Finite Group Databasebeta

← #11780186

Subgroups — #11780186

Order 1152.

351 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 351 conjugacy classes of subgroups — too many to draw. Only its 76 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#10589829C211yesmaximal, characteristic
2#10588758C211yesmaximal, characteristic, complemented
3#10588530C211yesmaximal, characteristic
4#10588513C211yesmaximal, characteristic, complemented
5C9×#332C211yesmaximal, characteristic, complemented
6#10588162C211yesmaximal, characteristic
7#10588160C211yesmaximal, characteristic, complemented
8#68461—31nomaximal
9C2×Q8×D9—21no—
10C9×C4⋊Q8C2211yescharacteristic
11#63508—21no—
12C2×Dic36—21no—
13#63458—22no—
14#63455—21no—
15#63450—21no—
16C4×D36C2211yescharacteristic
17#63431C2211yescharacteristic
18C4×Dic18C2211yescharacteristic
19C9×C4⋊C8C2211yescharacteristic
20C9×C4⋊C8C2211yescharacteristic
21#63380—21no—
22#63378—21no—
23#63376—21no—
24#63366—22no—
25C4×C9⋊C8C2211yescharacteristic
26#5727—31no—
27#5078—31no—
28#4849—31no—
29#4846—31no—
30C3×#332D311yescharacteristic
31#4484—31no—
32#4483—31no—
33C2×Q8×C9—21no—
34Q8×D9—42no—
35Q8×D9—42no—
36C2×D36D411yescharacteristic
37C2×C4×D9—22no—
38C2×C4×D9—21no—
39C2×Dic18—22no—
40C2×Dic18—21no—
41C2×Dic18D411yescharacteristic
42C2×C8×C9—21no—
43C2×C8×C9—21no—
44C9×C4⋊C4—21no—
45C9×C4⋊C4D412yes—
46C42×C9C2311yescharacteristic
47(C2×D9)⋊C4—22no—
48(C2×D9)⋊C4—21no—
49C4⋊Dic9—21no—
50C4⋊Dic9—21no—
51C4⋊Dic9D411yescharacteristic
52C4⋊Dic9D411yescharacteristic
53Dic9⋊C4—22no—
54Dic9⋊C4—21no—
55C4×Dic9—21no—
56C2×C9⋊C8—21no—
57Dic36—42no—
58#1649—91noSylow
59C2×D3×Q8—61no—
60C3×C4⋊Q8C2×D311yescharacteristic
61#946—61no—
62C2×Dic12—61no—
63#896—62no—
64#893—61no—
65#888—61no—
66C4×D12—31no—
67#869—31no—
68C4×Dic6—31no—
69C3×C4⋊C8C2×D311yescharacteristic
70C3×C4⋊C8C2×D311yescharacteristic
71#821—61no—
72#818—61no—
73#816—61no—
74#807—62no—
75C4×C3⋊C8—31no—
76C22×D9—21no—
77Q8×C9—41no—
78Q8×C9—41no—
79C2×C4×C9—22no—
80C2×C4×C9C2×D411yescharacteristic
81C2×C4×C9C2×D411yescharacteristic
82C2×C4×C9C2×D411yescharacteristic
83C2×Dic9—21no—
84C2×Dic9—21no—
85C2×Dic9—21no—
86C2×Dic9—41no—
87D36—21no—
88D36Q1612yescomplemented
89C4×D9—44no—
90C4×D9—41no—
91C4×D9—41no—
92Dic18—21no—
93Dic18—44no—
94Dic18—41no—
95Dic18—41no—
96Dic18D812yes—
97C8×C9—41no—
98C8×C9—41no—
99C9⋊C8—22no—
100D4×Q8—91no—
101#500—91no—
102#474—91no—
103#462—91no—
104#332D911yescharacteristic, complemented
105Q8⋊C8—91no—
106D4⋊C8—91no—
107C2×C3×Q8—21no—
108D3×Q8—122no—
109D3×Q8—122no—
110C2×D12—31no—
111C2×C4×D3—62no—
112C2×C4×D3—61no—
113C2×Dic6—31no—
114C2×Dic6—62no—
115C2×Dic6—61no—
116C2×C3×C8—21no—
117C2×C3×C8—21no—
118C3×C4⋊C4—21no—
119C3×C4⋊C4D1212yes—
120C3×C42C22×D311yescharacteristic
121(C2×D3)⋊C4—62no—
122(C2×D3)⋊C4—61no—
123C4⋊Dic3—31no—
124C4⋊Dic3—31no—
125C4⋊Dic3—61no—
126C4⋊Dic3—61no—
127Dic3⋊C4—62no—
128Dic3⋊C4—61no—
129C4×Dic3—61no—
130C2×C3⋊C8—61no—
131Dic12—122no—
132C22×C9#12011yescharacteristic
133C2×D9—22no—
134C2×D9—41no—
135C2×D9—41no—
136C4×C9—21no—
137C4×C9—42no—
138C4×C9C2×D811yescharacteristic
139C4×C9C2×Q1611yescharacteristic
140C4×C9AGL(1,ℤ/8)11yescharacteristic
141C4×C9#13711yescharacteristic
142Dic9—22no—
143Dic9—41no—
144Dic9—41no—
145Dic9—81no—
146C22×Q8—181no—
147C2×Q16—181no—
148C4⋊Q8—91no—
149C4⋊Q8—181no—
150C4⋊Q8C2×D911yescharacteristic
151C22⋊Q8—181no—
152C22⋊Q8—182no—
153C4×Q8—91no—
154C4×D4—91no—
155C4×D4—181no—
156#107—181no—
157#107—182no—
158C4⋊C8C2×D911yescharacteristic
159C4⋊C8C2×D911yescharacteristic
160#103—181no—
161#102—181no—
162C4×C8—91no—
163C22×D3—61no—
164C3×Q8—41no—
165C3×Q8—41no—
166C2×C3×C4—22no—
167C2×C3×C4C2×D1211yescharacteristic
168C2×C3×C4D3×D411yescharacteristic
169C2×C3×C4D3×D411yescharacteristic
170C2×Dic3—61no—
171C2×Dic3—61no—
172C2×Dic3—61no—
173C2×Dic3—121no—
174D12—32no—
175D12—61no—
176C4×D3—124no—
177C4×D3—121no—
178C4×D3—121no—
179Dic6—32no—
180Dic6—61no—
181Dic6—124no—
182Dic6—121no—
183Dic6—121no—
184C3×C8—41no—
185C3×C8—41no—
186C3⋊C8—62no—
187C2×C9#44711yescharacteristic
188C2×C9#45111yescharacteristic
189C2×C9#45611yescharacteristic
190D9—42no—
191C2×Q8—21no—
192C2×Q8—91no—
193C2×Q8—182no—
194C2×Q8—181no—
195C2×Q8—362no—
196C2×Q8—362no—
197C2×D4—91no—
198C22×C4—182no—
199C22×C4—181no—
200Q16—362no—
201C2×C8—21no—
202C2×C8—21no—
203C2×C8—181no—
204C4⋊C4—21no—
205C4⋊C4—91no—
206C4⋊C4—91no—
207C4⋊C4—182no—
208C4⋊C4—181no—
209C4⋊C4—181no—
210C4⋊C4—181no—
211C4⋊C4D3612yes—
212C22⋊C4—182no—
213C22⋊C4—181no—
214C42—181no—
215C42C22×D911yescharacteristic
216C22×C3#88211yescharacteristic
217C2×D3—62no—
218C2×D3—121no—
219C2×D3—121no—
220C3×C4—21no—
221C3×C4—42no—
222C3×C4D3×D811yescharacteristic
223C3×C4#91411yescharacteristic
224C3×C4#91511yescharacteristic
225C3×C4D3×Q1611yescharacteristic
226Dic3—62no—
227Dic3—121no—
228Dic3—121no—
229Dic3—241no—
230C9#164911yescharacteristic, complemented, Sylow
231C23—181no—
232Q8—41no—
233Q8—41no—
234Q8—92no—
235Q8—181no—
236Q8—364no—
237Q8—361no—
238Q8—361no—
239D4—92no—
240D4—181no—
241C2×C4—22no—
242C2×C4—181no—
243C2×C4—181no—
244C2×C4—181no—
245C2×C4—364no—
246C2×C4—361no—
247C2×C4—361no—
248C2×C4—361no—
249C2×C4C2×D3611yescharacteristic
250C2×C4D4×D911yescharacteristic
251C2×C4D4×D911yescharacteristic
252C8—41no—
253C8—41no—
254C8—182no—
255C2×C3#475211yescharacteristic
256C2×C3#477311yescharacteristic
257C2×C3#480911yescharacteristic
258D3—122no—
259C22—182no—
260C22—361no—
261C22—361no—
262C22#6344411yescharacteristic
263C4—21no—
264C4—42no—
265C4—182no—
266C4—361no—
267C4—361no—
268C4—721no—
269C4D8×D911yescharacteristic
270C4#6347611yescharacteristic
271C4#6347711yescharacteristic
272C4Q16×D911yescharacteristic
273C3#6846111yescharacteristic
274C2—362no—
275C2#1058843211yescharacteristic
276C2#1058845311yescharacteristic
277C2#1058848911yescharacteristic
subgroupG/H
centerC22#63444
commutator, cosocleC42×C9C23
FrattiniC3×C42C22×D3
FittingC9×#332C2
socleC22×C3#882
prime radicalC2×D36D4
hypercenter#332D9
hypocenterC9#1649
LCSG ▷ C42×C9 ▷ C22×C9 ▷ C9
UCSC1 ◁ C22 ◁ C42 ◁ #332

Complements

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

NH ≅ G/Ntype
2. #10588758C2semidirect
4. #10588513C2semidirect
5. C9×#332C2semidirect
7. #10588160C2semidirect
88. D36Q16semidirect
104. #332D9semidirect
230. C9#1649semidirect

Maximal subgroups

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

subgroupindex
#105898292
#105887582
#105885302
#105885132
C9×#3322
#105881622
#105881602
#684613