Finite Group Databasebeta

← #11867010

Subgroups — #11867010

Order 1152.

1049 conjugacy classes of subgroups; only the 176 normal subgroups are shown.

normal subgroups only

This group has 1049 conjugacy classes of subgroups — too many to draw. Only its 176 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×#63802C211yesmaximal, characteristic, complemented
2C2×#63791C211yesmaximal, characteristic
3#10594631C212yesmaximal
4C3⋊D3×#106C211yesmaximal, characteristic, complemented
5C3×#4867C212yesmaximal, complemented
6#10590854C212yesmaximal, complemented
7#10590601C212yesmaximal, complemented
8#10590520C214yesmaximal, complemented
9D3×#470—32nomaximal
10C2×C4×D32C2211yescharacteristic
11C2×#3797C2212yes—
12C2×C8×C3⋊D3C2211yescharacteristic
13C4⋊C4×C3⋊D3C2212yes—
14C2×C3×Dic12C2212yescomplemented
15C2×C3×ΓL(1,𝔽25)C2212yes—
16C3×#897C2214yes—
17#63921—22no—
18#63900—22no—
19#63899—24no—
20#63856C2214yes—
21C2×#3718C2212yescomplemented
22C2×#3711C2212yes—
23C2×#3710C2211yescharacteristic
24#63802—24no—
25#63791—24no—
26C32×#106C2211yescharacteristic, complemented
27#63644C2211yescharacteristic, complemented
28#63635C2212yescomplemented
29C3×#810C2214yescomplemented
30#63566C2214yescomplemented
31C2×D3×Q16—32no—
32C2×D3×M16—32no—
33D3×C22⋊Q8—34no—
34C3×#470—32no—
35#5189—32no—
36#5137—32no—
37#5052—34no—
38#4867D312yescomplemented
39D3×#106—32no—
40D3×#106—61no—
41#4816—34no—
42D3×#103—34no—
43C22×D32D411yescharacteristic
44C2×C4×C3⋊D3—22no—
45C2×C4×C3⋊D3C2311yescharacteristic
46C2×C3×C4×D3C2312yes—
47C2×C3×Dic6C2314yes—
48C2×#627—22no—
49C2×#624—22no—
50C2×#624D411yescharacteristic
51C2×D3×Dic3D412yes—
52C4×D32—22no—
53C4×D32—22no—
54#3797—24no—
55#3797—24no—
56C2×C32×C8C2311yescharacteristic
57C32×C4⋊C4C2312yes—
58C4⋊(C3⋊Dic3)C2312yes—
59#3750—22no—
60C2×C3⋊(C3⋊C8)C2311yescharacteristic
61C8×C3⋊D3D414yes—
62C3×(C2×D3)⋊C4—24no—
63C3×C4⋊Dic3—24no—
64C2×C3×C3⋊C8C2312yes—
65C3×Dic12—24no—
66C3×ΓL(1,𝔽25)—24no—
67#3724—24no—
68(C2×D3)⋊Dic3—24no—
69#3718—24no—
70#3711—24no—
71#3710—22no—
72C2×#470—91noSylow
73C2×D3×Q8—34no—
74C22×C4×D3—32no—
75C2×C3×Q16—32no—
76C2×C3×M16—32no—
77C3×C22⋊Q8—34no—
78#946—34no—
79C2×#216—34no—
80#924—34no—
81C2×#208—32no—
82D3×Q16—68no—
83D3×M16—68no—
84C2×Dic12C2×D312yescomplemented
85C2×ΓL(1,𝔽25)—32no—
86C2×ΓL(1,𝔽25)C2×D312yes—
87C2×D3×C8—32no—
88C2×D3×C8—32no—
89C2×D3×C8—61no—
90#897C2×D314yes—
91#896—64no—
92D3×C4⋊C4—34no—
93D3×C4⋊C4—62no—
94D3×C4⋊C4—64no—
95D3×C22⋊C4—64no—
96#878—64no—
97C3×#106—21no—
98C3×#106C2×D312yescomplemented
99C3×#103—34no—
100#835—34no—
101#817—32no—
102#817—61no—
103#816—34no—
104#810C2×D314yescomplemented
105#808—34no—
106#808—62no—
107C22×C3⋊D3C2×D411yescharacteristic
108C22×C3×D3C2×D412yes—
109C2×D32—22no—
110C2×D32—24no—
111C2×C32×C4—22no—
112C2×C32×C4C2411yescharacteristic
113C2×C3⋊Dic3—22no—
114C2×C3⋊Dic3C2×D411yescharacteristic
115C4×C3⋊D3—44no—
116C4×C3⋊D3C2×D412yes—
117C4×C3⋊D3#4112yes—
118C2×C3×Dic3—24no—
119C2×C3×Dic3C2×D412yes—
120C3×C4×D3—22no—
121C3×C4×D3—22no—
122C3×Dic6—24no—
123C3×Dic6—24no—
124#627—44no—
125#624—22no—
126#624—44no—
127D3×Dic3—24no—
128C32×C8C2×D412yes—
129C3⋊(C3⋊C8)C2×D412yes—
130C3×C3⋊C8—22no—
131C22×Q16—91no—
132C22×M16—91no—
133C2×C22⋊Q8—92no—
134#470—32no—
135#470—94no—
136#470—92no—
137C2×#106—91no—
138C2×#103—92no—
139C23×D3—32no—
140C2×C3×Q8—34no—
141C22×C3×C4—32no—
142C22×Dic3—32no—
143D3×Q8—68no—
144D3×Q8—68no—
145C2×C4×D3—32no—
146C2×C4×D3—32no—
147C2×C4×D3—32no—
148C2×C4×D3—61no—
149C2×C4×D3—64no—
150C2×C4×D3—64no—
151C2×C4×D3—64no—
152C2×C4×D3—64no—
153C2×C4×D3—122no—
154C2×C4×D3C22×D312yes—
155C2×Dic6—64no—
156C2×Dic6C22×D314yes—
157C3×Q16—64no—
158C3×M16—64no—
159C2×C3×C8—21no—
160C2×C3×C8—32no—
161C2×C3×C8C22×D312yes—
162C3×C4⋊C4—22no—
163C3×C4⋊C4—64no—
164C3×C4⋊C4C22×D314yes—
165C3×C22⋊C4—64no—
166#217—64no—
167#216—68no—
168(C2×D3)⋊C4—24no—
169(C2×D3)⋊C4—64no—
170C4⋊Dic3—24no—
171C4⋊Dic3—34no—
172C4⋊Dic3—62no—
173Dic3⋊C4—64no—
174Dic3⋊C4—64no—
175Dic3⋊C4—64no—
176Dic3⋊C4—122no—
177#208—64no—
178C2×C3⋊C8—32no—
179C2×C3⋊C8—61no—
180C2×C3⋊C8C22×D312yes—
181Dic12—24no—
182ΓL(1,𝔽25)—24no—
183ΓL(1,𝔽25)—64no—
184D3×C8—38no—
185D3×C8—64no—
186D3×C8—64no—
187C22×C32C22×D411yescharacteristic
188C2×C3⋊D3#12112yes—
189C2×C3⋊D3#13714yes—
190C2×C3×D3—22no—
191C2×C3×D3—24no—
192D32—44no—
193C32×C4—42no—
194C32×C4C22×D411yescharacteristic
195C32×C4C2×#4111yescharacteristic
196C3⋊Dic3—42no—
197C3⋊Dic3#12112yes—
198C3×Dic3—22no—
199C3×Dic3—44no—
200C22×Q8—92no—
201C23×C4—91no—
202C2×Q16—32no—
203C2×Q16—92no—
204C2×Q16—184no—
205C2×M16—32no—
206C2×M16—92no—
207C2×M16—184no—
208C22×C8—91no—
209C22×C8—91no—
210C22⋊Q8—34no—
211C22⋊Q8—94no—
212C22⋊Q8—184no—
213C2×C4⋊C4—92no—
214C2×C4⋊C4—182no—
215C2×C22⋊C4—182no—
216#106—91no—
217#106—92no—
218#106D3211yescharacteristic, complemented
219#103—34no—
220#103—94no—
221C23×C3—32no—
222C22×D3—32no—
223C22×D3—61no—
224C22×D3—64no—
225C22×D3—68no—
226C22×D3D3×D412yes—
227C3×Q8—64no—
228C3×Q8—64no—
229C2×C3×C4—24no—
230C2×C3×C4—21no—
231C2×C3×C4—32no—
232C2×C3×C4—42no—
233C2×C3×C4—62no—
234C2×C3×C4—62no—
235C2×C3×C4—64no—
236C2×C3×C4C23×D312yes—
237C2×Dic3—24no—
238C2×Dic3—32no—
239C2×Dic3—61no—
240C2×Dic3—64no—
241C2×Dic3—64no—
242C2×Dic3—122no—
243C2×Dic3D3×D412yes—
244C4×D3—22no—
245C4×D3—22no—
246C4×D3—34no—
247C4×D3—34no—
248C4×D3—62no—
249C4×D3—62no—
250C4×D3—64no—
251C4×D3—64no—
252C4×D3—128no—
253C4×D3—128no—
254C4×D3—244no—
255Dic6—24no—
256Dic6—24no—
257Dic6—128no—
258C3×C8—22no—
259C3×C8—62no—
260C3×C8D3×D414yes—
261C3⋊C8—22no—
262C3⋊C8—34no—
263C3⋊C8—62no—
264C2×C32C2×#12111yescharacteristic
265C2×C32C2×#13712yes—
266C3⋊D3#47014yescomplemented
267C3×D3—42no—
268C24—91no—
269C2×Q8—34no—
270C2×Q8—182no—
271C2×Q8—184no—
272C2×Q8—184no—
273C22×C4—32no—
274C22×C4—91no—
275C22×C4—92no—
276C22×C4—91no—
277C22×C4—182no—
278C22×C4—182no—
279C22×C4—182no—
280C22×C4—182no—
281Q16—64no—
282Q16—184no—
283M16—64no—
284M16—184no—
285C2×C8—32no—
286C2×C8—91no—
287C2×C8—94no—
288C2×C8—182no—
289C2×C8C2×D3211yescharacteristic
290C4⋊C4—64no—
291C4⋊C4—92no—
292C4⋊C4—182no—
293C4⋊C4—184no—
294C4⋊C4C2×D3212yes—
295C22⋊C4—64no—
296C22⋊C4—184no—
297C22×C3—21no—
298C22×C3—64no—
299C22×C3—62no—
300C22×C3C2×D3×D412yes—
301C2×D3—24no—
302C2×D3—22no—
303C2×D3—38no—
304C2×D3—34no—
305C2×D3—62no—
306C2×D3—64no—
307C2×D3—128no—
308C3×C4—21no—
309C3×C4—21no—
310C3×C4—44no—
311C3×C4—62no—
312C3×C4—82no—
313C3×C4—124no—
314C3×C4C2×D3×D412yes—
315C3×C4D3×#4112yes—
316Dic3—22no—
317Dic3—34no—
318Dic3—44no—
319Dic3—62no—
320Dic3—124no—
321Dic3—242no—
322C32C2×#47011yescharacteristic, complemented, Sylow
323C23—32no—
324C23—91no—
325C23—182no—
326C23—184no—
327Q8—64no—
328Q8—64no—
329Q8—364no—
330C2×C4—22no—
331C2×C4—32no—
332C2×C4—62no—
333C2×C4—62no—
334C2×C4—64no—
335C2×C4—91no—
336C2×C4—92no—
337C2×C4—92no—
338C2×C4—182no—
339C2×C4—184no—
340C2×C4—182no—
341C2×C4—364no—
342C2×C4—364no—
343C2×C4C22×D3211yescharacteristic
344C8—62no—
345C8—92no—
346C8#380212yes—
347C2×C3—21no—
348C2×C3—22no—
349C2×C3—122no—
350C2×C3D3×#12112yes—
351C2×C3D3×#13714yes—
352D3—38no—
353D3—42no—
354D3—64no—
355C22—62no—
356C22—64no—
357C22—92no—
358C22—94no—
359C22—364no—
360C22D32×D411yescharacteristic
361C4—42no—
362C4—62no—
363C4—92no—
364C4—124no—
365C4—362no—
366C4C2×#380211yescharacteristic
367C4#6431911yescharacteristic
368C3—21no—
369C3D3×#47012yescomplemented
370C2—94no—
371C2—122no—
372C2#1059461211yescharacteristic
373C2#1059474212yes—
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#106C22
socleC22×C32C22×D4
prime radicalC22×D32D4
hypercenter#106D32
hypocenterC32C2×#470
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #106

Complements

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

NH ≅ G/Ntype
1. C2×#63802C2semidirect
4. C3⋊D3×#106C2semidirect
5. C3×#4867C2semidirect
6. #10590854C2semidirect
7. #10590601C2semidirect
8. #10590520C2semidirect
14. C2×C3×Dic12C22semidirect
21. C2×#3718C22semidirect
26. C32×#106C22semidirect
27. #63644C22semidirect
28. #63635C22semidirect
29. C3×#810C22semidirect
30. #63566C22semidirect
38. #4867D3semidirect
84. C2×Dic12C2×D3semidirect
98. C3×#106C2×D3semidirect
104. #810C2×D3semidirect
218. #106D32semidirect
266. C3⋊D3#470semidirect
322. C32C2×#470semidirect
369. C3D3×#470semidirect

Maximal subgroups

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

subgroupindex
C2×#638022
C2×#637912
#105946312
C3⋊D3×#1062
C3×#48672
#105908542
#105906012
#105905202
D3×#4703