Finite Group Databasebeta

← #11920102

Subgroups — #11920102

Order 1152.

376 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 376 conjugacy classes of subgroups — too many to draw. Only its 58 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
1C2×Q8×C22⋊C9C211yesmaximal, characteristic
2C4⋊((C22⋊C9)⋊C4)C211yesmaximal, characteristic
3C2×(C22⋊C9)⋊C8C211yesmaximal, characteristic
4#72132—31nomaximal
5Q8×C22⋊C9—21no—
6Q8×C22⋊C9C412yescomplemented
7C2×C4×C22⋊C9—21no—
8C2×C4×C22⋊C9C2211yescharacteristic
9C2×(C22⋊C9)⋊C4—21no—
10(C22⋊C9)⋊C8—21no—
11#63395—41nomaximal
12C23×C3×Q8D311yescharacteristic
13C2×#835—31no—
14C2×#835—31no—
15C2×#835—31no—
16C2×#835—31no—
17#5212—31no—
18C2×#830—31no—
19C22×C22⋊C9D411yescharacteristic
20C2×Q8×C9—41no—
21C4×C22⋊C9—22no—
22C4×C22⋊C9C2×C411yescharacteristic
23C4×C22⋊C9D411yescharacteristic
24(C22⋊C9)⋊C4—41no—
25C4⋊Dic9—41no—
26C2×C9⋊C8—41no—
27#1787—91noSylow
28C22×C3×Q8—21no—
29C22×C3×Q8—31no—
30C22×C3×Q8—31no—
31C22×C3×Q8—32no—
32C22×C3×Q8—61no—
33C22×C3×Q8—61no—
34C22×C3×Q8Dic312yes—
35C23×C3×C4—21no—
36C23×C3×C4C2×D311yescharacteristic
37C2×#217—61no—
38C2×C4⋊Dic3—31no—
39C2×C4⋊Dic3—31no—
40C22×C3⋊C8—31no—
41C22×C3⋊C8—31no—
42#835—62no—
43#835—62no—
44#835—62no—
45#835—61no—
46#835—61no—
47C3⋊#95—61no—
48#830—61no—
49#830—61no—
50C2×C22⋊C9C22⋊C411yescharacteristic
51C2×C22⋊C9SD1611yescharacteristic
52C2×C22⋊C9Q1611yescharacteristic
53Q8×C9—42no—
54Q8×C9—81no—
55C2×C4×C9—41no—
56C2×C4×C9—81no—
57C2×Dic9—81no—
58C9⋊C8—81no—
59C23×Q8D911yescharacteristic
60C2×#103—91no—
61C2×#103—91no—
62C2×#103—91no—
63C2×#103—91no—
64C2×C22⋊C8—91no—
65#380—91no—
66C24×C3#6711yescharacteristic
67C2×C3×Q8—32no—
68C2×C3×Q8—32no—
69C2×C3×Q8—32no—
70C2×C3×Q8—32no—
71C2×C3×Q8—32no—
72C2×C3×Q8—31no—
73C2×C3×Q8—61no—
74C2×C3×Q8—61no—
75C2×C3×Q8—61no—
76C2×C3×Q8—62no—
77C2×C3×Q8—61no—
78C2×C3×Q8—61no—
79C2×C3×Q8—62no—
80C2×C3×Q8—64no—
81C2×C3×Q8S411yescharacteristic
82C22×C3×C4—22no—
83C22×C3×C4—31no—
84C22×C3×C4—31no—
85C22×C3×C4—31no—
86C22×C3×C4—31no—
87C22×C3×C4—61no—
88C22×C3×C4—62no—
89C22×C3×C4—61no—
90C22×C3×C4C2×Dic311yescharacteristic
91C22×C3×C4#6711yescharacteristic
92C22×Dic3—61no—
93C22×Dic3—61no—
94#217—121no—
95#217—121no—
96C4⋊Dic3—61no—
97C4⋊Dic3—61no—
98C4⋊Dic3—61no—
99C4⋊Dic3—61no—
100C2×C3⋊C8—61no—
101C2×C3⋊C8—61no—
102C2×C3⋊C8—61no—
103C2×C3⋊C8—61no—
104C2×C3⋊C8—61no—
105C2×C3⋊C8—61no—
106C22×C9—41no—
107C22⋊C9#10311yescharacteristic, complemented
108C4×C9—41no—
109C4×C9—41no—
110C4×C9—82no—
111Dic9—161no—
112C22×Q8—21no—
113C22×Q8—31no—
114C22×Q8—31no—
115C22×Q8—32no—
116C22×Q8—61no—
117C22×Q8—61no—
118C22×Q8Dic912yescomplemented
119C23×C4—21no—
120C23×C4C2×D911yescharacteristic
121C22×C8—91no—
122C22×C8—91no—
123C2×C4⋊C4—91no—
124C2×C4⋊C4—91no—
125C2×C22⋊C4—181no—
126#103—182no—
127#103—182no—
128#103—182no—
129#103—181no—
130#103—181no—
131C22⋊C8—181no—
132C22⋊C8—181no—
133#95—181no—
134C23×C3—31no—
135C23×C3—31no—
136C23×C3—31no—
137C23×C3—31no—
138C23×C3#21511yescharacteristic
139C23×C3#21611yescharacteristic
140C23×C3#21711yescharacteristic
141C3×Q8—21no—
142C3×Q8—34no—
143C3×Q8—32no—
144C3×Q8—62no—
145C3×Q8—62no—
146C3×Q8—62no—
147C3×Q8—61no—
148C3×Q8SL(2,ℤ/4)12yes—
149C2×C3×C4—21no—
150C2×C3×C4—31no—
151C2×C3×C4—31no—
152C2×C3×C4—31no—
153C2×C3×C4—31no—
154C2×C3×C4—31no—
155C2×C3×C4—31no—
156C2×C3×C4—31no—
157C2×C3×C4—62no—
158C2×C3×C4—62no—
159C2×C3×C4—61no—
160C2×C3×C4—62no—
161C2×C3×C4—61no—
162C2×C3×C4—62no—
163C2×C3×C4C2×S411yescharacteristic
164C2×Dic3—121no—
165C2×Dic3—121no—
166C2×Dic3—121no—
167C2×Dic3—121no—
168C2×Dic3—121no—
169C2×Dic3—121no—
170C3⋊C8—121no—
171C3⋊C8—121no—
172C2×C9—41no—
173C2×C9—41no—
174C2×C9—41no—
175C24#61111yescharacteristic
176C2×Q8—32no—
177C2×Q8—32no—
178C2×Q8—32no—
179C2×Q8—32no—
180C2×Q8—32no—
181C2×Q8—31no—
182C2×Q8—61no—
183C2×Q8—61no—
184C2×Q8—61no—
185C2×Q8—62no—
186C2×Q8—61no—
187C2×Q8—61no—
188C2×Q8—62no—
189C2×Q8—64no—
190C2×Q8(C22⋊C9)⋊C211yescharacteristic
191C22×C4—22no—
192C22×C4—31no—
193C22×C4—31no—
194C22×C4—31no—
195C22×C4—31no—
196C22×C4—61no—
197C22×C4—62no—
198C22×C4—61no—
199C22×C4—181no—
200C22×C4—181no—
201C22×C4C2×Dic911yescharacteristic
202C22×C4#61111yescharacteristic
203C2×C8—181no—
204C2×C8—181no—
205C2×C8—181no—
206C2×C8—181no—
207C2×C8—181no—
208C2×C8—181no—
209C4⋊C4—181no—
210C4⋊C4—181no—
211C4⋊C4—181no—
212C4⋊C4—181no—
213C22⋊C4—361no—
214C22⋊C4—361no—
215C22×C3—31no—
216C22×C3—31no—
217C22×C3—31no—
218C22×C3—31no—
219C22×C3—31no—
220C22×C3—31no—
221C22×C3—31no—
222C22×C3—31no—
223C22×C3—31no—
224C22×C3—61no—
225C22×C3#83511yescharacteristic
226C22×C3GL(2,ℤ/4)11yescharacteristic
227C3×C4—22no—
228C3×C4—31no—
229C3×C4—31no—
230C3×C4—62no—
231C3×C4C2×SL(2,ℤ/4)11yescharacteristic
232C3×C4GL(2,ℤ/4)11yescharacteristic
233Dic3—241no—
234Dic3—241no—
235C9—41noSylow
236C23—31no—
237C23—31no—
238C23—31no—
239C23—31no—
240C23#367411yescharacteristic
241C23#367511yescharacteristic
242C23#367611yescharacteristic
243Q8—21no—
244Q8—34no—
245Q8—32no—
246Q8—62no—
247Q8—62no—
248Q8—62no—
249Q8—61no—
250Q8(C22⋊C9)⋊C412yescomplemented
251C2×C4—21no—
252C2×C4—31no—
253C2×C4—31no—
254C2×C4—31no—
255C2×C4—31no—
256C2×C4—31no—
257C2×C4—31no—
258C2×C4—31no—
259C2×C4—62no—
260C2×C4—62no—
261C2×C4—61no—
262C2×C4—62no—
263C2×C4—61no—
264C2×C4—62no—
265C2×C4—361no—
266C2×C4—361no—
267C2×C4—361no—
268C2×C4—361no—
269C2×C4—361no—
270C2×C4—361no—
271C2×C4C2×(C22⋊C9)⋊C211yescharacteristic
272C8—361no—
273C8—361no—
274C2×C3—31no—
275C2×C3—31no—
276C2×C3—31no—
277C2×C3—31no—
278C2×C3#541611yescharacteristic
279C2×C3#541711yescharacteristic
280C2×C3#543211yescharacteristic
281C22—31no—
282C22—31no—
283C22—31no—
284C22—31no—
285C22—31no—
286C22—31no—
287C22—31no—
288C22—31no—
289C22—31no—
290C22—61no—
291C22#6339511yescharacteristic, complemented
292C22#6369411yescharacteristic
293C4—22no—
294C4—31no—
295C4—31no—
296C4—62no—
297C4—721no—
298C4—721no—
299C4C2×(C22⋊C9)⋊C411yescharacteristic
300C4#6369411yescharacteristic
301C3#7314711yescharacteristic
302C2—31no—
303C2—31no—
304C2—31no—
305C2—31no—
306C2#1058951811yescharacteristic
307C2#1058951911yescharacteristic
308C2#1058953411yescharacteristic
subgroupG/H
centerC22#63694
commutatorC4×C22⋊C9C2×C4
FrattiniC2×C3×C4C2×S4
FittingC23×C3×Q8D3
socle, prime radicalC24×C3#67
cosocleC2×C4×C22⋊C9C22
hypercenterC2×Q8(C22⋊C9)⋊C2
hypocenterC22⋊C9#103
LCSG ▷ C4×C22⋊C9 ▷ C2×C22⋊C9 ▷ C22⋊C9
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×Q8

Complements

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

NH ≅ G/Ntype
6. Q8×C22⋊C9C4semidirect
107. C22⋊C9#103semidirect
118. C22×Q8Dic9semidirect
250. Q8(C22⋊C9)⋊C4semidirect
291. C22#63395semidirect

Maximal subgroups

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

subgroupindex
C2×Q8×C22⋊C92
C4⋊((C22⋊C9)⋊C4)2
C2×(C22⋊C9)⋊C82
#721323
#633954