Finite Group Databasebeta

← #11868768

Subgroups — #11868768

Order 1152.

797 conjugacy classes of subgroups.

The subgroup lattice has 691 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×D3×Dic6C211yesmaximal, characteristic
2#10593874C211yesmaximal, characteristic
3#10592528C211yesmaximal, characteristic, complemented
4C3×#4837C211yesmaximal, characteristic
5C3×#4829C211yesmaximal, characteristic, complemented
6#10590948C211yesmaximal, characteristic
7#10590948C211yesmaximal, characteristic
8#10590805C211yesmaximal, characteristic, complemented
9#10590804C211yesmaximal, characteristic, complemented
10#10590803C211yesmaximal, characteristic, complemented
11#10590802C211yesmaximal, characteristic, complemented
12#10590683C211yesmaximal, characteristic
13#10590681C211yesmaximal, characteristic
14#10590302C211yesmaximal, characteristic, complemented
15#10590292C211yesmaximal, characteristic, complemented
16#81230—31nomaximal
17#79068—31nomaximal
18C2×D3×Dic6C2211yescharacteristic
19#64079C2211yescharacteristic
20C4×#634C2211yescharacteristic
21C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
22C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
23C3×C42×D3C2211yescharacteristic
24C3×#870C2211yescharacteristic
25C3×C4×Dic6C2211yescharacteristic
26#63918C2211yescharacteristic
27#63918C2211yescharacteristic
28C4×#627—21no—
29D3×C4⋊Dic3C2211yescharacteristic
30D3×Dic3⋊C4—21no—
31C4×D3×Dic3—21no—
32#63851—21no—
33#63851—21no—
34#63844C2211yescharacteristic
35Dic3×Dic6C2211yescharacteristic
36#63841C2211yescharacteristic
37#63841C2211yescharacteristic
38#63837—21no—
39#63837—21no—
40#63837—21no—
41C32×C4⋊C8C2211yescharacteristic
42#63645C2211yescharacteristic
43#63644C2211yescharacteristic
44#63643C2211yescharacteristic
45#63643C2211yescharacteristic
46C3×#818C2211yescharacteristic
47C3×#817C2211yescharacteristic
48C3×#816C2211yescharacteristic
49C3×#816C2211yescharacteristic
50C3×Dic3⋊C8C2211yescharacteristic
51C3×Dic3⋊C8C2211yescharacteristic
52C3×C4⋊(C3⋊C8)C2211yescharacteristic
53#63575C2211yescharacteristic
54#63575C2211yescharacteristic
55#63573C2211yescharacteristic
56#63573C2211yescharacteristic
57#63567C2211yescharacteristic
58#63567C2211yescharacteristic
59#63566C2211yescharacteristic
60#63566C2211yescharacteristic
61#5688—31no—
62C4×D3×Q8—31no—
63#5470—31no—
64C2×C4×Dic6—31no—
65C3×#479—31no—
66C3×#423—31no—
67#5121—31no—
68#5121—31no—
69#5120—31no—
70#5120—31no—
71#5063—31no—
72#5022—31no—
73#4881—31no—
74#4875—31no—
75#4861—31no—
76#4854—31no—
77#4851—31no—
78#4851—31no—
79#4850—31no—
80#4850—31no—
81#4837D311yescharacteristic
82#4829—31no—
83#4829—31no—
84#4829—31no—
85#4829—31no—
86#4829—61no—
87#4829D311yescharacteristic, complemented
88#4802—31no—
89#4802—31no—
90#4793—31no—
91#4791—31no—
92C2×#634C2311yescharacteristic
93C2×C3×C4×D3D411yescharacteristic
94C2×C3×C4×D3D411yescharacteristic
95C2×C3×C4×D3C2311yescharacteristic
96C2×C3×Dic6C2311yescharacteristic
97C2×#627—21no—
98C2×#627—21no—
99C2×#627—21no—
100C2×D3×Dic3—21no—
101C2×D3×Dic3—21no—
102D3×Dic6—22no—
103D3×Dic6Q814yescomplemented
104C2×C32×C8C2311yescharacteristic
105C2×C32×C8C2311yescharacteristic
106C32×C42C2311yescharacteristic
107C4⋊(C3⋊Dic3)C2311yescharacteristic
108C4⋊(C3⋊Dic3)C2311yescharacteristic
109C4⋊(C3⋊Dic3)C2311yescharacteristic
110#3750—21no—
111#3750—21no—
112#3750—21no—
113C4×C3⋊Dic3—21no—
114C3×C4⋊Dic3C2311yescharacteristic
115C3×C4⋊Dic3C2311yescharacteristic
116C3×C4⋊Dic3C2311yescharacteristic
117C3×Dic3⋊C4—21no—
118C3×Dic3⋊C4—21no—
119C3×Dic3⋊C4—21no—
120C3×C4×Dic3—21no—
121C3×C4×Dic3D411yescharacteristic
122C3×C4×Dic3D411yescharacteristic
123C3×C4×Dic3C2311yescharacteristic
124C2×C3×C3⋊C8C2311yescharacteristic
125C2×C3×C3⋊C8C2311yescharacteristic
126C3×ΓL(1,𝔽25)—22no—
127C3×ΓL(1,𝔽25)—22no—
128#3724—21no—
129Dic3⋊Dic3—21no—
130Dic3⋊Dic3—21no—
131Dic3⋊Dic3—21no—
132Dic3⋊Dic3—21no—
133(C2×D3)⋊Dic3—21no—
134(C2×D3)⋊Dic3—21no—
135Dic32—21no—
136Dic32—21no—
137Dic32—21no—
138Dic32—21no—
139#3078—91noSylow
140C2×D3×Q8—31no—
141C22×Dic6—31no—
142C2×C3×M16—31no—
143C2×C3×M16—31no—
144C3×#125—31no—
145C3×C4×Q8—31no—
146C2×C3×C42—31no—
147Q8×Dic3—31no—
148#926—31no—
149#926—31no—
150C2×C4⋊Dic3—31no—
151#924—61no—
152#924—61no—
153C2×Dic3⋊C4—61no—
154C2×C4×Dic3—61no—
155C2×ΓL(1,𝔽25)C2×D311yescharacteristic
156C2×ΓL(1,𝔽25)C2×D311yescharacteristic
157#896—61no—
158#896—61no—
159#892—31no—
160#892—31no—
161D3×C4⋊C4—31no—
162D3×C4⋊C4—61no—
163#888—31no—
164#888—31no—
165#887—31no—
166#887—61no—
167#887—61no—
168#887—61no—
169C42×D3—61no—
170C42×D3C2×D311yescharacteristic
171#870—31no—
172#870—31no—
173#870—61no—
174#870C2×D311yescharacteristic
175#869—31no—
176#869—31no—
177C4×Dic6—31no—
178C4×Dic6—31no—
179C4×Dic6—31no—
180C4×Dic6—31no—
181C4×Dic6—61no—
182C4×Dic6—61no—
183C4×Dic6—61no—
184C4×Dic6—61no—
185C4×Dic6—61no—
186C4×Dic6—61no—
187C4×Dic6C2×D311yescharacteristic
188C3×#107—31no—
189C3×#106—31no—
190C3×C4⋊C8—21no—
191C3×C4⋊C8—31no—
192C3×C4⋊C8—31no—
193C3×C4⋊C8—31no—
194C3×C4⋊C8C2×D311yescharacteristic
195C3×C4⋊C8C2×D311yescharacteristic
196C3×#103—31no—
197C3×#103—31no—
198#835—31no—
199#835—31no—
200#818—31no—
201#818—31no—
202#818—31no—
203#818—31no—
204#818—61no—
205#818C2×D311yescharacteristic
206#817—31no—
207#817—31no—
208#817—31no—
209#817—31no—
210#817—61no—
211#817C2×D311yescharacteristic
212#816—31no—
213#816—31no—
214#816—31no—
215#816—31no—
216#816—31no—
217#816—31no—
218#816—31no—
219#816—31no—
220#816—61no—
221#816—61no—
222#816C2×D311yescharacteristic
223#816C2×D311yescharacteristic
224Dic3⋊C8C2×D311yescharacteristic
225Dic3⋊C8C2×D311yescharacteristic
226#810—31no—
227#810—31no—
228#808—31no—
229#808—31no—
230#807—31no—
231#807—31no—
232C4⋊(C3⋊C8)C2×D311yescharacteristic
233C22×C3×D3C2×D411yescharacteristic
234C2×C32×C4C2×D411yescharacteristic
235C2×C32×C4C2×D411yescharacteristic
236C2×C32×C4C2411yescharacteristic
237C2×C3⋊Dic3—21no—
238C2×C3⋊Dic3—21no—
239C2×C3⋊Dic3—21no—
240C2×C3⋊Dic3—21no—
241#634—21no—
242#634C2×Q812yes—
243C2×C3×Dic3—21no—
244C2×C3×Dic3—21no—
245C2×C3×Dic3—21no—
246C2×C3×Dic3—21no—
247C2×C3×Dic3C2×D411yescharacteristic
248C2×C3×Dic3C2×D411yescharacteristic
249C2×C3×Dic3C2×D411yescharacteristic
250C3×C4×D3—22no—
251C3×C4×D3—41no—
252C3×C4×D3C2×Q812yes—
253C3×C4×D3#4112yes—
254C3×Dic6—21no—
255C3×Dic6C2×Q812yes—
256#627—24no—
257#627—42no—
258#627—42no—
259D3×Dic3—24no—
260D3×Dic3—42no—
261C32×C8—21no—
262C32×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—91no—
272#477—91no—
273#475—91no—
274#475—91no—
275#428—91no—
276#428—91no—
277#423—31no—
278#419—91no—
279#419—91no—
280C2×C3×Q8—31no—
281C22×C3×C4—31no—
282C22×C3×C4—31no—
283C22×C3×C4—31no—
284C22×Dic3—61no—
285C22×Dic3—61no—
286D3×Q8—34no—
287D3×Q8—62no—
288C2×C4×D3—61no—
289C2×C4×D3—61no—
290C2×C4×D3D1211yescharacteristic
291C2×C4×D3D1211yescharacteristic
292C2×C4×D3C22×D311yescharacteristic
293C2×Dic6—31no—
294C2×Dic6—31no—
295C2×Dic6—34no—
296C2×Dic6—61no—
297C2×Dic6—62no—
298C2×Dic6—61no—
299C2×Dic6—61no—
300C2×Dic6—61no—
301C2×Dic6—61no—
302C2×Dic6—61no—
303C2×Dic6—61no—
304C2×Dic6C22×D311yescharacteristic
305C3×M16—62no—
306C3×M16—62no—
307C2×C3×C8—21no—
308C2×C3×C8—21no—
309C2×C3×C8—31no—
310C2×C3×C8—31no—
311C2×C3×C8C22×D311yescharacteristic
312C2×C3×C8C22×D311yescharacteristic
313C2×C3×C8C22×D311yescharacteristic
314C2×C3×C8C22×D311yescharacteristic
315C3×C4⋊C4—31no—
316C3×C4⋊C4—31no—
317C3×C4⋊C4—31no—
318C3×C4⋊C4—61no—
319C3×C4⋊C4—61no—
320C3×C4⋊C4—61no—
321C3×C42—21no—
322C3×C42—31no—
323C3×C42—31no—
324C3×C42—31no—
325C3×C42—61no—
326C3×C42C22×D311yescharacteristic
327C3×C42C22×D311yescharacteristic
328#217—61no—
329#217—61no—
330(C2×D3)⋊C4—61no—
331(C2×D3)⋊C4—61no—
332C4⋊Dic3—31no—
333C4⋊Dic3—31no—
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
347C4⋊Dic3C22×D311yescharacteristic
348Dic3⋊C4—21no—
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—
361Dic3⋊C4—61no—
362Dic3⋊C4—61no—
363Dic3⋊C4—121no—
364Dic3⋊C4—121no—
365Dic3⋊C4—121no—
366C4×Dic3—21no—
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—61no—
376C4×Dic3—61no—
377C4×Dic3—121no—
378C4×Dic3D1211yescharacteristic
379C4×Dic3D1211yescharacteristic
380C4×Dic3C22×D311yescharacteristic
381C2×C3⋊C8C22×D311yescharacteristic
382C2×C3⋊C8C22×D311yescharacteristic
383ΓL(1,𝔽25)—22no—
384ΓL(1,𝔽25)—22no—
385C22×C32C22×D411yescharacteristic
386C2×C3×D3—21no—
387C2×C3×D3—21no—
388C2×C3×D3C22⋊Q812yes—
389C32×C4—21no—
390C32×C4—21no—
391C32×C4C22×Q811yescharacteristic
392C32×C4C2×#4111yescharacteristic
393C3⋊Dic3—22no—
394C3⋊Dic3—41no—
395C3⋊Dic3—41no—
396C3⋊Dic3—41no—
397C3×Dic3—22no—
398C3×Dic3—21no—
399C3×Dic3—41no—
400C3×Dic3—41no—
401C3×Dic3—41no—
402C3×Dic3C22⋊Q812yes—
403C3×Dic3#13712yes—
404C22×Q8—91no—
405C2×M16—31no—
406C2×M16—31no—
407C4⋊Q8—91no—
408C4⋊Q8—91no—
409#125—31no—
410#125—91no—
411C22⋊Q8—181no—
412C22⋊Q8—181no—
413C4×Q8—31no—
414C4×Q8—91no—
415C4×Q8—91no—
416C4×Q8—91no—
417C4×Q8—181no—
418C4×Q8—181no—
419C4×Q8—181no—
420C4×Q8—181no—
421#117—91no—
422#117—91no—
423C2×C4⋊C4—91no—
424C2×C4⋊C4—181no—
425C2×C42—31no—
426C2×C42—181no—
427#107—31no—
428#107—91no—
429#107—91no—
430#107—91no—
431#106—31no—
432#106—91no—
433#106—91no—
434#106—91no—
435C4⋊C8—31no—
436C4⋊C8—31no—
437C4⋊C8—31no—
438C4⋊C8D3211yescharacteristic
439#103—31no—
440#103—31no—
441#103—91no—
442#103—91no—
443#103—91no—
444#103—91no—
445#103—91no—
446#103—91no—
447C23×C3—31no—
448C22×D3C2×D1211yescharacteristic
449C3×Q8—32no—
450C3×Q8—61no—
451C2×C3×C4—21no—
452C2×C3×C4—21no—
453C2×C3×C4—21no—
454C2×C3×C4—31no—
455C2×C3×C4—31no—
456C2×C3×C4—32no—
457C2×C3×C4—32no—
458C2×C3×C4—31no—
459C2×C3×C4—62no—
460C2×C3×C4—61no—
461C2×C3×C4—61no—
462C2×C3×C4—61no—
463C2×C3×C4—61no—
464C2×C3×C4—121no—
465C2×C3×C4C2×D1211yescharacteristic
466C2×C3×C4C2×D1211yescharacteristic
467C2×C3×C4D3×D411yescharacteristic
468C2×C3×C4D3×D411yescharacteristic
469C2×C3×C4C23×D311yescharacteristic
470C2×C3×C4C23×D311yescharacteristic
471C2×Dic3—21no—
472C2×Dic3—21no—
473C2×Dic3—21no—
474C2×Dic3—21no—
475C2×Dic3—64no—
476C2×Dic3—61no—
477C2×Dic3—61no—
478C2×Dic3—61no—
479C2×Dic3—61no—
480C2×Dic3—61no—
481C2×Dic3—61no—
482C2×Dic3—61no—
483C2×Dic3—61no—
484C2×Dic3—121no—
485C2×Dic3—121no—
486C2×Dic3—121no—
487C2×Dic3—121no—
488C2×Dic3—122no—
489C2×Dic3C2×D1211yescharacteristic
490C2×Dic3C2×D1211yescharacteristic
491C2×Dic3C2×D1211yescharacteristic
492C4×D3—22no—
493C4×D3—41no—
494C4×D3—64no—
495C4×D3—122no—
496C4×D3#23712yes—
497C4×D3D3×Q812yes—
498Dic6—21no—
499Dic6—32no—
500Dic6—32no—
501Dic6—62no—
502Dic6—64no—
503Dic6—61no—
504Dic6—61no—
505Dic6—64no—
506Dic6—121no—
507Dic6—122no—
508Dic6—122no—
509Dic6—122no—
510Dic6—122no—
511Dic6D3×Q812yes—
512C3×C8—21no—
513C3×C8—21no—
514C3×C8—21no—
515C3×C8—21no—
516C3×C8—41no—
517C3×C8—41no—
518C3×C8—61no—
519C3×C8—61no—
520C3⋊C8—21no—
521C3⋊C8—21no—
522C2×C32C2×C22⋊Q811yescharacteristic
523C2×C32C2×#13711yescharacteristic
524C2×C32#57511yescharacteristic
525C3×D3—22no—
526C2×Q8—31no—
527C2×Q8—94no—
528C2×Q8—91no—
529C2×Q8—181no—
530C2×Q8—181no—
531C2×Q8—181no—
532C2×Q8—182no—
533C22×C4—31no—
534C22×C4—31no—
535C22×C4—31no—
536C22×C4—181no—
537C22×C4—181no—
538M16—62no—
539M16—62no—
540C2×C8—31no—
541C2×C8—31no—
542C2×C8C2×D3211yescharacteristic
543C2×C8C2×D3211yescharacteristic
544C4⋊C4—31no—
545C4⋊C4—31no—
546C4⋊C4—31no—
547C4⋊C4—61no—
548C4⋊C4—61no—
549C4⋊C4—61no—
550C4⋊C4—91no—
551C4⋊C4—91no—
552C4⋊C4—91no—
553C4⋊C4—181no—
554C4⋊C4—181no—
555C4⋊C4—181no—
556C4⋊C4—181no—
557C4⋊C4—181no—
558C4⋊C4—181no—
559C4⋊C4—181no—
560C4⋊C4—181no—
561C22⋊C4—181no—
562C22⋊C4—181no—
563C42—31no—
564C42—31no—
565C42—31no—
566C42—61no—
567C42—181no—
568C42—181no—
569C42—181no—
570C42—181no—
571C42—181no—
572C42C2×D3211yescharacteristic
573C22×C3—21no—
574C22×C3—32no—
575C22×C3—61no—
576C22×C3—61no—
577C22×C3C22×D1211yescharacteristic
578C22×C3C2×D3×D411yescharacteristic
579C2×D3—21no—
580C2×D3—21no—
581C2×D3#89712yes—
582C3×C4—21no—
583C3×C4—21no—
584C3×C4—21no—
585C3×C4—21no—
586C3×C4—21no—
587C3×C4—21no—
588C3×C4—32no—
589C3×C4—32no—
590C3×C4—41no—
591C3×C4—41no—
592C3×C4—62no—
593C3×C4—61no—
594C3×C4—121no—
595C3×C4—121no—
596C3×C4—121no—
597C3×C4C2×#23711yescharacteristic
598C3×C4C2×D3×Q811yescharacteristic
599C3×C4C2×D3×Q811yescharacteristic
600C3×C4D3×#4111yescharacteristic
601Dic3—21no—
602Dic3—22no—
603Dic3—41no—
604Dic3—41no—
605Dic3—41no—
606Dic3—62no—
607Dic3—62no—
608Dic3—122no—
609Dic3—121no—
610Dic3—121no—
611Dic3—121no—
612Dic3—121no—
613Dic3—121no—
614Dic3—121no—
615Dic3—241no—
616Dic3—241no—
617Dic3—241no—
618Dic3#89712yes—
619Dic3#90912yes—
620C32#307811yescharacteristic, complemented, Sylow
621C23—31no—
622Q8—32no—
623Q8—61no—
624Q8—92no—
625Q8—184no—
626Q8—181no—
627Q8—362no—
628Q8—362no—
629C2×C4—31no—
630C2×C4—31no—
631C2×C4—32no—
632C2×C4—32no—
633C2×C4—31no—
634C2×C4—62no—
635C2×C4—61no—
636C2×C4—61no—
637C2×C4—61no—
638C2×C4—61no—
639C2×C4—121no—
640C2×C4—184no—
641C2×C4—181no—
642C2×C4—181no—
643C2×C4—181no—
644C2×C4—181no—
645C2×C4—362no—
646C2×C4D3×D1211yescharacteristic
647C2×C4D3×D1211yescharacteristic
648C2×C4C22×D3211yescharacteristic
649C8—21no—
650C8—21no—
651C8—61no—
652C8—61no—
653C2×C3—21no—
654C2×C3—21no—
655C2×C3—21no—
656C2×C3—62no—
657C2×C3C2×#89711yescharacteristic
658C2×C3D3×C22⋊Q811yescharacteristic
659C2×C3C2×#90911yescharacteristic
660C2×C3#574811yescharacteristic
661C2×C3#576811yescharacteristic
662C2×C3D3×#13711yescharacteristic
663D3—22no—
664C22—32no—
665C22—61no—
666C22—61no—
667C22C2×D3×D1211yescharacteristic
668C4—21no—
669C4—21no—
670C4—32no—
671C4—32no—
672C4—62no—
673C4—61no—
674C4—121no—
675C4—121no—
676C4—121no—
677C4—182no—
678C4—361no—
679C4—361no—
680C4—361no—
681C4D3×#23711yescharacteristic
682C4D32×Q811yescharacteristic
683C3—21no—
684C3#7906811yescharacteristic, complemented
685C3#8123011yescharacteristic, complemented
686C2—62no—
687C2D3×#89711yescharacteristic
688C2#1059467611yescharacteristic
689C2D3×#90911yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊C8C22
socleC22×C32C22×D4
prime radicalC22×C3×D3C2×D4
hypercenterC4⋊C8D32
hypocenterC32#3078
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
3. #10592528C2semidirect
5. C3×#4829C2semidirect
8. #10590805C2semidirect
9. #10590804C2semidirect
10. #10590803C2semidirect
11. #10590802C2semidirect
14. #10590302C2semidirect
15. #10590292C2semidirect
87. #4829D3semidirect
103. D3×Dic6Q8semidirect
620. C32#3078semidirect
684. C3#79068semidirect
685. C3#81230semidirect

Maximal subgroups

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

subgroupindex
C4×D3×Dic62
#105938742
#105925282
C3×#48372
C3×#48292
#105909482
#105908052
#105908042
#105908032
#105908022
#105906832
#105906812
#105903022
#105902922
#812303
#790683