Finite Group Databasebeta

← #11779854

Subgroups — #11779854

Order 1152.

375 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 375 conjugacy classes of subgroups — too many to draw. Only its 74 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#10589820C211yesmaximal, characteristic
2#10588750C211yesmaximal, characteristic, complemented
3#10588525C211yesmaximal, characteristic, complemented
4#10588515C211yesmaximal, characteristic, complemented
5C9×#331C211yesmaximal, characteristic, complemented
6#10588162C211yesmaximal, characteristic, complemented
7#10588160C211yesmaximal, characteristic, complemented
8#68393—31nomaximal
9C2×#3699—21no—
10C9×#127C2211yescharacteristic
11#63502—21no—
12#63501—22no—
13#63500—21no—
14D4×Dic9—21no—
15C2×#3664—21no—
16C4×D36C2211yescharacteristic
17#63431C2211yescharacteristic
18C4×Dic18C2211yescharacteristic
19C9×C4⋊C8C2211yescharacteristic
20C9×C4⋊C8C2211yescharacteristic
21#63392—22no—
22#63377—21no—
23#63376—21no—
24#63376—21no—
25C4×C9⋊C8C2211yescharacteristic
26#5718—31no—
27#5070—31no—
28#4851—31no—
29#4841—31no—
30C3×#331D311yescharacteristic
31#4484—31no—
32#4483—31no—
33C2×D4×C9—21no—
34C2×D4×C9—21no—
35C2×D4×C9D412yes—
36C2×#611—22no—
37C2×#611—22no—
38C22×Dic9—22no—
39#3699—42no—
40#3699—42no—
41C2×D36D411yescharacteristic
42C2×C4×D9—21no—
43C2×Dic18—21no—
44C2×Dic18D411yescharacteristic
45C2×C8×C9—21no—
46C2×C8×C9—21no—
47C42×C9C2311yescharacteristic
48#3676—22no—
49(C2×D9)⋊C4—21no—
50C4⋊Dic9—21no—
51C4⋊Dic9—21no—
52C4⋊Dic9D411yescharacteristic
53C4⋊Dic9D411yescharacteristic
54Dic9⋊C4—21no—
55C4×Dic9—21no—
56C2×C9⋊C8—21no—
57#3664—42no—
58#1642—91noSylow
59C2×#237—61no—
60C3×#127C2×D311yescharacteristic
61#940—61no—
62#939—62no—
63#938—61no—
64D4×Dic3—61no—
65C2×#204—61no—
66C4×D12—31no—
67#869—31no—
68C4×Dic6—31no—
69C3×C4⋊C8C2×D311yescharacteristic
70C3×C4⋊C8C2×D311yescharacteristic
71#832—62no—
72#817—61no—
73#816—61no—
74#816—61no—
75C4×C3⋊C8—31no—
76C23×C9—22no—
77C22×D9—21no—
78D4×C9—42no—
79D4×C9—41no—
80D4×C9—41no—
81D4×C9—41no—
82D4×C9—41no—
83C2×C4×C9C2×D411yescharacteristic
84C2×C4×C9C2×D411yescharacteristic
85C2×C4×C9C2×D411yescharacteristic
86#611—44no—
87#611—82no—
88C2×Dic9—21no—
89C2×Dic9—21no—
90C2×Dic9—21no—
91C2×Dic9—44no—
92C2×Dic9—41no—
93D36—21no—
94D36—21no—
95C4×D9—41no—
96C4×D9—41no—
97Dic18—21no—
98Dic18—41no—
99Dic18—41no—
100Dic18SD1612yescomplemented
101C8×C9—41no—
102C8×C9—41no—
103C9⋊C8—41no—
104#550—91no—
105#486—91no—
106#475—91no—
107#461—91no—
108#331D911yescharacteristic, complemented
109Q8⋊C8—91no—
110D4⋊C8—91no—
111C2×C3×D4—21no—
112C2×C3×D4—21no—
113C2×C3×D4D1212yes—
114C2×#67—62no—
115C2×#67—62no—
116C22×Dic3—62no—
117#237—122no—
118#237—122no—
119C2×D12—31no—
120C2×C4×D3—61no—
121C2×Dic6—31no—
122C2×Dic6—61no—
123C2×C3×C8—21no—
124C2×C3×C8—21no—
125C3×C42C22×D311yescharacteristic
126#217—62no—
127(C2×D3)⋊C4—61no—
128C4⋊Dic3—31no—
129C4⋊Dic3—31no—
130C4⋊Dic3—61no—
131C4⋊Dic3—61no—
132Dic3⋊C4—61no—
133C4×Dic3—61no—
134C2×C3⋊C8—61no—
135#204—122no—
136C22×C9—42no—
137C22×C9—42no—
138C22×C9—42no—
139C22×C9#12011yescharacteristic
140C2×D9—41no—
141C2×D9—41no—
142C2×D9—41no—
143C4×C9—21no—
144C4×C9C2×SD1611yescharacteristic
145C4×C9#13511yescharacteristic
146C4×C9AGL(1,ℤ/8)11yescharacteristic
147C4×C9AGL(1,ℤ/8)11yescharacteristic
148Dic9—22no—
149Dic9—41no—
150Dic9—41no—
151Dic9—81no—
152C2×#41—181no—
153C2×SD16—181no—
154C4⋊Q8—91no—
155#127—181no—
156#127C2×D911yescharacteristic
157#121—181no—
158#121—182no—
159C4×Q8—91no—
160C4×D4—91no—
161C4×D4—181no—
162#106—181no—
163C4⋊C8C2×D911yescharacteristic
164C4⋊C8C2×D911yescharacteristic
165#103—181no—
166#103—181no—
167#102—182no—
168C4×C8—91no—
169C23×C3—22no—
170C22×D3—61no—
171C3×D4—42no—
172C3×D4—41no—
173C3×D4—41no—
174C3×D4—41no—
175C3×D4—41no—
176C2×C3×C4C2×D1211yescharacteristic
177C2×C3×C4D3×D411yescharacteristic
178C2×C3×C4D3×D411yescharacteristic
179#67—124no—
180#67—242no—
181C2×Dic3—61no—
182C2×Dic3—61no—
183C2×Dic3—61no—
184C2×Dic3—124no—
185C2×Dic3—121no—
186D12—61no—
187D12—61no—
188C4×D3—121no—
189C4×D3—121no—
190Dic6—32no—
191Dic6—61no—
192Dic6—121no—
193Dic6—121no—
194C3×C8—41no—
195C3×C8—41no—
196C3⋊C8—121no—
197C2×C9—82no—
198C2×C9#44911yescharacteristic
199C2×C9#45011yescharacteristic
200C2×C9#45511yescharacteristic
201D9—81no—
202#41—362no—
203#41—362no—
204C2×Q8—91no—
205C2×Q8—181no—
206C2×D4—21no—
207C2×D4—21no—
208C2×D4—91no—
209C2×D4—182no—
210C2×D4—182no—
211C2×D4D3612yes—
212C22×C4—182no—
213C22×C4—181no—
214SD16—362no—
215C2×C8—21no—
216C2×C8—21no—
217C2×C8—181no—
218C4⋊C4—91no—
219C4⋊C4—91no—
220C4⋊C4—181no—
221C4⋊C4—181no—
222C4⋊C4—181no—
223C22⋊C4—182no—
224C22⋊C4—181no—
225C42—181no—
226C42C22×D911yescharacteristic
227C22×C3—42no—
228C22×C3—42no—
229C22×C3—42no—
230C22×C3#88211yescharacteristic
231C2×D3—121no—
232C2×D3—121no—
233C2×D3—121no—
234C3×C4—21no—
235C3×C4#91111yescharacteristic
236C3×C4#91111yescharacteristic
237C3×C4D3×SD1611yescharacteristic
238C3×C4#91611yescharacteristic
239Dic3—62no—
240Dic3—121no—
241Dic3—121no—
242Dic3—241no—
243C9#164211yescharacteristic, complemented, Sylow
244C23—22no—
245C23—181no—
246Q8—92no—
247Q8—181no—
248Q8—361no—
249Q8—361no—
250D4—42no—
251D4—41no—
252D4—41no—
253D4—41no—
254D4—41no—
255D4—181no—
256D4—181no—
257D4—364no—
258D4—722no—
259C2×C4—181no—
260C2×C4—181no—
261C2×C4—181no—
262C2×C4—364no—
263C2×C4—361no—
264C2×C4—361no—
265C2×C4—361no—
266C2×C4C2×D3611yescharacteristic
267C2×C4D4×D911yescharacteristic
268C2×C4D4×D911yescharacteristic
269C8—41no—
270C8—41no—
271C8—361no—
272C2×C3—82no—
273C2×C3#474611yescharacteristic
274C2×C3#477611yescharacteristic
275C2×C3#478111yescharacteristic
276D3—241no—
277C22—42no—
278C22—42no—
279C22—42no—
280C22—361no—
281C22—361no—
282C22—361no—
283C22#6344411yescharacteristic
284C4—21no—
285C4—182no—
286C4—361no—
287C4—361no—
288C4—721no—
289C4#6347311yescharacteristic
290C4#6347311yescharacteristic
291C4SD16×D911yescharacteristic
292C4#6347811yescharacteristic
293C3#6839311yescharacteristic
294C2—82no—
295C2—721no—
296C2#1058842611yescharacteristic
297C2#1058845611yescharacteristic
298C2#1058846111yescharacteristic
subgroupG/H
centerC22#63444
commutator, cosocleC42×C9C23
FrattiniC3×C42C22×D3
FittingC9×#331C2
socleC22×C3#882
prime radical#10589820C2
hypercenter#331D9
hypocenterC9#1642
LCSG ▷ C42×C9 ▷ C22×C9 ▷ C9
UCSC1 ◁ C22 ◁ C42 ◁ #331

Complements

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

NH ≅ G/Ntype
2. #10588750C2semidirect
3. #10588525C2semidirect
4. #10588515C2semidirect
5. C9×#331C2semidirect
6. #10588162C2semidirect
7. #10588160C2semidirect
100. Dic18SD16semidirect
108. #331D9semidirect
243. C9#1642semidirect

Maximal subgroups

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

subgroupindex
#105898202
#105887502
#105885252
#105885152
C9×#3312
#105881622
#105881602
#683933