Finite Group Databasebeta

← #11799110

Subgroups — #11799110

Order 1152.

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

normal subgroups only

This group has 385 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
1#10592846C211yesmaximal, characteristic, complemented
2C3×#5151C211yesmaximal, characteristic, complemented
3#10590917C211yesmaximal, characteristic, complemented
4#10590633C211yesmaximal, characteristic, complemented
5C3×#4563C211yesmaximal, characteristic, complemented
6#10589134C211yesmaximal, characteristic, complemented
7#10589126C211yesmaximal, characteristic, complemented
8#71295—31nomaximal
9#69263—31nomaximal
10C2×C32×D8C2211yescharacteristic
11#64113C2211yescharacteristic
12C3×#940—21no—
13C2×C3×#213—21no—
14C2×C3×D24C2211yescharacteristic
15#63817—21no—
16#63654—21no—
17#63653—21no—
18#63639C2211yescharacteristic
19C3×#819C2211yescharacteristic
20C3×C8×Dic3C2211yescharacteristic
21C3×#812C2211yescharacteristic
22#63570—21no—
23#63548—21no—
24#63546—21no—
25C3×#493—31no—
26#5151D311yescharacteristic, complemented
27#5147—31no—
28#5147—31no—
29#5147—31no—
30#5147—61no—
31#4908—31no—
32#4895—31no—
33#4700—31no—
34C3×#361—31no—
35#4563—31no—
36#4563D311yescharacteristic, complemented
37#4511—31no—
38#4495—31no—
39#4463—31no—
40C2×C32×D4—21no—
41#3828—21no—
42C2×C3×#67—42no—
43C2×C3×D12—21no—
44C32×D8—21no—
45C32×D8—21no—
46C2×C32×C8C2311yescharacteristic
47#3746D411yescharacteristic, complemented
48#3745D411yescharacteristic, complemented
49#3744—21no—
50C3×#213—41no—
51C3×#213—41no—
52C3×C4×Dic3D411yescharacteristic
53C3×#208—21no—
54C2×C3×C3⋊C8D411yescharacteristic
55C3×D24—21no—
56C3×D24—21no—
57#3712—41no—
58#3710—41no—
59C3⋊(C3⋊C16)—21no—
60C3×C3⋊C16—21no—
61#2213—91noSylow
62C2×C3×D8—21no—
63C2×C3×D8—31no—
64C2×C3×D8—61no—
65C2×C3×D8C2×D311yescharacteristic
66C2×C3×D8C2×D311yescharacteristic
67C3×#127—61no—
68#940—21no—
69C2×#213—21no—
70#907—61no—
71#904—31no—
72#904—31no—
73#904—61no—
74C2×D24C2×D311yescharacteristic
75#901—61no—
76C3×M32—31no—
77C3×#108—31no—
78C3×C4×C8—31no—
79#827—61no—
80#827—61no—
81#827—61no—
82#827—62no—
83#826—61no—
84#826—61no—
85#826—61no—
86#826—62no—
87#825—61no—
88#819C2×D311yescharacteristic
89C8×Dic3C2×D311yescharacteristic
90#812—31no—
91#812—31no—
92#812—61no—
93#812C2×D311yescharacteristic
94#805—61no—
95#800—61no—
96D48—61no—
97C23×C32—41no—
98C22×C3×D3—41no—
99C32×D4—41no—
100C32×D4—41no—
101C2×C32×C4C2×D411yescharacteristic
102#638—41no—
103C4⋊(C3⋊D3)—21no—
104C4×C3⋊D3—41no—
105#634—21no—
106C3×#67—84no—
107C2×C3×Dic3—21no—
108C3×D12—41no—
109C3×D12—41no—
110C32×C8C2×D411yescharacteristic
111C32×C8#4111yescharacteristic
112C3×C3⋊C8—41no—
113C3×C3⋊C8D811yescharacteristic
114C3×C3⋊C8D811yescharacteristic
115#509—91no—
116#509—91no—
117#493—31no—
118#443—91no—
119#364—91no—
120#361—31no—
121#361—91no—
122C2×C3×D4—21no—
123C2×C3×D4—21no—
124C2×C3×D4—41no—
125C2×C3×D4—61no—
126C2×C3×D4—122no—
127C2×#67—42no—
128#235—61no—
129#235—61no—
130#235—121no—
131C2×D12—21no—
132C3×D8—22no—
133C3×D8—21no—
134C3×D8—21no—
135C3×D8—21no—
136C3×D8—21no—
137C3×D8—41no—
138C3×D8—61no—
139C3×D8—61no—
140C3×D8—121no—
141C3×D8—121no—
142C3×M16—61no—
143C2×C3×C8—21no—
144C2×C3×C8—31no—
145C2×C3×C8C22×D311yescharacteristic
146C2×C3×C8C22×D311yescharacteristic
147C3×C42—31no—
148#213—41no—
149#213—41no—
150C4×Dic3#6711yescharacteristic
151#208—21no—
152C2×C3⋊C8#6711yescharacteristic
153Dic12—31no—
154Dic12—31no—
155Dic12—61no—
156D24—21no—
157D24—21no—
158D24—31no—
159D24—31no—
160D24—61no—
161#204—61no—
162#204—61no—
163#204—121no—
164ΓL(1,𝔽25)—121no—
165ΓL(1,𝔽25)—121no—
166D3×C8—121no—
167D3×C8—121no—
168C3×C16—61no—
169C3⋊C16—21no—
170C3⋊C16—62no—
171C3⋊C16—61no—
172C3⋊C16—61no—
173C22×C32—81no—
174C22×C32—82no—
175C22×C32AGL(1,ℤ/8)11yescharacteristic
176C2×C3⋊D3—41no—
177C2×C3×D3—82no—
178C2×C3×D3—81no—
179C32×C4#12111yescharacteristic
180C32×C4C2×D811yescharacteristic
181C3⋊Dic3—41no—
182C3×Dic3—22no—
183#135—91no—
184C2×D8—31no—
185C2×D8—61no—
186C2×D8D3211yescharacteristic
187#131—181no—
188#127—61no—
189SD32—181no—
190SD32—181no—
191D16—181no—
192D16—181no—
193M32—31no—
194M32—91no—
195#108—31no—
196#104—181no—
197C4×C8—31no—
198C23×C3—41no—
199C23×C3—41no—
200C23×C3—81no—
201C23×C3—121no—
202C22×D3—41no—
203C3×D4—42no—
204C3×D4—41no—
205C3×D4—41no—
206C3×D4—41no—
207C3×D4—41no—
208C3×D4—81no—
209C3×D4—121no—
210C3×D4—121no—
211C3×D4—244no—
212C2×C3×C4—21no—
213C2×C3×C4—61no—
214C2×C3×C4D3×D411yescharacteristic
215C2×C3×C4C2×#6711yescharacteristic
216#67—84no—
217#67—121no—
218#67—121no—
219#67—241no—
220C2×Dic3—21no—
221D12—41no—
222D12—41no—
223D12—61no—
224D12—61no—
225D12—121no—
226C4×D3—121no—
227C4×D3—121no—
228C4×D3—241no—
229Dic6—61no—
230Dic6—61no—
231Dic6—121no—
232C3×C8—21no—
233C3×C8—21no—
234C3×C8—31no—
235C3×C8—31no—
236C3×C8—121no—
237C3×C8#23511yescharacteristic
238C3×C8D3×D411yescharacteristic
239C3×C8D3×D411yescharacteristic
240C3×C8#23711yescharacteristic
241C3⋊C8—41no—
242C3⋊C8#21311yescharacteristic
243C3⋊C8#21311yescharacteristic
244C2×C32—21no—
245C2×C32—161no—
246C2×C32#45911yescharacteristic
247C3⋊D3—81no—
248C3×D3—161no—
249#41—181no—
250C2×D4—21no—
251C2×D4—61no—
252C2×D4—122no—
253Q16—91no—
254SD16—181no—
255D8—21no—
256D8—21no—
257D8—61no—
258D8—61no—
259D8—91no—
260D8—121no—
261D8—121no—
262M16—61no—
263M16—361no—
264C2×C8—31no—
265C2×C8—361no—
266C2×C8C2×D3211yescharacteristic
267C42—31no—
268C16—61no—
269C16—181no—
270C22×C3—21no—
271C22×C3—82no—
272C22×C3—82no—
273C22×C3—82no—
274C22×C3—81no—
275C22×C3—81no—
276C22×C3—162no—
277C22×C3—242no—
278C22×C3—241no—
279C22×C3#91411yescharacteristic
280C22×C3#93211yescharacteristic
281C2×D3—82no—
282C2×D3—81no—
283C2×D3—121no—
284C2×D3—121no—
285C2×D3—241no—
286C3×C4—21no—
287C3×C4—21no—
288C3×C4—62no—
289C3×C4#88411yescharacteristic
290C3×C4D3×D811yescharacteristic
291C3×C4C2×#21311yescharacteristic
292C3×C4#93811yescharacteristic
293Dic3—22no—
294Dic3—121no—
295Dic3—121no—
296Dic3—241no—
297C32#221311yescharacteristic, complemented, Sylow
298C23—41no—
299C23—121no—
300Q8—181no—
301D4—41no—
302D4—41no—
303D4—121no—
304D4—121no—
305D4—181no—
306D4—244no—
307D4—361no—
308C2×C4—61no—
309C2×C4—361no—
310C2×C4D3×#6711yescharacteristic
311C8—31no—
312C8—31no—
313C8—121no—
314C8#380411yescharacteristic
315C8#381111yescharacteristic
316C2×C3—21no—
317C2×C3—21no—
318C2×C3—21no—
319C2×C3—41no—
320C2×C3—162no—
321C2×C3—161no—
322C2×C3—161no—
323C2×C3—481no—
324C2×C3#478611yescharacteristic
325C2×C3#507211yescharacteristic
326D3—161no—
327D3—241no—
328D3—241no—
329D3—481no—
330C22—82no—
331C22—81no—
332C22—242no—
333C22—241no—
334C22—361no—
335C22#6393411yescharacteristic
336C4—62no—
337C4—361no—
338C4D3×#21311yescharacteristic
339C4#6395811yescharacteristic
340C3—21no—
341C3#6926311yescharacteristic, complemented
342C3#7129511yescharacteristic, complemented
343C2—21no—
344C2—161no—
345C2—481no—
346C2—721no—
347C2#1059142911yescharacteristic
subgroupG/H
centerC2#10591429
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. #10592846C2semidirect
2. C3×#5151C2semidirect
3. #10590917C2semidirect
4. #10590633C2semidirect
5. C3×#4563C2semidirect
6. #10589134C2semidirect
7. #10589126C2semidirect
26. #5151D3semidirect
36. #4563D3semidirect
47. #3746D4semidirect
48. #3745D4semidirect
297. C32#2213semidirect
341. C3#69263semidirect
342. C3#71295semidirect

Maximal subgroups

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

subgroupindex
#105928462
C3×#51512
#105909172
#105906332
C3×#45632
#105891342
#105891262
#712953
#692633