Finite Group Databasebeta

← #11785619

Subgroups — #11785619

Order 1152.

530 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 530 conjugacy classes of subgroups — too many to draw. Only its 74 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
1C3⋊D3×#131C211yesmaximal, characteristic
2#10593840C212yesmaximal
3#10593771C211yesmaximal, characteristic, complemented
4C2×#63769C211yesmaximal, characteristic, complemented
5#10590188C212yesmaximal, complemented
6#41×C3⋊D3C2211yescharacteristic
7C2×C4⋊#157C2212yes—
8#64283C2212yes—
9C32×#131C411yescharacteristic, complemented
10#64157C411yescharacteristic, complemented
11#64116—21no—
12#64116C411yescharacteristic, complemented
13M16×C3⋊D3—21no—
14M16×C3⋊D3C2211yescharacteristic
15#64110—21no—
16#64110C411yescharacteristic, complemented
17C2×C8×C3⋊D3—21no—
18C2×C8×C3⋊D3C2211yescharacteristic
19#63784—22no—
20#63782—22no—
21#63771—21no—
22#63770—21no—
23#63769—21no—
24#63769—21no—
25D3×#131—62no—
26C22×#157—22no—
27C32×#41C2×C411yescharacteristic
28#3832Q811yescharacteristic
29Q8×C3⋊D3D411yescharacteristic
30#3830—21no—
31#3830Q811yescharacteristic
32D4×C3⋊D3—21no—
33D4×C3⋊D3D411yescharacteristic
34#3828—21no—
35#3828C2×C411yescharacteristic
36C2×C4×C3⋊D3—21no—
37C2×C4×C3⋊D3C2311yescharacteristic
38#3792—22no—
39C4⋊#157—22no—
40C4⋊#157—22no—
41#3788—22no—
42#3787—22no—
43C32×M16—21no—
44C32×M16C2×C411yescharacteristic
45C2×C32×C8—21no—
46C2×C32×C8C2×C411yescharacteristic
47#3748—21no—
48#3748C2×C411yescharacteristic
49C2×C3⋊(C3⋊C8)—21no—
50C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
51#3743—21no—
52#3743—21no—
53#3743—21no—
54C8×C3⋊D3—21no—
55C8×C3⋊D3—21no—
56C8×C3⋊D3—21no—
57C8×C3⋊D3D411yescharacteristic
58C8×C3⋊D3D411yescharacteristic
59C8×C3⋊D3D411yescharacteristic
60C8×C3⋊D3D411yescharacteristic
61#1816—91nomaximal, Sylow
62D3×#41—62no—
63C3×#131—22no—
64#948—62no—
65#907—62no—
66#907—64no—
67D3×M16—62no—
68D3×M16—64no—
69#901—62no—
70#901—64no—
71C2×D3×C8—62no—
72C2×D3×C8—64no—
73C22×C3⋊D3—21no—
74C22×C3⋊D3#4111yescharacteristic
75C2×#157—42no—
76C2×#157—82no—
77C32×Q8C4⋊C411yescharacteristic
78C32×D4—21no—
79C32×D4C4⋊C411yescharacteristic
80C2×C32×C4—21no—
81C2×C32×C4C22×C411yescharacteristic
82#638—21no—
83#638—21no—
84#638—21no—
85C2×C3⋊Dic3—21no—
86C2×C3⋊Dic3#4111yescharacteristic
87C4⋊(C3⋊D3)—21no—
88C4⋊(C3⋊D3)C4⋊C411yescharacteristic
89C4×C3⋊D3—21no—
90C4×C3⋊D3—21no—
91C4×C3⋊D3—21no—
92C4×C3⋊D3C2×D411yescharacteristic
93C4×C3⋊D3C2×D411yescharacteristic
94C4×C3⋊D3C2×D411yescharacteristic
95C4×C3⋊D3C2×Q811yescharacteristic
96#634—21no—
97#634C4⋊C411yescharacteristic
98#622—42no—
99C32×C8—21no—
100C32×C8C22⋊C411yescharacteristic
101C32×C8C22⋊C411yescharacteristic
102C3⋊(C3⋊C8)—21no—
103C3⋊(C3⋊C8)C22⋊C411yescharacteristic
104C3⋊(C3⋊C8)C22⋊C411yescharacteristic
105C2×#131—91no—
106C2×#108—91no—
107C2×#107—91no—
108#417—92no—
109#343—92no—
110C3×#41—22no—
111#239—62no—
112D3×Q8—62no—
113#237—62no—
114#237—64no—
115D3×D4—62no—
116D3×D4—64no—
117#235—62no—
118#235—64no—
119C2×C4×D3—62no—
120C2×C4×D3—64no—
121C3×M16—24no—
122C3×M16—22no—
123C2×C3×C8—24no—
124C2×C3×C8—22no—
125#208—62no—
126#208—64no—
127C2×C3⋊C8—62no—
128C2×C3⋊C8—64no—
129ΓL(1,𝔽25)—64no—
130ΓL(1,𝔽25)—64no—
131ΓL(1,𝔽25)—64no—
132D3×C8—62no—
133D3×C8—62no—
134D3×C8—62no—
135D3×C8—62no—
136D3×C8—64no—
137D3×C8—64no—
138D3×C8—64no—
139C22×C32—21no—
140C22×C32#11711yescharacteristic
141C2×C3⋊D3—21no—
142C2×C3⋊D3—21no—
143C2×C3⋊D3—21no—
144C2×C3⋊D3—41no—
145C2×C3⋊D3—41no—
146C2×C3⋊D3#12111yescharacteristic
147C2×C3⋊D3C22⋊Q811yescharacteristic
148#157—82no—
149C32×C4—21no—
150C32×C4C2×C22⋊C411yescharacteristic
151C32×C4C2×C4⋊C411yescharacteristic
152C3⋊Dic3—21no—
153C3⋊Dic3#12111yescharacteristic
154C3⋊Dic3C22⋊Q811yescharacteristic
155C2×#41—91no—
156#131—91no—
157#131—91no—
158#131—91no—
159#131—181no—
160#131—181no—
161#131#15711yescharacteristic, complemented
162C2×M16—91no—
163C2×M16—92no—
164C2×M16—181no—
165C22×C8—91no—
166C22×C8—181no—
167C2×C4⋊C4—92no—
168#108—181no—
169#108—181no—
170#107—181no—
171#107—181no—
172#103—182no—
173#102—182no—
174C22×D3—62no—
175C22×D3—64no—
176C3×Q8—22no—
177C3×D4—24no—
178C3×D4—22no—
179C2×C3×C4—24no—
180C2×C3×C4—22no—
181#67—64no—
182#67—64no—
183#67—64no—
184C2×Dic3—62no—
185C2×Dic3—64no—
186D12—62no—
187D12—64no—
188C4×D3—62no—
189C4×D3—62no—
190C4×D3—62no—
191C4×D3—62no—
192C4×D3—64no—
193C4×D3—64no—
194C4×D3—64no—
195Dic6—62no—
196Dic6—64no—
197C3×C8—24no—
198C3×C8—22no—
199C3×C8—22no—
200C3⋊C8—62no—
201C3⋊C8—62no—
202C3⋊C8—64no—
203C2×C32—21no—
204C2×C32—41no—
205C2×C32#38011yescharacteristic
206C3⋊D3—21no—
207C3⋊D3—41no—
208C3⋊D3#47211yescharacteristic
209C3⋊D3#47311yescharacteristic
210#41—91no—
211#41—91no—
212#41—91no—
213#41—181no—
214#41—181no—
215#41C2×#15711yescharacteristic
216C2×Q8—91no—
217C2×D4—91no—
218C2×D4—181no—
219C22×C4—91no—
220C22×C4—181no—
221C22×C4—182no—
222M16—21no—
223M16—91no—
224M16—181no—
225M16—181no—
226M16—181no—
227M16—181no—
228M16—182no—
229M16—182no—
230M16C2×#15711yescharacteristic
231C2×C8—21no—
232C2×C8—91no—
233C2×C8—91no—
234C2×C8—91no—
235C2×C8—91no—
236C2×C8—91no—
237C2×C8—181no—
238C2×C8—181no—
239C2×C8—181no—
240C2×C8—181no—
241C2×C8—182no—
242C2×C8C2×#15711yescharacteristic
243C4⋊C4—182no—
244C4⋊C4—182no—
245C22×C3—24no—
246C22×C3—22no—
247C2×D3—62no—
248C2×D3—62no—
249C2×D3—64no—
250C2×D3—122no—
251C2×D3—122no—
252C2×D3—124no—
253C2×D3—124no—
254C3×C4—24no—
255C3×C4—22no—
256C3×C4—22no—
257Dic3—62no—
258Dic3—62no—
259Dic3—64no—
260C32#181611yescharacteristic, complemented, Sylow
261C23—91no—
262C23—181no—
263Q8—91no—
264Q8—181no—
265Q8C4⋊#15711yescharacteristic
266D4—21no—
267D4—91no—
268D4—181no—
269D4—181no—
270D4—181no—
271D4—181no—
272D4C4⋊#15711yescharacteristic
273C2×C4—21no—
274C2×C4—91no—
275C2×C4—91no—
276C2×C4—91no—
277C2×C4—91no—
278C2×C4—91no—
279C2×C4—181no—
280C2×C4—181no—
281C2×C4—181no—
282C2×C4—181no—
283C2×C4—362no—
284C2×C4—722no—
285C2×C4C22×#15711yescharacteristic
286C8—21no—
287C8—91no—
288C8—91no—
289C8—181no—
290C8—362no—
291C8C22⋊#15711yescharacteristic
292C8C22⋊#15711yescharacteristic
293C2×C3—22no—
294C2×C3—42no—
295C2×C3—44no—
296D3—62no—
297D3—62no—
298D3—122no—
299D3—124no—
300C22—21no—
301C22—91no—
302C22—91no—
303C22—181no—
304C22—181no—
305C22—181no—
306C22—361no—
307C22—361no—
308C22#6428611yescharacteristic
309C4—21no—
310C4—91no—
311C4—91no—
312C4—181no—
313C4—722no—
314C4C2×C4⋊#15711yescharacteristic
315C4C2×C22⋊#15711yescharacteristic
316C3—22no—
317C2—21no—
318C2—41no—
319C2—91no—
320C2—91no—
321C2—181no—
322C2—361no—
323C2#1059381211yescharacteristic
subgroupG/H
centerC2#10593812
commutatorC2×C32×C4C22×C4
FrattiniC2×C4C22×#157
FittingC32×#131C4
socleC2×C32#380
prime radical#41×C3⋊D3C22
cosocleC2×C4×C3⋊D3C23
hypercenter#131#157
hypocenterC32#1816
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ #131

Complements

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

NH ≅ G/Ntype
3. #10593771C2semidirect
4. C2×#63769C2semidirect
5. #10590188C2semidirect
9. C32×#131C4semidirect
10. #64157C4semidirect
12. #64116C4semidirect
16. #64110C4semidirect
161. #131#157semidirect
260. C32#1816semidirect

Maximal subgroups

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

subgroupindex
C3⋊D3×#1312
#105938402
#105937712
C2×#637692
#105901882
#18169