Finite Group Databasebeta

← #11920205

Subgroups — #11920205

Order 1152.

454 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 454 conjugacy classes of subgroups — too many to draw. Only its 66 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⋊C4×C22⋊C9C211yesmaximal, characteristic
2C4⋊((C22⋊C9)⋊C4)C212yesmaximal
3C4⋊((C22⋊C9)⋊C4)C211yesmaximal, characteristic
4((C22⋊C9)⋊C4)⋊C4C212yesmaximal
5C4×(C22⋊C9)⋊C4C211yesmaximal, characteristic
6#82172—31nomaximal
7C2×C4×C22⋊C9C2212yes—
8C2×C4×C22⋊C9C2211yescharacteristic
9C2×(C22⋊C9)⋊C4C2211yescharacteristic
10C2×(C22⋊C9)⋊C4C2211yescharacteristic
11C2×(C22⋊C9)⋊C4C2212yes—
12#63452—41nomaximal
13C22×C3×C4⋊C4D311yescharacteristic
14C2×#890—31no—
15#5212—32no—
16#5212—31no—
17#5210—32no—
18C4×#217—31no—
19#4986—32no—
20#4984—31no—
21#4982—32no—
22#4977—31no—
23#4972—31no—
24C22×C22⋊C9C2311yescharacteristic
25C4×C22⋊C9—22no—
26C4×C22⋊C9Q812yes—
27(C22⋊C9)⋊C4—21no—
28(C22⋊C9)⋊C4—21no—
29(C22⋊C9)⋊C4—22no—
30C9×C4⋊C4—41no—
31C4⋊Dic9—42no—
32C4⋊Dic9—41no—
33Dic9⋊C4—42no—
34C4×Dic9—41no—
35#2442—91noSylow
36C23×C3×C4C2×D312yes—
37C23×C3×C4C2×D311yescharacteristic
38C2×C3×C4⋊C4—31no—
39C2×C3×C4⋊C4—31no—
40C2×C3×C4⋊C4—32no—
41C2×#217—31no—
42C2×#217—31no—
43C2×#217—32no—
44C2×C4⋊Dic3—31no—
45C2×C4⋊Dic3—31no—
46C2×C4⋊Dic3—32no—
47C2×C4⋊Dic3—32no—
48C2×Dic3⋊C4—32no—
49C2×Dic3⋊C4—32no—
50C2×C4×Dic3—31no—
51C2×C4×Dic3—31no—
52#890—62no—
53#890—61no—
54#890—61no—
55C3⋊#95—31no—
56C3⋊#95—31no—
57C3⋊#95—32no—
58C3⋊#95—32no—
59C3⋊#95—32no—
60C3⋊#95—32no—
61C3⋊#95—32no—
62C2×C22⋊C9C2×Q811yescharacteristic
63C2×C22⋊C9#4111yescharacteristic
64C2×C22⋊C9#4111yescharacteristic
65C2×C4×C9—41no—
66C2×C4×C9—42no—
67C2×Dic9—41no—
68C2×Dic9—41no—
69C2×Dic9—42no—
70C2×#125—91no—
71C22×C4⋊C4D911yescharacteristic
72#400—92no—
73#398—92no—
74#389—91no—
75#389—91no—
76#385—92no—
77#382—91no—
78#380—92no—
79#380—91no—
80C4×C22⋊C4—91no—
81C24×C3C22×D311yescharacteristic
82C22×C3×C4—22no—
83C22×C3×C4—31no—
84C22×C3×C4—31no—
85C22×C3×C4—32no—
86C22×C3×C4—32no—
87C22×C3×C4—32no—
88C22×C3×C4—62no—
89C22×C3×C4Dic612yes—
90C22×Dic3—31no—
91C22×Dic3—31no—
92C22×Dic3—31no—
93C22×Dic3—32no—
94C22×Dic3—32no—
95C22×Dic3—31no—
96C3×C4⋊C4—32no—
97C3×C4⋊C4—31no—
98C3×C4⋊C4—61no—
99C3×C4⋊C4S411yescharacteristic
100#217—61no—
101#217—62no—
102#217—61no—
103#217—61no—
104#217—61no—
105#217—62no—
106C4⋊Dic3—62no—
107C4⋊Dic3—61no—
108C4⋊Dic3—62no—
109C4⋊Dic3—62no—
110C4⋊Dic3—61no—
111C4⋊Dic3—122no—
112Dic3⋊C4—62no—
113Dic3⋊C4—62no—
114Dic3⋊C4—122no—
115C4×Dic3—61no—
116C4×Dic3—62no—
117C4×Dic3—61no—
118C22×C9—41no—
119C22⋊C9#12511yescharacteristic, complemented
120C4×C9—42no—
121C4×C9—82no—
122Dic9—81no—
123Dic9—81no—
124Dic9—82no—
125C23×C4C2×D912yes—
126C23×C4C2×D911yescharacteristic
127#125—182no—
128#125—181no—
129#125—181no—
130C2×C4⋊C4—31no—
131C2×C4⋊C4—31no—
132C2×C4⋊C4—32no—
133C2×C4⋊C4—91no—
134C2×C4⋊C4—92no—
135C2×C4⋊C4—92no—
136C2×C4⋊C4—91no—
137C2×C4⋊C4—92no—
138C2×C4⋊C4—92no—
139C2×C22⋊C4—91no—
140C2×C22⋊C4—91no—
141C2×C22⋊C4—92no—
142C2×C42—91no—
143C2×C42—91no—
144#95—91no—
145#95—91no—
146#95—92no—
147#95—92no—
148#95—92no—
149#95—92no—
150#95—92no—
151C23×C3—31no—
152C23×C3—31no—
153C23×C3—31no—
154C23×C3—31no—
155C23×C3C2×Dic611yescharacteristic
156C23×C3#23711yescharacteristic
157C23×C3#23911yescharacteristic
158C2×C3×C4—31no—
159C2×C3×C4—32no—
160C2×C3×C4—32no—
161C2×C3×C4—32no—
162C2×C3×C4—32no—
163C2×C3×C4—62no—
164C2×C3×C4—62no—
165C2×C3×C4—61no—
166C2×C3×C4—62no—
167C2×C3×C4—62no—
168C2×C3×C4C2×S412yes—
169C2×C3×C4C2×S411yescharacteristic
170C2×Dic3—61no—
171C2×Dic3—61no—
172C2×Dic3—61no—
173C2×Dic3—62no—
174C2×Dic3—62no—
175C2×Dic3—61no—
176C2×Dic3—61no—
177C2×Dic3—61no—
178C2×Dic3—62no—
179C2×Dic3—61no—
180C2×Dic3—61no—
181C2×Dic3—62no—
182C2×Dic3—61no—
183C2×Dic3—61no—
184C2×Dic3—62no—
185C2×Dic3—61no—
186C2×Dic3—61no—
187C2×Dic3—62no—
188C2×C9—41no—
189C2×C9—41no—
190C2×C9—41no—
191C24C22×D911yescharacteristic
192C22×C4—22no—
193C22×C4—31no—
194C22×C4—31no—
195C22×C4—32no—
196C22×C4—32no—
197C22×C4—32no—
198C22×C4—62no—
199C22×C4—91no—
200C22×C4—91no—
201C22×C4—91no—
202C22×C4—92no—
203C22×C4—92no—
204C22×C4—91no—
205C22×C4Dic1812yes—
206C4⋊C4—32no—
207C4⋊C4—31no—
208C4⋊C4—61no—
209C4⋊C4—182no—
210C4⋊C4—181no—
211C4⋊C4—182no—
212C4⋊C4—182no—
213C4⋊C4—182no—
214C4⋊C4—182no—
215C4⋊C4—181no—
216C4⋊C4—362no—
217C4⋊C4—362no—
218C4⋊C4(C22⋊C9)⋊C211yescharacteristic
219C22⋊C4—181no—
220C22⋊C4—182no—
221C22⋊C4—181no—
222C22⋊C4—181no—
223C22⋊C4—181no—
224C22⋊C4—182no—
225C42—181no—
226C42—182no—
227C42—181no—
228C22×C3—31no—
229C22×C3—31no—
230C22×C3—31no—
231C22×C3—31no—
232C22×C3—31no—
233C22×C3—31no—
234C22×C3—31no—
235C22×C3—31no—
236C22×C3—31no—
237C22×C3—61no—
238C22×C3#89011yescharacteristic
239C22×C3C22×S411yescharacteristic
240C3×C4—22no—
241C3×C4—32no—
242C3×C4—62no—
243C3×C4A4⋊Q812yes—
244Dic3—121no—
245Dic3—122no—
246Dic3—121no—
247Dic3—121no—
248Dic3—121no—
249Dic3—122no—
250C9—41noSylow
251C23—31no—
252C23—31no—
253C23—31no—
254C23—31no—
255C23C2×Dic1811yescharacteristic
256C23#369911yescharacteristic
257C23#370111yescharacteristic
258C2×C4—31no—
259C2×C4—32no—
260C2×C4—32no—
261C2×C4—32no—
262C2×C4—32no—
263C2×C4—62no—
264C2×C4—62no—
265C2×C4—61no—
266C2×C4—62no—
267C2×C4—62no—
268C2×C4—181no—
269C2×C4—181no—
270C2×C4—181no—
271C2×C4—181no—
272C2×C4—182no—
273C2×C4—181no—
274C2×C4—181no—
275C2×C4—182no—
276C2×C4—182no—
277C2×C4—182no—
278C2×C4—181no—
279C2×C4—181no—
280C2×C4—181no—
281C2×C4—181no—
282C2×C4—182no—
283C2×C4—181no—
284C2×C4—181no—
285C2×C4—182no—
286C2×C4C2×(C22⋊C9)⋊C212yes—
287C2×C4C2×(C22⋊C9)⋊C211yescharacteristic
288C2×C3—31no—
289C2×C3—31no—
290C2×C3—31no—
291C2×C3—31no—
292C2×C3C2×A4⋊Q811yescharacteristic
293C2×C3#591411yescharacteristic
294C2×C3#591911yescharacteristic
295C22—31no—
296C22—31no—
297C22—31no—
298C22—31no—
299C22—31no—
300C22—31no—
301C22—31no—
302C22—31no—
303C22—31no—
304C22—61no—
305C22#6345211yescharacteristic, complemented
306C22C22×(C22⋊C9)⋊C211yescharacteristic
307C4—22no—
308C4—32no—
309C4—62no—
310C4—361no—
311C4—362no—
312C4—361no—
313C4—361no—
314C4—361no—
315C4—362no—
316C4(C22⋊C9)⋊Q812yes—
317C3#8530511yescharacteristic
318C2—31no—
319C2—31no—
320C2—31no—
321C2—31no—
322C2C2×(C22⋊C9)⋊Q811yescharacteristic
323C2#1059308911yescharacteristic
324C2#1059309411yescharacteristic
subgroupG/H
centerC22C22×(C22⋊C9)⋊C2
commutator, cosocleC22×C22⋊C9C23
FrattiniC22×C3C22×S4
FittingC22×C3×C4⋊C4D3
socle, prime radicalC24×C3C22×D3
hypercenterC4⋊C4(C22⋊C9)⋊C2
hypocenterC22⋊C9#125
LCSG ▷ C22×C22⋊C9 ▷ C22⋊C9
UCSC1 ◁ C22 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
119. C22⋊C9#125semidirect
305. C22#63452semidirect

Maximal subgroups

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

subgroupindex
C4⋊C4×C22⋊C92
C4⋊((C22⋊C9)⋊C4)2
((C22⋊C9)⋊C4)⋊C42
C4×(C22⋊C9)⋊C42
#821723
#634524