Finite Group Databasebeta

← #11775861

Subgroups — #11775861

Order 1152.

388 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 388 conjugacy classes of subgroups — too many to draw. Only its 53 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
2C4×#3792C211yesmaximal, characteristic, complemented
3#10591066C211yesmaximal, characteristic, complemented
4#10590036C212yesmaximal, complemented
5#10590035C212yesmaximal, complemented
6C2×#3792—21no—
7C2×C4×C3⋊Dic3C2211yescharacteristic
8C3×#929—21no—
9#63982C411yescharacteristic
10#63980C411yescharacteristic
11#67⋊Dic3—21no—
12#63915C2211yescharacteristic
13#63902C411yescharacteristic
14#63878—21no—
15#63870C2211yescharacteristic
16#63862—21no—
17#63838C411yescharacteristic
18#63777C2212yes—
19C4×#622—21no—
20C3×#830—21no—
21#63572—21no—
22#63555C2212yes—
23#5649—61no—
24#4719—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—
32#3792—24no—
33C2×#622—22no—
34C4×C3⋊Dic3C2×C411yescharacteristic
35C4×C3⋊Dic3D411yescharacteristic
36C4×C3⋊Dic3D411yescharacteristic
37C4×C3⋊Dic3C2311yescharacteristic
38C3×#217—21no—
39C3×(C2×D3)⋊C4—21no—
40C3×(C2×D3)⋊C4—21no—
41C3×Dic3⋊C4—21no—
42C3×Dic3⋊C4—21no—
43C2×C3×C3⋊C8—22no—
44#3724C2×C411yescharacteristic
45#3724C2×C411yescharacteristic
46Dic3⋊Dic3—21no—
47Dic3⋊Dic3—21no—
48(C2×D3)⋊Dic3—21no—
49(C2×D3)⋊Dic3—21no—
50Dic32—21no—
51#1529—91nomaximal, Sylow
52C3×#123—61no—
53#939—61no—
54D4×Dic3—61no—
55#929—21no—
56C2×C4×Dic3—61no—
57C2×C4×Dic3—61no—
58#898—61no—
59#892—61no—
60#889—61no—
61#887—61no—
62#885—61no—
63#67⋊C4—61no—
64#67⋊C4—61no—
65#879—61no—
66#878—61no—
67#877—61no—
68C3×C22⋊C8—61no—
69#830—21no—
70#815—62no—
71Dic3⋊C8—62no—
72C23×C32C22⋊C411yescharacteristic
73C22×C3×D3—21no—
74C2×C32×C4—41no—
75C2×C32×C4C22⋊C411yescharacteristic
76C2×C32×C4C2×D411yescharacteristic
77C2×C3⋊Dic3—22no—
78C2×C3⋊Dic3—41no—
79C2×C3⋊Dic3C22⋊C411yescharacteristic
80C2×C3⋊Dic3C22⋊C411yescharacteristic
81C2×C3⋊Dic3C22×C411yescharacteristic
82C2×C3⋊Dic3C2×D411yescharacteristic
83C3×#67—42no—
84C2×C3×Dic3—21no—
85C2×C3×Dic3—21no—
86C2×C3×Dic3—21no—
87#627—41no—
88#625—41no—
89D3×Dic3—42no—
90#622—24no—
91C3×C3⋊C8—42no—
92#529—91no—
93#432—91no—
94C4×M16—91no—
95#330—92no—
96#329—92no—
97C2×C3×D4—61no—
98C22×C3×C4—21no—
99C22×C3×C4—21no—
100C2×#67—21no—
101C2×#67—61no—
102C22×Dic3—61no—
103C22×Dic3—61no—
104C22×Dic3—61no—
105C22×Dic3—61no—
106C22×Dic3—61no—
107C2×C4×D3—61no—
108C2×Dic6—61no—
109C2×C3×C8—62no—
110C3×C4⋊C4—61no—
111C3×C4⋊C4—61no—
112C3×C22⋊C4—61no—
113C3×C22⋊C4—61no—
114C3×C22⋊C4—61no—
115#217—21no—
116#217—61no—
117#217—61no—
118(C2×D3)⋊C4—21no—
119(C2×D3)⋊C4—21no—
120(C2×D3)⋊C4—61no—
121(C2×D3)⋊C4—61no—
122C4⋊Dic3—61no—
123C4⋊Dic3—61no—
124Dic3⋊C4—21no—
125Dic3⋊C4—21no—
126Dic3⋊C4—61no—
127Dic3⋊C4—61no—
128Dic3⋊C4—61no—
129Dic3⋊C4—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—
139C4×Dic3—61no—
140C2×C3⋊C8—22no—
141C22×C32—21no—
142C22×C32—21no—
143C22×C32—21no—
144C22×C32C2×C22⋊C411yescharacteristic
145C2×C3×D3—41no—
146C2×C3×D3—41no—
147C2×C3×D3—41no—
148C32×C4—21no—
149C32×C4—21no—
150C3⋊Dic3—21no—
151C3⋊Dic3—21no—
152C3⋊Dic3—21no—
153C3⋊Dic3#10412yes—
154C3×Dic3—41no—
155C3×Dic3—41no—
156C3×Dic3—41no—
157C2×M16—181no—
158#126—181no—
159#125—91no—
160#124—91no—
161#123—61no—
162C22⋊Q8—91no—
163#121—91no—
164C4×Q8—91no—
165C4×D4—91no—
166C4×D4—181no—
167#117—181no—
168C2×C42—91no—
169C4⋊C8—181no—
170C22⋊C8—61no—
171#97—92no—
172#97—92no—
173C4×C8—181no—
174C23×C3—21no—
175C23×C3—21no—
176C23×C3—61no—
177C22×D3—21no—
178C3×D4—122no—
179C2×C3×C4—21no—
180C2×C3×C4—21no—
181C2×C3×C4—21no—
182C2×C3×C4—21no—
183C2×C3×C4—42no—
184C2×C3×C4—42no—
185C2×C3×C4—61no—
186C2×C3×C4—61no—
187C2×C3×C4—61no—
188#67—42no—
189#67—122no—
190C2×Dic3—21no—
191C2×Dic3—21no—
192C2×Dic3—21no—
193C2×Dic3—61no—
194C2×Dic3—61no—
195C2×Dic3—61no—
196C2×Dic3—61no—
197C2×Dic3—61no—
198C2×Dic3—61no—
199C2×Dic3—61no—
200C2×Dic3—61no—
201C2×Dic3—122no—
202C2×Dic3—122no—
203C2×Dic3—122no—
204C2×Dic3—122no—
205C2×Dic3—122no—
206C4×D3—122no—
207Dic6—122no—
208C3×C8—122no—
209C3⋊C8—42no—
210C2×C32—41no—
211C2×C32#41311yescharacteristic
212C2×C32C2×#10411yescharacteristic
213C2×C32#42111yescharacteristic
214C3×D3—81no—
215C2×Q8—91no—
216C2×D4—61no—
217C2×D4—91no—
218C22×C4—91no—
219C22×C4—91no—
220C22×C4—181no—
221C22×C4GO+(4,𝔽2)11yescharacteristic
222M16—184no—
223C2×C8—62no—
224C2×C8—182no—
225C4⋊C4—61no—
226C4⋊C4—61no—
227C4⋊C4—91no—
228C4⋊C4—91no—
229C4⋊C4—181no—
230C4⋊C4—181no—
231C22⋊C4—61no—
232C22⋊C4—61no—
233C22⋊C4—61no—
234C22⋊C4—181no—
235C22⋊C4—181no—
236C42—91no—
237C42—91no—
238C42—91no—
239C42—91no—
240C42—181no—
241C22×C3—22no—
242C22×C3—22no—
243C22×C3—21no—
244C22×C3—21no—
245C22×C3—41no—
246C22×C3—41no—
247C22×C3—41no—
248C22×C3—41no—
249C22×C3—121no—
250C22×C3—121no—
251C22×C3—121no—
252C2×D3—41no—
253C2×D3—41no—
254C2×D3—41no—
255C3×C4—22no—
256C3×C4—41no—
257C3×C4—41no—
258C3×C4—41no—
259C3×C4—121no—
260C3×C4—121no—
261C3×C4—121no—
262Dic3—41no—
263Dic3—41no—
264Dic3—41no—
265Dic3—62no—
266Dic3—62no—
267Dic3—62no—
268Dic3—121no—
269Dic3—121no—
270Dic3—121no—
271Dic3—121no—
272Dic3—121no—
273C32#152911yescharacteristic, complemented, Sylow
274C23—61no—
275C23D32⋊C411yescharacteristic
276Q8—361no—
277D4—122no—
278D4—361no—
279C2×C4—41no—
280C2×C4—61no—
281C2×C4—61no—
282C2×C4—61no—
283C2×C4—91no—
284C2×C4—91no—
285C2×C4—91no—
286C2×C4—91no—
287C2×C4—182no—
288C2×C4—362no—
289C2×C4—361no—
290C2×C4D32⋊C411yescharacteristic
291C2×C4C2×GO+(4,𝔽2)11yescharacteristic
292C8—122no—
293C8—184no—
294C2×C3—21no—
295C2×C3—21no—
296C2×C3—21no—
297C2×C3—21no—
298C2×C3—21no—
299C2×C3—21no—
300C2×C3—42no—
301C2×C3—42no—
302C2×C3—241no—
303D3—81no—
304C22—21no—
305C22—21no—
306C22—21no—
307C22—121no—
308C22—121no—
309C22—121no—
310C22C2×D32⋊C411yescharacteristic
311C4—21no—
312C4—21no—
313C4—92no—
314C4—121no—
315C4—121no—
316C4—121no—
317C4—181no—
318C4—181no—
319C4—181no—
320C3—21no—
321C3—21no—
322C2—41no—
323C2—241no—
324C2#1059331111yescharacteristic
325C2#1059332511yescharacteristic
326C2#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#1529
LCSG ▷ C2×C3⋊Dic3 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
2. C4×#3792C2semidirect
3. #10591066C2semidirect
4. #10590036C2semidirect
5. #10590035C2semidirect
273. C32#1529semidirect

Maximal subgroups

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

subgroupindex
#105949632
C4×#37922
#105910662
#105900362
#105900352
#15299