Finite Group Databasebeta

← #11780274

Subgroups — #11780274

Order 1152.

351 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 351 conjugacy classes of subgroups — too many to draw. Only its 80 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
1Q8×D36C211yesmaximal, characteristic
2C9×#475C211yesmaximal, characteristic, complemented
3#10588768C211yesmaximal, characteristic
4#10588760C211yesmaximal, characteristic, complemented
5#10588212C211yesmaximal, characteristic, complemented
6#10588162C211yesmaximal, characteristic
7#10588159C211yesmaximal, characteristic, complemented
8#71127—31nomaximal
9C2×Q8×D9—21no—
10C9×C4⋊Q8C2211yescharacteristic
11C4×Q8×C9C2211yescharacteristic
12C2×#3675—21no—
13#63459—21no—
14#63459—22no—
15C4×D36—21no—
16C4×D36C2211yescharacteristic
17#63431—21no—
18#63431C2211yescharacteristic
19C9×#106—21no—
20C9×C4⋊C8C2211yescharacteristic
21C9×#103—21no—
22#63395—21no—
23#63367—22no—
24C4⋊(C9⋊C8)C2211yescharacteristic
25C4×C9⋊C8C2211yescharacteristic
26Q8×D12—31no—
27C3×#475D311yescharacteristic
28#5083—31no—
29#5080—31no—
30#4535—31no—
31#4483—31no—
32#4482—31no—
33C2×Q8×C9—21no—
34C2×Q8×C9D411yescharacteristic
35Q8×D9—42no—
36Q8×D9—42no—
37C2×D36D411yescharacteristic
38C2×C4×D9—22no—
39C2×C4×D9—21no—
40C2×Dic18—22no—
41C2×Dic18—21no—
42C2×C8×C9—21no—
43C9×C4⋊C4—21no—
44C9×C4⋊C4—21no—
45C9×C4⋊C4—21no—
46C9×C4⋊C4D411yescharacteristic
47C42×C9—21no—
48C42×C9C2311yescharacteristic
49#3675—42no—
50(C2×D9)⋊C4—22no—
51(C2×D9)⋊C4—21no—
52C4⋊Dic9—22no—
53C4⋊Dic9—21no—
54C4⋊Dic9D412yes—
55C4⋊Dic9D411yescharacteristic
56C2×C9⋊C8—21no—
57C2×C9⋊C8—21no—
58#1651—91noSylow
59C2×D3×Q8—61no—
60C3×C4⋊Q8C2×D311yescharacteristic
61C3×C4×Q8C2×D311yescharacteristic
62C2×#215—61no—
63#897—62no—
64#897—61no—
65C4×D12—31no—
66C4×D12—61no—
67#869—31no—
68#869—61no—
69C3×#106—21no—
70C3×C4⋊C8C2×D311yescharacteristic
71C3×#103—21no—
72#835—61no—
73#808—62no—
74C4⋊(C3⋊C8)—31no—
75C4×C3⋊C8—31no—
76C22×D9—21no—
77Q8×C9—21no—
78Q8×C9—41no—
79Q8×C9—41no—
80Q8×C9SD1612yescomplemented
81C2×C4×C9—21no—
82C2×C4×C9—21no—
83C2×C4×C9—41no—
84C2×C4×C9C2×D411yescharacteristic
85C2×C4×C9C2×D411yescharacteristic
86C2×C4×C9C2×D411yescharacteristic
87C2×Dic9—21no—
88C2×Dic9—22no—
89D36—21no—
90D36SD1612yes—
91C4×D9—44no—
92C4×D9—41no—
93C4×D9—41no—
94Dic18—44no—
95Dic18—41no—
96Dic18—41no—
97C8×C9—41no—
98C9⋊C8—22no—
99C9⋊C8—41no—
100D4×Q8—91no—
101#498—91no—
102#475D911yescharacteristic, complemented
103#461—91no—
104#332—91no—
105Q8⋊C8—91no—
106D4⋊C8—91no—
107C2×C3×Q8—21no—
108C2×C3×Q8#6711yescharacteristic
109D3×Q8—122no—
110D3×Q8—122no—
111C2×D12—31no—
112C2×C4×D3—62no—
113C2×C4×D3—61no—
114C2×Dic6—62no—
115C2×Dic6—61no—
116C2×C3×C8—21no—
117C3×C4⋊C4—21no—
118C3×C4⋊C4—21no—
119C3×C4⋊C4—21no—
120C3×C4⋊C4#6711yescharacteristic
121C3×C42—21no—
122C3×C42C22×D311yescharacteristic
123#215—122no—
124(C2×D3)⋊C4—62no—
125(C2×D3)⋊C4—61no—
126C4⋊Dic3—32no—
127C4⋊Dic3—31no—
128C4⋊Dic3—62no—
129C4⋊Dic3—61no—
130C2×C3⋊C8—61no—
131C2×C3⋊C8—61no—
132C22×C9#12011yescharacteristic
133C2×D9—22no—
134C2×D9—41no—
135C2×D9—41no—
136C4×C9—22no—
137C4×C9—21no—
138C4×C9—41no—
139C4×C9—81no—
140C4×C9C2×SD1611yescharacteristic
141C4×C9C2×SD1611yescharacteristic
142C4×C9AGL(1,ℤ/8)11yescharacteristic
143C4×C9#13711yescharacteristic
144Dic9—41no—
145Dic9—42no—
146C22×Q8—181no—
147C2×SD16—181no—
148C4⋊Q8—91no—
149C4⋊Q8—181no—
150C4⋊Q8C2×D911yescharacteristic
151C22⋊Q8—182no—
152C22⋊Q8—181no—
153C4×Q8C2×D911yescharacteristic
154C4×D4—91no—
155C4×D4—181no—
156#106—21no—
157#106—182no—
158C4⋊C8—91no—
159C4⋊C8C2×D911yescharacteristic
160#103—21no—
161#103—181no—
162C4×C8—91no—
163C22×D3—61no—
164C3×Q8—21no—
165C3×Q8—41no—
166C3×Q8—41no—
167C3×Q8#21512yes—
168C2×C3×C4—21no—
169C2×C3×C4—21no—
170C2×C3×C4—41no—
171C2×C3×C4D3×D411yescharacteristic
172C2×C3×C4D3×D411yescharacteristic
173C2×C3×C4C2×#6711yescharacteristic
174C2×Dic3—62no—
175C2×Dic3—61no—
176D12—32no—
177D12—61no—
178C4×D3—124no—
179C4×D3—121no—
180C4×D3—121no—
181Dic6—124no—
182Dic6—121no—
183Dic6—121no—
184C3×C8—41no—
185C3⋊C8—62no—
186C3⋊C8—121no—
187C2×C9#44811yescharacteristic
188C2×C9#45011yescharacteristic
189C2×C9#45611yescharacteristic
190D9—42no—
191C2×Q8—21no—
192C2×Q8—182no—
193C2×Q8—181no—
194C2×Q8—362no—
195C2×Q8—362no—
196C2×Q8#61111yescharacteristic
197C2×D4—91no—
198C22×C4—182no—
199C22×C4—181no—
200SD16—362no—
201C2×C8—21no—
202C2×C8—181no—
203C2×C8—181no—
204C4⋊C4—21no—
205C4⋊C4—21no—
206C4⋊C4—21no—
207C4⋊C4—91no—
208C4⋊C4—92no—
209C4⋊C4—182no—
210C4⋊C4—181no—
211C4⋊C4#61111yescharacteristic
212C22⋊C4—182no—
213C22⋊C4—181no—
214C42—21no—
215C42C22×D911yescharacteristic
216C22×C3#93711yescharacteristic
217C2×D3—62no—
218C2×D3—121no—
219C2×D3—121no—
220C3×C4—21no—
221C3×C4—22no—
222C3×C4—41no—
223C3×C4—81no—
224C3×C4D3×SD1611yescharacteristic
225C3×C4#91511yescharacteristic
226C3×C4C2×#21511yescharacteristic
227C3×C4#94911yescharacteristic
228Dic3—121no—
229Dic3—122no—
230C9#165111yescharacteristic, complemented, Sylow
231C23—181no—
232Q8—21no—
233Q8—41no—
234Q8—41no—
235Q8—364no—
236Q8—361no—
237Q8—361no—
238Q8#367512yescomplemented
239D4—92no—
240D4—181no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—41no—
244C2×C4—182no—
245C2×C4—181no—
246C2×C4—364no—
247C2×C4—361no—
248C2×C4—361no—
249C2×C4D4×D911yescharacteristic
250C2×C4D4×D911yescharacteristic
251C2×C4C2×#61111yescharacteristic
252C8—41no—
253C8—182no—
254C8—361no—
255C2×C3#504611yescharacteristic
256C2×C3#517011yescharacteristic
257C2×C3#520511yescharacteristic
258D3—122no—
259C22—182no—
260C22—361no—
261C22—361no—
262C22#6349911yescharacteristic
263C4—22no—
264C4—21no—
265C4—41no—
266C4—81no—
267C4—362no—
268C4—361no—
269C4SD16×D911yescharacteristic
270C4#6347711yescharacteristic
271C4C2×#367511yescharacteristic
272C4#6351211yescharacteristic
273C3#7112711yescharacteristic
274C2—362no—
275C2#1058872911yescharacteristic
276C2#1058885011yescharacteristic
277C2#1058888511yescharacteristic
subgroupG/H
centerC22#63499
commutator, cosocleC42×C9C23
FrattiniC3×C42C22×D3
FittingC9×#475C2
socleC22×C3#937
prime radicalC2×D36D4
hypercenter#475D9
hypocenterC9#1651
LCSG ▷ C42×C9 ▷ C22×C9 ▷ C9
UCSC1 ◁ C22 ◁ C42 ◁ #475

Complements

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

NH ≅ G/Ntype
2. C9×#475C2semidirect
4. #10588760C2semidirect
5. #10588212C2semidirect
7. #10588159C2semidirect
80. Q8×C9SD16semidirect
102. #475D9semidirect
230. C9#1651semidirect
238. Q8#3675semidirect

Maximal subgroups

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

subgroupindex
Q8×D362
C9×#4752
#105887682
#105887602
#105882122
#105881622
#105881592
#711273