Finite Group Databasebeta

← #11873300

Subgroups — #11873300

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#10595347C211yesmaximal, characteristic
2#10594346C211yesmaximal, characteristic
3#10592488C211yesmaximal, characteristic, complemented
4C3×#4809C211yesmaximal, characteristic
5C3×#4799C211yesmaximal, characteristic, complemented
6#10591625C211yesmaximal, characteristic, complemented
7#10591595C211yesmaximal, characteristic
8#10591581C211yesmaximal, characteristic, complemented
9#10590819C211yesmaximal, characteristic, complemented
10#10590800C211yesmaximal, characteristic, complemented
11#10590709C211yesmaximal, characteristic
12#10590699C211yesmaximal, characteristic
13#10590491C211yesmaximal, characteristic, complemented
14#10590482C211yesmaximal, characteristic, complemented
15#10590448C211yesmaximal, characteristic
16#81211—31nomaximal
17#80177—31nomaximal
18C2×C3×D3×Q8C2211yescharacteristic
19Q8×C3⋊Dic3C2211yescharacteristic
20C2×#3756C2211yescharacteristic
21#64096C2211yescharacteristic
22C3×Q8×Dic3C2211yescharacteristic
23C2×C3×#216C2211yescharacteristic
24C2×C3×Dic12C2211yescharacteristic
25C3×#897C2211yescharacteristic
26C3×#890C2211yescharacteristic
27#63872—21no—
28#63866C2211yescharacteristic
29#63862—21no—
30#63858—21no—
31#63857C2211yescharacteristic
32#63855—21no—
33#63855C2211yescharacteristic
34#63846—21no—
35#63843—21no—
36#63843C2211yescharacteristic
37#63843C2211yescharacteristic
38Dic3×Dic6—21no—
39Dic3×Dic6C2211yescharacteristic
40#63841—21no—
41#63841C2211yescharacteristic
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#5812—31no—
62#5698—31no—
63#5625—31no—
64#5572—31no—
65C3×#479—31no—
66C3×#451—31no—
67#5228—31no—
68#5184—31no—
69#5182—31no—
70#5182—31no—
71Dic3×Q16—31no—
72#5063—31no—
73#5045—31no—
74#5031—31no—
75#4888—31no—
76#4873—31no—
77#4868—31no—
78#4853—31no—
79#4849—31no—
80#4840—31no—
81#4809—31no—
82#4809D311yescharacteristic
83#4799D311yescharacteristic, complemented
84#4796—31no—
85#4790—31no—
86#4790—31no—
87#4789—31no—
88#4789—31no—
89#4789—61no—
90#4723—31no—
91#4720—31no—
92C2×C32×Q8C2311yescharacteristic
93C2×#634C2311yescharacteristic
94C3×D3×Q8—22no—
95C3×D3×Q8—22no—
96C2×C3×C4×D3—21no—
97C2×C3×C4×D3C2311yescharacteristic
98C2×C3×Dic6—21no—
99C2×C3×Dic6C2311yescharacteristic
100C2×C3×Dic6C2311yescharacteristic
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×C4⋊Dic3—21no—
114C3×C4⋊Dic3—21no—
115C3×C4⋊Dic3—21no—
116C3×C4⋊Dic3C2311yescharacteristic
117C3×C4⋊Dic3C2311yescharacteristic
118C3×Dic3⋊C4—21no—
119C3×C4×Dic3—21no—
120C3×C4×Dic3C2311yescharacteristic
121C2×C3×C3⋊C8C2311yescharacteristic
122C2×C3×C3⋊C8C2311yescharacteristic
123C3×Dic12—22no—
124Dic3⋊Dic3—21no—
125Dic3⋊Dic3—21no—
126Dic3⋊Dic3—21no—
127Dic3⋊Dic3—21no—
128Dic3⋊Dic3—21no—
129Dic3⋊Dic3—21no—
130Dic3⋊Dic3D411yescharacteristic
131Dic3⋊Dic3D411yescharacteristic
132(C2×D3)⋊Dic3—21no—
133(C2×D3)⋊Dic3—21no—
134(C2×D3)⋊Dic3D411yescharacteristic
135(C2×D3)⋊Dic3D411yescharacteristic
136Dic32—21no—
137Dic32—21no—
138Dic32—21no—
139Dic32—21no—
140#3719—22no—
141#3127—91noSylow
142C22×C3×Q8—31no—
143C2×D3×Q8C2×D311yescharacteristic
144C2×C3×Q16—31no—
145C2×C3×Q16—31no—
146C3×#125—31no—
147C3×C22⋊Q8—31no—
148C3×C4×Q8—31no—
149Q8×Dic3—31no—
150Q8×Dic3—31no—
151Q8×Dic3—31no—
152Q8×Dic3—31no—
153Q8×Dic3—31no—
154Q8×Dic3—61no—
155Q8×Dic3—61no—
156Q8×Dic3—61no—
157Q8×Dic3C2×D311yescharacteristic
158#944—31no—
159C2×#216—31no—
160C2×#216—31no—
161C2×#216—31no—
162C2×#216—61no—
163C2×#216C2×D311yescharacteristic
164#926—31no—
165#926—31no—
166#926—61no—
167#926—61no—
168#924—31no—
169C2×Dic12—31no—
170C2×Dic12C2×D311yescharacteristic
171#898—61no—
172#898—61no—
173#897—31no—
174#897C2×D311yescharacteristic
175#892—31no—
176#892—61no—
177#890—61no—
178#890—61no—
179#890—61no—
180#890C2×D311yescharacteristic
181#889—61no—
182#887—31no—
183#887—31no—
184#887—31no—
185#887—31no—
186#887—61no—
187#887—61no—
188#879—61no—
189#879—61no—
190#872—31no—
191#872—61no—
192#869—31no—
193C4×Dic6—31no—
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#4112yes—
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—21no—
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—24no—
255C3×C4×D3—21no—
256C3×C4×D3—21no—
257C3×Dic6—24no—
258C3×Dic6—21no—
259C3×Dic6—21no—
260C3×Dic6—21no—
261C3×Dic6#4112yes—
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—31no—
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×Q8—61no—
285C2×C3×Q8—62no—
286C2×C3×Q8—62no—
287C2×C3×Q8C22×D311yescharacteristic
288C2×C3×Q8C22×D311yescharacteristic
289C22×C3×C4—31no—
290C22×C3×C4—61no—
291D3×Q8—22no—
292D3×Q8—22no—
293C2×C4×D3—21no—
294C2×C4×D3C22×D311yescharacteristic
295C2×Dic6—21no—
296C2×Dic6—31no—
297C2×Dic6—31no—
298C2×Dic6—61no—
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×C42—31no—
319C3×C42—61no—
320#217—31no—
321#217—31no—
322#217—61no—
323#217—61no—
324#216—22no—
325#216—62no—
326#216—64no—
327#216—62no—
328#216—62no—
329(C2×D3)⋊C4—21no—
330(C2×D3)⋊C4—31no—
331(C2×D3)⋊C4—31no—
332(C2×D3)⋊C4—61no—
333(C2×D3)⋊C4—61no—
334C4⋊Dic3—21no—
335C4⋊Dic3—21no—
336C4⋊Dic3—21no—
337C4⋊Dic3—31no—
338C4⋊Dic3—31no—
339C4⋊Dic3—31no—
340C4⋊Dic3—31no—
341C4⋊Dic3—61no—
342C4⋊Dic3—61no—
343C4⋊Dic3—61no—
344C4⋊Dic3—61no—
345C4⋊Dic3—61no—
346C4⋊Dic3—61no—
347C4⋊Dic3—61no—
348C4⋊Dic3—61no—
349C4⋊Dic3—61no—
350C4⋊Dic3—121no—
351C4⋊Dic3C22×D311yescharacteristic
352C4⋊Dic3C22×D311yescharacteristic
353Dic3⋊C4—21no—
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×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—22no—
396C32×C4—41no—
397C32×C4C2×#4111yescharacteristic
398C32×C4C2×#4111yescharacteristic
399C3⋊Dic3—21no—
400C3⋊Dic3—21no—
401C3⋊Dic3—41no—
402C3⋊Dic3—41no—
403C3×Dic3—21no—
404C3×Dic3—22no—
405C3×Dic3—21no—
406C3×Dic3—21no—
407C3×Dic3—41no—
408C3×Dic3—41no—
409C3×Dic3—41no—
410C22×Q8—31no—
411C2×Q16—31no—
412C2×Q16—31no—
413C2×Q16—91no—
414C2×Q16—91no—
415C4⋊Q8—91no—
416#126—181no—
417#126—181no—
418#125—31no—
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—91no—
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—21no—
456C3×Q8—21no—
457C3×Q8—22no—
458C3×Q8—32no—
459C3×Q8—41no—
460C3×Q8—64no—
461C3×Q8—61no—
462C3×Q8—61no—
463C3×Q8—61no—
464C3×Q8#23712yes—
465C3×Q8#23912yes—
466C2×C3×C4—21no—
467C2×C3×C4—21no—
468C2×C3×C4—21no—
469C2×C3×C4—21no—
470C2×C3×C4—21no—
471C2×C3×C4—31no—
472C2×C3×C4—31no—
473C2×C3×C4—31no—
474C2×C3×C4—41no—
475C2×C3×C4—41no—
476C2×C3×C4—64no—
477C2×C3×C4—61no—
478C2×C3×C4—61no—
479C2×C3×C4—61no—
480C2×C3×C4—61no—
481C2×C3×C4—61no—
482C2×C3×C4—61no—
483C2×C3×C4C23×D311yescharacteristic
484C2×C3×C4C23×D311yescharacteristic
485C2×Dic3—21no—
486C2×Dic3—21no—
487C2×Dic3—21no—
488C2×Dic3—21no—
489C2×Dic3—31no—
490C2×Dic3—31no—
491C2×Dic3—31no—
492C2×Dic3—31no—
493C2×Dic3—61no—
494C2×Dic3—61no—
495C2×Dic3—61no—
496C2×Dic3—61no—
497C2×Dic3—61no—
498C2×Dic3—61no—
499C2×Dic3—121no—
500C2×Dic3—121no—
501C2×Dic3D3×D411yescharacteristic
502C2×Dic3D3×D411yescharacteristic
503C2×Dic3D3×D411yescharacteristic
504C4×D3—24no—
505C4×D3—21no—
506C4×D3—21no—
507Dic6—24no—
508Dic6—21no—
509Dic6—21no—
510Dic6—21no—
511Dic6—62no—
512Dic6—61no—
513Dic6—61no—
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—61no—
535C2×Q8—62no—
536C2×Q8—62no—
537C2×Q8—91no—
538C2×Q8C2×D3211yescharacteristic
539C22×C4—31no—
540C22×C4—61no—
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—91no—
569C22⋊C4—91no—
570C22⋊C4—181no—
571C22⋊C4—181no—
572C42—31no—
573C42—61no—
574C42—91no—
575C42—181no—
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—22no—
591C3×C4—22no—
592C3×C4—21no—
593C3×C4—21no—
594C3×C4—42no—
595C3×C4—41no—
596C3×C4—41no—
597C3×C4—61no—
598C3×C4—61no—
599C3×C4—61no—
600C3×C4—62no—
601C3×C4—81no—
602C3×C4—121no—
603C3×C4—121no—
604C3×C4—121no—
605C3×C4C2×#23711yescharacteristic
606C3×C4C2×#23711yescharacteristic
607C3×C4C2×#23911yescharacteristic
608C3×C4D3×#4111yescharacteristic
609Dic3—21no—
610Dic3—21no—
611Dic3—21no—
612Dic3—22no—
613Dic3—41no—
614Dic3—41no—
615Dic3—41no—
616Dic3—61no—
617Dic3—61no—
618Dic3—61no—
619Dic3—61no—
620Dic3—121no—
621Dic3—121no—
622Dic3—122no—
623Dic3—121no—
624Dic3—121no—
625Dic3—121no—
626Dic3—121no—
627Dic3—241no—
628C32#312711yescharacteristic, complemented, Sylow
629C23—31no—
630Q8—21no—
631Q8—32no—
632Q8—64no—
633Q8—61no—
634Q8—61no—
635Q8—61no—
636Q8—181no—
637Q8—181no—
638Q8#379612yes—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—31no—
642C2×C4—31no—
643C2×C4—31no—
644C2×C4—64no—
645C2×C4—61no—
646C2×C4—61no—
647C2×C4—61no—
648C2×C4—61no—
649C2×C4—61no—
650C2×C4—61no—
651C2×C4—91no—
652C2×C4—91no—
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#558611yescharacteristic
665C2×C3#562711yescharacteristic
666C2×C3#576611yescharacteristic
667C2×C3#577111yescharacteristic
668C2×C3#577911yescharacteristic
669C2×C3#577911yescharacteristic
670D3—41no—
671C22—61no—
672C22—61no—
673C22—61no—
674C22D32×D411yescharacteristic
675C4—22no—
676C4—41no—
677C4—61no—
678C4—62no—
679C4—61no—
680C4—61no—
681C4—121no—
682C4—121no—
683C4—121no—
684C4—181no—
685C4—181no—
686C4—361no—
687C4—361no—
688C4C2×#379611yescharacteristic
689C4D3×#23711yescharacteristic
690C3—21no—
691C3#8017711yescharacteristic, complemented
692C3#8121111yescharacteristic, complemented
693C2—121no—
694C2#1059405511yescharacteristic
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×#4799C2semidirect
6. #10591625C2semidirect
8. #10591581C2semidirect
9. #10590819C2semidirect
10. #10590800C2semidirect
13. #10590491C2semidirect
14. #10590482C2semidirect
83. #4799D3semidirect
628. C32#3127semidirect
691. C3#80177semidirect
692. C3#81211semidirect

Maximal subgroups

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

subgroupindex
#105953472
#105943462
#105924882
C3×#48092
C3×#47992
#105916252
#105915952
#105915812
#105908192
#105908002
#105907092
#105906992
#105904912
#105904822
#105904482
#812113
#801773