Finite Group Databasebeta

← #3567×D73 #33993418

Subgroups — #3567×D73 #33993418

Order 18688.

6662 conjugacy classes of subgroups.

The subgroup lattice has 1218 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22624621C211yesmaximal, characteristic, complemented
2#22624620C216yesmaximal, complemented
3#22624619C213yesmaximal, complemented
4#22624618C213yesmaximal, complemented
5#22624617C216yesmaximal, complemented
6#22624616C216yesmaximal, complemented
7#22624615C216yesmaximal, complemented
8#564×D73C211yesmaximal, characteristic, complemented
9#562×D73C213yesmaximal, complemented
10#553×D73C216yesmaximal, complemented
11#552×D73C216yesmaximal, complemented
12#540×D73C216yesmaximal, complemented
13#539×D73C216yesmaximal, complemented
14#529×D73C213yesmaximal, complemented
15C73×#3567C211yesmaximal, characteristic, complemented
16C73⋊#564C2216yescomplemented
17C73⋊#564C2216yescomplemented
18C73⋊#564C2213yescomplemented
19#17989335C2213yescomplemented
20#17989334C2216yescomplemented
21#17989334C2216yescomplemented
22#17989333C2216yescomplemented
23#17989333C2216yescomplemented
24#17989332C2216yescomplemented
25#17989332C2216yescomplemented
26#17989331C2213yescomplemented
27#17989331C2213yescomplemented
28#17989290C2216yescomplemented
29#17989289C2216yescomplemented
30#17989288C2216yescomplemented
31#17989288C2216yescomplemented
32#17989287C2216yescomplemented
33#17989286C2216yescomplemented
34#17989286C2216yescomplemented
35#17989285C2216yescomplemented
36#17989284C2216yescomplemented
37#17989283C2216yescomplemented
38#17989282C2216yescomplemented
39#17989282C2216yescomplemented
40#17989281C2216yescomplemented
41#17989280C2216yescomplemented
42#17989280C2216yescomplemented
43#17989279C2216yescomplemented
44#17989278C2216yescomplemented
45#17989277C2216yescomplemented
46#17989276C2216yescomplemented
47#17989275C2216yescomplemented
48#17989274C2216yescomplemented
49#17989274C2216yescomplemented
50#17989273C2216yescomplemented
51#17989273C2216yescomplemented
52#17989272C2216yescomplemented
53#17989271C2216yescomplemented
54#17989270C2216yescomplemented
55#17989270C2216yescomplemented
56#17989269C2216yescomplemented
57#17989269C2216yescomplemented
58#17989193C2216yescomplemented
59#17989192C2216yescomplemented
60#17989191C2216yescomplemented
61#17989190C2216yescomplemented
62#17989190C2216yescomplemented
63#17989189C2216yescomplemented
64#17989189C2216yescomplemented
65#17989189C2216yescomplemented
66#17989189C2216yescomplemented
67#17989188C2216yescomplemented
68#17989188C2216yescomplemented
69#17989187C2216yescomplemented
70#17989187C2216yescomplemented
71#17989187C2216yescomplemented
72#17989187C2216yescomplemented
73#17989186C2216yescomplemented
74#17989185C2216yescomplemented
75#17989185C2216yescomplemented
76#17989184C2216yescomplemented
77#17989183C2216yescomplemented
78#17989183C2216yescomplemented
79#17989182C2216yescomplemented
80#17989181C2216yescomplemented
81#17989181C2216yescomplemented
82#17989180C2216yescomplemented
83#17989180C2216yescomplemented
84#17989179C2216yescomplemented
85#17989179C2216yescomplemented
86#17989178C2216yescomplemented
87#17989178C2216yescomplemented
88#127×D73C2212yes—
89#17989124C2213yescomplemented
90#17989123C2213yescomplemented
91#17989122C2213yescomplemented
92#17989121C2213yescomplemented
93#17989120C2216yescomplemented
94#17989119C2213yescomplemented
95#17989118C2213yescomplemented
96#17989117C2216yescomplemented
97#17989116C2213yescomplemented
98#17989115C2216yescomplemented
99#17989114C2216yescomplemented
100#126×D73C2212yes—
101#126×D73C2216yes—
102#126×D73C2216yes—
103#125×D73C2216yes—
104#125×D73C2216yes—
105#125×D73C2216yes—
106#125×D73C2213yes—
107#124×D73C2213yes—
108#123×D73C2216yes—
109#123×D73C2216yes—
110#123×D73C2216yes—
111#123×D73C2216yes—
112#123×D73C2216yes—
113C22⋊Q8×D73C2213yes—
114C22⋊Q8×D73C2216yes—
115C22⋊Q8×D73C2216yes—
116#121×D73C2216yes—
117#121×D73C2213yes—
118#121×D73C2216yes—
119#121×D73C2216yes—
120#121×D73C2216yes—
121C4×Q8×D73C2213yes—
122C4×D4×D73C2216yes—
123C4×D4×D73C2216yes—
124C4×D4×D73C2216yes—
125C4×D4×D73C2213yes—
126#117×D73C2216yes—
127#117×D73C2216yes—
128C2×C4⋊C4×D73C2216yes—
129C2×C42×D73C2211yescharacteristic
130#564×C73C2211yescharacteristic, complemented
131#562×C73C2213yescomplemented
132#553×C73C2216yescomplemented
133#552×C73C2216yescomplemented
134#540×C73C2216yescomplemented
135#539×C73C2216yescomplemented
136#529×C73C2213yescomplemented
137C2×Q8×D73C2313yes—
138C2×D4×D73C2316yes—
139C2×D4×D73C2316yes—
140C2×D4×D73C2316yes—
141C2×D4×D73C2313yes—
142C22×C4×D73C2313yes—
143C22×C4×D73C2316yes—
144C22×C4×D73C2316yes—
145C22×C4×D73C2316yes—
146#14556588C2312yes—
147#14556587C2316yes—
148#14556587C2316yes—
149#14556586C2316yes—
150#14556586C2316yes—
151#14556586C2316yes—
152#14556586C2316yes—
153#14556586C2316yes—
154#14556586C2316yes—
155#14556586C2316yes—
156#14556585C2316yes—
157#14556585C2312yes—
158#14556585C2316yes—
159#14556584C2316yes—
160#14556584C2316yes—
161#14556584C2316yes—
162#14556584C2316yes—
163#14556584C2316yes—
164#14556584C2316yes—
165#14556584C2316yes—
166#14556583C2313yes—
167#14556583C2316yes—
168#14556583C2316yes—
169#14556583C2316yes—
170#14556582C2313yes—
171#14556582C2313yes—
172#14556582C2316yes—
173#14556582C2316yes—
174#14556582C2316yes—
175#14556582C2316yes—
176#14556582C2316yes—
177#14556582C2316yes—
178#14556581C2316yes—
179#14556581C2316yes—
180#14556581C2316yes—
181#14556581C2316yes—
182#14556581C2316yes—
183#14556581C2316yes—
184#14556581C2316yes—
185#14556581C2316yes—
186#14556581C2316yes—
187#14556581C2316yes—
188#14556581C2316yes—
189#14556581C2316yes—
190#14556581C2316yes—
191#14556581C2316yes—
192#14556580C2313yes—
193#14556579C2313yes—
194#14556578C2313yes—
195#14556577C2316yes—
196#14556577C2316yes—
197#14556576C2316yes—
198#14556576C2316yes—
199#14556576C2316yes—
200#14556576C2316yes—
201#14556576C2316yes—
202#14556576C2316yes—
203#14556576C2316yes—
204#14556576C2316yes—
205#14556576C2316yes—
206#14556576C2316yes—
207#14556575C2316yes—
208#14556575C2316yes—
209#14556575C2316yes—
210#14556575C2316yes—
211#14556575C2316yes—
212#14556574C2316yes—
213#14556574C2316yes—
214#14556574C2316yes—
215#14556574C2316yes—
216#14556574C2316yes—
217#14556573C2316yes—
218#14556573C2316yes—
219#14556573C2316yes—
220#14556573C2316yes—
221#14556573C2316yes—
222#14556573C2316yes—
223#14556573C2316yes—
224#14556573C2316yes—
225#14556573C2316yes—
226#14556573C2316yes—
227#14556572C2316yes—
228#14556572C2316yes—
229#14556572C2316yes—
230#14556572C2316yes—
231#14556572C2316yes—
232#14556571C2313yes—
233#14556571C2316yes—
234#14556571C2316yes—
235#14556570C2313yes—
236#14556570C2316yes—
237#14556570C2316yes—
238#14556569C2316yes—
239#14556569C2316yes—
240#14556569C2316yes—
241#14556569C2316yes—
242#14556569C2316yes—
243#14556568C2316yes—
244#14556568C2316yes—
245#14556568C2316yes—
246#14556568C2316yes—
247#14556568C2316yes—
248#14556567C2313yes—
249#14556567C2316yes—
250#14556567C2316yes—
251#14556566C2313yes—
252#14556566C2316yes—
253#14556566C2316yes—
254#14556566C2316yes—
255#14556566C2316yes—
256#14556565C2313yes—
257#14556565C2316yes—
258#14556565C2316yes—
259#14556565C2316yes—
260#14556565C2316yes—
261#14556564C2316yes—
262#14556564C2316yes—
263#14556564C2316yes—
264#14556564C2316yes—
265#14556564C2316yes—
266#14556564C2316yes—
267#14556564C2316yes—
268#14556564C2316yes—
269#14556564C2316yes—
270#14556563C2316yes—
271#14556563C2316yes—
272#14556563C2316yes—
273#14556563C2316yes—
274#14556563C2316yes—
275#14556563C2316yes—
276#14556563C2316yes—
277#14556563C2316yes—
278#14556563C2316yes—
279#14556562C2316yes—
280#14556562C2313yes—
281#14556562C2316yes—
282#14556562C2316yes—
283#14556562C2316yes—
284Q8×Dic73C2313yes—
285C4×Dic146C2313yes—
286C4×Dic146C2316yes—
287#14556556C2316yes—
288#14556556C2313yes—
289C4×D292C2313yes—
290C4×D292C2316yes—
291C4×D292C2316yes—
292C4×D292C2316yes—
293D4×Dic73C2316yes—
294D4×Dic73C2316yes—
295D4×Dic73C2316yes—
296D4×Dic73C2313yes—
297#14556553C2316yes—
298#14556553C2313yes—
299#14556553C2316yes—
300#14556553C2316yes—
301C4×C22⋊D73C2316yes—
302C4×C22⋊D73C2316yes—
303C4×C22⋊D73C2316yes—
304C4×C22⋊D73C2316yes—
305C4×C22⋊D73C2316yes—
306C4×C22⋊D73C2316yes—
307C4×C22⋊D73C2316yes—
308#14556551C2316yes—
309#14556551C2316yes—
310#14556551C2316yes—
311#14556551C2316yes—
312#14556551C2316yes—
313#14556551C2316yes—
314#14556551C2316yes—
315#14556550C2316yes—
316#14556550C2316yes—
317#14556549C2316yes—
318#14556549C2316yes—
319#14556549C2316yes—
320#14556549C2316yes—
321#14556548C2316yes—
322#14556548C2316yes—
323#14556548C2316yes—
324#14556548C2316yes—
325#14556547C2316yes—
326#14556547C2316yes—
327#14556547C2316yes—
328#14556547C2316yes—
329C2×C4⋊Dic73C2316yes—
330C2×#11924007C2316yes—
331C2×#11924007C2316yes—
332C4⋊C4×D73C2316yes—
333C4⋊C4×D73C2316yes—
334C4⋊C4×D73C2316yes—
335C4⋊C4×D73C2316yes—
336C4⋊C4×D73C2316yes—
337C4⋊C4×D73C2316yes—
338C4⋊C4×D73C2316yes—
339C4⋊C4×D73C2316yes—
340C4⋊C4×D73C2316yes—
341C4⋊C4×D73C2316yes—
342C4⋊C4×D73C2316yes—
343C4⋊C4×D73C2316yes—
344C4⋊C4×D73C2313yes—
345C4⋊C4×D73C2313yes—
346C22⋊C4×D73C2316yes—
347C22⋊C4×D73C2316yes—
348C22⋊C4×D73C2316yes—
349C22⋊C4×D73C2316yes—
350C22⋊C4×D73C2316yes—
351C22⋊C4×D73C2316yes—
352C22⋊C4×D73C2316yes—
353C2×C4×Dic73C2313yes—
354C42×D73C2313yes—
355C42×D73C2311yescharacteristic
356C42×D73C2312yes—
357C42×D73C2313yes—
358C42×D73C2311yescharacteristic
359C42×D73C2316yes—
360C42×D73C2312yes—
361#127×C73C2312yes—
362#126×C73C2316yes—
363#126×C73C2312yes—
364#126×C73C2316yes—
365#125×C73C2313yes—
366#125×C73C2316yes—
367#125×C73C2316yes—
368#125×C73C2316yes—
369#124×C73C2313yes—
370#123×C73C2316yes—
371#123×C73C2316yes—
372#123×C73C2316yes—
373#123×C73C2316yes—
374#123×C73C2316yes—
375C22⋊Q8×C73C2313yes—
376C22⋊Q8×C73C2316yes—
377C22⋊Q8×C73C2316yes—
378#121×C73C2316yes—
379#121×C73C2313yes—
380#121×C73C2316yes—
381#121×C73C2316yes—
382#121×C73C2316yes—
383C4×Q8×C73C2313yes—
384C4×D4×C73C2316yes—
385C4×D4×C73C2316yes—
386C4×D4×C73C2316yes—
387C4×D4×C73C2313yes—
388#117×C73C2316yes—
389#117×C73C2316yes—
390C2×C4⋊C4×C73C2316yes—
391C2×C42×C73C2311yescharacteristic
392C23×D73C2416yes—
393C23×D73C2411yescharacteristic
394C2×Dic146C2413yes—
395C2×Dic146C2416yes—
396Q8×D73—46no—
397C2×D292C2413yes—
398C2×D292C2416yes—
399C2×D292C2416yes—
400C2×D292C2416yes—
401C2×C22⋊D73C2416yes—
402C2×C22⋊D73C2416yes—
403C2×C22⋊D73C2416yes—
404C2×C22⋊D73C2416yes—
405C2×C22⋊D73C2416yes—
406C2×C22⋊D73C2416yes—
407C2×C22⋊D73C2416yes—
408D4×D73—412no—
409D4×D73—412no—
410D4×D73—412no—
411D4×D73—46no—
412C22×Dic73C2413yes—
413C22×Dic73C2416yes—
414C22×Dic73C2416yes—
415C22×Dic73C2416yes—
416C2×C4×D73—412no—
417C2×C4×D73—46no—
418C2×C4×D73—412no—
419C2×C4×D73—412no—
420C2×C4×D73C2413yes—
421C2×C4×D73C2413yes—
422C2×C4×D73C2416yes—
423C2×C4×D73C2416yes—
424C2×C4×D73C2416yes—
425C2×C4×D73C2413yes—
426C2×C4×D73C2413yes—
427C2×C4×D73C2416yes—
428C2×C4×D73C2416yes—
429C2×C4×D73C2416yes—
430C2×C4×D73C2416yes—
431C2×C4×D73C2416yes—
432C2×C4×D73C2416yes—
433C4⋊Dic73C2416yes—
434C4⋊Dic73C2416yes—
435C4⋊Dic73C2416yes—
436C4⋊Dic73C2416yes—
437C4⋊Dic73C2416yes—
438C4⋊Dic73C2416yes—
439C4⋊Dic73C2416yes—
440C4⋊Dic73C2416yes—
441C4⋊Dic73C2413yes—
442C4⋊Dic73C2413yes—
443#11924007C2416yes—
444#11924007C2416yes—
445#11924007C2416yes—
446#11924007C2416yes—
447#11924007C2416yes—
448#11924007C2416yes—
449#11924007C2416yes—
450#11924007C2416yes—
451#11924007C2416yes—
452#11924007C2416yes—
453#11924007C2416yes—
454#11924007C2416yes—
455#11924007C2416yes—
456#11924007C2416yes—
457#11924007C2416yes—
458#11924007C2416yes—
459#11924007C2416yes—
460#11924007C2416yes—
461C22⋊Dic73C2416yes—
462C22⋊Dic73C2416yes—
463C22⋊Dic73C2416yes—
464C22⋊Dic73C2416yes—
465C22⋊Dic73C2416yes—
466C22⋊Dic73C2416yes—
467C22⋊Dic73C2416yes—
468#11924005C2416yes—
469#11924005C2416yes—
470#11924005C2416yes—
471#11924005C2416yes—
472#11924005C2416yes—
473#11924005C2416yes—
474#11924005C2416yes—
475#11924005C2416yes—
476#11924005C2416yes—
477#11924005C2416yes—
478#11924005C2416yes—
479#11924005C2416yes—
480#11924005C2416yes—
481#11924005C2416yes—
482C4×Dic73C2413yes—
483C4×Dic73C2413yes—
484C4×Dic73C2413yes—
485C4×Dic73C2413yes—
486C4×Dic73C2416yes—
487C4×Dic73C2416yes—
488C4×Dic73C2416yes—
489C4×Dic73C2416yes—
490C4×Dic73C2416yes—
491C2×Q8×C73C2413yes—
492C2×D4×C73C2416yes—
493C2×D4×C73C2413yes—
494C2×D4×C73C2416yes—
495C2×D4×C73C2416yes—
496C22×C4×C73C2413yes—
497C22×C4×C73C2416yes—
498C22×C4×C73C2416yes—
499C22×C4×C73C2416yes—
500C4⋊C4×C73C2416yes—
501C4⋊C4×C73C2416yes—
502C4⋊C4×C73C2416yes—
503C4⋊C4×C73C2416yes—
504C4⋊C4×C73C2416yes—
505C4⋊C4×C73C2416yes—
506C4⋊C4×C73C2416yes—
507C4⋊C4×C73C2416yes—
508C4⋊C4×C73C2413yes—
509C4⋊C4×C73C2413yes—
510C22⋊C4×C73C2416yes—
511C22⋊C4×C73C2416yes—
512C22⋊C4×C73C2416yes—
513C22⋊C4×C73C2416yes—
514C22⋊C4×C73C2416yes—
515C22⋊C4×C73C2416yes—
516C22⋊C4×C73C2416yes—
517C42×C73C2413yes—
518C42×C73C2411yescharacteristic
519C42×C73C2412yes—
520C42×C73C2416yes—
521C42×C73C2412yes—
522C23×C73C2516yes—
523C23×C73C2511yescharacteristic
524C22×D73—212no—
525C22×D73—212no—
526C22×D73—26no—
527C22×D73—212no—
528C22×D73C2516yes—
529C22×D73C2511yescharacteristic
530C22×D73C2511yescharacteristic
531Q8×C73—43no—
532D4×C73—43no—
533D4×C73—46no—
534D4×C73—46no—
535D4×C73—46no—
536C2×C4×C73—46no—
537C2×C4×C73—46no—
538C2×C4×C73—43no—
539C2×C4×C73—46no—
540C2×C4×C73C2513yes—
541C2×C4×C73C2513yes—
542C2×C4×C73C2516yes—
543C2×C4×C73C2516yes—
544C2×C4×C73C2516yes—
545C22⋊D73—46no—
546C22⋊D73—46no—
547C22⋊D73—46no—
548C22⋊D73—46no—
549C22⋊D73—46no—
550C22⋊D73—46no—
551C22⋊D73—46no—
552C2×Dic73—46no—
553C2×Dic73—46no—
554C2×Dic73—43no—
555C2×Dic73—46no—
556C2×Dic73C2513yes—
557C2×Dic73C2513yes—
558C2×Dic73C2516yes—
559C2×Dic73C2516yes—
560C2×Dic73C2516yes—
561D292—43no—
562D292—46no—
563D292—46no—
564D292—46no—
565C4×D73—26no—
566C4×D73—212no—
567C4×D73—212no—
568C4×D73—212no—
569C4×D73—26no—
570C4×D73—46no—
571C4×D73—46no—
572C4×D73—43no—
573C4×D73—43no—
574C4×D73—46no—
575C4×D73—46no—
576C4×D73—46no—
577C4×D73—46no—
578Dic146—43no—
579Dic146—46no—
580C22×C73—26no—
581C22×C73—26no—
582C22×C73—23no—
583C22×C73—26no—
584C22×C73C2611yescharacteristic
585C2×D73—26no—
586C2×D73—26no—
587C2×D73—23no—
588C2×D73—26no—
589C2×D73—424no—
590C2×D73—44no—
591C2×D73#58516yes—
592C4×C73—26no—
593C4×C73—23no—
594C4×C73—23no—
595C4×C73—26no—
596C4×C73—26no—
597Dic73—26no—
598Dic73—23no—
599Dic73—23no—
600Dic73—26no—
601Dic73—26no—
602C2×#3567—731nomaximal, Sylow
603C2×C73—46no—
604C2×C73—41no—
605C2×C73C2×#58513yes—
606D73—46no—
607D73—41no—
608D73#356714yesdirect product factor
609#3567—731no—
610#3567—733no—
611#3567—736no—
612#3567—736no—
613#3567—736no—
614#3567—736no—
615#3567—733no—
616#3567D7311yescharacteristic, direct product factor
617C2×#564—731no—
618C2×#562—733no—
619C2×#553—736no—
620C2×#552—736no—
621C2×#540—736no—
622C2×#539—736no—
623C2×#529—733no—
624C73C2×#356711yescharacteristic, complemented, Sylow
625#564—736no—
626#564—736no—
627#564—733no—
628#564C2×D7311yescharacteristic, complemented
629#562—733no—
630#562—733no—
631#562—733no—
632#562—736no—
633#562—736no—
634#562—736no—
635#562—736no—
636#562—736no—
637#562—736no—
638#562C2×D7313yescomplemented
639#553—736no—
640#553—736no—
641#553—736no—
642#553—736no—
643#553—736no—
644#553—736no—
645#553—736no—
646#553—736no—
647#553—736no—
648#553—736no—
649#553—736no—
650#553—736no—
651#553—736no—
652#553—736no—
653#553—736no—
654#553C2×D7316yescomplemented
655#552—736no—
656#552—736no—
657#552—736no—
658#552—736no—
659#552—736no—
660#552—736no—
661#552—736no—
662#552—736no—
663#552—736no—
664#552—736no—
665#552—736no—
666#552—736no—
667#552—736no—
668#552—736no—
669#552—736no—
670#552C2×D7316yescomplemented
671#540—736no—
672#540—736no—
673#540—736no—
674#540—736no—
675#540—736no—
676#540—736no—
677#540—736no—
678#540—736no—
679#540—736no—
680#540—736no—
681#540—736no—
682#540—736no—
683#540—736no—
684#540—736no—
685#540—736no—
686#540C2×D7316yescomplemented
687#539—736no—
688#539—736no—
689#539—736no—
690#539—736no—
691#539—736no—
692#539—736no—
693#539—736no—
694#539—736no—
695#539—736no—
696#539—736no—
697#539—736no—
698#539—736no—
699#539—736no—
700#539—736no—
701#539—736no—
702#539C2×D7316yescomplemented
703C2×#127—732no—
704#529—736no—
705#529—733no—
706#529—733no—
707#529—736no—
708#529—733no—
709#529—733no—
710#529—733no—
711#529—736no—
712#529—733no—
713#529—736no—
714#529—733no—
715#529C2×D7313yescomplemented
716C2×#126—736no—
717C2×#126—732no—
718C2×#126—736no—
719C2×#125—733no—
720C2×#125—736no—
721C2×#125—736no—
722C2×#125—736no—
723C2×#124—733no—
724C2×#123—736no—
725C2×#123—736no—
726C2×#123—736no—
727C2×#123—736no—
728C2×#123—736no—
729C2×C22⋊Q8—733no—
730C2×C22⋊Q8—736no—
731C2×C22⋊Q8—736no—
732C2×#121—733no—
733C2×#121—736no—
734C2×#121—736no—
735C2×#121—736no—
736C2×#121—736no—
737C2×C4×Q8—733no—
738C2×C4×D4—736no—
739C2×C4×D4—733no—
740C2×C4×D4—736no—
741C2×C4×D4—736no—
742C2×#117—736no—
743C2×#117—736no—
744C22×C4⋊C4—736no—
745C22×C42—731no—
746C22×Q8—733no—
747C22×D4—736no—
748C22×D4—733no—
749C22×D4—736no—
750C22×D4—736no—
751C23×C4—736no—
752C23×C4—736no—
753C23×C4—736no—
754C23×C4—733no—
755#127—736no—
756#127—736no—
757#127—732no—
758#127C22×D7312yes—
759#126—736no—
760#126—736no—
761#126—736no—
762#126—736no—
763#126—736no—
764#126—736no—
765#126—736no—
766#126—736no—
767#126—736no—
768#126—736no—
769#126—736no—
770#126—736no—
771#126—736no—
772#126—736no—
773#126—736no—
774#126—732no—
775#126—736no—
776#126C22×D7316yes—
777#126C22×D7312yes—
778#126C22×D7316yes—
779#125—736no—
780#125—736no—
781#125—733no—
782#125—733no—
783#125—736no—
784#125—736no—
785#125—736no—
786#125—736no—
787#125—736no—
788#125—736no—
789#125—736no—
790#125—736no—
791#125—736no—
792#125—736no—
793#125—736no—
794#125—736no—
795#125—736no—
796#125—736no—
797#125—736no—
798#125—736no—
799#125—736no—
800#125—736no—
801#125—733no—
802#125—736no—
803#125—736no—
804#125—736no—
805#125C22×D7313yes—
806#125C22×D7316yes—
807#125C22×D7316yes—
808#125C22×D7316yes—
809#124—733no—
810#124—733no—
811#124—736no—
812#124—736no—
813#124—733no—
814#124C22×D7313yes—
815#123—736no—
816#123—736no—
817#123—736no—
818#123—736no—
819#123—736no—
820#123—736no—
821#123—736no—
822#123—736no—
823#123—736no—
824#123—736no—
825#123—736no—
826#123—736no—
827#123—736no—
828#123—736no—
829#123—736no—
830#123—736no—
831#123—736no—
832#123—736no—
833#123—736no—
834#123—736no—
835#123—736no—
836#123—736no—
837#123—736no—
838#123—736no—
839#123—736no—
840#123—736no—
841#123—736no—
842#123—736no—
843#123—736no—
844#123—736no—
845#123—736no—
846#123—736no—
847#123—736no—
848#123—736no—
849#123—736no—
850#123C22×D7316yes—
851#123C22×D7316yes—
852#123C22×D7316yes—
853#123C22×D7316yes—
854#123C22×D7316yes—
855C22⋊Q8—733no—
856C22⋊Q8—736no—
857C22⋊Q8—736no—
858C22⋊Q8—733no—
859C22⋊Q8—736no—
860C22⋊Q8—736no—
861C22⋊Q8—736no—
862C22⋊Q8—733no—
863C22⋊Q8—736no—
864C22⋊Q8—736no—
865C22⋊Q8—736no—
866C22⋊Q8—736no—
867C22⋊Q8—736no—
868C22⋊Q8—736no—
869C22⋊Q8—736no—
870C22⋊Q8—736no—
871C22⋊Q8—736no—
872C22⋊Q8—736no—
873C22⋊Q8—736no—
874C22⋊Q8C22×D7313yes—
875C22⋊Q8C22×D7316yes—
876C22⋊Q8C22×D7316yes—
877#121—733no—
878#121—736no—
879#121—736no—
880#121—736no—
881#121—736no—
882#121—736no—
883#121—736no—
884#121—736no—
885#121—736no—
886#121—736no—
887#121—736no—
888#121—736no—
889#121—736no—
890#121—736no—
891#121—733no—
892#121—736no—
893#121—736no—
894#121—736no—
895#121—736no—
896#121—733no—
897#121—736no—
898#121—736no—
899#121—736no—
900#121—736no—
901#121—736no—
902#121—736no—
903#121—736no—
904#121—736no—
905#121—736no—
906#121—736no—
907#121—736no—
908#121—736no—
909#121—736no—
910#121C22×D7313yes—
911#121C22×D7316yes—
912#121C22×D7316yes—
913#121C22×D7316yes—
914#121C22×D7316yes—
915C4×Q8—733no—
916C4×Q8—733no—
917C4×Q8—736no—
918C4×Q8—736no—
919C4×Q8—733no—
920C4×Q8C22×D7313yes—
921C4×D4—736no—
922C4×D4—733no—
923C4×D4—736no—
924C4×D4—736no—
925C4×D4—736no—
926C4×D4—736no—
927C4×D4—736no—
928C4×D4—736no—
929C4×D4—736no—
930C4×D4—736no—
931C4×D4—736no—
932C4×D4—736no—
933C4×D4—733no—
934C4×D4—736no—
935C4×D4—736no—
936C4×D4—736no—
937C4×D4—736no—
938C4×D4—736no—
939C4×D4—736no—
940C4×D4—736no—
941C4×D4—736no—
942C4×D4—736no—
943C4×D4—736no—
944C4×D4—733no—
945C4×D4—736no—
946C4×D4—736no—
947C4×D4C22×D7316yes—
948C4×D4C22×D7313yes—
949C4×D4C22×D7316yes—
950C4×D4C22×D7316yes—
951#117—736no—
952#117—736no—
953#117—736no—
954#117—736no—
955#117—736no—
956#117—736no—
957#117—736no—
958#117—736no—
959#117—736no—
960#117—736no—
961#117—736no—
962#117—736no—
963#117—736no—
964#117—736no—
965#117C22×D7316yes—
966#117C22×D7316yes—
967C2×C4⋊C4—736no—
968C2×C4⋊C4—736no—
969C2×C4⋊C4—736no—
970C2×C4⋊C4—736no—
971C2×C4⋊C4—736no—
972C2×C4⋊C4—736no—
973C2×C4⋊C4—736no—
974C2×C4⋊C4—736no—
975C2×C4⋊C4—736no—
976C2×C4⋊C4—736no—
977C2×C4⋊C4—736no—
978C2×C4⋊C4—736no—
979C2×C4⋊C4—736no—
980C2×C4⋊C4—736no—
981C2×C4⋊C4—736no—
982C2×C4⋊C4—733no—
983C2×C4⋊C4—733no—
984C2×C4⋊C4C22×D7316yes—
985C2×C22⋊C4—736no—
986C2×C22⋊C4—736no—
987C2×C22⋊C4—736no—
988C2×C22⋊C4—736no—
989C2×C22⋊C4—736no—
990C2×C22⋊C4—736no—
991C2×C22⋊C4—736no—
992C2×C42—733no—
993C2×C42—732no—
994C2×C42—736no—
995C2×C42—733no—
996C2×C42—732no—
997C2×C42—731no—
998C2×C42—731no—
999C2×C42—733no—
1000C2×C42C22×D7311yescharacteristic
1001C24—736no—
1002C24—731no—
1003C2×Q8—2926no—
1004C2×Q8—736no—
1005C2×Q8—733no—
1006C2×Q8C23×D7313yes—
1007C2×D4—29212no—
1008C2×D4—29212no—
1009C2×D4—29212no—
1010C2×D4—2926no—
1011C2×D4—736no—
1012C2×D4—736no—
1013C2×D4—736no—
1014C2×D4—736no—
1015C2×D4—736no—
1016C2×D4—736no—
1017C2×D4—736no—
1018C2×D4—736no—
1019C2×D4—733no—
1020C2×D4—736no—
1021C2×D4—736no—
1022C2×D4C23×D7316yes—
1023C2×D4C23×D7313yes—
1024C2×D4C23×D7316yes—
1025C2×D4C23×D7316yes—
1026C22×C4—29212no—
1027C22×C4—2926no—
1028C22×C4—29212no—
1029C22×C4—29212no—
1030C22×C4—733no—
1031C22×C4—736no—
1032C22×C4—736no—
1033C22×C4—736no—
1034C22×C4—733no—
1035C22×C4—733no—
1036C22×C4—736no—
1037C22×C4—736no—
1038C22×C4—736no—
1039C22×C4—736no—
1040C22×C4—736no—
1041C22×C4—736no—
1042C22×C4—733no—
1043C22×C4—733no—
1044C22×C4—736no—
1045C22×C4—736no—
1046C22×C4—736no—
1047C22×C4C23×D7313yes—
1048C22×C4C23×D7316yes—
1049C22×C4C23×D7316yes—
1050C22×C4C23×D7316yes—
1051C4⋊C4—736no—
1052C4⋊C4—736no—
1053C4⋊C4—736no—
1054C4⋊C4—736no—
1055C4⋊C4—736no—
1056C4⋊C4—736no—
1057C4⋊C4—736no—
1058C4⋊C4—736no—
1059C4⋊C4—736no—
1060C4⋊C4—736no—
1061C4⋊C4—736no—
1062C4⋊C4—736no—
1063C4⋊C4—736no—
1064C4⋊C4—736no—
1065C4⋊C4—736no—
1066C4⋊C4—736no—
1067C4⋊C4—736no—
1068C4⋊C4—736no—
1069C4⋊C4—736no—
1070C4⋊C4—736no—
1071C4⋊C4—736no—
1072C4⋊C4—736no—
1073C4⋊C4—736no—
1074C4⋊C4—736no—
1075C4⋊C4—736no—
1076C4⋊C4—736no—
1077C4⋊C4—733no—
1078C4⋊C4—733no—
1079C4⋊C4C23×D7316yes—
1080C4⋊C4C23×D7316yes—
1081C4⋊C4C23×D7316yes—
1082C4⋊C4C23×D7316yes—
1083C4⋊C4C23×D7316yes—
1084C4⋊C4C23×D7316yes—
1085C4⋊C4C23×D7316yes—
1086C4⋊C4C23×D7316yes—
1087C4⋊C4C23×D7313yes—
1088C4⋊C4C23×D7313yes—
1089C22⋊C4—736no—
1090C22⋊C4—736no—
1091C22⋊C4—736no—
1092C22⋊C4—736no—
1093C22⋊C4—736no—
1094C22⋊C4—736no—
1095C22⋊C4—736no—
1096C22⋊C4—736no—
1097C22⋊C4—736no—
1098C22⋊C4—736no—
1099C22⋊C4—736no—
1100C22⋊C4—736no—
1101C22⋊C4—736no—
1102C22⋊C4—736no—
1103C22⋊C4—736no—
1104C22⋊C4—736no—
1105C22⋊C4—736no—
1106C22⋊C4—736no—
1107C22⋊C4—736no—
1108C22⋊C4—736no—
1109C22⋊C4—736no—
1110C22⋊C4C23×D7316yes—
1111C22⋊C4C23×D7316yes—
1112C22⋊C4C23×D7316yes—
1113C22⋊C4C23×D7316yes—
1114C22⋊C4C23×D7316yes—
1115C22⋊C4C23×D7316yes—
1116C22⋊C4C23×D7316yes—
1117C42—733no—
1118C42—733no—
1119C42—733no—
1120C42—733no—
1121C42—736no—
1122C42—736no—
1123C42—736no—
1124C42—736no—
1125C42—736no—
1126C42C23×D7313yes—
1127C42C23×D7311yescharacteristic
1128C42C23×D7312yes—
1129C42C23×D7316yes—
1130C42C23×D7312yes—
1131C23—731no—
1132C23—736no—
1133C23—731no—
1134C23—14612no—
1135C23—14612no—
1136C23—1466no—
1137C23—14612no—
1138C23C24×D7316yes—
1139C23C24×D7311yescharacteristic
1140Q8—43no—
1141Q8—2926no—
1142Q8—2923no—
1143D4—46no—
1144D4—46no—
1145D4—46no—
1146D4—43no—
1147D4—2926no—
1148D4—2926no—
1149D4—2926no—
1150D4—2923no—
1151D4—2926no—
1152D4—2926no—
1153D4—2926no—
1154D4—2926no—
1155D4—2926no—
1156D4—2926no—
1157D4—2926no—
1158C2×C4—46no—
1159C2×C4—43no—
1160C2×C4—46no—
1161C2×C4—46no—
1162C2×C4—2926no—
1163C2×C4—2923no—
1164C2×C4—2926no—
1165C2×C4—2926no—
1166C2×C4—2926no—
1167C2×C4—2926no—
1168C2×C4—2926no—
1169C2×C4—2923no—
1170C2×C4—2926no—
1171C2×C4—2923no—
1172C2×C4—2926no—
1173C2×C4—2926no—
1174C2×C4—733no—
1175C2×C4—733no—
1176C2×C4—736no—
1177C2×C4—736no—
1178C2×C4—736no—
1179C2×C4—1466no—
1180C2×C4—14612no—
1181C2×C4—14612no—
1182C2×C4—14612no—
1183C2×C4—1466no—
1184C2×C4C24×D7313yes—
1185C2×C4C24×D7313yes—
1186C2×C4C24×D7316yes—
1187C2×C4C24×D7316yes—
1188C2×C4C24×D7316yes—
1189C22—26no—
1190C22—26no—
1191C22—23no—
1192C22—26no—
1193C22—29224no—
1194C22—2924no—
1195C22—736no—
1196C22—1466no—
1197C22—1466no—
1198C22—1463no—
1199C22—1466no—
1200C22C25×D7311yescharacteristic
1201C4—23no—
1202C4—26no—
1203C4—26no—
1204C4—26no—
1205C4—23no—
1206C4—1463no—
1207C4—1466no—
1208C4—1466no—
1209C4—1466no—
1210C4—1463no—
1211C2—46no—
1212C2—41no—
1213C2—2926no—
1214C2—2921no—
1215C2—734no—
1216C2#585×D7313yes—
subgroupG/H
center, FrattiniC22C25×D73
commutator, socle, cosocleC22×C73C26
FittingC73×#3567C2
hypercenter#3567D73
hypocenterC73C2×#3567
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ #3567

Complements

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

NH ≅ G/Ntype
1. #22624621C2semidirect
2. #22624620C2semidirect
3. #22624619C2semidirect
4. #22624618C2semidirect
5. #22624617C2semidirect
6. #22624616C2semidirect
7. #22624615C2semidirect
8. #564×D73C2semidirect
9. #562×D73C2semidirect
10. #553×D73C2semidirect
11. #552×D73C2semidirect
12. #540×D73C2semidirect
13. #539×D73C2semidirect
14. #529×D73C2semidirect
15. C73×#3567C2semidirect
16. C73⋊#564C22semidirect
17. C73⋊#564C22semidirect
18. C73⋊#564C22semidirect
19. #17989335C22semidirect
20. #17989334C22semidirect
21. #17989334C22semidirect
22. #17989333C22semidirect
23. #17989333C22semidirect
24. #17989332C22semidirect
25. #17989332C22semidirect
26. #17989331C22semidirect
27. #17989331C22semidirect
28. #17989290C22semidirect
29. #17989289C22semidirect
30. #17989288C22semidirect
31. #17989288C22semidirect
32. #17989287C22semidirect
33. #17989286C22semidirect
34. #17989286C22semidirect
35. #17989285C22semidirect
36. #17989284C22semidirect
37. #17989283C22semidirect
38. #17989282C22semidirect
39. #17989282C22semidirect
40. #17989281C22semidirect
41. #17989280C22semidirect
42. #17989280C22semidirect
43. #17989279C22semidirect
44. #17989278C22semidirect
45. #17989277C22semidirect
46. #17989276C22semidirect
47. #17989275C22semidirect
48. #17989274C22semidirect
49. #17989274C22semidirect
50. #17989273C22semidirect
51. #17989273C22semidirect
52. #17989272C22semidirect
53. #17989271C22semidirect
54. #17989270C22semidirect
55. #17989270C22semidirect
56. #17989269C22semidirect
57. #17989269C22semidirect
58. #17989193C22semidirect
59. #17989192C22semidirect
60. #17989191C22semidirect
61. #17989190C22semidirect
62. #17989190C22semidirect
63. #17989189C22semidirect
64. #17989189C22semidirect
65. #17989189C22semidirect
66. #17989189C22semidirect
67. #17989188C22semidirect
68. #17989188C22semidirect
69. #17989187C22semidirect
70. #17989187C22semidirect
71. #17989187C22semidirect
72. #17989187C22semidirect
73. #17989186C22semidirect
74. #17989185C22semidirect
75. #17989185C22semidirect
76. #17989184C22semidirect
77. #17989183C22semidirect
78. #17989183C22semidirect
79. #17989182C22semidirect
80. #17989181C22semidirect
81. #17989181C22semidirect
82. #17989180C22semidirect
83. #17989180C22semidirect
84. #17989179C22semidirect
85. #17989179C22semidirect
86. #17989178C22semidirect
87. #17989178C22semidirect
89. #17989124C22semidirect
90. #17989123C22semidirect
91. #17989122C22semidirect
92. #17989121C22semidirect
93. #17989120C22semidirect
94. #17989119C22semidirect
95. #17989118C22semidirect
96. #17989117C22semidirect
97. #17989116C22semidirect
98. #17989115C22semidirect
99. #17989114C22semidirect
130. #564×C73C22semidirect
131. #562×C73C22semidirect
132. #553×C73C22semidirect
133. #552×C73C22semidirect
134. #540×C73C22semidirect
135. #539×C73C22semidirect
136. #529×C73C22semidirect
608. D73#3567direct (N × H)
616. #3567D73direct (N × H)
624. C73C2×#3567semidirect
628. #564C2×D73semidirect
638. #562C2×D73semidirect
654. #553C2×D73semidirect
670. #552C2×D73semidirect
686. #540C2×D73semidirect
702. #539C2×D73semidirect
715. #529C2×D73semidirect

Maximal subgroups

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

subgroupindex
#226246212
#226246202
#226246192
#226246182
#226246172
#226246162
#226246152
#564×D732
#562×D732
#553×D732
#552×D732
#540×D732
#539×D732
#529×D732
C73×#35672
C2×#356773