Finite Group Databasebeta

← #11784129

Subgroups — #11784129

Order 1152.

462 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 462 conjugacy classes of subgroups — too many to draw. Only its 88 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#10596647C211yesmaximal, characteristic
2#10593841C211yesmaximal, characteristic
3#10593775C211yesmaximal, characteristic, complemented
4#10593723C211yesmaximal, characteristic, complemented
5C3⋊D3×#104C211yesmaximal, characteristic
6#10590190C211yesmaximal, characteristic, complemented
7#10590151C211yesmaximal, characteristic, complemented
8#41×C3⋊D3C2211yescharacteristic
9#64289C412yescomplemented
10#64287—22no—
11#64287C412yescomplemented
12#64286C2211yescharacteristic
13#64283—21no—
14#64283C2211yescharacteristic
15C2×#3787—21no—
16C2×#3787C2211yescharacteristic
17C2×#3787C2211yescharacteristic
18M16×C3⋊D3C2211yescharacteristic
19C42×C3⋊D3C2211yescharacteristic
20#63784C412yescomplemented
21#63782C412yescomplemented
22#63777—22no—
23#63767—21no—
24C8×#157—21no—
25C32×#104C411yescharacteristic, complemented
26#63664C411yescharacteristic, complemented
27#63652C411yescharacteristic, complemented
28#63632C411yescharacteristic, complemented
29D3×#104—62no—
30C32×#41C2×C411yescharacteristic
31#3832C2×C411yescharacteristic
32Q8×C3⋊D3C2×C411yescharacteristic
33#3830—21no—
34#3830C2×C411yescharacteristic
35D4×C3⋊D3—21no—
36D4×C3⋊D3C2×C411yescharacteristic
37#3828—21no—
38#3828C2×C411yescharacteristic
39C2×C4×C3⋊D3—21no—
40C2×C4×C3⋊D3—21no—
41C2×C4×C3⋊D3C2311yescharacteristic
42C22⋊#157—21no—
43#3792—21no—
44#3792—22no—
45C2×#622—21no—
46C2×#622—22no—
47C2×#622D412yes—
48C4⋊#157C2×C412yes—
49C4×#157—21no—
50#3788—22no—
51#3788C2×C412yes—
52#3787—21no—
53#3787—21no—
54#3787—22no—
55#3787C2×C412yes—
56#3787C2×C412yes—
57#3787D411yescharacteristic
58#3787D411yescharacteristic
59C32×M16C2×C411yescharacteristic
60C32×C42C2×C411yescharacteristic
61C4×C3⋊Dic3—21no—
62C4×C3⋊Dic3C2×C411yescharacteristic
63#3748C2×C411yescharacteristic
64#3743—21no—
65C8×C3⋊D3—21no—
66#1765—91nomaximal, Sylow
67D3×#41—62no—
68D3×M16—62no—
69C42×D3—62no—
70C3×#104—22no—
71#837—62no—
72#825—62no—
73#805—62no—
74C22×C3⋊D3—21no—
75C22×C3⋊D3#4111yescharacteristic
76C2×#157—22no—
77C32×Q8C4211yescharacteristic
78C32×D4—21no—
79C32×D4C4211yescharacteristic
80C2×C32×C4—21no—
81C2×C32×C4—21no—
82C2×C32×C4C22×C411yescharacteristic
83#638—21no—
84#638—21no—
85#638—21no—
86C2×C3⋊Dic3—21no—
87C2×C3⋊Dic3—21no—
88C2×C3⋊Dic3C2×D411yescharacteristic
89C4⋊(C3⋊D3)—21no—
90C4⋊(C3⋊D3)C4211yescharacteristic
91C4×C3⋊D3—21no—
92C4×C3⋊D3—21no—
93C4×C3⋊D3—21no—
94C4×C3⋊D3—42no—
95C4×C3⋊D3C22×C411yescharacteristic
96C4×C3⋊D3C22×C411yescharacteristic
97C4×C3⋊D3C2×D411yescharacteristic
98C4×C3⋊D3#4111yescharacteristic
99#634—21no—
100#634C4211yescharacteristic
101#622—22no—
102#622—22no—
103#622C22⋊C412yes—
104#622C22⋊C412yes—
105C32×C8—21no—
106C3⋊(C3⋊C8)—21no—
107C2×#131—91no—
108C2×#104—91no—
109#416—91no—
110#405—91no—
111C2×#97—91no—
112#341—91no—
113#339—91no—
114C3×#41—22no—
115#239—62no—
116D3×Q8—62no—
117#237—62no—
118#237—122no—
119D3×D4—62no—
120D3×D4—122no—
121#235—62no—
122#235—122no—
123C2×C4×D3—62no—
124C2×C4×D3—122no—
125C2×C4×D3—122no—
126C3×M16—22no—
127C3×C42—22no—
128C4×Dic3—62no—
129C4×Dic3—122no—
130#208—62no—
131ΓL(1,𝔽25)—122no—
132D3×C8—122no—
133C22×C32—21no—
134C22×C32C4×D411yescharacteristic
135C2×C3⋊D3—22no—
136C2×C3⋊D3—21no—
137C2×C3⋊D3—42no—
138C2×C3⋊D3#11711yescharacteristic
139C2×C3⋊D3C4×D411yescharacteristic
140#157—42no—
141C32×C4—21no—
142C32×C4—41no—
143C32×C4C2×C4211yescharacteristic
144C32×C4C4×D411yescharacteristic
145C3⋊Dic3—21no—
146C3⋊Dic3—41no—
147C3⋊Dic3C2×C22⋊C411yescharacteristic
148C3⋊Dic3C4×D411yescharacteristic
149C2×#41—91no—
150#131—92no—
151#131—92no—
152#131—182no—
153C2×M16—91no—
154C2×M16—91no—
155C2×M16—181no—
156C22×C8—91no—
157C22×C8—91no—
158C22×C8—181no—
159#117—91no—
160C2×C42—91no—
161#104—91no—
162#104—91no—
163#104—91no—
164#104#15711yescharacteristic, complemented
165#103—92no—
166#102—92no—
167#97—181no—
168#97—182no—
169C4×C8—181no—
170C22×D3—62no—
171C22×D3—122no—
172C3×Q8—22no—
173C3×D4—22no—
174C3×D4—42no—
175C2×C3×C4—22no—
176C2×C3×C4—42no—
177C2×C3×C4—42no—
178#67—122no—
179#67—122no—
180#67—122no—
181C2×Dic3—62no—
182C2×Dic3—122no—
183C2×Dic3—122no—
184D12—62no—
185D12—122no—
186C4×D3—62no—
187C4×D3—62no—
188C4×D3—62no—
189C4×D3—62no—
190C4×D3—122no—
191C4×D3—122no—
192C4×D3—122no—
193C4×D3—128no—
194Dic6—62no—
195Dic6—122no—
196C3×C8—42no—
197C3⋊C8—122no—
198C2×C32—21no—
199C2×C32—41no—
200C2×C32C4×C22⋊C411yescharacteristic
201C3⋊D3—21no—
202C3⋊D3—41no—
203C3⋊D3#44412yes—
204#41—91no—
205#41—91no—
206#41—91no—
207#41—181no—
208#41—181no—
209#41C2×#15711yescharacteristic
210C2×Q8—91no—
211C2×D4—91no—
212C2×D4—181no—
213C22×C4—91no—
214C22×C4—181no—
215C22×C4—181no—
216M16—92no—
217M16—91no—
218M16—181no—
219M16—182no—
220M16—182no—
221M16—181no—
222M16C2×#15711yescharacteristic
223C2×C8—91no—
224C2×C8—91no—
225C2×C8—92no—
226C2×C8—92no—
227C2×C8—92no—
228C2×C8—181no—
229C2×C8—182no—
230C2×C8—182no—
231C2×C8—181no—
232C2×C8—181no—
233C2×C8—181no—
234C4⋊C4—92no—
235C22⋊C4—181no—
236C42—91no—
237C42—181no—
238C42—181no—
239C42C2×#15711yescharacteristic
240C22×C3—22no—
241C22×C3—42no—
242C2×D3—62no—
243C2×D3—62no—
244C2×D3—124no—
245C2×D3—122no—
246C2×D3—244no—
247C3×C4—22no—
248C3×C4—22no—
249C3×C4—42no—
250C3×C4—44no—
251Dic3—62no—
252Dic3—62no—
253Dic3—122no—
254Dic3—124no—
255C32#176511yescharacteristic, complemented, Sylow
256C23—91no—
257C23—181no—
258Q8—91no—
259Q8—181no—
260Q8C4×#15711yescharacteristic
261D4—21no—
262D4—91no—
263D4—181no—
264D4—181no—
265D4—181no—
266D4—181no—
267D4C4×#15711yescharacteristic
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—91no—
271C2×C4—91no—
272C2×C4—91no—
273C2×C4—91no—
274C2×C4—91no—
275C2×C4—181no—
276C2×C4—181no—
277C2×C4—181no—
278C2×C4—181no—
279C2×C4—182no—
280C2×C4—181no—
281C2×C4—362no—
282C2×C4C22×#15711yescharacteristic
283C8—21no—
284C8—92no—
285C8—92no—
286C8—182no—
287C8—182no—
288C8—181no—
289C2×C3—22no—
290C2×C3—42no—
291C2×C3—82no—
292D3—64no—
293D3—122no—
294D3—242no—
295C22—21no—
296C22—91no—
297C22—91no—
298C22—182no—
299C22—181no—
300C22—362no—
301C22D4×#15711yescharacteristic
302C4—21no—
303C4—41no—
304C4—91no—
305C4—91no—
306C4—181no—
307C4—361no—
308C4—362no—
309C4C2×C4×#15711yescharacteristic
310C4D4×#15711yescharacteristic
311C3—22no—
312C2—21no—
313C2—41no—
314C2—92no—
315C2—181no—
316C2—361no—
317C2C22⋊C4×#15711yescharacteristic
subgroupG/H
centerC4D4×#157
commutatorC32×C4C2×C42
FrattiniC2×C4C22×#157
FittingC32×#104C4
socleC2×C32C4×C22⋊C4
prime radical#41×C3⋊D3C22
cosocleC2×C4×C3⋊D3C23
hypercenter#104#157
hypocenterC32#1765
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C2×C4 ◁ #104

Complements

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

NH ≅ G/Ntype
3. #10593775C2semidirect
4. #10593723C2semidirect
6. #10590190C2semidirect
7. #10590151C2semidirect
9. #64289C4semidirect
11. #64287C4semidirect
20. #63784C4semidirect
21. #63782C4semidirect
25. C32×#104C4semidirect
26. #63664C4semidirect
27. #63652C4semidirect
28. #63632C4semidirect
164. #104#157semidirect
255. C32#1765semidirect

Maximal subgroups

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

subgroupindex
#105966472
#105938412
#105937752
#105937232
C3⋊D3×#1042
#105901902
#105901512
#17659