Finite Group Databasebeta

← #11796866

Subgroups — #11796866

Order 1152.

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

normal subgroups only

This group has 414 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
1#10594684C211yesmaximal, characteristic
2#10593762C211yesmaximal, characteristic, complemented
3#10590714C211yesmaximal, characteristic, complemented
4#10590064C214yesmaximal, complemented
5#64306—21no—
6C2×C8×C3⋊D3C2211yescharacteristic
7C3×#904—21no—
8#63849—21no—
9#63822C2212yes—
10#63810—21no—
11#63809C412yescomplemented
12#63802C411yescharacteristic, complemented
13#63797C411yescharacteristic, complemented
14#63796—21no—
15#63773C2212yescomplemented
16#63765—21no—
17#63764—21no—
18C3×#818—21no—
19#63574C2212yescomplemented
20D3×#135—61no—
21#4880—61no—
22C2×C4×C3⋊D3D411yescharacteristic
23C3×#235—22no—
24#3811—41no—
25#3805—41no—
26#3802—21no—
27C4×D32—41no—
28#3798—41no—
29#3797—21no—
30#3796—22no—
31C2×C32×C8D411yescharacteristic
32C2×C3⋊(C3⋊C8)C2311yescharacteristic
33C8×C3⋊D3C2×C411yescharacteristic
34C8×C3⋊D3C2×C411yescharacteristic
35C8×C3⋊D3D411yescharacteristic
36C8×C3⋊D3D411yescharacteristic
37C3×C4⋊Dic3—22no—
38C3×Dic12—21no—
39C3×D24—21no—
40C3×#204—22no—
41#3722—41no—
42Dic32—41no—
43#3718C2×C412yes—
44#3715—22no—
45#3713C2×C412yes—
46#3708—22no—
47#2145—91nomaximal, Sylow
48D3×#41—62no—
49C3×#135—61no—
50#950—62no—
51#919—61no—
52D3×Q16—61no—
53#916—62no—
54D3×SD16—62no—
55#912—61no—
56D3×D8—61no—
57#904—21no—
58C2×D3×C8—61no—
59C2×D3×C8—61no—
60#892—62no—
61C3×#107—61no—
62#818—21no—
63#808—62no—
64C22×C3⋊D3D811yescharacteristic
65C2×D32—41no—
66C2×C32×C4C2×D411yescharacteristic
67C2×C3⋊Dic3D811yescharacteristic
68C4×C3⋊D3C22⋊C411yescharacteristic
69C4×C3⋊D3C22⋊C411yescharacteristic
70C4×C3⋊D3SD1611yescharacteristic
71C4×C3⋊D3SD1611yescharacteristic
72C3×#67—42no—
73C2×C3×Dic3—42no—
74C3×D12—22no—
75C3×C4×D3—42no—
76C3×Dic6—22no—
77#627—41no—
78#626—42no—
79#625—41no—
80#624—41no—
81D3×Dic3—42no—
82C32×C8C22⋊C411yescharacteristic
83C32×C8C22⋊C411yescharacteristic
84C3⋊(C3⋊C8)C22×C411yescharacteristic
85C3⋊(C3⋊C8)C2×D411yescharacteristic
86C2×#135—91no—
87C2×M32—91no—
88#427—91no—
89#360—94no—
90C3×#41—62no—
91#239—62no—
92D3×Q8—62no—
93#237—62no—
94#237—122no—
95D3×D4—62no—
96D3×D4—122no—
97#235—22no—
98#235—122no—
99C2×C4×D3—61no—
100C2×C4×D3—61no—
101C2×C4×D3—122no—
102C3×Q16—61no—
103C3×SD16—62no—
104C3×D8—61no—
105C2×C3×C8—21no—
106C2×C3×C8—21no—
107C3×C4⋊C4—62no—
108#216—62no—
109#215—62no—
110#214—62no—
111#213—62no—
112(C2×D3)⋊C4—122no—
113C4⋊Dic3—22no—
114C4×Dic3—122no—
115C2×C3⋊C8—61no—
116C2×C3⋊C8—61no—
117Dic12—21no—
118D24—21no—
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—
128C22×C32C2×D811yescharacteristic
129C2×C3⋊D3—41no—
130C2×C3⋊D3#10211yescharacteristic
131C2×C3⋊D3#10211yescharacteristic
132C2×C3×D3—42no—
133D32—82no—
134C32×C4C2×C22⋊C411yescharacteristic
135C32×C4C2×SD1611yescharacteristic
136C3⋊Dic3#10211yescharacteristic
137C3⋊Dic3#10211yescharacteristic
138C3×Dic3—42no—
139C3×Dic3—82no—
140C2×#41—181no—
141#135—61no—
142#135—92no—
143#135—92no—
144#135—181no—
145C2×Q16—91no—
146C2×SD16—181no—
147C2×D8—91no—
148C22×C8—91no—
149#117—181no—
150M32—92no—
151M32—181no—
152C2×C16—181no—
153#107—61no—
154#106—92no—
155C22×D3—61no—
156C22×D3—61no—
157C22×D3—122no—
158C3×Q8—62no—
159C3×D4—62no—
160C3×D4—122no—
161C2×C3×C4—21no—
162C2×C3×C4—21no—
163C2×C3×C4—122no—
164C2×C3×C4—122no—
165#67—42no—
166#67—122no—
167#67—122no—
168C2×Dic3—42no—
169C2×Dic3—61no—
170C2×Dic3—61no—
171C2×Dic3—122no—
172D12—22no—
173D12—122no—
174C4×D3—42no—
175C4×D3—61no—
176C4×D3—61no—
177C4×D3—61no—
178C4×D3—61no—
179C4×D3—61no—
180C4×D3—61no—
181C4×D3—61no—
182C4×D3—61no—
183C4×D3—122no—
184C4×D3—122no—
185Dic6—22no—
186Dic6—122no—
187C3×C8—21no—
188C3×C8—21no—
189C3×C8—21no—
190C3×C8—21no—
191C3⋊C8—61no—
192C3⋊C8—61no—
193C3⋊C8—61no—
194C3⋊C8—61no—
195C2×C32—21no—
196C2×C32C2×#10211yescharacteristic
197C3⋊D3—21no—
198C3⋊D3—21no—
199C3×D3—82no—
200#41—62no—
201#41—182no—
202#41—361no—
203#41—361no—
204C2×Q8—181no—
205C2×D4—181no—
206C2×D4—361no—
207C22×C4—91no—
208C22×C4—361no—
209Q16—61no—
210Q16—92no—
211SD16—62no—
212SD16—182no—
213D8—61no—
214D8—92no—
215C2×C8—91no—
216C2×C8—91no—
217C2×C8—91no—
218C2×C8—91no—
219C2×C8—91no—
220C2×C8GO+(4,𝔽2)11yescharacteristic
221C4⋊C4—62no—
222C22⋊C4—361no—
223C42—361no—
224C16—182no—
225C22×C3—21no—
226C22×C3—21no—
227C22×C3—122no—
228C2×D3—42no—
229C2×D3—61no—
230C2×D3—61no—
231C2×D3—61no—
232C2×D3—61no—
233C2×D3—122no—
234C2×D3—121no—
235C2×D3—121no—
236C2×D3—244no—
237C3×C4—21no—
238C3×C4—21no—
239C3×C4—21no—
240C3×C4—21no—
241C3×C4—122no—
242C3×C4—242no—
243Dic3—42no—
244Dic3—61no—
245Dic3—61no—
246Dic3—61no—
247Dic3—61no—
248Dic3—82no—
249C32#214511yescharacteristic, complemented, Sylow
250C23—91no—
251C23—361no—
252Q8—62no—
253Q8—361no—
254D4—62no—
255D4—122no—
256D4—361no—
257D4—362no—
258C2×C4—91no—
259C2×C4—91no—
260C2×C4—91no—
261C2×C4—91no—
262C2×C4—91no—
263C2×C4—122no—
264C2×C4—122no—
265C2×C4—362no—
266C2×C4—361no—
267C2×C4C2×GO+(4,𝔽2)11yescharacteristic
268C8—91no—
269C8—91no—
270C8D32⋊C411yescharacteristic
271C8D32⋊C411yescharacteristic
272C2×C3—21no—
273C2×C3—21no—
274C2×C3—21no—
275C2×C3—21no—
276C2×C3—41no—
277C2×C3—242no—
278D3—62no—
279D3—82no—
280D3—121no—
281D3—121no—
282D3—121no—
283C22—91no—
284C22—91no—
285C22—122no—
286C22—361no—
287C22—722no—
288C22#6422511yescharacteristic
289C4—91no—
290C4—91no—
291C4—122no—
292C4—242no—
293C4#6422711yescharacteristic
294C4C2×D32⋊C411yescharacteristic
295C3—21no—
296C3—21no—
297C2—21no—
298C2—181no—
299C2—181no—
300C2—242no—
301C2#1059336511yescharacteristic
subgroupG/H
centerC2#10593365
commutatorC3⋊(C3⋊C8)C22×C4
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC2×C32×C8D4
socleC2×C32C2×#102
prime radical#10594684C2
cosocleC2×C3⋊(C3⋊C8)C23
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. #10593762C2semidirect
3. #10590714C2semidirect
4. #10590064C2semidirect
11. #63809C4semidirect
12. #63802C4semidirect
13. #63797C4semidirect
15. #63773C22semidirect
19. #63574C22semidirect
249. C32#2145semidirect

Maximal subgroups

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

subgroupindex
#105946842
#105937622
#105907142
#105900642
#21459