Finite Group Databasebeta

← #11906060

Subgroups — #11906060

Order 1152.

2270 conjugacy classes of subgroups; only the 449 normal subgroups are shown.

normal subgroups only

This group has 2270 conjugacy classes of subgroups — too many to draw. Only its 449 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#10596694C212yesmaximal, complemented
2#41×#157C211yesmaximal, characteristic, complemented
3Q8×GO+(4,𝔽2)C214yesmaximal, complemented
4#10596519C2112yesmaximal, complemented
5#10596511C213yesmaximal, complemented
6C2×#64222C213yesmaximal, complemented
7#10596494C216yesmaximal, complemented
8#41×C3⋊D3C2211yescharacteristic
9C3×#1010—22no—
10D32×Q8C2214yes—
11#64316—22no—
12#64312C22112yes—
13#64309—26no—
14#64306C2216yes—
15C2×#3797C2216yes—
16#64297—26no—
17Q8×#157C2212yes—
18D4×#157C2216yes—
19#64286C2213yes—
20C2×C4×#157C2213yes—
21#64242C22112yes—
22C2×#3773C22112yes—
23#64233C22124yes—
24#64231C2211yescharacteristic
25C4×GO+(4,𝔽2)C22112yes—
26#64222C2216yes—
27#64222C2213yes—
28#64222C22112yes—
29#64221C2216yes—
30D32⋊Q8C22124yes—
31D3×2−1+4—62no—
32C22×#157C2316yes—
33C2×GO+(4,𝔽2)C2314yes—
34C32×#41D411yescharacteristic, complemented
35#3832D411yescharacteristic, complemented
36Q8×C3⋊D3C2311yescharacteristic
37#3830D413yescomplemented
38D4×C3⋊D3C2313yes—
39#3828D413yescomplemented
40C2×C4×C3⋊D3C2313yes—
41C3×D3×Q8—24no—
42C3×#237—212no—
43C3×#235—26no—
44C2×C3×Dic6—26no—
45#3811C23112yes—
46C2×#627—26no—
47C2×#624C23112yes—
48#3805—26no—
49#3804—224no—
50#3802C2312yes—
51C4×D32C23112yes—
52#3799—212no—
53#3798—26no—
54#3797—26no—
55#3797—26no—
56#3797C2316yes—
57#3797C23112yes—
58#3796—26no—
59D3×Dic6—212no—
60C22⋊#157C2316yes—
61C4⋊#157C2316yes—
62C4×#157C2311yescharacteristic
63C4×#157C2313yes—
64C4×#157C2316yes—
65#3773C23124yes—
66#3773C23112yes—
67D32⋊C4C23124yes—
68#3499—91nomaximal, Sylow
69C3×2−1+4—62no—
70#1010—22no—
71#1010—66no—
72#1010—612no—
73D3×#41—66no—
74D3×#41—612no—
75D3×#41—62no—
76#1007—66no—
77#1007—64no—
78C2×D3×Q8—66no—
79C2×D3×Q8—64no—
80C22×C3⋊D3C2413yes—
81C2×D32C2414yes—
82C2×#157—212no—
83C2×#157C2416yes—
84C2×#157C2412yes—
85GO+(4,𝔽2)—28no—
86C32×Q8C2×D411yescharacteristic
87C32×D4C2×D413yes—
88C2×C32×C4C2×D413yes—
89#638C2×D416yes—
90C2×C3⋊Dic3C2×D413yes—
91C4⋊(C3⋊D3)C2×D413yes—
92C4×C3⋊D3C2×D413yes—
93C4×C3⋊D3C2×D413yes—
94C4×C3⋊D3C2411yescharacteristic
95C4×C3⋊D3C2413yes—
96#634C2×D413yes—
97C3×#67—212no—
98C2×C3×Dic3—212no—
99C3×D12—22no—
100C3×C4×D3—212no—
101C3×Dic6—212no—
102C3×Dic6—26no—
103#627—212no—
104#627—26no—
105#626—212no—
106#625—22no—
107#624—212no—
108#624C24112yes—
109D3×Dic3—212no—
110C2×2−1+4—92no—
111D4×Q8—94no—
112#547—912no—
113#536—96no—
114#532—93no—
115C2×C4⋊Q8—93no—
116C4×#41—91no—
117C3×#41—22no—
118C3×#41—66no—
119C3×#41—612no—
120C2×C3×Q8—66no—
121C2×C3×Q8—64no—
122#239—62no—
123#239—612no—
124#239—66no—
125D3×Q8—24no—
126D3×Q8—612no—
127D3×Q8—66no—
128D3×Q8—62no—
129D3×Q8—612no—
130D3×Q8—612no—
131D3×Q8—612no—
132#237—212no—
133#237—66no—
134#237—66no—
135#237—624no—
136#237—612no—
137D3×D4—62no—
138D3×D4—612no—
139D3×D4—66no—
140#235—26no—
141#235—66no—
142#235—612no—
143#235—612no—
144#235—624no—
145C2×C4×D3—612no—
146C2×C4×D3—612no—
147C2×C4×D3—66no—
148C2×Dic6—26no—
149C2×Dic6—612no—
150C2×Dic6—612no—
151C22×C32C22×D413yes—
152C2×C3⋊D3—26no—
153C2×C3⋊D3C22×D413yes—
154C2×C3⋊D3C2511yescharacteristic
155C2×C3×D3—24no—
156D32—28no—
157#157—26no—
158#1572−1+414yescomplemented
159C32×C4C22×D411yescharacteristic
160C32×C4C22×D413yes—
161C3⋊Dic3C22×D413yes—
162C3⋊Dic3C22×D411yescharacteristic
163C3×Dic3—212no—
1642−1+4—62no—
1652−1+4—182no—
1662−1+4—186no—
1672−1+4—186no—
168C2×#41—96no—
169C2×#41—912no—
170C2×#41—91no—
171C22×Q8—96no—
172C22×Q8—94no—
173C4⋊Q8—93no—
174C4⋊Q8—96no—
175C4⋊Q8—912no—
176#127—91no—
177#124—96no—
178#123—924no—
179C22⋊Q8—924no—
180#121—912no—
181C4×Q8—92no—
182C4×D4—96no—
183C4×D4—912no—
184#117—93no—
185C2×C4⋊C4—912no—
186C2×C42—93no—
187C22×D3—64no—
188C22×D3—66no—
189C3×Q8—22no—
190C3×Q8—66no—
191C3×Q8—612no—
192C3×D4—26no—
193C3×D4—62no—
194C3×D4—612no—
195C2×C3×C4—26no—
196C2×C3×C4—612no—
197C2×C3×C4—612no—
198#67—212no—
199#67—612no—
200#67—612no—
201#67—64no—
202C2×Dic3—212no—
203C2×Dic3—66no—
204C2×Dic3—612no—
205D12—22no—
206D12—66no—
207D12—612no—
208C4×D3—212no—
209C4×D3—612no—
210C4×D3—66no—
211C4×D3—66no—
212C4×D3—62no—
213C4×D3—66no—
214C4×D3—624no—
215C4×D3—612no—
216Dic6—26no—
217Dic6—212no—
218Dic6—66no—
219Dic6—624no—
220Dic6—612no—
221C2×C32—23no—
222C2×C32C23×D411yescharacteristic
223C3⋊D3—23no—
224C3⋊D3C2×2−1+412yes—
225C3×D3—44no—
226#41—612no—
227#41—66no—
228#41—91no—
229#41—93no—
230#41—93no—
231#41—186no—
232#41—1824no—
233#41—1812no—
234#41—186no—
235#41—186no—
236#41GO+(4,𝔽2)11yescharacteristic, complemented
237C2×Q8—64no—
238C2×Q8—66no—
239C2×Q8—912no—
240C2×Q8—96no—
241C2×Q8—91no—
242C2×Q8—186no—
243C2×Q8—1812no—
244C2×Q8—186no—
245C2×Q8—186no—
246C2×D4—912no—
247C2×D4—92no—
248C2×D4—93no—
249C2×D4—94no—
250C22×C4—912no—
251C22×C4—912no—
252C22×C4—93no—
253C22×C4—96no—
254C4⋊C4—912no—
255C4⋊C4—924no—
256C4⋊C4—96no—
257C22⋊C4—96no—
258C22⋊C4—924no—
259C42—91no—
260C42—93no—
261C42—96no—
262C22×C3—26no—
263C22×C3—64no—
264C2×D3—24no—
265C2×D3—62no—
266C2×D3—66no—
267C2×D3—128no—
268C2×D3—1212no—
269C3×C4—22no—
270C3×C4—26no—
271C3×C4—612no—
272Dic3—212no—
273Dic3—62no—
274Dic3—66no—
275C32#349911yescharacteristic, complemented, Sylow
276C23—94no—
277C23—93no—
278Q8—612no—
279Q8—66no—
280Q8—93no—
281Q8—186no—
282Q8—1812no—
283Q8C2×GO+(4,𝔽2)11yescharacteristic
284D4—612no—
285D4—62no—
286D4—96no—
287D4—93no—
288D4—1812no—
289D4—182no—
290D4—188no—
291D4C2×GO+(4,𝔽2)13yes—
292C2×C4—612no—
293C2×C4—612no—
294C2×C4—912no—
295C2×C4—92no—
296C2×C4—93no—
297C2×C4—91no—
298C2×C4—93no—
299C2×C4—93no—
300C2×C4—93no—
301C2×C4—96no—
302C2×C4—1812no—
303C2×C4—1812no—
304C2×C4—1812no—
305C2×C4C2×GO+(4,𝔽2)13yes—
306C2×C3—22no—
307C2×C3—46no—
308C2×C3—124no—
309D3—44no—
310D3—64no—
311D3—126no—
312C22—64no—
313C22—91no—
314C22—93no—
315C22—186no—
316C22—188no—
317C22C22×GO+(4,𝔽2)13yes—
318C4—612no—
319C4—94no—
320C4—91no—
321C4—93no—
322C4—186no—
323C4C22×GO+(4,𝔽2)13yes—
324C4C22×GO+(4,𝔽2)11yescharacteristic
325C3—22no—
326C2—23no—
327C2—92no—
328C2—124no—
329C2—183no—
330C2C23×GO+(4,𝔽2)11yescharacteristic
subgroupG/H
center, FrattiniC2C23×GO+(4,𝔽2)
commutator, cosocleC2×C3⋊D3C25
FittingC32×#41D4
socleC2×C32C23×D4
hypercenter#41GO+(4,𝔽2)
hypocenterC32#3499
LCSG ▷ C2×C3⋊D3 ▷ C32
UCSC1 ◁ C2 ◁ #41

Complements

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

NH ≅ G/Ntype
1. #10596694C2semidirect
2. #41×#157C2semidirect
3. Q8×GO+(4,𝔽2)C2semidirect
4. #10596519C2semidirect
5. #10596511C2semidirect
6. C2×#64222C2semidirect
7. #10596494C2semidirect
34. C32×#41D4semidirect
35. #3832D4semidirect
37. #3830D4semidirect
39. #3828D4semidirect
158. #1572−1+4semidirect
236. #41GO+(4,𝔽2)semidirect
275. C32#3499semidirect

Maximal subgroups

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

subgroupindex
#105966942
#41×#1572
Q8×GO+(4,𝔽2)2
#105965192
#105965112
C2×#642222
#105964942
#34999