Finite Group Databasebeta

← #11774447

Subgroups — #11774447

Order 1152.

388 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 388 conjugacy classes of subgroups — too many to draw. Only its 55 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#10594963C211yesmaximal, characteristic
2#10593801C211yesmaximal, characteristic, complemented
3#10591061C211yesmaximal, characteristic, complemented
4#10590031C212yesmaximal, complemented
5#10590030C212yesmaximal, complemented
6C2×C4×C3⋊Dic3C2211yescharacteristic
7C3×#929—21no—
8#63982C411yescharacteristic
9#63980C411yescharacteristic
10#67⋊Dic3—21no—
11#63915C411yescharacteristic
12#63902C2211yescharacteristic
13#63878—21no—
14#63870C411yescharacteristic
15#63862—21no—
16#63838C2211yescharacteristic
17C22⋊#622—21no—
18#63779C2212yes—
19C4×#622—21no—
20C3×#830—21no—
21#63572—21no—
22#63553C2212yes—
23#5649—61no—
24#4718—61no—
25C22×C32×C4D411yescharacteristic
26C22×C3⋊Dic3C2×C411yescharacteristic
27C22×C3⋊Dic3D411yescharacteristic
28C2×C3×#67—21no—
29C2×#627C2×C411yescharacteristic
30C2×#625C2×C411yescharacteristic
31C2×D3×Dic3—21no—
32C2×#622—22no—
33C4×C3⋊Dic3C2×C411yescharacteristic
34C4×C3⋊Dic3D411yescharacteristic
35C4×C3⋊Dic3D411yescharacteristic
36C4×C3⋊Dic3C2311yescharacteristic
37C3×#217—21no—
38C3×(C2×D3)⋊C4—21no—
39C3×(C2×D3)⋊C4—21no—
40C3×Dic3⋊C4—21no—
41C3×Dic3⋊C4—21no—
42C2×C3×C3⋊C8—22no—
43#3724C2×C411yescharacteristic
44#3724C2×C411yescharacteristic
45Dic3⋊Dic3—21no—
46Dic3⋊Dic3—21no—
47(C2×D3)⋊Dic3—21no—
48(C2×D3)⋊Dic3—21no—
49Dic32—21no—
50#1482—91nomaximal, Sylow
51C3×#123—61no—
52#939—61no—
53D4×Dic3—61no—
54#929—21no—
55C2×C4×Dic3—61no—
56C2×C4×Dic3—61no—
57#898—61no—
58#892—61no—
59#889—61no—
60#887—61no—
61#885—61no—
62#67⋊C4—61no—
63#67⋊C4—61no—
64#879—61no—
65#878—61no—
66#877—61no—
67C3×C22⋊C8—61no—
68#830—21no—
69Dic3⋊C8—62no—
70C8×Dic3—62no—
71C23×C32C22⋊C411yescharacteristic
72C22×C3×D3—21no—
73C2×C32×C4—41no—
74C2×C32×C4C22⋊C411yescharacteristic
75C2×C32×C4C2×D411yescharacteristic
76C2×C3⋊Dic3—22no—
77C2×C3⋊Dic3—22no—
78C2×C3⋊Dic3C22⋊C411yescharacteristic
79C2×C3⋊Dic3C22⋊C411yescharacteristic
80C2×C3⋊Dic3C22×C411yescharacteristic
81C2×C3⋊Dic3C2×D411yescharacteristic
82C3×#67—42no—
83C2×C3×Dic3—21no—
84C2×C3×Dic3—21no—
85C2×C3×Dic3—21no—
86#627—22no—
87#625—22no—
88D3×Dic3—42no—
89#622—42no—
90C3×C3⋊C8—42no—
91#529—91no—
92#431—91no—
93#431—91no—
94Q8⋊C8—92no—
95D4⋊C8—92no—
96C2×C3×D4—61no—
97C22×C3×C4—21no—
98C22×C3×C4—21no—
99C2×#67—21no—
100C2×#67—61no—
101C22×Dic3—61no—
102C22×Dic3—61no—
103C22×Dic3—61no—
104C22×Dic3—61no—
105C22×Dic3—61no—
106C2×C4×D3—61no—
107C2×Dic6—61no—
108C2×C3×C8—62no—
109C3×C4⋊C4—61no—
110C3×C4⋊C4—61no—
111C3×C22⋊C4—61no—
112C3×C22⋊C4—61no—
113C3×C22⋊C4—61no—
114#217—21no—
115#217—61no—
116#217—61no—
117(C2×D3)⋊C4—21no—
118(C2×D3)⋊C4—21no—
119(C2×D3)⋊C4—61no—
120(C2×D3)⋊C4—61no—
121C4⋊Dic3—61no—
122C4⋊Dic3—61no—
123Dic3⋊C4—21no—
124Dic3⋊C4—21no—
125Dic3⋊C4—61no—
126Dic3⋊C4—61no—
127Dic3⋊C4—61no—
128Dic3⋊C4—61no—
129C4×Dic3—61no—
130C4×Dic3—61no—
131C4×Dic3—61no—
132C4×Dic3—61no—
133C4×Dic3—61no—
134C4×Dic3—61no—
135C4×Dic3—61no—
136C4×Dic3—61no—
137C4×Dic3—61no—
138C4×Dic3—61no—
139C2×C3⋊C8—22no—
140C22×C32—21no—
141C22×C32—21no—
142C22×C32—21no—
143C22×C32C2×C22⋊C411yescharacteristic
144C2×C3×D3—41no—
145C2×C3×D3—41no—
146C2×C3×D3—41no—
147C32×C4—21no—
148C32×C4—21no—
149C3⋊Dic3—21no—
150C3⋊Dic3—21no—
151C3⋊Dic3#13112yes—
152C3⋊Dic3#13512yes—
153C3×Dic3—41no—
154C3×Dic3—41no—
155C3×Dic3—41no—
156#126—181no—
157#125—91no—
158#124—91no—
159#123—61no—
160C22⋊Q8—91no—
161#121—91no—
162C4×Q8—91no—
163C4×D4—91no—
164C4×D4—181no—
165#117—181no—
166C2×C42—91no—
167C4⋊C8—92no—
168C4⋊C8—181no—
169C22⋊C8—61no—
170C22⋊C8—181no—
171C4×C8—92no—
172C4×C8—181no—
173C23×C3—21no—
174C23×C3—21no—
175C23×C3—61no—
176C22×D3—21no—
177C3×D4—122no—
178C2×C3×C4—21no—
179C2×C3×C4—21no—
180C2×C3×C4—21no—
181C2×C3×C4—21no—
182C2×C3×C4—42no—
183C2×C3×C4—42no—
184C2×C3×C4—61no—
185C2×C3×C4—61no—
186C2×C3×C4—61no—
187#67—42no—
188#67—122no—
189C2×Dic3—21no—
190C2×Dic3—21no—
191C2×Dic3—21no—
192C2×Dic3—61no—
193C2×Dic3—61no—
194C2×Dic3—61no—
195C2×Dic3—61no—
196C2×Dic3—61no—
197C2×Dic3—61no—
198C2×Dic3—61no—
199C2×Dic3—61no—
200C2×Dic3—64no—
201C2×Dic3—122no—
202C2×Dic3—122no—
203C2×Dic3—122no—
204C2×Dic3—122no—
205C4×D3—122no—
206Dic6—122no—
207C3×C8—122no—
208C3⋊C8—42no—
209C2×C32—41no—
210C2×C32#40811yescharacteristic
211C2×C32#41611yescharacteristic
212C2×C32#42111yescharacteristic
213C3×D3—81no—
214C2×Q8—91no—
215C2×D4—61no—
216C2×D4—91no—
217C22×C4—91no—
218C22×C4—91no—
219C22×C4—181no—
220C22×C4GO+(4,𝔽2)11yescharacteristic
221C2×C8—62no—
222C2×C8—182no—
223C4⋊C4—61no—
224C4⋊C4—61no—
225C4⋊C4—91no—
226C4⋊C4—91no—
227C4⋊C4—181no—
228C4⋊C4—181no—
229C22⋊C4—61no—
230C22⋊C4—61no—
231C22⋊C4—61no—
232C22⋊C4—181no—
233C22⋊C4—181no—
234C42—91no—
235C42—91no—
236C42—91no—
237C42—91no—
238C42—181no—
239C22×C3—22no—
240C22×C3—22no—
241C22×C3—21no—
242C22×C3—21no—
243C22×C3—41no—
244C22×C3—41no—
245C22×C3—41no—
246C22×C3—41no—
247C22×C3—121no—
248C22×C3—121no—
249C22×C3—121no—
250C2×D3—41no—
251C2×D3—41no—
252C2×D3—41no—
253C3×C4—22no—
254C3×C4—41no—
255C3×C4—41no—
256C3×C4—41no—
257C3×C4—121no—
258C3×C4—121no—
259C3×C4—121no—
260Dic3—41no—
261Dic3—41no—
262Dic3—41no—
263Dic3—62no—
264Dic3—62no—
265Dic3—62no—
266Dic3—62no—
267Dic3—62no—
268Dic3—121no—
269Dic3—121no—
270Dic3—121no—
271C32#148211yescharacteristic, complemented, Sylow
272C23—61no—
273C23D32⋊C411yescharacteristic
274Q8—182no—
275D4—122no—
276D4—182no—
277C2×C4—41no—
278C2×C4—61no—
279C2×C4—61no—
280C2×C4—61no—
281C2×C4—91no—
282C2×C4—91no—
283C2×C4—91no—
284C2×C4—91no—
285C2×C4—182no—
286C2×C4—182no—
287C2×C4—362no—
288C2×C4D32⋊C411yescharacteristic
289C2×C4C2×GO+(4,𝔽2)11yescharacteristic
290C8—122no—
291C8—362no—
292C2×C3—21no—
293C2×C3—21no—
294C2×C3—21no—
295C2×C3—21no—
296C2×C3—21no—
297C2×C3—21no—
298C2×C3—42no—
299C2×C3—42no—
300C2×C3—241no—
301D3—81no—
302C22—21no—
303C22—21no—
304C22—21no—
305C22—121no—
306C22—121no—
307C22—121no—
308C22C2×D32⋊C411yescharacteristic
309C4—21no—
310C4—21no—
311C4—92no—
312C4—92no—
313C4—121no—
314C4—121no—
315C4—121no—
316C4—181no—
317C4—181no—
318C3—21no—
319C3—21no—
320C2—41no—
321C2—241no—
322C2#1059330911yescharacteristic
323C2#1059331711yescharacteristic
324C2#1059350611yescharacteristic
subgroupG/H
centerC22C2×D32⋊C4
commutatorC2×C3⋊Dic3C22×C4
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC22×C32C2×C22⋊C4
prime radical#63980C4
cosocleC4×C3⋊Dic3C23
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32#1482
LCSG ▷ C2×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
2. #10593801C2semidirect
3. #10591061C2semidirect
4. #10590031C2semidirect
5. #10590030C2semidirect
271. C32#1482semidirect

Maximal subgroups

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

subgroupindex
#105949632
#105938012
#105910612
#105900312
#105900302
#14829