Finite Group Databasebeta

← #11860899

Subgroups — #11860899

Order 1152.

1035 conjugacy classes of subgroups.

The subgroup lattice has 530 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63808C211yesmaximal, characteristic
2#10594327C212yesmaximal, complemented
3#10592571C211yesmaximal, characteristic, complemented
4C3×D3×#107C211yesmaximal, characteristic, complemented
5C3×#4873C211yesmaximal, characteristic, complemented
6#10590818C211yesmaximal, characteristic, complemented
7#10590763C211yesmaximal, characteristic, complemented
8#10590692C211yesmaximal, characteristic, complemented
9#10590609C212yesmaximal, complemented
10#10590484C212yesmaximal, complemented
11#10590457C212yesmaximal, complemented
12#79721—31nomaximal
13#79136—31nomaximal
14C2×#3799C2212yes—
15C2×#3745C2211yescharacteristic
16#64102C2212yes—
17C2×C3×Dic12C2211yescharacteristic
18C2×C3×D3×C8C2211yescharacteristic
19C3×D3×C4⋊C4C2212yes—
20C3×#887C2212yes—
21#63904—22no—
22C4×#626—22no—
23#63894C2212yes—
24#63883—22no—
25#63855C2211yescharacteristic
26#63843C2212yes—
27#63836—22no—
28C2×#3717C2212yes—
29C2×#3711C2211yescharacteristic
30#63808C418yescomplemented
31C32×#107C2211yescharacteristic
32C8×C3⋊Dic3C2211yescharacteristic
33#63636C2212yes—
34C3×#818C2211yescharacteristic
35C3×C8×Dic3C2211yescharacteristic
36C3×#810C2212yes—
37C3×#807C2212yes—
38#63565C2212yes—
39#63564C2212yes—
40#63555C2211yescharacteristic
41#63554C2211yescharacteristic
42C2×#919—31no—
43C2×#904—31no—
44#5574—32no—
45#5504—32no—
46C3×C4×Q16—31no—
47C2×C3×#107—31no—
48Dic3×Q16—31no—
49#5101—31no—
50#5026—32no—
51#4966—32no—
52#4889—32no—
53#4889—32no—
54D3×#107D311yescharacteristic, complemented
55#4873—31no—
56#4873D311yescharacteristic, complemented
57#4872—31no—
58#4872—31no—
59#4872—31no—
60#4872—61no—
61#4817—32no—
62#4803—32no—
63C4×D24—31no—
64#4689—31no—
65C2×C4⋊(C3⋊D3)C2312yes—
66C2×C4×C3⋊D3—22no—
67C2×C3×C4×D3—22no—
68C2×C3×C4×D3C2311yescharacteristic
69C2×C3×Dic6C2312yes—
70C2×#626—22no—
71C2×#624—22no—
72C2×#624—22no—
73#3799—24no—
74#3799C2×C418yescomplemented
75C2×C32×C8C2311yescharacteristic
76C32×C4⋊C4C2312yes—
77#3752—22no—
78C4×C3⋊Dic3C2311yescharacteristic
79C2×C3⋊(C3⋊C8)C2311yescharacteristic
80#3745C2×C414yescomplemented
81C3×C4⋊Dic3C2312yes—
82C3×Dic3⋊C4—22no—
83C3×Dic3⋊C4—22no—
84C3×C4×Dic3—22no—
85C3×C4×Dic3C2311yescharacteristic
86C2×C3×C3⋊C8C2311yescharacteristic
87C2×C3×C3⋊C8C2311yescharacteristic
88C3×Dic12C2×C414yescomplemented
89C3×D3×C8C2×C414yescomplemented
90Dic3⋊Dic3—22no—
91Dic3⋊Dic3D411yescharacteristic
92Dic3⋊Dic3D411yescharacteristic
93#3722—22no—
94(C2×D3)⋊Dic3D411yescharacteristic
95(C2×D3)⋊Dic3D411yescharacteristic
96Dic32—22no—
97#3717C2×C418yescomplemented
98#3711—22no—
99#2951—91noSylow
100C2×#239—32no—
101C2×#235—32no—
102C2×C3×Q16—31no—
103C22×C3×C8—31no—
104C3×C4×Q8—32no—
105C2×C3×C4⋊C4—32no—
106Q8×Dic3—32no—
107C2×#215—32no—
108C4×#67—62no—
109C4×#67—62no—
110#926—31no—
111C2×#208—31no—
112#919—38no—
113C2×Dic12C2×D311yescharacteristic
114#904—38no—
115C2×D24—31no—
116C2×D24—31no—
117C2×D24—61no—
118C2×#204—32no—
119C2×ΓL(1,𝔽25)—31no—
120C2×D3×C8C2×D311yescharacteristic
121#893—32no—
122#893—32no—
123#893—32no—
124#893—62no—
125#893—62no—
126#892—62no—
127D3×C4⋊C4—62no—
128D3×C4⋊C4—62no—
129D3×C4⋊C4C2×D312yes—
130#887—32no—
131#887C2×D312yes—
132C4×D12—32no—
133C4×D12—62no—
134#872—31no—
135#872—62no—
136C3×#107—21no—
137C3×#107—31no—
138C3×#107—32no—
139C3×#107C2×D311yescharacteristic
140C3×#107C2×D311yescharacteristic
141C3×#103—32no—
142C3×C4×C8—31no—
143#835—32no—
144#821—32no—
145#818C2×D311yescharacteristic
146#815—31no—
147#815—31no—
148#815—31no—
149C8×Dic3—31no—
150C8×Dic3—31no—
151C8×Dic3—61no—
152C8×Dic3C2×D311yescharacteristic
153#810—32no—
154#810C2×D312yes—
155#809—32no—
156#809—32no—
157#809—32no—
158#809—62no—
159#807C2×D312yes—
160#803—31no—
161C22×C3⋊D3—22no—
162C22×C3×D3C2×D411yescharacteristic
163C2×C32×C4—22no—
164C2×C32×C4C2411yescharacteristic
165C2×C3⋊Dic3C2×D411yescharacteristic
166C2×C3⋊Dic3C2×D411yescharacteristic
167C4⋊(C3⋊D3)—22no—
168C4⋊(C3⋊D3)C22×C414yes—
169C4×C3⋊D3—82no—
170C2×C3×Dic3—22no—
171C2×C3×Dic3—22no—
172C2×C3×Dic3C2×D411yescharacteristic
173C2×C3×Dic3C2×D411yescharacteristic
174C2×C3×Dic3C2×D411yescharacteristic
175C3×C4×D3—82no—
176C3×C4×D3C22×C412yes—
177C3×C4×D3#4112yes—
178C3×Dic6—22no—
179C3×Dic6C22×C414yes—
180#626—28no—
181#624—28no—
182#624—82no—
183C32×C8C22×C412yes—
184C3⋊(C3⋊C8)—21no—
185C3×C3⋊C8—21no—
186C3×C3⋊C8C22×C412yes—
187C2×#135—91no—
188#520—92no—
189#440—92no—
190#440—92no—
191C4×Q16—31no—
192C4×Q16—91no—
193C4×D8—91no—
194C4×D8—91no—
195C2×#107—31no—
196#417—92no—
197#405—91no—
198C2×C3×Q8—32no—
199C22×C3×C4—31no—
200C22×C3×C4—62no—
201C2×#67—62no—
202#239—38no—
203#239—64no—
204#235—38no—
205#235—64no—
206C2×D12—32no—
207C2×D12—32no—
208C2×D12—62no—
209C2×D12—62no—
210C2×C4×D3—22no—
211C2×C4×D3—62no—
212C2×C4×D3—62no—
213C2×C4×D3—62no—
214C2×C4×D3—62no—
215C2×C4×D3—62no—
216C2×C4×D3—62no—
217C2×C4×D3—122no—
218C2×C4×D3C22×D311yescharacteristic
219C2×Dic6C22×D312yes—
220C3×Q16—34no—
221C2×C3×C8—21no—
222C2×C3×C8—31no—
223C2×C3×C8—34no—
224C2×C3×C8—31no—
225C2×C3×C8C22×D311yescharacteristic
226C2×C3×C8C22×D311yescharacteristic
227C3×C4⋊C4—22no—
228C3×C4⋊C4—32no—
229C3×C4⋊C4—62no—
230C3×C4⋊C4—62no—
231C3×C4⋊C4C22×D312yes—
232C3×C4⋊C4C22×D312yes—
233C3×C42—31no—
234C3×C42—62no—
235#217—31no—
236#217—31no—
237#215—38no—
238(C2×D3)⋊C4—31no—
239(C2×D3)⋊C4—31no—
240(C2×D3)⋊C4—62no—
241(C2×D3)⋊C4—62no—
242(C2×D3)⋊C4—62no—
243(C2×D3)⋊C4—62no—
244(C2×D3)⋊C4—122no—
245C4⋊Dic3—31no—
246C4⋊Dic3—31no—
247C4⋊Dic3—62no—
248C4⋊Dic3C22×D312yes—
249Dic3⋊C4—22no—
250Dic3⋊C4—22no—
251Dic3⋊C4—31no—
252Dic3⋊C4—31no—
253Dic3⋊C4—62no—
254C4×Dic3—22no—
255C4×Dic3—31no—
256C4×Dic3—31no—
257C4×Dic3—61no—
258C4×Dic3—62no—
259C4×Dic3—62no—
260C4×Dic3C22×D311yescharacteristic
261#208—62no—
262C2×C3⋊C8—31no—
263C2×C3⋊C8—31no—
264C2×C3⋊C8—61no—
265C2×C3⋊C8C22×D311yescharacteristic
266C2×C3⋊C8C22×D311yescharacteristic
267Dic12C4×D314yescomplemented
268D24—34no—
269D24—34no—
270D24—64no—
271#204—38no—
272ΓL(1,𝔽25)—62no—
273D3×C8C4×D314yescomplemented
274C22×C32C22×D411yescharacteristic
275C2×C3⋊D3—24no—
276C2×C3⋊D3—42no—
277C2×C3⋊D3—42no—
278C2×C3×D3—21no—
279C2×C3×D3—21no—
280C2×C3×D3C4×D412yes—
281C32×C4—42no—
282C32×C4C23×C411yescharacteristic
283C32×C4C2×#4111yescharacteristic
284C3⋊Dic3—21no—
285C3⋊Dic3—21no—
286C3×Dic3—24no—
287C3×Dic3—21no—
288C3×Dic3—21no—
289C3×Dic3—42no—
290C3×Dic3C4×D412yes—
291C2×#41—92no—
292#135—98no—
293C2×Q16—31no—
294C2×SD16—92no—
295C2×D8—91no—
296C2×M16—91no—
297C22×C8—31no—
298C4×Q8—32no—
299C4×Q8—92no—
300C4×D4—92no—
301C4×D4—92no—
302C4×D4—182no—
303C4×D4—182no—
304#117—91no—
305#117—182no—
306C2×C4⋊C4—32no—
307C2×C4⋊C4—182no—
308#107—31no—
309#107—32no—
310#107D3211yescharacteristic
311#103—32no—
312#103—92no—
313#102—92no—
314#102—92no—
315#97—91no—
316#97—91no—
317C4×C8—31no—
318C4×C8—91no—
319C23×C3—31no—
320C22×D3—62no—
321C22×D3—62no—
322C22×D3—122no—
323C22×D3D3×D411yescharacteristic
324C3×Q8—34no—
325C3×Q8—62no—
326C2×C3×C4—22no—
327C2×C3×C4—22no—
328C2×C3×C4—21no—
329C2×C3×C4—31no—
330C2×C3×C4—32no—
331C2×C3×C4—32no—
332C2×C3×C4—31no—
333C2×C3×C4—31no—
334C2×C3×C4—42no—
335C2×C3×C4—62no—
336C2×C3×C4—62no—
337C2×C3×C4—242no—
338C2×C3×C4C23×D311yescharacteristic
339C2×C3×C4C23×D311yescharacteristic
340#67—68no—
341C2×Dic3—22no—
342C2×Dic3—22no—
343C2×Dic3—31no—
344C2×Dic3—31no—
345C2×Dic3—31no—
346C2×Dic3—31no—
347C2×Dic3—61no—
348C2×Dic3—61no—
349C2×Dic3D3×D411yescharacteristic
350C2×Dic3D3×D411yescharacteristic
351C2×Dic3D3×D411yescharacteristic
352D12—34no—
353D12—34no—
354D12—64no—
355D12—68no—
356D12—62no—
357D12—62no—
358D12—122no—
359C4×D3—68no—
360C4×D3—68no—
361C4×D3—82no—
362C4×D3—242no—
363C4×D3—242no—
364C4×D3—242no—
365C4×D3—242no—
366C4×D3—244no—
367C4×D3C2×C4×D312yes—
368C4×D3#23912yes—
369Dic6—22no—
370Dic6C2×C4×D314yes—
371C3×C8—22no—
372C3×C8—32no—
373C3×C8—61no—
374C3×C8C2×C4×D312yes—
375C3×C8C2×C4×D312yes—
376C3⋊C8—21no—
377C3⋊C8—61no—
378C3⋊C8—61no—
379C3⋊C8—121no—
380C3⋊C8C2×C4×D312yes—
381C2×C32C2×C4×D411yescharacteristic
382C2×C32#57611yescharacteristic
383C2×C32#57811yescharacteristic
384C3⋊D3—44no—
385C3×D3—22no—
386#41—98no—
387#41—184no—
388C2×Q8—32no—
389C2×D4—92no—
390C2×D4—182no—
391C22×C4—31no—
392C22×C4—62no—
393C22×C4—182no—
394C22×C4—182no—
395C22×C4—182no—
396Q16—34no—
397SD16—98no—
398D8—94no—
399M16—182no—
400C2×C8—31no—
401C2×C8—34no—
402C2×C8—31no—
403C2×C8—91no—
404C2×C8C2×D3211yescharacteristic
405C4⋊C4—32no—
406C4⋊C4—62no—
407C4⋊C4—62no—
408C4⋊C4—91no—
409C4⋊C4—91no—
410C4⋊C4—182no—
411C4⋊C4C2×D3212yes—
412C22⋊C4—91no—
413C22⋊C4—91no—
414C22⋊C4—182no—
415C22⋊C4—182no—
416C42—31no—
417C42—62no—
418C42—91no—
419C42—182no—
420C22×C3—21no—
421C22×C3—32no—
422C22×C3—61no—
423C22×C3—61no—
424C22×C3C2×D3×D411yescharacteristic
425C22×C3C2×D3×D411yescharacteristic
426C2×D3—21no—
427C2×D3—21no—
428C2×D3—64no—
429C2×D3—64no—
430C2×D3—124no—
431C2×D3—122no—
432C2×D3—122no—
433C2×D3—122no—
434C2×D3—122no—
435C2×D3—242no—
436C2×D3—242no—
437C2×D3#89312yes—
438C3×C4—21no—
439C3×C4—21no—
440C3×C4—32no—
441C3×C4—42no—
442C3×C4—42no—
443C3×C4—61no—
444C3×C4—64no—
445C3×C4—61no—
446C3×C4—82no—
447C3×C4—122no—
448C3×C4C22×C4×D311yescharacteristic
449C3×C4C22×C4×D311yescharacteristic
450C3×C4C2×#23911yescharacteristic
451C3×C4D3×#4111yescharacteristic
452Dic3—21no—
453Dic3—21no—
454Dic3—24no—
455Dic3—42no—
456Dic3—62no—
457Dic3—61no—
458Dic3—61no—
459Dic3—61no—
460Dic3—61no—
461Dic3—121no—
462Dic3#89312yes—
463C32#295111yescharacteristic, complemented, Sylow
464C23—31no—
465C23—182no—
466Q8—34no—
467Q8—62no—
468D4—94no—
469D4—188no—
470D4—182no—
471C2×C4—22no—
472C2×C4—31no—
473C2×C4—32no—
474C2×C4—32no—
475C2×C4—31no—
476C2×C4—31no—
477C2×C4—62no—
478C2×C4—62no—
479C2×C4—91no—
480C2×C4—91no—
481C2×C4—188no—
482C2×C4—242no—
483C2×C4—722no—
484C2×C4—722no—
485C2×C4C22×D3211yescharacteristic
486C8—32no—
487C8—61no—
488C8—181no—
489C8C4×D3212yes—
490C2×C3—21no—
491C2×C3—21no—
492C2×C3—21no—
493C2×C3—62no—
494C2×C3C2×#89311yescharacteristic
495C2×C3C4×D3×D411yescharacteristic
496C2×C3#575711yescharacteristic
497C2×C3#576611yescharacteristic
498C2×C3#576611yescharacteristic
499C2×C3#576911yescharacteristic
500D3—22no—
501D3—124no—
502D3—124no—
503D3—244no—
504C22—32no—
505C22—61no—
506C22—61no—
507C22—184no—
508C22—362no—
509C22—362no—
510C22D32×D411yescharacteristic
511C4—32no—
512C4—42no—
513C4—64no—
514C4—61no—
515C4—61no—
516C4—122no—
517C4—181no—
518C4—181no—
519C4C2×C4×D3211yescharacteristic
520C4D3×#23911yescharacteristic
521C3—21no—
522C3#7913611yescharacteristic, complemented
523C3#7972111yescharacteristic, complemented
524C2—62no—
525C2—364no—
526C2D3×#89311yescharacteristic
527C2#1059473411yescharacteristic
528C2#1059476511yescharacteristic
subgroupG/H
centerC22D32×D4
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×#107C22
socleC22×C32C22×D4
prime radicalC2×#63808C2
cosocleC2×C32×C4C24
hypercenter#107D32
hypocenterC32#2951
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #107

Complements

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

NH ≅ G/Ntype
2. #10594327C2semidirect
3. #10592571C2semidirect
4. C3×D3×#107C2semidirect
5. C3×#4873C2semidirect
6. #10590818C2semidirect
7. #10590763C2semidirect
8. #10590692C2semidirect
9. #10590609C2semidirect
10. #10590484C2semidirect
11. #10590457C2semidirect
30. #63808C4semidirect
54. D3×#107D3semidirect
56. #4873D3semidirect
74. #3799C2×C4semidirect
80. #3745C2×C4semidirect
88. C3×Dic12C2×C4semidirect
89. C3×D3×C8C2×C4semidirect
97. #3717C2×C4semidirect
267. Dic12C4×D3semidirect
273. D3×C8C4×D3semidirect
463. C32#2951semidirect
522. C3#79136semidirect
523. C3#79721semidirect

Maximal subgroups

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

subgroupindex
C2×#638082
#105943272
#105925712
C3×D3×#1072
C3×#48732
#105908182
#105907632
#105906922
#105906092
#105904842
#105904572
#797213
#791363