Finite Group Databasebeta

← #11799467

Subgroups — #11799467

Order 1152.

338 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 338 conjugacy classes of subgroups — too many to draw. Only its 68 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#10592891C211yesmaximal, characteristic, complemented
2C2×C3×#828C211yesmaximal, characteristic, complemented
3#10590929C211yesmaximal, characteristic
4#10590624C211yesmaximal, characteristic, complemented
5C3×#4565C211yesmaximal, characteristic, complemented
6#10589143C211yesmaximal, characteristic, complemented
7#10589127C211yesmaximal, characteristic, complemented
8#71491—31nomaximal
9#69271—31nomaximal
10C2×C32×Q16C2211yescharacteristic
11#64151—21no—
12#64110C2211yescharacteristic
13C2×C3×D24C2211yescharacteristic
14#63830—21no—
15#63663—21no—
16#63646C2211yescharacteristic
17C3×#828—21no—
18C3×#828—21no—
19C3×#819C2211yescharacteristic
20C3×#812C2211yescharacteristic
21C2×C3×C3⋊C16C2211yescharacteristic
22#63558—21no—
23#63544—21no—
24#63542—21no—
25C2×C3×SD32—31no—
26#5192—31no—
27#5192—31no—
28#5192—61no—
29C2×#828D311yescharacteristic, complemented
30#5160—31no—
31#4907—31no—
32#4901—31no—
33#4897—31no—
34C3×#362—31no—
35#4565D311yescharacteristic, complemented
36#4563—31no—
37#4516—31no—
38#4506—31no—
39#4493—31no—
40C2×C32×Q8—21no—
41#3828D411yescharacteristic
42C2×C3×D12—21no—
43C32×Q16—21no—
44C32×Q16—21no—
45C2×C32×C8C2311yescharacteristic
46#3756—41no—
47#3755—41no—
48#3748—21no—
49#3748D411yescharacteristic
50#3743—21no—
51C8×C3⋊D3—21no—
52C3×#208—21no—
53C3×D24—21no—
54C3×D24—21no—
55#3716—41no—
56#3714—41no—
57C3×C3⋊C16—21no—
58C3×C3⋊C16D411yescharacteristic
59C3×C3⋊C16D411yescharacteristic
60#2223—91noSylow
61C2×C3×Q16—21no—
62C2×C3×Q16C2×D311yescharacteristic
63C2×C3×Q16C2×D311yescharacteristic
64C2×C3×D8—31no—
65#942—61no—
66#942—61no—
67#942—62no—
68#932—61no—
69#908—61no—
70C2×D24C2×D311yescharacteristic
71#901—31no—
72#901—31no—
73#901—61no—
74C3×SD32—61no—
75C3×SD32—61no—
76C3×M32—31no—
77C2×C3×C16—31no—
78C3×#108—31no—
79#836—61no—
80#836—61no—
81#836—62no—
82#833—61no—
83#828—21no—
84#828—21no—
85#823—61no—
86#819—31no—
87#819—31no—
88#819—61no—
89#819C2×D311yescharacteristic
90#812C2×D311yescharacteristic
91C2×C3⋊C16C2×D311yescharacteristic
92#798—61no—
93#798—61no—
94D3×C16—61no—
95D3×C16—61no—
96C22×C3×D3—41no—
97C32×Q8—41no—
98C32×Q8—41no—
99C2×C32×C4—41no—
100C2×C32×C4C2×D411yescharacteristic
101#638—21no—
102C4⋊(C3⋊D3)D811yescharacteristic
103C4×C3⋊D3—21no—
104#634D811yescharacteristic
105C3×D12—41no—
106C3×D12—41no—
107C32×C8C2×D411yescharacteristic
108C32×C8#4111yescharacteristic
109C3⋊(C3⋊C8)—21no—
110C3⋊(C3⋊C8)—41no—
111C3×C3⋊C8—41no—
112C2×SD32—31no—
113#504—91no—
114#473—91no—
115#472—91no—
116#368—91no—
117#362—31no—
118#361—91no—
119C2×C3×Q8—22no—
120C2×C3×Q8—21no—
121C2×C3×Q8—21no—
122C2×C3×D4—61no—
123#235—31no—
124#235—31no—
125#235—61no—
126C2×D12—21no—
127C3×Q16—21no—
128C3×Q16—21no—
129C3×Q16—21no—
130C3×Q16—21no—
131C3×Q16—41no—
132C3×Q16—41no—
133C3×D8—61no—
134C3×D8—61no—
135C3×M16—61no—
136C2×C3×C8—21no—
137C2×C3×C8C22×D311yescharacteristic
138C2×C3×C8C22×D311yescharacteristic
139#216—121no—
140#216—121no—
141#216—122no—
142#215—121no—
143#215—121no—
144#215—122no—
145#214—121no—
146#213—121no—
147#208—21no—
148#208—31no—
149#208—31no—
150#208—61no—
151#208—62no—
152#208—61no—
153#208—61no—
154D24—21no—
155D24—21no—
156D24—121no—
157#204—121no—
158ΓL(1,𝔽25)—61no—
159ΓL(1,𝔽25)—61no—
160ΓL(1,𝔽25)—121no—
161D3×C8—61no—
162D3×C8—61no—
163D3×C8—121no—
164C3×C16—31no—
165C3×C16—31no—
166C3×C16—61no—
167C3⋊C16—21no—
168C3⋊C16#6711yescharacteristic
169C3⋊C16#6711yescharacteristic
170C22×C32#13511yescharacteristic
171C2×C3⋊D3—21no—
172C2×C3×D3—81no—
173C2×C3×D3—161no—
174C32×C4—81no—
175C32×C4#12111yescharacteristic
176C32×C4C2×D811yescharacteristic
177C3⋊Dic3—21no—
178#137—181no—
179AGL(1,ℤ/8)—181no—
180C2×Q16D3211yescharacteristic
181C2×D8—31no—
182#131—91no—
183SD32—61no—
184SD32—61no—
185M32—31no—
186M32—181no—
187C2×C16—31no—
188C2×C16—181no—
189#108—31no—
190#108—91no—
191#101—181no—
192#100—181no—
193C23×C3—121no—
194C22×D3—41no—
195C3×Q8—42no—
196C3×Q8—42no—
197C3×Q8—41no—
198C3×Q8—41no—
199C3×Q8—41no—
200C3×Q8—41no—
201C3×D4—121no—
202C3×D4—121no—
203C2×C3×C4—21no—
204C2×C3×C4—42no—
205C2×C3×C4—41no—
206C2×C3×C4—41no—
207C2×C3×C4D3×D411yescharacteristic
208C2×C3×C4D3×D411yescharacteristic
209#67—61no—
210#67—61no—
211#67—121no—
212D12—31no—
213D12—31no—
214D12—41no—
215D12—41no—
216D12—61no—
217C4×D3—61no—
218C4×D3—61no—
219C4×D3—121no—
220Dic6—31no—
221Dic6—31no—
222Dic6—61no—
223C3×C8—21no—
224C3×C8—21no—
225C3×C8—121no—
226C3×C8#23511yescharacteristic
227C3×C8D3×D411yescharacteristic
228C3×C8#23711yescharacteristic
229C3×C8C2×#6711yescharacteristic
230C3⋊C8—41no—
231C3⋊C8—61no—
232C3⋊C8—61no—
233C3⋊C8—121no—
234C3⋊C8—122no—
235C3⋊C8—121no—
236C3⋊C8—121no—
237C2×C32—21no—
238C2×C32#46611yescharacteristic
239C3⋊D3—41no—
240C3×D3—161no—
241#41—91no—
242C2×Q8—21no—
243C2×D4—61no—
244Q16—21no—
245Q16—21no—
246Q16—361no—
247SD16—361no—
248SD16—361no—
249D8—61no—
250D8—61no—
251D8—361no—
252M16—61no—
253M16—91no—
254M16—181no—
255M16—181no—
256C2×C8—181no—
257C2×C8C2×D3211yescharacteristic
258C16—31no—
259C16—31no—
260C16—61no—
261C22×C3—21no—
262C22×C3—241no—
263C22×C3—481no—
264C22×C3#91211yescharacteristic
265C22×C3#91611yescharacteristic
266C2×D3—61no—
267C2×D3—61no—
268C2×D3—81no—
269C2×D3—121no—
270C2×D3—161no—
271C3×C4—21no—
272C3×C4—21no—
273C3×C4—82no—
274C3×C4—81no—
275C3×C4—81no—
276C3×C4#88411yescharacteristic
277C3×C4D3×D811yescharacteristic
278C3×C4D3×D811yescharacteristic
279C3×C4#93811yescharacteristic
280Dic3—61no—
281Dic3—61no—
282Dic3—121no—
283C32#222311yescharacteristic, complemented, Sylow
284C23—121no—
285Q8—41no—
286Q8—41no—
287Q8—91no—
288D4—91no—
289D4—121no—
290D4—121no—
291D4—181no—
292C2×C4—41no—
293C2×C4—181no—
294C2×C4#381111yescharacteristic
295C8—121no—
296C8—181no—
297C8—361no—
298C8#380411yescharacteristic
299C8D3×#6711yescharacteristic
300C2×C3—21no—
301C2×C3—21no—
302C2×C3—21no—
303C2×C3—41no—
304C2×C3—481no—
305C2×C3#477511yescharacteristic
306C2×C3#515711yescharacteristic
307D3—121no—
308D3—121no—
309D3—161no—
310D3—241no—
311C22—181no—
312C22—241no—
313C22—481no—
314C22#6393611yescharacteristic
315C4—81no—
316C4—181no—
317C4#6392611yescharacteristic
318C4#6395811yescharacteristic
319C3—21no—
320C3#6927111yescharacteristic, complemented
321C3#7149111yescharacteristic, complemented
322C2—21no—
323C2—361no—
324C2—481no—
325C2#1059145511yescharacteristic
subgroupG/H
centerC2#10591455
commutator, cosocleC2×C32×C8C23
FrattiniC2×C8C2×D32
FittingC2×C32×Q16C22
socleC2×C32#466
prime radical#10590929C2
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. #10592891C2semidirect
2. C2×C3×#828C2semidirect
4. #10590624C2semidirect
5. C3×#4565C2semidirect
6. #10589143C2semidirect
7. #10589127C2semidirect
29. C2×#828D3semidirect
35. #4565D3semidirect
283. C32#2223semidirect
320. C3#69271semidirect
321. C3#71491semidirect

Maximal subgroups

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

subgroupindex
#105928912
C2×C3×#8282
#105909292
#105906242
C3×#45652
#105891432
#105891272
#714913
#692713