Finite Group Databasebeta

← #11786734

Subgroups — #11786734

Order 1152.

456 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 68 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596650C211yesmaximal, characteristic
2#10593840C211yesmaximal, characteristic
3#10593774C211yesmaximal, characteristic, complemented
4#10593736C211yesmaximal, characteristic, complemented
5C3⋊D3×#104C211yesmaximal, characteristic
6#10590188C211yesmaximal, characteristic, complemented
7#10590151C211yesmaximal, characteristic, complemented
8#41×C3⋊D3C2211yescharacteristic
9Q8×#157—21no—
10D4×#157—21no—
11D4×#157—22no—
12#64286—21no—
13#64286C2211yescharacteristic
14C2×C4⋊#157—21no—
15C2×C4⋊#157C2211yescharacteristic
16C2×C4⋊#157C2211yescharacteristic
17#64283C2211yescharacteristic
18M16×C3⋊D3C2211yescharacteristic
19C42×C3⋊D3C2211yescharacteristic
20#63784—21no—
21#63782—21no—
22#63781—22no—
23#63769—21no—
24#63768—21no—
25C32×#104C411yescharacteristic, complemented
26#63664C411yescharacteristic, complemented
27#63652C411yescharacteristic, complemented
28#63632C411yescharacteristic, complemented
29D3×#104—62no—
30C22×#157—22no—
31C22×#157—21no—
32C22×#157D412yes—
33C32×#41C2×C411yescharacteristic
34#3832Q811yescharacteristic
35Q8×C3⋊D3D411yescharacteristic
36#3830—21no—
37#3830Q811yescharacteristic
38D4×C3⋊D3—21no—
39D4×C3⋊D3D411yescharacteristic
40#3828—21no—
41#3828C2×C411yescharacteristic
42C2×C4×C3⋊D3—21no—
43C2×C4×C3⋊D3—21no—
44C2×C4×C3⋊D3C2311yescharacteristic
45C22⋊#157—22no—
46C22⋊#157—21no—
47#3792—21no—
48C4⋊#157—22no—
49C4⋊#157—21no—
50C4⋊#157—21no—
51C4⋊#157—21no—
52C4⋊#157—21no—
53C4⋊#157D411yescharacteristic
54C4⋊#157D411yescharacteristic
55C4×#157—22no—
56C4×#157—21no—
57#3788—21no—
58#3787—21no—
59C32×M16C2×C411yescharacteristic, complemented
60C32×C42C2×C411yescharacteristic, complemented
61C4×C3⋊Dic3—21no—
62C4×C3⋊Dic3C2×C411yescharacteristic, complemented
63#3748C2×C411yescharacteristic, complemented
64#3743—21no—
65C8×C3⋊D3—21no—
66#1860—91nomaximal, Sylow
67D3×#41—62no—
68D3×M16—62no—
69C42×D3—62no—
70C3×#104—22no—
71#837—62no—
72#825—62no—
73#805—62no—
74C22×C3⋊D3—21no—
75C22×C3⋊D3C2×D411yescharacteristic
76C2×#157—21no—
77C2×#157—22no—
78C2×#157—21no—
79C2×#157—42no—
80C2×#157—42no—
81C2×#157—41no—
82C2×#157—82no—
83C32×Q8C4⋊C411yescharacteristic
84C32×D4—21no—
85C32×D4C4⋊C411yescharacteristic
86C2×C32×C4—21no—
87C2×C32×C4—21no—
88C2×C32×C4C22×C411yescharacteristic
89#638—21no—
90#638—21no—
91#638—21no—
92C2×C3⋊Dic3—21no—
93C2×C3⋊Dic3—21no—
94C2×C3⋊Dic3#4111yescharacteristic
95C4⋊(C3⋊D3)—21no—
96C4⋊(C3⋊D3)C4⋊C411yescharacteristic
97C4×C3⋊D3—21no—
98C4×C3⋊D3—21no—
99C4×C3⋊D3—21no—
100C4×C3⋊D3—41no—
101C4×C3⋊D3—41no—
102C4×C3⋊D3C2×D411yescharacteristic
103C4×C3⋊D3C2×D411yescharacteristic
104C4×C3⋊D3C2×Q811yescharacteristic
105C4×C3⋊D3#4111yescharacteristic
106#634—21no—
107#634C4⋊C411yescharacteristic
108#622—41no—
109C32×C8—21no—
110C3⋊(C3⋊C8)—21no—
111#520—91no—
112#428—91no—
113C2×#104—91no—
114#417—91no—
115#382—91no—
116#343—91no—
117#339—91no—
118C3×#41—22no—
119#239—62no—
120D3×Q8—62no—
121#237—62no—
122#237—122no—
123D3×D4—62no—
124D3×D4—122no—
125#235—62no—
126#235—122no—
127C2×C4×D3—62no—
128C2×C4×D3—122no—
129C2×C4×D3—122no—
130C3×M16—22no—
131C3×C42—22no—
132C4×Dic3—62no—
133C4×Dic3—122no—
134#208—62no—
135ΓL(1,𝔽25)—122no—
136D3×C8—122no—
137C22×C32—21no—
138C22×C32C4×D411yescharacteristic
139C2×C3⋊D3—21no—
140C2×C3⋊D3—21no—
141C2×C3⋊D3—21no—
142C2×C3⋊D3—41no—
143C2×C3⋊D3—41no—
144C2×C3⋊D3#12011yescharacteristic
145C2×C3⋊D3C22⋊Q811yescharacteristic
146#157—41no—
147#157—42no—
148#157—41no—
149#157—81no—
150C32×C4—21no—
151C32×C4—41no—
152C32×C4C2×C4⋊C411yescharacteristic
153C32×C4C4×D411yescharacteristic
154C3⋊Dic3—21no—
155C3⋊Dic3—41no—
156C3⋊Dic3C22⋊Q811yescharacteristic
157C3⋊Dic3#12311yescharacteristic
158C2×#41—91no—
159C2×M16—91no—
160C2×M16—91no—
161C4×Q8—181no—
162C4×D4—182no—
163C4×D4—181no—
164#117—91no—
165#117—181no—
166C2×C4⋊C4—91no—
167C2×C4⋊C4—91no—
168C2×C4⋊C4—181no—
169C2×C42—91no—
170#107—181no—
171#106—181no—
172#104—91no—
173#104—91no—
174#104—91no—
175#104#15711yescharacteristic, complemented
176#103—181no—
177#102—181no—
178#95—182no—
179C22×D3—62no—
180C22×D3—122no—
181C3×Q8—22no—
182C3×D4—22no—
183C3×D4—42no—
184C2×C3×C4—22no—
185C2×C3×C4—42no—
186C2×C3×C4—42no—
187#67—122no—
188#67—122no—
189#67—122no—
190C2×Dic3—62no—
191C2×Dic3—122no—
192C2×Dic3—122no—
193D12—62no—
194D12—122no—
195C4×D3—62no—
196C4×D3—62no—
197C4×D3—62no—
198C4×D3—62no—
199C4×D3—122no—
200C4×D3—122no—
201C4×D3—122no—
202C4×D3—124no—
203C4×D3—124no—
204Dic6—62no—
205Dic6—122no—
206C3×C8—42no—
207C3⋊C8—122no—
208C2×C32—21no—
209C2×C32—41no—
210C2×C32#38511yescharacteristic
211C3⋊D3—21no—
212C3⋊D3—41no—
213C3⋊D3#45411yescharacteristic
214C3⋊D3#45511yescharacteristic
215#41—91no—
216#41—91no—
217#41—91no—
218#41—181no—
219#41—181no—
220#41C2×#15711yescharacteristic
221C2×Q8—91no—
222C2×D4—91no—
223C2×D4—181no—
224C22×C4—91no—
225C22×C4—92no—
226C22×C4—181no—
227C22×C4—181no—
228C22×C4—182no—
229C22×C4—181no—
230M16—91no—
231M16—181no—
232M16—181no—
233M16—181no—
234M16C2×#15711yescharacteristic, complemented
235C2×C8—181no—
236C2×C8—181no—
237C4⋊C4—91no—
238C4⋊C4—91no—
239C4⋊C4—181no—
240C4⋊C4—181no—
241C4⋊C4—181no—
242C4⋊C4—181no—
243C4⋊C4—182no—
244C22⋊C4—181no—
245C22⋊C4—182no—
246C42—91no—
247C42—181no—
248C42—181no—
249C42—182no—
250C42C2×#15711yescharacteristic, complemented
251C22×C3—22no—
252C22×C3—42no—
253C2×D3—62no—
254C2×D3—62no—
255C2×D3—122no—
256C2×D3—122no—
257C2×D3—122no—
258C2×D3—242no—
259C2×D3—242no—
260C3×C4—22no—
261C3×C4—22no—
262C3×C4—42no—
263C3×C4—44no—
264Dic3—62no—
265Dic3—62no—
266Dic3—122no—
267Dic3—124no—
268C32#186011yescharacteristic, complemented, Sylow
269C23—91no—
270C23—181no—
271Q8—91no—
272Q8—181no—
273Q8C4⋊#15711yescharacteristic
274D4—21no—
275D4—91no—
276D4—181no—
277D4—181no—
278D4—181no—
279D4—181no—
280D4C4⋊#15711yescharacteristic
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—91no—
284C2×C4—91no—
285C2×C4—91no—
286C2×C4—91no—
287C2×C4—91no—
288C2×C4—181no—
289C2×C4—181no—
290C2×C4—181no—
291C2×C4—181no—
292C2×C4—181no—
293C2×C4—181no—
294C2×C4—182no—
295C2×C4—181no—
296C2×C4—361no—
297C2×C4—361no—
298C2×C4—362no—
299C2×C4—361no—
300C2×C4—362no—
301C2×C4—722no—
302C2×C4C22×#15711yescharacteristic
303C8—21no—
304C8—181no—
305C8—361no—
306C2×C3—22no—
307C2×C3—42no—
308C2×C3—82no—
309D3—62no—
310D3—62no—
311D3—122no—
312D3—242no—
313C22—21no—
314C22—91no—
315C22—91no—
316C22—181no—
317C22—181no—
318C22—181no—
319C22—361no—
320C22—361no—
321C22D4×#15711yescharacteristic
322C4—21no—
323C4—41no—
324C4—91no—
325C4—91no—
326C4—181no—
327C4—361no—
328C4—362no—
329C4—361no—
330C4—361no—
331C4—721no—
332C4C2×C4⋊#15711yescharacteristic
333C4D4×#15711yescharacteristic
334C3—22no—
335C2—21no—
336C2—41no—
337C2—91no—
338C2—91no—
339C2—181no—
340C2—361no—
341C2#1059374611yescharacteristic
subgroupG/H
centerC2#10593746
commutatorC2×C32×C4C22×C4
FrattiniC2×C4C22×#157
FittingC32×#104C4
socleC2×C32#385
prime radical#41×C3⋊D3C22
cosocleC2×C4×C3⋊D3C23
hypercenter#104#157
hypocenterC32#1860
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ #104

Complements

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

NH ≅ G/Ntype
3. #10593774C2semidirect
4. #10593736C2semidirect
6. #10590188C2semidirect
7. #10590151C2semidirect
25. C32×#104C4semidirect
26. #63664C4semidirect
27. #63652C4semidirect
28. #63632C4semidirect
59. C32×M16C2×C4semidirect
60. C32×C42C2×C4semidirect
62. C4×C3⋊Dic3C2×C4semidirect
63. #3748C2×C4semidirect
175. #104#157semidirect
234. M16C2×#157semidirect
250. C42C2×#157semidirect
268. C32#1860semidirect

Maximal subgroups

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

subgroupindex
#105966502
#105938402
#105937742
#105937362
C3⋊D3×#1042
#105901882
#105901512
#18609