Finite Group Databasebeta

← #11783401

Subgroups — #11783401

Order 1152.

1073 conjugacy classes of subgroups; only the 196 normal subgroups are shown.

normal subgroups only

This group has 1073 conjugacy classes of subgroups — too many to draw. Only its 196 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
1C2×C4⋊C4×C3⋊D3C211yesmaximal, characteristic
2C2×#63818C212yesmaximal
3C3×#4530C212yesmaximal, complemented
4#10589168C212yesmaximal, complemented
5D3×#343—32nomaximal
6C22×C4×C3⋊D3C412yes—
7C22×C4×C3⋊D3C2211yescharacteristic
8C2×C32×C4⋊C4C2211yescharacteristic
9C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
10C2×#3750C412yes—
11C4⋊C4×C3⋊D3—22no—
12C4⋊C4×C3⋊D3—22no—
13C2×C3×#208C2214yes—
14C2×#3712—22no—
15#63818—24no—
16#63818C418yescomplemented
17C2×#3710—22no—
18C2×D3×M16—34no—
19C2×D3×C4⋊C4—32no—
20C2×D3×C4⋊C4—61no—
21C3×#343—32no—
22#4554—34no—
23#4530D312yescomplemented
24C23×C3⋊D3C2×C411yescharacteristic
25C22×C32×C4C2×C412yes—
26C22×C32×C4C2311yescharacteristic
27C22×C3⋊Dic3C2×C412yes—
28C22×C3⋊Dic3C2×C411yescharacteristic
29C2×C4×C3⋊D3—22no—
30C2×C4×C3⋊D3—22no—
31C2×C4×C3⋊D3—44no—
32C2×C4×C3⋊D3C2×C414yes—
33C2×C4×C3⋊D3D412yes—
34C2×C4×C3⋊D3D412yes—
35C2×C4×C3⋊D3D412yes—
36C2×C4×C3⋊D3Q812yes—
37C32×C4⋊C4—22no—
38C4⋊(C3⋊Dic3)—22no—
39#3750—24no—
40C3×#208—24no—
41C3×#208C2×C418yescomplemented
42C2×C3×C3⋊C8—24no—
43#3712—28no—
44#3710—28no—
45C2×#343—91noSylow
46C22×C4×D3—32no—
47C22×C4×D3—34no—
48C22×C4×D3—61no—
49C22×C4×D3—62no—
50C2×C3×M16—34no—
51C2×C3×C4⋊C4—21no—
52C2×C3×C4⋊C4C2×D312yes—
53C2×C4⋊Dic3—32no—
54C2×C4⋊Dic3—61no—
55C2×Dic3⋊C4—34no—
56C2×Dic3⋊C4—62no—
57C2×#208C2×D314yes—
58D3×M16—316no—
59D3×M16—68no—
60C2×ΓL(1,𝔽25)—64no—
61C2×D3×C8—64no—
62D3×C4⋊C4—64no—
63D3×C4⋊C4—64no—
64D3×C4⋊C4—64no—
65D3×C4⋊C4—64no—
66C23×C32C22×C411yescharacteristic
67C22×C3⋊D3—22no—
68C22×C3⋊D3—22no—
69C22×C3⋊D3C4212yes—
70C22×C3⋊D3C22⋊C411yescharacteristic
71C22×C3⋊D3C22⋊C411yescharacteristic
72C22×C3⋊D3C4⋊C412yes—
73C2×C32×C4—22no—
74C2×C32×C4—42no—
75C2×C32×C4C22×C412yes—
76C2×C32×C4C2×D411yescharacteristic
77C2×C32×C4C2×D412yes—
78C2×C32×C4C2×Q811yescharacteristic
79C2×C3⋊Dic3—22no—
80C2×C3⋊Dic3—42no—
81C2×C3⋊Dic3C4212yes—
82C2×C3⋊Dic3C22⋊C412yes—
83C2×C3⋊Dic3C4⋊C412yes—
84C4×C3⋊D3—44no—
85C4×C3⋊D3—44no—
86C4×C3⋊D3C22⋊C414yes—
87C4×C3⋊D3C22⋊C414yes—
88C4×C3⋊D3C4⋊C414yes—
89C4×C3⋊D3C4⋊C414yes—
90C3×C3⋊C8—28no—
91C22×M16—92no—
92C22×C4⋊C4—91no—
93#343—32no—
94#343—92no—
95C23×D3—32no—
96C23×D3—61no—
97C22×C3×C4—22no—
98C22×C3×C4—21no—
99C22×C3×C4C4×D314yes—
100C22×C3×C4C22×D312yes—
101C22×Dic3—32no—
102C22×Dic3—34no—
103C22×Dic3—61no—
104C22×Dic3—62no—
105C2×C4×D3—38no—
106C2×C4×D3—34no—
107C2×C4×D3—34no—
108C2×C4×D3—34no—
109C2×C4×D3—34no—
110C2×C4×D3—62no—
111C2×C4×D3—62no—
112C2×C4×D3—64no—
113C2×C4×D3—62no—
114C2×C4×D3—62no—
115C2×C4×D3—64no—
116C2×C4×D3—64no—
117C2×C4×D3—64no—
118C2×C4×D3—64no—
119C2×C4×D3—128no—
120C2×C4×D3—128no—
121C3×M16—38no—
122C3×M16—64no—
123C2×C3×C8—64no—
124C3×C4⋊C4—24no—
125C3×C4⋊C4—24no—
126C4⋊Dic3—64no—
127C4⋊Dic3—64no—
128Dic3⋊C4—68no—
129Dic3⋊C4—68no—
130#208—24no—
131#208C4×D318yescomplemented
132C2×C3⋊C8—24no—
133ΓL(1,𝔽25)—616no—
134D3×C8—616no—
135C22×C32—21no—
136C22×C32—21no—
137C22×C32C2×C4211yescharacteristic
138C22×C32C2×C22⋊C411yescharacteristic
139C22×C32C2×C4⋊C411yescharacteristic
140C2×C3⋊D3—21no—
141C2×C3⋊D3—21no—
142C2×C3⋊D3—24no—
143C2×C3⋊D3—24no—
144C2×C3⋊D3#9512yes—
145C2×C3⋊D3#9512yes—
146C2×C3⋊D3#10012yes—
147C2×C3⋊D3#10112yes—
148C32×C4—42no—
149C32×C4C2×C22⋊C412yes—
150C32×C4C2×C4⋊C412yes—
151C3⋊Dic3—42no—
152C3⋊Dic3#9514yes—
153C23×C4—91no—
154C23×C4—92no—
155C2×M16—34no—
156C2×M16—98no—
157C2×M16—182no—
158C2×M16—184no—
159C22×C8—182no—
160C2×C4⋊C4—92no—
161C2×C4⋊C4—91no—
162C2×C4⋊C4—182no—
163C2×C4⋊C4—182no—
164C2×C4⋊C4D3211yescharacteristic
165C23×C3—21no—
166C23×C3C2×C4×D312yes—
167C22×D3—32no—
168C22×D3—34no—
169C22×D3—32no—
170C22×D3—34no—
171C22×D3—62no—
172C22×D3—61no—
173C22×D3—61no—
174C22×D3—62no—
175C22×D3—64no—
176C22×D3—64no—
177C22×D3—64no—
178C22×D3—64no—
179C2×C3×C4—24no—
180C2×C3×C4—24no—
181C2×C3×C4—21no—
182C2×C3×C4—22no—
183C2×C3×C4—21no—
184C2×C3×C4—22no—
185C2×C3×C4—44no—
186C2×C3×C4—44no—
187C2×C3×C4C2×C4×D314yes—
188C2×C3×C4D3×D412yes—
189C2×C3×C4D3×D414yes—
190C2×C3×C4D3×Q812yes—
191C2×Dic3—34no—
192C2×Dic3—34no—
193C2×Dic3—34no—
194C2×Dic3—62no—
195C2×Dic3—62no—
196C2×Dic3—62no—
197C2×Dic3—64no—
198C2×Dic3—64no—
199C2×Dic3—124no—
200C2×Dic3—124no—
201C4×D3—38no—
202C4×D3—38no—
203C4×D3—38no—
204C4×D3—38no—
205C4×D3—64no—
206C4×D3—64no—
207C4×D3—64no—
208C4×D3—64no—
209C4×D3—128no—
210C4×D3—128no—
211C4×D3—128no—
212C4×D3—128no—
213C3×C8—68no—
214C3⋊C8—28no—
215C2×C32—21no—
216C2×C32—21no—
217C2×C32C2×#9511yescharacteristic
218C2×C32C2×#10011yescharacteristic
219C2×C32C2×#10111yescharacteristic
220C3⋊D3—22no—
221C3⋊D3#34314yescomplemented
222C24—91no—
223C22×C4—91no—
224C22×C4—92no—
225C22×C4—94no—
226C22×C4—92no—
227C22×C4—92no—
228C22×C4—92no—
229C22×C4—92no—
230C22×C4—182no—
231C22×C4—182no—
232C22×C4—364no—
233C22×C4#62412yes—
234C22×C4C2×D3211yescharacteristic
235M16—38no—
236M16—64no—
237M16—188no—
238C2×C8—64no—
239C2×C8—188no—
240C4⋊C4—22no—
241C4⋊C4—184no—
242C4⋊C4—182no—
243C22×C3—22no—
244C22×C3—22no—
245C22×C3—22no—
246C22×C3—22no—
247C22×C3—21no—
248C22×C3—21no—
249C22×C3—21no—
250C22×C3C42×D312yes—
251C22×C3D3×C22⋊C412yes—
252C22×C3D3×C4⋊C412yes—
253C2×D3—34no—
254C2×D3—34no—
255C2×D3—34no—
256C2×D3—34no—
257C2×D3—62no—
258C2×D3—62no—
259C2×D3—62no—
260C2×D3—62no—
261C2×D3—68no—
262C2×D3—68no—
263C2×D3—62no—
264C2×D3—68no—
265C2×D3—68no—
266C2×D3—62no—
267C2×D3—62no—
268C2×D3—62no—
269C3×C4—22no—
270C3×C4—22no—
271C3×C4—44no—
272C3×C4—44no—
273C3×C4D3×C22⋊C414yes—
274C3×C4D3×C4⋊C414yes—
275Dic3—38no—
276Dic3—64no—
277Dic3—124no—
278Dic3—124no—
279C32C2×#34311yescharacteristic, complemented, Sylow
280C23—91no—
281C23—92no—
282C23—92no—
283C23—91no—
284C23—182no—
285C23—182no—
286C23C2×#62411yescharacteristic
287C2×C4—22no—
288C2×C4—42no—
289C2×C4—92no—
290C2×C4—92no—
291C2×C4—92no—
292C2×C4—94no—
293C2×C4—94no—
294C2×C4—94no—
295C2×C4—94no—
296C2×C4—182no—
297C2×C4—364no—
298C2×C4—364no—
299C2×C4—362no—
300C2×C4#379711yescharacteristic
301C2×C4C4×D3212yes—
302C2×C4#380211yescharacteristic
303C2×C4#381112yes—
304C8—68no—
305C2×C3—22no—
306C2×C3—22no—
307C2×C3—22no—
308C2×C3—22no—
309C2×C3—21no—
310C2×C3—21no—
311C2×C3—21no—
312C2×C3D3×#9512yes—
313C2×C3D3×#10012yes—
314C2×C3D3×#10112yes—
315D3—38no—
316D3—64no—
317D3—64no—
318D3—64no—
319C22—21no—
320C22—21no—
321C22—92no—
322C22—92no—
323C22—92no—
324C22—92no—
325C22—184no—
326C22—184no—
327C22—181no—
328C22—181no—
329C22C4×#62411yescharacteristic
330C22#6390011yescharacteristic
331C22#6397411yescharacteristic
332C4—42no—
333C4—94no—
334C4—362no—
335C4#6388312yes—
336C4#6392112yes—
337C3—21no—
338C3D3×#34312yescomplemented
339C2—21no—
340C2—21no—
341C2—94no—
342C2—182no—
343C2#1059137011yescharacteristic
344C2#1059150311yescharacteristic
345C2#1059163911yescharacteristic
subgroupG/H
centerC22#63974
commutatorC22×C32C2×C42
FrattiniC22×C4C2×D32
FittingC2×C32×C4⋊C4C22
socleC22×C32C2×C22⋊C4
prime radicalC23×C3⋊D3C2×C4
cosocleC22×C32×C4C23
hypercenterC2×C4⋊C4D32
hypocenterC32C2×#343
LCSG ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. C3×#4530C2semidirect
4. #10589168C2semidirect
16. #63818C4semidirect
23. #4530D3semidirect
41. C3×#208C2×C4semidirect
131. #208C4×D3semidirect
221. C3⋊D3#343semidirect
279. C32C2×#343semidirect
338. C3D3×#343semidirect

Maximal subgroups

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

subgroupindex
C2×C4⋊C4×C3⋊D32
C2×#638182
C3×#45302
#105891682
D3×#3433