Finite Group Databasebeta

← #11799119

Subgroups — #11799119

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×#4908C211yesmaximal, characteristic, complemented
2#10590915C211yesmaximal, characteristic, complemented
3#10590880C211yesmaximal, characteristic, complemented
4#10590634C211yesmaximal, characteristic, complemented
5#10589382C211yesmaximal, characteristic, complemented
6C3×#4511C211yesmaximal, characteristic, complemented
7#10589127C211yesmaximal, characteristic, complemented
8#71514—31nomaximal
9#69305—31nomaximal
10C2×#3745C2211yescharacteristic
11C3×#904C2211yescharacteristic
12C2×C3×D24C2211yescharacteristic
13#63911—21no—
14C2×#3714—21no—
15#63814—21no—
16C32×M32C2211yescharacteristic
17#63646C2211yescharacteristic
18C3×C8×Dic3C2211yescharacteristic
19C3×#812C2211yescharacteristic
20C3×#800—21no—
21C3×D48—21no—
22#63569—21no—
23#63549—21no—
24#63546—21no—
25C3×#509—31no—
26#5196—31no—
27#5193—31no—
28#5151—31no—
29#4908—31no—
30#4908D311yescharacteristic, complemented
31#4700—31no—
32#4695—31no—
33C3×#364—31no—
34#4563—31no—
35#4516—31no—
36#4516—31no—
37#4516—31no—
38#4516—61no—
39#4511D311yescharacteristic, complemented
40C2×C4⋊(C3⋊D3)—21no—
41C3×#235—21no—
42C2×C3×D12—21no—
43C2×#626—42no—
44C2×C32×C8C2311yescharacteristic
45#3748—21no—
46#3745—21no—
47#3745—21no—
48C3×C4×Dic3D411yescharacteristic
49C2×C3×C3⋊C8D411yescharacteristic
50C3×Dic12D411yescharacteristic, complemented
51C3×D24—21no—
52C3×D24—21no—
53C3×D24D411yescharacteristic, complemented
54C3×#204—21no—
55#3714—41no—
56#3714—41no—
57#3711—41no—
58D3×C3⋊C8—41no—
59C32×C16—21no—
60C3×C3⋊C16—21no—
61#2213—91noSylow
62C3×#135—31no—
63C2×C3×D8—31no—
64#948—61no—
65#940—61no—
66C2×#213—61no—
67#904C2×D311yescharacteristic
68C2×D24—31no—
69C2×D24—31no—
70C2×D24—61no—
71C2×D24—61no—
72C2×D24C2×D311yescharacteristic
73#901—61no—
74#874—61no—
75C3×SD32—61no—
76C3×D16—61no—
77C3×M32—21no—
78C3×M32—31no—
79C3×M32C2×D311yescharacteristic
80C3×M32C2×D311yescharacteristic
81C3×C4×C8—31no—
82#837—61no—
83#828—61no—
84#826—61no—
85#819—31no—
86#819—31no—
87#819—61no—
88C8×Dic3C2×D311yescharacteristic
89#812C2×D311yescharacteristic
90#805—61no—
91#800—21no—
92#800—61no—
93D48—21no—
94D48—61no—
95C22×C3⋊D3—41no—
96C22×C3×D3—41no—
97C2×C32×C4C2×D411yescharacteristic
98C4⋊(C3⋊D3)—41no—
99C4⋊(C3⋊D3)—41no—
100C3×#67—41no—
101C2×C3×Dic3—21no—
102C3×D12—21no—
103C3×D12—41no—
104C3×D12—41no—
105C3×C4×D3—41no—
106C3×Dic6—21no—
107#626—84no—
108C32×C8C2×D411yescharacteristic
109C32×C8#4111yescharacteristic
110C3⋊(C3⋊C8)—41no—
111C3×C3⋊C8D811yescharacteristic
112C3×C3⋊C8D811yescharacteristic
113#509—31no—
114#509—91no—
115#493—91no—
116#443—91no—
117#364—31no—
118#361—91no—
119#361—91no—
120C3×#41—61no—
121C2×C3×D4—61no—
122C2×#67—122no—
123#235—21no—
124C2×D12—21no—
125C2×D12—61no—
126C2×D12—61no—
127C2×D12—121no—
128C2×D12—122no—
129C3×Q16—31no—
130C3×SD16—61no—
131C3×D8—31no—
132C3×D8—61no—
133C3×D8—61no—
134C2×C3×C8—21no—
135C2×C3×C8—31no—
136C2×C3×C8C22×D311yescharacteristic
137C2×C3×C8C22×D311yescharacteristic
138C3×C42—31no—
139#213—121no—
140#213—121no—
141C4×Dic3D1211yescharacteristic
142#208—61no—
143#208—61no—
144#208—121no—
145#208—121no—
146C2×C3⋊C8—121no—
147C2×C3⋊C8D1211yescharacteristic
148Dic12#6711yescharacteristic, complemented
149D24—21no—
150D24—21no—
151D24—62no—
152D24—61no—
153D24—61no—
154D24—61no—
155D24—61no—
156D24—121no—
157D24—121no—
158D24—121no—
159D24#6711yescharacteristic, complemented
160#204—21no—
161ΓL(1,𝔽25)—121no—
162D3×C8—121no—
163C3×C16—21no—
164C3×C16—21no—
165C3×C16—41no—
166C3×C16—61no—
167C3⋊C16—21no—
168C22×C32AGL(1,ℤ/8)11yescharacteristic
169C2×C3⋊D3—81no—
170C2×C3⋊D3—82no—
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—91no—
181C2×D8—181no—
182#131—181no—
183#127—181no—
184SD32—61no—
185SD32—181no—
186D16—61no—
187D16—181no—
188M32—31no—
189M32D3211yescharacteristic
190#108—91no—
191#104—181no—
192C4×C8—31no—
193C23×C3—121no—
194C22×D3—41no—
195C22×D3—121no—
196C22×D3—121no—
197C22×D3—241no—
198C3×Q8—61no—
199C3×D4—61no—
200C3×D4—121no—
201C3×D4—121no—
202C3×D4—121no—
203C2×C3×C4—21no—
204C2×C3×C4—61no—
205C2×C3×C4—121no—
206C2×C3×C4C2×D1211yescharacteristic
207C2×C3×C4D3×D411yescharacteristic
208#67—41no—
209#67—244no—
210C2×Dic3—21no—
211D12—21no—
212D12—41no—
213D12—41no—
214D12—122no—
215D12—121no—
216D12—121no—
217D12—121no—
218D12—121no—
219D12—241no—
220D12—244no—
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#23911yescharacteristic
230C3×C8C2×#6711yescharacteristic
231C3⋊C8—121no—
232C3⋊C8—121no—
233C3⋊C8—241no—
234C3⋊C8D2411yescharacteristic
235C3⋊C8D2411yescharacteristic
236C2×C32—21no—
237C2×C32#45911yescharacteristic
238C3⋊D3—161no—
239C3×D3—81no—
240C3×D3—161no—
241#41—61no—
242C2×D4—61no—
243C2×D4—181no—
244C2×D4—362no—
245Q16—31no—
246SD16—61no—
247D8—31no—
248D8—61no—
249D8—61no—
250D8—181no—
251D8—181no—
252D8—361no—
253D8—361no—
254M16—181no—
255M16—361no—
256C2×C8—31no—
257C2×C8—361no—
258C2×C8C2×D3211yescharacteristic
259C42—31no—
260C16—21no—
261C16—61no—
262C22×C3—21no—
263C22×C3—121no—
264C22×C3—242no—
265C22×C3—241no—
266C22×C3#90811yescharacteristic
267C22×C3#91111yescharacteristic
268C2×D3—41no—
269C2×D3—82no—
270C2×D3—81no—
271C2×D3—242no—
272C2×D3—242no—
273C2×D3—242no—
274C2×D3—241no—
275C2×D3—241no—
276C2×D3—482no—
277C3×C4—21no—
278C3×C4—21no—
279C3×C4—62no—
280C3×C4—121no—
281C3×C4#89511yescharacteristic
282C3×C4C2×D2411yescharacteristic
283C3×C4D3×D811yescharacteristic
284C3×C4#93911yescharacteristic
285Dic3—22no—
286Dic3—41no—
287C32#221311yescharacteristic, complemented, Sylow
288C23—121no—
289C23—361no—
290Q8—61no—
291D4—61no—
292D4—121no—
293D4—121no—
294D4—121no—
295D4—361no—
296D4—361no—
297D4—724no—
298C2×C4—61no—
299C2×C4—121no—
300C2×C4D3×D1211yescharacteristic
301C8—31no—
302C8—31no—
303C8—361no—
304C8#379611yescharacteristic
305C8D3×#6711yescharacteristic
306C2×C3—21no—
307C2×C3—21no—
308C2×C3—21no—
309C2×C3—41no—
310C2×C3—241no—
311C2×C3—481no—
312C2×C3#484311yescharacteristic
313C2×C3#515011yescharacteristic
314D3—81no—
315D3—161no—
316D3—482no—
317D3—481no—
318D3—481no—
319C22—121no—
320C22—242no—
321C22—241no—
322C22—722no—
323C22—721no—
324C22#6379511yescharacteristic
325C4—62no—
326C4—121no—
327C4D3×D2411yescharacteristic
328C4#6388611yescharacteristic
329C3—21no—
330C3#6930511yescharacteristic, complemented
331C3#7151411yescharacteristic, complemented
332C2—21no—
333C2—241no—
334C2—481no—
335C2—1441no—
336C2#1059075311yescharacteristic
subgroupG/H
centerC2#10590753
commutator, cosocleC2×C32×C8C23
FrattiniC2×C8C2×D32
FittingC32×M32C22
socleC2×C32#459
hypercenterM32D32
hypocenterC32#2213
LCSG ▷ C2×C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ M32

Complements

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

NH ≅ G/Ntype
1. C3×#4908C2semidirect
2. #10590915C2semidirect
3. #10590880C2semidirect
4. #10590634C2semidirect
5. #10589382C2semidirect
6. C3×#4511C2semidirect
7. #10589127C2semidirect
30. #4908D3semidirect
39. #4511D3semidirect
50. C3×Dic12D4semidirect
53. C3×D24D4semidirect
148. Dic12#67semidirect
159. D24#67semidirect
287. C32#2213semidirect
330. C3#69305semidirect
331. C3#71514semidirect

Maximal subgroups

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

subgroupindex
C3×#49082
#105909152
#105908802
#105906342
#105893822
C3×#45112
#105891272
#715143
#693053