Finite Group Databasebeta

← #11805363

Subgroups — #11805363

Order 1152.

834 conjugacy classes of subgroups.

The subgroup lattice has 347 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3⋊D3×#117C211yesmaximal, characteristic
2#10593812C211yesmaximal, characteristic
3C4×C22⋊#157C211yesmaximal, characteristic
4#10593759C212yesmaximal, complemented
5C4⋊C4×#157C212yesmaximal, complemented
6#10593747C214yesmaximal
7#10593737C212yesmaximal, complemented
8C4×C4⋊#157C212yesmaximal, complemented
9C22×C4×C3⋊D3C2211yescharacteristic
10C2×C22⋊#157C2212yes—
11C2×C22⋊#157C2212yes—
12C2×C4⋊#157C2212yes—
13C2×C4⋊#157C2214yes—
14C2×C4×#157C2212yes—
15C2×C4×#157C2214yes—
16C32×#117C411yescharacteristic, complemented
17#64135C411yescharacteristic, complemented
18#64101C411yescharacteristic, complemented
19#64101C411yescharacteristic, complemented
20C4⋊C4×C3⋊D3C2211yescharacteristic
21C4⋊C4×C3⋊D3C2211yescharacteristic
22C22⋊C4×C3⋊D3C2212yes—
23#64086C412yescomplemented
24#64081C412yescomplemented
25C42×C3⋊D3C2212yes—
26#63781C2211yescharacteristic
27#63781C2211yescharacteristic
28#63781C2212yes—
29#63781C2214yes—
30#63781C2214yes—
31D3×#117—62no—
32C23×C3⋊D3C2311yescharacteristic
33C22×#157C2314yes—
34C22×#157C2312yes—
35C22×#157C2312yes—
36C22×C32×C4C2×C411yescharacteristic
37C22×C3⋊Dic3C2×C411yescharacteristic
38C2×C4×C3⋊D3—24no—
39C2×C4×C3⋊D3C2×C411yescharacteristic
40C2×C4×C3⋊D3C2×C411yescharacteristic
41C2×C4×C3⋊D3C2312yes—
42C2×C4×C3⋊D3C2312yes—
43C2×C4×C3⋊D3C2311yescharacteristic
44C2×C4×C3⋊D3C2311yescharacteristic
45C22⋊#157—24no—
46C22⋊#157—42no—
47C4⋊#157—28no—
48C4⋊#157—24no—
49C4×#157—24no—
50C4×#157—44no—
51C32×C4⋊C4C2×C411yescharacteristic
52C32×C4⋊C4C2×C411yescharacteristic
53C32×C22⋊C4C2×C412yes—
54C32×C42C2×C412yes—
55#3757C2×C412yes—
56#3752C2×C412yes—
57#3752C2×C412yes—
58C4⋊(C3⋊Dic3)C2×C411yescharacteristic
59C4⋊(C3⋊Dic3)C2×C411yescharacteristic
60#3750C2×C412yes—
61#3750C2×C412yes—
62C4×C3⋊Dic3C2×C412yes—
63C4×C3⋊Dic3C2×C412yes—
64C4×C3⋊Dic3C2×C412yes—
65#2347—91nomaximal, Sylow
66C22×C4×D3—62no—
67C3×#117—22no—
68#926—62no—
69#892—62no—
70#892—62no—
71D3×C4⋊C4—62no—
72D3×C4⋊C4—62no—
73D3×C22⋊C4—64no—
74#877—64no—
75#872—64no—
76C42×D3—64no—
77C23×C32C22×C411yescharacteristic
78C22×C3⋊D3—22no—
79C22×C3⋊D3—22no—
80C22×C3⋊D3—21no—
81C22×C3⋊D3—21no—
82C22×C3⋊D3C22×C411yescharacteristic
83C22×C3⋊D3C2411yescharacteristic
84C2×#157—22no—
85C2×#157—22no—
86C2×#157—22no—
87C2×#157—24no—
88C2×#157—24no—
89C2×#157—22no—
90C2×#157—24no—
91C2×#157—22no—
92C2×#157#4114yes—
93C2×C32×C4—22no—
94C2×C32×C4C22×C411yescharacteristic
95C2×C32×C4C22×C412yes—
96C2×C32×C4C22×C412yes—
97C2×C32×C4C22×C411yescharacteristic
98C2×C3⋊Dic3—22no—
99C2×C3⋊Dic3C22×C411yescharacteristic
100C2×C3⋊Dic3C22×C412yes—
101C2×C3⋊Dic3C22×C412yes—
102C2×C3⋊Dic3C22×C411yescharacteristic
103C4×C3⋊D3—22no—
104C4×C3⋊D3—22no—
105C4×C3⋊D3—22no—
106C4×C3⋊D3—24no—
107C4×C3⋊D3—22no—
108C4×C3⋊D3—22no—
109C4×C3⋊D3#4114yes—
110C2×#117—91no—
111#389—92no—
112#388—94no—
113#383—92no—
114#380—91no—
115C4×C4⋊C4—92no—
116C4×C4⋊C4—92no—
117C4×C22⋊C4—91no—
118C23×D3—62no—
119C22×C3×C4—22no—
120C22×Dic3—62no—
121C2×C4×D3—62no—
122C2×C4×D3—62no—
123C2×C4×D3—62no—
124C2×C4×D3—62no—
125C2×C4×D3—64no—
126C2×C4×D3—64no—
127C2×C4×D3—616no—
128C3×C4⋊C4—22no—
129C3×C4⋊C4—22no—
130C3×C22⋊C4—24no—
131C3×C42—24no—
132#217—64no—
133(C2×D3)⋊C4—64no—
134(C2×D3)⋊C4—64no—
135C4⋊Dic3—62no—
136C4⋊Dic3—62no—
137Dic3⋊C4—64no—
138Dic3⋊C4—64no—
139C4×Dic3—64no—
140C4×Dic3—64no—
141C4×Dic3—64no—
142C22×C32—21no—
143C22×C32—21no—
144C22×C32—21no—
145C22×C32C23×C411yescharacteristic
146C2×C3⋊D3—21no—
147C2×C3⋊D3—21no—
148C2×C3⋊D3—21no—
149C2×C3⋊D3—42no—
150C2×C3⋊D3—42no—
151C2×C3⋊D3C2×#4112yes—
152C2×C3⋊D3C2×#4112yes—
153C2×C3⋊D3H(5,𝔽2)11yescharacteristic
154C2×C3⋊D32−1+411yescharacteristic
155#157—24no—
156#157—44no—
157#157—42no—
158C32×C4—21no—
159C32×C4—22no—
160C32×C4—22no—
161C32×C4#11712yes—
162C3⋊Dic3—21no—
163C3⋊Dic3—22no—
164C3⋊Dic3—22no—
165C3⋊Dic3#11712yes—
166C23×C4—91no—
167#117—91no—
168#117—91no—
169#117—91no—
170#117—92no—
171#117—92no—
172#117#15711yescharacteristic, complemented
173C2×C4⋊C4—91no—
174C2×C4⋊C4—91no—
175C2×C4⋊C4—92no—
176C2×C4⋊C4—94no—
177C2×C22⋊C4—92no—
178C2×C22⋊C4—92no—
179C2×C22⋊C4—92no—
180C2×C42—92no—
181C2×C42—92no—
182C2×C42—94no—
183#95—91no—
184#95—91no—
185#95—92no—
186#95—94no—
187#95—94no—
188C23×C3—22no—
189C22×D3—62no—
190C22×D3—62no—
191C22×D3—68no—
192C22×D3—124no—
193C22×D3—122no—
194C22×D3—122no—
195C2×C3×C4—28no—
196C2×C3×C4—22no—
197C2×C3×C4—22no—
198C2×C3×C4—24no—
199C2×C3×C4—24no—
200C2×Dic3—62no—
201C2×Dic3—62no—
202C2×Dic3—64no—
203C2×Dic3—64no—
204C2×Dic3—68no—
205C4×D3—68no—
206C4×D3—68no—
207C4×D3—68no—
208C4×D3—68no—
209C4×D3—124no—
210C4×D3—128no—
211C4×D3—124no—
212C2×C32—41no—
213C2×C32C2×#11711yescharacteristic
214C2×C32C4×#4111yescharacteristic
215C2×C32#52011yescharacteristic
216C3⋊D3—41no—
217C3⋊D3#55312yes—
218C3⋊D3#55612yes—
219C24—91no—
220C22×C4—91no—
221C22×C4—92no—
222C22×C4—91no—
223C22×C4—91no—
224C22×C4—92no—
225C22×C4—92no—
226C22×C4—91no—
227C22×C4—91no—
228C22×C4—92no—
229C22×C4—94no—
230C22×C4—184no—
231C22×C4C2×#15711yescharacteristic
232C4⋊C4—92no—
233C4⋊C4—92no—
234C4⋊C4—91no—
235C4⋊C4—91no—
236C4⋊C4—184no—
237C4⋊C4—188no—
238C4⋊C4C2×#15711yescharacteristic
239C4⋊C4C2×#15711yescharacteristic
240C22⋊C4—92no—
241C22⋊C4—92no—
242C22⋊C4—92no—
243C22⋊C4—184no—
244C22⋊C4—362no—
245C22⋊C4C2×#15712yes—
246C42—92no—
247C42—92no—
248C42—92no—
249C42—184no—
250C42—364no—
251C42C2×#15712yes—
252C22×C3—24no—
253C22×C3—22no—
254C22×C3—42no—
255C22×C3—42no—
256C2×D3—64no—
257C2×D3—64no—
258C2×D3—62no—
259C2×D3—62no—
260C2×D3—64no—
261C2×D3—122no—
262C2×D3—122no—
263C2×D3—128no—
264C2×D3—128no—
265C3×C4—24no—
266C3×C4—24no—
267C3×C4—44no—
268C3×C4—44no—
269Dic3—64no—
270Dic3—64no—
271Dic3—124no—
272Dic3—124no—
273C32#234711yescharacteristic, complemented, Sylow
274C23—91no—
275C23—91no—
276C23—182no—
277C23—181no—
278C23—182no—
279C23—181no—
280C23C22×#15711yescharacteristic
281C2×C4—22no—
282C2×C4—91no—
283C2×C4—94no—
284C2×C4—94no—
285C2×C4—91no—
286C2×C4—92no—
287C2×C4—92no—
288C2×C4—182no—
289C2×C4—182no—
290C2×C4—184no—
291C2×C4—182no—
292C2×C4—182no—
293C2×C4—182no—
294C2×C4—182no—
295C2×C4—182no—
296C2×C4—182no—
297C2×C4—182no—
298C2×C4—184no—
299C2×C4—182no—
300C2×C4—184no—
301C2×C4—184no—
302C2×C4—182no—
303C2×C4C22×#15711yescharacteristic
304C2×C4C22×#15712yes—
305C2×C4C22×#15712yes—
306C2×C4C22×#15711yescharacteristic
307C2×C3—22no—
308C2×C3—22no—
309C2×C3—22no—
310C2×C3—44no—
311D3—64no—
312D3—64no—
313D3—124no—
314C22—21no—
315C22—21no—
316C22—21no—
317C22—92no—
318C22—92no—
319C22—91no—
320C22—91no—
321C22—181no—
322C22—181no—
323C22—181no—
324C22—362no—
325C22—362no—
326C22C23×#15711yescharacteristic
327C4—21no—
328C4—22no—
329C4—22no—
330C4—92no—
331C4—184no—
332C4—181no—
333C4—182no—
334C4—182no—
335C4—364no—
336C4—362no—
337C4#6428612yes—
338C3—22no—
339C2—41no—
340C2—92no—
341C2—92no—
342C2—361no—
343C2C2×#6428611yescharacteristic
344C2#41×#15711yescharacteristic
345C2#1059665011yescharacteristic
subgroupG/H
center, FrattiniC22C23×#157
commutator, socleC22×C32C23×C4
FittingC32×#117C4
prime radicalC23×C3⋊D3C23
cosocleC22×C3⋊D3C24
hypercenter#117#157
hypocenterC32#2347
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ #117

Complements

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

NH ≅ G/Ntype
4. #10593759C2semidirect
5. C4⋊C4×#157C2semidirect
7. #10593737C2semidirect
8. C4×C4⋊#157C2semidirect
16. C32×#117C4semidirect
17. #64135C4semidirect
18. #64101C4semidirect
19. #64101C4semidirect
23. #64086C4semidirect
24. #64081C4semidirect
172. #117#157semidirect
273. C32#2347semidirect

Maximal subgroups

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

subgroupindex
C3⋊D3×#1172
#105938122
C4×C22⋊#1572
#105937592
C4⋊C4×#1572
#105937472
#105937372
C4×C4⋊#1572
#23479