Finite Group Databasebeta

← #11796868

Subgroups — #11796868

Order 1152.

402 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 59 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
1C2×#63809C211yesmaximal, characteristic
2#10593768C211yesmaximal, characteristic, complemented
3#10590625C211yesmaximal, characteristic, complemented
4#10590019C214yesmaximal, complemented
5C2×#3796—21no—
6#64286—21no—
7C2×C8×C3⋊D3C2211yescharacteristic
8C2×C3×#204—21no—
9C2×#3718C411yescharacteristic, complemented
10C2×#3713C411yescharacteristic, complemented
11#63809—21no—
12#63809—21no—
13#63809C412yescomplemented
14#63809C2212yes—
15#63769—21no—
16#63768C2212yescomplemented
17C3×#812—21no—
18#63544C2212yescomplemented
19#63542—21no—
20C2×#916—61no—
21D3×M32—61no—
22C2×C4×C3⋊D3D411yescharacteristic
23C2×C3×D12—21no—
24C2×C3×Dic6—21no—
25C2×#626—41no—
26C2×D3×Dic3—41no—
27#3796—22no—
28#3796—22no—
29#3796—41no—
30#3796—41no—
31C22⋊#157—41no—
32C4⋊#157—22no—
33C4×#157—41no—
34C2×C32×C8D411yescharacteristic
35C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
36C8×C3⋊D3C2×C411yescharacteristic
37C8×C3⋊D3D411yescharacteristic
38C8×C3⋊D3D411yescharacteristic
39C8×C3⋊D3C2311yescharacteristic
40C3×#204—22no—
41C3×#204—22no—
42#3718—21no—
43#3718C2×C412yes—
44#3713—21no—
45#3713C2×C412yes—
46C3×C3⋊C16—22no—
47#2145—91nomaximal, Sylow
48C2×#239—61no—
49C2×#237—61no—
50C2×C3×SD16—61no—
51C2×#216—61no—
52C2×#213—61no—
53#916—62no—
54#916—62no—
55#916—62no—
56#916—62no—
57C2×#204—21no—
58C2×D3×C8—61no—
59C2×D3×C8—61no—
60C3×M32—61no—
61#812—21no—
62#798—62no—
63D3×C16—62no—
64C22×C3⋊D3D811yescharacteristic
65C22×C3×D3—41no—
66C2×#157—42no—
67C2×C32×C4C22⋊C411yescharacteristic
68C2×C3⋊Dic3SD1611yescharacteristic
69C4×C3⋊D3C22⋊C411yescharacteristic
70C4×C3⋊D3D811yescharacteristic
71C4×C3⋊D3SD1611yescharacteristic
72C4×C3⋊D3C2×D411yescharacteristic
73C2×C3×Dic3—41no—
74C3×D12—22no—
75C3×D12—41no—
76C3×Dic6—22no—
77C3×Dic6—41no—
78#626—42no—
79#626—42no—
80D3×Dic3—42no—
81D3×Dic3—42no—
82C32×C8C22⋊C411yescharacteristic
83C32×C8C2×D411yescharacteristic
84C3⋊(C3⋊C8)C22⋊C411yescharacteristic
85C3⋊(C3⋊C8)C22×C411yescharacteristic
86C2×#135—91no—
87C2×M32—91no—
88#427—91no—
89#360—94no—
90C2×C3×Q8—61no—
91C2×C3×D4—61no—
92C2×#67—121no—
93C22×Dic3—121no—
94#239—62no—
95#239—62no—
96#239—121no—
97#239—121no—
98#237—62no—
99#237—62no—
100#237—121no—
101#237—121no—
102C2×D12—21no—
103C2×D12—121no—
104C2×C4×D3—61no—
105C2×C4×D3—61no—
106C2×C4×D3—121no—
107C2×Dic6—21no—
108C3×SD16—62no—
109C3×SD16—62no—
110C2×C3×C8—21no—
111C2×C3×C8—21no—
112#216—62no—
113#216—62no—
114#213—62no—
115#213—62no—
116C2×C3⋊C8—61no—
117C2×C3⋊C8—61no—
118#204—22no—
119#204—22no—
120D3×C8—61no—
121D3×C8—61no—
122D3×C8—61no—
123D3×C8—61no—
124D3×C8—61no—
125D3×C8—61no—
126D3×C8—61no—
127D3×C8—61no—
128C3×C16—62no—
129C3⋊C16—22no—
130C22×C32#10211yescharacteristic
131C2×C3⋊D3—41no—
132C2×C3⋊D3#10211yescharacteristic
133C2×C3⋊D3C2×D811yescharacteristic
134C2×C3×D3—42no—
135C2×C3×D3—82no—
136#157—82no—
137C32×C4#10211yescharacteristic
138C32×C4C2×C22⋊C411yescharacteristic
139C3⋊Dic3#10211yescharacteristic
140C3⋊Dic3C2×SD1611yescharacteristic
141C3×Dic3—42no—
142C2×#41—181no—
143#135—92no—
144#135—92no—
145#135—181no—
146#135—181no—
147C2×Q16—91no—
148C2×SD16—61no—
149C2×D8—91no—
150C22×C8—91no—
151#117—181no—
152M32—61no—
153M32—92no—
154C2×C16—181no—
155#107—181no—
156#106—92no—
157C23×C3—121no—
158C22×D3—41no—
159C22×D3—61no—
160C22×D3—61no—
161C3×Q8—62no—
162C3×Q8—121no—
163C3×D4—62no—
164C3×D4—121no—
165C2×C3×C4—21no—
166C2×C3×C4—21no—
167C2×C3×C4—121no—
168#67—122no—
169#67—122no—
170C2×Dic3—41no—
171C2×Dic3—61no—
172C2×Dic3—61no—
173C2×Dic3—122no—
174C2×Dic3—122no—
175D12—22no—
176D12—41no—
177D12—122no—
178D12—122no—
179C4×D3—61no—
180C4×D3—61no—
181C4×D3—61no—
182C4×D3—61no—
183C4×D3—61no—
184C4×D3—61no—
185C4×D3—61no—
186C4×D3—61no—
187C4×D3—122no—
188C4×D3—122no—
189Dic6—22no—
190Dic6—41no—
191C3×C8—21no—
192C3×C8—21no—
193C3×C8—21no—
194C3×C8—21no—
195C3⋊C8—61no—
196C3⋊C8—61no—
197C3⋊C8—61no—
198C3⋊C8—61no—
199C2×C32—21no—
200C2×C32C2×#10211yescharacteristic
201C3⋊D3—21no—
202C3⋊D3—21no—
203C3×D3—82no—
204#41—182no—
205#41—182no—
206#41—361no—
207#41—361no—
208C2×Q8—61no—
209C2×D4—61no—
210C2×D4—361no—
211C22×C4—91no—
212C22×C4—361no—
213Q16—92no—
214Q16—181no—
215SD16—62no—
216SD16—62no—
217D8—92no—
218D8—181no—
219C2×C8—91no—
220C2×C8—91no—
221C2×C8—91no—
222C2×C8—91no—
223C2×C8—91no—
224C2×C8GO+(4,𝔽2)11yescharacteristic
225C4⋊C4—182no—
226C22⋊C4—361no—
227C42—361no—
228C16—62no—
229C22×C3—21no—
230C22×C3—21no—
231C22×C3—122no—
232C22×C3—242no—
233C2×D3—42no—
234C2×D3—61no—
235C2×D3—61no—
236C2×D3—61no—
237C2×D3—61no—
238C2×D3—82no—
239C2×D3—122no—
240C2×D3—122no—
241C3×C4—21no—
242C3×C4—21no—
243C3×C4—21no—
244C3×C4—21no—
245C3×C4—122no—
246Dic3—42no—
247Dic3—61no—
248Dic3—61no—
249Dic3—61no—
250Dic3—61no—
251C32#214511yescharacteristic, complemented, Sylow
252C23—91no—
253C23—121no—
254Q8—62no—
255Q8—121no—
256D4—62no—
257D4—121no—
258D4—362no—
259D4—362no—
260C2×C4—91no—
261C2×C4—91no—
262C2×C4—91no—
263C2×C4—91no—
264C2×C4—91no—
265C2×C4—121no—
266C2×C4—362no—
267C2×C4—362no—
268C2×C4—362no—
269C2×C4D32⋊C411yescharacteristic
270C8—91no—
271C8—91no—
272C8D32⋊C411yescharacteristic
273C8C2×GO+(4,𝔽2)11yescharacteristic
274C2×C3—22no—
275C2×C3—21no—
276C2×C3—21no—
277C2×C3—41no—
278C2×C3—242no—
279D3—62no—
280D3—82no—
281D3—121no—
282D3—121no—
283D3—121no—
284C22—91no—
285C22—91no—
286C22—122no—
287C22—242no—
288C22—361no—
289C22#6372911yescharacteristic
290C4—91no—
291C4—91no—
292C4—122no—
293C4—722no—
294C4#6372911yescharacteristic
295C4C2×D32⋊C411yescharacteristic
296C3—21no—
297C3—21no—
298C2—21no—
299C2—181no—
300C2—181no—
301C2—242no—
302C2C2×#6372911yescharacteristic
subgroupG/H
centerC2C2×#63729
commutatorC3⋊(C3⋊C8)C22×C4
FrattiniC8C2×GO+(4,𝔽2)
FittingC2×C32×C8D4
socleC2×C32C2×#102
prime radicalC2×#63809C2
cosocleC8×C3⋊D3C23
hypercenterC2×C8GO+(4,𝔽2)
hypocenterC32#2145
LCSG ▷ C3⋊(C3⋊C8) ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8

Complements

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

NH ≅ G/Ntype
2. #10593768C2semidirect
3. #10590625C2semidirect
4. #10590019C2semidirect
9. C2×#3718C4semidirect
10. C2×#3713C4semidirect
13. #63809C4semidirect
16. #63768C22semidirect
18. #63544C22semidirect
251. C32#2145semidirect

Maximal subgroups

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

subgroupindex
C2×#638092
#105937682
#105906252
#105900192
#21459