Finite Group Databasebeta

← #11859551

Subgroups — #11859551

Order 1152.

1041 conjugacy classes of subgroups; only the 244 normal subgroups are shown.

normal subgroups only

This group has 1041 conjugacy classes of subgroups — too many to draw. Only its 244 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#10595032C211yesmaximal, characteristic
2C2×#63815C212yesmaximal, complemented
3C2×#63642C211yesmaximal, characteristic, complemented
4C3×#5110C212yesmaximal, complemented
5#10591120C211yesmaximal, characteristic, complemented
6#10590725C218yesmaximal, complemented
7#78658—32nomaximal
8C2×C3×#235C2212yes—
9C22×C32×C8C2211yescharacteristic
10C2×C4×C3⋊Dic3C2211yescharacteristic
11C22×C3⋊(C3⋊C8)C2211yescharacteristic
12C2×C3×#208C2212yes—
13#63980C414yes—
14#63914C411yescharacteristic
15C4×#625C2214yes—
16#63873C411yescharacteristic
17#63863C412yes—
18C2×#3711C2214yes—
19#63815—28no—
20C2×D3×C3⋊C8C2214yes—
21#63642C2214yes—
22C3×(C2×D3)⋊C8C2218yes—
23#63572C2214yes—
24#5832—32no—
25C2×#948—32no—
26C2×#907—32no—
27C3×#408—32no—
28#5118—32no—
29#5110D312yescomplemented
30C2×#815—32no—
31C2×#815—61no—
32#4730—38no—
33#4728—38no—
34C22×C32×C4C2311yescharacteristic
35C22×C3⋊Dic3C2×C412yes—
36C2×C3×#67C2×C414yes—
37C3×#235—24no—
38C3×#235—24no—
39C2×C3×D12C2×C412yes—
40C2×C3×C4×D3C2314yes—
41C2×C3×Dic6C2×C412yes—
42C2×#625C2×C414yes—
43C2×C32×C8—22no—
44C2×C32×C8C2312yes—
45C4×C3⋊Dic3C2×C411yescharacteristic
46C4×C3⋊Dic3C2×C411yescharacteristic
47C4×C3⋊Dic3C2312yes—
48C2×C3⋊(C3⋊C8)D414yescomplemented
49C2×C3⋊(C3⋊C8)C2312yes—
50C3×#208—24no—
51C2×C3×C3⋊C8C2314yes—
52#3724C2×C414yes—
53(C2×D3)⋊Dic3C2×C418yes—
54#3711—28no—
55D3×C3⋊C8—28no—
56#2932—91noSylow
57C2×C3×#41—32no—
58C2×#235C2×D312yes—
59C2×C3×M16—32no—
60C22×C3×C8—21no—
61C22×C3×C8C2×D312yes—
62#948—68no—
63#947—32no—
64#944—32no—
65#940—32no—
66#939—38no—
67#936—32no—
68C4×#67—38no—
69C2×C4×Dic3—32no—
70C2×C4×Dic3—61no—
71C2×#208—34no—
72C2×#208C2×D312yes—
73C22×C3⋊C8—32no—
74C22×C3⋊C8—34no—
75C22×C3⋊C8—61no—
76#907—68no—
77C2×ΓL(1,𝔽25)—34no—
78C2×D3×C8—34no—
79C3×C22⋊C8—38no—
80(C2×D3)⋊C8C2×D318yes—
81#815—34no—
82#815—34no—
83#815—64no—
84Dic3⋊C8—38no—
85C23×C32C22×C411yescharacteristic
86C22×C3×D3C22×C414yes—
87C2×C32×C4C22×C411yescharacteristic
88C2×C32×C4C2×D412yes—
89C2×C32×C4#4112yes—
90C2×C32×C4C2411yescharacteristic
91C2×C3⋊Dic3—42no—
92C2×C3⋊Dic3C22×C412yes—
93C2×C3⋊Dic3C22×C412yes—
94C3×#67—28no—
95C2×C3×Dic3C22×C414yes—
96C3×D12—24no—
97C3×C4×D3—24no—
98C3×C4×D3—24no—
99C3×Dic6—24no—
100#625—44no—
101C32×C8—22no—
102C3⋊(C3⋊C8)C2×D414yes—
103C3×C3⋊C8—24no—
104C2×#131—92no—
105#532—91no—
106#435—98no—
107#423—91no—
108#408—32no—
109C2×#97—91no—
110C3×#41—64no—
111C3×#41—64no—
112C2×C3×Q8—32no—
113C2×C3×D4—34no—
114C2×C3×D4—32no—
115C22×C3×C4—21no—
116C22×C3×C4—34no—
117C22×C3×C4C22×D312yes—
118C2×#67—38no—
119C2×#67C4×D314yes—
120C22×Dic3—34no—
121C22×Dic3—62no—
122#235—24no—
123#235—24no—
124C2×D12C4×D312yes—
125C2×C4×D3C22×D314yes—
126C2×Dic6C4×D312yes—
127C3×M16—64no—
128C2×C3×C8—24no—
129C2×C3×C8—24no—
130C2×C3×C8—22no—
131C2×C3×C8—34no—
132C2×C3×C8C22×D314yes—
133#217—38no—
134(C2×D3)⋊C4—38no—
135Dic3⋊C4—38no—
136C4×Dic3—32no—
137C4×Dic3—32no—
138C4×Dic3—34no—
139C4×Dic3—62no—
140C4×Dic3—61no—
141C4×Dic3—61no—
142#208—24no—
143#208—68no—
144C2×C3⋊C8—38no—
145C2×C3⋊C8—32no—
146C2×C3⋊C8—32no—
147C2×C3⋊C8—62no—
148C2×C3⋊C8—64no—
149C2×C3⋊C8—68no—
150C2×C3⋊C8C22×D314yes—
151ΓL(1,𝔽25)—68no—
152D3×C8—68no—
153C22×C32—22no—
154C22×C32C4×D412yes—
155C22×C32C23×C411yescharacteristic
156C2×C3×D3—24no—
157C2×C3×D3—28no—
158C32×C4C4×D412yes—
159C32×C4C22×D411yescharacteristic
160C32×C4C2×#4111yescharacteristic
161C3⋊Dic3—22no—
162C3⋊Dic3—22no—
163C3×Dic3—24no—
164C2×#41—32no—
165#131—188no—
166C2×M16—32no—
167C2×M16—94no—
168C22×C8—94no—
169C22×C8—91no—
170C22×C8D3211yescharacteristic
171C4⋊Q8—91no—
172#127—91no—
173#124—92no—
174#121—94no—
175C4×D4—94no—
176C2×C42—91no—
177C4⋊C8—94no—
178C22⋊C8—38no—
179#97—94no—
180C23×C3—21no—
181C23×C3—34no—
182C23×C3C2×C4×D312yes—
183C22×D3C2×C4×D314yes—
184C3×Q8—64no—
185C3×D4—68no—
186C3×D4—64no—
187C2×C3×C4—21no—
188C2×C3×C4—21no—
189C2×C3×C4—22no—
190C2×C3×C4—22no—
191C2×C3×C4—34no—
192C2×C3×C4—64no—
193C2×C3×C4—64no—
194C2×C3×C4C2×C4×D312yes—
195C2×C3×C4D3×D414yes—
196C2×C3×C4#23714yes—
197C2×C3×C4C23×D312yes—
198#67—28no—
199#67—128no—
200C2×Dic3—34no—
201C2×Dic3—34no—
202C2×Dic3—62no—
203C2×Dic3—62no—
204C2×Dic3—124no—
205C2×Dic3—124no—
206C2×Dic3C2×C4×D314yes—
207D12—24no—
208C4×D3—24no—
209C4×D3—24no—
210Dic6—24no—
211C3×C8—24no—
212C3×C8—24no—
213C3×C8—64no—
214C3⋊C8—24no—
215C3⋊C8—34no—
216C3⋊C8—34no—
217C3⋊C8—64no—
218C2×C32—22no—
219C2×C32C2×C4×D411yescharacteristic
220C2×C32#56812yes—
221C3×D3—44no—
222#41—64no—
223#41—64no—
224C2×Q8—32no—
225C2×D4—34no—
226C2×D4—32no—
227C2×D4—94no—
228C22×C4—34no—
229C22×C4—92no—
230C22×C4C2×D3211yescharacteristic
231M16—64no—
232M16—188no—
233C2×C8—22no—
234C2×C8—34no—
235C2×C8—92no—
236C2×C8—94no—
237C2×C8—188no—
238C2×C8C2×D3212yes—
239C4⋊C4—94no—
240C22⋊C4—98no—
241C42—92no—
242C42—91no—
243C42—91no—
244C22×C3—24no—
245C22×C3—24no—
246C22×C3—21no—
247C22×C3—22no—
248C22×C3—64no—
249C22×C3—68no—
250C22×C3#67⋊C414yes—
251C22×C3C22×C4×D312yes—
252C2×D3—24no—
253C2×D3—28no—
254C3×C4—21no—
255C3×C4—21no—
256C3×C4—22no—
257C3×C4—64no—
258C3×C4#67⋊C414yes—
259C3×C4C2×D3×D412yes—
260C3×C4C2×#23712yes—
261Dic3—24no—
262Dic3—64no—
263Dic3—64no—
264Dic3—122no—
265Dic3—122no—
266C32#293211yescharacteristic, complemented, Sylow
267C23—34no—
268C23C4×D3211yescharacteristic
269Q8—64no—
270D4—68no—
271D4—64no—
272D4—364no—
273C2×C4—34no—
274C2×C4—64no—
275C2×C4—64no—
276C2×C4—92no—
277C2×C4—92no—
278C2×C4—362no—
279C2×C4C4×D3211yescharacteristic
280C2×C4#380212yes—
281C2×C4#380512yes—
282C2×C4C22×D3211yescharacteristic
283C8—22no—
284C8—64no—
285C8—94no—
286C2×C3—24no—
287C2×C3—24no—
288C2×C3—22no—
289C2×C3—21no—
290C2×C3—124no—
291C2×C3C2×#67⋊C412yes—
292C2×C3#575014yes—
293D3—44no—
294C22—22no—
295C22—68no—
296C22—64no—
297C22#6390212yes—
298C22C2×C4×D3211yescharacteristic
299C4—64no—
300C4—182no—
301C4—182no—
302C4#6390212yes—
303C4C2×#380211yescharacteristic
304C4C2×#380511yescharacteristic
305C3—21no—
306C3#7865812yescomplemented
307C2—22no—
308C2—124no—
309C2#1059467012yes—
310C2C2×#6390211yescharacteristic
subgroupG/H
center, FrattiniC2×C4C22×D32
commutator, socleC22×C32C23×C4
FittingC22×C32×C8C22
prime radical#10595032C2
cosocleC2×C32×C4C24
hypercenterC22×C8D32
hypocenterC32#2932
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
2. C2×#63815C2semidirect
3. C2×#63642C2semidirect
4. C3×#5110C2semidirect
5. #10591120C2semidirect
6. #10590725C2semidirect
29. #5110D3semidirect
48. C2×C3⋊(C3⋊C8)D4semidirect
266. C32#2932semidirect
306. C3#78658semidirect

Maximal subgroups

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

subgroupindex
#105950322
C2×#638152
C2×#636422
C3×#51102
#105911202
#105907252
#786583