Finite Group Databasebeta

← #11859508

Subgroups — #11859508

Order 1152.

766 conjugacy classes of subgroups; only the 153 normal subgroups are shown.

normal subgroups only

This group has 766 conjugacy classes of subgroups — too many to draw. Only its 153 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×C8×#157C211yesmaximal, characteristic, complemented
4#10593328C211yesmaximal, characteristic, complemented
5#10593309C212yesmaximal, complemented
6#10593283C214yesmaximal, complemented
7C8×GO+(4,𝔽2)C214yesmaximal, complemented
8#64306C2212yes—
9C2×C4×#157C2211yescharacteristic
10C2×#3787C2211yescharacteristic
11#64242C414yes—
12#64231C411yescharacteristic
13C4×GO+(4,𝔽2)C2214yes—
14#64222C411yescharacteristic
15#64221C412yes—
16C2×C8×C3⋊D3C2211yescharacteristic
17C3×#901—22no—
18#63818C2212yes—
19#63815—22no—
20#63805—22no—
21#63803—22no—
22#63791C2214yes—
23D32×C8C2214yes—
24C8×#157C2212yes—
25C8×#157C2212yes—
26#63732C2214yes—
27D32⋊C8C2218yes—
28D3×#131—62no—
29C22×#157C2×C412yes—
30C2×GO+(4,𝔽2)C2×C414yes—
31C2×C4×C3⋊D3C2311yescharacteristic
32C3×#235—22no—
33#3811C2×C414yes—
34#3805—22no—
35#3802C2×C412yes—
36C4×D32C2314yes—
37#3798—22no—
38#3797C2×C412yes—
39#3796—22no—
40C2×#622—21no—
41C4×#157C2×C411yescharacteristic
42C4×#157C2×C411yescharacteristic
43C4×#157C2312yes—
44#3787—21no—
45#3787C2312yes—
46#3773C2×C414yes—
47D32⋊C4C2×C418yes—
48C2×C32×C8D411yescharacteristic, complemented
49C2×C3⋊(C3⋊C8)D411yescharacteristic, complemented
50C8×C3⋊D3D411yescharacteristic, complemented
51C8×C3⋊D3D411yescharacteristic, complemented
52C8×C3⋊D3C2311yescharacteristic
53C8×C3⋊D3C2311yescharacteristic
54C3×#208—22no—
55C3×ΓL(1,𝔽25)—24no—
56C3×D3×C8—24no—
57#3712—22no—
58#3711—24no—
59#3710C2314yes—
60D3×C3⋊C8—24no—
61#2931—91nomaximal, Sylow
62D3×#41—62no—
63C3×#131—62no—
64#948—62no—
65#907—64no—
66#907—62no—
67D3×M16—64no—
68D3×M16—62no—
69#901—22no—
70#901—64no—
71C2×D3×C8—64no—
72C2×D3×C8—62no—
73C22×C3⋊D3C22×C411yescharacteristic
74C2×D32C22×C414yes—
75C2×#157—24no—
76C2×#157C22×C412yes—
77C2×#157C22×C412yes—
78GO+(4,𝔽2)—28no—
79C2×C32×C4C2×D411yescharacteristic
80C2×C3⋊Dic3#4111yescharacteristic
81C4×C3⋊D3C22×C411yescharacteristic
82C4×C3⋊D3C2×D411yescharacteristic
83C4×C3⋊D3#4111yescharacteristic
84C4×C3⋊D3C2411yescharacteristic
85C3×#67—24no—
86C3×D12—22no—
87C3×C4×D3—24no—
88C3×Dic6—22no—
89#627—22no—
90#626—24no—
91#625—22no—
92#624C22×C414yes—
93D3×Dic3—24no—
94#622—22no—
95C32×C8C2×D411yescharacteristic
96C32×C8C2×D411yescharacteristic
97C3⋊(C3⋊C8)C2×D411yescharacteristic
98C3⋊(C3⋊C8)C2×D411yescharacteristic
99C3×C3⋊C8—24no—
100C2×#131—92no—
101#532—91no—
102#436—94no—
103C8×D4—94no—
104#423—91no—
105#408—92no—
106C2×C4×C8—91no—
107C3×#41—62no—
108#239—62no—
109D3×Q8—62no—
110#237—62no—
111#237—64no—
112D3×D4—62no—
113D3×D4—64no—
114#235—22no—
115#235—64no—
116C2×C4×D3—64no—
117C2×C4×D3—62no—
118C3×M16—64no—
119C3×M16—62no—
120C2×C3×C8—22no—
121C2×C3×C8—64no—
122#208—22no—
123#208—64no—
124C2×C3⋊C8—62no—
125C2×C3⋊C8—64no—
126ΓL(1,𝔽25)—24no—
127ΓL(1,𝔽25)—64no—
128ΓL(1,𝔽25)—64no—
129D3×C8—24no—
130D3×C8—64no—
131D3×C8—62no—
132D3×C8—62no—
133D3×C8—62no—
134D3×C8—62no—
135D3×C8—64no—
136C22×C32C4×D411yescharacteristic
137C2×C3⋊D3—22no—
138C2×C3⋊D3C4×D411yescharacteristic
139C2×C3⋊D3C23×C411yescharacteristic
140C2×C3×D3—24no—
141D32—28no—
142#157—22no—
143#157#13114yescomplemented
144C32×C4C4×D411yescharacteristic
145C32×C4C22×D411yescharacteristic
146C3⋊Dic3C4×D411yescharacteristic
147C3⋊Dic3C2×#4111yescharacteristic
148C3×Dic3—24no—
149C2×#41—92no—
150#131—62no—
151#131—182no—
152#131—182no—
153#131—182no—
154C2×M16—92no—
155C2×M16—94no—
156C22×C8—94no—
157C22×C8—91no—
158C22×C8—91no—
159C4⋊Q8—91no—
160#127—91no—
161#124—92no—
162#121—94no—
163C4×D4—94no—
164C2×C42—91no—
165C4⋊C8—94no—
166C22⋊C8—98no—
167C4×C8—92no—
168C4×C8—92no—
169C22×D3—64no—
170C22×D3—62no—
171C3×Q8—62no—
172C3×D4—62no—
173C3×D4—64no—
174C2×C3×C4—22no—
175C2×C3×C4—64no—
176#67—24no—
177#67—64no—
178#67—64no—
179C2×Dic3—62no—
180C2×Dic3—64no—
181D12—22no—
182D12—64no—
183C4×D3—24no—
184C4×D3—64no—
185C4×D3—62no—
186C4×D3—62no—
187C4×D3—62no—
188C4×D3—62no—
189C4×D3—64no—
190Dic6—22no—
191Dic6—64no—
192C3×C8—22no—
193C3×C8—22no—
194C3×C8—64no—
195C3⋊C8—24no—
196C3⋊C8—62no—
197C3⋊C8—62no—
198C2×C32—21no—
199C2×C32C2×C4×D411yescharacteristic
200C3⋊D3—21no—
201C3⋊D3C2×#13112yes—
202C3×D3—44no—
203#41—62no—
204#41—182no—
205#41—182no—
206#41—182no—
207C2×Q8—92no—
208C2×D4—94no—
209C2×D4—92no—
210C2×D4—94no—
211C22×C4—94no—
212C22×C4—91no—
213C22×C4—92no—
214M16—62no—
215M16—64no—
216M16—182no—
217M16—184no—
218C2×C8—64no—
219C2×C8—94no—
220C2×C8—91no—
221C2×C8—91no—
222C2×C8—91no—
223C2×C8—91no—
224C2×C8—91no—
225C2×C8—92no—
226C2×C8—184no—
227C2×C8—181no—
228C2×C8—181no—
229C2×C8GO+(4,𝔽2)11yescharacteristic, complemented
230C4⋊C4—94no—
231C22⋊C4—98no—
232C42—92no—
233C42—91no—
234C42—91no—
235C22×C3—22no—
236C22×C3—64no—
237C2×D3—24no—
238C2×D3—62no—
239C2×D3—62no—
240C2×D3—128no—
241C2×D3—124no—
242C3×C4—22no—
243C3×C4—22no—
244C3×C4—64no—
245Dic3—24no—
246Dic3—62no—
247Dic3—62no—
248C32#293111yescharacteristic, complemented, Sylow
249C23—94no—
250C23—91no—
251Q8—62no—
252Q8—182no—
253D4—64no—
254D4—62no—
255D4—184no—
256D4—182no—
257D4—188no—
258C2×C4—64no—
259C2×C4—94no—
260C2×C4—92no—
261C2×C4—91no—
262C2×C4—91no—
263C2×C4—91no—
264C2×C4—91no—
265C2×C4—91no—
266C2×C4—92no—
267C2×C4—184no—
268C2×C4—184no—
269C2×C4C2×GO+(4,𝔽2)11yescharacteristic
270C8—64no—
271C8—91no—
272C8—91no—
273C8—182no—
274C8C2×GO+(4,𝔽2)11yescharacteristic
275C8C2×GO+(4,𝔽2)11yescharacteristic
276C2×C3—22no—
277C2×C3—42no—
278C2×C3—124no—
279D3—44no—
280D3—64no—
281D3—122no—
282C22—64no—
283C22—91no—
284C22—91no—
285C22—182no—
286C22—188no—
287C22C4×GO+(4,𝔽2)11yescharacteristic
288C4—64no—
289C4—94no—
290C4—91no—
291C4—91no—
292C4—182no—
293C4C4×GO+(4,𝔽2)11yescharacteristic
294C4C22×GO+(4,𝔽2)11yescharacteristic
295C3—22no—
296C2—21no—
297C2—92no—
298C2—124no—
299C2—181no—
300C2C2×C4×GO+(4,𝔽2)11yescharacteristic
subgroupG/H
centerC8C2×GO+(4,𝔽2)
commutatorC2×C3⋊D3C23×C4
FrattiniC4C22×GO+(4,𝔽2)
FittingC2×C32×C8D4
socleC2×C32C2×C4×D4
prime radical#10596511C2
cosocleC4×C3⋊D3C24
hypercenterC2×C8GO+(4,𝔽2)
hypocenterC32#2931
LCSG ▷ C2×C3⋊D3 ▷ C32
UCSC1 ◁ C8 ◁ C2×C8

Complements

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

NH ≅ G/Ntype
2. #10594669C2semidirect
3. C2×C8×#157C2semidirect
4. #10593328C2semidirect
5. #10593309C2semidirect
6. #10593283C2semidirect
7. C8×GO+(4,𝔽2)C2semidirect
48. C2×C32×C8D4semidirect
49. C2×C3⋊(C3⋊C8)D4semidirect
50. C8×C3⋊D3D4semidirect
51. C8×C3⋊D3D4semidirect
143. #157#131semidirect
229. C2×C8GO+(4,𝔽2)semidirect
248. C32#2931semidirect

Maximal subgroups

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

subgroupindex
#105965112
#105946692
C2×C8×#1572
#105933282
#105933092
#105932832
C8×GO+(4,𝔽2)2
#29319