Finite Group Databasebeta

← #11775394

Subgroups — #11775394

Order 1152.

616 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 616 conjugacy classes of subgroups — too many to draw. Only its 58 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#10596098C211yesmaximal, characteristic
2#10593812C211yesmaximal, characteristic, complemented
3#10593802C211yesmaximal, characteristic, complemented
4#10590215C212yesmaximal, complemented
5#10590157C212yesmaximal, complemented
6C2×#3832C411yescharacteristic, complemented
7C22×C4×C3⋊D3C2211yescharacteristic
8C2×C22⋊#157—21no—
9C2×#3792—21no—
10C2×C4⋊#157—21no—
11C32×C22⋊Q8C411yescharacteristic, complemented
12#64155C2211yescharacteristic
13#64139C411yescharacteristic, complemented
14#64104C2211yescharacteristic
15#64103—21no—
16#64102—21no—
17#64101C411yescharacteristic, complemented
18#64091—21no—
19#64090—21no—
20#63781C2212yes—
21#63778—21no—
22#63778C2212yes—
23#5627—62no—
24C23×C3⋊D3D411yescharacteristic
25C22×#157—22no—
26C2×C32×Q8C2×C411yescharacteristic
27C22×C32×C4C2×C411yescharacteristic
28C2×#638—21no—
29C22×C3⋊Dic3D411yescharacteristic
30#3832—42no—
31C2×C4⋊(C3⋊D3)—21no—
32C2×C4⋊(C3⋊D3)—21no—
33C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
34C2×C4×C3⋊D3—21no—
35C2×C4×C3⋊D3—42no—
36C2×C4×C3⋊D3C2×C411yescharacteristic
37C2×C4×C3⋊D3D411yescharacteristic
38C2×C4×C3⋊D3D411yescharacteristic
39C2×C4×C3⋊D3C2311yescharacteristic
40C22⋊#157—42no—
41#3792—42no—
42C2×#622—22no—
43C4⋊#157—42no—
44C32×C4⋊C4—21no—
45C32×C4⋊C4C2×C411yescharacteristic
46C32×C22⋊C4—21no—
47#3752—21no—
48#3752—21no—
49#3752—21no—
50#3752—21no—
51C4⋊(C3⋊Dic3)C2×C411yescharacteristic
52#3750—21no—
53C4×C3⋊Dic3—21no—
54#1513—91nomaximal, Sylow
55C2×#239—62no—
56C22×C4×D3—62no—
57C3×C22⋊Q8—22no—
58#946—62no—
59#930—62no—
60#895—62no—
61#894—64no—
62#893—64no—
63#892—62no—
64#882—64no—
65#67⋊C4—64no—
66C23×C32C22⋊C411yescharacteristic
67C22×C3⋊D3—21no—
68C22×C3⋊D3—21no—
69C22×C3⋊D3—21no—
70C22×C3⋊D3—41no—
71C22×C3⋊D3—41no—
72C22×C3⋊D3C22⋊C411yescharacteristic
73C22×C3⋊D3C2×D411yescharacteristic
74C2×#157—42no—
75C2×#157—42no—
76C2×#157—42no—
77C32×Q8—41no—
78C2×C32×C4—21no—
79C2×C32×C4—21no—
80C2×C32×C4—41no—
81C2×C32×C4C22⋊C411yescharacteristic
82C2×C32×C4C22×C411yescharacteristic
83#638—42no—
84C2×C3⋊Dic3—21no—
85C2×C3⋊Dic3—22no—
86C2×C3⋊Dic3C22⋊C411yescharacteristic
87C2×C3⋊Dic3C2×D411yescharacteristic
88C4⋊(C3⋊D3)—41no—
89C4⋊(C3⋊D3)—42no—
90C4⋊(C3⋊D3)—41no—
91C4⋊(C3⋊D3)—41no—
92C4×C3⋊D3—22no—
93C4×C3⋊D3—22no—
94C4×C3⋊D3—41no—
95C4×C3⋊D3—41no—
96C4×C3⋊D3—42no—
97#622—42no—
98#525—91no—
99#407—91no—
100#380—91no—
101#328—92no—
102#327—92no—
103C23×D3—62no—
104C2×C3×Q8—22no—
105C22×C3×C4—22no—
106C2×#67—64no—
107C22×Dic3—62no—
108#239—128no—
109C2×D12—62no—
110C2×D12—64no—
111C2×D12—64no—
112C2×C4×D3—62no—
113C2×C4×D3—62no—
114C2×C4×D3—62no—
115C2×C4×D3—62no—
116C2×C4×D3—64no—
117C2×C4×D3—128no—
118C3×C4⋊C4—24no—
119C3×C4⋊C4—22no—
120C3×C22⋊C4—24no—
121(C2×D3)⋊C4—64no—
122(C2×D3)⋊C4—64no—
123(C2×D3)⋊C4—64no—
124(C2×D3)⋊C4—64no—
125C4⋊Dic3—62no—
126Dic3⋊C4—64no—
127C4×Dic3—64no—
128C22×C32—21no—
129C22×C32—21no—
130C22×C32—21no—
131C22×C32C2×C22⋊C411yescharacteristic
132C2×C3⋊D3—21no—
133C2×C3⋊D3—21no—
134C2×C3⋊D3—21no—
135C2×C3⋊D3—21no—
136C2×C3⋊D3—21no—
137C2×C3⋊D3—42no—
138C2×C3⋊D3—42no—
139C2×C3⋊D3—41no—
140C2×C3⋊D3—41no—
141C2×C3⋊D3—41no—
142C2×C3⋊D3AGL(1,ℤ/8)11yescharacteristic
143C2×C3⋊D3#13711yescharacteristic
144#157—82no—
145C32×C4—21no—
146C32×C4—21no—
147C32×C4—41no—
148C32×C4—41no—
149C3⋊Dic3—21no—
150C3⋊Dic3—41no—
151C3⋊Dic3#9912yes—
152C2×#41—91no—
153C23×C4—91no—
154C2×M16—181no—
155#123—181no—
156C22⋊Q8—91no—
157C22⋊Q8#15711yescharacteristic, complemented
158#121—91no—
159#121—91no—
160#120—181no—
161C4×D4—181no—
162C4×D4—181no—
163#117—91no—
164C2×C4⋊C4—181no—
165C2×C22⋊C4—181no—
166C22⋊C8—92no—
167C22⋊C8—181no—
168#95—92no—
169C23×C3—22no—
170C22×D3—62no—
171C22×D3—62no—
172C22×D3—64no—
173C22×D3—122no—
174C22×D3—122no—
175C22×D3—124no—
176C22×D3—124no—
177C3×Q8—44no—
178C2×C3×C4—24no—
179C2×C3×C4—24no—
180C2×C3×C4—22no—
181C2×C3×C4—22no—
182C2×C3×C4—44no—
183#67—128no—
184C2×Dic3—62no—
185C2×Dic3—62no—
186C2×Dic3—64no—
187C2×Dic3—124no—
188D12—124no—
189D12—124no—
190D12—124no—
191D12—128no—
192C4×D3—68no—
193C4×D3—124no—
194C4×D3—128no—
195C4×D3—124no—
196C4×D3—124no—
197C2×C32—41no—
198C2×C32C2×#9911yescharacteristic
199C2×C32#41711yescharacteristic
200C2×C32#42111yescharacteristic
201C3⋊D3—21no—
202C3⋊D3—21no—
203C3⋊D3—41no—
204C3⋊D3—81no—
205C24—91no—
206#41—362no—
207C2×Q8C2×#15711yescharacteristic
208C2×D4—91no—
209C2×D4—181no—
210C2×D4—181no—
211C2×D4—181no—
212C22×C4—91no—
213C22×C4—91no—
214C22×C4—91no—
215C22×C4—91no—
216C22×C4—91no—
217C22×C4—181no—
218C22×C4—182no—
219C22×C4—362no—
220C22×C4C2×#15711yescharacteristic
221M16—362no—
222C2×C8—182no—
223C4⋊C4—21no—
224C4⋊C4—91no—
225C4⋊C4—181no—
226C4⋊C4—362no—
227C4⋊C4C2×#15711yescharacteristic
228C22⋊C4—21no—
229C22⋊C4—181no—
230C22⋊C4—181no—
231C22⋊C4—181no—
232C22⋊C4—181no—
233C22⋊C4—362no—
234C42—181no—
235C22×C3—24no—
236C22×C3—22no—
237C22×C3—42no—
238C22×C3—42no—
239C2×D3—62no—
240C2×D3—62no—
241C2×D3—64no—
242C2×D3—122no—
243C2×D3—122no—
244C2×D3—122no—
245C2×D3—122no—
246C2×D3—128no—
247C2×D3—128no—
248C2×D3—124no—
249C2×D3—124no—
250C2×D3—124no—
251C3×C4—24no—
252C3×C4—42no—
253C3×C4—44no—
254C3×C4—44no—
255Dic3—64no—
256Dic3—122no—
257Dic3—124no—
258C32#151311yescharacteristic, complemented, Sylow
259C23—91no—
260C23—91no—
261C23—181no—
262C23—181no—
263C23—181no—
264C23—361no—
265C23—361no—
266C23C22⋊#15711yescharacteristic
267Q8—41no—
268D4—361no—
269D4—361no—
270D4—361no—
271D4—362no—
272D4—362no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—41no—
276C2×C4—91no—
277C2×C4—91no—
278C2×C4—182no—
279C2×C4—182no—
280C2×C4—182no—
281C2×C4—181no—
282C2×C4—361no—
283C2×C4—361no—
284C2×C4—362no—
285C2×C4—362no—
286C2×C4—362no—
287C2×C4—362no—
288C2×C4C22⋊#15711yescharacteristic
289C2×C4C22×#15711yescharacteristic
290C8—362no—
291C2×C3—22no—
292C2×C3—22no—
293C2×C3—22no—
294C2×C3—44no—
295D3—122no—
296D3—122no—
297D3—124no—
298D3—244no—
299C22—21no—
300C22—21no—
301C22—21no—
302C22—91no—
303C22—91no—
304C22—181no—
305C22—181no—
306C22—181no—
307C22—181no—
308C22—181no—
309C22—362no—
310C22—362no—
311C22—361no—
312C22—361no—
313C22—361no—
314C22C2×C22⋊#15711yescharacteristic
315C4—21no—
316C4—21no—
317C4—41no—
318C4—41no—
319C4—92no—
320C4—181no—
321C4—361no—
322C4—722no—
323C3—22no—
324C2—41no—
325C2—181no—
326C2—181no—
327C2—361no—
328C2—721no—
329C2#1059381711yescharacteristic
330C2#1059383111yescharacteristic
331C2#1059384011yescharacteristic
subgroupG/H
centerC22C2×C22⋊#157
commutatorC2×C32×C4C22×C4
FrattiniC2×C4C22×#157
FittingC32×C22⋊Q8C4
socleC22×C32C2×C22⋊C4
prime radical#10596098C2
cosocleC2×C4×C3⋊D3C23
hypercenterC22⋊Q8#157
hypocenterC32#1513
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
2. #10593812C2semidirect
3. #10593802C2semidirect
4. #10590215C2semidirect
5. #10590157C2semidirect
6. C2×#3832C4semidirect
11. C32×C22⋊Q8C4semidirect
13. #64139C4semidirect
17. #64101C4semidirect
157. C22⋊Q8#157semidirect
258. C32#1513semidirect

Maximal subgroups

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

subgroupindex
#105960982
#105938122
#105938022
#105902152
#105901572
#15139