Finite Group Databasebeta

← #11803124

Subgroups — #11803124

Order 1152.

966 conjugacy classes of subgroups; only the 162 normal subgroups are shown.

normal subgroups only

This group has 966 conjugacy classes of subgroups — too many to draw. Only its 162 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
1C4×D4×C3⋊D3C211yesmaximal, characteristic
2#10593827C212yesmaximal
3#10593812C212yesmaximal, complemented
4#10593811C212yesmaximal, complemented
5#10593759C212yesmaximal, complemented
6#10593747C214yesmaximal, complemented
7C4×C4⋊#157C211yesmaximal, characteristic, complemented
8#10593733C211yesmaximal, characteristic, complemented
9C2×D4×C3⋊D3C2211yescharacteristic
10C22×C4×C3⋊D3C2212yes—
11C2×C22⋊#157C2214yes—
12C2×C22⋊#157C2214yes—
13C2×C4⋊#157C2212yes—
14C2×C4⋊#157C2214yes—
15C2×C4×#157C2212yes—
16C2×C4×#157C2212yes—
17C32×C4×D4C411yescharacteristic, complemented
18D4×C3⋊Dic3C411yescharacteristic, complemented
19C4×#638C412yescomplemented
20#64102C411yescharacteristic, complemented
21C4⋊C4×C3⋊D3C2211yescharacteristic
22#64090C412yescomplemented
23C22⋊C4×C3⋊D3C2212yes—
24C4×C4⋊(C3⋊D3)C411yescharacteristic, complemented
25C42×C3⋊D3C2211yescharacteristic
26#63781C2211yescharacteristic
27#63781C2212yes—
28#63781C2214yes—
29#63781C2211yescharacteristic
30#63781C2212yes—
31C4×D3×D4—62no—
32C23×C3⋊D3C2312yes—
33C22×#157C2312yes—
34C22×#157C2314yes—
35C22×#157C2312yes—
36C2×C32×D4C2×C411yescharacteristic
37C22×C32×C4C2×C412yes—
38C2×#638C2×C412yes—
39C22×C3⋊Dic3C2×C412yes—
40D4×C3⋊D3—24no—
41C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
42C2×C4×C3⋊D3—44no—
43C2×C4×C3⋊D3C2×C412yes—
44C2×C4×C3⋊D3C2×C412yes—
45C2×C4×C3⋊D3C2311yescharacteristic
46C2×C4×C3⋊D3C2312yes—
47C2×C4×C3⋊D3C2311yescharacteristic
48C2×C4×C3⋊D3C2311yescharacteristic
49C22⋊#157—44no—
50C22⋊#157—44no—
51C4⋊#157—24no—
52C4⋊#157—44no—
53C4×#157—24no—
54C4×#157—42no—
55C32×C4⋊C4C2×C411yescharacteristic
56C32×C22⋊C4C2×C412yes—
57C32×C42C2×C411yescharacteristic
58#3757C2×C412yes—
59#3752C2×C412yes—
60#3752C2×C412yes—
61C4⋊(C3⋊Dic3)C2×C411yescharacteristic
62#3750C2×C412yes—
63C4×C3⋊Dic3C2×C411yescharacteristic
64C4×C3⋊Dic3C2×C411yescharacteristic
65C4×C3⋊Dic3C2×C411yescharacteristic
66#2319—91nomaximal, Sylow
67C2×D3×D4—62no—
68C22×C4×D3—64no—
69C3×C4×D4—22no—
70D4×Dic3—62no—
71C4×#67—64no—
72#893—62no—
73D3×C4⋊C4—62no—
74#67⋊C4—64no—
75D3×C22⋊C4—64no—
76C4×D12—62no—
77C42×D3—62no—
78C23×C32C22×C412yes—
79C22×C3⋊D3—24no—
80C22×C3⋊D3—22no—
81C22×C3⋊D3—24no—
82C22×C3⋊D3—22no—
83C22×C3⋊D3C22×C412yes—
84C22×C3⋊D3C2411yescharacteristic
85C2×#157—22no—
86C2×#157—22no—
87C2×#157—24no—
88C2×#157—24no—
89C2×#157—22no—
90C2×#157—24no—
91C2×#157—22no—
92C2×#157—22no—
93C2×#157—22no—
94C32×D4—22no—
95C2×C32×C4—42no—
96C2×C32×C4C22×C411yescharacteristic
97C2×C32×C4C22×C411yescharacteristic
98C2×C32×C4C22×C412yes—
99C2×C32×C4C22×C411yescharacteristic
100#638—24no—
101C2×C3⋊Dic3—42no—
102C2×C3⋊Dic3C22×C411yescharacteristic
103C2×C3⋊Dic3C22×C411yescharacteristic
104C2×C3⋊Dic3C22×C412yes—
105C2×C3⋊Dic3C22×C411yescharacteristic
106C4⋊(C3⋊D3)—22no—
107C4×C3⋊D3—22no—
108C4×C3⋊D3—21no—
109C4×C3⋊D3—24no—
110C4×C3⋊D3—21no—
111C4×C3⋊D3—42no—
112C4×C3⋊D3—42no—
113C4×C3⋊D3#4114yes—
114C2×C4×D4—91no—
115#390—92no—
116#389—92no—
117#388—94no—
118#381—92no—
119#380—92no—
120C4×C4⋊C4—91no—
121#376—91no—
122C23×D3—64no—
123C2×C3×D4—22no—
124C22×C3×C4—24no—
125C2×#67—64no—
126C22×Dic3—64no—
127D3×D4—616no—
128C2×D12—62no—
129C2×C4×D3—62no—
130C2×C4×D3—62no—
131C2×C4×D3—62no—
132C2×C4×D3—64no—
133C2×C4×D3—64no—
134C2×C4×D3—64no—
135C2×C4×D3—1216no—
136C3×C4⋊C4—22no—
137C3×C22⋊C4—24no—
138C3×C42—22no—
139#217—64no—
140(C2×D3)⋊C4—64no—
141(C2×D3)⋊C4—64no—
142C4⋊Dic3—62no—
143Dic3⋊C4—64no—
144C4×Dic3—62no—
145C4×Dic3—62no—
146C4×Dic3—62no—
147C22×C32—22no—
148C22×C32—22no—
149C22×C32—22no—
150C22×C32C23×C411yescharacteristic
151C2×C3⋊D3—22no—
152C2×C3⋊D3—22no—
153C2×C3⋊D3—22no—
154C2×C3⋊D3—44no—
155C2×C3⋊D3—44no—
156C2×C3⋊D3C2×#4112yes—
157C2×C3⋊D3H(5,𝔽2)11yescharacteristic
158C2×C3⋊D3H(5,𝔽2)12yes—
159C2×C3⋊D32−1+411yescharacteristic
160#157—42no—
161#157—44no—
162#157—42no—
163C32×C4—21no—
164C32×C4—22no—
165C32×C4—21no—
166C32×C4#11712yes—
167C3⋊Dic3—21no—
168C3⋊Dic3—22no—
169C3⋊Dic3—21no—
170C3⋊Dic3#11712yes—
171C22×D4—91no—
172C23×C4—92no—
173C4×D4—91no—
174C4×D4—92no—
175C4×D4—91no—
176C4×D4—92no—
177C4×D4—91no—
178C4×D4#15711yescharacteristic, complemented
179C2×C4⋊C4—91no—
180C2×C4⋊C4—92no—
181C2×C4⋊C4—94no—
182C2×C22⋊C4—92no—
183C2×C22⋊C4—94no—
184C2×C22⋊C4—94no—
185C2×C42—91no—
186C2×C42—92no—
187C2×C42—92no—
188#95—91no—
189#95—91no—
190#95—92no—
191#95—92no—
192#95—94no—
193C23×C3—24no—
194C22×D3—62no—
195C22×D3—64no—
196C22×D3—616no—
197C22×D3—128no—
198C22×D3—124no—
199C22×D3—124no—
200C3×D4—28no—
201C2×C3×C4—22no—
202C2×C3×C4—22no—
203C2×C3×C4—22no—
204C2×C3×C4—24no—
205C2×C3×C4—48no—
206#67—616no—
207C2×Dic3—62no—
208C2×Dic3—62no—
209C2×Dic3—62no—
210C2×Dic3—64no—
211C2×Dic3—128no—
212D12—68no—
213C4×D3—68no—
214C4×D3—68no—
215C4×D3—122no—
216C4×D3—122no—
217C4×D3—128no—
218C4×D3—128no—
219C4×D3—128no—
220C2×C32—42no—
221C2×C32C2×#11711yescharacteristic
222C2×C32#51811yescharacteristic
223C2×C32#52011yescharacteristic
224C3⋊D3—42no—
225C3⋊D3#54012yes—
226C3⋊D3#54212yes—
227C24—92no—
228C2×D4—92no—
229C2×D4—91no—
230C2×D4—184no—
231C2×D4C2×#15711yescharacteristic
232C22×C4—91no—
233C22×C4—92no—
234C22×C4—91no—
235C22×C4—91no—
236C22×C4—92no—
237C22×C4—92no—
238C22×C4—92no—
239C22×C4—92no—
240C22×C4—92no—
241C22×C4—94no—
242C22×C4—364no—
243C22×C4C2×#15712yes—
244C4⋊C4—92no—
245C4⋊C4—91no—
246C4⋊C4—184no—
247C4⋊C4—364no—
248C4⋊C4C2×#15711yescharacteristic
249C22⋊C4—92no—
250C22⋊C4—92no—
251C22⋊C4—92no—
252C22⋊C4—364no—
253C22⋊C4—364no—
254C22⋊C4C2×#15712yes—
255C42—91no—
256C42—91no—
257C42—91no—
258C42—184no—
259C42—362no—
260C42C2×#15711yescharacteristic
261C22×C3—28no—
262C22×C3—22no—
263C22×C3—44no—
264C22×C3—44no—
265C2×D3—64no—
266C2×D3—64no—
267C2×D3—62no—
268C2×D3—62no—
269C2×D3—68no—
270C2×D3—124no—
271C2×D3—124no—
272C2×D3—1216no—
273C2×D3—1216no—
274C3×C4—24no—
275C3×C4—24no—
276C3×C4—44no—
277C3×C4—42no—
278Dic3—64no—
279Dic3—64no—
280Dic3—124no—
281Dic3—122no—
282C32#231911yescharacteristic, complemented, Sylow
283C23—91no—
284C23—92no—
285C23—182no—
286C23—184no—
287C23—184no—
288C23—182no—
289C23C22×#15712yes—
290D4—22no—
291D4—184no—
292D4—182no—
293C2×C4—42no—
294C2×C4—91no—
295C2×C4—94no—
296C2×C4—91no—
297C2×C4—91no—
298C2×C4—92no—
299C2×C4—181no—
300C2×C4—184no—
301C2×C4—182no—
302C2×C4—181no—
303C2×C4—182no—
304C2×C4—182no—
305C2×C4—184no—
306C2×C4—182no—
307C2×C4—182no—
308C2×C4—184no—
309C2×C4—184no—
310C2×C4—182no—
311C2×C4—182no—
312C2×C4—362no—
313C2×C4—362no—
314C2×C4—362no—
315C2×C4C22×#15711yescharacteristic
316C2×C4C22×#15711yescharacteristic
317C2×C4C22×#15712yes—
318C2×C4C22×#15711yescharacteristic
319C2×C3—22no—
320C2×C3—22no—
321C2×C3—22no—
322C2×C3—48no—
323D3—64no—
324D3—64no—
325D3—128no—
326C22—22no—
327C22—22no—
328C22—22no—
329C22—92no—
330C22—92no—
331C22—91no—
332C22—91no—
333C22—182no—
334C22—182no—
335C22—182no—
336C22—364no—
337C22—364no—
338C22C23×#15711yescharacteristic
339C4—21no—
340C4—22no—
341C4—21no—
342C4—92no—
343C4—181no—
344C4—182no—
345C4—181no—
346C4—362no—
347C4—364no—
348C4—362no—
349C4#6428612yes—
350C3—22no—
351C2—42no—
352C2—92no—
353C2—92no—
354C2—362no—
355C2C2×#6428611yescharacteristic
356C2#1059664211yescharacteristic
357C2#1059665011yescharacteristic
subgroupG/H
center, FrattiniC22C23×#157
commutator, socleC22×C32C23×C4
FittingC32×C4×D4C4
prime radicalC2×D4×C3⋊D3C22
cosocleC22×C3⋊D3C24
hypercenterC4×D4#157
hypocenterC32#2319
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
3. #10593812C2semidirect
4. #10593811C2semidirect
5. #10593759C2semidirect
6. #10593747C2semidirect
7. C4×C4⋊#157C2semidirect
8. #10593733C2semidirect
17. C32×C4×D4C4semidirect
18. D4×C3⋊Dic3C4semidirect
19. C4×#638C4semidirect
20. #64102C4semidirect
22. #64090C4semidirect
24. C4×C4⋊(C3⋊D3)C4semidirect
178. C4×D4#157semidirect
282. C32#2319semidirect

Maximal subgroups

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

subgroupindex
C4×D4×C3⋊D32
#105938272
#105938122
#105938112
#105937592
#105937472
C4×C4⋊#1572
#105937332
#23199