Finite Group Databasebeta

← #11785800

Subgroups — #11785800

Order 1152.

654 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 654 conjugacy classes of subgroups — too many to draw. Only its 81 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×#63900C211yesmaximal, characteristic
2#10593812C211yesmaximal, characteristic
3#10591152C211yesmaximal, characteristic
4#10590049C214yesmaximal, complemented
5C22×C4×C3⋊D3C2211yescharacteristic
6C22×#624—21no—
7C2×C22⋊#157—21no—
8C2×C4⋊#157C2212yes—
9C2×C3×C4⋊Dic3—21no—
10C2×#3724C412yescomplemented
11#63900—21no—
12#63900—21no—
13#63900C412yescomplemented
14#63900C2212yes—
15C2×#3710C2212yes—
16#63781—21no—
17C3×#830—21no—
18#63557—21no—
19C2×D3×C4⋊C4—61no—
20D3×C22⋊C8—61no—
21C23×C3⋊D3D411yescharacteristic
22C22×#157—22no—
23C22×C32×C4D411yescharacteristic
24C22×C3⋊Dic3C2×C411yescharacteristic
25C2×C4×C3⋊D3—24no—
26C2×C4×C3⋊D3C2×C411yescharacteristic
27C2×C4×C3⋊D3D411yescharacteristic
28C2×C4×C3⋊D3D411yescharacteristic
29C2×C4×C3⋊D3C2311yescharacteristic
30C22×C3×Dic3—22no—
31C2×#624—22no—
32C2×#624—22no—
33C2×#624—44no—
34C22⋊#157—42no—
35C4⋊#157—24no—
36C3×C4⋊Dic3—22no—
37C3×C4⋊Dic3—22no—
38C2×C3×C3⋊C8—22no—
39#3724—22no—
40#3724C2×C414yes—
41#3710—24no—
42#1824—91nomaximal, Sylow
43C22×C4×D3—61no—
44C22×C4×D3—61no—
45C22×C4×D3—62no—
46C2×C3×C4⋊C4—61no—
47C2×C4⋊Dic3—21no—
48C2×Dic3⋊C4—62no—
49C2×D3×C8—62no—
50D3×C4⋊C4—62no—
51D3×C4⋊C4—62no—
52D3×C4⋊C4—62no—
53D3×C4⋊C4—62no—
54C3×C22⋊C8—61no—
55#830—21no—
56(C2×D3)⋊C8—62no—
57C23×C32C22⋊C411yescharacteristic
58C22×C3⋊D3—22no—
59C22×C3⋊D3—22no—
60C22×C3⋊D3C22⋊C411yescharacteristic
61C22×C3⋊D3SD1612yes—
62C22×C3⋊D3Q1612yes—
63C22×C3⋊D3C2×D411yescharacteristic
64C2×#157—42no—
65C2×#157—42no—
66C2×#157—42no—
67C2×C32×C4—22no—
68C2×C32×C4C22⋊C411yescharacteristic
69C2×C32×C4C2×D411yescharacteristic
70C2×C3⋊Dic3—22no—
71C2×C3⋊Dic3C22⋊C411yescharacteristic
72C2×C3⋊Dic3C22×C411yescharacteristic
73C4×C3⋊D3—22no—
74C4×C3⋊D3—22no—
75C4×C3⋊D3—22no—
76C4×C3⋊D3#4114yes—
77C2×C3×Dic3—24no—
78C2×C3×Dic3—44no—
79#624—44no—
80#624—44no—
81C3×C3⋊C8—42no—
82C22×C4⋊C4—91no—
83C2×C22⋊C8—91no—
84#380—91no—
85#340—94no—
86C23×D3—61no—
87C23×D3—61no—
88C22×C3×C4—21no—
89C22×C3×C4—21no—
90C22×C3×C4—62no—
91C22×Dic3—22no—
92C22×Dic3—61no—
93C22×Dic3—61no—
94C2×C4×D3—61no—
95C2×C4×D3—61no—
96C2×C4×D3—61no—
97C2×C4×D3—61no—
98C2×C4×D3—61no—
99C2×C4×D3—61no—
100C2×C4×D3—61no—
101C2×C4×D3—61no—
102C2×C4×D3—68no—
103C2×C4×D3—64no—
104C2×C4×D3—64no—
105C2×C4×D3—124no—
106C2×C4×D3—128no—
107C2×C3×C8—62no—
108C3×C4⋊C4—62no—
109C3×C4⋊C4—62no—
110C4⋊Dic3—22no—
111C4⋊Dic3—22no—
112Dic3⋊C4—64no—
113Dic3⋊C4—64no—
114C2×C3⋊C8—22no—
115D3×C8—124no—
116C22×C32—21no—
117C22×C32—21no—
118C22×C32#10312yes—
119C22×C32C2×C22⋊C411yescharacteristic
120C2×C3⋊D3—21no—
121C2×C3⋊D3—21no—
122C2×C3⋊D3—24no—
123C2×C3⋊D3—24no—
124C2×C3⋊D3#10312yes—
125C2×C3⋊D3#12312yes—
126C2×C3⋊D3C2×SD1611yescharacteristic
127C2×C3⋊D3C2×Q1611yescharacteristic
128C2×C3⋊D3AGL(1,ℤ/8)12yes—
129#157—82no—
130C32×C4—21no—
131C32×C4#12312yes—
132C3⋊Dic3—21no—
133C3⋊Dic3#11712yes—
134C3×Dic3—44no—
135C23×C4—91no—
136C23×C4—181no—
137C22×C8—92no—
138C2×C4⋊C4—61no—
139C2×C4⋊C4—92no—
140C2×C4⋊C4—92no—
141C2×C4⋊C4—92no—
142C2×C4⋊C4—92no—
143C2×C4⋊C4—181no—
144C2×C4⋊C4—181no—
145C2×C22⋊C4—181no—
146C22⋊C8—61no—
147C22⋊C8—181no—
148#95—181no—
149C23×C3—21no—
150C23×C3—21no—
151C22×D3—61no—
152C22×D3—62no—
153C22×D3—62no—
154C22×D3—61no—
155C22×D3—61no—
156C22×D3—61no—
157C22×D3—62no—
158C22×D3—62no—
159C22×D3—64no—
160C22×D3—64no—
161C22×D3—122no—
162C22×D3—122no—
163C2×C3×C4—24no—
164C2×C3×C4—21no—
165C2×C3×C4—21no—
166C2×C3×C4—21no—
167C2×C3×C4—21no—
168C2×C3×C4—42no—
169C2×C3×C4—64no—
170C2×C3×C4—124no—
171C2×Dic3—24no—
172C2×Dic3—44no—
173C2×Dic3—61no—
174C2×Dic3—61no—
175C2×Dic3—61no—
176C2×Dic3—61no—
177C2×Dic3—64no—
178C2×Dic3—122no—
179C4×D3—64no—
180C4×D3—64no—
181C4×D3—64no—
182C4×D3—64no—
183C4×D3—64no—
184C4×D3—122no—
185C4×D3—122no—
186C4×D3—122no—
187C4×D3—128no—
188C4×D3—128no—
189C3×C8—122no—
190C3⋊C8—42no—
191C2×C32—22no—
192C2×C32#38111yescharacteristic
193C2×C32C2×#10311yescharacteristic
194C2×C32#41811yescharacteristic
195C3⋊D3—22no—
196C3⋊D3#48112yes—
197C3⋊D3#48412yes—
198C24—91no—
199C22×C4—62no—
200C22×C4—91no—
201C22×C4—91no—
202C22×C4—91no—
203C22×C4—91no—
204C22×C4—91no—
205C22×C4—184no—
206C22×C4—182no—
207C22×C4—182no—
208C22×C4—182no—
209C22×C4—364no—
210C22×C4GO+(4,𝔽2)11yescharacteristic
211C2×C8—62no—
212C2×C8—184no—
213C4⋊C4—62no—
214C4⋊C4—62no—
215C4⋊C4—94no—
216C4⋊C4—182no—
217C4⋊C4—184no—
218C22⋊C4—362no—
219C22×C3—22no—
220C22×C3—22no—
221C22×C3—21no—
222C22×C3—21no—
223C22×C3—22no—
224C22×C3—22no—
225C22×C3—41no—
226C22×C3—41no—
227C2×D3—62no—
228C2×D3—62no—
229C2×D3—62no—
230C2×D3—62no—
231C2×D3—61no—
232C2×D3—61no—
233C2×D3—61no—
234C2×D3—61no—
235C2×D3—62no—
236C2×D3—62no—
237C2×D3—62no—
238C2×D3—62no—
239C2×D3—68no—
240C2×D3—68no—
241C2×D3—124no—
242C2×D3—124no—
243C2×D3—121no—
244C2×D3—121no—
245C3×C4—22no—
246C3×C4—22no—
247C3×C4—22no—
248C3×C4—41no—
249C3×C4—124no—
250Dic3—44no—
251Dic3—62no—
252Dic3—62no—
253Dic3—62no—
254Dic3—121no—
255C32#182411yescharacteristic, complemented, Sylow
256C23—91no—
257C23—91no—
258C23—92no—
259C23—92no—
260C23—182no—
261C23—182no—
262C23D32⋊C411yescharacteristic
263C2×C4—22no—
264C2×C4—64no—
265C2×C4—91no—
266C2×C4—94no—
267C2×C4—91no—
268C2×C4—124no—
269C2×C4—182no—
270C2×C4—182no—
271C2×C4—182no—
272C2×C4—182no—
273C2×C4—364no—
274C2×C4—364no—
275C2×C4—362no—
276C2×C4—362no—
277C2×C4—362no—
278C2×C4D32⋊C411yescharacteristic
279C2×C4C2×GO+(4,𝔽2)11yescharacteristic
280C8—122no—
281C2×C3—24no—
282C2×C3—21no—
283C2×C3—21no—
284C2×C3—21no—
285C2×C3—21no—
286C2×C3—21no—
287C2×C3—21no—
288C2×C3—42no—
289D3—62no—
290D3—62no—
291D3—62no—
292D3—62no—
293D3—64no—
294D3—122no—
295C22—21no—
296C22—21no—
297C22—92no—
298C22—91no—
299C22—91no—
300C22—92no—
301C22—92no—
302C22—184no—
303C22—184no—
304C22—181no—
305C22—181no—
306C22#6373012yes—
307C22C2×D32⋊C411yescharacteristic
308C4—21no—
309C4—92no—
310C4—124no—
311C4—181no—
312C4—722no—
313C4#6423312yes—
314C3—21no—
315C3—21no—
316C2—22no—
317C2—92no—
318C2—92no—
319C2—182no—
320C2#1059331811yescharacteristic
321C2C2×#6373011yescharacteristic
322C2#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#1824
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
10. C2×#3724C4semidirect
13. #63900C4semidirect
255. C32#1824semidirect

Maximal subgroups

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

subgroupindex
C2×#639002
#105938122
#105911522
#105900492
#18249