Finite Group Databasebeta

← #11774383

Subgroups — #11774383

Order 1152.

324 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 92 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#10589680C211yesmaximal, characteristic
2D9×C4⋊C8C211yesmaximal, characteristic
3#10588367C211yesmaximal, characteristic
4C9×Q8⋊C8C211yesmaximal, characteristic, complemented
5#10588212C211yesmaximal, characteristic, complemented
6#10588160C211yesmaximal, characteristic, complemented
7#10588133C211yesmaximal, characteristic, complemented
8#68232—31nomaximal
9C4×Q8×C9C2211yescharacteristic
10#63508C411yescharacteristic
11#63506C411yescharacteristic
12C2×C8×D9—21no—
13#63459C411yescharacteristic
14#63458—21no—
15#63451—21no—
16#63450C411yescharacteristic
17#63434—21no—
18C42×D9C2211yescharacteristic
19C4×Dic18—21no—
20C4×Dic18C2211yescharacteristic
21C9×C4⋊C8C2211yescharacteristic
22C4×C8×C9C2211yescharacteristic
23(C2×D9)⋊C8—21no—
24Dic9⋊C8—21no—
25Dic9⋊C8—21no—
26C4⋊(C9⋊C8)C2211yescharacteristic
27C4×C9⋊C8C2211yescharacteristic
28#5578—31no—
29D3×C4⋊C8—31no—
30#4685—31no—
31C3×Q8⋊C8D311yescharacteristic
32#4535—31no—
33#4484—31no—
34#4456—31no—
35C2×Q8×C9C2×C411yescharacteristic
36C2×C4×D9C2×C411yescharacteristic
37C2×C4×D9D411yescharacteristic
38C2×C4×D9D411yescharacteristic
39C2×Dic18—21no—
40C2×Dic18C2×C411yescharacteristic
41C2×C8×C9—21no—
42C2×C8×C9—21no—
43C9×C4⋊C4—21no—
44C9×C4⋊C4C2×C411yescharacteristic
45C42×C9—21no—
46C42×C9C2311yescharacteristic
47(C2×D9)⋊C4—21no—
48(C2×D9)⋊C4—21no—
49C4⋊Dic9—21no—
50C4⋊Dic9C2×C411yescharacteristic
51Dic9⋊C4—21no—
52Dic9⋊C4—21no—
53Dic9⋊C4—21no—
54Dic9⋊C4—21no—
55Dic9⋊C4—21no—
56C4×Dic9—21no—
57C4×Dic9C2×C411yescharacteristic
58C4×Dic9D411yescharacteristic
59C4×Dic9D411yescharacteristic
60C2×C9⋊C8—21no—
61C2×C9⋊C8—21no—
62C8×D9—42no—
63#1481—91noSylow
64C3×C4×Q8C2×D311yescharacteristic
65#946—31no—
66#944—31no—
67C2×D3×C8—61no—
68#897—31no—
69#896—61no—
70#889—61no—
71#888—31no—
72#872—61no—
73C42×D3—31no—
74C4×Dic6—31no—
75C4×Dic6—61no—
76C3×C4⋊C8C2×D311yescharacteristic
77C3×C4×C8C2×D311yescharacteristic
78(C2×D3)⋊C8—61no—
79Dic3⋊C8—61no—
80Dic3⋊C8—61no—
81C4⋊(C3⋊C8)—31no—
82C4×C3⋊C8—31no—
83C22×D9C22⋊C411yescharacteristic
84Q8×C9—21no—
85Q8×C9—21no—
86C2×C4×C9—21no—
87C2×C4×C9—21no—
88C2×C4×C9C22×C411yescharacteristic
89C2×C4×C9C2×D411yescharacteristic
90C2×C4×C9C2×D411yescharacteristic
91C2×Dic9—21no—
92C2×Dic9—21no—
93C2×Dic9C22⋊C411yescharacteristic
94C2×Dic9C22⋊C411yescharacteristic
95C2×Dic9C22⋊C411yescharacteristic
96C4×D9—21no—
97C4×D9—21no—
98C4×D9—41no—
99C4×D9SD1612yes—
100C4×D9Q1612yes—
101Dic18—21no—
102Dic18—21no—
103Dic18—42no—
104C8×C9—41no—
105C8×C9—41no—
106C9⋊C8—41no—
107C9⋊C8—41no—
108#533—91no—
109#431—91no—
110C2×C4⋊C8—91no—
111Q8⋊C8—91no—
112Q8⋊C8—91no—
113Q8⋊C8—91no—
114Q8⋊C8D911yescharacteristic, complemented
115C2×C3×Q8C4×D311yescharacteristic
116C2×C4×D3—31no—
117C2×C4×D3—31no—
118C2×C4×D3—31no—
119C2×Dic6—31no—
120C2×Dic6—61no—
121C2×C3×C8—21no—
122C2×C3×C8—21no—
123C3×C4⋊C4—21no—
124C3×C4⋊C4C4×D311yescharacteristic
125C3×C42—21no—
126C3×C42C22×D311yescharacteristic
127(C2×D3)⋊C4—61no—
128(C2×D3)⋊C4—61no—
129C4⋊Dic3—31no—
130C4⋊Dic3—61no—
131Dic3⋊C4—61no—
132Dic3⋊C4—61no—
133Dic3⋊C4—61no—
134Dic3⋊C4—61no—
135Dic3⋊C4—61no—
136C4×Dic3—31no—
137C4×Dic3—31no—
138C4×Dic3—31no—
139C4×Dic3—61no—
140C2×C3⋊C8—61no—
141C2×C3⋊C8—61no—
142D3×C8—122no—
143C22×C9C2×C22⋊C411yescharacteristic
144C2×D9—21no—
145C2×D9—21no—
146C2×D9#10312yes—
147C4×C9—21no—
148C4×C9—41no—
149C4×C9—41no—
150C4×C9#13111yescharacteristic
151C4×C9#13111yescharacteristic
152C4×C9C2×SD1611yescharacteristic
153C4×C9C2×Q1611yescharacteristic
154Dic9—21no—
155Dic9—21no—
156Dic9—41no—
157Dic9—41no—
158Dic9#10312yes—
159C22×C8—181no—
160C4⋊Q8—91no—
161C4⋊Q8—91no—
162#125—181no—
163C22⋊Q8—91no—
164C22⋊Q8—91no—
165C22⋊Q8—181no—
166C4×Q8—91no—
167C4×Q8—181no—
168C4×Q8C2×D911yescharacteristic
169#117—181no—
170C2×C42—91no—
171C4⋊C8—91no—
172C4⋊C8—181no—
173C4⋊C8—181no—
174C4⋊C8C2×D911yescharacteristic
175C22⋊C8—181no—
176C4×C8—91no—
177C4×C8C2×D911yescharacteristic
178C22×D3—31no—
179C3×Q8—21no—
180C3×Q8—21no—
181C2×C3×C4—21no—
182C2×C3×C4—21no—
183C2×C3×C4C2×C4×D311yescharacteristic
184C2×C3×C4D3×D411yescharacteristic
185C2×C3×C4D3×D411yescharacteristic
186C2×Dic3—31no—
187C2×Dic3—31no—
188C2×Dic3—31no—
189C2×Dic3—61no—
190C2×Dic3—61no—
191C4×D3—32no—
192C4×D3—32no—
193C4×D3—61no—
194C4×D3—61no—
195C4×D3—121no—
196Dic6—61no—
197Dic6—61no—
198Dic6—122no—
199C3×C8—41no—
200C3×C8—41no—
201C3⋊C8—121no—
202C3⋊C8—121no—
203C2×C9#40811yescharacteristic
204C2×C9C2×#10311yescharacteristic
205C2×C9#42111yescharacteristic
206D9—22no—
207C2×Q8—91no—
208C2×Q8—181no—
209C2×Q8C4×D911yescharacteristic
210C22×C4—91no—
211C22×C4—91no—
212C22×C4—91no—
213C2×C8—21no—
214C2×C8—21no—
215C2×C8—181no—
216C2×C8—181no—
217C2×C8—362no—
218C4⋊C4—21no—
219C4⋊C4—91no—
220C4⋊C4—181no—
221C4⋊C4—181no—
222C4⋊C4—181no—
223C4⋊C4—181no—
224C4⋊C4—181no—
225C4⋊C4—181no—
226C4⋊C4C4×D911yescharacteristic
227C22⋊C4—181no—
228C22⋊C4—181no—
229C42—21no—
230C42—91no—
231C42—91no—
232C42—91no—
233C42—181no—
234C42C22×D911yescharacteristic
235C22×C3D3×C22⋊C411yescharacteristic
236C2×D3—32no—
237C2×D3—61no—
238C2×D3—61no—
239C3×C4—21no—
240C3×C4—41no—
241C3×C4—41no—
242C3×C4#90111yescharacteristic
243C3×C4#90711yescharacteristic
244C3×C4D3×SD1611yescharacteristic
245C3×C4D3×Q1611yescharacteristic
246Dic3—32no—
247Dic3—61no—
248Dic3—61no—
249Dic3—121no—
250Dic3—121no—
251C9#148111yescharacteristic, complemented, Sylow
252C23—91no—
253Q8—21no—
254Q8—21no—
255Q8—181no—
256Q8—181no—
257Q8—362no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—91no—
261C2×C4—92no—
262C2×C4—92no—
263C2×C4—91no—
264C2×C4—91no—
265C2×C4—181no—
266C2×C4—181no—
267C2×C4—181no—
268C2×C4—181no—
269C2×C4—361no—
270C2×C4C2×C4×D911yescharacteristic
271C2×C4D4×D911yescharacteristic
272C2×C4D4×D911yescharacteristic
273C8—41no—
274C8—41no—
275C8—361no—
276C8—361no—
277C2×C3#472711yescharacteristic
278C2×C3D3×#10311yescharacteristic
279C2×C3#482111yescharacteristic
280D3—62no—
281C22—92no—
282C22—181no—
283C22—181no—
284C22C22⋊C4×D911yescharacteristic
285C4—21no—
286C4—41no—
287C4—41no—
288C4—92no—
289C4—181no—
290C4—181no—
291C4—361no—
292C4—361no—
293C4#6346411yescharacteristic
294C4#6346911yescharacteristic
295C4SD16×D911yescharacteristic
296C4Q16×D911yescharacteristic
297C3#6823211yescharacteristic
298C2—182no—
299C2#1058840911yescharacteristic
300C2D9×#10311yescharacteristic
301C2#1058850111yescharacteristic
subgroupG/H
centerC2×C4D4×D9
commutatorC2×C4×C9C22×C4
FrattiniC3×C42C22×D3
FittingC9×Q8⋊C8C2
socleC22×C3D3×C22⋊C4
prime radicalC22×D9C22⋊C4
cosocleC42×C9C23
hypercenterQ8⋊C8D9
hypocenterC9#1481
LCSG ▷ C2×C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C2×C4 ◁ C42 ◁ Q8⋊C8

Complements

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

NH ≅ G/Ntype
4. C9×Q8⋊C8C2semidirect
5. #10588212C2semidirect
6. #10588160C2semidirect
7. #10588133C2semidirect
114. Q8⋊C8D9semidirect
251. C9#1481semidirect

Maximal subgroups

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

subgroupindex
#105896802
D9×C4⋊C82
#105883672
C9×Q8⋊C82
#105882122
#105881602
#105881332
#682323