Finite Group Databasebeta

← #11920007

Subgroups — #11920007

Order 1152.

324 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 50 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×(C22⋊C9)⋊Q8C211yesmaximal, characteristic
2C4⋊C4×C22⋊C9C211yesmaximal, characteristic
3C2×(C22⋊C9)⋊C8C211yesmaximal, characteristic
4#71559—31nomaximal
5C2×C4×C22⋊C9—21no—
6C2×C4×C22⋊C9C2211yescharacteristic
7C2×(C22⋊C9)⋊C4—21no—
8(C22⋊C9)⋊Q8—21no—
9(C22⋊C9)⋊Q8C412yescomplemented
10(C22⋊C9)⋊C8—21no—
11#63368—41nomaximal
12C22×C3×C4⋊C4D311yescharacteristic
13C2×#924—31no—
14C2×#830—31no—
15C2×#810—31no—
16C2×#810—31no—
17#4529—31no—
18#4529—31no—
19C22×C22⋊C9D411yescharacteristic
20C2×Dic18—41no—
21C4×C22⋊C9—41no—
22C4×C22⋊C9C2×C411yescharacteristic
23C4×C22⋊C9D411yescharacteristic
24(C22⋊C9)⋊C4—22no—
25C9×C4⋊C4—41no—
26C2×C9⋊C8—41no—
27#1872—91noSylow
28C23×C3×C4—21no—
29C23×C3×C4C2×D311yescharacteristic
30C22×Dic6—31no—
31C2×C3×C4⋊C4—31no—
32C2×C3×C4⋊C4—31no—
33C2×C3×C4⋊C4—61no—
34C2×#217—61no—
35C2×C4⋊Dic3—31no—
36#924—32no—
37#924—32no—
38#924—61no—
39#924—61no—
40C2×Dic3⋊C4—61no—
41C22×C3⋊C8—31no—
42C22×C3⋊C8—31no—
43#830—61no—
44#830—61no—
45#810—62no—
46#810—61no—
47#810—61no—
48C2×C22⋊C9C22⋊C411yescharacteristic
49C2×C22⋊C9SD1611yescharacteristic
50C2×C22⋊C9Q1611yescharacteristic
51C2×C4×C9—41no—
52C2×C4×C9—81no—
53C2×Dic9—81no—
54Dic18—42no—
55Dic18—81no—
56C9⋊C8—81no—
57C2×C22⋊Q8—91no—
58C22×C4⋊C4D911yescharacteristic
59C2×#103—91no—
60C2×#103—91no—
61C2×C22⋊C8—91no—
62#340—91no—
63#340—91no—
64C24×C3#6711yescharacteristic
65C22×C3×C4—31no—
66C22×C3×C4—31no—
67C22×C3×C4—31no—
68C22×C3×C4—31no—
69C22×C3×C4—41no—
70C22×C3×C4—61no—
71C22×C3×C4—61no—
72C22×C3×C4—121no—
73C22×C3×C4C4×D311yescharacteristic
74C22×C3×C4D1211yescharacteristic
75C22×Dic3—61no—
76C22×Dic3—61no—
77C2×Dic6—32no—
78C2×Dic6—61no—
79C2×Dic6—61no—
80C2×Dic6—61no—
81C2×Dic6—61no—
82C2×Dic6—61no—
83C3×C4⋊C4—32no—
84C3×C4⋊C4—31no—
85C3×C4⋊C4—61no—
86C3×C4⋊C4S411yescharacteristic
87#217—62no—
88#217—62no—
89C4⋊Dic3—32no—
90C4⋊Dic3—61no—
91Dic3⋊C4—62no—
92Dic3⋊C4—62no—
93C2×C3⋊C8—61no—
94C2×C3⋊C8—61no—
95C2×C3⋊C8—61no—
96C2×C3⋊C8—61no—
97C2×C3⋊C8—61no—
98C2×C3⋊C8—61no—
99C22×C9—41no—
100C22⋊C9#10311yescharacteristic, complemented
101C4×C9—41no—
102C4×C9—41no—
103C4×C9—161no—
104Dic9—82no—
105C22×Q8—91no—
106C23×C4—21no—
107C23×C4C2×D911yescharacteristic
108C22×C8—91no—
109C22×C8—91no—
110C22⋊Q8—92no—
111C22⋊Q8—92no—
112C22⋊Q8—181no—
113C22⋊Q8—181no—
114C2×C4⋊C4—31no—
115C2×C4⋊C4—31no—
116C2×C4⋊C4—61no—
117C2×C4⋊C4—91no—
118C2×C4⋊C4—181no—
119C2×C22⋊C4—181no—
120#103—182no—
121#103—181no—
122#103—181no—
123C22⋊C8—181no—
124C22⋊C8—181no—
125C23×C3—31no—
126C23×C3—31no—
127C23×C3—31no—
128C23×C3—31no—
129C23×C3(C2×D3)⋊C411yescharacteristic
130C23×C3#21411yescharacteristic
131C23×C3#21611yescharacteristic
132C2×C3×C4—21no—
133C2×C3×C4—31no—
134C2×C3×C4—31no—
135C2×C3×C4—31no—
136C2×C3×C4—31no—
137C2×C3×C4—31no—
138C2×C3×C4—31no—
139C2×C3×C4—31no—
140C2×C3×C4—61no—
141C2×C3×C4—61no—
142C2×C3×C4—121no—
143C2×C3×C4—121no—
144C2×C3×C4—121no—
145C2×C3×C4—121no—
146C2×C3×C4C2×S411yescharacteristic
147C2×Dic3—62no—
148C2×Dic3—62no—
149C2×Dic3—121no—
150C2×Dic3—121no—
151C2×Dic3—121no—
152C2×Dic3—121no—
153Dic6—62no—
154Dic6—62no—
155Dic6—121no—
156Dic6—121no—
157C3⋊C8—121no—
158C3⋊C8—121no—
159C2×C9—41no—
160C2×C9—41no—
161C2×C9—41no—
162C24#61111yescharacteristic
163C2×Q8—92no—
164C2×Q8—181no—
165C2×Q8—181no—
166C2×Q8—181no—
167C2×Q8—181no—
168C2×Q8—181no—
169C22×C4—31no—
170C22×C4—31no—
171C22×C4—31no—
172C22×C4—31no—
173C22×C4—41no—
174C22×C4—61no—
175C22×C4—61no—
176C22×C4—121no—
177C22×C4—181no—
178C22×C4—181no—
179C22×C4C4×D911yescharacteristic
180C22×C4D3611yescharacteristic
181C2×C8—181no—
182C2×C8—181no—
183C2×C8—181no—
184C2×C8—181no—
185C2×C8—181no—
186C2×C8—181no—
187C4⋊C4—32no—
188C4⋊C4—31no—
189C4⋊C4—61no—
190C4⋊C4—92no—
191C4⋊C4—181no—
192C4⋊C4—182no—
193C4⋊C4—182no—
194C4⋊C4(C22⋊C9)⋊C211yescharacteristic
195C22⋊C4—182no—
196C22⋊C4—182no—
197C22×C3—31no—
198C22×C3—31no—
199C22×C3—31no—
200C22×C3—31no—
201C22×C3—31no—
202C22×C3—31no—
203C22×C3—31no—
204C22×C3—31no—
205C22×C3—31no—
206C22×C3—61no—
207C22×C3#81011yescharacteristic
208C22×C3GL(2,ℤ/4)11yescharacteristic
209C3×C4—31no—
210C3×C4—31no—
211C3×C4—41no—
212C3×C4—121no—
213C3×C4C4×S411yescharacteristic
214C3×C4C4⋊S411yescharacteristic
215Dic3—122no—
216Dic3—122no—
217C9—41noSylow
218C23—31no—
219C23—31no—
220C23—31no—
221C23—31no—
222C23(C2×D9)⋊C411yescharacteristic
223C23#367211yescharacteristic
224C23#367411yescharacteristic
225Q8—182no—
226Q8—182no—
227Q8—361no—
228Q8—361no—
229C2×C4—21no—
230C2×C4—31no—
231C2×C4—31no—
232C2×C4—31no—
233C2×C4—31no—
234C2×C4—31no—
235C2×C4—31no—
236C2×C4—31no—
237C2×C4—61no—
238C2×C4—61no—
239C2×C4—121no—
240C2×C4—121no—
241C2×C4—121no—
242C2×C4—121no—
243C2×C4—182no—
244C2×C4—182no—
245C2×C4—361no—
246C2×C4—361no—
247C2×C4—361no—
248C2×C4—361no—
249C2×C4C2×(C22⋊C9)⋊C211yescharacteristic
250C8—361no—
251C8—361no—
252C2×C3—31no—
253C2×C3—31no—
254C2×C3—31no—
255C2×C3—31no—
256C2×C3(C2×S4)⋊C411yescharacteristic
257C2×C3#541411yescharacteristic
258C2×C3#541611yescharacteristic
259C22—31no—
260C22—31no—
261C22—31no—
262C22—31no—
263C22—31no—
264C22—31no—
265C22—31no—
266C22—31no—
267C22—31no—
268C22—61no—
269C22#6336811yescharacteristic, complemented
270C22#6369411yescharacteristic
271C4—31no—
272C4—31no—
273C4—41no—
274C4—121no—
275C4—362no—
276C4—362no—
277C4C4×(C22⋊C9)⋊C211yescharacteristic
278C4C4⋊((C22⋊C9)⋊C2)11yescharacteristic
279C3#7305211yescharacteristic
280C2—31no—
281C2—31no—
282C2—31no—
283C2—31no—
284C2(C2×(C22⋊C9)⋊C2)⋊C411yescharacteristic
285C2#1058951611yescharacteristic
286C2#1058951811yescharacteristic
subgroupG/H
centerC22#63694
commutatorC4×C22⋊C9C2×C4
FrattiniC2×C3×C4C2×S4
FittingC22×C3×C4⋊C4D3
socle, prime radicalC24×C3#67
cosocleC2×C4×C22⋊C9C22
hypercenterC4⋊C4(C22⋊C9)⋊C2
hypocenterC22⋊C9#103
LCSG ▷ C4×C22⋊C9 ▷ C2×C22⋊C9 ▷ C22⋊C9
UCSC1 ◁ C22 ◁ C2×C4 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
9. (C22⋊C9)⋊Q8C4semidirect
100. C22⋊C9#103semidirect
269. C22#63368semidirect

Maximal subgroups

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

subgroupindex
C2×(C22⋊C9)⋊Q82
C4⋊C4×C22⋊C92
C2×(C22⋊C9)⋊C82
#715593
#633684