Finite Group Databasebeta

← #11904495

Subgroups — #11904495

Order 1152.

3409 conjugacy classes of subgroups.

The subgroup lattice has 907 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×Q8×C3⋊D3C211yesmaximal, characteristic, complemented
2C2×#64315C211yesmaximal, characteristic, complemented
3C3×#5817C211yesmaximal, characteristic, complemented
4C3×Q8×#67C211yesmaximal, characteristic, complemented
5#10595414C211yesmaximal, characteristic, complemented
6Q8×#626C211yesmaximal, characteristic, complemented
7#10595405C213yesmaximal, complemented
8#10595364C213yesmaximal, complemented
9#10595362C213yesmaximal, complemented
10#10595361C213yesmaximal, complemented
11#10595339C211yesmaximal, characteristic, complemented
12#10595016C213yesmaximal, complemented
13#10594922C213yesmaximal, complemented
14#10594918C213yesmaximal, complemented
15#10594915C213yesmaximal, complemented
16#86759—31nomaximal
17#86735—31nomaximal
18C22×C32×Q8C2211yescharacteristic
19C2×Q8×C3⋊D3—28no—
20C2×Q8×C3⋊D3C2213yes—
21C2×Q8×C3⋊D3C2213yes—
22C2×Q8×C3⋊D3C2211yescharacteristic
23C2×Q8×C3⋊D3C2211yescharacteristic
24C22×C4×C3⋊D3C2213yes—
25C22×#634C2213yes—
26C2×C3×#239C2211yescharacteristic, complemented
27C2×C3×D3×Q8C2211yescharacteristic, complemented
28#64315—28no—
29C2×#3798C2213yes—
30C2×#3796C2213yes—
31C2×#3795C2213yescomplemented
32C2×D3×Dic6C2213yescomplemented
33C3×#947C2213yescomplemented
34C3×#946C2213yescomplemented
35C3×#946C2213yescomplemented
36C3×Q8×Dic3C2211yescharacteristic, complemented
37C3×Q8×Dic3C2211yescharacteristic, complemented
38C3×#944C2213yescomplemented
39C3×#930C2213yes—
40C3×C4×#67C2213yes—
41C3×C4×#67C2213yes—
42C3×#924C2213yes—
43#63982C2213yes—
44#63981C2213yes—
45#63981C2211yescharacteristic
46#63980C2213yes—
47#67⋊Dic3C2216yes—
48#63916C2213yes—
49#63913C2216yescomplemented
50#63912C2213yes—
51C4×#626C2213yes—
52C4×#626C2213yes—
53#63896C2216yescomplemented
54#63896C2216yescomplemented
55#63881C2216yes—
56#63874C2213yes—
57#63871C2213yes—
58#63866C2213yescomplemented
59#63865C2213yes—
60#63860C2213yescomplemented
61#63857C2213yescomplemented
62#63857C2213yescomplemented
63#63853C2213yes—
64#63853C2216yes—
65#63853C2213yes—
66#63849C2213yes—
67#63844C2213yescomplemented
68#63844C2213yescomplemented
69#63840C2216yescomplemented
70C2×#1010—31no—
71C2×#1007—31no—
72C22×D3×Q8—31no—
73C22×D3×Q8—31no—
74C22×D3×Q8—61no—
75C3×D4×Q8—31no—
76C3×#548—31no—
77#5831—31no—
78#5817D311yescharacteristic, complemented
79Q8×#67—31no—
80Q8×#67D311yescharacteristic, complemented
81#5727—33no—
82#5724—33no—
83#5677—33no—
84#5675—33no—
85#5633—33no—
86#5632—33no—
87#5632—33no—
88#5628—33no—
89#5628—33no—
90#5627—33no—
91#5606—33no—
92#5598—33no—
93#5576—31no—
94Q8×D12—31no—
95#5572—31no—
96#5572—31no—
97#5552—33no—
98#5547—33no—
99#5547—33no—
100D4×Dic6—33no—
101C23×C3⋊D3C2311yescharacteristic
102C2×C32×Q8—24no—
103C2×C32×Q8C2313yes—
104C2×C32×Q8C2311yescharacteristic
105C22×C32×C4C2313yes—
106C22×C3⋊Dic3C2313yes—
107Q8×C3⋊D3—24no—
108Q8×C3⋊D3—212no—
109Q8×C3⋊D3—212no—
110Q8×C3⋊D3D418yescomplemented
111C2×C4×C3⋊D3—212no—
112C2×C4×C3⋊D3C2313yes—
113C2×C4×C3⋊D3C2313yes—
114C2×C4×C3⋊D3C2313yes—
115C2×C4×C3⋊D3C2313yes—
116C2×#634—212no—
117C2×#634C2316yes—
118C2×#634C2313yes—
119C2×#634C2313yes—
120C2×C3×#67C2311yescharacteristic
121C2×C3×#67C2313yes—
122C3×#239—24no—
123C3×D3×Q8—24no—
124C2×C3×D12C2313yes—
125C2×C3×C4×D3C2313yes—
126C2×C3×C4×D3C2313yes—
127C2×C3×Dic6C2313yes—
128C2×#627C2313yes—
129C2×#626C2313yes—
130C2×#626C2311yescharacteristic
131C2×#626C2313yes—
132C2×#626C2311yescharacteristic
133C2×#625C2313yes—
134C2×D3×Dic3C2316yes—
135#3798—212no—
136#3796—212no—
137#3795—212no—
138D3×Dic6—212no—
139C3×#217C2313yes—
140C3×#217C2311yescharacteristic
141C3×(C2×D3)⋊C4C2313yes—
142C3×(C2×D3)⋊C4C2313yes—
143C3×(C2×D3)⋊C4C2316yes—
144C3×C4⋊Dic3C2313yes—
145C3×C4⋊Dic3C2313yes—
146C3×Dic3⋊C4C2316yes—
147C3×Dic3⋊C4C2313yes—
148C3×Dic3⋊C4C2313yes—
149C3×C4×Dic3C2313yes—
150C3×C4×Dic3C2313yes—
151#3724C2313yes—
152#3724C2313yes—
153Dic3⋊Dic3C2313yes—
154Dic3⋊Dic3C2316yes—
155Dic3⋊Dic3C2313yes—
156#3722C2313yes—
157#3722C2311yescharacteristic
158#3722C2311yescharacteristic
159#3722C2313yes—
160(C2×D3)⋊Dic3C2313yes—
161(C2×D3)⋊Dic3C2316yes—
162(C2×D3)⋊Dic3C2313yes—
163Dic32C2316yes—
164#3486—91noSylow
165C2×C3×#41—31no—
166C22×C3×Q8—21no—
167C22×C3×Q8—31no—
168C22×C3×Q8C2×D311yescharacteristic
169C22×C3×Q8C2×D311yescharacteristic
170#1010—68no—
171#1007—68no—
172C2×#239—33no—
173C2×#239C2×D311yescharacteristic, complemented
174C2×D3×Q8—31no—
175C2×D3×Q8—31no—
176C2×D3×Q8—33no—
177C2×D3×Q8—33no—
178C2×D3×Q8—33no—
179C2×D3×Q8—33no—
180C2×D3×Q8—31no—
181C2×D3×Q8—31no—
182C2×D3×Q8—33no—
183C2×D3×Q8—61no—
184C2×D3×Q8—63no—
185C2×D3×Q8—63no—
186C2×D3×Q8—61no—
187C2×D3×Q8—68no—
188C2×D3×Q8—68no—
189C2×D3×Q8—616no—
190C2×D3×Q8C2×D311yescharacteristic, complemented
191C2×#237—33no—
192C2×#237—33no—
193C2×#235—33no—
194C2×#235—33no—
195C2×#235—33no—
196C22×C4×D3—33no—
197C22×C4×D3—33no—
198C22×C4×D3—63no—
199C22×Dic6—33no—
200C22×Dic6—33no—
201C22×Dic6—33no—
202C22×Dic6—63no—
203C3×C4⋊Q8—33no—
204C3×#124—33no—
205C3×C22⋊Q8—33no—
206C3×C22⋊Q8—33no—
207C3×C22⋊Q8—33no—
208C3×#121—33no—
209C3×C4×Q8—31no—
210C3×C4×Q8—31no—
211C3×C4×D4—33no—
212C3×C4×D4—33no—
213#947C2×D313yescomplemented
214#946—33no—
215#946C2×D313yescomplemented
216#946C2×D313yescomplemented
217Q8×Dic3C2×D311yescharacteristic, complemented
218Q8×Dic3C2×D311yescharacteristic, complemented
219#944—33no—
220#944C2×D313yescomplemented
221#939—33no—
222#939—33no—
223#938—33no—
224#937—31no—
225#937—33no—
226#936—33no—
227D4×Dic3—36no—
228#930C2×D313yes—
229C4×#67—33no—
230C4×#67—33no—
231C4×#67C2×D313yes—
232C4×#67C2×D313yes—
233#924—33no—
234#924—33no—
235#924C2×D313yes—
236#897—33no—
237#897—33no—
238#897—33no—
239#896—36no—
240#896—36no—
241#896—33no—
242#896—33no—
243#895—33no—
244#894—33no—
245#894—36no—
246#894—33no—
247#893—36no—
248#892—33no—
249#892—33no—
250#888—36no—
251#888—36no—
252#887—33no—
253#887—33no—
254#885—36no—
255#885—36no—
256#884—33no—
257#884—33no—
258#883—33no—
259#883—36no—
260#883—33no—
261#882—31no—
262#882—33no—
263#67⋊C4—36no—
264#67⋊C4—36no—
265#878—33no—
266#878—33no—
267#878—36no—
268#878—36no—
269#875—33no—
270C4×D12—33no—
271C4×D12—33no—
272#872—33no—
273#872—33no—
274#869—33no—
275C4×Dic6—33no—
276C4×Dic6—33no—
277C23×C32C2411yescharacteristic
278C22×C3⋊D3—22no—
279C22×C3⋊D3—22no—
280C22×C3⋊D3—22no—
281C22×C3⋊D3C2411yescharacteristic
282C22×C3⋊D3C2411yescharacteristic
283C22×C3×D3C2413yes—
284C22×C3×D3C2411yescharacteristic
285C32×Q8—26no—
286C32×Q8C2×D414yes—
287C2×C32×C4—26no—
288C2×C32×C4C2413yes—
289C2×C32×C4C2413yes—
290C2×C3⋊Dic3—26no—
291C2×C3⋊Dic3C2413yes—
292C2×C3⋊Dic3C2413yes—
293C4×C3⋊D3—26no—
294C4×C3⋊D3—26no—
295C4×C3⋊D3—26no—
296C4×C3⋊D3C2×D4112yes—
297#634—26no—
298#634—212no—
299#634C2×D4112yes—
300C3×#67—22no—
301C3×#67—26no—
302C2×C3×Dic3C2413yes—
303C2×C3×Dic3C2413yes—
304C2×C3×Dic3C2411yescharacteristic
305C2×C3×Dic3C2411yescharacteristic
306C2×C3×Dic3C2413yes—
307C2×C3×Dic3C2411yescharacteristic
308C3×D12—26no—
309C3×C4×D3—26no—
310C3×C4×D3—26no—
311C3×Dic6—26no—
312#627—26no—
313#626—26no—
314#626—22no—
315#626—26no—
316#626—22no—
317#625—26no—
318D3×Dic3—212no—
319C2×2−1+4—91no—
320C23×Q8—91no—
321D4×Q8—31no—
322D4×Q8—93no—
323D4×Q8—91no—
324D4×Q8—93no—
325#548—31no—
326#548—93no—
327#548—91no—
328#548—93no—
329#536—93no—
330#536—93no—
331#525—93no—
332#525—93no—
333#519—91no—
334C23×D3—31no—
335C23×D3—31no—
336C23×D3—61no—
337C3×#41—64no—
338C2×C3×Q8—28no—
339C2×C3×Q8—24no—
340C2×C3×Q8—24no—
341C2×C3×Q8—23no—
342C2×C3×Q8—21no—
343C2×C3×Q8—33no—
344C2×C3×Q8—64no—
345C2×C3×Q8C22×D313yes—
346C2×C3×Q8C22×D313yes—
347C2×C3×Q8C22×D311yescharacteristic
348C2×C3×Q8C22×D311yescharacteristic
349C2×C3×D4—33no—
350C2×C3×D4—31no—
351C2×C3×D4—33no—
352C22×C3×C4—23no—
353C22×C3×C4—33no—
354C22×C3×C4—33no—
355C22×C3×C4C22×D313yes—
356C22×C3×C4C22×D313yes—
357C2×#67—33no—
358C2×#67—33no—
359C2×#67—33no—
360C2×#67—31no—
361C2×#67—33no—
362C2×#67—31no—
363C2×#67C22×D313yes—
364C2×#67C22×D311yescharacteristic
365C22×Dic3—33no—
366C22×Dic3—33no—
367C22×Dic3—36no—
368C22×Dic3—63no—
369#239—24no—
370#239—612no—
371D3×Q8—24no—
372D3×Q8—38no—
373D3×Q8—38no—
374D3×Q8—68no—
375D3×Q8—612no—
376D3×Q8—612no—
377D3×Q8—612no—
378D3×Q8—612no—
379D3×Q8—612no—
380D3×Q8—624no—
381D3×Q8—624no—
382D3×Q8—68no—
383D3×Q8—64no—
384D3×Q8—64no—
385#237—612no—
386#237—612no—
387#235—612no—
388#235—612no—
389#235—612no—
390C2×D12—31no—
391C2×D12—33no—
392C2×D12—31no—
393C2×D12—33no—
394C2×D12C22×D313yes—
395C2×C4×D3—33no—
396C2×C4×D3—33no—
397C2×C4×D3—36no—
398C2×C4×D3—33no—
399C2×C4×D3—33no—
400C2×C4×D3—33no—
401C2×C4×D3—33no—
402C2×C4×D3—33no—
403C2×C4×D3—33no—
404C2×C4×D3—63no—
405C2×C4×D3—63no—
406C2×C4×D3—63no—
407C2×C4×D3—63no—
408C2×C4×D3—612no—
409C2×C4×D3—612no—
410C2×C4×D3—624no—
411C2×C4×D3C22×D313yes—
412C2×C4×D3C22×D313yes—
413C2×Dic6—33no—
414C2×Dic6—33no—
415C2×Dic6—33no—
416C2×Dic6—33no—
417C2×Dic6—36no—
418C2×Dic6—36no—
419C2×Dic6—33no—
420C2×Dic6—33no—
421C2×Dic6—63no—
422C2×Dic6—66no—
423C2×Dic6—63no—
424C2×Dic6—612no—
425C2×Dic6—612no—
426C2×Dic6—612no—
427C2×Dic6—624no—
428C2×Dic6C22×D313yes—
429C3×C4⋊C4—33no—
430C3×C4⋊C4—33no—
431C3×C4⋊C4—33no—
432C3×C4⋊C4—36no—
433C3×C4⋊C4—33no—
434C3×C22⋊C4—31no—
435C3×C22⋊C4—33no—
436C3×C22⋊C4—33no—
437C3×C22⋊C4—36no—
438C3×C22⋊C4—33no—
439C3×C42—33no—
440C3×C42—33no—
441#217—33no—
442#217—36no—
443#217—33no—
444#217C22×D311yescharacteristic
445#217C22×D313yes—
446(C2×D3)⋊C4—33no—
447(C2×D3)⋊C4—33no—
448(C2×D3)⋊C4—36no—
449(C2×D3)⋊C4—31no—
450(C2×D3)⋊C4—31no—
451(C2×D3)⋊C4—33no—
452(C2×D3)⋊C4—33no—
453(C2×D3)⋊C4—31no—
454(C2×D3)⋊C4—33no—
455(C2×D3)⋊C4—33no—
456(C2×D3)⋊C4—31no—
457(C2×D3)⋊C4C22×D313yes—
458(C2×D3)⋊C4C22×D313yes—
459(C2×D3)⋊C4C22×D316yes—
460C4⋊Dic3—33no—
461C4⋊Dic3—36no—
462C4⋊Dic3—33no—
463C4⋊Dic3C22×D313yes—
464C4⋊Dic3C22×D313yes—
465Dic3⋊C4—33no—
466Dic3⋊C4—33no—
467Dic3⋊C4—33no—
468Dic3⋊C4—33no—
469Dic3⋊C4—33no—
470Dic3⋊C4—33no—
471Dic3⋊C4—36no—
472Dic3⋊C4C22×D313yes—
473Dic3⋊C4C22×D316yes—
474Dic3⋊C4C22×D313yes—
475C4×Dic3—36no—
476C4×Dic3—36no—
477C4×Dic3C22×D313yes—
478C4×Dic3C22×D313yes—
479C22×C32—21no—
480C22×C32—21no—
481C22×C322−1+412yescomplemented
482C22×C32C2511yescharacteristic
483C2×C3⋊D3—28no—
484C2×C3⋊D3—21no—
485C2×C3⋊D3—21no—
486C2×C3⋊D3—21no—
487C2×C3⋊D3—21no—
488C2×C3⋊D3C22×D412yes—
489C2×C3⋊D32−1+412yescomplemented
490C2×C3×D3—23no—
491C2×C3×D3—21no—
492C2×C3×D3—23no—
493C2×C3×D3—21no—
494C2×C3×D3—21no—
495C2×C3×D3—23no—
496C32×C4—23no—
497C32×C4C22×D416yes—
498C3⋊Dic3—23no—
499C3⋊Dic3C22×D416yes—
500C3×Dic3—23no—
501C3×Dic3—21no—
502C3×Dic3—23no—
503C3×Dic3—21no—
504C3×Dic3—21no—
505C3×Dic3—23no—
5062−1+4—188no—
507C2×#41—31no—
508C2×#41—93no—
509C2×#41—93no—
510C2×#41—93no—
511C22×Q8—31no—
512C22×Q8—93no—
513C22×Q8—91no—
514C22×Q8—93no—
515C22×Q8—93no—
516C22×Q8—91no—
517C22×Q8—93no—
518C22×Q8—188no—
519C22×Q8D3211yescharacteristic
520C23×C4—93no—
521C4⋊Q8—33no—
522C4⋊Q8—93no—
523C4⋊Q8—96no—
524#124—33no—
525#124—93no—
526#124—96no—
527#123—93no—
528#123—93no—
529#123—96no—
530C22⋊Q8—33no—
531C22⋊Q8—33no—
532C22⋊Q8—33no—
533C22⋊Q8—93no—
534C22⋊Q8—96no—
535C22⋊Q8—96no—
536C22⋊Q8—93no—
537C22⋊Q8—93no—
538C22⋊Q8—93no—
539C22⋊Q8—93no—
540#121—33no—
541#121—93no—
542#121—93no—
543#121—93no—
544#120—91no—
545#120—93no—
546C4×Q8—31no—
547C4×Q8—31no—
548C4×Q8—93no—
549C4×Q8—93no—
550C4×D4—33no—
551C4×D4—33no—
552C4×D4—93no—
553C4×D4—93no—
554C4×D4—96no—
555C4×D4—96no—
556#117—93no—
557#117—93no—
558C23×C3—21no—
559C23×C3—33no—
560C23×C3—31no—
561C23×C3C23×D311yescharacteristic
562C23×C3C23×D311yescharacteristic
563C22×D3—31no—
564C22×D3—31no—
565C22×D3—31no—
566C22×D3—31no—
567C22×D3—61no—
568C22×D3—61no—
569C22×D3—62no—
570C22×D3—62no—
571C22×D3—62no—
572C22×D3—62no—
573C22×D3—64no—
574C22×D3—64no—
575C22×D3—64no—
576C22×D3—62no—
577C22×D3—62no—
578C22×D3C23×D313yes—
579C22×D3C23×D311yescharacteristic
580C3×Q8—212no—
581C3×Q8—26no—
582C3×Q8—26no—
583C3×Q8—24no—
584C3×Q8—66no—
585C3×Q8D3×D414yes—
586C3×Q8D3×D414yes—
587C3×D4—66no—
588C3×D4—62no—
589C3×D4—66no—
590C2×C3×C4—212no—
591C2×C3×C4—26no—
592C2×C3×C4—26no—
593C2×C3×C4—23no—
594C2×C3×C4—23no—
595C2×C3×C4—33no—
596C2×C3×C4—33no—
597C2×C3×C4—31no—
598C2×C3×C4—31no—
599C2×C3×C4—31no—
600C2×C3×C4—33no—
601C2×C3×C4—66no—
602C2×C3×C4—66no—
603C2×C3×C4C23×D313yes—
604C2×C3×C4C23×D313yes—
605C2×C3×C4C23×D313yes—
606C2×C3×C4C23×D313yes—
607#67—22no—
608#67—26no—
609#67—62no—
610#67—66no—
611#67—62no—
612#67—66no—
613#67—66no—
614#67—66no—
615C2×Dic3—33no—
616C2×Dic3—33no—
617C2×Dic3—33no—
618C2×Dic3—33no—
619C2×Dic3—63no—
620C2×Dic3—63no—
621C2×Dic3—612no—
622C2×Dic3—66no—
623C2×Dic3—66no—
624C2×Dic3—612no—
625C2×Dic3C23×D313yes—
626C2×Dic3C23×D313yes—
627C2×Dic3C23×D311yescharacteristic
628C2×Dic3C23×D311yescharacteristic
629C2×Dic3C23×D311yescharacteristic
630C2×Dic3C23×D313yes—
631D12—26no—
632D12—66no—
633D12—62no—
634D12—62no—
635D12—66no—
636C4×D3—26no—
637C4×D3—26no—
638C4×D3—312no—
639C4×D3—312no—
640C4×D3—612no—
641C4×D3—66no—
642C4×D3—66no—
643C4×D3—612no—
644C4×D3—66no—
645C4×D3—66no—
646C4×D3—612no—
647C4×D3—612no—
648C4×D3—612no—
649C4×D3—66no—
650C4×D3—66no—
651Dic6—26no—
652Dic6—312no—
653Dic6—312no—
654Dic6—612no—
655Dic6—66no—
656Dic6—66no—
657Dic6—612no—
658Dic6—612no—
659Dic6—624no—
660Dic6—612no—
661Dic6—66no—
662Dic6—66no—
663C2×C32—22no—
664C2×C32C23×D411yescharacteristic
665C2×C32C2×2−1+411yescharacteristic
666C2×C32C2×2−1+411yescharacteristic
667C3⋊D3—22no—
668C3⋊D3—22no—
669C3×D3—43no—
670C3×D3—41no—
671C24—91no—
672#41—64no—
673#41—1812no—
674#41—1812no—
675#41—1812no—
676C2×Q8—24no—
677C2×Q8—33no—
678C2×Q8—64no—
679C2×Q8—93no—
680C2×Q8—98no—
681C2×Q8—93no—
682C2×Q8—96no—
683C2×Q8—93no—
684C2×Q8—1812no—
685C2×Q8—1812no—
686C2×Q8—1812no—
687C2×Q8—1812no—
688C2×Q8—184no—
689C2×Q8C2×D3213yes—
690C2×Q8C2×D3211yescharacteristic
691C2×D4—31no—
692C2×D4—33no—
693C2×D4—33no—
694C2×D4—91no—
695C2×D4—93no—
696C2×D4—91no—
697C2×D4—93no—
698C2×D4—93no—
699C22×C4—33no—
700C22×C4—33no—
701C22×C4—96no—
702C22×C4—93no—
703C22×C4—93no—
704C22×C4—93no—
705C22×C4—93no—
706C22×C4—93no—
707C22×C4—1812no—
708C22×C4C2×D3213yes—
709C4⋊C4—33no—
710C4⋊C4—33no—
711C4⋊C4—33no—
712C4⋊C4—33no—
713C4⋊C4—36no—
714C4⋊C4—93no—
715C4⋊C4—93no—
716C4⋊C4—93no—
717C4⋊C4—93no—
718C4⋊C4—96no—
719C22⋊C4—31no—
720C22⋊C4—33no—
721C22⋊C4—33no—
722C22⋊C4—33no—
723C22⋊C4—36no—
724C22⋊C4—91no—
725C22⋊C4—93no—
726C22⋊C4—91no—
727C22⋊C4—93no—
728C22⋊C4—93no—
729C22⋊C4—96no—
730C22⋊C4—93no—
731C42—33no—
732C42—33no—
733C42—96no—
734C22×C3—22no—
735C22×C3—22no—
736C22×C3—21no—
737C22×C3—21no—
738C22×C3—21no—
739C22×C3—21no—
740C22×C3—22no—
741C22×C3—21no—
742C22×C3—63no—
743C22×C3—61no—
744C22×C3—63no—
745C22×C3—61no—
746C22×C3—61no—
747C22×C3—63no—
748C22×C3#100712yescomplemented
749C22×C3#101012yescomplemented
750C22×C3C24×D311yescharacteristic
751C22×C3C24×D311yescharacteristic
752C2×D3—21no—
753C2×D3—23no—
754C2×D3—21no—
755C2×D3—23no—
756C2×D3—23no—
757C2×D3—21no—
758C2×D3—32no—
759C2×D3—32no—
760C2×D3—32no—
761C2×D3—32no—
762C2×D3—62no—
763C2×D3—62no—
764C2×D3—62no—
765C2×D3—616no—
766C2×D3—68no—
767C2×D3—68no—
768C2×D3—62no—
769C2×D3—62no—
770C2×D3—62no—
771C2×D3—61no—
772C2×D3—61no—
773C2×D3—61no—
774C2×D3—61no—
775C2×D3—61no—
776C2×D3—61no—
777C2×D3—61no—
778C2×D3—61no—
779C3×C4—26no—
780C3×C4—23no—
781C3×C4—23no—
782C3×C4—26no—
783C3×C4—61no—
784C3×C4—63no—
785C3×C4—63no—
786C3×C4—61no—
787C3×C4—63no—
788C3×C4—61no—
789C3×C4C2×D3×D416yes—
790C3×C4C2×D3×D416yes—
791Dic3—23no—
792Dic3—21no—
793Dic3—21no—
794Dic3—23no—
795Dic3—21no—
796Dic3—23no—
797Dic3—36no—
798Dic3—36no—
799Dic3—66no—
800Dic3—66no—
801Dic3—63no—
802Dic3—63no—
803C32#348611yescharacteristic, complemented, Sylow
804C23—31no—
805C23—33no—
806C23—91no—
807C23—91no—
808C23—182no—
809C23—182no—
810C23—182no—
811C23C22×D3211yescharacteristic
812Q8—26no—
813Q8—66no—
814Q8—912no—
815Q8—1812no—
816Q8—186no—
817Q8—186no—
818Q8#381114yes—
819D4—62no—
820D4—66no—
821D4—66no—
822D4—182no—
823D4—186no—
824D4—182no—
825D4—186no—
826D4—186no—
827C2×C4—26no—
828C2×C4—31no—
829C2×C4—31no—
830C2×C4—33no—
831C2×C4—33no—
832C2×C4—31no—
833C2×C4—33no—
834C2×C4—66no—
835C2×C4—66no—
836C2×C4—93no—
837C2×C4—912no—
838C2×C4—93no—
839C2×C4—186no—
840C2×C4—186no—
841C2×C4—1812no—
842C2×C4—186no—
843C2×C4—186no—
844C2×C4C22×D3213yes—
845C2×C4C22×D3213yes—
846C2×C3—24no—
847C2×C3—22no—
848C2×C3—22no—
849C2×C3—21no—
850C2×C3—21no—
851C2×C3—21no—
852C2×C3—121no—
853C2×C3—123no—
854C2×C3C22×D3×D411yescharacteristic
855C2×C3C22×D3×D411yescharacteristic
856C2×C3C2×#100711yescharacteristic
857C2×C3C2×#101011yescharacteristic
858C2×C3D3×2−1+411yescharacteristic
859C2×C3D3×2−1+411yescharacteristic
860D3—43no—
861D3—41no—
862D3—64no—
863D3—64no—
864D3—62no—
865D3—62no—
866D3—62no—
867D3—62no—
868C22—21no—
869C22—21no—
870C22—61no—
871C22—63no—
872C22—61no—
873C22—63no—
874C22—61no—
875C22—63no—
876C22—92no—
877C22—92no—
878C22—188no—
879C22—181no—
880C22—181no—
881C22—181no—
882C22—181no—
883C22#6431512yescomplemented
884C22C23×D3211yescharacteristic
885C4—23no—
886C4—61no—
887C4—63no—
888C4—61no—
889C4—63no—
890C4—61no—
891C4—63no—
892C4—96no—
893C4—183no—
894C4C2×#381116yes—
895C3—21no—
896C3#8673511yescharacteristic, complemented
897C3#8675911yescharacteristic, complemented
898C2—22no—
899C2—121no—
900C2—123no—
901C2—182no—
902C2—182no—
903C2C2×#6431511yescharacteristic
904C2#1059668711yescharacteristic
905C2C22×#381111yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC22×C32×Q8C22
hypercenterC22×Q8D32
hypocenterC32#3486
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
1. C22×Q8×C3⋊D3C2semidirect
2. C2×#64315C2semidirect
3. C3×#5817C2semidirect
4. C3×Q8×#67C2semidirect
5. #10595414C2semidirect
6. Q8×#626C2semidirect
7. #10595405C2semidirect
8. #10595364C2semidirect
9. #10595362C2semidirect
10. #10595361C2semidirect
11. #10595339C2semidirect
12. #10595016C2semidirect
13. #10594922C2semidirect
14. #10594918C2semidirect
15. #10594915C2semidirect
26. C2×C3×#239C22semidirect
27. C2×C3×D3×Q8C22semidirect
31. C2×#3795C22semidirect
32. C2×D3×Dic6C22semidirect
33. C3×#947C22semidirect
34. C3×#946C22semidirect
35. C3×#946C22semidirect
36. C3×Q8×Dic3C22semidirect
37. C3×Q8×Dic3C22semidirect
38. C3×#944C22semidirect
49. #63913C22semidirect
53. #63896C22semidirect
54. #63896C22semidirect
58. #63866C22semidirect
60. #63860C22semidirect
61. #63857C22semidirect
62. #63857C22semidirect
67. #63844C22semidirect
68. #63844C22semidirect
69. #63840C22semidirect
78. #5817D3semidirect
80. Q8×#67D3semidirect
110. Q8×C3⋊D3D4semidirect
173. C2×#239C2×D3semidirect
190. C2×D3×Q8C2×D3semidirect
213. #947C2×D3semidirect
215. #946C2×D3semidirect
216. #946C2×D3semidirect
217. Q8×Dic3C2×D3semidirect
218. Q8×Dic3C2×D3semidirect
220. #944C2×D3semidirect
481. C22×C322−1+4semidirect
489. C2×C3⋊D32−1+4semidirect
748. C22×C3#1007semidirect
749. C22×C3#1010semidirect
803. C32#3486semidirect
883. C22#64315semidirect
896. C3#86735semidirect
897. C3#86759semidirect

Maximal subgroups

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

subgroupindex
C22×Q8×C3⋊D32
C2×#643152
C3×#58172
C3×Q8×#672
#105954142
Q8×#6262
#105954052
#105953642
#105953622
#105953612
#105953392
#105950162
#105949222
#105949182
#105949152
#867593
#867353