Finite Group Databasebeta

← #11918952

Subgroups — #11918952

Order 1152.

2202 conjugacy classes of subgroups; only the 445 normal subgroups are shown.

normal subgroups only

This group has 2202 conjugacy classes of subgroups — too many to draw. Only its 445 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#10596647C211yesmaximal, characteristic, complemented
3#10596520C214yesmaximal, complemented
4#10596516C2112yesmaximal, complemented
5C2×#64228C213yesmaximal, complemented
6#10596505C216yesmaximal, complemented
7#10596500C213yesmaximal, complemented
8#41×C3⋊D3C2211yescharacteristic
9C3×#1010—22no—
10D32×Q8—22no—
11#64316C2214yescomplemented
12#64312—26no—
13#64309C22112yescomplemented
14#64306C2216yes—
15C2×#3797C2216yes—
16#64297—26no—
17#64289C2212yescomplemented
18#64287C2216yescomplemented
19#64283C2213yes—
20C2×#3787C2213yes—
21C2×#3776C22112yescomplemented
22#64239C22124yescomplemented
23#64237C22112yescomplemented
24#64228C2213yes—
25#64228C2216yes—
26#64228C22112yescomplemented
27#64227C2216yes—
28#64226C22124yescomplemented
29#64225C2211yescharacteristic
30#64223C22112yescomplemented
31D3×2−1+4—62no—
32C32×#41D411yescharacteristic
33#3832C2311yescharacteristic
34Q8×C3⋊D3D411yescharacteristic
35#3830C2313yes—
36D4×C3⋊D3D413yes—
37#3828D413yes—
38C2×C4×C3⋊D3C2313yes—
39C3×D3×Q8—24no—
40C3×#237—212no—
41C3×#235—26no—
42C2×C3×Dic6—26no—
43#3811—26no—
44C2×#627C23112yes—
45C2×#624—26no—
46#3805C23112yes—
47#3804—224no—
48#3802C2312yes—
49C4×D32—26no—
50#3799—212no—
51#3798C23112yes—
52#3797—26no—
53#3797—26no—
54#3797C2316yes—
55#3797C23112yes—
56#3796—26no—
57D3×Dic6—212no—
58#3792C2316yes—
59C2×#622C2316yes—
60#3788C2316yes—
61#3787C2311yescharacteristic
62#3787C2313yes—
63#3787C2316yes—
64#3776C23112yes—
65#3776C23124yes—
66#3775C23124yes—
67#3774C2314yes—
68C2×#578—91nomaximal, Sylow
69C3×2−1+4—62no—
70#1010—22no—
71#1010—612no—
72#1010—66no—
73D3×#41—66no—
74D3×#41—62no—
75D3×#41—612no—
76#1007—64no—
77#1007—66no—
78C2×D3×Q8—66no—
79C2×D3×Q8—64no—
80C22×C3⋊D3C2×D413yes—
81C2×D32—22no—
82C32×Q8C2×D411yescharacteristic
83C32×D4C2×D413yes—
84C2×C32×C4C2×D413yes—
85#638C2×D416yes—
86C2×C3⋊Dic3C2413yes—
87C4⋊(C3⋊D3)C2×D413yes—
88C4×C3⋊D3C2×D413yes—
89C4×C3⋊D3C2×D413yes—
90C4×C3⋊D3C2411yescharacteristic
91C4×C3⋊D3C2413yes—
92#634C2×D413yes—
93C3×#67—212no—
94C2×C3×Dic3—212no—
95C3×D12—22no—
96C3×C4×D3—212no—
97C3×Dic6—212no—
98C3×Dic6—26no—
99#627—212no—
100#627C24112yes—
101#626—212no—
102#625C2414yes—
103#624—26no—
104#624—212no—
105D3×Dic3—212no—
106#622C2412yes—
107#622C2416yes—
108C2×2−1+4—92no—
109#578—912no—
110#578—94no—
111C2×#137—96no—
112C2×#135—93no—
113C22×Q16—93no—
114C2×#131—91no—
115C3×#41—22no—
116C3×#41—66no—
117C3×#41—612no—
118C2×C3×Q8—66no—
119C2×C3×Q8—64no—
120#239—62no—
121#239—612no—
122#239—66no—
123D3×Q8—24no—
124D3×Q8—66no—
125D3×Q8—612no—
126D3×Q8—62no—
127D3×Q8—612no—
128D3×Q8—612no—
129D3×Q8—612no—
130#237—212no—
131#237—612no—
132#237—66no—
133#237—66no—
134#237—624no—
135D3×D4—62no—
136D3×D4—66no—
137D3×D4—612no—
138#235—26no—
139#235—612no—
140#235—66no—
141#235—612no—
142#235—624no—
143C2×C4×D3—66no—
144C2×C4×D3—612no—
145C2×C4×D3—612no—
146C2×Dic6—26no—
147C2×Dic6—612no—
148C2×Dic6—612no—
149C22×C32C22×D413yes—
150C2×C3⋊D3—26no—
151C2×C3⋊D3C22×D413yes—
152C2×C3⋊D3C22×D411yescharacteristic
153C2×C3×D3—24no—
154D32—44no—
155C32×C4C22×D411yescharacteristic
156C32×C4C22×D413yes—
157C3⋊Dic3C22×D413yes—
158C3⋊Dic3C2511yescharacteristic
159C3×Dic3—212no—
1602−1+4—62no—
1612−1+4—94no—
1622−1+4—912no—
1632−1+4—186no—
164C2×#41—91no—
165C2×#41—96no—
166C2×#41—186no—
167C22×Q8—96no—
168C22×Q8—182no—
169#137—924no—
170#137—924no—
171#135—912no—
172#135—912no—
173C2×Q16—93no—
174C2×Q16—96no—
175C2×Q16—912no—
176C2×Q16—912no—
177C2×SD16—96no—
178C2×D8—91no—
179#131—96no—
180#131—92no—
181C2×M16—93no—
182C22×C8—93no—
183C22×D3—66no—
184C22×D3—64no—
185C3×Q8—22no—
186C3×Q8—66no—
187C3×Q8—612no—
188C3×D4—26no—
189C3×D4—62no—
190C3×D4—612no—
191C2×C3×C4—26no—
192C2×C3×C4—612no—
193C2×C3×C4—612no—
194#67—212no—
195#67—64no—
196#67—612no—
197#67—612no—
198C2×Dic3—212no—
199C2×Dic3—66no—
200C2×Dic3—612no—
201D12—22no—
202D12—66no—
203D12—612no—
204C4×D3—212no—
205C4×D3—66no—
206C4×D3—66no—
207C4×D3—62no—
208C4×D3—66no—
209C4×D3—612no—
210C4×D3—624no—
211C4×D3—612no—
212Dic6—26no—
213Dic6—212no—
214Dic6—612no—
215Dic6—66no—
216Dic6—624no—
217C2×C32—23no—
218C2×C32C23×D411yescharacteristic
219C3⋊D3—23no—
220C3⋊D3#57812yescomplemented
221C3×D3—44no—
222#41—612no—
223#41—66no—
224#41—912no—
225#41—91no—
226#41—93no—
227#41—93no—
228#41—912no—
229#41—1824no—
230#41—1812no—
231#41—186no—
232#41GO+(4,𝔽2)11yescharacteristic
233C2×Q8—64no—
234C2×Q8—66no—
235C2×Q8—912no—
236C2×Q8—91no—
237C2×Q8—96no—
238C2×Q8—912no—
239C2×Q8—1812no—
240C2×Q8—186no—
241C2×Q8—186no—
242C2×D4—92no—
243C2×D4—93no—
244C2×D4—186no—
245C22×C4—93no—
246C22×C4—186no—
247C22×C4—186no—
248Q16—912no—
249Q16—924no—
250SD16—924no—
251D8—94no—
252M16—96no—
253M16—96no—
254C2×C8—91no—
255C2×C8—93no—
256C2×C8—96no—
257C2×C8—96no—
258C22×C3—26no—
259C22×C3—64no—
260C2×D3—24no—
261C2×D3—62no—
262C2×D3—66no—
263C2×D3—1212no—
264C2×D3—128no—
265C3×C4—22no—
266C3×C4—26no—
267C3×C4—612no—
268Dic3—212no—
269Dic3—66no—
270Dic3—62no—
271C32C2×#57811yescharacteristic, complemented, Sylow
272C23—93no—
273C23—182no—
274Q8—612no—
275Q8—66no—
276Q8—912no—
277Q8—93no—
278Q8—1812no—
279Q8C2×GO+(4,𝔽2)11yescharacteristic
280D4—612no—
281D4—62no—
282D4—94no—
283D4—96no—
284D4—93no—
285D4—1812no—
286D4C2×GO+(4,𝔽2)13yes—
287C2×C4—612no—
288C2×C4—612no—
289C2×C4—93no—
290C2×C4—91no—
291C2×C4—93no—
292C2×C4—93no—
293C2×C4—93no—
294C2×C4—186no—
295C2×C4—1812no—
296C2×C4—1812no—
297C2×C4C2×GO+(4,𝔽2)13yes—
298C8—92no—
299C8—96no—
300C2×C3—22no—
301C2×C3—46no—
302C2×C3—124no—
303D3—44no—
304D3—64no—
305D3—126no—
306C22—64no—
307C22—91no—
308C22—93no—
309C22—186no—
310C22—364no—
311C22C22×GO+(4,𝔽2)13yes—
312C4—612no—
313C4—91no—
314C4—93no—
315C4C22×GO+(4,𝔽2)13yes—
316C4C22×GO+(4,𝔽2)11yescharacteristic
317C3—22no—
318C2—23no—
319C2—92no—
320C2—124no—
321C2—183no—
322C2C23×GO+(4,𝔽2)11yescharacteristic
subgroupG/H
center, FrattiniC2C23×GO+(4,𝔽2)
commutator, cosocleC3⋊Dic3C25
FittingC32×#41D4
socleC2×C32C23×D4
hypercenter#41GO+(4,𝔽2)
hypocenterC32C2×#578
LCSG ▷ C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ #41

Complements

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

NH ≅ G/Ntype
1. #10596694C2semidirect
2. #10596647C2semidirect
3. #10596520C2semidirect
4. #10596516C2semidirect
5. C2×#64228C2semidirect
6. #10596505C2semidirect
7. #10596500C2semidirect
11. #64316C22semidirect
13. #64309C22semidirect
17. #64289C22semidirect
18. #64287C22semidirect
21. C2×#3776C22semidirect
22. #64239C22semidirect
23. #64237C22semidirect
26. #64228C22semidirect
28. #64226C22semidirect
30. #64223C22semidirect
220. C3⋊D3#578semidirect
271. C32C2×#578semidirect

Maximal subgroups

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

subgroupindex
#105966942
#105966472
#105965202
#105965162
C2×#642282
#105965052
#105965002
C2×#5789