Finite Group Databasebeta

← #11868743

Subgroups — #11868743

Order 1152.

827 conjugacy classes of subgroups.

The subgroup lattice has 703 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Q8×#624C211yesmaximal, characteristic
2#10594448C211yesmaximal, characteristic
3#10592501C211yesmaximal, characteristic
4C3×#4799C211yesmaximal, characteristic, complemented
5C3×#4793C211yesmaximal, characteristic, complemented
6#10591562C211yesmaximal, characteristic
7#10591545C211yesmaximal, characteristic, complemented
8#10591544C211yesmaximal, characteristic, complemented
9#10590814C211yesmaximal, characteristic, complemented
10#10590802C211yesmaximal, characteristic, complemented
11#10590688C211yesmaximal, characteristic
12#10590666C211yesmaximal, characteristic
13#10590582C211yesmaximal, characteristic
14#10590492C211yesmaximal, characteristic, complemented
15#10590488C211yesmaximal, characteristic, complemented
16#81230—31nomaximal
17#81108—31nomaximal
18C2×Q8×C3⋊D3C2211yescharacteristic
19C2×#3743C2211yescharacteristic
20#64101C2211yescharacteristic
21C3×Q8×Dic3C2211yescharacteristic
22C3×Q8×Dic3C2211yescharacteristic
23C3×#890C2211yescharacteristic
24C3×#888C2211yescharacteristic
25#63918C2211yescharacteristic
26#63900—21no—
27#63900C2211yescharacteristic
28#63895—21no—
29#63888—21no—
30C4×#624—21no—
31C4×#624C2211yescharacteristic
32#63869C2211yescharacteristic
33#63849C2211yescharacteristic
34#63844—21no—
35#63844—21no—
36#63844C2211yescharacteristic
37#63844C2211yescharacteristic
38#63843—21no—
39#63838—21no—
40C2×#3712C2211yescharacteristic
41C32×#103C2211yescharacteristic
42#63662C2211yescharacteristic
43#63643C2211yescharacteristic
44#63637C2211yescharacteristic
45C3×#835C2211yescharacteristic
46C3×#835C2211yescharacteristic
47C3×#818C2211yescharacteristic
48C3×#817C2211yescharacteristic
49C3×Dic3⋊C8C2211yescharacteristic
50C3×Dic3⋊C8C2211yescharacteristic
51C3×#807C2211yescharacteristic
52C3×#807C2211yescharacteristic
53#63576C2211yescharacteristic
54#63574C2211yescharacteristic
55#63573C2211yescharacteristic
56#63573C2211yescharacteristic
57Dic3⋊(C3⋊C8)C2211yescharacteristic
58Dic3⋊(C3⋊C8)C2211yescharacteristic
59#63567C2211yescharacteristic
60#63567C2211yescharacteristic
61#5728—31no—
62#5688—31no—
63C4×D3×Q8—31no—
64C4×D3×Q8—31no—
65C3×#479—31no—
66C3×#477—31no—
67#5091—31no—
68#5063—31no—
69#5022—31no—
70#5020—31no—
71#4881—31no—
72#4881—31no—
73#4881—31no—
74#4877—31no—
75#4877—31no—
76#4875—31no—
77#4861—31no—
78#4854—31no—
79#4851—31no—
80#4837—31no—
81#4837—31no—
82#4829—31no—
83#4802—31no—
84#4802—31no—
85#4802—31no—
86#4802—31no—
87#4802—61no—
88#4799—31no—
89#4799D311yescharacteristic, complemented
90#4793D311yescharacteristic, complemented
91#4791—31no—
92C2×C32×Q8C2311yescharacteristic
93Q8×C3⋊D3—22no—
94Q8×C3⋊D3Q814yescomplemented
95C2×C4×C3⋊D3—21no—
96C2×C4×C3⋊D3C2311yescharacteristic
97C2×#634—21no—
98C2×#634C2311yescharacteristic
99C2×C3×Dic6—21no—
100C2×#627—21no—
101C2×#624—21no—
102C2×#624D411yescharacteristic
103C2×#624D411yescharacteristic
104C2×C32×C8C2311yescharacteristic
105C32×C4⋊C4C2311yescharacteristic
106#3752—21no—
107C4⋊(C3⋊Dic3)C2311yescharacteristic
108C4×C3⋊Dic3—21no—
109C2×C3⋊(C3⋊C8)C2311yescharacteristic
110#3743—22no—
111C3×C4⋊Dic3—21no—
112C3×C4⋊Dic3—21no—
113C3×C4⋊Dic3—21no—
114C3×C4⋊Dic3C2311yescharacteristic
115C3×C4⋊Dic3C2311yescharacteristic
116C3×C4⋊Dic3C2311yescharacteristic
117C3×C4⋊Dic3C2311yescharacteristic
118C3×Dic3⋊C4—21no—
119C3×Dic3⋊C4—21no—
120C3×C4×Dic3—21no—
121C3×C4×Dic3—21no—
122C3×C4×Dic3C2311yescharacteristic
123C3×C4×Dic3C2311yescharacteristic
124C2×C3×C3⋊C8C2311yescharacteristic
125C2×C3×C3⋊C8C2311yescharacteristic
126#3724—21no—
127#3724—21no—
128#3724—21no—
129#3724—21no—
130Dic3⋊Dic3—21no—
131Dic3⋊Dic3—21no—
132#3722—21no—
133Dic32—21no—
134Dic32—21no—
135Dic32—21no—
136Dic32D411yescharacteristic
137Dic32D411yescharacteristic
138#3712—22no—
139#3078—91noSylow
140C2×D3×Q8—31no—
141C2×D3×Q8—31no—
142C2×D3×Q8—61no—
143C3×C4⋊Q8—31no—
144C3×#125—31no—
145C3×C4×Q8—31no—
146C3×C4×Q8—31no—
147#946—61no—
148Q8×Dic3—61no—
149Q8×Dic3C2×D311yescharacteristic
150Q8×Dic3C2×D311yescharacteristic
151C2×ΓL(1,𝔽25)—31no—
152C2×ΓL(1,𝔽25)—31no—
153C2×ΓL(1,𝔽25)—31no—
154C2×ΓL(1,𝔽25)—31no—
155C2×ΓL(1,𝔽25)—61no—
156#897—61no—
157#896—61no—
158#896—61no—
159#892—31no—
160#892—31no—
161#892—31no—
162#892—31no—
163#892—61no—
164D3×C4⋊C4—31no—
165D3×C4⋊C4—31no—
166D3×C4⋊C4—61no—
167D3×C4⋊C4—61no—
168#890—31no—
169#890C2×D311yescharacteristic
170#888—31no—
171#888C2×D311yescharacteristic
172#887—31no—
173#887—31no—
174#887—61no—
175#887—61no—
176#887—61no—
177#887—61no—
178#887—61no—
179C42×D3—31no—
180C42×D3—31no—
181C42×D3—61no—
182C42×D3—61no—
183#870—31no—
184#869—31no—
185C4×Dic6—31no—
186C4×Dic6—31no—
187C4×Dic6—61no—
188C4×Dic6—61no—
189C3×#107—31no—
190C3×#107—31no—
191C3×#107—31no—
192C3×#106—31no—
193C3×C4⋊C8—31no—
194C3×C4⋊C8—31no—
195C3×#103—21no—
196C3×#103—31no—
197C3×#103—31no—
198C3×#103C2×D311yescharacteristic
199C3×#103C2×D311yescharacteristic
200#835—31no—
201#835—31no—
202#835—61no—
203#835C2×D311yescharacteristic
204#835C2×D311yescharacteristic
205#818C2×D311yescharacteristic
206#817—31no—
207#817—31no—
208#817C2×D311yescharacteristic
209#816—31no—
210#816—31no—
211#816—31no—
212#816—31no—
213#816—61no—
214Dic3⋊C8—31no—
215Dic3⋊C8—31no—
216Dic3⋊C8C2×D311yescharacteristic
217Dic3⋊C8C2×D311yescharacteristic
218#810—31no—
219#810—31no—
220#810—31no—
221#810—31no—
222#810—61no—
223#808—31no—
224#808—31no—
225#808—31no—
226#808—31no—
227#807—31no—
228#807—31no—
229#807C2×D311yescharacteristic
230#807C2×D311yescharacteristic
231C4⋊(C3⋊C8)—31no—
232C4⋊(C3⋊C8)—31no—
233C22×C3⋊D3C2×D411yescharacteristic
234C32×Q8—21no—
235C32×Q8C2×Q812yes—
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—24no—
243C4×C3⋊D3C2×Q812yes—
244C4×C3⋊D3#4112yes—
245#634—21no—
246#634—24no—
247#634C2×Q812yes—
248C2×C3×Dic3—21no—
249C2×C3×Dic3—21no—
250C2×C3×Dic3—21no—
251C2×C3×Dic3—21no—
252C2×C3×Dic3C2×D411yescharacteristic
253C2×C3×Dic3C2×D411yescharacteristic
254C2×C3×Dic3C2×D411yescharacteristic
255C2×C3×Dic3C2×D411yescharacteristic
256C3×Dic6—42no—
257#627—42no—
258#624—22no—
259#624—41no—
260#624—42no—
261C32×C8—21no—
262C3⋊(C3⋊C8)—21no—
263C3×C3⋊C8—21no—
264C3×C3⋊C8—21no—
265#533—91no—
266C2×C4×Q8—91no—
267#479—31no—
268#479—91no—
269#479—91no—
270#479—91no—
271#477—31no—
272#477—91no—
273#475—91no—
274#475—91no—
275#428—91no—
276#428—91no—
277#423—91no—
278#419—91no—
279#419—91no—
280C2×C3×Q8—21no—
281C2×C3×Q8—61no—
282C2×C3×Q8C22×D311yescharacteristic
283C2×C3×Q8C22×D311yescharacteristic
284D3×Q8—34no—
285D3×Q8—34no—
286D3×Q8—64no—
287D3×Q8—62no—
288D3×Q8—62no—
289D3×Q8—122no—
290C2×C4×D3—31no—
291C2×C4×D3—31no—
292C2×C4×D3—31no—
293C2×C4×D3—31no—
294C2×C4×D3—31no—
295C2×C4×D3—31no—
296C2×C4×D3—61no—
297C2×C4×D3—61no—
298C2×C4×D3—61no—
299C2×C4×D3—61no—
300C2×C4×D3—61no—
301C2×C4×D3—121no—
302C2×Dic6—21no—
303C2×Dic6—31no—
304C2×Dic6—31no—
305C2×Dic6—61no—
306C2×Dic6—61no—
307C2×Dic6—61no—
308C2×Dic6—61no—
309C2×Dic6—61no—
310C2×Dic6—121no—
311C2×C3×C8—21no—
312C2×C3×C8—31no—
313C2×C3×C8—31no—
314C2×C3×C8C22×D311yescharacteristic
315C2×C3×C8C22×D311yescharacteristic
316C3×C4⋊C4—21no—
317C3×C4⋊C4—31no—
318C3×C4⋊C4—31no—
319C3×C4⋊C4—31no—
320C3×C4⋊C4—31no—
321C3×C4⋊C4—61no—
322C3×C4⋊C4—61no—
323C3×C4⋊C4—61no—
324C3×C4⋊C4—61no—
325C3×C4⋊C4—61no—
326C3×C4⋊C4C22×D311yescharacteristic
327C3×C4⋊C4C22×D311yescharacteristic
328C3×C42—31no—
329C3×C42—31no—
330C3×C42—61no—
331C3×C42—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—121no—
337C4⋊Dic3—21no—
338C4⋊Dic3—21no—
339C4⋊Dic3—21no—
340C4⋊Dic3—31no—
341C4⋊Dic3—31no—
342C4⋊Dic3—61no—
343C4⋊Dic3—61no—
344C4⋊Dic3—61no—
345C4⋊Dic3C22×D311yescharacteristic
346C4⋊Dic3C22×D311yescharacteristic
347C4⋊Dic3C22×D311yescharacteristic
348C4⋊Dic3C22×D311yescharacteristic
349Dic3⋊C4—21no—
350Dic3⋊C4—21no—
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—
361C4×Dic3—21no—
362C4×Dic3—21no—
363C4×Dic3—31no—
364C4×Dic3—31no—
365C4×Dic3—31no—
366C4×Dic3—31no—
367C4×Dic3—61no—
368C4×Dic3—61no—
369C4×Dic3—61no—
370C4×Dic3—61no—
371C4×Dic3—61no—
372C4×Dic3—61no—
373C4×Dic3—61no—
374C4×Dic3—61no—
375C4×Dic3—121no—
376C4×Dic3C22×D311yescharacteristic
377C4×Dic3C22×D311yescharacteristic
378C2×C3⋊C8—31no—
379C2×C3⋊C8—31no—
380C2×C3⋊C8—61no—
381C2×C3⋊C8C22×D311yescharacteristic
382C2×C3⋊C8C22×D311yescharacteristic
383ΓL(1,𝔽25)—62no—
384ΓL(1,𝔽25)—62no—
385ΓL(1,𝔽25)—62no—
386ΓL(1,𝔽25)—62no—
387ΓL(1,𝔽25)—122no—
388C22×C32C22×D411yescharacteristic
389C2×C3⋊D3—21no—
390C2×C3⋊D3—21no—
391C2×C3⋊D3C22⋊Q812yes—
392C32×C4—22no—
393C32×C4—41no—
394C32×C4C22×Q811yescharacteristic
395C32×C4C2×#4111yescharacteristic
396C3⋊Dic3—22no—
397C3⋊Dic3—41no—
398C3⋊Dic3C22⋊Q812yes—
399C3×Dic3—21no—
400C3×Dic3—21no—
401C3×Dic3—21no—
402C3×Dic3—41no—
403C3×Dic3—41no—
404C3×Dic3—41no—
405C3×Dic3—41no—
406C3×Dic3#13712yes—
407C22×Q8—91no—
408C2×M16—91no—
409C2×M16—91no—
410C4⋊Q8—31no—
411C4⋊Q8—91no—
412#125—31no—
413#125—91no—
414C22⋊Q8—181no—
415C22⋊Q8—181no—
416C4×Q8—31no—
417C4×Q8—31no—
418C4×Q8—91no—
419C4×Q8—91no—
420C4×Q8—181no—
421C4×Q8—181no—
422C4×Q8—181no—
423C4×Q8—181no—
424#117—91no—
425#117—91no—
426C2×C4⋊C4—91no—
427C2×C4⋊C4—181no—
428C2×C42—91no—
429C2×C42—181no—
430#107—31no—
431#107—31no—
432#107—31no—
433#107—91no—
434#106—31no—
435#106—91no—
436#106—91no—
437#106—91no—
438C4⋊C8—31no—
439C4⋊C8—31no—
440C4⋊C8—91no—
441C4⋊C8—91no—
442#103—31no—
443#103—31no—
444#103—91no—
445#103—91no—
446#103—91no—
447#103—91no—
448#103—91no—
449#103D3211yescharacteristic
450C22×D3—31no—
451C22×D3—31no—
452C22×D3—61no—
453C3×Q8—21no—
454C3×Q8—21no—
455C3×Q8—22no—
456C3×Q8—41no—
457C3×Q8—122no—
458C3×Q8D3×Q812yes—
459C3×Q8D3×Q812yes—
460C2×C3×C4—21no—
461C2×C3×C4—21no—
462C2×C3×C4—21no—
463C2×C3×C4—21no—
464C2×C3×C4—21no—
465C2×C3×C4—31no—
466C2×C3×C4—31no—
467C2×C3×C4—31no—
468C2×C3×C4—31no—
469C2×C3×C4—41no—
470C2×C3×C4—41no—
471C2×C3×C4—61no—
472C2×C3×C4—61no—
473C2×C3×C4—61no—
474C2×C3×C4—61no—
475C2×C3×C4C23×D311yescharacteristic
476C2×C3×C4C23×D311yescharacteristic
477C2×Dic3—21no—
478C2×Dic3—21no—
479C2×Dic3—21no—
480C2×Dic3—21no—
481C2×Dic3—31no—
482C2×Dic3—31no—
483C2×Dic3—61no—
484C2×Dic3—61no—
485C2×Dic3—61no—
486C2×Dic3—61no—
487C2×Dic3—61no—
488C2×Dic3—121no—
489C2×Dic3—121no—
490C2×Dic3D3×D411yescharacteristic
491C2×Dic3D3×D411yescharacteristic
492C2×Dic3D3×D411yescharacteristic
493C2×Dic3D3×D411yescharacteristic
494C4×D3—32no—
495C4×D3—32no—
496C4×D3—32no—
497C4×D3—32no—
498C4×D3—62no—
499C4×D3—62no—
500C4×D3—62no—
501C4×D3—64no—
502C4×D3—64no—
503C4×D3—62no—
504C4×D3—124no—
505C4×D3—121no—
506C4×D3—121no—
507C4×D3—122no—
508C4×D3—122no—
509Dic6—32no—
510Dic6—32no—
511Dic6—42no—
512Dic6—62no—
513Dic6—64no—
514Dic6—64no—
515Dic6—61no—
516Dic6—61no—
517Dic6—124no—
518Dic6—121no—
519Dic6—122no—
520Dic6—122no—
521C3×C8—21no—
522C3×C8—21no—
523C3×C8—41no—
524C3×C8—61no—
525C3×C8—61no—
526C3⋊C8—21no—
527C3⋊C8—21no—
528C3⋊C8—61no—
529C3⋊C8—61no—
530C3⋊C8—121no—
531C2×C32C2×C22⋊Q811yescharacteristic
532C2×C32C2×#13711yescharacteristic
533C2×C32#57511yescharacteristic
534C3⋊D3—22no—
535C2×Q8—61no—
536C2×Q8—94no—
537C2×Q8—91no—
538C2×Q8—181no—
539C2×Q8—181no—
540C2×Q8—182no—
541C2×Q8C2×D3211yescharacteristic
542C22×C4—91no—
543C22×C4—91no—
544C22×C4—91no—
545C22×C4—181no—
546C22×C4—181no—
547M16—182no—
548M16—182no—
549C2×C8—31no—
550C2×C8—31no—
551C2×C8—91no—
552C2×C8C2×D3211yescharacteristic
553C4⋊C4—31no—
554C4⋊C4—31no—
555C4⋊C4—31no—
556C4⋊C4—31no—
557C4⋊C4—61no—
558C4⋊C4—61no—
559C4⋊C4—61no—
560C4⋊C4—61no—
561C4⋊C4—61no—
562C4⋊C4—91no—
563C4⋊C4—181no—
564C4⋊C4—181no—
565C4⋊C4—181no—
566C4⋊C4—181no—
567C4⋊C4—181no—
568C4⋊C4—181no—
569C4⋊C4C2×D3211yescharacteristic
570C22⋊C4—181no—
571C22⋊C4—181no—
572C42—31no—
573C42—31no—
574C42—61no—
575C42—61no—
576C42—91no—
577C42—91no—
578C42—181no—
579C42—181no—
580C42—181no—
581C42—181no—
582C22×C3—21no—
583C22×C3C2×D3×D411yescharacteristic
584C22×C3C2×D3×D411yescharacteristic
585C2×D3—32no—
586C2×D3—32no—
587C2×D3—62no—
588C2×D3—61no—
589C2×D3—61no—
590C2×D3—61no—
591C2×D3—61no—
592C2×D3—121no—
593C2×D3—121no—
594C3×C4—22no—
595C3×C4—22no—
596C3×C4—21no—
597C3×C4—21no—
598C3×C4—32no—
599C3×C4—42no—
600C3×C4—41no—
601C3×C4—41no—
602C3×C4—61no—
603C3×C4—61no—
604C3×C4—61no—
605C3×C4—81no—
606C3×C4—121no—
607C3×C4—121no—
608C3×C4—121no—
609C3×C4—121no—
610C3×C4C2×D3×Q811yescharacteristic
611C3×C4C2×D3×Q811yescharacteristic
612C3×C4D3×#4111yescharacteristic
613C3×C4D3×#4111yescharacteristic
614Dic3—21no—
615Dic3—21no—
616Dic3—21no—
617Dic3—32no—
618Dic3—32no—
619Dic3—41no—
620Dic3—41no—
621Dic3—41no—
622Dic3—41no—
623Dic3—62no—
624Dic3—62no—
625Dic3—62no—
626Dic3—122no—
627Dic3—121no—
628Dic3—121no—
629Dic3—241no—
630Dic3#91812yes—
631C32#307811yescharacteristic, complemented, Sylow
632C23—91no—
633Q8—21no—
634Q8—92no—
635Q8—122no—
636Q8—184no—
637Q8—181no—
638Q8—362no—
639Q8#379712yes—
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—92no—
652C2×C4—92no—
653C2×C4—184no—
654C2×C4—182no—
655C2×C4—181no—
656C2×C4—181no—
657C2×C4—361no—
658C2×C4—362no—
659C2×C4C22×D3211yescharacteristic
660C8—21no—
661C8—61no—
662C8—61no—
663C8—181no—
664C2×C3—21no—
665C2×C3—21no—
666C2×C3—21no—
667C2×C3D3×C22⋊Q811yescharacteristic
668C2×C3D3×C22⋊Q811yescharacteristic
669C2×C3C2×#91811yescharacteristic
670C2×C3#576811yescharacteristic
671C2×C3#577311yescharacteristic
672C2×C3D3×#13711yescharacteristic
673D3—62no—
674D3—62no—
675D3—122no—
676C22—92no—
677C22—181no—
678C22—181no—
679C22D32×D411yescharacteristic
680C4—22no—
681C4—32no—
682C4—41no—
683C4—61no—
684C4—61no—
685C4—61no—
686C4—92no—
687C4—121no—
688C4—121no—
689C4—121no—
690C4—121no—
691C4—182no—
692C4—361no—
693C4C2×#379711yescharacteristic
694C4#6431211yescharacteristic
695C3—21no—
696C3#8110811yescharacteristic, complemented
697C3#8123011yescharacteristic, complemented
698C2—182no—
699C2#1059406711yescharacteristic
700C2#1059474511yescharacteristic
701C2D3×#91811yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#103C22
socleC22×C32C22×D4
prime radicalC22×C3⋊D3C2×D4
hypercenter#103D32
hypocenterC32#3078
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
4. C3×#4799C2semidirect
5. C3×#4793C2semidirect
7. #10591545C2semidirect
8. #10591544C2semidirect
9. #10590814C2semidirect
10. #10590802C2semidirect
14. #10590492C2semidirect
15. #10590488C2semidirect
89. #4799D3semidirect
90. #4793D3semidirect
94. Q8×C3⋊D3Q8semidirect
631. C32#3078semidirect
696. C3#81108semidirect
697. C3#81230semidirect

Maximal subgroups

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

subgroupindex
Q8×#6242
#105944482
#105925012
C3×#47992
C3×#47932
#105915622
#105915452
#105915442
#105908142
#105908022
#105906882
#105906662
#105905822
#105904922
#105904882
#812303
#811083