Finite Group Databasebeta

← #11783907

Subgroups — #11783907

Order 1152.

490 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 490 conjugacy classes of subgroups — too many to draw. Only its 88 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#41×#157C211yesmaximal, characteristic
2#10593839C211yesmaximal, characteristic
3M16×#157C211yesmaximal, characteristic, complemented
4#10593733C211yesmaximal, characteristic, complemented
5C3⋊D3×#104C211yesmaximal, characteristic
6#10590189C211yesmaximal, characteristic, complemented
7#10590151C211yesmaximal, characteristic, complemented
8#41×C3⋊D3C2211yescharacteristic
9Q8×#157C412yescomplemented
10D4×#157—22no—
11D4×#157C412yescomplemented
12#64286—21no—
13#64286C2211yescharacteristic
14C2×C4×#157—21no—
15C2×C4×#157C2211yescharacteristic
16C2×C4×#157C2211yescharacteristic
17#64283C2211yescharacteristic
18M16×C3⋊D3C2211yescharacteristic
19C42×C3⋊D3C2211yescharacteristic
20#63785C412yescomplemented
21#63783C412yescomplemented
22#63781—22no—
23#63767—21no—
24C8×#157—21no—
25C32×#104C411yescharacteristic, complemented
26#63664C411yescharacteristic, complemented
27#63652C411yescharacteristic, complemented
28#63632C411yescharacteristic, complemented
29D3×#104—62no—
30C22×#157—21no—
31C22×#157—22no—
32C22×#157D412yes—
33C32×#41C2×C411yescharacteristic
34#3832C2×C411yescharacteristic
35Q8×C3⋊D3C2×C411yescharacteristic
36#3830—21no—
37#3830C2×C411yescharacteristic
38D4×C3⋊D3—21no—
39D4×C3⋊D3C2×C411yescharacteristic
40#3828—21no—
41#3828C2×C411yescharacteristic
42C2×C4×C3⋊D3—21no—
43C2×C4×C3⋊D3—21no—
44C2×C4×C3⋊D3C2311yescharacteristic
45C22⋊#157—21no—
46C22⋊#157—22no—
47#3792—21no—
48C4⋊#157—22no—
49C4⋊#157C2×C412yes—
50C4×#157—22no—
51C4×#157—21no—
52C4×#157—21no—
53C4×#157C2×C412yes—
54C4×#157C2×C412yescomplemented
55C4×#157D411yescharacteristic
56C4×#157D411yescharacteristic
57#3788C2×C412yescomplemented
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#1759—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—22no—
77C2×#157—22no—
78C2×#157—42no—
79C2×#157—44no—
80C2×#157—42no—
81C2×#157C22⋊C412yes—
82C2×#157C22⋊C412yes—
83C32×Q8C4211yescharacteristic
84C32×D4—21no—
85C32×D4C4211yescharacteristic
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)C4211yescharacteristic
97C4×C3⋊D3—21no—
98C4×C3⋊D3—21no—
99C4×C3⋊D3—21no—
100C4×C3⋊D3—42no—
101C4×C3⋊D3C22×C411yescharacteristic
102C4×C3⋊D3C22×C411yescharacteristic
103C4×C3⋊D3C2×D411yescharacteristic
104C4×C3⋊D3#4111yescharacteristic
105#634—21no—
106#634C4211yescharacteristic
107#622—22no—
108C32×C8—21no—
109C3⋊(C3⋊C8)—21no—
110C4×#41—91no—
111C2×#104—91no—
112C2×#104—91no—
113C4×M16—91no—
114#376—91no—
115#339—91no—
116#339—91no—
117C3×#41—22no—
118#239—62no—
119D3×Q8—62no—
120#237—62no—
121#237—122no—
122D3×D4—62no—
123D3×D4—122no—
124#235—62no—
125#235—122no—
126C2×C4×D3—62no—
127C2×C4×D3—122no—
128C2×C4×D3—122no—
129C3×M16—22no—
130C3×C42—22no—
131C4×Dic3—62no—
132C4×Dic3—122no—
133#208—62no—
134ΓL(1,𝔽25)—122no—
135D3×C8—122no—
136C22×C32—21no—
137C22×C32C4×D411yescharacteristic
138C2×C3⋊D3—22no—
139C2×C3⋊D3—21no—
140C2×C3⋊D3—42no—
141C2×C3⋊D3C2×C22⋊C411yescharacteristic
142C2×C3⋊D3C4×D411yescharacteristic
143#157—22no—
144#157—22no—
145#157—42no—
146#157—42no—
147C32×C4—21no—
148C32×C4—41no—
149C32×C4C2×C4211yescharacteristic
150C32×C4C4×D411yescharacteristic
151C3⋊Dic3—21no—
152C3⋊Dic3—41no—
153C3⋊Dic3#11711yescharacteristic
154C3⋊Dic3C4×D411yescharacteristic
155C2×#41—91no—
156C2×M16—91no—
157C2×M16—91no—
158C4×Q8—92no—
159C4×D4—92no—
160C4×D4—182no—
161#117—91no—
162#117—181no—
163C2×C42—91no—
164C2×C42—91no—
165C2×C42—91no—
166C2×C42—181no—
167#104—92no—
168#104—92no—
169#104—91no—
170#104—91no—
171#104—91no—
172#104#15711yescharacteristic, complemented
173#97—181no—
174C4×C8—181no—
175#95—182no—
176C22×D3—62no—
177C22×D3—122no—
178C3×Q8—22no—
179C3×D4—22no—
180C3×D4—42no—
181C2×C3×C4—22no—
182C2×C3×C4—42no—
183C2×C3×C4—42no—
184#67—122no—
185#67—122no—
186#67—122no—
187C2×Dic3—62no—
188C2×Dic3—122no—
189C2×Dic3—122no—
190D12—62no—
191D12—122no—
192C4×D3—62no—
193C4×D3—62no—
194C4×D3—62no—
195C4×D3—62no—
196C4×D3—122no—
197C4×D3—122no—
198C4×D3—122no—
199C4×D3—128no—
200Dic6—62no—
201Dic6—122no—
202C3×C8—42no—
203C3⋊C8—122no—
204C2×C32—21no—
205C2×C32—41no—
206C2×C32C4×C22⋊C411yescharacteristic
207C3⋊D3—21no—
208C3⋊D3—41no—
209C3⋊D3#42112yes—
210#41—91no—
211#41—91no—
212#41—91no—
213#41—181no—
214#41—181no—
215#41C2×#15711yescharacteristic
216C2×Q8—91no—
217C2×D4—91no—
218C2×D4—181no—
219C22×C4—91no—
220C22×C4—92no—
221C22×C4—181no—
222C22×C4—181no—
223C22×C4—182no—
224C22×C4—181no—
225M16—92no—
226M16—91no—
227M16—181no—
228M16—181no—
229M16C2×#15711yescharacteristic, complemented
230C2×C8—181no—
231C2×C8—181no—
232C4⋊C4—92no—
233C4⋊C4—182no—
234C22⋊C4—182no—
235C22⋊C4—181no—
236C42—91no—
237C42—91no—
238C42—92no—
239C42—92no—
240C42—91no—
241C42—181no—
242C42—181no—
243C42—181no—
244C42—182no—
245C42C2×#15711yescharacteristic, complemented
246C22×C3—22no—
247C22×C3—42no—
248C2×D3—62no—
249C2×D3—62no—
250C2×D3—124no—
251C2×D3—122no—
252C2×D3—244no—
253C3×C4—22no—
254C3×C4—22no—
255C3×C4—42no—
256C3×C4—44no—
257Dic3—62no—
258Dic3—62no—
259Dic3—122no—
260Dic3—124no—
261C32#175911yescharacteristic, complemented, Sylow
262C23—91no—
263C23—181no—
264Q8—91no—
265Q8—181no—
266Q8C4×#15711yescharacteristic
267D4—21no—
268D4—91no—
269D4—181no—
270D4—181no—
271D4—181no—
272D4—181no—
273D4C4×#15711yescharacteristic
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—91no—
277C2×C4—91no—
278C2×C4—91no—
279C2×C4—91no—
280C2×C4—91no—
281C2×C4—92no—
282C2×C4—92no—
283C2×C4—181no—
284C2×C4—181no—
285C2×C4—181no—
286C2×C4—181no—
287C2×C4—182no—
288C2×C4—182no—
289C2×C4—181no—
290C2×C4—362no—
291C2×C4—362no—
292C2×C4—364no—
293C2×C4—362no—
294C2×C4C22×#15711yescharacteristic
295C8—21no—
296C8—182no—
297C8—181no—
298C2×C3—22no—
299C2×C3—42no—
300C2×C3—82no—
301D3—64no—
302D3—122no—
303D3—242no—
304C22—21no—
305C22—91no—
306C22—91no—
307C22—182no—
308C22—181no—
309C22—362no—
310C22D4×#15711yescharacteristic
311C4—21no—
312C4—41no—
313C4—91no—
314C4—91no—
315C4—182no—
316C4—182no—
317C4—181no—
318C4—361no—
319C4—362no—
320C4—362no—
321C4C2×C4×#15711yescharacteristic
322C4D4×#15711yescharacteristic
323C3—22no—
324C2—21no—
325C2—41no—
326C2—92no—
327C2—181no—
328C2—361no—
329C2C22⋊C4×#15711yescharacteristic
subgroupG/H
centerC4D4×#157
commutatorC32×C4C2×C42
FrattiniC2×C4C22×#157
FittingC32×#104C4
socleC2×C32C4×C22⋊C4
prime radical#41×C3⋊D3C22
cosocleC2×C4×C3⋊D3C23
hypercenter#104#157
hypocenterC32#1759
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C2×C4 ◁ #104

Complements

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

NH ≅ G/Ntype
3. M16×#157C2semidirect
4. #10593733C2semidirect
6. #10590189C2semidirect
7. #10590151C2semidirect
9. Q8×#157C4semidirect
11. D4×#157C4semidirect
20. #63785C4semidirect
21. #63783C4semidirect
25. C32×#104C4semidirect
26. #63664C4semidirect
27. #63652C4semidirect
28. #63632C4semidirect
54. C4×#157C2×C4semidirect
57. #3788C2×C4semidirect
59. C32×M16C2×C4semidirect
60. C32×C42C2×C4semidirect
62. C4×C3⋊Dic3C2×C4semidirect
63. #3748C2×C4semidirect
172. #104#157semidirect
229. M16C2×#157semidirect
245. C42C2×#157semidirect
261. C32#1759semidirect

Maximal subgroups

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

subgroupindex
#41×#1572
#105938392
M16×#1572
#105937332
C3⋊D3×#1042
#105901892
#105901512
#17599