Finite Group Databasebeta

← C2×#23777334 #35196232

Subgroups — C2×#23777334 #35196232

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#23777334C2132yesmaximal, direct product factor
2C2×#19099295C211yesmaximal, characteristic, complemented
3C2×#19099269C211yesmaximal, characteristic, complemented
4C2×#19099266C211yesmaximal, characteristic, complemented
5C2×#19099257C212yesmaximal, complemented
6C2×#19099255C211yesmaximal, characteristic, complemented
7C2×#19099242C212yesmaximal, complemented
8C2×#19099237C212yesmaximal, complemented
9C2×#19099213C211yesmaximal, characteristic, complemented
10C2×#19099208C212yesmaximal, complemented
11C2×#19099206C211yesmaximal, characteristic, complemented
12C2×#19099204C211yesmaximal, characteristic, complemented
13C2×#19099197C211yesmaximal, characteristic, complemented
14C2×#19099185C211yesmaximal, characteristic, complemented
15C2×#19099164C211yesmaximal, characteristic, complemented
16C2×#19099154C212yesmaximal, complemented
17C2×#19099152C212yesmaximal, complemented
18C2×#19099097C211yesmaximal, characteristic, complemented
19C2×#19099071C212yesmaximal, complemented
20C2×#123×D79C212yesmaximal, complemented
21C2×#19099045C211yesmaximal, characteristic, complemented
22C2×#19099035C211yesmaximal, characteristic, complemented
23C22×C4×D316C211yesmaximal, characteristic, complemented
24C2×#529×C79C211yesmaximal, characteristic, complemented
25C22×#11929625C2211yescharacteristic
26C22×#11929623C2212yescomplemented
27C23×D316C2211yescharacteristic
28C22×D4×D79C2211yescharacteristic
29C22×D4×D79C2212yes—
30C23×C4×D79C2212yescomplemented
31#19099295C22116yescomplemented
32#19099269C22116yescomplemented
33#19099266C22116yescomplemented
34#19099257C22132yescomplemented
35#19099255C22116yescomplemented
36#19099242C22132yescomplemented
37#19099237C22132yescomplemented
38#19099213C22116yescomplemented
39#19099208C22132yescomplemented
40#19099206C22116yescomplemented
41#19099204C22116yescomplemented
42#19099197C22116yescomplemented
43#19099185C22116yescomplemented
44#19099164C22116yescomplemented
45#19099154C22132yescomplemented
46#19099152C22132yescomplemented
47C2×#14579160C2211yescharacteristic, complemented
48C2×#14579157C2211yescharacteristic
49#19099097C22116yescomplemented
50C2×#14579156C2212yescomplemented
51C2×#14579156C2212yescomplemented
52C2×#14579155C2212yescomplemented
53C2×#14579155C2211yescharacteristic, complemented
54C2×#14579155C2211yescharacteristic, complemented
55C2×#14579153C2211yescharacteristic, complemented
56C2×#14579152C2212yescomplemented
57C2×#14579152C2211yescharacteristic, complemented
58C2×#14579150C2211yescharacteristic, complemented
59C2×#14579149C2212yescomplemented
60C2×#14579149C2211yescharacteristic, complemented
61C2×#14579147C2212yescomplemented
62#19099071C22132yescomplemented
63C2×#14579146C2212yescomplemented
64C2×#14579146C2212yescomplemented
65C2×#14579146C2212yescomplemented
66C2×#14579145C2212yes—
67C2×#14579145C2212yescomplemented
68C2×#14579144C2211yescharacteristic
69C2×#14579144C2211yescharacteristic, complemented
70C2×#14579144C2212yescomplemented
71C2×#14579143C2212yescomplemented
72C2×#14579143C2212yescomplemented
73C2×#14579143C2212yescomplemented
74C2×#14579143C2212yescomplemented
75C2×#14579142C2212yescomplemented
76#123×D79C22132yescomplemented
77C2×#14579141C2212yescomplemented
78C2×#14579140C2211yescharacteristic, complemented
79C2×#14579139C2212yescomplemented
80C2×#14579139C2212yescomplemented
81C2×#14579139C2212yescomplemented
82C2×#14579138C2212yescomplemented
83C2×#14579137C2211yescharacteristic, complemented
84C2×#14579136C2211yescharacteristic
85C2×#14579136C2212yescomplemented
86C2×#14579136C2211yescharacteristic, complemented
87C2×#14579136C2212yescomplemented
88C2×#14579135C2211yescharacteristic
89C2×#14579135C2212yescomplemented
90C2×#14579134C2212yes—
91C2×#14579134C2212yescomplemented
92C2×#14579134C2212yescomplemented
93C2×#14579132C2211yescharacteristic, complemented
94C2×#14579131C2212yes—
95C2×#14579131C2212yescomplemented
96C2×#14579131C2212yescomplemented
97C2×#14579129C2212yes—
98#19099045C22116yescomplemented
99#19099035C22116yescomplemented
100C2×Q8×Dic79C2211yescharacteristic, complemented
101C2×C4×Dic158C2211yescharacteristic, complemented
102C2×C4×D316C2211yescharacteristic
103C2×C4×D316C2211yescharacteristic
104C2×C4×D316C2211yescharacteristic, complemented
105C2×C4×D316C2212yescomplemented
106C2×C4×D316C2211yescharacteristic, complemented
107C2×C4×D316C2212yescomplemented
108C2×C4×D316C2211yescharacteristic, complemented
109C2×C4×D316C2212yescomplemented
110C2×C4×D316C22116yescomplemented
111C2×D4×Dic79C2211yescharacteristic, complemented
112C2×#14579123C2211yescharacteristic
113C2×#14579123C2211yescharacteristic
114C2×#14579123C2212yescomplemented
115C2×#14579123C2212yescomplemented
116C2×C4×C22⋊D79C2211yescharacteristic
117C2×C4×C22⋊D79C2212yescomplemented
118C2×C4×C22⋊D79C2211yescharacteristic, complemented
119C2×(C22⋊D79)⋊C4C2212yescomplemented
120C2×(C22⋊D79)⋊C4C2212yescomplemented
121C2×#14579119C2211yescharacteristic, complemented
122C2×#14579118C2211yescharacteristic, complemented
123C2×#14579118C2212yescomplemented
124C2×#14579118C2211yescharacteristic, complemented
125C2×#14579117C2212yescomplemented
126C22×C4⋊Dic79C2211yescharacteristic, complemented
127C2×C4⋊C4×D79C2211yescharacteristic, complemented
128C2×C4⋊C4×D79C2212yescomplemented
129C2×C4⋊C4×D79C2212yescomplemented
130C22×(C2×D79)⋊C4C2212yescomplemented
131C22×(C2×D79)⋊C4C2212yescomplemented
132C2×C22⋊C4×D79C2212yescomplemented
133C2×C22⋊C4×D79C2212yescomplemented
134C2×C22⋊C4×D79C2212yescomplemented
135#529×C79C22116yescomplemented
136C2×#126×C79C2212yescomplemented
137C2×#125×C79C2211yescharacteristic, complemented
138C2×#124×C79C2211yescharacteristic, complemented
139C2×#123×C79C2212yescomplemented
140C2×C22⋊Q8×C79C2211yescharacteristic, complemented
141C2×#121×C79C2211yescharacteristic
142C2×C4×Q8×C79C2211yescharacteristic, complemented
143C2×C4×D4×C79C2211yescharacteristic, complemented
144C2×C4×D4×C79C2212yescomplemented
145C2×#117×C79C2212yescomplemented
146C22×C42×C79C2211yescharacteristic, complemented
147C24×D79C2312yes—
148C24×D79C2312yes—
149C2×#11929625—28no—
150C2×#11929625C2318yes—
151C2×#11929623—48no—
152C2×#11929623C23116yescomplemented
153C22×Dic158C2311yescharacteristic
154C22×Dic158C2312yes—
155C22×D316—28no—
156C22×D316C2318yes—
157C22×D316C2312yes—
158C22×D316C2312yes—
159C22×D316C2311yescharacteristic
160C22×D316C2312yes—
161C22×D316C2311yescharacteristic
162C22×D316C2312yes—
163C22×D316C2311yescharacteristic
164C22×C22⋊D79C2312yes—
165C22×C22⋊D79C2311yescharacteristic
166C22×C22⋊D79C2311yescharacteristic
167C22×C22⋊D79C2312yes—
168C22×C22⋊D79C2312yes—
169C22×C22⋊D79C2312yes—
170C2×D4×D79—28no—
171C2×D4×D79—48no—
172C2×D4×D79C2318yes—
173C2×D4×D79C23116yes—
174C23×Dic79C2312yes—
175C23×Dic79C2312yes—
176C22×C4×D79—48no—
177C22×C4×D79C2312yes—
178C22×C4×D79C2311yescharacteristic
179C22×C4×D79C2311yescharacteristic
180C22×C4×D79C2312yes—
181C22×C4×D79C2312yes—
182C22×C4×D79C2312yes—
183C22×C4×D79C2312yes—
184C22×C4×D79C2312yes—
185C22×C4×D79C2312yes—
186C22×C4×D79C2312yes—
187C22×C4×D79C23116yescomplemented
188#14579160C2318yescomplemented
189#14579157C2318yes—
190#14579156C23116yescomplemented
191#14579156C23116yescomplemented
192#14579155C23116yescomplemented
193#14579155C2318yescomplemented
194#14579155C2318yescomplemented
195#14579153C2318yescomplemented
196#14579152C23116yescomplemented
197#14579152C2318yescomplemented
198#14579150C2318yescomplemented
199#14579149C2318yescomplemented
200#14579149C23116yescomplemented
201#14579147C23116yescomplemented
202#14579146C23116yescomplemented
203#14579146C23116yescomplemented
204#14579146C23116yescomplemented
205#14579145C23116yes—
206#14579145C23116yescomplemented
207#14579144C2318yes—
208#14579144C23116yescomplemented
209#14579144C2318yescomplemented
210#14579143C23116yescomplemented
211#14579143C23116yescomplemented
212#14579143C23116yescomplemented
213#14579143C23116yescomplemented
214#14579142C23116yescomplemented
215#14579141C23116yescomplemented
216#14579140C2318yescomplemented
217#14579139C23116yescomplemented
218#14579139C23116yescomplemented
219#14579139C23116yescomplemented
220#14579138C23116yescomplemented
221#14579137C2318yescomplemented
222#14579136C2318yes—
223#14579136C23116yescomplemented
224#14579136C23116yescomplemented
225#14579136C2318yescomplemented
226#14579135C2318yes—
227#14579135C23116yescomplemented
228#14579134C23116yes—
229#14579134C23116yescomplemented
230#14579134C23116yescomplemented
231#14579132C2318yescomplemented
232#14579131C23116yes—
233#14579131C23116yescomplemented
234#14579131C23116yescomplemented
235#14579129C23116yes—
236Q8×Dic79C2318yescomplemented
237C4×Dic158C2318yescomplemented
238C4×D316C2318yes—
239C4×D316C2318yes—
240C4×D316C23116yescomplemented
241C4×D316C2318yescomplemented
242C4×D316C2318yescomplemented
243C4×D316C23116yescomplemented
244C4×D316C23116yescomplemented
245C4×D316C2318yescomplemented
246D4×Dic79C2318yescomplemented
247#14579123C2318yes—
248#14579123C2318yes—
249#14579123C23116yescomplemented
250#14579123C23116yescomplemented
251C4×C22⋊D79C2318yes—
252C4×C22⋊D79C2318yescomplemented
253C4×C22⋊D79C23116yescomplemented
254(C22⋊D79)⋊C4C23116yescomplemented
255(C22⋊D79)⋊C4C23116yescomplemented
256#14579119C2318yescomplemented
257#14579118C2318yescomplemented
258#14579118C2318yescomplemented
259#14579118C23116yescomplemented
260#14579117C23116yescomplemented
261C2×C4⋊Dic79C2311yescharacteristic
262C2×C4⋊Dic79C2312yes—
263C2×C4⋊Dic79C2312yes—
264C2×C4⋊Dic79C2311yescharacteristic
265C2×C4⋊Dic79C2312yes—
266C2×C4⋊Dic79C2311yescharacteristic
267C2×C4⋊Dic79C2311yescharacteristic
268C2×C4⋊Dic79C2318yescomplemented
269C2×Dic79⋊C4C2312yes—
270C2×Dic79⋊C4C2311yescharacteristic
271C2×Dic79⋊C4C2311yescharacteristic
272C2×Dic79⋊C4C2312yes—
273C2×Dic79⋊C4C2312yes—
274C2×Dic79⋊C4C2312yes—
275C2×Dic79⋊C4C2311yescharacteristic
276C2×Dic79⋊C4C2311yescharacteristic
277C2×Dic79⋊C4C2311yescharacteristic
278C2×Dic79⋊C4C2311yescharacteristic
279C2×Dic79⋊C4C2311yescharacteristic
280C2×Dic79⋊C4C2311yescharacteristic
281C4⋊C4×D79C23116yescomplemented
282C4⋊C4×D79C2318yescomplemented
283C4⋊C4×D79C23116yescomplemented
284C2×C22⋊Dic79C2311yescharacteristic
285C2×C22⋊Dic79C2312yes—
286C2×C22⋊Dic79C2312yes—
287C2×C22⋊Dic79C2311yescharacteristic
288C2×(C2×D79)⋊C4C2311yescharacteristic
289C2×(C2×D79)⋊C4C2311yescharacteristic
290C2×(C2×D79)⋊C4C2312yes—
291C2×(C2×D79)⋊C4C2312yes—
292C2×(C2×D79)⋊C4C2312yes—
293C2×(C2×D79)⋊C4C2312yes—
294C2×(C2×D79)⋊C4C2312yes—
295C2×(C2×D79)⋊C4C2311yescharacteristic
296C2×(C2×D79)⋊C4C2312yes—
297C2×(C2×D79)⋊C4C2312yes—
298C2×(C2×D79)⋊C4C2312yes—
299C2×(C2×D79)⋊C4C2312yes—
300C2×(C2×D79)⋊C4C2312yes—
301C2×(C2×D79)⋊C4C2311yescharacteristic
302C2×(C2×D79)⋊C4C2311yescharacteristic
303C2×(C2×D79)⋊C4C2312yes—
304C2×(C2×D79)⋊C4C2311yescharacteristic
305C2×(C2×D79)⋊C4C2311yescharacteristic
306C2×(C2×D79)⋊C4C2311yescharacteristic
307C2×(C2×D79)⋊C4C2312yes—
308C2×(C2×D79)⋊C4C23116yescomplemented
309C2×(C2×D79)⋊C4C23116yescomplemented
310C22⋊C4×D79C23116yescomplemented
311C22⋊C4×D79C23116yescomplemented
312C22⋊C4×D79C23116yescomplemented
313C2×C4×Dic79C2312yes—
314C2×C4×Dic79C2312yes—
315C2×C4×Dic79C2311yescharacteristic
316C2×C4×Dic79C2311yescharacteristic
317C22×Q8×C79C2311yescharacteristic
318C22×D4×C79C2312yes—
319C22×D4×C79C2311yescharacteristic
320C23×C4×C79C2311yescharacteristic
321C23×C4×C79C2311yescharacteristic
322C23×C4×C79C2311yescharacteristic
323C23×C4×C79C2312yes—
324#126×C79C23116yescomplemented
325#125×C79C2318yescomplemented
326#124×C79C2318yescomplemented
327#123×C79C23116yescomplemented
328C22⋊Q8×C79C2318yescomplemented
329#121×C79C2318yes—
330C4×Q8×C79C2318yescomplemented
331C4×D4×C79C2318yescomplemented
332C4×D4×C79C23116yescomplemented
333#117×C79C23116yescomplemented
334C2×C4⋊C4×C79C2312yes—
335C2×C4⋊C4×C79C2312yes—
336C2×C4⋊C4×C79C2311yescharacteristic
337C2×C4⋊C4×C79C2312yes—
338C2×C4⋊C4×C79C2311yescharacteristic
339C2×C4⋊C4×C79C2312yes—
340C2×C22⋊C4×C79C2312yes—
341C2×C22⋊C4×C79C2312yes—
342C2×C22⋊C4×C79C2312yes—
343C2×C22⋊C4×C79C2312yes—
344C2×C22⋊C4×C79C2312yes—
345C2×C42×C79C2311yescharacteristic
346C2×C42×C79C2311yescharacteristic
347C2×C42×C79C2311yescharacteristic
348C2×C42×C79C2311yescharacteristic
349C2×C42×C79C2312yes—
350C2×C42×C79C2318yescomplemented
351C23×D79—28no—
352C23×D79—28no—
353C23×D79—28no—
354C23×D79—44no—
355C23×D79—44no—
356C23×D79—44no—
357C23×D79C2411yescharacteristic
358C23×D79C2412yes—
359C23×D79C2411yescharacteristic
360C23×D79C2418yes—
361C23×D79C2412yes—
362C23×D79C2418yes—
363#11929625—232no—
364#11929623—432no—
365C2×Dic158—42no—
366C2×Dic158—44no—
367C2×Dic158C2418yes—
368C2×Dic158C2414yes—
369C2×D316—232no—
370C2×D316—28no—
371C2×D316—28no—
372C2×D316—24no—
373C2×D316—44no—
374C2×D316—44no—
375C2×D316—42no—
376C2×D316#4118yescomplemented
377C2×D316C2418yes—
378C2×D316C2418yes—
379C2×D316C2414yes—
380C2×D316C2418yes—
381C2×D316C2414yes—
382C2×D316C2418yes—
383C2×D316C2414yes—
384C2×C22⋊D79—24no—
385C2×C22⋊D79—24no—
386C2×C22⋊D79—28no—
387C2×C22⋊D79—44no—
388C2×C22⋊D79—44no—
389C2×C22⋊D79—44no—
390C2×C22⋊D79C2414yes—
391C2×C22⋊D79C2418yes—
392C2×C22⋊D79C2414yes—
393C2×C22⋊D79C2418yes—
394C2×C22⋊D79C2418yes—
395C2×C22⋊D79C2418yes—
396D4×D79—232no—
397D4×D79—432no—
398C22×Dic79—28no—
399C22×Dic79—44no—
400C22×Dic79C2411yescharacteristic
401C22×Dic79C2411yescharacteristic
402C22×Dic79C2411yescharacteristic
403C22×Dic79C2412yes—
404C22×Dic79C2418yes—
405C22×Dic79C2411yescharacteristic
406C22×Dic79C2412yes—
407C22×Dic79C2411yescharacteristic
408C22×Dic79C2411yescharacteristic
409C22×Dic79C2418yes—
410C2×C4×D79—28no—
411C2×C4×D79—24no—
412C2×C4×D79—24no—
413C2×C4×D79—44no—
414C2×C4×D79—44no—
415C2×C4×D79—44no—
416C2×C4×D79—44no—
417C2×C4×D79—44no—
418C2×C4×D79—432no—
419C2×C4×D79—44no—
420C2×C4×D79—44no—
421C2×C4×D79C2418yes—
422C2×C4×D79C2414yes—
423C2×C4×D79C2414yes—
424C2×C4×D79C2418yes—
425C2×C4×D79C2418yes—
426C2×C4×D79C2418yes—
427C2×C4×D79C2418yes—
428C2×C4×D79C2418yes—
429C2×C4×D79C2418yes—
430C2×C4×D79C2418yes—
431C4⋊Dic79C2414yes—
432C4⋊Dic79C2418yes—
433C4⋊Dic79C2418yes—
434C4⋊Dic79C2414yes—
435C4⋊Dic79C2418yes—
436C4⋊Dic79C2414yes—
437C4⋊Dic79C2414yes—
438Dic79⋊C4C2418yes—
439Dic79⋊C4C2414yes—
440Dic79⋊C4C2414yes—
441Dic79⋊C4C2418yes—
442Dic79⋊C4C2418yes—
443Dic79⋊C4C2418yes—
444Dic79⋊C4C2414yes—
445Dic79⋊C4C2414yes—
446Dic79⋊C4C2414yes—
447Dic79⋊C4C2414yes—
448Dic79⋊C4C2414yes—
449Dic79⋊C4C2414yes—
450C22⋊Dic79C2414yes—
451C22⋊Dic79C2418yes—
452C22⋊Dic79C2418yes—
453C22⋊Dic79C2414yes—
454(C2×D79)⋊C4C2414yes—
455(C2×D79)⋊C4C2414yes—
456(C2×D79)⋊C4C2418yes—
457(C2×D79)⋊C4C2418yes—
458(C2×D79)⋊C4C2418yes—
459(C2×D79)⋊C4C2418yes—
460(C2×D79)⋊C4C2418yes—
461(C2×D79)⋊C4C2414yes—
462(C2×D79)⋊C4C2418yes—
463(C2×D79)⋊C4C2418yes—
464(C2×D79)⋊C4C2418yes—
465(C2×D79)⋊C4C2418yes—
466(C2×D79)⋊C4C2418yes—
467(C2×D79)⋊C4C2414yes—
468(C2×D79)⋊C4C2414yes—
469(C2×D79)⋊C4C2418yes—
470(C2×D79)⋊C4C2414yes—
471(C2×D79)⋊C4C2414yes—
472(C2×D79)⋊C4C2414yes—
473(C2×D79)⋊C4C2418yes—
474C4×Dic79C2418yes—
475C4×Dic79C2418yes—
476C4×Dic79C2414yes—
477C4×Dic79C2414yes—
478C24×C79C2412yes—
479C24×C79C2411yescharacteristic
480C2×Q8×C79—24no—
481C2×Q8×C79C2414yes—
482C2×D4×C79—28no—
483C2×D4×C79—24no—
484C2×D4×C79C2418yes—
485C2×D4×C79C2414yes—
486C22×C4×C79—24no—
487C22×C4×C79—24no—
488C22×C4×C79—44no—
489C22×C4×C79—42no—
490C22×C4×C79C2411yescharacteristic
491C22×C4×C79C2412yes—
492C22×C4×C79C2411yescharacteristic
493C22×C4×C79C2411yescharacteristic
494C22×C4×C79C2411yescharacteristic
495C22×C4×C79C2411yescharacteristic
496C22×C4×C79C2412yes—
497C22×C4×C79C2414yes—
498C22×C4×C79C2414yes—
499C22×C4×C79C2412yes—
500C22×C4×C79C2414yes—
501C22×C4×C79C2418yes—
502C22×C4×C79C2411yescharacteristic
503C4⋊C4×C79C2418yes—
504C4⋊C4×C79C2418yes—
505C4⋊C4×C79C2414yes—
506C4⋊C4×C79C2418yes—
507C4⋊C4×C79C2414yes—
508C4⋊C4×C79C2418yes—
509C22⋊C4×C79C2418yes—
510C22⋊C4×C79C2418yes—
511C22⋊C4×C79C2418yes—
512C22⋊C4×C79C2418yes—
513C22⋊C4×C79C2418yes—
514C42×C79C2414yes—
515C42×C79C2414yes—
516C42×C79C2414yes—
517C42×C79C2414yes—
518C42×C79C2418yes—
519C23×C79—22no—
520C23×C79—22no—
521C23×C79—24no—
522C23×C79—24no—
523C23×C79—24no—
524C23×C79H(5,𝔽2)14yes—
525C23×C79C2514yes—
526C23×C79C2512yes—
527C23×C79C2511yescharacteristic
528C22×D79—24no—
529C22×D79—24no—
530C22×D79—22no—
531C22×D79—22no—
532C22×D79—24no—
533C22×D79—216no—
534C22×D79—22no—
535C22×D79—24no—
536C22×D79—22no—
537C22×D79—24no—
538C22×D79—22no—
539C22×D79—22no—
540C22×D79—216no—
541C22×D79—216no—
542C22×D79—48no—
543C22×D79—48no—
544C22×D79—48no—
545C22×D79—432no—
546C22×D79—816no—
547C22×D79C2×#4118yes—
548C22×D79C2512yes—
549C22×D79C2514yes—
550C22×D79C2512yes—
551C22×D79C2514yes—
552Q8×C79—28no—
553D4×C79—216no—
554D4×C79—28no—
555C2×C4×C79—24no—
556C2×C4×C79—22no—
557C2×C4×C79—28no—
558C2×C4×C79—22no—
559C2×C4×C79—22no—
560C2×C4×C79—24no—
561C2×C4×C79—24no—
562C2×C4×C79—22no—
563C2×C4×C79—22no—
564C2×C4×C79—28no—
565C2×C4×C79—44no—
566C2×C4×C79—48no—
567C2×C4×C79C2×#4114yes—
568C2×C4×C79C2514yes—
569C2×C4×C79C2514yes—
570C2×C4×C79C2512yes—
571C2×C4×C79C2512yes—
572C2×C4×C79C2512yes—
573C2×C4×C79C2512yes—
574C2×C4×C79C2512yes—
575C2×C4×C79C2514yes—
576C2×C4×C79C2512yes—
577C22⋊D79—28no—
578C22⋊D79—28no—
579C22⋊D79—216no—
580C22⋊D79—48no—
581C22⋊D79—48no—
582C22⋊D79—48no—
583C2×Dic79—22no—
584C2×Dic79—22no—
585C2×Dic79—24no—
586C2×Dic79—24no—
587C2×Dic79—216no—
588C2×Dic79—22no—
589C2×Dic79—22no—
590C2×Dic79—22no—
591C2×Dic79—22no—
592C2×Dic79—48no—
593C2×Dic79C2512yes—
594C2×Dic79C2512yes—
595C2×Dic79C2514yes—
596C2×Dic79C2512yes—
597C2×Dic79C2512yes—
598C2×Dic79C2512yes—
599C2×Dic79C2512yes—
600C2×Dic79C2514yes—
601D316—216no—
602D316—216no—
603D316—28no—
604D316—48no—
605D316—44no—
606D316—48no—
607D316C2×#41116yescomplemented
608C4×D79—216no—
609C4×D79—28no—
610C4×D79—28no—
611C4×D79—48no—
612C4×D79—48no—
613C4×D79—48no—
614C4×D79—48no—
615C4×D79—48no—
616C4×D79—48no—
617C4×D79—48no—
618Dic158—44no—
619Dic158—48no—
620C22×C79—22no—
621C22×C79—22no—
622C22×C79—28no—
623C22×C79—24no—
624C22×C79—24no—
625C22×C79—24no—
626C22×C79—48no—
627C22×C79C22×#4112yes—
628C22×C79C2×H(5,𝔽2)14yes—
629C22×C79C2×H(5,𝔽2)12yes—
630C22×C79#58512yes—
631C22×C79C2611yescharacteristic
632C2×D79—24no—
633C2×D79—24no—
634C2×D79—216no—
635C2×D79—22no—
636C2×D79—24no—
637C2×D79—22no—
638C2×D79—22no—
639C2×D79—22no—
640C2×D79—24no—
641C2×D79—24no—
642C2×D79—22no—
643C2×D79—22no—
644C2×D79—432no—
645C2×D79—44no—
646C2×D79—48no—
647C2×D79—44no—
648C2×D79—816no—
649C2×D79C22×#4118yes—
650C4×C79—22no—
651C4×C79—24no—
652C4×C79—22no—
653C4×C79—22no—
654C4×C79—24no—
655C4×C79—22no—
656C4×C79—22no—
657C4×C79—24no—
658C4×C79C22×#4114yes—
659Dic79—22no—
660Dic79—22no—
661Dic79—22no—
662Dic79—22no—
663Dic79—24no—
664Dic79—24no—
665Dic79—22no—
666Dic79—22no—
667C2×#3513—791nomaximal, Sylow
668C2×C79—24no—
669C2×C79—44no—
670C2×C79#351314yescomplemented
671C2×C79C23×#4111yescharacteristic
672C2×C79C22×H(5,𝔽2)11yescharacteristic
673C2×C79C2×#58511yescharacteristic
674D79—28no—
675D79—42no—
676D79—44no—
677D79—42no—
678#3513—7932no—
679C2×#559—791no—
680C2×#554—791no—
681C2×#553—791no—
682C2×#553—792no—
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×#529D7911yescharacteristic, complemented
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#559—7916no—
710#554—7916no—
711#553—7916no—
712#553—7932no—
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×#127—791no—
727#529—7916no—
728#529C2×D79116yescomplemented
729C2×#126—792no—
730C2×#126—792no—
731C2×#126—791no—
732C2×#126—791no—
733C2×#126—792no—
734C2×#126C2×D7912yescomplemented
735C2×#125—792no—
736C2×#125—791no—
737C2×#125—791no—
738C2×#125C2×D7911yescharacteristic, complemented
739C2×#124—791no—
740C2×#124—792no—
741C2×#124—791no—
742C2×#124—792no—
743C2×#124C2×D7911yescharacteristic, complemented
744#525—7932no—
745C2×#123—792no—
746C2×#123—791no—
747C2×#123—791no—
748C2×#123—792no—
749C2×#123—7932no—
750C2×#123—792no—
751C2×#123—792no—
752C2×#123—792no—
753C2×#123—792no—
754C2×#123—792no—
755C2×#123—792no—
756C2×#123—792no—
757C2×#123—792no—
758C2×#123—792no—
759C2×#123C2×D7912yescomplemented
760C2×C22⋊Q8—791no—
761C2×C22⋊Q8—791no—
762C2×C22⋊Q8—792no—
763C2×C22⋊Q8—792no—
764C2×C22⋊Q8—792no—
765C2×C22⋊Q8—792no—
766C2×C22⋊Q8—792no—
767C2×C22⋊Q8C2×D7911yescharacteristic, complemented
768C2×#121—791no—
769C2×#121—791no—
770C2×#121—792no—
771C2×#121—792no—
772C2×#121—792no—
773C2×#121—791no—
774C2×#121—791no—
775C2×#121—792no—
776C2×#121—792no—
777C2×#121—792no—
778C2×#121C2×D7911yescharacteristic
779C2×#120—792no—
780C2×#120—792no—
781C2×#120—792no—
782C2×#120—792no—
783#520—7916no—
784#518—7916no—
785C2×C4×Q8—791no—
786C2×C4×Q8—791no—
787C2×C4×Q8C2×D7911yescharacteristic, complemented
788C2×C4×D4—791no—
789C2×C4×D4—792no—
790C2×C4×D4—791no—
791C2×C4×D4—791no—
792C2×C4×D4—791no—
793C2×C4×D4—792no—
794C2×C4×D4—791no—
795C2×C4×D4—792no—
796C2×C4×D4—792no—
797C2×C4×D4—792no—
798C2×C4×D4—791no—
799C2×C4×D4—792no—
800C2×C4×D4—791no—
801C2×C4×D4—791no—
802C2×C4×D4—792no—
803C2×C4×D4—791no—
804C2×C4×D4—792no—
805C2×C4×D4—791no—
806C2×C4×D4—7916no—
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×#117C2×D7912yescomplemented
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×C42C2×D7911yescharacteristic, complemented
825C25—792no—
826C25—792no—
827C2×#41—3168no—
828C2×#41—798no—
829C2×#41—7916no—
830C2×#41—1588no—
831C22×Q8—791no—
832C22×Q8—792no—
833C22×Q8C22×D7911yescharacteristic
834C22×D4—3168no—
835C22×D4—792no—
836C22×D4—792no—
837C22×D4—792no—
838C22×D4—7916no—
839C22×D4—792no—
840C22×D4—791no—
841C22×D4—791no—
842C22×D4—798no—
843C22×D4—791no—
844C22×D4—792no—
845C22×D4—792no—
846C22×D4—791no—
847C22×D4—792no—
848C22×D4—792no—
849C22×D4—791no—
850C22×D4—798no—
851C22×D4—1588no—
852C22×D4—1588no—
853C22×D4C22×D7911yescharacteristic
854C22×D4C22×D7912yes—
855C23×C4—3168no—
856C23×C4—792no—
857C23×C4—792no—
858C23×C4—792no—
859C23×C4—792no—
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×C4C22×D7911yescharacteristic
870C23×C4C22×D7911yescharacteristic
871C23×C4C22×D7911yescharacteristic
872C23×C4C22×D7912yes—
873C4⋊Q8—798no—
874#127—798no—
875#126—7916no—
876#126—7916no—
877#126—798no—
878#126—798no—
879#126—7916no—
880#126C22×D79116yescomplemented
881#125—7916no—
882#125—798no—
883#125—798no—
884#125C22×D7918yescomplemented
885#124—798no—
886#124—7916no—
887#124—798no—
888#124—7916no—
889#124C22×D7918yescomplemented
890#123—7916no—
891#123—798no—
892#123—798no—
893#123—7916no—
894#123—7916no—
895#123—7916no—
896#123—7916no—
897#123—7916no—
898#123—7916no—
899#123—7916no—
900#123—7916no—
901#123—7916no—
902#123—7916no—
903#123C22×D79116yescomplemented
904C22⋊Q8—798no—
905C22⋊Q8—798no—
906C22⋊Q8—7916no—
907C22⋊Q8—7916no—
908C22⋊Q8—7916no—
909C22⋊Q8—7916no—
910C22⋊Q8—7916no—
911C22⋊Q8C22×D7918yescomplemented
912#121—798no—
913#121—798no—
914#121—7916no—
915#121—7916no—
916#121—7916no—
917#121—798no—
918#121—798no—
919#121—7916no—
920#121—7916no—
921#121—7916no—
922#121C22×D7918yes—
923#120—7916no—
924#120—7916no—
925#120—7916no—
926#120—7916no—
927C4×Q8—798no—
928C4×Q8—798no—
929C4×Q8C22×D7918yescomplemented
930C4×D4—798no—
931C4×D4—7916no—
932C4×D4—798no—
933C4×D4—798no—
934C4×D4—798no—
935C4×D4—7916no—
936C4×D4—798no—
937C4×D4—7916no—
938C4×D4—7916no—
939C4×D4—7916no—
940C4×D4—798no—
941C4×D4—7916no—
942C4×D4—798no—
943C4×D4—798no—
944C4×D4—7916no—
945C4×D4—798no—
946C4×D4—7916no—
947C4×D4—798no—
948C4×D4C22×D7918yescomplemented
949C4×D4C22×D79116yescomplemented
950#117—798no—
951#117—7916no—
952#117—798no—
953#117—798no—
954#117—7916no—
955#117C22×D79116yescomplemented
956C2×C4⋊C4—791no—
957C2×C4⋊C4—792no—
958C2×C4⋊C4—791no—
959C2×C4⋊C4—791no—
960C2×C4⋊C4—791no—
961C2×C4⋊C4—792no—
962C2×C4⋊C4—798no—
963C2×C4⋊C4—792no—
964C2×C4⋊C4—792no—
965C2×C4⋊C4—792no—
966C2×C4⋊C4—791no—
967C2×C4⋊C4—791no—
968C2×C4⋊C4—791no—
969C2×C4⋊C4—792no—
970C2×C4⋊C4—792no—
971C2×C4⋊C4—791no—
972C2×C4⋊C4—791no—
973C2×C4⋊C4—791no—
974C2×C4⋊C4—791no—
975C2×C4⋊C4—791no—
976C2×C4⋊C4—7916no—
977C2×C4⋊C4—798no—
978C2×C4⋊C4—7916no—
979C2×C4⋊C4C22×D7912yes—
980C2×C4⋊C4C22×D7911yescharacteristic
981C2×C4⋊C4C22×D7912yes—
982C2×C4⋊C4C22×D7911yescharacteristic
983C2×C4⋊C4C22×D7912yes—
984C2×C4⋊C4C22×D7912yes—
985C2×C22⋊C4—791no—
986C2×C22⋊C4—792no—
987C2×C22⋊C4—792no—
988C2×C22⋊C4—791no—
989C2×C22⋊C4—792no—
990C2×C22⋊C4—792no—
991C2×C22⋊C4—791no—
992C2×C22⋊C4—791no—
993C2×C22⋊C4—791no—
994C2×C22⋊C4—792no—
995C2×C22⋊C4—792no—
996C2×C22⋊C4—792no—
997C2×C22⋊C4—792no—
998C2×C22⋊C4—7916no—
999C2×C22⋊C4—7916no—
1000C2×C22⋊C4—792no—
1001C2×C22⋊C4—792no—
1002C2×C22⋊C4—792no—
1003C2×C22⋊C4—792no—
1004C2×C22⋊C4—791no—
1005C2×C22⋊C4—791no—
1006C2×C22⋊C4—791no—
1007C2×C22⋊C4—791no—
1008C2×C22⋊C4—792no—
1009C2×C22⋊C4—792no—
1010C2×C22⋊C4—791no—
1011C2×C22⋊C4—7916no—
1012C2×C22⋊C4—7916no—
1013C2×C22⋊C4—7916no—
1014C2×C22⋊C4C22×D7912yes—
1015C2×C22⋊C4C22×D7912yes—
1016C2×C22⋊C4C22×D7912yes—
1017C2×C22⋊C4C22×D7912yes—
1018C2×C22⋊C4C22×D7912yes—
1019C2×C42—792no—
1020C2×C42—792no—
1021C2×C42—791no—
1022C2×C42—791no—
1023C2×C42C22×D7911yescharacteristic
1024C2×C42C22×D7912yes—
1025C2×C42C22×D7911yescharacteristic
1026C2×C42C22×D7911yescharacteristic
1027C2×C42C22×D7911yescharacteristic
1028C2×C42C22×D7918yescomplemented
1029C24—3164no—
1030C24—3164no—
1031C24—3164no—
1032C24—798no—
1033C24—798no—
1034C24—792no—
1035C24—791no—
1036C24—792no—
1037C24—791no—
1038C24—1588no—
1039C24—1588no—
1040C24—1588no—
1041C24C23×D7912yes—
1042C24C23×D7911yescharacteristic
1043#41—31632no—
1044#41—15832no—
1045C2×Q8—24no—
1046C2×Q8—3162no—
1047C2×Q8—3164no—
1048C2×Q8—794no—
1049C2×Q8—798no—
1050C2×Q8C23×D7914yes—
1051C2×D4—28no—
1052C2×D4—24no—
1053C2×D4—3164no—
1054C2×D4—3164no—
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—794no—
1065C2×D4—794no—
1066C2×D4—798no—
1067C2×D4—794no—
1068C2×D4—798no—
1069C2×D4—798no—
1070C2×D4—794no—
1071C2×D4—798no—
1072C2×D4—798no—
1073C2×D4—794no—
1074C2×D4—15832no—
1075C2×D4—1588no—
1076C2×D4—1588no—
1077C2×D4—15832no—
1078C2×D4—1588no—
1079C2×D4—1584no—
1080C2×D4—1584no—
1081C2×D4—1584no—
1082C2×D4C23×D7914yes—
1083C2×D4C23×D7918yes—
1084C22×C4—24no—
1085C22×C4—24no—
1086C22×C4—44no—
1087C22×C4—42no—
1088C22×C4—3164no—
1089C22×C4—3164no—
1090C22×C4—3164no—
1091C22×C4—3164no—
1092C22×C4—31632no—
1093C22×C4—3164no—
1094C22×C4—3164no—
1095C22×C4—3164no—
1096C22×C4—3164no—
1097C22×C4—798no—
1098C22×C4—798no—
1099C22×C4—798no—
1100C22×C4—798no—
1101C22×C4—798no—
1102C22×C4—798no—
1103C22×C4—798no—
1104C22×C4—798no—
1105C22×C4—798no—
1106C22×C4—791no—
1107C22×C4—791no—
1108C22×C4—792no—
1109C22×C4—791no—
1110C22×C4—791no—
1111C22×C4—791no—
1112C22×C4—791no—
1113C22×C4—792no—
1114C22×C4—798no—
1115C22×C4—794no—
1116C22×C4—794no—
1117C22×C4—1588no—
1118C22×C4—1588no—
1119C22×C4—1584no—
1120C22×C4—1584no—
1121C22×C4C23×D7914yes—
1122C22×C4C23×D7914yes—
1123C22×C4C23×D7912yes—
1124C22×C4C23×D7912yes—
1125C22×C4C23×D7911yescharacteristic
1126C22×C4C23×D7911yescharacteristic
1127C22×C4C23×D7911yescharacteristic
1128C22×C4C23×D7911yescharacteristic
1129C22×C4C23×D7911yescharacteristic
1130C22×C4C23×D7912yes—
1131C22×C4C23×D7914yes—
1132C22×C4C23×D7918yes—
1133C22×C4C23×D7911yescharacteristic
1134C4⋊C4—798no—
1135C4⋊C4—794no—
1136C4⋊C4—794no—
1137C4⋊C4—798no—
1138C4⋊C4—794no—
1139C4⋊C4—794no—
1140C4⋊C4—794no—
1141C4⋊C4—798no—
1142C4⋊C4—798no—
1143C4⋊C4—794no—
1144C4⋊C4—794no—
1145C4⋊C4—794no—
1146C4⋊C4—794no—
1147C4⋊C4—794no—
1148C4⋊C4—798no—
1149C4⋊C4—798no—
1150C4⋊C4—798no—
1151C4⋊C4—794no—
1152C4⋊C4—794no—
1153C4⋊C4C23×D7918yes—
1154C4⋊C4C23×D7914yes—
1155C4⋊C4C23×D7918yes—
1156C4⋊C4C23×D7914yes—
1157C4⋊C4C23×D7918yes—
1158C4⋊C4C23×D7918yes—
1159C22⋊C4—794no—
1160C22⋊C4—798no—
1161C22⋊C4—798no—
1162C22⋊C4—794no—
1163C22⋊C4—798no—
1164C22⋊C4—798no—
1165C22⋊C4—794no—
1166C22⋊C4—794no—
1167C22⋊C4—794no—
1168C22⋊C4—798no—
1169C22⋊C4—798no—
1170C22⋊C4—798no—
1171C22⋊C4—798no—
1172C22⋊C4—798no—
1173C22⋊C4—798no—
1174C22⋊C4—798no—
1175C22⋊C4—798no—
1176C22⋊C4—794no—
1177C22⋊C4—794no—
1178C22⋊C4—794no—
1179C22⋊C4—794no—
1180C22⋊C4—798no—
1181C22⋊C4—798no—
1182C22⋊C4—794no—
1183C22⋊C4C23×D7918yes—
1184C22⋊C4C23×D7918yes—
1185C22⋊C4C23×D7918yes—
1186C22⋊C4C23×D7918yes—
1187C22⋊C4C23×D7918yes—
1188C42—798no—
1189C42—798no—
1190C42—794no—
1191C42—794no—
1192C42C23×D7914yes—
1193C42C23×D7914yes—
1194C42C23×D7914yes—
1195C42C23×D7914yes—
1196C42C23×D7918yes—
1197C23—22no—
1198C23—22no—
1199C23—24no—
1200C23—24no—
1201C23—24no—
1202C23—31632no—
1203C23—3168no—
1204C23—3168no—
1205C23—3168no—
1206C23—794no—
1207C23—798no—
1208C23—792no—
1209C23—794no—
1210C23—792no—
1211C23—63216no—
1212C23—15816no—
1213C23—15816no—
1214C23—1582no—
1215C23—15816no—
1216C23—1584no—
1217C23—1582no—
1218C23—1582no—
1219C23—1584no—
1220C23—1582no—
1221C23—1582no—
1222C23—1582no—
1223C23—1584no—
1224C23—1584no—
1225C23—1584no—
1226C23#1457920714yes—
1227C23C24×D7914yes—
1228C23C24×D7912yes—
1229C23C24×D7911yescharacteristic
1230Q8—28no—
1231Q8—3168no—
1232Q8—3164no—
1233D4—216no—
1234D4—28no—
1235D4—3168no—
1236D4—3168no—
1237D4—3164no—
1238D4—3168no—
1239D4—3168no—
1240D4—3168no—
1241D4—7916no—
1242D4—15816no—
1243D4—15816no—
1244D4—15816no—
1245D4—1588no—
1246D4—1588no—
1247D4—1588no—
1248C2×C4—28no—
1249C2×C4—22no—
1250C2×C4—22no—
1251C2×C4—24no—
1252C2×C4—22no—
1253C2×C4—24no—
1254C2×C4—22no—
1255C2×C4—22no—
1256C2×C4—24no—
1257C2×C4—28no—
1258C2×C4—48no—
1259C2×C4—44no—
1260C2×C4—3168no—
1261C2×C4—3168no—
1262C2×C4—3168no—
1263C2×C4—3168no—
1264C2×C4—3168no—
1265C2×C4—3168no—
1266C2×C4—3168no—
1267C2×C4—3168no—
1268C2×C4—792no—
1269C2×C4—792no—
1270C2×C4—794no—
1271C2×C4—792no—
1272C2×C4—792no—
1273C2×C4—792no—
1274C2×C4—792no—
1275C2×C4—794no—
1276C2×C4—15816no—
1277C2×C4—1584no—
1278C2×C4—1584no—
1279C2×C4—15816no—
1280C2×C4—1582no—
1281C2×C4—1582no—
1282C2×C4—1582no—
1283C2×C4—1582no—
1284C2×C4—1582no—
1285C2×C4—1582no—
1286C2×C4—1588no—
1287C2×C4—1588no—
1288C2×C4#41×D7914yes—
1289C2×C4C24×D7914yes—
1290C2×C4C24×D7914yes—
1291C2×C4C24×D7912yes—
1292C2×C4C24×D7912yes—
1293C2×C4C24×D7912yes—
1294C2×C4C24×D7912yes—
1295C2×C4C24×D7912yes—
1296C2×C4C24×D7914yes—
1297C2×C4C24×D7912yes—
1298C22—28no—
1299C22—22no—
1300C22—22no—
1301C22—24no—
1302C22—24no—
1303C22—24no—
1304C22—48no—
1305C22—31632no—
1306C22—3168no—
1307C22—3164no—
1308C22—3164no—
1309C22—798no—
1310C22—63216no—
1311C22—1582no—
1312C22—1582no—
1313C22—1584no—
1314C22—1582no—
1315C22—1584no—
1316C22—1582no—
1317C22—1582no—
1318C22—1584no—
1319C22—1582no—
1320C22—15816no—
1321C22—1584no—
1322C22—1584no—
1323C22C2×#41×D7912yes—
1324C22C2×#1457920714yes—
1325C22C2×#1457920712yes—
1326C22#1909939912yes—
1327C22C25×D7911yescharacteristic
1328C4—22no—
1329C4—24no—
1330C4—22no—
1331C4—22no—
1332C4—24no—
1333C4—22no—
1334C4—24no—
1335C4—22no—
1336C4—1582no—
1337C4—1582no—
1338C4—1584no—
1339C4—1584no—
1340C4—1582no—
1341C4—1582no—
1342C4—1582no—
1343C4—1582no—
1344C4C2×#41×D7914yes—
1345C2—24no—
1346C2—44no—
1347C2—3164no—
1348C2—3162no—
1349C2—3162no—
1350C2—1588no—
1351C2#2377733414yesdirect product factor
1352C2C22×#41×D7911yescharacteristic
1353C2C22×#1457920711yescharacteristic
1354C2C2×#1909939911yescharacteristic
subgroupG/H
centerC23C24×D79
commutator, cosocleC22×C79C26
FrattiniC22C25×D79
FittingC2×#529×C79C2
socleC23×C79C25
hypercenterC2×#529D79
hypocenterC79C2×#3513
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×#529

Complements

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

NH ≅ G/Ntype
1. #23777334C2direct (N × H)
2. C2×#19099295C2semidirect
3. C2×#19099269C2semidirect
4. C2×#19099266C2semidirect
5. C2×#19099257C2semidirect
6. C2×#19099255C2semidirect
7. C2×#19099242C2semidirect
8. C2×#19099237C2semidirect
9. C2×#19099213C2semidirect
10. C2×#19099208C2semidirect
11. C2×#19099206C2semidirect
12. C2×#19099204C2semidirect
13. C2×#19099197C2semidirect
14. C2×#19099185C2semidirect
15. C2×#19099164C2semidirect
16. C2×#19099154C2semidirect
17. C2×#19099152C2semidirect
18. C2×#19099097C2semidirect
19. C2×#19099071C2semidirect
20. C2×#123×D79C2semidirect
21. C2×#19099045C2semidirect
22. C2×#19099035C2semidirect
23. C22×C4×D316C2semidirect
24. C2×#529×C79C2semidirect
26. C22×#11929623C22semidirect
30. C23×C4×D79C22semidirect
31. #19099295C22semidirect
32. #19099269C22semidirect
33. #19099266C22semidirect
34. #19099257C22semidirect
35. #19099255C22semidirect
36. #19099242C22semidirect
37. #19099237C22semidirect
38. #19099213C22semidirect
39. #19099208C22semidirect
40. #19099206C22semidirect
41. #19099204C22semidirect
42. #19099197C22semidirect
43. #19099185C22semidirect
44. #19099164C22semidirect
45. #19099154C22semidirect
46. #19099152C22semidirect
47. C2×#14579160C22semidirect
49. #19099097C22semidirect
50. C2×#14579156C22semidirect
51. C2×#14579156C22semidirect
52. C2×#14579155C22semidirect
53. C2×#14579155C22semidirect
54. C2×#14579155C22semidirect
55. C2×#14579153C22semidirect
56. C2×#14579152C22semidirect
57. C2×#14579152C22semidirect
58. C2×#14579150C22semidirect
59. C2×#14579149C22semidirect
60. C2×#14579149C22semidirect
61. C2×#14579147C22semidirect
62. #19099071C22semidirect
63. C2×#14579146C22semidirect
64. C2×#14579146C22semidirect
65. C2×#14579146C22semidirect
67. C2×#14579145C22semidirect
69. C2×#14579144C22semidirect
70. C2×#14579144C22semidirect
71. C2×#14579143C22semidirect
72. C2×#14579143C22semidirect
73. C2×#14579143C22semidirect
74. C2×#14579143C22semidirect
75. C2×#14579142C22semidirect
76. #123×D79C22semidirect
77. C2×#14579141C22semidirect
78. C2×#14579140C22semidirect
79. C2×#14579139C22semidirect
80. C2×#14579139C22semidirect
81. C2×#14579139C22semidirect
82. C2×#14579138C22semidirect
83. C2×#14579137C22semidirect
85. C2×#14579136C22semidirect
86. C2×#14579136C22semidirect
87. C2×#14579136C22semidirect
89. C2×#14579135C22semidirect
91. C2×#14579134C22semidirect
92. C2×#14579134C22semidirect
93. C2×#14579132C22semidirect
95. C2×#14579131C22semidirect
96. C2×#14579131C22semidirect
98. #19099045C22semidirect
99. #19099035C22semidirect
100. C2×Q8×Dic79C22semidirect
101. C2×C4×Dic158C22semidirect
104. C2×C4×D316C22semidirect
105. C2×C4×D316C22semidirect
106. C2×C4×D316C22semidirect
107. C2×C4×D316C22semidirect
108. C2×C4×D316C22semidirect
109. C2×C4×D316C22semidirect
110. C2×C4×D316C22semidirect
111. C2×D4×Dic79C22semidirect
114. C2×#14579123C22semidirect
115. C2×#14579123C22semidirect
117. C2×C4×C22⋊D79C22semidirect
118. C2×C4×C22⋊D79C22semidirect
119. C2×(C22⋊D79)⋊C4C22semidirect
120. C2×(C22⋊D79)⋊C4C22semidirect
121. C2×#14579119C22semidirect
122. C2×#14579118C22semidirect
123. C2×#14579118C22semidirect
124. C2×#14579118C22semidirect
125. C2×#14579117C22semidirect
126. C22×C4⋊Dic79C22semidirect
127. C2×C4⋊C4×D79C22semidirect
128. C2×C4⋊C4×D79C22semidirect
129. C2×C4⋊C4×D79C22semidirect
130. C22×(C2×D79)⋊C4C22semidirect
131. C22×(C2×D79)⋊C4C22semidirect
132. C2×C22⋊C4×D79C22semidirect
133. C2×C22⋊C4×D79C22semidirect
134. C2×C22⋊C4×D79C22semidirect
135. #529×C79C22semidirect
136. C2×#126×C79C22semidirect
137. C2×#125×C79C22semidirect
138. C2×#124×C79C22semidirect
139. C2×#123×C79C22semidirect
140. C2×C22⋊Q8×C79C22semidirect
142. C2×C4×Q8×C79C22semidirect
143. C2×C4×D4×C79C22semidirect
144. C2×C4×D4×C79C22semidirect
145. C2×#117×C79C22semidirect
146. C22×C42×C79C22semidirect
152. C2×#11929623C23semidirect
187. C22×C4×D79C23semidirect
188. #14579160C23semidirect
190. #14579156C23semidirect
191. #14579156C23semidirect
192. #14579155C23semidirect
193. #14579155C23semidirect
194. #14579155C23semidirect
195. #14579153C23semidirect
196. #14579152C23semidirect
197. #14579152C23semidirect
198. #14579150C23semidirect
199. #14579149C23semidirect
200. #14579149C23semidirect
201. #14579147C23semidirect
202. #14579146C23semidirect
203. #14579146C23semidirect
204. #14579146C23semidirect
206. #14579145C23semidirect
208. #14579144C23semidirect
209. #14579144C23semidirect
210. #14579143C23semidirect
211. #14579143C23semidirect
212. #14579143C23semidirect
213. #14579143C23semidirect
214. #14579142C23semidirect
215. #14579141C23semidirect
216. #14579140C23semidirect
217. #14579139C23semidirect
218. #14579139C23semidirect
219. #14579139C23semidirect
220. #14579138C23semidirect
221. #14579137C23semidirect
223. #14579136C23semidirect
224. #14579136C23semidirect
225. #14579136C23semidirect
227. #14579135C23semidirect
229. #14579134C23semidirect
230. #14579134C23semidirect
231. #14579132C23semidirect
233. #14579131C23semidirect
234. #14579131C23semidirect
236. Q8×Dic79C23semidirect
237. C4×Dic158C23semidirect
240. C4×D316C23semidirect
241. C4×D316C23semidirect
242. C4×D316C23semidirect
243. C4×D316C23semidirect
244. C4×D316C23semidirect
245. C4×D316C23semidirect
246. D4×Dic79C23semidirect
249. #14579123C23semidirect
250. #14579123C23semidirect
252. C4×C22⋊D79C23semidirect
253. C4×C22⋊D79C23semidirect
254. (C22⋊D79)⋊C4C23semidirect
255. (C22⋊D79)⋊C4C23semidirect
256. #14579119C23semidirect
257. #14579118C23semidirect
258. #14579118C23semidirect
259. #14579118C23semidirect
260. #14579117C23semidirect
268. C2×C4⋊Dic79C23semidirect
281. C4⋊C4×D79C23semidirect
282. C4⋊C4×D79C23semidirect
283. C4⋊C4×D79C23semidirect
308. C2×(C2×D79)⋊C4C23semidirect
309. C2×(C2×D79)⋊C4C23semidirect
310. C22⋊C4×D79C23semidirect
311. C22⋊C4×D79C23semidirect
312. C22⋊C4×D79C23semidirect
324. #126×C79C23semidirect
325. #125×C79C23semidirect
326. #124×C79C23semidirect
327. #123×C79C23semidirect
328. C22⋊Q8×C79C23semidirect
330. C4×Q8×C79C23semidirect
331. C4×D4×C79C23semidirect
332. C4×D4×C79C23semidirect
333. #117×C79C23semidirect
350. C2×C42×C79C23semidirect
376. C2×D316#41semidirect
607. D316C2×#41semidirect
670. C2×C79#3513semidirect
696. C2×#529D79semidirect
702. C79C2×#3513semidirect
728. #529C2×D79semidirect
734. C2×#126C2×D79semidirect
738. C2×#125C2×D79semidirect
743. C2×#124C2×D79semidirect
759. C2×#123C2×D79semidirect
767. C2×C22⋊Q8C2×D79semidirect
787. C2×C4×Q8C2×D79semidirect
807. C2×C4×D4C2×D79semidirect
808. C2×C4×D4C2×D79semidirect
814. C2×#117C2×D79semidirect
824. C22×C42C2×D79semidirect
880. #126C22×D79semidirect
884. #125C22×D79semidirect
889. #124C22×D79semidirect
903. #123C22×D79semidirect
911. C22⋊Q8C22×D79semidirect
929. C4×Q8C22×D79semidirect
948. C4×D4C22×D79semidirect
949. C4×D4C22×D79semidirect
955. #117C22×D79semidirect
1028. C2×C42C22×D79semidirect
1351. C2#23777334direct (N × H)

Maximal subgroups

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

subgroupindex
#237773342
C2×#190992952
C2×#190992692
C2×#190992662
C2×#190992572
C2×#190992552
C2×#190992422
C2×#190992372
C2×#190992132
C2×#190992082
C2×#190992062
C2×#190992042
C2×#190991972
C2×#190991852
C2×#190991642
C2×#190991542
C2×#190991522
C2×#190990972
C2×#190990712
C2×#123×D792
C2×#190990452
C2×#190990352
C22×C4×D3162
C2×#529×C792
C2×#351379