Finite Group Databasebeta

← #11799111

Subgroups — #11799111

Order 1152.

371 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 371 conjugacy classes of subgroups — too many to draw. Only its 72 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×#5151C211yesmaximal, characteristic, complemented
2C3×#5147C211yesmaximal, characteristic, complemented
3#10590915C211yesmaximal, characteristic, complemented
4#10590630C211yesmaximal, characteristic, complemented
5#10589429C211yesmaximal, characteristic, complemented
6#10589134C211yesmaximal, characteristic, complemented
7#10589127C211yesmaximal, characteristic, complemented
8#71514—31nomaximal
9#71295—31nomaximal
10C2×C32×D8C2211yescharacteristic
11C3×#940—21no—
12C2×C3×#213—21no—
13C3×#904C2211yescharacteristic
14C2×C3×D24C2211yescharacteristic
15#63814—21no—
16#63646C2211yescharacteristic
17#63639C2211yescharacteristic
18C3×#827—21no—
19C3×#826—21no—
20C3×C8×Dic3C2211yescharacteristic
21C3×#812C2211yescharacteristic
22#63569—21no—
23#63547—21no—
24#63545—21no—
25C3×#509—31no—
26C3×#493—31no—
27#5196—31no—
28#5193—31no—
29#5151D311yescharacteristic, complemented
30#5147—31no—
31#5147D311yescharacteristic, complemented
32#4700—31no—
33#4563—31no—
34#4563—31no—
35#4563—31no—
36#4563—61no—
37#4516—31no—
38#4511—31no—
39#4463—31no—
40C2×C32×D4—21no—
41C2×C3×#67—42no—
42C3×#235—21no—
43C2×C3×D12—21no—
44C32×D8—21no—
45C32×D8—21no—
46C2×C32×C8C2311yescharacteristic
47#3748—21no—
48C3×#213—41no—
49C3×#213—41no—
50C3×C4×Dic3D411yescharacteristic
51C2×C3×C3⋊C8D411yescharacteristic
52C3×Dic12D411yescharacteristic, complemented
53C3×D24—21no—
54C3×D24—21no—
55C3×D24D411yescharacteristic, complemented
56C3×#204—21no—
57#3711—41no—
58D3×C3⋊C8—41no—
59C3⋊(C3⋊C16)—21no—
60C3×C3⋊C16—21no—
61#2213—91noSylow
62C3×#135—31no—
63C2×C3×D8—21no—
64C2×C3×D8—31no—
65C2×C3×D8—61no—
66C2×C3×D8C2×D311yescharacteristic
67C2×C3×D8C2×D311yescharacteristic
68C3×#127—61no—
69#948—61no—
70#940—21no—
71C2×#213—21no—
72#904C2×D311yescharacteristic
73C2×D24C2×D311yescharacteristic
74#901—61no—
75C3×SD32—61no—
76C3×D16—61no—
77C3×M32—31no—
78C3×C4×C8—31no—
79#837—61no—
80#828—61no—
81#827—21no—
82#827—61no—
83#826—21no—
84#826—61no—
85#826—61no—
86#819—31no—
87#819—31no—
88#819—61no—
89C8×Dic3C2×D311yescharacteristic
90#812—31no—
91#812—31no—
92#812—61no—
93#812C2×D311yescharacteristic
94#805—61no—
95C23×C32—41no—
96C22×C3×D3—41no—
97C32×D4—41no—
98C32×D4—41no—
99C2×C32×C4C2×D411yescharacteristic
100C3×#67—41no—
101C3×#67—84no—
102C2×C3×Dic3—21no—
103C3×D12—21no—
104C3×D12—41no—
105C3×D12—41no—
106C3×C4×D3—41no—
107C3×Dic6—21no—
108C32×C8C2×D411yescharacteristic
109C32×C8#4111yescharacteristic
110C3⋊(C3⋊C8)—41no—
111C3×C3⋊C8D811yescharacteristic
112C3×C3⋊C8D811yescharacteristic
113#509—31no—
114#509—91no—
115#493—31no—
116#443—91no—
117#364—91no—
118#361—91no—
119#361—91no—
120C3×#41—61no—
121C2×C3×D4—21no—
122C2×C3×D4—21no—
123C2×C3×D4—41no—
124C2×C3×D4—61no—
125C2×C3×D4—122no—
126C2×#67—42no—
127#235—21no—
128C2×D12—21no—
129C3×Q16—31no—
130C3×SD16—61no—
131C3×D8—22no—
132C3×D8—21no—
133C3×D8—21no—
134C3×D8—21no—
135C3×D8—21no—
136C3×D8—31no—
137C3×D8—41no—
138C3×D8—61no—
139C3×D8—61no—
140C3×D8—121no—
141C3×D8—121no—
142C2×C3×C8—21no—
143C2×C3×C8—31no—
144C2×C3×C8C22×D311yescharacteristic
145C2×C3×C8C22×D311yescharacteristic
146C3×C42—31no—
147#213—41no—
148#213—41no—
149C4×Dic3#6711yescharacteristic
150#208—61no—
151#208—61no—
152#208—121no—
153#208—121no—
154C2×C3⋊C8—121no—
155C2×C3⋊C8#6711yescharacteristic
156Dic12#6711yescharacteristic, complemented
157D24—21no—
158D24—21no—
159D24#6711yescharacteristic, complemented
160#204—21no—
161ΓL(1,𝔽25)—121no—
162D3×C8—121no—
163C3×C16—61no—
164C3⋊C16—21no—
165C3⋊C16—61no—
166C3⋊C16—61no—
167C3⋊C16—121no—
168C22×C32—81no—
169C22×C32—82no—
170C22×C32AGL(1,ℤ/8)11yescharacteristic
171C2×C3×D3—41no—
172C2×C3×D3—82no—
173C2×C3×D3—81no—
174C32×C4#12111yescharacteristic
175C32×C4C2×D811yescharacteristic
176C3×Dic3—22no—
177C3×Dic3—41no—
178#135—31no—
179C2×D8—31no—
180C2×D8—61no—
181C2×D8D3211yescharacteristic
182#131—181no—
183#127—61no—
184SD32—61no—
185SD32—181no—
186D16—61no—
187D16—181no—
188M32—31no—
189M32—91no—
190#108—91no—
191#104—181no—
192C4×C8—31no—
193C23×C3—41no—
194C23×C3—41no—
195C23×C3—81no—
196C23×C3—121no—
197C22×D3—41no—
198C3×Q8—61no—
199C3×D4—42no—
200C3×D4—41no—
201C3×D4—41no—
202C3×D4—41no—
203C3×D4—41no—
204C3×D4—61no—
205C3×D4—81no—
206C3×D4—121no—
207C3×D4—121no—
208C3×D4—121no—
209C3×D4—244no—
210C2×C3×C4—21no—
211C2×C3×C4—61no—
212C2×C3×C4—121no—
213C2×C3×C4D3×D411yescharacteristic
214C2×C3×C4C2×#6711yescharacteristic
215#67—41no—
216#67—84no—
217C2×Dic3—21no—
218D12—21no—
219D12—41no—
220D12—41no—
221C4×D3—41no—
222Dic6—21no—
223C3×C8—21no—
224C3×C8—21no—
225C3×C8—31no—
226C3×C8—31no—
227C3×C8D3×D411yescharacteristic
228C3×C8#23711yescharacteristic
229C3×C8#23711yescharacteristic
230C3×C8C2×#6711yescharacteristic
231C3⋊C8—121no—
232C3⋊C8—121no—
233C3⋊C8—241no—
234C3⋊C8#21311yescharacteristic
235C3⋊C8#21311yescharacteristic
236C2×C32—21no—
237C2×C32—161no—
238C2×C32#45911yescharacteristic
239C3×D3—81no—
240C3×D3—161no—
241#41—61no—
242C2×D4—21no—
243C2×D4—61no—
244C2×D4—122no—
245Q16—31no—
246SD16—61no—
247D8—21no—
248D8—21no—
249D8—31no—
250D8—61no—
251D8—61no—
252D8—121no—
253D8—121no—
254M16—181no—
255M16—361no—
256C2×C8—31no—
257C2×C8—361no—
258C2×C8C2×D3211yescharacteristic
259C42—31no—
260C16—61no—
261C16—181no—
262C22×C3—21no—
263C22×C3—82no—
264C22×C3—82no—
265C22×C3—82no—
266C22×C3—81no—
267C22×C3—81no—
268C22×C3—121no—
269C22×C3—162no—
270C22×C3—242no—
271C22×C3—241no—
272C22×C3#91111yescharacteristic
273C22×C3#93211yescharacteristic
274C2×D3—41no—
275C2×D3—82no—
276C2×D3—81no—
277C3×C4—21no—
278C3×C4—21no—
279C3×C4—62no—
280C3×C4—121no—
281C3×C4D3×D811yescharacteristic
282C3×C4C2×#21311yescharacteristic
283C3×C4#93811yescharacteristic
284C3×C4#93911yescharacteristic
285Dic3—22no—
286Dic3—41no—
287C32#221311yescharacteristic, complemented, Sylow
288C23—41no—
289C23—121no—
290Q8—61no—
291D4—41no—
292D4—41no—
293D4—61no—
294D4—121no—
295D4—121no—
296D4—121no—
297D4—244no—
298C2×C4—61no—
299C2×C4—121no—
300C2×C4D3×#6711yescharacteristic
301C8—31no—
302C8—31no—
303C8—361no—
304C8#380511yescharacteristic
305C8D3×#6711yescharacteristic
306C2×C3—21no—
307C2×C3—21no—
308C2×C3—21no—
309C2×C3—41no—
310C2×C3—162no—
311C2×C3—161no—
312C2×C3—161no—
313C2×C3—241no—
314C2×C3—481no—
315C2×C3#507211yescharacteristic
316C2×C3#515011yescharacteristic
317D3—81no—
318D3—161no—
319C22—82no—
320C22—81no—
321C22—121no—
322C22—242no—
323C22—241no—
324C22#6393211yescharacteristic
325C4—62no—
326C4—121no—
327C4D3×#21311yescharacteristic
328C4#6397011yescharacteristic
329C3—21no—
330C3#7129511yescharacteristic, complemented
331C3#7151411yescharacteristic, complemented
332C2—21no—
333C2—161no—
334C2—241no—
335C2—481no—
336C2#1059142811yescharacteristic
subgroupG/H
centerC2#10591428
commutator, cosocleC2×C32×C8C23
FrattiniC2×C8C2×D32
FittingC2×C32×D8C22
socleC2×C32#459
hypercenterC2×D8D32
hypocenterC32#2213
LCSG ▷ C2×C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×D8

Complements

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

NH ≅ G/Ntype
1. C3×#5151C2semidirect
2. C3×#5147C2semidirect
3. #10590915C2semidirect
4. #10590630C2semidirect
5. #10589429C2semidirect
6. #10589134C2semidirect
7. #10589127C2semidirect
29. #5151D3semidirect
31. #5147D3semidirect
52. C3×Dic12D4semidirect
55. C3×D24D4semidirect
156. Dic12#67semidirect
159. D24#67semidirect
287. C32#2213semidirect
330. C3#71295semidirect
331. C3#71514semidirect

Maximal subgroups

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

subgroupindex
C3×#51512
C3×#51472
#105909152
#105906302
#105894292
#105891342
#105891272
#715143
#712953