Finite Group Databasebeta

← #11895851

Subgroups — #11895851

Order 1152.

794 conjugacy classes of subgroups.

The subgroup lattice has 721 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Dic6×D12C211yesmaximal, characteristic, complemented
2#10593850C211yesmaximal, characteristic, complemented
3#10592413C211yesmaximal, characteristic, complemented
4C3×#4710C211yesmaximal, characteristic, complemented
5C3×#4701C211yesmaximal, characteristic, complemented
6#10590893C211yesmaximal, characteristic, complemented
7#10590890C211yesmaximal, characteristic, complemented
8#10590805C211yesmaximal, characteristic, complemented
9#10590764C211yesmaximal, characteristic, complemented
10#10590754C211yesmaximal, characteristic
11#10590752C211yesmaximal, characteristic, complemented
12#10590747C211yesmaximal, characteristic, complemented
13#10590745C211yesmaximal, characteristic
14#10590366C211yesmaximal, characteristic
15#10590283C211yesmaximal, characteristic, complemented
16#79970—31nomaximal
17#79751—31nomaximal
18C2×D3×Dic6—21no—
19#64084C2211yescharacteristic
20#64078C2211yescharacteristic
21C2×C3×#204C2211yescharacteristic
22C3×C4×D12C2211yescharacteristic
23C3×C4×Dic6C2211yescharacteristic
24C3×C4×Dic6C2211yescharacteristic
25#63918C2211yescharacteristic
26#63918C2211yescharacteristic
27#63894C2211yescharacteristic
28#63893—21no—
29#63893—21no—
30Dic3×D12C2211yescharacteristic
31Dic3×D12C2211yescharacteristic
32#63888—21no—
33#63868—21no—
34#63866C2211yescharacteristic
35#63864C2211yescharacteristic
36#63857—21no—
37#63848—21no—
38#63844C2211yescharacteristic
39#63836—21no—
40C2×#3716C2211yescharacteristic
41C2×#3714C2211yescharacteristic
42C32×#97C2211yescharacteristic
43#63648C2211yescharacteristic
44#63648C2211yescharacteristic
45#63643C2211yescharacteristic
46#63643C2211yescharacteristic
47C3×#821C2211yescharacteristic
48C3×#818C2211yescharacteristic
49C3×#816C2211yescharacteristic
50C3×#815C2211yescharacteristic
51C3×Dic3⋊C8C2211yescharacteristic
52C3×Dic3⋊C8C2211yescharacteristic
53C3×C8×Dic3C2211yescharacteristic
54C3×C4⋊(C3⋊C8)C2211yescharacteristic
55#63575C2211yescharacteristic
56#63575C2211yescharacteristic
57#63567C2211yescharacteristic
58#63566C2211yescharacteristic
59#63566C2211yescharacteristic
60#63564C2211yescharacteristic
61#5584—31no—
62Q8×D12—31no—
63#5568—31no—
64D4×Dic6—31no—
65C3×#446—31no—
66C3×#440—31no—
67#5165—31no—
68#5162—31no—
69#5021—31no—
70#5016—31no—
71#4890—31no—
72#4875—31no—
73#4850—31no—
74#4850—31no—
75#4846—31no—
76#4844—31no—
77#4844—31no—
78#4841—31no—
79#4794—31no—
80#4792—31no—
81#4757—31no—
82#4756—31no—
83#4714—31no—
84#4714—31no—
85#4714—31no—
86#4714—61no—
87#4710—31no—
88#4710D311yescharacteristic, complemented
89#4701D311yescharacteristic, complemented
90C4×D24—31no—
91#4681—31no—
92C2×C4⋊(C3⋊D3)C2311yescharacteristic
93C2×#634—21no—
94C2×#634C2311yescharacteristic
95C2×C3×D12C2311yescharacteristic
96C2×C3×C4×D3—21no—
97C2×C3×Dic6D411yescharacteristic
98C2×C3×Dic6C2311yescharacteristic
99C2×#627—21no—
100C2×#627—21no—
101C2×#624—21no—
102C2×D3×Dic3—21no—
103C2×D3×Dic3—21no—
104D3×Dic6—44no—
105C2×C32×C8C2311yescharacteristic
106C2×C32×C8C2311yescharacteristic
107C32×C42C2311yescharacteristic
108#3752—21no—
109#3752—21no—
110C4⋊(C3⋊Dic3)—21no—
111C4⋊(C3⋊Dic3)C2311yescharacteristic
112C4⋊(C3⋊Dic3)C2311yescharacteristic
113C3×(C2×D3)⋊C4—21no—
114C3×C4⋊Dic3D411yescharacteristic
115C3×C4⋊Dic3C2311yescharacteristic
116C3×C4⋊Dic3C2311yescharacteristic
117C3×Dic3⋊C4—21no—
118C3×Dic3⋊C4D411yescharacteristic
119C3×Dic3⋊C4D411yescharacteristic
120C3×C4×Dic3—21no—
121C3×C4×Dic3C2311yescharacteristic
122C3×C4×Dic3C2311yescharacteristic
123C2×C3×C3⋊C8C2311yescharacteristic
124C2×C3×C3⋊C8C2311yescharacteristic
125C3×#204—22no—
126#3724—21no—
127Dic3⋊Dic3—21no—
128Dic3⋊Dic3—21no—
129Dic3⋊Dic3—21no—
130Dic3⋊Dic3—21no—
131#3722—21no—
132#3722—21no—
133#3722—21no—
134(C2×D3)⋊Dic3—21no—
135(C2×D3)⋊Dic3—21no—
136Dic32—21no—
137#3716—22no—
138#3714—22no—
139#3367—91noSylow
140C2×D3×Q8—61no—
141C22×Dic6—61no—
142C2×C3×SD16—31no—
143C3×C4×Q8—31no—
144C3×C4×Q8—31no—
145C3×C4×D4—31no—
146#947—31no—
147#946—61no—
148#944—31no—
149D4×Dic3—31no—
150D4×Dic3—31no—
151C2×#214—31no—
152C2×#213—31no—
153#924—61no—
154C2×D24—31no—
155C2×#204—31no—
156C2×#204C2×D311yescharacteristic
157#898—61no—
158#898—61no—
159#898—61no—
160#897—61no—
161#897—61no—
162#897—61no—
163#896—61no—
164#893—31no—
165#892—61no—
166#888—31no—
167#888—31no—
168#887—31no—
169#878—61no—
170#878—61no—
171#876—61no—
172#875—31no—
173#875—31no—
174#875—31no—
175#875—61no—
176C4×D12—31no—
177C4×D12—31no—
178C4×D12—31no—
179C4×D12C2×D311yescharacteristic
180#872—61no—
181#869—31no—
182#869—31no—
183#869—31no—
184#869—31no—
185#869—31no—
186#869—61no—
187C4×Dic6—31no—
188C4×Dic6C2×D311yescharacteristic
189C4×Dic6C2×D311yescharacteristic
190C3×#107—31no—
191C3×C4⋊C8—31no—
192C3×C4⋊C8—31no—
193C3×C4⋊C8—31no—
194C3×#103—31no—
195C3×#102—31no—
196C3×#97—21no—
197C3×#97—31no—
198C3×#97C2×D311yescharacteristic
199C3×#97C2×D311yescharacteristic
200C3×C4×C8—31no—
201#835—31no—
202#835—31no—
203#821—31no—
204#821—31no—
205#821—31no—
206#821—31no—
207#821—31no—
208#821—61no—
209#821—61no—
210#821C2×D311yescharacteristic
211#818—31no—
212#818—31no—
213#818C2×D311yescharacteristic
214#816—31no—
215#816—31no—
216#816—31no—
217#816—31no—
218#816—31no—
219#816—31no—
220#816—31no—
221#816—61no—
222#816—61no—
223#816C2×D311yescharacteristic
224#815C2×D311yescharacteristic
225Dic3⋊C8C2×D311yescharacteristic
226Dic3⋊C8C2×D311yescharacteristic
227C8×Dic3C2×D311yescharacteristic
228#810—31no—
229#809—31no—
230#807—31no—
231#807—31no—
232C4⋊(C3⋊C8)C2×D311yescharacteristic
233C22×C3⋊D3—21no—
234C22×C3×D3—21no—
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)—21no—
243#634—21no—
244#634—21no—
245#634—42no—
246C2×C3×Dic3—21no—
247C2×C3×Dic3—21no—
248C2×C3×Dic3—21no—
249C2×C3×Dic3C2×D411yescharacteristic
250C2×C3×Dic3C2×D411yescharacteristic
251C2×C3×Dic3C2×D411yescharacteristic
252C2×C3×Dic3C2×D411yescharacteristic
253C3×D12—21no—
254C3×D12#4112yes—
255C3×C4×D3—42no—
256C3×Dic6—22no—
257C3×Dic6—21no—
258C3×Dic6—21no—
259#627—42no—
260#627—42no—
261#624—42no—
262D3×Dic3—42no—
263D3×Dic3—42no—
264C32×C8—21no—
265C32×C8—21no—
266C3×C3⋊C8—21no—
267C3×C3⋊C8—21no—
268#556—91no—
269D4×Q8—91no—
270#489—91no—
271#489—91no—
272#487—91no—
273#477—91no—
274#477—91no—
275#474—91no—
276#463—91no—
277#463—91no—
278#461—91no—
279#446—31no—
280#440—31no—
281#440—91no—
282C4×D8—91no—
283C2×C3×Q8—31no—
284C2×C3×Q8—31no—
285C2×C3×D4—31no—
286C22×C3×C4—61no—
287C22×Dic3—61no—
288C22×Dic3—61no—
289D3×Q8—124no—
290C2×D12—31no—
291C2×D12—31no—
292C2×D12—61no—
293C2×D12C22×D311yescharacteristic
294C2×C4×D3—21no—
295C2×C4×D3—61no—
296C2×C4×D3—61no—
297C2×C4×D3—61no—
298C2×C4×D3—61no—
299C2×Dic6—31no—
300C2×Dic6—31no—
301C2×Dic6—61no—
302C2×Dic6—61no—
303C2×Dic6—61no—
304C2×Dic6—61no—
305C2×Dic6—61no—
306C2×Dic6—61no—
307C2×Dic6—61no—
308C2×Dic6—121no—
309C2×Dic6—124no—
310C2×Dic6D1211yescharacteristic
311C2×Dic6C22×D311yescharacteristic
312C3×SD16—62no—
313C2×C3×C8—21no—
314C2×C3×C8—21no—
315C2×C3×C8—31no—
316C2×C3×C8—31no—
317C2×C3×C8C22×D311yescharacteristic
318C2×C3×C8C22×D311yescharacteristic
319C2×C3×C8C22×D311yescharacteristic
320C2×C3×C8C22×D311yescharacteristic
321C3×C4⋊C4—31no—
322C3×C4⋊C4—31no—
323C3×C4⋊C4—31no—
324C3×C4⋊C4—31no—
325C3×C4⋊C4—31no—
326C3×C4⋊C4—61no—
327C3×C22⋊C4—61no—
328C3×C42—21no—
329C3×C42—31no—
330C3×C42—31no—
331C3×C42—61no—
332C3×C42C22×D311yescharacteristic
333C3×C42C22×D311yescharacteristic
334#217—61no—
335#217—61no—
336#214—62no—
337#213—62no—
338(C2×D3)⋊C4—21no—
339(C2×D3)⋊C4—61no—
340(C2×D3)⋊C4—61no—
341(C2×D3)⋊C4—61no—
342(C2×D3)⋊C4—61no—
343(C2×D3)⋊C4—61no—
344(C2×D3)⋊C4—61no—
345(C2×D3)⋊C4—61no—
346(C2×D3)⋊C4—61no—
347(C2×D3)⋊C4—61no—
348(C2×D3)⋊C4—61no—
349(C2×D3)⋊C4—61no—
350(C2×D3)⋊C4—61no—
351(C2×D3)⋊C4—121no—
352(C2×D3)⋊C4—121no—
353C4⋊Dic3—31no—
354C4⋊Dic3—31no—
355C4⋊Dic3—31no—
356C4⋊Dic3—31no—
357C4⋊Dic3—61no—
358C4⋊Dic3—61no—
359C4⋊Dic3—61no—
360C4⋊Dic3—61no—
361C4⋊Dic3—61no—
362C4⋊Dic3—61no—
363C4⋊Dic3—61no—
364C4⋊Dic3—61no—
365C4⋊Dic3—121no—
366C4⋊Dic3D1211yescharacteristic
367C4⋊Dic3C22×D311yescharacteristic
368C4⋊Dic3C22×D311yescharacteristic
369Dic3⋊C4—21no—
370Dic3⋊C4—61no—
371Dic3⋊C4—61no—
372Dic3⋊C4—61no—
373Dic3⋊C4—61no—
374Dic3⋊C4—61no—
375Dic3⋊C4—61no—
376Dic3⋊C4D1211yescharacteristic
377Dic3⋊C4D1211yescharacteristic
378C4×Dic3—21no—
379C4×Dic3—61no—
380C4×Dic3—61no—
381C4×Dic3C22×D311yescharacteristic
382C4×Dic3C22×D311yescharacteristic
383C2×C3⋊C8C22×D311yescharacteristic
384C2×C3⋊C8C22×D311yescharacteristic
385D24—62no—
386#204—22no—
387#204—62no—
388C22×C32C22×D411yescharacteristic
389C2×C3⋊D3—41no—
390C2×C3⋊D3—41no—
391C2×C3⋊D3—41no—
392C2×C3×D3—22no—
393C2×C3×D3—41no—
394C2×C3×D3—41no—
395C32×C4—21no—
396C32×C4—21no—
397C32×C4C2×#4111yescharacteristic
398C32×C42−1+411yescharacteristic
399C3⋊Dic3—41no—
400C3⋊Dic3—41no—
401C3⋊Dic3—41no—
402C3×Dic3—21no—
403C3×Dic3—21no—
404C3×Dic3—21no—
405C3×Dic3—41no—
406C3×Dic3—41no—
407C3×Dic3—41no—
408C3×Dic3AGL(1,ℤ/8)12yes—
409C22×Q8—181no—
410C2×SD16—31no—
411C2×SD16—91no—
412C2×D8—91no—
413C4⋊Q8—91no—
414C4⋊Q8—91no—
415C4⋊Q8—91no—
416C4⋊Q8—91no—
417#126—181no—
418#126—181no—
419#124—91no—
420#124—91no—
421C22⋊Q8—181no—
422C22⋊Q8—181no—
423C22⋊Q8—181no—
424C22⋊Q8—181no—
425C4×Q8—31no—
426C4×Q8—31no—
427C4×Q8—91no—
428C4×D4—31no—
429C4×D4—91no—
430C4×D4—91no—
431C4×D4—91no—
432#117—181no—
433#107—31no—
434#107—91no—
435#107—91no—
436C4⋊C8—31no—
437C4⋊C8—31no—
438C4⋊C8—31no—
439#103—31no—
440#103—91no—
441#103—91no—
442#103—91no—
443#103—91no—
444#103—91no—
445#102—31no—
446#102—91no—
447#102—91no—
448#102—91no—
449#97—31no—
450#97D3211yescharacteristic
451C4×C8—31no—
452C23×C3—61no—
453C22×D3—21no—
454C22×D3—61no—
455C22×D3—61no—
456C22×D3—121no—
457C3×Q8—62no—
458C3×Q8—61no—
459C3×Q8—61no—
460C3×D4—32no—
461C3×D4—61no—
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—61no—
470C2×C3×C4—61no—
471C2×C3×C4—61no—
472C2×C3×C4—122no—
473C2×C3×C4C2×D1211yescharacteristic
474C2×C3×C4C2×D1211yescharacteristic
475C2×C3×C4D3×D411yescharacteristic
476C2×C3×C4D3×D411yescharacteristic
477C2×C3×C4C23×D311yescharacteristic
478C2×C3×C4C23×D311yescharacteristic
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×Dic3—122no—
492C2×Dic3—122no—
493C2×Dic3C2×D1211yescharacteristic
494C2×Dic3C2×D1211yescharacteristic
495C2×Dic3C2×D1211yescharacteristic
496C2×Dic3C2×D1211yescharacteristic
497D12—21no—
498D12—61no—
499D12—61no—
500D12—61no—
501D12—61no—
502D12—121no—
503D12—121no—
504D12#23512yes—
505C4×D3—42no—
506C4×D3—122no—
507C4×D3—122no—
508C4×D3—122no—
509C4×D3—122no—
510Dic6—22no—
511Dic6—21no—
512Dic6—21no—
513Dic6—61no—
514Dic6—61no—
515Dic6—61no—
516Dic6—61no—
517Dic6—121no—
518Dic6—121no—
519Dic6—122no—
520Dic6—122no—
521Dic6—122no—
522Dic6—122no—
523Dic6—122no—
524Dic6—122no—
525Dic6—242no—
526C3×C8—21no—
527C3×C8—21no—
528C3×C8—21no—
529C3×C8—21no—
530C3×C8—41no—
531C3×C8—41no—
532C3×C8—61no—
533C3×C8—61no—
534C3⋊C8—21no—
535C3⋊C8—21no—
536C2×C32#54811yescharacteristic
537C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
538C2×C32#57811yescharacteristic
539C3⋊D3—81no—
540C3×D3—42no—
541C2×Q8—31no—
542C2×Q8—31no—
543C2×Q8—91no—
544C2×Q8—181no—
545C2×Q8—181no—
546C2×Q8—181no—
547C2×Q8—364no—
548C2×D4—31no—
549C2×D4—91no—
550C22×C4—61no—
551C22×C4—181no—
552C22×C4—181no—
553C22×C4—181no—
554SD16—62no—
555SD16—182no—
556D8—182no—
557C2×C8—31no—
558C2×C8—31no—
559C2×C8C2×D3211yescharacteristic
560C2×C8C2×D3211yescharacteristic
561C4⋊C4—31no—
562C4⋊C4—31no—
563C4⋊C4—31no—
564C4⋊C4—31no—
565C4⋊C4—31no—
566C4⋊C4—61no—
567C4⋊C4—91no—
568C4⋊C4—91no—
569C4⋊C4—181no—
570C4⋊C4—181no—
571C4⋊C4—181no—
572C4⋊C4—181no—
573C4⋊C4—181no—
574C4⋊C4—181no—
575C22⋊C4—61no—
576C22⋊C4—181no—
577C22⋊C4—181no—
578C22⋊C4—181no—
579C22⋊C4—181no—
580C22⋊C4—181no—
581C22⋊C4—181no—
582C22⋊C4—181no—
583C42—31no—
584C42—31no—
585C42—61no—
586C42—181no—
587C42C2×D3211yescharacteristic
588C22×C3—21no—
589C22×C3—62no—
590C22×C3—121no—
591C22×C3—121no—
592C22×C3C22×D1211yescharacteristic
593C22×C3C2×D3×D411yescharacteristic
594C2×D3—22no—
595C2×D3—41no—
596C2×D3—41no—
597C2×D3—121no—
598C2×D3—121no—
599C2×D3—121no—
600C2×D3—121no—
601C2×D3—121no—
602C2×D3—121no—
603C2×D3—241no—
604C2×D3—241no—
605C2×D3—241no—
606C3×C4—21no—
607C3×C4—21no—
608C3×C4—21no—
609C3×C4—21no—
610C3×C4—21no—
611C3×C4—21no—
612C3×C4—32no—
613C3×C4—41no—
614C3×C4—41no—
615C3×C4—61no—
616C3×C4—61no—
617C3×C4—61no—
618C3×C4—121no—
619C3×C4—121no—
620C3×C4—121no—
621C3×C4C2×#23511yescharacteristic
622C3×C4#100711yescharacteristic
623C3×C4D3×#4111yescharacteristic
624C3×C4#101011yescharacteristic
625Dic3—21no—
626Dic3—21no—
627Dic3—21no—
628Dic3—41no—
629Dic3—41no—
630Dic3—41no—
631Dic3—121no—
632Dic3—121no—
633Dic3—121no—
634Dic3—121no—
635Dic3—121no—
636Dic3—121no—
637Dic3—241no—
638Dic3—241no—
639Dic3—241no—
640Dic3#90812yes—
641C32#336711yescharacteristic, complemented, Sylow
642C23—61no—
643C23—181no—
644Q8—62no—
645Q8—61no—
646Q8—61no—
647Q8—181no—
648Q8—181no—
649Q8—362no—
650Q8—362no—
651Q8—362no—
652D4—32no—
653D4—61no—
654D4—181no—
655D4—181no—
656C2×C4—31no—
657C2×C4—31no—
658C2×C4—31no—
659C2×C4—31no—
660C2×C4—61no—
661C2×C4—61no—
662C2×C4—61no—
663C2×C4—122no—
664C2×C4—181no—
665C2×C4—181no—
666C2×C4—181no—
667C2×C4—362no—
668C2×C4—362no—
669C2×C4—362no—
670C2×C4D3×D1211yescharacteristic
671C2×C4D3×D1211yescharacteristic
672C2×C4C22×D3211yescharacteristic
673C8—21no—
674C8—21no—
675C8—61no—
676C8—61no—
677C2×C3—21no—
678C2×C3—21no—
679C2×C3—21no—
680C2×C3—122no—
681C2×C3#555211yescharacteristic
682C2×C3#557611yescharacteristic
683C2×C3C2×#90811yescharacteristic
684C2×C3#575311yescharacteristic
685C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
686C2×C3#577911yescharacteristic
687D3—42no—
688D3—241no—
689D3—241no—
690D3—481no—
691C22—62no—
692C22—121no—
693C22—121no—
694C22—361no—
695C22—361no—
696C22—361no—
697C22C2×D3×D1211yescharacteristic
698C4—21no—
699C4—21no—
700C4—32no—
701C4—61no—
702C4—61no—
703C4—61no—
704C4—121no—
705C4—121no—
706C4—121no—
707C4—361no—
708C4—361no—
709C4—361no—
710C4#6429711yescharacteristic
711C4D3×#23511yescharacteristic
712C3—21no—
713C3#7975111yescharacteristic, complemented
714C3#7997011yescharacteristic, complemented
715C2—122no—
716C2—721no—
717C2#1059389911yescharacteristic
718C2D3×#90811yescharacteristic
719C2#1059472111yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#97C22
socleC22×C32C22×D4
prime radicalC2×#3714C22
hypercenter#97D32
hypocenterC32#3367
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #97

Complements

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

NH ≅ G/Ntype
1. Dic6×D12C2semidirect
2. #10593850C2semidirect
3. #10592413C2semidirect
4. C3×#4710C2semidirect
5. C3×#4701C2semidirect
6. #10590893C2semidirect
7. #10590890C2semidirect
8. #10590805C2semidirect
9. #10590764C2semidirect
11. #10590752C2semidirect
12. #10590747C2semidirect
15. #10590283C2semidirect
88. #4710D3semidirect
89. #4701D3semidirect
641. C32#3367semidirect
713. C3#79751semidirect
714. C3#79970semidirect

Maximal subgroups

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

subgroupindex
Dic6×D122
#105938502
#105924132
C3×#47102
C3×#47012
#105908932
#105908902
#105908052
#105907642
#105907542
#105907522
#105907472
#105907452
#105903662
#105902832
#799703
#797513