Finite Group Databasebeta

← #11790603

Subgroups — #11790603

Order 1152.

666 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 666 conjugacy classes of subgroups — too many to draw. Only its 79 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
2#10593723C211yesmaximal, characteristic, complemented
3C2×D32⋊C8C214yesmaximal, complemented
4#10590331C211yesmaximal, characteristic, complemented
5C2×#3802C411yescharacteristic
6C2×C4×D32C2212yes—
7C2×#3787C2212yes—
8C42×C3⋊D3C2211yescharacteristic
9C3×C4×D12—21no—
10#63921C412yes—
11#63902—21no—
12C4×#625—21no—
13#63900C411yescharacteristic
14#63898—21no—
15C2×#3710C2212yes—
16#63777—21no—
17#63777—21no—
18D32⋊C8—28no—
19C3×C4⋊(C3⋊C8)—21no—
20#63572—21no—
21C4×D3×D4—61no—
22D3×C4⋊C8—61no—
23C22×D32C2×C412yes—
24C2×C4×C3⋊D3C2×C411yescharacteristic
25C2×C4×C3⋊D3C2×C411yescharacteristic
26C2×C4×C3⋊D3C2311yescharacteristic
27C2×C3×D12—21no—
28C2×C3×C4×D3—22no—
29C2×#625—21no—
30C2×#624C2×C412yes—
31C2×D3×Dic3—22no—
32#3802—24no—
33C4×D32—24no—
34C4×D32—24no—
35C2×#622—22no—
36#3787—22no—
37#3787D414yescomplemented
38C32×C42D411yescharacteristic
39C4×C3⋊Dic3D411yescharacteristic
40C4×C3⋊Dic3D411yescharacteristic
41C4×C3⋊Dic3D411yescharacteristic
42C3×(C2×D3)⋊C4—22no—
43C3×C4⋊Dic3—21no—
44C2×C3×C3⋊C8—22no—
45#3724—21no—
46(C2×D3)⋊Dic3—22no—
47#3710—24no—
48#1955—91nomaximal, Sylow
49C2×D3×D4—61no—
50C22×C4×D3—62no—
51C3×C4×D4—61no—
52D4×Dic3—61no—
53C4×#67—62no—
54C2×D3×C8—62no—
55#893—61no—
56D3×C4⋊C4—61no—
57#67⋊C4—62no—
58D3×C22⋊C4—62no—
59C4×D12—21no—
60C42×D3—61no—
61C42×D3—61no—
62C3×C4⋊C8—61no—
63Dic3⋊C8—62no—
64C4⋊(C3⋊C8)—21no—
65C22×C3⋊D3C22×C411yescharacteristic
66C22×C3×D3—22no—
67C2×D32—22no—
68C2×D32—24no—
69C2×D32—24no—
70C2×D32M1614yes—
71C2×C32×C4C22⋊C411yescharacteristic
72C2×C32×C4C22⋊C411yescharacteristic
73C2×C32×C4C2×D411yescharacteristic
74C2×C3⋊Dic3C22⋊C411yescharacteristic
75C2×C3⋊Dic3C22⋊C411yescharacteristic
76C2×C3⋊Dic3C2×D411yescharacteristic
77C4×C3⋊D3—22no—
78C4×C3⋊D3—22no—
79C4×C3⋊D3C2×D412yes—
80C4×C3⋊D3#4112yes—
81C2×C3×Dic3—22no—
82C3×D12—24no—
83C3×C4×D3—42no—
84C3×C4×D3—42no—
85#625—24no—
86#624—24no—
87D3×Dic3—44no—
88#622—24no—
89C3×C3⋊C8—42no—
90C2×C4×D4—91no—
91C2×C4⋊C8—91no—
92C2×C22⋊C8—94no—
93C2×#97—91no—
94C23×D3—62no—
95C2×C3×D4—61no—
96C22×C3×C4—62no—
97C2×#67—62no—
98C22×Dic3—62no—
99D3×D4—68no—
100C2×D12—21no—
101C2×C4×D3—22no—
102C2×C4×D3—61no—
103C2×C4×D3—61no—
104C2×C4×D3—61no—
105C2×C4×D3—61no—
106C2×C4×D3—62no—
107C2×C4×D3—61no—
108C2×C4×D3—61no—
109C2×C4×D3—62no—
110C2×C4×D3—124no—
111C2×C4×D3—124no—
112C2×C3×C8—62no—
113C3×C4⋊C4—61no—
114C3×C22⋊C4—62no—
115C3×C42—21no—
116C3×C42—21no—
117#217—62no—
118(C2×D3)⋊C4—22no—
119(C2×D3)⋊C4—62no—
120C4⋊Dic3—21no—
121Dic3⋊C4—62no—
122C4×Dic3—61no—
123C4×Dic3—61no—
124C4×Dic3—61no—
125C4×Dic3—61no—
126C4×Dic3—61no—
127C4×Dic3—61no—
128C2×C3⋊C8—22no—
129D3×C8—124no—
130C22×C32C2×C22⋊C411yescharacteristic
131C2×C3⋊D3C4×D412yes—
132C2×C3⋊D3C2×M1612yes—
133C2×C3⋊D3#13112yes—
134C2×C3×D3—24no—
135C2×C3×D3—42no—
136C2×C3×D3—42no—
137D32—28no—
138D32—44no—
139C32×C4—21no—
140C32×C4—21no—
141C32×C4#12411yescharacteristic
142C32×C4#12711yescharacteristic
143C3⋊Dic3—21no—
144C3⋊Dic3—21no—
145C3⋊Dic3#12112yes—
146C3×Dic3—42no—
147C22×D4—91no—
148C23×C4—92no—
149C22×C8—92no—
150C22×C8—92no—
151C4×D4—61no—
152C4×D4—181no—
153C4×D4—181no—
154C4×D4—181no—
155C2×C4⋊C4—91no—
156C2×C22⋊C4—92no—
157C2×C42—91no—
158C4⋊C8—61no—
159C4⋊C8—181no—
160C22⋊C8—188no—
161#97—181no—
162#97—181no—
163C23×C3—62no—
164C22×D3—22no—
165C22×D3—64no—
166C22×D3—61no—
167C22×D3—61no—
168C22×D3—64no—
169C22×D3—124no—
170C22×D3—124no—
171C3×D4—64no—
172C2×C3×C4—21no—
173C2×C3×C4—21no—
174C2×C3×C4—21no—
175C2×C3×C4—21no—
176C2×C3×C4—21no—
177C2×C3×C4—21no—
178C2×C3×C4—62no—
179C2×C3×C4—122no—
180C2×C3×C4—122no—
181#67—68no—
182C2×Dic3—22no—
183C2×Dic3—61no—
184C2×Dic3—61no—
185C2×Dic3—61no—
186C2×Dic3—61no—
187C2×Dic3—61no—
188C2×Dic3—61no—
189C2×Dic3—124no—
190D12—24no—
191C4×D3—42no—
192C4×D3—42no—
193C4×D3—62no—
194C4×D3—62no—
195C4×D3—62no—
196C4×D3—62no—
197C4×D3—64no—
198C4×D3—64no—
199C4×D3—124no—
200C4×D3—122no—
201C4×D3—122no—
202C4×D3—124no—
203C3×C8—122no—
204C3⋊C8—42no—
205C2×C32#39011yescharacteristic
206C2×C32#40711yescharacteristic
207C2×C32#40811yescharacteristic
208C3⋊D3#43514yes—
209C3×D3—44no—
210C24—92no—
211C2×D4—61no—
212C2×D4—181no—
213C2×D4—184no—
214C22×C4—62no—
215C22×C4—92no—
216C22×C4—91no—
217C22×C4—91no—
218C22×C4—91no—
219C22×C4—182no—
220C22×C4—184no—
221C22×C4—184no—
222C2×C8—62no—
223C2×C8—94no—
224C2×C8—184no—
225C2×C8—182no—
226C2×C8—182no—
227C4⋊C4—61no—
228C4⋊C4—181no—
229C22⋊C4—62no—
230C22⋊C4—182no—
231C42—91no—
232C42—91no—
233C42—91no—
234C42GO+(4,𝔽2)11yescharacteristic
235C22×C3—21no—
236C22×C3—21no—
237C22×C3—64no—
238C22×C3—122no—
239C22×C3—122no—
240C2×D3—24no—
241C2×D3—42no—
242C2×D3—42no—
243C2×D3—62no—
244C2×D3—62no—
245C2×D3—62no—
246C2×D3—62no—
247C2×D3—62no—
248C2×D3—62no—
249C2×D3—128no—
250C2×D3—128no—
251C3×C4—22no—
252C3×C4—22no—
253C3×C4—21no—
254C3×C4—21no—
255C3×C4—21no—
256C3×C4—21no—
257C3×C4—41no—
258C3×C4—41no—
259C3×C4—122no—
260Dic3—42no—
261Dic3—62no—
262Dic3—62no—
263Dic3—62no—
264Dic3—62no—
265Dic3—121no—
266Dic3—121no—
267C32#195511yescharacteristic, complemented, Sylow
268C23—62no—
269C23—94no—
270C23—91no—
271C23—182no—
272C23—184no—
273C23—184no—
274D4—64no—
275D4—184no—
276C2×C4—62no—
277C2×C4—91no—
278C2×C4—92no—
279C2×C4—92no—
280C2×C4—91no—
281C2×C4—91no—
282C2×C4—122no—
283C2×C4—122no—
284C2×C4—182no—
285C2×C4—182no—
286C2×C4—184no—
287C2×C4—364no—
288C2×C4D32⋊C411yescharacteristic
289C2×C4D32⋊C411yescharacteristic
290C2×C4C2×GO+(4,𝔽2)11yescharacteristic
291C8—122no—
292C8—184no—
293C2×C3—21no—
294C2×C3—21no—
295C2×C3—21no—
296C2×C3—21no—
297C2×C3—21no—
298C2×C3—21no—
299C2×C3—124no—
300D3—44no—
301D3—64no—
302D3—64no—
303C22—64no—
304C22—92no—
305C22—92no—
306C22—92no—
307C22—122no—
308C22—122no—
309C22—188no—
310C22—364no—
311C22C2×D32⋊C411yescharacteristic
312C4—21no—
313C4—21no—
314C4—92no—
315C4—122no—
316C4—181no—
317C4—181no—
318C4#6422111yescharacteristic
319C4#6423111yescharacteristic
320C3—21no—
321C3—21no—
322C2—94no—
323C2—124no—
324C2#1059330711yescharacteristic
325C2#1059330811yescharacteristic
326C2#1059340711yescharacteristic
subgroupG/H
center, FrattiniC2×C4C2×GO+(4,𝔽2)
commutatorC22×C3⋊D3C22×C4
FittingC32×C42D4
socleC22×C32C2×C22⋊C4
prime radicalC2×#3802C4
cosocleC2×C4×C3⋊D3C23
hypercenterC42GO+(4,𝔽2)
hypocenterC32#1955
LCSG ▷ C22×C3⋊D3 ▷ C32
UCSC1 ◁ C2×C4 ◁ C42

Complements

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

NH ≅ G/Ntype
2. #10593723C2semidirect
3. C2×D32⋊C8C2semidirect
4. #10590331C2semidirect
37. #3787D4semidirect
267. C32#1955semidirect

Maximal subgroups

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

subgroupindex
C4×#38022
#105937232
C2×D32⋊C82
#105903312
#19559