Finite Group Databasebeta

← #11868610

Subgroups — #11868610

Order 1152.

827 conjugacy classes of subgroups.

The subgroup lattice has 711 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#3799C211yesmaximal, characteristic
2#10593874C211yesmaximal, characteristic, complemented
3#10592546C211yesmaximal, characteristic, complemented
4C3×D3×C4⋊C8C211yesmaximal, characteristic, complemented
5C3×#4829C211yesmaximal, characteristic, complemented
6#10590804C211yesmaximal, characteristic, complemented
7#10590803C211yesmaximal, characteristic, complemented
8#10590764C211yesmaximal, characteristic, complemented
9#10590759C211yesmaximal, characteristic, complemented
10#10590707C211yesmaximal, characteristic, complemented
11#10590706C211yesmaximal, characteristic, complemented
12#10590690C211yesmaximal, characteristic
13#10590690C211yesmaximal, characteristic
14#10590308C211yesmaximal, characteristic, complemented
15#10590302C211yesmaximal, characteristic, complemented
16#81229—31nomaximal
17#79025—31nomaximal
18C2×#3799C2211yescharacteristic
19C4×C4⋊(C3⋊D3)C2211yescharacteristic
20#64079C2211yescharacteristic
21C2×C3×D3×C8C2211yescharacteristic
22C2×C3×D3×C8C2211yescharacteristic
23C3×C42×D3C2211yescharacteristic
24C3×#870C2211yescharacteristic
25C3×C4×Dic6C2211yescharacteristic
26#63918C2211yescharacteristic
27#63918C2211yescharacteristic
28#63904—21no—
29C4×#626—21no—
30#63894C2211yescharacteristic
31C4×#624—21no—
32#63851—21no—
33#63851—21no—
34Dic3×Dic6C2211yescharacteristic
35#63841C2211yescharacteristic
36#63841C2211yescharacteristic
37#63841C2211yescharacteristic
38#63837—21no—
39#63837—21no—
40#63836—21no—
41C32×C4⋊C8C2211yescharacteristic
42#63648C2211yescharacteristic
43#63648C2211yescharacteristic
44#63645C2211yescharacteristic
45#63644C2211yescharacteristic
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#63566C2211yescharacteristic
58#63566C2211yescharacteristic
59#63564C2211yescharacteristic
60#63564C2211yescharacteristic
61#5688—31no—
62C4×#239—31no—
63C4×#235—31no—
64#5470—31no—
65C3×#479—31no—
66C2×C3×C4⋊C8—31no—
67#5113—31no—
68#5113—31no—
69#5106—31no—
70#5106—31no—
71#5066—31no—
72#5022—31no—
73#4890—31no—
74#4880—31no—
75#4870—31no—
76#4860—31no—
77#4851—31no—
78#4850—31no—
79#4847—31no—
80#4847—31no—
81#4847—31no—
82#4847—61no—
83#4846—31no—
84#4842—31no—
85D3×C4⋊C8D311yescharacteristic, complemented
86#4829—31no—
87#4829D311yescharacteristic, complemented
88#4804—31no—
89#4804—31no—
90#4793—31no—
91#4791—31no—
92C2×C4⋊(C3⋊D3)C2311yescharacteristic
93C2×C4×C3⋊D3—21no—
94C2×C3×C4×D3D411yescharacteristic
95C2×C3×C4×D3D411yescharacteristic
96C2×C3×C4×D3C2311yescharacteristic
97C2×C3×Dic6C2311yescharacteristic
98C2×#627—21no—
99C2×#627—21no—
100C2×#626—21no—
101C2×#624—21no—
102C2×#624—21no—
103#3799—22no—
104#3799Q814yescomplemented
105C2×C32×C8C2311yescharacteristic
106C2×C32×C8C2311yescharacteristic
107C32×C42C2311yescharacteristic
108#3752—21no—
109C4⋊(C3⋊Dic3)C2311yescharacteristic
110C4⋊(C3⋊Dic3)C2311yescharacteristic
111C4⋊(C3⋊Dic3)C2311yescharacteristic
112#3750—21no—
113#3750—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×D3×C8—22no—
127C3×D3×C8—22no—
128Dic3⋊Dic3—21no—
129Dic3⋊Dic3—21no—
130Dic3⋊Dic3—21no—
131#3722—21no—
132(C2×D3)⋊Dic3—21no—
133(C2×D3)⋊Dic3—21no—
134(C2×D3)⋊Dic3—21no—
135Dic32—21no—
136Dic32—21no—
137Dic32—21no—
138Dic32—21no—
139#3076—91noSylow
140C2×#239—31no—
141C2×#235—31no—
142C22×C3×C8—31no—
143C22×C3×C8—31no—
144C3×#125—31no—
145C3×C4×Q8—31no—
146C2×C3×C42—31no—
147Q8×Dic3—31no—
148C4×#67—61no—
149C4×#67—61no—
150#926—31no—
151#926—31no—
152#926—31no—
153#924—61no—
154#924—61no—
155C2×D3×C8C2×D311yescharacteristic
156C2×D3×C8C2×D311yescharacteristic
157#896—61no—
158#896—61no—
159#893—31no—
160#893—61no—
161#892—31no—
162#892—31no—
163#892—31no—
164#892—61no—
165#888—31no—
166#888—31no—
167#887—61no—
168#887—61no—
169C4×D12—31no—
170C4×D12—31no—
171C4×D12—31no—
172C4×D12—61no—
173C4×D12—61no—
174#872—61no—
175C42×D3—61no—
176C42×D3—61no—
177C42×D3C2×D311yescharacteristic
178#870—31no—
179#870—31no—
180#870—61no—
181#870C2×D311yescharacteristic
182#869—31no—
183#869—31no—
184C4×Dic6—31no—
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#821—31no—
201#821—31no—
202#821—31no—
203#821—31no—
204#821—31no—
205#821—31no—
206#821—61no—
207#821—61no—
208#818—31no—
209#818—31no—
210#818—31no—
211#818—31no—
212#818—61no—
213#818C2×D311yescharacteristic
214#817—31no—
215#817—31no—
216#817—31no—
217#817—31no—
218#817—61no—
219#817C2×D311yescharacteristic
220#816—31no—
221#816—31no—
222#816C2×D311yescharacteristic
223#816C2×D311yescharacteristic
224Dic3⋊C8C2×D311yescharacteristic
225Dic3⋊C8C2×D311yescharacteristic
226#809—31no—
227#809—31no—
228#808—31no—
229#808—31no—
230#807—31no—
231#807—31no—
232C4⋊(C3⋊C8)C2×D311yescharacteristic
233C22×C3⋊D3—21no—
234C22×C3×D3C2×D411yescharacteristic
235C2×C32×C4C2×D411yescharacteristic
236C2×C32×C4C2×D411yescharacteristic
237C2×C32×C4C2411yescharacteristic
238C2×C3⋊Dic3—21no—
239C2×C3⋊Dic3—21no—
240C2×C3⋊Dic3—21no—
241C4⋊(C3⋊D3)—21no—
242C4⋊(C3⋊D3)C2×Q812yes—
243C4×C3⋊D3—42no—
244C2×C3×Dic3—21no—
245C2×C3×Dic3—21no—
246C2×C3×Dic3—21no—
247C2×C3×Dic3—21no—
248C2×C3×Dic3C2×D411yescharacteristic
249C2×C3×Dic3C2×D411yescharacteristic
250C2×C3×Dic3C2×D411yescharacteristic
251C3×C4×D3—22no—
252C3×C4×D3—41no—
253C3×C4×D3C2×Q812yes—
254C3×C4×D3#4112yes—
255C3×Dic6—21no—
256C3×Dic6C2×Q812yes—
257#627—42no—
258#627—42no—
259#626—24no—
260#624—24no—
261#624—42no—
262C32×C8—21no—
263C32×C8—21no—
264C3×C3⋊C8—21no—
265C3×C3⋊C8—21no—
266#533—91no—
267C4×#41—91no—
268#479—31no—
269#479—91no—
270#478—91no—
271#478—91no—
272#477—91no—
273#476—91no—
274#475—91no—
275#474—91no—
276#427—91no—
277#427—91no—
278C2×C4⋊C8—31no—
279#416—91no—
280#416—91no—
281C2×C3×Q8—31no—
282C22×C3×C4—31no—
283C22×C3×C4—31no—
284C22×C3×C4—31no—
285C2×#67—61no—
286#239—34no—
287#239—62no—
288#235—34no—
289#235—62no—
290C2×D12—31no—
291C2×D12—31no—
292C2×D12—61no—
293C2×D12—61no—
294C2×C4×D3—61no—
295C2×C4×D3—61no—
296C2×C4×D3—61no—
297C2×C4×D3—61no—
298C2×C4×D3—61no—
299C2×C4×D3—61no—
300C2×C4×D3—121no—
301C2×C4×D3D1211yescharacteristic
302C2×C4×D3D1211yescharacteristic
303C2×C4×D3C22×D311yescharacteristic
304C2×Dic6—61no—
305C2×Dic6—61no—
306C2×Dic6—61no—
307C2×Dic6—61no—
308C2×Dic6C22×D311yescharacteristic
309C2×C3×C8—21no—
310C2×C3×C8—21no—
311C2×C3×C8—31no—
312C2×C3×C8—31no—
313C2×C3×C8—62no—
314C2×C3×C8—62no—
315C2×C3×C8C22×D311yescharacteristic
316C2×C3×C8C22×D311yescharacteristic
317C2×C3×C8C22×D311yescharacteristic
318C2×C3×C8C22×D311yescharacteristic
319C3×C4⋊C4—31no—
320C3×C4⋊C4—31no—
321C3×C4⋊C4—31no—
322C3×C4⋊C4—61no—
323C3×C4⋊C4—61no—
324C3×C4⋊C4—61no—
325C3×C42—21no—
326C3×C42—31no—
327C3×C42—31no—
328C3×C42—31no—
329C3×C42—61no—
330C3×C42C22×D311yescharacteristic
331C3×C42C22×D311yescharacteristic
332#217—61no—
333#217—61no—
334#217—61no—
335(C2×D3)⋊C4—61no—
336(C2×D3)⋊C4—61no—
337(C2×D3)⋊C4—61no—
338(C2×D3)⋊C4—61no—
339(C2×D3)⋊C4—61no—
340(C2×D3)⋊C4—61no—
341(C2×D3)⋊C4—61no—
342(C2×D3)⋊C4—121no—
343C4⋊Dic3—31no—
344C4⋊Dic3—31no—
345C4⋊Dic3—31no—
346C4⋊Dic3—31no—
347C4⋊Dic3—31no—
348C4⋊Dic3—31no—
349C4⋊Dic3—61no—
350C4⋊Dic3—61no—
351C4⋊Dic3—61no—
352C4⋊Dic3—61no—
353C4⋊Dic3—61no—
354C4⋊Dic3—61no—
355C4⋊Dic3C22×D311yescharacteristic
356C4⋊Dic3C22×D311yescharacteristic
357C4⋊Dic3C22×D311yescharacteristic
358Dic3⋊C4—21no—
359Dic3⋊C4—21no—
360Dic3⋊C4—21no—
361Dic3⋊C4—61no—
362Dic3⋊C4—61no—
363Dic3⋊C4—61no—
364Dic3⋊C4—61no—
365Dic3⋊C4—61no—
366Dic3⋊C4—61no—
367Dic3⋊C4—61no—
368Dic3⋊C4—121no—
369Dic3⋊C4—121no—
370C4×Dic3—21no—
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×Dic3D1211yescharacteristic
380C4×Dic3D1211yescharacteristic
381C4×Dic3C22×D311yescharacteristic
382C2×C3⋊C8C22×D311yescharacteristic
383C2×C3⋊C8C22×D311yescharacteristic
384D3×C8—22no—
385D3×C8—22no—
386C22×C32C22×D411yescharacteristic
387C2×C3⋊D3—22no—
388C2×C3⋊D3—41no—
389C2×C3⋊D3—41no—
390C2×C3×D3—21no—
391C2×C3×D3—21no—
392C2×C3×D3C22⋊Q812yes—
393C32×C4—21no—
394C32×C4—21no—
395C32×C4C22×Q811yescharacteristic
396C32×C4C2×#4111yescharacteristic
397C3⋊Dic3—41no—
398C3⋊Dic3—41no—
399C3⋊Dic3—41no—
400C3×Dic3—22no—
401C3×Dic3—21no—
402C3×Dic3—41no—
403C3×Dic3—41no—
404C3×Dic3—41no—
405C3×Dic3C22⋊Q812yes—
406C3×Dic3#13512yes—
407C2×#41—91no—
408C22×C8—31no—
409C22×C8—31no—
410C4⋊Q8—91no—
411C4⋊Q8—91no—
412#125—31no—
413#125—91no—
414C22⋊Q8—181no—
415C22⋊Q8—181no—
416C4×Q8—31no—
417C4×Q8—91no—
418C4×Q8—181no—
419C4×Q8—181no—
420C4×D4—91no—
421C4×D4—91no—
422C4×D4—181no—
423C4×D4—181no—
424#117—91no—
425#117—91no—
426#117—91no—
427#117—181no—
428C2×C42—31no—
429C2×C42—181no—
430#107—31no—
431#107—91no—
432#107—91no—
433#107—91no—
434#106—31no—
435#106—91no—
436#106—91no—
437#106—91no—
438C4⋊C8—31no—
439C4⋊C8—31no—
440C4⋊C8—31no—
441C4⋊C8D3211yescharacteristic
442#103—31no—
443#103—31no—
444#103—91no—
445#103—91no—
446#102—91no—
447#102—91no—
448#102—91no—
449#102—91no—
450C23×C3—31no—
451C22×D3—61no—
452C22×D3—61no—
453C22×D3—121no—
454C22×D3C2×D1211yescharacteristic
455C3×Q8—32no—
456C3×Q8—61no—
457C2×C3×C4—21no—
458C2×C3×C4—21no—
459C2×C3×C4—21no—
460C2×C3×C4—31no—
461C2×C3×C4—31no—
462C2×C3×C4—32no—
463C2×C3×C4—32no—
464C2×C3×C4—31no—
465C2×C3×C4—62no—
466C2×C3×C4—61no—
467C2×C3×C4—61no—
468C2×C3×C4—61no—
469C2×C3×C4—61no—
470C2×C3×C4—121no—
471C2×C3×C4C2×D1211yescharacteristic
472C2×C3×C4C2×D1211yescharacteristic
473C2×C3×C4D3×D411yescharacteristic
474C2×C3×C4D3×D411yescharacteristic
475C2×C3×C4C23×D311yescharacteristic
476C2×C3×C4C23×D311yescharacteristic
477#67—64no—
478C2×Dic3—21no—
479C2×Dic3—21no—
480C2×Dic3—21no—
481C2×Dic3—21no—
482C2×Dic3—61no—
483C2×Dic3—61no—
484C2×Dic3—61no—
485C2×Dic3—61no—
486C2×Dic3—61no—
487C2×Dic3—61no—
488C2×Dic3—121no—
489C2×Dic3—121no—
490C2×Dic3—121no—
491C2×Dic3C2×D1211yescharacteristic
492C2×Dic3C2×D1211yescharacteristic
493C2×Dic3C2×D1211yescharacteristic
494D12—32no—
495D12—32no—
496D12—62no—
497D12—64no—
498D12—61no—
499D12—61no—
500D12—121no—
501C4×D3—22no—
502C4×D3—41no—
503C4×D3—64no—
504C4×D3—64no—
505C4×D3—122no—
506C4×D3—122no—
507C4×D3—122no—
508C4×D3—122no—
509C4×D3—242no—
510C4×D3#23712yes—
511C4×D3D3×Q812yes—
512Dic6—21no—
513Dic6—122no—
514Dic6—122no—
515Dic6—122no—
516Dic6—122no—
517Dic6D3×Q812yes—
518C3×C8—21no—
519C3×C8—21no—
520C3×C8—21no—
521C3×C8—21no—
522C3×C8—41no—
523C3×C8—41no—
524C3×C8—61no—
525C3×C8—61no—
526C3⋊C8—21no—
527C3⋊C8—21no—
528C2×C32C2×C22⋊Q811yescharacteristic
529C2×C32C2×#13511yescharacteristic
530C2×C32#57511yescharacteristic
531C3⋊D3—42no—
532C3×D3—22no—
533#41—94no—
534#41—182no—
535C2×Q8—31no—
536C2×Q8—181no—
537C2×Q8—181no—
538C2×D4—91no—
539C2×D4—181no—
540C22×C4—31no—
541C22×C4—31no—
542C22×C4—31no—
543C22×C4—181no—
544C22×C4—181no—
545C22×C4—181no—
546C2×C8—31no—
547C2×C8—31no—
548C2×C8—62no—
549C2×C8—62no—
550C2×C8C2×D3211yescharacteristic
551C2×C8C2×D3211yescharacteristic
552C4⋊C4—31no—
553C4⋊C4—31no—
554C4⋊C4—31no—
555C4⋊C4—61no—
556C4⋊C4—61no—
557C4⋊C4—61no—
558C4⋊C4—91no—
559C4⋊C4—91no—
560C4⋊C4—91no—
561C4⋊C4—181no—
562C4⋊C4—181no—
563C4⋊C4—181no—
564C4⋊C4—181no—
565C4⋊C4—181no—
566C22⋊C4—181no—
567C22⋊C4—181no—
568C22⋊C4—181no—
569C22⋊C4—181no—
570C22⋊C4—181no—
571C42—31no—
572C42—31no—
573C42—31no—
574C42—61no—
575C42—181no—
576C42—181no—
577C42—181no—
578C42—181no—
579C42C2×D3211yescharacteristic
580C22×C3—21no—
581C22×C3—32no—
582C22×C3—61no—
583C22×C3—61no—
584C22×C3C22×D1211yescharacteristic
585C22×C3C2×D3×D411yescharacteristic
586C2×D3—21no—
587C2×D3—21no—
588C2×D3—62no—
589C2×D3—62no—
590C2×D3—122no—
591C2×D3—121no—
592C2×D3—121no—
593C2×D3—121no—
594C2×D3—121no—
595C2×D3—241no—
596C2×D3—241no—
597C2×D3#89712yes—
598C3×C4—21no—
599C3×C4—21no—
600C3×C4—21no—
601C3×C4—21no—
602C3×C4—21no—
603C3×C4—21no—
604C3×C4—32no—
605C3×C4—32no—
606C3×C4—41no—
607C3×C4—41no—
608C3×C4—62no—
609C3×C4—61no—
610C3×C4—121no—
611C3×C4—121no—
612C3×C4—121no—
613C3×C4C2×#23711yescharacteristic
614C3×C4C2×D3×Q811yescharacteristic
615C3×C4C2×D3×Q811yescharacteristic
616C3×C4D3×#4111yescharacteristic
617Dic3—21no—
618Dic3—22no—
619Dic3—41no—
620Dic3—41no—
621Dic3—41no—
622Dic3—121no—
623Dic3—121no—
624Dic3—121no—
625Dic3—121no—
626Dic3—121no—
627Dic3—121no—
628Dic3—241no—
629Dic3—241no—
630Dic3—241no—
631Dic3#89712yes—
632Dic3#90412yes—
633C32#307611yescharacteristic, complemented, Sylow
634C23—31no—
635C23—181no—
636Q8—32no—
637Q8—61no—
638Q8—362no—
639Q8—362no—
640D4—92no—
641D4—184no—
642D4—181no—
643C2×C4—31no—
644C2×C4—31no—
645C2×C4—32no—
646C2×C4—32no—
647C2×C4—31no—
648C2×C4—62no—
649C2×C4—61no—
650C2×C4—61no—
651C2×C4—61no—
652C2×C4—61no—
653C2×C4—121no—
654C2×C4—184no—
655C2×C4—181no—
656C2×C4—181no—
657C2×C4—181no—
658C2×C4—362no—
659C2×C4—362no—
660C2×C4D3×D1211yescharacteristic
661C2×C4D3×D1211yescharacteristic
662C2×C4C22×D3211yescharacteristic
663C8—21no—
664C8—21no—
665C8—61no—
666C8—61no—
667C2×C3—21no—
668C2×C3—21no—
669C2×C3—21no—
670C2×C3—62no—
671C2×C3C2×#89711yescharacteristic
672C2×C3D3×C22⋊Q811yescharacteristic
673C2×C3C2×#90411yescharacteristic
674C2×C3#574811yescharacteristic
675C2×C3D3×#13511yescharacteristic
676C2×C3#577711yescharacteristic
677D3—22no—
678D3—122no—
679D3—122no—
680D3—242no—
681C22—32no—
682C22—61no—
683C22—61no—
684C22—182no—
685C22—361no—
686C22—361no—
687C22C2×D3×D1211yescharacteristic
688C4—21no—
689C4—21no—
690C4—32no—
691C4—32no—
692C4—62no—
693C4—61no—
694C4—121no—
695C4—121no—
696C4—121no—
697C4—361no—
698C4—361no—
699C4—361no—
700C4D3×#23711yescharacteristic
701C4D32×Q811yescharacteristic
702C3—21no—
703C3#7902511yescharacteristic, complemented
704C3#8122911yescharacteristic, complemented
705C2—62no—
706C2—362no—
707C2D3×#89711yescharacteristic
708C2D3×#90411yescharacteristic
709C2#1059471111yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊C8C22
socleC22×C32C22×D4
prime radicalC2×#3799C22
hypercenterC4⋊C8D32
hypocenterC32#3076
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
2. #10593874C2semidirect
3. #10592546C2semidirect
4. C3×D3×C4⋊C8C2semidirect
5. C3×#4829C2semidirect
6. #10590804C2semidirect
7. #10590803C2semidirect
8. #10590764C2semidirect
9. #10590759C2semidirect
10. #10590707C2semidirect
11. #10590706C2semidirect
14. #10590308C2semidirect
15. #10590302C2semidirect
85. D3×C4⋊C8D3semidirect
87. #4829D3semidirect
104. #3799Q8semidirect
633. C32#3076semidirect
703. C3#79025semidirect
704. C3#81229semidirect

Maximal subgroups

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

subgroupindex
C4×#37992
#105938742
#105925462
C3×D3×C4⋊C82
C3×#48292
#105908042
#105908032
#105907642
#105907592
#105907072
#105907062
#105906902
#105903082
#105903022
#812293
#790253