Finite Group Databasebeta

← #35197073

Subgroups — #35197073

Order 20224.

6636 conjugacy classes of subgroups.

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

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23778057C218yesmaximal, complemented
2#23778026C214yesmaximal, complemented
3#23777942C214yesmaximal, complemented
4#23777905C212yesmaximal, complemented
5#23777824C212yesmaximal, complemented
6#23777649C211yesmaximal, characteristic, complemented
7#23777622C212yesmaximal, complemented
8#23777384C214yesmaximal, complemented
9#23777371C214yesmaximal, complemented
10#23777352C214yesmaximal, complemented
11#23777325C218yesmaximal, complemented
12#23777325C214yesmaximal, complemented
13#23777319C212yesmaximal, complemented
14#23777295C212yesmaximal, complemented
15#23777115C214yesmaximal, complemented
16#23777097C214yesmaximal, complemented
17#23776692C211yesmaximal, characteristic, complemented
18C2×#19099094C212yesmaximal, complemented
19C79×#3537C211yesmaximal, characteristic, complemented
20#19099316C2214yescomplemented
21#19099316C2218yescomplemented
22#19099313C2214yescomplemented
23#19099308C2218yescomplemented
24#19099302C2214yescomplemented
25#19099299C2218yescomplemented
26#19099299C2214yescomplemented
27#19099290C2214yescomplemented
28#19099283C2214yescomplemented
29#19099282C2218yescomplemented
30#19099280C2218yescomplemented
31#19099277C2218yescomplemented
32#19099275C2214yescomplemented
33#19099272C2214yescomplemented
34#19099272C2218yescomplemented
35#19099268C2214yescomplemented
36#19099260C2218yescomplemented
37#19099260C2214yescomplemented
38#19099258C2218yescomplemented
39#19099256C2218yescomplemented
40#19099256C2218yescomplemented
41#19099256C2218yescomplemented
42#19099253C2214yescomplemented
43#19099253C2218yescomplemented
44#19099252C2214yescomplemented
45#19099250C2218yescomplemented
46#19099250C2218yescomplemented
47#19099250C2218yescomplemented
48#19099250C2218yescomplemented
49#19099249C2218yescomplemented
50#19099244C2218yescomplemented
51#19099244C2218yescomplemented
52#19099244C2218yescomplemented
53#19099244C2218yescomplemented
54#19099244C2214yescomplemented
55#19099244C2214yescomplemented
56#19099244C2218yescomplemented
57#19099244C2218yescomplemented
58D4×Dic158C2214yescomplemented
59#19099219C2214yescomplemented
60#19099219C2214yescomplemented
61#19099213C2214yescomplemented
62#19099213C2218yescomplemented
63#19099207C2214yescomplemented
64#19099207C2218yescomplemented
65#19099207C2218yescomplemented
66#19099207C2214yescomplemented
67#19099207C2218yescomplemented
68#19099192C2214yescomplemented
69#19099189C2214yescomplemented
70#19099181C2218yescomplemented
71#19099180C2218yescomplemented
72#19099180C2218yescomplemented
73#19099180C2214yescomplemented
74#19099180C2214yescomplemented
75#19099176C2212yescomplemented
76#19099175C2212yescomplemented
77#19099170C2218yescomplemented
78#19099170C2218yescomplemented
79#19099167C2218yescomplemented
80#19099167C2212yescomplemented
81#19099158C2218yescomplemented
82#19099158C2218yescomplemented
83#19099158C2218yescomplemented
84#19099158C2214yescomplemented
85#19099158C2214yescomplemented
86#19099156C2218yescomplemented
87#19099151C2214yescomplemented
88#19099148C2218yescomplemented
89#19099148C2218yescomplemented
90#19099148C2218yescomplemented
91#19099148C2218yescomplemented
92#19099142C2214yescomplemented
93#19099140C2214yescomplemented
94#19099134C2212yescomplemented
95#19099116C2212yescomplemented
96#19099116C2211yescharacteristic, complemented
97#19099115C2212yescomplemented
98#19099111C2212yescomplemented
99#19099109C2211yescharacteristic, complemented
100#19099108C2212yescomplemented
101#19099099C2212yescomplemented
102#19099095C2214yescomplemented
103#19099094C2214yescomplemented
104#19099094C2214yescomplemented
105#19099094C2214yescomplemented
106#19099094C2214yescomplemented
107#19099094C2214yescomplemented
108#19099094C2218yescomplemented
109#19099094C2214yescomplemented
110#19099094C2214yescomplemented
111#19099094C2212yescomplemented
112#19099094C2214yescomplemented
113#19099094C2214yescomplemented
114#19099093C2218yescomplemented
115#19099093C2214yescomplemented
116#19099090C2214yescomplemented
117C2×#14579154C2214yescomplemented
118C2×#14579152C2212yescomplemented
119#125×D79C2212yescomplemented
120C2×#14579148C2212yescomplemented
121C2×#14579148C2212yescomplemented
122#19099074C2211yescharacteristic, complemented
123#19099069C2218yescomplemented
124#19099069C2214yescomplemented
125C2×#14579142C2218yescomplemented
126C2×#14579142C2214yescomplemented
127C2×#14579140C2212yescomplemented
128#19099042C2214yescomplemented
129#19099042C2218yescomplemented
130#19099040C2212yescomplemented
131#19099038C2212yescomplemented
132#19099038C2218yescomplemented
133#41×Dic79C2211yescharacteristic, complemented
134#19099031C2211yescharacteristic, complemented
135C4×#11929623C2214yescomplemented
136C2×#14579126C2212yescomplemented
137C2×D4×Dic79C2214yescomplemented
138C2×D4×Dic79C2212yescomplemented
139C2×#14579117C2214yescomplemented
140C22×C4×Dic79C2211yescharacteristic, complemented
141#560×C79C2214yes—
142#553×C79C2214yes—
143D42×C79C2214yes—
144D42×C79C2214yes—
145#540×C79C2212yes—
146#538×C79C2214yes—
147#535×C79C2212yes—
148#534×C79C2214yes—
149#525×C79C2211yescharacteristic
150C2×#121×C79C2212yes—
151C2×#11929624C2311yescharacteristic
152C2×#11929623C2318yes—
153C2×#11929623C2314yes—
154C2×#11929623C2314yes—
155C22×Dic158C2312yes—
156C22×Dic158C2312yes—
157C23×Dic79C2312yes—
158C23×Dic79C2314yes—
159#14579161C2312yes—
160#14579160C2318yes—
161#14579160C2318yes—
162#14579160C2314yes—
163#14579160C2312yes—
164#14579159C2314yes—
165#14579159C2311yescharacteristic
166#14579157C2311yescharacteristic
167#14579156C2318yes—
168#14579156C2314yes—
169#14579154C2318yes—
170#14579154C2318yes—
171#14579154C2318yes—
172#14579154C2318yes—
173#14579154C2318yes—
174#14579154C2318yes—
175#14579154C2318yes—
176#14579154C2318yes—
177#14579154C2318yes—
178#14579154C2318yes—
179#14579154C2318yes—
180#14579154C2318yes—
181#14579154C2314yes—
182#14579154C2318yes—
183#14579154C2318yes—
184#14579153C2318yes—
185#14579153C2312yes—
186#14579152C2314yes—
187#14579152C2318yes—
188#14579152C2314yes—
189#14579152C2312yes—
190#14579152C2314yes—
191#14579152C2314yes—
192#14579151C2318yes—
193#14579151C2314yes—
194#14579151C2318yes—
195#14579151C2318yes—
196#14579151C2318yes—
197#14579151C2318yes—
198#14579151C2318yes—
199#14579150C2311yescharacteristic
200#14579148C2314yes—
201#14579148C2314yes—
202#14579148C2318yes—
203#14579148C2318yes—
204#14579148C2318yes—
205#14579148C2314yes—
206#14579148C2318yes—
207#14579148C2314yes—
208#14579148C2311yescharacteristic
209#14579148C2314yes—
210#14579148C2314yes—
211#14579147C2314yes—
212#14579147C2318yes—
213#14579147C2318yes—
214#14579145C2314yes—
215#14579144C2312yes—
216#14579143C2318yes—
217#14579143C2318yes—
218#14579143C2318yes—
219#14579142C2318yes—
220#14579142C2318yes—
221#14579142C2318yes—
222#14579142C2318yes—
223#14579142C2318yes—
224#14579142C2318yes—
225#14579142C2318yes—
226#14579142C2318yes—
227#14579142C2318yes—
228#14579142C2314yes—
229#14579142C2318yes—
230#14579142C2318yes—
231#14579142C2318yes—
232#14579142C2314yes—
233#14579142C2318yes—
234#14579142C2318yes—
235#14579142C2314yes—
236#14579142C2318yes—
237#14579141C2314yes—
238#14579140C2314yes—
239#14579140C2314yes—
240#14579140C2318yes—
241#14579140C2312yes—
242#14579140C2318yes—
243#14579140C2318yes—
244#14579140C2314yes—
245#14579140C2314yes—
246#14579140C2314yes—
247#14579139C2318yes—
248#14579138C2318yes—
249#14579138C2318yes—
250#14579138C2318yes—
251#14579138C2318yes—
252#14579138C2318yes—
253#14579138C2318yes—
254#14579138C2318yes—
255#14579138C2314yes—
256#14579138C2318yes—
257#14579138C2318yes—
258#14579138C2318yes—
259#14579138C2318yes—
260#14579138C2314yes—
261#14579135C2312yes—
262#14579134C2318yes—
263#14579133C2318yes—
264#14579133C2318yes—
265#14579133C2318yes—
266#14579133C2314yes—
267#14579133C2318yes—
268#14579133C2318yes—
269#14579133C2318yes—
270#14579133C2314yes—
271#14579132C2318yes—
272#14579132C2314yes—
273#14579132C2318yes—
274#14579132C2318yes—
275#14579130C2318yes—
276#14579130C2318yes—
277#14579130C2312yes—
278Q8×Dic79C2312yes—
279C4×Dic158C2318yes—
280C4×Dic158C2318yes—
281C4×Dic158C2314yes—
282C4×Dic158C2314yes—
283#14579126C2314yes—
284#14579126C2314yes—
285#14579126C2314yes—
286#14579126C2314yes—
287#14579126C2318yes—
288#14579126C2314yes—
289#14579126C2312yes—
290#14579126C2314yes—
291D4×Dic79C2314yes—
292D4×Dic79C2318yes—
293D4×Dic79C2318yes—
294D4×Dic79C2318yes—
295D4×Dic79C2314yes—
296D4×Dic79C2318yes—
297D4×Dic79C2318yes—
298D4×Dic79C2318yes—
299D4×Dic79C2318yes—
300D4×Dic79C2314yes—
301D4×Dic79C2318yes—
302D4×Dic79C2314yes—
303D4×Dic79C2318yes—
304D4×Dic79C2318yes—
305D4×Dic79C2314yes—
306D4×Dic79C2312yes—
307D4×Dic79C2314yes—
308D4×Dic79C2314yes—
309D4×Dic79C2318yes—
310#14579123C2312yes—
311C4×C22⋊D79C2318yes—
312C4×C22⋊D79C2318yes—
313C4×C22⋊D79C2318yes—
314C4×C22⋊D79C2314yes—
315C4×C22⋊D79C2314yes—
316(C22⋊D79)⋊C4C2314yes—
317(C22⋊D79)⋊C4C2314yes—
318(C22⋊D79)⋊C4C2318yes—
319(C22⋊D79)⋊C4C2318yes—
320(C22⋊D79)⋊C4C2314yes—
321#14579120C2311yescharacteristic
322#14579120C2312yes—
323#14579120C2318yes—
324#14579120C2318yes—
325#14579120C2312yes—
326#14579119C2314yes—
327#14579118C2312yes—
328#14579118C2318yes—
329#14579117C2318yes—
330#14579117C2318yes—
331#14579117C2318yes—
332#14579117C2318yes—
333#14579117C2314yes—
334#14579117C2314yes—
335#14579117C2318yes—
336#14579117C2318yes—
337#14579117C2318yes—
338#14579117C2318yes—
339C2×C4⋊Dic79C2312yes—
340C2×C4⋊Dic79C2314yes—
341C2×Dic79⋊C4C2314yes—
342C2×Dic79⋊C4C2314yes—
343C2×Dic79⋊C4C2318yes—
344C2×Dic79⋊C4C2318yes—
345C2×Dic79⋊C4C2314yes—
346C4⋊C4×D79C2314yes—
347C4⋊C4×D79C2318yes—
348C2×C22⋊Dic79C2314yes—
349C2×C22⋊Dic79C2318yes—
350C2×C22⋊Dic79C2318yes—
351C2×C22⋊Dic79C2318yes—
352C2×C22⋊Dic79C2318yes—
353C2×C22⋊Dic79C2314yes—
354C2×C22⋊Dic79C2314yes—
355C2×C22⋊Dic79C2314yes—
356C2×C4×Dic79C2312yes—
357C2×C4×Dic79C2312yes—
358C2×C4×Dic79C2312yes—
359C2×C4×Dic79C2311yescharacteristic
360C2×C4×Dic79C2312yes—
361C2×C4×Dic79C2312yes—
362C2×C4×Dic79C2311yescharacteristic
363C2×C4×Dic79C2314yes—
364C2×C4×Dic79C2312yes—
365C42×D79C2312yes—
366C2×#41×C79C2311yescharacteristic
367C22×D4×C79C2314yes—
368C22×D4×C79C2312yes—
369C22×D4×C79C2318yes—
370C22×D4×C79C2312yes—
371C23×C4×C79C2311yescharacteristic
372#127×C79C2314yes—
373#127×C79C2312yes—
374#126×C79C2318yes—
375#125×C79C2312yes—
376#124×C79C2314yes—
377#123×C79C2318yes—
378#123×C79C2312yes—
379#123×C79C2318yes—
380C22⋊Q8×C79C2312yes—
381#121×C79C2314yes—
382#121×C79C2314yes—
383#121×C79C2312yes—
384#121×C79C2318yes—
385#121×C79C2318yes—
386#121×C79C2318yes—
387#121×C79C2314yes—
388#121×C79C2314yes—
389#121×C79C2314yes—
390#120×C79C2318yes—
391#120×C79C2314yes—
392#120×C79C2318yes—
393#120×C79C2312yes—
394#120×C79C2314yes—
395C4×D4×C79C2314yes—
396C4×D4×C79C2318yes—
397C4×D4×C79C2314yes—
398#117×C79C2311yescharacteristic
399#117×C79C2312yes—
400C2×C4⋊C4×C79C2312yes—
401C2×C22⋊C4×C79C2314yes—
402#11929624—42no—
403#11929623—416no—
404#11929623—48no—
405#11929623—48no—
406C2×Dic158—44no—
407C2×Dic158—44no—
408C2×Dic158C2414yes—
409C2×Dic158C2414yes—
410C2×Dic158C2414yes—
411C2×Dic158C2418yes—
412C2×Dic158C2414yes—
413C2×Dic158C2411yescharacteristic
414C2×D316C2411yescharacteristic
415C2×C22⋊D79C2414yes—
416C2×C22⋊D79C2418yes—
417C2×C22⋊D79C2418yes—
418C2×C22⋊D79C2414yes—
419C2×C22⋊D79C2412yes—
420C22×Dic79—44no—
421C22×Dic79—48no—
422C22×Dic79C2412yes—
423C22×Dic79C2414yes—
424C22×Dic79C2412yes—
425C22×Dic79C2414yes—
426C22×Dic79C2414yes—
427C22×Dic79C2414yes—
428C22×Dic79C2418yes—
429C22×Dic79C2418yes—
430C22×Dic79C2412yes—
431C22×Dic79C2412yes—
432C22×Dic79C2412yes—
433C22×Dic79C2412yes—
434C22×Dic79C2418yes—
435C22×Dic79C2418yes—
436C2×C4×D79C2412yes—
437C2×C4×D79C2414yes—
438C2×C4×D79C2418yes—
439C4⋊Dic79C2414yes—
440C4⋊Dic79C2418yes—
441C4⋊Dic79C2418yes—
442C4⋊Dic79C2414yes—
443C4⋊Dic79C2414yes—
444C4⋊Dic79C2414yes—
445C4⋊Dic79C2418yes—
446C4⋊Dic79C2418yes—
447C4⋊Dic79C2412yes—
448Dic79⋊C4C2418yes—
449Dic79⋊C4C2418yes—
450Dic79⋊C4C2418yes—
451Dic79⋊C4C2418yes—
452Dic79⋊C4C2414yes—
453Dic79⋊C4C2414yes—
454Dic79⋊C4C2418yes—
455Dic79⋊C4C2418yes—
456Dic79⋊C4C2418yes—
457Dic79⋊C4C2418yes—
458Dic79⋊C4C2418yes—
459Dic79⋊C4C2418yes—
460Dic79⋊C4C2418yes—
461Dic79⋊C4C2414yes—
462Dic79⋊C4C2414yes—
463Dic79⋊C4C2414yes—
464Dic79⋊C4C2418yes—
465C22⋊Dic79C2418yes—
466C22⋊Dic79C2418yes—
467C22⋊Dic79C2414yes—
468C22⋊Dic79C2414yes—
469C22⋊Dic79C2418yes—
470C22⋊Dic79C2418yes—
471C22⋊Dic79C2414yes—
472C22⋊Dic79C2418yes—
473C22⋊Dic79C2414yes—
474C22⋊Dic79C2418yes—
475C22⋊Dic79C2418yes—
476C22⋊Dic79C2418yes—
477C22⋊Dic79C2418yes—
478C22⋊Dic79C2418yes—
479C22⋊Dic79C2418yes—
480C22⋊Dic79C2418yes—
481C22⋊Dic79C2418yes—
482C22⋊Dic79C2412yes—
483(C2×D79)⋊C4C2414yes—
484(C2×D79)⋊C4C2414yes—
485(C2×D79)⋊C4C2418yes—
486(C2×D79)⋊C4C2414yes—
487C4×Dic79C2411yescharacteristic
488C4×Dic79C2414yes—
489C4×Dic79C2411yescharacteristic
490C4×Dic79C2412yes—
491C4×Dic79C2412yes—
492C4×Dic79C2412yes—
493C4×Dic79C2411yescharacteristic
494C4×Dic79C2412yes—
495C4×Dic79C2412yes—
496C4×Dic79C2412yes—
497C4×Dic79C2411yescharacteristic
498C4×Dic79C2418yes—
499C4×Dic79C2414yes—
500C4×Dic79C2418yes—
501C4×Dic79C2412yes—
502C4×Dic79C2414yes—
503C4×Dic79C2418yes—
504C4×Dic79C2418yes—
505C24×C79C2411yescharacteristic
506C24×C79C2414yes—
507C24×C79C2414yes—
508#41×C79—42no—
509C2×Q8×C79C2411yescharacteristic
510C2×D4×C79—44no—
511C2×D4×C79—44no—
512C2×D4×C79—48no—
513C2×D4×C79—416no—
514C2×D4×C79C2418yes—
515C2×D4×C79C2414yes—
516C2×D4×C79C2414yes—
517C2×D4×C79C2411yescharacteristic
518C2×D4×C79C2412yes—
519C2×D4×C79C2414yes—
520C2×D4×C79C2418yes—
521C2×D4×C79C2418yes—
522C2×D4×C79C2414yes—
523C2×D4×C79C2418yes—
524C22×C4×C79—42no—
525C22×C4×C79C2412yes—
526C22×C4×C79C2412yes—
527C22×C4×C79C2411yescharacteristic
528C22×C4×C79C2412yes—
529C22×C4×C79C2414yes—
530C22×C4×C79C2418yes—
531C22×C4×C79C2411yescharacteristic
532C4⋊C4×C79C2414yes—
533C4⋊C4×C79C2414yes—
534C4⋊C4×C79C2412yes—
535C4⋊C4×C79C2414yes—
536C4⋊C4×C79C2418yes—
537C22⋊C4×C79C2418yes—
538C22⋊C4×C79C2418yes—
539C22⋊C4×C79C2414yes—
540C22⋊C4×C79C2412yes—
541C22⋊C4×C79C2414yes—
542C22⋊C4×C79C2418yes—
543C22⋊C4×C79C2418yes—
544C22⋊C4×C79C2414yes—
545C42×C79C2412yes—
546C42×C79C2414yes—
547C23×C79—24no—
548C23×C79—28no—
549C23×C79—41no—
550C23×C79—44no—
551C23×C79—44no—
552C23×C79—44no—
553C23×C79—48no—
554C23×C79C2512yes—
555C23×C79C2518yes—
556C23×C79C2511yescharacteristic
557C23×C79C2512yes—
558C22×D79C2512yes—
559Q8×C79—41no—
560D4×C79—216no—
561D4×C79—28no—
562D4×C79—28no—
563D4×C79—44no—
564D4×C79—44no—
565D4×C79—48no—
566D4×C79—48no—
567D4×C79—48no—
568D4×C79—41no—
569D4×C79—42no—
570C2×C4×C79—24no—
571C2×C4×C79—24no—
572C2×C4×C79—22no—
573C2×C4×C79—41no—
574C2×C4×C79—42no—
575C2×C4×C79—44no—
576C2×C4×C79—48no—
577C2×C4×C79C2512yes—
578C2×C4×C79C2512yes—
579C2×C4×C79C2511yescharacteristic
580C2×C4×C79C2514yes—
581C2×C4×C79C2518yes—
582C2×C4×C79C2511yescharacteristic
583C22⋊D79—28no—
584C22⋊D79—44no—
585C22⋊D79—48no—
586C22⋊D79—48no—
587C22⋊D79—42no—
588C2×Dic79—24no—
589C2×Dic79—24no—
590C2×Dic79—28no—
591C2×Dic79—42no—
592C2×Dic79—42no—
593C2×Dic79—48no—
594C2×Dic79—48no—
595C2×Dic79—42no—
596C2×Dic79—42no—
597C2×Dic79—44no—
598C2×Dic79—44no—
599C2×Dic79—48no—
600C2×Dic79—44no—
601C2×Dic79—48no—
602C2×Dic79C2512yes—
603C2×Dic79C2512yes—
604C2×Dic79C2512yes—
605C2×Dic79C2514yes—
606C2×Dic79C2518yes—
607C2×Dic79C2512yes—
608C2×Dic79C2512yes—
609C2×Dic79C2518yes—
610D316—41no—
611C4×D79—24no—
612C4×D79—48no—
613C4×D79—44no—
614Dic158—28no—
615Dic158—44no—
616Dic158—44no—
617Dic158—44no—
618Dic158—48no—
619Dic158—41no—
620C22×C79—22no—
621C22×C79—22no—
622C22×C79—21no—
623C22×C79—28no—
624C22×C79—28no—
625C22×C79—24no—
626C22×C79—22no—
627C22×C79—28no—
628C22×C79—22no—
629C22×C79—44no—
630C22×C79—88no—
631C22×C79—164no—
632C22×C79#58514yes—
633C22×C79C2611yescharacteristic
634C2×D79—24no—
635C2×D79—22no—
636C4×C79—22no—
637C4×C79—21no—
638C4×C79—22no—
639C4×C79—28no—
640C4×C79—24no—
641C4×C79#58512yes—
642Dic79—24no—
643Dic79—22no—
644Dic79—28no—
645Dic79—22no—
646Dic79—28no—
647Dic79—22no—
648Dic79—22no—
649Dic79—22no—
650#62829—791nomaximal, Sylow
651C2×C79—24no—
652C2×C79—41no—
653C2×C79—48no—
654C2×C79—42no—
655C2×C79C2×#58512yes—
656C2×C79C2×#58511yescharacteristic
657D79—42no—
658#3566—798no—
659#3564—794no—
660#3560—794no—
661#3557—792no—
662#3551—792no—
663#3538—791no—
664#3537D7911yescharacteristic, complemented
665#3536—792no—
666#3516—794no—
667#3515—794no—
668#3514—794no—
669#3513—798no—
670#3513—794no—
671#3512—792no—
672#3510—792no—
673#3493—794no—
674#3491—794no—
675#3444—791no—
676C2×#529—792no—
677C79#6282911yescharacteristic, complemented, Sylow
678#563—794no—
679#563—794no—
680#563—798no—
681#562—798no—
682#560—794no—
683#560C2×D7914yes—
684#559—798no—
685#559—794no—
686#557—794no—
687#556—798no—
688#556—798no—
689#556—794no—
690#555—794no—
691#555—798no—
692#554—794no—
693#554—798no—
694#554—794no—
695#553—798no—
696#553—798no—
697#553—798no—
698#553—798no—
699#553—798no—
700#553—794no—
701#553C2×D7914yes—
702#552—798no—
703#552—798no—
704#552—798no—
705#552—798no—
706#552—798no—
707#552—794no—
708#552—798no—
709#552—794no—
710#551—794no—
711#551—798no—
712#551—798no—
713#551—798no—
714#551—798no—
715#551—794no—
716#551—798no—
717#551—798no—
718D4×Q8—794no—
719#548—794no—
720#548—794no—
721#547—794no—
722#547—798no—
723#546—798no—
724#546—798no—
725#546—794no—
726#546—794no—
727#546—798no—
728D42C2×D7914yes—
729D42C2×D7914yes—
730#544—794no—
731#543—794no—
732#542—798no—
733#542—794no—
734#542—794no—
735#542—798no—
736#542—798no—
737#541—798no—
738#541—798no—
739#541—792no—
740#541—792no—
741#540—792no—
742#540—798no—
743#540C2×D7912yes—
744#539—798no—
745#539—798no—
746#539—794no—
747#539—794no—
748#539—798no—
749#539—798no—
750#538—798no—
751#538—798no—
752#538—798no—
753#538—798no—
754#538—794no—
755#538C2×D7914yes—
756#537—794no—
757#537—794no—
758#536—792no—
759#535C2×D7912yes—
760#534C2×D7914yes—
761#533—792no—
762#533—791no—
763#533—792no—
764#532—791no—
765#532—792no—
766#532—792no—
767#529—794no—
768#529—792no—
769#529—794no—
770#529—794no—
771#529—794no—
772#529—794no—
773#529—794no—
774#529—794no—
775#529—794no—
776#529—794no—
777#529—792no—
778#529—798no—
779#529—794no—
780#529—794no—
781#529—798no—
782#529—794no—
783C2×#126—794no—
784C2×#125—792no—
785C2×#125—792no—
786C2×#124—792no—
787C2×#124—792no—
788#525—791no—
789#525—794no—
790#525—798no—
791#525C2×D7911yescharacteristic
792C2×#123—794no—
793C2×#123—798no—
794C2×C22⋊Q8—792no—
795C2×#121C2×D7912yes—
796#520—798no—
797#520—794no—
798#519—792no—
799#518—798no—
800#518—792no—
801C4×#41—791no—
802C4×#41—794no—
803C4×#41—791no—
804C2×C4×Q8—792no—
805C2×C4×D4—794no—
806C2×C4×D4—792no—
807C2×#117—794no—
808C22×C42—791no—
809C2×#41—794no—
810C2×#41—798no—
811C2×#41—794no—
812C2×#41—791no—
813C2×#41C22×D7911yescharacteristic
814C22×Q8—792no—
815C22×Q8—792no—
816C22×D4C22×D7914yes—
817C22×D4C22×D7912yes—
818C22×D4C22×D7918yes—
819C22×D4C22×D7912yes—
820C23×C4—794no—
821C23×C4—792no—
822C23×C4C22×D7911yescharacteristic
823C4⋊Q8—791no—
824C4⋊Q8—794no—
825C4⋊Q8—792no—
826C4⋊Q8—794no—
827C4⋊Q8—798no—
828C4⋊Q8—798no—
829C4⋊Q8—792no—
830#127—791no—
831#127C22×D7912yes—
832#127C22×D7914yes—
833#126—794no—
834#126—798no—
835#126—798no—
836#126—798no—
837#126—798no—
838#126—798no—
839#126—794no—
840#126—798no—
841#126—798no—
842#126—798no—
843#126—798no—
844#126—798no—
845#126—798no—
846#126—798no—
847#126—798no—
848#126—798no—
849#126—798no—
850#126C22×D7918yes—
851#125—794no—
852#125—794no—
853#125—794no—
854#125—794no—
855#125—798no—
856#125—794no—
857#125—792no—
858#125—798no—
859#125—798no—
860#125—798no—
861#125—798no—
862#125—798no—
863#125—798no—
864#125—792no—
865#125—798no—
866#125C22×D7912yes—
867#124—791no—
868#124—794no—
869#124—794no—
870#124—794no—
871#124—794no—
872#124—798no—
873#124—794no—
874#124—791no—
875#124—798no—
876#124—794no—
877#124—798no—
878#124—798no—
879#124—794no—
880#124—798no—
881#124—798no—
882#124C22×D7914yes—
883#123—798no—
884#123—794no—
885#123—798no—
886#123—798no—
887#123—798no—
888#123—798no—
889#123—798no—
890#123—798no—
891#123—798no—
892#123—798no—
893#123—798no—
894#123—798no—
895#123—794no—
896#123—794no—
897#123—798no—
898#123—798no—
899#123—798no—
900#123—798no—
901#123—792no—
902#123—794no—
903#123—798no—
904#123—798no—
905#123—798no—
906#123C22×D7912yes—
907#123C22×D7918yes—
908#123C22×D7918yes—
909C22⋊Q8—794no—
910C22⋊Q8—794no—
911C22⋊Q8—794no—
912C22⋊Q8—794no—
913C22⋊Q8—792no—
914C22⋊Q8—794no—
915C22⋊Q8—798no—
916C22⋊Q8—798no—
917C22⋊Q8—798no—
918C22⋊Q8—794no—
919C22⋊Q8—798no—
920C22⋊Q8—794no—
921C22⋊Q8—794no—
922C22⋊Q8—798no—
923C22⋊Q8—798no—
924C22⋊Q8—798no—
925C22⋊Q8—798no—
926C22⋊Q8—798no—
927C22⋊Q8—798no—
928C22⋊Q8—798no—
929C22⋊Q8—798no—
930C22⋊Q8—798no—
931C22⋊Q8—798no—
932C22⋊Q8—798no—
933C22⋊Q8C22×D7912yes—
934#121—794no—
935#121—794no—
936#121—798no—
937#121—798no—
938#121—798no—
939#121—794no—
940#121—798no—
941#121—798no—
942#121—798no—
943#121—798no—
944#121—798no—
945#121—798no—
946#121—792no—
947#121—798no—
948#121C22×D7914yes—
949#121C22×D7914yes—
950#121C22×D7914yes—
951#121C22×D7914yes—
952#121C22×D7912yes—
953#121C22×D7918yes—
954#121C22×D7914yes—
955#121C22×D7918yes—
956#121C22×D7918yes—
957#120—792no—
958#120—798no—
959#120—798no—
960#120C22×D7912yes—
961#120C22×D7918yes—
962#120C22×D7914yes—
963#120C22×D7918yes—
964#120C22×D7914yes—
965C4×Q8—792no—
966C4×Q8—794no—
967C4×Q8—794no—
968C4×Q8—794no—
969C4×Q8—794no—
970C4×Q8—794no—
971C4×Q8—792no—
972C4×Q8—794no—
973C4×Q8—798no—
974C4×Q8—794no—
975C4×Q8—798no—
976C4×Q8—794no—
977C4×Q8—798no—
978C4×D4—798no—
979C4×D4—794no—
980C4×D4—794no—
981C4×D4—798no—
982C4×D4—798no—
983C4×D4—794no—
984C4×D4—794no—
985C4×D4—798no—
986C4×D4—794no—
987C4×D4—794no—
988C4×D4—792no—
989C4×D4—798no—
990C4×D4—798no—
991C4×D4—798no—
992C4×D4—798no—
993C4×D4—798no—
994C4×D4—798no—
995C4×D4—794no—
996C4×D4—798no—
997C4×D4—794no—
998C4×D4—794no—
999C4×D4—798no—
1000C4×D4—798no—
1001C4×D4—798no—
1002C4×D4—792no—
1003C4×D4—794no—
1004C4×D4—794no—
1005C4×D4—794no—
1006C4×D4—798no—
1007C4×D4—798no—
1008C4×D4C22×D7914yes—
1009C4×D4C22×D7918yes—
1010C4×D4C22×D7914yes—
1011#117—792no—
1012#117—791no—
1013#117—798no—
1014#117—798no—
1015#117—792no—
1016#117—794no—
1017#117—798no—
1018#117—798no—
1019#117—798no—
1020#117—798no—
1021#117—794no—
1022#117—794no—
1023#117—798no—
1024#117—798no—
1025#117—798no—
1026#117—798no—
1027#117—792no—
1028#117—798no—
1029#117C22×D7911yescharacteristic
1030#117C22×D7912yes—
1031C2×C4⋊C4—794no—
1032C2×C4⋊C4—794no—
1033C2×C4⋊C4—792no—
1034C2×C4⋊C4—794no—
1035C2×C4⋊C4—794no—
1036C2×C4⋊C4—798no—
1037C2×C4⋊C4—798no—
1038C2×C4⋊C4—794no—
1039C2×C4⋊C4—798no—
1040C2×C4⋊C4C22×D7912yes—
1041C2×C22⋊C4—794no—
1042C2×C22⋊C4—794no—
1043C2×C22⋊C4—794no—
1044C2×C22⋊C4—794no—
1045C2×C22⋊C4—798no—
1046C2×C22⋊C4—798no—
1047C2×C22⋊C4—798no—
1048C2×C22⋊C4—798no—
1049C2×C22⋊C4C22×D7914yes—
1050C2×C42—792no—
1051C2×C42—794no—
1052C2×C42—792no—
1053C2×C42—792no—
1054C2×C42—792no—
1055C2×C42—791no—
1056C2×C42—792no—
1057C2×C42—792no—
1058C2×C42—791no—
1059C2×C42—792no—
1060C24C23×D7911yescharacteristic
1061C24C23×D7914yes—
1062C24C23×D7914yes—
1063#41—42no—
1064#41—3162no—
1065#41—3168no—
1066#41—3168no—
1067#41—31616no—
1068C2×Q8—3164no—
1069C2×Q8—3164no—
1070C2×Q8—791no—
1071C2×Q8—798no—
1072C2×Q8—794no—
1073C2×Q8—794no—
1074C2×Q8—794no—
1075C2×Q8—794no—
1076C2×Q8C23×D7911yescharacteristic
1077C2×D4—44no—
1078C2×D4—44no—
1079C2×D4—48no—
1080C2×D4—416no—
1081C2×D4—798no—
1082C2×D4—798no—
1083C2×D4—794no—
1084C2×D4—792no—
1085C2×D4—794no—
1086C2×D4—791no—
1087C2×D4C23×D7918yes—
1088C2×D4C23×D7914yes—
1089C2×D4C23×D7914yes—
1090C2×D4C23×D7911yescharacteristic
1091C2×D4C23×D7912yes—
1092C2×D4C23×D7914yes—
1093C2×D4C23×D7918yes—
1094C2×D4C23×D7918yes—
1095C2×D4C23×D7914yes—
1096C2×D4C23×D7918yes—
1097C22×C4—42no—
1098C22×C4—3164no—
1099C22×C4—3168no—
1100C22×C4—792no—
1101C22×C4—792no—
1102C22×C4—792no—
1103C22×C4—792no—
1104C22×C4—794no—
1105C22×C4—794no—
1106C22×C4—798no—
1107C22×C4—798no—
1108C22×C4—794no—
1109C22×C4—798no—
1110C22×C4—798no—
1111C22×C4—794no—
1112C22×C4—798no—
1113C22×C4—792no—
1114C22×C4—792no—
1115C22×C4—794no—
1116C22×C4—792no—
1117C22×C4C23×D7912yes—
1118C22×C4C23×D7911yescharacteristic
1119C22×C4C23×D7912yes—
1120C22×C4C23×D7912yes—
1121C22×C4C23×D7911yescharacteristic
1122C22×C4C23×D7914yes—
1123C22×C4C23×D7918yes—
1124C4⋊C4—798no—
1125C4⋊C4—798no—
1126C4⋊C4—794no—
1127C4⋊C4—798no—
1128C4⋊C4—794no—
1129C4⋊C4—798no—
1130C4⋊C4—798no—
1131C4⋊C4—798no—
1132C4⋊C4—798no—
1133C4⋊C4—798no—
1134C4⋊C4—798no—
1135C4⋊C4—798no—
1136C4⋊C4—798no—
1137C4⋊C4—794no—
1138C4⋊C4—794no—
1139C4⋊C4—794no—
1140C4⋊C4—798no—
1141C4⋊C4—794no—
1142C4⋊C4—798no—
1143C4⋊C4—798no—
1144C4⋊C4—794no—
1145C4⋊C4—794no—
1146C4⋊C4—794no—
1147C4⋊C4—798no—
1148C4⋊C4—798no—
1149C4⋊C4—792no—
1150C4⋊C4C23×D7914yes—
1151C4⋊C4C23×D7918yes—
1152C4⋊C4C23×D7914yes—
1153C4⋊C4C23×D7914yes—
1154C4⋊C4C23×D7912yes—
1155C22⋊C4—798no—
1156C22⋊C4—798no—
1157C22⋊C4—794no—
1158C22⋊C4—798no—
1159C22⋊C4—794no—
1160C22⋊C4—798no—
1161C22⋊C4—794no—
1162C22⋊C4—798no—
1163C22⋊C4—794no—
1164C22⋊C4—798no—
1165C22⋊C4—798no—
1166C22⋊C4—798no—
1167C22⋊C4—798no—
1168C22⋊C4—798no—
1169C22⋊C4—798no—
1170C22⋊C4—798no—
1171C22⋊C4—798no—
1172C22⋊C4—792no—
1173C22⋊C4—794no—
1174C22⋊C4—794no—
1175C22⋊C4—798no—
1176C22⋊C4—794no—
1177C22⋊C4C23×D7918yes—
1178C22⋊C4C23×D7918yes—
1179C22⋊C4C23×D7914yes—
1180C22⋊C4C23×D7914yes—
1181C22⋊C4C23×D7918yes—
1182C22⋊C4C23×D7918yes—
1183C22⋊C4C23×D7914yes—
1184C22⋊C4C23×D7912yes—
1185C42—791no—
1186C42—792no—
1187C42—791no—
1188C42—791no—
1189C42—792no—
1190C42—792no—
1191C42—792no—
1192C42—792no—
1193C42—792no—
1194C42—791no—
1195C42—794no—
1196C42—798no—
1197C42—798no—
1198C42—794no—
1199C42—792no—
1200C42—798no—
1201C42—794no—
1202C42—798no—
1203C42C23×D7912yes—
1204C42C23×D7914yes—
1205C23—24no—
1206C23—28no—
1207C23—41no—
1208C23—44no—
1209C23—44no—
1210C23—44no—
1211C23—48no—
1212C23—792no—
1213C23C24×D7912yes—
1214C23C24×D7918yes—
1215C23C24×D7911yescharacteristic
1216C23C24×D7912yes—
1217Q8—41no—
1218Q8—3164no—
1219Q8—3164no—
1220Q8—3161no—
1221Q8—3168no—
1222Q8—3164no—
1223Q8—1588no—
1224D4—216no—
1225D4—28no—
1226D4—28no—
1227D4—44no—
1228D4—44no—
1229D4—48no—
1230D4—48no—
1231D4—48no—
1232D4—41no—
1233D4—42no—
1234D4—3161no—
1235D4—3162no—
1236D4—3168no—
1237D4—3168no—
1238D4—3164no—
1239D4—1588no—
1240C2×C4—24no—
1241C2×C4—22no—
1242C2×C4—24no—
1243C2×C4—41no—
1244C2×C4—42no—
1245C2×C4—44no—
1246C2×C4—48no—
1247C2×C4—3164no—
1248C2×C4—3168no—
1249C2×C4—3162no—
1250C2×C4—3162no—
1251C2×C4—3168no—
1252C2×C4—3168no—
1253C2×C4—3162no—
1254C2×C4—3162no—
1255C2×C4—3164no—
1256C2×C4—3164no—
1257C2×C4—3164no—
1258C2×C4—3168no—
1259C2×C4—3168no—
1260C2×C4—792no—
1261C2×C4—792no—
1262C2×C4—792no—
1263C2×C4—798no—
1264C2×C4—794no—
1265C2×C4—792no—
1266C2×C4—792no—
1267C2×C4—798no—
1268C2×C4—1584no—
1269C2×C4—1584no—
1270C2×C4—1588no—
1271C2×C4—1584no—
1272C2×C4C24×D7912yes—
1273C2×C4C24×D7912yes—
1274C2×C4C24×D7911yescharacteristic
1275C2×C4C24×D7914yes—
1276C2×C4C24×D7918yes—
1277C2×C4C24×D7911yescharacteristic
1278C22—22no—
1279C22—22no—
1280C22—21no—
1281C22—22no—
1282C22—28no—
1283C22—22no—
1284C22—28no—
1285C22—28no—
1286C22—24no—
1287C22—44no—
1288C22—88no—
1289C22—164no—
1290C22—1584no—
1291C22—1582no—
1292C22#1909939814yes—
1293C22C25×D7911yescharacteristic
1294C4—22no—
1295C4—21no—
1296C4—22no—
1297C4—28no—
1298C4—24no—
1299C4—1582no—
1300C4—1582no—
1301C4—1582no—
1302C4—1588no—
1303C4—1582no—
1304C4—1588no—
1305C4—1584no—
1306C4—1582no—
1307C4#1909939812yes—
1308C2—24no—
1309C2—41no—
1310C2—48no—
1311C2—42no—
1312C2—3162no—
1313C2C2×#1909939812yes—
1314C2C2×#1909939811yescharacteristic
subgroupG/H
center, FrattiniC22C25×D79
commutator, socle, cosocleC22×C79C26
FittingC79×#3537C2
hypercenter#3537D79
hypocenterC79#62829
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C22 ◁ #3537

Complements

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

NH ≅ G/Ntype
1. #23778057C2semidirect
2. #23778026C2semidirect
3. #23777942C2semidirect
4. #23777905C2semidirect
5. #23777824C2semidirect
6. #23777649C2semidirect
7. #23777622C2semidirect
8. #23777384C2semidirect
9. #23777371C2semidirect
10. #23777352C2semidirect
11. #23777325C2semidirect
12. #23777325C2semidirect
13. #23777319C2semidirect
14. #23777295C2semidirect
15. #23777115C2semidirect
16. #23777097C2semidirect
17. #23776692C2semidirect
18. C2×#19099094C2semidirect
19. C79×#3537C2semidirect
20. #19099316C22semidirect
21. #19099316C22semidirect
22. #19099313C22semidirect
23. #19099308C22semidirect
24. #19099302C22semidirect
25. #19099299C22semidirect
26. #19099299C22semidirect
27. #19099290C22semidirect
28. #19099283C22semidirect
29. #19099282C22semidirect
30. #19099280C22semidirect
31. #19099277C22semidirect
32. #19099275C22semidirect
33. #19099272C22semidirect
34. #19099272C22semidirect
35. #19099268C22semidirect
36. #19099260C22semidirect
37. #19099260C22semidirect
38. #19099258C22semidirect
39. #19099256C22semidirect
40. #19099256C22semidirect
41. #19099256C22semidirect
42. #19099253C22semidirect
43. #19099253C22semidirect
44. #19099252C22semidirect
45. #19099250C22semidirect
46. #19099250C22semidirect
47. #19099250C22semidirect
48. #19099250C22semidirect
49. #19099249C22semidirect
50. #19099244C22semidirect
51. #19099244C22semidirect
52. #19099244C22semidirect
53. #19099244C22semidirect
54. #19099244C22semidirect
55. #19099244C22semidirect
56. #19099244C22semidirect
57. #19099244C22semidirect
58. D4×Dic158C22semidirect
59. #19099219C22semidirect
60. #19099219C22semidirect
61. #19099213C22semidirect
62. #19099213C22semidirect
63. #19099207C22semidirect
64. #19099207C22semidirect
65. #19099207C22semidirect
66. #19099207C22semidirect
67. #19099207C22semidirect
68. #19099192C22semidirect
69. #19099189C22semidirect
70. #19099181C22semidirect
71. #19099180C22semidirect
72. #19099180C22semidirect
73. #19099180C22semidirect
74. #19099180C22semidirect
75. #19099176C22semidirect
76. #19099175C22semidirect
77. #19099170C22semidirect
78. #19099170C22semidirect
79. #19099167C22semidirect
80. #19099167C22semidirect
81. #19099158C22semidirect
82. #19099158C22semidirect
83. #19099158C22semidirect
84. #19099158C22semidirect
85. #19099158C22semidirect
86. #19099156C22semidirect
87. #19099151C22semidirect
88. #19099148C22semidirect
89. #19099148C22semidirect
90. #19099148C22semidirect
91. #19099148C22semidirect
92. #19099142C22semidirect
93. #19099140C22semidirect
94. #19099134C22semidirect
95. #19099116C22semidirect
96. #19099116C22semidirect
97. #19099115C22semidirect
98. #19099111C22semidirect
99. #19099109C22semidirect
100. #19099108C22semidirect
101. #19099099C22semidirect
102. #19099095C22semidirect
103. #19099094C22semidirect
104. #19099094C22semidirect
105. #19099094C22semidirect
106. #19099094C22semidirect
107. #19099094C22semidirect
108. #19099094C22semidirect
109. #19099094C22semidirect
110. #19099094C22semidirect
111. #19099094C22semidirect
112. #19099094C22semidirect
113. #19099094C22semidirect
114. #19099093C22semidirect
115. #19099093C22semidirect
116. #19099090C22semidirect
117. C2×#14579154C22semidirect
118. C2×#14579152C22semidirect
119. #125×D79C22semidirect
120. C2×#14579148C22semidirect
121. C2×#14579148C22semidirect
122. #19099074C22semidirect
123. #19099069C22semidirect
124. #19099069C22semidirect
125. C2×#14579142C22semidirect
126. C2×#14579142C22semidirect
127. C2×#14579140C22semidirect
128. #19099042C22semidirect
129. #19099042C22semidirect
130. #19099040C22semidirect
131. #19099038C22semidirect
132. #19099038C22semidirect
133. #41×Dic79C22semidirect
134. #19099031C22semidirect
135. C4×#11929623C22semidirect
136. C2×#14579126C22semidirect
137. C2×D4×Dic79C22semidirect
138. C2×D4×Dic79C22semidirect
139. C2×#14579117C22semidirect
140. C22×C4×Dic79C22semidirect
664. #3537D79semidirect
677. C79#62829semidirect

Maximal subgroups

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

subgroupindex
#237780572
#237780262
#237779422
#237779052
#237778242
#237776492
#237776222
#237773842
#237773712
#237773522
#237773252
#237773192
#237772952
#237771152
#237770972
#237766922
C2×#190990942
C79×#35372
#6282979