Finite Group Databasebeta

← #11785598

Subgroups — #11785598

Order 1152.

450 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 450 conjugacy classes of subgroups — too many to draw. Only its 69 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
2C2×#63768C211yesmaximal, characteristic, complemented
3#10593319C212yesmaximal
4#10590913C211yesmaximal, characteristic, complemented
5#10590053C212yesmaximal, complemented
6#64306C2211yescharacteristic
7C2×C4⋊#157C2212yes—
8C2×C8×C3⋊D3C2211yescharacteristic
9C3×#901—21no—
10#63818C2212yes—
11#63818C2211yescharacteristic
12#63815—21no—
13#63805C412yescomplemented
14#63803C412yescomplemented
15#63791—21no—
16D32×C8—21no—
17#63768—21no—
18#63768—21no—
19#63730—22no—
20#63729—22no—
21C3×#819—21no—
22#63578—21no—
23D3×#131—61no—
24D3×#108—61no—
25C22×#157—22no—
26C2×C4×C3⋊D3C2311yescharacteristic
27C3×#235—21no—
28#3811—21no—
29#3805Q812yes—
30#3802D411yescharacteristic
31C4×D32—21no—
32#3798C2×C412yes—
33#3797D411yescharacteristic
34#3796—21no—
35C4⋊#157—22no—
36C4⋊#157—22no—
37C2×C32×C8D411yescharacteristic
38C2×C3⋊(C3⋊C8)D411yescharacteristic
39C8×C3⋊D3C2×C411yescharacteristic
40C8×C3⋊D3C2×C411yescharacteristic
41C8×C3⋊D3D411yescharacteristic
42C8×C3⋊D3D411yescharacteristic
43C3×#208—21no—
44C3×#208—22no—
45C3×ΓL(1,𝔽25)—22no—
46C3×D3×C8—22no—
47#3712—22no—
48#3712C2×C412yes—
49#3711—22no—
50#3710—21no—
51#3710—22no—
52D3×C3⋊C8—22no—
53#1815—91nomaximal, Sylow
54D3×#41—61no—
55C3×#131—61no—
56#948—61no—
57#907—62no—
58#907—61no—
59D3×M16—61no—
60D3×M16—62no—
61D3×M16—62no—
62#901—21no—
63#901—62no—
64C2×D3×C8—61no—
65C2×D3×C8—61no—
66C2×D3×C8—62no—
67C3×#108—61no—
68#822—62no—
69#819—21no—
70C22×C3⋊D3#4111yescharacteristic
71C2×D32—21no—
72C2×#157—42no—
73C2×#157—82no—
74C2×C32×C4C2×D411yescharacteristic
75C2×C3⋊Dic3C2×Q811yescharacteristic
76C4×C3⋊D3C22×C411yescharacteristic
77C4×C3⋊D3C2×D411yescharacteristic
78C4×C3⋊D3C2×D411yescharacteristic
79C4×C3⋊D3#4111yescharacteristic
80C3×#67—22no—
81C3×D12—21no—
82C3×C4×D3—22no—
83C3×Dic6—21no—
84#627C4⋊C412yes—
85#626—22no—
86#625C4⋊C412yes—
87#624—21no—
88D3×Dic3—22no—
89C32×C8C22⋊C411yescharacteristic
90C32×C8C22⋊C411yescharacteristic
91C3⋊(C3⋊C8)C22⋊C411yescharacteristic
92C3⋊(C3⋊C8)C22⋊C411yescharacteristic
93C3×C3⋊C8—22no—
94C3×C3⋊C8—42no—
95C2×#131—91no—
96C2×#108—91no—
97C2×#106—91no—
98#417—92no—
99#343—92no—
100C3×#41—61no—
101#239—61no—
102D3×Q8—61no—
103#237—62no—
104#237—61no—
105D3×D4—61no—
106D3×D4—62no—
107#235—21no—
108#235—62no—
109C2×C4×D3—61no—
110C2×C4×D3—61no—
111C2×C4×D3—62no—
112C3×M16—62no—
113C3×M16—61no—
114C3×M16—62no—
115C2×C3×C8—21no—
116C2×C3×C8—21no—
117C2×C3×C8—62no—
118#208—21no—
119#208—22no—
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—
127ΓL(1,𝔽25)—122no—
128D3×C8—22no—
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—
138D3×C8—62no—
139D3×C8—122no—
140C22×C32C22⋊Q811yescharacteristic
141C2×C3⋊D3—22no—
142C2×C3⋊D3#11711yescharacteristic
143C2×C3⋊D3#12111yescharacteristic
144C2×C3×D3—22no—
145D32—42no—
146#157—82no—
147C32×C4C2×C22⋊C411yescharacteristic
148C32×C4#12111yescharacteristic
149C3⋊Dic3C2×C4⋊C411yescharacteristic
150C3⋊Dic3C22⋊Q811yescharacteristic
151C3×Dic3—22no—
152C2×#41—91no—
153#131—61no—
154#131—92no—
155#131—92no—
156#131—181no—
157C2×M16—91no—
158C2×M16—92no—
159C2×M16—181no—
160C22×C8—91no—
161C22×C8—181no—
162C2×C4⋊C4—92no—
163#108—61no—
164#108—181no—
165#106—181no—
166#106—181no—
167#103—182no—
168#102—182no—
169C22×D3—61no—
170C22×D3—61no—
171C22×D3—62no—
172C3×Q8—61no—
173C3×D4—61no—
174C3×D4—62no—
175C2×C3×C4—21no—
176C2×C3×C4—21no—
177C2×C3×C4—62no—
178#67—22no—
179#67—62no—
180#67—62no—
181C2×Dic3—61no—
182C2×Dic3—61no—
183C2×Dic3—62no—
184D12—21no—
185D12—62no—
186C4×D3—22no—
187C4×D3—61no—
188C4×D3—61no—
189C4×D3—61no—
190C4×D3—61no—
191C4×D3—61no—
192C4×D3—61no—
193C4×D3—61no—
194C4×D3—61no—
195C4×D3—62no—
196C4×D3—62no—
197Dic6—21no—
198Dic6—62no—
199C3×C8—21no—
200C3×C8—21no—
201C3×C8—21no—
202C3×C8—21no—
203C3×C8—62no—
204C3×C8—122no—
205C3⋊C8—22no—
206C3⋊C8—42no—
207C3⋊C8—61no—
208C3⋊C8—61no—
209C3⋊C8—61no—
210C3⋊C8—61no—
211C2×C32—21no—
212C2×C32#38011yescharacteristic
213C3⋊D3—21no—
214C3⋊D3#47112yes—
215C3×D3—42no—
216#41—61no—
217#41—92no—
218#41—92no—
219#41—181no—
220C2×Q8—91no—
221C2×D4—91no—
222C2×D4—181no—
223C22×C4—91no—
224C22×C4—181no—
225C22×C4—182no—
226M16—61no—
227M16—62no—
228M16—62no—
229M16—92no—
230M16—182no—
231M16—182no—
232C2×C8—62no—
233C2×C8—91no—
234C2×C8—91no—
235C2×C8—91no—
236C2×C8—91no—
237C2×C8—91no—
238C2×C8—181no—
239C2×C8—182no—
240C2×C8—182no—
241C2×C8GO+(4,𝔽2)11yescharacteristic
242C4⋊C4—182no—
243C4⋊C4—182no—
244C22×C3—21no—
245C22×C3—21no—
246C22×C3—62no—
247C2×D3—22no—
248C2×D3—61no—
249C2×D3—61no—
250C2×D3—61no—
251C2×D3—61no—
252C2×D3—122no—
253C2×D3—122no—
254C2×D3—124no—
255C3×C4—21no—
256C3×C4—21no—
257C3×C4—21no—
258C3×C4—21no—
259C3×C4—62no—
260Dic3—22no—
261Dic3—61no—
262Dic3—61no—
263Dic3—61no—
264Dic3—61no—
265C32#181511yescharacteristic, complemented, Sylow
266C23—91no—
267C23—181no—
268Q8—61no—
269Q8—92no—
270D4—62no—
271D4—61no—
272D4—92no—
273D4—182no—
274C2×C4—62no—
275C2×C4—91no—
276C2×C4—91no—
277C2×C4—91no—
278C2×C4—91no—
279C2×C4—91no—
280C2×C4—181no—
281C2×C4—182no—
282C2×C4—362no—
283C2×C4—722no—
284C2×C4C2×GO+(4,𝔽2)11yescharacteristic
285C8—62no—
286C8—91no—
287C8—91no—
288C8—122no—
289C8D32⋊C411yescharacteristic
290C8D32⋊C411yescharacteristic
291C2×C3—21no—
292C2×C3—21no—
293C2×C3—41no—
294C2×C3—41no—
295C2×C3—122no—
296D3—42no—
297D3—62no—
298D3—62no—
299D3—121no—
300D3—121no—
301C22—62no—
302C22—91no—
303C22—91no—
304C22—182no—
305C22—362no—
306C22D32⋊Q811yescharacteristic
307C4—62no—
308C4—91no—
309C4—91no—
310C4—722no—
311C4#6423011yescharacteristic
312C4C2×D32⋊C411yescharacteristic
313C3—21no—
314C3—21no—
315C2—21no—
316C2—92no—
317C2—122no—
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#1815
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. C2×#63768C2semidirect
4. #10590913C2semidirect
5. #10590053C2semidirect
13. #63805C4semidirect
14. #63803C4semidirect
265. C32#1815semidirect

Maximal subgroups

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

subgroupindex
#105946692
C2×#637682
#105933192
#105909132
#105900532
#18159