Finite Group Databasebeta

← #11774693

Subgroups — #11774693

Order 1152.

703 conjugacy classes of subgroups; only the 108 normal subgroups are shown.

normal subgroups only

This group has 703 conjugacy classes of subgroups — too many to draw. Only its 108 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
1C4×#3802C211yesmaximal, characteristic
2C4×#3743C211yesmaximal, characteristic, complemented
3#10590260C211yesmaximal, characteristic, complemented
4C3×#4459C212yesmaximal, complemented
5#10589080C212yesmaximal, complemented
6#68175—32nomaximal
7C2×#3802C411yescharacteristic
8C2×C4×D32—21no—
9C2×#3743—21no—
10C42×C3⋊D3C2211yescharacteristic
11C3×C4×D12C2212yes—
12#63921—21no—
13#63902—21no—
14C4×#625—21no—
15#63900C411yescharacteristic
16#63898C412yes—
17C32×C4×C8C2211yescharacteristic, complemented
18#63642—21no—
19C4×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
20C3×C4⋊(C3⋊C8)C2212yescomplemented
21#63557—21no—
22#63555—21no—
23C4×D3×D4—32no—
24#4835—32no—
25C4×ΓL(1,𝔽25)—32no—
26C4×ΓL(1,𝔽25)—61no—
27C3×D4⋊C8—32no—
28D4⋊(C3⋊C8)—32no—
29#4483—32no—
30#4459D312yescomplemented
31C22×D32—21no—
32C2×C4×C3⋊D3C2×C411yescharacteristic
33C2×C4×C3⋊D3D411yescharacteristic
34C2×C4×C3⋊D3D411yescharacteristic
35C2×C3×D12C2×C412yes—
36C2×C3×C4×D3—22no—
37C2×#625—21no—
38C2×#624—21no—
39C2×D3×Dic3—22no—
40#3802—24no—
41C4×D32—44no—
42C2×C32×C8—21no—
43C32×C42C2311yescharacteristic
44C4×C3⋊Dic3C2×C411yescharacteristic
45C4×C3⋊Dic3D411yescharacteristic
46C4×C3⋊Dic3D411yescharacteristic
47C2×C3⋊(C3⋊C8)—21no—
48#3743—24no—
49C3×(C2×D3)⋊C4—22no—
50C3×C4⋊Dic3C2×C412yes—
51C2×C3×C3⋊C8—22no—
52#3724—21no—
53(C2×D3)⋊Dic3—22no—
54#1490—91noSylow
55C2×D3×D4—32no—
56C22×C4×D3—62no—
57C3×C4×D4—32no—
58D4×Dic3—32no—
59C4×#67—62no—
60C2×ΓL(1,𝔽25)—62no—
61C2×ΓL(1,𝔽25)—62no—
62#893—32no—
63D3×C4⋊C4—32no—
64#67⋊C4—62no—
65D3×C22⋊C4—62no—
66C4×D12C2×D312yes—
67C42×D3—32no—
68C42×D3—61no—
69C3×C4⋊C8—32no—
70C3×C4×C8—21no—
71C3×C4×C8C2×D312yescomplemented
72(C2×D3)⋊C8—62no—
73#815—62no—
74#815—62no—
75#815—62no—
76C4⋊(C3⋊C8)C2×D312yescomplemented
77C4×C3⋊C8—32no—
78C4×C3⋊C8—61no—
79C22×C3⋊D3C22⋊C411yescharacteristic
80C22×C3×D3—22no—
81C2×D32—24no—
82C2×D32—42no—
83C2×D32—42no—
84C2×C32×C4C22×C411yescharacteristic
85C2×C32×C4C2×D411yescharacteristic
86C2×C32×C4C2×D411yescharacteristic
87C2×C3⋊Dic3C22⋊C411yescharacteristic
88C2×C3⋊Dic3C22⋊C411yescharacteristic
89C2×C3⋊Dic3C22⋊C411yescharacteristic
90C4×C3⋊D3—22no—
91C4×C3⋊D3—22no—
92C4×C3⋊D3—22no—
93C2×C3×Dic3—22no—
94C3×D12—22no—
95C3×D12M1614yescomplemented
96C3×C4×D3—42no—
97C3×C4×D3—42no—
98#625—24no—
99#624—42no—
100D3×Dic3—44no—
101C32×C8—22no—
102C3⋊(C3⋊C8)—22no—
103C3×C3⋊C8—42no—
104C2×C4×D4—91no—
105#432—91no—
106C4×M16—91no—
107D4⋊C8—32no—
108D4⋊C8—92no—
109C23×D3—62no—
110C2×C3×D4—32no—
111C22×C3×C4—62no—
112C2×#67—62no—
113C22×Dic3—62no—
114D3×D4—64no—
115D3×D4—64no—
116C2×D12C4×D312yes—
117C2×C4×D3—22no—
118C2×C4×D3—32no—
119C2×C4×D3—32no—
120C2×C4×D3—32no—
121C2×C4×D3—61no—
122C2×C4×D3—61no—
123C2×C4×D3—61no—
124C2×C4×D3—62no—
125C2×C4×D3—62no—
126C2×C4×D3—124no—
127C2×C4×D3—124no—
128C2×C3×C8—22no—
129C2×C3×C8—22no—
130C2×C3×C8—62no—
131C3×C4⋊C4—32no—
132C3×C22⋊C4—62no—
133C3×C42—21no—
134C3×C42C22×D312yes—
135#217—62no—
136(C2×D3)⋊C4—22no—
137(C2×D3)⋊C4—62no—
138C4⋊Dic3C4×D312yes—
139Dic3⋊C4—62no—
140C4×Dic3—32no—
141C4×Dic3—32no—
142C4×Dic3—32no—
143C4×Dic3—61no—
144C4×Dic3—61no—
145C4×Dic3—61no—
146C2×C3⋊C8—22no—
147C2×C3⋊C8—62no—
148C2×C3⋊C8—62no—
149ΓL(1,𝔽25)—68no—
150ΓL(1,𝔽25)—68no—
151C22×C32C2×C22⋊C411yescharacteristic
152C2×C3⋊D3—21no—
153C2×C3⋊D3—21no—
154C2×C3⋊D3#10412yes—
155C2×C3×D3—24no—
156C2×C3×D3—42no—
157C2×C3×D3—42no—
158D32—48no—
159C32×C4—21no—
160C32×C4C2×M1612yes—
161C32×C4AGL(1,ℤ/8)12yes—
162C3⋊Dic3—21no—
163C3⋊Dic3—21no—
164C3⋊Dic3—21no—
165C3×Dic3—42no—
166C22×D4—91no—
167C23×C4—181no—
168C2×M16—181no—
169C4×D4—32no—
170C4×D4—92no—
171C4×D4—181no—
172C4×D4—181no—
173C2×C4⋊C4—91no—
174C2×C22⋊C4—181no—
175C2×C42—91no—
176C4⋊C8—32no—
177C22⋊C8—181no—
178#97—181no—
179#97—181no—
180C4×C8—91no—
181C4×C8D3211yescharacteristic, complemented
182C23×C3—62no—
183C22×D3—22no—
184C22×D3—32no—
185C22×D3—61no—
186C22×D3—68no—
187C22×D3—124no—
188C22×D3—124no—
189C3×D4—34no—
190C3×D4—62no—
191C2×C3×C4—21no—
192C2×C3×C4—21no—
193C2×C3×C4—21no—
194C2×C3×C4—62no—
195C2×C3×C4—122no—
196C2×C3×C4—122no—
197C2×C3×C4C2×C4×D312yes—
198C2×C3×C4D3×D412yes—
199C2×C3×C4D3×D412yes—
200#67—68no—
201C2×Dic3—22no—
202C2×Dic3—32no—
203C2×Dic3—32no—
204C2×Dic3—32no—
205C2×Dic3—61no—
206C2×Dic3—61no—
207C2×Dic3—61no—
208C2×Dic3—124no—
209D12—22no—
210D12ΓL(1,𝔽25)14yescomplemented
211C4×D3—42no—
212C4×D3—42no—
213C4×D3—64no—
214C4×D3—64no—
215C4×D3—62no—
216C4×D3—62no—
217C4×D3—62no—
218C4×D3—62no—
219C4×D3—122no—
220C4×D3—122no—
221C4×D3—124no—
222C4×D3—124no—
223C3×C8—24no—
224C3×C8—24no—
225C3×C8—122no—
226C3⋊C8—42no—
227C3⋊C8—64no—
228C3⋊C8—64no—
229C2×C32#40711yescharacteristic
230C2×C32#41811yescharacteristic
231C2×C32C2×#10411yescharacteristic
232C3⋊D3—22no—
233C3×D3—44no—
234C24—181no—
235C2×D4—32no—
236C2×D4—181no—
237C2×D4—184no—
238C22×C4—62no—
239C22×C4—91no—
240C22×C4—91no—
241C22×C4—91no—
242C22×C4—181no—
243C22×C4—182no—
244C22×C4—364no—
245M16—184no—
246C2×C8—21no—
247C2×C8—62no—
248C2×C8—181no—
249C4⋊C4—32no—
250C4⋊C4—181no—
251C22⋊C4—62no—
252C22⋊C4—182no—
253C42—91no—
254C42—91no—
255C42—91no—
256C42C2×D3211yescharacteristic
257C22×C3—21no—
258C22×C3—64no—
259C22×C3—122no—
260C22×C3—122no—
261C22×C3D3×C22⋊C412yes—
262C2×D3—24no—
263C2×D3—34no—
264C2×D3—42no—
265C2×D3—42no—
266C2×D3—62no—
267C2×D3—62no—
268C2×D3—62no—
269C2×D3—121no—
270C2×D3—121no—
271C2×D3—1216no—
272C3×C4—22no—
273C3×C4—22no—
274C3×C4—22no—
275C3×C4—22no—
276C3×C4—122no—
277C3×C4C2×ΓL(1,𝔽25)12yes—
278C3×C4D3×M1612yes—
279C3×C4#91112yes—
280C3×C4#91412yes—
281Dic3—42no—
282Dic3—62no—
283Dic3—62no—
284Dic3—62no—
285Dic3—62no—
286Dic3—121no—
287Dic3—121no—
288C32#149011yescharacteristic, complemented, Sylow
289C23—62no—
290C23—91no—
291C23—184no—
292C23—362no—
293C23—362no—
294D4—34no—
295D4—62no—
296D4—184no—
297C2×C4—62no—
298C2×C4—91no—
299C2×C4—91no—
300C2×C4—91no—
301C2×C4—122no—
302C2×C4—122no—
303C2×C4—182no—
304C2×C4—182no—
305C2×C4—182no—
306C2×C4—362no—
307C2×C4—364no—
308C2×C4C4×D3211yescharacteristic
309C2×C4#380211yescharacteristic
310C2×C4#381111yescharacteristic
311C8—22no—
312C8—122no—
313C8—182no—
314C2×C3—21no—
315C2×C3—21no—
316C2×C3—21no—
317C2×C3—124no—
318C2×C3#472612yes—
319C2×C3#477012yes—
320C2×C3D3×#10412yes—
321D3—44no—
322D3—64no—
323D3—122no—
324C22—64no—
325C22—92no—
326C22—122no—
327C22—122no—
328C22—181no—
329C22—181no—
330C22—368no—
331C22#6392111yescharacteristic
332C4—21no—
333C4—122no—
334C4—181no—
335C4—181no—
336C4—181no—
337C4D3×ΓL(1,𝔽25)12yes—
338C4#6379812yes—
339C3—21no—
340C3#6817512yescomplemented
341C2—124no—
342C2—182no—
343C2#1059039311yescharacteristic
344C2#1059093711yescharacteristic
345C2#1059094111yescharacteristic
subgroupG/H
centerC2×C4#3802
commutatorC2×C32×C4C22×C4
FrattiniC42C2×D32
FittingC32×C4×C8C22
socleC22×C32C2×C22⋊C4
prime radicalC2×#3802C4
cosocleC32×C42C23
hypercenterC4×C8D32
hypocenterC32#1490
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×C8

Complements

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

NH ≅ G/Ntype
2. C4×#3743C2semidirect
3. #10590260C2semidirect
4. C3×#4459C2semidirect
5. #10589080C2semidirect
17. C32×C4×C8C22semidirect
19. C4×C3⋊(C3⋊C8)C22semidirect
20. C3×C4⋊(C3⋊C8)C22semidirect
30. #4459D3semidirect
71. C3×C4×C8C2×D3semidirect
76. C4⋊(C3⋊C8)C2×D3semidirect
95. C3×D12M16semidirect
181. C4×C8D32semidirect
210. D12ΓL(1,𝔽25)semidirect
288. C32#1490semidirect
340. C3#68175semidirect

Maximal subgroups

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

subgroupindex
C4×#38022
C4×#37432
#105902602
C3×#44592
#105890802
#681753