Finite Group Databasebeta

← #11779950

Subgroups — #11779950

Order 1152.

312 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 74 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#10589832C211yesmaximal, characteristic
2#10588759C211yesmaximal, characteristic, complemented
3#10588530C211yesmaximal, characteristic
4#10588513C211yesmaximal, characteristic, complemented
5C9×#333C211yesmaximal, characteristic, complemented
6#10588162C211yesmaximal, characteristic
7#10588160C211yesmaximal, characteristic, complemented
8#68506—31nomaximal
9C9×C4⋊Q8C2211yescharacteristic
10#63508—22no—
11C2×Dic36—21no—
12#63459—21no—
13#63455—21no—
14C4⋊C4×D9—21no—
15#63452—21no—
16C4×D36C2211yescharacteristic
17#63431C2211yescharacteristic
18C4×Dic18C2211yescharacteristic
19C9×C4⋊C8C2211yescharacteristic
20C9×C4⋊C8C2211yescharacteristic
21#63395—22no—
22#63380—21no—
23#63378—21no—
24#63376—21no—
25C4×C9⋊C8C2211yescharacteristic
26#5730—31no—
27#5079—31no—
28#4849—31no—
29#4846—31no—
30C3×#333D311yescharacteristic
31#4484—31no—
32#4483—31no—
33C2×Q8×C9D412yes—
34C2×D36D411yescharacteristic
35C2×C4×D9—21no—
36C2×C4×D9—22no—
37C2×Dic18—21no—
38C2×Dic18D411yescharacteristic
39C2×C8×C9—21no—
40C2×C8×C9—21no—
41C9×C4⋊C4—21no—
42C9×C4⋊C4—21no—
43C42×C9C2311yescharacteristic
44(C2×D9)⋊C4—22no—
45(C2×D9)⋊C4—21no—
46C4⋊Dic9—22no—
47C4⋊Dic9—21no—
48C4⋊Dic9—21no—
49C4⋊Dic9D411yescharacteristic
50C4⋊Dic9D411yescharacteristic
51Dic9⋊C4—22no—
52Dic9⋊C4—21no—
53C4×Dic9—21no—
54C2×C9⋊C8—21no—
55Dic36—42no—
56#1644—91noSylow
57C3×C4⋊Q8C2×D311yescharacteristic
58#946—62no—
59C2×Dic12—61no—
60#897—61no—
61#893—61no—
62D3×C4⋊C4—61no—
63#890—61no—
64C4×D12—31no—
65#869—31no—
66C4×Dic6—31no—
67C3×C4⋊C8C2×D311yescharacteristic
68C3×C4⋊C8C2×D311yescharacteristic
69#835—62no—
70#821—61no—
71#818—61no—
72#816—61no—
73C4×C3⋊C8—31no—
74C22×D9—21no—
75Q8×C9—42no—
76C2×C4×C9—22no—
77C2×C4×C9C2×D411yescharacteristic
78C2×C4×C9C2×D411yescharacteristic
79C2×C4×C9C2×D411yescharacteristic
80C2×Dic9—21no—
81C2×Dic9—21no—
82C2×Dic9—21no—
83C2×Dic9—41no—
84D36—21no—
85D36Q1612yescomplemented
86C4×D9—41no—
87C4×D9—41no—
88C4×D9—82no—
89Dic18—21no—
90Dic18—21no—
91Dic18—41no—
92Dic18—41no—
93C8×C9—41no—
94C8×C9—41no—
95C9⋊C8—41no—
96#554—91no—
97#487—91no—
98#474—91no—
99#462—91no—
100#333D911yescharacteristic, complemented
101Q8⋊C8—91no—
102D4⋊C8—91no—
103C2×C3×Q8D1212yes—
104C2×D12—31no—
105C2×C4×D3—61no—
106C2×C4×D3—62no—
107C2×Dic6—31no—
108C2×Dic6—61no—
109C2×C3×C8—21no—
110C2×C3×C8—21no—
111C3×C4⋊C4—21no—
112C3×C4⋊C4—21no—
113C3×C42C22×D311yescharacteristic
114(C2×D3)⋊C4—62no—
115(C2×D3)⋊C4—61no—
116C4⋊Dic3—31no—
117C4⋊Dic3—31no—
118C4⋊Dic3—62no—
119C4⋊Dic3—61no—
120C4⋊Dic3—61no—
121Dic3⋊C4—62no—
122Dic3⋊C4—61no—
123C4×Dic3—61no—
124C2×C3⋊C8—61no—
125Dic12—122no—
126C22×C9#12011yescharacteristic
127C2×D9—22no—
128C2×D9—41no—
129C2×D9—41no—
130C4×C9—21no—
131C4×C9—42no—
132C4×C9C2×Q1611yescharacteristic
133C4×C9#13511yescharacteristic
134C4×C9AGL(1,ℤ/8)11yescharacteristic
135C4×C9#13711yescharacteristic
136Dic9—41no—
137Dic9—41no—
138Dic9—41no—
139Dic9—81no—
140C2×Q16—181no—
141C4⋊Q8—91no—
142C4⋊Q8C2×D911yescharacteristic
143#125—181no—
144C22⋊Q8—181no—
145C22⋊Q8—182no—
146C4×Q8—91no—
147C4×D4—91no—
148C4×D4—181no—
149C2×C4⋊C4—181no—
150#107—181no—
151C4⋊C8C2×D911yescharacteristic
152C4⋊C8C2×D911yescharacteristic
153#103—181no—
154#103—182no—
155#102—181no—
156C4×C8—91no—
157C22×D3—61no—
158C3×Q8—42no—
159C2×C3×C4—22no—
160C2×C3×C4C2×D1211yescharacteristic
161C2×C3×C4D3×D411yescharacteristic
162C2×C3×C4D3×D411yescharacteristic
163C2×Dic3—61no—
164C2×Dic3—61no—
165C2×Dic3—61no—
166C2×Dic3—121no—
167D12—32no—
168D12—61no—
169C4×D3—121no—
170C4×D3—121no—
171C4×D3—242no—
172Dic6—61no—
173Dic6—61no—
174Dic6—121no—
175Dic6—121no—
176C3×C8—41no—
177C3×C8—41no—
178C3⋊C8—121no—
179C2×C9#44911yescharacteristic
180C2×C9#45111yescharacteristic
181C2×C9#45511yescharacteristic
182D9—42no—
183C2×Q8—91no—
184C2×Q8—181no—
185C2×Q8D3612yes—
186C2×D4—91no—
187C22×C4—182no—
188C22×C4—181no—
189Q16—362no—
190C2×C8—21no—
191C2×C8—21no—
192C2×C8—181no—
193C4⋊C4—21no—
194C4⋊C4—21no—
195C4⋊C4—91no—
196C4⋊C4—91no—
197C4⋊C4—182no—
198C4⋊C4—182no—
199C4⋊C4—181no—
200C4⋊C4—181no—
201C4⋊C4—181no—
202C22⋊C4—182no—
203C22⋊C4—181no—
204C42—181no—
205C42C22×D911yescharacteristic
206C22×C3#88211yescharacteristic
207C2×D3—62no—
208C2×D3—121no—
209C2×D3—121no—
210C3×C4—21no—
211C3×C4—42no—
212C3×C4#91411yescharacteristic
213C3×C4#91511yescharacteristic
214C3×C4D3×Q1611yescharacteristic
215C3×C4#91911yescharacteristic
216Dic3—121no—
217Dic3—121no—
218Dic3—121no—
219Dic3—241no—
220C9#164411yescharacteristic, complemented, Sylow
221C23—181no—
222Q8—42no—
223Q8—181no—
224Q8—181no—
225Q8—361no—
226Q8—361no—
227D4—92no—
228D4—181no—
229C2×C4—22no—
230C2×C4—181no—
231C2×C4—181no—
232C2×C4—181no—
233C2×C4—361no—
234C2×C4—361no—
235C2×C4—361no—
236C2×C4—722no—
237C2×C4C2×D3611yescharacteristic
238C2×C4D4×D911yescharacteristic
239C2×C4D4×D911yescharacteristic
240C8—41no—
241C8—41no—
242C8—361no—
243C2×C3#474611yescharacteristic
244C2×C3#480911yescharacteristic
245C2×C3#481011yescharacteristic
246D3—122no—
247C22—182no—
248C22—361no—
249C22—361no—
250C22#6344411yescharacteristic
251C4—21no—
252C4—42no—
253C4—361no—
254C4—361no—
255C4—361no—
256C4—721no—
257C4#6347611yescharacteristic
258C4#6347711yescharacteristic
259C4Q16×D911yescharacteristic
260C4#6348111yescharacteristic
261C3#6850611yescharacteristic
262C2—362no—
263C2#1058842611yescharacteristic
264C2#1058848911yescharacteristic
265C2#1058849011yescharacteristic
subgroupG/H
centerC22#63444
commutator, cosocleC42×C9C23
FrattiniC3×C42C22×D3
FittingC9×#333C2
socleC22×C3#882
prime radicalC2×D36D4
hypercenter#333D9
hypocenterC9#1644
LCSG ▷ C42×C9 ▷ C22×C9 ▷ C9
UCSC1 ◁ C22 ◁ C42 ◁ #333

Complements

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

NH ≅ G/Ntype
2. #10588759C2semidirect
4. #10588513C2semidirect
5. C9×#333C2semidirect
7. #10588160C2semidirect
85. D36Q16semidirect
100. #333D9semidirect
220. C9#1644semidirect

Maximal subgroups

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

subgroupindex
#105898322
#105887592
#105885302
#105885132
C9×#3332
#105881622
#105881602
#685063