Finite Group Databasebeta

← #11774322

Subgroups — #11774322

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
1C2×C4×#625C211yesmaximal, characteristic
2#10593801C211yesmaximal, characteristic, complemented
3#10591061C211yesmaximal, characteristic, complemented
4#10590029C214yesmaximal, complemented
5C22×C3×C4×D3—21no—
6C22×#625C411yescharacteristic
7C2×C4×C3⋊Dic3C2211yescharacteristic
8C2×#3724C411yescharacteristic
9C2×(C2×D3)⋊Dic3—21no—
10C4×#625—21no—
11C4×#625—21no—
12C4×#625C412yes—
13C4×#625C2212yes—
14C22⋊#622—21no—
15#63779—21no—
16C4×#622C2212yescomplemented
17C3×#830—21no—
18#63572C2212yescomplemented
19#63553—21no—
20C2×C4×#67—61no—
21#4718—61no—
22C23×C3×D3—21no—
23C22×C32×C4D411yescharacteristic
24C22×C3⋊Dic3C2×C411yescharacteristic
25C22×C3⋊Dic3D411yescharacteristic
26C22×C3×Dic3—21no—
27C2×C3×C4×D3—22no—
28C2×C3×C4×D3—22no—
29C2×C3×C4×D3—44no—
30C2×#625—21no—
31C2×#625—22no—
32C2×#625C814yescomplemented
33C2×#625C2×C412yes—
34C2×#622—22no—
35C4×C3⋊Dic3C2×C411yescharacteristic
36C4×C3⋊Dic3D411yescharacteristic
37C4×C3⋊Dic3D411yescharacteristic
38C4×C3⋊Dic3C2311yescharacteristic
39C2×C3×C3⋊C8—22no—
40#3724—21no—
41#3724C2×C412yes—
42(C2×D3)⋊Dic3—22no—
43(C2×D3)⋊Dic3—22no—
44#1478—91nomaximal, Sylow
45C23×C3×C4—61no—
46C22×#67—61no—
47C22×C4×D3—21no—
48C2×#217—61no—
49C4×#67—62no—
50C4×#67—62no—
51C4×#67—62no—
52C4×#67—62no—
53C2×(C2×D3)⋊C4—61no—
54C2×Dic3⋊C4—61no—
55C2×C4×Dic3—61no—
56C2×C4×Dic3—61no—
57C3×C22⋊C8—61no—
58#830—21no—
59Dic3⋊C8—62no—
60C8×Dic3—62no—
61C23×C32C22⋊C411yescharacteristic
62C22×C3×D3—24no—
63C22×C3×D3—22no—
64C22×C3×D3—42no—
65C22×C3×D3—42no—
66C2×C32×C4—22no—
67C2×C32×C4C22⋊C411yescharacteristic
68C2×C32×C4C2×D411yescharacteristic
69C2×C3⋊Dic3—41no—
70C2×C3⋊Dic3C22⋊C411yescharacteristic
71C2×C3⋊Dic3C22⋊C411yescharacteristic
72C2×C3⋊Dic3C2×C812yes—
73C2×C3⋊Dic3M1612yes—
74C2×C3⋊Dic3C22×C411yescharacteristic
75C2×C3⋊Dic3C2×D411yescharacteristic
76C2×C3×Dic3—22no—
77C2×C3×Dic3—42no—
78C3×C4×D3—44no—
79C3×C4×D3—44no—
80#625—24no—
81#625—22no—
82#625C2×C814yes—
83#622—42no—
84C3×C3⋊C8—42no—
85C2×C4×D4—91no—
86#431—91no—
87#431—91no—
88D4⋊C8—94no—
89C24×C3—61no—
90C23×D3—21no—
91C22×C3×C4—21no—
92C22×C3×C4—21no—
93C22×C3×C4—62no—
94C22×C3×C4—62no—
95C22×C3×C4—61no—
96C22×C3×C4—124no—
97C2×#67—62no—
98C2×#67—64no—
99C2×#67—62no—
100C2×#67—64no—
101C22×Dic3—21no—
102C22×Dic3—61no—
103C22×Dic3—61no—
104C22×Dic3—61no—
105C22×Dic3—61no—
106C2×C4×D3—22no—
107C2×C4×D3—22no—
108C2×C4×D3—44no—
109C2×C3×C8—62no—
110#217—62no—
111#217—62no—
112(C2×D3)⋊C4—62no—
113(C2×D3)⋊C4—62no—
114Dic3⋊C4—62no—
115Dic3⋊C4—62no—
116C4×Dic3—61no—
117C4×Dic3—61no—
118C4×Dic3—61no—
119C4×Dic3—61no—
120C4×Dic3—61no—
121C4×Dic3—61no—
122C4×Dic3—61no—
123C4×Dic3—61no—
124C2×C3⋊C8—22no—
125C22×C32—21no—
126C22×C32—21no—
127C22×C32C22⋊C812yes—
128C22×C32C2×C22⋊C411yescharacteristic
129C2×C3×D3—24no—
130C2×C3×D3—48no—
131C2×C3×D3—42no—
132C2×C3×D3—42no—
133C32×C4—21no—
134C32×C4AGL(1,ℤ/8)12yes—
135C3⋊Dic3—21no—
136C3⋊Dic3—21no—
137C3⋊Dic3C22⋊C812yes—
138C3⋊Dic3C22×C811yescharacteristic
139C3⋊Dic3C2×M1611yescharacteristic
140C3×Dic3—42no—
141C22×D4—91no—
142C23×C4—61no—
143C4×D4—92no—
144C4×D4—92no—
145C4×D4—181no—
146C4×D4—181no—
147C2×C4⋊C4—91no—
148C2×C22⋊C4—181no—
149C2×C42—91no—
150C4⋊C8—92no—
151C4⋊C8—181no—
152C22⋊C8—61no—
153C22⋊C8—181no—
154C4×C8—92no—
155C4×C8—181no—
156C23×C3—21no—
157C23×C3—21no—
158C23×C3—62no—
159C23×C3—64no—
160C23×C3—122no—
161C23×C3—122no—
162C22×D3—22no—
163C22×D3—24no—
164C22×D3—42no—
165C22×D3—42no—
166C2×C3×C4—24no—
167C2×C3×C4—21no—
168C2×C3×C4—21no—
169C2×C3×C4—21no—
170C2×C3×C4—21no—
171C2×C3×C4—42no—
172C2×C3×C4—62no—
173C2×C3×C4—124no—
174C2×C3×C4—124no—
175C2×C3×C4—122no—
176#67—64no—
177#67—68no—
178#67—64no—
179C2×Dic3—22no—
180C2×Dic3—42no—
181C2×Dic3—61no—
182C2×Dic3—61no—
183C2×Dic3—61no—
184C2×Dic3—62no—
185C2×Dic3—62no—
186C2×Dic3—62no—
187C2×Dic3—62no—
188C2×Dic3—61no—
189C2×Dic3—61no—
190C2×Dic3—61no—
191C2×Dic3—61no—
192C2×Dic3—61no—
193C2×Dic3—122no—
194C2×Dic3—122no—
195C4×D3—44no—
196C4×D3—44no—
197C3×C8—122no—
198C3⋊C8—42no—
199C2×C32—22no—
200C2×C32C2×C22⋊C811yescharacteristic
201C2×C32#41811yescharacteristic
202C2×C32#42111yescharacteristic
203C3×D3—44no—
204C24—61no—
205C2×D4—92no—
206C2×D4—94no—
207C2×D4—181no—
208C2×D4—182no—
209C22×C4—61no—
210C22×C4—62no—
211C22×C4—62no—
212C22×C4—91no—
213C22×C4—91no—
214C22×C4—124no—
215C22×C4GO+(4,𝔽2)11yescharacteristic
216C2×C8—62no—
217C2×C8—182no—
218C4⋊C4—92no—
219C4⋊C4—181no—
220C22⋊C4—182no—
221C22⋊C4—182no—
222C42—91no—
223C42—91no—
224C42—91no—
225C42—91no—
226C22×C3—22no—
227C22×C3—22no—
228C22×C3—21no—
229C22×C3—21no—
230C22×C3—22no—
231C22×C3—22no—
232C22×C3—41no—
233C22×C3—41no—
234C22×C3—64no—
235C22×C3—122no—
236C22×C3—128no—
237C22×C3—122no—
238C2×D3—24no—
239C2×D3—42no—
240C2×D3—48no—
241C2×D3—42no—
242C3×C4—22no—
243C3×C4—22no—
244C3×C4—22no—
245C3×C4—41no—
246C3×C4—122no—
247Dic3—42no—
248Dic3—62no—
249Dic3—61no—
250Dic3—61no—
251Dic3—62no—
252Dic3—61no—
253Dic3—61no—
254Dic3—62no—
255Dic3—121no—
256Dic3—121no—
257Dic3—121no—
258C32#147811yescharacteristic, complemented, Sylow
259C23—62no—
260C23—64no—
261C23—122no—
262C23—122no—
263C23D32⋊C411yescharacteristic
264D4—94no—
265D4—182no—
266D4—184no—
267C2×C4—22no—
268C2×C4—62no—
269C2×C4—91no—
270C2×C4—91no—
271C2×C4—92no—
272C2×C4—92no—
273C2×C4—91no—
274C2×C4—91no—
275C2×C4—124no—
276C2×C4—122no—
277C2×C4—124no—
278C2×C4—361no—
279C2×C4D32⋊C411yescharacteristic
280C2×C4C2×GO+(4,𝔽2)11yescharacteristic
281C8—122no—
282C8—362no—
283C2×C3—24no—
284C2×C3—21no—
285C2×C3—21no—
286C2×C3—21no—
287C2×C3—21no—
288C2×C3—21no—
289C2×C3—21no—
290C2×C3—42no—
291C2×C3—124no—
292D3—44no—
293C22—21no—
294C22—21no—
295C22—64no—
296C22—128no—
297C22—122no—
298C22—122no—
299C22D32⋊C812yes—
300C22C2×D32⋊C411yescharacteristic
301C4—21no—
302C4—91no—
303C4—91no—
304C4—92no—
305C4—122no—
306C4—181no—
307C4—181no—
308C4#6423612yes—
309C3—21no—
310C3—21no—
311C2—22no—
312C2—124no—
313C2C2×D32⋊C811yescharacteristic
314C2#1059332311yescharacteristic
315C2#1059349311yescharacteristic
subgroupG/H
center, FrattiniC2×C4C2×GO+(4,𝔽2)
commutatorC3⋊Dic3C22×C8
FittingC22×C32×C4D4
socleC22×C32C2×C22⋊C4
prime radicalC22×#625C4
cosocleC4×C3⋊Dic3C23
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32#1478
LCSG ▷ C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
2. #10593801C2semidirect
3. #10591061C2semidirect
4. #10590029C2semidirect
16. C4×#622C22semidirect
18. #63572C22semidirect
32. C2×#625C8semidirect
258. C32#1478semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#6252
#105938012
#105910612
#105900292
#14789