Finite Group Databasebeta

← #11860004

Subgroups — #11860004

Order 1152.

1155 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595993C211yesmaximal, characteristic, complemented
2#10594958C211yesmaximal, characteristic, complemented
3C2×#63829C211yesmaximal, characteristic
4C3×#5002C211yesmaximal, characteristic, complemented
5C3×#4998C211yesmaximal, characteristic, complemented
6#10591105C211yesmaximal, characteristic, complemented
7C2×#63553C211yesmaximal, characteristic, complemented
8#10590483C212yesmaximal, complemented
9#10590482C212yesmaximal, complemented
10#10590460C212yesmaximal, complemented
11#10590459C212yesmaximal, complemented
12#79165—31nomaximal
13#78818—31nomaximal
14C2×#3828C2211yescharacteristic
15C2×C3×#235C2211yescharacteristic
16C32×#117C2211yescharacteristic
17C2×C4×C3⋊Dic3C2211yescharacteristic
18#64102C2212yes—
19#64096C2212yes—
20#64090—22no—
21#64081—21no—
22C42×C3⋊D3—21no—
23C3×#926C2211yescharacteristic
24C22×C3×C3⋊C8C2211yescharacteristic
25C22×C3×C3⋊C8C2211yescharacteristic
26#67⋊Dic3—22no—
27#63898C2212yes—
28C4×D3×Dic3—21no—
29#63855—21no—
30#63843C2212yes—
31C2×#3719C2211yescharacteristic
32C2×#3717C2211yescharacteristic
33#63829C418yescomplemented
34C2×#3716C2211yescharacteristic
35C2×#3714C2211yescharacteristic
36C3×#810C2212yes—
37C3×#809C2212yes—
38C3×#808C2212yes—
39C3×#807C2212yes—
40#63567C2212yes—
41#63564C2212yes—
42#63553C2212yes—
43#63553C2212yes—
44Dic3×#41—31no—
45C2×#950—31no—
46C2×#904—31no—
47#5522—31no—
48#5522—31no—
49#5522—31no—
50#5522—61no—
51C3×#427—31no—
52C3×#416—31no—
53#5113—31no—
54C2×C8×Dic3—31no—
55C2×C8×Dic3—31no—
56#5002—31no—
57#5002D311yescharacteristic, complemented
58#4998D311yescharacteristic, complemented
59#4873—32no—
60#4872—32no—
61#4852—32no—
62#4852—32no—
63#4790—32no—
64#4788—32no—
65#4758—32no—
66#4756—32no—
67C22×C32×C4C2311yescharacteristic
68C2×#638—21no—
69C22×C3⋊Dic3D412yes—
70#3828—22no—
71#3828C2×C414yescomplemented
72C2×C4⋊(C3⋊D3)C2311yescharacteristic
73C2×C4×C3⋊D3—21no—
74C2×C4×C3⋊D3—22no—
75C2×#634C2311yescharacteristic
76C2×C3×#67—21no—
77C3×#235—22no—
78C3×#235C2×C414yescomplemented
79C2×C3×D12C2311yescharacteristic
80C2×C3×C4×D3—21no—
81C2×C3×Dic6C2311yescharacteristic
82C2×D3×Dic3—22no—
83C32×C4⋊C4C2312yes—
84C32×C22⋊C4—21no—
85C32×C42—21no—
86#3752—22no—
87#3750—22no—
88C4×C3⋊Dic3—22no—
89C4×C3⋊Dic3D411yescharacteristic
90C4×C3⋊Dic3D411yescharacteristic
91C4×C3⋊Dic3C2312yes—
92C3×#217—21no—
93C3×C4⋊Dic3C2312yes—
94C3×C4×Dic3—21no—
95C2×C3×C3⋊C8—22no—
96C2×C3×C3⋊C8C2×C414yescomplemented
97C2×C3×C3⋊C8C2312yes—
98C2×C3×C3⋊C8C2311yescharacteristic
99C2×C3×C3⋊C8C2311yescharacteristic
100Dic3⋊Dic3—22no—
101(C2×D3)⋊Dic3—22no—
102Dic32—22no—
103#3719C2×C414yescomplemented
104#3717C2×C414yescomplemented
105#3716C2×C414yescomplemented
106#3714C2×C414yescomplemented
107C4×#135—91noSylow
108C2×C3×#41—31no—
109C2×#235—31no—
110C2×#235—31no—
111C2×#235—61no—
112C2×#235C2×D311yescharacteristic
113C22×C3×C8—31no—
114C22×C3×C8—31no—
115C3×#117—21no—
116C3×#117—31no—
117C3×#117C2×D311yescharacteristic
118C3×#117C2×D311yescharacteristic
119#950—38no—
120Q8×Dic3—32no—
121C2×#216—31no—
122C2×#215—31no—
123D4×Dic3—32no—
124D4×Dic3—62no—
125C2×#214—31no—
126C2×#213—31no—
127#926—61no—
128#926C2×D311yescharacteristic
129C2×C4×Dic3—31no—
130C2×C4×Dic3—31no—
131C2×C4×Dic3—61no—
132C2×C4×Dic3—61no—
133C22×C3⋊C8C2×D311yescharacteristic
134C22×C3⋊C8C2×D311yescharacteristic
135C2×Dic12—31no—
136#904—38no—
137C2×D24—31no—
138C2×#204—31no—
139C2×#204—31no—
140#893—32no—
141#893—32no—
142#893—32no—
143#893—62no—
144#887—32no—
145#887—32no—
146#887—32no—
147#887—62no—
148#67⋊C4—62no—
149#67⋊C4—62no—
150#67⋊C4—64no—
151#67⋊C4—62no—
152#872—61no—
153#872—61no—
154#872—61no—
155#872—62no—
156C42×D3—61no—
157C42×D3—61no—
158C42×D3—61no—
159C42×D3—62no—
160C3×#107—32no—
161C3×#106—32no—
162C3×#103—32no—
163C3×#102—32no—
164#821—32no—
165#816—32no—
166C8×Dic3—32no—
167C8×Dic3—32no—
168C8×Dic3—32no—
169C8×Dic3—32no—
170#810—32no—
171#810C2×D312yes—
172#809—32no—
173#809C2×D312yes—
174#808C2×D312yes—
175#807C2×D312yes—
176C23×C32C2×D411yescharacteristic
177C22×C3⋊D3—21no—
178C22×C3×D3—21no—
179C2×C32×C4—22no—
180C2×C32×C4C22×C412yes—
181C2×C32×C4C2×D411yescharacteristic
182C2×C32×C4#4112yes—
183C2×C32×C4C2411yescharacteristic
184#638—24no—
185C2×C3⋊Dic3—21no—
186C2×C3⋊Dic3—24no—
187C2×C3⋊Dic3C2×D412yes—
188C2×C3⋊Dic3C2×D412yes—
189C4⋊(C3⋊D3)—21no—
190C4⋊(C3⋊D3)C22×C412yes—
191C4×C3⋊D3—24no—
192C4×C3⋊D3—44no—
193#634—21no—
194#634C22×C412yes—
195C3×#67—24no—
196C2×C3×Dic3—21no—
197C2×C3×Dic3—22no—
198C3×D12—21no—
199C3×D12C22×C412yes—
200C3×C4×D3—24no—
201C3×Dic6—21no—
202C3×Dic6C22×C412yes—
203D3×Dic3—44no—
204C3×C3⋊C8—22no—
205C3×C3⋊C8C22×C412yes—
206C3×C3⋊C8C22×C412yes—
207C2×#135—91no—
208C4×#41—91no—
209C4×#41—91no—
210C4×Q16—92no—
211C4×SD16—92no—
212C4×SD16—92no—
213C4×D8—92no—
214#427—31no—
215#416—31no—
216#416—91no—
217C2×C4×C8—91no—
218C3×#41—34no—
219C3×#41—62no—
220C2×C3×Q8—31no—
221C2×C3×D4—31no—
222C2×C3×D4—61no—
223C22×C3×C4—21no—
224C22×C3×C4—61no—
225C22×C3×C4C22×D311yescharacteristic
226C22×C3×C4C22×D311yescharacteristic
227C2×#67—21no—
228C2×#67—62no—
229C2×#67—61no—
230C2×#67—61no—
231C22×Dic3—32no—
232C22×Dic3—32no—
233C22×Dic3—62no—
234C22×Dic3—62no—
235#235—22no—
236#235—34no—
237#235—34no—
238#235—64no—
239#235—64no—
240#235—62no—
241#235—62no—
242#235C4×D314yescomplemented
243C2×D12—31no—
244C2×D12—31no—
245C2×D12—61no—
246C2×D12C22×D311yescharacteristic
247C2×C4×D3—21no—
248C2×C4×D3—62no—
249C2×C4×D3—61no—
250C2×C4×D3—61no—
251C2×C4×D3—62no—
252C2×C4×D3—62no—
253C2×C4×D3—62no—
254C2×C4×D3—64no—
255C2×Dic6—31no—
256C2×Dic6—31no—
257C2×Dic6—61no—
258C2×Dic6C22×D311yescharacteristic
259C2×C3×C8—34no—
260C2×C3×C8—31no—
261C2×C3×C8—31no—
262C2×C3×C8—32no—
263C2×C3×C8—62no—
264C3×C4⋊C4—22no—
265C3×C4⋊C4—32no—
266C3×C4⋊C4C22×D312yes—
267C3×C4⋊C4C22×D312yes—
268C3×C22⋊C4—22no—
269C3×C22⋊C4—21no—
270C3×C22⋊C4—21no—
271C3×C22⋊C4—61no—
272C3×C42—22no—
273C3×C42—21no—
274C3×C42—21no—
275C3×C42—61no—
276#217—21no—
277#217—62no—
278#216—34no—
279#215—34no—
280#214—34no—
281#213—34no—
282(C2×D3)⋊C4—62no—
283(C2×D3)⋊C4—62no—
284(C2×D3)⋊C4—62no—
285(C2×D3)⋊C4—64no—
286C4⋊Dic3—62no—
287C4⋊Dic3C22×D312yes—
288Dic3⋊C4—62no—
289Dic3⋊C4—62no—
290Dic3⋊C4—62no—
291Dic3⋊C4—64no—
292C4×Dic3—21no—
293C4×Dic3—31no—
294C4×Dic3—31no—
295C4×Dic3—31no—
296C4×Dic3—31no—
297C4×Dic3—32no—
298C4×Dic3—32no—
299C4×Dic3—61no—
300C4×Dic3—61no—
301C4×Dic3—62no—
302C4×Dic3—62no—
303C4×Dic3—62no—
304C4×Dic3—62no—
305C4×Dic3—62no—
306C4×Dic3—64no—
307C2×C3⋊C8—22no—
308C2×C3⋊C8C4×D314yescomplemented
309C2×C3⋊C8C22×D312yes—
310C2×C3⋊C8C22×D311yescharacteristic
311C2×C3⋊C8C22×D311yescharacteristic
312Dic12—34no—
313D24—34no—
314#204—34no—
315#204—34no—
316C22×C32—22no—
317C22×C32C4×D412yes—
318C22×C32C22×D411yescharacteristic
319C2×C3⋊D3—22no—
320C2×C3⋊D3—42no—
321C2×C3×D3—22no—
322C2×C3×D3—42no—
323C32×C4—42no—
324C32×C4C4×D412yes—
325C32×C4C23×C411yescharacteristic
326C32×C4C2×#4111yescharacteristic
327C3⋊Dic3—22no—
328C3⋊Dic3—22no—
329C3⋊Dic3#13514yescomplemented
330C3×Dic3—22no—
331C3×Dic3—42no—
332C2×#41—31no—
333C2×#41—91no—
334#135—98no—
335C2×Q16—91no—
336C2×SD16—91no—
337C2×SD16—91no—
338C2×D8—91no—
339C22×C8—31no—
340C22×C8—31no—
341C4×Q8—92no—
342C4×Q8—92no—
343C4×D4—92no—
344C4×D4—92no—
345C4×D4—182no—
346C4×D4—182no—
347#117—31no—
348#117—181no—
349#117—181no—
350#117D3211yescharacteristic
351C2×C42—91no—
352C2×C42—181no—
353C2×C42—181no—
354#107—32no—
355#106—32no—
356#103—32no—
357#103—92no—
358#102—32no—
359#102—92no—
360C4×C8—92no—
361C4×C8—92no—
362C23×C3—21no—
363C23×C3—61no—
364C23×C3D3×D411yescharacteristic
365C23×C3D3×D411yescharacteristic
366C22×D3—21no—
367C22×D3—62no—
368C22×D3—61no—
369C22×D3—61no—
370C3×Q8—32no—
371C3×Q8—61no—
372C3×D4—32no—
373C3×D4—64no—
374C3×D4—61no—
375C2×C3×C4—24no—
376C2×C3×C4—22no—
377C2×C3×C4—22no—
378C2×C3×C4—21no—
379C2×C3×C4—22no—
380C2×C3×C4—22no—
381C2×C3×C4—21no—
382C2×C3×C4—61no—
383C2×C3×C4—64no—
384C2×C3×C4—62no—
385C2×C3×C4C2×C4×D312yes—
386C2×C3×C4C2×C4×D312yes—
387C2×C3×C4D3×D411yescharacteristic
388C2×C3×C4D3×D411yescharacteristic
389C2×C3×C4#23712yes—
390C2×C3×C4#23912yes—
391C2×C3×C4C23×D311yescharacteristic
392C2×C3×C4C23×D311yescharacteristic
393#67—24no—
394#67—68no—
395#67—64no—
396#67—64no—
397C2×Dic3—21no—
398C2×Dic3—22no—
399C2×Dic3—32no—
400C2×Dic3—32no—
401C2×Dic3—32no—
402C2×Dic3—32no—
403C2×Dic3—62no—
404C2×Dic3—62no—
405C2×Dic3—64no—
406C2×Dic3—64no—
407C2×Dic3—62no—
408C2×Dic3—61no—
409C2×Dic3—61no—
410C2×Dic3—124no—
411C2×Dic3—124no—
412D12—21no—
413D12—32no—
414D12—32no—
415D12—62no—
416D12—62no—
417D12—61no—
418D12—61no—
419D12C2×C4×D312yes—
420C4×D3—24no—
421C4×D3—68no—
422C4×D3—64no—
423C4×D3—64no—
424C4×D3—124no—
425C4×D3—124no—
426C4×D3—124no—
427C4×D3—128no—
428Dic6—21no—
429Dic6—32no—
430Dic6—32no—
431Dic6—62no—
432Dic6—62no—
433Dic6—61no—
434Dic6—61no—
435Dic6C2×C4×D312yes—
436C3×C8—32no—
437C3×C8—32no—
438C3×C8—62no—
439C3⋊C8—22no—
440C3⋊C8C2×C4×D312yes—
441C3⋊C8C2×C4×D312yes—
442C2×C32—22no—
443C2×C32C2×C4×D411yescharacteristic
444C2×C32C2×#13512yes—
445C3⋊D3—42no—
446C3×D3—42no—
447#41—34no—
448#41—62no—
449#41—94no—
450#41—182no—
451C2×Q8—31no—
452C2×Q8—91no—
453C2×D4—31no—
454C2×D4—61no—
455C2×D4—91no—
456C2×D4—181no—
457C22×C4—61no—
458C22×C4—92no—
459C22×C4—182no—
460C22×C4—182no—
461C22×C4—181no—
462C22×C4C2×D3211yescharacteristic
463Q16—94no—
464SD16—94no—
465SD16—94no—
466D8—94no—
467C2×C8—31no—
468C2×C8—31no—
469C2×C8—34no—
470C2×C8—32no—
471C2×C8—62no—
472C4⋊C4—32no—
473C4⋊C4—182no—
474C4⋊C4—182no—
475C4⋊C4C2×D3212yes—
476C22⋊C4—21no—
477C22⋊C4—61no—
478C22⋊C4—182no—
479C22⋊C4—182no—
480C42—21no—
481C42—61no—
482C42—92no—
483C42—91no—
484C42—91no—
485C42—182no—
486C42—182no—
487C22×C3—22no—
488C22×C3—22no—
489C22×C3—21no—
490C22×C3—22no—
491C22×C3—42no—
492C22×C3—62no—
493C22×C3—122no—
494C22×C3#67⋊C412yes—
495C22×C3#89312yes—
496C22×C3C2×D3×D411yescharacteristic
497C22×C3C2×D3×D411yescharacteristic
498C2×D3—22no—
499C2×D3—42no—
500C2×D3—64no—
501C2×D3—62no—
502C2×D3—62no—
503C2×D3—124no—
504C2×D3—122no—
505C2×D3—122no—
506C3×C4—21no—
507C3×C4—21no—
508C3×C4—22no—
509C3×C4—44no—
510C3×C4—42no—
511C3×C4—42no—
512C3×C4—62no—
513C3×C4—122no—
514C3×C4#67⋊C412yes—
515C3×C4#89312yes—
516C3×C4C22×C4×D311yescharacteristic
517C3×C4C22×C4×D311yescharacteristic
518C3×C4C2×#23711yescharacteristic
519C3×C4C2×#23911yescharacteristic
520Dic3—22no—
521Dic3—34no—
522Dic3—34no—
523Dic3—42no—
524Dic3—64no—
525Dic3—64no—
526Dic3—62no—
527Dic3—62no—
528Dic3—62no—
529Dic3—62no—
530Dic3—122no—
531C32C4×#13511yescharacteristic, complemented, Sylow
532C23—61no—
533C23—181no—
534C23#381111yescharacteristic
535Q8—32no—
536Q8—61no—
537Q8—92no—
538Q8—181no—
539D4—32no—
540D4—64no—
541D4—61no—
542D4—92no—
543D4—184no—
544D4—181no—
545C2×C4—22no—
546C2×C4—61no—
547C2×C4—64no—
548C2×C4—62no—
549C2×C4—92no—
550C2×C4—92no—
551C2×C4—184no—
552C2×C4—181no—
553C2×C4—184no—
554C2×C4—364no—
555C2×C4—364no—
556C2×C4#379612yes—
557C2×C4C4×D3212yes—
558C2×C4#381111yescharacteristic
559C2×C4C22×D3211yescharacteristic
560C8—32no—
561C8—32no—
562C8—62no—
563C2×C3—22no—
564C2×C3—22no—
565C2×C3—21no—
566C2×C3—22no—
567C2×C3—42no—
568C2×C3—122no—
569C2×C3C2×#67⋊C411yescharacteristic
570C2×C3C2×#89311yescharacteristic
571C2×C3D3×#13512yes—
572C2×C3D3×#13512yes—
573D3—42no—
574D3—124no—
575D3—122no—
576D3—122no—
577C22—22no—
578C22—62no—
579C22—122no—
580C22—182no—
581C22—362no—
582C22#6388112yes—
583C22C2×#381111yescharacteristic
584C4—42no—
585C4—62no—
586C4—94no—
587C4—122no—
588C4—182no—
589C4—182no—
590C4#6388112yes—
591C4C2×#379611yescharacteristic
592C4C2×C4×D3211yescharacteristic
593C3—21no—
594C3#7881811yescharacteristic, complemented
595C3#7916511yescharacteristic, complemented
596C2—22no—
597C2—122no—
598C2—362no—
599C2C2×#6388111yescharacteristic
600C2#1059545912yes—
subgroupG/H
centerC2×C4#3811
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×#117C22
socleC22×C32C22×D4
prime radicalC2×#63829C2
cosocleC2×C32×C4C24
hypercenter#117D32
hypocenterC32C4×#135
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
1. #10595993C2semidirect
2. #10594958C2semidirect
4. C3×#5002C2semidirect
5. C3×#4998C2semidirect
6. #10591105C2semidirect
7. C2×#63553C2semidirect
8. #10590483C2semidirect
9. #10590482C2semidirect
10. #10590460C2semidirect
11. #10590459C2semidirect
33. #63829C4semidirect
57. #5002D3semidirect
58. #4998D3semidirect
71. #3828C2×C4semidirect
78. C3×#235C2×C4semidirect
96. C2×C3×C3⋊C8C2×C4semidirect
103. #3719C2×C4semidirect
104. #3717C2×C4semidirect
105. #3716C2×C4semidirect
106. #3714C2×C4semidirect
242. #235C4×D3semidirect
308. C2×C3⋊C8C4×D3semidirect
329. C3⋊Dic3#135semidirect
531. C32C4×#135semidirect
594. C3#78818semidirect
595. C3#79165semidirect

Maximal subgroups

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

subgroupindex
#105959932
#105949582
C2×#638292
C3×#50022
C3×#49982
#105911052
C2×#635532
#105904832
#105904822
#105904602
#105904592
#791653
#788183