Finite Group Databasebeta

← C2×#23777339 #35196241

Subgroups — C2×#23777339 #35196241

Order 20224.

8082 conjugacy classes of subgroups.

The subgroup lattice has 1356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23777339C2132yesmaximal, direct product factor
2C2×#19099273C211yesmaximal, characteristic, complemented
3C2×#19099263C211yesmaximal, characteristic, complemented
4C2×#19099258C212yesmaximal, complemented
5C2×#19099254C211yesmaximal, characteristic, complemented
6C2×#19099243C212yesmaximal, complemented
7C2×#19099242C212yesmaximal, complemented
8C2×#19099218C211yesmaximal, characteristic, complemented
9C2×#19099206C211yesmaximal, characteristic, complemented
10C2×#19099206C211yesmaximal, characteristic, complemented
11C2×#19099205C212yesmaximal, complemented
12C2×#19099198C211yesmaximal, characteristic, complemented
13C2×#19099182C211yesmaximal, characteristic, complemented
14C2×#19099167C211yesmaximal, characteristic, complemented
15C2×#19099156C212yesmaximal, complemented
16C2×#19099147C212yesmaximal, complemented
17C2×#19099100C211yesmaximal, characteristic, complemented
18C2×#19099092C211yesmaximal, characteristic, complemented
19C2×#19099072C212yesmaximal, complemented
20C2×#123×D79C212yesmaximal, complemented
21C2×#19099045C211yesmaximal, characteristic, complemented
22C2×#19099035C211yesmaximal, characteristic, complemented
23C2×C4×D4×D79C211yesmaximal, characteristic, complemented
24C2×#559×C79C211yesmaximal, characteristic, complemented
25C22×#11929625C2211yescharacteristic
26C22×#11929624C2212yescomplemented
27C22×D4×D79C2211yescharacteristic
28C22×D4×D79C2211yescharacteristic
29C22×D4×D79C2212yes—
30C23×C4×D79C2212yescomplemented
31#19099273C22116yescomplemented
32#19099263C22116yescomplemented
33#19099258C22132yescomplemented
34#19099254C22116yescomplemented
35#19099243C22132yescomplemented
36#19099242C22132yescomplemented
37#19099218C22116yescomplemented
38#19099206C22116yescomplemented
39#19099206C22116yescomplemented
40#19099205C22132yescomplemented
41#19099198C22116yescomplemented
42#19099182C22116yescomplemented
43#19099167C22116yescomplemented
44#19099156C22132yescomplemented
45#19099147C22132yescomplemented
46C2×#14579161C2211yescharacteristic, complemented
47#19099100C22116yescomplemented
48#19099092C22116yescomplemented
49C2×#14579156C2211yescharacteristic, complemented
50C2×#14579156C2211yescharacteristic, complemented
51C2×#14579155C2212yescomplemented
52C2×#14579154C2212yescomplemented
53C2×#14579154C2212yescomplemented
54C2×#14579154C2212yescomplemented
55C2×#14579153C2211yescharacteristic, complemented
56C2×#14579153C2211yescharacteristic, complemented
57C2×#14579152C2211yescharacteristic, complemented
58C2×#14579151C2212yescomplemented
59C2×#14579150C2211yescharacteristic, complemented
60C2×#14579147C2212yescomplemented
61#19099072C22132yescomplemented
62C2×#14579146C2212yes—
63C2×#14579146C2211yescharacteristic
64C2×#14579146C2211yescharacteristic, complemented
65C2×#14579145C2212yescomplemented
66C2×#14579144C2212yescomplemented
67C2×#14579143C2212yescomplemented
68C2×#14579143C2212yescomplemented
69C2×#14579143C2212yescomplemented
70C2×#14579143C2212yescomplemented
71C2×#14579143C2212yescomplemented
72C2×#14579142C2212yescomplemented
73C2×#14579142C2212yescomplemented
74#123×D79C22132yescomplemented
75C2×#14579140C2212yescomplemented
76C2×#14579139C2212yescomplemented
77C2×#14579139C2212yescomplemented
78C2×#14579138C2212yescomplemented
79C2×#14579137C2211yescharacteristic, complemented
80C2×#14579137C2211yescharacteristic, complemented
81C2×#14579137C2211yescharacteristic, complemented
82C2×#14579137C2212yescomplemented
83C2×#14579136C2211yescharacteristic
84C2×#14579134C2212yescomplemented
85C2×#14579134C2212yescomplemented
86C2×#14579134C2212yescomplemented
87C2×#14579133C2212yescomplemented
88C2×#14579133C2212yescomplemented
89C2×#14579132C2211yescharacteristic
90C2×#14579132C2211yescharacteristic
91C2×#14579132C2212yes—
92C2×#14579132C2211yescharacteristic, complemented
93C2×#14579132C2211yescharacteristic, complemented
94C2×#14579131C2212yescomplemented
95C2×#14579131C2212yescomplemented
96C2×#14579129C2212yes—
97C2×#14579129C2212yes—
98#19099045C22116yescomplemented
99#19099035C22116yescomplemented
100C2×Q8×Dic79C2211yescharacteristic, complemented
101C2×C4×D316C2211yescharacteristic
102C2×C4×D316C2211yescharacteristic
103C2×C4×D316C2211yescharacteristic
104C2×C4×D316C2211yescharacteristic
105C2×C4×D316C2211yescharacteristic, complemented
106C2×C4×D316C2211yescharacteristic, complemented
107C2×C4×D316C2212yescomplemented
108C2×D4×Dic79C2211yescharacteristic, complemented
109C2×D4×Dic79C2211yescharacteristic, complemented
110C2×#14579123C2211yescharacteristic
111C2×#14579123C2212yescomplemented
112C2×C4×C22⋊D79C2212yescomplemented
113C2×C4×C22⋊D79C2212yescomplemented
114C2×C4×C22⋊D79C2212yescomplemented
115C2×(C22⋊D79)⋊C4C2212yescomplemented
116C2×(C22⋊D79)⋊C4C2212yescomplemented
117C2×(C22⋊D79)⋊C4C2212yescomplemented
118C4×D4×D79C22116yescomplemented
119C2×#14579119C2211yescharacteristic, complemented
120C2×#14579118C2211yescharacteristic, complemented
121C2×#14579118C2212yescomplemented
122C2×#14579118C2211yescharacteristic, complemented
123C2×#14579118C2212yescomplemented
124C2×#14579117C2212yescomplemented
125C2×C4⋊C4×D79C2211yescharacteristic, complemented
126C2×C4⋊C4×D79C2211yescharacteristic, complemented
127C2×C4⋊C4×D79C2212yescomplemented
128C2×C4⋊C4×D79C2212yescomplemented
129C22×(C2×D79)⋊C4C2212yescomplemented
130C2×C22⋊C4×D79C2212yescomplemented
131C2×C22⋊C4×D79C2212yescomplemented
132C2×C22⋊C4×D79C2212yescomplemented
133C2×C22⋊C4×D79C2212yescomplemented
134C2×C42×D79C2211yescharacteristic, complemented
135#559×C79C22116yescomplemented
136C2×#127×C79C2211yescharacteristic
137C2×#124×C79C2211yescharacteristic, complemented
138C2×#124×C79C2211yescharacteristic, complemented
139C2×#124×C79C2212yescomplemented
140C2×#123×C79C2212yescomplemented
141C2×#123×C79C2212yescomplemented
142C2×C4×Q8×C79C2211yescharacteristic, complemented
143C2×C4×Q8×C79C2211yescharacteristic, complemented
144C2×C4×D4×C79C2211yescharacteristic, complemented
145C2×C4×D4×C79C2211yescharacteristic, complemented
146C2×C4×D4×C79C2212yescomplemented
147C24×D79C2312yes—
148C24×D79C2312yes—
149C2×#11929625—28no—
150C2×#11929625C2318yes—
151C2×#11929624—48no—
152C2×#11929624C23116yescomplemented
153C22×Dic158C2312yes—
154C22×D316C2312yes—
155C22×D316C2311yescharacteristic
156C22×D316C2311yescharacteristic
157C22×D316C2311yescharacteristic
158C22×D316C2311yescharacteristic
159C22×C22⋊D79C2312yes—
160C22×C22⋊D79C2312yes—
161C22×C22⋊D79C2312yes—
162C22×C22⋊D79C2312yes—
163C22×C22⋊D79C2312yes—
164C22×C22⋊D79C2312yes—
165C2×D4×D79—28no—
166C2×D4×D79—28no—
167C2×D4×D79—48no—
168C2×D4×D79C2318yes—
169C2×D4×D79C2318yes—
170C2×D4×D79C23116yes—
171C23×Dic79C2312yes—
172C23×Dic79C2312yes—
173C22×C4×D79—48no—
174C22×C4×D79C2311yescharacteristic
175C22×C4×D79C2311yescharacteristic
176C22×C4×D79C2312yes—
177C22×C4×D79C2312yes—
178C22×C4×D79C2311yescharacteristic
179C22×C4×D79C2311yescharacteristic
180C22×C4×D79C2311yescharacteristic
181C22×C4×D79C2312yes—
182C22×C4×D79C2312yes—
183C22×C4×D79C2312yes—
184C22×C4×D79C2312yes—
185C22×C4×D79C2312yes—
186C22×C4×D79C23116yescomplemented
187#14579161C2318yescomplemented
188#14579156C2318yescomplemented
189#14579156C2318yescomplemented
190#14579155C23116yescomplemented
191#14579154C23116yescomplemented
192#14579154C23116yescomplemented
193#14579154C23116yescomplemented
194#14579153C2318yescomplemented
195#14579153C2318yescomplemented
196#14579152C2318yescomplemented
197#14579151C23116yescomplemented
198#14579150C2318yescomplemented
199#14579147C23116yescomplemented
200#14579146C23116yes—
201#14579146C2318yes—
202#14579146C2318yescomplemented
203#14579145C23116yescomplemented
204#14579144C23116yescomplemented
205#14579143C23116yescomplemented
206#14579143C23116yescomplemented
207#14579143C23116yescomplemented
208#14579143C23116yescomplemented
209#14579143C23116yescomplemented
210#14579142C23116yescomplemented
211#14579142C23116yescomplemented
212#14579140C23116yescomplemented
213#14579139C23116yescomplemented
214#14579139C23116yescomplemented
215#14579138C23116yescomplemented
216#14579137C23116yescomplemented
217#14579137C2318yescomplemented
218#14579137C2318yescomplemented
219#14579137C2318yescomplemented
220#14579136C2318yes—
221#14579134C23116yescomplemented
222#14579134C23116yescomplemented
223#14579134C23116yescomplemented
224#14579133C23116yescomplemented
225#14579133C23116yescomplemented
226#14579132C23116yes—
227#14579132C2318yes—
228#14579132C2318yes—
229#14579132C2318yescomplemented
230#14579132C2318yescomplemented
231#14579131C23116yescomplemented
232#14579131C23116yescomplemented
233#14579129C23116yes—
234#14579129C23116yes—
235Q8×Dic79C2318yescomplemented
236C4×D316C2318yes—
237C4×D316C2318yes—
238C4×D316C2318yes—
239C4×D316C2318yes—
240C4×D316C23116yescomplemented
241C4×D316C2318yescomplemented
242C4×D316C2318yescomplemented
243D4×Dic79C2318yescomplemented
244D4×Dic79C2318yescomplemented
245#14579123C2318yes—
246#14579123C23116yescomplemented
247C4×C22⋊D79C23116yescomplemented
248C4×C22⋊D79C23116yescomplemented
249C4×C22⋊D79C23116yescomplemented
250(C22⋊D79)⋊C4C23116yescomplemented
251(C22⋊D79)⋊C4C23116yescomplemented
252(C22⋊D79)⋊C4C23116yescomplemented
253#14579119C2318yescomplemented
254#14579118C2318yescomplemented
255#14579118C2318yescomplemented
256#14579118C23116yescomplemented
257#14579118C23116yescomplemented
258#14579117C23116yescomplemented
259C2×C4⋊Dic79C2311yescharacteristic
260C2×C4⋊Dic79C2311yescharacteristic
261C2×C4⋊Dic79C2312yes—
262C2×C4⋊Dic79C2312yes—
263C2×C4⋊Dic79C2311yescharacteristic
264C2×C4⋊Dic79C2311yescharacteristic
265C2×C4⋊Dic79C2311yescharacteristic
266C2×C4⋊Dic79C2311yescharacteristic
267C2×Dic79⋊C4C2312yes—
268C2×Dic79⋊C4C2311yescharacteristic
269C2×Dic79⋊C4C2312yes—
270C2×Dic79⋊C4C2312yes—
271C2×Dic79⋊C4C2312yes—
272C2×Dic79⋊C4C2312yes—
273C2×Dic79⋊C4C2311yescharacteristic
274C2×Dic79⋊C4C2311yescharacteristic
275C2×Dic79⋊C4C2311yescharacteristic
276C2×Dic79⋊C4C2312yes—
277C2×Dic79⋊C4C2312yes—
278C2×Dic79⋊C4C2312yes—
279C4⋊C4×D79C23116yescomplemented
280C4⋊C4×D79C2318yescomplemented
281C4⋊C4×D79C2318yescomplemented
282C4⋊C4×D79C23116yescomplemented
283C2×C22⋊Dic79C2312yes—
284C2×C22⋊Dic79C2312yes—
285C2×C22⋊Dic79C2312yes—
286C2×C22⋊Dic79C2312yes—
287C2×C22⋊Dic79C2312yes—
288C2×C22⋊Dic79C2312yes—
289C2×(C2×D79)⋊C4C2311yescharacteristic
290C2×(C2×D79)⋊C4C2311yescharacteristic
291C2×(C2×D79)⋊C4C2311yescharacteristic
292C2×(C2×D79)⋊C4C2312yes—
293C2×(C2×D79)⋊C4C2312yes—
294C2×(C2×D79)⋊C4C2312yes—
295C2×(C2×D79)⋊C4C2312yes—
296C2×(C2×D79)⋊C4C2312yes—
297C2×(C2×D79)⋊C4C2311yescharacteristic
298C2×(C2×D79)⋊C4C2312yes—
299C2×(C2×D79)⋊C4C2311yescharacteristic
300C2×(C2×D79)⋊C4C2311yescharacteristic
301C2×(C2×D79)⋊C4C2312yes—
302C2×(C2×D79)⋊C4C2311yescharacteristic
303C2×(C2×D79)⋊C4C2311yescharacteristic
304C2×(C2×D79)⋊C4C2311yescharacteristic
305C2×(C2×D79)⋊C4C2311yescharacteristic
306C2×(C2×D79)⋊C4C23116yescomplemented
307C22⋊C4×D79C23116yescomplemented
308C22⋊C4×D79C23116yescomplemented
309C22⋊C4×D79C23116yescomplemented
310C22⋊C4×D79C23116yescomplemented
311C2×C4×Dic79C2311yescharacteristic
312C2×C4×Dic79C2311yescharacteristic
313C2×C4×Dic79C2311yescharacteristic
314C2×C4×Dic79C2312yes—
315C2×C4×Dic79C2312yes—
316C42×D79C2318yescomplemented
317C22×Q8×C79C2311yescharacteristic
318C22×Q8×C79C2311yescharacteristic
319C22×D4×C79C2311yescharacteristic
320C22×D4×C79C2311yescharacteristic
321C22×D4×C79C2312yes—
322C22×D4×C79C2312yes—
323C23×C4×C79C2312yes—
324C23×C4×C79C2312yes—
325#127×C79C2318yes—
326#124×C79C23116yescomplemented
327#124×C79C2318yescomplemented
328#124×C79C2318yescomplemented
329#123×C79C23116yescomplemented
330#123×C79C23116yescomplemented
331C4×Q8×C79C2318yescomplemented
332C4×Q8×C79C2318yescomplemented
333C4×D4×C79C2318yescomplemented
334C4×D4×C79C23116yescomplemented
335C4×D4×C79C2318yescomplemented
336C2×C4⋊C4×C79C2311yescharacteristic
337C2×C4⋊C4×C79C2311yescharacteristic
338C2×C4⋊C4×C79C2311yescharacteristic
339C2×C4⋊C4×C79C2312yes—
340C2×C4⋊C4×C79C2311yescharacteristic
341C2×C22⋊C4×C79C2312yes—
342C2×C22⋊C4×C79C2312yes—
343C2×C22⋊C4×C79C2312yes—
344C2×C22⋊C4×C79C2312yes—
345C2×C22⋊C4×C79C2312yes—
346C2×C22⋊C4×C79C2312yes—
347C2×C42×C79C2311yescharacteristic
348C2×C42×C79C2312yes—
349C2×C42×C79C2311yescharacteristic
350C2×C42×C79C2311yescharacteristic
351C23×D79—28no—
352C23×D79—28no—
353C23×D79—28no—
354C23×D79—44no—
355C23×D79—44no—
356C23×D79—44no—
357C23×D79C2411yescharacteristic
358C23×D79C2411yescharacteristic
359C23×D79C2418yes—
360C23×D79C2412yes—
361C23×D79C2411yescharacteristic
362C23×D79C2418yes—
363#11929625—232no—
364#11929624—432no—
365C2×Dic158—44no—
366C2×Dic158C2418yes—
367C2×D316—28no—
368C2×D316—24no—
369C2×D316—24no—
370C2×D316—42no—
371C2×D316#4118yescomplemented
372C2×D316C2414yes—
373C2×D316C2418yes—
374C2×D316C2414yes—
375C2×D316C2414yes—
376C2×D316C2414yes—
377C2×C22⋊D79—28no—
378C2×C22⋊D79—28no—
379C2×C22⋊D79—28no—
380C2×C22⋊D79—44no—
381C2×C22⋊D79—44no—
382C2×C22⋊D79—44no—
383C2×C22⋊D79C2418yes—
384C2×C22⋊D79C2418yes—
385C2×C22⋊D79C2418yes—
386C2×C22⋊D79C2418yes—
387C2×C22⋊D79C2418yes—
388C2×C22⋊D79C2418yes—
389D4×D79—232no—
390D4×D79—232no—
391D4×D79—432no—
392C22×Dic79—44no—
393C22×Dic79—44no—
394C22×Dic79C2412yes—
395C22×Dic79C2412yes—
396C22×Dic79C2411yescharacteristic
397C22×Dic79C2411yescharacteristic
398C22×Dic79C2411yescharacteristic
399C22×Dic79C2411yescharacteristic
400C22×Dic79C2412yes—
401C22×Dic79C2411yescharacteristic
402C22×Dic79C2418yes—
403C22×Dic79C2418yes—
404C2×C4×D79—28no—
405C2×C4×D79—28no—
406C2×C4×D79—24no—
407C2×C4×D79—24no—
408C2×C4×D79—24no—
409C2×C4×D79—24no—
410C2×C4×D79—44no—
411C2×C4×D79—44no—
412C2×C4×D79—44no—
413C2×C4×D79—44no—
414C2×C4×D79—42no—
415C2×C4×D79—44no—
416C2×C4×D79—432no—
417C2×C4×D79C2418yes—
418C2×C4×D79C2418yes—
419C2×C4×D79C2414yes—
420C2×C4×D79C2414yes—
421C2×C4×D79C2414yes—
422C2×C4×D79C2414yes—
423C2×C4×D79C2418yes—
424C2×C4×D79C2414yes—
425C2×C4×D79C2418yes—
426C2×C4×D79C2418yes—
427C2×C4×D79C2418yes—
428C2×C4×D79C2418yes—
429C4⋊Dic79C2414yes—
430C4⋊Dic79C2414yes—
431C4⋊Dic79C2418yes—
432C4⋊Dic79C2418yes—
433C4⋊Dic79C2414yes—
434C4⋊Dic79C2414yes—
435C4⋊Dic79C2414yes—
436C4⋊Dic79C2414yes—
437Dic79⋊C4C2418yes—
438Dic79⋊C4C2414yes—
439Dic79⋊C4C2418yes—
440Dic79⋊C4C2418yes—
441Dic79⋊C4C2418yes—
442Dic79⋊C4C2418yes—
443Dic79⋊C4C2414yes—
444Dic79⋊C4C2414yes—
445Dic79⋊C4C2414yes—
446Dic79⋊C4C2418yes—
447Dic79⋊C4C2418yes—
448Dic79⋊C4C2418yes—
449C22⋊Dic79C2418yes—
450C22⋊Dic79C2418yes—
451C22⋊Dic79C2418yes—
452C22⋊Dic79C2418yes—
453C22⋊Dic79C2418yes—
454C22⋊Dic79C2418yes—
455(C2×D79)⋊C4C2414yes—
456(C2×D79)⋊C4C2414yes—
457(C2×D79)⋊C4C2414yes—
458(C2×D79)⋊C4C2418yes—
459(C2×D79)⋊C4C2418yes—
460(C2×D79)⋊C4C2418yes—
461(C2×D79)⋊C4C2418yes—
462(C2×D79)⋊C4C2418yes—
463(C2×D79)⋊C4C2414yes—
464(C2×D79)⋊C4C2418yes—
465(C2×D79)⋊C4C2414yes—
466(C2×D79)⋊C4C2414yes—
467(C2×D79)⋊C4C2418yes—
468(C2×D79)⋊C4C2414yes—
469(C2×D79)⋊C4C2414yes—
470(C2×D79)⋊C4C2414yes—
471(C2×D79)⋊C4C2414yes—
472C4×Dic79C2414yes—
473C4×Dic79C2414yes—
474C4×Dic79C2414yes—
475C4×Dic79C2418yes—
476C4×Dic79C2418yes—
477C24×C79C2412yes—
478C24×C79C2412yes—
479C2×Q8×C79—24no—
480C2×Q8×C79—42no—
481C2×Q8×C79C2414yes—
482C2×Q8×C79C2414yes—
483C2×D4×C79—24no—
484C2×D4×C79—24no—
485C2×D4×C79—44no—
486C2×D4×C79—44no—
487C2×D4×C79C2414yes—
488C2×D4×C79C2414yes—
489C2×D4×C79C2418yes—
490C2×D4×C79C2418yes—
491C22×C4×C79—44no—
492C22×C4×C79—44no—
493C22×C4×C79C2411yescharacteristic
494C22×C4×C79C2411yescharacteristic
495C22×C4×C79C2412yes—
496C22×C4×C79C2411yescharacteristic
497C22×C4×C79C2411yescharacteristic
498C22×C4×C79C2411yescharacteristic
499C22×C4×C79C2412yes—
500C22×C4×C79C2411yescharacteristic
501C22×C4×C79C2418yes—
502C22×C4×C79C2418yes—
503C22×C4×C79C2411yescharacteristic
504C4⋊C4×C79C2414yes—
505C4⋊C4×C79C2414yes—
506C4⋊C4×C79C2414yes—
507C4⋊C4×C79C2418yes—
508C4⋊C4×C79C2414yes—
509C22⋊C4×C79C2418yes—
510C22⋊C4×C79C2418yes—
511C22⋊C4×C79C2418yes—
512C22⋊C4×C79C2418yes—
513C22⋊C4×C79C2418yes—
514C22⋊C4×C79C2418yes—
515C42×C79C2414yes—
516C42×C79C2418yes—
517C42×C79C2414yes—
518C42×C79C2414yes—
519C23×C79—24no—
520C23×C79—24no—
521C23×C79—24no—
522C23×C79—24no—
523C23×C79—24no—
524C23×C79—24no—
525C23×C79C2514yes—
526C23×C79C2514yes—
527C23×C79C2511yescharacteristic
528C22×D79—22no—
529C22×D79—24no—
530C22×D79—22no—
531C22×D79—24no—
532C22×D79—22no—
533C22×D79—22no—
534C22×D79—22no—
535C22×D79—22no—
536C22×D79—22no—
537C22×D79—22no—
538C22×D79—216no—
539C22×D79—216no—
540C22×D79—216no—
541C22×D79—48no—
542C22×D79—432no—
543C22×D79—48no—
544C22×D79—48no—
545C22×D79—816no—
546C22×D79C2×#4118yes—
547C22×D79H(5,𝔽2)14yes—
548C22×D79C2512yes—
549C22×D79C2512yes—
550C22×D79C2514yes—
551C22×D79C2512yes—
552Q8×C79—28no—
553Q8×C79—44no—
554D4×C79—28no—
555D4×C79—28no—
556D4×C79—48no—
557D4×C79—48no—
558C2×C4×C79—24no—
559C2×C4×C79—24no—
560C2×C4×C79—22no—
561C2×C4×C79—22no—
562C2×C4×C79—22no—
563C2×C4×C79—22no—
564C2×C4×C79—22no—
565C2×C4×C79—22no—
566C2×C4×C79—48no—
567C2×C4×C79—48no—
568C2×C4×C79C2×#4114yes—
569C2×C4×C79C2514yes—
570C2×C4×C79C2512yes—
571C2×C4×C79C2512yes—
572C2×C4×C79C2514yes—
573C2×C4×C79C2512yes—
574C2×C4×C79C2512yes—
575C2×C4×C79C2512yes—
576C2×C4×C79C2512yes—
577C2×C4×C79C2512yes—
578C22⋊D79—216no—
579C22⋊D79—216no—
580C22⋊D79—216no—
581C22⋊D79—48no—
582C22⋊D79—48no—
583C22⋊D79—48no—
584C2×Dic79—22no—
585C2×Dic79—22no—
586C2×Dic79—22no—
587C2×Dic79—22no—
588C2×Dic79—24no—
589C2×Dic79—24no—
590C2×Dic79—22no—
591C2×Dic79—24no—
592C2×Dic79—48no—
593C2×Dic79—48no—
594C2×Dic79C2512yes—
595C2×Dic79C2512yes—
596C2×Dic79C2512yes—
597C2×Dic79C2512yes—
598C2×Dic79C2514yes—
599C2×Dic79C2514yes—
600C2×Dic79C2512yes—
601C2×Dic79C2514yes—
602D316—216no—
603D316—28no—
604D316—28no—
605D316—44no—
606D316C2×#41116yescomplemented
607C4×D79—216no—
608C4×D79—28no—
609C4×D79—216no—
610C4×D79—28no—
611C4×D79—28no—
612C4×D79—28no—
613C4×D79—48no—
614C4×D79—48no—
615C4×D79—48no—
616C4×D79—44no—
617C4×D79—48no—
618C4×D79—48no—
619Dic158—48no—
620C22×C79—24no—
621C22×C79—24no—
622C22×C79—24no—
623C22×C79—24no—
624C22×C79—24no—
625C22×C79—24no—
626C22×C79—48no—
627C22×C79—48no—
628C22×C79C22×#4112yes—
629C22×C79C2×H(5,𝔽2)12yes—
630C22×C79#58512yes—
631C22×C79C2611yescharacteristic
632C2×D79—22no—
633C2×D79—24no—
634C2×D79—22no—
635C2×D79—24no—
636C2×D79—28no—
637C2×D79—216no—
638C2×D79—22no—
639C2×D79—22no—
640C2×D79—22no—
641C2×D79—22no—
642C2×D79—22no—
643C2×D79—22no—
644C2×D79—432no—
645C2×D79—44no—
646C2×D79—44no—
647C2×D79—816no—
648C2×D79C22×#4118yes—
649C2×D79C2×H(5,𝔽2)14yes—
650C4×C79—24no—
651C4×C79—22no—
652C4×C79—22no—
653C4×C79—24no—
654C4×C79—22no—
655C4×C79—22no—
656C4×C79—22no—
657C4×C79—22no—
658C4×C79C22×#4114yes—
659Dic79—22no—
660Dic79—22no—
661Dic79—22no—
662Dic79—24no—
663Dic79—24no—
664Dic79—22no—
665Dic79—24no—
666Dic79—22no—
667C2×#3513—791nomaximal, Sylow
668C2×C79—44no—
669C2×C79—44no—
670C2×C79#351314yescomplemented
671C2×C79C23×#4111yescharacteristic
672C2×C79C22×H(5,𝔽2)11yescharacteristic
673C2×C79C2×#58511yescharacteristic
674D79—24no—
675D79—28no—
676D79—42no—
677D79—42no—
678#3513—7932no—
679C2×#559D7911yescharacteristic, complemented
680C2×#554—791no—
681C2×#553—792no—
682C2×#553—791no—
683C2×#552—791no—
684C2×#551—792no—
685C2×#551—792no—
686C2×#547—791no—
687C2×#546—791no—
688C2×#546—791no—
689C2×#546—792no—
690C2×D42—791no—
691C2×#542—791no—
692C2×#540—791no—
693C2×#539—792no—
694C2×#538—792no—
695C2×#529—791no—
696C2×#529—791no—
697C2×#525—792no—
698C22×#123—792no—
699C2×#520—791no—
700C2×#518—791no—
701C22×C4×D4—791no—
702C79C2×#351311yescharacteristic, complemented, Sylow
703C22×#41—791no—
704C22×#41—792no—
705C23×D4—792no—
706C23×D4—791no—
707C23×D4—791no—
708C24×C4—792no—
709#559C2×D79116yescomplemented
710#554—7916no—
711#553—7932no—
712#553—7916no—
713#552—7916no—
714#551—7932no—
715#551—7932no—
716#547—7916no—
717#546—7916no—
718#546—7916no—
719#546—7932no—
720D42—7916no—
721#542—7916no—
722#540—7916no—
723#539—7932no—
724#538—7932no—
725C2×C4⋊Q8—791no—
726C2×#127C2×D7911yescharacteristic
727#529—7916no—
728#529—7916no—
729C2×#126—791no—
730C2×#126—791no—
731C2×#126—792no—
732C2×#126—792no—
733C2×#126—792no—
734C2×#126—792no—
735C2×#125—791no—
736C2×#125—792no—
737C2×#125—791no—
738C2×#125—791no—
739C2×#124—791no—
740C2×#124—792no—
741C2×#124C2×D7911yescharacteristic, complemented
742C2×#124C2×D7912yescomplemented
743C2×#124C2×D7911yescharacteristic, complemented
744#525—7932no—
745C2×#123—792no—
746C2×#123—792no—
747C2×#123—792no—
748C2×#123—7932no—
749C2×#123—791no—
750C2×#123—792no—
751C2×#123—791no—
752C2×#123—792no—
753C2×#123—792no—
754C2×#123—792no—
755C2×#123—792no—
756C2×#123—792no—
757C2×#123—792no—
758C2×#123C2×D7912yescomplemented
759C2×#123C2×D7912yescomplemented
760C2×C22⋊Q8—791no—
761C2×C22⋊Q8—791no—
762C2×C22⋊Q8—792no—
763C2×C22⋊Q8—791no—
764C2×C22⋊Q8—792no—
765C2×C22⋊Q8—792no—
766C2×C22⋊Q8—792no—
767C2×C22⋊Q8—792no—
768C2×#121—792no—
769C2×#121—791no—
770C2×#121—792no—
771C2×#121—791no—
772C2×#121—791no—
773C2×#121—792no—
774C2×#121—791no—
775C2×#121—791no—
776C2×#121—792no—
777C2×#121—792no—
778C2×#121—792no—
779C2×#120—792no—
780C2×#120—792no—
781C2×#120—792no—
782C2×#120—792no—
783#520—7916no—
784#518—7916no—
785C2×C4×Q8—791no—
786C2×C4×Q8C2×D7911yescharacteristic, complemented
787C2×C4×Q8C2×D7911yescharacteristic, complemented
788C2×C4×D4—791no—
789C2×C4×D4—791no—
790C2×C4×D4—792no—
791C2×C4×D4—792no—
792C2×C4×D4—792no—
793C2×C4×D4—7916no—
794C2×C4×D4—791no—
795C2×C4×D4—792no—
796C2×C4×D4—792no—
797C2×C4×D4—792no—
798C2×C4×D4—792no—
799C2×C4×D4—791no—
800C2×C4×D4—791no—
801C2×C4×D4—792no—
802C2×C4×D4—791no—
803C2×C4×D4—791no—
804C2×C4×D4—791no—
805C2×C4×D4—791no—
806C2×C4×D4C2×D7911yescharacteristic, complemented
807C2×C4×D4C2×D7911yescharacteristic, complemented
808C2×C4×D4C2×D7912yescomplemented
809C2×#117—791no—
810C2×#117—792no—
811C2×#117—791no—
812C2×#117—791no—
813C2×#117—792no—
814C2×#117—792no—
815C22×C4⋊C4—791no—
816C22×C4⋊C4—792no—
817C22×C4⋊C4—791no—
818C22×C4⋊C4—792no—
819C22×C22⋊C4—792no—
820C22×C22⋊C4—792no—
821C22×C22⋊C4—792no—
822C22×C22⋊C4—792no—
823C22×C22⋊C4—792no—
824C22×C42—791no—
825C25—792no—
826C25—792no—
827C2×#41—3168no—
828C2×#41—798no—
829C2×#41—7916no—
830C2×#41—1588no—
831C22×Q8—792no—
832C22×Q8C22×D7911yescharacteristic
833C22×Q8C22×D7911yescharacteristic
834C22×D4—3168no—
835C22×D4—792no—
836C22×D4—792no—
837C22×D4—792no—
838C22×D4—7916no—
839C22×D4—792no—
840C22×D4—792no—
841C22×D4—792no—
842C22×D4—798no—
843C22×D4—798no—
844C22×D4—791no—
845C22×D4—791no—
846C22×D4—792no—
847C22×D4—791no—
848C22×D4—791no—
849C22×D4—1588no—
850C22×D4—1588no—
851C22×D4C22×D7911yescharacteristic
852C22×D4C22×D7911yescharacteristic
853C22×D4C22×D7912yes—
854C22×D4C22×D7912yes—
855C23×C4—3168no—
856C23×C4—792no—
857C23×C4—792no—
858C23×C4—792no—
859C23×C4—791no—
860C23×C4—792no—
861C23×C4—792no—
862C23×C4—792no—
863C23×C4—792no—
864C23×C4—7916no—
865C23×C4—792no—
866C23×C4—792no—
867C23×C4—791no—
868C23×C4—791no—
869C23×C4—791no—
870C23×C4—791no—
871C23×C4C22×D7912yes—
872C23×C4C22×D7912yes—
873C4⋊Q8—798no—
874#127C22×D7918yes—
875#126—798no—
876#126—798no—
877#126—7916no—
878#126—7916no—
879#126—7916no—
880#126—7916no—
881#125—798no—
882#125—7916no—
883#125—798no—
884#125—798no—
885#124—798no—
886#124—7916no—
887#124C22×D7918yescomplemented
888#124C22×D79116yescomplemented
889#124C22×D7918yescomplemented
890#123—7916no—
891#123—7916no—
892#123—7916no—
893#123—798no—
894#123—7916no—
895#123—798no—
896#123—7916no—
897#123—7916no—
898#123—7916no—
899#123—7916no—
900#123—7916no—
901#123—7916no—
902#123C22×D79116yescomplemented
903#123C22×D79116yescomplemented
904C22⋊Q8—798no—
905C22⋊Q8—798no—
906C22⋊Q8—7916no—
907C22⋊Q8—798no—
908C22⋊Q8—7916no—
909C22⋊Q8—7916no—
910C22⋊Q8—7916no—
911C22⋊Q8—7916no—
912#121—7916no—
913#121—798no—
914#121—7916no—
915#121—798no—
916#121—798no—
917#121—7916no—
918#121—798no—
919#121—798no—
920#121—7916no—
921#121—7916no—
922#121—7916no—
923#120—7916no—
924#120—7916no—
925#120—7916no—
926#120—7916no—
927C4×Q8—798no—
928C4×Q8C22×D7918yescomplemented
929C4×Q8C22×D7918yescomplemented
930C4×D4—798no—
931C4×D4—798no—
932C4×D4—7916no—
933C4×D4—7916no—
934C4×D4—7916no—
935C4×D4—798no—
936C4×D4—7916no—
937C4×D4—7916no—
938C4×D4—7916no—
939C4×D4—7916no—
940C4×D4—798no—
941C4×D4—798no—
942C4×D4—7916no—
943C4×D4—798no—
944C4×D4—798no—
945C4×D4—798no—
946C4×D4—798no—
947C4×D4C22×D7918yescomplemented
948C4×D4C22×D7918yescomplemented
949C4×D4C22×D79116yescomplemented
950#117—798no—
951#117—7916no—
952#117—798no—
953#117—798no—
954#117—7916no—
955#117—7916no—
956C2×C4⋊C4—792no—
957C2×C4⋊C4—791no—
958C2×C4⋊C4—792no—
959C2×C4⋊C4—791no—
960C2×C4⋊C4—792no—
961C2×C4⋊C4—791no—
962C2×C4⋊C4—792no—
963C2×C4⋊C4—792no—
964C2×C4⋊C4—792no—
965C2×C4⋊C4—791no—
966C2×C4⋊C4—791no—
967C2×C4⋊C4—791no—
968C2×C4⋊C4—791no—
969C2×C4⋊C4—792no—
970C2×C4⋊C4—792no—
971C2×C4⋊C4—792no—
972C2×C4⋊C4—791no—
973C2×C4⋊C4—792no—
974C2×C4⋊C4—791no—
975C2×C4⋊C4—791no—
976C2×C4⋊C4—798no—
977C2×C4⋊C4—7916no—
978C2×C4⋊C4—798no—
979C2×C4⋊C4—7916no—
980C2×C4⋊C4C22×D7911yescharacteristic
981C2×C4⋊C4C22×D7911yescharacteristic
982C2×C4⋊C4C22×D7912yes—
983C2×C4⋊C4C22×D7911yescharacteristic
984C2×C4⋊C4C22×D7911yescharacteristic
985C2×C22⋊C4—792no—
986C2×C22⋊C4—792no—
987C2×C22⋊C4—792no—
988C2×C22⋊C4—792no—
989C2×C22⋊C4—792no—
990C2×C22⋊C4—792no—
991C2×C22⋊C4—792no—
992C2×C22⋊C4—792no—
993C2×C22⋊C4—791no—
994C2×C22⋊C4—791no—
995C2×C22⋊C4—791no—
996C2×C22⋊C4—791no—
997C2×C22⋊C4—792no—
998C2×C22⋊C4—792no—
999C2×C22⋊C4—792no—
1000C2×C22⋊C4—7916no—
1001C2×C22⋊C4—792no—
1002C2×C22⋊C4—791no—
1003C2×C22⋊C4—792no—
1004C2×C22⋊C4—791no—
1005C2×C22⋊C4—791no—
1006C2×C22⋊C4—791no—
1007C2×C22⋊C4—791no—
1008C2×C22⋊C4—791no—
1009C2×C22⋊C4—7916no—
1010C2×C22⋊C4—7916no—
1011C2×C22⋊C4—7916no—
1012C2×C22⋊C4—7916no—
1013C2×C22⋊C4C22×D7912yes—
1014C2×C22⋊C4C22×D7912yes—
1015C2×C22⋊C4C22×D7912yes—
1016C2×C22⋊C4C22×D7912yes—
1017C2×C22⋊C4C22×D7912yes—
1018C2×C22⋊C4C22×D7912yes—
1019C2×C42—791no—
1020C2×C42—792no—
1021C2×C42—792no—
1022C2×C42—791no—
1023C2×C42—791no—
1024C2×C42—798no—
1025C2×C42C22×D7912yes—
1026C2×C42C22×D7911yescharacteristic
1027C2×C42C22×D7911yescharacteristic
1028C2×C42C22×D7911yescharacteristic
1029C24—3164no—
1030C24—3164no—
1031C24—3164no—
1032C24—798no—
1033C24—798no—
1034C24—791no—
1035C24—792no—
1036C24—791no—
1037C24—791no—
1038C24—1588no—
1039C24—1588no—
1040C24—1588no—
1041C24C23×D7912yes—
1042C24C23×D7912yes—
1043#41—31632no—
1044#41—15832no—
1045C2×Q8—24no—
1046C2×Q8—42no—
1047C2×Q8—3164no—
1048C2×Q8—798no—
1049C2×Q8C23×D7914yes—
1050C2×Q8C23×D7914yes—
1051C2×D4—24no—
1052C2×D4—24no—
1053C2×D4—44no—
1054C2×D4—44no—
1055C2×D4—3162no—
1056C2×D4—31632no—
1057C2×D4—3164no—
1058C2×D4—3164no—
1059C2×D4—3164no—
1060C2×D4—798no—
1061C2×D4—798no—
1062C2×D4—798no—
1063C2×D4—798no—
1064C2×D4—798no—
1065C2×D4—798no—
1066C2×D4—798no—
1067C2×D4—794no—
1068C2×D4—794no—
1069C2×D4—798no—
1070C2×D4—794no—
1071C2×D4—794no—
1072C2×D4—1584no—
1073C2×D4—1584no—
1074C2×D4—1588no—
1075C2×D4—15832no—
1076C2×D4—15832no—
1077C2×D4—1588no—
1078C2×D4—1588no—
1079C2×D4—1588no—
1080C2×D4C23×D7914yes—
1081C2×D4C23×D7914yes—
1082C2×D4C23×D7918yes—
1083C2×D4C23×D7918yes—
1084C22×C4—44no—
1085C22×C4—44no—
1086C22×C4—3164no—
1087C22×C4—3164no—
1088C22×C4—3164no—
1089C22×C4—3162no—
1090C22×C4—3164no—
1091C22×C4—3164no—
1092C22×C4—31632no—
1093C22×C4—3164no—
1094C22×C4—3164no—
1095C22×C4—798no—
1096C22×C4—798no—
1097C22×C4—794no—
1098C22×C4—798no—
1099C22×C4—798no—
1100C22×C4—798no—
1101C22×C4—798no—
1102C22×C4—798no—
1103C22×C4—791no—
1104C22×C4—791no—
1105C22×C4—791no—
1106C22×C4—791no—
1107C22×C4—792no—
1108C22×C4—792no—
1109C22×C4—791no—
1110C22×C4—792no—
1111C22×C4—794no—
1112C22×C4—794no—
1113C22×C4—798no—
1114C22×C4—798no—
1115C22×C4—794no—
1116C22×C4—794no—
1117C22×C4—1584no—
1118C22×C4—1588no—
1119C22×C4—1588no—
1120C22×C4—1584no—
1121C22×C4—1584no—
1122C22×C4—1584no—
1123C22×C4C23×D7911yescharacteristic
1124C22×C4C23×D7912yes—
1125C22×C4C23×D7912yes—
1126C22×C4C23×D7911yescharacteristic
1127C22×C4C23×D7911yescharacteristic
1128C22×C4C23×D7911yescharacteristic
1129C22×C4C23×D7911yescharacteristic
1130C22×C4C23×D7911yescharacteristic
1131C22×C4C23×D7918yes—
1132C22×C4C23×D7918yes—
1133C22×C4C23×D7911yescharacteristic
1134C4⋊C4—798no—
1135C4⋊C4—794no—
1136C4⋊C4—798no—
1137C4⋊C4—798no—
1138C4⋊C4—798no—
1139C4⋊C4—794no—
1140C4⋊C4—794no—
1141C4⋊C4—794no—
1142C4⋊C4—798no—
1143C4⋊C4—798no—
1144C4⋊C4—798no—
1145C4⋊C4—798no—
1146C4⋊C4—794no—
1147C4⋊C4—794no—
1148C4⋊C4—798no—
1149C4⋊C4—798no—
1150C4⋊C4—794no—
1151C4⋊C4—794no—
1152C4⋊C4—794no—
1153C4⋊C4—794no—
1154C4⋊C4C23×D7914yes—
1155C4⋊C4C23×D7914yes—
1156C4⋊C4C23×D7918yes—
1157C4⋊C4C23×D7914yes—
1158C4⋊C4C23×D7914yes—
1159C22⋊C4—798no—
1160C22⋊C4—798no—
1161C22⋊C4—798no—
1162C22⋊C4—798no—
1163C22⋊C4—798no—
1164C22⋊C4—798no—
1165C22⋊C4—798no—
1166C22⋊C4—798no—
1167C22⋊C4—794no—
1168C22⋊C4—794no—
1169C22⋊C4—794no—
1170C22⋊C4—794no—
1171C22⋊C4—798no—
1172C22⋊C4—798no—
1173C22⋊C4—798no—
1174C22⋊C4—798no—
1175C22⋊C4—794no—
1176C22⋊C4—798no—
1177C22⋊C4—794no—
1178C22⋊C4—794no—
1179C22⋊C4—794no—
1180C22⋊C4—794no—
1181C22⋊C4—794no—
1182C22⋊C4C23×D7918yes—
1183C22⋊C4C23×D7918yes—
1184C22⋊C4C23×D7918yes—
1185C22⋊C4C23×D7918yes—
1186C22⋊C4C23×D7918yes—
1187C22⋊C4C23×D7918yes—
1188C42—794no—
1189C42—794no—
1190C42—794no—
1191C42—798no—
1192C42—798no—
1193C42C23×D7914yes—
1194C42C23×D7918yes—
1195C42C23×D7914yes—
1196C42C23×D7914yes—
1197C23—24no—
1198C23—24no—
1199C23—24no—
1200C23—24no—
1201C23—24no—
1202C23—24no—
1203C23—3168no—
1204C23—3168no—
1205C23—3168no—
1206C23—31632no—
1207C23—794no—
1208C23—794no—
1209C23—792no—
1210C23—798no—
1211C23—792no—
1212C23—792no—
1213C23—63216no—
1214C23—15816no—
1215C23—15816no—
1216C23—15816no—
1217C23—1582no—
1218C23—1582no—
1219C23—1582no—
1220C23—1582no—
1221C23—1582no—
1222C23—1582no—
1223C23—1584no—
1224C23—1582no—
1225C23—1584no—
1226C23—1582no—
1227C23C24×D7914yes—
1228C23C24×D7914yes—
1229C23C24×D7911yescharacteristic
1230Q8—28no—
1231Q8—44no—
1232Q8—3168no—
1233D4—28no—
1234D4—28no—
1235D4—48no—
1236D4—48no—
1237D4—3164no—
1238D4—3168no—
1239D4—3168no—
1240D4—3168no—
1241D4—7916no—
1242D4—1588no—
1243D4—1588no—
1244D4—15816no—
1245D4—15816no—
1246D4—15816no—
1247D4—15816no—
1248C2×C4—22no—
1249C2×C4—24no—
1250C2×C4—22no—
1251C2×C4—22no—
1252C2×C4—22no—
1253C2×C4—22no—
1254C2×C4—22no—
1255C2×C4—24no—
1256C2×C4—48no—
1257C2×C4—48no—
1258C2×C4—3168no—
1259C2×C4—3168no—
1260C2×C4—3168no—
1261C2×C4—3168no—
1262C2×C4—3168no—
1263C2×C4—3164no—
1264C2×C4—3168no—
1265C2×C4—3168no—
1266C2×C4—792no—
1267C2×C4—792no—
1268C2×C4—792no—
1269C2×C4—792no—
1270C2×C4—794no—
1271C2×C4—794no—
1272C2×C4—792no—
1273C2×C4—794no—
1274C2×C4—1588no—
1275C2×C4—15816no—
1276C2×C4—15816no—
1277C2×C4—1582no—
1278C2×C4—1584no—
1279C2×C4—1584no—
1280C2×C4—1582no—
1281C2×C4—1584no—
1282C2×C4—1582no—
1283C2×C4—1582no—
1284C2×C4—1582no—
1285C2×C4—1588no—
1286C2×C4—1588no—
1287C2×C4—1588no—
1288C2×C4#41×D7914yes—
1289C2×C4C24×D7914yes—
1290C2×C4C24×D7912yes—
1291C2×C4C24×D7912yes—
1292C2×C4C24×D7914yes—
1293C2×C4C24×D7912yes—
1294C2×C4C24×D7912yes—
1295C2×C4C24×D7912yes—
1296C2×C4C24×D7912yes—
1297C2×C4C24×D7912yes—
1298C22—24no—
1299C22—24no—
1300C22—24no—
1301C22—24no—
1302C22—24no—
1303C22—24no—
1304C22—48no—
1305C22—48no—
1306C22—31632no—
1307C22—3164no—
1308C22—3164no—
1309C22—798no—
1310C22—794no—
1311C22—63216no—
1312C22—1582no—
1313C22—1582no—
1314C22—1582no—
1315C22—1582no—
1316C22—1582no—
1317C22—1582no—
1318C22—1588no—
1319C22—15816no—
1320C22—1582no—
1321C22—1584no—
1322C22—1582no—
1323C22—1584no—
1324C22C2×#41×D7912yes—
1325C22H(5,𝔽2)×D7912yes—
1326C22#1909939912yes—
1327C22C25×D7911yescharacteristic
1328C4—24no—
1329C4—22no—
1330C4—24no—
1331C4—22no—
1332C4—22no—
1333C4—22no—
1334C4—22no—
1335C4—22no—
1336C4—1582no—
1337C4—1582no—
1338C4—1582no—
1339C4—1582no—
1340C4—1584no—
1341C4—1584no—
1342C4—1582no—
1343C4—1584no—
1344C4C2×#41×D7914yes—
1345C2—44no—
1346C2—44no—
1347C2—3162no—
1348C2—3162no—
1349C2—1584no—
1350C2—1588no—
1351C2#2377733914yesdirect product factor
1352C2C22×#41×D7911yescharacteristic
1353C2C2×H(5,𝔽2)×D7911yescharacteristic
1354C2C2×#1909939911yescharacteristic
subgroupG/H
centerC23C24×D79
commutator, cosocleC22×C79C26
FrattiniC22C25×D79
FittingC2×#559×C79C2
socleC23×C79C25
hypercenterC2×#559D79
hypocenterC79C2×#3513
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×#559

Complements

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

NH ≅ G/Ntype
1. #23777339C2direct (N × H)
2. C2×#19099273C2semidirect
3. C2×#19099263C2semidirect
4. C2×#19099258C2semidirect
5. C2×#19099254C2semidirect
6. C2×#19099243C2semidirect
7. C2×#19099242C2semidirect
8. C2×#19099218C2semidirect
9. C2×#19099206C2semidirect
10. C2×#19099206C2semidirect
11. C2×#19099205C2semidirect
12. C2×#19099198C2semidirect
13. C2×#19099182C2semidirect
14. C2×#19099167C2semidirect
15. C2×#19099156C2semidirect
16. C2×#19099147C2semidirect
17. C2×#19099100C2semidirect
18. C2×#19099092C2semidirect
19. C2×#19099072C2semidirect
20. C2×#123×D79C2semidirect
21. C2×#19099045C2semidirect
22. C2×#19099035C2semidirect
23. C2×C4×D4×D79C2semidirect
24. C2×#559×C79C2semidirect
26. C22×#11929624C22semidirect
30. C23×C4×D79C22semidirect
31. #19099273C22semidirect
32. #19099263C22semidirect
33. #19099258C22semidirect
34. #19099254C22semidirect
35. #19099243C22semidirect
36. #19099242C22semidirect
37. #19099218C22semidirect
38. #19099206C22semidirect
39. #19099206C22semidirect
40. #19099205C22semidirect
41. #19099198C22semidirect
42. #19099182C22semidirect
43. #19099167C22semidirect
44. #19099156C22semidirect
45. #19099147C22semidirect
46. C2×#14579161C22semidirect
47. #19099100C22semidirect
48. #19099092C22semidirect
49. C2×#14579156C22semidirect
50. C2×#14579156C22semidirect
51. C2×#14579155C22semidirect
52. C2×#14579154C22semidirect
53. C2×#14579154C22semidirect
54. C2×#14579154C22semidirect
55. C2×#14579153C22semidirect
56. C2×#14579153C22semidirect
57. C2×#14579152C22semidirect
58. C2×#14579151C22semidirect
59. C2×#14579150C22semidirect
60. C2×#14579147C22semidirect
61. #19099072C22semidirect
64. C2×#14579146C22semidirect
65. C2×#14579145C22semidirect
66. C2×#14579144C22semidirect
67. C2×#14579143C22semidirect
68. C2×#14579143C22semidirect
69. C2×#14579143C22semidirect
70. C2×#14579143C22semidirect
71. C2×#14579143C22semidirect
72. C2×#14579142C22semidirect
73. C2×#14579142C22semidirect
74. #123×D79C22semidirect
75. C2×#14579140C22semidirect
76. C2×#14579139C22semidirect
77. C2×#14579139C22semidirect
78. C2×#14579138C22semidirect
79. C2×#14579137C22semidirect
80. C2×#14579137C22semidirect
81. C2×#14579137C22semidirect
82. C2×#14579137C22semidirect
84. C2×#14579134C22semidirect
85. C2×#14579134C22semidirect
86. C2×#14579134C22semidirect
87. C2×#14579133C22semidirect
88. C2×#14579133C22semidirect
92. C2×#14579132C22semidirect
93. C2×#14579132C22semidirect
94. C2×#14579131C22semidirect
95. C2×#14579131C22semidirect
98. #19099045C22semidirect
99. #19099035C22semidirect
100. C2×Q8×Dic79C22semidirect
105. C2×C4×D316C22semidirect
106. C2×C4×D316C22semidirect
107. C2×C4×D316C22semidirect
108. C2×D4×Dic79C22semidirect
109. C2×D4×Dic79C22semidirect
111. C2×#14579123C22semidirect
112. C2×C4×C22⋊D79C22semidirect
113. C2×C4×C22⋊D79C22semidirect
114. C2×C4×C22⋊D79C22semidirect
115. C2×(C22⋊D79)⋊C4C22semidirect
116. C2×(C22⋊D79)⋊C4C22semidirect
117. C2×(C22⋊D79)⋊C4C22semidirect
118. C4×D4×D79C22semidirect
119. C2×#14579119C22semidirect
120. C2×#14579118C22semidirect
121. C2×#14579118C22semidirect
122. C2×#14579118C22semidirect
123. C2×#14579118C22semidirect
124. C2×#14579117C22semidirect
125. C2×C4⋊C4×D79C22semidirect
126. C2×C4⋊C4×D79C22semidirect
127. C2×C4⋊C4×D79C22semidirect
128. C2×C4⋊C4×D79C22semidirect
129. C22×(C2×D79)⋊C4C22semidirect
130. C2×C22⋊C4×D79C22semidirect
131. C2×C22⋊C4×D79C22semidirect
132. C2×C22⋊C4×D79C22semidirect
133. C2×C22⋊C4×D79C22semidirect
134. C2×C42×D79C22semidirect
135. #559×C79C22semidirect
137. C2×#124×C79C22semidirect
138. C2×#124×C79C22semidirect
139. C2×#124×C79C22semidirect
140. C2×#123×C79C22semidirect
141. C2×#123×C79C22semidirect
142. C2×C4×Q8×C79C22semidirect
143. C2×C4×Q8×C79C22semidirect
144. C2×C4×D4×C79C22semidirect
145. C2×C4×D4×C79C22semidirect
146. C2×C4×D4×C79C22semidirect
152. C2×#11929624C23semidirect
186. C22×C4×D79C23semidirect
187. #14579161C23semidirect
188. #14579156C23semidirect
189. #14579156C23semidirect
190. #14579155C23semidirect
191. #14579154C23semidirect
192. #14579154C23semidirect
193. #14579154C23semidirect
194. #14579153C23semidirect
195. #14579153C23semidirect
196. #14579152C23semidirect
197. #14579151C23semidirect
198. #14579150C23semidirect
199. #14579147C23semidirect
202. #14579146C23semidirect
203. #14579145C23semidirect
204. #14579144C23semidirect
205. #14579143C23semidirect
206. #14579143C23semidirect
207. #14579143C23semidirect
208. #14579143C23semidirect
209. #14579143C23semidirect
210. #14579142C23semidirect
211. #14579142C23semidirect
212. #14579140C23semidirect
213. #14579139C23semidirect
214. #14579139C23semidirect
215. #14579138C23semidirect
216. #14579137C23semidirect
217. #14579137C23semidirect
218. #14579137C23semidirect
219. #14579137C23semidirect
221. #14579134C23semidirect
222. #14579134C23semidirect
223. #14579134C23semidirect
224. #14579133C23semidirect
225. #14579133C23semidirect
229. #14579132C23semidirect
230. #14579132C23semidirect
231. #14579131C23semidirect
232. #14579131C23semidirect
235. Q8×Dic79C23semidirect
240. C4×D316C23semidirect
241. C4×D316C23semidirect
242. C4×D316C23semidirect
243. D4×Dic79C23semidirect
244. D4×Dic79C23semidirect
246. #14579123C23semidirect
247. C4×C22⋊D79C23semidirect
248. C4×C22⋊D79C23semidirect
249. C4×C22⋊D79C23semidirect
250. (C22⋊D79)⋊C4C23semidirect
251. (C22⋊D79)⋊C4C23semidirect
252. (C22⋊D79)⋊C4C23semidirect
253. #14579119C23semidirect
254. #14579118C23semidirect
255. #14579118C23semidirect
256. #14579118C23semidirect
257. #14579118C23semidirect
258. #14579117C23semidirect
279. C4⋊C4×D79C23semidirect
280. C4⋊C4×D79C23semidirect
281. C4⋊C4×D79C23semidirect
282. C4⋊C4×D79C23semidirect
306. C2×(C2×D79)⋊C4C23semidirect
307. C22⋊C4×D79C23semidirect
308. C22⋊C4×D79C23semidirect
309. C22⋊C4×D79C23semidirect
310. C22⋊C4×D79C23semidirect
316. C42×D79C23semidirect
326. #124×C79C23semidirect
327. #124×C79C23semidirect
328. #124×C79C23semidirect
329. #123×C79C23semidirect
330. #123×C79C23semidirect
331. C4×Q8×C79C23semidirect
332. C4×Q8×C79C23semidirect
333. C4×D4×C79C23semidirect
334. C4×D4×C79C23semidirect
335. C4×D4×C79C23semidirect
371. C2×D316#41semidirect
606. D316C2×#41semidirect
670. C2×C79#3513semidirect
679. C2×#559D79semidirect
702. C79C2×#3513semidirect
709. #559C2×D79semidirect
741. C2×#124C2×D79semidirect
742. C2×#124C2×D79semidirect
743. C2×#124C2×D79semidirect
758. C2×#123C2×D79semidirect
759. C2×#123C2×D79semidirect
786. C2×C4×Q8C2×D79semidirect
787. C2×C4×Q8C2×D79semidirect
806. C2×C4×D4C2×D79semidirect
807. C2×C4×D4C2×D79semidirect
808. C2×C4×D4C2×D79semidirect
887. #124C22×D79semidirect
888. #124C22×D79semidirect
889. #124C22×D79semidirect
902. #123C22×D79semidirect
903. #123C22×D79semidirect
928. C4×Q8C22×D79semidirect
929. C4×Q8C22×D79semidirect
947. C4×D4C22×D79semidirect
948. C4×D4C22×D79semidirect
949. C4×D4C22×D79semidirect
1351. C2#23777339direct (N × H)

Maximal subgroups

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

subgroupindex
#237773392
C2×#190992732
C2×#190992632
C2×#190992582
C2×#190992542
C2×#190992432
C2×#190992422
C2×#190992182
C2×#190992062
C2×#190992052
C2×#190991982
C2×#190991822
C2×#190991672
C2×#190991562
C2×#190991472
C2×#190991002
C2×#190990922
C2×#190990722
C2×#123×D792
C2×#190990452
C2×#190990352
C2×C4×D4×D792
C2×#559×C792
C2×#351379