Finite Group Databasebeta

← #11774826

Subgroups — #11774826

Order 1152.

324 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 84 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#10589682C211yesmaximal, characteristic
2#10588521C211yesmaximal, characteristic, complemented
3#10588367C211yesmaximal, characteristic, complemented
4C9×Q8⋊C8C211yesmaximal, characteristic, complemented
5#10588212C211yesmaximal, characteristic, complemented
6#10588162C211yesmaximal, characteristic, complemented
7#10588136C211yesmaximal, characteristic, complemented
8#68242—31nomaximal
9C4×Q8×C9C2211yescharacteristic
10#63509C411yescharacteristic
11#63508C411yescharacteristic
12C2×#3663—21no—
13#63460—21no—
14#63457C411yescharacteristic
15#63456—21no—
16#63452C411yescharacteristic
17C4×D36—21no—
18C4×D36C2211yescharacteristic
19#63434—21no—
20C42×D9C2211yescharacteristic
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#5580—31no—
29#4837—31no—
30#4685—31no—
31C3×Q8⋊C8D311yescharacteristic
32#4535—31no—
33#4483—31no—
34#4459—31no—
35C2×Q8×C9C2×C411yescharacteristic
36C2×D36—21no—
37C2×D36C2×C411yescharacteristic
38C2×C4×D9—21no—
39C2×C4×D9C2×C411yescharacteristic
40C2×C4×D9D411yescharacteristic
41C2×C4×D9D411yescharacteristic
42C2×C8×C9—21no—
43C2×C8×C9—21no—
44C9×C4⋊C4—21no—
45C9×C4⋊C4C2×C411yescharacteristic
46C42×C9—21no—
47C42×C9C2311yescharacteristic
48(C2×D9)⋊C4—21no—
49(C2×D9)⋊C4—21no—
50(C2×D9)⋊C4—21no—
51(C2×D9)⋊C4—21no—
52(C2×D9)⋊C4—21no—
53C4⋊Dic9—21no—
54C4⋊Dic9C2×C411yescharacteristic
55Dic9⋊C4—21no—
56Dic9⋊C4—21no—
57C4×Dic9C2×C411yescharacteristic
58C4×Dic9D411yescharacteristic
59C4×Dic9D411yescharacteristic
60C2×C9⋊C8—21no—
61C2×C9⋊C8—21no—
62#3663—42no—
63#1495—91noSylow
64C3×C4×Q8C2×D311yescharacteristic
65#947—31no—
66#946—31no—
67C2×ΓL(1,𝔽25)—61no—
68#898—61no—
69#895—31no—
70#894—61no—
71#890—31no—
72C4×D12—31no—
73C4×D12—61no—
74#872—61no—
75C42×D3—31no—
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×D9—21no—
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×Dic9C22⋊C411yescharacteristic
94C2×Dic9C22⋊C411yescharacteristic
95C2×Dic9C22⋊C411yescharacteristic
96D36—21no—
97D36—21no—
98D36—42no—
99C4×D9—21no—
100C4×D9—21no—
101C4×D9—21no—
102C4×D9—21no—
103C4×D9—41no—
104C4×D9—41no—
105C4×D9—41no—
106C8×C9—41no—
107C8×C9—41no—
108C9⋊C8—41no—
109C9⋊C8—41no—
110#529—91no—
111#431—91no—
112#423—91no—
113Q8⋊C8—91no—
114Q8⋊C8D911yescharacteristic, complemented
115D4⋊C8—91no—
116D4⋊C8—91no—
117C2×C3×Q8C4×D311yescharacteristic
118C2×D12—31no—
119C2×D12—61no—
120C2×C4×D3—31no—
121C2×C4×D3—31no—
122C2×C4×D3—31no—
123C2×C4×D3—61no—
124C2×C3×C8—21no—
125C2×C3×C8—21no—
126C3×C4⋊C4—21no—
127C3×C4⋊C4C4×D311yescharacteristic
128C3×C42—21no—
129C3×C42C22×D311yescharacteristic
130(C2×D3)⋊C4—61no—
131(C2×D3)⋊C4—61no—
132(C2×D3)⋊C4—61no—
133(C2×D3)⋊C4—61no—
134(C2×D3)⋊C4—61no—
135C4⋊Dic3—31no—
136C4⋊Dic3—61no—
137Dic3⋊C4—61no—
138Dic3⋊C4—61no—
139C4×Dic3—31no—
140C4×Dic3—31no—
141C4×Dic3—31no—
142C2×C3⋊C8—61no—
143C2×C3⋊C8—61no—
144ΓL(1,𝔽25)—122no—
145C22×C9C2×C22⋊C411yescharacteristic
146C2×D9—21no—
147C2×D9—21no—
148C2×D9—21no—
149C2×D9—41no—
150C2×D9—41no—
151C2×D9—41no—
152C4×C9—21no—
153C4×C9—41no—
154C4×C9—41no—
155C4×C9#13111yescharacteristic
156C4×C9#13111yescharacteristic
157C4×C9AGL(1,ℤ/8)11yescharacteristic
158C4×C9#13711yescharacteristic
159Dic9—21no—
160Dic9—21no—
161Dic9—21no—
162Dic9—41no—
163C2×M16—181no—
164#126—181no—
165#125—91no—
166#124—91no—
167#123—181no—
168C22⋊Q8—91no—
169#121—91no—
170C4×Q8C2×D911yescharacteristic
171C4×D4—91no—
172C4×D4—181no—
173#117—181no—
174C2×C42—91no—
175C4⋊C8—91no—
176C4⋊C8—181no—
177C4⋊C8—181no—
178C4⋊C8C2×D911yescharacteristic
179C22⋊C8—181no—
180C4×C8—91no—
181C4×C8C2×D911yescharacteristic
182C22×D3—31no—
183C22×D3—61no—
184C3×Q8—21no—
185C3×Q8—21no—
186C2×C3×C4—21no—
187C2×C3×C4—21no—
188C2×C3×C4C2×C4×D311yescharacteristic
189C2×C3×C4D3×D411yescharacteristic
190C2×C3×C4D3×D411yescharacteristic
191C2×Dic3—31no—
192C2×Dic3—31no—
193C2×Dic3—31no—
194C2×Dic3—61no—
195D12—61no—
196D12—61no—
197D12—122no—
198C4×D3—61no—
199C4×D3—61no—
200C4×D3—61no—
201C4×D3—61no—
202C4×D3—121no—
203C4×D3—121no—
204C4×D3—121no—
205C3×C8—41no—
206C3×C8—41no—
207C3⋊C8—121no—
208C3⋊C8—121no—
209C2×C9#40811yescharacteristic
210C2×C9#41711yescharacteristic
211C2×C9#42111yescharacteristic
212D9—41no—
213D9—81no—
214C2×Q8C4×D911yescharacteristic
215C2×D4—91no—
216C2×D4—181no—
217C22×C4—91no—
218C22×C4—91no—
219C22×C4—91no—
220C22×C4—181no—
221M16—362no—
222C2×C8—21no—
223C2×C8—21no—
224C2×C8—181no—
225C2×C8—181no—
226C4⋊C4—21no—
227C4⋊C4—91no—
228C4⋊C4—181no—
229C4⋊C4—181no—
230C4⋊C4—181no—
231C4⋊C4C4×D911yescharacteristic
232C22⋊C4—181no—
233C22⋊C4—181no—
234C22⋊C4—181no—
235C22⋊C4—181no—
236C22⋊C4—181no—
237C42—21no—
238C42—91no—
239C42—91no—
240C42—91no—
241C42C22×D911yescharacteristic
242C22×C3D3×C22⋊C411yescharacteristic
243C2×D3—61no—
244C2×D3—61no—
245C2×D3—61no—
246C2×D3—121no—
247C2×D3—121no—
248C2×D3—121no—
249C3×C4—21no—
250C3×C4—41no—
251C3×C4—41no—
252C3×C4#90111yescharacteristic
253C3×C4#90711yescharacteristic
254C3×C4#91411yescharacteristic
255C3×C4#91811yescharacteristic
256Dic3—61no—
257Dic3—61no—
258Dic3—61no—
259Dic3—121no—
260C9#149511yescharacteristic, complemented, Sylow
261C23—91no—
262C23—181no—
263Q8—21no—
264Q8—21no—
265D4—181no—
266D4—181no—
267D4—362no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—91no—
271C2×C4—91no—
272C2×C4—91no—
273C2×C4—181no—
274C2×C4—181no—
275C2×C4—181no—
276C2×C4—181no—
277C2×C4—181no—
278C2×C4—361no—
279C2×C4—361no—
280C2×C4—361no—
281C2×C4C2×C4×D911yescharacteristic
282C2×C4D4×D911yescharacteristic
283C2×C4D4×D911yescharacteristic
284C8—41no—
285C8—41no—
286C8—361no—
287C8—361no—
288C2×C3#472711yescharacteristic
289C2×C3#480311yescharacteristic
290C2×C3#482111yescharacteristic
291D3—121no—
292D3—241no—
293C22—181no—
294C22—181no—
295C22—181no—
296C22—361no—
297C22—361no—
298C22—361no—
299C22C22⋊C4×D911yescharacteristic
300C4—21no—
301C4—41no—
302C4—41no—
303C4—181no—
304C4—181no—
305C4—181no—
306C4—361no—
307C4#6346411yescharacteristic
308C4#6346911yescharacteristic
309C4#6347611yescharacteristic
310C4#6348011yescharacteristic
311C3#6824211yescharacteristic
312C2—361no—
313C2—721no—
314C2#1058840911yescharacteristic
315C2#1058848311yescharacteristic
316C2#1058850111yescharacteristic
subgroupG/H
centerC2×C4D4×D9
commutatorC2×C4×C9C22×C4
FrattiniC3×C42C22×D3
FittingC9×Q8⋊C8C2
socleC22×C3D3×C22⋊C4
prime radical#63457C4
cosocleC42×C9C23
hypercenterQ8⋊C8D9
hypocenterC9#1495
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
2. #10588521C2semidirect
3. #10588367C2semidirect
4. C9×Q8⋊C8C2semidirect
5. #10588212C2semidirect
6. #10588162C2semidirect
7. #10588136C2semidirect
114. Q8⋊C8D9semidirect
260. C9#1495semidirect

Maximal subgroups

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

subgroupindex
#105896822
#105885212
#105883672
C9×Q8⋊C82
#105882122
#105881622
#105881362
#682423