Finite Group Databasebeta

← #35197090

Subgroups — #35197090

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#23778076C218yesmaximal, complemented
2#23778028C214yesmaximal, complemented
3#23777956C214yesmaximal, complemented
4#23777906C212yesmaximal, complemented
5#23777827C212yesmaximal, complemented
6#23777649C211yesmaximal, characteristic, complemented
7#23777639C211yesmaximal, characteristic, complemented
8#23777627C212yesmaximal, complemented
9#23777389C214yesmaximal, complemented
10#23777378C214yesmaximal, complemented
11#23777361C214yesmaximal, complemented
12#23777344C214yesmaximal, complemented
13#23777326C218yesmaximal, complemented
14#23777322C212yesmaximal, complemented
15#23777296C212yesmaximal, complemented
16#23777112C214yesmaximal, complemented
17#23777092C214yesmaximal, complemented
18C2×#19099097C212yesmaximal, complemented
19C79×#3444C211yesmaximal, characteristic, complemented
20#19099316C2214yescomplemented
21#19099312C2214yescomplemented
22#19099312C2218yescomplemented
23#19099310C2218yescomplemented
24#19099303C2214yes—
25#19099300C2214yescomplemented
26#19099298C2214yescomplemented
27#19099296C2218yescomplemented
28#19099291C2214yescomplemented
29#19099286C2214yescomplemented
30#19099285C2218yescomplemented
31#19099280C2218yescomplemented
32#19099276C2218yescomplemented
33#19099275C2214yescomplemented
34#19099273C2214yescomplemented
35#19099270C2214yescomplemented
36#19099267C2218yescomplemented
37#19099264C2218yescomplemented
38#19099263C2218yescomplemented
39#19099262C2218yescomplemented
40#19099262C2218yescomplemented
41#19099259C2214yes—
42#19099259C2214yescomplemented
43#19099256C2218yescomplemented
44#19099254C2218yescomplemented
45#19099253C2214yescomplemented
46#19099253C2214yescomplemented
47#19099252C2218yescomplemented
48#19099249C2218yescomplemented
49#19099246C2218yescomplemented
50#19099246C2218yescomplemented
51#19099245C2218yescomplemented
52#19099244C2214yescomplemented
53#19099243C2214yescomplemented
54#19099242C2218yescomplemented
55#19099242C2218yescomplemented
56#19099240C2218yescomplemented
57#19099238C2218yescomplemented
58#19099237C2218yescomplemented
59#19099237C2218yescomplemented
60D4×Dic158C2214yescomplemented
61#19099222C2214yescomplemented
62#19099222C2214yescomplemented
63#19099217C2214yescomplemented
64#19099212C2218yescomplemented
65#19099209C2214yescomplemented
66#19099209C2214yescomplemented
67#19099202C2218yescomplemented
68#19099201C2218yescomplemented
69#19099200C2218yescomplemented
70D4×D316C2214yes—
71#19099195C2214yes—
72#19099192C2214yescomplemented
73#19099188C2214yescomplemented
74#19099185C2218yescomplemented
75#19099184C2214yescomplemented
76#19099184C2214yescomplemented
77#19099183C2218yescomplemented
78#19099177C2218yescomplemented
79#19099175C2212yescomplemented
80#19099175C2212yescomplemented
81#19099172C2218yescomplemented
82#19099171C2218yescomplemented
83#19099168C2212yes—
84#19099168C2212yescomplemented
85#19099163C2218yescomplemented
86#19099162C2214yescomplemented
87#19099161C2218yescomplemented
88#19099159C2218yescomplemented
89#19099158C2214yescomplemented
90#19099155C2218yescomplemented
91#19099155C2218yescomplemented
92#19099153C2214yes—
93#19099150C2214yescomplemented
94#19099147C2218yescomplemented
95#19099146C2218yescomplemented
96#19099146C2218yescomplemented
97#19099145C2218yescomplemented
98#19099141C2214yescomplemented
99#19099140C2214yescomplemented
100#19099134C2212yescomplemented
101#19099127C2212yes—
102#19099121C2214yes—
103#19099120C2212yescomplemented
104#19099113C2212yescomplemented
105#19099097C2214yescomplemented
106#19099097C2214yescomplemented
107#19099097C2214yescomplemented
108#19099097C2214yescomplemented
109#19099097C2214yescomplemented
110#19099097C2214yescomplemented
111#19099097C2214yescomplemented
112#19099097C2214yescomplemented
113#19099097C2214yescomplemented
114#19099097C2214yescomplemented
115#19099090C2218yescomplemented
116#19099090C2218yescomplemented
117C2×#14579155C2214yescomplemented
118C2×#14579153C2212yescomplemented
119C2×#14579153C2212yescomplemented
120C2×#14579149C2212yescomplemented
121C2×#14579149C2212yescomplemented
122#19099071C2218yescomplemented
123C2×#14579144C2214yescomplemented
124#123×D79C2218yescomplemented
125C2×#14579140C2212yescomplemented
126C2×#14579135C2212yes—
127#19099043C2214yescomplemented
128#19099042C2218yescomplemented
129#19099040C2212yescomplemented
130#19099037C2212yescomplemented
131#19099035C2218yescomplemented
132C2×C4×Dic158C2212yescomplemented
133C2×C4×D316C2212yescomplemented
134C2×C4×C22⋊D79C2214yescomplemented
135C2×#14579118C2214yescomplemented
136#533×C79C2211yescharacteristic, complemented
137#533×C79C2212yescomplemented
138#532×C79C2211yescharacteristic, complemented
139#532×C79C2212yescomplemented
140#529×C79C2214yescomplemented
141#529×C79C2214yescomplemented
142#529×C79C2212yescomplemented
143#529×C79C2212yescomplemented
144#525×C79C2211yescharacteristic
145#525×C79C2214yescomplemented
146#525×C79C2211yescharacteristic, complemented
147C4×#41×C79C2211yescharacteristic, complemented
148C4×#41×C79C2211yescharacteristic, complemented
149C4×#41×C79C2214yescomplemented
150C22×C42×C79C2211yescharacteristic, complemented
151C2×#11929624C2314yes—
152C2×#11929623C2318yes—
153C22×Dic158C2312yes—
154C22×Dic158C2312yes—
155C22×D316C2312yes—
156C22×D316C2312yes—
157C22×C22⋊D79C2314yes—
158C2×D4×D79C2318yes—
159C22×C4×D79C2314yes—
160#14579161C2312yes—
161#14579161C2314yes—
162#14579160C2318yes—
163#14579159C2318yes—
164#14579159C2314yes—
165#14579158C2312yes—
166#14579157C2314yes—
167#14579156C2318yes—
168#14579156C2318yes—
169#14579156C2318yes—
170#14579156C2318yes—
171#14579156C2318yes—
172#14579156C2318yes—
173#14579155C2318yes—
174#14579155C2318yes—
175#14579155C2318yes—
176#14579155C2318yes—
177#14579155C2318yes—
178#14579155C2318yes—
179#14579154C2318yes—
180#14579154C2318yes—
181#14579154C2318yes—
182#14579154C2318yes—
183#14579153C2314yes—
184#14579153C2318yes—
185#14579153C2312yes—
186#14579153C2312yes—
187#14579153C2314yes—
188#14579153C2314yes—
189#14579153C2314yes—
190#14579152C2318yes—
191#14579151C2318yes—
192#14579151C2318yes—
193#14579151C2318yes—
194#14579151C2318yes—
195#14579151C2318yes—
196#14579151C2318yes—
197#14579150C2318yes—
198#14579150C2314yes—
199#14579149C2314yes—
200#14579149C2318yes—
201#14579149C2314yes—
202#14579149C2314yes—
203#14579149C2314yes—
204#14579149C2314yes—
205#14579148C2314yes—
206#14579147C2318yes—
207#14579147C2318yes—
208#14579147C2318yes—
209#14579147C2318yes—
210#14579146C2318yes—
211#14579146C2318yes—
212#14579146C2318yes—
213#14579146C2318yes—
214#14579146C2318yes—
215#14579146C2318yes—
216#14579145C2318yes—
217#14579145C2318yes—
218#14579144C2318yes—
219#14579144C2318yes—
220#14579144C2318yes—
221#14579144C2318yes—
222#14579144C2318yes—
223#14579144C2318yes—
224#14579143C2318yes—
225#14579143C2318yes—
226#14579143C2318yes—
227#14579143C2318yes—
228#14579142C2318yes—
229#14579142C2318yes—
230#14579142C2314yes—
231#14579142C2314yes—
232#14579141C2318yes—
233#14579140C2314yes—
234#14579140C2314yes—
235#14579140C2314yes—
236#14579140C2318yes—
237#14579140C2314yes—
238#14579140C2314yes—
239#14579140C2314yes—
240#14579139C2318yes—
241#14579139C2318yes—
242#14579139C2318yes—
243#14579139C2318yes—
244#14579139C2318yes—
245#14579139C2318yes—
246#14579138C2318yes—
247#14579138C2318yes—
248#14579138C2318yes—
249#14579138C2318yes—
250#14579137C2318yes—
251#14579137C2318yes—
252#14579137C2318yes—
253#14579136C2318yes—
254#14579135C2314yes—
255#14579135C2314yes—
256#14579135C2314yes—
257#14579135C2318yes—
258#14579135C2314yes—
259#14579135C2314yes—
260#14579135C2314yes—
261#14579134C2318yes—
262#14579134C2318yes—
263#14579134C2318yes—
264#14579134C2318yes—
265#14579133C2318yes—
266#14579133C2318yes—
267#14579133C2318yes—
268#14579133C2318yes—
269#14579133C2318yes—
270#14579133C2318yes—
271#14579132C2318yes—
272#14579131C2318yes—
273#14579131C2318yes—
274#14579129C2314yes—
275#14579129C2318yes—
276#14579129C2318yes—
277#14579129C2314yes—
278C4×Dic158C2318yes—
279C4×Dic158C2314yes—
280C4×Dic158C2314yes—
281C4×Dic158C2314yes—
282C4×Dic158C2314yes—
283C4×Dic158C2314yes—
284C4×Dic158C2314yes—
285#14579126C2318yes—
286#14579126C2318yes—
287C4×D316C2314yes—
288C4×D316C2314yes—
289C4×D316C2314yes—
290C4×D316C2314yes—
291C4×D316C2318yes—
292C4×D316C2314yes—
293C4×D316C2314yes—
294D4×Dic79C2318yes—
295D4×Dic79C2318yes—
296#14579123C2318yes—
297#14579123C2318yes—
298C4×C22⋊D79C2318yes—
299C4×C22⋊D79C2318yes—
300C4×C22⋊D79C2318yes—
301C4×C22⋊D79C2318yes—
302C4×C22⋊D79C2318yes—
303C4×C22⋊D79C2318yes—
304(C22⋊D79)⋊C4C2318yes—
305(C22⋊D79)⋊C4C2318yes—
306(C22⋊D79)⋊C4C2318yes—
307(C22⋊D79)⋊C4C2318yes—
308(C22⋊D79)⋊C4C2318yes—
309(C22⋊D79)⋊C4C2318yes—
310#14579120C2312yes—
311#14579120C2312yes—
312#14579119C2318yes—
313#14579119C2318yes—
314#14579118C2318yes—
315#14579118C2318yes—
316#14579118C2318yes—
317#14579118C2318yes—
318#14579118C2318yes—
319#14579118C2318yes—
320#14579117C2318yes—
321#14579117C2318yes—
322#14579117C2318yes—
323C2×C4⋊Dic79C2314yes—
324C2×C4⋊Dic79C2312yes—
325C2×C4⋊Dic79C2312yes—
326C2×Dic79⋊C4C2314yes—
327C2×Dic79⋊C4C2314yes—
328C2×Dic79⋊C4C2318yes—
329C2×Dic79⋊C4C2314yes—
330C2×Dic79⋊C4C2314yes—
331C4⋊C4×D79C2318yes—
332C4⋊C4×D79C2318yes—
333C2×C22⋊Dic79C2314yes—
334C2×(C2×D79)⋊C4C2314yes—
335C2×(C2×D79)⋊C4C2318yes—
336C2×(C2×D79)⋊C4C2314yes—
337C2×(C2×D79)⋊C4C2314yes—
338C2×(C2×D79)⋊C4C2314yes—
339C22⋊C4×D79C2318yes—
340C22⋊C4×D79C2318yes—
341C22⋊C4×D79C2318yes—
342C2×C4×Dic79C2314yes—
343C2×#41×C79C2311yescharacteristic
344C2×#41×C79C2314yes—
345C2×#41×C79C2311yescharacteristic
346C23×C4×C79C2311yescharacteristic
347C23×C4×C79C2312yes—
348C4⋊Q8×C79C2312yes—
349C4⋊Q8×C79C2311yescharacteristic
350#127×C79C2311yescharacteristic
351#126×C79C2314yes—
352#126×C79C2314yes—
353#125×C79C2314yes—
354#125×C79C2312yes—
355#124×C79C2314yes—
356#124×C79C2311yescharacteristic
357#124×C79C2311yescharacteristic
358#123×C79C2312yes—
359#123×C79C2312yes—
360#123×C79C2314yes—
361#123×C79C2314yes—
362C22⋊Q8×C79C2312yes—
363C22⋊Q8×C79C2314yes—
364C22⋊Q8×C79C2312yes—
365C22⋊Q8×C79C2314yes—
366#121×C79C2312yes—
367#121×C79C2314yes—
368#121×C79C2312yes—
369#121×C79C2314yes—
370#120×C79C2312yes—
371#120×C79C2312yes—
372C4×Q8×C79C2314yes—
373C4×Q8×C79C2312yes—
374C4×Q8×C79C2314yes—
375C4×Q8×C79C2312yes—
376C4×D4×C79C2314yes—
377C4×D4×C79C2314yes—
378C4×D4×C79C2314yes—
379C4×D4×C79C2314yes—
380C4×D4×C79C2314yes—
381C4×D4×C79C2314yes—
382C4×D4×C79C2312yes—
383C4×D4×C79C2314yes—
384C4×D4×C79C2314yes—
385C4×D4×C79C2312yes—
386#117×C79C2311yescharacteristic
387#117×C79C2312yes—
388#117×C79C2311yescharacteristic
389#117×C79C2312yes—
390#117×C79C2314yes—
391#117×C79C2314yes—
392#117×C79C2314yes—
393C2×C42×C79C2312yes—
394C2×C42×C79C2311yescharacteristic
395C2×C42×C79C2312yes—
396C2×C42×C79C2312yes—
397C2×C42×C79C2312yes—
398C2×C42×C79C2312yes—
399C2×C42×C79C2311yescharacteristic
400C2×C42×C79C2312yes—
401C2×C42×C79C2312yes—
402C23×D79C2414yes—
403C23×D79C2414yes—
404#11929624—48no—
405#11929623—416no—
406C2×Dic158—44no—
407C2×Dic158—44no—
408C2×Dic158C2414yes—
409C2×Dic158C2414yes—
410C2×Dic158C2414yes—
411C2×Dic158C2418yes—
412C2×D316—44no—
413C2×D316—44no—
414C2×D316C2414yes—
415C2×D316C2414yes—
416C2×D316C2418yes—
417C2×D316C2414yes—
418C2×C22⋊D79—48no—
419C2×C22⋊D79C2418yes—
420C2×C22⋊D79C2418yes—
421C2×C22⋊D79C2418yes—
422C2×C22⋊D79C2418yes—
423C2×C22⋊D79C2418yes—
424D4×D79—416no—
425C22×Dic79C2414yes—
426C22×Dic79C2414yes—
427C22×Dic79C2414yes—
428C22×Dic79C2418yes—
429C22×Dic79C2414yes—
430C2×C4×D79—48no—
431C2×C4×D79C2418yes—
432C2×C4×D79C2418yes—
433C2×C4×D79C2418yes—
434C2×C4×D79C2418yes—
435C2×C4×D79C2418yes—
436C4⋊Dic79C2418yes—
437C4⋊Dic79C2418yes—
438C4⋊Dic79C2414yes—
439C4⋊Dic79C2414yes—
440C4⋊Dic79C2414yes—
441C4⋊Dic79C2414yes—
442C4⋊Dic79C2418yes—
443Dic79⋊C4C2418yes—
444Dic79⋊C4C2418yes—
445Dic79⋊C4C2418yes—
446Dic79⋊C4C2418yes—
447Dic79⋊C4C2418yes—
448Dic79⋊C4C2418yes—
449Dic79⋊C4C2418yes—
450Dic79⋊C4C2418yes—
451Dic79⋊C4C2418yes—
452Dic79⋊C4C2418yes—
453Dic79⋊C4C2418yes—
454Dic79⋊C4C2418yes—
455Dic79⋊C4C2418yes—
456Dic79⋊C4C2418yes—
457C22⋊Dic79C2414yes—
458C22⋊Dic79C2418yes—
459C22⋊Dic79C2418yes—
460C22⋊Dic79C2418yes—
461C22⋊Dic79C2414yes—
462C22⋊Dic79C2418yes—
463(C2×D79)⋊C4C2418yes—
464(C2×D79)⋊C4C2418yes—
465(C2×D79)⋊C4C2418yes—
466(C2×D79)⋊C4C2418yes—
467(C2×D79)⋊C4C2418yes—
468(C2×D79)⋊C4C2418yes—
469(C2×D79)⋊C4C2418yes—
470(C2×D79)⋊C4C2418yes—
471(C2×D79)⋊C4C2418yes—
472(C2×D79)⋊C4C2418yes—
473(C2×D79)⋊C4C2418yes—
474(C2×D79)⋊C4C2418yes—
475(C2×D79)⋊C4C2418yes—
476(C2×D79)⋊C4C2418yes—
477C4×Dic79C2418yes—
478C4×Dic79C2418yes—
479C4×Dic79C2414yes—
480C4×Dic79C2414yes—
481C4×Dic79C2418yes—
482C4×Dic79C2418yes—
483C24×C79C2411yescharacteristic
484#41×C79—42no—
485#41×C79—42no—
486#41×C79—48no—
487C2×Q8×C79C2411yescharacteristic
488C2×Q8×C79C2414yes—
489C2×Q8×C79C2411yescharacteristic
490C2×D4×C79C2414yes—
491C2×D4×C79C2414yes—
492C2×D4×C79C2412yes—
493C2×D4×C79C2412yes—
494C2×D4×C79C2411yescharacteristic
495C2×D4×C79C2414yes—
496C2×D4×C79C2411yescharacteristic
497C22×C4×C79—42no—
498C22×C4×C79—44no—
499C22×C4×C79C2412yes—
500C22×C4×C79C2412yes—
501C22×C4×C79C2412yes—
502C22×C4×C79C2412yes—
503C22×C4×C79C2411yescharacteristic
504C22×C4×C79C2412yes—
505C22×C4×C79C2412yes—
506C22×C4×C79C2412yes—
507C22×C4×C79C2412yes—
508C22×C4×C79C2412yes—
509C22×C4×C79C2412yes—
510C22×C4×C79C2411yescharacteristic
511C22×C4×C79C2414yes—
512C22×C4×C79C2414yes—
513C4⋊C4×C79C2412yes—
514C4⋊C4×C79C2414yes—
515C4⋊C4×C79C2414yes—
516C4⋊C4×C79C2412yes—
517C4⋊C4×C79C2414yes—
518C4⋊C4×C79C2414yes—
519C4⋊C4×C79C2414yes—
520C4⋊C4×C79C2414yes—
521C4⋊C4×C79C2414yes—
522C4⋊C4×C79C2414yes—
523C22⋊C4×C79C2414yes—
524C22⋊C4×C79C2414yes—
525C22⋊C4×C79C2412yes—
526C22⋊C4×C79C2412yes—
527C22⋊C4×C79C2414yes—
528C22⋊C4×C79C2414yes—
529C22⋊C4×C79C2414yes—
530C22⋊C4×C79C2414yes—
531C22⋊C4×C79C2414yes—
532C22⋊C4×C79C2414yes—
533C42×C79C2411yescharacteristic
534C42×C79C2412yes—
535C42×C79C2411yescharacteristic
536C42×C79C2412yes—
537C42×C79C2412yes—
538C42×C79C2412yes—
539C42×C79C2411yescharacteristic
540C42×C79C2412yes—
541C42×C79C2412yes—
542C42×C79C2411yescharacteristic
543C42×C79C2414yes—
544C42×C79C2414yes—
545C42×C79C2412yes—
546C42×C79C2412yes—
547C23×C79—24no—
548C23×C79—41no—
549C23×C79C2512yes—
550C23×C79C2511yescharacteristic
551C23×C79C2512yes—
552C23×C79C2512yes—
553C22×D79—28no—
554C22×D79—44no—
555C22×D79—44no—
556C22×D79—48no—
557C22×D79—44no—
558C22×D79C2518yes—
559Q8×C79—41no—
560Q8×C79—41no—
561Q8×C79—44no—
562D4×C79—28no—
563D4×C79—28no—
564D4×C79—41no—
565D4×C79—44no—
566D4×C79—41no—
567D4×C79—42no—
568D4×C79—42no—
569C2×C4×C79—24no—
570C2×C4×C79—24no—
571C2×C4×C79—24no—
572C2×C4×C79—24no—
573C2×C4×C79—24no—
574C2×C4×C79—22no—
575C2×C4×C79—42no—
576C2×C4×C79—42no—
577C2×C4×C79—42no—
578C2×C4×C79—42no—
579C2×C4×C79—42no—
580C2×C4×C79—41no—
581C2×C4×C79—44no—
582C2×C4×C79—44no—
583C2×C4×C79C2512yes—
584C2×C4×C79C2512yes—
585C2×C4×C79C2512yes—
586C2×C4×C79C2514yes—
587C2×C4×C79C2514yes—
588C2×C4×C79C2512yes—
589C2×C4×C79C2511yescharacteristic
590C2×C4×C79C2512yes—
591C2×C4×C79C2512yes—
592C2×C4×C79C2512yes—
593C2×C4×C79C2511yescharacteristic
594C22⋊D79—216no—
595C22⋊D79—48no—
596C22⋊D79—48no—
597C22⋊D79—48no—
598C22⋊D79—48no—
599C2×Dic79—28no—
600C2×Dic79—44no—
601C2×Dic79—44no—
602C2×Dic79—44no—
603C2×Dic79—48no—
604C2×Dic79C2518yes—
605C2×Dic79C2518yes—
606C2×Dic79C2518yes—
607D316—28no—
608D316—48no—
609D316—44no—
610D316—44no—
611C4×D79—48no—
612C4×D79—48no—
613C4×D79—48no—
614C4×D79—48no—
615C4×D79—48no—
616Dic158—28no—
617Dic158—44no—
618Dic158—44no—
619Dic158—48no—
620C22×C79—22no—
621C22×C79—22no—
622C22×C79—22no—
623C22×C79—22no—
624C22×C79—24no—
625C22×C79—24no—
626C22×C79—21no—
627C22×C79—22no—
628C22×C79—44no—
629C22×C79#58514yes—
630C22×C79C2611yescharacteristic
631C2×D79—28no—
632C2×D79—28no—
633C2×D79—28no—
634C2×D79—88no—
635C2×D79—164no—
636C4×C79—22no—
637C4×C79—22no—
638C4×C79—21no—
639C4×C79—22no—
640C4×C79—22no—
641C4×C79—22no—
642C4×C79—22no—
643C4×C79—22no—
644C4×C79—24no—
645C4×C79—24no—
646C4×C79#58512yes—
647Dic79—28no—
648Dic79—28no—
649Dic79—28no—
650#62829—791nomaximal, Sylow
651C2×C79—24no—
652C2×C79—42no—
653C2×C79—42no—
654C2×C79—41no—
655C2×C79C2×#58512yes—
656C2×C79C2×#58511yescharacteristic
657D79—48no—
658#3566—798no—
659#3564—794no—
660#3560—794no—
661#3557—792no—
662#3551—792no—
663#3538—791no—
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#3444D7911yescharacteristic, complemented
676C2×#529—792no—
677C79#6282911yescharacteristic, complemented, Sylow
678#563—794no—
679#563—798no—
680#563—794no—
681#562—798no—
682#560—794no—
683#560—794no—
684#559—794no—
685#559—798no—
686#557—794no—
687#556—798no—
688#556—798no—
689#556—794no—
690#555—794no—
691#555—798no—
692#554—798no—
693#554—794no—
694#554—794no—
695#553—798no—
696#553—798no—
697#553—794no—
698#553—794no—
699#553—798no—
700#553—798no—
701#553—798no—
702#552—798no—
703#552—798no—
704#552—798no—
705#552—794no—
706#552—794no—
707#552—798no—
708#552—798no—
709#552—798no—
710#551—798no—
711#551—794no—
712#551—798no—
713#551—794no—
714#551—798no—
715#551—798no—
716#551—798no—
717#551—798no—
718D4×Q8—794no—
719#548—794no—
720#548—794no—
721#547—798no—
722#547—794no—
723#546—798no—
724#546—798no—
725#546—798no—
726#546—794no—
727#546—794no—
728D42—794no—
729D42—794no—
730#544—794no—
731#543—794no—
732#542—798no—
733#542—798no—
734#542—798no—
735#542—794no—
736#542—794no—
737#541—798no—
738#541—798no—
739#541—792no—
740#541—792no—
741#540—798no—
742#540—792no—
743#540—792no—
744#539—798no—
745#539—798no—
746#539—794no—
747#539—794no—
748#539—798no—
749#539—798no—
750#538—798no—
751#538—794no—
752#538—798no—
753#538—794no—
754#538—798no—
755#538—798no—
756#537—794no—
757#537—794no—
758#536—792no—
759#535—792no—
760#534—794no—
761#533—792no—
762#533C2×D7911yescharacteristic, complemented
763#533C2×D7912yescomplemented
764#532—792no—
765#532C2×D7911yescharacteristic, complemented
766#532C2×D7912yescomplemented
767#529—798no—
768#529—798no—
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—794no—
778#529—794no—
779#529C2×D7912yescomplemented
780#529C2×D7912yescomplemented
781#529C2×D7914yescomplemented
782#529C2×D7914yescomplemented
783C2×#126—794no—
784C2×#125—792no—
785C2×#125—792no—
786C2×#124—792no—
787C2×#124—792no—
788#525—798no—
789#525C2×D7911yescharacteristic
790#525C2×D7914yescomplemented
791#525C2×D7911yescharacteristic, complemented
792C2×#123—794no—
793C2×#123—798no—
794C2×C22⋊Q8—792no—
795C2×#121—792no—
796#520—798no—
797#520—794no—
798#519—792no—
799#518—798no—
800#518—792no—
801C4×#41C2×D7911yescharacteristic, complemented
802C4×#41C2×D7911yescharacteristic, complemented
803C4×#41C2×D7914yescomplemented
804C2×C4×Q8—792no—
805C2×C4×D4—794no—
806C2×C4×D4—792no—
807C2×#117—794no—
808C22×C42C2×D7911yescharacteristic, complemented
809C2×#41—798no—
810C2×#41—794no—
811C2×#41C22×D7911yescharacteristic
812C2×#41C22×D7911yescharacteristic
813C2×#41C22×D7914yes—
814C22×Q8—792no—
815C22×Q8—792no—
816C22×D4—794no—
817C22×D4—798no—
818C22×D4—792no—
819C22×D4—792no—
820C23×C4—794no—
821C23×C4C22×D7912yes—
822C23×C4C22×D7911yescharacteristic
823C4⋊Q8—794no—
824C4⋊Q8—798no—
825C4⋊Q8—798no—
826C4⋊Q8—792no—
827C4⋊Q8—794no—
828C4⋊Q8C22×D7912yes—
829C4⋊Q8C22×D7911yescharacteristic
830#127—794no—
831#127—792no—
832#127C22×D7911yescharacteristic
833#126—798no—
834#126—798no—
835#126—798no—
836#126—798no—
837#126—798no—
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—798no—
847#126—798no—
848#126—798no—
849#126C22×D7914yes—
850#126C22×D7914yes—
851#125—798no—
852#125—798no—
853#125—798no—
854#125—798no—
855#125—798no—
856#125—798no—
857#125—798no—
858#125—794no—
859#125—794no—
860#125—794no—
861#125—794no—
862#125—798no—
863#125—792no—
864#125—792no—
865#125C22×D7914yes—
866#125C22×D7912yes—
867#124—794no—
868#124—798no—
869#124—794no—
870#124—798no—
871#124—798no—
872#124—798no—
873#124—798no—
874#124—794no—
875#124—794no—
876#124—794no—
877#124—794no—
878#124—798no—
879#124—794no—
880#124C22×D7914yes—
881#124C22×D7911yescharacteristic
882#124C22×D7911yescharacteristic
883#123—798no—
884#123—794no—
885#123—794no—
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—798no—
901#123—798no—
902#123—798no—
903#123—798no—
904#123—798no—
905#123C22×D7914yes—
906#123C22×D7914yes—
907#123C22×D7912yes—
908#123C22×D7912yes—
909C22⋊Q8—798no—
910C22⋊Q8—798no—
911C22⋊Q8—798no—
912C22⋊Q8—794no—
913C22⋊Q8—794no—
914C22⋊Q8—794no—
915C22⋊Q8—794no—
916C22⋊Q8—794no—
917C22⋊Q8—794no—
918C22⋊Q8—798no—
919C22⋊Q8—798no—
920C22⋊Q8—798no—
921C22⋊Q8—798no—
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⋊Q8C22×D7912yes—
931C22⋊Q8C22×D7914yes—
932C22⋊Q8C22×D7912yes—
933C22⋊Q8C22×D7914yes—
934#121—798no—
935#121—798no—
936#121—798no—
937#121—798no—
938#121—798no—
939#121—798no—
940#121—798no—
941#121—794no—
942#121—794no—
943#121—794no—
944#121—794no—
945#121—794no—
946#121—794no—
947#121—798no—
948#121—798no—
949#121—798no—
950#121—798no—
951#121—798no—
952#121—798no—
953#121C22×D7912yes—
954#121C22×D7912yes—
955#121C22×D7914yes—
956#121C22×D7914yes—
957#120—798no—
958#120—794no—
959#120—794no—
960#120—798no—
961#120—798no—
962#120—798no—
963#120C22×D7912yes—
964#120C22×D7912yes—
965C4×Q8—798no—
966C4×Q8—798no—
967C4×Q8—794no—
968C4×Q8—794no—
969C4×Q8—794no—
970C4×Q8—794no—
971C4×Q8—794no—
972C4×Q8—794no—
973C4×Q8—798no—
974C4×Q8C22×D7914yes—
975C4×Q8C22×D7912yes—
976C4×Q8C22×D7914yes—
977C4×Q8C22×D7912yes—
978C4×D4—798no—
979C4×D4—798no—
980C4×D4—798no—
981C4×D4—798no—
982C4×D4—798no—
983C4×D4—798no—
984C4×D4—798no—
985C4×D4—798no—
986C4×D4—798no—
987C4×D4—798no—
988C4×D4—798no—
989C4×D4—798no—
990C4×D4—798no—
991C4×D4—798no—
992C4×D4—798no—
993C4×D4—798no—
994C4×D4—794no—
995C4×D4—794no—
996C4×D4—794no—
997C4×D4—794no—
998C4×D4—794no—
999C4×D4—798no—
1000C4×D4—794no—
1001C4×D4C22×D7914yes—
1002C4×D4C22×D7914yes—
1003C4×D4C22×D7914yes—
1004C4×D4C22×D7914yes—
1005C4×D4C22×D7914yes—
1006C4×D4C22×D7914yes—
1007C4×D4C22×D7914yes—
1008C4×D4C22×D7914yes—
1009C4×D4C22×D7912yes—
1010C4×D4C22×D7912yes—
1011#117—792no—
1012#117—792no—
1013#117—798no—
1014#117—798no—
1015#117—798no—
1016#117—798no—
1017#117—798no—
1018#117—798no—
1019#117—798no—
1020#117—798no—
1021#117—798no—
1022#117—798no—
1023#117—798no—
1024#117C22×D7912yes—
1025#117C22×D7912yes—
1026#117C22×D7911yescharacteristic
1027#117C22×D7911yescharacteristic
1028#117C22×D7914yes—
1029#117C22×D7914yes—
1030#117C22×D7914yes—
1031C2×C4⋊C4—794no—
1032C2×C4⋊C4—794no—
1033C2×C4⋊C4—792no—
1034C2×C4⋊C4—794no—
1035C2×C4⋊C4—792no—
1036C2×C4⋊C4—794no—
1037C2×C4⋊C4—794no—
1038C2×C4⋊C4—798no—
1039C2×C4⋊C4—798no—
1040C2×C4⋊C4—798no—
1041C2×C22⋊C4—794no—
1042C2×C22⋊C4—794no—
1043C2×C22⋊C4—794no—
1044C2×C22⋊C4—794no—
1045C2×C22⋊C4—794no—
1046C2×C22⋊C4—798no—
1047C2×C22⋊C4—798no—
1048C2×C22⋊C4—798no—
1049C2×C22⋊C4—798no—
1050C2×C42—794no—
1051C2×C42C22×D7912yes—
1052C2×C42C22×D7912yes—
1053C2×C42C22×D7912yes—
1054C2×C42C22×D7912yes—
1055C2×C42C22×D7912yes—
1056C2×C42C22×D7911yescharacteristic
1057C2×C42C22×D7912yes—
1058C2×C42C22×D7912yes—
1059C2×C42C22×D7911yescharacteristic
1060C24—794no—
1061C24—794no—
1062C24C23×D7911yescharacteristic
1063#41—42no—
1064#41—42no—
1065#41—48no—
1066#41—3168no—
1067#41—31616no—
1068C2×Q8—3164no—
1069C2×Q8—3164no—
1070C2×Q8—798no—
1071C2×Q8—794no—
1072C2×Q8—794no—
1073C2×Q8—794no—
1074C2×Q8C23×D7911yescharacteristic
1075C2×Q8C23×D7914yes—
1076C2×Q8C23×D7911yescharacteristic
1077C2×D4—3164no—
1078C2×D4—3164no—
1079C2×D4—31616no—
1080C2×D4—3168no—
1081C2×D4—798no—
1082C2×D4—798no—
1083C2×D4—798no—
1084C2×D4—798no—
1085C2×D4—798no—
1086C2×D4—794no—
1087C2×D4—798no—
1088C2×D4—794no—
1089C2×D4—794no—
1090C2×D4C23×D7914yes—
1091C2×D4C23×D7914yes—
1092C2×D4C23×D7911yescharacteristic
1093C2×D4C23×D7912yes—
1094C2×D4C23×D7914yes—
1095C2×D4C23×D7912yes—
1096C2×D4C23×D7911yescharacteristic
1097C22×C4—42no—
1098C22×C4—44no—
1099C22×C4—3168no—
1100C22×C4—794no—
1101C22×C4—794no—
1102C22×C4—794no—
1103C22×C4—798no—
1104C22×C4—798no—
1105C22×C4—798no—
1106C22×C4—798no—
1107C22×C4—798no—
1108C22×C4—798no—
1109C22×C4—794no—
1110C22×C4C23×D7912yes—
1111C22×C4C23×D7912yes—
1112C22×C4C23×D7912yes—
1113C22×C4C23×D7911yescharacteristic
1114C22×C4C23×D7912yes—
1115C22×C4C23×D7912yes—
1116C22×C4C23×D7912yes—
1117C22×C4C23×D7912yes—
1118C22×C4C23×D7912yes—
1119C22×C4C23×D7912yes—
1120C22×C4C23×D7912yes—
1121C22×C4C23×D7911yescharacteristic
1122C22×C4C23×D7914yes—
1123C22×C4C23×D7914yes—
1124C4⋊C4—798no—
1125C4⋊C4—798no—
1126C4⋊C4—798no—
1127C4⋊C4—798no—
1128C4⋊C4—798no—
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—798no—
1138C4⋊C4—794no—
1139C4⋊C4—794no—
1140C4⋊C4—798no—
1141C4⋊C4—794no—
1142C4⋊C4—798no—
1143C4⋊C4—794no—
1144C4⋊C4—798no—
1145C4⋊C4C23×D7914yes—
1146C4⋊C4C23×D7914yes—
1147C4⋊C4C23×D7914yes—
1148C4⋊C4C23×D7914yes—
1149C4⋊C4C23×D7914yes—
1150C4⋊C4C23×D7912yes—
1151C4⋊C4C23×D7914yes—
1152C4⋊C4C23×D7914yes—
1153C4⋊C4C23×D7912yes—
1154C4⋊C4C23×D7914yes—
1155C22⋊C4—798no—
1156C22⋊C4—794no—
1157C22⋊C4—798no—
1158C22⋊C4—798no—
1159C22⋊C4—794no—
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—798no—
1173C22⋊C4—798no—
1174C22⋊C4—798no—
1175C22⋊C4C23×D7914yes—
1176C22⋊C4C23×D7914yes—
1177C22⋊C4C23×D7914yes—
1178C22⋊C4C23×D7914yes—
1179C22⋊C4C23×D7914yes—
1180C22⋊C4C23×D7914yes—
1181C22⋊C4C23×D7914yes—
1182C22⋊C4C23×D7912yes—
1183C22⋊C4C23×D7912yes—
1184C22⋊C4C23×D7914yes—
1185C42—798no—
1186C42—798no—
1187C42—798no—
1188C42—794no—
1189C42—798no—
1190C42—794no—
1191C42C23×D7911yescharacteristic
1192C42C23×D7911yescharacteristic
1193C42C23×D7912yes—
1194C42C23×D7912yes—
1195C42C23×D7912yes—
1196C42C23×D7911yescharacteristic
1197C42C23×D7912yes—
1198C42C23×D7912yes—
1199C42C23×D7912yes—
1200C42C23×D7911yescharacteristic
1201C42C23×D7914yes—
1202C42C23×D7914yes—
1203C42C23×D7912yes—
1204C42C23×D7912yes—
1205C23—24no—
1206C23—41no—
1207C23—3164no—
1208C23—3164no—
1209C23—3164no—
1210C23—3168no—
1211C23—798no—
1212C23—1588no—
1213C23C24×D7912yes—
1214C23C24×D7911yescharacteristic
1215C23C24×D7912yes—
1216C23C24×D7912yes—
1217Q8—41no—
1218Q8—41no—
1219Q8—44no—
1220Q8—3164no—
1221Q8—3164no—
1222Q8—3168no—
1223Q8—1588no—
1224D4—28no—
1225D4—28no—
1226D4—41no—
1227D4—41no—
1228D4—44no—
1229D4—42no—
1230D4—42no—
1231D4—3164no—
1232D4—3164no—
1233D4—3168no—
1234D4—3168no—
1235D4—3168no—
1236D4—3168no—
1237D4—3168no—
1238D4—15816no—
1239D4—1588no—
1240C2×C4—24no—
1241C2×C4—24no—
1242C2×C4—24no—
1243C2×C4—22no—
1244C2×C4—24no—
1245C2×C4—24no—
1246C2×C4—42no—
1247C2×C4—42no—
1248C2×C4—42no—
1249C2×C4—42no—
1250C2×C4—42no—
1251C2×C4—41no—
1252C2×C4—44no—
1253C2×C4—44no—
1254C2×C4—3168no—
1255C2×C4—3168no—
1256C2×C4—3168no—
1257C2×C4—3168no—
1258C2×C4—3168no—
1259C2×C4—3164no—
1260C2×C4—3164no—
1261C2×C4—3164no—
1262C2×C4—3168no—
1263C2×C4—798no—
1264C2×C4—798no—
1265C2×C4—798no—
1266C2×C4—1588no—
1267C2×C4C24×D7912yes—
1268C2×C4C24×D7912yes—
1269C2×C4C24×D7912yes—
1270C2×C4C24×D7914yes—
1271C2×C4C24×D7914yes—
1272C2×C4C24×D7912yes—
1273C2×C4C24×D7911yescharacteristic
1274C2×C4C24×D7912yes—
1275C2×C4C24×D7912yes—
1276C2×C4C24×D7912yes—
1277C2×C4C24×D7911yescharacteristic
1278C22—22no—
1279C22—22no—
1280C22—21no—
1281C22—22no—
1282C22—22no—
1283C22—22no—
1284C22—24no—
1285C22—24no—
1286C22—44no—
1287C22—6328no—
1288C22—1588no—
1289C22—1588no—
1290C22—1588no—
1291C22—12644no—
1292C22#1909939914yes—
1293C22C25×D7911yescharacteristic
1294C4—22no—
1295C4—22no—
1296C4—22no—
1297C4—22no—
1298C4—21no—
1299C4—22no—
1300C4—22no—
1301C4—22no—
1302C4—24no—
1303C4—24no—
1304C4—1588no—
1305C4—1588no—
1306C4—1588no—
1307C4#1909939912yes—
1308C2—24no—
1309C2—41no—
1310C2—42no—
1311C2—42no—
1312C2—3168no—
1313C2C2×#1909939912yes—
1314C2C2×#1909939911yescharacteristic
subgroupG/H
center, FrattiniC22C25×D79
commutator, socle, cosocleC22×C79C26
FittingC79×#3444C2
hypercenter#3444D79
hypocenterC79#62829
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C22 ◁ #3444

Complements

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

NH ≅ G/Ntype
1. #23778076C2semidirect
2. #23778028C2semidirect
3. #23777956C2semidirect
4. #23777906C2semidirect
5. #23777827C2semidirect
6. #23777649C2semidirect
7. #23777639C2semidirect
8. #23777627C2semidirect
9. #23777389C2semidirect
10. #23777378C2semidirect
11. #23777361C2semidirect
12. #23777344C2semidirect
13. #23777326C2semidirect
14. #23777322C2semidirect
15. #23777296C2semidirect
16. #23777112C2semidirect
17. #23777092C2semidirect
18. C2×#19099097C2semidirect
19. C79×#3444C2semidirect
20. #19099316C22semidirect
21. #19099312C22semidirect
22. #19099312C22semidirect
23. #19099310C22semidirect
25. #19099300C22semidirect
26. #19099298C22semidirect
27. #19099296C22semidirect
28. #19099291C22semidirect
29. #19099286C22semidirect
30. #19099285C22semidirect
31. #19099280C22semidirect
32. #19099276C22semidirect
33. #19099275C22semidirect
34. #19099273C22semidirect
35. #19099270C22semidirect
36. #19099267C22semidirect
37. #19099264C22semidirect
38. #19099263C22semidirect
39. #19099262C22semidirect
40. #19099262C22semidirect
42. #19099259C22semidirect
43. #19099256C22semidirect
44. #19099254C22semidirect
45. #19099253C22semidirect
46. #19099253C22semidirect
47. #19099252C22semidirect
48. #19099249C22semidirect
49. #19099246C22semidirect
50. #19099246C22semidirect
51. #19099245C22semidirect
52. #19099244C22semidirect
53. #19099243C22semidirect
54. #19099242C22semidirect
55. #19099242C22semidirect
56. #19099240C22semidirect
57. #19099238C22semidirect
58. #19099237C22semidirect
59. #19099237C22semidirect
60. D4×Dic158C22semidirect
61. #19099222C22semidirect
62. #19099222C22semidirect
63. #19099217C22semidirect
64. #19099212C22semidirect
65. #19099209C22semidirect
66. #19099209C22semidirect
67. #19099202C22semidirect
68. #19099201C22semidirect
69. #19099200C22semidirect
72. #19099192C22semidirect
73. #19099188C22semidirect
74. #19099185C22semidirect
75. #19099184C22semidirect
76. #19099184C22semidirect
77. #19099183C22semidirect
78. #19099177C22semidirect
79. #19099175C22semidirect
80. #19099175C22semidirect
81. #19099172C22semidirect
82. #19099171C22semidirect
84. #19099168C22semidirect
85. #19099163C22semidirect
86. #19099162C22semidirect
87. #19099161C22semidirect
88. #19099159C22semidirect
89. #19099158C22semidirect
90. #19099155C22semidirect
91. #19099155C22semidirect
93. #19099150C22semidirect
94. #19099147C22semidirect
95. #19099146C22semidirect
96. #19099146C22semidirect
97. #19099145C22semidirect
98. #19099141C22semidirect
99. #19099140C22semidirect
100. #19099134C22semidirect
103. #19099120C22semidirect
104. #19099113C22semidirect
105. #19099097C22semidirect
106. #19099097C22semidirect
107. #19099097C22semidirect
108. #19099097C22semidirect
109. #19099097C22semidirect
110. #19099097C22semidirect
111. #19099097C22semidirect
112. #19099097C22semidirect
113. #19099097C22semidirect
114. #19099097C22semidirect
115. #19099090C22semidirect
116. #19099090C22semidirect
117. C2×#14579155C22semidirect
118. C2×#14579153C22semidirect
119. C2×#14579153C22semidirect
120. C2×#14579149C22semidirect
121. C2×#14579149C22semidirect
122. #19099071C22semidirect
123. C2×#14579144C22semidirect
124. #123×D79C22semidirect
125. C2×#14579140C22semidirect
127. #19099043C22semidirect
128. #19099042C22semidirect
129. #19099040C22semidirect
130. #19099037C22semidirect
131. #19099035C22semidirect
132. C2×C4×Dic158C22semidirect
133. C2×C4×D316C22semidirect
134. C2×C4×C22⋊D79C22semidirect
135. C2×#14579118C22semidirect
136. #533×C79C22semidirect
137. #533×C79C22semidirect
138. #532×C79C22semidirect
139. #532×C79C22semidirect
140. #529×C79C22semidirect
141. #529×C79C22semidirect
142. #529×C79C22semidirect
143. #529×C79C22semidirect
145. #525×C79C22semidirect
146. #525×C79C22semidirect
147. C4×#41×C79C22semidirect
148. C4×#41×C79C22semidirect
149. C4×#41×C79C22semidirect
150. C22×C42×C79C22semidirect
675. #3444D79semidirect
677. C79#62829semidirect
762. #533C2×D79semidirect
763. #533C2×D79semidirect
765. #532C2×D79semidirect
766. #532C2×D79semidirect
779. #529C2×D79semidirect
780. #529C2×D79semidirect
781. #529C2×D79semidirect
782. #529C2×D79semidirect
790. #525C2×D79semidirect
791. #525C2×D79semidirect
801. C4×#41C2×D79semidirect
802. C4×#41C2×D79semidirect
803. C4×#41C2×D79semidirect
808. C22×C42C2×D79semidirect

Maximal subgroups

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

subgroupindex
#237780762
#237780282
#237779562
#237779062
#237778272
#237776492
#237776392
#237776272
#237773892
#237773782
#237773612
#237773442
#237773262
#237773222
#237772962
#237771122
#237770922
C2×#190990972
C79×#34442
#6282979