Finite Group Databasebeta

← #3231×D73 #33958046

Subgroups — #3231×D73 #33958046

Order 18688.

1778 conjugacy classes of subgroups.

The subgroup lattice has 976 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#533×D73C211yesmaximal, characteristic
2#533×D73C211yesmaximal, characteristic
3#22621093C211yesmaximal, characteristic, complemented
4#22621092C211yesmaximal, characteristic, complemented
5#22621091C211yesmaximal, characteristic, complemented
6#22621090C211yesmaximal, characteristic, complemented
7#22621089C214yesmaximal, complemented
8#22621088C214yesmaximal, complemented
9#22621087C211yesmaximal, characteristic, complemented
10#22621086C211yesmaximal, characteristic, complemented
11#22621085C211yesmaximal, characteristic, complemented
12#500×D73C211yesmaximal, characteristic, complemented
13#498×D73C211yesmaximal, characteristic, complemented
14#487×D73C211yesmaximal, characteristic, complemented
15#487×D73C211yesmaximal, characteristic, complemented
16#485×D73C214yesmaximal
17#479×D73C214yesmaximal, complemented
18#431×D73C211yesmaximal, characteristic
19C73×#3231C211yesmaximal, characteristic, complemented
20#17989144C2211yescharacteristic
21#17989144C2211yescharacteristic
22#17989143—21no—
23#17989143C2212yes—
24#17989142C2211yescharacteristic
25#17989142C2211yescharacteristic
26#17989142C2211yescharacteristic
27#17989142C2211yescharacteristic
28#17989141—21no—
29#17989141—21no—
30#17989141—21no—
31#17989141C2212yes—
32#17989140—21no—
33#17989140C2212yes—
34#17989139—21no—
35#17989139—21no—
36#17989139—21no—
37#17989139C2212yes—
38C4⋊Q8×D73C2211yescharacteristic
39C4⋊Q8×D73C2211yescharacteristic
40C4⋊Q8×D73C2211yescharacteristic
41C4⋊Q8×D73C2211yescharacteristic
42#125×D73—21no—
43#125×D73C2212yes—
44C22⋊Q8×D73—21no—
45C22⋊Q8×D73—21no—
46C22⋊Q8×D73—21no—
47C22⋊Q8×D73C2212yes—
48C4×Q8×D73—21no—
49C4×Q8×D73—21no—
50C4×Q8×D73—21no—
51C4×Q8×D73C2212yes—
52#117×D73—21no—
53#117×D73C2212yes—
54C2×C42×D73C2211yescharacteristic
55#17988992C2211yescharacteristic, complemented
56#17988991C2214yescomplemented
57#17988990C2211yescharacteristic, complemented
58#17988990C2211yescharacteristic, complemented
59#17988985C2211yescharacteristic, complemented
60#17988984C2214yescomplemented
61#17988983C2211yescharacteristic, complemented
62#17988983C2211yescharacteristic, complemented
63#17988939C2211yescharacteristic, complemented
64#17988939C2211yescharacteristic, complemented
65#17988938C2211yescharacteristic, complemented
66#17988938C2211yescharacteristic, complemented
67#17988937C2211yescharacteristic, complemented
68#17988937C2211yescharacteristic, complemented
69#17988936C2214yescomplemented
70#17988936C2214yescomplemented
71#17988931C2214yes—
72#17988930C2214yes—
73#17988929C2214yes—
74#17988928C2214yes—
75#17988927C2214yes—
76#17988926C2214yes—
77#17988925C2214yes—
78#17988897C2214yescomplemented
79#17988896C2214yescomplemented
80#17988895C2214yescomplemented
81#17988894C2214yescomplemented
82#17988893C2214yescomplemented
83#17988892C2214yescomplemented
84#17988891C2214yescomplemented
85#17988640C2211yescharacteristic
86#17988639C2212yes—
87#17988638C2211yescharacteristic
88#17988638C2211yescharacteristic
89#17988637C2212yes—
90#107×D73C2214yes—
91#106×D73C2214yes—
92C4⋊C8×D73C2212yes—
93#103×D73C2214yes—
94#103×D73C2214yes—
95C22⋊C8×D73C2212yes—
96C4×C8×D73C2211yescharacteristic
97C4×C8×D73C2211yescharacteristic
98#533×C73C2211yescharacteristic
99#533×C73C2211yescharacteristic
100#500×C73C2211yescharacteristic, complemented
101#498×C73C2211yescharacteristic, complemented
102#487×C73C2211yescharacteristic, complemented
103#487×C73C2211yescharacteristic, complemented
104#485×C73C2214yes—
105#479×C73C2214yescomplemented
106#431×C73C2211yescharacteristic
107C2×Q8×D73—21no—
108C2×Q8×D73—21no—
109C2×Q8×D73—21no—
110C2×Q8×D73C2312yes—
111C22×C4×D73D411yescharacteristic
112C22×C4×D73D411yescharacteristic
113C22×C4×D73C2311yescharacteristic
114C2×C8×D73C2312yes—
115C2×C8×D73C2312yes—
116#14556591C2311yescharacteristic
117#14556591C2311yescharacteristic
118#14556591C2311yescharacteristic
119#14556591C2311yescharacteristic
120#14556590—21no—
121#14556590—21no—
122#14556590—21no—
123#14556590—21no—
124#14556590—21no—
125#14556590C2312yes—
126#14556590C2312yes—
127#14556590C2312yes—
128#14556589—21no—
129#14556589—21no—
130#14556589—21no—
131#14556589C2312yes—
132#14556583—21no—
133#14556583C2312yes—
134#14556582—21no—
135#14556582—21no—
136#14556582C2312yes—
137#14556582C2312yes—
138#14556581—22no—
139#14556581—22no—
140#14556581—22no—
141#14556581—22no—
142#14556571—21no—
143#14556571—21no—
144#14556571—21no—
145#14556571C2312yes—
146#14556570—21no—
147#14556570—21no—
148#14556570—21no—
149#14556570C2312yes—
150#14556569—22no—
151#14556569—22no—
152#14556569—22no—
153#14556569—22no—
154#14556568—22no—
155#14556568—22no—
156#14556568—22no—
157#14556568—22no—
158#14556567—21no—
159#14556567—21no—
160#14556567—21no—
161#14556567C2312yes—
162Q8×Dic73—21no—
163Q8×Dic73—21no—
164Q8×Dic73—21no—
165Q8×Dic73C2312yes—
166C4×Dic146—22no—
167C4×Dic146—22no—
168C4×Dic146—22no—
169C4×Dic146—22no—
170C4×Dic146—21no—
171C4×Dic146—21no—
172C4×Dic146—21no—
173C4×Dic146C2312yes—
174#14556556—21no—
175#14556556—21no—
176#14556556—21no—
177#14556556—22no—
178#14556556—22no—
179#14556556—22no—
180#14556556—22no—
181#14556556C2312yes—
182#14556550—21no—
183#14556550C2312yes—
184#14556549—21no—
185#14556549—21no—
186#14556549C2312yes—
187#14556549C2312yes—
188#14556548—22no—
189#14556548—22no—
190#14556547—22no—
191#14556547—22no—
192C4⋊C4×D73—21no—
193C4⋊C4×D73—21no—
194C4⋊C4×D73—21no—
195C4⋊C4×D73—21no—
196C4⋊C4×D73—21no—
197C4⋊C4×D73—22no—
198C4⋊C4×D73—22no—
199C4⋊C4×D73—22no—
200C4⋊C4×D73—22no—
201C4⋊C4×D73C2312yes—
202C4⋊C4×D73C2312yes—
203C4⋊C4×D73C2312yes—
204C22⋊C4×D73—22no—
205C22⋊C4×D73—22no—
206C2×C4×Dic73D411yescharacteristic
207C2×C4×Dic73D411yescharacteristic
208C2×C4×Dic73C2311yescharacteristic
209C42×D73—22no—
210C42×D73—22no—
211C42×D73D411yescharacteristic
212C42×D73D411yescharacteristic
213C42×D73D411yescharacteristic
214C42×D73D411yescharacteristic
215C42×D73C2311yescharacteristic
216C42×D73C2311yescharacteristic
217C42×D73C2311yescharacteristic
218C42×D73C2311yescharacteristic
219#14556525C2314yes—
220#14556524C2314yes—
221#14556524C2314yes—
222#14556523C2314yes—
223#14556522C2314yes—
224#14556522C2314yes—
225C4⋊#10596831C2312yes—
226#14556520C2312yes—
227#14556520C2312yes—
228#14556516C2314yes—
229#14556516C2314yes—
230#14556515C2314yes—
231#14556515C2314yes—
232#14556514C2314yes—
233#14556514C2314yes—
234C22⋊#10596831C2312yes—
235#14556503C2312yes—
236#14556503C2312yes—
237C4×#10596831C2311yescharacteristic
238C4×#10596831C2311yescharacteristic
239C8×Dic73C2312yes—
240C8×Dic73C2312yes—
241C4⋊Q8×C73C2311yescharacteristic
242C4⋊Q8×C73C2311yescharacteristic
243C4⋊Q8×C73C2311yescharacteristic
244C4⋊Q8×C73C2311yescharacteristic
245#125×C73—21no—
246#125×C73C2312yes—
247C22⋊Q8×C73—21no—
248C22⋊Q8×C73—21no—
249C22⋊Q8×C73—21no—
250C22⋊Q8×C73C2312yes—
251C4×Q8×C73—21no—
252C4×Q8×C73—21no—
253C4×Q8×C73—21no—
254C4×Q8×C73C2312yes—
255#117×C73—21no—
256#117×C73C2312yes—
257C2×C42×C73C2311yescharacteristic
258#107×C73C2314yes—
259#106×C73C2314yes—
260C4⋊C8×C73C2312yes—
261#103×C73C2314yes—
262#103×C73C2314yes—
263C22⋊C8×C73C2312yes—
264C4×C8×C73C2311yescharacteristic
265C4×C8×C73C2311yescharacteristic
266C23×D73C2×D411yescharacteristic
267C2×Dic146—21no—
268C2×Dic146—21no—
269C2×Dic146—21no—
270C2×Dic146—22no—
271C2×Dic146—22no—
272C2×Dic146—22no—
273C2×Dic146—22no—
274C2×Dic146C2412yes—
275Q8×D73—28no—
276Q8×D73—44no—
277Q8×D73—44no—
278Q8×D73—44no—
279C22×Dic73C2×D411yescharacteristic
280C22×Dic73C2×D411yescharacteristic
281C22×Dic73C2×D411yescharacteristic
282C2×C4×D73—24no—
283C2×C4×D73—24no—
284C2×C4×D73—24no—
285C2×C4×D73—22no—
286C2×C4×D73—22no—
287C2×C4×D73—22no—
288C2×C4×D73—22no—
289C2×C4×D73C2×D411yescharacteristic
290C2×C4×D73C2×D411yescharacteristic
291C2×C4×D73C2×D411yescharacteristic
292C2×C4×D73C2×D411yescharacteristic
293C2×C4×D73C2×D411yescharacteristic
294C2×C4×D73C2×D411yescharacteristic
295C2×C4×D73C2×D411yescharacteristic
296C2×C4×D73C2×D411yescharacteristic
297C2×C4×D73C2×D411yescharacteristic
298C2×C4×D73C2×D411yescharacteristic
299C2×C4×D73C2411yescharacteristic
300C2×C4×D73C2411yescharacteristic
301C2×#10596831C2412yes—
302C2×#10596831C2412yes—
303C8×D73—24no—
304C8×D73—24no—
305C4⋊Dic73—21no—
306C4⋊Dic73—21no—
307C4⋊Dic73—21no—
308C4⋊Dic73—21no—
309C4⋊Dic73—21no—
310C4⋊Dic73—22no—
311C4⋊Dic73—22no—
312C4⋊Dic73—22no—
313C4⋊Dic73—22no—
314C4⋊Dic73C2412yes—
315C4⋊Dic73C2412yes—
316C4⋊Dic73C2412yes—
317#11924007—22no—
318#11924007—22no—
319#11924007—22no—
320#11924007—22no—
321#11924007—22no—
322#11924007—22no—
323#11924007—22no—
324#11924007—22no—
325#11924007—22no—
326#11924007—22no—
327#11924007—22no—
328#11924007—22no—
329#11924007—22no—
330#11924007—22no—
331#11924007—22no—
332#11924007—22no—
333C22⋊Dic73—22no—
334C22⋊Dic73—22no—
335#11924005—22no—
336#11924005—22no—
337#11924005—22no—
338#11924005—22no—
339C4×Dic73—22no—
340C4×Dic73—22no—
341C4×Dic73—22no—
342C4×Dic73—22no—
343C4×Dic73—22no—
344C4×Dic73—22no—
345C4×Dic73C2×D411yescharacteristic
346C4×Dic73C2×D411yescharacteristic
347C4×Dic73C2×D411yescharacteristic
348C4×Dic73C2×D411yescharacteristic
349C4×Dic73C2×D411yescharacteristic
350C4×Dic73C2×D411yescharacteristic
351C4×Dic73C2×D411yescharacteristic
352C4×Dic73C2×D411yescharacteristic
353C4×Dic73C2×D411yescharacteristic
354C4×Dic73C2×D411yescharacteristic
355C4×Dic73C2411yescharacteristic
356C4×Dic73C2411yescharacteristic
357C2×Q8×C73—21no—
358C2×Q8×C73—21no—
359C2×Q8×C73—21no—
360C2×Q8×C73C2412yes—
361C22×C4×C73C2×D411yescharacteristic
362C22×C4×C73C2×D411yescharacteristic
363C22×C4×C73C2411yescharacteristic
364C2×C8×C73C2412yes—
365C2×C8×C73C2412yes—
366C4⋊C4×C73—21no—
367C4⋊C4×C73—21no—
368C4⋊C4×C73—22no—
369C4⋊C4×C73—22no—
370C4⋊C4×C73—21no—
371C4⋊C4×C73—21no—
372C4⋊C4×C73—21no—
373C4⋊C4×C73—22no—
374C4⋊C4×C73—22no—
375C4⋊C4×C73C2412yes—
376C4⋊C4×C73C2412yes—
377C4⋊C4×C73C2412yes—
378C22⋊C4×C73—22no—
379C22⋊C4×C73—22no—
380C42×C73—22no—
381C42×C73—22no—
382C42×C73C2×D411yescharacteristic
383C42×C73C2×D411yescharacteristic
384C42×C73C2411yescharacteristic
385C42×C73C2411yescharacteristic
386C23×C73C22×D411yescharacteristic
387C22×D73—22no—
388C22×D73—22no—
389C22×D73—22no—
390C22×D73C22×D411yescharacteristic
391C22×D73C22×D411yescharacteristic
392Q8×C73—24no—
393Q8×C73—42no—
394Q8×C73—42no—
395Q8×C73—42no—
396C2×C4×C73—22no—
397C2×C4×C73—22no—
398C2×C4×C73—22no—
399C2×C4×C73—22no—
400C2×C4×C73—22no—
401C2×C4×C73—22no—
402C2×C4×C73—22no—
403C2×C4×C73C22×D411yescharacteristic
404C2×C4×C73C22×D411yescharacteristic
405C2×C4×C73C22×D411yescharacteristic
406C2×C4×C73C22×D411yescharacteristic
407C2×C4×C73C22×D411yescharacteristic
408C2×C4×C73C2511yescharacteristic
409C2×Dic73—22no—
410C2×Dic73—22no—
411C2×Dic73—22no—
412C2×Dic73—22no—
413C2×Dic73—22no—
414C2×Dic73—22no—
415C2×Dic73—22no—
416C2×Dic73C22×D411yescharacteristic
417C2×Dic73C22×D411yescharacteristic
418C2×Dic73C22×D411yescharacteristic
419C2×Dic73C22×D411yescharacteristic
420C2×Dic73C22×D411yescharacteristic
421C2×Dic73C22×D411yescharacteristic
422C4×D73—22no—
423C4×D73—22no—
424C4×D73—22no—
425C4×D73—22no—
426C4×D73—22no—
427C4×D73—22no—
428C4×D73—22no—
429C4×D73—22no—
430C4×D73—22no—
431C4×D73—44no—
432C4×D73—44no—
433C4×D73—44no—
434C4×D73—44no—
435C4×D73#13514yes—
436C4×D73#13714yes—
437C4×D732−1+414yes—
438Dic146—24no—
439Dic146—42no—
440Dic146—42no—
441Dic146—42no—
442Dic146—44no—
443Dic146—44no—
444Dic146—44no—
445Dic146—44no—
446C8×C73—22no—
447C8×C73—22no—
448#10596831—22no—
449#10596831—22no—
450C22×C73—21no—
451C22×C73—21no—
452C22×C73—21no—
453C22×C73C23×D411yescharacteristic
454C2×D73—21no—
455C2×D73—21no—
456C2×D73—21no—
457C2×D73—44no—
458C2×D73#53612yes—
459C2×D73C2×#13512yes—
460C2×D73C2×#13712yes—
461C4×C73—21no—
462C4×C73—21no—
463C4×C73—21no—
464C4×C73—42no—
465C4×C73—42no—
466C4×C73—42no—
467C4×C73—42no—
468C4×C73C2×#13512yes—
469C4×C73C2×#13712yes—
470C4×C73C2×2−1+412yes—
471Dic73—21no—
472Dic73—21no—
473Dic73—21no—
474Dic73—42no—
475Dic73—42no—
476Dic73—42no—
477Dic73—42no—
478Dic73#53612yes—
479Dic73C2×#13512yes—
480Dic73C2×#13712yes—
481C2×#3231—731nomaximal, Sylow
482C2×C73—41no—
483C2×C73C2×#53611yescharacteristic
484C2×C73C22×#13511yescharacteristic
485C2×C73C22×#13711yescharacteristic
486D73—41no—
487D73#323114yesdirect product factor
488C2×#533—731no—
489C2×#533—731no—
490#3231—731no—
491#3231—731no—
492#3231—731no—
493#3231—731no—
494#3231—734no—
495#3231—734no—
496#3231—731no—
497#3231—731no—
498#3231—731no—
499#3231D7311yescharacteristic, direct product factor
500C2×#500—731no—
501C2×#498—731no—
502C2×#487—731no—
503C2×#487—731no—
504C2×#485—734no—
505C2×#479—734no—
506C2×#431—731no—
507C73C2×#323111yescharacteristic, complemented, Sylow
508#533—731no—
509#533—731no—
510#533—732no—
511#533—732no—
512#533—731no—
513#533—731no—
514#533—732no—
515#533—732no—
516#533—731no—
517#533—731no—
518#533—1461no—
519#533—1461no—
520#533—1461no—
521#533—1461no—
522#533—1461no—
523#533—1461no—
524#533—1461no—
525#533—1461no—
526#533C2×D7311yescharacteristic
527#533C2×D7311yescharacteristic
528C2×C4⋊Q8—731no—
529C2×C4⋊Q8—731no—
530C2×C4⋊Q8—731no—
531C2×C4⋊Q8—731no—
532C2×#125—732no—
533C2×#125—1461no—
534C2×C22⋊Q8—732no—
535C2×C22⋊Q8—1461no—
536C2×C22⋊Q8—1461no—
537C2×C22⋊Q8—1461no—
538C2×C4×Q8—732no—
539C2×C4×Q8—1461no—
540C2×C4×Q8—1461no—
541C2×C4×Q8—1461no—
542C2×#117—732no—
543C2×#117—1461no—
544C22×C42—731no—
545#500—731no—
546#500—731no—
547#500—734no—
548#500—731no—
549#500C2×D7311yescharacteristic, complemented
550#498—731no—
551#498—731no—
552#498—734no—
553#498—731no—
554#498C2×D7311yescharacteristic, complemented
555#487—731no—
556#487—731no—
557#487—731no—
558#487—731no—
559#487—734no—
560#487—734no—
561#487—731no—
562#487—731no—
563#487C2×D7311yescharacteristic, complemented
564#487C2×D7311yescharacteristic, complemented
565#485—734no—
566#485—734no—
567#485—734no—
568#485—734no—
569#485—734no—
570#485—734no—
571#485—734no—
572#485C2×D7314yes—
573#479—734no—
574#479—734no—
575#479—734no—
576#479—734no—
577#479—734no—
578#479—734no—
579#479—734no—
580#479C2×D7314yescomplemented
581#431—731no—
582#431—732no—
583#431—732no—
584#431—731no—
585#431—731no—
586#431C2×D7311yescharacteristic
587C2×#107—734no—
588C2×#106—734no—
589C2×C4⋊C8—732no—
590C2×#103—734no—
591C2×#103—734no—
592C2×C22⋊C8—732no—
593C2×C4×C8—731no—
594C2×C4×C8—731no—
595C22×Q8—732no—
596C22×Q8—1461no—
597C22×Q8—1461no—
598C22×Q8—1461no—
599C23×C4—731no—
600C23×C4—731no—
601C23×C4—731no—
602C22×C8—732no—
603C22×C8—732no—
604C4⋊Q8—732no—
605C4⋊Q8—732no—
606C4⋊Q8—732no—
607C4⋊Q8—732no—
608C4⋊Q8—731no—
609C4⋊Q8—731no—
610C4⋊Q8—731no—
611C4⋊Q8—731no—
612C4⋊Q8—1461no—
613C4⋊Q8—1461no—
614C4⋊Q8—1461no—
615C4⋊Q8—1461no—
616C4⋊Q8—1461no—
617C4⋊Q8—1461no—
618C4⋊Q8—1461no—
619C4⋊Q8—1461no—
620C4⋊Q8C22×D7311yescharacteristic
621C4⋊Q8C22×D7311yescharacteristic
622C4⋊Q8C22×D7311yescharacteristic
623C4⋊Q8C22×D7311yescharacteristic
624#125—21no—
625#125—732no—
626#125—732no—
627#125—732no—
628#125—1462no—
629#125—1462no—
630#125—1462no—
631#125—1462no—
632#125—1461no—
633#125—1461no—
634#125—1461no—
635#125C22×D7312yes—
636C22⋊Q8—21no—
637C22⋊Q8—21no—
638C22⋊Q8—21no—
639C22⋊Q8—732no—
640C22⋊Q8—732no—
641C22⋊Q8—732no—
642C22⋊Q8—1462no—
643C22⋊Q8—1462no—
644C22⋊Q8—1462no—
645C22⋊Q8—1462no—
646C22⋊Q8—1462no—
647C22⋊Q8—1462no—
648C22⋊Q8—1462no—
649C22⋊Q8—1462no—
650C22⋊Q8—1461no—
651C22⋊Q8—1461no—
652C22⋊Q8—1461no—
653C22⋊Q8—1461no—
654C22⋊Q8—1461no—
655C22⋊Q8—1461no—
656C22⋊Q8—1461no—
657C22⋊Q8—1461no—
658C22⋊Q8—1461no—
659C22⋊Q8C22×D7312yes—
660C4×Q8—21no—
661C4×Q8—21no—
662C4×Q8—21no—
663C4×Q8—732no—
664C4×Q8—732no—
665C4×Q8—732no—
666C4×Q8—1462no—
667C4×Q8—1462no—
668C4×Q8—1462no—
669C4×Q8—1462no—
670C4×Q8—1462no—
671C4×Q8—1462no—
672C4×Q8—1461no—
673C4×Q8—1461no—
674C4×Q8—1462no—
675C4×Q8—1462no—
676C4×Q8—1461no—
677C4×Q8—1461no—
678C4×Q8—1461no—
679C4×Q8—1461no—
680C4×Q8—1461no—
681C4×Q8—1461no—
682C4×Q8—1461no—
683C4×Q8C22×D7312yes—
684#117—21no—
685#117—732no—
686#117—732no—
687#117—732no—
688#117—1462no—
689#117—1462no—
690#117—1462no—
691#117—1462no—
692#117—1461no—
693#117—1461no—
694#117—1461no—
695#117C22×D7312yes—
696C2×C4⋊C4—732no—
697C2×C4⋊C4—732no—
698C2×C4⋊C4—732no—
699C2×C4⋊C4—1461no—
700C2×C4⋊C4—1461no—
701C2×C4⋊C4—1462no—
702C2×C4⋊C4—1462no—
703C2×C4⋊C4—1462no—
704C2×C4⋊C4—1462no—
705C2×C4⋊C4—1461no—
706C2×C4⋊C4—1461no—
707C2×C4⋊C4—1461no—
708C2×C22⋊C4—1462no—
709C2×C22⋊C4—1462no—
710C2×C42—731no—
711C2×C42—731no—
712C2×C42—731no—
713C2×C42—731no—
714C2×C42—731no—
715C2×C42—731no—
716C2×C42—731no—
717C2×C42—731no—
718C2×C42—731no—
719C2×C42—731no—
720C2×C42—731no—
721C2×C42—1462no—
722C2×C42—1462no—
723C2×C42C22×D7311yescharacteristic
724#107—734no—
725#107—734no—
726#107—734no—
727#107C22×D7314yes—
728#106—734no—
729#106—734no—
730#106—734no—
731#106C22×D7314yes—
732C4⋊C8—732no—
733C4⋊C8—732no—
734C4⋊C8—732no—
735C4⋊C8C22×D7312yes—
736#103—734no—
737#103—734no—
738#103—734no—
739#103—734no—
740#103—734no—
741#103—734no—
742#103C22×D7314yes—
743#103C22×D7314yes—
744C22⋊C8—732no—
745C22⋊C8—732no—
746C22⋊C8—732no—
747C22⋊C8C22×D7312yes—
748C4×C8—732no—
749C4×C8—732no—
750C4×C8—731no—
751C4×C8—731no—
752C4×C8C22×D7311yescharacteristic
753C4×C8C22×D7311yescharacteristic
754C24—731no—
755C2×Q8—21no—
756C2×Q8—21no—
757C2×Q8—21no—
758C2×Q8—2924no—
759C2×Q8—2924no—
760C2×Q8—2924no—
761C2×Q8—732no—
762C2×Q8—1462no—
763C2×Q8—1462no—
764C2×Q8—1462no—
765C2×Q8—1462no—
766C2×Q8—1468no—
767C2×Q8—1461no—
768C2×Q8—1461no—
769C2×Q8—1461no—
770C2×Q8C23×D7312yes—
771C22×C4—731no—
772C22×C4—731no—
773C22×C4—731no—
774C22×C4—731no—
775C22×C4—731no—
776C22×C4—731no—
777C22×C4—731no—
778C22×C4—731no—
779C22×C4—731no—
780C22×C4—731no—
781C22×C4—731no—
782C22×C4—731no—
783C22×C4—731no—
784C22×C4—731no—
785C22×C4—731no—
786C22×C4—1462no—
787C22×C4—1462no—
788C22×C4—1462no—
789C22×C4—1462no—
790C22×C4—1464no—
791C22×C4—1464no—
792C22×C4—1464no—
793C22×C4D4×D7311yescharacteristic
794C22×C4D4×D7311yescharacteristic
795C22×C4C23×D7311yescharacteristic
796C2×C8—732no—
797C2×C8—732no—
798C2×C8—1464no—
799C2×C8—1464no—
800C2×C8C23×D7312yes—
801C2×C8C23×D7312yes—
802C4⋊C4—21no—
803C4⋊C4—21no—
804C4⋊C4—22no—
805C4⋊C4—22no—
806C4⋊C4—21no—
807C4⋊C4—21no—
808C4⋊C4—21no—
809C4⋊C4—22no—
810C4⋊C4—22no—
811C4⋊C4—732no—
812C4⋊C4—732no—
813C4⋊C4—732no—
814C4⋊C4—1462no—
815C4⋊C4—1462no—
816C4⋊C4—1462no—
817C4⋊C4—1462no—
818C4⋊C4—1462no—
819C4⋊C4—1462no—
820C4⋊C4—1462no—
821C4⋊C4—1462no—
822C4⋊C4—1462no—
823C4⋊C4—1462no—
824C4⋊C4—1462no—
825C4⋊C4—1462no—
826C4⋊C4—1462no—
827C4⋊C4—1462no—
828C4⋊C4—1462no—
829C4⋊C4—1462no—
830C4⋊C4—1462no—
831C4⋊C4—1462no—
832C4⋊C4—1462no—
833C4⋊C4—1462no—
834C4⋊C4—1461no—
835C4⋊C4—1461no—
836C4⋊C4—1461no—
837C4⋊C4—1461no—
838C4⋊C4—1461no—
839C4⋊C4C23×D7312yes—
840C4⋊C4C23×D7312yes—
841C4⋊C4C23×D7312yes—
842C22⋊C4—22no—
843C22⋊C4—22no—
844C22⋊C4—1462no—
845C22⋊C4—1462no—
846C22⋊C4—1462no—
847C22⋊C4—1462no—
848C22⋊C4—1462no—
849C22⋊C4—1462no—
850C42—22no—
851C42—22no—
852C42—731no—
853C42—731no—
854C42—731no—
855C42—731no—
856C42—731no—
857C42—731no—
858C42—731no—
859C42—731no—
860C42—731no—
861C42—731no—
862C42—731no—
863C42—731no—
864C42—1462no—
865C42—1462no—
866C42—1462no—
867C42—1462no—
868C42—1462no—
869C42—1462no—
870C42D4×D7311yescharacteristic
871C42D4×D7311yescharacteristic
872C42C23×D7311yescharacteristic
873C42C23×D7311yescharacteristic
874C23—731no—
875C23—731no—
876C23—1462no—
877C23—1462no—
878C23—1462no—
879C23C2×D4×D7311yescharacteristic
880Q8—24no—
881Q8—42no—
882Q8—42no—
883Q8—42no—
884Q8—2924no—
885Q8—2924no—
886Q8—2924no—
887Q8—2924no—
888Q8—2922no—
889Q8—2922no—
890Q8—2922no—
891Q8—1464no—
892C2×C4—22no—
893C2×C4—22no—
894C2×C4—22no—
895C2×C4—22no—
896C2×C4—22no—
897C2×C4—22no—
898C2×C4—22no—
899C2×C4—2924no—
900C2×C4—2924no—
901C2×C4—2924no—
902C2×C4—2924no—
903C2×C4—731no—
904C2×C4—731no—
905C2×C4—731no—
906C2×C4—734no—
907C2×C4—734no—
908C2×C4—734no—
909C2×C4—731no—
910C2×C4—731no—
911C2×C4—731no—
912C2×C4—1462no—
913C2×C4—1462no—
914C2×C4—1462no—
915C2×C4—1462no—
916C2×C4—1462no—
917C2×C4—1462no—
918C2×C4—1462no—
919C2×C4—1462no—
920C2×C4—1462no—
921C2×C4—1462no—
922C2×C4—1462no—
923C2×C4—1462no—
924C2×C4—1462no—
925C2×C4—1462no—
926C2×C4—1462no—
927C2×C4—1462no—
928C2×C4C2×D4×D7311yescharacteristic
929C2×C4C2×D4×D7311yescharacteristic
930C2×C4C2×D4×D7311yescharacteristic
931C2×C4C2×D4×D7311yescharacteristic
932C2×C4C2×D4×D7311yescharacteristic
933C2×C4C24×D7311yescharacteristic
934C8—22no—
935C8—22no—
936C8—1462no—
937C8—1462no—
938C22—21no—
939C22—21no—
940C22—21no—
941C22—2924no—
942C22—732no—
943C22—732no—
944C22—732no—
945C22—1461no—
946C22—1461no—
947C22—1461no—
948C22C22×D4×D7311yescharacteristic
949C4—21no—
950C4—21no—
951C4—21no—
952C4—42no—
953C4—42no—
954C4—42no—
955C4—42no—
956C4—2922no—
957C4—2922no—
958C4—2922no—
959C4—2922no—
960C4—732no—
961C4—732no—
962C4—732no—
963C4—1461no—
964C4—1461no—
965C4—1461no—
966C4#135×D7312yes—
967C4#137×D7312yes—
968C42−1+4×D7312yes—
969C2—41no—
970C2—2921no—
971C2—734no—
972C2#536×D7311yescharacteristic
973C2C2×#135×D7311yescharacteristic
974C2C2×#137×D7311yescharacteristic
subgroupG/H
centerC22C22×D4×D73
commutator, cosocleC2×C4×C73C25
FrattiniC2×C4C24×D73
FittingC73×#3231C2
socleC22×C73C23×D4
prime radicalC23×D73C2×D4
hypercenter#3231D73
hypocenterC73C2×#3231
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3231

Complements

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

NH ≅ G/Ntype
3. #22621093C2semidirect
4. #22621092C2semidirect
5. #22621091C2semidirect
6. #22621090C2semidirect
7. #22621089C2semidirect
8. #22621088C2semidirect
9. #22621087C2semidirect
10. #22621086C2semidirect
11. #22621085C2semidirect
12. #500×D73C2semidirect
13. #498×D73C2semidirect
14. #487×D73C2semidirect
15. #487×D73C2semidirect
17. #479×D73C2semidirect
19. C73×#3231C2semidirect
55. #17988992C22semidirect
56. #17988991C22semidirect
57. #17988990C22semidirect
58. #17988990C22semidirect
59. #17988985C22semidirect
60. #17988984C22semidirect
61. #17988983C22semidirect
62. #17988983C22semidirect
63. #17988939C22semidirect
64. #17988939C22semidirect
65. #17988938C22semidirect
66. #17988938C22semidirect
67. #17988937C22semidirect
68. #17988937C22semidirect
69. #17988936C22semidirect
70. #17988936C22semidirect
78. #17988897C22semidirect
79. #17988896C22semidirect
80. #17988895C22semidirect
81. #17988894C22semidirect
82. #17988893C22semidirect
83. #17988892C22semidirect
84. #17988891C22semidirect
100. #500×C73C22semidirect
101. #498×C73C22semidirect
102. #487×C73C22semidirect
103. #487×C73C22semidirect
105. #479×C73C22semidirect
487. D73#3231direct (N × H)
499. #3231D73direct (N × H)
507. C73C2×#3231semidirect
549. #500C2×D73semidirect
554. #498C2×D73semidirect
563. #487C2×D73semidirect
564. #487C2×D73semidirect
580. #479C2×D73semidirect

Maximal subgroups

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

subgroupindex
#533×D732
#226210932
#226210922
#226210912
#226210902
#226210892
#226210882
#226210872
#226210862
#226210852
#500×D732
#498×D732
#487×D732
#485×D732
#479×D732
#431×D732
C73×#32312
C2×#323173