Finite Group Databasebeta

← #11774640

Subgroups — #11774640

Order 1152.

399 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 399 conjugacy classes of subgroups — too many to draw. Only its 94 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
1C4×#3701C211yesmaximal, characteristic
2#10588521C211yesmaximal, characteristic, complemented
3C4×#3663C211yesmaximal, characteristic, complemented
4C9×Q8⋊C8C211yesmaximal, characteristic, complemented
5#10588212C211yesmaximal, characteristic, complemented
6#10588162C211yesmaximal, characteristic, complemented
7#10588136C211yesmaximal, characteristic, complemented
8#68238—31nomaximal
9C2×#3701C411yescharacteristic
10C4×Q8×C9C2211yescharacteristic
11Q8×Dic9C411yescharacteristic
12C2×#3663—21no—
13C2×#3663—21no—
14#63455—21no—
15#63455C411yescharacteristic
16#63454—21no—
17#63454C411yescharacteristic
18C4×D36—21no—
19C4×D36C2211yescharacteristic
20C42×D9—21no—
21C42×D9C2211yescharacteristic
22C9×C4⋊C8C2211yescharacteristic
23C4×C8×C9C2211yescharacteristic
24#63375—21no—
25Dic9⋊C8—21no—
26C4⋊(C9⋊C8)C2211yescharacteristic
27C4×C9⋊C8C2211yescharacteristic
28C4×#239—31no—
29#4837—31no—
30C4×ΓL(1,𝔽25)—31no—
31C3×Q8⋊C8D311yescharacteristic
32#4535—31no—
33#4483—31no—
34#4459—31no—
35C2×Q8×C9C2×C411yescharacteristic
36#3701—22no—
37#3701—22no—
38C2×D36—21no—
39C2×D36C2×C411yescharacteristic
40C2×C4×D9—21no—
41C2×C4×D9—21no—
42C2×C4×D9—21no—
43C2×C4×D9C2×C411yescharacteristic
44C2×C4×D9D411yescharacteristic
45C2×C4×D9D411yescharacteristic
46C2×C8×C9—21no—
47C2×C8×C9—21no—
48C9×C4⋊C4—21no—
49C9×C4⋊C4C2×C411yescharacteristic
50C42×C9—21no—
51C42×C9C2311yescharacteristic
52(C2×D9)⋊C4—21no—
53(C2×D9)⋊C4—21no—
54(C2×D9)⋊C4—21no—
55C4⋊Dic9—21no—
56C4⋊Dic9C2×C411yescharacteristic
57C4×Dic9—21no—
58C4×Dic9—21no—
59C4×Dic9C2×C411yescharacteristic
60C4×Dic9D411yescharacteristic
61C4×Dic9D411yescharacteristic
62C2×C9⋊C8—21no—
63C2×C9⋊C8—21no—
64#3663—24no—
65#3663—42no—
66#1489—91noSylow
67C2×#239—31no—
68C3×C4×Q8C2×D311yescharacteristic
69Q8×Dic3—31no—
70C2×ΓL(1,𝔽25)—61no—
71C2×ΓL(1,𝔽25)—61no—
72#893—31no—
73#893—61no—
74#892—31no—
75#892—61no—
76C4×D12—31no—
77C4×D12—61no—
78C42×D3—31no—
79C42×D3—61no—
80C3×C4⋊C8C2×D311yescharacteristic
81C3×C4×C8C2×D311yescharacteristic
82#815—61no—
83Dic3⋊C8—61no—
84C4⋊(C3⋊C8)—31no—
85C4×C3⋊C8—31no—
86C22×D9—21no—
87C22×D9C22⋊C411yescharacteristic
88Q8×C9—21no—
89Q8×C9M1612yescomplemented
90C2×C4×C9—21no—
91C2×C4×C9—21no—
92C2×C4×C9C22×C411yescharacteristic
93C2×C4×C9C2×D411yescharacteristic
94C2×C4×C9C2×D411yescharacteristic
95C2×Dic9—21no—
96C2×Dic9C22⋊C411yescharacteristic
97C2×Dic9C22⋊C411yescharacteristic
98C2×Dic9C22⋊C411yescharacteristic
99D36—24no—
100D36—21no—
101D36M1612yescomplemented
102C4×D9—24no—
103C4×D9—21no—
104C4×D9—21no—
105C4×D9—21no—
106C4×D9—21no—
107C4×D9—22no—
108C4×D9—41no—
109C4×D9—41no—
110C4×D9—42no—
111C8×C9—22no—
112C8×C9—41no—
113C9⋊C8—22no—
114C9⋊C8—41no—
115C4×#41—91no—
116#423—91no—
117C4×M16—91no—
118Q8⋊C8—91no—
119Q8⋊C8D911yescharacteristic, complemented
120D4⋊C8—91no—
121D4⋊C8—91no—
122C2×C3×Q8C4×D311yescharacteristic
123#239—62no—
124#239—62no—
125C2×D12—31no—
126C2×D12—61no—
127C2×C4×D3—31no—
128C2×C4×D3—31no—
129C2×C4×D3—31no—
130C2×C4×D3—61no—
131C2×C4×D3—61no—
132C2×C4×D3—61no—
133C2×C3×C8—21no—
134C2×C3×C8—21no—
135C3×C4⋊C4—21no—
136C3×C4⋊C4C4×D311yescharacteristic
137C3×C42—21no—
138C3×C42C22×D311yescharacteristic
139(C2×D3)⋊C4—61no—
140(C2×D3)⋊C4—61no—
141(C2×D3)⋊C4—61no—
142C4⋊Dic3—31no—
143C4⋊Dic3—61no—
144C4×Dic3—31no—
145C4×Dic3—31no—
146C4×Dic3—31no—
147C4×Dic3—61no—
148C4×Dic3—61no—
149C2×C3⋊C8—61no—
150C2×C3⋊C8—61no—
151ΓL(1,𝔽25)—64no—
152ΓL(1,𝔽25)—122no—
153C22×C9C2×C22⋊C411yescharacteristic
154C2×D9—21no—
155C2×D9—22no—
156C2×D9—21no—
157C2×D9—21no—
158C2×D9—41no—
159C2×D9—41no—
160C4×C9—22no—
161C4×C9—21no—
162C4×C9—41no—
163C4×C9C2×M1611yescharacteristic
164C4×C9C2×M1611yescharacteristic
165C4×C9AGL(1,ℤ/8)11yescharacteristic
166C4×C9#13711yescharacteristic
167Dic9—21no—
168Dic9—21no—
169Dic9—41no—
170Dic9#10412yes—
171C2×#41—91no—
172C2×M16—181no—
173C2×M16—181no—
174C4×Q8—91no—
175C4×Q8C2×D911yescharacteristic
176C4×D4—91no—
177C4×D4—91no—
178C4×D4—181no—
179C4×D4—181no—
180#117—91no—
181#117—181no—
182C2×C42—91no—
183C2×C42—181no—
184C4⋊C8—91no—
185C4⋊C8—181no—
186C4⋊C8C2×D911yescharacteristic
187#97—181no—
188C4×C8—91no—
189C4×C8C2×D911yescharacteristic
190C22×D3—31no—
191C22×D3—61no—
192C3×Q8—21no—
193C3×Q8ΓL(1,𝔽25)12yes—
194C2×C3×C4—21no—
195C2×C3×C4—21no—
196C2×C3×C4C2×C4×D311yescharacteristic
197C2×C3×C4D3×D411yescharacteristic
198C2×C3×C4D3×D411yescharacteristic
199C2×Dic3—31no—
200C2×Dic3—31no—
201C2×Dic3—31no—
202C2×Dic3—61no—
203D12—32no—
204D12—64no—
205D12—61no—
206C4×D3—62no—
207C4×D3—64no—
208C4×D3—61no—
209C4×D3—61no—
210C4×D3—61no—
211C4×D3—61no—
212C4×D3—122no—
213C4×D3—121no—
214C4×D3—121no—
215C3×C8—22no—
216C3×C8—41no—
217C3⋊C8—62no—
218C3⋊C8—121no—
219C2×C9#40711yescharacteristic
220C2×C9#41711yescharacteristic
221C2×C9C2×#10411yescharacteristic
222D9—41no—
223D9—42no—
224#41—182no—
225#41—182no—
226C2×Q8C4×D911yescharacteristic
227C2×D4—91no—
228C2×D4—181no—
229C22×C4—91no—
230C22×C4—91no—
231C22×C4—91no—
232C22×C4—181no—
233C22×C4—181no—
234C22×C4—181no—
235M16—184no—
236M16—362no—
237C2×C8—21no—
238C2×C8—21no—
239C2×C8—181no—
240C2×C8—181no—
241C4⋊C4—21no—
242C4⋊C4—91no—
243C4⋊C4—181no—
244C4⋊C4C4×D911yescharacteristic
245C22⋊C4—181no—
246C22⋊C4—181no—
247C22⋊C4—181no—
248C42—21no—
249C42—91no—
250C42—91no—
251C42—91no—
252C42—181no—
253C42—181no—
254C42C22×D911yescharacteristic
255C22×C3D3×C22⋊C411yescharacteristic
256C2×D3—62no—
257C2×D3—61no—
258C2×D3—61no—
259C2×D3—61no—
260C2×D3—121no—
261C2×D3—121no—
262C3×C4—22no—
263C3×C4—21no—
264C3×C4—41no—
265C3×C4C2×ΓL(1,𝔽25)11yescharacteristic
266C3×C4D3×M1611yescharacteristic
267C3×C4#91411yescharacteristic
268C3×C4#91811yescharacteristic
269Dic3—32no—
270Dic3—61no—
271Dic3—61no—
272Dic3—121no—
273C9#148911yescharacteristic, complemented, Sylow
274C23—91no—
275C23—181no—
276Q8—21no—
277Q8#366312yescomplemented
278D4—92no—
279D4—184no—
280D4—181no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—91no—
284C2×C4—91no—
285C2×C4—91no—
286C2×C4—182no—
287C2×C4—184no—
288C2×C4—181no—
289C2×C4—181no—
290C2×C4—181no—
291C2×C4—181no—
292C2×C4—181no—
293C2×C4—362no—
294C2×C4—361no—
295C2×C4—361no—
296C2×C4C2×C4×D911yescharacteristic
297C2×C4D4×D911yescharacteristic
298C2×C4D4×D911yescharacteristic
299C8—22no—
300C8—41no—
301C8—182no—
302C8—361no—
303C2×C3#472611yescharacteristic
304C2×C3#480311yescharacteristic
305C2×C3D3×#10411yescharacteristic
306D3—121no—
307D3—122no—
308C22—181no—
309C22—181no—
310C22—182no—
311C22—181no—
312C22—361no—
313C22—361no—
314C22C22⋊C4×D911yescharacteristic
315C4—21no—
316C4—22no—
317C4—41no—
318C4—92no—
319C4—181no—
320C4—181no—
321C4—361no—
322C4C2×#366311yescharacteristic
323C4M16×D911yescharacteristic
324C4#6347611yescharacteristic
325C4#6348011yescharacteristic
326C3#6823811yescharacteristic
327C2—361no—
328C2—362no—
329C2#1058840811yescharacteristic
330C2#1058848311yescharacteristic
331C2D9×#10411yescharacteristic
subgroupG/H
centerC2×C4D4×D9
commutatorC2×C4×C9C22×C4
FrattiniC3×C42C22×D3
FittingC9×Q8⋊C8C2
socleC22×C3D3×C22⋊C4
prime radicalC2×#3701C4
cosocleC42×C9C23
hypercenterQ8⋊C8D9
hypocenterC9#1489
LCSG ▷ C2×C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C2×C4 ◁ C42 ◁ Q8⋊C8

Complements

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

NH ≅ G/Ntype
2. #10588521C2semidirect
3. C4×#3663C2semidirect
4. C9×Q8⋊C8C2semidirect
5. #10588212C2semidirect
6. #10588162C2semidirect
7. #10588136C2semidirect
89. Q8×C9M16semidirect
101. D36M16semidirect
119. Q8⋊C8D9semidirect
273. C9#1489semidirect
277. Q8#3663semidirect

Maximal subgroups

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

subgroupindex
C4×#37012
#105885212
C4×#36632
C9×Q8⋊C82
#105882122
#105881622
#105881362
#682383