Finite Group Databasebeta

← #11895900

Subgroups — #11895900

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
1#10595387C211yesmaximal, characteristic, complemented
2#10594376C211yesmaximal, characteristic, complemented
3#10592493C211yesmaximal, characteristic, complemented
4C3×#4818C211yesmaximal, characteristic, complemented
5C3×#4793C211yesmaximal, characteristic, complemented
6#10591623C211yesmaximal, characteristic, complemented
7#10591570C211yesmaximal, characteristic
8#10591566C211yesmaximal, characteristic, complemented
9#10590779C211yesmaximal, characteristic, complemented
10#10590764C211yesmaximal, characteristic, complemented
11#10590754C211yesmaximal, characteristic
12#10590646C211yesmaximal, characteristic, complemented
13#10590535C211yesmaximal, characteristic, complemented
14#10590496C211yesmaximal, characteristic, complemented
15#10590456C211yesmaximal, characteristic
16#81100—31nomaximal
17#80416—31nomaximal
18C2×D3×Dic6—21no—
19#64156C2211yescharacteristic
20#64097C2211yescharacteristic
21C3×Q8×Dic3C2211yescharacteristic
22C3×#944C2211yescharacteristic
23C2×C3×#215C2211yescharacteristic
24C2×C3×#204C2211yescharacteristic
25C3×#893C2211yescharacteristic
26C3×#888C2211yescharacteristic
27#63918C2211yescharacteristic
28C4×#627C2211yescharacteristic
29#63898C2211yescharacteristic
30#63896—21no—
31#63895—21no—
32#63894C2211yescharacteristic
33Dic3×D12C2211yescharacteristic
34#63887—21no—
35#63868—21no—
36#63864C2211yescharacteristic
37#63851—21no—
38#63848—21no—
39#63843C2211yescharacteristic
40#63836—21no—
41C2×#3714C2211yescharacteristic
42C32×#103C2211yescharacteristic
43#63662C2211yescharacteristic
44#63648C2211yescharacteristic
45#63642C2211yescharacteristic
46#63636C2211yescharacteristic
47C3×#835C2211yescharacteristic
48C3×#818C2211yescharacteristic
49C3×Dic3⋊C8C2211yescharacteristic
50C3×Dic3⋊C8C2211yescharacteristic
51C3×#810C2211yescharacteristic
52C3×#807C2211yescharacteristic
53#63575C2211yescharacteristic
54#63572C2211yescharacteristic
55#63566C2211yescharacteristic
56#63565C2211yescharacteristic
57#63564C2211yescharacteristic
58#63562C2211yescharacteristic
59#63554C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic
61#5732—31no—
62#5727—31no—
63#5568—31no—
64D4×Dic6—31no—
65C3×#477—31no—
66C3×#461—31no—
67#5165—31no—
68#5165—31no—
69#5164—31no—
70#5164—31no—
71#5089—31no—
72#5079—31no—
73#5026—31no—
74C4×#213—31no—
75#4890—31no—
76#4889—31no—
77#4875—31no—
78#4872—31no—
79#4846—31no—
80#4844—31no—
81#4831—31no—
82#4828—31no—
83#4819—31no—
84#4818D311yescharacteristic, complemented
85#4794—31no—
86#4794—31no—
87#4794—31no—
88#4794—61no—
89#4793—31no—
90#4793D311yescharacteristic, complemented
91#4792—31no—
92C2×C32×Q8C2311yescharacteristic
93C2×C4⋊(C3⋊D3)C2311yescharacteristic
94C2×#634—21no—
95C2×C3×D12C2311yescharacteristic
96C2×C3×C4×D3—21no—
97C2×C3×Dic6—21no—
98C2×C3×Dic6C2311yescharacteristic
99C2×#627—21no—
100C2×#627D411yescharacteristic
101C2×#624—21no—
102C2×D3×Dic3—21no—
103C2×D3×Dic3—21no—
104D3×Dic6—44no—
105C2×C32×C8C2311yescharacteristic
106C32×C4⋊C4C2311yescharacteristic
107#3752—21no—
108#3752—21no—
109C4⋊(C3⋊Dic3)C2311yescharacteristic
110#3750—21no—
111C4×C3⋊Dic3C2311yescharacteristic
112C2×C3⋊(C3⋊C8)C2311yescharacteristic
113C3×#215—22no—
114C3×(C2×D3)⋊C4—21no—
115C3×C4⋊Dic3—21no—
116C3×C4⋊Dic3C2311yescharacteristic
117C3×C4⋊Dic3C2311yescharacteristic
118C3×Dic3⋊C4—21no—
119C3×Dic3⋊C4—21no—
120C3×Dic3⋊C4—21no—
121C3×C4×Dic3—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#3722—21no—
133#3722—21no—
134#3722—21no—
135(C2×D3)⋊Dic3—21no—
136(C2×D3)⋊Dic3—21no—
137Dic32—21no—
138#3714—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×C4×Q8—31no—
147C3×C4×D4—31no—
148#947—31no—
149#947—31no—
150#947—31no—
151#947—61no—
152#946—61no—
153Q8×Dic3—31no—
154Q8×Dic3C2×D311yescharacteristic
155#944C2×D311yescharacteristic
156C2×#215C2×D311yescharacteristic
157D4×Dic3—31no—
158D4×Dic3—31no—
159C2×#213—31no—
160#924—61no—
161C2×D24—31no—
162C2×#204C2×D311yescharacteristic
163#898—61no—
164#898—61no—
165#898—61no—
166#897—61no—
167#896—61no—
168#896—61no—
169#896—61no—
170#893—31no—
171#893—31no—
172#893C2×D311yescharacteristic
173#892—61no—
174#888—31no—
175#888—31no—
176#888—31no—
177#888—61no—
178#888C2×D311yescharacteristic
179#887—31no—
180#878—61no—
181#878—61no—
182#876—61no—
183#875—31no—
184C4×D12—31no—
185C4×D12—31no—
186#872—61no—
187#869—31no—
188C4×Dic6—31no—
189C4×Dic6—31no—
190C3×#107—31no—
191C3×#107—31no—
192C3×C4⋊C8—31no—
193C3×C4⋊C8—31no—
194C3×#103—21no—
195C3×#103—31no—
196C3×#103—31no—
197C3×#103C2×D311yescharacteristic
198C3×#103C2×D311yescharacteristic
199#835—31no—
200#835—31no—
201#835—31no—
202#835—31no—
203#835—61no—
204#835C2×D311yescharacteristic
205#832—31no—
206#821—31no—
207#821—31no—
208#821—31no—
209#821—61no—
210#818—31no—
211#818C2×D311yescharacteristic
212#816—31no—
213#815—31no—
214#815—31no—
215#815—31no—
216#815—61no—
217Dic3⋊C8—31no—
218Dic3⋊C8—31no—
219Dic3⋊C8C2×D311yescharacteristic
220Dic3⋊C8C2×D311yescharacteristic
221C8×Dic3—31no—
222#810—31no—
223#810C2×D311yescharacteristic
224#809—31no—
225#809—31no—
226#809—31no—
227#809—31no—
228#809—61no—
229#807—31no—
230#807C2×D311yescharacteristic
231#803—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⋊Dic3C2×D411yescharacteristic
242C2×C3⋊Dic3C2×D411yescharacteristic
243C4⋊(C3⋊D3)—21no—
244C4⋊(C3⋊D3)—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—21no—
257C3×Dic6—21no—
258C3×Dic6—42no—
259#627—22no—
260#627—42no—
261#624—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—91no—
271#489—91no—
272#487—91no—
273#477—31no—
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—
289C22×C3×C4—61no—
290C22×Dic3—61no—
291C22×Dic3—61no—
292D3×Q8—124no—
293C2×D12—31no—
294C2×D12—31no—
295C2×D12—61no—
296C2×D12C22×D311yescharacteristic
297C2×C4×D3—21no—
298C2×C4×D3—61no—
299C2×C4×D3—61no—
300C2×C4×D3—61no—
301C2×C4×D3—61no—
302C2×Dic6—21no—
303C2×Dic6—31no—
304C2×Dic6—31no—
305C2×Dic6—61no—
306C2×Dic6—61no—
307C2×Dic6—61no—
308C2×Dic6—61no—
309C2×Dic6—121no—
310C2×Dic6—124no—
311C2×Dic6C22×D311yescharacteristic
312C3×SD16—62no—
313C3×SD16—62no—
314C2×C3×C8—21no—
315C2×C3×C8—31no—
316C2×C3×C8—31no—
317C2×C3×C8C22×D311yescharacteristic
318C2×C3×C8C22×D311yescharacteristic
319C3×C4⋊C4—21no—
320C3×C4⋊C4—31no—
321C3×C4⋊C4—31no—
322C3×C4⋊C4—61no—
323C3×C4⋊C4—61no—
324C3×C4⋊C4—61no—
325C3×C4⋊C4—61no—
326C3×C4⋊C4C22×D311yescharacteristic
327C3×C4⋊C4C22×D311yescharacteristic
328C3×C22⋊C4—61no—
329C3×C42—31no—
330C3×C42—31no—
331C3×C42—61no—
332#217—61no—
333#217—61no—
334#215—22no—
335#213—62no—
336(C2×D3)⋊C4—21no—
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—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—121no—
350(C2×D3)⋊C4—121no—
351C4⋊Dic3—21no—
352C4⋊Dic3—31no—
353C4⋊Dic3—31no—
354C4⋊Dic3—31no—
355C4⋊Dic3—31no—
356C4⋊Dic3—61no—
357C4⋊Dic3—61no—
358C4⋊Dic3—61no—
359C4⋊Dic3C22×D311yescharacteristic
360C4⋊Dic3C22×D311yescharacteristic
361Dic3⋊C4—21no—
362Dic3⋊C4—21no—
363Dic3⋊C4—21no—
364Dic3⋊C4—31no—
365Dic3⋊C4—31no—
366Dic3⋊C4—31no—
367Dic3⋊C4—31no—
368Dic3⋊C4—61no—
369Dic3⋊C4—61no—
370Dic3⋊C4—61no—
371Dic3⋊C4—61no—
372Dic3⋊C4—121no—
373C4×Dic3—21no—
374C4×Dic3—31no—
375C4×Dic3—31no—
376C4×Dic3—61no—
377C4×Dic3—61no—
378C4×Dic3—61no—
379C4×Dic3C22×D311yescharacteristic
380C4×Dic3C22×D311yescharacteristic
381C2×C3⋊C8—31no—
382C2×C3⋊C8—31no—
383C2×C3⋊C8—61no—
384C2×C3⋊C8C22×D311yescharacteristic
385C2×C3⋊C8C22×D311yescharacteristic
386D24—62no—
387#204—22no—
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—41no—
396C32×C4—41no—
397C32×C4C2×#4111yescharacteristic
398C32×C42−1+411yescharacteristic
399C3⋊Dic3—21no—
400C3⋊Dic3—21no—
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—31no—
412C2×D8—91no—
413C4⋊Q8—31no—
414C4⋊Q8—31no—
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—91no—
427C4×Q8—91no—
428C4×D4—31no—
429C4×D4—91no—
430C4×D4—91no—
431C4×D4—91no—
432#117—181no—
433#107—31no—
434#107—31no—
435#107—91no—
436C4⋊C8—31no—
437C4⋊C8—31no—
438C4⋊C8—91no—
439#103—31no—
440#103—31no—
441#103—91no—
442#103—91no—
443#103—91no—
444#103D3211yescharacteristic
445#102—91no—
446#102—91no—
447#102—91no—
448#102—91no—
449#97—91no—
450#97—91no—
451C4×C8—91no—
452C23×C3—61no—
453C22×D3—21no—
454C22×D3—61no—
455C22×D3—61no—
456C22×D3—121no—
457C3×Q8—21no—
458C3×Q8—21no—
459C3×Q8—21no—
460C3×Q8—21no—
461C3×Q8—41no—
462C3×Q8—41no—
463C3×Q8—61no—
464C3×Q8—61no—
465C3×Q8—122no—
466C3×D4—32no—
467C3×D4—61no—
468C2×C3×C4—21no—
469C2×C3×C4—21no—
470C2×C3×C4—21no—
471C2×C3×C4—21no—
472C2×C3×C4—21no—
473C2×C3×C4—31no—
474C2×C3×C4—31no—
475C2×C3×C4—31no—
476C2×C3×C4—31no—
477C2×C3×C4—41no—
478C2×C3×C4—41no—
479C2×C3×C4—61no—
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—21no—
488C2×Dic3—31no—
489C2×Dic3—31no—
490C2×Dic3—31no—
491C2×Dic3—31no—
492C2×Dic3—61no—
493C2×Dic3—61no—
494C2×Dic3—61no—
495C2×Dic3—61no—
496C2×Dic3—121no—
497C2×Dic3—122no—
498C2×Dic3—122no—
499C2×Dic3D3×D411yescharacteristic
500C2×Dic3D3×D411yescharacteristic
501C2×Dic3D3×D411yescharacteristic
502C2×Dic3D3×D411yescharacteristic
503D12—21no—
504D12—61no—
505D12—61no—
506D12—61no—
507D12—61no—
508D12—121no—
509D12—121no—
510D12#23712yes—
511C4×D3—42no—
512C4×D3—122no—
513C4×D3—122no—
514C4×D3—122no—
515C4×D3—122no—
516Dic6—21no—
517Dic6—21no—
518Dic6—42no—
519Dic6—62no—
520Dic6—62no—
521Dic6—122no—
522Dic6—122no—
523Dic6—122no—
524Dic6—122no—
525Dic6—242no—
526C3×C8—21no—
527C3×C8—21no—
528C3×C8—41no—
529C3×C8—61no—
530C3×C8—61no—
531C3⋊C8—21no—
532C3⋊C8—21no—
533C3⋊C8—61no—
534C3⋊C8—61no—
535C3⋊C8—121no—
536C2×C32#54811yescharacteristic
537C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
538C2×C32#57811yescharacteristic
539C3⋊D3—81no—
540C3×D3—42no—
541C2×Q8—31no—
542C2×Q8—61no—
543C2×Q8—91no—
544C2×Q8—181no—
545C2×Q8—181no—
546C2×Q8—364no—
547C2×Q8C2×D3211yescharacteristic
548C2×D4—31no—
549C2×D4—91no—
550C22×C4—61no—
551C22×C4—181no—
552C22×C4—181no—
553C22×C4—181no—
554SD16—62no—
555SD16—62no—
556D8—182no—
557C2×C8—31no—
558C2×C8—31no—
559C2×C8—91no—
560C2×C8C2×D3211yescharacteristic
561C4⋊C4—31no—
562C4⋊C4—31no—
563C4⋊C4—61no—
564C4⋊C4—61no—
565C4⋊C4—61no—
566C4⋊C4—61no—
567C4⋊C4—91no—
568C4⋊C4—91no—
569C4⋊C4—91no—
570C4⋊C4—91no—
571C4⋊C4—181no—
572C4⋊C4—181no—
573C4⋊C4—181no—
574C4⋊C4C2×D3211yescharacteristic
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—91no—
587C42—181no—
588C22×C3—21no—
589C22×C3—62no—
590C22×C3—121no—
591C22×C3—121no—
592C22×C3C2×D3×D411yescharacteristic
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—32no—
609C3×C4—41no—
610C3×C4—41no—
611C3×C4—41no—
612C3×C4—41no—
613C3×C4—61no—
614C3×C4—61no—
615C3×C4—61no—
616C3×C4—81no—
617C3×C4—81no—
618C3×C4—121no—
619C3×C4—121no—
620C3×C4—121no—
621C3×C4C2×#23711yescharacteristic
622C3×C4#100711yescharacteristic
623C3×C4D3×#4111yescharacteristic
624C3×C4#101011yescharacteristic
625Dic3—21no—
626Dic3—21no—
627Dic3—21no—
628Dic3—41no—
629Dic3—41no—
630Dic3—41no—
631Dic3—61no—
632Dic3—61no—
633Dic3—61no—
634Dic3—61no—
635Dic3—121no—
636Dic3—121no—
637Dic3—121no—
638Dic3—121no—
639Dic3—241no—
640Dic3#91412yes—
641C32#336711yescharacteristic, complemented, Sylow
642C23—61no—
643C23—181no—
644Q8—21no—
645Q8—21no—
646Q8—61no—
647Q8—61no—
648Q8—122no—
649Q8—182no—
650Q8—362no—
651Q8—362no—
652D4—32no—
653D4—61no—
654D4—181no—
655D4—181no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—31no—
659C2×C4—31no—
660C2×C4—31no—
661C2×C4—31no—
662C2×C4—61no—
663C2×C4—61no—
664C2×C4—61no—
665C2×C4—91no—
666C2×C4—91no—
667C2×C4—122no—
668C2×C4—181no—
669C2×C4—362no—
670C2×C4—362no—
671C2×C4—362no—
672C2×C4C22×D3211yescharacteristic
673C8—21no—
674C8—61no—
675C8—61no—
676C8—181no—
677C2×C3—21no—
678C2×C3—21no—
679C2×C3—21no—
680C2×C3—122no—
681C2×C3#559811yescharacteristic
682C2×C3#563311yescharacteristic
683C2×C3C2×#91411yescharacteristic
684C2×C3#576611yescharacteristic
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—
697C22D32×D411yescharacteristic
698C4—32no—
699C4—41no—
700C4—41no—
701C4—61no—
702C4—61no—
703C4—61no—
704C4—121no—
705C4—121no—
706C4—121no—
707C4—181no—
708C4—181no—
709C4—361no—
710C4#6429711yescharacteristic
711C4D3×#23711yescharacteristic
712C3—21no—
713C3#8041611yescharacteristic, complemented
714C3#8110011yescharacteristic, complemented
715C2—122no—
716C2—721no—
717C2#1059407411yescharacteristic
718C2D3×#91411yescharacteristic
719C2#1059476611yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#103C22
socleC22×C32C22×D4
prime radicalC2×#3714C22
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. #10595387C2semidirect
2. #10594376C2semidirect
3. #10592493C2semidirect
4. C3×#4818C2semidirect
5. C3×#4793C2semidirect
6. #10591623C2semidirect
8. #10591566C2semidirect
9. #10590779C2semidirect
10. #10590764C2semidirect
12. #10590646C2semidirect
13. #10590535C2semidirect
14. #10590496C2semidirect
84. #4818D3semidirect
90. #4793D3semidirect
641. C32#3367semidirect
713. C3#80416semidirect
714. C3#81100semidirect

Maximal subgroups

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

subgroupindex
#105953872
#105943762
#105924932
C3×#48182
C3×#47932
#105916232
#105915702
#105915662
#105907792
#105907642
#105907542
#105906462
#105905352
#105904962
#105904562
#811003
#804163