Finite Group Databasebeta

← #35197091

Subgroups — #35197091

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#23778081C218yesmaximal, complemented
2#23778021C214yesmaximal, complemented
3#23777957C214yesmaximal, complemented
4#23777908C212yesmaximal, complemented
5#23777829C212yesmaximal, complemented
6#23777639C211yesmaximal, characteristic, complemented
7#23777629C212yesmaximal, complemented
8#23777394C214yesmaximal, complemented
9#23777375C214yesmaximal, complemented
10#23777362C214yesmaximal, complemented
11#23777345C214yesmaximal, complemented
12#23777327C218yesmaximal, complemented
13#23777323C212yesmaximal, complemented
14#23777299C212yesmaximal, complemented
15#23777121C214yesmaximal, complemented
16#23777094C214yesmaximal, complemented
17#23776692C211yesmaximal, characteristic, complemented
18C2×#19099099C212yesmaximal, complemented
19C79×#3538C211yesmaximal, characteristic, complemented
20#19099317C2218yescomplemented
21#19099312C2214yescomplemented
22#19099309C2218yescomplemented
23#19099303C2214yes—
24#19099303C2214yescomplemented
25#19099298C2214yescomplemented
26#19099295C2218yescomplemented
27#19099289C2214yescomplemented
28#19099287C2218yescomplemented
29#19099287C2218yescomplemented
30#19099287C2214yescomplemented
31#19099279C2218yescomplemented
32#19099279C2214yescomplemented
33#19099271C2218yescomplemented
34#19099271C2214yescomplemented
35#19099269C2214yescomplemented
36#19099266C2218yescomplemented
37#19099266C2218yescomplemented
38#19099264C2218yescomplemented
39#19099264C2218yescomplemented
40#19099259C2214yes—
41#19099259C2218yescomplemented
42#19099257C2214yescomplemented
43#19099251C2218yescomplemented
44#19099251C2218yescomplemented
45#19099249C2218yescomplemented
46#19099247C2218yescomplemented
47#19099247C2214yescomplemented
48#19099246C2218yescomplemented
49#19099245C2218yescomplemented
50#19099241C2214yescomplemented
51#19099240C2218yescomplemented
52#19099240C2218yescomplemented
53#19099238C2218yescomplemented
54#19099237C2218yescomplemented
55#19099236C2218yescomplemented
56#19099236C2218yescomplemented
57#19099224C2214yescomplemented
58#19099224C2214yescomplemented
59#19099214C2214yescomplemented
60#19099211C2218yescomplemented
61#19099208C2218yescomplemented
62#19099205C2218yescomplemented
63#19099204C2214yescomplemented
64#19099204C2214yescomplemented
65#19099203C2218yescomplemented
66D4×D316C2214yes—
67#19099195C2214yes—
68#19099188C2214yescomplemented
69#19099187C2218yescomplemented
70#19099186C2214yescomplemented
71#19099186C2214yescomplemented
72#19099186C2218yescomplemented
73#19099179C2218yescomplemented
74#19099174C2218yescomplemented
75#19099174C2212yescomplemented
76#19099172C2218yescomplemented
77#19099169C2212yescomplemented
78#19099168C2212yes—
79#19099165C2218yescomplemented
80#19099161C2218yescomplemented
81#19099160C2214yescomplemented
82#19099157C2218yescomplemented
83#19099154C2218yescomplemented
84#19099154C2218yescomplemented
85#19099153C2214yes—
86#19099153C2218yescomplemented
87#19099153C2218yescomplemented
88#19099153C2214yescomplemented
89#19099152C2218yescomplemented
90#19099147C2218yescomplemented
91#19099144C2214yescomplemented
92#19099143C2214yescomplemented
93#19099127C2212yes—
94#19099121C2214yes—
95#19099116C2212yescomplemented
96#19099116C2211yescharacteristic, complemented
97#19099115C2212yescomplemented
98#19099114C2212yescomplemented
99#19099109C2211yescharacteristic, complemented
100#19099108C2212yescomplemented
101#19099100C2214yescomplemented
102#19099099C2214yescomplemented
103#19099099C2214yescomplemented
104#19099099C2214yescomplemented
105#19099099C2214yescomplemented
106#19099099C2214yescomplemented
107#19099099C2218yescomplemented
108#19099099C2214yescomplemented
109#19099099C2214yescomplemented
110#19099099C2214yescomplemented
111#19099099C2212yescomplemented
112#19099099C2214yescomplemented
113#19099094C2212yescomplemented
114#19099093C2218yescomplemented
115#19099093C2214yescomplemented
116#19099090C2214yescomplemented
117C2×#14579156C2214yescomplemented
118C2×#14579152C2212yescomplemented
119#125×D79C2212yescomplemented
120C2×#14579150C2212yescomplemented
121C2×#14579150C2212yescomplemented
122#19099075C2218yescomplemented
123#19099074C2211yescharacteristic, complemented
124#19099069C2214yescomplemented
125C2×#14579145C2214yescomplemented
126#123×D79C2218yescomplemented
127C2×#14579135C2212yes—
128#19099045C2214yescomplemented
129#19099043C2218yescomplemented
130#19099041C2212yescomplemented
131#19099037C2212yescomplemented
132#19099035C2218yescomplemented
133#41×Dic79C2211yescharacteristic, complemented
134#19099031C2211yescharacteristic, complemented
135C4×#11929623C2214yescomplemented
136C2×Q8×Dic79C2212yescomplemented
137C2×#14579123C2212yescomplemented
138C2×(C22⋊D79)⋊C4C2214yescomplemented
139C2×#14579119C2214yescomplemented
140C22×C4×Dic79C2211yescharacteristic, complemented
141#563×C79C2214yescomplemented
142#552×C79C2214yescomplemented
143#551×C79C2214yescomplemented
144D4×Q8×C79C2214yescomplemented
145#544×C79C2214yescomplemented
146#541×C79C2212yescomplemented
147#539×C79C2214yescomplemented
148#536×C79C2212yescomplemented
149#525×C79C2211yescharacteristic
150C2×C22⋊Q8×C79C2212yescomplemented
151C2×#11929625C2314yes—
152C2×#11929624C2311yescharacteristic
153C2×#11929624C2318yes—
154C2×#11929623C2314yes—
155C22×D316C2312yes—
156C22×D316C2312yes—
157C22×C22⋊D79C2314yes—
158C2×D4×D79C2318yes—
159C23×Dic79C2312yes—
160C22×C4×D79C2314yes—
161#14579160C2318yes—
162#14579160C2314yes—
163#14579160C2312yes—
164#14579159C2311yescharacteristic
165#14579158C2312yes—
166#14579157C2314yes—
167#14579157C2311yescharacteristic
168#14579156C2318yes—
169#14579156C2318yes—
170#14579156C2318yes—
171#14579156C2318yes—
172#14579156C2318yes—
173#14579156C2318yes—
174#14579156C2318yes—
175#14579156C2318yes—
176#14579156C2318yes—
177#14579156C2318yes—
178#14579156C2318yes—
179#14579156C2314yes—
180#14579156C2318yes—
181#14579155C2318yes—
182#14579154C2318yes—
183#14579154C2314yes—
184#14579153C2318yes—
185#14579153C2312yes—
186#14579152C2314yes—
187#14579152C2318yes—
188#14579152C2314yes—
189#14579152C2314yes—
190#14579152C2312yes—
191#14579152C2314yes—
192#14579151C2318yes—
193#14579151C2318yes—
194#14579151C2314yes—
195#14579151C2318yes—
196#14579151C2318yes—
197#14579150C2318yes—
198#14579150C2314yes—
199#14579150C2318yes—
200#14579150C2314yes—
201#14579150C2318yes—
202#14579150C2314yes—
203#14579150C2314yes—
204#14579150C2314yes—
205#14579150C2311yescharacteristic
206#14579150C2314yes—
207#14579149C2318yes—
208#14579148C2311yescharacteristic
209#14579147C2314yes—
210#14579147C2318yes—
211#14579147C2318yes—
212#14579146C2318yes—
213#14579146C2318yes—
214#14579146C2318yes—
215#14579146C2318yes—
216#14579146C2318yes—
217#14579146C2318yes—
218#14579146C2318yes—
219#14579146C2318yes—
220#14579145C2318yes—
221#14579145C2318yes—
222#14579145C2318yes—
223#14579145C2318yes—
224#14579145C2318yes—
225#14579145C2314yes—
226#14579144C2318yes—
227#14579144C2312yes—
228#14579143C2318yes—
229#14579143C2318yes—
230#14579143C2318yes—
231#14579143C2318yes—
232#14579143C2318yes—
233#14579142C2314yes—
234#14579141C2318yes—
235#14579141C2318yes—
236#14579141C2318yes—
237#14579141C2318yes—
238#14579141C2318yes—
239#14579140C2312yes—
240#14579139C2318yes—
241#14579139C2318yes—
242#14579139C2318yes—
243#14579139C2318yes—
244#14579138C2314yes—
245#14579138C2318yes—
246#14579138C2318yes—
247#14579138C2314yes—
248#14579137C2314yes—
249#14579137C2318yes—
250#14579137C2318yes—
251#14579136C2318yes—
252#14579136C2314yes—
253#14579136C2318yes—
254#14579136C2318yes—
255#14579136C2318yes—
256#14579136C2318yes—
257#14579136C2318yes—
258#14579135C2314yes—
259#14579135C2312yes—
260#14579135C2314yes—
261#14579135C2318yes—
262#14579135C2318yes—
263#14579135C2314yes—
264#14579135C2314yes—
265#14579135C2314yes—
266#14579134C2318yes—
267#14579134C2318yes—
268#14579134C2318yes—
269#14579134C2318yes—
270#14579133C2314yes—
271#14579133C2318yes—
272#14579133C2314yes—
273#14579131C2318yes—
274#14579131C2318yes—
275#14579131C2318yes—
276#14579131C2318yes—
277#14579130C2312yes—
278#14579129C2314yes—
279#14579129C2314yes—
280Q8×Dic79C2314yes—
281Q8×Dic79C2314yes—
282Q8×Dic79C2318yes—
283Q8×Dic79C2314yes—
284Q8×Dic79C2314yes—
285Q8×Dic79C2314yes—
286Q8×Dic79C2312yes—
287C4×Dic158C2318yes—
288C4×Dic158C2318yes—
289C4×Dic158C2314yes—
290#14579126C2314yes—
291#14579126C2312yes—
292C4×D316C2318yes—
293C4×D316C2318yes—
294C4×D316C2318yes—
295C4×D316C2318yes—
296C4×D316C2318yes—
297C4×D316C2314yes—
298D4×Dic79C2314yes—
299D4×Dic79C2312yes—
300D4×Dic79C2314yes—
301#14579123C2314yes—
302#14579123C2314yes—
303#14579123C2314yes—
304#14579123C2318yes—
305#14579123C2318yes—
306#14579123C2314yes—
307#14579123C2314yes—
308#14579123C2312yes—
309C4×C22⋊D79C2318yes—
310C4×C22⋊D79C2318yes—
311C4×C22⋊D79C2314yes—
312C4×C22⋊D79C2314yes—
313(C22⋊D79)⋊C4C2318yes—
314(C22⋊D79)⋊C4C2318yes—
315(C22⋊D79)⋊C4C2314yes—
316(C22⋊D79)⋊C4C2314yes—
317(C22⋊D79)⋊C4C2318yes—
318(C22⋊D79)⋊C4C2318yes—
319(C22⋊D79)⋊C4C2318yes—
320(C22⋊D79)⋊C4C2318yes—
321(C22⋊D79)⋊C4C2318yes—
322(C22⋊D79)⋊C4C2314yes—
323#14579120C2311yescharacteristic
324#14579120C2312yes—
325#14579120C2318yes—
326#14579120C2312yes—
327#14579119C2318yes—
328#14579119C2318yes—
329#14579119C2318yes—
330#14579119C2318yes—
331#14579119C2318yes—
332#14579119C2318yes—
333#14579119C2318yes—
334#14579119C2314yes—
335#14579118C2312yes—
336#14579118C2318yes—
337#14579118C2318yes—
338#14579117C2314yes—
339#14579117C2314yes—
340C2×C4⋊Dic79C2314yes—
341C2×C4⋊Dic79C2312yes—
342C2×C4⋊Dic79C2314yes—
343C2×Dic79⋊C4C2314yes—
344C4⋊C4×D79C2314yes—
345C4⋊C4×D79C2318yes—
346C4⋊C4×D79C2318yes—
347C4⋊C4×D79C2318yes—
348C2×(C2×D79)⋊C4C2314yes—
349C2×(C2×D79)⋊C4C2314yes—
350C2×(C2×D79)⋊C4C2318yes—
351C2×(C2×D79)⋊C4C2314yes—
352C2×(C2×D79)⋊C4C2314yes—
353C22⋊C4×D79C2318yes—
354C22⋊C4×D79C2318yes—
355C22⋊C4×D79C2318yes—
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×Q8×C79C2312yes—
368C22×Q8×C79C2312yes—
369C23×C4×C79C2311yescharacteristic
370C4⋊Q8×C79C2318yes—
371C4⋊Q8×C79C2312yes—
372C4⋊Q8×C79C2314yes—
373#126×C79C2318yes—
374#126×C79C2318yes—
375#125×C79C2318yes—
376#125×C79C2312yes—
377#125×C79C2318yes—
378#124×C79C2314yes—
379#123×C79C2318yes—
380#123×C79C2314yes—
381#123×C79C2314yes—
382#123×C79C2312yes—
383C22⋊Q8×C79C2314yes—
384C22⋊Q8×C79C2312yes—
385C22⋊Q8×C79C2318yes—
386C22⋊Q8×C79C2314yes—
387C22⋊Q8×C79C2318yes—
388C22⋊Q8×C79C2314yes—
389C22⋊Q8×C79C2314yes—
390C22⋊Q8×C79C2314yes—
391#121×C79C2312yes—
392#120×C79C2312yes—
393C4×Q8×C79C2314yes—
394C4×D4×C79C2314yes—
395C4×D4×C79C2318yes—
396#117×C79C2311yescharacteristic
397#117×C79C2318yes—
398#117×C79C2312yes—
399C2×C4⋊C4×C79C2314yes—
400C2×C4⋊C4×C79C2312yes—
401C2×C22⋊C4×C79C2314yes—
402C23×D79C2414yes—
403C23×D79C2414yes—
404#11929625—48no—
405#11929624—416no—
406#11929624—42no—
407#11929623—48no—
408C2×Dic158C2414yes—
409C2×Dic158C2411yescharacteristic
410C2×Dic158C2418yes—
411C2×D316—44no—
412C2×D316—44no—
413C2×D316C2414yes—
414C2×D316C2411yescharacteristic
415C2×D316C2418yes—
416C2×D316C2418yes—
417C2×D316C2414yes—
418C2×D316C2418yes—
419C2×D316C2414yes—
420C2×C22⋊D79—48no—
421C2×C22⋊D79C2414yes—
422C2×C22⋊D79C2418yes—
423C2×C22⋊D79C2414yes—
424C2×C22⋊D79C2412yes—
425C2×C22⋊D79C2418yes—
426C2×C22⋊D79C2418yes—
427D4×D79—416no—
428C22×Dic79—44no—
429C22×Dic79C2412yes—
430C22×Dic79C2412yes—
431C22×Dic79C2414yes—
432C22×Dic79C2412yes—
433C22×Dic79C2412yes—
434C22×Dic79C2412yes—
435C22×Dic79C2412yes—
436C22×Dic79C2414yes—
437C2×C4×D79—48no—
438C2×C4×D79C2412yes—
439C2×C4×D79C2414yes—
440C2×C4×D79C2418yes—
441C2×C4×D79C2418yes—
442C2×C4×D79C2418yes—
443C2×C4×D79C2418yes—
444C2×C4×D79C2418yes—
445C2×C4×D79C2418yes—
446C4⋊Dic79C2418yes—
447C4⋊Dic79C2418yes—
448C4⋊Dic79C2414yes—
449C4⋊Dic79C2418yes—
450C4⋊Dic79C2414yes—
451C4⋊Dic79C2418yes—
452C4⋊Dic79C2414yes—
453C4⋊Dic79C2414yes—
454C4⋊Dic79C2412yes—
455C4⋊Dic79C2418yes—
456Dic79⋊C4C2414yes—
457Dic79⋊C4C2414yes—
458Dic79⋊C4C2418yes—
459Dic79⋊C4C2418yes—
460Dic79⋊C4C2418yes—
461Dic79⋊C4C2418yes—
462Dic79⋊C4C2418yes—
463Dic79⋊C4C2414yes—
464Dic79⋊C4C2414yes—
465Dic79⋊C4C2414yes—
466Dic79⋊C4C2418yes—
467C22⋊Dic79C2414yes—
468C22⋊Dic79C2414yes—
469C22⋊Dic79C2414yes—
470C22⋊Dic79C2414yes—
471C22⋊Dic79C2412yes—
472(C2×D79)⋊C4C2418yes—
473(C2×D79)⋊C4C2418yes—
474(C2×D79)⋊C4C2418yes—
475(C2×D79)⋊C4C2418yes—
476(C2×D79)⋊C4C2418yes—
477(C2×D79)⋊C4C2418yes—
478(C2×D79)⋊C4C2418yes—
479(C2×D79)⋊C4C2418yes—
480(C2×D79)⋊C4C2418yes—
481(C2×D79)⋊C4C2418yes—
482(C2×D79)⋊C4C2418yes—
483(C2×D79)⋊C4C2418yes—
484(C2×D79)⋊C4C2414yes—
485(C2×D79)⋊C4C2418yes—
486(C2×D79)⋊C4C2414yes—
487(C2×D79)⋊C4C2414yes—
488(C2×D79)⋊C4C2418yes—
489(C2×D79)⋊C4C2418yes—
490C4×Dic79C2411yescharacteristic
491C4×Dic79C2414yes—
492C4×Dic79C2412yes—
493C4×Dic79C2411yescharacteristic
494C4×Dic79C2411yescharacteristic
495C4×Dic79C2412yes—
496C4×Dic79C2412yes—
497C4×Dic79C2412yes—
498C4×Dic79C2412yes—
499C4×Dic79C2412yes—
500C4×Dic79C2411yescharacteristic
501C4×Dic79C2414yes—
502C4×Dic79C2418yes—
503C4×Dic79C2418yes—
504C4×Dic79C2412yes—
505C4×Dic79C2418yes—
506C4×Dic79C2414yes—
507C24×C79C2411yescharacteristic
508#41×C79—42no—
509C2×Q8×C79—44no—
510C2×Q8×C79—44no—
511C2×Q8×C79C2414yes—
512C2×Q8×C79C2414yes—
513C2×Q8×C79C2414yes—
514C2×Q8×C79C2411yescharacteristic
515C2×D4×C79C2414yes—
516C2×D4×C79C2412yes—
517C2×D4×C79C2411yescharacteristic
518C22×C4×C79—42no—
519C22×C4×C79C2414yes—
520C22×C4×C79C2411yescharacteristic
521C22×C4×C79C2412yes—
522C22×C4×C79C2412yes—
523C22×C4×C79C2414yes—
524C22×C4×C79C2412yes—
525C22×C4×C79C2414yes—
526C22×C4×C79C2411yescharacteristic
527C4⋊C4×C79C2414yes—
528C4⋊C4×C79C2418yes—
529C4⋊C4×C79C2418yes—
530C4⋊C4×C79C2414yes—
531C4⋊C4×C79C2412yes—
532C4⋊C4×C79C2418yes—
533C4⋊C4×C79C2418yes—
534C4⋊C4×C79C2418yes—
535C4⋊C4×C79C2414yes—
536C4⋊C4×C79C2418yes—
537C22⋊C4×C79C2418yes—
538C22⋊C4×C79C2418yes—
539C22⋊C4×C79C2414yes—
540C22⋊C4×C79C2412yes—
541C22⋊C4×C79C2414yes—
542C22⋊C4×C79C2414yes—
543C22⋊C4×C79C2418yes—
544C42×C79C2414yes—
545C42×C79C2412yes—
546C42×C79C2418yes—
547C23×C79—24no—
548C23×C79—41no—
549C23×C79C2512yes—
550C23×C79C2511yescharacteristic
551C23×C79C2512yes—
552C22×D79—28no—
553C22×D79—44no—
554C22×D79—44no—
555C22×D79—48no—
556C22×D79—44no—
557C22×D79C2518yes—
558C22×D79C2512yes—
559Q8×C79—28no—
560Q8×C79—44no—
561Q8×C79—44no—
562Q8×C79—41no—
563D4×C79—28no—
564D4×C79—41no—
565D4×C79—42no—
566C2×C4×C79—28no—
567C2×C4×C79—24no—
568C2×C4×C79—24no—
569C2×C4×C79—22no—
570C2×C4×C79—42no—
571C2×C4×C79—41no—
572C2×C4×C79—44no—
573C2×C4×C79—44no—
574C2×C4×C79C2511yescharacteristic
575C2×C4×C79C2512yes—
576C2×C4×C79C2512yes—
577C2×C4×C79C2518yes—
578C2×C4×C79C2514yes—
579C2×C4×C79C2518yes—
580C2×C4×C79C2511yescharacteristic
581C22⋊D79—216no—
582C22⋊D79—28no—
583C22⋊D79—48no—
584C22⋊D79—48no—
585C22⋊D79—44no—
586C22⋊D79—42no—
587C2×Dic79—24no—
588C2×Dic79—24no—
589C2×Dic79—42no—
590C2×Dic79—42no—
591C2×Dic79—42no—
592C2×Dic79—42no—
593C2×Dic79—44no—
594C2×Dic79—44no—
595C2×Dic79C2512yes—
596C2×Dic79C2512yes—
597C2×Dic79C2512yes—
598C2×Dic79C2512yes—
599C2×Dic79C2514yes—
600C2×Dic79C2518yes—
601C2×Dic79C2512yes—
602D316—28no—
603D316—48no—
604D316—44no—
605D316—44no—
606D316—41no—
607D316—48no—
608D316—48no—
609C4×D79—24no—
610C4×D79—48no—
611C4×D79—48no—
612C4×D79—48no—
613C4×D79—44no—
614C4×D79—48no—
615C4×D79—48no—
616C4×D79—48no—
617Dic158—44no—
618Dic158—48no—
619Dic158—41no—
620C22×C79—22no—
621C22×C79—22no—
622C22×C79—22no—
623C22×C79—24no—
624C22×C79—21no—
625C22×C79—22no—
626C22×C79—44no—
627C22×C79#58514yes—
628C22×C79C2611yescharacteristic
629C2×D79—28no—
630C2×D79—24no—
631C2×D79—28no—
632C2×D79—22no—
633C2×D79—28no—
634C2×D79—88no—
635C2×D79—164no—
636C4×C79—21no—
637C4×C79—22no—
638C4×C79—22no—
639C4×C79—28no—
640C4×C79—28no—
641C4×C79—24no—
642C4×C79#58512yes—
643Dic79—28no—
644Dic79—24no—
645Dic79—22no—
646Dic79—22no—
647Dic79—22no—
648Dic79—22no—
649Dic79—22no—
650#62829—791nomaximal, Sylow
651C2×C79—24no—
652C2×C79—42no—
653C2×C79—41no—
654C2×C79C2×#58511yescharacteristic
655C2×C79C2×#58512yes—
656D79—42no—
657D79—48no—
658#3566—798no—
659#3564—794no—
660#3560—794no—
661#3557—792no—
662#3551—792no—
663#3538D7911yescharacteristic, complemented
664#3537—791no—
665#3536—792no—
666#3516—794no—
667#3515—794no—
668#3514—794no—
669#3513—794no—
670#3513—798no—
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—798no—
680#563C2×D7914yescomplemented
681#562—798no—
682#560—794no—
683#560—794no—
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—794no—
700#553—798no—
701#553—794no—
702#552—798no—
703#552—798no—
704#552—798no—
705#552—798no—
706#552—798no—
707#552—794no—
708#552—798no—
709#552C2×D7914yescomplemented
710#551—798no—
711#551—798no—
712#551—798no—
713#551—794no—
714#551—798no—
715#551—798no—
716#551—798no—
717#551C2×D7914yescomplemented
718D4×Q8C2×D7914yescomplemented
719#548—794no—
720#548—794no—
721#547—798no—
722#547—794no—
723#546—798no—
724#546—794no—
725#546—794no—
726#546—798no—
727#546—798no—
728D42—794no—
729D42—794no—
730#544C2×D7914yescomplemented
731#543—794no—
732#542—798no—
733#542—798no—
734#542—794no—
735#542—794no—
736#542—798no—
737#541—792no—
738#541—798no—
739#541—798no—
740#541C2×D7912yescomplemented
741#540—792no—
742#540—798no—
743#540—792no—
744#539—798no—
745#539—798no—
746#539—798no—
747#539—798no—
748#539—794no—
749#539C2×D7914yescomplemented
750#538—798no—
751#538—798no—
752#538—794no—
753#538—798no—
754#538—794no—
755#538—798no—
756#537—794no—
757#537—794no—
758#536C2×D7912yescomplemented
759#535—792no—
760#534—794no—
761#533—792no—
762#533—791no—
763#533—792no—
764#532—791no—
765#532—792no—
766#532—792no—
767#529—794no—
768#529—794no—
769#529—794no—
770#529—794no—
771#529—794no—
772#529—794no—
773#529—794no—
774#529—794no—
775#529—794no—
776#529—792no—
777#529—798no—
778#529—794no—
779#529—792no—
780#529—794no—
781#529—794no—
782#529—798no—
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—798no—
793C2×#123—794no—
794C2×C22⋊Q8C2×D7912yescomplemented
795C2×#121—792no—
796#520—794no—
797#520—798no—
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—792no—
806C2×C4×D4—794no—
807C2×#117—794no—
808C22×C42—791no—
809C2×#41—794no—
810C2×#41—794no—
811C2×#41—791no—
812C2×#41—798no—
813C2×#41C22×D7911yescharacteristic
814C22×Q8C22×D7912yes—
815C22×Q8C22×D7912yes—
816C22×D4—794no—
817C22×D4—798no—
818C22×D4—792no—
819C22×D4—792no—
820C23×C4—792no—
821C23×C4—794no—
822C23×C4C22×D7911yescharacteristic
823C4⋊Q8—791no—
824C4⋊Q8—792no—
825C4⋊Q8—794no—
826C4⋊Q8—798no—
827C4⋊Q8C22×D7912yes—
828C4⋊Q8C22×D7914yes—
829C4⋊Q8C22×D7918yes—
830#127—791no—
831#127—794no—
832#127—792no—
833#126—798no—
834#126—798no—
835#126—798no—
836#126—798no—
837#126—794no—
838#126—798no—
839#126—798no—
840#126—798no—
841#126—798no—
842#126—798no—
843#126—798no—
844#126—798no—
845#126—798no—
846#126—794no—
847#126—798no—
848#126—798no—
849#126C22×D7918yes—
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—792no—
863#125—798no—
864#125C22×D7912yes—
865#125C22×D7918yes—
866#125C22×D7918yes—
867#124—794no—
868#124—794no—
869#124—794no—
870#124—794no—
871#124—798no—
872#124—794no—
873#124—791no—
874#124—798no—
875#124—794no—
876#124—798no—
877#124—791no—
878#124—794no—
879#124—798no—
880#124—798no—
881#124—798no—
882#124C22×D7914yes—
883#123—794no—
884#123—798no—
885#123—792no—
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—798no—
896#123—798no—
897#123—798no—
898#123—798no—
899#123—798no—
900#123—794no—
901#123—798no—
902#123—798no—
903#123—798no—
904#123—798no—
905#123C22×D7918yes—
906#123C22×D7912yes—
907#123C22×D7914yes—
908#123C22×D7914yes—
909C22⋊Q8—794no—
910C22⋊Q8—798no—
911C22⋊Q8—798no—
912C22⋊Q8—792no—
913C22⋊Q8—798no—
914C22⋊Q8—798no—
915C22⋊Q8—798no—
916C22⋊Q8—798no—
917C22⋊Q8—798no—
918C22⋊Q8—798no—
919C22⋊Q8—798no—
920C22⋊Q8—798no—
921C22⋊Q8—798no—
922C22⋊Q8—794no—
923C22⋊Q8—794no—
924C22⋊Q8—798no—
925C22⋊Q8—798no—
926C22⋊Q8C22×D7914yes—
927C22⋊Q8C22×D7914yes—
928C22⋊Q8C22×D7914yes—
929C22⋊Q8C22×D7914yes—
930C22⋊Q8C22×D7912yes—
931C22⋊Q8C22×D7914yes—
932C22⋊Q8C22×D7918yes—
933C22⋊Q8C22×D7918yes—
934#121—794no—
935#121—794no—
936#121—798no—
937#121—794no—
938#121—794no—
939#121—794no—
940#121—794no—
941#121—792no—
942#121—794no—
943#121—798no—
944#121—798no—
945#121—798no—
946#121—798no—
947#121—794no—
948#121—798no—
949#121—798no—
950#121—798no—
951#121—798no—
952#121—798no—
953#121—798no—
954#121—798no—
955#121—798no—
956#121C22×D7912yes—
957#120—792no—
958#120—794no—
959#120—794no—
960#120—798no—
961#120—798no—
962#120—798no—
963#120—798no—
964#120C22×D7912yes—
965C4×Q8—794no—
966C4×Q8—794no—
967C4×Q8—794no—
968C4×Q8—794no—
969C4×Q8—792no—
970C4×Q8—798no—
971C4×Q8—794no—
972C4×Q8—794no—
973C4×Q8—792no—
974C4×Q8—794no—
975C4×Q8—798no—
976C4×Q8—798no—
977C4×Q8C22×D7914yes—
978C4×D4—794no—
979C4×D4—794no—
980C4×D4—792no—
981C4×D4—794no—
982C4×D4—794no—
983C4×D4—798no—
984C4×D4—798no—
985C4×D4—794no—
986C4×D4—794no—
987C4×D4—794no—
988C4×D4—794no—
989C4×D4—792no—
990C4×D4—794no—
991C4×D4—798no—
992C4×D4—798no—
993C4×D4—798no—
994C4×D4—798no—
995C4×D4—798no—
996C4×D4—798no—
997C4×D4—794no—
998C4×D4—794no—
999C4×D4—794no—
1000C4×D4—798no—
1001C4×D4—798no—
1002C4×D4—798no—
1003C4×D4—798no—
1004C4×D4—798no—
1005C4×D4—798no—
1006C4×D4—798no—
1007C4×D4—798no—
1008C4×D4—794no—
1009C4×D4C22×D7914yes—
1010C4×D4C22×D7918yes—
1011#117—792no—
1012#117—791no—
1013#117—798no—
1014#117—792no—
1015#117—798no—
1016#117—798no—
1017#117—798no—
1018#117—798no—
1019#117—794no—
1020#117—798no—
1021#117—798no—
1022#117—798no—
1023#117—794no—
1024#117—794no—
1025#117—792no—
1026#117—798no—
1027#117—798no—
1028#117C22×D7911yescharacteristic
1029#117C22×D7912yes—
1030#117C22×D7918yes—
1031C2×C4⋊C4—794no—
1032C2×C4⋊C4—794no—
1033C2×C4⋊C4—792no—
1034C2×C4⋊C4—794no—
1035C2×C4⋊C4—798no—
1036C2×C4⋊C4—798no—
1037C2×C4⋊C4—794no—
1038C2×C4⋊C4—798no—
1039C2×C4⋊C4C22×D7914yes—
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—
1060C24—794no—
1061C24—794no—
1062C24C23×D7911yescharacteristic
1063#41—42no—
1064#41—31616no—
1065#41—3162no—
1066#41—3168no—
1067#41—3168no—
1068C2×Q8—44no—
1069C2×Q8—44no—
1070C2×Q8—791no—
1071C2×Q8—798no—
1072C2×Q8—794no—
1073C2×Q8C23×D7914yes—
1074C2×Q8C23×D7914yes—
1075C2×Q8C23×D7914yes—
1076C2×Q8C23×D7911yescharacteristic
1077C2×D4—3164no—
1078C2×D4—3164no—
1079C2×D4—31616no—
1080C2×D4—3168no—
1081C2×D4—794no—
1082C2×D4—798no—
1083C2×D4—792no—
1084C2×D4—798no—
1085C2×D4—794no—
1086C2×D4—798no—
1087C2×D4—798no—
1088C2×D4—798no—
1089C2×D4—794no—
1090C2×D4—798no—
1091C2×D4—794no—
1092C2×D4—791no—
1093C2×D4—794no—
1094C2×D4C23×D7914yes—
1095C2×D4C23×D7911yescharacteristic
1096C2×D4C23×D7912yes—
1097C22×C4—42no—
1098C22×C4—3168no—
1099C22×C4—3164no—
1100C22×C4—792no—
1101C22×C4—792no—
1102C22×C4—792no—
1103C22×C4—792no—
1104C22×C4—794no—
1105C22×C4—794no—
1106C22×C4—794no—
1107C22×C4—798no—
1108C22×C4—798no—
1109C22×C4—798no—
1110C22×C4—798no—
1111C22×C4—798no—
1112C22×C4—798no—
1113C22×C4—792no—
1114C22×C4—792no—
1115C22×C4—792no—
1116C22×C4C23×D7912yes—
1117C22×C4C23×D7911yescharacteristic
1118C22×C4C23×D7912yes—
1119C22×C4C23×D7914yes—
1120C22×C4C23×D7912yes—
1121C22×C4C23×D7911yescharacteristic
1122C22×C4C23×D7914yes—
1123C22×C4C23×D7914yes—
1124C4⋊C4—794no—
1125C4⋊C4—798no—
1126C4⋊C4—794no—
1127C4⋊C4—798no—
1128C4⋊C4—798no—
1129C4⋊C4—798no—
1130C4⋊C4—798no—
1131C4⋊C4—798no—
1132C4⋊C4—794no—
1133C4⋊C4—794no—
1134C4⋊C4—794no—
1135C4⋊C4—798no—
1136C4⋊C4—798no—
1137C4⋊C4—794no—
1138C4⋊C4—798no—
1139C4⋊C4—794no—
1140C4⋊C4—798no—
1141C4⋊C4—794no—
1142C4⋊C4—794no—
1143C4⋊C4—792no—
1144C4⋊C4—798no—
1145C4⋊C4C23×D7918yes—
1146C4⋊C4C23×D7914yes—
1147C4⋊C4C23×D7918yes—
1148C4⋊C4C23×D7918yes—
1149C4⋊C4C23×D7918yes—
1150C4⋊C4C23×D7914yes—
1151C4⋊C4C23×D7918yes—
1152C4⋊C4C23×D7918yes—
1153C4⋊C4C23×D7914yes—
1154C4⋊C4C23×D7912yes—
1155C22⋊C4—794no—
1156C22⋊C4—794no—
1157C22⋊C4—794no—
1158C22⋊C4—794no—
1159C22⋊C4—792no—
1160C22⋊C4—798no—
1161C22⋊C4—798no—
1162C22⋊C4—798no—
1163C22⋊C4—798no—
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—794no—
1173C22⋊C4—794no—
1174C22⋊C4—798no—
1175C22⋊C4—798no—
1176C22⋊C4—798no—
1177C22⋊C4—794no—
1178C22⋊C4C23×D7914yes—
1179C22⋊C4C23×D7918yes—
1180C22⋊C4C23×D7918yes—
1181C22⋊C4C23×D7918yes—
1182C22⋊C4C23×D7914yes—
1183C22⋊C4C23×D7914yes—
1184C22⋊C4C23×D7912yes—
1185C42—791no—
1186C42—791no—
1187C42—792no—
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—
1202C42C23×D7912yes—
1203C42C23×D7918yes—
1204C42C23×D7914yes—
1205C23—24no—
1206C23—41no—
1207C23—3164no—
1208C23—3164no—
1209C23—3164no—
1210C23—3168no—
1211C23—798no—
1212C23—792no—
1213C23—1588no—
1214C23C24×D7912yes—
1215C23C24×D7911yescharacteristic
1216C23C24×D7912yes—
1217Q8—28no—
1218Q8—44no—
1219Q8—44no—
1220Q8—41no—
1221Q8—3161no—
1222Q8—3168no—
1223Q8—3164no—
1224D4—28no—
1225D4—41no—
1226D4—42no—
1227D4—3164no—
1228D4—3164no—
1229D4—3168no—
1230D4—3161no—
1231D4—3168no—
1232D4—3168no—
1233D4—3168no—
1234D4—3168no—
1235D4—3162no—
1236D4—3164no—
1237D4—15816no—
1238D4—1588no—
1239D4—1588no—
1240C2×C4—28no—
1241C2×C4—24no—
1242C2×C4—22no—
1243C2×C4—24no—
1244C2×C4—42no—
1245C2×C4—41no—
1246C2×C4—44no—
1247C2×C4—44no—
1248C2×C4—3168no—
1249C2×C4—3168no—
1250C2×C4—3168no—
1251C2×C4—3168no—
1252C2×C4—3168no—
1253C2×C4—3168no—
1254C2×C4—3164no—
1255C2×C4—3162no—
1256C2×C4—3162no—
1257C2×C4—3162no—
1258C2×C4—3162no—
1259C2×C4—3164no—
1260C2×C4—3164no—
1261C2×C4—792no—
1262C2×C4—792no—
1263C2×C4—792no—
1264C2×C4—794no—
1265C2×C4—792no—
1266C2×C4—798no—
1267C2×C4—792no—
1268C2×C4—1584no—
1269C2×C4—1584no—
1270C2×C4—1584no—
1271C2×C4C24×D7912yes—
1272C2×C4C24×D7911yescharacteristic
1273C2×C4C24×D7912yes—
1274C2×C4C24×D7918yes—
1275C2×C4C24×D7914yes—
1276C2×C4C24×D7918yes—
1277C2×C4C24×D7911yescharacteristic
1278C22—22no—
1279C22—22no—
1280C22—22no—
1281C22—21no—
1282C22—22no—
1283C22—24no—
1284C22—44no—
1285C22—6328no—
1286C22—1588no—
1287C22—1582no—
1288C22—1584no—
1289C22—1588no—
1290C22—1588no—
1291C22—12644no—
1292C22#1909940014yes—
1293C22C25×D7911yescharacteristic
1294C4—21no—
1295C4—22no—
1296C4—22no—
1297C4—28no—
1298C4—28no—
1299C4—24no—
1300C4—1582no—
1301C4—1582no—
1302C4—1582no—
1303C4—1582no—
1304C4—1588no—
1305C4—1584no—
1306C4—1582no—
1307C4#1909939812yes—
1308C2—24no—
1309C2—41no—
1310C2—42no—
1311C2—3168no—
1312C2—3162no—
1313C2C2×#1909939811yescharacteristic
1314C2C2×#1909940012yes—
subgroupG/H
center, FrattiniC22C25×D79
commutator, socle, cosocleC22×C79C26
FittingC79×#3538C2
hypercenter#3538D79
hypocenterC79#62829
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C22 ◁ #3538

Complements

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

NH ≅ G/Ntype
1. #23778081C2semidirect
2. #23778021C2semidirect
3. #23777957C2semidirect
4. #23777908C2semidirect
5. #23777829C2semidirect
6. #23777639C2semidirect
7. #23777629C2semidirect
8. #23777394C2semidirect
9. #23777375C2semidirect
10. #23777362C2semidirect
11. #23777345C2semidirect
12. #23777327C2semidirect
13. #23777323C2semidirect
14. #23777299C2semidirect
15. #23777121C2semidirect
16. #23777094C2semidirect
17. #23776692C2semidirect
18. C2×#19099099C2semidirect
19. C79×#3538C2semidirect
20. #19099317C22semidirect
21. #19099312C22semidirect
22. #19099309C22semidirect
24. #19099303C22semidirect
25. #19099298C22semidirect
26. #19099295C22semidirect
27. #19099289C22semidirect
28. #19099287C22semidirect
29. #19099287C22semidirect
30. #19099287C22semidirect
31. #19099279C22semidirect
32. #19099279C22semidirect
33. #19099271C22semidirect
34. #19099271C22semidirect
35. #19099269C22semidirect
36. #19099266C22semidirect
37. #19099266C22semidirect
38. #19099264C22semidirect
39. #19099264C22semidirect
41. #19099259C22semidirect
42. #19099257C22semidirect
43. #19099251C22semidirect
44. #19099251C22semidirect
45. #19099249C22semidirect
46. #19099247C22semidirect
47. #19099247C22semidirect
48. #19099246C22semidirect
49. #19099245C22semidirect
50. #19099241C22semidirect
51. #19099240C22semidirect
52. #19099240C22semidirect
53. #19099238C22semidirect
54. #19099237C22semidirect
55. #19099236C22semidirect
56. #19099236C22semidirect
57. #19099224C22semidirect
58. #19099224C22semidirect
59. #19099214C22semidirect
60. #19099211C22semidirect
61. #19099208C22semidirect
62. #19099205C22semidirect
63. #19099204C22semidirect
64. #19099204C22semidirect
65. #19099203C22semidirect
68. #19099188C22semidirect
69. #19099187C22semidirect
70. #19099186C22semidirect
71. #19099186C22semidirect
72. #19099186C22semidirect
73. #19099179C22semidirect
74. #19099174C22semidirect
75. #19099174C22semidirect
76. #19099172C22semidirect
77. #19099169C22semidirect
79. #19099165C22semidirect
80. #19099161C22semidirect
81. #19099160C22semidirect
82. #19099157C22semidirect
83. #19099154C22semidirect
84. #19099154C22semidirect
86. #19099153C22semidirect
87. #19099153C22semidirect
88. #19099153C22semidirect
89. #19099152C22semidirect
90. #19099147C22semidirect
91. #19099144C22semidirect
92. #19099143C22semidirect
95. #19099116C22semidirect
96. #19099116C22semidirect
97. #19099115C22semidirect
98. #19099114C22semidirect
99. #19099109C22semidirect
100. #19099108C22semidirect
101. #19099100C22semidirect
102. #19099099C22semidirect
103. #19099099C22semidirect
104. #19099099C22semidirect
105. #19099099C22semidirect
106. #19099099C22semidirect
107. #19099099C22semidirect
108. #19099099C22semidirect
109. #19099099C22semidirect
110. #19099099C22semidirect
111. #19099099C22semidirect
112. #19099099C22semidirect
113. #19099094C22semidirect
114. #19099093C22semidirect
115. #19099093C22semidirect
116. #19099090C22semidirect
117. C2×#14579156C22semidirect
118. C2×#14579152C22semidirect
119. #125×D79C22semidirect
120. C2×#14579150C22semidirect
121. C2×#14579150C22semidirect
122. #19099075C22semidirect
123. #19099074C22semidirect
124. #19099069C22semidirect
125. C2×#14579145C22semidirect
126. #123×D79C22semidirect
128. #19099045C22semidirect
129. #19099043C22semidirect
130. #19099041C22semidirect
131. #19099037C22semidirect
132. #19099035C22semidirect
133. #41×Dic79C22semidirect
134. #19099031C22semidirect
135. C4×#11929623C22semidirect
136. C2×Q8×Dic79C22semidirect
137. C2×#14579123C22semidirect
138. C2×(C22⋊D79)⋊C4C22semidirect
139. C2×#14579119C22semidirect
140. C22×C4×Dic79C22semidirect
141. #563×C79C22semidirect
142. #552×C79C22semidirect
143. #551×C79C22semidirect
144. D4×Q8×C79C22semidirect
145. #544×C79C22semidirect
146. #541×C79C22semidirect
147. #539×C79C22semidirect
148. #536×C79C22semidirect
150. C2×C22⋊Q8×C79C22semidirect
663. #3538D79semidirect
677. C79#62829semidirect
680. #563C2×D79semidirect
709. #552C2×D79semidirect
717. #551C2×D79semidirect
718. D4×Q8C2×D79semidirect
730. #544C2×D79semidirect
740. #541C2×D79semidirect
749. #539C2×D79semidirect
758. #536C2×D79semidirect
794. C2×C22⋊Q8C2×D79semidirect

Maximal subgroups

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

subgroupindex
#237780812
#237780212
#237779572
#237779082
#237778292
#237776392
#237776292
#237773942
#237773752
#237773622
#237773452
#237773272
#237773232
#237772992
#237771212
#237770942
#237766922
C2×#190990992
C79×#35382
#6282979