Finite Group Databasebeta

← #11791469

Subgroups — #11791469

Order 1152.

746 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 746 conjugacy classes of subgroups — too many to draw. Only its 85 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#10594008C211yesmaximal, characteristic
2C4×C4⋊#157C211yesmaximal, characteristic, complemented
3C2×#63729C214yesmaximal, complemented
4#10590331C211yesmaximal, characteristic, complemented
5C2×#3802—21no—
6C2×#3802—21no—
7C2×#3802C2212yes—
8C2×C4⋊#157C2212yes—
9C2×C4×#157—21no—
10C42×C3⋊D3C2211yescharacteristic
11C3×#874—21no—
12#63914—21no—
13#63914C412yescomplemented
14#63914C412yescomplemented
15C2×#3710C2212yes—
16#63781—21no—
17#63729—28no—
18C3×C4⋊(C3⋊C8)—21no—
19#63572—21no—
20D3×#127—61no—
21D3×C4⋊C8—61no—
22C22×D32—22no—
23C22×#157—22no—
24C2×C4×C3⋊D3D411yescharacteristic
25C2×C4×C3⋊D3D411yescharacteristic
26C2×C4×C3⋊D3C2311yescharacteristic
27C2×C3×D12—22no—
28C2×C3×D12—22no—
29C2×C3×D12—22no—
30C2×#625—22no—
31C2×#625—22no—
32C2×#625C2×C414yes—
33#3802—24no—
34#3802—24no—
35#3802—44no—
36#3802—42no—
37#3802—42no—
38C4⋊#157—22no—
39C4⋊#157D414yescomplemented
40C4×#157—42no—
41C32×C42D411yescharacteristic
42C4×C3⋊Dic3C2×C411yescharacteristic
43C4×C3⋊Dic3C2×C411yescharacteristic
44C4×C3⋊Dic3D411yescharacteristic
45C2×C3×C3⋊C8—22no—
46#3710—24no—
47#1982—91nomaximal, Sylow
48C2×D3×D4—62no—
49C2×D3×D4—62no—
50C2×D3×D4—62no—
51C3×#127—61no—
52#940—62no—
53#940—62no—
54#940—62no—
55C2×D3×C8—62no—
56#874—21no—
57C42×D3—61no—
58C42×D3—61no—
59C3×C4⋊C8—61no—
60Dic3⋊C8—62no—
61C4⋊(C3⋊C8)—21no—
62C22×C3⋊D3C2×D411yescharacteristic
63C22×C3×D3—24no—
64C2×D32—44no—
65C2×D32—42no—
66C2×D32—42no—
67C2×D32—44no—
68C2×#157—24no—
69C2×#157—42no—
70C2×#157—42no—
71C2×C32×C4C22⋊C411yescharacteristic
72C2×C32×C4C22⋊C411yescharacteristic
73C2×C32×C4C2×D411yescharacteristic
74C2×C3⋊Dic3C22⋊C411yescharacteristic
75C2×C3⋊Dic3C22⋊C411yescharacteristic
76C2×C3⋊Dic3C22×C411yescharacteristic
77C4×C3⋊D3—22no—
78C4×C3⋊D3D812yes—
79C4×C3⋊D3SD1612yes—
80C4×C3⋊D3C2×D412yes—
81C4×C3⋊D3#4112yes—
82C3×D12—44no—
83C3×D12—44no—
84C3×D12—42no—
85C3×D12—42no—
86#625—28no—
87#625—44no—
88#625—44no—
89C3×C3⋊C8—42no—
90C2×#127—91no—
91C2×C4⋊C8—91no—
92C2×#102—94no—
93C4×C4⋊C4—91no—
94C23×D3—64no—
95C2×C3×D4—62no—
96C2×C3×D4—62no—
97C2×C3×D4—62no—
98C2×#67—64no—
99C2×#67—64no—
100C2×#67—64no—
101D3×D4—124no—
102D3×D4—124no—
103D3×D4—124no—
104D3×D4—124no—
105D3×D4—128no—
106C2×D12—22no—
107C2×D12—22no—
108C2×D12—22no—
109C2×C4×D3—61no—
110C2×C4×D3—61no—
111C2×C4×D3—61no—
112C2×C4×D3—61no—
113C2×C4×D3—61no—
114C2×C4×D3—61no—
115C2×C3×C8—62no—
116C3×C42—21no—
117C3×C42—21no—
118C4×Dic3—61no—
119C4×Dic3—61no—
120C4×Dic3—61no—
121C4×Dic3—61no—
122C4×Dic3—61no—
123C4×Dic3—61no—
124C2×C3⋊C8—22no—
125D3×C8—124no—
126C22×C32C2×C22⋊C411yescharacteristic
127C2×C3⋊D3#12112yes—
128C2×C3⋊D3C2×D811yescharacteristic
129C2×C3⋊D3C2×SD1611yescharacteristic
130C2×C3⋊D3AGL(1,ℤ/8)12yes—
131C2×C3×D3—44no—
132C2×C3×D3—44no—
133C2×C3×D3—44no—
134D32—84no—
135D32—84no—
136#157—44no—
137C32×C4—21no—
138C32×C4#10212yescomplemented
139C32×C4#12411yescharacteristic
140C32×C4#12711yescharacteristic
141C3⋊Dic3—21no—
142C3⋊Dic3#10212yescomplemented
143C3⋊Dic3C4×D412yes—
144C22×D4—92no—
145C22×D4—181no—
146C22×D4—181no—
147C22×C8—92no—
148#127—61no—
149#127—92no—
150#127—92no—
151#127—181no—
152C2×C4⋊C4—92no—
153C2×C42—91no—
154C2×C42—181no—
155C4⋊C8—61no—
156C4⋊C8—181no—
157#102—188no—
158#95—181no—
159C23×C3—64no—
160C22×D3—24no—
161C22×D3—61no—
162C22×D3—61no—
163C22×D3—128no—
164C22×D3—124no—
165C22×D3—124no—
166C22×D3—128no—
167C3×D4—124no—
168C3×D4—122no—
169C3×D4—122no—
170C3×D4—124no—
171C2×C3×C4—21no—
172C2×C3×C4—21no—
173C2×C3×C4—21no—
174C2×C3×C4—21no—
175C2×C3×C4—21no—
176C2×C3×C4—21no—
177#67—128no—
178#67—128no—
179#67—128no—
180C2×Dic3—61no—
181C2×Dic3—61no—
182C2×Dic3—61no—
183C2×Dic3—61no—
184C2×Dic3—61no—
185C2×Dic3—61no—
186D12—44no—
187D12—42no—
188D12—42no—
189D12—44no—
190C4×D3—62no—
191C4×D3—62no—
192C4×D3—62no—
193C4×D3—62no—
194C4×D3—62no—
195C4×D3—62no—
196C4×D3—62no—
197C4×D3—62no—
198C4×D3—64no—
199C4×D3—122no—
200C3×C8—122no—
201C3⋊C8—42no—
202C2×C32#39011yescharacteristic
203C2×C32C2×#10211yescharacteristic
204C2×C32#41811yescharacteristic
205C3⋊D3#45912yes—
206C3⋊D3#46012yes—
207C3×D3—84no—
208C24—182no—
209C2×D4—62no—
210C2×D4—62no—
211C2×D4—62no—
212C2×D4—94no—
213C2×D4—184no—
214C2×D4—184no—
215C2×D4—182no—
216C2×D4—182no—
217C2×D4—362no—
218C2×D4—362no—
219C2×D4—364no—
220C22×C4—91no—
221C22×C4—91no—
222C22×C4—91no—
223C22×C4—182no—
224C2×C8—62no—
225C2×C8—184no—
226C4⋊C4—94no—
227C4⋊C4—182no—
228C42—91no—
229C42—91no—
230C42—91no—
231C42—362no—
232C42GO+(4,𝔽2)11yescharacteristic
233C22×C3—21no—
234C22×C3—21no—
235C22×C3—124no—
236C22×C3—124no—
237C22×C3—124no—
238C2×D3—44no—
239C2×D3—44no—
240C2×D3—44no—
241C2×D3—62no—
242C2×D3—61no—
243C2×D3—61no—
244C2×D3—62no—
245C2×D3—62no—
246C2×D3—61no—
247C2×D3—61no—
248C2×D3—62no—
249C2×D3—248no—
250C2×D3—248no—
251C3×C4—22no—
252C3×C4—21no—
253C3×C4—21no—
254C3×C4—21no—
255C3×C4—21no—
256C3×C4—22no—
257C3×C4—22no—
258C3×C4—41no—
259Dic3—62no—
260Dic3—62no—
261Dic3—62no—
262Dic3—62no—
263Dic3—62no—
264Dic3—121no—
265C32#198211yescharacteristic, complemented, Sylow
266C23—64no—
267C23—91no—
268C23—364no—
269C23—362no—
270C23—362no—
271C23—364no—
272D4—124no—
273D4—122no—
274D4—122no—
275D4—124no—
276D4—188no—
277D4—364no—
278D4—364no—
279C2×C4—91no—
280C2×C4—91no—
281C2×C4—92no—
282C2×C4—92no—
283C2×C4—92no—
284C2×C4—92no—
285C2×C4—91no—
286C2×C4—182no—
287C2×C4—184no—
288C2×C4—362no—
289C2×C4—362no—
290C2×C4D32⋊C411yescharacteristic
291C2×C4D32⋊C411yescharacteristic
292C2×C4C2×GO+(4,𝔽2)11yescharacteristic
293C8—122no—
294C2×C3—21no—
295C2×C3—21no—
296C2×C3—21no—
297C2×C3—21no—
298C2×C3—21no—
299C2×C3—21no—
300C2×C3—244no—
301D3—62no—
302D3—62no—
303D3—62no—
304D3—62no—
305D3—84no—
306C22—91no—
307C22—91no—
308C22—92no—
309C22—92no—
310C22—124no—
311C22—124no—
312C22—124no—
313C22—724no—
314C22—724no—
315C22C2×D32⋊C411yescharacteristic
316C4—21no—
317C4—92no—
318C4—92no—
319C4—181no—
320C4—364no—
321C4#6372912yescomplemented
322C4#6422111yescharacteristic
323C4#6423111yescharacteristic
324C3—21no—
325C3—21no—
326C2—92no—
327C2—92no—
328C2—244no—
329C2C2×#6372911yescharacteristic
330C2#1059331811yescharacteristic
331C2#1059340711yescharacteristic
subgroupG/H
centerC22C2×D32⋊C4
commutatorC2×C3⋊Dic3C22×C4
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC32×C42D4
socleC22×C32C2×C22⋊C4
prime radical#10594008C2
cosocleC2×C4×C3⋊D3C23
hypercenterC42GO+(4,𝔽2)
hypocenterC32#1982
LCSG ▷ C2×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42

Complements

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

NH ≅ G/Ntype
2. C4×C4⋊#157C2semidirect
3. C2×#63729C2semidirect
4. #10590331C2semidirect
13. #63914C4semidirect
14. #63914C4semidirect
39. C4⋊#157D4semidirect
138. C32×C4#102semidirect
142. C3⋊Dic3#102semidirect
265. C32#1982semidirect
321. C4#63729semidirect

Maximal subgroups

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

subgroupindex
#105940082
C4×C4⋊#1572
C2×#637292
#105903312
#19829