Finite Group Databasebeta

← #11859557

Subgroups — #11859557

Order 1152.

750 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 750 conjugacy classes of subgroups — too many to draw. Only its 149 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#10596511C211yesmaximal, characteristic
2#10594669C212yesmaximal, complemented
3C2×#63767C211yesmaximal, characteristic, complemented
4#10593328C211yesmaximal, characteristic, complemented
5#10593309C212yesmaximal, complemented
6#10593282C218yesmaximal, complemented
7#64306C2212yes—
8C2×C4×#157C2211yescharacteristic
9C2×#3787C2211yescharacteristic
10#64242C414yes—
11#64231C411yescharacteristic
12C4×GO+(4,𝔽2)C2214yes—
13#64222C411yescharacteristic
14#64221C412yes—
15C2×C8×C3⋊D3C2211yescharacteristic
16C3×#901—22no—
17#63818C2212yes—
18#63815—22no—
19#63805—22no—
20#63803—22no—
21#63791C2214yes—
22D32×C8C2214yes—
23#63767C2214yes—
24#63732C2214yes—
25D32⋊C8C2218yes—
26D3×#131—62no—
27C22×#157C2×C412yes—
28C2×GO+(4,𝔽2)C2×C414yes—
29C2×C4×C3⋊D3C2311yescharacteristic
30C3×#235—22no—
31#3811C2×C414yes—
32#3805—22no—
33#3802C2×C412yes—
34C4×D32C2314yes—
35#3798—22no—
36#3797C2×C412yes—
37#3796—22no—
38C2×#622—21no—
39C4×#157C2×C411yescharacteristic
40C4×#157C2×C411yescharacteristic
41C4×#157C2312yes—
42#3787—21no—
43#3787C2312yes—
44#3773C2×C414yes—
45D32⋊C4C2×C418yes—
46C2×C32×C8D411yescharacteristic, complemented
47C2×C3⋊(C3⋊C8)D411yescharacteristic, complemented
48C8×C3⋊D3D412yescomplemented
49C8×C3⋊D3C2312yes—
50C3×#208—22no—
51C3×ΓL(1,𝔽25)—24no—
52C3×D3×C8—24no—
53#3712—22no—
54#3711—24no—
55#3710C2314yes—
56D3×C3⋊C8—24no—
57#2932—91nomaximal, Sylow
58D3×#41—62no—
59C3×#131—62no—
60#948—62no—
61#907—64no—
62#907—62no—
63D3×M16—64no—
64D3×M16—62no—
65#901—22no—
66#901—64no—
67C2×D3×C8—64no—
68C2×D3×C8—62no—
69C22×C3⋊D3C22×C411yescharacteristic
70C2×D32C22×C414yes—
71C2×#157—42no—
72C2×#157C22×C412yes—
73C2×#157C22×C412yes—
74GO+(4,𝔽2)—44no—
75C2×C32×C4C2×D411yescharacteristic
76C2×C3⋊Dic3#4111yescharacteristic
77C4×C3⋊D3C22×C411yescharacteristic
78C4×C3⋊D3C2×D411yescharacteristic
79C4×C3⋊D3#4111yescharacteristic
80C4×C3⋊D3C2411yescharacteristic
81C3×#67—24no—
82C3×D12—22no—
83C3×C4×D3—24no—
84C3×Dic6—22no—
85#627—22no—
86#626—24no—
87#625—22no—
88#624C22×C414yes—
89D3×Dic3—24no—
90#622—22no—
91C32×C8C2×D412yes—
92C3⋊(C3⋊C8)C2×D412yes—
93C3×C3⋊C8—24no—
94C2×#131—92no—
95#532—91no—
96#435—98no—
97#423—91no—
98#408—92no—
99C2×#97—91no—
100C3×#41—62no—
101#239—62no—
102D3×Q8—62no—
103#237—62no—
104#237—64no—
105D3×D4—62no—
106D3×D4—64no—
107#235—22no—
108#235—64no—
109C2×C4×D3—64no—
110C2×C4×D3—62no—
111C3×M16—64no—
112C3×M16—62no—
113C2×C3×C8—22no—
114C2×C3×C8—64no—
115#208—22no—
116#208—64no—
117C2×C3⋊C8—62no—
118C2×C3⋊C8—64no—
119ΓL(1,𝔽25)—24no—
120ΓL(1,𝔽25)—64no—
121ΓL(1,𝔽25)—64no—
122D3×C8—24no—
123D3×C8—64no—
124D3×C8—62no—
125D3×C8—62no—
126D3×C8—62no—
127D3×C8—62no—
128D3×C8—64no—
129C22×C32C4×D411yescharacteristic
130C2×C3⋊D3—22no—
131C2×C3⋊D3C4×D411yescharacteristic
132C2×C3⋊D3C23×C411yescharacteristic
133C2×C3×D3—24no—
134D32—28no—
135#157—22no—
136#157—22no—
137C32×C4C4×D411yescharacteristic
138C32×C4C22×D411yescharacteristic
139C3⋊Dic3C4×D411yescharacteristic
140C3⋊Dic3C2×#4111yescharacteristic
141C3×Dic3—24no—
142C2×#41—92no—
143#131—62no—
144#131—182no—
145#131—182no—
146#131—182no—
147C2×M16—92no—
148C2×M16—94no—
149C22×C8—94no—
150C22×C8—91no—
151C22×C8—91no—
152C4⋊Q8—91no—
153#127—91no—
154#124—92no—
155#121—94no—
156C4×D4—94no—
157C2×C42—91no—
158C4⋊C8—94no—
159C22⋊C8—98no—
160#97—94no—
161C22×D3—64no—
162C22×D3—62no—
163C3×Q8—62no—
164C3×D4—62no—
165C3×D4—64no—
166C2×C3×C4—22no—
167C2×C3×C4—64no—
168#67—24no—
169#67—64no—
170#67—64no—
171C2×Dic3—62no—
172C2×Dic3—64no—
173D12—22no—
174D12—64no—
175C4×D3—24no—
176C4×D3—64no—
177C4×D3—62no—
178C4×D3—62no—
179C4×D3—62no—
180C4×D3—62no—
181C4×D3—64no—
182Dic6—22no—
183Dic6—64no—
184C3×C8—22no—
185C3×C8—22no—
186C3×C8—64no—
187C3⋊C8—24no—
188C3⋊C8—62no—
189C3⋊C8—62no—
190C2×C32—21no—
191C2×C32C2×C4×D411yescharacteristic
192C3⋊D3—21no—
193C3⋊D3#56812yes—
194C3×D3—44no—
195#41—62no—
196#41—182no—
197#41—182no—
198#41—182no—
199C2×Q8—92no—
200C2×D4—94no—
201C2×D4—92no—
202C2×D4—94no—
203C22×C4—94no—
204C22×C4—91no—
205C22×C4—92no—
206M16—62no—
207M16—64no—
208M16—182no—
209M16—184no—
210C2×C8—64no—
211C2×C8—94no—
212C2×C8—91no—
213C2×C8—92no—
214C2×C8—92no—
215C2×C8—92no—
216C2×C8—184no—
217C2×C8—181no—
218C2×C8—181no—
219C2×C8GO+(4,𝔽2)11yescharacteristic, complemented
220C4⋊C4—94no—
221C22⋊C4—98no—
222C42—92no—
223C42—91no—
224C42—91no—
225C22×C3—22no—
226C22×C3—64no—
227C2×D3—24no—
228C2×D3—62no—
229C2×D3—62no—
230C2×D3—128no—
231C2×D3—124no—
232C3×C4—22no—
233C3×C4—22no—
234C3×C4—64no—
235Dic3—24no—
236Dic3—62no—
237Dic3—62no—
238C32#293211yescharacteristic, complemented, Sylow
239C23—94no—
240C23—91no—
241Q8—62no—
242Q8—182no—
243D4—64no—
244D4—62no—
245D4—184no—
246D4—182no—
247D4—364no—
248C2×C4—64no—
249C2×C4—94no—
250C2×C4—91no—
251C2×C4—91no—
252C2×C4—91no—
253C2×C4—91no—
254C2×C4—91no—
255C2×C4—92no—
256C2×C4—92no—
257C2×C4—184no—
258C2×C4—362no—
259C2×C4C2×GO+(4,𝔽2)11yescharacteristic
260C8—64no—
261C8—92no—
262C8—182no—
263C8C2×GO+(4,𝔽2)12yes—
264C2×C3—22no—
265C2×C3—42no—
266C2×C3—124no—
267D3—44no—
268D3—64no—
269D3—122no—
270C22—64no—
271C22—91no—
272C22—91no—
273C22—182no—
274C22—188no—
275C22C4×GO+(4,𝔽2)11yescharacteristic
276C4—64no—
277C4—91no—
278C4—91no—
279C4—182no—
280C4—182no—
281C4C4×GO+(4,𝔽2)11yescharacteristic
282C4C22×GO+(4,𝔽2)11yescharacteristic
283C3—22no—
284C2—21no—
285C2—92no—
286C2—124no—
287C2—181no—
288C2C2×C4×GO+(4,𝔽2)11yescharacteristic
subgroupG/H
center, FrattiniC4C22×GO+(4,𝔽2)
commutatorC2×C3⋊D3C23×C4
FittingC2×C32×C8D4
socleC2×C32C2×C4×D4
prime radical#10596511C2
cosocleC4×C3⋊D3C24
hypercenterC2×C8GO+(4,𝔽2)
hypocenterC32#2932
LCSG ▷ C2×C3⋊D3 ▷ C32
UCSC1 ◁ C4 ◁ C2×C8

Complements

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

NH ≅ G/Ntype
2. #10594669C2semidirect
3. C2×#63767C2semidirect
4. #10593328C2semidirect
5. #10593309C2semidirect
6. #10593282C2semidirect
46. C2×C32×C8D4semidirect
47. C2×C3⋊(C3⋊C8)D4semidirect
48. C8×C3⋊D3D4semidirect
219. C2×C8GO+(4,𝔽2)semidirect
238. C32#2932semidirect

Maximal subgroups

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

subgroupindex
#105965112
#105946692
C2×#637672
#105933282
#105933092
#105932822
#29329