Finite Group Databasebeta

← #3228×D73 #33958036

Subgroups — #3228×D73 #33958036

Order 18688.

2058 conjugacy classes of subgroups.

The subgroup lattice has 1044 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#533×D73C211yesmaximal, characteristic, complemented
2#532×D73C211yesmaximal, characteristic
3#22621070C211yesmaximal, characteristic, complemented
4#22621069C211yesmaximal, characteristic, complemented
5#22621068C211yesmaximal, characteristic, complemented
6#22621067C211yesmaximal, characteristic, complemented
7#22621066C214yesmaximal, complemented
8#22621065C214yesmaximal, complemented
9#22621064C211yesmaximal, characteristic, complemented
10#22621063C211yesmaximal, characteristic, complemented
11#22621062C211yesmaximal, characteristic, complemented
12#500×D73C211yesmaximal, characteristic, complemented
13#498×D73C211yesmaximal, characteristic, complemented
14#486×D73C211yesmaximal, characteristic, complemented
15#486×D73C211yesmaximal, characteristic, complemented
16#482×D73C214yesmaximal, complemented
17#478×D73C214yesmaximal, complemented
18#431×D73C211yesmaximal, characteristic, complemented
19C73×#3228C211yesmaximal, characteristic, complemented
20C2×#41×D73—21no—
21#17989144C2211yescharacteristic, complemented
22#17989143C2212yescomplemented
23#17989142C2211yescharacteristic, complemented
24#17989142C2211yescharacteristic, complemented
25#17989141—21no—
26#17989141—21no—
27#17989140C2212yescomplemented
28#17989139—21no—
29#17989139—21no—
30#17989138C2211yescharacteristic
31#17989137C2211yescharacteristic
32#17989136—21no—
33#17989135C2211yescharacteristic
34#17989134—21no—
35#17989134C2212yes—
36#17989133—21no—
37#17989132—21no—
38#17989132C2212yes—
39C4⋊Q8×D73C2211yescharacteristic
40C4⋊Q8×D73C2211yescharacteristic
41C4⋊Q8×D73C2211yescharacteristic
42#127×D73C2211yescharacteristic
43#125×D73C2212yes—
44#124×D73—21no—
45C22⋊Q8×D73—21no—
46C22⋊Q8×D73—21no—
47#121×D73—21no—
48#121×D73C2212yes—
49C4×Q8×D73—21no—
50C4×Q8×D73—21no—
51C4×D4×D73—21no—
52C4×D4×D73C2212yes—
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#17988935C2211yescharacteristic, complemented
64#17988935C2211yescharacteristic, complemented
65#17988934C2211yescharacteristic, complemented
66#17988934C2211yescharacteristic, complemented
67#17988933C2211yescharacteristic, complemented
68#17988933C2211yescharacteristic, complemented
69#17988932C2214yescomplemented
70#17988932C2214yescomplemented
71#17988914C2214yescomplemented
72#17988913C2214yescomplemented
73#17988912C2214yescomplemented
74#17988911C2214yescomplemented
75#17988910C2214yescomplemented
76#17988909C2214yescomplemented
77#17988908C2214yescomplemented
78#17988890C2214yescomplemented
79#17988889C2214yescomplemented
80#17988888C2214yescomplemented
81#17988887C2214yescomplemented
82#17988886C2214yescomplemented
83#17988885C2214yescomplemented
84#17988884C2214yescomplemented
85#17988640C2211yescharacteristic, complemented
86#17988639C2212yescomplemented
87#17988638C2211yescharacteristic, complemented
88#17988638C2211yescharacteristic, complemented
89#17988637C2212yescomplemented
90#107×D73C2214yes—
91#106×D73C2214yes—
92C4⋊C8×D73C2212yes—
93#102×D73C2214yes—
94#102×D73C2214yes—
95C22⋊C8×D73C2212yes—
96C4×C8×D73C2211yescharacteristic
97C4×C8×D73C2211yescharacteristic
98#533×C73C2211yescharacteristic, complemented
99#532×C73C2211yescharacteristic
100#500×C73C2211yescharacteristic, complemented
101#498×C73C2211yescharacteristic, complemented
102#486×C73C2211yescharacteristic, complemented
103#486×C73C2211yescharacteristic, complemented
104#482×C73C2214yescomplemented
105#478×C73C2214yescomplemented
106#431×C73C2211yescharacteristic, complemented
107C2×#11924029—21no—
108C2×#11924028—22no—
109C2×#11924028—21no—
110C2×#11924027—22no—
111C2×#11924027—21no—
112#41×D73—48no—
113C2×Q8×D73—21no—
114C2×Q8×D73—21no—
115C2×Q8×D73—21no—
116C2×D4×D73—22no—
117C2×D4×D73—21no—
118C2×D4×D73—21no—
119C2×D4×D73C2312yes—
120C22×C4×D73—22no—
121C22×C4×D73D411yescharacteristic
122C22×C4×D73D411yescharacteristic
123C22×C4×D73C2311yescharacteristic
124C2×C8×D73C2312yes—
125C2×C8×D73C2312yes—
126#14556591C2311yescharacteristic
127#14556591C2311yescharacteristic
128#14556591C2311yescharacteristic
129#14556590—21no—
130#14556590—21no—
131#14556590—21no—
132#14556590C2312yes—
133#14556590C2312yes—
134#14556590C2312yes—
135#14556589—21no—
136#14556589—21no—
137#14556589—21no—
138#14556588C2311yescharacteristic
139#14556587—21no—
140#14556587—21no—
141#14556587C2312yes—
142#14556583C2312yes—
143#14556582C2312yes—
144#14556582C2312yes—
145#14556581—22no—
146#14556581—22no—
147#14556580—21no—
148#14556579—21no—
149#14556578—21no—
150#14556577—22no—
151#14556577—22no—
152#14556571—21no—
153#14556571—21no—
154#14556570—21no—
155#14556570—21no—
156#14556569—22no—
157#14556569—22no—
158#14556568—22no—
159#14556568—22no—
160#14556567—21no—
161#14556567—21no—
162#14556566—21no—
163#14556566C2312yes—
164#14556565—21no—
165#14556565C2312yes—
166#14556564—22no—
167#14556564—22no—
168#14556563—22no—
169#14556563—22no—
170#14556562—21no—
171#14556562C2312yes—
172Q8×Dic73—21no—
173Q8×Dic73—21no—
174C4×Dic146—22no—
175C4×Dic146—22no—
176C4×Dic146—21no—
177C4×Dic146—21no—
178#14556556—21no—
179#14556556—21no—
180#14556556—22no—
181#14556556—22no—
182C4×D292—21no—
183C4×D292C2312yes—
184D4×Dic73—21no—
185D4×Dic73C2312yes—
186#14556553—21no—
187#14556553C2312yes—
188C4×C22⋊D73—22no—
189C4×C22⋊D73—22no—
190#14556551—22no—
191#14556551—22no—
192#14556550C2312yes—
193#14556549C2312yes—
194#14556549C2312yes—
195#14556548—22no—
196#14556547—22no—
197C4⋊C4×D73—21no—
198C4⋊C4×D73—21no—
199C4⋊C4×D73—21no—
200C4⋊C4×D73—22no—
201C4⋊C4×D73—22no—
202C4⋊C4×D73C2312yes—
203C4⋊C4×D73C2312yes—
204C4⋊C4×D73C2312yes—
205C22⋊C4×D73—22no—
206C22⋊C4×D73—22no—
207C22⋊C4×D73—22no—
208C2×C4×Dic73D411yescharacteristic
209C2×C4×Dic73D411yescharacteristic
210C2×C4×Dic73C2311yescharacteristic
211C42×D73—22no—
212C42×D73D411yescharacteristic
213C42×D73D411yescharacteristic
214C42×D73D411yescharacteristic
215C42×D73D411yescharacteristic
216C42×D73C2311yescharacteristic
217C42×D73C2311yescharacteristic
218C42×D73C2311yescharacteristic
219C42×D73C2311yescharacteristic
220#14556525C2314yes—
221#14556524C2314yes—
222#14556524C2314yes—
223#14556523C2314yes—
224#14556522C2314yes—
225#14556522C2314yes—
226C4⋊#10596831C2312yes—
227#14556520C2312yes—
228#14556520C2312yes—
229#14556513C2314yes—
230#14556513C2314yes—
231#14556512C2314yes—
232#14556512C2314yes—
233#14556511C2314yes—
234#14556511C2314yes—
235C22⋊#10596831C2312yes—
236#14556503C2312yes—
237#14556503C2312yes—
238C4×#10596831C2311yescharacteristic
239C4×#10596831C2311yescharacteristic
240C8×Dic73C2312yes—
241C8×Dic73C2312yes—
242C2×#41×C73—21no—
243C4⋊Q8×C73C2311yescharacteristic
244C4⋊Q8×C73C2311yescharacteristic
245C4⋊Q8×C73C2311yescharacteristic
246#127×C73C2311yescharacteristic
247#125×C73C2312yes—
248#124×C73—21no—
249C22⋊Q8×C73—21no—
250C22⋊Q8×C73—21no—
251#121×C73—21no—
252#121×C73C2312yes—
253C4×Q8×C73—21no—
254C4×Q8×C73—21no—
255C4×D4×C73—21no—
256C4×D4×C73C2312yes—
257#117×C73C2312yes—
258C2×C42×C73C2311yescharacteristic
259#107×C73C2314yes—
260#106×C73C2314yes—
261C4⋊C8×C73C2312yes—
262#102×C73C2314yes—
263#102×C73C2314yes—
264C22⋊C8×C73C2312yes—
265C4×C8×C73C2311yescharacteristic
266C4×C8×C73C2311yescharacteristic
267C23×D73—22no—
268C23×D73C2×D411yescharacteristic
269#11924029—44no—
270#11924028—48no—
271#11924028—44no—
272#11924027—44no—
273#11924027—48no—
274C2×Dic146—21no—
275C2×Dic146—21no—
276C2×Dic146—21no—
277C2×Dic146—22no—
278C2×Dic146—22no—
279C2×Dic146—22no—
280Q8×D73—44no—
281Q8×D73—44no—
282Q8×D73—44no—
283C2×D292—22no—
284C2×D292—21no—
285C2×D292—21no—
286C2×D292C2412yes—
287C2×C22⋊D73—22no—
288C2×C22⋊D73—22no—
289C2×C22⋊D73—22no—
290C2×C22⋊D73—22no—
291C2×C22⋊D73—22no—
292D4×D73—28no—
293D4×D73—48no—
294D4×D73—44no—
295D4×D73—44no—
296C22×Dic73—22no—
297C22×Dic73C2×D411yescharacteristic
298C22×Dic73C2×D411yescharacteristic
299C22×Dic73C2×D411yescharacteristic
300C2×C4×D73—24no—
301C2×C4×D73—24no—
302C2×C4×D73—24no—
303C2×C4×D73—22no—
304C2×C4×D73—22no—
305C2×C4×D73—22no—
306C2×C4×D73—22no—
307C2×C4×D73—22no—
308C2×C4×D73—48no—
309C2×C4×D73C2×D411yescharacteristic
310C2×C4×D73C2×D411yescharacteristic
311C2×C4×D73C2×D411yescharacteristic
312C2×C4×D73C2×D411yescharacteristic
313C2×C4×D73C2×D411yescharacteristic
314C2×C4×D73C2×D411yescharacteristic
315C2×C4×D73C2×D411yescharacteristic
316C2×C4×D73C2×D411yescharacteristic
317C2×C4×D73C2×D411yescharacteristic
318C2×C4×D73C2×D411yescharacteristic
319C2×C4×D73C2411yescharacteristic
320C2×C4×D73C2411yescharacteristic
321C2×#10596831C2412yes—
322C2×#10596831C2412yes—
323C8×D73—24no—
324C8×D73—24no—
325C4⋊Dic73—21no—
326C4⋊Dic73—21no—
327C4⋊Dic73—21no—
328C4⋊Dic73—22no—
329C4⋊Dic73—22no—
330C4⋊Dic73C2412yes—
331C4⋊Dic73C2412yes—
332C4⋊Dic73C2412yes—
333#11924007—22no—
334#11924007—22no—
335#11924007—22no—
336#11924007—22no—
337#11924007—22no—
338#11924007—22no—
339#11924007—22no—
340#11924007—22no—
341#11924007—22no—
342#11924007—22no—
343C22⋊Dic73—22no—
344C22⋊Dic73—22no—
345C22⋊Dic73—22no—
346#11924005—22no—
347#11924005—22no—
348#11924005—22no—
349#11924005—22no—
350#11924005—22no—
351#11924005—22no—
352C4×Dic73—22no—
353C4×Dic73—22no—
354C4×Dic73—22no—
355C4×Dic73C2×D411yescharacteristic
356C4×Dic73C2×D411yescharacteristic
357C4×Dic73C2×D411yescharacteristic
358C4×Dic73C2×D411yescharacteristic
359C4×Dic73C2×D411yescharacteristic
360C4×Dic73C2×D411yescharacteristic
361C4×Dic73C2×D411yescharacteristic
362C4×Dic73C2×D411yescharacteristic
363C4×Dic73C2×D411yescharacteristic
364C4×Dic73C2×D411yescharacteristic
365C4×Dic73C2411yescharacteristic
366C4×Dic73C2411yescharacteristic
367#41×C73—44no—
368C2×Q8×C73—21no—
369C2×Q8×C73—21no—
370C2×Q8×C73—21no—
371C2×D4×C73—22no—
372C2×D4×C73—21no—
373C2×D4×C73—21no—
374C2×D4×C73C2412yes—
375C22×C4×C73—22no—
376C22×C4×C73C2×D411yescharacteristic
377C22×C4×C73C2×D411yescharacteristic
378C22×C4×C73C2411yescharacteristic
379C2×C8×C73C2412yes—
380C2×C8×C73C2412yes—
381C4⋊C4×C73—21no—
382C4⋊C4×C73—22no—
383C4⋊C4×C73—22no—
384C4⋊C4×C73—21no—
385C4⋊C4×C73—21no—
386C4⋊C4×C73C2412yes—
387C4⋊C4×C73C2412yes—
388C4⋊C4×C73C2412yes—
389C22⋊C4×C73—22no—
390C22⋊C4×C73—22no—
391C22⋊C4×C73—22no—
392C42×C73—22no—
393C42×C73C2×D411yescharacteristic
394C42×C73C2×D411yescharacteristic
395C42×C73C2411yescharacteristic
396C42×C73C2411yescharacteristic
397C23×C73—22no—
398C23×C73C22×D411yescharacteristic
399C22×D73—22no—
400C22×D73—22no—
401C22×D73—22no—
402C22×D73—22no—
403C22×D73—44no—
404C22×D73—44no—
405C22×D73—44no—
406C22×D73C22×D411yescharacteristic
407C22×D73C22×D411yescharacteristic
408Q8×C73—42no—
409Q8×C73—42no—
410Q8×C73—42no—
411D4×C73—24no—
412D4×C73—44no—
413D4×C73—42no—
414D4×C73—42no—
415C2×C4×C73—22no—
416C2×C4×C73—22no—
417C2×C4×C73—22no—
418C2×C4×C73—22no—
419C2×C4×C73—22no—
420C2×C4×C73—22no—
421C2×C4×C73—44no—
422C2×C4×C73C22×D411yescharacteristic
423C2×C4×C73C22×D411yescharacteristic
424C2×C4×C73C22×D411yescharacteristic
425C2×C4×C73C22×D411yescharacteristic
426C2×C4×C73C22×D411yescharacteristic
427C2×C4×C73C2511yescharacteristic
428C22⋊D73—44no—
429C22⋊D73—44no—
430C22⋊D73—44no—
431C22⋊D73—44no—
432C22⋊D73—44no—
433C2×Dic73—22no—
434C2×Dic73—22no—
435C2×Dic73—22no—
436C2×Dic73—22no—
437C2×Dic73—22no—
438C2×Dic73—22no—
439C2×Dic73—44no—
440C2×Dic73C22×D411yescharacteristic
441C2×Dic73C22×D411yescharacteristic
442C2×Dic73C22×D411yescharacteristic
443C2×Dic73C22×D411yescharacteristic
444C2×Dic73C22×D411yescharacteristic
445C2×Dic73C22×D411yescharacteristic
446D292—24no—
447D292—44no—
448D292—42no—
449D292—42no—
450C4×D73—22no—
451C4×D73—22no—
452C4×D73—22no—
453C4×D73—22no—
454C4×D73—22no—
455C4×D73—22no—
456C4×D73—22no—
457C4×D73—22no—
458C4×D73—22no—
459C4×D73—44no—
460C4×D73—44no—
461C4×D73—44no—
462C4×D73—44no—
463C4×D73—44no—
464C4×D73#13514yes—
465C4×D73AGL(1,ℤ/8)14yes—
466C4×D732−1+414yes—
467Dic146—42no—
468Dic146—42no—
469Dic146—42no—
470Dic146—44no—
471Dic146—44no—
472Dic146—44no—
473C8×C73—22no—
474C8×C73—22no—
475#10596831—22no—
476#10596831—22no—
477C22×C73—21no—
478C22×C73—21no—
479C22×C73—21no—
480C22×C73—42no—
481C22×C73—42no—
482C22×C73—42no—
483C22×C73C23×D411yescharacteristic
484C2×D73—21no—
485C2×D73—21no—
486C2×D73—21no—
487C2×D73—44no—
488C2×D73—42no—
489C2×D73—42no—
490C2×D73—42no—
491C2×D73—88no—
492C2×D73#53612yes—
493C2×D73C2×#13512yes—
494C2×D73C2×AGL(1,ℤ/8)12yes—
495C4×C73—21no—
496C4×C73—21no—
497C4×C73—21no—
498C4×C73—42no—
499C4×C73—42no—
500C4×C73—42no—
501C4×C73C2×#13512yes—
502C4×C73C2×AGL(1,ℤ/8)12yes—
503C4×C73C2×2−1+412yes—
504Dic73—21no—
505Dic73—21no—
506Dic73—21no—
507Dic73—42no—
508Dic73—42no—
509Dic73—42no—
510Dic73#53612yes—
511Dic73C2×#13512yes—
512Dic73C2×AGL(1,ℤ/8)12yes—
513C2×#3228—731nomaximal, Sylow
514C2×C73—41no—
515C2×C73—82no—
516C2×C73C2×#53611yescharacteristic
517C2×C73C22×#13511yescharacteristic
518C2×C73C22×AGL(1,ℤ/8)11yescharacteristic
519D73—41no—
520D73—82no—
521D73#322814yesdirect product factor
522C2×#533—731no—
523C2×#532—731no—
524#3228—731no—
525#3228—731no—
526#3228—731no—
527#3228—731no—
528#3228—734no—
529#3228—734no—
530#3228—731no—
531#3228—731no—
532#3228—731no—
533#3228D7311yescharacteristic, direct product factor
534C2×#500—731no—
535C2×#498—731no—
536C2×#486—731no—
537C2×#486—731no—
538C2×#482—734no—
539C2×#478—734no—
540C2×#431—731no—
541C73C2×#322811yescharacteristic, complemented, Sylow
542C22×#41—1461no—
543#533—731no—
544#533—731no—
545#533—732no—
546#533—732no—
547#533—731no—
548#533—1461no—
549#533—1461no—
550#533—1461no—
551#533—1461no—
552#533C2×D7311yescharacteristic, complemented
553#532—731no—
554#532—731no—
555#532—732no—
556#532—732no—
557#532—731no—
558#532—1461no—
559#532—1461no—
560#532—1461no—
561#532—1461no—
562#532C2×D7311yescharacteristic
563C2×C4⋊Q8—731no—
564C2×C4⋊Q8—731no—
565C2×C4⋊Q8—731no—
566C2×#127—731no—
567C2×#125—732no—
568C2×#124—1461no—
569C2×C22⋊Q8—1461no—
570C2×C22⋊Q8—1461no—
571C2×#121—732no—
572C2×#121—1461no—
573C2×C4×Q8—1461no—
574C2×C4×Q8—1461no—
575C2×C4×D4—732no—
576C2×C4×D4—1461no—
577C2×#117—732no—
578C22×C42—731no—
579#500—731no—
580#500—731no—
581#500—734no—
582#500—731no—
583#500C2×D7311yescharacteristic, complemented
584#498—731no—
585#498—731no—
586#498—734no—
587#498—731no—
588#498C2×D7311yescharacteristic, complemented
589#486—731no—
590#486—731no—
591#486—731no—
592#486—731no—
593#486—734no—
594#486—734no—
595#486—731no—
596#486—731no—
597#486C2×D7311yescharacteristic, complemented
598#486C2×D7311yescharacteristic, complemented
599#482—734no—
600#482—734no—
601#482—734no—
602#482—734no—
603#482—734no—
604#482—734no—
605#482—734no—
606#482C2×D7314yescomplemented
607#478—734no—
608#478—734no—
609#478—734no—
610#478—734no—
611#478—734no—
612#478—734no—
613#478—734no—
614#478C2×D7314yescomplemented
615#431—731no—
616#431—732no—
617#431—732no—
618#431—731no—
619#431—731no—
620#431C2×D7311yescharacteristic, complemented
621C2×#107—734no—
622C2×#106—734no—
623C2×C4⋊C8—732no—
624C2×#102—734no—
625C2×#102—734no—
626C2×C22⋊C8—732no—
627C2×C4×C8—731no—
628C2×C4×C8—731no—
629C2×#41—21no—
630C2×#41—2928no—
631C2×#41—1462no—
632C2×#41—1462no—
633C2×#41—1461no—
634C2×#41—1461no—
635C2×#41—1461no—
636C22×Q8—1461no—
637C22×Q8—1461no—
638C22×Q8—1461no—
639C22×D4—732no—
640C22×D4—1461no—
641C22×D4—1461no—
642C22×D4—1462no—
643C23×C4—731no—
644C23×C4—731no—
645C23×C4—731no—
646C23×C4—1462no—
647C22×C8—732no—
648C22×C8—732no—
649C4⋊Q8—732no—
650C4⋊Q8—732no—
651C4⋊Q8—732no—
652C4⋊Q8—731no—
653C4⋊Q8—731no—
654C4⋊Q8—731no—
655C4⋊Q8—1461no—
656C4⋊Q8—1461no—
657C4⋊Q8—1461no—
658C4⋊Q8—1461no—
659C4⋊Q8—1461no—
660C4⋊Q8—1461no—
661C4⋊Q8C22×D7311yescharacteristic
662C4⋊Q8C22×D7311yescharacteristic
663C4⋊Q8C22×D7311yescharacteristic
664#127—732no—
665#127—731no—
666#127—1461no—
667#127—1461no—
668#127C22×D7311yescharacteristic
669#125—732no—
670#125—732no—
671#125—732no—
672#125—1462no—
673#125—1462no—
674#125C22×D7312yes—
675#124—21no—
676#124—1462no—
677#124—1462no—
678#124—1461no—
679#124—1461no—
680#124—1461no—
681C22⋊Q8—21no—
682C22⋊Q8—21no—
683C22⋊Q8—1462no—
684C22⋊Q8—1462no—
685C22⋊Q8—1462no—
686C22⋊Q8—1462no—
687C22⋊Q8—1461no—
688C22⋊Q8—1461no—
689C22⋊Q8—1461no—
690C22⋊Q8—1461no—
691C22⋊Q8—1461no—
692C22⋊Q8—1461no—
693#121—21no—
694#121—732no—
695#121—732no—
696#121—732no—
697#121—1462no—
698#121—1462no—
699#121—1461no—
700#121—1462no—
701#121—1461no—
702#121—1462no—
703#121—1461no—
704#121C22×D7312yes—
705C4×Q8—21no—
706C4×Q8—21no—
707C4×Q8—1462no—
708C4×Q8—1462no—
709C4×Q8—1462no—
710C4×Q8—1461no—
711C4×Q8—1462no—
712C4×Q8—1461no—
713C4×Q8—1461no—
714C4×Q8—1461no—
715C4×Q8—1461no—
716C4×Q8—1461no—
717C4×D4—21no—
718C4×D4—732no—
719C4×D4—732no—
720C4×D4—732no—
721C4×D4—1462no—
722C4×D4—1462no—
723C4×D4—1461no—
724C4×D4—1462no—
725C4×D4—1462no—
726C4×D4—1461no—
727C4×D4—1461no—
728C4×D4C22×D7312yes—
729#117—732no—
730#117—732no—
731#117—732no—
732#117—1462no—
733#117—1462no—
734#117C22×D7312yes—
735C2×C4⋊C4—732no—
736C2×C4⋊C4—732no—
737C2×C4⋊C4—732no—
738C2×C4⋊C4—1461no—
739C2×C4⋊C4—1462no—
740C2×C4⋊C4—1462no—
741C2×C4⋊C4—1461no—
742C2×C4⋊C4—1461no—
743C2×C22⋊C4—1462no—
744C2×C22⋊C4—1462no—
745C2×C22⋊C4—1462no—
746C2×C42—731no—
747C2×C42—731no—
748C2×C42—731no—
749C2×C42—731no—
750C2×C42—731no—
751C2×C42—731no—
752C2×C42—731no—
753C2×C42—731no—
754C2×C42—731no—
755C2×C42—731no—
756C2×C42—731no—
757C2×C42—1462no—
758C2×C42C22×D7311yescharacteristic
759#107—734no—
760#107—734no—
761#107—734no—
762#107C22×D7314yes—
763#106—734no—
764#106—734no—
765#106—734no—
766#106C22×D7314yes—
767C4⋊C8—732no—
768C4⋊C8—732no—
769C4⋊C8—732no—
770C4⋊C8C22×D7312yes—
771#102—734no—
772#102—734no—
773#102—734no—
774#102—734no—
775#102—734no—
776#102—734no—
777#102C22×D7314yes—
778#102C22×D7314yes—
779C22⋊C8—732no—
780C22⋊C8—732no—
781C22⋊C8—732no—
782C22⋊C8C22×D7312yes—
783C4×C8—732no—
784C4×C8—732no—
785C4×C8—731no—
786C4×C8—731no—
787C4×C8C22×D7311yescharacteristic
788C4×C8C22×D7311yescharacteristic
789C24—731no—
790C24—1462no—
791#41—44no—
792#41—2924no—
793#41—2928no—
794#41—2928no—
795#41—2924no—
796#41—2924no—
797C2×Q8—21no—
798C2×Q8—21no—
799C2×Q8—21no—
800C2×Q8—2924no—
801C2×Q8—2924no—
802C2×Q8—2924no—
803C2×Q8—1462no—
804C2×Q8—1462no—
805C2×Q8—1462no—
806C2×Q8—1461no—
807C2×Q8—1461no—
808C2×Q8—1461no—
809C2×D4—22no—
810C2×D4—21no—
811C2×D4—21no—
812C2×D4—2928no—
813C2×D4—2924no—
814C2×D4—2924no—
815C2×D4—732no—
816C2×D4—1462no—
817C2×D4—1468no—
818C2×D4—1462no—
819C2×D4—1462no—
820C2×D4—1462no—
821C2×D4—1462no—
822C2×D4—1462no—
823C2×D4—1461no—
824C2×D4—1461no—
825C2×D4C23×D7312yes—
826C22×C4—22no—
827C22×C4—2928no—
828C22×C4—731no—
829C22×C4—731no—
830C22×C4—731no—
831C22×C4—731no—
832C22×C4—731no—
833C22×C4—731no—
834C22×C4—731no—
835C22×C4—731no—
836C22×C4—731no—
837C22×C4—731no—
838C22×C4—731no—
839C22×C4—731no—
840C22×C4—731no—
841C22×C4—731no—
842C22×C4—731no—
843C22×C4—1462no—
844C22×C4—1462no—
845C22×C4—1462no—
846C22×C4—1462no—
847C22×C4—1464no—
848C22×C4—1464no—
849C22×C4—1464no—
850C22×C4—1462no—
851C22×C4—1462no—
852C22×C4D4×D7311yescharacteristic
853C22×C4D4×D7311yescharacteristic
854C22×C4C23×D7311yescharacteristic
855C2×C8—732no—
856C2×C8—732no—
857C2×C8—1464no—
858C2×C8—1464no—
859C2×C8C23×D7312yes—
860C2×C8C23×D7312yes—
861C4⋊C4—21no—
862C4⋊C4—22no—
863C4⋊C4—22no—
864C4⋊C4—21no—
865C4⋊C4—21no—
866C4⋊C4—732no—
867C4⋊C4—732no—
868C4⋊C4—732no—
869C4⋊C4—1462no—
870C4⋊C4—1462no—
871C4⋊C4—1462no—
872C4⋊C4—1462no—
873C4⋊C4—1462no—
874C4⋊C4—1462no—
875C4⋊C4—1462no—
876C4⋊C4—1462no—
877C4⋊C4—1462no—
878C4⋊C4—1462no—
879C4⋊C4—1462no—
880C4⋊C4—1462no—
881C4⋊C4—1461no—
882C4⋊C4—1461no—
883C4⋊C4—1461no—
884C4⋊C4C23×D7312yes—
885C4⋊C4C23×D7312yes—
886C4⋊C4C23×D7312yes—
887C22⋊C4—22no—
888C22⋊C4—22no—
889C22⋊C4—22no—
890C22⋊C4—1462no—
891C22⋊C4—1462no—
892C22⋊C4—1462no—
893C22⋊C4—1462no—
894C22⋊C4—1462no—
895C22⋊C4—1462no—
896C22⋊C4—1462no—
897C22⋊C4—1462no—
898C22⋊C4—1462no—
899C42—22no—
900C42—731no—
901C42—731no—
902C42—731no—
903C42—731no—
904C42—731no—
905C42—731no—
906C42—731no—
907C42—731no—
908C42—731no—
909C42—731no—
910C42—731no—
911C42—731no—
912C42—1462no—
913C42—1462no—
914C42—1462no—
915C42D4×D7311yescharacteristic
916C42D4×D7311yescharacteristic
917C42C23×D7311yescharacteristic
918C42C23×D7311yescharacteristic
919C23—22no—
920C23—2924no—
921C23—2924no—
922C23—2924no—
923C23—731no—
924C23—731no—
925C23—1462no—
926C23—1462no—
927C23—1462no—
928C23—1462no—
929C23C2×D4×D7311yescharacteristic
930Q8—42no—
931Q8—42no—
932Q8—42no—
933Q8—2924no—
934Q8—2924no—
935Q8—2924no—
936Q8—2922no—
937Q8—2922no—
938Q8—2922no—
939D4—24no—
940D4—44no—
941D4—42no—
942D4—42no—
943D4—2924no—
944D4—2924no—
945D4—2924no—
946D4—2924no—
947D4—2924no—
948D4—2924no—
949D4—2922no—
950D4—2922no—
951D4—1464no—
952C2×C4—22no—
953C2×C4—22no—
954C2×C4—22no—
955C2×C4—22no—
956C2×C4—22no—
957C2×C4—22no—
958C2×C4—44no—
959C2×C4—2924no—
960C2×C4—2924no—
961C2×C4—2924no—
962C2×C4—2924no—
963C2×C4—2924no—
964C2×C4—2924no—
965C2×C4—731no—
966C2×C4—731no—
967C2×C4—731no—
968C2×C4—734no—
969C2×C4—734no—
970C2×C4—734no—
971C2×C4—731no—
972C2×C4—731no—
973C2×C4—731no—
974C2×C4—1462no—
975C2×C4—1462no—
976C2×C4—1462no—
977C2×C4—1462no—
978C2×C4—1462no—
979C2×C4—1462no—
980C2×C4—1462no—
981C2×C4—1462no—
982C2×C4—1462no—
983C2×C4—1462no—
984C2×C4—1462no—
985C2×C4—1462no—
986C2×C4—1462no—
987C2×C4—1462no—
988C2×C4—1462no—
989C2×C4C2×D4×D7311yescharacteristic
990C2×C4C2×D4×D7311yescharacteristic
991C2×C4C2×D4×D7311yescharacteristic
992C2×C4C2×D4×D7311yescharacteristic
993C2×C4C2×D4×D7311yescharacteristic
994C2×C4C24×D7311yescharacteristic
995C8—22no—
996C8—22no—
997C8—1462no—
998C8—1462no—
999C22—21no—
1000C22—21no—
1001C22—21no—
1002C22—42no—
1003C22—42no—
1004C22—42no—
1005C22—2924no—
1006C22—2922no—
1007C22—2922no—
1008C22—2922no—
1009C22—5848no—
1010C22—732no—
1011C22—732no—
1012C22—732no—
1013C22—1461no—
1014C22—1461no—
1015C22—1461no—
1016C22C22×D4×D7311yescharacteristic
1017C4—21no—
1018C4—21no—
1019C4—21no—
1020C4—42no—
1021C4—42no—
1022C4—42no—
1023C4—2922no—
1024C4—2922no—
1025C4—2922no—
1026C4—732no—
1027C4—732no—
1028C4—732no—
1029C4—1461no—
1030C4—1461no—
1031C4—1461no—
1032C4#135×D7312yes—
1033C4AGL(1,ℤ/8)×D7312yes—
1034C42−1+4×D7312yes—
1035C2—41no—
1036C2—82no—
1037C2—2921no—
1038C2—5842no—
1039C2—734no—
1040C2#536×D7311yescharacteristic
1041C2C2×#135×D7311yescharacteristic
1042C2C2×AGL(1,ℤ/8)×D7311yescharacteristic
subgroupG/H
centerC22C22×D4×D73
commutator, cosocleC2×C4×C73C25
FrattiniC2×C4C24×D73
FittingC73×#3228C2
socleC22×C73C23×D4
prime radical#532×D73C2
hypercenter#3228D73
hypocenterC73C2×#3228
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3228

Complements

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

NH ≅ G/Ntype
1. #533×D73C2semidirect
3. #22621070C2semidirect
4. #22621069C2semidirect
5. #22621068C2semidirect
6. #22621067C2semidirect
7. #22621066C2semidirect
8. #22621065C2semidirect
9. #22621064C2semidirect
10. #22621063C2semidirect
11. #22621062C2semidirect
12. #500×D73C2semidirect
13. #498×D73C2semidirect
14. #486×D73C2semidirect
15. #486×D73C2semidirect
16. #482×D73C2semidirect
17. #478×D73C2semidirect
18. #431×D73C2semidirect
19. C73×#3228C2semidirect
21. #17989144C22semidirect
22. #17989143C22semidirect
23. #17989142C22semidirect
24. #17989142C22semidirect
27. #17989140C22semidirect
55. #17988992C22semidirect
56. #17988991C22semidirect
57. #17988990C22semidirect
58. #17988990C22semidirect
59. #17988985C22semidirect
60. #17988984C22semidirect
61. #17988983C22semidirect
62. #17988983C22semidirect
63. #17988935C22semidirect
64. #17988935C22semidirect
65. #17988934C22semidirect
66. #17988934C22semidirect
67. #17988933C22semidirect
68. #17988933C22semidirect
69. #17988932C22semidirect
70. #17988932C22semidirect
71. #17988914C22semidirect
72. #17988913C22semidirect
73. #17988912C22semidirect
74. #17988911C22semidirect
75. #17988910C22semidirect
76. #17988909C22semidirect
77. #17988908C22semidirect
78. #17988890C22semidirect
79. #17988889C22semidirect
80. #17988888C22semidirect
81. #17988887C22semidirect
82. #17988886C22semidirect
83. #17988885C22semidirect
84. #17988884C22semidirect
85. #17988640C22semidirect
86. #17988639C22semidirect
87. #17988638C22semidirect
88. #17988638C22semidirect
89. #17988637C22semidirect
98. #533×C73C22semidirect
100. #500×C73C22semidirect
101. #498×C73C22semidirect
102. #486×C73C22semidirect
103. #486×C73C22semidirect
104. #482×C73C22semidirect
105. #478×C73C22semidirect
106. #431×C73C22semidirect
521. D73#3228direct (N × H)
533. #3228D73direct (N × H)
541. C73C2×#3228semidirect
552. #533C2×D73semidirect
583. #500C2×D73semidirect
588. #498C2×D73semidirect
597. #486C2×D73semidirect
598. #486C2×D73semidirect
606. #482C2×D73semidirect
614. #478C2×D73semidirect
620. #431C2×D73semidirect

Maximal subgroups

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

subgroupindex
#533×D732
#532×D732
#226210702
#226210692
#226210682
#226210672
#226210662
#226210652
#226210642
#226210632
#226210622
#500×D732
#498×D732
#486×D732
#482×D732
#478×D732
#431×D732
C73×#32282
C2×#322873