Finite Group Databasebeta

← #11775180

Subgroups — #11775180

Order 1152.

545 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 545 conjugacy classes of subgroups — too many to draw. Only its 92 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#10594810C211yesmaximal, characteristic
2#10592347C211yesmaximal, characteristic
3#10591066C211yesmaximal, characteristic
4C3×#4452C212yesmaximal
5#10589152C212yesmaximal
6#68310—32nomaximal
7C2×C4×C3⋊Dic3—21no—
8C2×C4×C3⋊Dic3C2211yescharacteristic
9C3×#924C2212yes—
10#63982—21no—
11#63957—21no—
12#63919C411yescharacteristic, complemented
13#63873C411yescharacteristic, complemented
14#63870—21no—
15#63843C412yescomplemented
16#63838—21no—
17C32×#95C2211yescharacteristic
18#63658—21no—
19#63658C2211yescharacteristic
20C3×#830C2212yes—
21#63572—21no—
22#63555—21no—
23#5622—32no—
24#4719—32no—
25#4648—32no—
26#4648—61no—
27C3×#328—32no—
28#4538—32no—
29#4467—32no—
30#4452D312yes—
31C22×C32×C4—21no—
32C22×C32×C4C2311yescharacteristic
33C22×C3⋊Dic3—21no—
34C22×C3⋊Dic3D411yescharacteristic
35C22×C3⋊Dic3D411yescharacteristic
36C2×C3×Dic6C2×C412yes—
37C2×#627—21no—
38C4×C3⋊Dic3—24no—
39C4×C3⋊Dic3C2×C411yescharacteristic
40C4×C3⋊Dic3C2×C411yescharacteristic
41C4×C3⋊Dic3D411yescharacteristic
42C4×C3⋊Dic3D411yescharacteristic
43C3×#217—22no—
44C3×C4⋊Dic3C2×C412yes—
45C3×Dic3⋊C4—22no—
46C2×C3×C3⋊C8—22no—
47#3724—21no—
48#3724—21no—
49#3724—21no—
50Dic3⋊Dic3—22no—
51Dic32—22no—
52#1506—91noSylow
53C3×C22⋊Q8—32no—
54Q8×Dic3—32no—
55#944—32no—
56#924C2×D312yes—
57C2×C4×Dic3—32no—
58C2×C4×Dic3—61no—
59C2×C4×Dic3—62no—
60C2×C4×Dic3—62no—
61#889—62no—
62#888—32no—
63#887—32no—
64#887—62no—
65#878—62no—
66#877—62no—
67C3×C22⋊C8—32no—
68C3×#95—21no—
69C3×#95C2×D312yes—
70C3⋊#95—32no—
71C3⋊#95—61no—
72C3⋊#95—62no—
73C3⋊#95—62no—
74#830C2×D312yes—
75#815—62no—
76Dic3⋊C8—62no—
77C23×C32C2×D411yescharacteristic
78C2×C32×C4—22no—
79C2×C32×C4—41no—
80C2×C32×C4—41no—
81C2×C32×C4—41no—
82C2×C32×C4C22×C411yescharacteristic
83C2×C32×C4C2×D411yescharacteristic
84C2×C3⋊Dic3—22no—
85C2×C3⋊Dic3—22no—
86C2×C3⋊Dic3—21no—
87C2×C3⋊Dic3—21no—
88C2×C3⋊Dic3—41no—
89C2×C3⋊Dic3—41no—
90C2×C3⋊Dic3C22⋊C411yescharacteristic
91C2×C3⋊Dic3C22⋊C411yescharacteristic
92C2×C3⋊Dic3C22⋊C411yescharacteristic
93C2×C3⋊Dic3C22⋊C411yescharacteristic
94C2×C3×Dic3—22no—
95C2×C3×Dic3—22no—
96C3×Dic6—42no—
97#627—42no—
98C3×C3⋊C8—42no—
99#533—91no—
100#432—91no—
101#376—91no—
102#328—32no—
103#328—92no—
104C2×C3×Q8—32no—
105C22×C3×C4—22no—
106C22×C3×C4—22no—
107C22×C3×C4—21no—
108C22×C3×C4C22×D312yes—
109C22×Dic3—32no—
110C22×Dic3—32no—
111C22×Dic3—61no—
112C22×Dic3—61no—
113C22×Dic3—62no—
114C22×Dic3—62no—
115C2×Dic6—62no—
116C2×Dic6C4×D312yes—
117C2×C3×C8—62no—
118C3×C4⋊C4—32no—
119C3×C4⋊C4—62no—
120C3×C22⋊C4—62no—
121#217—22no—
122C4⋊Dic3—62no—
123C4⋊Dic3C4×D312yes—
124Dic3⋊C4—22no—
125Dic3⋊C4—62no—
126Dic3⋊C4—62no—
127Dic3⋊C4—62no—
128Dic3⋊C4—62no—
129C4×Dic3—32no—
130C4×Dic3—32no—
131C4×Dic3—32no—
132C4×Dic3—32no—
133C4×Dic3—61no—
134C4×Dic3—61no—
135C4×Dic3—61no—
136C4×Dic3—61no—
137C4×Dic3—62no—
138C4×Dic3—62no—
139C4×Dic3—68no—
140C4×Dic3—68no—
141C2×C3⋊C8—22no—
142C22×C32—21no—
143C22×C32—21no—
144C22×C32C2×C22⋊C411yescharacteristic
145C22×C32#13711yescharacteristic
146C22×C32#13711yescharacteristic
147C32×C4—21no—
148C32×C4—21no—
149C32×C4—42no—
150C3⋊Dic3—21no—
151C3⋊Dic3—21no—
152C3⋊Dic3—21no—
153C3⋊Dic3—42no—
154C3⋊Dic3#10412yes—
155C3×Dic3—42no—
156C3×Dic3—42no—
157C4⋊Q8—91no—
158C4⋊Q8—91no—
159#125—181no—
160C22⋊Q8—32no—
161C22⋊Q8—181no—
162C4×Q8—92no—
163C4×Q8—181no—
164#117—181no—
165C2×C42—91no—
166C2×C42—181no—
167C4⋊C8—181no—
168C22⋊C8—32no—
169#97—181no—
170#95—91no—
171#95—181no—
172#95D3211yescharacteristic
173C23×C3—21no—
174C23×C3D3×D412yes—
175C3×Q8—122no—
176C2×C3×C4—24no—
177C2×C3×C4—24no—
178C2×C3×C4—21no—
179C2×C3×C4—21no—
180C2×C3×C4—42no—
181C2×C3×C4—42no—
182C2×C3×C4—42no—
183C2×C3×C4—42no—
184C2×C3×C4—42no—
185C2×C3×C4—42no—
186C2×C3×C4—62no—
187C2×C3×C4—62no—
188C2×C3×C4C2×C4×D312yes—
189C2×C3×C4D3×D412yes—
190C2×Dic3—22no—
191C2×Dic3—22no—
192C2×Dic3—32no—
193C2×Dic3—32no—
194C2×Dic3—32no—
195C2×Dic3—32no—
196C2×Dic3—61no—
197C2×Dic3—61no—
198C2×Dic3—61no—
199C2×Dic3—61no—
200C2×Dic3—64no—
201C2×Dic3—64no—
202C2×Dic3—62no—
203C2×Dic3—62no—
204C2×Dic3—64no—
205C2×Dic3—64no—
206C2×Dic3—121no—
207C2×Dic3—121no—
208C2×Dic3—122no—
209C2×Dic3—122no—
210C2×Dic3—122no—
211C2×Dic3—122no—
212Dic6—42no—
213Dic6—124no—
214C3×C8—122no—
215C3⋊C8—42no—
216C2×C32—21no—
217C2×C32—21no—
218C2×C32#41011yescharacteristic
219C2×C32#41911yescharacteristic
220C2×C32C2×#10411yescharacteristic
221C2×Q8—32no—
222C2×Q8—181no—
223C22×C4—21no—
224C22×C4—91no—
225C22×C4—91no—
226C22×C4—181no—
227C22×C4C2×D3211yescharacteristic
228C2×C8—62no—
229C4⋊C4—32no—
230C4⋊C4—62no—
231C4⋊C4—181no—
232C4⋊C4—181no—
233C4⋊C4—182no—
234C4⋊C4—181no—
235C22⋊C4—62no—
236C42—91no—
237C42—91no—
238C42—91no—
239C42—91no—
240C42—184no—
241C42—182no—
242C22×C3—22no—
243C22×C3—22no—
244C22×C3—22no—
245C22×C3—22no—
246C22×C3—21no—
247C22×C3—21no—
248C22×C3—21no—
249C22×C3D3×C22⋊C412yes—
250C22×C3#91512yes—
251C22×C3#91812yes—
252C3×C4—22no—
253C3×C4—22no—
254C3×C4—41no—
255C3×C4—41no—
256C3×C4—44no—
257C3×C4—44no—
258C3×C4—122no—
259C3×C4—122no—
260Dic3—34no—
261Dic3—42no—
262Dic3—42no—
263Dic3—62no—
264Dic3—62no—
265Dic3—62no—
266Dic3—62no—
267Dic3—62no—
268Dic3—121no—
269Dic3—121no—
270Dic3—124no—
271Dic3—124no—
272C32#150611yescharacteristic, complemented, Sylow
273C23#381111yescharacteristic
274Q8—122no—
275Q8—362no—
276C2×C4—22no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—62no—
281C2×C4—62no—
282C2×C4—91no—
283C2×C4—91no—
284C2×C4—91no—
285C2×C4—91no—
286C2×C4—182no—
287C2×C4—181no—
288C2×C4—181no—
289C2×C4—182no—
290C2×C4—361no—
291C2×C4—361no—
292C2×C4C4×D3211yescharacteristic
293C2×C4#380211yescharacteristic
294C8—122no—
295C2×C3—22no—
296C2×C3—22no—
297C2×C3—22no—
298C2×C3—22no—
299C2×C3—21no—
300C2×C3—21no—
301C2×C3—21no—
302C2×C3#474012yes—
303C2×C3#480212yes—
304C2×C3D3×#10412yes—
305C22—21no—
306C22—21no—
307C22#6392111yescharacteristic
308C22#6393111yescharacteristic
309C22#6394511yescharacteristic
310C4—21no—
311C4—21no—
312C4—42no—
313C4—92no—
314C4—122no—
315C4—122no—
316C4—181no—
317C4—181no—
318C4—181no—
319C4—362no—
320C3—21no—
321C3#6831012yescomplemented
322C2—21no—
323C2—21no—
324C2#1059039311yescharacteristic
325C2#1059040611yescharacteristic
326C2#1059060211yescharacteristic
subgroupG/H
centerC22#63921
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC32×#95C22
socleC22×C32C2×C22⋊C4
prime radicalC23×C32C2×D4
cosocleC22×C32×C4C23
hypercenter#95D32
hypocenterC32#1506
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #95

Complements

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

NH ≅ G/Ntype
12. #63919C4semidirect
13. #63873C4semidirect
15. #63843C4semidirect
272. C32#1506semidirect
321. C3#68310semidirect

Maximal subgroups

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

subgroupindex
#105948102
#105923472
#105910662
C3×#44522
#105891522
#683103