Finite Group Databasebeta

← #11873327

Subgroups — #11873327

Order 1152.

764 conjugacy classes of subgroups.

The subgroup lattice has 700 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10593867C211yesmaximal, characteristic
2#10593848C211yesmaximal, characteristic
3#10592539C211yesmaximal, characteristic
4C3×#4849C211yesmaximal, characteristic, complemented
5C3×#4829C211yesmaximal, characteristic, complemented
6#10590950C211yesmaximal, characteristic
7#10590950C211yesmaximal, characteristic
8#10590819C211yesmaximal, characteristic, complemented
9#10590818C211yesmaximal, characteristic, complemented
10#10590791C211yesmaximal, characteristic, complemented
11#10590790C211yesmaximal, characteristic, complemented
12#10590715C211yesmaximal, characteristic
13#10590713C211yesmaximal, characteristic
14#10590384C211yesmaximal, characteristic, complemented
15#10590286C211yesmaximal, characteristic, complemented
16#81211—31nomaximal
17#80461—31nomaximal
18C2×#3797C2211yescharacteristic
19#64081C2211yescharacteristic
20C2×C3×Dic12C2211yescharacteristic
21C2×C3×Dic12C2211yescharacteristic
22C3×#870C2211yescharacteristic
23C3×#869C2211yescharacteristic
24C3×C4×Dic6C2211yescharacteristic
25C3×C4×Dic6C2211yescharacteristic
26#63871C2211yescharacteristic
27#63871C2211yescharacteristic
28#63849C2211yescharacteristic
29#63848—21no—
30#63848—21no—
31#63846—21no—
32#63846—21no—
33#63843C2211yescharacteristic
34#63843C2211yescharacteristic
35#63843C2211yescharacteristic
36#63843C2211yescharacteristic
37#63837—21no—
38#63837—21no—
39#63836—21no—
40#63836—21no—
41C2×#3718C2211yescharacteristic
42C2×#3718C2211yescharacteristic
43C32×C4⋊C8C2211yescharacteristic
44#63647C2211yescharacteristic
45#63647C2211yescharacteristic
46#63642C2211yescharacteristic
47C8×C3⋊Dic3C2211yescharacteristic
48C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
49C3×#818C2211yescharacteristic
50C3×#817C2211yescharacteristic
51C3×#816C2211yescharacteristic
52C3×#816C2211yescharacteristic
53C3×#816C2211yescharacteristic
54C3×#816C2211yescharacteristic
55#63576C2211yescharacteristic
56#63574C2211yescharacteristic
57#63565C2211yescharacteristic
58#63565C2211yescharacteristic
59#63565C2211yescharacteristic
60#63565C2211yescharacteristic
61#5731—31no—
62#5698—31no—
63#5572—31no—
64#5572—31no—
65C3×#479—31no—
66C3×#462—31no—
67#5186—31no—
68#5186—31no—
69#5184—31no—
70Dic3×Q16—31no—
71#5090—31no—
72#5063—31no—
73#5031—31no—
74#5022—31no—
75#4888—31no—
76#4873—31no—
77#4868—31no—
78#4853—31no—
79#4849D311yescharacteristic, complemented
80#4840—31no—
81#4840—31no—
82#4840—61no—
83#4829D311yescharacteristic, complemented
84#4815—31no—
85#4814—31no—
86#4809—31no—
87#4809—31no—
88#4790—31no—
89#4790—31no—
90#4789—31no—
91#4789—31no—
92C2×C4×C3⋊D3C2311yescharacteristic
93C2×C3×Dic6C2311yescharacteristic
94C2×C3×Dic6C2311yescharacteristic
95C2×C3×Dic6C2311yescharacteristic
96C2×C3×Dic6C2311yescharacteristic
97C2×#627—21no—
98C2×#624—21no—
99#3797—22no—
100#3797—22no—
101C2×C32×C8C2311yescharacteristic
102C2×C32×C8C2311yescharacteristic
103C32×C42C2311yescharacteristic
104#3752D411yescharacteristic
105#3752D411yescharacteristic
106#3750D411yescharacteristic
107#3750D411yescharacteristic
108C4×C3⋊Dic3C2311yescharacteristic
109C2×C3⋊(C3⋊C8)C2311yescharacteristic
110C2×C3⋊(C3⋊C8)C2311yescharacteristic
111C3×C4⋊Dic3—21no—
112C3×C4⋊Dic3—21no—
113C3×C4⋊Dic3C2311yescharacteristic
114C3×C4⋊Dic3C2311yescharacteristic
115C3×C4⋊Dic3C2311yescharacteristic
116C3×C4⋊Dic3C2311yescharacteristic
117C3×Dic3⋊C4—21no—
118C3×Dic3⋊C4—21no—
119C3×Dic3⋊C4—21no—
120C3×Dic3⋊C4—21no—
121C3×C4×Dic3—21no—
122C3×C4×Dic3—21no—
123C3×Dic12—22no—
124C3×Dic12—22no—
125Dic3⋊Dic3—21no—
126Dic3⋊Dic3—21no—
127Dic3⋊Dic3—21no—
128Dic3⋊Dic3—21no—
129Dic3⋊Dic3—21no—
130Dic3⋊Dic3—21no—
131#3722—21no—
132#3722—21no—
133#3722—21no—
134Dic32—21no—
135Dic32—21no—
136Dic32—21no—
137Dic32—21no—
138Dic32—21no—
139#3718—22no—
140#3718—22no—
141#3127—91noSylow
142C2×D3×Q8—31no—
143C2×D3×Q8—31no—
144C2×C3×Q16—31no—
145C2×C3×Q16—31no—
146C3×C4⋊Q8—31no—
147C3×#125—31no—
148C3×C4×Q8—31no—
149C3×C4×Q8—31no—
150#946—31no—
151#946—31no—
152Q8×Dic3—31no—
153Q8×Dic3—31no—
154Q8×Dic3—31no—
155Q8×Dic3—31no—
156C2×#216—31no—
157C2×#216—31no—
158C2×#216—31no—
159C2×#216—31no—
160C2×Dic12C2×D311yescharacteristic
161C2×Dic12C2×D311yescharacteristic
162#898—61no—
163#898—61no—
164#898—61no—
165#898—61no—
166#897—31no—
167#897—31no—
168#892—31no—
169#892—31no—
170#892—61no—
171#892—61no—
172#890—61no—
173#890—61no—
174#889—61no—
175#889—61no—
176#887—31no—
177#887—31no—
178#887—31no—
179#887—31no—
180#887—61no—
181#887—61no—
182#872—31no—
183#872—31no—
184#872—61no—
185#872—61no—
186#872—61no—
187#870C2×D311yescharacteristic
188#869C2×D311yescharacteristic
189C4×Dic6—61no—
190C4×Dic6—61no—
191C4×Dic6C2×D311yescharacteristic
192C4×Dic6C2×D311yescharacteristic
193C3×#107—31no—
194C3×#106—31no—
195C3×C4⋊C8—21no—
196C3×C4⋊C8C2×D311yescharacteristic
197C3×C4⋊C8C2×D311yescharacteristic
198C3×#103—31no—
199C3×#103—31no—
200C3×#103—31no—
201C3×#103—31no—
202#835—31no—
203#835—31no—
204#835—31no—
205#835—31no—
206(C2×D3)⋊C8—31no—
207(C2×D3)⋊C8—31no—
208(C2×D3)⋊C8—31no—
209(C2×D3)⋊C8—31no—
210(C2×D3)⋊C8—61no—
211(C2×D3)⋊C8—61no—
212#818C2×D311yescharacteristic
213#817C2×D311yescharacteristic
214#816C2×D311yescharacteristic
215#816C2×D311yescharacteristic
216#816C2×D311yescharacteristic
217#816C2×D311yescharacteristic
218#815—31no—
219#815—31no—
220#815—61no—
221C8×Dic3—31no—
222C8×Dic3—31no—
223C8×Dic3—61no—
224#810—31no—
225#810—31no—
226#810—31no—
227#810—31no—
228#808—31no—
229#808—31no—
230#807—31no—
231#807—31no—
232C4⋊(C3⋊C8)—31no—
233C4⋊(C3⋊C8)—31no—
234C4⋊(C3⋊C8)—61no—
235C22×C3⋊D3C2×D411yescharacteristic
236C2×C32×C4C2×D411yescharacteristic
237C2×C32×C4C2×D411yescharacteristic
238C2×C32×C4C2411yescharacteristic
239C2×C3⋊Dic3C2×D411yescharacteristic
240C2×C3⋊Dic3C2×D411yescharacteristic
241C2×C3⋊Dic3C2×D411yescharacteristic
242C4×C3⋊D3—21no—
243C4×C3⋊D3—21no—
244C2×C3×Dic3—21no—
245C2×C3×Dic3—21no—
246C2×C3×Dic3—21no—
247C2×C3×Dic3—21no—
248C2×C3×Dic3—21no—
249C2×C3×Dic3—21no—
250C2×C3×Dic3—21no—
251C2×C3×Dic3—21no—
252C3×Dic6—21no—
253C3×Dic6—21no—
254C3×Dic6—21no—
255C3×Dic6—21no—
256C3×Dic6—21no—
257C3×Dic6—21no—
258C3×Dic6#4112yes—
259C3×Dic6#4112yes—
260#627—24no—
261#624—24no—
262C32×C8—21no—
263C32×C8—21no—
264C3⋊(C3⋊C8)—21no—
265C3⋊(C3⋊C8)—21no—
266#541—91no—
267#519—91no—
268#485—91no—
269#485—91no—
270#479—31no—
271#479—91no—
272#462—31no—
273#462—91no—
274#451—91no—
275#451—91no—
276#441—91no—
277#441—91no—
278C4×Q16—91no—
279C4×Q16—91no—
280#433—91no—
281C2×C3×Q8—31no—
282C2×C3×Q8—31no—
283C2×C3×Q8—31no—
284C2×C3×Q8—31no—
285D3×Q8—62no—
286D3×Q8—62no—
287D3×Q8—62no—
288D3×Q8—62no—
289C2×C4×D3—31no—
290C2×C4×D3—31no—
291C2×C4×D3—61no—
292C2×C4×D3—61no—
293C2×C4×D3—61no—
294C2×Dic6—61no—
295C2×Dic6—61no—
296C2×Dic6C22×D311yescharacteristic
297C2×Dic6C22×D311yescharacteristic
298C2×Dic6C22×D311yescharacteristic
299C2×Dic6C22×D311yescharacteristic
300C3×Q16—62no—
301C3×Q16—62no—
302C2×C3×C8—21no—
303C2×C3×C8—21no—
304C2×C3×C8C22×D311yescharacteristic
305C2×C3×C8C22×D311yescharacteristic
306C2×C3×C8C22×D311yescharacteristic
307C2×C3×C8C22×D311yescharacteristic
308C3×C4⋊C4—31no—
309C3×C4⋊C4—31no—
310C3×C4⋊C4—31no—
311C3×C4⋊C4—31no—
312C3×C4⋊C4—61no—
313C3×C4⋊C4—61no—
314C3×C4⋊C4—61no—
315C3×C4⋊C4—61no—
316C3×C4⋊C4—61no—
317C3×C4⋊C4—61no—
318C3×C42—21no—
319C3×C42—61no—
320C3×C42—61no—
321C3×C42C22×D311yescharacteristic
322C3×C42C22×D311yescharacteristic
323#216—62no—
324#216—62no—
325#216—62no—
326#216—62no—
327(C2×D3)⋊C4—31no—
328(C2×D3)⋊C4—31no—
329(C2×D3)⋊C4—31no—
330(C2×D3)⋊C4—31no—
331(C2×D3)⋊C4—61no—
332(C2×D3)⋊C4—61no—
333(C2×D3)⋊C4—61no—
334(C2×D3)⋊C4—61no—
335(C2×D3)⋊C4—61no—
336(C2×D3)⋊C4—61no—
337(C2×D3)⋊C4—61no—
338(C2×D3)⋊C4—61no—
339C4⋊Dic3—21no—
340C4⋊Dic3—21no—
341C4⋊Dic3—61no—
342C4⋊Dic3—61no—
343C4⋊Dic3—61no—
344C4⋊Dic3—61no—
345C4⋊Dic3—61no—
346C4⋊Dic3—61no—
347C4⋊Dic3C22×D311yescharacteristic
348C4⋊Dic3C22×D311yescharacteristic
349C4⋊Dic3C22×D311yescharacteristic
350C4⋊Dic3C22×D311yescharacteristic
351Dic3⋊C4—21no—
352Dic3⋊C4—21no—
353Dic3⋊C4—21no—
354Dic3⋊C4—21no—
355Dic3⋊C4—31no—
356Dic3⋊C4—31no—
357Dic3⋊C4—31no—
358Dic3⋊C4—31no—
359Dic3⋊C4—61no—
360Dic3⋊C4—61no—
361Dic3⋊C4—61no—
362Dic3⋊C4—61no—
363Dic3⋊C4—61no—
364Dic3⋊C4—61no—
365Dic3⋊C4—61no—
366Dic3⋊C4—61no—
367C4×Dic3—21no—
368C4×Dic3—21no—
369C4×Dic3—31no—
370C4×Dic3—31no—
371C4×Dic3—61no—
372C4×Dic3—61no—
373C4×Dic3—61no—
374C4×Dic3—61no—
375C4×Dic3—61no—
376C4×Dic3—61no—
377C4×Dic3—61no—
378C4×Dic3—61no—
379C4×Dic3—61no—
380C4×Dic3—61no—
381C4×Dic3—61no—
382C2×C3⋊C8—31no—
383C2×C3⋊C8—31no—
384C2×C3⋊C8—31no—
385C2×C3⋊C8—31no—
386C2×C3⋊C8—61no—
387C2×C3⋊C8—61no—
388Dic12—22no—
389Dic12—22no—
390C22×C32C22×D411yescharacteristic
391C2×C3⋊D3—21no—
392C2×C3⋊D3—21no—
393C2×C3⋊D3—21no—
394C32×C4—21no—
395C32×C4—21no—
396C32×C4C2×#4111yescharacteristic
397C32×C4C2×#4111yescharacteristic
398C3⋊Dic3—21no—
399C3⋊Dic3—21no—
400C3⋊Dic3—21no—
401C3×Dic3—22no—
402C3×Dic3—22no—
403C3×Dic3—41no—
404C3×Dic3—41no—
405C3×Dic3—41no—
406C3×Dic3—41no—
407C3×Dic3—41no—
408C3×Dic3—41no—
409C22×Q8—91no—
410C2×Q16—31no—
411C2×Q16—31no—
412C2×Q16—91no—
413C2×Q16—91no—
414C4⋊Q8—31no—
415#126—181no—
416#126—181no—
417#125—31no—
418#125—181no—
419#125—181no—
420C22⋊Q8—91no—
421C22⋊Q8—91no—
422C4×Q8—31no—
423C4×Q8—31no—
424C4×Q8—91no—
425C4×Q8—91no—
426C4×Q8—91no—
427C4×Q8—91no—
428C4×Q8—181no—
429C4×Q8—181no—
430#117—91no—
431#117—91no—
432#117—181no—
433#117—181no—
434#107—31no—
435#107—91no—
436#106—31no—
437#106—91no—
438C4⋊C8—91no—
439C4⋊C8D3211yescharacteristic
440#103—31no—
441#103—31no—
442#103—31no—
443#103—31no—
444#103—91no—
445#103—91no—
446#103—91no—
447#103—91no—
448C22⋊C8—91no—
449C22⋊C8—91no—
450#97—91no—
451C4×C8—91no—
452C22×D3—31no—
453C22×D3—31no—
454C22×D3—61no—
455C3×Q8—32no—
456C3×Q8—32no—
457C3×Q8—61no—
458C3×Q8—61no—
459C3×Q8—61no—
460C3×Q8—61no—
461C3×Q8—61no—
462C3×Q8—61no—
463C2×C3×C4—21no—
464C2×C3×C4—21no—
465C2×C3×C4—21no—
466C2×C3×C4—61no—
467C2×C3×C4—61no—
468C2×C3×C4—61no—
469C2×C3×C4—61no—
470C2×C3×C4—61no—
471C2×C3×C4—61no—
472C2×C3×C4—61no—
473C2×C3×C4—61no—
474C2×C3×C4D3×D411yescharacteristic
475C2×C3×C4D3×D411yescharacteristic
476C2×C3×C4D3×D411yescharacteristic
477C2×C3×C4D3×D411yescharacteristic
478C2×C3×C4C23×D311yescharacteristic
479C2×C3×C4C23×D311yescharacteristic
480C2×Dic3—21no—
481C2×Dic3—21no—
482C2×Dic3—21no—
483C2×Dic3—21no—
484C2×Dic3—21no—
485C2×Dic3—21no—
486C2×Dic3—21no—
487C2×Dic3—21no—
488C2×Dic3—31no—
489C2×Dic3—31no—
490C2×Dic3—31no—
491C2×Dic3—31no—
492C2×Dic3—31no—
493C2×Dic3—31no—
494C2×Dic3—61no—
495C2×Dic3—61no—
496C2×Dic3—61no—
497C4×D3—64no—
498C4×D3—64no—
499C4×D3—61no—
500C4×D3—61no—
501C4×D3—61no—
502C4×D3—61no—
503C4×D3—121no—
504C4×D3—121no—
505Dic6—21no—
506Dic6—21no—
507Dic6—21no—
508Dic6—21no—
509Dic6—21no—
510Dic6—21no—
511Dic6—64no—
512Dic6—64no—
513Dic6#23712yes—
514Dic6#23912yes—
515C3×C8—21no—
516C3×C8—21no—
517C3×C8—21no—
518C3×C8—21no—
519C3×C8—41no—
520C3×C8—41no—
521C3⋊C8—61no—
522C3⋊C8—61no—
523C3⋊C8—61no—
524C3⋊C8—61no—
525C3⋊C8—121no—
526C3⋊C8—121no—
527C2×C32#52511yescharacteristic
528C2×C32#57811yescharacteristic
529C2×C32#57811yescharacteristic
530C3⋊D3—41no—
531C2×Q8—31no—
532C2×Q8—31no—
533C2×Q8—31no—
534C2×Q8—31no—
535C2×Q8—181no—
536C2×Q8—182no—
537C2×Q8—182no—
538C22×C4—91no—
539C22×C4—181no—
540Q16—62no—
541Q16—62no—
542Q16—182no—
543Q16—182no—
544C2×C8—91no—
545C2×C8—91no—
546C2×C8C2×D3211yescharacteristic
547C2×C8C2×D3211yescharacteristic
548C4⋊C4—31no—
549C4⋊C4—31no—
550C4⋊C4—31no—
551C4⋊C4—31no—
552C4⋊C4—61no—
553C4⋊C4—61no—
554C4⋊C4—61no—
555C4⋊C4—61no—
556C4⋊C4—61no—
557C4⋊C4—61no—
558C4⋊C4—91no—
559C4⋊C4—91no—
560C4⋊C4—181no—
561C4⋊C4—181no—
562C4⋊C4—181no—
563C4⋊C4—181no—
564C4⋊C4—181no—
565C4⋊C4—181no—
566C22⋊C4—91no—
567C22⋊C4—91no—
568C22⋊C4—181no—
569C22⋊C4—181no—
570C22⋊C4—181no—
571C42—61no—
572C42—61no—
573C42—91no—
574C42—181no—
575C42—181no—
576C42—181no—
577C42—181no—
578C42—181no—
579C42C2×D3211yescharacteristic
580C22×C3—21no—
581C22×C3C2×D3×D411yescharacteristic
582C22×C3C2×D3×D411yescharacteristic
583C2×D3—61no—
584C2×D3—61no—
585C2×D3—61no—
586C2×D3—61no—
587C2×D3—61no—
588C2×D3—61no—
589C2×D3—121no—
590C2×D3—121no—
591C2×D3—121no—
592C3×C4—21no—
593C3×C4—21no—
594C3×C4—21no—
595C3×C4—21no—
596C3×C4—21no—
597C3×C4—21no—
598C3×C4—41no—
599C3×C4—41no—
600C3×C4—62no—
601C3×C4—62no—
602C3×C4—121no—
603C3×C4—121no—
604C3×C4—121no—
605C3×C4—121no—
606C3×C4—121no—
607C3×C4—121no—
608C3×C4C2×#23711yescharacteristic
609C3×C4C2×#23911yescharacteristic
610C3×C4D3×#4111yescharacteristic
611C3×C4D3×#4111yescharacteristic
612Dic3—22no—
613Dic3—22no—
614Dic3—41no—
615Dic3—41no—
616Dic3—41no—
617Dic3—41no—
618Dic3—41no—
619Dic3—41no—
620Dic3—61no—
621Dic3—61no—
622Dic3—61no—
623Dic3—61no—
624Dic3—61no—
625Dic3—61no—
626Dic3—121no—
627Dic3—121no—
628Dic3—121no—
629C32#312711yescharacteristic, complemented, Sylow
630C23—91no—
631Q8—32no—
632Q8—32no—
633Q8—61no—
634Q8—61no—
635Q8—61no—
636Q8—61no—
637Q8—61no—
638Q8—61no—
639Q8—184no—
640C2×C4—61no—
641C2×C4—61no—
642C2×C4—61no—
643C2×C4—61no—
644C2×C4—61no—
645C2×C4—61no—
646C2×C4—61no—
647C2×C4—61no—
648C2×C4—91no—
649C2×C4—91no—
650C2×C4—91no—
651C2×C4—184no—
652C2×C4—181no—
653C2×C4—181no—
654C2×C4#380211yescharacteristic
655C2×C4#380211yescharacteristic
656C2×C4C22×D3211yescharacteristic
657C8—21no—
658C8—21no—
659C8—181no—
660C8—181no—
661C2×C3—21no—
662C2×C3—21no—
663C2×C3—21no—
664C2×C3#560611yescharacteristic
665C2×C3#562711yescharacteristic
666C2×C3#576611yescharacteristic
667C2×C3#577111yescharacteristic
668C2×C3#577911yescharacteristic
669C2×C3#577911yescharacteristic
670D3—121no—
671D3—121no—
672D3—241no—
673C22—181no—
674C22—181no—
675C22—181no—
676C22C2×#380211yescharacteristic
677C4—21no—
678C4—21no—
679C4—62no—
680C4—62no—
681C4—121no—
682C4—121no—
683C4—121no—
684C4—121no—
685C4—121no—
686C4—121no—
687C4—181no—
688C4—181no—
689C4—181no—
690C4D3×#23711yescharacteristic
691C4D3×#23911yescharacteristic
692C3—21no—
693C3#8046111yescharacteristic, complemented
694C3#8121111yescharacteristic, complemented
695C2—361no—
696C2#1059463211yescharacteristic
697C2#1059470311yescharacteristic
698C2#1059472311yescharacteristic
subgroupG/H
centerC22C2×#3802
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊C8C22
socleC22×C32C22×D4
prime radicalC22×C3⋊D3C2×D4
hypercenterC4⋊C8D32
hypocenterC32#3127
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
4. C3×#4849C2semidirect
5. C3×#4829C2semidirect
8. #10590819C2semidirect
9. #10590818C2semidirect
10. #10590791C2semidirect
11. #10590790C2semidirect
14. #10590384C2semidirect
15. #10590286C2semidirect
79. #4849D3semidirect
83. #4829D3semidirect
629. C32#3127semidirect
693. C3#80461semidirect
694. C3#81211semidirect

Maximal subgroups

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

subgroupindex
#105938672
#105938482
#105925392
C3×#48492
C3×#48292
#105909502
#105908192
#105908182
#105907912
#105907902
#105907152
#105907132
#105903842
#105902862
#812113
#804613