Finite Group Databasebeta

← #11799466

Subgroups — #11799466

Order 1152.

333 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 333 conjugacy classes of subgroups — too many to draw. Only its 70 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×#63655C211yesmaximal, characteristic, complemented
2C3×#5192C211yesmaximal, characteristic, complemented
3#10590927C211yesmaximal, characteristic
4#10590622C211yesmaximal, characteristic, complemented
5C3×#4565C211yesmaximal, characteristic, complemented
6#10589144C211yesmaximal, characteristic, complemented
7#10589128C211yesmaximal, characteristic, complemented
8#71097—31nomaximal
9#69271—31nomaximal
10C2×C32×Q16C2211yescharacteristic
11C2×#3745C2211yescharacteristic
12C3×#942—21no—
13C3×#901C2211yescharacteristic
14#63825—21no—
15#63655—21no—
16#63655—21no—
17C2×C3⋊(C3⋊C16)C2211yescharacteristic
18C3×#836—21no—
19C3×#819C2211yescharacteristic
20C3×#819C2211yescharacteristic
21C3×#812C2211yescharacteristic
22#63559—21no—
23#63543—21no—
24D3×C3⋊C16—21no—
25C3×#473—31no—
26#5192D311yescharacteristic, complemented
27C2×#828—31no—
28C2×#828—31no—
29C2×#828—61no—
30#5142—31no—
31#5140—31no—
32#4907—31no—
33#4897—31no—
34C3×#362—31no—
35#4565D311yescharacteristic, complemented
36#4516—31no—
37#4495—31no—
38#4493—31no—
39#4493—31no—
40C2×C32×Q8—21no—
41C2×C4⋊(C3⋊D3)—21no—
42C3×#235D411yescharacteristic
43C32×Q16—21no—
44C32×Q16—21no—
45C2×C32×C8C2311yescharacteristic
46#3745—21no—
47#3745—21no—
48C3×#216—41no—
49C3×#215—41no—
50C3×#208—21no—
51C3×#208—21no—
52C3×#208D411yescharacteristic
53C3×ΓL(1,𝔽25)—21no—
54C3×D3×C8—21no—
55#3717—41no—
56#3714—41no—
57C3⋊(C3⋊C16)D411yescharacteristic
58C3⋊(C3⋊C16)D411yescharacteristic
59C3×C3⋊C16—21no—
60#2223—91noSylow
61C3×#137—61no—
62C2×C3×Q16—21no—
63C2×C3×Q16C2×D311yescharacteristic
64C2×C3×Q16C2×D311yescharacteristic
65C3×#131—31no—
66#949—61no—
67#942—21no—
68#908—61no—
69C2×D24—31no—
70C2×D24—31no—
71C2×D24—61no—
72#901C2×D311yescharacteristic
73C3×M32—31no—
74C3×#108—31no—
75C3×#108—31no—
76C3×#101—61no—
77#836—21no—
78#828—61no—
79#828—61no—
80#828—61no—
81#828—61no—
82#828—62no—
83#828—62no—
84#823—61no—
85#823—61no—
86#819C2×D311yescharacteristic
87#819C2×D311yescharacteristic
88#812—61no—
89#812C2×D311yescharacteristic
90C2×C3⋊C16—31no—
91C2×C3⋊C16—31no—
92C2×C3⋊C16—61no—
93C2×C3⋊C16—61no—
94#798—61no—
95D3×C16—61no—
96C22×C3⋊D3—41no—
97C32×Q8—41no—
98C32×Q8—41no—
99C2×C32×C4—41no—
100C2×C32×C4C2×D411yescharacteristic
101C4⋊(C3⋊D3)—41no—
102C4⋊(C3⋊D3)—41no—
103C3×#67—21no—
104C3×D12D811yescharacteristic
105C3×C4×D3—21no—
106C3×Dic6D811yescharacteristic
107C32×C8C2×D411yescharacteristic
108C32×C8#4111yescharacteristic
109C3×C3⋊C8—21no—
110C3×C3⋊C8—41no—
111C3×C3⋊C8—41no—
112C2×SD32—91no—
113#504—91no—
114#473—31no—
115#472—91no—
116#368—91no—
117#362—31no—
118#361—91no—
119C3×#41—31no—
120C2×C3×Q8—21no—
121C2×C3×Q8—21no—
122C2×C3×Q8—41no—
123#235#6711yescharacteristic
124C2×D12—61no—
125C2×D12—61no—
126C2×D12—121no—
127C3×Q16—22no—
128C3×Q16—21no—
129C3×Q16—21no—
130C3×Q16—21no—
131C3×Q16—21no—
132C3×Q16—41no—
133C3×Q16—121no—
134C3×SD16—121no—
135C3×M16—31no—
136C3×M16—61no—
137C3×M16—61no—
138C3×M16—61no—
139C2×C3×C8—21no—
140C2×C3×C8—61no—
141C2×C3×C8C22×D311yescharacteristic
142C2×C3×C8C22×D311yescharacteristic
143#216—41no—
144#215—41no—
145#215—121no—
146#213—121no—
147#208—21no—
148#208—21no—
149#208#6711yescharacteristic
150D24—62no—
151D24—61no—
152D24—61no—
153D24—61no—
154D24—61no—
155D24—121no—
156D24—121no—
157#204—121no—
158ΓL(1,𝔽25)—21no—
159D3×C8—21no—
160C3×C16—61no—
161C3⋊C16—21no—
162C3⋊C16—31no—
163C3⋊C16—31no—
164C3⋊C16—31no—
165C3⋊C16—31no—
166C3⋊C16—61no—
167C3⋊C16—61no—
168C22×C32#13511yescharacteristic
169C2×C3⋊D3—81no—
170C2×C3⋊D3—161no—
171C2×C3×D3—21no—
172C32×C4—81no—
173C32×C4#12111yescharacteristic
174C32×C4C2×D811yescharacteristic
175C3×Dic3—21no—
176#137—61no—
177AGL(1,ℤ/8)—181no—
178C2×Q16D3211yescharacteristic
179C2×D8—91no—
180#131—31no—
181SD32—181no—
182SD32—181no—
183M32—31no—
184M32—181no—
185C2×C16—91no—
186C2×C16—181no—
187#108—31no—
188#108—31no—
189#101—61no—
190#100—181no—
191C22×D3—121no—
192C22×D3—121no—
193C22×D3—241no—
194C3×Q8—31no—
195C3×Q8—42no—
196C3×Q8—41no—
197C3×Q8—41no—
198C3×Q8—41no—
199C3×Q8—41no—
200C3×Q8—81no—
201C3×D4—31no—
202C3×D4—61no—
203C2×C3×C4—21no—
204C2×C3×C4—41no—
205C2×C3×C4—41no—
206C2×C3×C4—61no—
207C2×C3×C4—81no—
208C2×C3×C4D3×D411yescharacteristic
209C2×C3×C4C2×#6711yescharacteristic
210#67—21no—
211D12—122no—
212D12—121no—
213D12—121no—
214D12—121no—
215D12—121no—
216D12—241no—
217D12#21311yescharacteristic
218C4×D3—21no—
219Dic6#21311yescharacteristic
220C3×C8—21no—
221C3×C8—21no—
222C3×C8—61no—
223C3×C8—121no—
224C3×C8—121no—
225C3×C8#23511yescharacteristic
226C3×C8D3×D411yescharacteristic
227C3×C8D3×D411yescharacteristic
228C3×C8#23711yescharacteristic
229C3⋊C8—21no—
230C3⋊C8—41no—
231C3⋊C8—41no—
232C2×C32—21no—
233C2×C32#46611yescharacteristic
234C3⋊D3—161no—
235C3×D3—41no—
236#41—31no—
237C2×Q8—21no—
238C2×D4—181no—
239Q16—21no—
240Q16—21no—
241Q16—121no—
242SD16—121no—
243SD16—361no—
244D8—181no—
245D8—181no—
246D8—361no—
247M16—31no—
248M16—61no—
249M16—61no—
250M16—61no—
251C2×C8—61no—
252C2×C8C2×D3211yescharacteristic
253C16—61no—
254C16—91no—
255C16—91no—
256C22×C3—21no—
257C22×C3—61no—
258C22×C3#91611yescharacteristic
259C22×C3#95011yescharacteristic
260C2×D3—21no—
261C2×D3—242no—
262C2×D3—241no—
263C2×D3—241no—
264C2×D3—482no—
265C2×D3—481no—
266C2×D3—481no—
267C3×C4—21no—
268C3×C4—21no—
269C3×C4—61no—
270C3×C4—82no—
271C3×C4—81no—
272C3×C4—81no—
273C3×C4#88411yescharacteristic
274C3×C4D3×D811yescharacteristic
275C3×C4C2×#21311yescharacteristic
276C3×C4#93911yescharacteristic
277Dic3—21no—
278C32#222311yescharacteristic, complemented, Sylow
279C23—361no—
280Q8—31no—
281Q8—41no—
282Q8—41no—
283D4—31no—
284D4—61no—
285D4—361no—
286D4—361no—
287C2×C4—41no—
288C2×C4—61no—
289C2×C4D3×#6711yescharacteristic
290C8—61no—
291C8—121no—
292C8—121no—
293C8#380411yescharacteristic
294C8#381111yescharacteristic
295C2×C3—22no—
296C2×C3—21no—
297C2×C3—21no—
298C2×C3—21no—
299C2×C3—121no—
300C2×C3#477511yescharacteristic
301C2×C3#503811yescharacteristic
302D3—41no—
303D3—482no—
304D3—481no—
305D3—481no—
306C22—61no—
307C22—721no—
308C22—1441no—
309C22#6393511yescharacteristic
310C4—61no—
311C4—81no—
312C4D3×#21311yescharacteristic
313C4#6397111yescharacteristic
314C3—21no—
315C3#6927111yescharacteristic, complemented
316C3#7109711yescharacteristic, complemented
317C2—21no—
318C2—121no—
319C2—1441no—
320C2#1059144911yescharacteristic
subgroupG/H
centerC2#10591449
commutator, cosocleC2×C32×C8C23
FrattiniC2×C8C2×D32
FittingC2×C32×Q16C22
socleC2×C32#466
prime radical#10590927C2
hypercenterC2×Q16D32
hypocenterC32#2223
LCSG ▷ C2×C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×Q16

Complements

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

NH ≅ G/Ntype
1. C2×#63655C2semidirect
2. C3×#5192C2semidirect
4. #10590622C2semidirect
5. C3×#4565C2semidirect
6. #10589144C2semidirect
7. #10589128C2semidirect
26. #5192D3semidirect
35. #4565D3semidirect
278. C32#2223semidirect
315. C3#69271semidirect
316. C3#71097semidirect

Maximal subgroups

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

subgroupindex
C2×#636552
C3×#51922
#105909272
#105906222
C3×#45652
#105891442
#105891282
#710973
#692713