Finite Group Databasebeta

← #11868619

Subgroups — #11868619

Order 1152.

824 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Dic3×#239C211yesmaximal, characteristic
2#10594477C211yesmaximal, characteristic, complemented
3#10592492C211yesmaximal, characteristic, complemented
4C3×#4804C211yesmaximal, characteristic
5C3×#4796C211yesmaximal, characteristic, complemented
6#10591630C211yesmaximal, characteristic, complemented
7#10591556C211yesmaximal, characteristic
8#10591545C211yesmaximal, characteristic, complemented
9#10590778C211yesmaximal, characteristic, complemented
10#10590767C211yesmaximal, characteristic, complemented
11#10590707C211yesmaximal, characteristic, complemented
12D3×Dic3⋊C8C211yesmaximal, characteristic, complemented
13#10590572C211yesmaximal, characteristic, complemented
14#10590472C211yesmaximal, characteristic, complemented
15#10590467C211yesmaximal, characteristic, complemented
16#81229—31nomaximal
17#78822—31nomaximal
18C2×C3×#239C2211yescharacteristic
19Q8×C3⋊Dic3C2211yescharacteristic
20#64097C2211yescharacteristic
21C3×Q8×Dic3C2211yescharacteristic
22C2×C3×D3×C8C2211yescharacteristic
23C3×#892C2211yescharacteristic
24C3×#890C2211yescharacteristic
25#63919C2211yescharacteristic
26#63899—21no—
27#63898—21no—
28#63898C2211yescharacteristic
29#63896—21no—
30Dic3×D12—21no—
31Dic3×D12C2211yescharacteristic
32C4×D3×Dic3—21no—
33C4×D3×Dic3C2211yescharacteristic
34#63869C2211yescharacteristic
35#63844—21no—
36#63841—21no—
37#63841C2211yescharacteristic
38#63841C2211yescharacteristic
39#63837—21no—
40C2×D3×C3⋊C8C2211yescharacteristic
41C32×#103C2211yescharacteristic
42#63662C2211yescharacteristic
43#63645C2211yescharacteristic
44#63641C2211yescharacteristic
45#63634C2211yescharacteristic
46C3×#835C2211yescharacteristic
47C3×#835C2211yescharacteristic
48C3×#821C2211yescharacteristic
49C3×#818C2211yescharacteristic
50C3×Dic3⋊C8C2211yescharacteristic
51C3×#809C2211yescharacteristic
52C3×#808C2211yescharacteristic
53#63576C2211yescharacteristic
54#63573C2211yescharacteristic
55#63573C2211yescharacteristic
56#63573C2211yescharacteristic
57#63572C2211yescharacteristic
58Dic3⋊(C3⋊C8)C2211yescharacteristic
59#63563C2211yescharacteristic
60#63562C2211yescharacteristic
61Dic3×#41—31no—
62#5688—31no—
63C4×#239—31no—
64#5517—31no—
65C3×#479—31no—
66C3×#416—31no—
67#5233—31no—
68#5106—31no—
69C2×Dic3⋊C8—31no—
70#5066—31no—
71#5022—31no—
72#4998—31no—
73#4890—31no—
74#4880—31no—
75#4870—31no—
76#4860—31no—
77#4847—31no—
78D3×C4⋊C8—31no—
79#4804—31no—
80#4804D311yescharacteristic
81#4799—31no—
82#4796D311yescharacteristic, complemented
83#4793—31no—
84#4793—31no—
85#4793—61no—
86#4791—31no—
87#4791—31no—
88#4766—31no—
89#4763—31no—
90#4761—31no—
91#4759—31no—
92C2×C32×Q8C2311yescharacteristic
93C2×#634—21no—
94C3×#239—22no—
95C3×#239Q814yescomplemented
96C2×C3×D12—21no—
97C2×C3×D12C2311yescharacteristic
98C2×C3×C4×D3—21no—
99C2×C3×C4×D3C2311yescharacteristic
100C2×#627—21no—
101C2×D3×Dic3—21no—
102C2×D3×Dic3—21no—
103C2×D3×Dic3D411yescharacteristic
104C2×D3×Dic3D411yescharacteristic
105C2×C32×C8C2311yescharacteristic
106C32×C4⋊C4C2311yescharacteristic
107C4⋊(C3⋊Dic3)—21no—
108C4⋊(C3⋊Dic3)C2311yescharacteristic
109C4⋊(C3⋊Dic3)C2311yescharacteristic
110#3750—21no—
111C4×C3⋊Dic3—21no—
112C4×C3⋊Dic3C2311yescharacteristic
113C2×C3⋊(C3⋊C8)C2311yescharacteristic
114C3×(C2×D3)⋊C4—21no—
115C3×C4⋊Dic3—21no—
116C3×C4⋊Dic3—21no—
117C3×C4⋊Dic3C2311yescharacteristic
118C3×C4⋊Dic3C2311yescharacteristic
119C3×C4⋊Dic3C2311yescharacteristic
120C3×Dic3⋊C4—21no—
121C3×C4×Dic3—21no—
122C3×C4×Dic3—21no—
123C3×C4×Dic3C2311yescharacteristic
124C2×C3×C3⋊C8C2311yescharacteristic
125C2×C3×C3⋊C8C2311yescharacteristic
126C3×D3×C8—22no—
127#3724—21no—
128#3724—21no—
129Dic3⋊Dic3—21no—
130(C2×D3)⋊Dic3—21no—
131(C2×D3)⋊Dic3—21no—
132(C2×D3)⋊Dic3—21no—
133(C2×D3)⋊Dic3—21no—
134Dic32—21no—
135Dic32—21no—
136Dic32D411yescharacteristic
137Dic32D411yescharacteristic
138D3×C3⋊C8—22no—
139#3076—91noSylow
140C2×C3×#41—31no—
141C2×#239C2×D311yescharacteristic
142C22×C3×C8—31no—
143C3×#125—31no—
144C3×C4×Q8—31no—
145C3×#117—31no—
146Q8×Dic3—31no—
147Q8×Dic3—31no—
148Q8×Dic3—61no—
149Q8×Dic3C2×D311yescharacteristic
150D4×Dic3—31no—
151D4×Dic3—31no—
152D4×Dic3—61no—
153D4×Dic3—61no—
154#926—31no—
155#926—31no—
156#926—61no—
157C2×C4×Dic3—31no—
158C2×C4×Dic3—61no—
159C22×C3⋊C8—31no—
160C2×D3×C8—31no—
161C2×D3×C8C2×D311yescharacteristic
162#896—61no—
163#896—61no—
164#893—31no—
165#893—61no—
166#892—31no—
167#892—31no—
168#892—61no—
169#892C2×D311yescharacteristic
170#890—31no—
171#890C2×D311yescharacteristic
172#888—31no—
173#888—31no—
174#888—31no—
175#888—31no—
176#888—61no—
177#887—61no—
178#887—61no—
179#878—61no—
180#878—61no—
181C4×D12—31no—
182C4×D12—61no—
183C42×D3—31no—
184C42×D3—61no—
185#870—31no—
186C4×Dic6—61no—
187C4×Dic6—61no—
188C3×#107—31no—
189C3×#106—31no—
190C3×C4⋊C8—31no—
191C3×#103—21no—
192C3×#103—31no—
193C3×#103—31no—
194C3×#103C2×D311yescharacteristic
195C3×#103C2×D311yescharacteristic
196C3×#102—31no—
197C3×#102—31no—
198#835—31no—
199#835—31no—
200#835—61no—
201#835C2×D311yescharacteristic
202#835C2×D311yescharacteristic
203#832—31no—
204#832—31no—
205#821—31no—
206#821C2×D311yescharacteristic
207#818—31no—
208#818—31no—
209#818—61no—
210#818C2×D311yescharacteristic
211#817—31no—
212#817—31no—
213#817—31no—
214Dic3⋊C8—31no—
215Dic3⋊C8—31no—
216Dic3⋊C8—31no—
217Dic3⋊C8—31no—
218Dic3⋊C8—31no—
219Dic3⋊C8—61no—
220Dic3⋊C8C2×D311yescharacteristic
221#809—31no—
222#809C2×D311yescharacteristic
223#808—31no—
224#808—31no—
225#808—31no—
226#808C2×D311yescharacteristic
227#807—31no—
228#807—31no—
229#807—31no—
230#807—31no—
231#807—61no—
232C4⋊(C3⋊C8)—31no—
233C22×C3×D3—21no—
234C22×C3×D3C2×D411yescharacteristic
235C32×Q8—21no—
236C32×Q8C2×Q812yes—
237C2×C32×C4—21no—
238C2×C32×C4—21no—
239C2×C32×C4C2411yescharacteristic
240C2×C3⋊Dic3—21no—
241C2×C3⋊Dic3—21no—
242C2×C3⋊Dic3C2×D411yescharacteristic
243C2×C3⋊Dic3C2×D411yescharacteristic
244#634—42no—
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×D12—24no—
252C3×D12—21no—
253C3×D12C2×Q812yes—
254C3×C4×D3—24no—
255C3×C4×D3C2×Q812yes—
256C3×C4×D3#4112yes—
257#627—42no—
258D3×Dic3—22no—
259D3×Dic3—41no—
260D3×Dic3—42no—
261D3×Dic3—42no—
262C32×C8—21no—
263C3⋊(C3⋊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—91no—
279#416—31no—
280#416—91no—
281C3×#41—34no—
282C3×#41—62no—
283C2×C3×Q8—21no—
284C2×C3×Q8C22×D311yescharacteristic
285C2×C3×Q8C22×D311yescharacteristic
286C2×C3×D4—31no—
287C2×C3×D4—61no—
288C22×C3×C4—31no—
289C22×C3×C4—61no—
290C22×Dic3—31no—
291C22×Dic3—31no—
292C22×Dic3—61no—
293C22×Dic3—61no—
294#239—22no—
295#239Dic614yescomplemented
296C2×D12—21no—
297C2×D12C22×D311yescharacteristic
298C2×C4×D3—21no—
299C2×C4×D3—31no—
300C2×C4×D3—31no—
301C2×C4×D3—61no—
302C2×C4×D3—61no—
303C2×C4×D3C22×D311yescharacteristic
304C2×Dic6—61no—
305C2×Dic6—61no—
306C2×Dic6—61no—
307C2×Dic6—61no—
308C2×Dic6—121no—
309C2×C3×C8—21no—
310C2×C3×C8—31no—
311C2×C3×C8—31no—
312C2×C3×C8—62no—
313C2×C3×C8C22×D311yescharacteristic
314C2×C3×C8C22×D311yescharacteristic
315C3×C4⋊C4—21no—
316C3×C4⋊C4—31no—
317C3×C4⋊C4—31no—
318C3×C4⋊C4—31no—
319C3×C4⋊C4—61no—
320C3×C4⋊C4—61no—
321C3×C4⋊C4—61no—
322C3×C4⋊C4C22×D311yescharacteristic
323C3×C4⋊C4C22×D311yescharacteristic
324C3×C22⋊C4—61no—
325C3×C42—31no—
326C3×C42—61no—
327C3×C42—61no—
328#217—61no—
329#217—61no—
330#217—61no—
331#217—61no—
332(C2×D3)⋊C4—21no—
333(C2×D3)⋊C4—61no—
334(C2×D3)⋊C4—61no—
335(C2×D3)⋊C4—61no—
336(C2×D3)⋊C4—61no—
337C4⋊Dic3—21no—
338C4⋊Dic3—21no—
339C4⋊Dic3—31no—
340C4⋊Dic3—31no—
341C4⋊Dic3—31no—
342C4⋊Dic3—31no—
343C4⋊Dic3—61no—
344C4⋊Dic3—61no—
345C4⋊Dic3—61no—
346C4⋊Dic3—61no—
347C4⋊Dic3—61no—
348C4⋊Dic3—121no—
349C4⋊Dic3C22×D311yescharacteristic
350C4⋊Dic3C22×D311yescharacteristic
351C4⋊Dic3C22×D311yescharacteristic
352Dic3⋊C4—21no—
353Dic3⋊C4—61no—
354Dic3⋊C4—61no—
355Dic3⋊C4—61no—
356Dic3⋊C4—61no—
357Dic3⋊C4—61no—
358Dic3⋊C4—61no—
359Dic3⋊C4—61no—
360Dic3⋊C4—121no—
361C4×Dic3—21no—
362C4×Dic3—21no—
363C4×Dic3—31no—
364C4×Dic3—31no—
365C4×Dic3—31no—
366C4×Dic3—31no—
367C4×Dic3—31no—
368C4×Dic3—31no—
369C4×Dic3—61no—
370C4×Dic3—61no—
371C4×Dic3—61no—
372C4×Dic3—61no—
373C4×Dic3—61no—
374C4×Dic3—61no—
375C4×Dic3—61no—
376C4×Dic3—121no—
377C4×Dic3C22×D311yescharacteristic
378C2×C3⋊C8—31no—
379C2×C3⋊C8—31no—
380C2×C3⋊C8—61no—
381C2×C3⋊C8—62no—
382C2×C3⋊C8C22×D311yescharacteristic
383C2×C3⋊C8C22×D311yescharacteristic
384D3×C8—22no—
385D3×C8—62no—
386C22×C32C22×D411yescharacteristic
387C2×C3×D3—21no—
388C2×C3×D3—21no—
389C2×C3×D3—22no—
390C2×C3×D3—41no—
391C2×C3×D3—41no—
392C2×C3×D3C22⋊Q812yes—
393C32×C4—22no—
394C32×C4—41no—
395C32×C4C22×Q811yescharacteristic
396C32×C4C2×#4111yescharacteristic
397C3⋊Dic3—21no—
398C3⋊Dic3—41no—
399C3⋊Dic3—41no—
400C3⋊Dic3#13512yes—
401C3×Dic3—21no—
402C3×Dic3—21no—
403C3×Dic3—41no—
404C3×Dic3—41no—
405C3×Dic3—41no—
406C3×Dic3C22⋊Q812yes—
407C2×#41—31no—
408C22×C8—31no—
409C22×C8—91no—
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—31no—
425#117—91no—
426#117—91no—
427#117—181no—
428C2×C42—91no—
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—91no—
440C4⋊C8—91no—
441C4⋊C8—91no—
442#103—31no—
443#103—31no—
444#103—91no—
445#103D3211yescharacteristic
446#102—31no—
447#102—31no—
448#102—91no—
449#102—91no—
450C23×C3—31no—
451C23×C3—61no—
452C22×D3—21no—
453C22×D3D3×D411yescharacteristic
454C3×Q8—21no—
455C3×Q8—21no—
456C3×Q8—22no—
457C3×Q8—41no—
458C3×Q8C2×Dic612yes—
459C3×Q8D3×Q812yes—
460C3×D4—32no—
461C3×D4—64no—
462C3×D4—61no—
463C2×C3×C4—21no—
464C2×C3×C4—21no—
465C2×C3×C4—21no—
466C2×C3×C4—21no—
467C2×C3×C4—21no—
468C2×C3×C4—31no—
469C2×C3×C4—32no—
470C2×C3×C4—32no—
471C2×C3×C4—31no—
472C2×C3×C4—31no—
473C2×C3×C4—41no—
474C2×C3×C4—41no—
475C2×C3×C4—64no—
476C2×C3×C4—61no—
477C2×C3×C4—61no—
478C2×C3×C4—61no—
479C2×C3×C4C23×D311yescharacteristic
480C2×C3×C4C23×D311yescharacteristic
481C2×Dic3—21no—
482C2×Dic3—21no—
483C2×Dic3—21no—
484C2×Dic3—31no—
485C2×Dic3—31no—
486C2×Dic3—31no—
487C2×Dic3—31no—
488C2×Dic3—61no—
489C2×Dic3—61no—
490C2×Dic3—62no—
491C2×Dic3—61no—
492C2×Dic3—61no—
493C2×Dic3—61no—
494C2×Dic3—61no—
495C2×Dic3—121no—
496C2×Dic3—121no—
497C2×Dic3—121no—
498C2×Dic3—122no—
499C2×Dic3—122no—
500C2×Dic3D3×D411yescharacteristic
501C2×Dic3D3×D411yescharacteristic
502C2×Dic3D3×D411yescharacteristic
503D12—24no—
504D12—21no—
505D12C2×Dic612yes—
506C4×D3—24no—
507C4×D3—62no—
508C4×D3—122no—
509C4×D3—121no—
510C4×D3—122no—
511C4×D3C2×Dic612yes—
512C4×D3#23712yes—
513Dic6—122no—
514Dic6—122no—
515Dic6—122no—
516Dic6—122no—
517Dic6—242no—
518C3×C8—21no—
519C3×C8—21no—
520C3×C8—41no—
521C3×C8—61no—
522C3×C8—61no—
523C3⋊C8—21no—
524C3⋊C8—21no—
525C3⋊C8—61no—
526C3⋊C8—61no—
527C3⋊C8—121no—
528C2×C32C2×C22⋊Q811yescharacteristic
529C2×C32C2×#13511yescharacteristic
530C2×C32#57511yescharacteristic
531C3×D3—22no—
532C3×D3—42no—
533#41—34no—
534#41—62no—
535C2×Q8—181no—
536C2×Q8—181no—
537C2×Q8C2×D3211yescharacteristic
538C2×D4—31no—
539C2×D4—61no—
540C22×C4—31no—
541C22×C4—61no—
542C22×C4—91no—
543C22×C4—91no—
544C22×C4—181no—
545C22×C4—181no—
546C2×C8—31no—
547C2×C8—31no—
548C2×C8—62no—
549C2×C8—91no—
550C2×C8—182no—
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—181no—
561C4⋊C4—181no—
562C4⋊C4—181no—
563C4⋊C4—181no—
564C4⋊C4—181no—
565C4⋊C4C2×D3211yescharacteristic
566C22⋊C4—61no—
567C22⋊C4—181no—
568C22⋊C4—181no—
569C22⋊C4—181no—
570C22⋊C4—181no—
571C42—31no—
572C42—61no—
573C42—61no—
574C42—91no—
575C42—91no—
576C42—91no—
577C42—181no—
578C42—181no—
579C42—181no—
580C22×C3—21no—
581C22×C3—32no—
582C22×C3—61no—
583C22×C3—61no—
584C22×C3—62no—
585C22×C3—121no—
586C22×C3—121no—
587C22×C3C2×D3×D411yescharacteristic
588C22×C3C2×D3×D411yescharacteristic
589C2×D3—21no—
590C2×D3—21no—
591C2×D3—22no—
592C2×D3—41no—
593C2×D3—41no—
594C2×D3#87812yes—
595C3×C4—22no—
596C3×C4—22no—
597C3×C4—21no—
598C3×C4—21no—
599C3×C4—32no—
600C3×C4—42no—
601C3×C4—41no—
602C3×C4—41no—
603C3×C4—61no—
604C3×C4—61no—
605C3×C4—81no—
606C3×C4—121no—
607C3×C4—121no—
608C3×C4—121no—
609C3×C4C22×Dic611yescharacteristic
610C3×C4C2×#23711yescharacteristic
611C3×C4C2×D3×Q811yescharacteristic
612C3×C4D3×#4111yescharacteristic
613Dic3—21no—
614Dic3—21no—
615Dic3—32no—
616Dic3—32no—
617Dic3—41no—
618Dic3—41no—
619Dic3—41no—
620Dic3—62no—
621Dic3—61no—
622Dic3—61no—
623Dic3—121no—
624Dic3—121no—
625Dic3—121no—
626Dic3—121no—
627Dic3—121no—
628Dic3—241no—
629Dic3—241no—
630Dic3#87812yes—
631C32#307611yescharacteristic, complemented, Sylow
632C23—31no—
633C23—61no—
634Q8—21no—
635Q8—362no—
636Q8—362no—
637Q8D3×Dic612yes—
638D4—32no—
639D4—64no—
640D4—61no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—31no—
644C2×C4—32no—
645C2×C4—32no—
646C2×C4—31no—
647C2×C4—31no—
648C2×C4—64no—
649C2×C4—61no—
650C2×C4—61no—
651C2×C4—61no—
652C2×C4—91no—
653C2×C4—91no—
654C2×C4—182no—
655C2×C4—181no—
656C2×C4—181no—
657C2×C4—361no—
658C2×C4—362no—
659C2×C4—362no—
660C2×C4C22×D3211yescharacteristic
661C8—21no—
662C8—61no—
663C8—61no—
664C8—181no—
665C2×C3—21no—
666C2×C3—21no—
667C2×C3—21no—
668C2×C3—62no—
669C2×C3—122no—
670C2×C3C2×#87811yescharacteristic
671C2×C3D3×C22⋊Q811yescharacteristic
672C2×C3D3×#13511yescharacteristic
673C2×C3D3×#13511yescharacteristic
674C2×C3#576811yescharacteristic
675C2×C3#577711yescharacteristic
676D3—22no—
677D3—42no—
678C22—32no—
679C22—61no—
680C22—61no—
681C22—62no—
682C22—121no—
683C22—121no—
684C22D32×D411yescharacteristic
685C4—22no—
686C4—32no—
687C4—41no—
688C4—61no—
689C4—61no—
690C4—92no—
691C4—121no—
692C4—121no—
693C4—121no—
694C4—181no—
695C4—361no—
696C4—361no—
697C4C2×D3×Dic611yescharacteristic
698C4D3×#23711yescharacteristic
699C3—21no—
700C3#7882211yescharacteristic, complemented
701C3#8122911yescharacteristic, complemented
702C2—62no—
703C2—122no—
704C2D3×#87811yescharacteristic
705C2#1059474611yescharacteristic
706C2#1059476411yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#103C22
socleC22×C32C22×D4
prime radicalC2×C3×#239C22
hypercenter#103D32
hypocenterC32#3076
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
2. #10594477C2semidirect
3. #10592492C2semidirect
5. C3×#4796C2semidirect
6. #10591630C2semidirect
8. #10591545C2semidirect
9. #10590778C2semidirect
10. #10590767C2semidirect
11. #10590707C2semidirect
12. D3×Dic3⋊C8C2semidirect
13. #10590572C2semidirect
14. #10590472C2semidirect
15. #10590467C2semidirect
82. #4796D3semidirect
95. C3×#239Q8semidirect
295. #239Dic6semidirect
631. C32#3076semidirect
700. C3#78822semidirect
701. C3#81229semidirect

Maximal subgroups

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

subgroupindex
Dic3×#2392
#105944772
#105924922
C3×#48042
C3×#47962
#105916302
#105915562
#105915452
#105907782
#105907672
#105907072
D3×Dic3⋊C82
#105905722
#105904722
#105904672
#812293
#788223