Finite Group Databasebeta

← #11785527

Subgroups — #11785527

Order 1152.

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

normal subgroups only

This group has 438 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
2C2×#63770C211yesmaximal, characteristic, complemented
3#10593313C212yesmaximal
4#10590913C211yesmaximal, characteristic, complemented
5#10590046C212yesmaximal, complemented
6#64306C2211yescharacteristic
7C2×#3788C2212yes—
8C2×C8×C3⋊D3C2211yescharacteristic
9C3×#901—21no—
10#63818C2212yes—
11#63818C2211yescharacteristic
12#63815—21no—
13#63805—21no—
14#63803—21no—
15#63791C412yes—
16D32×C8C412yes—
17#63770—21no—
18#63770—21no—
19#63728—22no—
20#63727—22no—
21C3×#819—21no—
22#63578—21no—
23D3×#131—61no—
24D3×#108—61no—
25C2×C4×C3⋊D3C2311yescharacteristic
26C3×#235—21no—
27#3811Q812yes—
28#3805—21no—
29#3802D411yescharacteristic
30C4×D32C2×C412yes—
31#3798—21no—
32#3797D411yescharacteristic
33#3796—21no—
34C2×#622—22no—
35#3788—22no—
36#3788—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—21no—
48#3712—22no—
49#3711—22no—
50#3710—22no—
51#3710C2×C412yes—
52D3×C3⋊C8—22no—
53#1813—91nomaximal, Sylow
54D3×#41—61no—
55C3×#131—61no—
56#948—61no—
57#907—62no—
58#907—61no—
59D3×M16—62no—
60D3×M16—61no—
61D3×M16—62no—
62#901—21no—
63#901—62no—
64C2×D3×C8—62no—
65C2×D3×C8—61no—
66C2×D3×C8—61no—
67C3×#108—61no—
68#822—62no—
69#819—21no—
70C22×C3⋊D3C2×Q811yescharacteristic
71C2×D32C4⋊C412yes—
72C2×C32×C4C2×D411yescharacteristic
73C2×C3⋊Dic3#4111yescharacteristic
74C4×C3⋊D3C22×C411yescharacteristic
75C4×C3⋊D3C2×D411yescharacteristic
76C4×C3⋊D3C2×D411yescharacteristic
77C4×C3⋊D3#4111yescharacteristic
78C3×#67—22no—
79C3×D12—21no—
80C3×C4×D3—22no—
81C3×Dic6—21no—
82#627—21no—
83#626—22no—
84#625—21no—
85#624C4⋊C412yes—
86D3×Dic3—22no—
87#622—42no—
88C32×C8C22⋊C411yescharacteristic
89C32×C8C22⋊C411yescharacteristic
90C3⋊(C3⋊C8)C22⋊C411yescharacteristic
91C3⋊(C3⋊C8)C22⋊C411yescharacteristic
92C3×C3⋊C8—22no—
93C3×C3⋊C8—42no—
94C2×#131—91no—
95C2×#108—91no—
96C2×#108—91no—
97#413—92no—
98#338—92no—
99C3×#41—61no—
100#239—61no—
101D3×Q8—61no—
102#237—61no—
103#237—62no—
104D3×D4—61no—
105D3×D4—62no—
106#235—21no—
107#235—62no—
108C2×C4×D3—62no—
109C2×C4×D3—61no—
110C2×C4×D3—61no—
111C3×M16—62no—
112C3×M16—61no—
113C3×M16—62no—
114C2×C3×C8—21no—
115C2×C3×C8—21no—
116C2×C3×C8—62no—
117#208—21no—
118#208—22no—
119#208—62no—
120C2×C3⋊C8—61no—
121C2×C3⋊C8—61no—
122C2×C3⋊C8—62no—
123ΓL(1,𝔽25)—22no—
124ΓL(1,𝔽25)—62no—
125ΓL(1,𝔽25)—62no—
126ΓL(1,𝔽25)—122no—
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—
138D3×C8—122no—
139C22×C32C22⋊Q811yescharacteristic
140C2×C3⋊D3—41no—
141C2×C3⋊D3C2×C4⋊C411yescharacteristic
142C2×C3⋊D3C22⋊Q811yescharacteristic
143C2×C3×D3—22no—
144D32—42no—
145C32×C4C2×C22⋊C411yescharacteristic
146C32×C4#12111yescharacteristic
147C3⋊Dic3#11711yescharacteristic
148C3⋊Dic3#12111yescharacteristic
149C3×Dic3—22no—
150C2×#41—91no—
151#131—61no—
152#131—181no—
153#131—181no—
154#131—181no—
155C2×M16—91no—
156C2×M16—92no—
157C2×M16—92no—
158C2×M16—92no—
159C22×C8—92no—
160C22×C8—91no—
161#108—61no—
162#108—181no—
163#108—181no—
164#108—181no—
165#101—182no—
166#100—182no—
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—
176#67—22no—
177#67—62no—
178#67—62no—
179C2×Dic3—61no—
180C2×Dic3—61no—
181C2×Dic3—62no—
182D12—21no—
183D12—62no—
184C4×D3—22no—
185C4×D3—62no—
186C4×D3—61no—
187C4×D3—61no—
188C4×D3—61no—
189C4×D3—61no—
190C4×D3—61no—
191C4×D3—61no—
192C4×D3—61no—
193C4×D3—61no—
194C4×D3—62no—
195Dic6—21no—
196Dic6—62no—
197C3×C8—21no—
198C3×C8—21no—
199C3×C8—21no—
200C3×C8—21no—
201C3×C8—62no—
202C3×C8—122no—
203C3⋊C8—22no—
204C3⋊C8—42no—
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—91no—
220C2×D4—92no—
221C22×C4—92no—
222C22×C4—91no—
223M16—61no—
224M16—62no—
225M16—62no—
226M16—181no—
227M16—182no—
228M16—182no—
229M16—182no—
230M16—182no—
231C2×C8—62no—
232C2×C8—92no—
233C2×C8—91no—
234C2×C8—91no—
235C2×C8—91no—
236C2×C8—91no—
237C2×C8—91no—
238C2×C8—182no—
239C2×C8—182no—
240C2×C8—182no—
241C2×C8GO+(4,𝔽2)11yescharacteristic
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—
258Dic3—22no—
259Dic3—61no—
260Dic3—61no—
261Dic3—61no—
262Dic3—61no—
263C32#181311yescharacteristic, complemented, Sylow
264C23—92no—
265C23—91no—
266Q8—61no—
267Q8—181no—
268D4—62no—
269D4—61no—
270D4—182no—
271D4—181no—
272C2×C4—62no—
273C2×C4—92no—
274C2×C4—91no—
275C2×C4—91no—
276C2×C4—91no—
277C2×C4—91no—
278C2×C4—91no—
279C2×C4—182no—
280C2×C4C2×GO+(4,𝔽2)11yescharacteristic
281C8—62no—
282C8—91no—
283C8—91no—
284C8—122no—
285C8—362no—
286C8D32⋊C411yescharacteristic
287C8D32⋊C411yescharacteristic
288C2×C3—21no—
289C2×C3—21no—
290C2×C3—41no—
291C2×C3—41no—
292C2×C3—122no—
293D3—42no—
294D3—62no—
295D3—62no—
296D3—121no—
297D3—121no—
298C22—62no—
299C22—91no—
300C22—91no—
301C22—361no—
302C22—362no—
303C22D32⋊Q811yescharacteristic
304C4—62no—
305C4—91no—
306C4—91no—
307C4#6423011yescharacteristic
308C4C2×D32⋊C411yescharacteristic
309C3—21no—
310C3—21no—
311C2—21no—
312C2—122no—
313C2—181no—
314C2—181no—
315C2#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#1813
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×#63770C2semidirect
4. #10590913C2semidirect
5. #10590046C2semidirect
263. C32#1813semidirect

Maximal subgroups

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

subgroupindex
#105946692
C2×#637702
#105933132
#105909132
#105900462
#18139