Finite Group Databasebeta

← #11895686

Subgroups — #11895686

Order 1152.

747 conjugacy classes of subgroups.

The subgroup lattice has 707 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595199C211yesmaximal, characteristic
2#10594317C211yesmaximal, characteristic, complemented
3#10592465C211yesmaximal, characteristic, complemented
4C3×#4767C211yesmaximal, characteristic, complemented
5C3×#4760C211yesmaximal, characteristic
6#10591478C211yesmaximal, characteristic, complemented
7#10591445C211yesmaximal, characteristic, complemented
8#10591438C211yesmaximal, characteristic
9Dic3×Dic12C211yesmaximal, characteristic, complemented
10#10590797C211yesmaximal, characteristic, complemented
11#10590767C211yesmaximal, characteristic, complemented
12#10590644C211yesmaximal, characteristic, complemented
13#10590539C211yesmaximal, characteristic, complemented
14#10590486C211yesmaximal, characteristic, complemented
15#10590453C211yesmaximal, characteristic, complemented
16#81589—31nomaximal
17#80581—31nomaximal
18D4×C3⋊Dic3C2211yescharacteristic
19#64099C2211yescharacteristic
20C3×#940C2211yescharacteristic
21C3×#936C2211yescharacteristic
22C2×C3×#214C2211yescharacteristic
23C2×C3×Dic12C2211yescharacteristic
24C3×#888C2211yescharacteristic
25C3×#887C2211yescharacteristic
26#67⋊Dic3—21no—
27#63969—21no—
28#63962—21no—
29#63959—21no—
30C4×#627C2211yescharacteristic
31Dic3×D12C2211yescharacteristic
32#63869C2211yescharacteristic
33#63867—21no—
34#63863C2211yescharacteristic
35#63845—21no—
36#63843C2211yescharacteristic
37Dic3×Dic6—21no—
38Dic3×Dic6C2211yescharacteristic
39Dic3×Dic6C2211yescharacteristic
40#63839—21no—
41C2×#3715C2211yescharacteristic
42C32×#102C2211yescharacteristic
43#63659C2211yescharacteristic
44#63645C2211yescharacteristic
45#63641C2211yescharacteristic
46#63635C2211yescharacteristic
47C3×#832C2211yescharacteristic
48C3×#821C2211yescharacteristic
49C3×Dic3⋊C8C2211yescharacteristic
50C3×C8×Dic3C2211yescharacteristic
51C3×#810C2211yescharacteristic
52C3×#809C2211yescharacteristic
53#63573C2211yescharacteristic
54Dic3⋊(C3⋊C8)C2211yescharacteristic
55#63566C2211yescharacteristic
56#63566C2211yescharacteristic
57#63565C2211yescharacteristic
58#63563C2211yescharacteristic
59#63553C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic
61#5721—31no—
62#5713—31no—
63#5681—31no—
64#5569—31no—
65C3×#486—31no—
66C3×#464—31no—
67#5185—31no—
68Dic3×Q16—31no—
69#5163—31no—
70Dic3×SD16—31no—
71#5094—31no—
72#5075—31no—
73#5056—31no—
74C4×#215—31no—
75#4847—31no—
76#4830—31no—
77#4800—31no—
78#4791—31no—
79#4768—31no—
80#4768—31no—
81#4767—31no—
82#4767D311yescharacteristic, complemented
83#4766—31no—
84#4766—31no—
85#4766—31no—
86#4766—61no—
87#4760D311yescharacteristic
88#4758—31no—
89#4758—31no—
90C4×Dic12—31no—
91C8×Dic6—31no—
92C2×C32×D4C2311yescharacteristic
93C22×C3⋊Dic3—21no—
94C2×C3×#67—21no—
95C2×C3×#67—21no—
96C2×C3×D12C2311yescharacteristic
97C2×C3×Dic6—21no—
98C2×C3×Dic6C2311yescharacteristic
99C2×C3×Dic6C2311yescharacteristic
100C2×#627D411yescharacteristic
101C2×D3×Dic3—21no—
102C2×C32×C8C2311yescharacteristic
103C32×C4⋊C4C2311yescharacteristic
104#3757—21no—
105C4⋊(C3⋊Dic3)—21no—
106C4⋊(C3⋊Dic3)C2311yescharacteristic
107C4⋊(C3⋊Dic3)C2311yescharacteristic
108#3750—21no—
109C4×C3⋊Dic3C2311yescharacteristic
110C2×C3⋊(C3⋊C8)C2311yescharacteristic
111C3×#217—21no—
112C3×#217—21no—
113C3×#214—22no—
114C3×C4⋊Dic3C2311yescharacteristic
115C3×Dic3⋊C4—21no—
116C3×Dic3⋊C4—21no—
117C3×C4×Dic3—21no—
118C3×C4×Dic3C2311yescharacteristic
119C3×C4×Dic3C2311yescharacteristic
120C2×C3×C3⋊C8C2311yescharacteristic
121C2×C3×C3⋊C8C2311yescharacteristic
122C3×Dic12—22no—
123#3724—21no—
124#3724D411yescharacteristic
125Dic3⋊Dic3—21no—
126Dic3⋊Dic3—21no—
127Dic3⋊Dic3—21no—
128Dic3⋊Dic3—21no—
129Dic3⋊Dic3D411yescharacteristic
130Dic3⋊Dic3D411yescharacteristic
131(C2×D3)⋊Dic3—21no—
132(C2×D3)⋊Dic3—21no—
133(C2×D3)⋊Dic3—21no—
134Dic32—21no—
135Dic32—21no—
136Dic32—21no—
137#3715—22no—
138#3365—91noSylow
139C2×C3×Q16—31no—
140C2×C3×SD16—31no—
141C3×C4⋊Q8—31no—
142C3×#127—31no—
143C3×#124—31no—
144C3×C4×Q8—31no—
145#947—31no—
146Q8×Dic3—31no—
147Q8×Dic3—31no—
148Q8×Dic3—31no—
149Q8×Dic3—61no—
150#944—61no—
151C2×#215—31no—
152#940C2×D311yescharacteristic
153#936—31no—
154#936—61no—
155#936C2×D311yescharacteristic
156#935—61no—
157#935—61no—
158D4×Dic3—31no—
159D4×Dic3—31no—
160D4×Dic3—31no—
161D4×Dic3—61no—
162D4×Dic3—61no—
163C2×#214—31no—
164C2×#214C2×D311yescharacteristic
165C2×Dic12C2×D311yescharacteristic
166#890—31no—
167#890—31no—
168#890—31no—
169#890—61no—
170#890—61no—
171#889—61no—
172#889—61no—
173#888—61no—
174#888C2×D311yescharacteristic
175#887—31no—
176#887C2×D311yescharacteristic
177#886—61no—
178#885—61no—
179#883—61no—
180#67⋊C4—61no—
181C4×D12—31no—
182#870—31no—
183#870—61no—
184C4×Dic6—31no—
185C4×Dic6—31no—
186C4×Dic6—31no—
187C4×Dic6—31no—
188C4×Dic6—61no—
189C3×C4⋊C8—31no—
190C3×#103—31no—
191C3×#102—21no—
192C3×#102—31no—
193C3×#102—31no—
194C3×#102—31no—
195C3×#102C2×D311yescharacteristic
196C3×#102C2×D311yescharacteristic
197C3×C4×C8—31no—
198#835—31no—
199#835—31no—
200#835—31no—
201#832—31no—
202#832—31no—
203#832—31no—
204#832—61no—
205#832C2×D311yescharacteristic
206#821—31no—
207#821C2×D311yescharacteristic
208#818—31no—
209#818—31no—
210#818—61no—
211#817—31no—
212#816—31no—
213#816—31no—
214Dic3⋊C8—31no—
215Dic3⋊C8—31no—
216Dic3⋊C8—31no—
217Dic3⋊C8—61no—
218Dic3⋊C8C2×D311yescharacteristic
219C8×Dic3—31no—
220C8×Dic3—31no—
221C8×Dic3—31no—
222C8×Dic3C2×D311yescharacteristic
223#810—31no—
224#810C2×D311yescharacteristic
225#809C2×D311yescharacteristic
226#808—31no—
227#808—31no—
228#808—31no—
229#808—61no—
230C4⋊(C3⋊C8)—31no—
231C4×C3⋊C8—31no—
232C23×C32—21no—
233C22×C3×D3—21no—
234C32×D4—21no—
235C32×D4—21no—
236C2×C32×C4—21no—
237C2×C32×C4C2411yescharacteristic
238C2×C3⋊Dic3—21no—
239C2×C3⋊Dic3—21no—
240C2×C3⋊Dic3—81no—
241C2×C3⋊Dic3C2×D411yescharacteristic
242C2×C3⋊Dic3C2×D411yescharacteristic
243C3×#67—42no—
244C3×#67—81no—
245C2×C3×Dic3—21no—
246C2×C3×Dic3—21no—
247C2×C3×Dic3—21no—
248C2×C3×Dic3C2×D411yescharacteristic
249C2×C3×Dic3C2×D411yescharacteristic
250C2×C3×Dic3C2×D411yescharacteristic
251C2×C3×Dic3C2×D411yescharacteristic
252C3×D12—21no—
253C3×D12—21no—
254C3×Dic6—21no—
255C3×Dic6—21no—
256C3×Dic6—21no—
257C3×Dic6—42no—
258C3×Dic6#4112yes—
259#627—22no—
260D3×Dic3—81no—
261C32×C8—21no—
262C3⋊(C3⋊C8)—21no—
263C3×C3⋊C8—21no—
264C3×C3⋊C8—21no—
265#559—91no—
266#557—91no—
267#488—91no—
268#488—91no—
269#486—31no—
270#478—91no—
271#478—91no—
272#475—91no—
273#464—31no—
274#464—91no—
275#460—91no—
276C8×Q8—91no—
277C4×Q16—91no—
278C4×SD16—91no—
279C4×SD16—91no—
280C2×C3×Q8—31no—
281C2×C3×Q8—31no—
282C2×C3×Q8—61no—
283C2×C3×D4—21no—
284C2×C3×D4—31no—
285C2×C3×D4—61no—
286C2×C3×D4—61no—
287C2×C3×D4C22×D311yescharacteristic
288C2×C3×D4C22×D311yescharacteristic
289C2×#67—21no—
290C2×#67—21no—
291C22×Dic3—61no—
292C22×Dic3—61no—
293C22×Dic3—61no—
294C22×Dic3—121no—
295C2×D12C22×D311yescharacteristic
296C2×C4×D3—61no—
297C2×Dic6—21no—
298C2×Dic6—31no—
299C2×Dic6—31no—
300C2×Dic6C22×D311yescharacteristic
301C2×Dic6C22×D311yescharacteristic
302C3×Q16—62no—
303C3×SD16—62no—
304C2×C3×C8—21no—
305C2×C3×C8—31no—
306C2×C3×C8—31no—
307C2×C3×C8C22×D311yescharacteristic
308C2×C3×C8C22×D311yescharacteristic
309C3×C4⋊C4—21no—
310C3×C4⋊C4—31no—
311C3×C4⋊C4—61no—
312C3×C4⋊C4—61no—
313C3×C4⋊C4C22×D311yescharacteristic
314C3×C4⋊C4C22×D311yescharacteristic
315C3×C22⋊C4—61no—
316C3×C22⋊C4—61no—
317C3×C42—31no—
318C3×C42—31no—
319C3×C42—61no—
320#217—21no—
321#217—21no—
322#217—61no—
323#217—61no—
324#217—61no—
325#217—61no—
326#217—61no—
327#217—121no—
328#215—62no—
329#214—22no—
330#214—62no—
331(C2×D3)⋊C4—61no—
332(C2×D3)⋊C4—61no—
333(C2×D3)⋊C4—61no—
334C4⋊Dic3—31no—
335C4⋊Dic3—31no—
336C4⋊Dic3—31no—
337C4⋊Dic3—31no—
338C4⋊Dic3—31no—
339C4⋊Dic3—31no—
340C4⋊Dic3—61no—
341C4⋊Dic3—61no—
342C4⋊Dic3—61no—
343C4⋊Dic3—61no—
344C4⋊Dic3—61no—
345C4⋊Dic3—61no—
346C4⋊Dic3—61no—
347C4⋊Dic3—61no—
348C4⋊Dic3—121no—
349C4⋊Dic3C22×D311yescharacteristic
350Dic3⋊C4—21no—
351Dic3⋊C4—21no—
352Dic3⋊C4—31no—
353Dic3⋊C4—31no—
354Dic3⋊C4—31no—
355Dic3⋊C4—31no—
356Dic3⋊C4—61no—
357Dic3⋊C4—61no—
358Dic3⋊C4—61no—
359Dic3⋊C4—61no—
360Dic3⋊C4—61no—
361Dic3⋊C4—61no—
362Dic3⋊C4—61no—
363Dic3⋊C4—61no—
364Dic3⋊C4—121no—
365C4×Dic3—21no—
366C4×Dic3—31no—
367C4×Dic3—31no—
368C4×Dic3—61no—
369C4×Dic3—61no—
370C4×Dic3—61no—
371C4×Dic3—61no—
372C4×Dic3—61no—
373C4×Dic3—61no—
374C4×Dic3—61no—
375C4×Dic3C22×D311yescharacteristic
376C4×Dic3C22×D311yescharacteristic
377C2×C3⋊C8—31no—
378C2×C3⋊C8—31no—
379C2×C3⋊C8—61no—
380C2×C3⋊C8C22×D311yescharacteristic
381C2×C3⋊C8C22×D311yescharacteristic
382Dic12—22no—
383C22×C32—41no—
384C22×C32—41no—
385C22×C32—41no—
386C22×C32C22×D411yescharacteristic
387C2×C3×D3—41no—
388C2×C3×D3—41no—
389C2×C3×D3—41no—
390C32×C4—41no—
391C32×C4C2×#4111yescharacteristic
392C32×C42−1+411yescharacteristic
393C3⋊Dic3—21no—
394C3⋊Dic3—21no—
395C3⋊Dic3—41no—
396C3⋊Dic3—41no—
397C3×Dic3—22no—
398C3×Dic3—21no—
399C3×Dic3—21no—
400C3×Dic3—21no—
401C3×Dic3—41no—
402C3×Dic3—41no—
403C3×Dic3#13512yes—
404C2×Q16—31no—
405C2×SD16—31no—
406C2×SD16—91no—
407C4⋊Q8—31no—
408C4⋊Q8—181no—
409#127—31no—
410#125—91no—
411#125—91no—
412#125—181no—
413#125—181no—
414#124—31no—
415#124—91no—
416#124—181no—
417#123—181no—
418#123—181no—
419C4×Q8—31no—
420C4×Q8—91no—
421C4×Q8—91no—
422C4×Q8—91no—
423C4×Q8—91no—
424C4×Q8—181no—
425C4×D4—91no—
426C4×D4—91no—
427C4×D4—181no—
428#107—91no—
429#106—91no—
430#106—91no—
431C4⋊C8—31no—
432C4⋊C8—91no—
433C4⋊C8—91no—
434#103—31no—
435#103—91no—
436#103—91no—
437#103—91no—
438#102—31no—
439#102—31no—
440#102—31no—
441#102—91no—
442#102—91no—
443#102D3211yescharacteristic
444C4×C8—31no—
445C4×C8—91no—
446C4×C8—91no—
447C23×C3—21no—
448C23×C3—21no—
449C23×C3—41no—
450C23×C3—61no—
451C22×D3—21no—
452C3×Q8—32no—
453C3×Q8—61no—
454C3×Q8—61no—
455C3×Q8—61no—
456C3×Q8—122no—
457C3×D4—22no—
458C3×D4—21no—
459C3×D4—21no—
460C3×D4—21no—
461C3×D4—21no—
462C3×D4—41no—
463C3×D4—61no—
464C3×D4—61no—
465C3×D4—122no—
466C3×D4—241no—
467C2×C3×C4—21no—
468C2×C3×C4—21no—
469C2×C3×C4—21no—
470C2×C3×C4—31no—
471C2×C3×C4—31no—
472C2×C3×C4—31no—
473C2×C3×C4—31no—
474C2×C3×C4—41no—
475C2×C3×C4—61no—
476C2×C3×C4—61no—
477C2×C3×C4—61no—
478C2×C3×C4C23×D311yescharacteristic
479C2×C3×C4C23×D311yescharacteristic
480#67—42no—
481#67—81no—
482C2×Dic3—21no—
483C2×Dic3—21no—
484C2×Dic3—21no—
485C2×Dic3—31no—
486C2×Dic3—31no—
487C2×Dic3—31no—
488C2×Dic3—31no—
489C2×Dic3—61no—
490C2×Dic3—61no—
491C2×Dic3—61no—
492C2×Dic3—61no—
493C2×Dic3—61no—
494C2×Dic3—61no—
495C2×Dic3—121no—
496C2×Dic3—121no—
497C2×Dic3—241no—
498C2×Dic3—241no—
499C2×Dic3—241no—
500C2×Dic3—242no—
501C2×Dic3D3×D411yescharacteristic
502C2×Dic3D3×D411yescharacteristic
503C2×Dic3D3×D411yescharacteristic
504C2×Dic3D3×D411yescharacteristic
505D12—21no—
506D12—21no—
507C4×D3—241no—
508Dic6—21no—
509Dic6—21no—
510Dic6—21no—
511Dic6—42no—
512Dic6—62no—
513Dic6—62no—
514Dic6#23712yes—
515C3×C8—21no—
516C3×C8—21no—
517C3×C8—41no—
518C3×C8—61no—
519C3×C8—61no—
520C3⋊C8—21no—
521C3⋊C8—21no—
522C3⋊C8—61no—
523C3⋊C8—61no—
524C3⋊C8—121no—
525C2×C32—81no—
526C2×C32#54811yescharacteristic
527C2×C32C2×#13511yescharacteristic
528C2×C32#57711yescharacteristic
529C3×D3—81no—
530C2×Q8—31no—
531C2×Q8—31no—
532C2×Q8—61no—
533C2×Q8—91no—
534C2×D4—31no—
535C2×D4—61no—
536C2×D4—61no—
537C2×D4C2×D3211yescharacteristic
538C22×C4—181no—
539C22×C4—181no—
540Q16—62no—
541SD16—62no—
542SD16—182no—
543C2×C8—31no—
544C2×C8—31no—
545C2×C8—91no—
546C2×C8C2×D3211yescharacteristic
547C4⋊C4—31no—
548C4⋊C4—61no—
549C4⋊C4—61no—
550C4⋊C4—91no—
551C4⋊C4—91no—
552C4⋊C4—91no—
553C4⋊C4—91no—
554C4⋊C4—91no—
555C4⋊C4—181no—
556C4⋊C4—181no—
557C4⋊C4—181no—
558C4⋊C4—181no—
559C4⋊C4—181no—
560C4⋊C4—181no—
561C4⋊C4—181no—
562C4⋊C4C2×D3211yescharacteristic
563C22⋊C4—61no—
564C22⋊C4—61no—
565C22⋊C4—181no—
566C22⋊C4—181no—
567C22⋊C4—181no—
568C22⋊C4—181no—
569C42—31no—
570C42—31no—
571C42—61no—
572C42—91no—
573C42—181no—
574C42—181no—
575C42—181no—
576C22×C3—21no—
577C22×C3—42no—
578C22×C3—41no—
579C22×C3—41no—
580C22×C3—41no—
581C22×C3—41no—
582C22×C3—41no—
583C22×C3—41no—
584C22×C3—81no—
585C22×C3—81no—
586C22×C3—121no—
587C22×C3—121no—
588C22×C3—121no—
589C22×C3C2×D3×D411yescharacteristic
590C22×C3C2×D3×D411yescharacteristic
591C2×D3—41no—
592C2×D3—41no—
593C2×D3—41no—
594C3×C4—21no—
595C3×C4—21no—
596C3×C4—32no—
597C3×C4—41no—
598C3×C4—41no—
599C3×C4—62no—
600C3×C4—61no—
601C3×C4—61no—
602C3×C4—61no—
603C3×C4—81no—
604C3×C4—121no—
605C3×C4—121no—
606C3×C4C2×#23711yescharacteristic
607C3×C4D3×#4111yescharacteristic
608C3×C4#101011yescharacteristic
609C3×C4#101011yescharacteristic
610Dic3—21no—
611Dic3—21no—
612Dic3—21no—
613Dic3—22no—
614Dic3—41no—
615Dic3—41no—
616Dic3—61no—
617Dic3—61no—
618Dic3—61no—
619Dic3—61no—
620Dic3—121no—
621Dic3—121no—
622Dic3—121no—
623Dic3—121no—
624Dic3—121no—
625Dic3—121no—
626Dic3—241no—
627Dic3—241no—
628Dic3#91212yes—
629C32#336511yescharacteristic, complemented, Sylow
630C23—21no—
631C23—61no—
632Q8—32no—
633Q8—61no—
634Q8—61no—
635Q8—61no—
636Q8—122no—
637Q8—182no—
638D4—21no—
639D4—21no—
640D4—61no—
641D4—61no—
642D4—122no—
643D4—241no—
644C2×C4—21no—
645C2×C4—31no—
646C2×C4—31no—
647C2×C4—31no—
648C2×C4—31no—
649C2×C4—61no—
650C2×C4—61no—
651C2×C4—61no—
652C2×C4—91no—
653C2×C4—91no—
654C2×C4—181no—
655C2×C4—181no—
656C2×C4—721no—
657C2×C4—721no—
658C2×C4C22×D3211yescharacteristic
659C8—21no—
660C8—61no—
661C8—61no—
662C8—181no—
663C2×C3—21no—
664C2×C3—21no—
665C2×C3—21no—
666C2×C3—82no—
667C2×C3—81no—
668C2×C3—81no—
669C2×C3—241no—
670C2×C3#559811yescharacteristic
671C2×C3#567711yescharacteristic
672C2×C3C2×#91211yescharacteristic
673C2×C3#576211yescharacteristic
674C2×C3D3×#13511yescharacteristic
675C2×C3#577811yescharacteristic
676D3—81no—
677C22—41no—
678C22—41no—
679C22—41no—
680C22—121no—
681C22—121no—
682C22—121no—
683C22D32×D411yescharacteristic
684C4—32no—
685C4—41no—
686C4—62no—
687C4—61no—
688C4—61no—
689C4—61no—
690C4—121no—
691C4—121no—
692C4—181no—
693C4—181no—
694C4—361no—
695C4—361no—
696C4#6429811yescharacteristic
697C4D3×#23711yescharacteristic
698C3—21no—
699C3#8058111yescharacteristic, complemented
700C3#8158911yescharacteristic, complemented
701C2—81no—
702C2—241no—
703C2#1059407611yescharacteristic
704C2D3×#91211yescharacteristic
705C2#1059475111yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#102C22
socleC22×C32C22×D4
prime radicalC3×#940C22
hypercenter#102D32
hypocenterC32#3365
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #102

Complements

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

NH ≅ G/Ntype
2. #10594317C2semidirect
3. #10592465C2semidirect
4. C3×#4767C2semidirect
6. #10591478C2semidirect
7. #10591445C2semidirect
9. Dic3×Dic12C2semidirect
10. #10590797C2semidirect
11. #10590767C2semidirect
12. #10590644C2semidirect
13. #10590539C2semidirect
14. #10590486C2semidirect
15. #10590453C2semidirect
82. #4767D3semidirect
629. C32#3365semidirect
699. C3#80581semidirect
700. C3#81589semidirect

Maximal subgroups

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

subgroupindex
#105951992
#105943172
#105924652
C3×#47672
C3×#47602
#105914782
#105914452
#105914382
Dic3×Dic122
#105907972
#105907672
#105906442
#105905392
#105904862
#105904532
#815893
#805813