Finite Group Databasebeta

← #11780174

Subgroups — #11780174

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
2C9×#500C211yesmaximal, characteristic, complemented
3#10588772C211yesmaximal, characteristic
4#10588763C211yesmaximal, characteristic, complemented
5#10588224C211yesmaximal, characteristic, complemented
6#10588136C211yesmaximal, characteristic
7#10588133C211yesmaximal, characteristic, complemented
8#71376—31nomaximal
9C2×Q8×D9—21no—
10C9×C4⋊Q8C2211yescharacteristic
11C9×C4⋊Q8C2211yescharacteristic
12#63508—21no—
13C2×#3674—21no—
14#63458—22no—
15#63455—21no—
16#63450—21no—
17C4×D36C2211yescharacteristic
18C4×Dic18C2211yescharacteristic
19C9×#107—22no—
20C4×C8×C9C2211yescharacteristic
21#63395—21no—
22#63369—21no—
23#63366—21no—
24C4⋊(C9⋊C8)C2211yescharacteristic
25C4⋊(C9⋊C8)C2211yescharacteristic
26#5727—31no—
27C3×#500D311yescharacteristic
28#5090—31no—
29#5087—31no—
30#4547—31no—
31#4459—31no—
32#4456—31no—
33C2×Q8×C9—21no—
34C2×Q8×C9—21no—
35Q8×D9—42no—
36Q8×D9—42no—
37C2×D36D411yescharacteristic
38C2×C4×D9—22no—
39C2×C4×D9—21no—
40C2×Dic18—22no—
41C2×Dic18D411yescharacteristic
42C2×C8×C9—21no—
43C9×C4⋊C4—21no—
44C9×C4⋊C4—21no—
45C9×C4⋊C4—21no—
46C9×C4⋊C4D412yes—
47C42×C9C2311yescharacteristic
48#3674—42no—
49(C2×D9)⋊C4—22no—
50(C2×D9)⋊C4—21no—
51C4⋊Dic9D411yescharacteristic
52C4⋊Dic9D411yescharacteristic
53Dic9⋊C4—22no—
54Dic9⋊C4—21no—
55C4×Dic9—21no—
56C2×C9⋊C8—21no—
57C2×C9⋊C8—21no—
58#1649—91noSylow
59C2×D3×Q8—61no—
60C3×C4⋊Q8C2×D311yescharacteristic
61C3×C4⋊Q8C2×D311yescharacteristic
62#946—61no—
63C2×#216—61no—
64#896—62no—
65#893—61no—
66#888—61no—
67C4×D12—31no—
68C4×Dic6—31no—
69C3×#107—22no—
70C3×C4×C8C2×D311yescharacteristic
71#835—61no—
72#809—61no—
73#807—61no—
74C4⋊(C3⋊C8)—31no—
75C4⋊(C3⋊C8)—31no—
76C22×D9—21no—
77Q8×C9—41no—
78Q8×C9—41no—
79Q8×C9—41no—
80Q8×C9—41no—
81C2×C4×C9—22no—
82C2×C4×C9—41no—
83C2×C4×C9C2×D411yescharacteristic
84C2×C4×C9C2×D411yescharacteristic
85C2×C4×C9C2×D411yescharacteristic
86C2×Dic9—21no—
87C2×Dic9—21no—
88C2×Dic9—21no—
89D36—21no—
90D36Q1612yescomplemented
91C4×D9—44no—
92C4×D9—41no—
93C4×D9—41no—
94Dic18—21no—
95Dic18—44no—
96Dic18D812yes—
97C8×C9—22no—
98C9⋊C8—41no—
99C9⋊C8—41no—
100D4×Q8—91no—
101#500D911yescharacteristic, complemented
102#474—91no—
103#462—91no—
104#332—91no—
105Q8⋊C8—91no—
106D4⋊C8—91no—
107C2×C3×Q8—21no—
108C2×C3×Q8—21no—
109D3×Q8—122no—
110D3×Q8—122no—
111C2×D12—31no—
112C2×C4×D3—62no—
113C2×C4×D3—61no—
114C2×Dic6—31no—
115C2×Dic6—62no—
116C2×C3×C8—21no—
117C3×C4⋊C4—21no—
118C3×C4⋊C4—21no—
119C3×C4⋊C4—21no—
120C3×C4⋊C4#6712yes—
121C3×C42C22×D311yescharacteristic
122#216—122no—
123(C2×D3)⋊C4—62no—
124(C2×D3)⋊C4—61no—
125C4⋊Dic3—31no—
126C4⋊Dic3—31no—
127Dic3⋊C4—62no—
128Dic3⋊C4—61no—
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—21no—
137C4×C9—42no—
138C4×C9—81no—
139C4×C9C2×D811yescharacteristic
140C4×C9C2×Q1611yescharacteristic
141C4×C9AGL(1,ℤ/8)11yescharacteristic
142C4×C9#13711yescharacteristic
143Dic9—22no—
144Dic9—41no—
145Dic9—41no—
146C22×Q8—181no—
147C2×Q16—181no—
148C4⋊Q8—181no—
149C4⋊Q8C2×D911yescharacteristic
150C4⋊Q8C2×D911yescharacteristic
151C22⋊Q8—181no—
152C22⋊Q8—182no—
153C4×Q8—91no—
154C4×D4—91no—
155C4×D4—181no—
156#107—22no—
157#107—181no—
158C4⋊C8—91no—
159C4⋊C8—91no—
160#103—181no—
161#102—181no—
162C4×C8C2×D911yescharacteristic
163C22×D3—61no—
164C3×Q8—41no—
165C3×Q8—41no—
166C3×Q8—41no—
167C3×Q8—41no—
168C2×C3×C4—22no—
169C2×C3×C4—41no—
170C2×C3×C4D3×D411yescharacteristic
171C2×C3×C4D3×D411yescharacteristic
172C2×C3×C4C2×#6711yescharacteristic
173C2×Dic3—61no—
174C2×Dic3—61no—
175C2×Dic3—61no—
176D12—32no—
177D12—61no—
178C4×D3—124no—
179C4×D3—121no—
180C4×D3—121no—
181Dic6—32no—
182Dic6—61no—
183Dic6—124no—
184C3×C8—22no—
185C3⋊C8—121no—
186C3⋊C8—121no—
187C2×C9#44711yescharacteristic
188C2×C9#45111yescharacteristic
189C2×C9#45611yescharacteristic
190D9—42no—
191C2×Q8—21no—
192C2×Q8—21no—
193C2×Q8—91no—
194C2×Q8—182no—
195C2×Q8—362no—
196C2×Q8—362no—
197C2×D4—91no—
198C22×C4—182no—
199C22×C4—181no—
200Q16—362no—
201C2×C8—21no—
202C2×C8—181no—
203C2×C8—181no—
204C4⋊C4—21no—
205C4⋊C4—21no—
206C4⋊C4—21no—
207C4⋊C4—91no—
208C4⋊C4—91no—
209C4⋊C4—182no—
210C4⋊C4—181no—
211C4⋊C4#61112yes—
212C22⋊C4—182no—
213C22⋊C4—181no—
214C42—181no—
215C42C22×D911yescharacteristic
216C22×C3#93711yescharacteristic
217C2×D3—62no—
218C2×D3—121no—
219C2×D3—121no—
220C3×C4—21no—
221C3×C4—42no—
222C3×C4—81no—
223C3×C4D3×D811yescharacteristic
224C3×C4#91111yescharacteristic
225C3×C4D3×Q1611yescharacteristic
226C3×C4#91811yescharacteristic
227Dic3—62no—
228Dic3—121no—
229Dic3—121no—
230C9#164911yescharacteristic, complemented, Sylow
231C23—181no—
232Q8—41no—
233Q8—41no—
234Q8—41no—
235Q8—41no—
236Q8—92no—
237Q8—181no—
238Q8—364no—
239D4—92no—
240D4—181no—
241C2×C4—22no—
242C2×C4—41no—
243C2×C4—181no—
244C2×C4—181no—
245C2×C4—181no—
246C2×C4—364no—
247C2×C4—361no—
248C2×C4—361no—
249C2×C4D4×D911yescharacteristic
250C2×C4D4×D911yescharacteristic
251C2×C4C2×#61111yescharacteristic
252C8—22no—
253C8—361no—
254C8—361no—
255C2×C3#509511yescharacteristic
256C2×C3#515611yescharacteristic
257C2×C3#518611yescharacteristic
258D3—122no—
259C22—182no—
260C22—361no—
261C22—361no—
262C22#6349911yescharacteristic
263C4—21no—
264C4—42no—
265C4—81no—
266C4—182no—
267C4—361no—
268C4—361no—
269C4D8×D911yescharacteristic
270C4#6347311yescharacteristic
271C4Q16×D911yescharacteristic
272C4#6348011yescharacteristic
273C3#7137611yescharacteristic
274C2—362no—
275C2#1058877511yescharacteristic
276C2#1058883611yescharacteristic
277C2#1058886611yescharacteristic
subgroupG/H
centerC22#63499
commutator, cosocleC42×C9C23
FrattiniC3×C42C22×D3
FittingC9×#500C2
socleC22×C3#937
prime radicalC2×D36D4
hypercenter#500D9
hypocenterC9#1649
LCSG ▷ C42×C9 ▷ C22×C9 ▷ C9
UCSC1 ◁ C22 ◁ C42 ◁ #500

Complements

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

NH ≅ G/Ntype
2. C9×#500C2semidirect
4. #10588763C2semidirect
5. #10588224C2semidirect
7. #10588133C2semidirect
90. D36Q16semidirect
101. #500D9semidirect
230. C9#1649semidirect

Maximal subgroups

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

subgroupindex
#105898292
C9×#5002
#105887722
#105887632
#105882242
#105881362
#105881332
#713763