Finite Group Databasebeta

← #11865763

Subgroups — #11865763

Order 1152.

1046 conjugacy classes of subgroups.

The subgroup lattice has 643 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63807C212yesmaximal, complemented
2#10593897C211yesmaximal, characteristic, complemented
3C4×#3795C211yesmaximal, characteristic, complemented
4#10592548C211yesmaximal, characteristic, complemented
5C3×#4843C211yesmaximal, characteristic, complemented
6C3×D3×C4⋊C8C211yesmaximal, characteristic, complemented
7#10590954C212yesmaximal, complemented
8#10590861C212yesmaximal, complemented
9#10590755C212yesmaximal, complemented
10#10590377C211yesmaximal, characteristic, complemented
11#10590365C211yesmaximal, characteristic, complemented
12#80331—31nomaximal
13#79021—31nomaximal
14C2×#3795C2212yes—
15C2×#3795C2211yescharacteristic
16C2×#3746C2212yes—
17#64078C2211yescharacteristic
18C4×#634C2211yescharacteristic
19C2×C3×D24C2212yes—
20C2×C3×D3×C8C2212yes—
21C3×#874C2211yescharacteristic
22C3×C4×D12C2211yescharacteristic
23C3×C42×D3C2211yescharacteristic
24#63908—21no—
25#63908—21no—
26C4×#625—21no—
27Dic3×D12—21no—
28Dic3×D12—21no—
29Dic3×D12C2211yescharacteristic
30#63879—21no—
31#63877—21no—
32C4×D3×Dic3—21no—
33#63860C2212yes—
34#63844C2211yescharacteristic
35#63841C2211yescharacteristic
36C2×#3716C2212yes—
37C2×#3716C2212yes—
38#63807—28no—
39C32×C4⋊C8C2211yescharacteristic
40#63643C2212yes—
41C3×#821C2212yes—
42C3×Dic3⋊C8C2212yes—
43C3×C4⋊(C3⋊C8)C2211yescharacteristic
44#63567C2212yes—
45#63563C2212yes—
46C2×#912—32no—
47C2×#904—32no—
48#5716—31no—
49C4×#237—31no—
50#5477—31no—
51C4×#235—31no—
52C3×#459—31no—
53C2×C3×C4⋊C8—31no—
54#5153—32no—
55#5113—32no—
56#5075—31no—
57#5019—31no—
58#4849—31no—
59#4849—31no—
60#4849—61no—
61#4848—31no—
62#4845—32no—
63#4844—32no—
64#4843D311yescharacteristic, complemented
65#4841—31no—
66D3×C4⋊C8D311yescharacteristic, complemented
67#4772—32no—
68#4767—32no—
69C2×#634C2312yes—
70C2×#634C2311yescharacteristic
71C2×C3×D12—21no—
72C2×C3×D12—21no—
73C2×C3×D12C2312yes—
74C2×C3×D12C2311yescharacteristic
75C2×C3×C4×D3—21no—
76C2×C3×C4×D3D411yescharacteristic
77C2×C3×C4×D3D411yescharacteristic
78C2×C3×C4×D3C2311yescharacteristic
79C2×#625—21no—
80C2×#625—22no—
81C2×D3×Dic3—21no—
82C2×D3×Dic3—22no—
83C2×D3×Dic3—21no—
84#3795—22no—
85#3795—24no—
86#3795—24no—
87#3795D414yescomplemented
88C2×C32×C8C2312yes—
89C32×C42C2311yescharacteristic
90C4⋊(C3⋊Dic3)—21no—
91C4⋊(C3⋊Dic3)—21no—
92C4⋊(C3⋊Dic3)C2311yescharacteristic
93#3750—21no—
94C4×C3⋊Dic3—21no—
95#3746—24no—
96C3×(C2×D3)⋊C4—21no—
97C3×C4⋊Dic3C2311yescharacteristic
98C3×C4×Dic3D411yescharacteristic
99C3×C4×Dic3D411yescharacteristic
100C3×C4×Dic3C2311yescharacteristic
101C2×C3×C3⋊C8C2312yes—
102C3×D24—24no—
103C3×D3×C8—24no—
104#3724—21no—
105(C2×D3)⋊Dic3—21no—
106(C2×D3)⋊Dic3—22no—
107(C2×D3)⋊Dic3—22no—
108(C2×D3)⋊Dic3—21no—
109Dic32—21no—
110Dic32—21no—
111#3716—24no—
112#3716—24no—
113#3035—91noSylow
114C2×#237—31no—
115C2×#237—32no—
116C2×#235—31no—
117C2×#235—32no—
118C2×C3×D8—32no—
119C22×C3×C8—32no—
120C3×#127—31no—
121C3×C4×D4—31no—
122C2×C3×C42—31no—
123#938—61no—
124#938—61no—
125#936—32no—
126D4×Dic3—31no—
127D4×Dic3—61no—
128D4×Dic3—61no—
129C2×#214—32no—
130C2×#214—32no—
131#930—61no—
132#930—61no—
133C4×#67—61no—
134C4×#67—61no—
135C4×#67—61no—
136#926—31no—
137C2×C4×Dic3—61no—
138#912—68no—
139C2×Dic12—32no—
140C2×Dic12—32no—
141C2×Dic12—62no—
142#904—68no—
143C2×D24C2×D312yes—
144C2×#204—32no—
145C2×#204—32no—
146C2×D3×C8C2×D312yes—
147#892—31no—
148#887—31no—
149#67⋊C4—61no—
150#877—61no—
151#875—32no—
152#874C2×D311yescharacteristic
153C4×D12—31no—
154C4×D12—61no—
155C4×D12—61no—
156C4×D12C2×D311yescharacteristic
157#872—61no—
158C42×D3—61no—
159C42×D3C2×D311yescharacteristic
160#869—31no—
161#869—31no—
162#869—61no—
163C4×Dic6—31no—
164C4×Dic6—31no—
165C4×Dic6—31no—
166C4×Dic6—61no—
167C3×C4⋊C8—21no—
168C3×C4⋊C8—32no—
169C3×C4⋊C8—31no—
170C3×C4⋊C8C2×D311yescharacteristic
171C3×C4⋊C8C2×D311yescharacteristic
172C3×#102—32no—
173#832—32no—
174#821—32no—
175#821C2×D312yes—
176#816—32no—
177#816—32no—
178#816—32no—
179#816—62no—
180Dic3⋊C8C2×D312yes—
181#810—32no—
182C4⋊(C3⋊C8)C2×D311yescharacteristic
183C22×C3×D3—21no—
184C22×C3×D3—22no—
185C22×C3×D3C2×D411yescharacteristic
186C2×C32×C4C2×D411yescharacteristic
187C2×C32×C4C2×D411yescharacteristic
188C2×C32×C4C2411yescharacteristic
189C2×C3⋊Dic3—21no—
190C2×C3⋊Dic3—21no—
191C2×C3⋊Dic3—22no—
192#634—21no—
193#634—22no—
194#634—22no—
195#634C2×D412yes—
196C2×C3×Dic3—21no—
197C2×C3×Dic3C2×D411yescharacteristic
198C2×C3×Dic3C2×D411yescharacteristic
199C2×C3×Dic3C2×D411yescharacteristic
200C3×D12—22no—
201C3×D12—21no—
202C3×D12—22no—
203C3×D12—42no—
204C3×D12—42no—
205C3×D12C2×D412yes—
206C3×C4×D3—22no—
207C3×C4×D3—41no—
208C3×C4×D3—42no—
209C3×C4×D3C2×D412yes—
210C3×C4×D3#4112yes—
211#625—24no—
212#625—44no—
213D3×Dic3—24no—
214D3×Dic3—42no—
215D3×Dic3—44no—
216C32×C8—22no—
217C3×C3⋊C8—22no—
218C2×#135—92no—
219#532—91no—
220C4×#41—91no—
221#464—92no—
222#463—92no—
223#462—91no—
224#461—91no—
225#460—91no—
226#459—31no—
227C2×C4⋊C8—31no—
228#416—92no—
229C2×C3×D4—31no—
230C2×C3×D4—32no—
231C2×C3×D4—61no—
232C2×C3×D4—61no—
233C22×C3×C4—31no—
234C22×C3×C4—31no—
235C22×C3×C4—31no—
236C22×C3×C4—61no—
237C2×#67—61no—
238C2×#67—61no—
239C2×#67—62no—
240C2×#67—62no—
241C22×Dic3—61no—
242C22×Dic3—61no—
243C22×Dic3—62no—
244#237—34no—
245#237—64no—
246#237—62no—
247#237—64no—
248#235—34no—
249#235—62no—
250#235—64no—
251#235—64no—
252C2×D12—21no—
253C2×D12—21no—
254C2×D12C22×D312yes—
255C2×D12C22×D311yescharacteristic
256C2×C4×D3—21no—
257C2×C4×D3—61no—
258C2×C4×D3—61no—
259C2×C4×D3—62no—
260C2×C4×D3D1211yescharacteristic
261C2×C4×D3D1211yescharacteristic
262C2×C4×D3C22×D311yescharacteristic
263C2×Dic6—31no—
264C2×Dic6—31no—
265C2×Dic6—32no—
266C2×Dic6—32no—
267C2×Dic6—61no—
268C2×Dic6—62no—
269C3×D8—64no—
270C2×C3×C8—22no—
271C2×C3×C8—32no—
272C2×C3×C8—64no—
273C2×C3×C8C22×D312yes—
274C2×C3×C8C22×D312yes—
275C3×C4⋊C4—31no—
276C3×C22⋊C4—61no—
277C3×C42—21no—
278C3×C42—31no—
279C3×C42—31no—
280C3×C42—31no—
281C3×C42C22×D311yescharacteristic
282C3×C42C22×D311yescharacteristic
283#217—61no—
284#217—61no—
285#217—62no—
286#217—62no—
287#214—64no—
288#214—64no—
289(C2×D3)⋊C4—21no—
290(C2×D3)⋊C4—61no—
291(C2×D3)⋊C4—62no—
292(C2×D3)⋊C4—62no—
293(C2×D3)⋊C4—61no—
294C4⋊Dic3—31no—
295C4⋊Dic3—31no—
296C4⋊Dic3—61no—
297C4⋊Dic3—61no—
298C4⋊Dic3—61no—
299C4⋊Dic3—61no—
300C4⋊Dic3—61no—
301C4⋊Dic3—121no—
302C4⋊Dic3—121no—
303C4⋊Dic3C22×D311yescharacteristic
304Dic3⋊C4—61no—
305Dic3⋊C4—61no—
306Dic3⋊C4—61no—
307Dic3⋊C4—61no—
308Dic3⋊C4—121no—
309C4×Dic3—61no—
310C4×Dic3—61no—
311C4×Dic3—61no—
312C4×Dic3—61no—
313C4×Dic3—61no—
314C4×Dic3—61no—
315C4×Dic3—121no—
316C4×Dic3D1211yescharacteristic
317C4×Dic3D1211yescharacteristic
318C4×Dic3C22×D311yescharacteristic
319C2×C3⋊C8C22×D312yes—
320Dic12—64no—
321Dic12—64no—
322Dic12—124no—
323D24—24no—
324#204—64no—
325#204—64no—
326D3×C8—24no—
327C22×C32C22×D411yescharacteristic
328C2×C3×D3—21no—
329C2×C3×D3—21no—
330C2×C3×D3—22no—
331C2×C3×D3—41no—
332C2×C3×D3—41no—
333C2×C3×D3—42no—
334C2×C3×D3—42no—
335C2×C3×D3—42no—
336C2×C3×D3#12112yes—
337C32×C4—21no—
338C32×C4#13512yescomplemented
339C32×C4C22×D411yescharacteristic
340C32×C4C2×#4111yescharacteristic
341C3⋊Dic3—22no—
342C3⋊Dic3—42no—
343C3⋊Dic3—41no—
344C3×Dic3—21no—
345C3×Dic3—21no—
346C3×Dic3—41no—
347C3×Dic3#12112yes—
348C2×#41—91no—
349C2×#41—92no—
350#135—188no—
351C2×Q16—92no—
352C2×SD16—92no—
353C2×SD16—92no—
354C2×D8—32no—
355C22×C8—32no—
356C4⋊Q8—91no—
357#127—31no—
358#124—92no—
359#121—181no—
360#121—181no—
361C4×Q8—91no—
362C4×Q8—91no—
363C4×D4—31no—
364C4×D4—91no—
365C4×D4—181no—
366C4×D4—181no—
367C4×D4—181no—
368C4×D4—181no—
369#117—91no—
370#117—181no—
371C2×C42—31no—
372C2×C42—181no—
373C4⋊C8—32no—
374C4⋊C8—31no—
375C4⋊C8D3211yescharacteristic
376#103—92no—
377#103—92no—
378#102—32no—
379#102—92no—
380C23×C3—31no—
381C23×C3—61no—
382C23×C3—62no—
383C22×D3—21no—
384C22×D3—22no—
385C22×D3C2×D1211yescharacteristic
386C3×D4—32no—
387C3×D4—62no—
388C3×D4—61no—
389C3×D4—62no—
390C3×D4—122no—
391C3×D4—122no—
392C2×C3×C4—21no—
393C2×C3×C4—21no—
394C2×C3×C4—21no—
395C2×C3×C4—31no—
396C2×C3×C4—32no—
397C2×C3×C4—32no—
398C2×C3×C4—31no—
399C2×C3×C4—31no—
400C2×C3×C4—62no—
401C2×C3×C4—61no—
402C2×C3×C4—121no—
403C2×C3×C4—122no—
404C2×C3×C4C2×D1211yescharacteristic
405C2×C3×C4C2×D1211yescharacteristic
406C2×C3×C4D3×D411yescharacteristic
407C2×C3×C4D3×D411yescharacteristic
408C2×C3×C4C23×D311yescharacteristic
409C2×C3×C4C23×D311yescharacteristic
410#67—64no—
411#67—64no—
412#67—124no—
413#67—124no—
414C2×Dic3—21no—
415C2×Dic3—61no—
416C2×Dic3—61no—
417C2×Dic3—64no—
418C2×Dic3—61no—
419C2×Dic3—62no—
420C2×Dic3—61no—
421C2×Dic3—62no—
422C2×Dic3—121no—
423C2×Dic3—121no—
424C2×Dic3—122no—
425C2×Dic3—122no—
426C2×Dic3—124no—
427C2×Dic3C2×D1211yescharacteristic
428C2×Dic3C2×D1211yescharacteristic
429C2×Dic3C2×D1211yescharacteristic
430D12—22no—
431D12—21no—
432D12—22no—
433D12—42no—
434D12—42no—
435D12D3×D412yes—
436C4×D3—22no—
437C4×D3—41no—
438C4×D3—42no—
439C4×D3—64no—
440C4×D3—124no—
441C4×D3—122no—
442C4×D3D3×D412yes—
443C4×D3#23912yes—
444Dic6—32no—
445Dic6—32no—
446Dic6—62no—
447Dic6—61no—
448Dic6—61no—
449Dic6—62no—
450Dic6—62no—
451Dic6—62no—
452Dic6—62no—
453Dic6—121no—
454Dic6—122no—
455Dic6—122no—
456C3×C8—22no—
457C3×C8—22no—
458C3×C8—42no—
459C3×C8—62no—
460C3⋊C8—22no—
461C2×C32C2×#12111yescharacteristic
462C2×C32C2×#13511yescharacteristic
463C2×C32#57511yescharacteristic
464C3×D3—22no—
465C3×D3—42no—
466C3×D3—82no—
467#41—94no—
468#41—182no—
469#41—184no—
470#41—184no—
471C2×Q8—91no—
472C2×Q8—92no—
473C2×D4—31no—
474C2×D4—32no—
475C2×D4—61no—
476C2×D4—61no—
477C2×D4—181no—
478C2×D4—182no—
479C22×C4—31no—
480C22×C4—31no—
481C22×C4—31no—
482C22×C4—61no—
483C22×C4—181no—
484C22×C4—181no—
485C22×C4—182no—
486Q16—184no—
487SD16—184no—
488SD16—184no—
489D8—64no—
490C2×C8—32no—
491C2×C8—64no—
492C2×C8C2×D3212yes—
493C4⋊C4—31no—
494C4⋊C4—91no—
495C4⋊C4—181no—
496C4⋊C4—181no—
497C4⋊C4—181no—
498C4⋊C4—181no—
499C22⋊C4—61no—
500C22⋊C4—181no—
501C22⋊C4—182no—
502C22⋊C4—182no—
503C22⋊C4—181no—
504C42—31no—
505C42—31no—
506C42—31no—
507C42—181no—
508C42—181no—
509C42—181no—
510C42C2×D3211yescharacteristic
511C22×C3—21no—
512C22×C3—32no—
513C22×C3—61no—
514C22×C3—61no—
515C22×C3—62no—
516C22×C3—121no—
517C22×C3—121no—
518C22×C3—122no—
519C22×C3—122no—
520C22×C3—122no—
521C22×C3C22×D1211yescharacteristic
522C22×C3C2×D3×D411yescharacteristic
523C2×D3—21no—
524C2×D3—21no—
525C2×D3—22no—
526C2×D3—41no—
527C2×D3—41no—
528C2×D3—42no—
529C2×D3—42no—
530C2×D3—42no—
531C2×D3#89512yes—
532C3×C4—21no—
533C3×C4—21no—
534C3×C4—21no—
535C3×C4—21no—
536C3×C4—22no—
537C3×C4—32no—
538C3×C4—41no—
539C3×C4—61no—
540C3×C4—61no—
541C3×C4—121no—
542C3×C4#90412yescomplemented
543C3×C4#91212yescomplemented
544C3×C4C2×D3×D411yescharacteristic
545C3×C4C2×D3×D411yescharacteristic
546C3×C4C2×#23911yescharacteristic
547C3×C4D3×#4111yescharacteristic
548Dic3—21no—
549Dic3—21no—
550Dic3—41no—
551Dic3—62no—
552Dic3—62no—
553Dic3—122no—
554Dic3—121no—
555Dic3—122no—
556Dic3—121no—
557Dic3—122no—
558Dic3—242no—
559Dic3—241no—
560Dic3#89512yes—
561C32#303511yescharacteristic, complemented, Sylow
562C23—31no—
563C23—61no—
564C23—62no—
565Q8—92no—
566Q8—181no—
567Q8—182no—
568Q8—182no—
569D4—32no—
570D4—62no—
571D4—61no—
572D4—62no—
573D4—122no—
574D4—122no—
575D4—184no—
576D4—364no—
577C2×C4—31no—
578C2×C4—32no—
579C2×C4—32no—
580C2×C4—31no—
581C2×C4—31no—
582C2×C4—62no—
583C2×C4—61no—
584C2×C4—121no—
585C2×C4—122no—
586C2×C4—184no—
587C2×C4—181no—
588C2×C4—181no—
589C2×C4—182no—
590C2×C4—364no—
591C2×C4—362no—
592C2×C4D3×D1211yescharacteristic
593C2×C4D3×D1211yescharacteristic
594C2×C4C22×D3211yescharacteristic
595C8—22no—
596C8—62no—
597C2×C3—21no—
598C2×C3—21no—
599C2×C3—21no—
600C2×C3—62no—
601C2×C3—122no—
602C2×C3—242no—
603C2×C3C2×#89511yescharacteristic
604C2×C3D3×#12111yescharacteristic
605C2×C3C2×#90411yescharacteristic
606C2×C3#574811yescharacteristic
607C2×C3C2×#91211yescharacteristic
608C2×C3#577311yescharacteristic
609D3—22no—
610D3—42no—
611D3—82no—
612C22—32no—
613C22—61no—
614C22—61no—
615C22—62no—
616C22—121no—
617C22—121no—
618C22—122no—
619C22—122no—
620C22—122no—
621C22C2×D3×D1211yescharacteristic
622C4—21no—
623C4—32no—
624C4—61no—
625C4—61no—
626C4—121no—
627C4—182no—
628C4—362no—
629C4—361no—
630C4#6380712yescomplemented
631C4D32×D411yescharacteristic
632C4D3×#23911yescharacteristic
633C3—21no—
634C3#7902111yescharacteristic, complemented
635C3#8033111yescharacteristic, complemented
636C2—62no—
637C2—122no—
638C2—242no—
639C2D3×#89511yescharacteristic
640C2C2×#6380711yescharacteristic
641C2#1059471211yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊C8C22
socleC22×C32C22×D4
hypercenterC4⋊C8D32
hypocenterC32#3035
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
1. C2×#63807C2semidirect
2. #10593897C2semidirect
3. C4×#3795C2semidirect
4. #10592548C2semidirect
5. C3×#4843C2semidirect
6. C3×D3×C4⋊C8C2semidirect
7. #10590954C2semidirect
8. #10590861C2semidirect
9. #10590755C2semidirect
10. #10590377C2semidirect
11. #10590365C2semidirect
64. #4843D3semidirect
66. D3×C4⋊C8D3semidirect
87. #3795D4semidirect
338. C32×C4#135semidirect
542. C3×C4#904semidirect
543. C3×C4#912semidirect
561. C32#3035semidirect
630. C4#63807semidirect
634. C3#79021semidirect
635. C3#80331semidirect

Maximal subgroups

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

subgroupindex
C2×#638072
#105938972
C4×#37952
#105925482
C3×#48432
C3×D3×C4⋊C82
#105909542
#105908612
#105907552
#105903772
#105903652
#803313
#790213