Finite Group Databasebeta

← #11873343

Subgroups — #11873343

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#10595349C211yesmaximal, characteristic
2#10594357C211yesmaximal, characteristic
3#10592488C211yesmaximal, characteristic, complemented
4C3×#4815C211yesmaximal, characteristic
5C3×#4795C211yesmaximal, characteristic, complemented
6#10591653C211yesmaximal, characteristic
7#10591581C211yesmaximal, characteristic, complemented
8#10591575C211yesmaximal, characteristic, complemented
9#10590949C211yesmaximal, characteristic
10#10590819C211yesmaximal, characteristic, complemented
11#10590809C211yesmaximal, characteristic, complemented
12#10590699C211yesmaximal, characteristic
13#10590544C211yesmaximal, characteristic, complemented
14#10590519C211yesmaximal, characteristic
15#10590482C211yesmaximal, characteristic, complemented
16#81499—31nomaximal
17#80461—31nomaximal
18C2×D3×Dic6C2211yescharacteristic
19Q8×C3⋊Dic3C2211yescharacteristic
20C2×#3756C2211yescharacteristic
21#64096C2211yescharacteristic
22C3×#946C2211yescharacteristic
23C3×#944C2211yescharacteristic
24C2×C3×#216C2211yescharacteristic
25C2×C3×Dic12C2211yescharacteristic
26C3×#892C2211yescharacteristic
27C3×#887C2211yescharacteristic
28C4×#627—21no—
29#63878—21no—
30#63877—21no—
31#63870—21no—
32#63869C2211yescharacteristic
33#63862—21no—
34#63861—21no—
35#63856C2211yescharacteristic
36#63855C2211yescharacteristic
37#63845—21no—
38#63844C2211yescharacteristic
39#63843C2211yescharacteristic
40#63843C2211yescharacteristic
41#63837—21no—
42C2×#3719C2211yescharacteristic
43C32×#103C2211yescharacteristic
44#63643C2211yescharacteristic
45#63642C2211yescharacteristic
46#63635C2211yescharacteristic
47C3×#835C2211yescharacteristic
48C3×(C2×D3)⋊C8C2211yescharacteristic
49C3×#817C2211yescharacteristic
50C3×Dic3⋊C8C2211yescharacteristic
51C3×#810C2211yescharacteristic
52C3×#807C2211yescharacteristic
53#63575C2211yescharacteristic
54Dic3⋊(C3⋊C8)C2211yescharacteristic
55#63567C2211yescharacteristic
56#63566C2211yescharacteristic
57#63565C2211yescharacteristic
58#63565C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60#63553C2211yescharacteristic
61#5731—31no—
62#5625—31no—
63#5572—31no—
64#5516—31no—
65C3×#485—31no—
66C3×#462—31no—
67#5186—31no—
68#5186—31no—
69#5184—31no—
70Dic3×Q16—31no—
71#5090—31no—
72#5050—31no—
73#5022—31no—
74#4996—31no—
75#4877—31no—
76#4873—31no—
77#4857—31no—
78#4853—31no—
79#4840—31no—
80#4829—31no—
81#4815D311yescharacteristic
82#4814—31no—
83#4795—31no—
84#4795D311yescharacteristic, complemented
85#4790—31no—
86#4790—31no—
87#4789—31no—
88#4789—31no—
89#4789—61no—
90#4739—31no—
91#4720—31no—
92C2×C32×Q8C2311yescharacteristic
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
102C32×C4⋊C4C2311yescharacteristic
103#3756—22no—
104C4⋊(C3⋊Dic3)—21no—
105C4⋊(C3⋊Dic3)C2311yescharacteristic
106#3750—21no—
107C4×C3⋊Dic3—21no—
108C4×C3⋊Dic3—21no—
109C4×C3⋊Dic3C2311yescharacteristic
110C2×C3⋊(C3⋊C8)C2311yescharacteristic
111C3×#216—22no—
112C3×(C2×D3)⋊C4—21no—
113C3×(C2×D3)⋊C4—21no—
114C3×C4⋊Dic3C2311yescharacteristic
115C3×C4⋊Dic3C2311yescharacteristic
116C3×Dic3⋊C4—21no—
117C3×Dic3⋊C4—21no—
118C3×Dic3⋊C4—21no—
119C3×Dic3⋊C4—21no—
120C3×C4×Dic3—21no—
121C3×C4×Dic3—21no—
122C3×C4×Dic3C2311yescharacteristic
123C2×C3×C3⋊C8C2311yescharacteristic
124C2×C3×C3⋊C8C2311yescharacteristic
125C3×Dic12—22no—
126#3724—21no—
127#3724—21no—
128#3724—21no—
129Dic3⋊Dic3—21no—
130Dic3⋊Dic3—21no—
131Dic3⋊Dic3—21no—
132Dic3⋊Dic3D411yescharacteristic
133Dic3⋊Dic3D411yescharacteristic
134(C2×D3)⋊Dic3—21no—
135(C2×D3)⋊Dic3D411yescharacteristic
136(C2×D3)⋊Dic3D411yescharacteristic
137Dic32—21no—
138Dic32—21no—
139Dic32—21no—
140#3719—22no—
141#3127—91noSylow
142C2×D3×Q8—31no—
143C22×Dic6—31no—
144C2×C3×Q16—31no—
145C2×C3×Q16—31no—
146C3×C4⋊Q8—31no—
147C3×C22⋊Q8—31no—
148C3×C4×Q8—31no—
149C3×#117—31no—
150#946—31no—
151#946C2×D311yescharacteristic
152Q8×Dic3—31no—
153Q8×Dic3—31no—
154Q8×Dic3—31no—
155Q8×Dic3—31no—
156Q8×Dic3—61no—
157#944C2×D311yescharacteristic
158C2×#216—31no—
159C2×#216—31no—
160C2×#216—31no—
161C2×#216—61no—
162C2×#216C2×D311yescharacteristic
163#926—31no—
164#924—31no—
165C2×Dic12—31no—
166C2×Dic12C2×D311yescharacteristic
167#898—61no—
168#898—61no—
169#892—61no—
170#892C2×D311yescharacteristic
171#890—31no—
172#890—61no—
173#889—61no—
174#889—61no—
175#889—61no—
176#887—31no—
177#887—31no—
178#887—31no—
179#887—31no—
180#887—31no—
181#887—61no—
182#887—61no—
183#887C2×D311yescharacteristic
184#879—61no—
185#879—61no—
186#877—61no—
187#877—61no—
188#872—31no—
189#872—61no—
190#870—31no—
191C4×Dic6—31no—
192C4×Dic6—61no—
193C4×Dic6—61no—
194C4×Dic6—61no—
195C3×#107—31no—
196C3×#106—31no—
197C3×C4⋊C8—31no—
198C3×#103—21no—
199C3×#103—31no—
200C3×#103—31no—
201C3×#103C2×D311yescharacteristic
202C3×#103C2×D311yescharacteristic
203C3×C22⋊C8—31no—
204#835—31no—
205#835—31no—
206#835—31no—
207#835C2×D311yescharacteristic
208#830—31no—
209(C2×D3)⋊C8—31no—
210(C2×D3)⋊C8C2×D311yescharacteristic
211#818—31no—
212#817C2×D311yescharacteristic
213#816—31no—
214#816—31no—
215#816—31no—
216#816—31no—
217#816—61no—
218#815—31no—
219#815—31no—
220#815—61no—
221Dic3⋊C8—31no—
222Dic3⋊C8C2×D311yescharacteristic
223C8×Dic3—31no—
224C8×Dic3—31no—
225#810—31no—
226#810—31no—
227#810—31no—
228#810C2×D311yescharacteristic
229#808—31no—
230#808—31no—
231#808—61no—
232#807—31no—
233#807C2×D311yescharacteristic
234C4⋊(C3⋊C8)—31no—
235C22×C3×D3C2×D411yescharacteristic
236C32×Q8—21no—
237C32×Q8—21no—
238C2×C32×C4—21no—
239C2×C32×C4—21no—
240C2×C32×C4C2411yescharacteristic
241C2×C3⋊Dic3—21no—
242C2×C3⋊Dic3—21no—
243C2×C3⋊Dic3C2×D411yescharacteristic
244C2×C3⋊Dic3C2×D411yescharacteristic
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—
263C3⋊(C3⋊C8)—21no—
264C3×C3⋊C8—21no—
265C3×C3⋊C8—21no—
266#541—91no—
267#519—91no—
268#485—31no—
269#485—91no—
270#479—91no—
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—21no—
282C2×C3×Q8—31no—
283C2×C3×Q8—31no—
284C2×C3×Q8C22×D311yescharacteristic
285C2×C3×Q8C22×D311yescharacteristic
286C22×C3×C4—31no—
287C22×Dic3—61no—
288D3×Q8—62no—
289D3×Q8—62no—
290C2×C4×D3—61no—
291C2×C4×D3C22×D311yescharacteristic
292C2×Dic6—31no—
293C2×Dic6—31no—
294C2×Dic6—61no—
295C2×Dic6—62no—
296C2×Dic6—61no—
297C2×Dic6—61no—
298C2×Dic6—62no—
299C2×Dic6C22×D311yescharacteristic
300C2×Dic6C22×D311yescharacteristic
301C3×Q16—62no—
302C3×Q16—62no—
303C2×C3×C8—21no—
304C2×C3×C8—31no—
305C2×C3×C8—31no—
306C2×C3×C8C22×D311yescharacteristic
307C2×C3×C8C22×D311yescharacteristic
308C3×C4⋊C4—21no—
309C3×C4⋊C4—31no—
310C3×C4⋊C4—31no—
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×C22⋊C4—61no—
318C3×C22⋊C4—61no—
319C3×C42—31no—
320C3×C42—61no—
321C3×C42—61no—
322#217—31no—
323#217—31no—
324#217—61no—
325#216—22no—
326#216—62no—
327#216—62no—
328#216—62no—
329#216—64no—
330(C2×D3)⋊C4—21no—
331(C2×D3)⋊C4—21no—
332(C2×D3)⋊C4—31no—
333(C2×D3)⋊C4—31no—
334(C2×D3)⋊C4—61no—
335C4⋊Dic3—31no—
336C4⋊Dic3—31no—
337C4⋊Dic3—31no—
338C4⋊Dic3—31no—
339C4⋊Dic3—61no—
340C4⋊Dic3—61no—
341C4⋊Dic3—61no—
342C4⋊Dic3—61no—
343C4⋊Dic3—61no—
344C4⋊Dic3—61no—
345C4⋊Dic3—121no—
346C4⋊Dic3C22×D311yescharacteristic
347C4⋊Dic3C22×D311yescharacteristic
348Dic3⋊C4—21no—
349Dic3⋊C4—21no—
350Dic3⋊C4—21no—
351Dic3⋊C4—21no—
352Dic3⋊C4—31no—
353Dic3⋊C4—31no—
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—61no—
365Dic3⋊C4—121no—
366C4×Dic3—21no—
367C4×Dic3—21no—
368C4×Dic3—31no—
369C4×Dic3—31no—
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—61no—
381C4×Dic3—121no—
382C4×Dic3—121no—
383C4×Dic3C22×D311yescharacteristic
384C2×C3⋊C8—31no—
385C2×C3⋊C8—31no—
386C2×C3⋊C8—61no—
387C2×C3⋊C8C22×D311yescharacteristic
388C2×C3⋊C8C22×D311yescharacteristic
389Dic12—22no—
390Dic12—62no—
391C22×C32C22×D411yescharacteristic
392C2×C3×D3—21no—
393C2×C3×D3—21no—
394C2×C3×D3—21no—
395C32×C4—41no—
396C32×C4—41no—
397C32×C4C2×#4111yescharacteristic
398C32×C4C2×#4111yescharacteristic
399C3⋊Dic3—22no—
400C3⋊Dic3—21no—
401C3⋊Dic3—21no—
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—31no—
413C2×Q16—91no—
414C2×Q16—91no—
415C4⋊Q8—31no—
416#126—181no—
417#126—181no—
418#125—91no—
419#125—181no—
420#125—181no—
421C22⋊Q8—31no—
422C22⋊Q8—91no—
423C4×Q8—31no—
424C4×Q8—91no—
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—31no—
436#107—91no—
437#106—31no—
438#106—91no—
439C4⋊C8—31no—
440C4⋊C8—91no—
441#103—31no—
442#103—31no—
443#103—91no—
444#103—91no—
445#103—91no—
446#103—91no—
447#103—91no—
448#103D3211yescharacteristic
449C22⋊C8—31no—
450C22⋊C8—91no—
451#97—91no—
452C4×C8—91no—
453C23×C3—31no—
454C22×D3D3×D411yescharacteristic
455C3×Q8—22no—
456C3×Q8—21no—
457C3×Q8—21no—
458C3×Q8—21no—
459C3×Q8—21no—
460C3×Q8—32no—
461C3×Q8—41no—
462C3×Q8—61no—
463C3×Q8—61no—
464C3×Q8—61no—
465C2×C3×C4—21no—
466C2×C3×C4—21no—
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—41no—
474C2×C3×C4—41no—
475C2×C3×C4—61no—
476C2×C3×C4—61no—
477C2×C3×C4—61no—
478C2×C3×C4—61no—
479C2×C3×C4—61no—
480C2×C3×C4—61no—
481C2×C3×C4C23×D311yescharacteristic
482C2×C3×C4C23×D311yescharacteristic
483C2×Dic3—21no—
484C2×Dic3—21no—
485C2×Dic3—21no—
486C2×Dic3—21no—
487C2×Dic3—31no—
488C2×Dic3—31no—
489C2×Dic3—31no—
490C2×Dic3—31no—
491C2×Dic3—61no—
492C2×Dic3—61no—
493C2×Dic3—64no—
494C2×Dic3—61no—
495C2×Dic3—61no—
496C2×Dic3—61no—
497C2×Dic3—61no—
498C2×Dic3—121no—
499C2×Dic3—121no—
500C2×Dic3D3×D411yescharacteristic
501C2×Dic3D3×D411yescharacteristic
502C2×Dic3D3×D411yescharacteristic
503C4×D3—21no—
504C4×D3—21no—
505C4×D3—64no—
506Dic6—21no—
507Dic6—21no—
508Dic6—21no—
509Dic6—32no—
510Dic6—32no—
511Dic6—62no—
512Dic6—64no—
513Dic6—64no—
514Dic6—61no—
515Dic6—61no—
516Dic6—121no—
517Dic6#23712yes—
518C3×C8—21no—
519C3×C8—21no—
520C3×C8—41no—
521C3×C8—61no—
522C3×C8—61no—
523C3⋊C8—21no—
524C3⋊C8—21no—
525C3⋊C8—62no—
526C3⋊C8—61no—
527C3⋊C8—61no—
528C2×C32#52511yescharacteristic
529C2×C32#57811yescharacteristic
530C2×C32#57811yescharacteristic
531C3×D3—41no—
532C2×Q8—31no—
533C2×Q8—31no—
534C2×Q8—91no—
535C2×Q8—181no—
536C2×Q8—182no—
537C2×Q8—182no—
538C2×Q8C2×D3211yescharacteristic
539C22×C4—31no—
540C22×C4—181no—
541Q16—62no—
542Q16—62no—
543Q16—182no—
544Q16—182no—
545C2×C8—31no—
546C2×C8—31no—
547C2×C8—91no—
548C2×C8C2×D3211yescharacteristic
549C4⋊C4—31no—
550C4⋊C4—31no—
551C4⋊C4—61no—
552C4⋊C4—61no—
553C4⋊C4—61no—
554C4⋊C4—61no—
555C4⋊C4—91no—
556C4⋊C4—91no—
557C4⋊C4—91no—
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⋊C4C2×D3211yescharacteristic
567C22⋊C4—61no—
568C22⋊C4—61no—
569C22⋊C4—91no—
570C22⋊C4—91no—
571C22⋊C4—181no—
572C42—31no—
573C42—61no—
574C42—61no—
575C42—91no—
576C42—181no—
577C42—181no—
578C42—181no—
579C42—181no—
580C42—181no—
581C22×C3—21no—
582C22×C3—61no—
583C22×C3—61no—
584C22×C3—61no—
585C22×C3C2×D3×D411yescharacteristic
586C22×C3C2×D3×D411yescharacteristic
587C2×D3—21no—
588C2×D3—21no—
589C2×D3—21no—
590C3×C4—21no—
591C3×C4—21no—
592C3×C4—42no—
593C3×C4—41no—
594C3×C4—41no—
595C3×C4—41no—
596C3×C4—41no—
597C3×C4—62no—
598C3×C4—61no—
599C3×C4—61no—
600C3×C4—61no—
601C3×C4—81no—
602C3×C4—121no—
603C3×C4—121no—
604C3×C4—121no—
605C3×C4C2×#23711yescharacteristic
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—61no—
618Dic3—61no—
619Dic3—61no—
620Dic3—61no—
621Dic3—62no—
622Dic3—122no—
623Dic3—121no—
624Dic3—121no—
625Dic3—121no—
626Dic3—121no—
627Dic3—241no—
628C32#312711yescharacteristic, complemented, Sylow
629C23—31no—
630Q8—21no—
631Q8—21no—
632Q8—32no—
633Q8—61no—
634Q8—61no—
635Q8—61no—
636Q8—92no—
637Q8—184no—
638Q8—181no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—31no—
642C2×C4—31no—
643C2×C4—31no—
644C2×C4—61no—
645C2×C4—61no—
646C2×C4—61no—
647C2×C4—61no—
648C2×C4—61no—
649C2×C4—61no—
650C2×C4—91no—
651C2×C4—91no—
652C2×C4—184no—
653C2×C4—181no—
654C2×C4—181no—
655C2×C4C22×D3211yescharacteristic
656C8—21no—
657C8—61no—
658C8—61no—
659C8—181no—
660C2×C3—21no—
661C2×C3—21no—
662C2×C3—21no—
663C2×C3—121no—
664C2×C3#560611yescharacteristic
665C2×C3#565611yescharacteristic
666C2×C3#576611yescharacteristic
667C2×C3#577111yescharacteristic
668C2×C3#577911yescharacteristic
669C2×C3#577911yescharacteristic
670D3—41no—
671C22—61no—
672C22—61no—
673C22—61no—
674C22D32×D411yescharacteristic
675C4—41no—
676C4—41no—
677C4—61no—
678C4—61no—
679C4—61no—
680C4—62no—
681C4—121no—
682C4—121no—
683C4—121no—
684C4—181no—
685C4—181no—
686C4—182no—
687C4—361no—
688C4#6430611yescharacteristic
689C4D3×#23711yescharacteristic
690C3—21no—
691C3#8046111yescharacteristic, complemented
692C3#8149911yescharacteristic, complemented
693C2—121no—
694C2#1059426711yescharacteristic
695C2#1059475611yescharacteristic
696C2#1059476611yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#103C22
socleC22×C32C22×D4
prime radicalC22×C3×D3C2×D4
hypercenter#103D32
hypocenterC32#3127
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #103

Complements

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

NH ≅ G/Ntype
3. #10592488C2semidirect
5. C3×#4795C2semidirect
7. #10591581C2semidirect
8. #10591575C2semidirect
10. #10590819C2semidirect
11. #10590809C2semidirect
13. #10590544C2semidirect
15. #10590482C2semidirect
84. #4795D3semidirect
628. C32#3127semidirect
691. C3#80461semidirect
692. C3#81499semidirect

Maximal subgroups

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

subgroupindex
#105953492
#105943572
#105924882
C3×#48152
C3×#47952
#105916532
#105915812
#105915752
#105909492
#105908192
#105908092
#105906992
#105905442
#105905192
#105904822
#814993
#804613