Finite Group Databasebeta

← #11873339

Subgroups — #11873339

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#10594355C211yesmaximal, characteristic
2#10594347C211yesmaximal, characteristic
3#10592587C211yesmaximal, characteristic
4C3×#4877C211yesmaximal, characteristic, complemented
5C3×#4873C211yesmaximal, characteristic, complemented
6#10590950C211yesmaximal, characteristic
7#10590800C211yesmaximal, characteristic, complemented
8#10590793C211yesmaximal, characteristic, complemented
9#10590648C211yesmaximal, characteristic
10#10590605C211yesmaximal, characteristic
11#10590561C211yesmaximal, characteristic, complemented
12#10590527C211yesmaximal, characteristic
13#10590491C211yesmaximal, characteristic, complemented
14#10590480C211yesmaximal, characteristic, complemented
15#10590477C211yesmaximal, characteristic, complemented
16#81211—31nomaximal
17#79724—31nomaximal
18C2×#3797C2211yescharacteristic
19#64106C2211yescharacteristic
20#64101C2211yescharacteristic
21C2×C3×Dic12C2211yescharacteristic
22C3×#890C2211yescharacteristic
23C3×#887C2211yescharacteristic
24C3×#887C2211yescharacteristic
25C3×#887C2211yescharacteristic
26C4×#627—21no—
27#63874C2211yescharacteristic
28#63871C2211yescharacteristic
29#63869—21no—
30#63868—21no—
31#63866C2211yescharacteristic
32#63848—21no—
33#63845—21no—
34#63844C2211yescharacteristic
35Dic3×Dic6C2211yescharacteristic
36Dic3×Dic6C2211yescharacteristic
37#63838—21no—
38#63836—21no—
39#63836—21no—
40C2×#3719C2211yescharacteristic
41C2×#3719C2211yescharacteristic
42C2×#3718C2211yescharacteristic
43C32×#107C2211yescharacteristic
44#63647C2211yescharacteristic
45#63643C2211yescharacteristic
46#63637C2211yescharacteristic
47#63635C2211yescharacteristic
48C3×#816C2211yescharacteristic
49C3×Dic3⋊C8C2211yescharacteristic
50C3×C8×Dic3C2211yescharacteristic
51C3×#810C2211yescharacteristic
52C3×#810C2211yescharacteristic
53C3×#810C2211yescharacteristic
54C3×#808C2211yescharacteristic
55#63575C2211yescharacteristic
56Dic3⋊(C3⋊C8)C2211yescharacteristic
57#63566C2211yescharacteristic
58#63565C2211yescharacteristic
59#63557C2211yescharacteristic
60#63554C2211yescharacteristic
61#5698—31no—
62#5583—31no—
63#5572—31no—
64#5572—31no—
65C3×#479—31no—
66C3×C4×Q16—31no—
67#5186—31no—
68#5182—31no—
69#5063—31no—
70#5031—31no—
71#5030—31no—
72#5030—31no—
73#4888—31no—
74#4888—31no—
75#4888—61no—
76#4877D311yescharacteristic, complemented
77#4873D311yescharacteristic, complemented
78#4868—31no—
79#4853—31no—
80#4849—31no—
81#4840—31no—
82#4814—31no—
83#4809—31no—
84#4809—31no—
85#4809—31no—
86#4796—31no—
87#4795—31no—
88#4790—31no—
89#4789—31no—
90C4×Dic12—31no—
91#4690—31no—
92C2×C4×C3⋊D3C2311yescharacteristic
93C2×#634C2311yescharacteristic
94C2×C3×Dic6C2311yescharacteristic
95C2×C3×Dic6C2311yescharacteristic
96C2×C3×Dic6C2311yescharacteristic
97C2×#627—21no—
98C2×#624—21no—
99#3797—22no—
100#3797—22no—
101C2×C32×C8C2311yescharacteristic
102C32×C4⋊C4C2311yescharacteristic
103C32×C4⋊C4C2311yescharacteristic
104#3752—21no—
105#3752—21no—
106C4⋊(C3⋊Dic3)—21no—
107C4⋊(C3⋊Dic3)C2311yescharacteristic
108C4×C3⋊Dic3—21no—
109C2×C3⋊(C3⋊C8)C2311yescharacteristic
110C3×C4⋊Dic3—21no—
111C3×C4⋊Dic3C2311yescharacteristic
112C3×Dic3⋊C4—21no—
113C3×Dic3⋊C4—21no—
114C3×Dic3⋊C4—21no—
115C3×Dic3⋊C4—21no—
116C3×C4×Dic3—21no—
117C3×C4×Dic3—21no—
118C3×C4×Dic3—21no—
119C3×C4×Dic3C2311yescharacteristic
120C3×C4×Dic3C2311yescharacteristic
121C2×C3×C3⋊C8C2311yescharacteristic
122C2×C3×C3⋊C8C2311yescharacteristic
123C3×Dic12—22no—
124#3724—21no—
125#3724D411yescharacteristic
126#3724D411yescharacteristic
127Dic3⋊Dic3—21no—
128Dic3⋊Dic3—21no—
129Dic3⋊Dic3—21no—
130Dic3⋊Dic3—21no—
131Dic3⋊Dic3—21no—
132#3722—21no—
133#3722D411yescharacteristic
134#3722D411yescharacteristic
135Dic32—21no—
136Dic32—21no—
137Dic32—21no—
138#3719—22no—
139#3719—22no—
140#3718—22no—
141#3127—91noSylow
142C2×D3×Q8—31no—
143C2×D3×Q8—31no—
144C2×C3×Q16—31no—
145C3×#125—31no—
146C3×C4×Q8—31no—
147C3×C4×Q8—31no—
148C3×C4×Q8—31no—
149#946—31no—
150Q8×Dic3—31no—
151Q8×Dic3—31no—
152#944—31no—
153C2×#216—31no—
154C2×#216—31no—
155C2×#216—31no—
156C2×#216—31no—
157C2×Dic12—31no—
158C2×Dic12—31no—
159C2×Dic12C2×D311yescharacteristic
160#898—61no—
161#898—61no—
162#898—61no—
163#897—31no—
164#897—31no—
165#897—31no—
166#897—61no—
167#892—31no—
168#892—31no—
169#892—61no—
170#892—61no—
171#892—61no—
172#890—61no—
173#890—61no—
174#890C2×D311yescharacteristic
175#889—61no—
176#887—31no—
177#887—61no—
178#887—61no—
179#887C2×D311yescharacteristic
180#887C2×D311yescharacteristic
181#887C2×D311yescharacteristic
182#876—61no—
183#872—31no—
184#872—31no—
185#872—61no—
186#872—61no—
187#870—61no—
188#869—31no—
189C4×Dic6—31no—
190C4×Dic6—31no—
191C4×Dic6—31no—
192C4×Dic6—61no—
193C4×Dic6—61no—
194C3×#107—21no—
195C3×#107C2×D311yescharacteristic
196C3×#107C2×D311yescharacteristic
197C3×#106—31no—
198C3×C4⋊C8—31no—
199C3×#103—31no—
200C3×#103—31no—
201C3×#103—31no—
202C3×#103—31no—
203C3×C4×C8—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#818—31no—
212#816—31no—
213#816—31no—
214#816—31no—
215#816—61no—
216#816C2×D311yescharacteristic
217#815—31no—
218Dic3⋊C8—31no—
219Dic3⋊C8C2×D311yescharacteristic
220C8×Dic3C2×D311yescharacteristic
221#810—31no—
222#810—31no—
223#810—31no—
224#810—61no—
225#810C2×D311yescharacteristic
226#810C2×D311yescharacteristic
227#810C2×D311yescharacteristic
228#808—31no—
229#808—31no—
230#808—61no—
231#808C2×D311yescharacteristic
232#807—31no—
233C4⋊(C3⋊C8)—31no—
234#803—31no—
235C22×C3⋊D3C2×D411yescharacteristic
236C2×C32×C4—21no—
237C2×C32×C4—21no—
238C2×C32×C4C2411yescharacteristic
239C2×C3⋊Dic3—21no—
240C2×C3⋊Dic3—21no—
241C2×C3⋊Dic3C2×D411yescharacteristic
242C4×C3⋊D3—21no—
243C4×C3⋊D3—21no—
244#634—21no—
245#634—21no—
246C2×C3×Dic3—21no—
247C2×C3×Dic3—21no—
248C2×C3×Dic3—21no—
249C2×C3×Dic3—21no—
250C2×C3×Dic3C2×D411yescharacteristic
251C2×C3×Dic3C2×D411yescharacteristic
252C2×C3×Dic3C2×D411yescharacteristic
253C2×C3×Dic3C2×D411yescharacteristic
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—
263C3⋊(C3⋊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—91no—
273#462—91no—
274#451—91no—
275#451—91no—
276#441—91no—
277#441—91no—
278C4×Q16—31no—
279C4×Q16—91no—
280#433—91no—
281C2×C3×Q8—31no—
282C2×C3×Q8—31no—
283C2×C3×Q8—31no—
284D3×Q8—62no—
285D3×Q8—62no—
286D3×Q8—62no—
287D3×Q8—62no—
288C2×C4×D3—31no—
289C2×C4×D3—31no—
290C2×C4×D3—61no—
291C2×C4×D3—61no—
292C2×C4×D3—61no—
293C2×Dic6—31no—
294C2×Dic6—31no—
295C2×Dic6—61no—
296C2×Dic6—61no—
297C2×Dic6—61no—
298C2×Dic6C22×D311yescharacteristic
299C2×Dic6C22×D311yescharacteristic
300C2×Dic6C22×D311yescharacteristic
301C3×Q16—62no—
302C2×C3×C8—21no—
303C2×C3×C8—31no—
304C2×C3×C8—31no—
305C2×C3×C8C22×D311yescharacteristic
306C2×C3×C8C22×D311yescharacteristic
307C3×C4⋊C4—21no—
308C3×C4⋊C4—21no—
309C3×C4⋊C4—31no—
310C3×C4⋊C4—61no—
311C3×C4⋊C4—61no—
312C3×C4⋊C4—61no—
313C3×C4⋊C4—61no—
314C3×C4⋊C4—61no—
315C3×C4⋊C4C22×D311yescharacteristic
316C3×C4⋊C4C22×D311yescharacteristic
317C3×C4⋊C4C22×D311yescharacteristic
318C3×C4⋊C4C22×D311yescharacteristic
319C3×C42—31no—
320C3×C42—31no—
321C3×C42—61no—
322C3×C42—61no—
323C3×C42—61no—
324#216—62no—
325#216—62no—
326#216—62no—
327#216—62no—
328(C2×D3)⋊C4—31no—
329(C2×D3)⋊C4—31no—
330(C2×D3)⋊C4—31no—
331(C2×D3)⋊C4—31no—
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—121no—
339(C2×D3)⋊C4—121no—
340C4⋊Dic3—21no—
341C4⋊Dic3—31no—
342C4⋊Dic3—31no—
343C4⋊Dic3—61no—
344C4⋊Dic3—61no—
345C4⋊Dic3—61no—
346C4⋊Dic3—61no—
347C4⋊Dic3—61no—
348C4⋊Dic3—61no—
349C4⋊Dic3—61no—
350C4⋊Dic3—61no—
351C4⋊Dic3—121no—
352C4⋊Dic3C22×D311yescharacteristic
353Dic3⋊C4—21no—
354Dic3⋊C4—21no—
355Dic3⋊C4—21no—
356Dic3⋊C4—21no—
357Dic3⋊C4—31no—
358Dic3⋊C4—31no—
359Dic3⋊C4—31no—
360Dic3⋊C4—31no—
361Dic3⋊C4—61no—
362Dic3⋊C4—61no—
363Dic3⋊C4—61no—
364Dic3⋊C4—61no—
365Dic3⋊C4—61no—
366Dic3⋊C4—61no—
367Dic3⋊C4—61no—
368C4×Dic3—21no—
369C4×Dic3—21no—
370C4×Dic3—21no—
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—121no—
380C4×Dic3C22×D311yescharacteristic
381C4×Dic3C22×D311yescharacteristic
382C2×C3⋊C8—31no—
383C2×C3⋊C8—31no—
384C2×C3⋊C8—61no—
385C2×C3⋊C8C22×D311yescharacteristic
386C2×C3⋊C8C22×D311yescharacteristic
387Dic12—22no—
388Dic12—62no—
389Dic12—62no—
390C22×C32C22×D411yescharacteristic
391C2×C3⋊D3—21no—
392C2×C3⋊D3—21no—
393C2×C3⋊D3—21no—
394C32×C4—41no—
395C32×C4—41no—
396C32×C4C2×#4111yescharacteristic
397C32×C4C2×#4111yescharacteristic
398C3⋊Dic3—21no—
399C3⋊Dic3—41no—
400C3⋊Dic3—41no—
401C3×Dic3—22no—
402C3×Dic3—22no—
403C3×Dic3—21no—
404C3×Dic3—21no—
405C3×Dic3—21no—
406C3×Dic3—21no—
407C3×Dic3—41no—
408C3×Dic3—41no—
409C22×Q8—91no—
410C2×Q16—31no—
411C2×Q16—91no—
412C2×Q16—91no—
413C2×Q16—91no—
414C4⋊Q8—91no—
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—31no—
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—91no—
435#107D3211yescharacteristic
436#106—31no—
437#106—91no—
438C4⋊C8—31no—
439C4⋊C8—91no—
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—31no—
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—
461C2×C3×C4—21no—
462C2×C3×C4—21no—
463C2×C3×C4—21no—
464C2×C3×C4—21no—
465C2×C3×C4—21no—
466C2×C3×C4—31no—
467C2×C3×C4—31no—
468C2×C3×C4—31no—
469C2×C3×C4—31no—
470C2×C3×C4—41no—
471C2×C3×C4—41no—
472C2×C3×C4—61no—
473C2×C3×C4—61no—
474C2×C3×C4—61no—
475C2×C3×C4—61no—
476C2×C3×C4C23×D311yescharacteristic
477C2×C3×C4C23×D311yescharacteristic
478C2×Dic3—21no—
479C2×Dic3—21no—
480C2×Dic3—21no—
481C2×Dic3—21no—
482C2×Dic3—31no—
483C2×Dic3—31no—
484C2×Dic3—61no—
485C2×Dic3—61no—
486C2×Dic3—61no—
487C2×Dic3—61no—
488C2×Dic3—61no—
489C2×Dic3—121no—
490C2×Dic3—121no—
491C2×Dic3D3×D411yescharacteristic
492C2×Dic3D3×D411yescharacteristic
493C2×Dic3D3×D411yescharacteristic
494C2×Dic3D3×D411yescharacteristic
495C4×D3—64no—
496C4×D3—64no—
497C4×D3—61no—
498C4×D3—61no—
499C4×D3—61no—
500C4×D3—61no—
501C4×D3—121no—
502C4×D3—121no—
503Dic6—21no—
504Dic6—21no—
505Dic6—21no—
506Dic6—21no—
507Dic6—64no—
508Dic6—64no—
509Dic6—61no—
510Dic6—61no—
511Dic6—61no—
512Dic6—61no—
513Dic6—121no—
514Dic6—121no—
515Dic6#23512yes—
516Dic6#23912yes—
517C3×C8—21no—
518C3×C8—21no—
519C3×C8—41no—
520C3×C8—61no—
521C3×C8—61no—
522C3⋊C8—21no—
523C3⋊C8—21no—
524C3⋊C8—61no—
525C3⋊C8—61no—
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—91no—
535C2×Q8—181no—
536C2×Q8—182no—
537C2×Q8—182no—
538C22×C4—91no—
539C22×C4—181no—
540Q16—62no—
541Q16—182no—
542Q16—182no—
543Q16—182no—
544C2×C8—31no—
545C2×C8—31no—
546C2×C8—91no—
547C2×C8C2×D3211yescharacteristic
548C4⋊C4—31no—
549C4⋊C4—61no—
550C4⋊C4—61no—
551C4⋊C4—61no—
552C4⋊C4—61no—
553C4⋊C4—61no—
554C4⋊C4—91no—
555C4⋊C4—91no—
556C4⋊C4—91no—
557C4⋊C4—181no—
558C4⋊C4—181no—
559C4⋊C4—181no—
560C4⋊C4—181no—
561C4⋊C4—181no—
562C4⋊C4—181no—
563C4⋊C4—181no—
564C4⋊C4C2×D3211yescharacteristic
565C4⋊C4C2×D3211yescharacteristic
566C22⋊C4—91no—
567C22⋊C4—91no—
568C22⋊C4—181no—
569C22⋊C4—181no—
570C22⋊C4—181no—
571C42—31no—
572C42—31no—
573C42—61no—
574C42—61no—
575C42—61no—
576C42—181no—
577C42—181no—
578C42—181no—
579C42—181no—
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—41no—
595C3×C4—41no—
596C3×C4—41no—
597C3×C4—41no—
598C3×C4—61no—
599C3×C4—61no—
600C3×C4—61no—
601C3×C4—61no—
602C3×C4—62no—
603C3×C4—62no—
604C3×C4—81no—
605C3×C4—81no—
606C3×C4—121no—
607C3×C4—121no—
608C3×C4C2×#23511yescharacteristic
609C3×C4C2×#23911yescharacteristic
610C3×C4D3×#4111yescharacteristic
611C3×C4D3×#4111yescharacteristic
612Dic3—21no—
613Dic3—21no—
614Dic3—21no—
615Dic3—21no—
616Dic3—22no—
617Dic3—22no—
618Dic3—41no—
619Dic3—41no—
620Dic3—61no—
621Dic3—61no—
622Dic3—121no—
623Dic3—121no—
624Dic3—121no—
625Dic3—121no—
626Dic3—121no—
627Dic3—241no—
628Dic3—241no—
629C32#312711yescharacteristic, complemented, Sylow
630C23—91no—
631Q8—32no—
632Q8—32no—
633Q8—61no—
634Q8—61no—
635Q8—61no—
636Q8—61no—
637Q8—184no—
638Q8—181no—
639Q8—181no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—31no—
643C2×C4—31no—
644C2×C4—31no—
645C2×C4—31no—
646C2×C4—61no—
647C2×C4—61no—
648C2×C4—61no—
649C2×C4—61no—
650C2×C4—91no—
651C2×C4—184no—
652C2×C4—181no—
653C2×C4—181no—
654C2×C4—181no—
655C2×C4—181no—
656C2×C4C22×D3211yescharacteristic
657C8—21no—
658C8—61no—
659C8—61no—
660C8—181no—
661C2×C3—21no—
662C2×C3—21no—
663C2×C3—21no—
664C2×C3#554711yescharacteristic
665C2×C3#562711yescharacteristic
666C2×C3#576611yescharacteristic
667C2×C3#577111yescharacteristic
668C2×C3#577111yescharacteristic
669C2×C3#577911yescharacteristic
670D3—121no—
671D3—121no—
672D3—241no—
673C22—181no—
674C22—181no—
675C22—181no—
676C22D32×D411yescharacteristic
677C4—41no—
678C4—41no—
679C4—62no—
680C4—62no—
681C4—61no—
682C4—61no—
683C4—61no—
684C4—61no—
685C4—121no—
686C4—121no—
687C4—181no—
688C4—361no—
689C4—361no—
690C4D3×#23511yescharacteristic
691C4D3×#23911yescharacteristic
692C3—21no—
693C3#7972411yescharacteristic, complemented
694C3#8121111yescharacteristic, complemented
695C2—361no—
696C2#1059462311yescharacteristic
697C2#1059473711yescharacteristic
698C2#1059476611yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#107C22
socleC22×C32C22×D4
prime radicalC22×C3⋊D3C2×D4
hypercenter#107D32
hypocenterC32#3127
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #107

Complements

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

NH ≅ G/Ntype
4. C3×#4877C2semidirect
5. C3×#4873C2semidirect
7. #10590800C2semidirect
8. #10590793C2semidirect
11. #10590561C2semidirect
13. #10590491C2semidirect
14. #10590480C2semidirect
15. #10590477C2semidirect
76. #4877D3semidirect
77. #4873D3semidirect
629. C32#3127semidirect
693. C3#79724semidirect
694. C3#81211semidirect

Maximal subgroups

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

subgroupindex
#105943552
#105943472
#105925872
C3×#48772
C3×#48732
#105909502
#105908002
#105907932
#105906482
#105906052
#105905612
#105905272
#105904912
#105904802
#105904772
#812113
#797243