Finite Group Databasebeta

← #11878889

Subgroups — #11878889

Order 1152.

576 conjugacy classes of subgroups; only the 154 normal subgroups are shown.

normal subgroups only

This group has 576 conjugacy classes of subgroups — too many to draw. Only its 154 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#10589830C211yesmaximal, characteristic
2D9×C4⋊Q8C211yesmaximal, characteristic
3C9×#487C211yesmaximal, characteristic, complemented
4#10588766C211yesmaximal, characteristic, complemented
5#10588765C211yesmaximal, characteristic, complemented
6#10588489C214yesmaximal
7#10588475C214yesmaximal, complemented
8#10588367C211yesmaximal, characteristic
9#10588365C211yesmaximal, characteristic, complemented
10#81604—31nomaximal
11C2×Q8×D9C2212yes—
12C9×C4⋊Q8C2211yescharacteristic
13C9×C4⋊Q8C2211yescharacteristic
14#63508—21no—
15Q8×Dic9—21no—
16#63506C2212yes—
17C2×#3674C2214yes—
18C2×Dic36C2214yes—
19#63459C2212yes—
20#63454—21no—
21C4⋊C4×D9—21no—
22C4⋊C4×D9—21no—
23#63452—21no—
24#63450—21no—
25#63450—21no—
26#63449C2212yes—
27C42×D9C2211yescharacteristic
28#63431C2211yescharacteristic
29#63431C2211yescharacteristic
30C9×#103C2214yes—
31C4×C8×C9C2211yescharacteristic
32(C2×D9)⋊C8C2212yes—
33Dic9⋊C8C2212yes—
34#63368C2214yes—
35C4×C9⋊C8C2211yescharacteristic
36#5728—31no—
37D3×C4⋊Q8—31no—
38C3×#487D311yescharacteristic
39#5093—31no—
40#5092—31no—
41#4809—34no—
42#4795—34no—
43#4699—31no—
44#4685—31no—
45C2×Q8×C9—21no—
46C2×Q8×C9C2312yes—
47Q8×D9—44no—
48C2×C4×D9—22no—
49C2×C4×D9D411yescharacteristic
50C2×C4×D9D411yescharacteristic
51C2×C4×D9C2311yescharacteristic
52C2×Dic18—22no—
53C2×Dic18C2312yes—
54C2×Dic18C2312yes—
55C2×C8×C9C2312yes—
56C9×C4⋊C4—21no—
57C9×C4⋊C4—21no—
58C9×C4⋊C4—21no—
59C9×C4⋊C4C2312yes—
60C42×C9C2311yescharacteristic
61#3674—44no—
62(C2×D9)⋊C4—22no—
63C4⋊Dic9—21no—
64C4⋊Dic9—21no—
65C4⋊Dic9—21no—
66C4⋊Dic9—21no—
67C4⋊Dic9—22no—
68Dic9⋊C4—22no—
69Dic9⋊C4—22no—
70Dic9⋊C4—22no—
71C4×Dic9—22no—
72C4×Dic9D411yescharacteristic
73C4×Dic9D411yescharacteristic
74C4×Dic9C2311yescharacteristic
75C2×C9⋊C8C2312yes—
76Dic36—44no—
77#3209—91noSylow
78C2×D3×Q8—32no—
79C3×C4⋊Q8C2×D311yescharacteristic
80C3×C4⋊Q8C2×D311yescharacteristic
81#946—61no—
82Q8×Dic3—61no—
83#944—32no—
84C2×#216—34no—
85C2×Dic12—34no—
86#897—32no—
87#892—61no—
88D3×C4⋊C4—61no—
89D3×C4⋊C4—61no—
90#890—61no—
91#888—61no—
92#888—61no—
93#887—32no—
94C42×D3—31no—
95#869—31no—
96#869—31no—
97C3×#103C2×D314yes—
98C3×C4×C8C2×D311yescharacteristic
99(C2×D3)⋊C8—32no—
100Dic3⋊C8—32no—
101#810—34no—
102C4×C3⋊C8—31no—
103C22×D9C2×D411yescharacteristic
104Q8×C9—24no—
105Q8×C9—42no—
106C2×C4×C9—22no—
107C2×C4×C9—22no—
108C2×C4×C9C2×D411yescharacteristic
109C2×C4×C9C2×D411yescharacteristic
110C2×C4×C9C2411yescharacteristic
111C2×Dic9—22no—
112C2×Dic9—22no—
113C2×Dic9C2×D411yescharacteristic
114C2×Dic9C2×D411yescharacteristic
115C2×Dic9C2×D411yescharacteristic
116C4×D9—22no—
117C4×D9—22no—
118C4×D9—44no—
119C4×D9Q1614yescomplemented
120Dic18—24no—
121Dic18—24no—
122Dic18—44no—
123C8×C9—22no—
124C9⋊C8—22no—
125#533—91no—
126C2×C4⋊Q8—91no—
127#494—91no—
128#494—91no—
129#487—91no—
130#487D911yescharacteristic, complemented
131#462—94no—
132#451—94no—
133#431—91no—
134C2×C3×Q8—21no—
135C2×C3×Q8C22×D312yes—
136D3×Q8—124no—
137C2×C4×D3—31no—
138C2×C4×D3—31no—
139C2×C4×D3—31no—
140C2×C4×D3—62no—
141C2×Dic6—32no—
142C2×Dic6—32no—
143C2×Dic6—62no—
144C2×C3×C8C22×D312yes—
145C3×C4⋊C4—21no—
146C3×C4⋊C4—21no—
147C3×C4⋊C4—21no—
148C3×C4⋊C4C22×D312yes—
149C3×C42C22×D311yescharacteristic
150#216—124no—
151(C2×D3)⋊C4—62no—
152C4⋊Dic3—62no—
153C4⋊Dic3—61no—
154C4⋊Dic3—61no—
155C4⋊Dic3—61no—
156C4⋊Dic3—61no—
157Dic3⋊C4—62no—
158Dic3⋊C4—62no—
159Dic3⋊C4—62no—
160C4×Dic3—31no—
161C4×Dic3—31no—
162C4×Dic3—31no—
163C4×Dic3—62no—
164C2×C3⋊C8—32no—
165Dic12—124no—
166C22×C9C22×D411yescharacteristic
167C2×D9—21no—
168C2×D9—21no—
169C2×D9C2×Q1612yes—
170C4×C9—42no—
171C4×C9—42no—
172C4×C9C2×Q1612yes—
173C4×C9#13712yes—
174C4×C9H(5,𝔽2)12yes—
175Dic9—21no—
176Dic9—21no—
177Dic9—42no—
178Dic9—42no—
179Dic9C2×Q1612yes—
180C22×Q8—92no—
181C2×Q16—94no—
182C2×Q16—94no—
183C4⋊Q8—92no—
184C4⋊Q8—91no—
185C4⋊Q8—91no—
186C4⋊Q8—181no—
187C4⋊Q8—181no—
188C4⋊Q8C2×D911yescharacteristic
189C4⋊Q8C2×D911yescharacteristic
190#125—181no—
191C22⋊Q8—92no—
192C22⋊Q8—181no—
193C4×Q8—92no—
194C4×Q8—181no—
195#117—181no—
196C2×C4⋊C4—181no—
197C2×C4⋊C4—181no—
198C2×C42—91no—
199C4⋊C8—92no—
200#103—94no—
201#103C2×D914yes—
202C22⋊C8—92no—
203C4×C8—91no—
204C4×C8C2×D911yescharacteristic
205C22×D3—31no—
206C3×Q8—24no—
207C3×Q8—42no—
208C2×C3×C4—22no—
209C2×C3×C4—22no—
210C2×C3×C4D3×D411yescharacteristic
211C2×C3×C4D3×D411yescharacteristic
212C2×C3×C4C23×D311yescharacteristic
213C2×Dic3—31no—
214C2×Dic3—31no—
215C2×Dic3—31no—
216C2×Dic3—62no—
217C2×Dic3—62no—
218C4×D3—34no—
219C4×D3—62no—
220C4×D3—62no—
221C4×D3—124no—
222Dic6—64no—
223Dic6—64no—
224Dic6—124no—
225C3×C8—22no—
226C3⋊C8—62no—
227C2×C9#53511yescharacteristic
228C2×C9C22×Q1611yescharacteristic
229C2×C9C2×#13711yescharacteristic
230D9—22no—
231C2×Q8—21no—
232C2×Q8—92no—
233C2×Q8—92no—
234C2×Q8—182no—
235C2×Q8—364no—
236C2×Q8C22×D912yes—
237C22×C4—91no—
238C22×C4—91no—
239C22×C4—91no—
240C22×C4—182no—
241Q16—364no—
242Q16—364no—
243C2×C8—92no—
244C2×C8C22×D912yes—
245C4⋊C4—21no—
246C4⋊C4—21no—
247C4⋊C4—21no—
248C4⋊C4—182no—
249C4⋊C4—182no—
250C4⋊C4—182no—
251C4⋊C4—182no—
252C4⋊C4—181no—
253C4⋊C4—181no—
254C4⋊C4—181no—
255C4⋊C4—181no—
256C4⋊C4C22×D912yes—
257C22⋊C4—182no—
258C42—91no—
259C42—91no—
260C42—91no—
261C42—182no—
262C42C22×D911yescharacteristic
263C22×C3C2×D3×D411yescharacteristic
264C2×D3—32no—
265C2×D3—61no—
266C2×D3—61no—
267C3×C4—42no—
268C3×C4—42no—
269C3×C4#91512yes—
270C3×C4D3×Q1612yes—
271C3×C4#100912yes—
272Dic3—32no—
273Dic3—61no—
274Dic3—61no—
275Dic3—122no—
276Dic3—122no—
277C9#320911yescharacteristic, complemented, Sylow
278C23—91no—
279Q8—24no—
280Q8—42no—
281Q8—184no—
282Q8—184no—
283Q8—364no—
284C2×C4—22no—
285C2×C4—22no—
286C2×C4—91no—
287C2×C4—94no—
288C2×C4—91no—
289C2×C4—91no—
290C2×C4—182no—
291C2×C4—182no—
292C2×C4—182no—
293C2×C4—182no—
294C2×C4—364no—
295C2×C4D4×D911yescharacteristic
296C2×C4D4×D911yescharacteristic
297C2×C4C23×D911yescharacteristic
298C8—22no—
299C8—182no—
300C2×C3#567411yescharacteristic
301C2×C3C2×#91511yescharacteristic
302C2×C3C2×D3×Q1611yescharacteristic
303D3—62no—
304C22—92no—
305C22—181no—
306C22—181no—
307C22C2×D4×D911yescharacteristic
308C4—42no—
309C4—42no—
310C4—92no—
311C4—181no—
312C4—181no—
313C4—362no—
314C4—362no—
315C4#6347712yes—
316C4Q16×D912yes—
317C4#6371512yes—
318C3#8160411yescharacteristic
319C2—182no—
320C2#1058977611yescharacteristic
321C2C2×#6347711yescharacteristic
322C2C2×Q16×D911yescharacteristic
subgroupG/H
centerC22C2×D4×D9
commutator, cosocleC2×C4×C9C24
FrattiniC2×C3×C4C23×D3
FittingC9×#487C2
socleC22×C3C2×D3×D4
prime radicalC22×D9C2×D4
hypercenter#487D9
hypocenterC9#3209
LCSG ▷ C2×C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
3. C9×#487C2semidirect
4. #10588766C2semidirect
5. #10588765C2semidirect
7. #10588475C2semidirect
9. #10588365C2semidirect
119. C4×D9Q16semidirect
130. #487D9semidirect
277. C9#3209semidirect

Maximal subgroups

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

subgroupindex
#105898302
D9×C4⋊Q82
C9×#4872
#105887662
#105887652
#105884892
#105884752
#105883672
#105883652
#816043