Finite Group Databasebeta

← C2×#23777086 #35196180

Subgroups — C2×#23777086 #35196180

Order 20224.

9502 conjugacy classes of subgroups.

The subgroup lattice has 1316 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23777086C2132yesmaximal, direct product factor
2C2×#19099243C212yesmaximal, complemented
3C2×#19099241C212yesmaximal, complemented
4C2×#19099238C212yesmaximal, complemented
5C2×#19099238C212yesmaximal, complemented
6C2×#19099210C212yesmaximal, complemented
7C2×#19099206C212yesmaximal, complemented
8C2×#19099205C212yesmaximal, complemented
9C2×#19099202C212yesmaximal, complemented
10C2×#19099188C211yesmaximal, characteristic, complemented
11C2×#19099151C211yesmaximal, characteristic, complemented
12C2×#19099148C212yesmaximal, complemented
13C2×#19099121C211yesmaximal, characteristic, complemented
14C2×#19099076C211yesmaximal, characteristic, complemented
15C2×#19099073C211yesmaximal, characteristic, complemented
16C2×#19099072C212yesmaximal, complemented
17C2×#120×D79C212yesmaximal, complemented
18C2×#19099035C212yesmaximal, complemented
19C22×C22⋊C4×D79C211yesmaximal, characteristic, complemented
20C2×#538×C79C211yesmaximal, characteristic, complemented
21C25×D79C2211yescharacteristic
22C22×#11929625C2211yescharacteristic, complemented
23C22×#11929624C2212yescomplemented
24C22×#11929623C2211yescharacteristic, complemented
25C22×D4×D79C2212yes—
26C22×D4×D79C2212yescomplemented
27C22×D4×D79C2212yescomplemented
28C23×C4×D79C2211yescharacteristic, complemented
29C23×C4×D79C2211yescharacteristic, complemented
30#19099243C22132yescomplemented
31#19099241C22132yescomplemented
32#19099238C22132yescomplemented
33#19099238C22132yescomplemented
34#19099210C22132yescomplemented
35#19099206C22132yescomplemented
36#19099205C22132yescomplemented
37#19099202C22132yescomplemented
38#19099188C22116yescomplemented
39#19099151C22116yescomplemented
40#19099148C22132yescomplemented
41#19099121C22116yescomplemented
42C2×#14579154C2212yescomplemented
43C2×#14579154C2212yescomplemented
44C2×#14579154C2212yescomplemented
45C2×#14579148C2212yescomplemented
46C2×#14579147C2212yescomplemented
47C2×#14579147C2212yescomplemented
48#19099076C22116yescomplemented
49#19099073C22116yescomplemented
50#19099072C22132yescomplemented
51C2×#14579146C2212yescomplemented
52C2×#14579146C2212yescomplemented
53C2×#14579146C2212yescomplemented
54C2×#14579143C2212yescomplemented
55C2×#14579143C2212yescomplemented
56C2×#14579143C2212yescomplemented
57C2×#14579143C2212yescomplemented
58C2×#14579143C2212yescomplemented
59C2×#14579142C2212yescomplemented
60C2×#14579141C2212yescomplemented
61C2×#14579141C2211yescharacteristic, complemented
62C2×#14579140C2211yescharacteristic, complemented
63C2×#14579139C2212yescomplemented
64C2×#14579139C2212yescomplemented
65C2×#14579139C2212yescomplemented
66C2×#14579138C2212yescomplemented
67C2×#14579137C2212yescomplemented
68C2×#14579137C2211yescharacteristic, complemented
69C2×#14579136C2211yescharacteristic, complemented
70C2×#14579135C2211yescharacteristic, complemented
71C2×#14579134C2212yescomplemented
72C2×#14579134C2212yescomplemented
73C2×#14579133C2212yescomplemented
74C2×#14579133C2212yescomplemented
75C2×#14579132C2212yescomplemented
76C2×#14579132C2211yescharacteristic, complemented
77C2×#14579131C2212yes—
78C2×#14579131C2212yes—
79C2×#14579131C2212yescomplemented
80C2×#14579131C2212yescomplemented
81C2×#14579130C2212yescomplemented
82C2×#14579129C2212yes—
83C2×#14579129C2212yes—
84C2×#14579129C2212yescomplemented
85C2×#14579129C2212yescomplemented
86#120×D79C22132yescomplemented
87#19099035C22132yescomplemented
88C2×C4×D316C2212yescomplemented
89C2×C4×D316C2212yescomplemented
90C2×D4×Dic79C2212yescomplemented
91C2×#14579123C2212yescomplemented
92C2×#14579123C2212yescomplemented
93C2×C4×C22⋊D79C2212yescomplemented
94C2×C4×C22⋊D79C2212yescomplemented
95C2×C4×C22⋊D79C2212yescomplemented
96C2×(C22⋊D79)⋊C4C2212yescomplemented
97C2×(C22⋊D79)⋊C4C2212yescomplemented
98C2×(C22⋊D79)⋊C4C2212yescomplemented
99C2×#14579119C2212yescomplemented
100C2×#14579119C2211yescharacteristic, complemented
101C2×#14579119C2211yescharacteristic, complemented
102C2×#14579118C2212yescomplemented
103C2×#14579118C2212yescomplemented
104C22×C22⋊Dic79C2211yescharacteristic, complemented
105C22×(C2×D79)⋊C4C2211yescharacteristic
106C22×(C2×D79)⋊C4C2211yescharacteristic
107C22×(C2×D79)⋊C4C2212yescomplemented
108C2×C22⋊C4×D79C2212yes—
109C2×C22⋊C4×D79C2212yescomplemented
110C2×C22⋊C4×D79C2212yescomplemented
111C2×C22⋊C4×D79C2212yescomplemented
112C2×C22⋊C4×D79C2212yescomplemented
113C2×C22⋊C4×D79C2212yescomplemented
114C2×C22⋊C4×D79C2212yescomplemented
115C2×C22⋊C4×D79C22116yescomplemented
116C2×C22⋊C4×D79C2212yescomplemented
117#538×C79C22116yescomplemented
118C2×#126×C79C2212yescomplemented
119C2×#124×C79C2212yescomplemented
120C2×#123×C79C2212yescomplemented
121C2×C22⋊Q8×C79C2211yescharacteristic, complemented
122C2×#121×C79C2212yescomplemented
123C2×#121×C79C2211yescharacteristic, complemented
124C2×#120×C79C2212yescomplemented
125C2×C4×D4×C79C2212yescomplemented
126C22×C22⋊C4×C79C2211yescharacteristic, complemented
127C24×D79—28no—
128C24×D79—44no—
129C24×D79—44no—
130C24×D79C2311yescharacteristic
131C24×D79C2312yes—
132C24×D79C2312yes—
133C24×D79C2318yes—
134C24×D79C2312yes—
135C24×D79C2311yescharacteristic
136C2×#11929625—44no—
137C2×#11929625C2318yescomplemented
138C2×#11929624—48no—
139C2×#11929624C23116yescomplemented
140C2×#11929623—44no—
141C2×#11929623C2318yescomplemented
142C22×Dic158C2312yescomplemented
143C22×Dic158C2311yescharacteristic, complemented
144C22×D316C2312yes—
145C22×D316C2312yes—
146C22×D316C2312yes—
147C22×D316C2311yescharacteristic, complemented
148C22×C22⋊D79C2312yes—
149C22×C22⋊D79C2312yes—
150C22×C22⋊D79C2312yes—
151C22×C22⋊D79C2312yes—
152C22×C22⋊D79C2312yes—
153C22×C22⋊D79C2312yes—
154C22×C22⋊D79C2312yescomplemented
155C2×D4×D79—216no—
156C2×D4×D79—48no—
157C2×D4×D79—48no—
158C2×D4×D79C23116yes—
159C2×D4×D79C23116yescomplemented
160C2×D4×D79C23116yescomplemented
161C23×Dic79C2311yescharacteristic
162C23×Dic79C2311yescharacteristic
163C23×Dic79C2312yescomplemented
164C22×C4×D79—44no—
165C22×C4×D79—44no—
166C22×C4×D79C2312yes—
167C22×C4×D79C2312yes—
168C22×C4×D79C2311yescharacteristic
169C22×C4×D79C2311yescharacteristic
170C22×C4×D79C2312yes—
171C22×C4×D79C2312yes—
172C22×C4×D79C2311yescharacteristic
173C22×C4×D79C2312yes—
174C22×C4×D79C2311yescharacteristic
175C22×C4×D79C2318yescomplemented
176C22×C4×D79C2318yescomplemented
177C22×C4×D79C2312yescomplemented
178C22×C4×D79C2312yescomplemented
179#14579154C23116yescomplemented
180#14579154C23116yescomplemented
181#14579154C23116yescomplemented
182#14579148C23116yescomplemented
183#14579147C23116yescomplemented
184#14579147C23116yescomplemented
185#14579146C23116yescomplemented
186#14579146C23116yescomplemented
187#14579146C23116yescomplemented
188#14579143C23116yescomplemented
189#14579143C23116yescomplemented
190#14579143C23116yescomplemented
191#14579143C23116yescomplemented
192#14579143C23116yescomplemented
193#14579142C23116yescomplemented
194#14579141C23116yescomplemented
195#14579141C2318yescomplemented
196#14579140C2318yescomplemented
197#14579139C23116yescomplemented
198#14579139C23116yescomplemented
199#14579139C23116yescomplemented
200#14579138C23116yescomplemented
201#14579137C23116yescomplemented
202#14579137C2318yescomplemented
203#14579136C2318yescomplemented
204#14579135C2318yescomplemented
205#14579134C23116yescomplemented
206#14579134C23116yescomplemented
207#14579133C23116yescomplemented
208#14579133C23116yescomplemented
209#14579132C23116yescomplemented
210#14579132C2318yescomplemented
211#14579131C23116yes—
212#14579131C23116yes—
213#14579131C23116yescomplemented
214#14579131C23116yescomplemented
215#14579130C23116yescomplemented
216#14579129C23116yes—
217#14579129C23116yes—
218#14579129C23116yescomplemented
219#14579129C23116yescomplemented
220C4×D316C23116yescomplemented
221C4×D316C23116yescomplemented
222D4×Dic79C23116yescomplemented
223#14579123C23116yescomplemented
224#14579123C23116yescomplemented
225C4×C22⋊D79C23116yescomplemented
226C4×C22⋊D79C23116yescomplemented
227C4×C22⋊D79C23116yescomplemented
228(C22⋊D79)⋊C4C23116yescomplemented
229(C22⋊D79)⋊C4C23116yescomplemented
230(C22⋊D79)⋊C4C23116yescomplemented
231#14579119C2318yescomplemented
232#14579119C23116yescomplemented
233#14579119C2318yescomplemented
234#14579118C23116yescomplemented
235#14579118C23116yescomplemented
236C2×C4⋊Dic79C2312yescomplemented
237C2×C4⋊Dic79C2311yescharacteristic, complemented
238C2×C4⋊Dic79C2311yescharacteristic, complemented
239C2×C4⋊Dic79C2312yescomplemented
240C2×Dic79⋊C4C2312yescomplemented
241C2×Dic79⋊C4C2312yescomplemented
242C2×Dic79⋊C4C2312yescomplemented
243C2×Dic79⋊C4C2312yescomplemented
244C2×Dic79⋊C4C2312yescomplemented
245C2×Dic79⋊C4C2312yescomplemented
246C2×C22⋊Dic79C2312yes—
247C2×C22⋊Dic79C2312yes—
248C2×C22⋊Dic79C2312yes—
249C2×C22⋊Dic79C2312yes—
250C2×C22⋊Dic79C2312yes—
251C2×C22⋊Dic79C2318yescomplemented
252C2×C22⋊Dic79C2312yescomplemented
253C2×C22⋊Dic79C2312yescomplemented
254C2×(C2×D79)⋊C4C2318yes—
255C2×(C2×D79)⋊C4C2312yes—
256C2×(C2×D79)⋊C4C2312yes—
257C2×(C2×D79)⋊C4C2312yes—
258C2×(C2×D79)⋊C4C2312yes—
259C2×(C2×D79)⋊C4C2318yes—
260C2×(C2×D79)⋊C4C2312yes—
261C2×(C2×D79)⋊C4C2312yes—
262C2×(C2×D79)⋊C4C2312yes—
263C2×(C2×D79)⋊C4C2312yes—
264C2×(C2×D79)⋊C4C2312yes—
265C2×(C2×D79)⋊C4C2312yes—
266C2×(C2×D79)⋊C4C23116yescomplemented
267C2×(C2×D79)⋊C4C2312yescomplemented
268C2×(C2×D79)⋊C4C2312yescomplemented
269C2×(C2×D79)⋊C4C2312yescomplemented
270C2×(C2×D79)⋊C4C2312yescomplemented
271C22⋊C4×D79C23116yes—
272C22⋊C4×D79C23116yescomplemented
273C22⋊C4×D79C23116yescomplemented
274C22⋊C4×D79C23116yescomplemented
275C22⋊C4×D79C23116yescomplemented
276C22⋊C4×D79C23116yescomplemented
277C22⋊C4×D79C23116yescomplemented
278C22⋊C4×D79C23116yescomplemented
279C2×C4×Dic79C2312yescomplemented
280C2×C4×Dic79C2312yescomplemented
281C2×C4×Dic79C2312yescomplemented
282C25×C79C2311yescharacteristic
283C22×Q8×C79C2311yescharacteristic, complemented
284C22×D4×C79C2312yes—
285C22×D4×C79C2312yes—
286C22×D4×C79C2312yes—
287C22×D4×C79C2311yescharacteristic, complemented
288C23×C4×C79C2311yescharacteristic
289C23×C4×C79C2311yescharacteristic
290C23×C4×C79C2312yescomplemented
291#126×C79C23116yescomplemented
292#124×C79C23116yescomplemented
293#123×C79C23116yescomplemented
294C22⋊Q8×C79C2318yescomplemented
295#121×C79C23116yescomplemented
296#121×C79C2318yescomplemented
297#120×C79C23116yescomplemented
298C4×D4×C79C23116yescomplemented
299C2×C4⋊C4×C79C2312yescomplemented
300C2×C4⋊C4×C79C2312yescomplemented
301C2×C4⋊C4×C79C2311yescharacteristic, complemented
302C2×C4⋊C4×C79C2311yescharacteristic, complemented
303C2×C22⋊C4×C79C2312yes—
304C2×C22⋊C4×C79C2312yes—
305C2×C22⋊C4×C79C2312yes—
306C2×C22⋊C4×C79C2312yes—
307C2×C22⋊C4×C79C2312yes—
308C2×C22⋊C4×C79C2318yescomplemented
309C2×C22⋊C4×C79C2312yescomplemented
310C2×C22⋊C4×C79C2312yescomplemented
311C2×C42×C79C2312yescomplemented
312C23×D79—24no—
313C23×D79—24no—
314C23×D79—24no—
315C23×D79—28no—
316C23×D79—28no—
317C23×D79—232no—
318C23×D79—28no—
319C23×D79—28no—
320C23×D79—28no—
321C23×D79—416no—
322C23×D79—416no—
323C23×D79—44no—
324C23×D79—44no—
325C23×D79—42no—
326C23×D79—42no—
327C23×D79—44no—
328C23×D79—44no—
329C23×D79—464no—
330C23×D79#4118yescomplemented
331C23×D79C2414yes—
332C23×D79C2412yes—
333C23×D79C2418yes—
334C23×D79C2418yes—
335C23×D79C2412yes—
336C23×D79C2411yescharacteristic
337C23×D79C2411yescharacteristic
338C23×D79C2418yes—
339C23×D79C2414yes—
340#11929625—416no—
341#11929624—432no—
342#11929623—416no—
343C2×Dic158—42no—
344C2×Dic158—44no—
345C2×Dic158C2414yescomplemented
346C2×Dic158C2418yescomplemented
347C2×D316—28no—
348C2×D316—28no—
349C2×D316—28no—
350C2×D316—42no—
351C2×D316C2418yes—
352C2×D316C2418yes—
353C2×D316C2418yes—
354C2×D316C2414yescomplemented
355C2×C22⋊D79—28no—
356C2×C22⋊D79—28no—
357C2×C22⋊D79—28no—
358C2×C22⋊D79—28no—
359C2×C22⋊D79—44no—
360C2×C22⋊D79—44no—
361C2×C22⋊D79—44no—
362C2×C22⋊D79C2418yes—
363C2×C22⋊D79C2418yes—
364C2×C22⋊D79C2418yes—
365C2×C22⋊D79C2418yes—
366C2×C22⋊D79C2418yes—
367C2×C22⋊D79C2418yes—
368C2×C22⋊D79C2418yescomplemented
369D4×D79—264no—
370D4×D79—432no—
371D4×D79—432no—
372C22×Dic79—44no—
373C22×Dic79—42no—
374C22×Dic79—42no—
375C22×Dic79C2412yes—
376C22×Dic79C2412yes—
377C22×Dic79C2412yes—
378C22×Dic79C2411yescharacteristic
379C22×Dic79C2412yes—
380C22×Dic79C2411yescharacteristic
381C22×Dic79C2414yes—
382C22×Dic79C2414yes—
383C22×Dic79C2418yescomplemented
384C2×C4×D79—28no—
385C2×C4×D79—24no—
386C2×C4×D79—28no—
387C2×C4×D79—24no—
388C2×C4×D79—44no—
389C2×C4×D79—44no—
390C2×C4×D79—44no—
391C2×C4×D79—42no—
392C2×C4×D79—42no—
393C2×C4×D79—44no—
394C2×C4×D79—44no—
395C2×C4×D79—416no—
396C2×C4×D79—416no—
397C2×C4×D79C2414yes—
398C2×C4×D79C2418yes—
399C2×C4×D79C2414yes—
400C2×C4×D79C2418yes—
401C2×C4×D79C2418yes—
402C2×C4×D79C2418yes—
403C2×C4×D79C2414yes—
404C2×C4×D79C2418yes—
405C2×C4×D79C2414yes—
406C2×C4×D79C2418yescomplemented
407C2×C4×D79C2418yescomplemented
408C4⋊Dic79C2418yescomplemented
409C4⋊Dic79C2414yescomplemented
410C4⋊Dic79C2414yescomplemented
411C4⋊Dic79C2418yescomplemented
412Dic79⋊C4C2418yescomplemented
413Dic79⋊C4C2418yescomplemented
414Dic79⋊C4C2418yescomplemented
415Dic79⋊C4C2418yescomplemented
416Dic79⋊C4C2418yescomplemented
417Dic79⋊C4C2418yescomplemented
418C22⋊Dic79C2418yes—
419C22⋊Dic79C2418yes—
420C22⋊Dic79C2418yes—
421C22⋊Dic79C2418yes—
422C22⋊Dic79C2418yes—
423C22⋊Dic79C2418yescomplemented
424C22⋊Dic79C2418yescomplemented
425(C2×D79)⋊C4C2418yes—
426(C2×D79)⋊C4C2418yes—
427(C2×D79)⋊C4C2418yes—
428(C2×D79)⋊C4C2418yes—
429(C2×D79)⋊C4C2418yes—
430(C2×D79)⋊C4C2418yes—
431(C2×D79)⋊C4C2418yes—
432(C2×D79)⋊C4C2418yes—
433(C2×D79)⋊C4C2418yes—
434(C2×D79)⋊C4C2418yes—
435(C2×D79)⋊C4C2418yescomplemented
436(C2×D79)⋊C4C2418yescomplemented
437(C2×D79)⋊C4C2418yescomplemented
438(C2×D79)⋊C4C2418yescomplemented
439C4×Dic79C2418yescomplemented
440C4×Dic79C2418yescomplemented
441C4×Dic79C2418yescomplemented
442C24×C79—24no—
443C24×C79—42no—
444C24×C79—42no—
445C24×C79C2412yes—
446C24×C79C2412yes—
447C24×C79C2411yescharacteristic
448C24×C79C2414yes—
449C2×Q8×C79—42no—
450C2×Q8×C79C2414yescomplemented
451C2×D4×C79—28no—
452C2×D4×C79—42no—
453C2×D4×C79—44no—
454C2×D4×C79—44no—
455C2×D4×C79C2418yes—
456C2×D4×C79C2418yes—
457C2×D4×C79C2418yes—
458C2×D4×C79C2414yescomplemented
459C22×C4×C79—44no—
460C22×C4×C79—42no—
461C22×C4×C79—42no—
462C22×C4×C79C2411yescharacteristic
463C22×C4×C79C2412yes—
464C22×C4×C79C2412yes—
465C22×C4×C79C2412yes—
466C22×C4×C79C2412yes—
467C22×C4×C79C2411yescharacteristic
468C22×C4×C79C2414yes—
469C22×C4×C79C2414yes—
470C22×C4×C79C2418yescomplemented
471C4⋊C4×C79C2418yescomplemented
472C4⋊C4×C79C2418yescomplemented
473C4⋊C4×C79C2414yescomplemented
474C4⋊C4×C79C2414yescomplemented
475C22⋊C4×C79C2418yes—
476C22⋊C4×C79C2418yes—
477C22⋊C4×C79C2418yes—
478C22⋊C4×C79C2418yes—
479C22⋊C4×C79C2418yes—
480C22⋊C4×C79C2418yescomplemented
481C22⋊C4×C79C2418yescomplemented
482C42×C79C2418yescomplemented
483C23×C79—22no—
484C23×C79—22no—
485C23×C79—24no—
486C23×C79—28no—
487C23×C79—24no—
488C23×C79—24no—
489C23×C79—24no—
490C23×C79—24no—
491C23×C79—24no—
492C23×C79—44no—
493C23×C79—44no—
494C23×C79—416no—
495C23×C79C2×#4114yes—
496C23×C79C2514yes—
497C23×C79C2514yes—
498C23×C79C2512yes—
499C23×C79C2511yescharacteristic
500C22×D79—232no—
501C22×D79—28no—
502C22×D79—22no—
503C22×D79—22no—
504C22×D79—22no—
505C22×D79—22no—
506C22×D79—24no—
507C22×D79—24no—
508C22×D79—28no—
509C22×D79—28no—
510C22×D79—24no—
511C22×D79—24no—
512C22×D79—24no—
513C22×D79—216no—
514C22×D79—216no—
515C22×D79—216no—
516C22×D79—216no—
517C22×D79—216no—
518C22×D79—416no—
519C22×D79—44no—
520C22×D79—44no—
521C22×D79—48no—
522C22×D79—48no—
523C22×D79—432no—
524C22×D79—432no—
525C22×D79—48no—
526C22×D79—48no—
527C22×D79—4128no—
528C22×D79—816no—
529C22×D79C2×#4118yes—
530C22×D79C2×#41116yescomplemented
531C22×D79H(5,𝔽2)14yes—
532C22×D79H(5,𝔽2)14yes—
533C22×D79C2514yes—
534C22×D79C2514yes—
535C22×D79C2512yes—
536C22×D79C2512yes—
537Q8×C79—44no—
538D4×C79—216no—
539D4×C79—48no—
540D4×C79—48no—
541D4×C79—44no—
542C2×C4×C79—24no—
543C2×C4×C79—24no—
544C2×C4×C79—22no—
545C2×C4×C79—22no—
546C2×C4×C79—24no—
547C2×C4×C79—24no—
548C2×C4×C79—44no—
549C2×C4×C79—44no—
550C2×C4×C79—48no—
551C2×C4×C79C2514yes—
552C2×C4×C79C2514yes—
553C2×C4×C79C2514yes—
554C2×C4×C79C2512yes—
555C2×C4×C79C2512yes—
556C2×C4×C79C2514yes—
557C22⋊D79—216no—
558C22⋊D79—216no—
559C22⋊D79—216no—
560C22⋊D79—216no—
561C22⋊D79—48no—
562C22⋊D79—48no—
563C22⋊D79—48no—
564C2×Dic79—24no—
565C2×Dic79—22no—
566C2×Dic79—22no—
567C2×Dic79—24no—
568C2×Dic79—24no—
569C2×Dic79—24no—
570C2×Dic79—44no—
571C2×Dic79—44no—
572C2×Dic79—48no—
573C2×Dic79C2512yes—
574C2×Dic79C2514yes—
575C2×Dic79C2512yes—
576C2×Dic79C2514yes—
577C2×Dic79C2514yes—
578C2×Dic79C2514yes—
579D316—216no—
580D316—216no—
581D316—216no—
582D316—44no—
583C4×D79—216no—
584C4×D79—28no—
585C4×D79—216no—
586C4×D79—28no—
587C4×D79—48no—
588C4×D79—44no—
589C4×D79—44no—
590C4×D79—48no—
591C4×D79—48no—
592C4×D79—48no—
593C4×D79—48no—
594Dic158—44no—
595Dic158—48no—
596C22×C79—22no—
597C22×C79—22no—
598C22×C79—28no—
599C22×C79—24no—
600C22×C79—24no—
601C22×C79—24no—
602C22×C79—24no—
603C22×C79—24no—
604C22×C79—24no—
605C22×C79—416no—
606C22×C79—48no—
607C22×C79—48no—
608C22×C79C22×#4114yes—
609C22×C79C22×#4112yes—
610C22×C79C2×H(5,𝔽2)12yes—
611C22×C79C2×H(5,𝔽2)12yes—
612C22×C79C2611yescharacteristic
613C2×D79—232no—
614C2×D79—22no—
615C2×D79—22no—
616C2×D79—24no—
617C2×D79—24no—
618C2×D79—22no—
619C2×D79—22no—
620C2×D79—28no—
621C2×D79—28no—
622C2×D79—216no—
623C2×D79—24no—
624C2×D79—24no—
625C2×D79—24no—
626C2×D79—416no—
627C2×D79—432no—
628C2×D79—432no—
629C2×D79—48no—
630C2×D79—816no—
631C2×D79C22×#4118yes—
632C2×D79C2×H(5,𝔽2)14yes—
633C2×D79C2×H(5,𝔽2)14yes—
634C4×C79—24no—
635C4×C79—24no—
636C4×C79—22no—
637C4×C79—24no—
638C4×C79—22no—
639C4×C79—24no—
640Dic79—24no—
641Dic79—24no—
642Dic79—24no—
643Dic79—24no—
644Dic79—22no—
645Dic79—22no—
646C2×#3490—791nomaximal, Sylow
647C2×C79—24no—
648C2×C79—44no—
649C2×C79—44no—
650C2×C79#349014yescomplemented
651C2×C79C23×#4111yescharacteristic
652C2×C79C22×H(5,𝔽2)11yescharacteristic
653C2×C79C22×H(5,𝔽2)11yescharacteristic
654D79—24no—
655D79—24no—
656D79—28no—
657D79—44no—
658#3490—7932no—
659C2×#551—792no—
660C2×#551—792no—
661C2×#551—792no—
662C2×#551—792no—
663C2×#546—792no—
664C2×#546—792no—
665C2×#546—792no—
666C2×#546—792no—
667C2×#543—791no—
668C2×#538—792no—
669C2×#538—791no—
670C2×#538D7911yescharacteristic, complemented
671C2×#534—791no—
672C2×#525—791no—
673C2×#525—791no—
674C2×#525—792no—
675C22×#120—792no—
676C2×#518—792no—
677C23×C22⋊C4—791no—
678C79C2×#349011yescharacteristic, complemented, Sylow
679C26—791no—
680C22×#41—791no—
681C22×#41—791no—
682C22×#41—792no—
683C23×D4—792no—
684C23×D4—792no—
685C23×D4—792no—
686C24×C4—791no—
687C24×C4—791no—
688#551—7932no—
689#551—7932no—
690#551—7932no—
691#551—7932no—
692#546—7932no—
693#546—7932no—
694#546—7932no—
695#546—7932no—
696#543—7916no—
697#538—7932no—
698#538—7916no—
699#538C2×D79116yescomplemented
700#534—7916no—
701C2×#126—792no—
702C2×#126—792no—
703C2×#126—792no—
704C2×#126C2×D7912yescomplemented
705C2×#124—792no—
706C2×#124—792no—
707C2×#124—792no—
708C2×#124C2×D7912yescomplemented
709#525—7916no—
710#525—7916no—
711#525—7932no—
712C2×#123—792no—
713C2×#123—792no—
714C2×#123—792no—
715C2×#123—792no—
716C2×#123—792no—
717C2×#123—792no—
718C2×#123—792no—
719C2×#123—792no—
720C2×#123—792no—
721C2×#123C2×D7912yescomplemented
722C2×C22⋊Q8—791no—
723C2×C22⋊Q8—792no—
724C2×C22⋊Q8—791no—
725C2×C22⋊Q8—792no—
726C2×C22⋊Q8—791no—
727C2×C22⋊Q8—792no—
728C2×C22⋊Q8—792no—
729C2×C22⋊Q8—792no—
730C2×C22⋊Q8—792no—
731C2×C22⋊Q8C2×D7911yescharacteristic, complemented
732C2×#121—792no—
733C2×#121—792no—
734C2×#121—792no—
735C2×#121—791no—
736C2×#121—791no—
737C2×#121—791no—
738C2×#121—792no—
739C2×#121—792no—
740C2×#121C2×D7912yescomplemented
741C2×#121C2×D7911yescharacteristic, complemented
742C2×#120—792no—
743C2×#120—792no—
744C2×#120—792no—
745C2×#120—792no—
746C2×#120—792no—
747C2×#120—7932no—
748C2×#120—792no—
749C2×#120—792no—
750C2×#120—792no—
751C2×#120—792no—
752C2×#120C2×D7912yescomplemented
753#518—7932no—
754C2×C4×D4—792no—
755C2×C4×D4—792no—
756C2×C4×D4—792no—
757C2×C4×D4—792no—
758C2×C4×D4—792no—
759C2×C4×D4—792no—
760C2×C4×D4—792no—
761C2×C4×D4—792no—
762C2×C4×D4—792no—
763C2×C4×D4—792no—
764C2×C4×D4—792no—
765C2×C4×D4C2×D7912yescomplemented
766C2×#117—792no—
767C2×#117—791no—
768C2×#117—791no—
769C2×#117—792no—
770C2×#117—792no—
771C22×C22⋊C4—791no—
772C22×C22⋊C4—791no—
773C22×C22⋊C4—791no—
774C22×C22⋊C4—792no—
775C22×C22⋊C4—792no—
776C22×C22⋊C4—792no—
777C22×C22⋊C4—792no—
778C22×C22⋊C4—792no—
779C22×C22⋊C4—792no—
780C22×C22⋊C4—792no—
781C22×C22⋊C4—792no—
782C22×C22⋊C4—7916no—
783C22×C22⋊C4—792no—
784C22×C22⋊C4C2×D7911yescharacteristic, complemented
785C25—3164no—
786C25—3164no—
787C25—791no—
788C25—798no—
789C25—792no—
790C25—792no—
791C25—792no—
792C25—791no—
793C25—1588no—
794C25C22×D7911yescharacteristic
795C2×#41—3168no—
796C2×#41—3164no—
797C2×#41—3164no—
798C2×#41—798no—
799C2×#41—798no—
800C2×#41—7916no—
801C22×Q8—791no—
802C22×Q8—792no—
803C22×Q8C22×D7911yescharacteristic, complemented
804C22×D4—3168no—
805C22×D4—3168no—
806C22×D4—792no—
807C22×D4—792no—
808C22×D4—792no—
809C22×D4—7916no—
810C22×D4—7916no—
811C22×D4—792no—
812C22×D4—792no—
813C22×D4—792no—
814C22×D4—792no—
815C22×D4—7916no—
816C22×D4—791no—
817C22×D4—792no—
818C22×D4—792no—
819C22×D4—792no—
820C22×D4—15816no—
821C22×D4C22×D7912yes—
822C22×D4C22×D7912yes—
823C22×D4C22×D7912yes—
824C22×D4C22×D7911yescharacteristic, complemented
825C23×C4—3164no—
826C23×C4—3164no—
827C23×C4—791no—
828C23×C4—791no—
829C23×C4—792no—
830C23×C4—791no—
831C23×C4—791no—
832C23×C4—792no—
833C23×C4—792no—
834C23×C4—792no—
835C23×C4—798no—
836C23×C4—798no—
837C23×C4—792no—
838C23×C4—792no—
839C23×C4—792no—
840C23×C4—791no—
841C23×C4—791no—
842C23×C4—792no—
843C23×C4C22×D7911yescharacteristic
844C23×C4C22×D7911yescharacteristic
845C23×C4C22×D7912yescomplemented
846#126—7916no—
847#126—7916no—
848#126—7916no—
849#126C22×D79116yescomplemented
850#124—7916no—
851#124—7916no—
852#124—7916no—
853#124C22×D79116yescomplemented
854#123—7916no—
855#123—7916no—
856#123—7916no—
857#123—7916no—
858#123—7916no—
859#123—7916no—
860#123—7916no—
861#123—7916no—
862#123—7916no—
863#123C22×D79116yescomplemented
864C22⋊Q8—798no—
865C22⋊Q8—7916no—
866C22⋊Q8—798no—
867C22⋊Q8—7916no—
868C22⋊Q8—798no—
869C22⋊Q8—7916no—
870C22⋊Q8—7916no—
871C22⋊Q8—7916no—
872C22⋊Q8—7916no—
873C22⋊Q8C22×D7918yescomplemented
874#121—7916no—
875#121—7916no—
876#121—7916no—
877#121—798no—
878#121—798no—
879#121—798no—
880#121—7916no—
881#121—7916no—
882#121C22×D79116yescomplemented
883#121C22×D7918yescomplemented
884#120—7916no—
885#120—7916no—
886#120—7916no—
887#120—7916no—
888#120—7916no—
889#120—7916no—
890#120—7916no—
891#120—7916no—
892#120—7916no—
893#120C22×D79116yescomplemented
894C4×D4—7916no—
895C4×D4—7916no—
896C4×D4—7916no—
897C4×D4—7916no—
898C4×D4—7916no—
899C4×D4—7916no—
900C4×D4—7916no—
901C4×D4—7916no—
902C4×D4—7916no—
903C4×D4—7916no—
904C4×D4—7916no—
905C4×D4C22×D79116yescomplemented
906#117—7916no—
907#117—798no—
908#117—798no—
909#117—7916no—
910#117—7916no—
911C2×C4⋊C4—792no—
912C2×C4⋊C4—792no—
913C2×C4⋊C4—792no—
914C2×C4⋊C4—792no—
915C2×C4⋊C4—791no—
916C2×C4⋊C4—792no—
917C2×C4⋊C4—791no—
918C2×C4⋊C4—792no—
919C2×C4⋊C4—792no—
920C2×C4⋊C4—792no—
921C2×C4⋊C4C22×D7912yescomplemented
922C2×C4⋊C4C22×D7911yescharacteristic, complemented
923C2×C4⋊C4C22×D7911yescharacteristic, complemented
924C2×C4⋊C4C22×D7912yescomplemented
925C2×C22⋊C4—792no—
926C2×C22⋊C4—792no—
927C2×C22⋊C4—798no—
928C2×C22⋊C4—792no—
929C2×C22⋊C4—792no—
930C2×C22⋊C4—792no—
931C2×C22⋊C4—792no—
932C2×C22⋊C4—792no—
933C2×C22⋊C4—792no—
934C2×C22⋊C4—792no—
935C2×C22⋊C4—798no—
936C2×C22⋊C4—792no—
937C2×C22⋊C4—792no—
938C2×C22⋊C4—798no—
939C2×C22⋊C4—792no—
940C2×C22⋊C4—792no—
941C2×C22⋊C4—792no—
942C2×C22⋊C4—792no—
943C2×C22⋊C4—792no—
944C2×C22⋊C4—792no—
945C2×C22⋊C4—792no—
946C2×C22⋊C4—792no—
947C2×C22⋊C4—792no—
948C2×C22⋊C4—792no—
949C2×C22⋊C4—7916no—
950C2×C22⋊C4—7916no—
951C2×C22⋊C4—7916no—
952C2×C22⋊C4—7916no—
953C2×C22⋊C4—7916no—
954C2×C22⋊C4—7916no—
955C2×C22⋊C4—7916no—
956C2×C22⋊C4—7916no—
957C2×C22⋊C4—7916no—
958C2×C22⋊C4C22×D7912yes—
959C2×C22⋊C4C22×D7912yes—
960C2×C22⋊C4C22×D7912yes—
961C2×C22⋊C4C22×D7912yes—
962C2×C22⋊C4C22×D7912yes—
963C2×C22⋊C4C22×D7918yescomplemented
964C2×C22⋊C4C22×D7912yescomplemented
965C2×C22⋊C4C22×D7912yescomplemented
966C2×C42—792no—
967C2×C42—792no—
968C2×C42—792no—
969C2×C42C22×D7912yescomplemented
970C24—24no—
971C24—42no—
972C24—42no—
973C24—3162no—
974C24—3162no—
975C24—3164no—
976C24—3164no—
977C24—3164no—
978C24—3164no—
979C24—31664no—
980C24—31616no—
981C24—31616no—
982C24—798no—
983C24—794no—
984C24—798no—
985C24—798no—
986C24—798no—
987C24—792no—
988C24—791no—
989C24—791no—
990C24—794no—
991C24—792no—
992C24—1588no—
993C24—1588no—
994C24—15832no—
995C24—1588no—
996C24—1588no—
997C24—1588no—
998C24—1584no—
999C24—1584no—
1000C24—1584no—
1001C24C23×D7912yes—
1002C24C23×D7912yes—
1003C24C23×D7911yescharacteristic
1004C24C23×D7914yes—
1005#41—31632no—
1006#41—31616no—
1007#41—31616no—
1008C2×Q8—42no—
1009C2×Q8—3162no—
1010C2×Q8—3164no—
1011C2×Q8—794no—
1012C2×Q8—798no—
1013C2×Q8C23×D7914yescomplemented
1014C2×D4—28no—
1015C2×D4—44no—
1016C2×D4—44no—
1017C2×D4—42no—
1018C2×D4—3162no—
1019C2×D4—31632no—
1020C2×D4—31632no—
1021C2×D4—3164no—
1022C2×D4—3164no—
1023C2×D4—3164no—
1024C2×D4—798no—
1025C2×D4—798no—
1026C2×D4—798no—
1027C2×D4—798no—
1028C2×D4—798no—
1029C2×D4—798no—
1030C2×D4—798no—
1031C2×D4—794no—
1032C2×D4—798no—
1033C2×D4—798no—
1034C2×D4—798no—
1035C2×D4—1588no—
1036C2×D4—1588no—
1037C2×D4—1588no—
1038C2×D4—15864no—
1039C2×D4—1588no—
1040C2×D4—1588no—
1041C2×D4—1588no—
1042C2×D4—1588no—
1043C2×D4C23×D7918yes—
1044C2×D4C23×D7918yes—
1045C2×D4C23×D7918yes—
1046C2×D4C23×D7914yescomplemented
1047C22×C4—42no—
1048C22×C4—42no—
1049C22×C4—44no—
1050C22×C4—3164no—
1051C22×C4—3162no—
1052C22×C4—3162no—
1053C22×C4—3164no—
1054C22×C4—3164no—
1055C22×C4—3164no—
1056C22×C4—3164no—
1057C22×C4—31616no—
1058C22×C4—31616no—
1059C22×C4—3162no—
1060C22×C4—3162no—
1061C22×C4—3164no—
1062C22×C4—794no—
1063C22×C4—794no—
1064C22×C4—798no—
1065C22×C4—794no—
1066C22×C4—794no—
1067C22×C4—798no—
1068C22×C4—798no—
1069C22×C4—798no—
1070C22×C4—798no—
1071C22×C4—798no—
1072C22×C4—792no—
1073C22×C4—791no—
1074C22×C4—791no—
1075C22×C4—792no—
1076C22×C4—792no—
1077C22×C4—792no—
1078C22×C4—798no—
1079C22×C4—794no—
1080C22×C4—794no—
1081C22×C4—798no—
1082C22×C4—1588no—
1083C22×C4—1584no—
1084C22×C4—1584no—
1085C22×C4—1588no—
1086C22×C4C23×D7912yes—
1087C22×C4C23×D7912yes—
1088C22×C4C23×D7912yes—
1089C22×C4C23×D7912yes—
1090C22×C4C23×D7911yescharacteristic
1091C22×C4C23×D7911yescharacteristic
1092C22×C4C23×D7914yes—
1093C22×C4C23×D7914yes—
1094C22×C4C23×D7918yescomplemented
1095C4⋊C4—798no—
1096C4⋊C4—798no—
1097C4⋊C4—798no—
1098C4⋊C4—798no—
1099C4⋊C4—798no—
1100C4⋊C4—798no—
1101C4⋊C4—798no—
1102C4⋊C4—794no—
1103C4⋊C4—794no—
1104C4⋊C4—798no—
1105C4⋊C4C23×D7918yescomplemented
1106C4⋊C4C23×D7914yescomplemented
1107C4⋊C4C23×D7914yescomplemented
1108C4⋊C4C23×D7918yescomplemented
1109C22⋊C4—798no—
1110C22⋊C4—798no—
1111C22⋊C4—798no—
1112C22⋊C4—798no—
1113C22⋊C4—798no—
1114C22⋊C4—798no—
1115C22⋊C4—798no—
1116C22⋊C4—798no—
1117C22⋊C4—798no—
1118C22⋊C4—798no—
1119C22⋊C4—798no—
1120C22⋊C4—798no—
1121C22⋊C4—798no—
1122C22⋊C4—798no—
1123C22⋊C4—798no—
1124C22⋊C4—798no—
1125C22⋊C4—798no—
1126C22⋊C4—798no—
1127C22⋊C4—798no—
1128C22⋊C4—798no—
1129C22⋊C4—798no—
1130C22⋊C4C23×D7918yes—
1131C22⋊C4C23×D7918yes—
1132C22⋊C4C23×D7918yes—
1133C22⋊C4C23×D7918yes—
1134C22⋊C4C23×D7918yes—
1135C22⋊C4C23×D7918yescomplemented
1136C22⋊C4C23×D7918yescomplemented
1137C42—798no—
1138C42—798no—
1139C42—798no—
1140C42C23×D7918yescomplemented
1141C23—22no—
1142C23—22no—
1143C23—24no—
1144C23—24no—
1145C23—24no—
1146C23—24no—
1147C23—24no—
1148C23—28no—
1149C23—24no—
1150C23—44no—
1151C23—44no—
1152C23—416no—
1153C23—31616no—
1154C23—3164no—
1155C23—3164no—
1156C23—3168no—
1157C23—3168no—
1158C23—3168no—
1159C23—3168no—
1160C23—316128no—
1161C23—31632no—
1162C23—31632no—
1163C23—7916no—
1164C23—794no—
1165C23—794no—
1166C23—794no—
1167C23—792no—
1168C23—792no—
1169C23—798no—
1170C23—794no—
1171C23—63216no—
1172C23—15816no—
1173C23—15816no—
1174C23—15816no—
1175C23—15816no—
1176C23—15816no—
1177C23—1588no—
1178C23—1588no—
1179C23—15832no—
1180C23—1584no—
1181C23—1584no—
1182C23—1584no—
1183C23—1582no—
1184C23—1582no—
1185C23—1584no—
1186C23—1584no—
1187C23—1588no—
1188C23—1582no—
1189C23—1582no—
1190C23#41×D7914yes—
1191C23C24×D7914yes—
1192C23C24×D7914yes—
1193C23C24×D7912yes—
1194C23C24×D7911yescharacteristic
1195Q8—44no—
1196Q8—3164no—
1197Q8—3168no—
1198D4—216no—
1199D4—48no—
1200D4—48no—
1201D4—44no—
1202D4—3164no—
1203D4—3168no—
1204D4—3168no—
1205D4—3168no—
1206D4—15816no—
1207D4—15816no—
1208D4—15816no—
1209D4—15816no—
1210D4—15816no—
1211D4—15816no—
1212D4—15816no—
1213C2×C4—24no—
1214C2×C4—22no—
1215C2×C4—22no—
1216C2×C4—24no—
1217C2×C4—24no—
1218C2×C4—24no—
1219C2×C4—44no—
1220C2×C4—44no—
1221C2×C4—48no—
1222C2×C4—3168no—
1223C2×C4—3164no—
1224C2×C4—3164no—
1225C2×C4—3168no—
1226C2×C4—3168no—
1227C2×C4—3168no—
1228C2×C4—3168no—
1229C2×C4—3164no—
1230C2×C4—3164no—
1231C2×C4—3168no—
1232C2×C4—794no—
1233C2×C4—792no—
1234C2×C4—792no—
1235C2×C4—794no—
1236C2×C4—794no—
1237C2×C4—794no—
1238C2×C4—15816no—
1239C2×C4—1588no—
1240C2×C4—1588no—
1241C2×C4—15816no—
1242C2×C4—1582no—
1243C2×C4—1582no—
1244C2×C4—1584no—
1245C2×C4—1584no—
1246C2×C4—1584no—
1247C2×C4—1584no—
1248C2×C4C24×D7914yes—
1249C2×C4C24×D7914yes—
1250C2×C4C24×D7914yes—
1251C2×C4C24×D7914yes—
1252C2×C4C24×D7912yes—
1253C2×C4C24×D7912yes—
1254C22—28no—
1255C22—22no—
1256C22—22no—
1257C22—24no—
1258C22—24no—
1259C22—24no—
1260C22—24no—
1261C22—24no—
1262C22—24no—
1263C22—416no—
1264C22—48no—
1265C22—48no—
1266C22—31616no—
1267C22—31632no—
1268C22—31632no—
1269C22—3168no—
1270C22—798no—
1271C22—794no—
1272C22—794no—
1273C22—63216no—
1274C22—15832no—
1275C22—1584no—
1276C22—1584no—
1277C22—1584no—
1278C22—15816no—
1279C22—1588no—
1280C22—1588no—
1281C22—1582no—
1282C22—1582no—
1283C22—1582no—
1284C22—1582no—
1285C22—1584no—
1286C22—1584no—
1287C22C2×#41×D7914yes—
1288C22C2×#41×D7912yes—
1289C22H(5,𝔽2)×D7912yes—
1290C22H(5,𝔽2)×D7912yes—
1291C22C25×D7911yescharacteristic
1292C4—24no—
1293C4—24no—
1294C4—22no—
1295C4—22no—
1296C4—24no—
1297C4—24no—
1298C4—1584no—
1299C4—1582no—
1300C4—1582no—
1301C4—1584no—
1302C4—1584no—
1303C4—1584no—
1304C2—24no—
1305C2—44no—
1306C2—44no—
1307C2—3164no—
1308C2—1588no—
1309C2—1584no—
1310C2—1584no—
1311C2#2377708614yesdirect product factor
1312C2C22×#41×D7911yescharacteristic
1313C2C2×H(5,𝔽2)×D7911yescharacteristic
1314C2C2×H(5,𝔽2)×D7911yescharacteristic
subgroupG/H
centerC23C24×D79
commutator, cosocleC22×C79C26
FrattiniC22C25×D79
FittingC2×#538×C79C2
socleC23×C79C25
hypercenterC2×#538D79
hypocenterC79C2×#3490
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×#538

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #23777086C2direct (N × H)
2. C2×#19099243C2semidirect
3. C2×#19099241C2semidirect
4. C2×#19099238C2semidirect
5. C2×#19099238C2semidirect
6. C2×#19099210C2semidirect
7. C2×#19099206C2semidirect
8. C2×#19099205C2semidirect
9. C2×#19099202C2semidirect
10. C2×#19099188C2semidirect
11. C2×#19099151C2semidirect
12. C2×#19099148C2semidirect
13. C2×#19099121C2semidirect
14. C2×#19099076C2semidirect
15. C2×#19099073C2semidirect
16. C2×#19099072C2semidirect
17. C2×#120×D79C2semidirect
18. C2×#19099035C2semidirect
19. C22×C22⋊C4×D79C2semidirect
20. C2×#538×C79C2semidirect
22. C22×#11929625C22semidirect
23. C22×#11929624C22semidirect
24. C22×#11929623C22semidirect
26. C22×D4×D79C22semidirect
27. C22×D4×D79C22semidirect
28. C23×C4×D79C22semidirect
29. C23×C4×D79C22semidirect
30. #19099243C22semidirect
31. #19099241C22semidirect
32. #19099238C22semidirect
33. #19099238C22semidirect
34. #19099210C22semidirect
35. #19099206C22semidirect
36. #19099205C22semidirect
37. #19099202C22semidirect
38. #19099188C22semidirect
39. #19099151C22semidirect
40. #19099148C22semidirect
41. #19099121C22semidirect
42. C2×#14579154C22semidirect
43. C2×#14579154C22semidirect
44. C2×#14579154C22semidirect
45. C2×#14579148C22semidirect
46. C2×#14579147C22semidirect
47. C2×#14579147C22semidirect
48. #19099076C22semidirect
49. #19099073C22semidirect
50. #19099072C22semidirect
51. C2×#14579146C22semidirect
52. C2×#14579146C22semidirect
53. C2×#14579146C22semidirect
54. C2×#14579143C22semidirect
55. C2×#14579143C22semidirect
56. C2×#14579143C22semidirect
57. C2×#14579143C22semidirect
58. C2×#14579143C22semidirect
59. C2×#14579142C22semidirect
60. C2×#14579141C22semidirect
61. C2×#14579141C22semidirect
62. C2×#14579140C22semidirect
63. C2×#14579139C22semidirect
64. C2×#14579139C22semidirect
65. C2×#14579139C22semidirect
66. C2×#14579138C22semidirect
67. C2×#14579137C22semidirect
68. C2×#14579137C22semidirect
69. C2×#14579136C22semidirect
70. C2×#14579135C22semidirect
71. C2×#14579134C22semidirect
72. C2×#14579134C22semidirect
73. C2×#14579133C22semidirect
74. C2×#14579133C22semidirect
75. C2×#14579132C22semidirect
76. C2×#14579132C22semidirect
79. C2×#14579131C22semidirect
80. C2×#14579131C22semidirect
81. C2×#14579130C22semidirect
84. C2×#14579129C22semidirect
85. C2×#14579129C22semidirect
86. #120×D79C22semidirect
87. #19099035C22semidirect
88. C2×C4×D316C22semidirect
89. C2×C4×D316C22semidirect
90. C2×D4×Dic79C22semidirect
91. C2×#14579123C22semidirect
92. C2×#14579123C22semidirect
93. C2×C4×C22⋊D79C22semidirect
94. C2×C4×C22⋊D79C22semidirect
95. C2×C4×C22⋊D79C22semidirect
96. C2×(C22⋊D79)⋊C4C22semidirect
97. C2×(C22⋊D79)⋊C4C22semidirect
98. C2×(C22⋊D79)⋊C4C22semidirect
99. C2×#14579119C22semidirect
100. C2×#14579119C22semidirect
101. C2×#14579119C22semidirect
102. C2×#14579118C22semidirect
103. C2×#14579118C22semidirect
104. C22×C22⋊Dic79C22semidirect
107. C22×(C2×D79)⋊C4C22semidirect
109. C2×C22⋊C4×D79C22semidirect
110. C2×C22⋊C4×D79C22semidirect
111. C2×C22⋊C4×D79C22semidirect
112. C2×C22⋊C4×D79C22semidirect
113. C2×C22⋊C4×D79C22semidirect
114. C2×C22⋊C4×D79C22semidirect
115. C2×C22⋊C4×D79C22semidirect
116. C2×C22⋊C4×D79C22semidirect
117. #538×C79C22semidirect
118. C2×#126×C79C22semidirect
119. C2×#124×C79C22semidirect
120. C2×#123×C79C22semidirect
121. C2×C22⋊Q8×C79C22semidirect
122. C2×#121×C79C22semidirect
123. C2×#121×C79C22semidirect
124. C2×#120×C79C22semidirect
125. C2×C4×D4×C79C22semidirect
126. C22×C22⋊C4×C79C22semidirect
137. C2×#11929625C23semidirect
139. C2×#11929624C23semidirect
141. C2×#11929623C23semidirect
142. C22×Dic158C23semidirect
143. C22×Dic158C23semidirect
147. C22×D316C23semidirect
154. C22×C22⋊D79C23semidirect
159. C2×D4×D79C23semidirect
160. C2×D4×D79C23semidirect
163. C23×Dic79C23semidirect
175. C22×C4×D79C23semidirect
176. C22×C4×D79C23semidirect
177. C22×C4×D79C23semidirect
178. C22×C4×D79C23semidirect
179. #14579154C23semidirect
180. #14579154C23semidirect
181. #14579154C23semidirect
182. #14579148C23semidirect
183. #14579147C23semidirect
184. #14579147C23semidirect
185. #14579146C23semidirect
186. #14579146C23semidirect
187. #14579146C23semidirect
188. #14579143C23semidirect
189. #14579143C23semidirect
190. #14579143C23semidirect
191. #14579143C23semidirect
192. #14579143C23semidirect
193. #14579142C23semidirect
194. #14579141C23semidirect
195. #14579141C23semidirect
196. #14579140C23semidirect
197. #14579139C23semidirect
198. #14579139C23semidirect
199. #14579139C23semidirect
200. #14579138C23semidirect
201. #14579137C23semidirect
202. #14579137C23semidirect
203. #14579136C23semidirect
204. #14579135C23semidirect
205. #14579134C23semidirect
206. #14579134C23semidirect
207. #14579133C23semidirect
208. #14579133C23semidirect
209. #14579132C23semidirect
210. #14579132C23semidirect
213. #14579131C23semidirect
214. #14579131C23semidirect
215. #14579130C23semidirect
218. #14579129C23semidirect
219. #14579129C23semidirect
220. C4×D316C23semidirect
221. C4×D316C23semidirect
222. D4×Dic79C23semidirect
223. #14579123C23semidirect
224. #14579123C23semidirect
225. C4×C22⋊D79C23semidirect
226. C4×C22⋊D79C23semidirect
227. C4×C22⋊D79C23semidirect
228. (C22⋊D79)⋊C4C23semidirect
229. (C22⋊D79)⋊C4C23semidirect
230. (C22⋊D79)⋊C4C23semidirect
231. #14579119C23semidirect
232. #14579119C23semidirect
233. #14579119C23semidirect
234. #14579118C23semidirect
235. #14579118C23semidirect
236. C2×C4⋊Dic79C23semidirect
237. C2×C4⋊Dic79C23semidirect
238. C2×C4⋊Dic79C23semidirect
239. C2×C4⋊Dic79C23semidirect
240. C2×Dic79⋊C4C23semidirect
241. C2×Dic79⋊C4C23semidirect
242. C2×Dic79⋊C4C23semidirect
243. C2×Dic79⋊C4C23semidirect
244. C2×Dic79⋊C4C23semidirect
245. C2×Dic79⋊C4C23semidirect
251. C2×C22⋊Dic79C23semidirect
252. C2×C22⋊Dic79C23semidirect
253. C2×C22⋊Dic79C23semidirect
266. C2×(C2×D79)⋊C4C23semidirect
267. C2×(C2×D79)⋊C4C23semidirect
268. C2×(C2×D79)⋊C4C23semidirect
269. C2×(C2×D79)⋊C4C23semidirect
270. C2×(C2×D79)⋊C4C23semidirect
272. C22⋊C4×D79C23semidirect
273. C22⋊C4×D79C23semidirect
274. C22⋊C4×D79C23semidirect
275. C22⋊C4×D79C23semidirect
276. C22⋊C4×D79C23semidirect
277. C22⋊C4×D79C23semidirect
278. C22⋊C4×D79C23semidirect
279. C2×C4×Dic79C23semidirect
280. C2×C4×Dic79C23semidirect
281. C2×C4×Dic79C23semidirect
283. C22×Q8×C79C23semidirect
287. C22×D4×C79C23semidirect
290. C23×C4×C79C23semidirect
291. #126×C79C23semidirect
292. #124×C79C23semidirect
293. #123×C79C23semidirect
294. C22⋊Q8×C79C23semidirect
295. #121×C79C23semidirect
296. #121×C79C23semidirect
297. #120×C79C23semidirect
298. C4×D4×C79C23semidirect
299. C2×C4⋊C4×C79C23semidirect
300. C2×C4⋊C4×C79C23semidirect
301. C2×C4⋊C4×C79C23semidirect
302. C2×C4⋊C4×C79C23semidirect
308. C2×C22⋊C4×C79C23semidirect
309. C2×C22⋊C4×C79C23semidirect
310. C2×C22⋊C4×C79C23semidirect
311. C2×C42×C79C23semidirect
330. C23×D79#41semidirect
345. C2×Dic158C24semidirect
346. C2×Dic158C24semidirect
354. C2×D316C24semidirect
368. C2×C22⋊D79C24semidirect
383. C22×Dic79C24semidirect
406. C2×C4×D79C24semidirect
407. C2×C4×D79C24semidirect
408. C4⋊Dic79C24semidirect
409. C4⋊Dic79C24semidirect
410. C4⋊Dic79C24semidirect
411. C4⋊Dic79C24semidirect
412. Dic79⋊C4C24semidirect
413. Dic79⋊C4C24semidirect
414. Dic79⋊C4C24semidirect
415. Dic79⋊C4C24semidirect
416. Dic79⋊C4C24semidirect
417. Dic79⋊C4C24semidirect
423. C22⋊Dic79C24semidirect
424. C22⋊Dic79C24semidirect
435. (C2×D79)⋊C4C24semidirect
436. (C2×D79)⋊C4C24semidirect
437. (C2×D79)⋊C4C24semidirect
438. (C2×D79)⋊C4C24semidirect
439. C4×Dic79C24semidirect
440. C4×Dic79C24semidirect
441. C4×Dic79C24semidirect
450. C2×Q8×C79C24semidirect
458. C2×D4×C79C24semidirect
470. C22×C4×C79C24semidirect
471. C4⋊C4×C79C24semidirect
472. C4⋊C4×C79C24semidirect
473. C4⋊C4×C79C24semidirect
474. C4⋊C4×C79C24semidirect
480. C22⋊C4×C79C24semidirect
481. C22⋊C4×C79C24semidirect
482. C42×C79C24semidirect
530. C22×D79C2×#41semidirect
650. C2×C79#3490semidirect
670. C2×#538D79semidirect
678. C79C2×#3490semidirect
699. #538C2×D79semidirect
704. C2×#126C2×D79semidirect
708. C2×#124C2×D79semidirect
721. C2×#123C2×D79semidirect
731. C2×C22⋊Q8C2×D79semidirect
740. C2×#121C2×D79semidirect
741. C2×#121C2×D79semidirect
752. C2×#120C2×D79semidirect
765. C2×C4×D4C2×D79semidirect
784. C22×C22⋊C4C2×D79semidirect
803. C22×Q8C22×D79semidirect
824. C22×D4C22×D79semidirect
845. C23×C4C22×D79semidirect
849. #126C22×D79semidirect
853. #124C22×D79semidirect
863. #123C22×D79semidirect
873. C22⋊Q8C22×D79semidirect
882. #121C22×D79semidirect
883. #121C22×D79semidirect
893. #120C22×D79semidirect
905. C4×D4C22×D79semidirect
921. C2×C4⋊C4C22×D79semidirect
922. C2×C4⋊C4C22×D79semidirect
923. C2×C4⋊C4C22×D79semidirect
924. C2×C4⋊C4C22×D79semidirect
963. C2×C22⋊C4C22×D79semidirect
964. C2×C22⋊C4C22×D79semidirect
965. C2×C22⋊C4C22×D79semidirect
969. C2×C42C22×D79semidirect
1013. C2×Q8C23×D79semidirect
1046. C2×D4C23×D79semidirect
1094. C22×C4C23×D79semidirect
1105. C4⋊C4C23×D79semidirect
1106. C4⋊C4C23×D79semidirect
1107. C4⋊C4C23×D79semidirect
1108. C4⋊C4C23×D79semidirect
1135. C22⋊C4C23×D79semidirect
1136. C22⋊C4C23×D79semidirect
1140. C42C23×D79semidirect
1311. C2#23777086direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#237770862
C2×#190992432
C2×#190992412
C2×#190992382
C2×#190992102
C2×#190992062
C2×#190992052
C2×#190992022
C2×#190991882
C2×#190991512
C2×#190991482
C2×#190991212
C2×#190990762
C2×#190990732
C2×#190990722
C2×#120×D792
C2×#190990352
C22×C22⋊C4×D792
C2×#538×C792
C2×#349079