Finite Group Databasebeta

← #11873323

Subgroups — #11873323

Order 1152.

770 conjugacy classes of subgroups.

The subgroup lattice has 698 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10593885C211yesmaximal, characteristic
2#10593880C211yesmaximal, characteristic
3#10592415C211yesmaximal, characteristic, complemented
4C3×#4716C211yesmaximal, characteristic, complemented
5C3×#4709C211yesmaximal, characteristic
6#10590952C211yesmaximal, characteristic
7#10590949C211yesmaximal, characteristic
8#10590815C211yesmaximal, characteristic, complemented
9#10590809C211yesmaximal, characteristic, complemented
10#10590808C211yesmaximal, characteristic, complemented
11#10590800C211yesmaximal, characteristic, complemented
12#10590711C211yesmaximal, characteristic
13#10590709C211yesmaximal, characteristic
14C4×#3719C211yesmaximal, characteristic, complemented
15C4×#3719C211yesmaximal, characteristic, complemented
16#79836—31nomaximal
17#79396—31nomaximal
18C2×D3×Dic6C2211yescharacteristic
19C2×#3746C2211yescharacteristic
20C4×#634C2211yescharacteristic
21C4×#634C2211yescharacteristic
22C2×C3×Dic12C2211yescharacteristic
23C3×#872C2211yescharacteristic
24C3×C4×Dic6C2211yescharacteristic
25C3×C4×Dic6C2211yescharacteristic
26#63878—21no—
27#63877—21no—
28#63870—21no—
29#63869C2211yescharacteristic
30#63867—21no—
31#63866C2211yescharacteristic
32#63862—21no—
33#63859—21no—
34#63857C2211yescharacteristic
35#63856C2211yescharacteristic
36#63844C2211yescharacteristic
37Dic3×Dic6C2211yescharacteristic
38#63841C2211yescharacteristic
39#63838—21no—
40#63837—21no—
41C2×#3719C2211yescharacteristic
42C2×#3719C2211yescharacteristic
43C32×#97C2211yescharacteristic
44#63644C2211yescharacteristic
45#63643C2211yescharacteristic
46#63643C2211yescharacteristic
47C3×(C2×D3)⋊C8C2211yescharacteristic
48C3×(C2×D3)⋊C8C2211yescharacteristic
49C3×#817C2211yescharacteristic
50C3×#816C2211yescharacteristic
51C3×#816C2211yescharacteristic
52C3×Dic3⋊C8C2211yescharacteristic
53C3×Dic3⋊C8C2211yescharacteristic
54C3×C4×C3⋊C8C2211yescharacteristic
55#63575C2211yescharacteristic
56#63575C2211yescharacteristic
57#63567C2211yescharacteristic
58#63567C2211yescharacteristic
59#63566C2211yescharacteristic
60#63566C2211yescharacteristic
61#5583—31no—
62#5572—31no—
63#5518—31no—
64#5516—31no—
65C3×#441—31no—
66C3×#433—31no—
67#5186—31no—
68#5182—31no—
69C4×#216—31no—
70C4×#216—31no—
71#4868—31no—
72#4857—31no—
73#4849—31no—
74#4849—31no—
75#4829—31no—
76#4829—31no—
77#4815—31no—
78#4809—31no—
79#4799—31no—
80#4795—31no—
81#4739—31no—
82#4739—31no—
83#4723—31no—
84#4723—31no—
85#4716—31no—
86#4716—31no—
87#4716—61no—
88#4716D311yescharacteristic, complemented
89#4709D311yescharacteristic
90C4×Dic12—31no—
91C4×Dic12—31no—
92C2×#634C2311yescharacteristic
93C2×#634C2311yescharacteristic
94C2×C3×C4×D3C2311yescharacteristic
95C2×C3×Dic6C2311yescharacteristic
96C2×C3×Dic6C2311yescharacteristic
97C2×#627—21no—
98C2×D3×Dic3—21no—
99D3×Dic6—22no—
100D3×Dic6—22no—
101C2×C32×C8C2311yescharacteristic
102C2×C32×C8C2311yescharacteristic
103C32×C42C2311yescharacteristic
104C4⋊(C3⋊Dic3)C2311yescharacteristic
105C4⋊(C3⋊Dic3)C2311yescharacteristic
106#3750—21no—
107#3750—21no—
108C4×C3⋊Dic3—21no—
109C4×C3⋊Dic3—21no—
110#3746—22no—
111C3×(C2×D3)⋊C4D411yescharacteristic
112C3×(C2×D3)⋊C4D411yescharacteristic
113C3×C4⋊Dic3C2311yescharacteristic
114C3×C4⋊Dic3C2311yescharacteristic
115C3×Dic3⋊C4—21no—
116C3×Dic3⋊C4—21no—
117C3×Dic3⋊C4D411yescharacteristic
118C3×Dic3⋊C4D411yescharacteristic
119C3×C4×Dic3—21no—
120C3×C4×Dic3—21no—
121C3×C4×Dic3C2311yescharacteristic
122C2×C3×C3⋊C8C2311yescharacteristic
123C2×C3×C3⋊C8C2311yescharacteristic
124C3×Dic12—22no—
125#3724—21no—
126#3724—21no—
127#3724—21no—
128Dic3⋊Dic3—21no—
129Dic3⋊Dic3—21no—
130Dic3⋊Dic3—21no—
131Dic3⋊Dic3—21no—
132Dic3⋊Dic3—21no—
133(C2×D3)⋊Dic3—21no—
134(C2×D3)⋊Dic3—21no—
135(C2×D3)⋊Dic3—21no—
136Dic32—21no—
137Dic32—21no—
138Dic32—21no—
139#3719—22no—
140#3719—22no—
141#3127—91noSylow
142C2×D3×Q8—31no—
143C22×Dic6—31no—
144C2×C3×Q16—31no—
145C3×C4×Q8—31no—
146C3×C4×Q8—31no—
147C3×#117—31no—
148#946—31no—
149Q8×Dic3—31no—
150#944—31no—
151C2×#216—31no—
152C2×#216—31no—
153#926—31no—
154#924—31no—
155#924—31no—
156C2×Dic12—31no—
157C2×Dic12—31no—
158C2×Dic12—31no—
159C2×Dic12—31no—
160C2×Dic12—61no—
161C2×Dic12C2×D311yescharacteristic
162#898—61no—
163#897—31no—
164#892—31no—
165#892—61no—
166#890—31no—
167#889—61no—
168#889—61no—
169#889—61no—
170#887—31no—
171#887—61no—
172#887—61no—
173#887—61no—
174#879—61no—
175#879—61no—
176#877—61no—
177#877—61no—
178#876—61no—
179#872—61no—
180#872C2×D311yescharacteristic
181#870—31no—
182#870—61no—
183#869—31no—
184C4×Dic6—31no—
185C4×Dic6—31no—
186C4×Dic6—31no—
187C4×Dic6—31no—
188C4×Dic6—31no—
189C4×Dic6—31no—
190C4×Dic6—61no—
191C4×Dic6—61no—
192C4×Dic6—61no—
193C4×Dic6C2×D311yescharacteristic
194C4×Dic6C2×D311yescharacteristic
195C3×#106—31no—
196C3×C4⋊C8—31no—
197C3×C4⋊C8—31no—
198C3×#103—31no—
199C3×#103—31no—
200C3×C22⋊C8—31no—
201C3×C22⋊C8—31no—
202C3×#97—21no—
203C3×#97C2×D311yescharacteristic
204C3×#97C2×D311yescharacteristic
205C3×C4×C8—31no—
206#835—31no—
207#835—31no—
208(C2×D3)⋊C8C2×D311yescharacteristic
209(C2×D3)⋊C8C2×D311yescharacteristic
210#818—31no—
211#818—31no—
212#817—31no—
213#817—31no—
214#817—61no—
215#817C2×D311yescharacteristic
216#816—31no—
217#816—31no—
218#816—31no—
219#816—31no—
220#816—31no—
221#816—31no—
222#816—31no—
223#816—31no—
224#816—61no—
225#816—61no—
226#816C2×D311yescharacteristic
227#816C2×D311yescharacteristic
228Dic3⋊C8C2×D311yescharacteristic
229Dic3⋊C8C2×D311yescharacteristic
230#810—31no—
231#810—31no—
232#807—31no—
233#807—31no—
234C4×C3⋊C8C2×D311yescharacteristic
235C22×C3×D3C2×D411yescharacteristic
236C2×C32×C4C2×D411yescharacteristic
237C2×C32×C4C2×D411yescharacteristic
238C2×C32×C4C2411yescharacteristic
239C2×C3⋊Dic3—21no—
240C2×C3⋊Dic3—21no—
241C2×C3⋊Dic3—21no—
242C2×C3⋊Dic3—21no—
243#634—21no—
244#634—21no—
245#634—21no—
246#634#4112yes—
247C2×C3×Dic3—21no—
248C2×C3×Dic3—21no—
249C2×C3×Dic3—21no—
250C2×C3×Dic3—21no—
251C2×C3×Dic3C2×D411yescharacteristic
252C2×C3×Dic3C2×D411yescharacteristic
253C2×C3×Dic3C2×D411yescharacteristic
254C3×C4×D3—21no—
255C3×C4×D3—21no—
256C3×Dic6—21no—
257C3×Dic6—21no—
258C3×Dic6—21no—
259C3×Dic6#4112yes—
260#627—24no—
261D3×Dic3—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—91no—
271#479—91no—
272#462—91no—
273#462—91no—
274#451—91no—
275#451—91no—
276#441—31no—
277#441—91no—
278C4×Q16—91no—
279C4×Q16—91no—
280#433—31no—
281C2×C3×Q8—31no—
282C2×C3×Q8—31no—
283C22×C3×C4—31no—
284C22×Dic3—61no—
285D3×Q8—62no—
286D3×Q8—62no—
287C2×C4×D3—61no—
288C2×C4×D3C22×D311yescharacteristic
289C2×Dic6—31no—
290C2×Dic6—31no—
291C2×Dic6—31no—
292C2×Dic6—31no—
293C2×Dic6—61no—
294C2×Dic6—61no—
295C2×Dic6—62no—
296C2×Dic6—61no—
297C2×Dic6—61no—
298C2×Dic6—62no—
299C2×Dic6C22×D311yescharacteristic
300C2×Dic6C22×D311yescharacteristic
301C3×Q16—62no—
302C2×C3×C8—21no—
303C2×C3×C8—21no—
304C2×C3×C8—31no—
305C2×C3×C8—31no—
306C2×C3×C8C22×D311yescharacteristic
307C2×C3×C8C22×D311yescharacteristic
308C2×C3×C8C22×D311yescharacteristic
309C2×C3×C8C22×D311yescharacteristic
310C3×C4⋊C4—31no—
311C3×C4⋊C4—31no—
312C3×C4⋊C4—31no—
313C3×C4⋊C4—31no—
314C3×C4⋊C4—61no—
315C3×C4⋊C4—61no—
316C3×C22⋊C4—31no—
317C3×C22⋊C4—31no—
318C3×C42—21no—
319C3×C42—31no—
320C3×C42—61no—
321C3×C42—61no—
322C3×C42C22×D311yescharacteristic
323C3×C42C22×D311yescharacteristic
324#217—61no—
325#217—61no—
326#217—61no—
327#216—62no—
328#216—62no—
329(C2×D3)⋊C4—61no—
330(C2×D3)⋊C4—61no—
331(C2×D3)⋊C4—61no—
332(C2×D3)⋊C4D1211yescharacteristic
333(C2×D3)⋊C4D1211yescharacteristic
334C4⋊Dic3—31no—
335C4⋊Dic3—31no—
336C4⋊Dic3—31no—
337C4⋊Dic3—31no—
338C4⋊Dic3—61no—
339C4⋊Dic3—61no—
340C4⋊Dic3—61no—
341C4⋊Dic3—61no—
342C4⋊Dic3—61no—
343C4⋊Dic3—61no—
344C4⋊Dic3—61no—
345C4⋊Dic3C22×D311yescharacteristic
346C4⋊Dic3C22×D311yescharacteristic
347Dic3⋊C4—21no—
348Dic3⋊C4—21no—
349Dic3⋊C4—61no—
350Dic3⋊C4—61no—
351Dic3⋊C4—61no—
352Dic3⋊C4—61no—
353Dic3⋊C4—61no—
354Dic3⋊C4—61no—
355Dic3⋊C4—61no—
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—
365Dic3⋊C4—121no—
366Dic3⋊C4D1211yescharacteristic
367Dic3⋊C4D1211yescharacteristic
368C4×Dic3—21no—
369C4×Dic3—21no—
370C4×Dic3—61no—
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—121no—
381C4×Dic3—121no—
382C4×Dic3C22×D311yescharacteristic
383C2×C3⋊C8C22×D311yescharacteristic
384C2×C3⋊C8C22×D311yescharacteristic
385Dic12—22no—
386Dic12—62no—
387Dic12—62no—
388Dic12—64no—
389Dic12—62no—
390Dic12—62no—
391C22×C32C22×D411yescharacteristic
392C2×C3×D3—21no—
393C2×C3×D3—21no—
394C2×C3×D3—21no—
395C32×C4—21no—
396C32×C4—21no—
397C32×C4C2×#4111yescharacteristic
398C32×C4C2×#4111yescharacteristic
399C3⋊Dic3—22no—
400C3⋊Dic3—41no—
401C3⋊Dic3—41no—
402C3⋊Dic3—41no—
403C3×Dic3—22no—
404C3×Dic3—21no—
405C3×Dic3—21no—
406C3×Dic3—21no—
407C3×Dic3—41no—
408C3×Dic3—41no—
409C3×Dic3—41no—
410C22×Q8—91no—
411C2×Q16—31no—
412C2×Q16—91no—
413C2×Q16—91no—
414C2×Q16—91no—
415C4⋊Q8—91no—
416#126—181no—
417#126—181no—
418#125—91no—
419#125—181no—
420#125—181no—
421C22⋊Q8—91no—
422C22⋊Q8—91no—
423C4×Q8—31no—
424C4×Q8—31no—
425C4×Q8—91no—
426C4×Q8—91no—
427C4×Q8—91no—
428C4×Q8—91no—
429C4×Q8—181no—
430C4×Q8—181no—
431#117—31no—
432#117—91no—
433#117—181no—
434#117—181no—
435#107—91no—
436#107—91no—
437#106—31no—
438#106—91no—
439C4⋊C8—31no—
440C4⋊C8—31no—
441#103—31no—
442#103—31no—
443#103—91no—
444#103—91no—
445#103—91no—
446#103—91no—
447#103—91no—
448#103—91no—
449C22⋊C8—31no—
450C22⋊C8—31no—
451#97D3211yescharacteristic
452C4×C8—31no—
453C23×C3—31no—
454C22×D3C2×D1211yescharacteristic
455C3×Q8—32no—
456C3×Q8—61no—
457C3×Q8—61no—
458C3×Q8—61no—
459C2×C3×C4—21no—
460C2×C3×C4—21no—
461C2×C3×C4—21no—
462C2×C3×C4—31no—
463C2×C3×C4—31no—
464C2×C3×C4—31no—
465C2×C3×C4—61no—
466C2×C3×C4—61no—
467C2×C3×C4—61no—
468C2×C3×C4—61no—
469C2×C3×C4—61no—
470C2×C3×C4—61no—
471C2×C3×C4C2×D1211yescharacteristic
472C2×C3×C4C2×D1211yescharacteristic
473C2×C3×C4D3×D411yescharacteristic
474C2×C3×C4D3×D411yescharacteristic
475C2×C3×C4C23×D311yescharacteristic
476C2×C3×C4C23×D311yescharacteristic
477C2×Dic3—21no—
478C2×Dic3—21no—
479C2×Dic3—21no—
480C2×Dic3—21no—
481C2×Dic3—64no—
482C2×Dic3—61no—
483C2×Dic3—61no—
484C2×Dic3—61no—
485C2×Dic3—61no—
486C2×Dic3—61no—
487C2×Dic3—61no—
488C2×Dic3—61no—
489C2×Dic3—61no—
490C2×Dic3—121no—
491C2×Dic3—121no—
492C2×Dic3—121no—
493C2×Dic3—121no—
494C2×Dic3C2×D1211yescharacteristic
495C2×Dic3C2×D1211yescharacteristic
496C2×Dic3C2×D1211yescharacteristic
497C4×D3—21no—
498C4×D3—21no—
499C4×D3—64no—
500Dic6—21no—
501Dic6—21no—
502Dic6—21no—
503Dic6—32no—
504Dic6—32no—
505Dic6—62no—
506Dic6—64no—
507Dic6—64no—
508Dic6—61no—
509Dic6—61no—
510Dic6—62no—
511Dic6—61no—
512Dic6—61no—
513Dic6—61no—
514Dic6—61no—
515Dic6—121no—
516Dic6—121no—
517Dic6#23512yes—
518C3×C8—22no—
519C3×C8—21no—
520C3×C8—21no—
521C3×C8—21no—
522C3×C8—21no—
523C3×C8—41no—
524C3×C8—61no—
525C3×C8—61no—
526C3⋊C8—21no—
527C3⋊C8—21no—
528C2×C32#52511yescharacteristic
529C2×C32#57811yescharacteristic
530C2×C32#57811yescharacteristic
531C3×D3—41no—
532C2×Q8—31no—
533C2×Q8—31no—
534C2×Q8—91no—
535C2×Q8—91no—
536C2×Q8—181no—
537C2×Q8—182no—
538C2×Q8—182no—
539C22×C4—31no—
540C22×C4—181no—
541Q16—62no—
542Q16—182no—
543Q16—182no—
544Q16—182no—
545C2×C8—31no—
546C2×C8—31no—
547C2×C8C2×D3211yescharacteristic
548C2×C8C2×D3211yescharacteristic
549C4⋊C4—31no—
550C4⋊C4—31no—
551C4⋊C4—31no—
552C4⋊C4—31no—
553C4⋊C4—61no—
554C4⋊C4—61no—
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⋊C4—181no—
565C4⋊C4—181no—
566C4⋊C4—181no—
567C22⋊C4—31no—
568C22⋊C4—31no—
569C22⋊C4—181no—
570C22⋊C4—181no—
571C22⋊C4—181no—
572C42—31no—
573C42—61no—
574C42—61no—
575C42—181no—
576C42—181no—
577C42—181no—
578C42—181no—
579C42—181no—
580C42C2×D3211yescharacteristic
581C22×C3—21no—
582C22×C3—61no—
583C22×C3—61no—
584C22×C3—61no—
585C22×C3C22×D1211yescharacteristic
586C22×C3C2×D3×D411yescharacteristic
587C2×D3—21no—
588C2×D3—21no—
589C2×D3—21no—
590C3×C4—21no—
591C3×C4—21no—
592C3×C4—21no—
593C3×C4—21no—
594C3×C4—21no—
595C3×C4—21no—
596C3×C4—41no—
597C3×C4—41no—
598C3×C4—61no—
599C3×C4—61no—
600C3×C4—62no—
601C3×C4—61no—
602C3×C4—121no—
603C3×C4—121no—
604C3×C4—121no—
605C3×C4C2×#23511yescharacteristic
606C3×C4D3×#4111yescharacteristic
607C3×C4D3×#4111yescharacteristic
608C3×C4D3×#4111yescharacteristic
609Dic3—21no—
610Dic3—21no—
611Dic3—21no—
612Dic3—22no—
613Dic3—41no—
614Dic3—41no—
615Dic3—41no—
616Dic3—62no—
617Dic3—62no—
618Dic3—122no—
619Dic3—122no—
620Dic3—121no—
621Dic3—121no—
622Dic3—121no—
623Dic3—121no—
624Dic3—121no—
625Dic3—121no—
626Dic3—241no—
627Dic3—241no—
628C32#312711yescharacteristic, complemented, Sylow
629C23—31no—
630Q8—32no—
631Q8—61no—
632Q8—61no—
633Q8—61no—
634Q8—92no—
635Q8—184no—
636Q8—181no—
637Q8—181no—
638Q8—181no—
639C2×C4—31no—
640C2×C4—31no—
641C2×C4—31no—
642C2×C4—61no—
643C2×C4—61no—
644C2×C4—61no—
645C2×C4—61no—
646C2×C4—61no—
647C2×C4—61no—
648C2×C4—184no—
649C2×C4—181no—
650C2×C4—181no—
651C2×C4—181no—
652C2×C4—181no—
653C2×C4D3×D1211yescharacteristic
654C2×C4D3×D1211yescharacteristic
655C2×C4C22×D3211yescharacteristic
656C8—21no—
657C8—21no—
658C8—61no—
659C8—61no—
660C2×C3—21no—
661C2×C3—21no—
662C2×C3—21no—
663C2×C3—121no—
664C2×C3#552411yescharacteristic
665C2×C3#554711yescharacteristic
666C2×C3#575311yescharacteristic
667C2×C3#575311yescharacteristic
668C2×C3#577911yescharacteristic
669C2×C3#577911yescharacteristic
670D3—41no—
671C22—61no—
672C22—61no—
673C22—61no—
674C22C2×D3×D1211yescharacteristic
675C4—21no—
676C4—21no—
677C4—61no—
678C4—61no—
679C4—61no—
680C4—62no—
681C4—121no—
682C4—121no—
683C4—121no—
684C4—182no—
685C4—361no—
686C4—361no—
687C4—361no—
688C4D3×#23511yescharacteristic
689C4#6430611yescharacteristic
690C3—21no—
691C3#7939611yescharacteristic, complemented
692C3#7983611yescharacteristic, complemented
693C2—121no—
694C2#1059399711yescharacteristic
695C2#1059472111yescharacteristic
696C2#1059472111yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#97C22
socleC22×C32C22×D4
prime radicalC22×C3×D3C2×D4
hypercenter#97D32
hypocenterC32#3127
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #97

Complements

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

NH ≅ G/Ntype
3. #10592415C2semidirect
4. C3×#4716C2semidirect
8. #10590815C2semidirect
9. #10590809C2semidirect
10. #10590808C2semidirect
11. #10590800C2semidirect
14. C4×#3719C2semidirect
15. C4×#3719C2semidirect
88. #4716D3semidirect
628. C32#3127semidirect
691. C3#79396semidirect
692. C3#79836semidirect

Maximal subgroups

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

subgroupindex
#105938852
#105938802
#105924152
C3×#47162
C3×#47092
#105909522
#105909492
#105908152
#105908092
#105908082
#105908002
#105907112
#105907092
C4×#37192
#798363
#793963