Finite Group Databasebeta

← #33994379

Subgroups — #33994379

Order 18688.

7856 conjugacy classes of subgroups.

The subgroup lattice has 1034 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22624017C212yesmaximal, complemented
2#22623964C216yesmaximal, complemented
3#22623938C212yesmaximal, complemented
4#22623893C216yesmaximal, complemented
5#22623844C213yesmaximal, complemented
6#22623808C213yesmaximal, complemented
7#22623709C211yesmaximal, characteristic, complemented
8#22623669C216yesmaximal, complemented
9#22623601C212yesmaximal, complemented
10#22623558C212yesmaximal, complemented
11#22623542C216yesmaximal, complemented
12#22623531C212yesmaximal, complemented
13D4×#11924029C216yesmaximal, complemented
14#22623354C216yesmaximal, complemented
15#22623228C213yesmaximal, complemented
16C2×#17989138C213yesmaximal, complemented
17#22623137C212yesmaximal, complemented
18C4×#41×D73C211yesmaximal, characteristic, complemented
19C73×#3503C211yesmaximal, characteristic, complemented
20C2×#14556637C2212yes—
21C22×#11924029C2216yescomplemented
22C2×#41×D73C2211yescharacteristic
23#17989322C2216yescomplemented
24#17989322C2216yescomplemented
25#17989311C2216yescomplemented
26#17989303C2216yescomplemented
27#17989303C22112yescomplemented
28#17989298C2216yescomplemented
29#17989290C22112yescomplemented
30#17989290C22112yescomplemented
31#17989285C22112yescomplemented
32#17989264C22124yescomplemented
33#17989259C2212yescomplemented
34#17989259C2212yescomplemented
35#17989259C2216yescomplemented
36#17989259C2216yescomplemented
37#17989259C2214yescomplemented
38#17989249C2214yescomplemented
39#17989248C22112yescomplemented
40#17989240C22112yescomplemented
41#17989240C2216yescomplemented
42#17989232C22112yescomplemented
43#17989228C22112yescomplemented
44#17989228C22112yescomplemented
45#17989228C22124yescomplemented
46D4×D292C2216yescomplemented
47D4×D292C22112yescomplemented
48D4×D292C2216yescomplemented
49#17989211C22112yescomplemented
50#17989211C22112yescomplemented
51#17989193C22112yescomplemented
52#17989193C22112yescomplemented
53#17989177C22124yescomplemented
54#17989168C2216yescomplemented
55#17989156C2216yescomplemented
56#17989156C2216yescomplemented
57#17989142C2213yescomplemented
58#17989142C2211yescharacteristic, complemented
59#17989138C2216yescomplemented
60#17989138C2216yescomplemented
61#17989138C2216yescomplemented
62#17989138C2213yescomplemented
63#17989138C2216yescomplemented
64#17989138C22112yescomplemented
65#17989138C2216yescomplemented
66#17989138C2216yescomplemented
67#17989138C2216yescomplemented
68#17989138C2213yescomplemented
69#17989137C2213yescomplemented
70C2×#14556588C2213yescomplemented
71#17989124C2216yescomplemented
72#17989124C2216yescomplemented
73#17989123C2216yescomplemented
74#17989123C2216yescomplemented
75#17989122C22112yescomplemented
76#17989122C2216yescomplemented
77#17989122C2216yescomplemented
78C2×#14556580C2216yescomplemented
79#17989100C22124yescomplemented
80#17989100C2216yescomplemented
81#17989100C2216yescomplemented
82#17989099C2216yescomplemented
83C2×#14556566C2216yescomplemented
84C2×#14556566C2216yescomplemented
85#17989069C2214yescomplemented
86#17989068C2216yescomplemented
87#17989061C2216yescomplemented
88#17989059C22112yescomplemented
89#41×Dic73C2211yescharacteristic
90C4×#11924029C2214yescomplemented
91C4×#11924029C2216yescomplemented
92C4×#11924029C2216yescomplemented
93C4×#11924029C2211yescharacteristic, complemented
94C4×#11924029C2211yescharacteristic, complemented
95C4×#11924028C2213yescomplemented
96#17989055C2213yescomplemented
97#17989055C2216yescomplemented
98C4×#11924027C2213yescomplemented
99C4×#11924027C2213yescomplemented
100C4×Q8×D73C2211yescharacteristic, complemented
101C4×Q8×D73C2211yescharacteristic, complemented
102C2×#14556553C2216yescomplemented
103C2×#14556553C2216yescomplemented
104C4×D4×D73C22112yescomplemented
105C4×D4×D73C2213yescomplemented
106C4×D4×D73C2213yescomplemented
107#117×D73C2213yescomplemented
108C2×C42×D73C2213yescomplemented
109Q82×C73C2212yescomplemented
110#557×C73C2212yescomplemented
111#554×C73C2216yescomplemented
112D4×Q8×C73C2216yescomplemented
113#544×C73C2216yescomplemented
114#533×C73C2213yescomplemented
115C2×C4⋊Q8×C73C2213yescomplemented
116#520×C73C2212yes—
117C4×#41×C73C2211yescharacteristic
118#14556637—216no—
119C2×#11924029—424no—
120C2×#11924029C2316yes—
121C2×#11924029C2311yescharacteristic
122C2×#11924029C2314yes—
123C2×#11924029C23112yes—
124C2×#11924029C23112yes—
125C2×#11924029C23112yes—
126C2×#11924029C2316yes—
127C2×#11924028C2316yes—
128C2×#11924028C2313yes—
129C2×#11924027C2313yes—
130#41×D73—28no—
131C2×Q8×D73C2311yescharacteristic
132C22×D292C2316yes—
133C22×D292C2316yes—
134C22×D292C2316yes—
135C22×D292C23112yes—
136C2×D4×D73C2313yes—
137C2×D4×D73C23112yes—
138C22×C4×D73C2313yes—
139C22×C4×D73C2313yes—
140C22×C4×D73C23112yes—
141C22×C4×D73C2313yes—
142#14556591C2311yescharacteristic
143#14556588C2313yes—
144#14556588C2316yes—
145#14556588C2316yes—
146#14556588C2316yes—
147#14556588C23112yes—
148#14556586C23112yes—
149#14556586C23112yes—
150#14556586C23124yes—
151#14556582C2312yes—
152#14556582C2316yes—
153#14556580C2316yes—
154#14556580C2316yes—
155#14556580C23112yes—
156#14556580C23112yes—
157#14556580C23112yes—
158#14556580C23124yes—
159#14556579C2316yes—
160#14556579C23112yes—
161#14556576C23112yes—
162#14556576C23112yes—
163#14556576C23124yes—
164#14556576C23124yes—
165#14556576C23124yes—
166#14556575C23112yes—
167#14556571C2312yes—
168#14556571C2316yes—
169#14556571C23112yes—
170#14556567C2312yes—
171#14556567C2316yes—
172#14556567C23124yes—
173#14556566C2316yes—
174#14556566C2316yes—
175#14556566C23112yes—
176#14556566C2316yes—
177#14556566C2316yes—
178#14556566C23112yes—
179#14556566C23112yes—
180#14556566C23112yes—
181#14556566C23112yes—
182#14556566C23112yes—
183#14556566C23112yes—
184#14556566C23112yes—
185#14556566C23112yes—
186#14556566C23124yes—
187#14556566C23124yes—
188#14556565C2316yes—
189#14556565C2316yes—
190#14556565C23124yes—
191#14556561C23124yes—
192#14556561C23124yes—
193#14556561C23112yes—
194Q8×Dic73C2312yes—
195Q8×Dic73C2316yes—
196Q8×Dic73C2311yescharacteristic
197Q8×Dic73C2311yescharacteristic
198C4×Dic146C2313yes—
199C4×Dic146C2313yes—
200#14556556C2313yes—
201#14556556C2312yes—
202#14556556C2316yes—
203#14556556C2313yes—
204C4×D292C2316yes—
205C4×D292C2316yes—
206C4×D292C23112yes—
207C4×D292C23112yes—
208C4×D292C2313yes—
209C4×D292C23112yes—
210C4×D292C2313yes—
211C4×D292C23112yes—
212D4×Dic73C2313yes—
213D4×Dic73C2313yes—
214#14556553C23112yes—
215#14556553C23112yes—
216#14556553C2316yes—
217#14556553C23112yes—
218#14556553C2316yes—
219#14556553C23112yes—
220#14556553C2316yes—
221#14556553C2316yes—
222#14556553C2313yes—
223#14556553C23112yes—
224#14556553C23112yes—
225#14556553C23112yes—
226#14556553C23112yes—
227#14556553C2313yes—
228C4×C22⋊D73C2316yes—
229C4×C22⋊D73C2316yes—
230C4×C22⋊D73C23124yes—
231#14556551C23112yes—
232#14556551C23112yes—
233#14556551C2316yes—
234#14556551C2316yes—
235#14556550C2313yes—
236#14556549C23112yes—
237#14556549C23112yes—
238#14556549C2316yes—
239#14556549C2312yes—
240#14556549C2313yes—
241#14556549C23112yes—
242#14556549C2313yes—
243#14556548C23112yes—
244#14556548C2316yes—
245#14556547C2316yes—
246C4⋊C4×D73C2313yes—
247C4⋊C4×D73C23112yes—
248C4⋊C4×D73C2313yes—
249C2×#11924005C23112yes—
250C2×#11924005C23112yes—
251C22⋊C4×D73C2316yes—
252C22⋊C4×D73C23124yes—
253C2×C4×Dic73C2313yes—
254C2×C4×Dic73C2313yes—
255C2×C4×Dic73C2313yes—
256C42×D73C2313yes—
257C42×D73C2313yes—
258C42×D73C23112yes—
259C42×D73C2313yes—
260C42×D73C2313yes—
261C42×D73C2311yescharacteristic
262C42×D73C2313yes—
263C42×D73C2313yes—
264C42×D73C2313yes—
265C2×#41×C73C2311yescharacteristic
266C22×Q8×C73C2316yes—
267C4⋊Q8×C73C2313yes—
268C4⋊Q8×C73C2311yescharacteristic
269C4⋊Q8×C73C2316yes—
270C4⋊Q8×C73C2316yes—
271C4⋊Q8×C73C2316yes—
272C4⋊Q8×C73C23112yes—
273#125×C73C2316yes—
274#125×C73C23112yes—
275C22⋊Q8×C73C2316yes—
276C22⋊Q8×C73C2316yes—
277C22⋊Q8×C73C23124yes—
278C4×Q8×C73C2316yes—
279C4×Q8×C73C2316yes—
280C4×Q8×C73C2314yes—
281C4×Q8×C73C2311yescharacteristic
282C4×Q8×C73C2311yescharacteristic
283C4×D4×C73C2313yes—
284C4×D4×C73C2313yes—
285C4×D4×C73C23112yes—
286#117×C73C2313yes—
287#117×C73C2316yes—
288C2×C4⋊C4×C73C2316yes—
289C2×C4⋊C4×C73C2316yes—
290C2×C42×C73C2313yes—
291C23×D73C2413yes—
292C23×D73C24112yes—
293#11924029—24no—
294#11924029—216no—
295#11924029—224no—
296#11924029—424no—
297#11924029—424no—
298#11924029—424no—
299#11924029—412no—
300#11924028—212no—
301#11924028—224no—
302#11924027—212no—
303C2×Dic146C2412yes—
304C2×Dic146C2413yes—
305Q8×D73—24no—
306C2×D292—224no—
307C2×D292—412no—
308C2×D292—412no—
309C2×D292—424no—
310C2×D292C2416yes—
311C2×D292C2416yes—
312C2×D292C24112yes—
313C2×D292C2413yes—
314C2×D292C24112yes—
315C2×D292C2416yes—
316C2×D292C24112yes—
317C2×D292C24112yes—
318C2×D292C24112yes—
319C2×D292C24124yes—
320C2×C22⋊D73C2416yes—
321C2×C22⋊D73C24112yes—
322D4×D73—212no—
323D4×D73—248no—
324C22×Dic73C2413yes—
325C22×Dic73C2413yes—
326C22×Dic73C2413yes—
327C2×C4×D73—212no—
328C2×C4×D73—212no—
329C2×C4×D73—424no—
330C2×C4×D73—46no—
331C2×C4×D73C2411yescharacteristic
332C2×C4×D73C2411yescharacteristic
333C2×C4×D73C2413yes—
334C2×C4×D73C2413yes—
335C2×C4×D73C2413yes—
336C2×C4×D73C2413yes—
337C2×C4×D73C2413yes—
338C2×C4×D73C2413yes—
339C2×C4×D73C2413yes—
340C2×C4×D73C24112yes—
341C2×C4×D73C24112yes—
342C2×C4×D73C2413yes—
343C2×C4×D73C2413yes—
344C2×C4×D73C24112yes—
345C2×C4×D73C24124yes—
346C2×C4×D73C2411yescharacteristic
347C4⋊Dic73C2413yes—
348C4⋊Dic73C2413yes—
349C4⋊Dic73C2412yes—
350C4⋊Dic73C2414yes—
351C4⋊Dic73C2412yes—
352C4⋊Dic73C24112yes—
353#11924007C24112yes—
354#11924007C2416yes—
355#11924007C2416yes—
356#11924007C2414yes—
357C22⋊Dic73C2416yes—
358#11924005C24112yes—
359#11924005C24124yes—
360#11924005C2416yes—
361#11924005C2416yes—
362#11924005C24112yes—
363#11924005C24112yes—
364#11924005C24124yes—
365#11924005C2414yes—
366#11924005C24112yes—
367#11924005C24112yes—
368#11924005C24112yes—
369#11924005C24112yes—
370C4×Dic73C2413yes—
371C4×Dic73C2411yescharacteristic
372C4×Dic73C2411yescharacteristic
373C4×Dic73C2411yescharacteristic
374C4×Dic73C2414yes—
375C4×Dic73C2413yes—
376C4×Dic73C2413yes—
377C4×Dic73C2413yes—
378C4×Dic73C2413yes—
379C4×Dic73C2413yes—
380C4×Dic73C2413yes—
381C4×Dic73C2413yes—
382C4×Dic73C2413yes—
383C4×Dic73C24112yes—
384#41×C73#4118yescomplemented
385C2×Q8×C73—412no—
386C2×Q8×C73C2412yes—
387C2×Q8×C73C2416yes—
388C2×Q8×C73C24112yes—
389C2×Q8×C73C2411yescharacteristic
390C2×D4×C73C2413yes—
391C22×C4×C73C2413yes—
392C22×C4×C73C2413yes—
393C22×C4×C73C24112yes—
394C22×C4×C73C2413yes—
395C4⋊C4×C73C2416yes—
396C4⋊C4×C73C2416yes—
397C4⋊C4×C73C24112yes—
398C4⋊C4×C73C24112yes—
399C4⋊C4×C73C2412yes—
400C4⋊C4×C73C2413yes—
401C4⋊C4×C73C2413yes—
402C4⋊C4×C73C2412yes—
403C4⋊C4×C73C24112yes—
404C4⋊C4×C73C24112yes—
405C22⋊C4×C73C24112yes—
406C22⋊C4×C73C2416yes—
407C42×C73C2411yescharacteristic
408C42×C73C2413yes—
409C42×C73C2413yes—
410C42×C73C2413yes—
411C42×C73C24112yes—
412C23×C73C2513yes—
413C22×D73—26no—
414C22×D73—224no—
415C22×D73—26no—
416C22×D73—43no—
417C22×D73—412no—
418C22×D73—412no—
419C22×D73C25112yes—
420C22×D73C2513yes—
421C22×D73C2511yescharacteristic
422Q8×C73—212no—
423Q8×C73—24no—
424Q8×C73—412no—
425Q8×C73C2×#4114yescomplemented
426D4×C73C2×#41112yescomplemented
427C2×C4×C73—26no—
428C2×C4×C73—26no—
429C2×C4×C73—412no—
430C2×C4×C73C2×#41112yescomplemented
431C2×C4×C73C2514yes—
432C2×C4×C73C2513yes—
433C2×C4×C73C2513yes—
434C2×C4×C73C25112yes—
435C2×C4×C73C2513yes—
436C2×C4×C73C2511yescharacteristic
437C2×C4×C73C2511yescharacteristic
438C2×C4×C73C2511yescharacteristic
439C22⋊D73—224no—
440C22⋊D73—212no—
441C2×Dic73—26no—
442C2×Dic73—26no—
443C2×Dic73—43no—
444C2×Dic73C2511yescharacteristic
445C2×Dic73C2511yescharacteristic
446C2×Dic73C2513yes—
447C2×Dic73C2513yes—
448C2×Dic73C2514yes—
449C2×Dic73C2513yes—
450C2×Dic73C2511yescharacteristic
451D292—224no—
452D292—224no—
453D292—26no—
454D292—212no—
455D292—212no—
456D292—212no—
457D292—412no—
458D292—412no—
459D292—424no—
460D292—412no—
461C4×D73—26no—
462C4×D73—22no—
463C4×D73—26no—
464C4×D73—26no—
465C4×D73—26no—
466C4×D73—224no—
467C4×D73—26no—
468C4×D73—22no—
469C4×D73—26no—
470C4×D73—26no—
471C4×D73—224no—
472C4×D73—43no—
473C4×D73—43no—
474C4×D73—424no—
475C4×D73—412no—
476C4×D73H(5,𝔽2)14yescomplemented
477Dic146—26no—
478Dic146—24no—
479C22×C73—23no—
480C22×C73—23no—
481C22×C73C22×#4116yes—
482C22×C73C2611yescharacteristic
483C2×D73—21no—
484C2×D73—21no—
485C2×D73—23no—
486C2×D73—212no—
487C2×D73—23no—
488C2×D73—212no—
489C2×D73—23no—
490C2×D73—212no—
491C2×D73—412no—
492C2×D73—824no—
493C2×D73C2×H(5,𝔽2)12yes—
494C4×C73—23no—
495C4×C73—212no—
496C4×C73—24no—
497C4×C73—23no—
498C4×C73C22×#4112yes—
499C4×C73C22×#4116yes—
500C4×C73C2×H(5,𝔽2)12yes—
501C4×C73#58512yes—
502Dic73—23no—
503Dic73—24no—
504Dic73—21no—
505Dic73—23no—
506Dic73—23no—
507Dic73—21no—
508Dic73C2×H(5,𝔽2)12yes—
509#62800—731nomaximal, Sylow
510C2×C73—26no—
511C2×C73C23×#4111yescharacteristic
512C2×C73C22×H(5,𝔽2)11yescharacteristic
513C2×C73C2×#58511yescharacteristic
514D73—22no—
515D73—43no—
516D73—412no—
517#3522—732no—
518#3519—736no—
519#3517—732no—
520#3514—736no—
521#3511—733no—
522#3508—733no—
523#3503D7311yescharacteristic, complemented
524#3498—731no—
525#3494—736no—
526#3488—732no—
527#3483—732no—
528#3481—736no—
529#3480—732no—
530D4×#41—736no—
531#3460—736no—
532#3444—733no—
533C2×#532—733no—
534C4×H(5,𝔽2)—732no—
535C2×C4×#41—731no—
536C73#6280011yescharacteristic, complemented, Sylow
537C2×H(5,𝔽2)—732no—
538C22×#41—731no—
539C22×#41—736no—
540#559—736no—
541#559—736no—
542Q82C2×D7312yescomplemented
543#557C2×D7312yescomplemented
544#556—736no—
545#555—7312no—
546#555—736no—
547#554—736no—
548#554C2×D7316yescomplemented
549#553—7312no—
550#553—7312no—
551#553—7312no—
552#551—7324no—
553#550—736no—
554#550—732no—
555#550—734no—
556#550—732no—
557#550—736no—
558D4×Q8C2×D7316yescomplemented
559#548—7312no—
560#548—734no—
561#547—7312no—
562#547—736no—
563#546—7324no—
564#546—7312no—
565#546—7312no—
566#546—7312no—
567D42—7312no—
568D42—736no—
569D42—736no—
570#544C2×D7316yescomplemented
571#542—7312no—
572#542—7312no—
573#540—7312no—
574#540—7312no—
575#538—7324no—
576#537—736no—
577#535—736no—
578#535—736no—
579#533—731no—
580#533—733no—
581#533C2×D7313yescomplemented
582#532—733no—
583#532—736no—
584#532—736no—
585#532—736no—
586#532—736no—
587#532—736no—
588#532—736no—
589#532—736no—
590#532—733no—
591#532—7312no—
592#532—733no—
593C2×C4⋊Q8C2×D7313yescomplemented
594C2×#127—733no—
595#529—736no—
596#529—736no—
597#529—7312no—
598#529—736no—
599#529—736no—
600#529—736no—
601#529—736no—
602C2×#124—736no—
603#525—736no—
604#525—736no—
605#525—7324no—
606#525—736no—
607C2×#121—736no—
608C2×#121—736no—
609#520—734no—
610#520—736no—
611#520C2×D7312yes—
612#518—7312no—
613#518—736no—
614C4×#41—731no—
615C4×#41—731no—
616C4×#41—731no—
617C4×#41—734no—
618C4×#41—736no—
619C4×#41—736no—
620C4×#41—733no—
621C4×#41—733no—
622C4×#41—733no—
623C4×#41—736no—
624C4×#41—733no—
625C4×#41C2×D7311yescharacteristic
626C2×C4×Q8—731no—
627C2×C4×Q8—731no—
628C2×C4×D4—733no—
629C2×C4×D4—733no—
630C2×C4×D4—7312no—
631C2×C4×D4—736no—
632C2×C4×D4—736no—
633C2×#117—733no—
634C22×C42—733no—
635H(5,𝔽2)—14616no—
636C2×#41—29224no—
637C2×#41—736no—
638C2×#41—7312no—
639C2×#41—7312no—
640C2×#41—7312no—
641C2×#41—731no—
642C2×#41—734no—
643C2×#41—736no—
644C2×#41—733no—
645C2×#41—733no—
646C2×#41—736no—
647C2×#41—1468no—
648C2×#41C22×D7311yescharacteristic
649C22×Q8—731no—
650C22×Q8C22×D7316yes—
651C22×D4—733no—
652C22×D4—7312no—
653C22×D4—736no—
654C22×D4—7312no—
655C22×D4—736no—
656C22×D4—736no—
657C23×C4—7312no—
658C23×C4—733no—
659C23×C4—733no—
660C23×C4—733no—
661C4⋊Q8—731no—
662C4⋊Q8C22×D7313yes—
663C4⋊Q8C22×D7316yes—
664C4⋊Q8C22×D7316yes—
665C4⋊Q8C22×D7316yes—
666C4⋊Q8C22×D7311yescharacteristic
667C4⋊Q8C22×D73112yes—
668#127—733no—
669#127—736no—
670#127—736no—
671#127—736no—
672#127—7312no—
673#126—7312no—
674#126—7312no—
675#126—7324no—
676#125—732no—
677#125—736no—
678#125C22×D7316yes—
679#125C22×D73112yes—
680#124—736no—
681#124—7312no—
682#124—7312no—
683#124—7312no—
684#124—736no—
685#124—7324no—
686#124—736no—
687#124—7312no—
688#123—7312no—
689#123—7312no—
690#123—7324no—
691#123—7324no—
692#123—7324no—
693#123—7312no—
694C22⋊Q8—732no—
695C22⋊Q8—736no—
696C22⋊Q8—7324no—
697C22⋊Q8—732no—
698C22⋊Q8—736no—
699C22⋊Q8—7312no—
700C22⋊Q8C22×D7316yes—
701C22⋊Q8C22×D7316yes—
702C22⋊Q8C22×D73124yes—
703#121—736no—
704#121—736no—
705#121—7324no—
706#121—736no—
707#121—736no—
708#121—7312no—
709#121—7312no—
710#121—7312no—
711#121—7312no—
712#121—7312no—
713#121—7312no—
714#121—736no—
715#121—736no—
716#121—7324no—
717#121—7312no—
718#121—7312no—
719#121—7312no—
720#121—7324no—
721#120—7312no—
722#120—7324no—
723#120—7324no—
724C4×Q8—731no—
725C4×Q8—731no—
726C4×Q8—732no—
727C4×Q8—736no—
728C4×Q8—733no—
729C4×Q8—733no—
730C4×Q8—732no—
731C4×Q8—736no—
732C4×Q8—733no—
733C4×Q8—733no—
734C4×Q8C22×D7311yescharacteristic
735C4×Q8C22×D7311yescharacteristic
736C4×Q8C22×D7314yes—
737C4×Q8C22×D7316yes—
738C4×Q8C22×D7316yes—
739C4×D4—733no—
740C4×D4—733no—
741C4×D4—736no—
742C4×D4—736no—
743C4×D4—7324no—
744C4×D4—7312no—
745C4×D4—736no—
746C4×D4—736no—
747C4×D4—733no—
748C4×D4—733no—
749C4×D4—7312no—
750C4×D4—7312no—
751C4×D4—7312no—
752C4×D4—7312no—
753C4×D4—7312no—
754C4×D4—736no—
755C4×D4—7312no—
756C4×D4—7312no—
757C4×D4—736no—
758C4×D4—7312no—
759C4×D4—736no—
760C4×D4—736no—
761C4×D4—7312no—
762C4×D4—733no—
763C4×D4—733no—
764C4×D4—7312no—
765C4×D4—7312no—
766C4×D4—7312no—
767C4×D4—7312no—
768C4×D4—736no—
769C4×D4—736no—
770C4×D4C22×D7313yes—
771C4×D4C22×D7313yes—
772C4×D4C22×D73112yes—
773#117—733no—
774#117—733no—
775#117—733no—
776#117—732no—
777#117—7312no—
778#117—7312no—
779#117—736no—
780#117—7312no—
781#117—736no—
782#117—736no—
783#117—7312no—
784#117C22×D7313yes—
785#117C22×D7316yes—
786C2×C4⋊C4—733no—
787C2×C4⋊C4—733no—
788C2×C4⋊C4—7312no—
789C2×C4⋊C4C22×D7316yes—
790C2×C4⋊C4C22×D7316yes—
791C2×C22⋊C4—7312no—
792C2×C22⋊C4—7312no—
793C2×C22⋊C4—736no—
794C2×C22⋊C4—7324no—
795C2×C42—733no—
796C2×C42—733no—
797C2×C42—733no—
798C2×C42—733no—
799C2×C42—733no—
800C2×C42—733no—
801C2×C42—7312no—
802C2×C42—733no—
803C2×C42—733no—
804C2×C42—733no—
805C2×C42—733no—
806C2×C42—731no—
807C2×C42C22×D7313yes—
808C24—7312no—
809C24—733no—
810#41—29224no—
811#41—29212no—
812#41—29224no—
813#41—29224no—
814#41—14624no—
815#41—1464no—
816#41—14616no—
817#41—14612no—
818#41—14612no—
819#41—14624no—
820#41#1192402918yescomplemented
821C2×Q8—412no—
822C2×Q8—733no—
823C2×Q8—732no—
824C2×Q8—1464no—
825C2×Q8C23×D7312yes—
826C2×Q8C23×D7316yes—
827C2×Q8C23×D73112yes—
828C2×Q8C23×D7311yescharacteristic
829C2×D4—29212no—
830C2×D4—29212no—
831C2×D4—29224no—
832C2×D4—736no—
833C2×D4—7312no—
834C2×D4—7312no—
835C2×D4—7312no—
836C2×D4—7312no—
837C2×D4—7324no—
838C2×D4—736no—
839C2×D4—7312no—
840C2×D4—736no—
841C2×D4—733no—
842C2×D4—7312no—
843C2×D4—736no—
844C2×D4—14612no—
845C2×D4—14648no—
846C2×D4—14624no—
847C2×D4C23×D7313yes—
848C22×C4—2926no—
849C22×C4—29224no—
850C22×C4—733no—
851C22×C4—733no—
852C22×C4—733no—
853C22×C4—7312no—
854C22×C4—7324no—
855C22×C4—731no—
856C22×C4—733no—
857C22×C4—733no—
858C22×C4—731no—
859C22×C4—731no—
860C22×C4—733no—
861C22×C4—733no—
862C22×C4—733no—
863C22×C4—733no—
864C22×C4—733no—
865C22×C4—733no—
866C22×C4—733no—
867C22×C4—7312no—
868C22×C4—7312no—
869C22×C4—14612no—
870C22×C4—14612no—
871C22×C4C23×D7313yes—
872C22×C4C23×D7313yes—
873C22×C4C23×D73112yes—
874C22×C4C23×D7313yes—
875C4⋊C4—7312no—
876C4⋊C4—736no—
877C4⋊C4—736no—
878C4⋊C4—734no—
879C4⋊C4—733no—
880C4⋊C4—733no—
881C4⋊C4—732no—
882C4⋊C4—734no—
883C4⋊C4—732no—
884C4⋊C4—7312no—
885C4⋊C4C23×D73112yes—
886C4⋊C4C23×D7313yes—
887C4⋊C4C23×D7313yes—
888C4⋊C4C23×D7316yes—
889C4⋊C4C23×D7316yes—
890C4⋊C4C23×D73112yes—
891C4⋊C4C23×D7312yes—
892C4⋊C4C23×D73112yes—
893C4⋊C4C23×D73112yes—
894C4⋊C4C23×D7312yes—
895C22⋊C4—736no—
896C22⋊C4—7312no—
897C22⋊C4—7324no—
898C22⋊C4—7312no—
899C22⋊C4—7312no—
900C22⋊C4—736no—
901C22⋊C4—736no—
902C22⋊C4—7324no—
903C22⋊C4—734no—
904C22⋊C4—7312no—
905C22⋊C4—7312no—
906C22⋊C4—7312no—
907C22⋊C4—7312no—
908C22⋊C4C23×D73112yes—
909C22⋊C4C23×D7316yes—
910C42—731no—
911C42—733no—
912C42—731no—
913C42—731no—
914C42—733no—
915C42—733no—
916C42—734no—
917C42—733no—
918C42—733no—
919C42—733no—
920C42—733no—
921C42—733no—
922C42—733no—
923C42—7312no—
924C42C23×D7311yescharacteristic
925C42C23×D7313yes—
926C42C23×D7313yes—
927C42C23×D7313yes—
928C42C23×D73112yes—
929C23—2923no—
930C23—29212no—
931C23—29212no—
932C23—731no—
933C23—7312no—
934C23—733no—
935C23—1466no—
936C23—1466no—
937C23—14624no—
938C23C24×D7313yes—
939Q8—212no—
940Q8—24no—
941Q8—412no—
942Q8—1466no—
943Q8—1464no—
944Q8C2×#1192402914yescomplemented
945D4—29212no—
946D4—29224no—
947D4—29212no—
948D4—29212no—
949D4—14624no—
950D4—14624no—
951D4—14612no—
952D4—14624no—
953D4—14612no—
954D4—1466no—
955D4—14612no—
956D4—14612no—
957D4C2×#11924029112yescomplemented
958C2×C4—26no—
959C2×C4—26no—
960C2×C4—412no—
961C2×C4—29224no—
962C2×C4—2923no—
963C2×C4—2923no—
964C2×C4—29212no—
965C2×C4—2923no—
966C2×C4—731no—
967C2×C4—734no—
968C2×C4—731no—
969C2×C4—731no—
970C2×C4—733no—
971C2×C4—733no—
972C2×C4—734no—
973C2×C4—733no—
974C2×C4—14624no—
975C2×C4—1466no—
976C2×C4—1466no—
977C2×C4—1466no—
978C2×C4—1466no—
979C2×C4—1462no—
980C2×C4—1466no—
981C2×C4—1466no—
982C2×C4—1466no—
983C2×C4—14624no—
984C2×C4—1466no—
985C2×C4—1462no—
986C2×C4—1466no—
987C2×C4C2×#11924029112yescomplemented
988C2×C4C24×D7313yes—
989C2×C4C24×D7313yes—
990C2×C4C24×D7314yes—
991C2×C4C24×D73112yes—
992C2×C4C24×D7311yescharacteristic
993C2×C4C24×D7313yes—
994C2×C4C24×D7311yescharacteristic
995C2×C4C24×D7311yescharacteristic
996C22—23no—
997C22—23no—
998C22—29212no—
999C22—58424no—
1000C22—732no—
1001C22—1463no—
1002C22—14612no—
1003C22—14612no—
1004C22—1463no—
1005C22—1463no—
1006C22—14612no—
1007C22—1461no—
1008C22—1461no—
1009C22C22×#1192402916yes—
1010C22C25×D7311yescharacteristic
1011C4—23no—
1012C4—212no—
1013C4—23no—
1014C4—24no—
1015C4—732no—
1016C4—1461no—
1017C4—1464no—
1018C4—1463no—
1019C4—1463no—
1020C4—1461no—
1021C4—1463no—
1022C4C22×#1192402916yes—
1023C4C22×#1192402912yes—
1024C4H(5,𝔽2)×D7312yes—
1025C4#1798942412yes—
1026C2—26no—
1027C2—2923no—
1028C2—29212no—
1029C2—1462no—
1030C2C23×#1192402911yescharacteristic
1031C2C2×H(5,𝔽2)×D7311yescharacteristic
1032C2C2×#1798942411yescharacteristic
subgroupG/H
center, FrattiniC22C25×D73
commutator, socle, cosocleC22×C73C26
FittingC73×#3503C2
hypercenter#3503D73
hypocenterC73#62800
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ #3503

Complements

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

NH ≅ G/Ntype
1. #22624017C2semidirect
2. #22623964C2semidirect
3. #22623938C2semidirect
4. #22623893C2semidirect
5. #22623844C2semidirect
6. #22623808C2semidirect
7. #22623709C2semidirect
8. #22623669C2semidirect
9. #22623601C2semidirect
10. #22623558C2semidirect
11. #22623542C2semidirect
12. #22623531C2semidirect
13. D4×#11924029C2semidirect
14. #22623354C2semidirect
15. #22623228C2semidirect
16. C2×#17989138C2semidirect
17. #22623137C2semidirect
18. C4×#41×D73C2semidirect
19. C73×#3503C2semidirect
21. C22×#11924029C22semidirect
23. #17989322C22semidirect
24. #17989322C22semidirect
25. #17989311C22semidirect
26. #17989303C22semidirect
27. #17989303C22semidirect
28. #17989298C22semidirect
29. #17989290C22semidirect
30. #17989290C22semidirect
31. #17989285C22semidirect
32. #17989264C22semidirect
33. #17989259C22semidirect
34. #17989259C22semidirect
35. #17989259C22semidirect
36. #17989259C22semidirect
37. #17989259C22semidirect
38. #17989249C22semidirect
39. #17989248C22semidirect
40. #17989240C22semidirect
41. #17989240C22semidirect
42. #17989232C22semidirect
43. #17989228C22semidirect
44. #17989228C22semidirect
45. #17989228C22semidirect
46. D4×D292C22semidirect
47. D4×D292C22semidirect
48. D4×D292C22semidirect
49. #17989211C22semidirect
50. #17989211C22semidirect
51. #17989193C22semidirect
52. #17989193C22semidirect
53. #17989177C22semidirect
54. #17989168C22semidirect
55. #17989156C22semidirect
56. #17989156C22semidirect
57. #17989142C22semidirect
58. #17989142C22semidirect
59. #17989138C22semidirect
60. #17989138C22semidirect
61. #17989138C22semidirect
62. #17989138C22semidirect
63. #17989138C22semidirect
64. #17989138C22semidirect
65. #17989138C22semidirect
66. #17989138C22semidirect
67. #17989138C22semidirect
68. #17989138C22semidirect
69. #17989137C22semidirect
70. C2×#14556588C22semidirect
71. #17989124C22semidirect
72. #17989124C22semidirect
73. #17989123C22semidirect
74. #17989123C22semidirect
75. #17989122C22semidirect
76. #17989122C22semidirect
77. #17989122C22semidirect
78. C2×#14556580C22semidirect
79. #17989100C22semidirect
80. #17989100C22semidirect
81. #17989100C22semidirect
82. #17989099C22semidirect
83. C2×#14556566C22semidirect
84. C2×#14556566C22semidirect
85. #17989069C22semidirect
86. #17989068C22semidirect
87. #17989061C22semidirect
88. #17989059C22semidirect
90. C4×#11924029C22semidirect
91. C4×#11924029C22semidirect
92. C4×#11924029C22semidirect
93. C4×#11924029C22semidirect
94. C4×#11924029C22semidirect
95. C4×#11924028C22semidirect
96. #17989055C22semidirect
97. #17989055C22semidirect
98. C4×#11924027C22semidirect
99. C4×#11924027C22semidirect
100. C4×Q8×D73C22semidirect
101. C4×Q8×D73C22semidirect
102. C2×#14556553C22semidirect
103. C2×#14556553C22semidirect
104. C4×D4×D73C22semidirect
105. C4×D4×D73C22semidirect
106. C4×D4×D73C22semidirect
107. #117×D73C22semidirect
108. C2×C42×D73C22semidirect
109. Q82×C73C22semidirect
110. #557×C73C22semidirect
111. #554×C73C22semidirect
112. D4×Q8×C73C22semidirect
113. #544×C73C22semidirect
114. #533×C73C22semidirect
115. C2×C4⋊Q8×C73C22semidirect
384. #41×C73#41semidirect
425. Q8×C73C2×#41semidirect
426. D4×C73C2×#41semidirect
430. C2×C4×C73C2×#41semidirect
476. C4×D73H(5,𝔽2)semidirect
523. #3503D73semidirect
536. C73#62800semidirect
542. Q82C2×D73semidirect
543. #557C2×D73semidirect
548. #554C2×D73semidirect
558. D4×Q8C2×D73semidirect
570. #544C2×D73semidirect
581. #533C2×D73semidirect
593. C2×C4⋊Q8C2×D73semidirect
820. #41#11924029semidirect
944. Q8C2×#11924029semidirect
957. D4C2×#11924029semidirect
987. C2×C4C2×#11924029semidirect

Maximal subgroups

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

subgroupindex
#226240172
#226239642
#226239382
#226238932
#226238442
#226238082
#226237092
#226236692
#226236012
#226235582
#226235422
#226235312
D4×#119240292
#226233542
#226232282
C2×#179891382
#226231372
C4×#41×D732
C73×#35032
#6280073