Finite Group Databasebeta

← #11775339

Subgroups — #11775339

Order 1152.

530 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 530 conjugacy classes of subgroups — too many to draw. Only its 55 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#10594925C211yesmaximal, characteristic
2#10593811C211yesmaximal, characteristic
3#10591159C211yesmaximal, characteristic
4#10590034C214yesmaximal, complemented
5C22×C4×C3⋊D3C2211yescharacteristic
6C2×#3797C411yescharacteristic, complemented
7C2×C22⋊#157—21no—
8C3×#924—21no—
9#63982C412yescomplemented
10#63974—21no—
11#63900C411yescharacteristic, complemented
12#63883—21no—
13#63871—21no—
14#63865C2212yes—
15C2×#3712—21no—
16#63781—21no—
17#63781C2212yes—
18C3×#830—21no—
19#63557C2212yes—
20D3×C22⋊Q8—61no—
21#4726—61no—
22C23×C3⋊D3D411yescharacteristic
23C22×#157—22no—
24C22×C32×C4D411yescharacteristic
25C22×C3⋊Dic3C2×C411yescharacteristic
26C2×C4×C3⋊D3—42no—
27C2×C4×C3⋊D3C2×C411yescharacteristic
28C2×C4×C3⋊D3D411yescharacteristic
29C2×C4×C3⋊D3D411yescharacteristic
30C2×C4×C3⋊D3C2311yescharacteristic
31C2×C3×Dic6—21no—
32C2×#627C2×C412yes—
33C2×#624—21no—
34C2×#624—21no—
35#3797—42no—
36C22⋊#157—42no—
37C3×#217—22no—
38C3×C4⋊Dic3—21no—
39C3×Dic3⋊C4—22no—
40C2×C3×C3⋊C8—22no—
41#3724C2×C412yes—
42Dic3⋊Dic3—22no—
43#3722—22no—
44#3712—42no—
45#1511—91nomaximal, Sylow
46C2×D3×Q8—61no—
47C22×C4×D3—61no—
48C22×C4×D3—61no—
49C3×C22⋊Q8—61no—
50#946—61no—
51#924—21no—
52C2×ΓL(1,𝔽25)—62no—
53#897—61no—
54#896—62no—
55D3×C4⋊C4—61no—
56D3×C4⋊C4—62no—
57D3×C22⋊C4—62no—
58#878—62no—
59C3×C22⋊C8—61no—
60#830—21no—
61(C2×D3)⋊C8—62no—
62C23×C32C22⋊C411yescharacteristic
63C22×C3⋊D3—22no—
64C22×C3⋊D3—22no—
65C22×C3⋊D3—41no—
66C22×C3⋊D3C22⋊C411yescharacteristic
67C22×C3⋊D3C2×D411yescharacteristic
68C2×#157—42no—
69C2×#157—42no—
70C2×#157—42no—
71C2×C32×C4—41no—
72C2×C32×C4C22⋊C411yescharacteristic
73C2×C32×C4C2×D411yescharacteristic
74C2×C3⋊Dic3—41no—
75C2×C3⋊Dic3C22⋊C411yescharacteristic
76C2×C3⋊Dic3C22×C411yescharacteristic
77C4×C3⋊D3—22no—
78C4×C3⋊D3—22no—
79C4×C3⋊D3—41no—
80C4×C3⋊D3—41no—
81C2×C3×Dic3—22no—
82C2×C3×Dic3—22no—
83C3×Dic6—42no—
84#627—42no—
85#624—42no—
86#624—42no—
87C3×C3⋊C8—42no—
88C2×C22⋊Q8—91no—
89#407—91no—
90#381—91no—
91#328—94no—
92C23×D3—61no—
93C23×D3—61no—
94C2×C3×Q8—61no—
95C22×C3×C4—21no—
96C22×C3×C4—21no—
97C22×Dic3—61no—
98C22×Dic3—61no—
99D3×Q8—124no—
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—62no—
109C2×C4×D3—62no—
110C2×C4×D3—124no—
111C2×C4×D3—124no—
112C2×Dic6—21no—
113C2×Dic6—62no—
114C2×C3×C8—62no—
115C3×C4⋊C4—62no—
116C3×C4⋊C4—61no—
117C3×C22⋊C4—62no—
118#217—22no—
119(C2×D3)⋊C4—62no—
120(C2×D3)⋊C4—62no—
121C4⋊Dic3—21no—
122C4⋊Dic3—62no—
123Dic3⋊C4—22no—
124Dic3⋊C4—62no—
125Dic3⋊C4—62no—
126C2×C3⋊C8—22no—
127ΓL(1,𝔽25)—124no—
128C22×C32—21no—
129C22×C32—21no—
130C22×C32—21no—
131C22×C32C2×C22⋊C411yescharacteristic
132C2×C3⋊D3—21no—
133C2×C3⋊D3—21no—
134C2×C3⋊D3—21no—
135C2×C3⋊D3—21no—
136C2×C3⋊D3—44no—
137C2×C3⋊D3#9912yes—
138C2×C3⋊D3#13712yes—
139#157—82no—
140C32×C4—21no—
141C32×C4—21no—
142C3⋊Dic3—21no—
143C3⋊Dic3—21no—
144C3×Dic3—42no—
145C3×Dic3—42no—
146C22×Q8—91no—
147C23×C4—91no—
148C2×M16—181no—
149C22⋊Q8—61no—
150C22⋊Q8—92no—
151C22⋊Q8—92no—
152C22⋊Q8—181no—
153C2×C4⋊C4—91no—
154C2×C4⋊C4—181no—
155C2×C22⋊C4—181no—
156C2×C22⋊C4—181no—
157C22⋊C8—61no—
158C22⋊C8—92no—
159#95—92no—
160#95—181no—
161C23×C3—21no—
162C23×C3—21no—
163C22×D3—61no—
164C22×D3—61no—
165C22×D3—61no—
166C22×D3—61no—
167C22×D3—64no—
168C22×D3—122no—
169C22×D3—122no—
170C22×D3—122no—
171C22×D3—122no—
172C22×D3—122no—
173C3×Q8—122no—
174C2×C3×C4—21no—
175C2×C3×C4—21no—
176C2×C3×C4—21no—
177C2×C3×C4—21no—
178C2×C3×C4—42no—
179C2×C3×C4—42no—
180C2×C3×C4—62no—
181C2×C3×C4—62no—
182C2×Dic3—22no—
183C2×Dic3—22no—
184C2×Dic3—61no—
185C2×Dic3—61no—
186C2×Dic3—61no—
187C2×Dic3—61no—
188C2×Dic3—122no—
189C2×Dic3—122no—
190C4×D3—64no—
191C4×D3—64no—
192C4×D3—122no—
193C4×D3—122no—
194C4×D3—124no—
195C4×D3—124no—
196C4×D3—122no—
197C4×D3—122no—
198C4×D3—122no—
199C4×D3—122no—
200Dic6—42no—
201Dic6—124no—
202C3×C8—122no—
203C3⋊C8—42no—
204C2×C32—41no—
205C2×C32C2×#9911yescharacteristic
206C2×C32#41911yescharacteristic
207C2×C32#42111yescharacteristic
208C3⋊D3—22no—
209C3⋊D3—22no—
210C24—91no—
211C2×Q8—61no—
212C2×Q8—92no—
213C2×Q8—362no—
214C22×C4—91no—
215C22×C4—91no—
216C22×C4—91no—
217C22×C4—91no—
218C22×C4—91no—
219C22×C4—181no—
220C22×C4—181no—
221C22×C4—182no—
222C22×C4—362no—
223C22×C4GO+(4,𝔽2)11yescharacteristic
224M16—362no—
225C2×C8—62no—
226C4⋊C4—62no—
227C4⋊C4—61no—
228C4⋊C4—92no—
229C4⋊C4—182no—
230C22⋊C4—62no—
231C22⋊C4—182no—
232C22⋊C4—362no—
233C22×C3—22no—
234C22×C3—22no—
235C22×C3—21no—
236C22×C3—21no—
237C22×C3—41no—
238C22×C3—41no—
239C22×C3—41no—
240C22×C3—41no—
241C2×D3—62no—
242C2×D3—62no—
243C2×D3—62no—
244C2×D3—62no—
245C2×D3—62no—
246C2×D3—62no—
247C2×D3—121no—
248C2×D3—121no—
249C2×D3—121no—
250C2×D3—121no—
251C2×D3—121no—
252C2×D3—121no—
253C2×D3—128no—
254C2×D3—128no—
255C3×C4—22no—
256C3×C4—22no—
257C3×C4—41no—
258C3×C4—41no—
259C3×C4—122no—
260C3×C4—122no—
261Dic3—42no—
262Dic3—42no—
263Dic3—62no—
264Dic3—62no—
265Dic3—121no—
266Dic3—121no—
267C32#151111yescharacteristic, complemented, Sylow
268C23—91no—
269C23—91no—
270C23—182no—
271C23—182no—
272C23—361no—
273C23D32⋊C411yescharacteristic
274Q8—122no—
275Q8—362no—
276C2×C4—41no—
277C2×C4—62no—
278C2×C4—62no—
279C2×C4—91no—
280C2×C4—91no—
281C2×C4—182no—
282C2×C4—182no—
283C2×C4—361no—
284C2×C4—361no—
285C2×C4—362no—
286C2×C4—362no—
287C2×C4—361no—
288C2×C4—362no—
289C2×C4—362no—
290C2×C4—362no—
291C2×C4D32⋊C411yescharacteristic
292C2×C4C2×GO+(4,𝔽2)11yescharacteristic
293C8—122no—
294C2×C3—21no—
295C2×C3—21no—
296C2×C3—21no—
297C2×C3—21no—
298C2×C3—21no—
299C2×C3—21no—
300C2×C3—42no—
301C2×C3—42no—
302D3—64no—
303D3—122no—
304D3—122no—
305D3—122no—
306C22—21no—
307C22—21no—
308C22—21no—
309C22—92no—
310C22—92no—
311C22—181no—
312C22—181no—
313C22—181no—
314C22—181no—
315C22—364no—
316C22C2×D32⋊C411yescharacteristic
317C4—21no—
318C4—21no—
319C4—122no—
320C4—122no—
321C4—181no—
322C4—181no—
323C4—722no—
324C3—21no—
325C3—21no—
326C2—41no—
327C2—182no—
328C2—182no—
329C2#1059332111yescharacteristic
330C2#1059332411yescharacteristic
331C2#1059349011yescharacteristic
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#1511
LCSG ▷ C2×C3⋊Dic3 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
4. #10590034C2semidirect
6. C2×#3797C4semidirect
9. #63982C4semidirect
11. #63900C4semidirect
267. C32#1511semidirect

Maximal subgroups

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

subgroupindex
#105949252
#105938112
#105911592
#105900342
#15119