Finite Group Databasebeta

← #11796359

Subgroups — #11796359

Order 1152.

387 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 387 conjugacy classes of subgroups — too many to draw. Only its 68 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#10589770C211yesmaximal, characteristic
2#10588420C212yesmaximal, complemented
3C9×#354C211yesmaximal, characteristic, complemented
4#10588218C211yesmaximal, characteristic, complemented
5#10588151C212yesmaximal, complemented
6#69158—31nomaximal
7C2×#3701C411yescharacteristic, complemented
8C2×#3699C2211yescharacteristic
9C9×#124C2211yescharacteristic
10#63506C411yescharacteristic, complemented
11#63502C2211yescharacteristic
12#63446—22no—
13#611⋊C4—22no—
14#63439—22no—
15#63437C411yescharacteristic, complemented
16C42×D9C411yescharacteristic, complemented
17C9×#99C2212yes—
18#63393C2212yes—
19#63365—22no—
20#5668—31no—
21#4740—32no—
22C3×#354D311yescharacteristic
23#4541—31no—
24#4474—32no—
25C2×Q8×C9C2×C411yescharacteristic
26C2×D4×C9C2311yescharacteristic
27C2×#611—22no—
28C2×#611D412yes—
29C22×Dic9D412yes—
30#3701—41no—
31#3701—41no—
32#3699—41no—
33#3699—41no—
34C2×D36—21no—
35C2×D36C2×C411yescharacteristic
36C2×C4×D9—21no—
37C2×C4×D9—21no—
38C2×C4×D9C2×C411yescharacteristic
39C2×Dic18C2×C411yescharacteristic
40C9×C22⋊C4—22no—
41C9×C22⋊C4—22no—
42C42×C9C2×C411yescharacteristic
43#3676—22no—
44(C2×D9)⋊C4—22no—
45Dic9⋊C4—22no—
46Dic9⋊C4—42no—
47C4×Dic9—21no—
48C4×Dic9—42no—
49C4×Dic9C2×C411yescharacteristic
50#2126—91noSylow
51C2×#239—31no—
52C2×#237—31no—
53C3×#124C2×D311yescharacteristic
54#944—31no—
55#940—31no—
56#884—62no—
57#67⋊C4—62no—
58#877—62no—
59#875—31no—
60C42×D3—31no—
61C3×#99C2×D312yes—
62#834—32no—
63#806—62no—
64C23×C9C2×D412yes—
65C22×D9—21no—
66C22×D9C22⋊C411yescharacteristic
67Q8×C9—41no—
68D4×C9—41no—
69C2×C4×C9—21no—
70C2×C4×C9—21no—
71C2×C4×C9—42no—
72C2×C4×C9C22×C411yescharacteristic
73#611—42no—
74#611—44no—
75C2×Dic9—21no—
76C2×Dic9—22no—
77C2×Dic9—22no—
78C2×Dic9—42no—
79C2×Dic9C22⋊C412yes—
80C2×Dic9C22⋊C411yescharacteristic
81D36—41no—
82D36—42no—
83C4×D9—21no—
84C4×D9—21no—
85C4×D9—42no—
86C4×D9—41no—
87C4×D9—41no—
88Dic18—41no—
89#532—91no—
90#410—92no—
91#354—91no—
92#354D911yescharacteristic, complemented
93#353—92no—
94C2×C3×Q8C4×D311yescharacteristic
95C2×C3×D4C22×D311yescharacteristic
96C2×#67—32no—
97C2×#67—62no—
98C22×Dic3—32no—
99#239—121no—
100#239—121no—
101#237—121no—
102#237—121no—
103C2×D12—31no—
104C2×D12—61no—
105C2×C4×D3—31no—
106C2×C4×D3—61no—
107C2×C4×D3—61no—
108C2×Dic6—31no—
109C3×C22⋊C4—22no—
110C3×C22⋊C4—22no—
111C3×C42C4×D311yescharacteristic
112#217—62no—
113(C2×D3)⋊C4—62no—
114Dic3⋊C4—62no—
115Dic3⋊C4—122no—
116C4×Dic3—31no—
117C4×Dic3—61no—
118C4×Dic3—122no—
119C22×C9—22no—
120C22×C9—42no—
121C22×C9C2×C22⋊C411yescharacteristic
122C2×D9—21no—
123C2×D9—41no—
124C2×D9—42no—
125C2×D9—41no—
126C4×C9—21no—
127C4×C9—41no—
128C4×C9—41no—
129C4×C9—82no—
130Dic9—22no—
131Dic9—22no—
132Dic9—82no—
133Dic9#9911yescharacteristic
134Dic9#9911yescharacteristic
135C2×#41—91no—
136C2×#41—91no—
137C4⋊Q8—91no—
138#127—91no—
139#124—91no—
140#124C2×D911yescharacteristic
141#121—182no—
142C4×D4—182no—
143#117—182no—
144C2×C42—91no—
145#99—92no—
146#99—182no—
147#99C2×D912yes—
148C23×C3D3×D412yes—
149C22×D3—31no—
150C22×D3—61no—
151C3×Q8—41no—
152C3×D4—41no—
153C2×C3×C4—21no—
154C2×C3×C4—21no—
155C2×C3×C4—42no—
156C2×C3×C4C2×C4×D311yescharacteristic
157#67—122no—
158#67—124no—
159C2×Dic3—31no—
160C2×Dic3—32no—
161C2×Dic3—62no—
162C2×Dic3—62no—
163C2×Dic3—61no—
164C2×Dic3—122no—
165D12—121no—
166D12—122no—
167C4×D3—61no—
168C4×D3—61no—
169C4×D3—121no—
170C4×D3—121no—
171C4×D3—122no—
172Dic6—121no—
173C2×C9—21no—
174C2×C9—42no—
175C2×C9C2×#9911yescharacteristic
176D9—41no—
177D9—81no—
178#41—361no—
179#41—361no—
180#41—361no—
181#41—361no—
182C2×Q8—91no—
183C2×Q8C4×D911yescharacteristic
184C2×D4—92no—
185C2×D4—91no—
186C2×D4—181no—
187C2×D4—182no—
188C2×D4C22×D911yescharacteristic
189C22×C4—92no—
190C22×C4—91no—
191C22×C4—181no—
192C22×C4—181no—
193C4⋊C4—182no—
194C4⋊C4—362no—
195C22⋊C4—22no—
196C22⋊C4—22no—
197C22⋊C4—182no—
198C22⋊C4—182no—
199C42—91no—
200C42—181no—
201C42—362no—
202C42C4×D911yescharacteristic
203C22×C3—22no—
204C22×C3—42no—
205C22×C3D3×C22⋊C411yescharacteristic
206C2×D3—61no—
207C2×D3—121no—
208C2×D3—122no—
209C2×D3—121no—
210C3×C4—21no—
211C3×C4—41no—
212C3×C4—41no—
213C3×C4—82no—
214Dic3—31no—
215Dic3—31no—
216Dic3—62no—
217Dic3—62no—
218Dic3—242no—
219C9#212611yescharacteristic, complemented, Sylow
220C23—91no—
221C23—181no—
222C23D4×D912yes—
223Q8—41no—
224Q8—361no—
225D4—41no—
226D4—361no—
227D4—362no—
228D4—362no—
229D4—364no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—42no—
233C2×C4—91no—
234C2×C4—92no—
235C2×C4—181no—
236C2×C4—181no—
237C2×C4—182no—
238C2×C4—182no—
239C2×C4—181no—
240C2×C4—361no—
241C2×C4—361no—
242C2×C4—362no—
243C2×C4—362no—
244C2×C4C2×C4×D911yescharacteristic
245C2×C3—21no—
246C2×C3—42no—
247C2×C3D3×#9911yescharacteristic
248D3—121no—
249D3—241no—
250C22—22no—
251C22—42no—
252C22—181no—
253C22—361no—
254C22—362no—
255C22—361no—
256C22C22⋊C4×D911yescharacteristic
257C4—21no—
258C4—41no—
259C4—41no—
260C4—82no—
261C4—91no—
262C4—91no—
263C4—182no—
264C4—182no—
265C4—722no—
266C3#6915811yescharacteristic
267C2—21no—
268C2—42no—
269C2—361no—
270C2—721no—
271C2D9×#9911yescharacteristic
subgroupG/H
centerC2D9×#99
commutatorC2×C4×C9C22×C4
FrattiniC2×C3×D4C22×D3
FittingC9×#354C2
socleC2×C3D3×#99
prime radical#10589770C2
cosocleC2×D4×C9C23
hypercenter#354D9
hypocenterC9#2126
LCSG ▷ C2×C4×C9 ▷ C22×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #354

Complements

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

NH ≅ G/Ntype
2. #10588420C2semidirect
3. C9×#354C2semidirect
4. #10588218C2semidirect
5. #10588151C2semidirect
7. C2×#3701C4semidirect
10. #63506C4semidirect
15. #63437C4semidirect
16. C42×D9C4semidirect
92. #354D9semidirect
219. C9#2126semidirect

Maximal subgroups

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

subgroupindex
#105897702
#105884202
C9×#3542
#105882182
#105881512
#691583