Finite Group Databasebeta

← #11785774

Subgroups — #11785774

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—42no—
34C2×#624—42no—
35C22⋊#157—42no—
36C4⋊#157—24no—
37C3×C4⋊Dic3—22no—
38C3×C4⋊Dic3—22no—
39C2×C3×C3⋊C8—22no—
40#3724—22no—
41#3724C2×C414yes—
42#3710—24no—
43#1823—91nomaximal, Sylow
44C22×C4×D3—61no—
45C22×C4×D3—61no—
46C22×C4×D3—62no—
47C2×C3×C4⋊C4—61no—
48C2×C4⋊Dic3—21no—
49C2×Dic3⋊C4—62no—
50C2×D3×C8—62no—
51D3×C4⋊C4—62no—
52D3×C4⋊C4—62no—
53D3×C4⋊C4—62no—
54D3×C4⋊C4—62no—
55C3×C22⋊C8—61no—
56#830—21no—
57(C2×D3)⋊C8—62no—
58C23×C32C22⋊C411yescharacteristic
59C22×C3⋊D3—22no—
60C22×C3⋊D3—22no—
61C22×C3⋊D3C22⋊C411yescharacteristic
62C22×C3⋊D3D812yes—
63C22×C3⋊D3SD1612yes—
64C22×C3⋊D3C2×D411yescharacteristic
65C2×#157—42no—
66C2×#157—42no—
67C2×#157—42no—
68C2×C32×C4—22no—
69C2×C32×C4C22⋊C411yescharacteristic
70C2×C32×C4C2×D411yescharacteristic
71C2×C3⋊Dic3—22no—
72C2×C3⋊Dic3C22⋊C411yescharacteristic
73C2×C3⋊Dic3C22×C411yescharacteristic
74C4×C3⋊D3—22no—
75C4×C3⋊D3—22no—
76C4×C3⋊D3—22no—
77C4×C3⋊D3#4114yes—
78C2×C3×Dic3—24no—
79C2×C3×Dic3—44no—
80#624—44no—
81#624—42no—
82#624—42no—
83C3×C3⋊C8—42no—
84C22×C4⋊C4—91no—
85C2×C22⋊C8—91no—
86#380—91no—
87#340—94no—
88C23×D3—61no—
89C23×D3—61no—
90C22×C3×C4—21no—
91C22×C3×C4—21no—
92C22×C3×C4—62no—
93C22×Dic3—22no—
94C22×Dic3—61no—
95C22×Dic3—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—61no—
103C2×C4×D3—61no—
104C2×C4×D3—68no—
105C2×C4×D3—64no—
106C2×C4×D3—64no—
107C2×C4×D3—124no—
108C2×C4×D3—124no—
109C2×C4×D3—124no—
110C2×C3×C8—62no—
111C3×C4⋊C4—62no—
112C3×C4⋊C4—62no—
113C4⋊Dic3—22no—
114C4⋊Dic3—22no—
115Dic3⋊C4—64no—
116Dic3⋊C4—64no—
117C2×C3⋊C8—22no—
118D3×C8—124no—
119C22×C32—21no—
120C22×C32—21no—
121C22×C32#10212yes—
122C22×C32C2×C22⋊C411yescharacteristic
123C2×C3⋊D3—21no—
124C2×C3⋊D3—21no—
125C2×C3⋊D3—24no—
126C2×C3⋊D3—24no—
127C2×C3⋊D3#10212yes—
128C2×C3⋊D3#12312yes—
129C2×C3⋊D3C2×D811yescharacteristic
130C2×C3⋊D3C2×SD1611yescharacteristic
131C2×C3⋊D3#13712yes—
132#157—82no—
133C32×C4—21no—
134C32×C4#12312yes—
135C3⋊Dic3—21no—
136C3⋊Dic3#11712yes—
137C3×Dic3—44no—
138C23×C4—91no—
139C23×C4—181no—
140C22×C8—92no—
141C2×C4⋊C4—61no—
142C2×C4⋊C4—92no—
143C2×C4⋊C4—92no—
144C2×C4⋊C4—92no—
145C2×C4⋊C4—92no—
146C2×C4⋊C4—181no—
147C2×C4⋊C4—181no—
148C2×C22⋊C4—181no—
149C22⋊C8—61no—
150C22⋊C8—181no—
151#95—181no—
152C23×C3—21no—
153C23×C3—21no—
154C22×D3—61no—
155C22×D3—62no—
156C22×D3—62no—
157C22×D3—61no—
158C22×D3—61no—
159C22×D3—61no—
160C22×D3—62no—
161C22×D3—62no—
162C22×D3—64no—
163C22×D3—64no—
164C22×D3—122no—
165C22×D3—122no—
166C2×C3×C4—24no—
167C2×C3×C4—21no—
168C2×C3×C4—21no—
169C2×C3×C4—21no—
170C2×C3×C4—21no—
171C2×C3×C4—42no—
172C2×C3×C4—64no—
173C2×C3×C4—124no—
174C2×Dic3—24no—
175C2×Dic3—44no—
176C2×Dic3—61no—
177C2×Dic3—61no—
178C2×Dic3—61no—
179C2×Dic3—61no—
180C2×Dic3—64no—
181C2×Dic3—122no—
182C4×D3—64no—
183C4×D3—64no—
184C4×D3—64no—
185C4×D3—64no—
186C4×D3—64no—
187C4×D3—122no—
188C4×D3—122no—
189C4×D3—122no—
190C4×D3—128no—
191C4×D3—124no—
192C4×D3—124no—
193C3×C8—122no—
194C3⋊C8—42no—
195C2×C32—22no—
196C2×C32#38111yescharacteristic
197C2×C32C2×#10211yescharacteristic
198C2×C32#41911yescharacteristic
199C3⋊D3—22no—
200C3⋊D3#48012yes—
201C3⋊D3#48312yes—
202C24—91no—
203C22×C4—62no—
204C22×C4—91no—
205C22×C4—91no—
206C22×C4—91no—
207C22×C4—91no—
208C22×C4—91no—
209C22×C4—184no—
210C22×C4—182no—
211C22×C4—182no—
212C22×C4—182no—
213C22×C4—362no—
214C22×C4—362no—
215C22×C4GO+(4,𝔽2)11yescharacteristic
216C2×C8—62no—
217C2×C8—184no—
218C4⋊C4—62no—
219C4⋊C4—62no—
220C4⋊C4—94no—
221C4⋊C4—182no—
222C4⋊C4—184no—
223C22⋊C4—362no—
224C22×C3—22no—
225C22×C3—22no—
226C22×C3—21no—
227C22×C3—21no—
228C22×C3—22no—
229C22×C3—22no—
230C22×C3—41no—
231C22×C3—41no—
232C2×D3—62no—
233C2×D3—62no—
234C2×D3—62no—
235C2×D3—61no—
236C2×D3—61no—
237C2×D3—61no—
238C2×D3—61no—
239C2×D3—62no—
240C2×D3—62no—
241C2×D3—62no—
242C2×D3—62no—
243C2×D3—68no—
244C2×D3—68no—
245C2×D3—62no—
246C2×D3—124no—
247C2×D3—124no—
248C2×D3—121no—
249C2×D3—121no—
250C3×C4—22no—
251C3×C4—22no—
252C3×C4—22no—
253C3×C4—41no—
254C3×C4—124no—
255Dic3—44no—
256Dic3—62no—
257Dic3—62no—
258Dic3—62no—
259Dic3—121no—
260C32#182311yescharacteristic, complemented, Sylow
261C23—91no—
262C23—91no—
263C23—92no—
264C23—92no—
265C23—182no—
266C23—182no—
267C23D32⋊C411yescharacteristic
268C2×C4—22no—
269C2×C4—64no—
270C2×C4—91no—
271C2×C4—94no—
272C2×C4—91no—
273C2×C4—124no—
274C2×C4—182no—
275C2×C4—182no—
276C2×C4—182no—
277C2×C4—182no—
278C2×C4—362no—
279C2×C4—362no—
280C2×C4—364no—
281C2×C4—362no—
282C2×C4—362no—
283C2×C4—362no—
284C2×C4D32⋊C411yescharacteristic
285C2×C4C2×GO+(4,𝔽2)11yescharacteristic
286C8—122no—
287C2×C3—24no—
288C2×C3—21no—
289C2×C3—21no—
290C2×C3—21no—
291C2×C3—21no—
292C2×C3—21no—
293C2×C3—21no—
294C2×C3—42no—
295D3—62no—
296D3—62no—
297D3—62no—
298D3—62no—
299D3—64no—
300D3—122no—
301C22—21no—
302C22—21no—
303C22—91no—
304C22—91no—
305C22—92no—
306C22—92no—
307C22—92no—
308C22—184no—
309C22—184no—
310C22—181no—
311C22—181no—
312C22#6372912yes—
313C22C2×D32⋊C411yescharacteristic
314C4—21no—
315C4—92no—
316C4—124no—
317C4—181no—
318C4—722no—
319C4#6423312yes—
320C3—21no—
321C3—21no—
322C2—22no—
323C2—92no—
324C2—92no—
325C2—182no—
326C2C2×#6372911yescharacteristic
327C2#1059332111yescharacteristic
328C2#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#1823
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
260. C32#1823semidirect

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
#18239