Finite Group Databasebeta

← #11775298

Subgroups — #11775298

Order 1152.

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

normal subgroups only

This group has 752 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
1C3⋊D3×#121C211yesmaximal, characteristic
2#10593811C211yesmaximal, characteristic, complemented
3#10593803C211yesmaximal, characteristic, complemented
4#10590209C212yesmaximal, complemented
5#10590157C212yesmaximal, complemented
6C2×D4×C3⋊D3—21no—
7C2×D4×C3⋊D3C411yescharacteristic, complemented
8C22×C4×C3⋊D3C2211yescharacteristic
9C2×C22⋊#157—21no—
10C2×#3788—21no—
11C32×#121C411yescharacteristic, complemented
12#64148—21no—
13#64147C2211yescharacteristic
14#64139C411yescharacteristic, complemented
15#64104C2211yescharacteristic
16C4⋊C4×C3⋊D3C411yescharacteristic, complemented
17#64093—21no—
18C22⋊C4×C3⋊D3—21no—
19C22⋊#622—21no—
20#63781—21no—
21#63781C2212yescomplemented
22#63778C2212yescomplemented
23D3×#121—62no—
24C23×C3⋊D3—21no—
25C23×C3⋊D3D411yescharacteristic
26C22×#157—22no—
27C2×C32×D4—21no—
28C2×C32×D4C2×C411yescharacteristic
29C22×C32×C4C2×C411yescharacteristic
30C2×#638—21no—
31C2×#638—21no—
32C2×#638—21no—
33C22×C3⋊Dic3D411yescharacteristic
34D4×C3⋊D3—42no—
35D4×C3⋊D3—44no—
36C2×C4⋊(C3⋊D3)—21no—
37C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
38C2×C4×C3⋊D3—21no—
39C2×C4×C3⋊D3—42no—
40C2×C4×C3⋊D3C2×C411yescharacteristic
41C2×C4×C3⋊D3D411yescharacteristic
42C2×C4×C3⋊D3D411yescharacteristic
43C2×C4×C3⋊D3C2311yescharacteristic
44C22⋊#157—42no—
45C2×#622—22no—
46#3788—42no—
47C32×C4⋊C4C2×C411yescharacteristic
48C32×C22⋊C4—21no—
49#3757—21no—
50#3752—21no—
51#3752—21no—
52C4⋊(C3⋊Dic3)C2×C411yescharacteristic
53#3750—21no—
54#1510—91nomaximal, Sylow
55C2×D3×D4—62no—
56C2×D3×D4—64no—
57C22×C4×D3—62no—
58C3×#121—22no—
59#939—64no—
60#938—62no—
61#930—62no—
62#895—62no—
63D3×C4⋊C4—62no—
64#884—64no—
65D3×C22⋊C4—64no—
66C23×C32—21no—
67C23×C32C22⋊C411yescharacteristic
68C22×C3⋊D3—22no—
69C22×C3⋊D3—21no—
70C22×C3⋊D3—22no—
71C22×C3⋊D3—41no—
72C22×C3⋊D3—42no—
73C22×C3⋊D3—42no—
74C22×C3⋊D3—42no—
75C22×C3⋊D3C22⋊C411yescharacteristic
76C22×C3⋊D3C2×D411yescharacteristic
77C2×#157—42no—
78C2×#157—42no—
79C2×#157—42no—
80C32×D4—41no—
81C32×D4—42no—
82C2×C32×C4—21no—
83C2×C32×C4—41no—
84C2×C32×C4C22⋊C411yescharacteristic
85C2×C32×C4C22×C411yescharacteristic
86#638—42no—
87#638—42no—
88#638—42no—
89C2×C3⋊Dic3—21no—
90C2×C3⋊Dic3—41no—
91C2×C3⋊Dic3C22⋊C411yescharacteristic
92C2×C3⋊Dic3C2×D411yescharacteristic
93C4⋊(C3⋊D3)—41no—
94C4⋊(C3⋊D3)—42no—
95C4×C3⋊D3—22no—
96C4×C3⋊D3—22no—
97C4×C3⋊D3—41no—
98C4×C3⋊D3—41no—
99C4×C3⋊D3—42no—
100#622—42no—
101C2×#121—91no—
102#407—91no—
103#381—91no—
104#327—92no—
105#327—92no—
106C23×D3—62no—
107C23×D3—64no—
108C2×C3×D4—24no—
109C2×C3×D4—22no—
110C22×C3×C4—22no—
111C2×#67—64no—
112C2×#67—64no—
113C2×#67—64no—
114C22×Dic3—62no—
115D3×D4—128no—
116D3×D4—1216no—
117C2×D12—62no—
118C2×D12—64no—
119C2×C4×D3—62no—
120C2×C4×D3—62no—
121C2×C4×D3—62no—
122C2×C4×D3—62no—
123C2×C4×D3—64no—
124C2×C4×D3—128no—
125C3×C4⋊C4—22no—
126C3×C22⋊C4—24no—
127#217—64no—
128(C2×D3)⋊C4—64no—
129(C2×D3)⋊C4—64no—
130C4⋊Dic3—62no—
131Dic3⋊C4—64no—
132C22×C32—21no—
133C22×C32—21no—
134C22×C32—21no—
135C22×C32—41no—
136C22×C32—41no—
137C22×C32—41no—
138C22×C32C2×C22⋊C411yescharacteristic
139C2×C3⋊D3—21no—
140C2×C3⋊D3—21no—
141C2×C3⋊D3—21no—
142C2×C3⋊D3—21no—
143C2×C3⋊D3—44no—
144C2×C3⋊D3—41no—
145C2×C3⋊D3—41no—
146C2×C3⋊D3—41no—
147C2×C3⋊D3—84no—
148C2×C3⋊D3#9912yes—
149C2×C3⋊D3AGL(1,ℤ/8)12yes—
150#157—82no—
151C32×C4—21no—
152C32×C4—21no—
153C32×C4—41no—
154C3⋊Dic3—21no—
155C3⋊Dic3—21no—
156C3⋊Dic3—41no—
157C22×D4—91no—
158C22×D4—181no—
159C23×C4—91no—
160C2×M16—181no—
161#121—91no—
162#121—91no—
163#121—91no—
164#121—181no—
165#121—181no—
166#121#15711yescharacteristic, complemented
167C2×C4⋊C4—91no—
168C2×C22⋊C4—181no—
169C2×C22⋊C4—181no—
170C22⋊C8—92no—
171C22⋊C8—181no—
172#95—92no—
173#95—181no—
174C23×C3—24no—
175C23×C3—22no—
176C22×D3—62no—
177C22×D3—62no—
178C22×D3—68no—
179C22×D3—64no—
180C22×D3—124no—
181C22×D3—124no—
182C22×D3—128no—
183C22×D3—128no—
184C22×D3—128no—
185C3×D4—44no—
186C3×D4—48no—
187C2×C3×C4—24no—
188C2×C3×C4—22no—
189C2×C3×C4—22no—
190C2×C3×C4—44no—
191#67—128no—
192#67—128no—
193#67—128no—
194C2×Dic3—62no—
195C2×Dic3—62no—
196C2×Dic3—64no—
197C2×Dic3—124no—
198D12—124no—
199D12—128no—
200C4×D3—68no—
201C4×D3—124no—
202C4×D3—124no—
203C4×D3—124no—
204C4×D3—128no—
205C2×C32—41no—
206C2×C32—81no—
207C2×C32C2×#9911yescharacteristic
208C2×C32#41811yescharacteristic
209C2×C32#42111yescharacteristic
210C3⋊D3—22no—
211C3⋊D3—22no—
212C3⋊D3—81no—
213C24—91no—
214C24—181no—
215C2×D4—21no—
216C2×D4—91no—
217C2×D4—181no—
218C2×D4—181no—
219C2×D4—181no—
220C2×D4—181no—
221C2×D4—362no—
222C2×D4—364no—
223C2×D4C2×#15711yescharacteristic
224C22×C4—91no—
225C22×C4—91no—
226C22×C4—91no—
227C22×C4—91no—
228C22×C4—91no—
229C22×C4—181no—
230C22×C4—182no—
231C22×C4—362no—
232C22×C4C2×#15711yescharacteristic
233M16—362no—
234C2×C8—182no—
235C4⋊C4—91no—
236C4⋊C4—181no—
237C4⋊C4C2×#15711yescharacteristic
238C22⋊C4—21no—
239C22⋊C4—181no—
240C22⋊C4—181no—
241C22⋊C4—181no—
242C22⋊C4—362no—
243C22×C3—24no—
244C22×C3—22no—
245C22×C3—42no—
246C22×C3—42no—
247C22×C3—44no—
248C22×C3—44no—
249C22×C3—44no—
250C2×D3—64no—
251C2×D3—64no—
252C2×D3—64no—
253C2×D3—64no—
254C2×D3—122no—
255C2×D3—122no—
256C2×D3—1216no—
257C2×D3—124no—
258C2×D3—124no—
259C2×D3—124no—
260C2×D3—2416no—
261C3×C4—24no—
262C3×C4—42no—
263C3×C4—44no—
264Dic3—64no—
265Dic3—122no—
266Dic3—124no—
267C32#151011yescharacteristic, complemented, Sylow
268C23—21no—
269C23—91no—
270C23—91no—
271C23—182no—
272C23—182no—
273C23—181no—
274C23—361no—
275C23—362no—
276C23—362no—
277C23—362no—
278C23C22⋊#15711yescharacteristic
279D4—41no—
280D4—42no—
281D4—361no—
282D4—362no—
283D4—362no—
284D4—362no—
285D4—362no—
286C2×C4—21no—
287C2×C4—41no—
288C2×C4—91no—
289C2×C4—91no—
290C2×C4—182no—
291C2×C4—182no—
292C2×C4—181no—
293C2×C4—361no—
294C2×C4—361no—
295C2×C4—362no—
296C2×C4—361no—
297C2×C4—362no—
298C2×C4—362no—
299C2×C4—362no—
300C2×C4C22⋊#15711yescharacteristic
301C2×C4C22×#15711yescharacteristic
302C8—362no—
303C2×C3—22no—
304C2×C3—22no—
305C2×C3—22no—
306C2×C3—44no—
307C2×C3—84no—
308D3—68no—
309D3—124no—
310D3—244no—
311C22—21no—
312C22—21no—
313C22—21no—
314C22—41no—
315C22—41no—
316C22—41no—
317C22—92no—
318C22—92no—
319C22—181no—
320C22—181no—
321C22—181no—
322C22—181no—
323C22—364no—
324C22—361no—
325C22—361no—
326C22—361no—
327C22—724no—
328C22C2×C22⋊#15711yescharacteristic
329C4—21no—
330C4—21no—
331C4—41no—
332C4—181no—
333C4—181no—
334C4—361no—
335C4—722no—
336C3—22no—
337C2—41no—
338C2—81no—
339C2—182no—
340C2—182no—
341C2—721no—
342C2#1059381411yescharacteristic
343C2#1059381711yescharacteristic
344C2#1059384211yescharacteristic
subgroupG/H
centerC22C2×C22⋊#157
commutatorC2×C32×C4C22×C4
FrattiniC2×C4C22×#157
FittingC32×#121C4
socleC22×C32C2×C22⋊C4
prime radicalC3⋊D3×#121C2
cosocleC2×C4×C3⋊D3C23
hypercenter#121#157
hypocenterC32#1510
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #121

Complements

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

NH ≅ G/Ntype
2. #10593811C2semidirect
3. #10593803C2semidirect
4. #10590209C2semidirect
5. #10590157C2semidirect
7. C2×D4×C3⋊D3C4semidirect
11. C32×#121C4semidirect
14. #64139C4semidirect
16. C4⋊C4×C3⋊D3C4semidirect
21. #63781C22semidirect
22. #63778C22semidirect
166. #121#157semidirect
267. C32#1510semidirect

Maximal subgroups

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

subgroupindex
C3⋊D3×#1212
#105938112
#105938032
#105902092
#105901572
#15109