Finite Group Databasebeta

← #11774321

Subgroups — #11774321

Order 1152.

584 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 584 conjugacy classes of subgroups — too many to draw. Only its 75 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#10593727C211yesmaximal, characteristic, complemented
3#10590297C211yesmaximal, characteristic, complemented
4#10590029C214yesmaximal, complemented
5C2×#3802C411yescharacteristic
6C2×C4×D32—21no—
7C42×C3⋊D3C2211yescharacteristic
8C3×C4×D12—21no—
9#63921—21no—
10#63902C412yes—
11C4×#625C2212yes—
12#63900C411yescharacteristic
13#63898—21no—
14#63778—21no—
15C4⋊#622—21no—
16C4×#622C2212yescomplemented
17C3×C4×C3⋊C8—21no—
18#63572C2212yescomplemented
19#63557—21no—
20C4×D3×D4—61no—
21#4685—61no—
22C22×D32—21no—
23C2×C4×C3⋊D3C2×C411yescharacteristic
24C2×C4×C3⋊D3D411yescharacteristic
25C2×C4×C3⋊D3D411yescharacteristic
26C2×C3×D12—21no—
27C2×C3×C4×D3—22no—
28C2×#625C2×C412yes—
29C2×#624—21no—
30C2×D3×Dic3—22no—
31#3802—22no—
32#3802C814yescomplemented
33C4×D32—44no—
34C2×#622—22no—
35C32×C42D411yescharacteristic
36C4×C3⋊Dic3C2×C411yescharacteristic
37C4×C3⋊Dic3D411yescharacteristic
38C4×C3⋊Dic3C2311yescharacteristic
39C3×(C2×D3)⋊C4—22no—
40C3×C4⋊Dic3—21no—
41C2×C3×C3⋊C8—22no—
42#3724C2×C412yes—
43(C2×D3)⋊Dic3—22no—
44#1478—91nomaximal, Sylow
45C2×D3×D4—61no—
46C22×C4×D3—62no—
47C3×C4×D4—61no—
48D4×Dic3—61no—
49C4×#67—62no—
50#893—61no—
51D3×C4⋊C4—61no—
52#67⋊C4—62no—
53D3×C22⋊C4—62no—
54C4×D12—21no—
55C42×D3—61no—
56C42×D3—61no—
57C3×C4×C8—61no—
58(C2×D3)⋊C8—62no—
59Dic3⋊C8—62no—
60C4×C3⋊C8—21no—
61C22×C3⋊D3C22⋊C411yescharacteristic
62C22×C3×D3—22no—
63C2×D32—24no—
64C2×D32—42no—
65C2×D32—42no—
66C2×C32×C4C22⋊C411yescharacteristic
67C2×C32×C4C22⋊C411yescharacteristic
68C2×C32×C4C2×D411yescharacteristic
69C2×C3⋊Dic3C22⋊C411yescharacteristic
70C2×C3⋊Dic3C22×C411yescharacteristic
71C2×C3⋊Dic3C2×D411yescharacteristic
72C4×C3⋊D3—22no—
73C4×C3⋊D3—41no—
74C4×C3⋊D3C2×C812yes—
75C4×C3⋊D3M1612yes—
76C2×C3×Dic3—22no—
77C3×D12—24no—
78C3×C4×D3—44no—
79#625—22no—
80#625C2×C814yes—
81#624—42no—
82D3×Dic3—44no—
83#622—42no—
84C3×C3⋊C8—42no—
85C2×C4×D4—91no—
86#431—91no—
87#431—91no—
88D4⋊C8—94no—
89C23×D3—62no—
90C2×C3×D4—61no—
91C22×C3×C4—62no—
92C2×#67—62no—
93C22×Dic3—62no—
94D3×D4—64no—
95D3×D4—64no—
96C2×D12—21no—
97C2×C4×D3—22no—
98C2×C4×D3—61no—
99C2×C4×D3—61no—
100C2×C4×D3—61no—
101C2×C4×D3—61no—
102C2×C4×D3—61no—
103C2×C4×D3—61no—
104C2×C4×D3—62no—
105C2×C4×D3—62no—
106C2×C4×D3—128no—
107C2×C3×C8—62no—
108C3×C4⋊C4—61no—
109C3×C22⋊C4—62no—
110C3×C42—21no—
111C3×C42—21no—
112#217—62no—
113(C2×D3)⋊C4—22no—
114(C2×D3)⋊C4—62no—
115C4⋊Dic3—21no—
116Dic3⋊C4—62no—
117C4×Dic3—61no—
118C4×Dic3—61no—
119C4×Dic3—61no—
120C4×Dic3—61no—
121C4×Dic3—61no—
122C4×Dic3—61no—
123C2×C3⋊C8—22no—
124C22×C32C2×C22⋊C411yescharacteristic
125C2×C3⋊D3—21no—
126C2×C3⋊D3—21no—
127C2×C3⋊D3C22⋊C812yes—
128C2×C3×D3—24no—
129C2×C3×D3—42no—
130C2×C3×D3—42no—
131D32—48no—
132C32×C4—21no—
133C32×C4C22⋊C812yes—
134C32×C4AGL(1,ℤ/8)12yes—
135C3⋊Dic3—21no—
136C3⋊Dic3—21no—
137C3⋊Dic3C22×C811yescharacteristic
138C3⋊Dic3C2×M1611yescharacteristic
139C3×Dic3—42no—
140C22×D4—91no—
141C23×C4—181no—
142C4×D4—61no—
143C4×D4—92no—
144C4×D4—92no—
145C4×D4—181no—
146C2×C4⋊C4—91no—
147C2×C22⋊C4—181no—
148C2×C42—91no—
149C4⋊C8—92no—
150C4⋊C8—181no—
151C22⋊C8—181no—
152C22⋊C8—181no—
153C4×C8—61no—
154C4×C8—92no—
155C23×C3—62no—
156C22×D3—22no—
157C22×D3—61no—
158C22×D3—61no—
159C22×D3—68no—
160C22×D3—124no—
161C22×D3—124no—
162C3×D4—64no—
163C2×C3×C4—21no—
164C2×C3×C4—21no—
165C2×C3×C4—21no—
166C2×C3×C4—21no—
167C2×C3×C4—21no—
168C2×C3×C4—21no—
169C2×C3×C4—62no—
170C2×C3×C4—124no—
171#67—64no—
172#67—64no—
173C2×Dic3—22no—
174C2×Dic3—61no—
175C2×Dic3—61no—
176C2×Dic3—61no—
177C2×Dic3—61no—
178C2×Dic3—61no—
179C2×Dic3—61no—
180C2×Dic3—124no—
181D12—24no—
182C4×D3—44no—
183C4×D3—62no—
184C4×D3—62no—
185C4×D3—62no—
186C4×D3—62no—
187C4×D3—64no—
188C4×D3—122no—
189C4×D3—124no—
190C4×D3—124no—
191C4×D3—122no—
192C4×D3—122no—
193C3×C8—122no—
194C3⋊C8—42no—
195C2×C32C2×C22⋊C811yescharacteristic
196C2×C32#41811yescharacteristic
197C2×C32#42111yescharacteristic
198C3⋊D3—22no—
199C3×D3—44no—
200C24—181no—
201C2×D4—61no—
202C2×D4—94no—
203C2×D4—92no—
204C2×D4—182no—
205C22×C4—62no—
206C22×C4—91no—
207C22×C4—91no—
208C22×C4—91no—
209C22×C4—181no—
210C22×C4—182no—
211C22×C4—364no—
212C2×C8—62no—
213C2×C8—182no—
214C4⋊C4—61no—
215C4⋊C4—92no—
216C22⋊C4—62no—
217C22⋊C4—182no—
218C42—91no—
219C42—91no—
220C42—91no—
221C42GO+(4,𝔽2)11yescharacteristic
222C22×C3—21no—
223C22×C3—21no—
224C22×C3—64no—
225C22×C3—122no—
226C22×C3—122no—
227C2×D3—24no—
228C2×D3—42no—
229C2×D3—42no—
230C2×D3—62no—
231C2×D3—62no—
232C2×D3—62no—
233C2×D3—62no—
234C2×D3—121no—
235C2×D3—121no—
236C2×D3—1216no—
237C3×C4—22no—
238C3×C4—22no—
239C3×C4—22no—
240C3×C4—22no—
241C3×C4—22no—
242C3×C4—41no—
243C3×C4—122no—
244Dic3—42no—
245Dic3—61no—
246Dic3—61no—
247Dic3—61no—
248Dic3—61no—
249Dic3—62no—
250Dic3—121no—
251Dic3—121no—
252Dic3—121no—
253C32#147811yescharacteristic, complemented, Sylow
254C23—62no—
255C23—91no—
256C23—184no—
257C23—362no—
258C23—362no—
259D4—64no—
260D4—94no—
261D4—182no—
262C2×C4—62no—
263C2×C4—91no—
264C2×C4—92no—
265C2×C4—92no—
266C2×C4—91no—
267C2×C4—91no—
268C2×C4—124no—
269C2×C4—182no—
270C2×C4—361no—
271C2×C4—362no—
272C2×C4—364no—
273C2×C4D32⋊C411yescharacteristic
274C2×C4D32⋊C411yescharacteristic
275C2×C4C2×GO+(4,𝔽2)11yescharacteristic
276C8—122no—
277C8—362no—
278C2×C3—21no—
279C2×C3—21no—
280C2×C3—21no—
281C2×C3—21no—
282C2×C3—21no—
283C2×C3—21no—
284C2×C3—124no—
285D3—44no—
286D3—64no—
287D3—122no—
288C22—64no—
289C22—92no—
290C22—122no—
291C22—122no—
292C22—181no—
293C22—181no—
294C22—368no—
295C22C2×D32⋊C411yescharacteristic
296C4—21no—
297C4—91no—
298C4—91no—
299C4—122no—
300C4—181no—
301C4—181no—
302C4D32⋊C812yes—
303C4#6422412yes—
304C3—21no—
305C3—21no—
306C2—124no—
307C2—182no—
308C2C2×D32⋊C811yescharacteristic
309C2#1059332411yescharacteristic
310C2#1059336311yescharacteristic
subgroupG/H
center, FrattiniC2×C4C2×GO+(4,𝔽2)
commutatorC3⋊Dic3C22×C8
FittingC32×C42D4
socleC22×C32C2×C22⋊C4
prime radicalC2×#3802C4
cosocleC4×C3⋊Dic3C23
hypercenterC42GO+(4,𝔽2)
hypocenterC32#1478
LCSG ▷ C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C42

Complements

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

NH ≅ G/Ntype
2. #10593727C2semidirect
3. #10590297C2semidirect
4. #10590029C2semidirect
16. C4×#622C22semidirect
18. #63572C22semidirect
32. #3802C8semidirect
253. C32#1478semidirect

Maximal subgroups

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

subgroupindex
C4×#38022
#105937272
#105902972
#105900292
#14789