Finite Group Databasebeta

← #11783281

Subgroups — #11783281

Order 1152.

866 conjugacy classes of subgroups; only the 138 normal subgroups are shown.

normal subgroups only

This group has 866 conjugacy classes of subgroups — too many to draw. Only its 138 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
1C2×#64286C211yesmaximal, characteristic
2C2×#64283C211yesmaximal, characteristic
3C2×C4⋊C4×C3⋊D3C211yesmaximal, characteristic
4#10590163C214yesmaximal, complemented
5C22×C4×C3⋊D3—21no—
6C22×C4×C3⋊D3C2211yescharacteristic
7C2×C22⋊#157—21no—
8C2×#3792—21no—
9#64286—22no—
10#64286C414yescomplemented
11C2×C4⋊#157C2212yes—
12C2×C4×#157—21no—
13#64283—22no—
14#64283C414yescomplemented
15C2×#3788—21no—
16C2×#3787C2212yes—
17C2×C32×C4⋊C4C411yescharacteristic, complemented
18C2×C4⋊(C3⋊Dic3)C411yescharacteristic, complemented
19C2×#3750—21no—
20C4⋊C4×C3⋊D3—21no—
21C4⋊C4×C3⋊D3—21no—
22C4⋊C4×C3⋊D3C412yescomplemented
23C4⋊C4×C3⋊D3C2212yes—
24C2×D3×C4⋊C4—62no—
25C23×C3⋊D3D411yescharacteristic
26C22×#157—22no—
27C22×C32×C4—21no—
28C22×C32×C4C2×C411yescharacteristic
29C22×C3⋊Dic3—21no—
30C22×C3⋊Dic3D411yescharacteristic
31C2×C4×C3⋊D3—22no—
32C2×C4×C3⋊D3—22no—
33C2×C4×C3⋊D3—44no—
34C2×C4×C3⋊D3C2×C411yescharacteristic
35C2×C4×C3⋊D3C2×C412yes—
36C2×C4×C3⋊D3C2×C412yes—
37C2×C4×C3⋊D3D411yescharacteristic
38C2×C4×C3⋊D3D411yescharacteristic
39C2×C4×C3⋊D3D412yes—
40C2×C4×C3⋊D3Q812yes—
41C2×C4×C3⋊D3C2311yescharacteristic
42C22⋊#157—24no—
43#3792—24no—
44C2×#622—22no—
45C4⋊#157—22no—
46C4⋊#157C2×C414yescomplemented
47C4×#157—24no—
48#3788—24no—
49#3787—22no—
50#3787C2×C414yescomplemented
51C32×C4⋊C4—21no—
52C32×C4⋊C4C2×C412yes—
53C4⋊(C3⋊Dic3)—21no—
54C4⋊(C3⋊Dic3)C2×C412yes—
55#3750—22no—
56#3750—22no—
57#1736—91nomaximal, Sylow
58C22×C4×D3—62no—
59C22×C4×D3—64no—
60C2×C3×C4⋊C4—22no—
61C2×C4⋊Dic3—62no—
62C2×Dic3⋊C4—64no—
63D3×C4⋊C4—64no—
64D3×C4⋊C4—64no—
65D3×C4⋊C4—64no—
66D3×C4⋊C4—64no—
67C23×C32C22⋊C411yescharacteristic
68C22×C3⋊D3—22no—
69C22×C3⋊D3—22no—
70C22×C3⋊D3C22⋊C411yescharacteristic
71C22×C3⋊D3C22⋊C412yes—
72C22×C3⋊D3C4⋊C412yes—
73C22×C3⋊D3C2×D411yescharacteristic
74C2×#157—24no—
75C2×#157—42no—
76C2×#157—42no—
77C2×C32×C4—22no—
78C2×C32×C4—42no—
79C2×C32×C4C4212yes—
80C2×C32×C4C22⋊C411yescharacteristic
81C2×C32×C4C4⋊C412yes—
82C2×C32×C4C22×C411yescharacteristic
83C2×C3⋊Dic3—22no—
84C2×C3⋊Dic3—42no—
85C2×C3⋊Dic3C22⋊C411yescharacteristic
86C2×C3⋊Dic3C22⋊C412yes—
87C2×C3⋊Dic3C4⋊C412yes—
88C2×C3⋊Dic3C2×D411yescharacteristic
89C4×C3⋊D3—44no—
90C4×C3⋊D3—44no—
91C4×C3⋊D3C4212yes—
92C4×C3⋊D3C22⋊C412yes—
93C4×C3⋊D3C22⋊C412yes—
94C4×C3⋊D3C4⋊C412yes—
95C4×C3⋊D3C4⋊C412yes—
96C4×C3⋊D3C4⋊C412yes—
97C4×C3⋊D3C22×C411yescharacteristic
98C4×C3⋊D3C22×C411yescharacteristic
99C4×C3⋊D3C2×D411yescharacteristic
100C4×C3⋊D3C2×Q811yescharacteristic
101#622—24no—
102C22×M16—91no—
103C2×#117—91no—
104C22×C4⋊C4—91no—
105#340—94no—
106C23×D3—62no—
107C22×C3×C4—24no—
108C22×C3×C4—22no—
109C22×Dic3—62no—
110C22×Dic3—64no—
111C2×C4×D3—62no—
112C2×C4×D3—62no—
113C2×C4×D3—62no—
114C2×C4×D3—62no—
115C2×C4×D3—64no—
116C2×C4×D3—64no—
117C2×C4×D3—64no—
118C2×C4×D3—64no—
119C2×C4×D3—68no—
120C2×C4×D3—68no—
121C2×C4×D3—1216no—
122C3×C4⋊C4—24no—
123C3×C4⋊C4—24no—
124C4⋊Dic3—64no—
125C4⋊Dic3—64no—
126Dic3⋊C4—68no—
127Dic3⋊C4—68no—
128C22×C32—21no—
129C22×C32—21no—
130C22×C32#9512yes—
131C22×C32C2×C22⋊C411yescharacteristic
132C2×C3⋊D3—21no—
133C2×C3⋊D3—21no—
134C2×C3⋊D3—24no—
135C2×C3⋊D3—24no—
136C2×C3⋊D3#9512yes—
137C2×C3⋊D3C2×C22⋊C411yescharacteristic
138C2×C3⋊D3C2×C4⋊C411yescharacteristic
139C2×C3⋊D3AGL(1,ℤ/8)12yes—
140C2×C3⋊D3#13712yes—
141#157—44no—
142C32×C4—42no—
143C32×C4#9512yes—
144C32×C4C2×C4211yescharacteristic
145C32×C4C2×C4⋊C411yescharacteristic
146C3⋊Dic3—42no—
147C3⋊Dic3#9512yes—
148C3⋊Dic3C2×C22⋊C411yescharacteristic
149C3⋊Dic3C2×C4⋊C411yescharacteristic
150C23×C4—91no—
151C23×C4—181no—
152C2×M16—94no—
153C2×M16—181no—
154C2×M16—182no—
155C2×M16—181no—
156C22×C8—92no—
157#117—94no—
158#117—182no—
159C2×C4⋊C4—92no—
160C2×C4⋊C4—91no—
161C2×C4⋊C4—92no—
162C2×C4⋊C4—92no—
163C2×C4⋊C4—181no—
164C2×C4⋊C4—181no—
165C2×C4⋊C4—181no—
166C2×C4⋊C4#15711yescharacteristic, complemented
167C2×C22⋊C4—181no—
168C2×C42—181no—
169C23×C3—22no—
170C22×D3—62no—
171C22×D3—64no—
172C22×D3—64no—
173C22×D3—62no—
174C22×D3—68no—
175C22×D3—68no—
176C2×C3×C4—28no—
177C2×C3×C4—22no—
178C2×C3×C4—24no—
179C2×C3×C4—24no—
180C2×C3×C4—22no—
181C2×C3×C4—48no—
182C2×Dic3—62no—
183C2×Dic3—64no—
184C2×Dic3—64no—
185C2×Dic3—62no—
186C2×Dic3—68no—
187C2×Dic3—128no—
188C4×D3—64no—
189C4×D3—64no—
190C4×D3—64no—
191C4×D3—64no—
192C4×D3—64no—
193C4×D3—64no—
194C4×D3—62no—
195C4×D3—62no—
196C4×D3—62no—
197C4×D3—62no—
198C4×D3—1216no—
199C4×D3—1216no—
200C2×C32—22no—
201C2×C32C2×#9511yescharacteristic
202C2×C32#41811yescharacteristic
203C2×C32#41911yescharacteristic
204C3⋊D3—22no—
205C3⋊D3#41712yes—
206C3⋊D3#42812yes—
207C24—91no—
208C22×C4—21no—
209C22×C4—91no—
210C22×C4—91no—
211C22×C4—91no—
212C22×C4—92no—
213C22×C4—92no—
214C22×C4—92no—
215C22×C4—92no—
216C22×C4—91no—
217C22×C4—91no—
218C22×C4—182no—
219C22×C4—182no—
220C22×C4—182no—
221C22×C4—181no—
222C22×C4—364no—
223C22×C4C2×#15711yescharacteristic
224M16—184no—
225M16—184no—
226C2×C8—94no—
227C2×C8—182no—
228C2×C8—182no—
229C4⋊C4—21no—
230C4⋊C4—94no—
231C4⋊C4—92no—
232C4⋊C4—182no—
233C4⋊C4—182no—
234C4⋊C4—182no—
235C4⋊C4—181no—
236C4⋊C4C2×#15712yes—
237C22⋊C4—184no—
238C42—184no—
239C22×C3—24no—
240C22×C3—24no—
241C22×C3—24no—
242C22×C3—22no—
243C2×D3—64no—
244C2×D3—62no—
245C2×D3—62no—
246C2×D3—64no—
247C2×D3—64no—
248C2×D3—64no—
249C2×D3—616no—
250C2×D3—616no—
251C2×D3—64no—
252C3×C4—22no—
253C3×C4—22no—
254C3×C4—24no—
255C3×C4—48no—
256Dic3—64no—
257Dic3—62no—
258Dic3—62no—
259Dic3—128no—
260C32#173611yescharacteristic, complemented, Sylow
261C23—91no—
262C23—92no—
263C23—92no—
264C23—91no—
265C23—182no—
266C23—182no—
267C23C22⋊#15711yescharacteristic
268C2×C4—22no—
269C2×C4—42no—
270C2×C4—92no—
271C2×C4—92no—
272C2×C4—91no—
273C2×C4—91no—
274C2×C4—91no—
275C2×C4—91no—
276C2×C4—92no—
277C2×C4—91no—
278C2×C4—91no—
279C2×C4—92no—
280C2×C4—92no—
281C2×C4—92no—
282C2×C4—92no—
283C2×C4—92no—
284C2×C4—184no—
285C2×C4—182no—
286C2×C4—364no—
287C2×C4—364no—
288C2×C4—362no—
289C2×C4—362no—
290C2×C4—362no—
291C2×C4C4×#15712yes—
292C2×C4C4⋊#15712yes—
293C2×C4C22⋊#15711yescharacteristic
294C2×C4C22×#15711yescharacteristic
295C8—184no—
296C2×C3—28no—
297C2×C3—22no—
298C2×C3—22no—
299C2×C3—22no—
300D3—64no—
301D3—64no—
302D3—68no—
303C22—21no—
304C22—21no—
305C22—91no—
306C22—91no—
307C22—92no—
308C22—92no—
309C22—92no—
310C22—184no—
311C22—184no—
312C22—181no—
313C22—181no—
314C22#6378112yes—
315C22C2×C22⋊#15711yescharacteristic
316C4—42no—
317C4—91no—
318C4—92no—
319C4—91no—
320C4—364no—
321C4—362no—
322C4#6378112yes—
323C4C2×C4×#15711yescharacteristic
324C4C2×C4⋊#15711yescharacteristic
325C3—22no—
326C2—22no—
327C2—92no—
328C2—92no—
329C2—182no—
330C2C2×#6378111yescharacteristic
331C2#1059381411yescharacteristic
332C2#1059382911yescharacteristic
subgroupG/H
centerC22C2×C22⋊#157
commutatorC32×C4C2×C42
FrattiniC2×C4C22×#157
FittingC2×C32×C4⋊C4C4
socleC22×C32C2×C22⋊C4
prime radicalC23×C3⋊D3D4
cosocleC2×C4×C3⋊D3C23
hypercenterC2×C4⋊C4#157
hypocenterC32#1736
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
4. #10590163C2semidirect
10. #64286C4semidirect
14. #64283C4semidirect
17. C2×C32×C4⋊C4C4semidirect
18. C2×C4⋊(C3⋊Dic3)C4semidirect
22. C4⋊C4×C3⋊D3C4semidirect
46. C4⋊#157C2×C4semidirect
50. #3787C2×C4semidirect
166. C2×C4⋊C4#157semidirect
260. C32#1736semidirect

Maximal subgroups

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

subgroupindex
C2×#642862
C2×#642832
C2×C4⋊C4×C3⋊D32
#105901632
#17369