Finite Group Databasebeta

← #11774755

Subgroups — #11774755

Order 1152.

348 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 348 conjugacy classes of subgroups — too many to draw. Only its 94 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
2#10588521C211yesmaximal, characteristic
3C4×C8×D9C211yesmaximal, characteristic
4C9×Q8⋊C8C211yesmaximal, characteristic, complemented
5#10588212C211yesmaximal, characteristic, complemented
6#10588160C211yesmaximal, characteristic, complemented
7#10588133C211yesmaximal, characteristic, complemented
8#68240—31nomaximal
9C4×Q8×C9C2211yescharacteristic
10#63508C411yescharacteristic
11#63506C411yescharacteristic
12C2×#3663—21no—
13C2×C8×D9—21no—
14#63459C411yescharacteristic
15#63458—21no—
16#63451—21no—
17#63450C411yescharacteristic
18#63434—21no—
19C42×D9C2211yescharacteristic
20C4×Dic18—21no—
21C4×Dic18C2211yescharacteristic
22C9×C4⋊C8C2211yescharacteristic
23C4×C8×C9C2211yescharacteristic
24Dic9⋊C8—21no—
25C8×Dic9—21no—
26C4⋊(C9⋊C8)C2211yescharacteristic
27C4×C9⋊C8C2211yescharacteristic
28#5578—31no—
29#4837—31no—
30C4×D3×C8—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—
62#3663—42no—
63C8×D9—24no—
64#1493—91noSylow
65C3×C4×Q8C2×D311yescharacteristic
66#946—31no—
67#944—31no—
68C2×ΓL(1,𝔽25)—61no—
69C2×D3×C8—61no—
70#897—31no—
71#896—61no—
72#889—61no—
73#888—31no—
74#872—61no—
75C42×D3—31no—
76C4×Dic6—31no—
77C4×Dic6—61no—
78C3×C4⋊C8C2×D311yescharacteristic
79C3×C4×C8C2×D311yescharacteristic
80Dic3⋊C8—61no—
81C8×Dic3—61no—
82C4⋊(C3⋊C8)—31no—
83C4×C3⋊C8—31no—
84C22×D9C22⋊C411yescharacteristic
85Q8×C9—21no—
86Q8×C9—21no—
87C2×C4×C9—21no—
88C2×C4×C9—21no—
89C2×C4×C9C22×C411yescharacteristic
90C2×C4×C9C2×D411yescharacteristic
91C2×C4×C9C2×D411yescharacteristic
92C2×Dic9—21no—
93C2×Dic9—21no—
94C2×Dic9C22⋊C411yescharacteristic
95C2×Dic9C22⋊C411yescharacteristic
96C2×Dic9C22⋊C411yescharacteristic
97C4×D9—21no—
98C4×D9—21no—
99C4×D9—22no—
100C4×D9SD1612yes—
101C4×D9Q1612yes—
102Dic18—21no—
103Dic18—21no—
104Dic18—42no—
105C8×C9—22no—
106C8×C9—41no—
107C9⋊C8—22no—
108C9⋊C8—41no—
109#533—91no—
110#423—91no—
111C2×C4×C8—91no—
112Q8⋊C8—91no—
113Q8⋊C8—91no—
114Q8⋊C8—91no—
115Q8⋊C8D911yescharacteristic, complemented
116C2×C3×Q8C4×D311yescharacteristic
117C2×C4×D3—31no—
118C2×C4×D3—31no—
119C2×C4×D3—31no—
120C2×Dic6—31no—
121C2×Dic6—61no—
122C2×C3×C8—21no—
123C2×C3×C8—21no—
124C3×C4⋊C4—21no—
125C3×C4⋊C4C4×D311yescharacteristic
126C3×C42—21no—
127C3×C42C22×D311yescharacteristic
128(C2×D3)⋊C4—61no—
129(C2×D3)⋊C4—61no—
130C4⋊Dic3—31no—
131C4⋊Dic3—61no—
132Dic3⋊C4—61no—
133Dic3⋊C4—61no—
134Dic3⋊C4—61no—
135Dic3⋊C4—61no—
136Dic3⋊C4—61no—
137C4×Dic3—31no—
138C4×Dic3—31no—
139C4×Dic3—31no—
140C4×Dic3—61no—
141C2×C3⋊C8—61no—
142C2×C3⋊C8—61no—
143ΓL(1,𝔽25)—122no—
144D3×C8—64no—
145C22×C9C2×C22⋊C411yescharacteristic
146C2×D9—21no—
147C2×D9—21no—
148C2×D9#10312yes—
149C4×C9—21no—
150C4×C9—41no—
151C4×C9—41no—
152C4×C9#13111yescharacteristic
153C4×C9#13111yescharacteristic
154C4×C9C2×SD1611yescharacteristic
155C4×C9C2×Q1611yescharacteristic
156Dic9—21no—
157Dic9—41no—
158Dic9—41no—
159Dic9#10312yes—
160Dic9#10412yes—
161C2×M16—181no—
162C22×C8—181no—
163C4⋊Q8—91no—
164C4⋊Q8—91no—
165#125—181no—
166C22⋊Q8—91no—
167C22⋊Q8—91no—
168C22⋊Q8—181no—
169C4×Q8—91no—
170C4×Q8—181no—
171C4×Q8C2×D911yescharacteristic
172#117—181no—
173C2×C42—91no—
174C4⋊C8—91no—
175C4⋊C8—181no—
176C4⋊C8C2×D911yescharacteristic
177C4×C8—91no—
178C4×C8—181no—
179C4×C8C2×D911yescharacteristic
180C22×D3—31no—
181C3×Q8—21no—
182C3×Q8—21no—
183C2×C3×C4—21no—
184C2×C3×C4—21no—
185C2×C3×C4C2×C4×D311yescharacteristic
186C2×C3×C4D3×D411yescharacteristic
187C2×C3×C4D3×D411yescharacteristic
188C2×Dic3—31no—
189C2×Dic3—31no—
190C2×Dic3—31no—
191C2×Dic3—61no—
192C2×Dic3—61no—
193C4×D3—32no—
194C4×D3—32no—
195C4×D3—62no—
196C4×D3—61no—
197C4×D3—61no—
198Dic6—61no—
199Dic6—61no—
200Dic6—122no—
201C3×C8—22no—
202C3×C8—41no—
203C3⋊C8—62no—
204C3⋊C8—121no—
205C2×C9#40811yescharacteristic
206C2×C9C2×#10311yescharacteristic
207C2×C9C2×#10411yescharacteristic
208D9—22no—
209C2×Q8—91no—
210C2×Q8—181no—
211C2×Q8C4×D911yescharacteristic
212C22×C4—91no—
213C22×C4—91no—
214C22×C4—91no—
215M16—362no—
216C2×C8—21no—
217C2×C8—21no—
218C2×C8—184no—
219C2×C8—181no—
220C2×C8—181no—
221C4⋊C4—21no—
222C4⋊C4—91no—
223C4⋊C4—181no—
224C4⋊C4—181no—
225C4⋊C4—181no—
226C4⋊C4—181no—
227C4⋊C4—181no—
228C4⋊C4—181no—
229C4⋊C4C4×D911yescharacteristic
230C22⋊C4—181no—
231C22⋊C4—181no—
232C42—21no—
233C42—91no—
234C42—91no—
235C42—91no—
236C42—181no—
237C42C22×D911yescharacteristic
238C22×C3D3×C22⋊C411yescharacteristic
239C2×D3—32no—
240C2×D3—61no—
241C2×D3—61no—
242C3×C4—21no—
243C3×C4—41no—
244C3×C4—41no—
245C3×C4#90111yescharacteristic
246C3×C4#90711yescharacteristic
247C3×C4D3×SD1611yescharacteristic
248C3×C4D3×Q1611yescharacteristic
249Dic3—32no—
250Dic3—32no—
251Dic3—61no—
252Dic3—121no—
253Dic3—121no—
254C9#149311yescharacteristic, complemented, Sylow
255C23—91no—
256Q8—21no—
257Q8—21no—
258Q8—181no—
259Q8—181no—
260Q8—362no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—91no—
264C2×C4—91no—
265C2×C4—92no—
266C2×C4—92no—
267C2×C4—91no—
268C2×C4—182no—
269C2×C4—181no—
270C2×C4—181no—
271C2×C4—181no—
272C2×C4—181no—
273C2×C4C2×C4×D911yescharacteristic
274C2×C4D4×D911yescharacteristic
275C2×C4D4×D911yescharacteristic
276C8—22no—
277C8—41no—
278C8—182no—
279C8—361no—
280C2×C3#472711yescharacteristic
281C2×C3D3×#10311yescharacteristic
282C2×C3D3×#10411yescharacteristic
283D3—62no—
284C22—92no—
285C22—181no—
286C22—181no—
287C22C22⋊C4×D911yescharacteristic
288C4—21no—
289C4—41no—
290C4—41no—
291C4—92no—
292C4—92no—
293C4—181no—
294C4—361no—
295C4—361no—
296C4#6346411yescharacteristic
297C4#6346911yescharacteristic
298C4SD16×D911yescharacteristic
299C4Q16×D911yescharacteristic
300C3#6824011yescharacteristic
301C2—182no—
302C2#1058840911yescharacteristic
303C2D9×#10311yescharacteristic
304C2D9×#10411yescharacteristic
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#1493
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
115. Q8⋊C8D9semidirect
254. C9#1493semidirect

Maximal subgroups

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

subgroupindex
#105896802
#105885212
C4×C8×D92
C9×Q8⋊C82
#105882122
#105881602
#105881332
#682403