Finite Group Databasebeta

← #11799118

Subgroups — #11799118

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#10592607C211yesmaximal, characteristic, complemented
2#10590917C211yesmaximal, characteristic, complemented
3#10590880C211yesmaximal, characteristic, complemented
4#10590633C211yesmaximal, characteristic, complemented
5C3×#4516C211yesmaximal, characteristic, complemented
6C3×#4511C211yesmaximal, characteristic, complemented
7#10589128C211yesmaximal, characteristic, complemented
8#69305—31nomaximal
9#69263—31nomaximal
10#64113C2211yescharacteristic
11C2×#3745C2211yescharacteristic
12C2×C3×D24C2211yescharacteristic
13#63911—21no—
14C2×#3714—21no—
15#63817—21no—
16C32×M32C2211yescharacteristic
17#63627—21no—
18#63626—21no—
19C3×#819C2211yescharacteristic
20C3×C8×Dic3C2211yescharacteristic
21C3×#812C2211yescharacteristic
22#63570—21no—
23#63548—21no—
24#63546—21no—
25#5151—31no—
26#5147—31no—
27#4908—31no—
28#4908—31no—
29#4908—31no—
30#4908—61no—
31#4895—31no—
32#4700—31no—
33#4695—31no—
34C3×#364—31no—
35C3×#361—31no—
36#4516—31no—
37#4516D311yescharacteristic, complemented
38#4511D311yescharacteristic, complemented
39#4495—31no—
40#3828—21no—
41C2×C4⋊(C3⋊D3)—21no—
42C2×C3×D12—21no—
43C2×#626—42no—
44C2×C32×C8C2311yescharacteristic
45#3746D411yescharacteristic, complemented
46#3745—21no—
47#3745—21no—
48#3745D411yescharacteristic, complemented
49#3744—21no—
50C3×C4×Dic3D411yescharacteristic
51C3×#208—21no—
52C2×C3×C3⋊C8D411yescharacteristic
53C3×D24—21no—
54C3×D24—21no—
55#3714—41no—
56#3714—41no—
57#3712—41no—
58#3710—41no—
59C32×C16—21no—
60C3×C3⋊C16—21no—
61#2213—91noSylow
62C2×C3×D8—31no—
63#940—61no—
64C2×#213—61no—
65#907—61no—
66#904—31no—
67#904—31no—
68#904—61no—
69C2×D24—31no—
70C2×D24—31no—
71C2×D24—61no—
72C2×D24—61no—
73C2×D24C2×D311yescharacteristic
74#901—61no—
75#874—61no—
76C3×M32—21no—
77C3×M32—31no—
78C3×M32C2×D311yescharacteristic
79C3×M32C2×D311yescharacteristic
80C3×#108—31no—
81C3×C4×C8—31no—
82#827—61no—
83#826—61no—
84#825—61no—
85#819C2×D311yescharacteristic
86C8×Dic3C2×D311yescharacteristic
87#812C2×D311yescharacteristic
88#805—61no—
89#800—61no—
90#800—61no—
91#800—62no—
92#800—61no—
93D48—61no—
94D48—61no—
95D48—62no—
96D48—61no—
97C22×C3⋊D3—41no—
98C22×C3×D3—41no—
99C2×C32×C4C2×D411yescharacteristic
100#638—41no—
101C4⋊(C3⋊D3)—21no—
102C4⋊(C3⋊D3)—41no—
103C4⋊(C3⋊D3)—41no—
104C4×C3⋊D3—41no—
105#634—21no—
106C2×C3×Dic3—21no—
107C3×D12—41no—
108C3×D12—41no—
109#626—84no—
110C32×C8C2×D411yescharacteristic
111C32×C8#4111yescharacteristic
112C3×C3⋊C8—41no—
113C3×C3⋊C8D811yescharacteristic
114C3×C3⋊C8D811yescharacteristic
115#509—91no—
116#509—91no—
117#493—91no—
118#443—91no—
119#364—31no—
120#361—31no—
121#361—91no—
122C2×C3×D4—61no—
123C2×#67—122no—
124#235—61no—
125#235—61no—
126#235—121no—
127C2×D12—21no—
128C2×D12—61no—
129C2×D12—61no—
130C2×D12—121no—
131C2×D12—122no—
132C3×D8—61no—
133C3×D8—61no—
134C3×M16—61no—
135C2×C3×C8—21no—
136C2×C3×C8—31no—
137C2×C3×C8C22×D311yescharacteristic
138C2×C3×C8C22×D311yescharacteristic
139C3×C42—31no—
140#213—121no—
141#213—121no—
142C4×Dic3D1211yescharacteristic
143#208—21no—
144C2×C3⋊C8D1211yescharacteristic
145Dic12—31no—
146Dic12—31no—
147Dic12—61no—
148D24—21no—
149D24—21no—
150D24—31no—
151D24—31no—
152D24—61no—
153D24—62no—
154D24—61no—
155D24—61no—
156D24—61no—
157D24—61no—
158D24—121no—
159D24—121no—
160D24—121no—
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—22no—
169C3×C16—21no—
170C3×C16—21no—
171C3×C16—61no—
172C3⋊C16—21no—
173C22×C32AGL(1,ℤ/8)11yescharacteristic
174C2×C3⋊D3—41no—
175C2×C3⋊D3—81no—
176C2×C3⋊D3—82no—
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—91no—
186C2×D8—181no—
187#131—181no—
188#127—181no—
189SD32—181no—
190SD32—181no—
191D16—181no—
192D16—181no—
193M32—31no—
194M32D3211yescharacteristic
195#108—31no—
196#104—181no—
197C4×C8—31no—
198C23×C3—121no—
199C22×D3—41no—
200C22×D3—121no—
201C22×D3—121no—
202C22×D3—241no—
203C3×D4—121no—
204C3×D4—121no—
205C2×C3×C4—21no—
206C2×C3×C4—61no—
207C2×C3×C4C2×D1211yescharacteristic
208C2×C3×C4D3×D411yescharacteristic
209#67—121no—
210#67—121no—
211#67—241no—
212#67—244no—
213C2×Dic3—21no—
214D12—41no—
215D12—41no—
216D12—61no—
217D12—61no—
218D12—121no—
219D12—122no—
220D12—121no—
221D12—121no—
222D12—121no—
223D12—121no—
224D12—241no—
225D12—244no—
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#23911yescharacteristic
241C3⋊C8—41no—
242C3⋊C8D2411yescharacteristic
243C3⋊C8D2411yescharacteristic
244C2×C32—21no—
245C2×C32#45911yescharacteristic
246C3⋊D3—81no—
247C3⋊D3—161no—
248C3×D3—161no—
249#41—181no—
250C2×D4—61no—
251C2×D4—181no—
252C2×D4—362no—
253Q16—91no—
254SD16—181no—
255D8—61no—
256D8—61no—
257D8—91no—
258D8—181no—
259D8—181no—
260D8—361no—
261D8—361no—
262M16—61no—
263M16—361no—
264C2×C8—31no—
265C2×C8—361no—
266C2×C8C2×D3211yescharacteristic
267C42—31no—
268C16—21no—
269C16—61no—
270C22×C3—21no—
271C22×C3—242no—
272C22×C3—241no—
273C22×C3#90811yescharacteristic
274C22×C3#91411yescharacteristic
275C2×D3—82no—
276C2×D3—81no—
277C2×D3—121no—
278C2×D3—121no—
279C2×D3—241no—
280C2×D3—242no—
281C2×D3—242no—
282C2×D3—242no—
283C2×D3—241no—
284C2×D3—241no—
285C2×D3—482no—
286C3×C4—21no—
287C3×C4—21no—
288C3×C4—62no—
289C3×C4#88411yescharacteristic
290C3×C4#89511yescharacteristic
291C3×C4C2×D2411yescharacteristic
292C3×C4D3×D811yescharacteristic
293Dic3—22no—
294Dic3—121no—
295Dic3—121no—
296Dic3—241no—
297C32#221311yescharacteristic, complemented, Sylow
298C23—121no—
299C23—361no—
300Q8—181no—
301D4—121no—
302D4—121no—
303D4—181no—
304D4—361no—
305D4—361no—
306D4—361no—
307D4—724no—
308C2×C4—61no—
309C2×C4—361no—
310C2×C4D3×D1211yescharacteristic
311C8—31no—
312C8—31no—
313C8—121no—
314C8#379911yescharacteristic
315C8#381111yescharacteristic
316C2×C3—21no—
317C2×C3—21no—
318C2×C3—21no—
319C2×C3—41no—
320C2×C3—481no—
321C2×C3#478611yescharacteristic
322C2×C3#484311yescharacteristic
323D3—161no—
324D3—241no—
325D3—241no—
326D3—481no—
327D3—482no—
328D3—481no—
329D3—481no—
330C22—242no—
331C22—241no—
332C22—361no—
333C22—722no—
334C22—721no—
335C22#6379411yescharacteristic
336C4—62no—
337C4—361no—
338C4D3×D2411yescharacteristic
339C4#6391011yescharacteristic
340C3—21no—
341C3#6926311yescharacteristic, complemented
342C3#6930511yescharacteristic, complemented
343C2—21no—
344C2—481no—
345C2—721no—
346C2—1441no—
347C2#1059076511yescharacteristic
subgroupG/H
centerC2#10590765
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. #10592607C2semidirect
2. #10590917C2semidirect
3. #10590880C2semidirect
4. #10590633C2semidirect
5. C3×#4516C2semidirect
6. C3×#4511C2semidirect
7. #10589128C2semidirect
37. #4516D3semidirect
38. #4511D3semidirect
45. #3746D4semidirect
48. #3745D4semidirect
297. C32#2213semidirect
341. C3#69263semidirect
342. C3#69305semidirect

Maximal subgroups

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

subgroupindex
#105926072
#105909172
#105908802
#105906332
C3×#45162
C3×#45112
#105891282
#693053
#692633