Finite Group Databasebeta

← #35197284

Subgroups — #35197284

Order 20224.

7130 conjugacy classes of subgroups.

The subgroup lattice has 1006 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23777203C211yesmaximal, characteristic, complemented
2#23777202C212yesmaximal, complemented
3#23777201C212yesmaximal, complemented
4#23777200C214yesmaximal, complemented
5#23777199C218yesmaximal, complemented
6#23777199C218yesmaximal, complemented
7#23777198C212yesmaximal, complemented
8#23777197C218yesmaximal, complemented
9#23777196C214yesmaximal, complemented
10#23777195C218yesmaximal, complemented
11#23776804C212yesmaximal, complemented
12#23776803C212yesmaximal, complemented
13C2×#19099188C214yesmaximal, complemented
14#543×D79C214yesmaximal, complemented
15C2×#19099035C211yesmaximal, characteristic
16#518×D79C212yesmaximal
17C79×#3501C211yesmaximal, characteristic, complemented
18C22×D4×D79C2211yescharacteristic
19#19099274C2214yescomplemented
20#19099274C2218yescomplemented
21#19099273C2218yescomplemented
22#19099273C2214yescomplemented
23#19099272C2218yescomplemented
24#19099272C2218yescomplemented
25#19099272C2218yescomplemented
26#19099271C22116yescomplemented
27#19099271C2218yescomplemented
28#19099270C2218yescomplemented
29#19099270C2214yescomplemented
30#19099269C2218yescomplemented
31#19099269C2218yescomplemented
32#19099269C2218yescomplemented
33#19099268C22116yescomplemented
34#19099268C2218yescomplemented
35#19099267C22116yescomplemented
36#19099267C22116yescomplemented
37#19099267C22116yescomplemented
38Q8×D316C2214yescomplemented
39D4×Dic158C2218yescomplemented
40D4×Dic158C2214yescomplemented
41#19099228C2218yescomplemented
42#19099228C2214yescomplemented
43Q8×C22⋊D79C2218yescomplemented
44#19099226C2218yescomplemented
45#19099226C22116yescomplemented
46#19099194C2212yescomplemented
47#19099193C2214yescomplemented
48#19099193C2214yescomplemented
49#19099193C2218yescomplemented
50#19099192C2214yescomplemented
51#19099192C2214yescomplemented
52#19099191C2214yescomplemented
53#19099190C2214yescomplemented
54#19099190C2214yescomplemented
55#19099190C2218yescomplemented
56#19099189C2218yescomplemented
57#19099189C2214yescomplemented
58#19099188C2214yes—
59#19099188C2218yes—
60#19099188C2214yes—
61#19099188C2218yescomplemented
62#19099188C2218yescomplemented
63#19099188C22116yescomplemented
64#19099188C22116yescomplemented
65#19099188C22116yescomplemented
66#19099188C22116yescomplemented
67#19099120C2212yescomplemented
68#19099119C2218yescomplemented
69#19099118C2218yescomplemented
70#19099117C2218yescomplemented
71#19099117C2218yescomplemented
72#19099116C2214yescomplemented
73#19099115C2218yescomplemented
74C2×#14579141C2218yescomplemented
75C2×#14579140C2214yescomplemented
76C2×#14579139C2218yescomplemented
77C2×#14579139C2218yescomplemented
78C2×#14579138C2218yescomplemented
79C2×#14579137C2218yescomplemented
80C22⋊Q8×D79C2218yescomplemented
81C22⋊Q8×D79C2218yescomplemented
82C22⋊Q8×D79C22116yescomplemented
83C22⋊Q8×D79C22116yescomplemented
84#19099038C2212yes—
85#19099037C2214yes—
86#19099036C2218yes—
87#19099035C2218yes—
88#19099035C2218yes—
89#19099035C2218yes—
90#19099035C2218yes—
91C2×C4×D316C2211yescharacteristic
92C2×D4×Dic79C2211yescharacteristic
93C2×#14579123C2211yescharacteristic
94C2×C4×C22⋊D79C2212yes—
95C2×(C22⋊D79)⋊C4C2212yes—
96C4×D4×D79C2218yes—
97C4×D4×D79C2218yes—
98C2×#14579119C2211yescharacteristic
99C2×#14579118C2211yescharacteristic
100#117×D79C2214yes—
101C22×(C2×D79)⋊C4C2212yes—
102C2×C22⋊C4×D79C2212yes—
103C2×C22⋊C4×D79C2218yes—
104#554×C79C2218yescomplemented
105#554×C79C2214yescomplemented
106D4×Q8×C79C2214yescomplemented
107#544×C79C2212yescomplemented
108#543×C79C2214yescomplemented
109#533×C79C2212yescomplemented
110C2×C22⋊Q8×C79C2214yescomplemented
111#518×C79C2212yes—
112C2×C4×D4×C79C2211yescharacteristic
113C24×D79C2312yes—
114C22×Dic158C2318yescomplemented
115C22×Dic158C2314yescomplemented
116C2×Q8×D79C2318yescomplemented
117C2×Q8×D79C2318yescomplemented
118C22×D316C2311yescharacteristic
119C22×C22⋊D79C2312yes—
120C2×D4×D79Q8116yescomplemented
121C2×D4×D79C2318yes—
122C23×Dic79C2312yes—
123C22×C4×D79C2318yes—
124C22×C4×D79C2318yes—
125C22×C4×D79C2312yes—
126C22×C4×D79C2312yes—
127C22×C4×D79C2311yescharacteristic
128#14579161C2318yescomplemented
129#14579161C2312yescomplemented
130#14579161C2312yescomplemented
131#14579160C2314yescomplemented
132#14579160C2314yescomplemented
133#14579160C2318yescomplemented
134#14579160C2318yescomplemented
135#14579160C2318yescomplemented
136#14579160C2318yescomplemented
137#14579160C2318yescomplemented
138#14579159C2318yescomplemented
139#14579159C2318yescomplemented
140#14579159C2318yescomplemented
141#14579153C2314yescomplemented
142#14579153C2318yescomplemented
143#14579152C2318yescomplemented
144#14579152C2314yescomplemented
145#14579152C2314yescomplemented
146#14579152C2318yescomplemented
147#14579151C2318yescomplemented
148#14579151C2318yescomplemented
149#14579151C23116yescomplemented
150#14579151C2318yescomplemented
151#14579151C2318yescomplemented
152#14579141C2318yes—
153#14579141C23116yes—
154#14579141C2318yes—
155#14579141C2318yescomplemented
156#14579141C23116yescomplemented
157#14579141C23116yescomplemented
158#14579141C2318yescomplemented
159#14579140C2314yes—
160#14579140C2318yes—
161#14579140C2314yes—
162#14579140C2318yescomplemented
163#14579140C2318yescomplemented
164#14579140C23116yescomplemented
165#14579140C23116yescomplemented
166#14579139C2318yes—
167#14579139C23116yes—
168#14579139C2318yes—
169#14579139C2318yes—
170#14579139C23116yes—
171#14579139C2318yes—
172#14579139C23116yescomplemented
173#14579139C23116yescomplemented
174#14579139C23116yescomplemented
175#14579139C23116yescomplemented
176#14579139C23116yescomplemented
177#14579139C23116yescomplemented
178#14579138C2318yes—
179#14579138C23116yes—
180#14579138C2318yes—
181#14579138C23116yescomplemented
182#14579138C23116yescomplemented
183#14579138C23116yescomplemented
184#14579138C23116yescomplemented
185#14579138C23116yescomplemented
186#14579138C23116yescomplemented
187#14579137C2318yes—
188#14579137C23116yes—
189#14579137C2318yes—
190#14579137C23116yescomplemented
191#14579137C2318yescomplemented
192#14579137C2318yescomplemented
193#14579137C23116yescomplemented
194Q8×Dic79C2318yescomplemented
195C4×Dic158C2318yescomplemented
196C4×Dic158C2314yescomplemented
197C4×Dic158C2314yescomplemented
198C4×Dic158C2318yescomplemented
199#14579126C23116yescomplemented
200#14579126C2318yescomplemented
201C4×D316C2318yes—
202C4×D316C2314yes—
203C4×D316C2314yes—
204C4×D316C2318yes—
205D4×Dic79C2318yes—
206D4×Dic79C2318yes—
207D4×Dic79C2318yes—
208#14579123C2318yes—
209#14579123C2318yes—
210#14579123C2318yes—
211C4×C22⋊D79C23116yes—
212C4×C22⋊D79C2318yes—
213C4×C22⋊D79C2318yes—
214C4×C22⋊D79C23116yes—
215(C22⋊D79)⋊C4C23116yes—
216(C22⋊D79)⋊C4C23116yes—
217(C22⋊D79)⋊C4C23116yes—
218#14579120C2314yes—
219#14579119C2314yes—
220#14579119C2314yes—
221#14579119C2318yes—
222#14579118C2314yes—
223#14579118C2318yes—
224#14579118C2314yes—
225#14579117C2318yes—
226C2×C4⋊Dic79C2311yescharacteristic
227C2×C4⋊Dic79C2318yescomplemented
228C2×C4⋊Dic79C2314yescomplemented
229C2×Dic79⋊C4C2311yescharacteristic
230C2×Dic79⋊C4C2311yescharacteristic
231C2×Dic79⋊C4C2318yescomplemented
232C2×Dic79⋊C4C2318yescomplemented
233C2×Dic79⋊C4C2318yescomplemented
234C4⋊C4×D79C2314yes—
235C4⋊C4×D79C2314yes—
236C4⋊C4×D79C2318yescomplemented
237C4⋊C4×D79C23116yescomplemented
238C4⋊C4×D79C23116yescomplemented
239C4⋊C4×D79C2318yescomplemented
240C2×C22⋊Dic79C2312yes—
241C2×C22⋊Dic79C2318yes—
242C2×(C2×D79)⋊C4C2311yescharacteristic
243C2×(C2×D79)⋊C4C2312yes—
244C2×(C2×D79)⋊C4C2311yescharacteristic
245C2×(C2×D79)⋊C4C2312yes—
246C2×(C2×D79)⋊C4C2312yes—
247C2×(C2×D79)⋊C4C2318yes—
248C2×(C2×D79)⋊C4C2318yes—
249C2×(C2×D79)⋊C4C2318yes—
250C2×(C2×D79)⋊C4C2318yes—
251C22⋊C4×D79C2318yes—
252C22⋊C4×D79C23116yes—
253C22⋊C4×D79C23116yes—
254C22⋊C4×D79C23116yes—
255C22⋊C4×D79C23116yes—
256C2×C4×Dic79C2311yescharacteristic
257C2×C4×Dic79C2312yes—
258C42×D79C2318yes—
259C22×Q8×C79C2314yescomplemented
260C22×D4×C79C2311yescharacteristic
261C23×C4×C79C2312yes—
262C4⋊Q8×C79C2312yescomplemented
263C4⋊Q8×C79C2312yescomplemented
264C4⋊Q8×C79C2318yescomplemented
265#125×C79C2314yescomplemented
266#125×C79C2318yescomplemented
267C22⋊Q8×C79C2314yes—
268C22⋊Q8×C79C2318yes—
269C22⋊Q8×C79C2314yes—
270C22⋊Q8×C79C2318yescomplemented
271C22⋊Q8×C79C2318yescomplemented
272C22⋊Q8×C79C23116yescomplemented
273C22⋊Q8×C79C23116yescomplemented
274C4×Q8×C79C2314yescomplemented
275C4×Q8×C79C2314yescomplemented
276C4×D4×C79C2314yes—
277C4×D4×C79C2318yes—
278C4×D4×C79C2314yes—
279C4×D4×C79C2318yes—
280#117×C79C2314yes—
281C2×C4⋊C4×C79C2311yescharacteristic
282C2×C4⋊C4×C79C2314yescomplemented
283C2×C4⋊C4×C79C2318yescomplemented
284C2×C22⋊C4×C79C2312yes—
285C2×C22⋊C4×C79C2318yes—
286C2×C42×C79C2311yescharacteristic
287C23×D79—82no—
288C23×D79—82no—
289C23×D79C2×Q8116yescomplemented
290C23×D79C2411yescharacteristic
291C23×D79C2412yes—
292C23×D79C2418yes—
293C2×Dic158—88no—
294C2×Dic158—84no—
295C2×Dic158C2418yes—
296C2×Dic158C2414yes—
297C2×Dic158C24116yes—
298C2×Dic158C2418yes—
299C2×Dic158C2418yes—
300C2×Dic158C2414yes—
301Q8×D79—88no—
302Q8×D79—88no—
303C2×D316C2×Q818yescomplemented
304C2×D316C2414yes—
305C2×C22⋊D79C2×Q8116yescomplemented
306C2×C22⋊D79C2418yes—
307D4×D79C2×Q8164yescomplemented
308C22×Dic79—82no—
309C22×Dic79C2418yes—
310C22×Dic79C2418yes—
311C22×Dic79C2418yes—
312C22×Dic79C2411yescharacteristic
313C22×Dic79C2412yes—
314C22×Dic79C2411yescharacteristic
315C22×Dic79C2411yescharacteristic
316C2×C4×D79—82no—
317C2×C4×D79—88no—
318C2×C4×D79—82no—
319C2×C4×D79—88no—
320C2×C4×D79C2×Q818yescomplemented
321C2×C4×D79C2418yes—
322C2×C4×D79C24116yes—
323C2×C4×D79C24116yes—
324C2×C4×D79C2418yes—
325C2×C4×D79C2418yes—
326C2×C4×D79C2418yes—
327C2×C4×D79C2414yes—
328C4⋊Dic79C2414yes—
329C4⋊Dic79C2414yes—
330C4⋊Dic79C2418yes—
331C4⋊Dic79C2414yes—
332C4⋊Dic79C24116yes—
333C4⋊Dic79C2418yes—
334C4⋊Dic79C2414yes—
335C4⋊Dic79C2418yes—
336C4⋊Dic79C2414yes—
337Dic79⋊C4C2418yes—
338Dic79⋊C4C2418yes—
339Dic79⋊C4C2418yes—
340Dic79⋊C4C2418yes—
341Dic79⋊C4C2418yes—
342Dic79⋊C4C24116yes—
343Dic79⋊C4C24116yes—
344Dic79⋊C4C24116yes—
345Dic79⋊C4C2414yes—
346Dic79⋊C4C2412yes—
347Dic79⋊C4C2412yes—
348Dic79⋊C4C2418yes—
349Dic79⋊C4C2418yes—
350Dic79⋊C4C2418yes—
351C22⋊Dic79C2418yes—
352C22⋊Dic79C2418yes—
353C22⋊Dic79C24116yes—
354(C2×D79)⋊C4C2414yes—
355(C2×D79)⋊C4C2418yes—
356(C2×D79)⋊C4C2418yes—
357(C2×D79)⋊C4C2418yes—
358(C2×D79)⋊C4C24116yes—
359(C2×D79)⋊C4C24116yes—
360(C2×D79)⋊C4C2412yes—
361(C2×D79)⋊C4C2412yes—
362(C2×D79)⋊C4C2418yes—
363(C2×D79)⋊C4C2414yes—
364(C2×D79)⋊C4C2414yes—
365C4×Dic79C2418yes—
366C4×Dic79C2418yes—
367C4×Dic79C2418yes—
368C4×Dic79C2414yes—
369C4×Dic79C2418yes—
370C24×C79C2412yes—
371C2×Q8×C79—84no—
372C2×Q8×C79C2414yes—
373C2×Q8×C79C2418yes—
374C2×Q8×C79C2414yes—
375C2×D4×C79C2×Q818yescomplemented
376C2×D4×C79C2414yes—
377C22×C4×C79—82no—
378C22×C4×C79C2418yes—
379C22×C4×C79C2414yes—
380C22×C4×C79C2411yescharacteristic
381C22×C4×C79C2411yescharacteristic
382C22×C4×C79C2412yes—
383C22×C4×C79C2418yes—
384C22×C4×C79C2414yes—
385C22×C4×C79C2411yescharacteristic
386C4⋊C4×C79C2414yes—
387C4⋊C4×C79C2418yes—
388C4⋊C4×C79C2414yes—
389C4⋊C4×C79C2418yes—
390C4⋊C4×C79C24116yes—
391C4⋊C4×C79C2414yes—
392C4⋊C4×C79C2414yes—
393C4⋊C4×C79C2418yes—
394C4⋊C4×C79C2414yes—
395C22⋊C4×C79C2418yes—
396C22⋊C4×C79C2418yes—
397C22⋊C4×C79C24116yes—
398C42×C79C2412yes—
399C42×C79C2412yes—
400C42×C79C2418yes—
401C23×C79—42no—
402C23×C79—42no—
403C23×C79C22×Q818yes—
404C23×C79C2511yescharacteristic
405C23×C79C2514yes—
406C22×D79—48no—
407C22×D79—48no—
408C22×D79—42no—
409C22×D79—42no—
410C22×D79—41no—
411C22×D79—41no—
412C22×D79—816no—
413C22×D79C22×Q814yes—
414C22×D79C22×Q8132yes—
415C22×D79C22×Q818yes—
416C22×D79C2512yes—
417C22×D79C2514yes—
418Q8×C79—44no—
419Q8×C79—48no—
420Q8×C79—44no—
421D4×C79C22×Q8116yes—
422C2×C4×C79—41no—
423C2×C4×C79—48no—
424C2×C4×C79—42no—
425C2×C4×C79—48no—
426C2×C4×C79—44no—
427C2×C4×C79—41no—
428C2×C4×C79—44no—
429C2×C4×C79C22×Q814yes—
430C2×C4×C79C2514yes—
431C2×C4×C79C2518yes—
432C2×C4×C79C2518yes—
433C2×C4×C79C2511yescharacteristic
434C2×C4×C79C2511yescharacteristic
435C2×C4×C79C2512yes—
436C2×C4×C79C2512yes—
437C22⋊D79C22×Q8132yes—
438C2×Dic79—41no—
439C2×Dic79—42no—
440C2×Dic79—48no—
441C2×Dic79—48no—
442C2×Dic79—41no—
443C2×Dic79—48no—
444C2×Dic79C22×Q814yes—
445C2×Dic79C2512yes—
446C2×Dic79C2514yes—
447C2×Dic79C2518yes—
448C2×Dic79C2518yes—
449C2×Dic79C2512yes—
450C2×Dic79C2512yes—
451D316C22×Q8116yes—
452C4×D79—48no—
453C4×D79—48no—
454C4×D79—48no—
455C4×D79—416no—
456C4×D79—416no—
457C4×D79—48no—
458C4×D79C22×Q8116yes—
459Dic158—48no—
460Dic158—44no—
461Dic158—48no—
462Dic158—416no—
463Dic158—44no—
464Dic158—48no—
465C22×C79—24no—
466C22×C79—21no—
467C22×C79—24no—
468C22×C79—21no—
469C22×C79—48no—
470C22×C79C23×Q818yes—
471C22×C79C23×Q812yes—
472C22×C79C2611yescharacteristic
473C2×D79—22no—
474C2×D79—22no—
475C2×D79—24no—
476C2×D79—24no—
477C2×D79—44no—
478C2×D79—432no—
479C2×D79—48no—
480C2×D79C23×Q818yes—
481C2×D79C23×Q814yes—
482C4×C79—21no—
483C4×C79—21no—
484C4×C79—24no—
485C4×C79—28no—
486C4×C79—28no—
487C4×C79—22no—
488C4×C79C23×Q814yes—
489Dic79—22no—
490Dic79—28no—
491Dic79—28no—
492Dic79—24no—
493Dic79—22no—
494Dic79C23×Q814yes—
495#62843—791nomaximal, Sylow
496C2×C79—22no—
497C2×C79—28no—
498C2×C79C24×Q811yescharacteristic
499C2×C79H(7,𝔽2)11yescharacteristic
500C2×C79H(7,𝔽2)11yescharacteristic
501D79—24no—
502D79—28no—
503#3501—798no—
504#3501—798no—
505#3501—798no—
506#3501—798no—
507#3501—792no—
508#3501—794no—
509#3501—792no—
510#3501—794no—
511#3501—792no—
512#3501—791no—
513#3501D7911yescharacteristic, complemented
514#3458—792no—
515#3458—792no—
516C2×#543—794no—
517C2×#543—794no—
518C2×#518—792no—
519C2×#518—791no—
520C79#6284311yescharacteristic, complemented, Sylow
521C23×D4—791no—
522#554—798no—
523#554—794no—
524#554—798no—
525#554—798no—
526#554—798no—
527#554—7916no—
528#554—7916no—
529#554—7916no—
530#554—7916no—
531#554—798no—
532#554—794no—
533#554—798no—
534#554—798no—
535#554—794no—
536#554—798no—
537#554—798no—
538#554—798no—
539#554—7916no—
540#554—798no—
541#554C2×D7914yescomplemented
542#554C2×D7918yescomplemented
543D4×Q8—798no—
544D4×Q8—798no—
545D4×Q8—794no—
546D4×Q8—7916no—
547D4×Q8—798no—
548D4×Q8—794no—
549D4×Q8—798no—
550D4×Q8—794no—
551D4×Q8C2×D7914yescomplemented
552#544—798no—
553#544—794no—
554#544—794no—
555#544—798no—
556#544—794no—
557#544—794no—
558#544—794no—
559#544—794no—
560#544—794no—
561#544—792no—
562#544C2×D7912yescomplemented
563#543—794no—
564#543—798no—
565#543—794no—
566#543—798no—
567#543—798no—
568#543—7916no—
569#543—7916no—
570#543—7916no—
571#543—7916no—
572#543—798no—
573#543—794no—
574#543C2×D7914yescomplemented
575#533—798no—
576#533—798no—
577#533—798no—
578#533—798no—
579#533—798no—
580#533—794no—
581#533—792no—
582#533C2×D7912yescomplemented
583C2×C22⋊Q8—798no—
584C2×C22⋊Q8—794no—
585C2×C22⋊Q8—798no—
586C2×C22⋊Q8—798no—
587C2×C22⋊Q8—7916no—
588C2×C22⋊Q8—7916no—
589C2×C22⋊Q8—798no—
590C2×C22⋊Q8—798no—
591C2×C22⋊Q8—798no—
592C2×C22⋊Q8—798no—
593C2×C22⋊Q8C2×D7914yescomplemented
594#518—792no—
595#518—798no—
596#518—798no—
597#518—798no—
598#518—798no—
599#518—794no—
600#518—798no—
601#518C2×D7912yes—
602C2×C4×D4—791no—
603C2×C4×D4—792no—
604C2×C4×D4—798no—
605C2×C4×D4—798no—
606C2×C4×D4—791no—
607C2×C4×D4—792no—
608C2×C4×D4—791no—
609C2×C4×D4C2×D7911yescharacteristic
610C2×#117—794no—
611C2×#117—791no—
612C2×#117—791no—
613C22×C22⋊C4—792no—
614C22×C22⋊C4—792no—
615C22×C22⋊C4—798no—
616C25—792no—
617C22×Q8—798no—
618C22×Q8—798no—
619C22×Q8—794no—
620C22×Q8—798no—
621C22×Q8C22×D7914yescomplemented
622C22×D4—792no—
623C22×D4—7916no—
624C22×D4—798no—
625C22×D4—791no—
626C22×D4C22×D7911yescharacteristic
627C23×C4—791no—
628C23×C4—792no—
629C23×C4—792no—
630C23×C4—792no—
631C23×C4—798no—
632C23×C4—798no—
633C23×C4C22×D7912yes—
634C4⋊Q8—798no—
635C4⋊Q8—798no—
636C4⋊Q8—798no—
637C4⋊Q8—794no—
638C4⋊Q8—798no—
639C4⋊Q8—794no—
640C4⋊Q8—798no—
641C4⋊Q8—798no—
642C4⋊Q8—798no—
643C4⋊Q8—798no—
644C4⋊Q8—798no—
645C4⋊Q8—792no—
646C4⋊Q8—792no—
647C4⋊Q8C22×D7918yescomplemented
648C4⋊Q8C22×D7912yescomplemented
649C4⋊Q8C22×D7912yescomplemented
650#125—798no—
651#125—798no—
652#125—7916no—
653#125—798no—
654#125—798no—
655#125—798no—
656#125—794no—
657#125—794no—
658#125—798no—
659#125—798no—
660#125—794no—
661#125C22×D7918yescomplemented
662#125C22×D7914yescomplemented
663C22⋊Q8—7916no—
664C22⋊Q8—798no—
665C22⋊Q8—798no—
666C22⋊Q8—7916no—
667C22⋊Q8—798no—
668C22⋊Q8—7916no—
669C22⋊Q8—798no—
670C22⋊Q8—798no—
671C22⋊Q8—794no—
672C22⋊Q8—794no—
673C22⋊Q8—798no—
674C22⋊Q8—798no—
675C22⋊Q8—7916no—
676C22⋊Q8—7916no—
677C22⋊Q8—798no—
678C22⋊Q8—798no—
679C22⋊Q8—7916no—
680C22⋊Q8—7916no—
681C22⋊Q8—798no—
682C22⋊Q8—798no—
683C22⋊Q8—798no—
684C22⋊Q8—7916no—
685C22⋊Q8—798no—
686C22⋊Q8—7916no—
687C22⋊Q8—7916no—
688C22⋊Q8—7916no—
689C22⋊Q8—7916no—
690C22⋊Q8—7916no—
691C22⋊Q8—7916no—
692C22⋊Q8—798no—
693C22⋊Q8—7916no—
694C22⋊Q8—798no—
695C22⋊Q8—7916no—
696C22⋊Q8—798no—
697C22⋊Q8—7916no—
698C22⋊Q8—798no—
699C22⋊Q8—7916no—
700C22⋊Q8—7916no—
701C22⋊Q8—7916no—
702C22⋊Q8—7916no—
703C22⋊Q8—7916no—
704C22⋊Q8—7916no—
705C22⋊Q8C22×D7914yes—
706C22⋊Q8C22×D7918yes—
707C22⋊Q8C22×D7914yes—
708C22⋊Q8C22×D79116yescomplemented
709C22⋊Q8C22×D79116yescomplemented
710C22⋊Q8C22×D7918yescomplemented
711C22⋊Q8C22×D7918yescomplemented
712C4×Q8—798no—
713C4×Q8—7916no—
714C4×Q8—798no—
715C4×Q8—798no—
716C4×Q8—798no—
717C4×Q8—794no—
718C4×Q8—794no—
719C4×Q8C22×D7914yescomplemented
720C4×Q8C22×D7914yescomplemented
721C4×D4—798no—
722C4×D4—798no—
723C4×D4—798no—
724C4×D4—798no—
725C4×D4—798no—
726C4×D4—7916no—
727C4×D4—7916no—
728C4×D4—798no—
729C4×D4—798no—
730C4×D4—798no—
731C4×D4—7916no—
732C4×D4—7916no—
733C4×D4—7916no—
734C4×D4—798no—
735C4×D4—798no—
736C4×D4—794no—
737C4×D4—794no—
738C4×D4C22×D7918yes—
739C4×D4C22×D7918yes—
740C4×D4C22×D7914yes—
741C4×D4C22×D7914yes—
742#117—794no—
743#117—794no—
744#117—794no—
745#117—798no—
746#117—798no—
747#117—798no—
748#117—794no—
749#117—794no—
750#117C22×D7914yes—
751C2×C4⋊C4—791no—
752C2×C4⋊C4—791no—
753C2×C4⋊C4—791no—
754C2×C4⋊C4—798no—
755C2×C4⋊C4—798no—
756C2×C4⋊C4—798no—
757C2×C4⋊C4—794no—
758C2×C4⋊C4—798no—
759C2×C4⋊C4—794no—
760C2×C4⋊C4—794no—
761C2×C4⋊C4—798no—
762C2×C4⋊C4—7916no—
763C2×C4⋊C4—7916no—
764C2×C4⋊C4—798no—
765C2×C4⋊C4C22×D7911yescharacteristic
766C2×C4⋊C4C22×D7918yescomplemented
767C2×C4⋊C4C22×D7914yescomplemented
768C2×C22⋊C4—792no—
769C2×C22⋊C4—798no—
770C2×C22⋊C4—792no—
771C2×C22⋊C4—791no—
772C2×C22⋊C4—791no—
773C2×C22⋊C4—792no—
774C2×C22⋊C4—792no—
775C2×C22⋊C4—798no—
776C2×C22⋊C4—798no—
777C2×C22⋊C4—798no—
778C2×C22⋊C4—798no—
779C2×C22⋊C4—798no—
780C2×C22⋊C4—7916no—
781C2×C22⋊C4—7916no—
782C2×C22⋊C4—7916no—
783C2×C22⋊C4—7916no—
784C2×C22⋊C4C22×D7912yes—
785C2×C22⋊C4C22×D7918yes—
786C2×C42—791no—
787C2×C42—792no—
788C2×C42—798no—
789C2×C42C22×D7911yescharacteristic
790C24—791no—
791C24—798no—
792C24—792no—
793C24—7916no—
794C24—6322no—
795C24—6322no—
796C24C23×D7912yes—
797C2×Q8—84no—
798C2×Q8—798no—
799C2×Q8—798no—
800C2×Q8—7916no—
801C2×Q8—798no—
802C2×Q8—794no—
803C2×Q8—794no—
804C2×Q8—6324no—
805C2×Q8—6328no—
806C2×Q8—6328no—
807C2×Q8—6328no—
808C2×Q8C23×D7918yes—
809C2×Q8C23×D7914yes—
810C2×Q8C23×D7914yes—
811C2×D4—7916no—
812C2×D4—798no—
813C2×D4—7964no—
814C2×D4—798no—
815C2×D4—794no—
816C2×D4Q8×D7918yescomplemented
817C2×D4C23×D7914yes—
818C22×C4—82no—
819C22×C4—791no—
820C22×C4—792no—
821C22×C4—791no—
822C22×C4—798no—
823C22×C4—798no—
824C22×C4—798no—
825C22×C4—798no—
826C22×C4—798no—
827C22×C4—798no—
828C22×C4—7916no—
829C22×C4—7916no—
830C22×C4—798no—
831C22×C4—791no—
832C22×C4—798no—
833C22×C4—794no—
834C22×C4—6322no—
835C22×C4—6322no—
836C22×C4—6328no—
837C22×C4—6328no—
838C22×C4—6322no—
839C22×C4C23×D7912yes—
840C22×C4C23×D7911yescharacteristic
841C22×C4C23×D7911yescharacteristic
842C22×C4C23×D7914yes—
843C22×C4C23×D7914yes—
844C22×C4C23×D7918yes—
845C22×C4C23×D7918yes—
846C22×C4C23×D7911yescharacteristic
847C4⋊C4—7916no—
848C4⋊C4—798no—
849C4⋊C4—7916no—
850C4⋊C4—798no—
851C4⋊C4—798no—
852C4⋊C4—7916no—
853C4⋊C4—798no—
854C4⋊C4—798no—
855C4⋊C4—798no—
856C4⋊C4—798no—
857C4⋊C4—798no—
858C4⋊C4—792no—
859C4⋊C4—792no—
860C4⋊C4—794no—
861C4⋊C4—798no—
862C4⋊C4—7916no—
863C4⋊C4—798no—
864C4⋊C4—798no—
865C4⋊C4—794no—
866C4⋊C4—794no—
867C4⋊C4—794no—
868C4⋊C4—794no—
869C4⋊C4—794no—
870C4⋊C4C23×D7914yes—
871C4⋊C4C23×D7918yes—
872C4⋊C4C23×D79116yes—
873C4⋊C4C23×D7918yes—
874C4⋊C4C23×D7914yes—
875C4⋊C4C23×D7914yes—
876C4⋊C4C23×D7914yes—
877C4⋊C4C23×D7914yes—
878C4⋊C4C23×D7918yes—
879C22⋊C4—798no—
880C22⋊C4—798no—
881C22⋊C4—7916no—
882C22⋊C4—798no—
883C22⋊C4—798no—
884C22⋊C4—798no—
885C22⋊C4—792no—
886C22⋊C4—792no—
887C22⋊C4—794no—
888C22⋊C4—798no—
889C22⋊C4—7916no—
890C22⋊C4—7916no—
891C22⋊C4—794no—
892C22⋊C4—794no—
893C22⋊C4C23×D7918yes—
894C22⋊C4C23×D7918yes—
895C22⋊C4C23×D79116yes—
896C42—798no—
897C42—798no—
898C42—798no—
899C42—798no—
900C42—794no—
901C42C23×D7918yes—
902C42C23×D7912yes—
903C42C23×D7912yes—
904C23—42no—
905C23—42no—
906C23—3168no—
907C23—3162no—
908C23—3168no—
909C23—3162no—
910C23—3161no—
911C23—3161no—
912C23—794no—
913C23—7932no—
914C23—798no—
915C23—792no—
916C23—794no—
917C23—63216no—
918C23C2×Q8×D7918yes—
919C23C24×D7911yescharacteristic
920C23C24×D7914yes—
921Q8—44no—
922Q8—48no—
923Q8—44no—
924Q8—3164no—
925Q8—3168no—
926Q8—3168no—
927Q8—3168no—
928Q8—31616no—
929Q8—3164no—
930D4—7932no—
931D4—7916no—
932D4C2×Q8×D79116yes—
933C2×C4—41no—
934C2×C4—42no—
935C2×C4—44no—
936C2×C4—44no—
937C2×C4—41no—
938C2×C4—48no—
939C2×C4—48no—
940C2×C4—3168no—
941C2×C4—3168no—
942C2×C4—3168no—
943C2×C4—31616no—
944C2×C4—31616no—
945C2×C4—3168no—
946C2×C4—3161no—
947C2×C4—3162no—
948C2×C4—3161no—
949C2×C4—3168no—
950C2×C4—3168no—
951C2×C4—3168no—
952C2×C4—792no—
953C2×C4—794no—
954C2×C4—7916no—
955C2×C4—798no—
956C2×C4—792no—
957C2×C4—798no—
958C2×C4—794no—
959C2×C4—792no—
960C2×C4C2×Q8×D7914yes—
961C2×C4C24×D7914yes—
962C2×C4C24×D7918yes—
963C2×C4C24×D7918yes—
964C2×C4C24×D7911yescharacteristic
965C2×C4C24×D7911yescharacteristic
966C2×C4C24×D7912yes—
967C2×C4C24×D7912yes—
968C22—24no—
969C22—21no—
970C22—24no—
971C22—21no—
972C22—48no—
973C22—3164no—
974C22—3168no—
975C22—31632no—
976C22—794no—
977C22—798no—
978C22—1584no—
979C22—1582no—
980C22—1584no—
981C22—1582no—
982C22C22×Q8×D7912yes—
983C22C22×Q8×D7918yes—
984C22C25×D7911yescharacteristic
985C4—21no—
986C4—21no—
987C4—24no—
988C4—28no—
989C4—28no—
990C4—22no—
991C4—794no—
992C4—1588no—
993C4—1582no—
994C4—1588no—
995C4—1584no—
996C4—1582no—
997C4C22×Q8×D7914yes—
998C2—22no—
999C2—28no—
1000C2—1584no—
1001C2—1588no—
1002C2C23×Q8×D7911yescharacteristic
1003C2#2377821011yescharacteristic
1004C2#2377821111yescharacteristic
subgroupG/H
center, FrattiniC22C25×D79
commutator, socle, cosocleC22×C79C26
FittingC79×#3501C2
prime radicalC22×D4×D79C22
hypercenter#3501D79
hypocenterC79#62843
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C22 ◁ #3501

Complements

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

NH ≅ G/Ntype
1. #23777203C2semidirect
2. #23777202C2semidirect
3. #23777201C2semidirect
4. #23777200C2semidirect
5. #23777199C2semidirect
6. #23777199C2semidirect
7. #23777198C2semidirect
8. #23777197C2semidirect
9. #23777196C2semidirect
10. #23777195C2semidirect
11. #23776804C2semidirect
12. #23776803C2semidirect
13. C2×#19099188C2semidirect
14. #543×D79C2semidirect
17. C79×#3501C2semidirect
19. #19099274C22semidirect
20. #19099274C22semidirect
21. #19099273C22semidirect
22. #19099273C22semidirect
23. #19099272C22semidirect
24. #19099272C22semidirect
25. #19099272C22semidirect
26. #19099271C22semidirect
27. #19099271C22semidirect
28. #19099270C22semidirect
29. #19099270C22semidirect
30. #19099269C22semidirect
31. #19099269C22semidirect
32. #19099269C22semidirect
33. #19099268C22semidirect
34. #19099268C22semidirect
35. #19099267C22semidirect
36. #19099267C22semidirect
37. #19099267C22semidirect
38. Q8×D316C22semidirect
39. D4×Dic158C22semidirect
40. D4×Dic158C22semidirect
41. #19099228C22semidirect
42. #19099228C22semidirect
43. Q8×C22⋊D79C22semidirect
44. #19099226C22semidirect
45. #19099226C22semidirect
46. #19099194C22semidirect
47. #19099193C22semidirect
48. #19099193C22semidirect
49. #19099193C22semidirect
50. #19099192C22semidirect
51. #19099192C22semidirect
52. #19099191C22semidirect
53. #19099190C22semidirect
54. #19099190C22semidirect
55. #19099190C22semidirect
56. #19099189C22semidirect
57. #19099189C22semidirect
61. #19099188C22semidirect
62. #19099188C22semidirect
63. #19099188C22semidirect
64. #19099188C22semidirect
65. #19099188C22semidirect
66. #19099188C22semidirect
67. #19099120C22semidirect
68. #19099119C22semidirect
69. #19099118C22semidirect
70. #19099117C22semidirect
71. #19099117C22semidirect
72. #19099116C22semidirect
73. #19099115C22semidirect
74. C2×#14579141C22semidirect
75. C2×#14579140C22semidirect
76. C2×#14579139C22semidirect
77. C2×#14579139C22semidirect
78. C2×#14579138C22semidirect
79. C2×#14579137C22semidirect
80. C22⋊Q8×D79C22semidirect
81. C22⋊Q8×D79C22semidirect
82. C22⋊Q8×D79C22semidirect
83. C22⋊Q8×D79C22semidirect
104. #554×C79C22semidirect
105. #554×C79C22semidirect
106. D4×Q8×C79C22semidirect
107. #544×C79C22semidirect
108. #543×C79C22semidirect
109. #533×C79C22semidirect
110. C2×C22⋊Q8×C79C22semidirect
114. C22×Dic158C23semidirect
115. C22×Dic158C23semidirect
116. C2×Q8×D79C23semidirect
117. C2×Q8×D79C23semidirect
120. C2×D4×D79Q8semidirect
128. #14579161C23semidirect
129. #14579161C23semidirect
130. #14579161C23semidirect
131. #14579160C23semidirect
132. #14579160C23semidirect
133. #14579160C23semidirect
134. #14579160C23semidirect
135. #14579160C23semidirect
136. #14579160C23semidirect
137. #14579160C23semidirect
138. #14579159C23semidirect
139. #14579159C23semidirect
140. #14579159C23semidirect
141. #14579153C23semidirect
142. #14579153C23semidirect
143. #14579152C23semidirect
144. #14579152C23semidirect
145. #14579152C23semidirect
146. #14579152C23semidirect
147. #14579151C23semidirect
148. #14579151C23semidirect
149. #14579151C23semidirect
150. #14579151C23semidirect
151. #14579151C23semidirect
155. #14579141C23semidirect
156. #14579141C23semidirect
157. #14579141C23semidirect
158. #14579141C23semidirect
162. #14579140C23semidirect
163. #14579140C23semidirect
164. #14579140C23semidirect
165. #14579140C23semidirect
172. #14579139C23semidirect
173. #14579139C23semidirect
174. #14579139C23semidirect
175. #14579139C23semidirect
176. #14579139C23semidirect
177. #14579139C23semidirect
181. #14579138C23semidirect
182. #14579138C23semidirect
183. #14579138C23semidirect
184. #14579138C23semidirect
185. #14579138C23semidirect
186. #14579138C23semidirect
190. #14579137C23semidirect
191. #14579137C23semidirect
192. #14579137C23semidirect
193. #14579137C23semidirect
194. Q8×Dic79C23semidirect
195. C4×Dic158C23semidirect
196. C4×Dic158C23semidirect
197. C4×Dic158C23semidirect
198. C4×Dic158C23semidirect
199. #14579126C23semidirect
200. #14579126C23semidirect
227. C2×C4⋊Dic79C23semidirect
228. C2×C4⋊Dic79C23semidirect
231. C2×Dic79⋊C4C23semidirect
232. C2×Dic79⋊C4C23semidirect
233. C2×Dic79⋊C4C23semidirect
236. C4⋊C4×D79C23semidirect
237. C4⋊C4×D79C23semidirect
238. C4⋊C4×D79C23semidirect
239. C4⋊C4×D79C23semidirect
259. C22×Q8×C79C23semidirect
262. C4⋊Q8×C79C23semidirect
263. C4⋊Q8×C79C23semidirect
264. C4⋊Q8×C79C23semidirect
265. #125×C79C23semidirect
266. #125×C79C23semidirect
270. C22⋊Q8×C79C23semidirect
271. C22⋊Q8×C79C23semidirect
272. C22⋊Q8×C79C23semidirect
273. C22⋊Q8×C79C23semidirect
274. C4×Q8×C79C23semidirect
275. C4×Q8×C79C23semidirect
282. C2×C4⋊C4×C79C23semidirect
283. C2×C4⋊C4×C79C23semidirect
289. C23×D79C2×Q8semidirect
303. C2×D316C2×Q8semidirect
305. C2×C22⋊D79C2×Q8semidirect
307. D4×D79C2×Q8semidirect
320. C2×C4×D79C2×Q8semidirect
375. C2×D4×C79C2×Q8semidirect
513. #3501D79semidirect
520. C79#62843semidirect
541. #554C2×D79semidirect
542. #554C2×D79semidirect
551. D4×Q8C2×D79semidirect
562. #544C2×D79semidirect
574. #543C2×D79semidirect
582. #533C2×D79semidirect
593. C2×C22⋊Q8C2×D79semidirect
621. C22×Q8C22×D79semidirect
647. C4⋊Q8C22×D79semidirect
648. C4⋊Q8C22×D79semidirect
649. C4⋊Q8C22×D79semidirect
661. #125C22×D79semidirect
662. #125C22×D79semidirect
708. C22⋊Q8C22×D79semidirect
709. C22⋊Q8C22×D79semidirect
710. C22⋊Q8C22×D79semidirect
711. C22⋊Q8C22×D79semidirect
719. C4×Q8C22×D79semidirect
720. C4×Q8C22×D79semidirect
766. C2×C4⋊C4C22×D79semidirect
767. C2×C4⋊C4C22×D79semidirect
816. C2×D4Q8×D79semidirect

Maximal subgroups

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

subgroupindex
#237772032
#237772022
#237772012
#237772002
#237771992
#237771982
#237771972
#237771962
#237771952
#237768042
#237768032
C2×#190991882
#543×D792
C2×#190990352
#518×D792
C79×#35012
#6284379