Finite Group Databasebeta

← #11860223

Subgroups — #11860223

Order 1152.

1063 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5522C211yesmaximal, characteristic, complemented
2#10594954C211yesmaximal, characteristic, complemented
3C2×#63829C211yesmaximal, characteristic
4#10592701C211yesmaximal, characteristic, complemented
5C3×#4998C211yesmaximal, characteristic, complemented
6#10591083C211yesmaximal, characteristic, complemented
7C2×#63554C211yesmaximal, characteristic, complemented
8#10590590C212yesmaximal, complemented
9#10590589C212yesmaximal, complemented
10#10590480C212yesmaximal, complemented
11#10590457C212yesmaximal, complemented
12#82506—31nomaximal
13#79166—31nomaximal
14C2×#3828C2211yescharacteristic
15C2×C3×#235C2211yescharacteristic
16C32×#117C2211yescharacteristic
17C22×C3⋊(C3⋊C8)C2211yescharacteristic
18C3×#926C2211yescharacteristic
19C2×C3×C4×Dic3C2211yescharacteristic
20C22×C3×C3⋊C8C2211yescharacteristic
21C3×#893C2212yes—
22C3×#887C2212yes—
23C3×#67⋊C4—22no—
24C3×#872—21no—
25C3×C42×D3—21no—
26#63952—22no—
27#63894C2212yes—
28C4×#624—21no—
29#63874—21no—
30#63844C2212yes—
31C2×#3719C2211yescharacteristic
32C2×#3717C2211yescharacteristic
33#63829C418yescomplemented
34C2×#3716C2211yescharacteristic
35C2×#3714C2211yescharacteristic
36#63637C2212yes—
37#63636C2212yes—
38C3×#808C2212yes—
39C3×#807C2212yes—
40#63565C2212yes—
41#63562C2212yes—
42#63554C2212yes—
43#63554C2212yes—
44C3×C4×#41—31no—
45C2×#950—31no—
46C2×#904—31no—
47#5522—31no—
48#5522D311yescharacteristic, complemented
49C4×#235—31no—
50C3×#427—31no—
51#5233—31no—
52C2×#815—31no—
53#5030—32no—
54#5026—32no—
55#5018—32no—
56#5014—32no—
57#5002—31no—
58#5002—31no—
59#5002—31no—
60#5002—61no—
61#4998D311yescharacteristic, complemented
62C2×#803—31no—
63#4889—32no—
64#4889—32no—
65#4869—32no—
66#4853—32no—
67C22×C32×C4C2311yescharacteristic
68C2×#638—21no—
69#3828—22no—
70#3828C2×C414yescomplemented
71C2×C4⋊(C3⋊D3)C2311yescharacteristic
72C2×C4×C3⋊D3—21no—
73C2×#634C2311yescharacteristic
74C2×C3×#67—21no—
75C22×C3×Dic3D412yes—
76C3×#235—22no—
77C3×#235C2×C414yescomplemented
78C2×C3×D12C2311yescharacteristic
79C2×C3×C4×D3—21no—
80C2×C3×C4×D3—22no—
81C2×C3×Dic6C2311yescharacteristic
82C2×#624—22no—
83C32×C4⋊C4C2312yes—
84C32×C22⋊C4—21no—
85C32×C42—21no—
86C2×C3⋊(C3⋊C8)—22no—
87C2×C3⋊(C3⋊C8)C2312yes—
88C3×#217—21no—
89C3×(C2×D3)⋊C4—22no—
90C3×C4⋊Dic3C2312yes—
91C3×Dic3⋊C4—22no—
92C3×C4×Dic3—21no—
93C3×C4×Dic3—22no—
94C3×C4×Dic3D411yescharacteristic
95C3×C4×Dic3D411yescharacteristic
96C3×C4×Dic3C2312yes—
97C2×C3×C3⋊C8C2×C414yescomplemented
98C2×C3×C3⋊C8C2311yescharacteristic
99C2×C3×C3⋊C8C2311yescharacteristic
100#3724—22no—
101#3722—22no—
102Dic32—22no—
103#3719C2×C414yescomplemented
104#3717C2×C414yescomplemented
105#3716C2×C414yescomplemented
106#3714C2×C414yescomplemented
107#2943—91noSylow
108C2×C3×#41—31no—
109C2×#235—31no—
110C2×#235—31no—
111C2×#235—61no—
112C2×#235C2×D311yescharacteristic
113C22×C3×C8—31no—
114C3×C4×Q8—32no—
115C3×C4×D4—32no—
116C3×C4×D4—62no—
117C3×#117—21no—
118C3×#117—31no—
119C3×#117—61no—
120C3×#117C2×D311yescharacteristic
121C3×#117C2×D311yescharacteristic
122C2×C3×C42—31no—
123C2×C3×C42—61no—
124#950—38no—
125C2×#216—31no—
126C2×#215—31no—
127C2×#214—31no—
128C2×#213—31no—
129C4×#67—62no—
130#926C2×D311yescharacteristic
131C2×C4×Dic3C2×D311yescharacteristic
132C22×C3⋊C8—31no—
133C22×C3⋊C8—31no—
134C22×C3⋊C8—61no—
135C22×C3⋊C8C2×D311yescharacteristic
136C2×Dic12—31no—
137#904—38no—
138C2×D24—31no—
139C2×#204—31no—
140C2×#204—31no—
141#893—32no—
142#893C2×D312yes—
143#887—32no—
144#887C2×D312yes—
145#67⋊C4—22no—
146#67⋊C4—62no—
147C4×D12—32no—
148#872—21no—
149#872—61no—
150#872—61no—
151C42×D3—21no—
152C42×D3—61no—
153C42×D3—61no—
154C4×Dic6—32no—
155C3×#107—32no—
156C3×#106—32no—
157#835—32no—
158#832—32no—
159#815—32no—
160#815—32no—
161#810—32no—
162#810—32no—
163#810—32no—
164#810—62no—
165#809—32no—
166#809—32no—
167#809—32no—
168#809—62no—
169#808C2×D312yes—
170#807C2×D312yes—
171#803—32no—
172#803—32no—
173C23×C32C2×D411yescharacteristic
174C22×C3⋊D3—21no—
175C22×C3×D3—21no—
176C2×C32×C4—22no—
177C2×C32×C4C22×C412yes—
178C2×C32×C4C2×D411yescharacteristic
179C2×C32×C4#4112yes—
180C2×C32×C4C2411yescharacteristic
181#638—24no—
182C2×C3⋊Dic3—21no—
183C4⋊(C3⋊D3)—21no—
184C4⋊(C3⋊D3)C22×C412yes—
185C4×C3⋊D3—24no—
186#634—21no—
187#634C22×C412yes—
188C3×#67—24no—
189C2×C3×Dic3—21no—
190C2×C3×Dic3—22no—
191C2×C3×Dic3—42no—
192C2×C3×Dic3C2×D412yes—
193C2×C3×Dic3C2×D412yes—
194C3×D12—21no—
195C3×D12C22×C412yes—
196C3×C4×D3—24no—
197C3×C4×D3—44no—
198C3×Dic6—21no—
199C3×Dic6C22×C412yes—
200#624—44no—
201C3⋊(C3⋊C8)—22no—
202C3×C3⋊C8C22×C412yes—
203C3×C3⋊C8C22×C412yes—
204C2×#135—91no—
205C4×#41—31no—
206C4×#41—91no—
207#442—92no—
208#441—92no—
209#440—92no—
210#440—92no—
211#427—31no—
212#416—91no—
213#416—91no—
214C2×#97—91no—
215C3×#41—34no—
216C3×#41—62no—
217C2×C3×Q8—31no—
218C2×C3×D4—31no—
219C2×C3×D4—61no—
220C22×C3×C4—21no—
221C22×C3×C4—32no—
222C22×C3×C4—62no—
223C22×C3×C4—61no—
224C22×C3×C4C22×D311yescharacteristic
225C22×C3×C4C22×D311yescharacteristic
226C2×#67—21no—
227C2×#67—61no—
228C2×#67—61no—
229C2×#67—121no—
230C22×Dic3#6712yes—
231#235—22no—
232#235—34no—
233#235—34no—
234#235—64no—
235#235—62no—
236#235—62no—
237#235—122no—
238#235C4×D314yescomplemented
239C2×D12—31no—
240C2×D12—31no—
241C2×D12—61no—
242C2×D12C22×D311yescharacteristic
243C2×C4×D3—21no—
244C2×C4×D3—22no—
245C2×C4×D3—61no—
246C2×C4×D3—61no—
247C2×C4×D3—62no—
248C2×C4×D3—62no—
249C2×C4×D3—121no—
250C2×Dic6—31no—
251C2×Dic6—31no—
252C2×Dic6—61no—
253C2×Dic6C22×D311yescharacteristic
254C2×C3×C8—34no—
255C2×C3×C8—31no—
256C2×C3×C8—31no—
257C3×C4⋊C4—22no—
258C3×C4⋊C4—32no—
259C3×C4⋊C4—62no—
260C3×C4⋊C4C22×D312yes—
261C3×C4⋊C4C22×D312yes—
262C3×C22⋊C4—21no—
263C3×C22⋊C4—21no—
264C3×C22⋊C4—41no—
265C3×C22⋊C4—62no—
266C3×C22⋊C4—61no—
267C3×C42—21no—
268C3×C42—21no—
269C3×C42—31no—
270C3×C42—31no—
271C3×C42—32no—
272C3×C42—41no—
273C3×C42—62no—
274C3×C42—61no—
275#217—21no—
276#216—34no—
277#215—34no—
278#214—34no—
279#213—34no—
280(C2×D3)⋊C4—22no—
281(C2×D3)⋊C4—62no—
282(C2×D3)⋊C4—62no—
283C4⋊Dic3C22×D312yes—
284Dic3⋊C4—22no—
285Dic3⋊C4—62no—
286Dic3⋊C4—62no—
287C4×Dic3—21no—
288C4×Dic3—22no—
289C4×Dic3—62no—
290C4×Dic3—62no—
291C4×Dic3#6711yescharacteristic
292C4×Dic3#6711yescharacteristic
293C4×Dic3C22×D312yes—
294C2×C3⋊C8—32no—
295C2×C3⋊C8—32no—
296C2×C3⋊C8—62no—
297C2×C3⋊C8—62no—
298C2×C3⋊C8—62no—
299C2×C3⋊C8—122no—
300C2×C3⋊C8C4×D314yescomplemented
301C2×C3⋊C8C22×D311yescharacteristic
302C2×C3⋊C8C22×D311yescharacteristic
303Dic12—34no—
304D24—34no—
305#204—34no—
306#204—34no—
307C22×C32—22no—
308C22×C32C4×D412yes—
309C22×C32C22×D411yescharacteristic
310C2×C3⋊D3—22no—
311C2×C3⋊D3—42no—
312C2×C3×D3—22no—
313C2×C3×D3—42no—
314C32×C4—42no—
315C32×C4C4×D412yes—
316C32×C4C23×C411yescharacteristic
317C32×C4C2×#4111yescharacteristic
318C3⋊Dic3—22no—
319C3×Dic3—22no—
320C3×Dic3—22no—
321C3×Dic3—22no—
322C3×Dic3—42no—
323C2×#41—31no—
324C2×#41—91no—
325#135—98no—
326C2×Q16—91no—
327C2×SD16—91no—
328C2×SD16—91no—
329C2×D8—91no—
330C22×C8—31no—
331C22×C8—91no—
332C4×Q8—32no—
333C4×Q8—92no—
334C4×D4—32no—
335C4×D4—62no—
336C4×D4—92no—
337C4×D4—182no—
338#117—31no—
339#117—61no—
340#117—181no—
341#117D3211yescharacteristic
342C2×C42—31no—
343C2×C42—61no—
344C2×C42—181no—
345#107—32no—
346#106—32no—
347#103—92no—
348#103—92no—
349#102—92no—
350#102—92no—
351#97—92no—
352#97—92no—
353C23×C3—21no—
354C23×C3—61no—
355C23×C3D3×D411yescharacteristic
356C23×C3C2×#6711yescharacteristic
357C22×D3—21no—
358C22×D3—61no—
359C22×D3—61no—
360C22×D3—121no—
361C3×Q8—32no—
362C3×Q8—61no—
363C3×D4—32no—
364C3×D4—64no—
365C3×D4—61no—
366C2×C3×C4—22no—
367C2×C3×C4—22no—
368C2×C3×C4—21no—
369C2×C3×C4—22no—
370C2×C3×C4—22no—
371C2×C3×C4—21no—
372C2×C3×C4—32no—
373C2×C3×C4—32no—
374C2×C3×C4—42no—
375C2×C3×C4—61no—
376C2×C3×C4—64no—
377C2×C3×C4—62no—
378C2×C3×C4—124no—
379C2×C3×C4—122no—
380C2×C3×C4C2×C4×D312yes—
381C2×C3×C4C2×C4×D312yes—
382C2×C3×C4#23512yes—
383C2×C3×C4D3×D411yescharacteristic
384C2×C3×C4#23912yes—
385C2×C3×C4C2×#6711yescharacteristic
386C2×C3×C4C23×D311yescharacteristic
387C2×C3×C4C23×D311yescharacteristic
388#67—24no—
389#67—64no—
390#67—64no—
391#67—124no—
392C2×Dic3—21no—
393C2×Dic3—22no—
394C2×Dic3—42no—
395C2×Dic3—61no—
396C2×Dic3—61no—
397C2×Dic3—121no—
398C2×Dic3C2×#6712yes—
399C2×Dic3C2×#6712yes—
400D12—21no—
401D12—32no—
402D12—32no—
403D12—62no—
404D12—61no—
405D12—61no—
406D12—121no—
407D12C2×C4×D312yes—
408C4×D3—24no—
409C4×D3—44no—
410C4×D3—64no—
411C4×D3—64no—
412C4×D3—124no—
413C4×D3—124no—
414C4×D3—124no—
415Dic6—21no—
416Dic6—32no—
417Dic6—32no—
418Dic6—62no—
419Dic6—61no—
420Dic6—61no—
421Dic6—121no—
422Dic6C2×C4×D312yes—
423C3×C8—32no—
424C3×C8—32no—
425C3⋊C8—62no—
426C3⋊C8—62no—
427C3⋊C8—122no—
428C3⋊C8C2×C4×D312yes—
429C3⋊C8C2×C4×D312yes—
430C2×C32—22no—
431C2×C32C2×C4×D411yescharacteristic
432C2×C32#57512yes—
433C3⋊D3—42no—
434C3×D3—42no—
435#41—34no—
436#41—62no—
437#41—94no—
438#41—182no—
439C2×Q8—31no—
440C2×Q8—91no—
441C2×D4—31no—
442C2×D4—61no—
443C2×D4—91no—
444C2×D4—181no—
445C22×C4—32no—
446C22×C4—62no—
447C22×C4—61no—
448C22×C4—182no—
449C22×C4—181no—
450C22×C4C2×D3211yescharacteristic
451Q16—94no—
452SD16—94no—
453SD16—94no—
454D8—94no—
455C2×C8—31no—
456C2×C8—31no—
457C2×C8—34no—
458C2×C8—92no—
459C2×C8—182no—
460C4⋊C4—32no—
461C4⋊C4—62no—
462C4⋊C4—182no—
463C4⋊C4C2×D3212yes—
464C22⋊C4—21no—
465C22⋊C4—62no—
466C22⋊C4—61no—
467C22⋊C4—182no—
468C42—21no—
469C42—32no—
470C42—31no—
471C42—31no—
472C42—62no—
473C42—61no—
474C42—182no—
475C22×C3—22no—
476C22×C3—22no—
477C22×C3—21no—
478C22×C3—22no—
479C22×C3—42no—
480C22×C3—62no—
481C22×C3—122no—
482C22×C3#89312yes—
483C22×C3C4×#6712yes—
484C22×C3C2×D3×D411yescharacteristic
485C22×C3C22×#6711yescharacteristic
486C2×D3—22no—
487C2×D3—42no—
488C2×D3—62no—
489C2×D3—62no—
490C2×D3—122no—
491C2×D3—122no—
492C2×D3—122no—
493C2×D3—242no—
494C3×C4—21no—
495C3×C4—21no—
496C3×C4—22no—
497C3×C4—42no—
498C3×C4—42no—
499C3×C4—62no—
500C3×C4—62no—
501C3×C4—62no—
502C3×C4—82no—
503C3×C4—122no—
504C3×C4#89312yes—
505C3×C4C4×#6712yes—
506C3×C4C22×C4×D311yescharacteristic
507C3×C4C22×C4×D311yescharacteristic
508C3×C4C2×#23511yescharacteristic
509C3×C4C2×#23911yescharacteristic
510Dic3—22no—
511Dic3—22no—
512Dic3—22no—
513Dic3—42no—
514Dic3—62no—
515Dic3—62no—
516Dic3—122no—
517C32#294311yescharacteristic, complemented, Sylow
518C23—61no—
519C23—181no—
520C23D3×#6711yescharacteristic
521Q8—32no—
522Q8—61no—
523Q8—92no—
524Q8—181no—
525D4—32no—
526D4—64no—
527D4—61no—
528D4—92no—
529D4—184no—
530D4—181no—
531C2×C4—22no—
532C2×C4—32no—
533C2×C4—32no—
534C2×C4—61no—
535C2×C4—64no—
536C2×C4—62no—
537C2×C4—124no—
538C2×C4—122no—
539C2×C4—181no—
540C2×C4—184no—
541C2×C4—364no—
542C2×C4#379912yes—
543C2×C4C4×D3212yes—
544C2×C4D3×#6711yescharacteristic
545C2×C4C22×D3211yescharacteristic
546C8—32no—
547C8—32no—
548C8—182no—
549C2×C3—22no—
550C2×C3—22no—
551C2×C3—22no—
552C2×C3—21no—
553C2×C3—42no—
554C2×C3—122no—
555C2×C3C2×#89311yescharacteristic
556C2×C3#576812yes—
557C2×C3C2×C4×#6711yescharacteristic
558C2×C3#582212yes—
559D3—42no—
560D3—122no—
561D3—122no—
562D3—242no—
563C22—22no—
564C22—62no—
565C22—122no—
566C22—182no—
567C22—362no—
568C22#6390412yes—
569C22C2×D3×#6711yescharacteristic
570C4—42no—
571C4—62no—
572C4—62no—
573C4—62no—
574C4—122no—
575C4—182no—
576C4#6390412yes—
577C4C2×#379911yescharacteristic
578C4C2×C4×D3211yescharacteristic
579C3—21no—
580C3#7916611yescharacteristic, complemented
581C3#8250611yescharacteristic, complemented
582C2—22no—
583C2—122no—
584C2—362no—
585C2C2×#6390411yescharacteristic
586C2#1059545312yes—
subgroupG/H
centerC2×C4D3×#67
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×#117C22
socleC22×C32C22×D4
prime radicalC2×#63829C2
cosocleC2×C32×C4C24
hypercenter#117D32
hypocenterC32#2943
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. C3×#5522C2semidirect
2. #10594954C2semidirect
4. #10592701C2semidirect
5. C3×#4998C2semidirect
6. #10591083C2semidirect
7. C2×#63554C2semidirect
8. #10590590C2semidirect
9. #10590589C2semidirect
10. #10590480C2semidirect
11. #10590457C2semidirect
33. #63829C4semidirect
48. #5522D3semidirect
61. #4998D3semidirect
70. #3828C2×C4semidirect
77. C3×#235C2×C4semidirect
97. C2×C3×C3⋊C8C2×C4semidirect
103. #3719C2×C4semidirect
104. #3717C2×C4semidirect
105. #3716C2×C4semidirect
106. #3714C2×C4semidirect
238. #235C4×D3semidirect
300. C2×C3⋊C8C4×D3semidirect
517. C32#2943semidirect
580. C3#79166semidirect
581. C3#82506semidirect

Maximal subgroups

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

subgroupindex
C3×#55222
#105949542
C2×#638292
#105927012
C3×#49982
#105910832
C2×#635542
#105905902
#105905892
#105904802
#105904572
#825063
#791663