Finite Group Databasebeta

← #11877009

Subgroups — #11877009

Order 1152.

963 conjugacy classes of subgroups; only the 168 normal subgroups are shown.

normal subgroups only

This group has 963 conjugacy classes of subgroups — too many to draw. Only its 168 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#10593907C212yesmaximal, complemented
2C4×#3743C211yesmaximal, characteristic, complemented
3C3×#4694C212yesmaximal, complemented
4#10590840C214yesmaximal, complemented
5#10590741C214yesmaximal, complemented
6#10590352C211yesmaximal, characteristic, complemented
7#10590309C211yesmaximal, characteristic, complemented
8#81560—32nomaximal
9C2×#3796—22no—
10C2×#3743C2212yes—
11C42×C3⋊D3C2211yescharacteristic
12C3×#874C2212yes—
13C3×#869C2212yes—
14#63916—22no—
15#63916C2214yes—
16#63898—22no—
17#63898C2214yes—
18#63863—22no—
19C2×#3713C2214yes—
20C32×C4×C8C2211yescharacteristic
21#63642C2212yes—
22C4×C3⋊(C3⋊C8)C2211yescharacteristic
23C3×#821C2218yes—
24#63574C2214yes—
25#5725—32no—
26#5716—32no—
27C3×#486—32no—
28#5080—32no—
29#5073—32no—
30#4785—38no—
31#4782—38no—
32#4694D312yescomplemented
33C4×ΓL(1,𝔽25)—32no—
34C4×ΓL(1,𝔽25)—61no—
35C2×C4×C3⋊D3D412yes—
36C2×C4×C3⋊D3C2311yescharacteristic
37C2×C3×D12—22no—
38C2×C3×D12—22no—
39C2×C3×D12C2314yes—
40C2×C3×Dic6—22no—
41C2×#626—24no—
42C2×D3×Dic3—24no—
43#3796—48no—
44C2×C32×C8C2312yes—
45C32×C42C2311yescharacteristic
46C4×C3⋊Dic3D412yes—
47C4×C3⋊Dic3C2311yescharacteristic
48C2×C3⋊(C3⋊C8)C2312yes—
49#3743—24no—
50C3×C4⋊Dic3—22no—
51C3×C4⋊Dic3C2314yes—
52(C2×D3)⋊Dic3—24no—
53(C2×D3)⋊Dic3—24no—
54#3713—28no—
55#3184—91noSylow
56C2×#239—62no—
57C2×#237—62no—
58C3×C4⋊Q8—32no—
59C3×#127—32no—
60#947—62no—
61#938—34no—
62#938—62no—
63#936—62no—
64D4×Dic3—34no—
65D4×Dic3—62no—
66C2×#213—38no—
67C2×ΓL(1,𝔽25)—34no—
68C2×ΓL(1,𝔽25)—62no—
69#895—34no—
70#895—62no—
71#893—34no—
72#893—62no—
73#874C2×D312yes—
74C42×D3—32no—
75C42×D3—61no—
76#869C2×D312yes—
77C3×#102—38no—
78C3×C4×C8—21no—
79C3×C4×C8C2×D312yes—
80#821C2×D318yes—
81#815—34no—
82#815—62no—
83#808—38no—
84C4×C3⋊C8—32no—
85C4×C3⋊C8—61no—
86C22×C3⋊D3C2×D411yescharacteristic
87C22×C3×D3—24no—
88C2×C32×C4C2×D412yes—
89C2×C32×C4C2411yescharacteristic
90C2×C3⋊Dic3C2×D411yescharacteristic
91C2×C3⋊Dic3C2×D412yes—
92C4×C3⋊D3—22no—
93C4×C3⋊D3—24no—
94C2×C3×Dic3—24no—
95C3×D12—28no—
96C3×D12—44no—
97C3×D12—44no—
98C3×Dic6—44no—
99#626—48no—
100D3×Dic3—48no—
101C32×C8—22no—
102C3⋊(C3⋊C8)#4114yescomplemented
103#532—92no—
104#498—91no—
105#493—91no—
106#486—32no—
107#469—94no—
108#442—94no—
109C4×M16—91no—
110C2×C3×Q8—62no—
111C2×C3×D4—34no—
112C2×C3×D4—62no—
113C2×C3×D4—62no—
114C2×#67—64no—
115C22×Dic3—64no—
116#239—128no—
117#237—128no—
118C2×D12—22no—
119C2×D12—22no—
120C2×D12—64no—
121C2×D12C22×D314yes—
122C2×C4×D3—32no—
123C2×C4×D3—32no—
124C2×C4×D3—32no—
125C2×C4×D3—61no—
126C2×C4×D3—62no—
127C2×C4×D3—64no—
128C2×Dic6—22no—
129C2×C3×C8—22no—
130C2×C3×C8C22×D314yes—
131C3×C4⋊C4—34no—
132C3×C4⋊C4—62no—
133C3×C42—21no—
134C3×C42C22×D312yes—
135#217—64no—
136#217—64no—
137#213—616no—
138(C2×D3)⋊C4—64no—
139(C2×D3)⋊C4—64no—
140C4⋊Dic3—22no—
141C4⋊Dic3C22×D314yes—
142C4×Dic3—32no—
143C4×Dic3—32no—
144C4×Dic3—32no—
145C4×Dic3—61no—
146C4×Dic3—62no—
147C2×C3⋊C8—34no—
148C2×C3⋊C8—62no—
149ΓL(1,𝔽25)—68no—
150ΓL(1,𝔽25)—68no—
151C22×C32C22×D411yescharacteristic
152C2×C3⋊D3—21no—
153C2×C3⋊D3—22no—
154C2×C3×D3—44no—
155C2×C3×D3—44no—
156C2×C3×D3—44no—
157C32×C4AGL(1,ℤ/8)14yes—
158C32×C4C2×#4112yes—
159C3⋊Dic3—21no—
160C3⋊Dic3—22no—
161C3×Dic3—44no—
162C2×#41—182no—
163C2×D8—94no—
164C2×M16—92no—
165C4⋊Q8—32no—
166#127—32no—
167#124—182no—
168#121—94no—
169#121—182no—
170C4×D4—94no—
171C4×D4—182no—
172C2×C42—91no—
173#106—94no—
174#102—38no—
175#97—92no—
176C4×C8—91no—
177C4×C8D3211yescharacteristic
178C23×C3—64no—
179C22×D3—24no—
180C22×D3—32no—
181C22×D3—61no—
182C3×Q8—124no—
183C3×D4—68no—
184C3×D4—124no—
185C3×D4—124no—
186C2×C3×C4—21no—
187C2×C3×C4—22no—
188C2×C3×C4—64no—
189C2×C3×C4D3×D412yes—
190C2×C3×C4D3×D412yes—
191C2×C3×C4C23×D312yes—
192#67—128no—
193C2×Dic3—24no—
194C2×Dic3—32no—
195C2×Dic3—32no—
196C2×Dic3—32no—
197C2×Dic3—61no—
198C2×Dic3—62no—
199C2×Dic3—128no—
200D12—28no—
201D12—44no—
202D12—44no—
203D12—128no—
204C4×D3—64no—
205C4×D3—64no—
206C4×D3—64no—
207C4×D3—64no—
208C4×D3—124no—
209C4×D3—128no—
210Dic6—44no—
211C3×C8—24no—
212C3×C8—24no—
213C3⋊C8—38no—
214C3⋊C8—64no—
215C2×C32#53211yescharacteristic
216C2×C32C2×AGL(1,ℤ/8)12yes—
217C3⋊D3—41no—
218C3×D3—84no—
219#41—368no—
220C2×Q8—62no—
221C2×D4—34no—
222C2×D4—62no—
223C2×D4—62no—
224C2×D4—184no—
225C22×C4—91no—
226C22×C4—92no—
227C22×C4—184no—
228D8—188no—
229M16—184no—
230C2×C8—92no—
231C2×C8C2×D3212yes—
232C4⋊C4—34no—
233C4⋊C4—62no—
234C22⋊C4—184no—
235C22⋊C4—184no—
236C42—91no—
237C42—92no—
238C42C2×D3211yescharacteristic
239C22×C3—21no—
240C22×C3—124no—
241C22×C3—124no—
242C22×C3—124no—
243C22×C3C2×D3×D412yes—
244C2×D3—44no—
245C2×D3—44no—
246C2×D3—44no—
247C2×D3—62no—
248C2×D3—62no—
249C2×D3—62no—
250C2×D3—62no—
251C2×D3—122no—
252C3×C4—22no—
253C3×C4—24no—
254C3×C4—124no—
255C3×C4#91114yes—
256C3×C4#91414yes—
257C3×C4D3×#4114yes—
258Dic3—44no—
259Dic3—62no—
260Dic3—62no—
261Dic3—62no—
262Dic3—62no—
263Dic3—122no—
264C32#318411yescharacteristic, complemented, Sylow
265C23—64no—
266C23—91no—
267Q8—124no—
268D4—68no—
269D4—124no—
270D4—124no—
271D4—368no—
272C2×C4—64no—
273C2×C4—91no—
274C2×C4—92no—
275C2×C4—182no—
276C2×C4—184no—
277C2×C4—368no—
278C2×C4#380212yes—
279C2×C4C22×D3211yescharacteristic
280C8—22no—
281C8—94no—
282C2×C3—22no—
283C2×C3—21no—
284C2×C3—244no—
285C2×C3#566812yes—
286C2×C3C2×#91112yes—
287C2×C3C2×#91412yes—
288D3—84no—
289D3—122no—
290D3—122no—
291C22—124no—
292C22—124no—
293C22—124no—
294C22—182no—
295C22—181no—
296C22C2×#380211yescharacteristic
297C4—124no—
298C4—182no—
299C4—181no—
300C4#6379814yes—
301C4#6430612yes—
302C3—21no—
303C3#8156012yescomplemented
304C2—244no—
305C2—361no—
306C2#1059397111yescharacteristic
307C2C2×#6379812yes—
subgroupG/H
centerC22C2×#3802
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×C8C22
socleC22×C32C22×D4
hypercenterC4×C8D32
hypocenterC32#3184
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8

Complements

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

NH ≅ G/Ntype
1. #10593907C2semidirect
2. C4×#3743C2semidirect
3. C3×#4694C2semidirect
4. #10590840C2semidirect
5. #10590741C2semidirect
6. #10590352C2semidirect
7. #10590309C2semidirect
32. #4694D3semidirect
102. C3⋊(C3⋊C8)#41semidirect
264. C32#3184semidirect
303. C3#81560semidirect

Maximal subgroups

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

subgroupindex
#105939072
C4×#37432
C3×#46942
#105908402
#105907412
#105903522
#105903092
#815603