Finite Group Databasebeta

← #11785499

Subgroups — #11785499

Order 1152.

450 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 450 conjugacy classes of subgroups — too many to draw. Only its 67 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#10594669C211yesmaximal, characteristic
2#10593768C211yesmaximal, characteristic, complemented
3#10593346C212yesmaximal
4#10590712C211yesmaximal, characteristic, complemented
5#10590045C212yesmaximal, complemented
6#64306C2211yescharacteristic
7#64286C2212yes—
8C2×C8×C3⋊D3C2211yescharacteristic
9C3×#901—21no—
10#63849C2212yes—
11#63818C2211yescharacteristic
12#63815—21no—
13#63805—21no—
14#63803—21no—
15#63791C412yescomplemented
16D32×C8C412yescomplemented
17#63769—21no—
18#63768—21no—
19#63738—24no—
20C3×#817—21no—
21#63576—21no—
22D3×#131—61no—
23#4860—61no—
24C2×C4×C3⋊D3C2311yescharacteristic
25C3×#235—21no—
26#3811D412yes—
27#3805—21no—
28#3802Q811yescharacteristic
29C4×D32C2×C412yes—
30#3798—21no—
31#3797Q811yescharacteristic
32#3796—21no—
33C22⋊#157—22no—
34C4⋊#157—22no—
35C4×#157—22no—
36C2×C32×C8D411yescharacteristic
37C2×C3⋊(C3⋊C8)D411yescharacteristic
38C8×C3⋊D3C2×C411yescharacteristic
39C8×C3⋊D3C2×C411yescharacteristic
40C8×C3⋊D3D411yescharacteristic
41C8×C3⋊D3D411yescharacteristic
42C3×C4⋊Dic3—22no—
43C3×#208—21no—
44C3×ΓL(1,𝔽25)—22no—
45C3×D3×C8—22no—
46#3722—22no—
47Dic32—22no—
48#3712—21no—
49#3711—22no—
50#3710C2×C412yes—
51D3×C3⋊C8—22no—
52#1812—91nomaximal, Sylow
53D3×#41—61no—
54C3×#131—61no—
55#948—61no—
56#907—62no—
57#907—61no—
58D3×M16—62no—
59D3×M16—61no—
60#901—21no—
61#901—62no—
62C2×D3×C8—62no—
63C2×D3×C8—61no—
64C2×D3×C8—61no—
65#892—62no—
66C3×#106—61no—
67#817—21no—
68#807—62no—
69C22×C3⋊D3C2×D411yescharacteristic
70C2×D32C4⋊C412yes—
71C2×#157—42no—
72C2×C32×C4C2×D411yescharacteristic
73C2×C3⋊Dic3#4111yescharacteristic
74C4×C3⋊D3C22×C411yescharacteristic
75C4×C3⋊D3C2×D411yescharacteristic
76C4×C3⋊D3C2×Q811yescharacteristic
77C4×C3⋊D3#4111yescharacteristic
78C3×#67—22no—
79C2×C3×Dic3—42no—
80C3×D12—21no—
81C3×C4×D3—22no—
82C3×Dic6—21no—
83#627—21no—
84#626—22no—
85#625—21no—
86#624C4⋊C412yes—
87D3×Dic3—22no—
88C32×C8C22⋊C411yescharacteristic
89C32×C8C22⋊C411yescharacteristic
90C3⋊(C3⋊C8)C22⋊C411yescharacteristic
91C3⋊(C3⋊C8)C22⋊C411yescharacteristic
92C3×C3⋊C8—22no—
93C2×#131—91no—
94#427—91no—
95#427—91no—
96#410—92no—
97H(3,ℤ/4)—92no—
98C3×#41—61no—
99#239—61no—
100D3×Q8—61no—
101#237—61no—
102#237—62no—
103D3×D4—61no—
104D3×D4—62no—
105#235—21no—
106#235—62no—
107C2×C4×D3—62no—
108C2×C4×D3—61no—
109C2×C4×D3—61no—
110C3×M16—62no—
111C3×M16—61no—
112C2×C3×C8—21no—
113C2×C3×C8—21no—
114C2×C3×C8—62no—
115C3×C4⋊C4—62no—
116(C2×D3)⋊C4—122no—
117C4⋊Dic3—22no—
118C4×Dic3—122no—
119#208—21no—
120#208—62no—
121C2×C3⋊C8—61no—
122C2×C3⋊C8—61no—
123C2×C3⋊C8—62no—
124ΓL(1,𝔽25)—22no—
125ΓL(1,𝔽25)—62no—
126ΓL(1,𝔽25)—62no—
127D3×C8—22no—
128D3×C8—62no—
129D3×C8—61no—
130D3×C8—61no—
131D3×C8—61no—
132D3×C8—61no—
133D3×C8—61no—
134D3×C8—61no—
135D3×C8—61no—
136D3×C8—61no—
137D3×C8—62no—
138C22×C32#12111yescharacteristic
139C2×C3⋊D3—41no—
140C2×C3⋊D3C2×C4⋊C411yescharacteristic
141C2×C3⋊D3#12111yescharacteristic
142C2×C3×D3—22no—
143D32—42no—
144#157—82no—
145C32×C4C2×C22⋊C411yescharacteristic
146C32×C4C22⋊Q811yescharacteristic
147C3⋊Dic3#11711yescharacteristic
148C3⋊Dic3C22⋊Q811yescharacteristic
149C3×Dic3—22no—
150C3×Dic3—82no—
151C2×#41—91no—
152#131—61no—
153#131—181no—
154#131—181no—
155#131—181no—
156C2×M16—91no—
157C2×M16—92no—
158C22×C8—92no—
159C22×C8—91no—
160#117—92no—
161#117—92no—
162#107—181no—
163#107—181no—
164#106—61no—
165#106—181no—
166#99—184no—
167C22×D3—62no—
168C22×D3—61no—
169C22×D3—61no—
170C3×Q8—61no—
171C3×D4—61no—
172C3×D4—62no—
173C2×C3×C4—21no—
174C2×C3×C4—21no—
175C2×C3×C4—62no—
176C2×C3×C4—122no—
177#67—22no—
178#67—62no—
179#67—62no—
180C2×Dic3—42no—
181C2×Dic3—61no—
182C2×Dic3—61no—
183C2×Dic3—62no—
184D12—21no—
185D12—62no—
186C4×D3—22no—
187C4×D3—62no—
188C4×D3—61no—
189C4×D3—61no—
190C4×D3—61no—
191C4×D3—61no—
192C4×D3—61no—
193C4×D3—61no—
194C4×D3—61no—
195C4×D3—61no—
196C4×D3—62no—
197Dic6—21no—
198Dic6—62no—
199C3×C8—21no—
200C3×C8—21no—
201C3×C8—21no—
202C3×C8—21no—
203C3×C8—62no—
204C3⋊C8—22no—
205C3⋊C8—61no—
206C3⋊C8—61no—
207C3⋊C8—61no—
208C3⋊C8—61no—
209C2×C32—21no—
210C2×C32#38011yescharacteristic
211C3⋊D3—21no—
212C3⋊D3—21no—
213C3×D3—42no—
214#41—61no—
215#41—181no—
216#41—181no—
217#41—181no—
218C2×Q8—91no—
219C2×D4—92no—
220C2×D4—91no—
221C22×C4—92no—
222C22×C4—91no—
223M16—61no—
224M16—62no—
225M16—181no—
226M16—182no—
227C2×C8—62no—
228C2×C8—92no—
229C2×C8—91no—
230C2×C8—91no—
231C2×C8—91no—
232C2×C8—91no—
233C2×C8—91no—
234C2×C8—182no—
235C2×C8GO+(4,𝔽2)11yescharacteristic
236C4⋊C4—62no—
237C4⋊C4—182no—
238C22⋊C4—182no—
239C22⋊C4—182no—
240C42—182no—
241C42—182no—
242C22×C3—21no—
243C22×C3—21no—
244C22×C3—62no—
245C2×D3—22no—
246C2×D3—61no—
247C2×D3—61no—
248C2×D3—61no—
249C2×D3—61no—
250C2×D3—124no—
251C2×D3—122no—
252C2×D3—122no—
253C3×C4—21no—
254C3×C4—21no—
255C3×C4—21no—
256C3×C4—21no—
257C3×C4—62no—
258C3×C4—242no—
259Dic3—22no—
260Dic3—61no—
261Dic3—61no—
262Dic3—61no—
263Dic3—61no—
264Dic3—82no—
265C32#181211yescharacteristic, complemented, Sylow
266C23—92no—
267C23—91no—
268Q8—61no—
269Q8—181no—
270D4—62no—
271D4—61no—
272D4—182no—
273D4—181no—
274C2×C4—62no—
275C2×C4—92no—
276C2×C4—91no—
277C2×C4—91no—
278C2×C4—91no—
279C2×C4—91no—
280C2×C4—91no—
281C2×C4—122no—
282C2×C4—182no—
283C2×C4—362no—
284C2×C4C2×GO+(4,𝔽2)11yescharacteristic
285C8—62no—
286C8—91no—
287C8—91no—
288C8D32⋊C411yescharacteristic
289C8D32⋊C411yescharacteristic
290C2×C3—22no—
291C2×C3—21no—
292C2×C3—21no—
293C2×C3—41no—
294C2×C3—122no—
295D3—42no—
296D3—62no—
297D3—121no—
298D3—121no—
299D3—121no—
300C22—62no—
301C22—91no—
302C22—91no—
303C22—361no—
304C22—362no—
305C22#6423011yescharacteristic
306C4—62no—
307C4—91no—
308C4—91no—
309C4—242no—
310C4—722no—
311C4D32⋊Q811yescharacteristic
312C4C2×D32⋊C411yescharacteristic
313C3—21no—
314C3—21no—
315C2—21no—
316C2—122no—
317C2—181no—
318C2—181no—
319C2#1059340311yescharacteristic
subgroupG/H
centerC2#10593403
commutatorC4×C3⋊D3C22×C4
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC2×C32×C8D4
socleC2×C32#380
prime radical#64306C22
cosocleC2×C4×C3⋊D3C23
hypercenterC2×C8GO+(4,𝔽2)
hypocenterC32#1812
LCSG ▷ C4×C3⋊D3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8

Complements

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

NH ≅ G/Ntype
2. #10593768C2semidirect
4. #10590712C2semidirect
5. #10590045C2semidirect
15. #63791C4semidirect
16. D32×C8C4semidirect
265. C32#1812semidirect

Maximal subgroups

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

subgroupindex
#105946692
#105937682
#105933462
#105907122
#105900452
#18129