Finite Group Databasebeta

← #11895902

Subgroups — #11895902

Order 1152.

792 conjugacy classes of subgroups.

The subgroup lattice has 716 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595384C211yesmaximal, characteristic, complemented
2#10594376C211yesmaximal, characteristic, complemented
3#10592492C211yesmaximal, characteristic, complemented
4C3×#4818C211yesmaximal, characteristic, complemented
5C3×#4794C211yesmaximal, characteristic, complemented
6#10591623C211yesmaximal, characteristic, complemented
7#10591572C211yesmaximal, characteristic, complemented
8#10591567C211yesmaximal, characteristic
9#10590786C211yesmaximal, characteristic, complemented
10#10590766C211yesmaximal, characteristic, complemented
11#10590762C211yesmaximal, characteristic, complemented
12#10590750C211yesmaximal, characteristic
13#10590541C211yesmaximal, characteristic, complemented
14#10590489C211yesmaximal, characteristic, complemented
15#10590452C211yesmaximal, characteristic
16#81670—31nomaximal
17#80416—31nomaximal
18C2×D3×Dic6—21no—
19Q8×C3⋊Dic3C2211yescharacteristic
20#64097C2211yescharacteristic
21C3×#947C2211yescharacteristic
22C3×#944C2211yescharacteristic
23C2×C3×#215C2211yescharacteristic
24C2×C3×#204C2211yescharacteristic
25C3×#893C2211yescharacteristic
26C3×#888C2211yescharacteristic
27#63918C2211yescharacteristic
28C4×#627C2211yescharacteristic
29#63898C2211yescharacteristic
30#63896—21no—
31#63893—21no—
32Dic3×D12C2211yescharacteristic
33Dic3×D12C2211yescharacteristic
34#63887—21no—
35#63878—21no—
36#63863C2211yescharacteristic
37#63862—21no—
38#63861—21no—
39#63851—21no—
40Dic3×Dic6C2211yescharacteristic
41C2×#3713C2211yescharacteristic
42C32×#103C2211yescharacteristic
43#63662C2211yescharacteristic
44#63645C2211yescharacteristic
45#63641C2211yescharacteristic
46#63634C2211yescharacteristic
47C3×#835C2211yescharacteristic
48C3×#821C2211yescharacteristic
49C3×#815C2211yescharacteristic
50C3×Dic3⋊C8C2211yescharacteristic
51C3×#810C2211yescharacteristic
52C3×#809C2211yescharacteristic
53#63575C2211yescharacteristic
54Dic3⋊(C3⋊C8)C2211yescharacteristic
55#63566C2211yescharacteristic
56#63565C2211yescharacteristic
57#63563C2211yescharacteristic
58#63563C2211yescharacteristic
59#63555C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic
61#5732—31no—
62#5727—31no—
63#5671—31no—
64D4×Dic6—31no—
65C3×#489—31no—
66C3×#461—31no—
67#5165—31no—
68#5165—31no—
69#5164—31no—
70#5164—31no—
71#5091—31no—
72#5079—31no—
73#5057—31no—
74C4×#213—31no—
75#4846—31no—
76#4831—31no—
77#4818D311yescharacteristic, complemented
78#4817—31no—
79#4794—31no—
80#4794D311yescharacteristic, complemented
81#4793—31no—
82#4793—31no—
83#4793—31no—
84#4793—61no—
85#4792—31no—
86#4787—31no—
87#4765—31no—
88#4759—31no—
89#4756—31no—
90#4710—31no—
91#4701—31no—
92C2×C32×Q8C2311yescharacteristic
93C2×#634—21no—
94C2×C3×D12C2311yescharacteristic
95C2×C3×D12C2311yescharacteristic
96C2×C3×C4×D3—21no—
97C2×C3×Dic6—21no—
98C2×C3×Dic6C2311yescharacteristic
99C2×#627—21no—
100C2×#627D411yescharacteristic
101C2×D3×Dic3—21no—
102C2×D3×Dic3—21no—
103C2×D3×Dic3—21no—
104D3×Dic6—44no—
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×#215—22no—
115C3×(C2×D3)⋊C4—21no—
116C3×(C2×D3)⋊C4—21no—
117C3×(C2×D3)⋊C4—21no—
118C3×C4⋊Dic3C2311yescharacteristic
119C3×Dic3⋊C4—21no—
120C3×Dic3⋊C4—21no—
121C3×Dic3⋊C4—21no—
122C3×C4×Dic3C2311yescharacteristic
123C3×C4×Dic3C2311yescharacteristic
124C2×C3×C3⋊C8C2311yescharacteristic
125C2×C3×C3⋊C8C2311yescharacteristic
126C3×#204—22no—
127#3724D411yescharacteristic
128Dic3⋊Dic3—21no—
129Dic3⋊Dic3—21no—
130Dic3⋊Dic3D411yescharacteristic
131Dic3⋊Dic3D411yescharacteristic
132(C2×D3)⋊Dic3—21no—
133(C2×D3)⋊Dic3—21no—
134(C2×D3)⋊Dic3—21no—
135(C2×D3)⋊Dic3—21no—
136(C2×D3)⋊Dic3—21no—
137Dic32—21no—
138#3713—22no—
139#3367—91noSylow
140C2×D3×Q8—61no—
141C22×Dic6—61no—
142C2×C3×SD16—31no—
143C2×C3×SD16—31no—
144C3×C4⋊Q8—31no—
145C3×C4⋊Q8—31no—
146C3×#124—31no—
147C3×C4×D4—31no—
148#947—31no—
149#947C2×D311yescharacteristic
150#946—61no—
151Q8×Dic3—31no—
152Q8×Dic3—31no—
153Q8×Dic3—31no—
154Q8×Dic3—61no—
155#944C2×D311yescharacteristic
156C2×#215C2×D311yescharacteristic
157#936—31no—
158D4×Dic3—31no—
159D4×Dic3—31no—
160D4×Dic3—31no—
161C2×#213—31no—
162C2×#213—31no—
163#924—61no—
164C2×#204C2×D311yescharacteristic
165#898—61no—
166#898—61no—
167#897—61no—
168#896—61no—
169#896—61no—
170#893—31no—
171#893C2×D311yescharacteristic
172#892—61no—
173#888—31no—
174#888—31no—
175#888—31no—
176#888—61no—
177#888C2×D311yescharacteristic
178#879—61no—
179#879—61no—
180#878—61no—
181#878—61no—
182#878—61no—
183#877—61no—
184C4×D12—31no—
185C4×D12—31no—
186#869—31no—
187C4×Dic6—31no—
188C4×Dic6—31no—
189C4×Dic6—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—
198C3×#97—31no—
199#835—31no—
200#835—31no—
201#835—31no—
202#835—31no—
203#835—61no—
204#835C2×D311yescharacteristic
205#832—31no—
206#832—31no—
207#821—31no—
208#821—31no—
209#821C2×D311yescharacteristic
210#818—31no—
211#818—31no—
212#818—31no—
213#818—61no—
214#816—31no—
215#815—31no—
216#815—31no—
217#815C2×D311yescharacteristic
218Dic3⋊C8—31no—
219Dic3⋊C8—31no—
220Dic3⋊C8—31no—
221Dic3⋊C8—61no—
222Dic3⋊C8C2×D311yescharacteristic
223C8×Dic3—31no—
224#810—31no—
225#810C2×D311yescharacteristic
226#809C2×D311yescharacteristic
227#807—31no—
228#807—31no—
229#807—31no—
230#807—61no—
231C4⋊(C3⋊C8)—31no—
232C4×C3⋊C8—31no—
233C22×C3×D3—21no—
234C22×C3×D3—21no—
235C32×Q8—21no—
236C32×Q8—21no—
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×Dic3C2×D411yescharacteristic
248C2×C3×Dic3C2×D411yescharacteristic
249C2×C3×Dic3C2×D411yescharacteristic
250C2×C3×Dic3C2×D411yescharacteristic
251C3×D12—21no—
252C3×D12—21no—
253C3×D12—21no—
254C3×D12#4112yes—
255C3×C4×D3—42no—
256C3×Dic6—21no—
257C3×Dic6—21no—
258C3×Dic6—42no—
259#627—22no—
260#627—42no—
261D3×Dic3—42no—
262D3×Dic3—42no—
263D3×Dic3—42no—
264C32×C8—21no—
265C3⋊(C3⋊C8)—21no—
266C3×C3⋊C8—21no—
267C3×C3⋊C8—21no—
268#556—91no—
269D4×Q8—91no—
270#489—31no—
271#489—91no—
272#487—91no—
273#477—91no—
274#477—91no—
275#474—91no—
276#463—91no—
277#463—91no—
278#461—31no—
279#446—91no—
280#440—91no—
281#440—91no—
282C4×D8—91no—
283C2×C3×Q8—21no—
284C2×C3×Q8—31no—
285C2×C3×Q8—61no—
286C2×C3×Q8C22×D311yescharacteristic
287C2×C3×Q8C22×D311yescharacteristic
288C2×C3×D4—31no—
289C2×C3×D4—31no—
290C22×C3×C4—61no—
291C22×Dic3—61no—
292C22×Dic3—61no—
293C22×Dic3—61no—
294D3×Q8—124no—
295C2×D12C22×D311yescharacteristic
296C2×D12C22×D311yescharacteristic
297C2×C4×D3—21no—
298C2×C4×D3—61no—
299C2×C4×D3—61no—
300C2×C4×D3—61no—
301C2×Dic6—21no—
302C2×Dic6—31no—
303C2×Dic6—31no—
304C2×Dic6—61no—
305C2×Dic6—61no—
306C2×Dic6—61no—
307C2×Dic6—61no—
308C2×Dic6—121no—
309C2×Dic6—124no—
310C2×Dic6C22×D311yescharacteristic
311C3×SD16—62no—
312C3×SD16—62no—
313C2×C3×C8—21no—
314C2×C3×C8—31no—
315C2×C3×C8—31no—
316C2×C3×C8C22×D311yescharacteristic
317C2×C3×C8C22×D311yescharacteristic
318C3×C4⋊C4—21no—
319C3×C4⋊C4—31no—
320C3×C4⋊C4—61no—
321C3×C4⋊C4—61no—
322C3×C4⋊C4—61no—
323C3×C4⋊C4C22×D311yescharacteristic
324C3×C4⋊C4C22×D311yescharacteristic
325C3×C22⋊C4—61no—
326C3×C22⋊C4—61no—
327C3×C22⋊C4—61no—
328C3×C42—31no—
329C3×C42—31no—
330#217—61no—
331#217—61no—
332#217—61no—
333#217—61no—
334#217—61no—
335#215—22no—
336#213—62no—
337#213—62no—
338(C2×D3)⋊C4—21no—
339(C2×D3)⋊C4—21no—
340(C2×D3)⋊C4—21no—
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—
346C4⋊Dic3—31no—
347C4⋊Dic3—31no—
348C4⋊Dic3—31no—
349C4⋊Dic3—31no—
350C4⋊Dic3—31no—
351C4⋊Dic3—31no—
352C4⋊Dic3—61no—
353C4⋊Dic3—61no—
354C4⋊Dic3—61no—
355C4⋊Dic3—61no—
356C4⋊Dic3—61no—
357C4⋊Dic3—61no—
358C4⋊Dic3—121no—
359C4⋊Dic3C22×D311yescharacteristic
360Dic3⋊C4—21no—
361Dic3⋊C4—21no—
362Dic3⋊C4—21no—
363Dic3⋊C4—31no—
364Dic3⋊C4—31no—
365Dic3⋊C4—31no—
366Dic3⋊C4—31no—
367Dic3⋊C4—61no—
368Dic3⋊C4—61no—
369Dic3⋊C4—61no—
370Dic3⋊C4—61no—
371Dic3⋊C4—121no—
372C4×Dic3—31no—
373C4×Dic3—31no—
374C4×Dic3—61no—
375C4×Dic3—61no—
376C4×Dic3—61no—
377C4×Dic3—61no—
378C4×Dic3—61no—
379C4×Dic3—121no—
380C4×Dic3C22×D311yescharacteristic
381C4×Dic3C22×D311yescharacteristic
382C2×C3⋊C8—31no—
383C2×C3⋊C8—31no—
384C2×C3⋊C8—61no—
385C2×C3⋊C8C22×D311yescharacteristic
386C2×C3⋊C8C22×D311yescharacteristic
387#204—22no—
388C22×C32C22×D411yescharacteristic
389C2×C3×D3—22no—
390C2×C3×D3—41no—
391C2×C3×D3—41no—
392C2×C3×D3—41no—
393C2×C3×D3—41no—
394C2×C3×D3—41no—
395C32×C4—41no—
396C32×C4—41no—
397C32×C4C2×#4111yescharacteristic
398C32×C42−1+411yescharacteristic
399C3⋊Dic3—21no—
400C3⋊Dic3—21no—
401C3⋊Dic3—41no—
402C3⋊Dic3—41no—
403C3×Dic3—21no—
404C3×Dic3—21no—
405C3×Dic3—21no—
406C3×Dic3—41no—
407C3×Dic3—41no—
408C3×Dic3AGL(1,ℤ/8)12yes—
409C22×Q8—181no—
410C2×SD16—31no—
411C2×SD16—31no—
412C2×D8—91no—
413C4⋊Q8—31no—
414C4⋊Q8—31no—
415C4⋊Q8—91no—
416C4⋊Q8—91no—
417#126—181no—
418#126—181no—
419#124—31no—
420#124—91no—
421C22⋊Q8—181no—
422C22⋊Q8—181no—
423C22⋊Q8—181no—
424C22⋊Q8—181no—
425C4×Q8—91no—
426C4×Q8—91no—
427C4×Q8—91no—
428C4×D4—31no—
429C4×D4—91no—
430C4×D4—91no—
431C4×D4—91no—
432#117—181no—
433#107—91no—
434#107—91no—
435#107—91no—
436C4⋊C8—31no—
437C4⋊C8—91no—
438C4⋊C8—91no—
439#103—31no—
440#103—31no—
441#103—91no—
442#103—91no—
443#103—91no—
444#103D3211yescharacteristic
445#102—31no—
446#102—31no—
447#102—91no—
448#102—91no—
449#97—31no—
450#97—91no—
451C4×C8—91no—
452C23×C3—61no—
453C23×C3—61no—
454C22×D3—21no—
455C22×D3—21no—
456C3×Q8—22no—
457C3×Q8—21no—
458C3×Q8—21no—
459C3×Q8—21no—
460C3×Q8—21no—
461C3×Q8—41no—
462C3×Q8—61no—
463C3×Q8—61no—
464C3×Q8—122no—
465C3×D4—32no—
466C3×D4—61no—
467C3×D4—61no—
468C3×D4—61no—
469C2×C3×C4—21no—
470C2×C3×C4—21no—
471C2×C3×C4—21no—
472C2×C3×C4—21no—
473C2×C3×C4—21no—
474C2×C3×C4—31no—
475C2×C3×C4—31no—
476C2×C3×C4—31no—
477C2×C3×C4—31no—
478C2×C3×C4—41no—
479C2×C3×C4—41no—
480C2×C3×C4—61no—
481C2×C3×C4—61no—
482C2×C3×C4—122no—
483C2×C3×C4C23×D311yescharacteristic
484C2×C3×C4C23×D311yescharacteristic
485C2×Dic3—21no—
486C2×Dic3—21no—
487C2×Dic3—31no—
488C2×Dic3—31no—
489C2×Dic3—31no—
490C2×Dic3—31no—
491C2×Dic3—61no—
492C2×Dic3—61no—
493C2×Dic3—61no—
494C2×Dic3—61no—
495C2×Dic3—61no—
496C2×Dic3—61no—
497C2×Dic3—121no—
498C2×Dic3—121no—
499C2×Dic3—122no—
500C2×Dic3—122no—
501C2×Dic3—122no—
502C2×Dic3D3×D411yescharacteristic
503C2×Dic3D3×D411yescharacteristic
504C2×Dic3D3×D411yescharacteristic
505C2×Dic3D3×D411yescharacteristic
506D12—21no—
507D12—21no—
508D12—21no—
509D12#23712yes—
510C4×D3—42no—
511C4×D3—122no—
512C4×D3—122no—
513C4×D3—122no—
514Dic6—21no—
515Dic6—21no—
516Dic6—42no—
517Dic6—62no—
518Dic6—62no—
519Dic6—122no—
520Dic6—122no—
521Dic6—122no—
522Dic6—122no—
523Dic6—242no—
524C3×C8—21no—
525C3×C8—21no—
526C3×C8—41no—
527C3×C8—61no—
528C3×C8—61no—
529C3⋊C8—21no—
530C3⋊C8—21no—
531C3⋊C8—61no—
532C3⋊C8—61no—
533C3⋊C8—121no—
534C2×C32#54811yescharacteristic
535C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
536C2×C32#57811yescharacteristic
537C3×D3—42no—
538C3×D3—81no—
539C2×Q8—31no—
540C2×Q8—61no—
541C2×Q8—91no—
542C2×Q8—181no—
543C2×Q8—181no—
544C2×Q8—364no—
545C2×Q8C2×D3211yescharacteristic
546C2×D4—31no—
547C2×D4—31no—
548C22×C4—61no—
549C22×C4—181no—
550C22×C4—181no—
551C22×C4—181no—
552SD16—62no—
553SD16—62no—
554D8—182no—
555C2×C8—31no—
556C2×C8—31no—
557C2×C8—91no—
558C2×C8C2×D3211yescharacteristic
559C4⋊C4—31no—
560C4⋊C4—61no—
561C4⋊C4—61no—
562C4⋊C4—61no—
563C4⋊C4—91no—
564C4⋊C4—91no—
565C4⋊C4—91no—
566C4⋊C4—91no—
567C4⋊C4—91no—
568C4⋊C4—181no—
569C4⋊C4—181no—
570C4⋊C4—181no—
571C4⋊C4—181no—
572C4⋊C4C2×D3211yescharacteristic
573C22⋊C4—61no—
574C22⋊C4—61no—
575C22⋊C4—61no—
576C22⋊C4—181no—
577C22⋊C4—181no—
578C22⋊C4—181no—
579C22⋊C4—181no—
580C22⋊C4—181no—
581C42—31no—
582C42—31no—
583C42—91no—
584C42—181no—
585C42—181no—
586C22×C3—21no—
587C22×C3—62no—
588C22×C3—121no—
589C22×C3—121no—
590C22×C3—121no—
591C22×C3—121no—
592C22×C3—121no—
593C22×C3C2×D3×D411yescharacteristic
594C22×C3C2×D3×D411yescharacteristic
595C2×D3—22no—
596C2×D3—41no—
597C2×D3—41no—
598C2×D3—41no—
599C2×D3—41no—
600C2×D3—41no—
601C3×C4—21no—
602C3×C4—21no—
603C3×C4—32no—
604C3×C4—42no—
605C3×C4—41no—
606C3×C4—41no—
607C3×C4—41no—
608C3×C4—41no—
609C3×C4—61no—
610C3×C4—61no—
611C3×C4—61no—
612C3×C4—81no—
613C3×C4—121no—
614C3×C4—121no—
615C3×C4C2×#23711yescharacteristic
616C3×C4D3×#4111yescharacteristic
617C3×C4#101011yescharacteristic
618C3×C4#101011yescharacteristic
619Dic3—21no—
620Dic3—21no—
621Dic3—21no—
622Dic3—41no—
623Dic3—41no—
624Dic3—62no—
625Dic3—61no—
626Dic3—61no—
627Dic3—61no—
628Dic3—61no—
629Dic3—121no—
630Dic3—121no—
631Dic3—121no—
632Dic3—121no—
633Dic3—121no—
634Dic3—241no—
635Dic3—241no—
636Dic3#91412yes—
637C32#336711yescharacteristic, complemented, Sylow
638C23—61no—
639C23—61no—
640Q8—21no—
641Q8—21no—
642Q8—61no—
643Q8—61no—
644Q8—122no—
645Q8—182no—
646Q8—362no—
647Q8—362no—
648D4—32no—
649D4—61no—
650D4—61no—
651D4—61no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—31no—
655C2×C4—31no—
656C2×C4—31no—
657C2×C4—31no—
658C2×C4—61no—
659C2×C4—61no—
660C2×C4—91no—
661C2×C4—91no—
662C2×C4—122no—
663C2×C4—181no—
664C2×C4—181no—
665C2×C4—362no—
666C2×C4—362no—
667C2×C4—362no—
668C2×C4C22×D3211yescharacteristic
669C8—21no—
670C8—61no—
671C8—61no—
672C8—181no—
673C2×C3—21no—
674C2×C3—21no—
675C2×C3—21no—
676C2×C3—122no—
677C2×C3—241no—
678C2×C3#559811yescharacteristic
679C2×C3#567711yescharacteristic
680C2×C3C2×#91411yescharacteristic
681C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
682C2×C3#577911yescharacteristic
683C2×C3#577911yescharacteristic
684D3—42no—
685D3—81no—
686C22—62no—
687C22—121no—
688C22—121no—
689C22—121no—
690C22—121no—
691C22—121no—
692C22D32×D411yescharacteristic
693C4—32no—
694C4—41no—
695C4—41no—
696C4—61no—
697C4—61no—
698C4—61no—
699C4—121no—
700C4—121no—
701C4—181no—
702C4—181no—
703C4—361no—
704C4—361no—
705C4#6429811yescharacteristic
706C4D3×#23711yescharacteristic
707C3—21no—
708C3#8041611yescharacteristic, complemented
709C3#8167011yescharacteristic, complemented
710C2—122no—
711C2—241no—
712C2#1059407611yescharacteristic
713C2D3×#91411yescharacteristic
714C2#1059476911yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#103C22
socleC22×C32C22×D4
prime radicalC2×#3713C22
hypercenter#103D32
hypocenterC32#3367
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
1. #10595384C2semidirect
2. #10594376C2semidirect
3. #10592492C2semidirect
4. C3×#4818C2semidirect
5. C3×#4794C2semidirect
6. #10591623C2semidirect
7. #10591572C2semidirect
9. #10590786C2semidirect
10. #10590766C2semidirect
11. #10590762C2semidirect
13. #10590541C2semidirect
14. #10590489C2semidirect
77. #4818D3semidirect
80. #4794D3semidirect
637. C32#3367semidirect
708. C3#80416semidirect
709. C3#81670semidirect

Maximal subgroups

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

subgroupindex
#105953842
#105943762
#105924922
C3×#48182
C3×#47942
#105916232
#105915722
#105915672
#105907862
#105907662
#105907622
#105907502
#105905412
#105904892
#105904522
#816703
#804163