Finite Group Databasebeta

← #11796853

Subgroups — #11796853

Order 1152.

490 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 490 conjugacy classes of subgroups — too many to draw. Only its 62 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
1C3⋊D3×#135C211yesmaximal, characteristic
2#10593768C211yesmaximal, characteristic, complemented
3C2×#63765C211yesmaximal, characteristic, complemented
4#10590196C212yesmaximal, complemented
5#10590192C212yesmaximal, complemented
6#41×C3⋊D3—21no—
7#64286—21no—
8C32×#135C411yescharacteristic, complemented
9#64159—21no—
10#64128C2211yescharacteristic
11Q16×C3⋊D3C411yescharacteristic, complemented
12#64125—21no—
13SD16×C3⋊D3—21no—
14#64121C2211yescharacteristic
15D8×C3⋊D3C411yescharacteristic, complemented
16#64113C411yescharacteristic, complemented
17C2×C8×C3⋊D3C2211yescharacteristic
18C2×#3708—21no—
19#63769—21no—
20#63768C2212yescomplemented
21#63765—21no—
22#63765C2212yescomplemented
23D3×#135—62no—
24C32×#41—21no—
25#3832—21no—
26Q8×C3⋊D3—21no—
27#3830—21no—
28#3830—41no—
29D4×C3⋊D3—21no—
30D4×C3⋊D3—41no—
31#3828—21no—
32#3828—41no—
33C2×C4×C3⋊D3—41no—
34C2×C4×C3⋊D3D411yescharacteristic
35C22⋊#157—41no—
36C4⋊#157—22no—
37C4×#157—41no—
38C32×Q16C2×C411yescharacteristic
39C32×SD16—21no—
40C32×D8C2×C411yescharacteristic
41C2×C32×C8C2×C411yescharacteristic
42#3756—21no—
43#3755—21no—
44#3754—21no—
45#3753—21no—
46C2×C3⋊(C3⋊C8)D411yescharacteristic
47#3746C2×C411yescharacteristic
48#3745C2×C411yescharacteristic
49#3744—21no—
50C8×C3⋊D3C2×C411yescharacteristic
51C8×C3⋊D3D411yescharacteristic
52C8×C3⋊D3D411yescharacteristic
53C8×C3⋊D3C2311yescharacteristic
54#3708—22no—
55#2145—91nomaximal, Sylow
56D3×#41—64no—
57C3×#135—22no—
58#950—64no—
59#919—62no—
60D3×Q16—62no—
61#916—64no—
62D3×SD16—64no—
63#912—62no—
64D3×D8—62no—
65#904—62no—
66C2×D3×C8—62no—
67C22×C3⋊D3—41no—
68C22×C3⋊D3D811yescharacteristic
69C2×#157—42no—
70C32×Q8—21no—
71C32×D4—21no—
72C32×D4—41no—
73C2×C32×C4—41no—
74C2×C32×C4C22⋊C411yescharacteristic
75#638—41no—
76#638—41no—
77#638—41no—
78C2×C3⋊Dic3—41no—
79C2×C3⋊Dic3SD1611yescharacteristic
80C4⋊(C3⋊D3)—21no—
81C4⋊(C3⋊D3)—41no—
82C4×C3⋊D3—41no—
83C4×C3⋊D3—41no—
84C4×C3⋊D3—41no—
85C4×C3⋊D3C22⋊C411yescharacteristic
86C4×C3⋊D3D811yescharacteristic
87C4×C3⋊D3SD1611yescharacteristic
88C4×C3⋊D3C2×D411yescharacteristic
89#634—21no—
90#634—41no—
91C32×C8C22⋊C411yescharacteristic
92C32×C8C22×C411yescharacteristic
93C3⋊(C3⋊C8)C22⋊C411yescharacteristic
94C3⋊(C3⋊C8)C2×D411yescharacteristic
95C2×#135—91no—
96C2×M32—91no—
97#427—91no—
98#360—92no—
99#360—92no—
100C3×#41—24no—
101#239—64no—
102D3×Q8—64no—
103#237—64no—
104#237—124no—
105D3×D4—64no—
106D3×D4—124no—
107#235—64no—
108#235—124no—
109C2×C4×D3—62no—
110C2×C4×D3—124no—
111C3×Q16—22no—
112C3×SD16—24no—
113C3×D8—22no—
114C2×C3×C8—22no—
115#216—64no—
116#215—64no—
117#214—64no—
118#213—64no—
119C2×C3⋊C8—62no—
120Dic12—62no—
121D24—62no—
122#204—64no—
123D3×C8—62no—
124D3×C8—62no—
125D3×C8—62no—
126D3×C8—62no—
127C22×C32—41no—
128C22×C32#10211yescharacteristic
129C2×C3⋊D3—41no—
130C2×C3⋊D3—41no—
131C2×C3⋊D3—82no—
132C2×C3⋊D3#10211yescharacteristic
133C2×C3⋊D3C2×D811yescharacteristic
134#157—82no—
135C32×C4—41no—
136C32×C4#10211yescharacteristic
137C32×C4C2×C22⋊C411yescharacteristic
138C3⋊Dic3—41no—
139C3⋊Dic3#10211yescharacteristic
140C3⋊Dic3C2×SD1611yescharacteristic
141C2×#41—181no—
142#135—91no—
143#135—91no—
144#135—91no—
145#135—181no—
146#135—181no—
147#135#15711yescharacteristic, complemented
148C2×Q16—91no—
149C2×SD16—181no—
150C2×D8—91no—
151C22×C8—91no—
152#117—181no—
153M32—92no—
154M32—181no—
155C2×C16—181no—
156#107—181no—
157#106—92no—
158C22×D3—62no—
159C22×D3—124no—
160C3×Q8—24no—
161C3×D4—24no—
162C3×D4—44no—
163C2×C3×C4—22no—
164C2×C3×C4—44no—
165#67—124no—
166#67—124no—
167#67—124no—
168C2×Dic3—62no—
169C2×Dic3—124no—
170D12—64no—
171D12—124no—
172C4×D3—62no—
173C4×D3—62no—
174C4×D3—62no—
175C4×D3—62no—
176C4×D3—124no—
177C4×D3—124no—
178C4×D3—124no—
179Dic6—64no—
180Dic6—124no—
181C3×C8—22no—
182C3×C8—22no—
183C3⋊C8—62no—
184C3⋊C8—62no—
185C2×C32—21no—
186C2×C32—81no—
187C2×C32C2×#10211yescharacteristic
188C3⋊D3—21no—
189C3⋊D3—21no—
190C3⋊D3—81no—
191#41—21no—
192#41—181no—
193#41—181no—
194#41—181no—
195#41—361no—
196#41—361no—
197C2×Q8—181no—
198C2×D4—181no—
199C2×D4—361no—
200C22×C4—91no—
201C22×C4—361no—
202Q16—91no—
203Q16—181no—
204Q16C2×#15711yescharacteristic
205SD16—21no—
206SD16—181no—
207SD16—181no—
208SD16—181no—
209D8—91no—
210D8—181no—
211D8C2×#15711yescharacteristic
212C2×C8—91no—
213C2×C8—91no—
214C2×C8—91no—
215C2×C8—91no—
216C2×C8—91no—
217C2×C8C2×#15711yescharacteristic
218C4⋊C4—182no—
219C22⋊C4—361no—
220C42—361no—
221C16—182no—
222C22×C3—22no—
223C22×C3—44no—
224C2×D3—62no—
225C2×D3—62no—
226C2×D3—124no—
227C2×D3—124no—
228C2×D3—248no—
229C3×C4—22no—
230C3×C4—22no—
231C3×C4—44no—
232Dic3—62no—
233Dic3—62no—
234Dic3—124no—
235C32#214511yescharacteristic, complemented, Sylow
236C23—91no—
237C23—361no—
238Q8—21no—
239Q8—181no—
240Q8—361no—
241D4—21no—
242D4—41no—
243D4—181no—
244D4—361no—
245D4—361no—
246D4—361no—
247D4—361no—
248C2×C4—41no—
249C2×C4—91no—
250C2×C4—91no—
251C2×C4—91no—
252C2×C4—91no—
253C2×C4—91no—
254C2×C4—361no—
255C2×C4—361no—
256C2×C4—361no—
257C2×C4—361no—
258C2×C4—362no—
259C2×C4C22⋊#15711yescharacteristic
260C8—91no—
261C8—91no—
262C8C22⋊#15711yescharacteristic
263C8C22×#15711yescharacteristic
264C2×C3—22no—
265C2×C3—42no—
266C2×C3—84no—
267D3—64no—
268D3—122no—
269D3—244no—
270C22—41no—
271C22—91no—
272C22—91no—
273C22—361no—
274C22—361no—
275C22—722no—
276C22#6378211yescharacteristic
277C4—41no—
278C4—91no—
279C4—91no—
280C4—361no—
281C4—722no—
282C4#6378211yescharacteristic
283C4C2×C22⋊#15711yescharacteristic
284C3—22no—
285C2—21no—
286C2—81no—
287C2—181no—
288C2—181no—
289C2—721no—
290C2C2×#6378211yescharacteristic
subgroupG/H
centerC4#63782
commutatorC32×C8C22×C4
FrattiniC8C22×#157
FittingC32×#135C4
socleC2×C32C2×#102
prime radicalC3⋊D3×#135C2
cosocleC8×C3⋊D3C23
hypercenter#135#157
hypocenterC32#2145
LCSG ▷ C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×C8 ◁ #135

Complements

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

NH ≅ G/Ntype
2. #10593768C2semidirect
3. C2×#63765C2semidirect
4. #10590196C2semidirect
5. #10590192C2semidirect
8. C32×#135C4semidirect
11. Q16×C3⋊D3C4semidirect
15. D8×C3⋊D3C4semidirect
16. #64113C4semidirect
20. #63768C22semidirect
22. #63765C22semidirect
147. #135#157semidirect
235. C32#2145semidirect

Maximal subgroups

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

subgroupindex
C3⋊D3×#1352
#105937682
C2×#637652
#105901962
#105901922
#21459