Finite Group Databasebeta

← #33994536

Subgroups — #33994536

Order 18688.

6930 conjugacy classes of subgroups.

The subgroup lattice has 1074 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22623751C218yesmaximal, complemented
2#22623745C214yesmaximal, complemented
3#22623742C214yesmaximal, complemented
4#22623739C212yesmaximal, complemented
5#22623736C212yesmaximal, complemented
6#22623734C211yesmaximal, characteristic, complemented
7#22623731C214yesmaximal, complemented
8#22623729C212yesmaximal, complemented
9#22623727C214yesmaximal, complemented
10#22623510C218yesmaximal, complemented
11#22623510C214yesmaximal, complemented
12Q8×#11924027C214yesmaximal, complemented
13#22623335C212yesmaximal, complemented
14#22623333C214yesmaximal, complemented
15C2×#17989139C214yesmaximal, complemented
16#533×D73C212yesmaximal, complemented
17#22623129C212yesmaximal
18C2×C4×#11924027C211yesmaximal, characteristic
19C73×#3501C211yesmaximal, characteristic, complemented
20C22×#11924027C2211yescharacteristic
21Q8×Dic146C2214yescomplemented
22#17989317C2214yescomplemented
23#17989317C2218yescomplemented
24#17989315C2218yescomplemented
25#17989315C2214yescomplemented
26#17989314C2218yescomplemented
27#17989314C2218yescomplemented
28#17989314C2218yescomplemented
29#17989312C2218yescomplemented
30#17989312C2214yescomplemented
31#17989296C2218yescomplemented
32#17989296C2218yescomplemented
33#17989296C2218yescomplemented
34#17989295C2218yescomplemented
35#17989295C22116yescomplemented
36#17989294C2214yescomplemented
37#17989294C2218yescomplemented
38#17989292C2218yescomplemented
39#17989292C22116yescomplemented
40#17989291C22116yescomplemented
41#17989291C22116yescomplemented
42#17989291C22116yescomplemented
43D4×Dic146C2218yescomplemented
44D4×Dic146C2214yescomplemented
45Q8×C22⋊D73C2218yescomplemented
46#17989250C22116yescomplemented
47#17989250C2218yescomplemented
48#17989218C2212yes—
49#17989217C2218yescomplemented
50#17989216C2218yes—
51#17989216C2218yes—
52#17989216C22116yescomplemented
53#17989216C22116yescomplemented
54#17989215C2214yes—
55#17989214C2218yescomplemented
56#17989213C2218yes—
57#17989213C2214yes—
58#17989212C2218yes—
59#17989144C2212yes—
60#17989143C2218yescomplemented
61#17989143C2214yescomplemented
62#17989142C2212yescomplemented
63#17989142C2218yescomplemented
64#17989142C2212yescomplemented
65#17989141C2214yescomplemented
66#17989141C2214yescomplemented
67#17989140C2214yes—
68#17989139C2214yes—
69#17989139C2218yes—
70#17989139C2218yes—
71#17989139C2214yes—
72#17989139C2218yes—
73#17989139C2218yescomplemented
74#17989139C2218yescomplemented
75#17989139C22116yescomplemented
76#17989139C2218yescomplemented
77#17989139C22116yescomplemented
78#17989139C2218yescomplemented
79C2×#14556590C2214yescomplemented
80C2×#14556589C2214yescomplemented
81C4⋊Q8×D73C2212yescomplemented
82C4⋊Q8×D73C2212yescomplemented
83C2×#14556581C2218yescomplemented
84#125×D73C2214yescomplemented
85C2×#14556570C2214yes—
86C2×#14556568C2218yes—
87C22⋊Q8×D73C2214yes—
88C22⋊Q8×D73C2214yes—
89#17989066C2218yes—
90#17989066C2218yes—
91#17989064C2214yes—
92#17989062C2212yes—
93#17989060C2218yes—
94C4×#11924027C2214yes—
95C4×#11924027C2214yes—
96C4×#11924027C2214yes—
97C4×#11924027C2218yes—
98C4×#11924027C2214yes—
99C4×#11924027C2218yes—
100C2×Q8×Dic73C2214yescomplemented
101C2×C4×Dic146C2211yescharacteristic
102C2×#14556556C2211yescharacteristic
103C2×#14556556C2214yescomplemented
104C2×#14556556C2218yescomplemented
105C4×Q8×D73C2214yescomplemented
106C4×Q8×D73C2214yescomplemented
107C2×D4×Dic73C2211yescharacteristic
108C2×C4×C22⋊D73C2212yes—
109C2×#14556551C2212yes—
110C2×#14556549C2211yescharacteristic
111C2×#14556547C2212yes—
112C2×#14556547C2218yes—
113#117×D73C2214yes—
114C22×C4×Dic73C2212yes—
115C2×C42×D73C2211yescharacteristic
116#554×C73C2214yescomplemented
117#554×C73C2218yescomplemented
118D4×Q8×C73C2214yescomplemented
119#544×C73C2212yes—
120#543×C73C2214yes—
121#533×C73C2212yes—
122C2×C22⋊Q8×C73C2214yes—
123#518×C73C2212yes—
124C2×C4×D4×C73C2211yescharacteristic
125C2×#11924027Q8116yescomplemented
126C2×#11924027C2314yes—
127C2×#11924027C2314yes—
128C22×Dic146C2314yes—
129C22×Dic146C2318yes—
130C22×Dic146C2311yescharacteristic
131C2×Q8×D73C2314yes—
132C2×Q8×D73C2314yes—
133C22×C22⋊D73C2312yes—
134C23×Dic73C2312yes—
135C23×Dic73C2312yes—
136C22×C4×D73C2311yescharacteristic
137C22×C4×D73C2311yescharacteristic
138C22×C4×D73C2311yescharacteristic
139#14556591C2312yes—
140#14556591C2312yes—
141#14556591C2318yes—
142#14556590C2314yes—
143#14556590C2314yes—
144#14556590C2314yes—
145#14556590C2314yes—
146#14556590C2318yes—
147#14556590C2318yes—
148#14556590C2318yes—
149#14556590C23116yes—
150#14556590C23116yes—
151#14556590C2318yes—
152#14556590C2318yes—
153#14556589C2314yes—
154#14556589C2314yes—
155#14556589C2318yes—
156#14556589C2318yes—
157#14556589C2318yes—
158#14556589C23116yes—
159#14556589C23116yes—
160#14556583C2314yes—
161#14556583C2318yes—
162#14556582C2314yes—
163#14556582C2314yes—
164#14556582C2318yes—
165#14556582C2318yes—
166#14556581C2318yes—
167#14556581C23116yes—
168#14556581C23116yes—
169#14556581C23116yes—
170#14556581C2318yes—
171#14556581C23116yes—
172#14556581C23116yes—
173#14556581C23116yes—
174#14556581C23116yes—
175#14556571C2314yes—
176#14556571C2314yes—
177#14556571C23116yes—
178#14556570C2314yes—
179#14556570C2318yes—
180#14556570C2314yes—
181#14556570C2318yes—
182#14556570C2318yes—
183#14556570C23116yes—
184#14556570C23116yes—
185#14556569C2318yes—
186#14556569C2318yes—
187#14556569C23116yes—
188#14556569C23116yes—
189#14556568C2318yes—
190#14556568C23116yes—
191#14556568C2318yes—
192#14556568C23116yes—
193#14556568C23116yes—
194#14556568C23116yes—
195#14556568C23116yes—
196#14556568C23116yes—
197#14556568C23116yes—
198#14556567C2314yes—
199#14556567C2314yes—
200#14556567C23116yes—
201Q8×Dic73C2314yes—
202Q8×Dic73C2318yes—
203Q8×Dic73C2314yes—
204Q8×Dic73C2318yes—
205Q8×Dic73C2318yes—
206C4×Dic146C2318yes—
207C4×Dic146C2318yes—
208C4×Dic146C2314yes—
209C4×Dic146C2314yes—
210C4×Dic146C2314yes—
211C4×Dic146C2314yes—
212C4×Dic146C2318yes—
213C4×Dic146C2318yes—
214#14556556C2314yes—
215#14556556C2318yes—
216#14556556C23116yes—
217#14556556C2318yes—
218#14556556C2314yes—
219#14556556C2318yes—
220#14556556C23116yes—
221#14556556C2318yes—
222#14556556C2318yes—
223#14556556C23116yes—
224#14556556C2314yes—
225#14556556C2314yes—
226#14556556C2318yes—
227#14556556C2318yes—
228D4×Dic73C2314yes—
229D4×Dic73C2318yes—
230D4×Dic73C2318yes—
231D4×Dic73C2314yes—
232C4×C22⋊D73C2318yes—
233C4×C22⋊D73C23116yes—
234C4×C22⋊D73C23116yes—
235C4×C22⋊D73C2318yes—
236#14556551C2318yes—
237#14556551C23116yes—
238#14556551C23116yes—
239#14556551C2318yes—
240#14556550C2314yes—
241#14556549C2314yes—
242#14556549C2314yes—
243#14556549C2314yes—
244#14556549C2314yes—
245#14556548C2318yes—
246#14556547C2318yes—
247#14556547C23116yes—
248#14556547C2318yes—
249#14556547C23116yes—
250#14556547C23116yes—
251#14556547C2318yes—
252C2×C4⋊Dic73C2314yes—
253C2×C4⋊Dic73C2311yescharacteristic
254C2×C4⋊Dic73C2318yes—
255C2×#11924007C2318yes—
256C2×#11924007C2318yes—
257C2×#11924007C2318yes—
258C2×#11924007C2312yes—
259C2×#11924007C2312yes—
260C2×#11924007C2318yes—
261C2×#11924007C2318yes—
262C4⋊C4×D73C2314yes—
263C4⋊C4×D73C2314yes—
264C4⋊C4×D73C2314yes—
265C4⋊C4×D73C2314yes—
266C4⋊C4×D73C2318yes—
267C4⋊C4×D73C2318yes—
268C2×C22⋊Dic73C2312yes—
269C2×C22⋊Dic73C2318yes—
270C2×#11924005C2312yes—
271C22⋊C4×D73C2318yes—
272C2×C4×Dic73C2314yes—
273C2×C4×Dic73C2311yescharacteristic
274C2×C4×Dic73C2311yescharacteristic
275C2×C4×Dic73C2312yes—
276C2×C4×Dic73C2312yes—
277C2×C4×Dic73C2312yes—
278C2×C4×Dic73C2314yes—
279C2×C4×Dic73C2314yes—
280C2×C4×Dic73C2314yes—
281C2×C4×Dic73C2318yes—
282C2×C4×Dic73C2318yes—
283C2×C4×Dic73C2311yescharacteristic
284C42×D73C2312yes—
285C42×D73C2312yes—
286C42×D73C2312yes—
287C42×D73C2318yes—
288C42×D73C2312yes—
289C22×Q8×C73C2314yes—
290C22×D4×C73C2311yescharacteristic
291C23×C4×C73C2312yes—
292C4⋊Q8×C73C2312yes—
293C4⋊Q8×C73C2312yes—
294C4⋊Q8×C73C2318yes—
295#125×C73C2318yes—
296#125×C73C2314yes—
297C22⋊Q8×C73C2314yes—
298C22⋊Q8×C73C2318yes—
299C22⋊Q8×C73C2314yes—
300C22⋊Q8×C73C2318yes—
301C22⋊Q8×C73C2318yes—
302C22⋊Q8×C73C23116yes—
303C22⋊Q8×C73C23116yes—
304C4×Q8×C73C2314yes—
305C4×Q8×C73C2314yes—
306C4×D4×C73C2314yes—
307C4×D4×C73C2318yes—
308C4×D4×C73C2314yes—
309C4×D4×C73C2318yes—
310#117×C73C2314yes—
311C2×C4⋊C4×C73C2314yes—
312C2×C4⋊C4×C73C2311yescharacteristic
313C2×C4⋊C4×C73C2318yes—
314C2×C22⋊C4×C73C2312yes—
315C2×C22⋊C4×C73C2318yes—
316C2×C42×C73C2311yescharacteristic
317C23×D73C2411yescharacteristic
318#11924027C2×Q8132yescomplemented
319#11924027C2×Q8132yescomplemented
320C2×Dic146—416no—
321C2×Dic146—48no—
322C2×Dic146C2×Q818yescomplemented
323C2×Dic146C2418yes—
324C2×Dic146C2414yes—
325C2×Dic146C24116yes—
326C2×Dic146C2418yes—
327C2×Dic146C2414yes—
328C2×Dic146C2418yes—
329C2×Dic146C2414yes—
330Q8×D73—48no—
331Q8×D73—48no—
332C2×C22⋊D73C2×Q8116yescomplemented
333C2×C22⋊D73C2418yes—
334C22×Dic73—44no—
335C22×Dic73C2×Q8116yescomplemented
336C22×Dic73C2411yescharacteristic
337C22×Dic73C2414yes—
338C22×Dic73C2412yes—
339C22×Dic73C2411yescharacteristic
340C22×Dic73C2414yes—
341C22×Dic73C2418yes—
342C22×Dic73C2418yes—
343C22×Dic73C2414yes—
344C22×Dic73C2411yescharacteristic
345C22×Dic73C2414yes—
346C22×Dic73C2412yes—
347C2×C4×D73—42no—
348C2×C4×D73—42no—
349C2×C4×D73C2×Q818yescomplemented
350C2×C4×D73C2412yes—
351C2×C4×D73C2412yes—
352C2×C4×D73C2412yes—
353C2×C4×D73C2412yes—
354C2×C4×D73C2418yes—
355C2×C4×D73C2418yes—
356C2×C4×D73C2412yes—
357C2×C4×D73C2412yes—
358C4⋊Dic73C2414yes—
359C4⋊Dic73C2418yes—
360C4⋊Dic73C2414yes—
361C4⋊Dic73C2414yes—
362C4⋊Dic73C2414yes—
363C4⋊Dic73C2418yes—
364C4⋊Dic73C2414yes—
365C4⋊Dic73C24116yes—
366C4⋊Dic73C2418yes—
367#11924007C2418yes—
368#11924007C2418yes—
369#11924007C2418yes—
370#11924007C2418yes—
371#11924007C2418yes—
372#11924007C2418yes—
373#11924007C2418yes—
374#11924007C2418yes—
375#11924007C2418yes—
376#11924007C24116yes—
377#11924007C24116yes—
378#11924007C2418yes—
379#11924007C24116yes—
380#11924007C24116yes—
381#11924007C24116yes—
382C22⋊Dic73C2418yes—
383C22⋊Dic73C2418yes—
384C22⋊Dic73C24116yes—
385#11924005C2418yes—
386#11924005C2418yes—
387#11924005C2418yes—
388C4×Dic73C2411yescharacteristic
389C4×Dic73C2411yescharacteristic
390C4×Dic73C2411yescharacteristic
391C4×Dic73C2411yescharacteristic
392C4×Dic73C2412yes—
393C4×Dic73C2412yes—
394C4×Dic73C2412yes—
395C4×Dic73C2412yes—
396C4×Dic73C2418yes—
397C4×Dic73C2418yes—
398C4×Dic73C2418yes—
399C4×Dic73C2414yes—
400C4×Dic73C2414yes—
401C4×Dic73C2414yes—
402C4×Dic73C2414yes—
403C4×Dic73C2414yes—
404C4×Dic73C2414yes—
405C4×Dic73C24116yes—
406C4×Dic73C24116yes—
407C24×C73C2412yes—
408C2×Q8×C73—48no—
409C2×Q8×C73C2414yes—
410C2×Q8×C73C2414yes—
411C2×Q8×C73C2418yes—
412C2×D4×C73C2×Q818yescomplemented
413C2×D4×C73C2414yes—
414C22×C4×C73—44no—
415C22×C4×C73C2411yescharacteristic
416C22×C4×C73C2414yes—
417C22×C4×C73C2411yescharacteristic
418C22×C4×C73C2418yes—
419C22×C4×C73C2418yes—
420C22×C4×C73C2412yes—
421C22×C4×C73C2414yes—
422C22×C4×C73C2411yescharacteristic
423C4⋊C4×C73C2418yes—
424C4⋊C4×C73C2414yes—
425C4⋊C4×C73C2414yes—
426C4⋊C4×C73C2418yes—
427C4⋊C4×C73C24116yes—
428C4⋊C4×C73C2414yes—
429C4⋊C4×C73C2414yes—
430C4⋊C4×C73C2418yes—
431C4⋊C4×C73C2414yes—
432C22⋊C4×C73C2418yes—
433C22⋊C4×C73C2418yes—
434C22⋊C4×C73C24116yes—
435C42×C73C2412yes—
436C42×C73C2412yes—
437C42×C73C2418yes—
438C23×C73—42no—
439C23×C73—42no—
440C23×C73C22×Q818yes—
441C23×C73C2511yescharacteristic
442C23×C73C2514yes—
443C22×D73—41no—
444C22×D73—41no—
445C22×D73C22×Q814yes—
446C22×D73C2512yes—
447Q8×C73—28no—
448Q8×C73—48no—
449Q8×C73—44no—
450D4×C73C22×Q8116yes—
451C2×C4×C73—22no—
452C2×C4×C73—28no—
453C2×C4×C73—42no—
454C2×C4×C73—44no—
455C2×C4×C73—48no—
456C2×C4×C73—41no—
457C2×C4×C73—48no—
458C2×C4×C73C22×Q814yes—
459C2×C4×C73C2512yes—
460C2×C4×C73C2511yescharacteristic
461C2×C4×C73C2518yes—
462C2×C4×C73C2518yes—
463C2×C4×C73C2514yes—
464C2×C4×C73C2512yes—
465C2×C4×C73C2511yescharacteristic
466C22⋊D73C22×Q8132yes—
467C2×Dic73—22no—
468C2×Dic73—28no—
469C2×Dic73—41no—
470C2×Dic73—42no—
471C2×Dic73—44no—
472C2×Dic73—48no—
473C2×Dic73—48no—
474C2×Dic73C22×Q814yes—
475C2×Dic73C22×Q818yes—
476C2×Dic73C22×Q8116yes—
477C2×Dic73C22×Q8116yes—
478C2×Dic73C2511yescharacteristic
479C2×Dic73C2514yes—
480C2×Dic73C2518yes—
481C2×Dic73C2518yes—
482C2×Dic73C2512yes—
483C2×Dic73C2511yescharacteristic
484C2×Dic73C2514yes—
485C2×Dic73C2511yescharacteristic
486C2×Dic73C2511yescharacteristic
487C4×D73—24no—
488C4×D73—24no—
489C4×D73—42no—
490C4×D73—42no—
491C4×D73—48no—
492C4×D73—48no—
493C4×D73C22×Q818yes—
494C4×D73C22×Q818yes—
495Dic146—28no—
496Dic146—216no—
497Dic146—44no—
498Dic146—48no—
499Dic146—48no—
500Dic146—416no—
501Dic146C22×Q8116yes—
502C22×C73—24no—
503C22×C73—21no—
504C22×C73—24no—
505C22×C73—21no—
506C22×C73—48no—
507C22×C73C23×Q812yes—
508C22×C73C23×Q818yes—
509C22×C73C2611yescharacteristic
510C2×D73—22no—
511C2×D73—22no—
512C2×D73—44no—
513C2×D73C23×Q814yes—
514C4×C73—28no—
515C4×C73—22no—
516C4×C73—24no—
517C4×C73—28no—
518C4×C73—21no—
519C4×C73C23×Q814yes—
520C4×C73#58512yes—
521Dic73—28no—
522Dic73—28no—
523Dic73—22no—
524Dic73—24no—
525Dic73—21no—
526Dic73C23×Q818yes—
527Dic73C23×Q812yes—
528Dic73C23×Q812yes—
529Dic73#58512yes—
530#62813—731nomaximal, Sylow
531C2×C73—22no—
532C2×C73—28no—
533C2×C73C24×Q811yescharacteristic
534C2×C73C2×#58511yescharacteristic
535C2×C73C2×#58511yescharacteristic
536D73—24no—
537#3504—738no—
538#3503—734no—
539#3503—734no—
540#3502—732no—
541#3502—732no—
542#3501—734no—
543#3501—734no—
544#3501—732no—
545#3501—731no—
546#3501D7311yescharacteristic, complemented
547Q8×#41—734no—
548Q8×#41—738no—
549Q8×#41—734no—
550#3458—732no—
551#3458—734no—
552C2×#533—732no—
553C2×#533—734no—
554#3428—732no—
555C2×C4×#41—731no—
556C73#6281311yescharacteristic, complemented, Sylow
557C22×#41—731no—
558Q82—738no—
559Q82—734no—
560Q82—734no—
561#557—734no—
562#557—738no—
563#557—738no—
564#557—738no—
565#557—738no—
566#557—734no—
567#557—738no—
568#554—7316no—
569#554—7316no—
570#554—7316no—
571#554—738no—
572#554—7316no—
573#554—734no—
574#554—738no—
575#554—738no—
576#554—738no—
577#554—738no—
578#554—738no—
579#554—7316no—
580#554C2×D7314yescomplemented
581#554C2×D7318yescomplemented
582D4×Q8—738no—
583D4×Q8—738no—
584D4×Q8—7316no—
585D4×Q8—738no—
586D4×Q8—734no—
587D4×Q8C2×D7314yescomplemented
588#544—738no—
589#544—738no—
590#544—738no—
591#544—738no—
592#544—7316no—
593#544—7316no—
594#544—734no—
595#544—732no—
596#544C2×D7312yes—
597#543—738no—
598#543—738no—
599#543—734no—
600#543C2×D7314yes—
601#533—732no—
602#533—732no—
603#533—738no—
604#533—734no—
605#533—738no—
606#533—734no—
607#533—734no—
608#533—738no—
609#533—738no—
610#533—738no—
611#533—738no—
612#533—738no—
613#533—738no—
614#533—738no—
615#533—7316no—
616#533—7316no—
617#533—734no—
618#533—734no—
619#533—734no—
620#533—732no—
621#533C2×D7312yes—
622C2×C4⋊Q8—734no—
623C2×C4⋊Q8—732no—
624C2×C4⋊Q8—732no—
625C2×C4⋊Q8—734no—
626C2×#125—734no—
627C2×#125—738no—
628C2×C22⋊Q8—734no—
629C2×C22⋊Q8—734no—
630C2×C22⋊Q8—734no—
631C2×C22⋊Q8—738no—
632C2×C22⋊Q8C2×D7314yes—
633#520—738no—
634#520—738no—
635#519—734no—
636#518—732no—
637#518—738no—
638#518C2×D7312yes—
639C4×#41—734no—
640C4×#41—734no—
641C4×#41—734no—
642C4×#41—734no—
643C4×#41—738no—
644C4×#41—738no—
645C2×C4×Q8—734no—
646C2×C4×Q8—734no—
647C2×C4×Q8—734no—
648C2×C4×Q8—731no—
649C2×C4×Q8—734no—
650C2×C4×Q8—738no—
651C2×C4×Q8—731no—
652C2×C4×D4—731no—
653C2×C4×D4—732no—
654C2×C4×D4—732no—
655C2×C4×D4C2×D7311yescharacteristic
656C2×#117—734no—
657C2×#117—731no—
658C2×#117—732no—
659C2×#117—738no—
660C22×C42—732no—
661C22×C42—731no—
662C2×#41—7316no—
663C2×#41—734no—
664C2×#41—734no—
665C22×Q8—734no—
666C22×Q8—734no—
667C22×Q8—734no—
668C22×Q8—738no—
669C22×Q8—731no—
670C22×Q8C22×D7314yes—
671C22×D4—732no—
672C22×D4C22×D7311yescharacteristic
673C23×C4—732no—
674C23×C4—731no—
675C23×C4—731no—
676C23×C4—732no—
677C23×C4—731no—
678C23×C4C22×D7312yes—
679C4⋊Q8—734no—
680C4⋊Q8—738no—
681C4⋊Q8—734no—
682C4⋊Q8—738no—
683C4⋊Q8—738no—
684C4⋊Q8—7316no—
685C4⋊Q8—7316no—
686C4⋊Q8—734no—
687C4⋊Q8—734no—
688C4⋊Q8—738no—
689C4⋊Q8—738no—
690C4⋊Q8—734no—
691C4⋊Q8—734no—
692C4⋊Q8—738no—
693C4⋊Q8—7316no—
694C4⋊Q8—7316no—
695C4⋊Q8—738no—
696C4⋊Q8—738no—
697C4⋊Q8—732no—
698C4⋊Q8—732no—
699C4⋊Q8—738no—
700C4⋊Q8C22×D7312yes—
701C4⋊Q8C22×D7312yes—
702C4⋊Q8C22×D7318yes—
703#125—738no—
704#125—738no—
705#125—7316no—
706#125—7316no—
707#125—7316no—
708#125—734no—
709#125—734no—
710#125—7316no—
711#125—7316no—
712#125—7316no—
713#125—7316no—
714#125—738no—
715#125—738no—
716#125—734no—
717#125—738no—
718#125C22×D7314yes—
719#125C22×D7318yes—
720C22⋊Q8—734no—
721C22⋊Q8—734no—
722C22⋊Q8—7316no—
723C22⋊Q8—734no—
724C22⋊Q8—738no—
725C22⋊Q8—734no—
726C22⋊Q8—738no—
727C22⋊Q8—738no—
728C22⋊Q8—7316no—
729C22⋊Q8—7316no—
730C22⋊Q8—738no—
731C22⋊Q8—734no—
732C22⋊Q8—738no—
733C22⋊Q8—734no—
734C22⋊Q8—7316no—
735C22⋊Q8—7316no—
736C22⋊Q8—7316no—
737C22⋊Q8—738no—
738C22⋊Q8—738no—
739C22⋊Q8—7316no—
740C22⋊Q8—7316no—
741C22⋊Q8—7316no—
742C22⋊Q8—7316no—
743C22⋊Q8—7316no—
744C22⋊Q8—7316no—
745C22⋊Q8—7316no—
746C22⋊Q8C22×D7314yes—
747C22⋊Q8C22×D7314yes—
748C22⋊Q8C22×D7318yes—
749C22⋊Q8C22×D7318yes—
750C22⋊Q8C22×D7318yes—
751C22⋊Q8C22×D73116yes—
752C22⋊Q8C22×D73116yes—
753C4×Q8—734no—
754C4×Q8—738no—
755C4×Q8—734no—
756C4×Q8—738no—
757C4×Q8—738no—
758C4×Q8—734no—
759C4×Q8—738no—
760C4×Q8—734no—
761C4×Q8—734no—
762C4×Q8—734no—
763C4×Q8—738no—
764C4×Q8—7316no—
765C4×Q8—738no—
766C4×Q8—7316no—
767C4×Q8—738no—
768C4×Q8—738no—
769C4×Q8—7316no—
770C4×Q8—738no—
771C4×Q8—738no—
772C4×Q8—734no—
773C4×Q8—734no—
774C4×Q8—738no—
775C4×Q8—734no—
776C4×Q8—738no—
777C4×Q8—734no—
778C4×Q8—738no—
779C4×Q8—738no—
780C4×Q8C22×D7314yes—
781C4×Q8C22×D7314yes—
782C4×D4—734no—
783C4×D4—734no—
784C4×D4—738no—
785C4×D4—738no—
786C4×D4—738no—
787C4×D4—738no—
788C4×D4—7316no—
789C4×D4—7316no—
790C4×D4—738no—
791C4×D4—738no—
792C4×D4—7316no—
793C4×D4—7316no—
794C4×D4C22×D7314yes—
795C4×D4C22×D7314yes—
796C4×D4C22×D7318yes—
797C4×D4C22×D7318yes—
798#117—734no—
799#117—734no—
800#117—734no—
801#117—734no—
802#117—734no—
803#117—738no—
804#117—738no—
805#117—7316no—
806#117—738no—
807#117—7316no—
808#117—7316no—
809#117—738no—
810#117C22×D7314yes—
811C2×C4⋊C4—732no—
812C2×C4⋊C4—732no—
813C2×C4⋊C4—731no—
814C2×C4⋊C4—738no—
815C2×C4⋊C4—738no—
816C2×C4⋊C4—738no—
817C2×C4⋊C4—738no—
818C2×C4⋊C4—738no—
819C2×C4⋊C4—738no—
820C2×C4⋊C4—734no—
821C2×C4⋊C4—734no—
822C2×C4⋊C4—734no—
823C2×C4⋊C4—738no—
824C2×C4⋊C4—738no—
825C2×C4⋊C4—734no—
826C2×C4⋊C4—734no—
827C2×C4⋊C4C22×D7311yescharacteristic
828C2×C4⋊C4C22×D7318yes—
829C2×C4⋊C4C22×D7314yes—
830C2×C22⋊C4—732no—
831C2×C22⋊C4—738no—
832C2×C22⋊C4—732no—
833C2×C22⋊C4—738no—
834C2×C22⋊C4C22×D7312yes—
835C2×C22⋊C4C22×D7318yes—
836C2×C42—732no—
837C2×C42—731no—
838C2×C42—738no—
839C2×C42—738no—
840C2×C42—732no—
841C2×C42—731no—
842C2×C42—732no—
843C2×C42—734no—
844C2×C42—734no—
845C2×C42—734no—
846C2×C42—734no—
847C2×C42—731no—
848C2×C42—738no—
849C2×C42—732no—
850C2×C42—732no—
851C2×C42—732no—
852C2×C42—732no—
853C2×C42C22×D7311yescharacteristic
854C24—731no—
855C24C23×D7312yes—
856#41—7332no—
857#41—7332no—
858C2×Q8—48no—
859C2×Q8—2928no—
860C2×Q8—29216no—
861C2×Q8—2928no—
862C2×Q8—2928no—
863C2×Q8—738no—
864C2×Q8—738no—
865C2×Q8—738no—
866C2×Q8—7316no—
867C2×Q8—734no—
868C2×Q8—734no—
869C2×Q8—738no—
870C2×Q8—734no—
871C2×Q8C23×D7314yes—
872C2×Q8C23×D7318yes—
873C2×Q8C23×D7314yes—
874C2×D4—7316no—
875C2×D4—738no—
876C2×D4Q8×D7318yescomplemented
877C2×D4C23×D7314yes—
878C22×C4—44no—
879C22×C4—2922no—
880C22×C4—2922no—
881C22×C4—2924no—
882C22×C4—732no—
883C22×C4—731no—
884C22×C4—734no—
885C22×C4—738no—
886C22×C4—738no—
887C22×C4—732no—
888C22×C4—732no—
889C22×C4—738no—
890C22×C4—738no—
891C22×C4—7316no—
892C22×C4—734no—
893C22×C4—731no—
894C22×C4—734no—
895C22×C4—732no—
896C22×C4—738no—
897C22×C4—732no—
898C22×C4—732no—
899C22×C4—731no—
900C22×C4—734no—
901C22×C4—732no—
902C22×C4—732no—
903C22×C4C23×D7311yescharacteristic
904C22×C4C23×D7314yes—
905C22×C4C23×D7312yes—
906C22×C4C23×D7314yes—
907C22×C4C23×D7311yescharacteristic
908C22×C4C23×D7318yes—
909C22×C4C23×D7318yes—
910C22×C4C23×D7311yescharacteristic
911C4⋊C4—738no—
912C4⋊C4—738no—
913C4⋊C4—738no—
914C4⋊C4—738no—
915C4⋊C4—738no—
916C4⋊C4—738no—
917C4⋊C4—7316no—
918C4⋊C4—7316no—
919C4⋊C4—738no—
920C4⋊C4—7316no—
921C4⋊C4—738no—
922C4⋊C4—7316no—
923C4⋊C4—738no—
924C4⋊C4—7316no—
925C4⋊C4—738no—
926C4⋊C4—738no—
927C4⋊C4—734no—
928C4⋊C4—734no—
929C4⋊C4—734no—
930C4⋊C4—734no—
931C4⋊C4—738no—
932C4⋊C4—7316no—
933C4⋊C4—738no—
934C4⋊C4—734no—
935C4⋊C4C23×D7318yes—
936C4⋊C4C23×D7314yes—
937C4⋊C4C23×D7314yes—
938C4⋊C4C23×D7314yes—
939C4⋊C4C23×D7314yes—
940C4⋊C4C23×D7318yes—
941C4⋊C4C23×D7314yes—
942C4⋊C4C23×D73116yes—
943C4⋊C4C23×D7318yes—
944C22⋊C4—738no—
945C22⋊C4—738no—
946C22⋊C4—7316no—
947C22⋊C4—738no—
948C22⋊C4—738no—
949C22⋊C4—738no—
950C22⋊C4C23×D7318yes—
951C22⋊C4C23×D7318yes—
952C22⋊C4C23×D73116yes—
953C42—731no—
954C42—731no—
955C42—731no—
956C42—731no—
957C42—734no—
958C42—738no—
959C42—738no—
960C42—732no—
961C42—734no—
962C42—732no—
963C42—734no—
964C42—734no—
965C42—732no—
966C42—734no—
967C42—734no—
968C42—732no—
969C42—7316no—
970C42—7316no—
971C42—738no—
972C42C23×D7312yes—
973C42C23×D7312yes—
974C42C23×D7318yes—
975C23—42no—
976C23—42no—
977C23—2921no—
978C23—2921no—
979C23—734no—
980C23—732no—
981C23C2×Q8×D7318yes—
982C23C24×D7311yescharacteristic
983C23C24×D7314yes—
984Q8—28no—
985Q8—48no—
986Q8—44no—
987Q8—29216no—
988Q8—2924no—
989Q8—2928no—
990Q8—2928no—
991Q8—7316no—
992Q8—14616no—
993Q8—1468no—
994D4—7332no—
995D4C2×Q8×D73116yes—
996C2×C4—22no—
997C2×C4—28no—
998C2×C4—44no—
999C2×C4—42no—
1000C2×C4—41no—
1001C2×C4—48no—
1002C2×C4—48no—
1003C2×C4—2922no—
1004C2×C4—2922no—
1005C2×C4—2928no—
1006C2×C4—2928no—
1007C2×C4—2924no—
1008C2×C4—2922no—
1009C2×C4—2921no—
1010C2×C4—2928no—
1011C2×C4—2928no—
1012C2×C4—734no—
1013C2×C4—738no—
1014C2×C4—7316no—
1015C2×C4—7316no—
1016C2×C4—731no—
1017C2×C4—734no—
1018C2×C4—731no—
1019C2×C4—731no—
1020C2×C4—738no—
1021C2×C4—738no—
1022C2×C4—731no—
1023C2×C4—738no—
1024C2×C4—734no—
1025C2×C4—738no—
1026C2×C4—732no—
1027C2×C4—1464no—
1028C2×C4—1462no—
1029C2×C4—1468no—
1030C2×C4—1464no—
1031C2×C4C2×Q8×D7314yes—
1032C2×C4C24×D7311yescharacteristic
1033C2×C4C24×D7314yes—
1034C2×C4C24×D7318yes—
1035C2×C4C24×D7318yes—
1036C2×C4C24×D7312yes—
1037C2×C4C24×D7312yes—
1038C2×C4C24×D7311yescharacteristic
1039C22—24no—
1040C22—21no—
1041C22—24no—
1042C22—21no—
1043C22—48no—
1044C22—2924no—
1045C22—734no—
1046C22—1462no—
1047C22—1462no—
1048C22C22×Q8×D7312yes—
1049C22C22×Q8×D7318yes—
1050C22C25×D7311yescharacteristic
1051C4—28no—
1052C4—22no—
1053C4—21no—
1054C4—24no—
1055C4—28no—
1056C4—732no—
1057C4—732no—
1058C4—738no—
1059C4—732no—
1060C4—1461no—
1061C4—1468no—
1062C4—1464no—
1063C4—1468no—
1064C4—1462no—
1065C4C22×Q8×D7314yes—
1066C4#1798942212yes—
1067C2—22no—
1068C2—28no—
1069C2—1464no—
1070C2C23×Q8×D7311yescharacteristic
1071C2#585×D7311yescharacteristic
1072C2C2×#1798942211yescharacteristic
subgroupG/H
center, FrattiniC22C25×D73
commutator, socle, cosocleC22×C73C26
FittingC73×#3501C2
prime radicalC22×#11924027C22
hypercenter#3501D73
hypocenterC73#62813
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ #3501

Complements

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

NH ≅ G/Ntype
1. #22623751C2semidirect
2. #22623745C2semidirect
3. #22623742C2semidirect
4. #22623739C2semidirect
5. #22623736C2semidirect
6. #22623734C2semidirect
7. #22623731C2semidirect
8. #22623729C2semidirect
9. #22623727C2semidirect
10. #22623510C2semidirect
11. #22623510C2semidirect
12. Q8×#11924027C2semidirect
13. #22623335C2semidirect
14. #22623333C2semidirect
15. C2×#17989139C2semidirect
16. #533×D73C2semidirect
19. C73×#3501C2semidirect
21. Q8×Dic146C22semidirect
22. #17989317C22semidirect
23. #17989317C22semidirect
24. #17989315C22semidirect
25. #17989315C22semidirect
26. #17989314C22semidirect
27. #17989314C22semidirect
28. #17989314C22semidirect
29. #17989312C22semidirect
30. #17989312C22semidirect
31. #17989296C22semidirect
32. #17989296C22semidirect
33. #17989296C22semidirect
34. #17989295C22semidirect
35. #17989295C22semidirect
36. #17989294C22semidirect
37. #17989294C22semidirect
38. #17989292C22semidirect
39. #17989292C22semidirect
40. #17989291C22semidirect
41. #17989291C22semidirect
42. #17989291C22semidirect
43. D4×Dic146C22semidirect
44. D4×Dic146C22semidirect
45. Q8×C22⋊D73C22semidirect
46. #17989250C22semidirect
47. #17989250C22semidirect
49. #17989217C22semidirect
52. #17989216C22semidirect
53. #17989216C22semidirect
55. #17989214C22semidirect
60. #17989143C22semidirect
61. #17989143C22semidirect
62. #17989142C22semidirect
63. #17989142C22semidirect
64. #17989142C22semidirect
65. #17989141C22semidirect
66. #17989141C22semidirect
73. #17989139C22semidirect
74. #17989139C22semidirect
75. #17989139C22semidirect
76. #17989139C22semidirect
77. #17989139C22semidirect
78. #17989139C22semidirect
79. C2×#14556590C22semidirect
80. C2×#14556589C22semidirect
81. C4⋊Q8×D73C22semidirect
82. C4⋊Q8×D73C22semidirect
83. C2×#14556581C22semidirect
84. #125×D73C22semidirect
100. C2×Q8×Dic73C22semidirect
103. C2×#14556556C22semidirect
104. C2×#14556556C22semidirect
105. C4×Q8×D73C22semidirect
106. C4×Q8×D73C22semidirect
116. #554×C73C22semidirect
117. #554×C73C22semidirect
118. D4×Q8×C73C22semidirect
125. C2×#11924027Q8semidirect
318. #11924027C2×Q8semidirect
319. #11924027C2×Q8semidirect
322. C2×Dic146C2×Q8semidirect
332. C2×C22⋊D73C2×Q8semidirect
335. C22×Dic73C2×Q8semidirect
349. C2×C4×D73C2×Q8semidirect
412. C2×D4×C73C2×Q8semidirect
546. #3501D73semidirect
556. C73#62813semidirect
580. #554C2×D73semidirect
581. #554C2×D73semidirect
587. D4×Q8C2×D73semidirect
876. C2×D4Q8×D73semidirect

Maximal subgroups

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

subgroupindex
#226237512
#226237452
#226237422
#226237392
#226237362
#226237342
#226237312
#226237292
#226237272
#226235102
Q8×#119240272
#226233352
#226233332
C2×#179891392
#533×D732
#226231292
C2×C4×#119240272
C73×#35012
#6281373