Finite Group Databasebeta

← #11785833

Subgroups — #11785833

Order 1152.

566 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 566 conjugacy classes of subgroups — too many to draw. Only its 71 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#10594969C211yesmaximal, characteristic
2#10593812C211yesmaximal, characteristic
3#10591152C211yesmaximal, characteristic
4#10590049C212yesmaximal, complemented
5#10590049C212yesmaximal, complemented
6C22×C4×C3⋊D3C2211yescharacteristic
7C2×C22⋊#157—21no—
8C2×C4⋊#157C2212yes—
9C3×#926—21no—
10#63974—21no—
11#63957C412yescomplemented
12#63900C2211yescharacteristic
13#63900C2211yescharacteristic
14C4×#624—21no—
15#63874C412yescomplemented
16#63849—21no—
17C2×#3710C2212yes—
18#63781—21no—
19C3×#830—21no—
20#63557—21no—
21D3×#117—61no—
22D3×C22⋊C8—61no—
23C23×C3⋊D3D411yescharacteristic
24C22×#157—22no—
25C22×C32×C4D411yescharacteristic
26C22×C3⋊Dic3C2×C411yescharacteristic
27C2×C4×C3⋊D3—24no—
28C2×C4×C3⋊D3C2×C411yescharacteristic
29C2×C4×C3⋊D3D411yescharacteristic
30C2×C4×C3⋊D3D411yescharacteristic
31C2×C4×C3⋊D3C2311yescharacteristic
32C2×#624—21no—
33C2×#624—21no—
34C22⋊#157—42no—
35C4⋊#157—24no—
36C3×#217—22no—
37C3×C4⋊Dic3—21no—
38C3×C4⋊Dic3—21no—
39C3×C4×Dic3—22no—
40C2×C3×C3⋊C8—22no—
41#3724C2×C412yes—
42#3724C2×C412yes—
43#3722—22no—
44Dic32—22no—
45#3710—24no—
46#1825—91nomaximal, Sylow
47C22×C4×D3—61no—
48C22×C4×D3—61no—
49C3×#117—61no—
50#926—21no—
51C2×D3×C8—62no—
52#892—61no—
53#892—61no—
54D3×C4⋊C4—61no—
55D3×C4⋊C4—61no—
56D3×C22⋊C4—62no—
57#877—62no—
58#872—62no—
59C42×D3—62no—
60C3×C22⋊C8—61no—
61#830—21no—
62(C2×D3)⋊C8—62no—
63C23×C32C22⋊C411yescharacteristic
64C22×C3⋊D3—22no—
65C22×C3⋊D3—22no—
66C22×C3⋊D3—21no—
67C22×C3⋊D3—21no—
68C22×C3⋊D3C22⋊C411yescharacteristic
69C22×C3⋊D3C2×D411yescharacteristic
70C2×#157—42no—
71C2×#157—42no—
72C2×#157—42no—
73C2×C32×C4—22no—
74C2×C32×C4C22⋊C411yescharacteristic
75C2×C32×C4C2×D411yescharacteristic
76C2×C3⋊Dic3—22no—
77C2×C3⋊Dic3C22⋊C411yescharacteristic
78C2×C3⋊Dic3C22×C411yescharacteristic
79C4×C3⋊D3—22no—
80C4×C3⋊D3—22no—
81C4×C3⋊D3—22no—
82C4×C3⋊D3#4114yes—
83C2×C3×Dic3—22no—
84C2×C3×Dic3—22no—
85#624—42no—
86#624—41no—
87#624—41no—
88C3×C3⋊C8—42no—
89C2×#117—91no—
90C2×C22⋊C8—91no—
91#380—91no—
92#340—92no—
93#340—92no—
94C23×D3—61no—
95C23×D3—61no—
96C22×C3×C4—21no—
97C22×C3×C4—21no—
98C22×Dic3—61no—
99C22×Dic3—61no—
100C2×C4×D3—61no—
101C2×C4×D3—61no—
102C2×C4×D3—61no—
103C2×C4×D3—61no—
104C2×C4×D3—61no—
105C2×C4×D3—61no—
106C2×C4×D3—61no—
107C2×C4×D3—61no—
108C2×C4×D3—68no—
109C2×C4×D3—62no—
110C2×C4×D3—62no—
111C2×C4×D3—124no—
112C2×C3×C8—62no—
113C3×C4⋊C4—61no—
114C3×C4⋊C4—61no—
115C3×C22⋊C4—62no—
116C3×C42—62no—
117#217—22no—
118(C2×D3)⋊C4—62no—
119(C2×D3)⋊C4—62no—
120C4⋊Dic3—21no—
121C4⋊Dic3—21no—
122Dic3⋊C4—62no—
123Dic3⋊C4—62no—
124C4×Dic3—22no—
125C4×Dic3—62no—
126C4×Dic3—62no—
127C2×C3⋊C8—22no—
128D3×C8—124no—
129C22×C32—21no—
130C22×C32—21no—
131C22×C32—21no—
132C22×C32C2×C22⋊C411yescharacteristic
133C2×C3⋊D3—21no—
134C2×C3⋊D3—21no—
135C2×C3⋊D3—21no—
136C2×C3⋊D3—42no—
137C2×C3⋊D3—42no—
138C2×C3⋊D3#12312yes—
139C2×C3⋊D3#13512yes—
140C2×C3⋊D3AGL(1,ℤ/8)11yescharacteristic
141C2×C3⋊D3#13711yescharacteristic
142#157—82no—
143C32×C4—21no—
144C32×C4#12312yes—
145C3⋊Dic3—21no—
146C3⋊Dic3#11712yes—
147C3×Dic3—42no—
148C3×Dic3—42no—
149C23×C4—91no—
150C22×C8—92no—
151#117—61no—
152#117—92no—
153#117—92no—
154#117—181no—
155C2×C4⋊C4—91no—
156C2×C4⋊C4—91no—
157C2×C4⋊C4—92no—
158C2×C22⋊C4—181no—
159C2×C22⋊C4—181no—
160C2×C42—181no—
161C22⋊C8—61no—
162C22⋊C8—181no—
163#95—181no—
164C23×C3—21no—
165C23×C3—21no—
166C22×D3—61no—
167C22×D3—61no—
168C22×D3—61no—
169C22×D3—61no—
170C22×D3—64no—
171C22×D3—64no—
172C22×D3—122no—
173C22×D3—121no—
174C22×D3—121no—
175C22×D3—122no—
176C22×D3—121no—
177C22×D3—121no—
178C2×C3×C4—24no—
179C2×C3×C4—21no—
180C2×C3×C4—21no—
181C2×C3×C4—21no—
182C2×C3×C4—21no—
183C2×C3×C4—42no—
184C2×C3×C4—62no—
185C2×C3×C4—62no—
186C2×Dic3—22no—
187C2×Dic3—22no—
188C2×Dic3—61no—
189C2×Dic3—61no—
190C2×Dic3—61no—
191C2×Dic3—61no—
192C2×Dic3—64no—
193C2×Dic3—122no—
194C4×D3—64no—
195C4×D3—64no—
196C4×D3—64no—
197C4×D3—64no—
198C4×D3—64no—
199C4×D3—122no—
200C4×D3—122no—
201C4×D3—122no—
202C4×D3—124no—
203C4×D3—122no—
204C4×D3—122no—
205C3×C8—122no—
206C3⋊C8—42no—
207C2×C32—41no—
208C2×C32#38111yescharacteristic
209C2×C32#41611yescharacteristic
210C2×C32#41711yescharacteristic
211C3⋊D3—41no—
212C3⋊D3#48212yes—
213C3⋊D3#48512yes—
214C24—91no—
215C22×C4—91no—
216C22×C4—91no—
217C22×C4—91no—
218C22×C4—91no—
219C22×C4—91no—
220C22×C4—184no—
221C22×C4—181no—
222C22×C4—181no—
223C22×C4—182no—
224C22×C4GO+(4,𝔽2)11yescharacteristic
225C2×C8—62no—
226C2×C8—184no—
227C4⋊C4—61no—
228C4⋊C4—61no—
229C4⋊C4—92no—
230C4⋊C4—92no—
231C4⋊C4—184no—
232C22⋊C4—62no—
233C22⋊C4—182no—
234C22⋊C4—362no—
235C42—62no—
236C42—182no—
237C22×C3—22no—
238C22×C3—22no—
239C22×C3—21no—
240C22×C3—21no—
241C22×C3—41no—
242C22×C3—41no—
243C22×C3—41no—
244C22×C3—41no—
245C2×D3—62no—
246C2×D3—62no—
247C2×D3—62no—
248C2×D3—61no—
249C2×D3—61no—
250C2×D3—62no—
251C2×D3—61no—
252C2×D3—61no—
253C2×D3—62no—
254C2×D3—62no—
255C2×D3—121no—
256C2×D3—121no—
257C2×D3—121no—
258C2×D3—121no—
259C2×D3—124no—
260C2×D3—124no—
261C2×D3—124no—
262C2×D3—124no—
263C3×C4—22no—
264C3×C4—22no—
265C3×C4—22no—
266C3×C4—41no—
267C3×C4—122no—
268C3×C4—122no—
269Dic3—42no—
270Dic3—42no—
271Dic3—62no—
272Dic3—62no—
273Dic3—62no—
274Dic3—121no—
275C32#182511yescharacteristic, complemented, Sylow
276C23—91no—
277C23—91no—
278C23—181no—
279C23—182no—
280C23—182no—
281C23—181no—
282C23D32⋊C411yescharacteristic
283C2×C4—22no—
284C2×C4—62no—
285C2×C4—62no—
286C2×C4—91no—
287C2×C4—94no—
288C2×C4—91no—
289C2×C4—182no—
290C2×C4—182no—
291C2×C4—182no—
292C2×C4—182no—
293C2×C4—362no—
294C2×C4—361no—
295C2×C4—361no—
296C2×C4—362no—
297C2×C4—362no—
298C2×C4—362no—
299C2×C4D32⋊C411yescharacteristic
300C2×C4C2×GO+(4,𝔽2)11yescharacteristic
301C8—122no—
302C2×C3—21no—
303C2×C3—21no—
304C2×C3—21no—
305C2×C3—21no—
306C2×C3—21no—
307C2×C3—21no—
308C2×C3—42no—
309C2×C3—42no—
310D3—62no—
311D3—62no—
312D3—62no—
313D3—62no—
314D3—122no—
315D3—122no—
316C22—21no—
317C22—21no—
318C22—21no—
319C22—92no—
320C22—91no—
321C22—91no—
322C22—92no—
323C22—181no—
324C22—181no—
325C22—181no—
326C22—362no—
327C22—362no—
328C22C2×D32⋊C411yescharacteristic
329C4—21no—
330C4—92no—
331C4—122no—
332C4—122no—
333C4—181no—
334C4—722no—
335C4#6423312yes—
336C3—21no—
337C3—21no—
338C2—41no—
339C2—92no—
340C2—92no—
341C2—361no—
342C2#1059331711yescharacteristic
343C2#1059331911yescharacteristic
344C2#1059348811yescharacteristic
subgroupG/H
centerC22C2×D32⋊C4
commutatorC2×C3⋊Dic3C22×C4
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC22×C32C2×C22⋊C4
prime radicalC23×C3⋊D3D4
cosocleC2×C4×C3⋊D3C23
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32#1825
LCSG ▷ C2×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
4. #10590049C2semidirect
5. #10590049C2semidirect
11. #63957C4semidirect
15. #63874C4semidirect
275. C32#1825semidirect

Maximal subgroups

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

subgroupindex
#105949692
#105938122
#105911522
#105900492
#18259