Finite Group Databasebeta

← #11782360

Subgroups — #11782360

Order 1152.

340 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 340 conjugacy classes of subgroups — too many to draw. Only its 84 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×#4838C211yesmaximal, characteristic
2#10590287C211yesmaximal, characteristic, complemented
3#10590269C211yesmaximal, characteristic
4#10590268C211yesmaximal, characteristic
5#10589347C211yesmaximal, characteristic, complemented
6C3×#4482C211yesmaximal, characteristic, complemented
7#10589097C211yesmaximal, characteristic, complemented
8#70876—31nomaximal
9#68455—31nomaximal
10#64078C2211yescharacteristic
11C2×C3×ΓL(1,𝔽25)—21no—
12C3×C4×D12C2211yescharacteristic
13C3×#869C2211yescharacteristic
14C32×C4⋊C8C2211yescharacteristic
15C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
16C3×(C2×D3)⋊C8—21no—
17C3×C4⋊(C3⋊C8)C2211yescharacteristic
18C3×C4×C3⋊C8C2211yescharacteristic
19#63576—21no—
20#63573—21no—
21#63566—21no—
22#63566—21no—
23#63563—21no—
24#63562—21no—
25C3×#436—31no—
26#5087—31no—
27#5079—31no—
28#5008—31no—
29#5007—31no—
30#4842—31no—
31#4838D311yescharacteristic
32#4681—31no—
33C3×#332—31no—
34#4482D311yescharacteristic, complemented
35#4481—31no—
36#4481—31no—
37#4481—61no—
38#4480—31no—
39#4457—31no—
40C2×#634—21no—
41C2×C3×D12D411yescharacteristic
42C2×C3×C4×D3—21no—
43C2×C3×Dic6—21no—
44C2×C32×C8—21no—
45C32×C42C2311yescharacteristic
46C4⋊(C3⋊Dic3)—21no—
47C4⋊(C3⋊Dic3)—21no—
48C2×C3⋊(C3⋊C8)—21no—
49C3×(C2×D3)⋊C4—21no—
50C3×C4⋊Dic3—21no—
51C3×C4⋊Dic3—21no—
52C3×C4⋊Dic3D411yescharacteristic
53C2×C3×C3⋊C8—21no—
54C2×C3×C3⋊C8D411yescharacteristic
55C2×C3×C3⋊C8D411yescharacteristic
56C3×ΓL(1,𝔽25)—42no—
57#1703—91noSylow
58C2×C3×M16—61no—
59C3×C4⋊Q8—31no—
60C3×C4×D4—31no—
61C2×ΓL(1,𝔽25)—21no—
62C4×D12C2×D311yescharacteristic
63#869—31no—
64#869—31no—
65#869—61no—
66#869C2×D311yescharacteristic
67C3×C4⋊C8—21no—
68C3×C4⋊C8—31no—
69C3×C4⋊C8C2×D311yescharacteristic
70C3×C4⋊C8C2×D311yescharacteristic
71C3×C22⋊C8—61no—
72C3×C4×C8—31no—
73#835—61no—
74#835—61no—
75#832—61no—
76#832—61no—
77#821—61no—
78(C2×D3)⋊C8—21no—
79#817—61no—
80#816—61no—
81#816—61no—
82#809—61no—
83#808—61no—
84#807—61no—
85#807—61no—
86C4⋊(C3⋊C8)—31no—
87C4⋊(C3⋊C8)—31no—
88C4⋊(C3⋊C8)—61no—
89C4⋊(C3⋊C8)C2×D311yescharacteristic
90C4×C3⋊C8C2×D311yescharacteristic
91C22×C3×D3—21no—
92C2×C32×C4C2×D411yescharacteristic
93C2×C32×C4C2×D411yescharacteristic
94C2×C32×C4#4111yescharacteristic
95C2×C3⋊Dic3—41no—
96#634—81no—
97C2×C3×Dic3—21no—
98C2×C3×Dic3—41no—
99C3×D12—21no—
100C3×D12—21no—
101C3×C4×D3—41no—
102C3×C4×D3—41no—
103C3×Dic6—41no—
104C3×Dic6—41no—
105C32×C8—41no—
106C3⋊(C3⋊C8)—41no—
107C3×C3⋊C8—21no—
108C3×C3⋊C8—21no—
109C3×C3⋊C8—41no—
110#487—91no—
111#476—91no—
112#474—91no—
113#436—31no—
114#334—91no—
115#333—91no—
116#332—31no—
117C2×C3×Q8—61no—
118C2×C3×D4—31no—
119C22×C3×C4—61no—
120C2×D12D1211yescharacteristic
121C2×C4×D3—21no—
122C2×Dic6—21no—
123C2×Dic6—62no—
124C2×Dic6—61no—
125C2×Dic6—61no—
126C3×M16—122no—
127C2×C3×C8—21no—
128C2×C3×C8—21no—
129C2×C3×C8—31no—
130C2×C3×C8—31no—
131C2×C3×C8—41no—
132C2×C3×C8—61no—
133C3×C4⋊C4—31no—
134C3×C4⋊C4—61no—
135C3×C4⋊C4—61no—
136C3×C22⋊C4—61no—
137C3×C42—21no—
138C3×C42C22×D311yescharacteristic
139C3×C42C22×D311yescharacteristic
140(C2×D3)⋊C4—21no—
141C4⋊Dic3—21no—
142C4⋊Dic3—21no—
143C4⋊Dic3—61no—
144C4⋊Dic3—61no—
145C4⋊Dic3—61no—
146C4⋊Dic3—61no—
147C4⋊Dic3—121no—
148C4⋊Dic3—121no—
149C4⋊Dic3D1211yescharacteristic
150C2×C3⋊C8—21no—
151C2×C3⋊C8—61no—
152C2×C3⋊C8—61no—
153C2×C3⋊C8—121no—
154C2×C3⋊C8#6711yescharacteristic
155C2×C3⋊C8#6711yescharacteristic
156ΓL(1,𝔽25)—42no—
157C22×C32#12111yescharacteristic
158C2×C3×D3—41no—
159C2×C3×D3—41no—
160C2×C3×D3—41no—
161C32×C4—21no—
162C32×C4#13511yescharacteristic
163C32×C4AGL(1,ℤ/8)11yescharacteristic
164C32×C4#13711yescharacteristic
165C32×C4#13711yescharacteristic
166C3⋊Dic3—81no—
167C3×Dic3—41no—
168C3×Dic3—81no—
169C2×M16—61no—
170C4⋊Q8—31no—
171C4⋊Q8—91no—
172C4×D4—31no—
173#107—181no—
174#106—181no—
175C4⋊C8—31no—
176C4⋊C8—91no—
177C4⋊C8D3211yescharacteristic
178#103—181no—
179#103—181no—
180#102—181no—
181#102—181no—
182C22⋊C8—61no—
183C4×C8—31no—
184C23×C3—61no—
185C22×D3—21no—
186C3×Q8—121no—
187C3×Q8—121no—
188C3×D4—61no—
189C3×D4—61no—
190C2×C3×C4—21no—
191C2×C3×C4—21no—
192C2×C3×C4—21no—
193C2×C3×C4—61no—
194C2×C3×C4—121no—
195C2×C3×C4—121no—
196C2×C3×C4—121no—
197C2×C3×C4C2×D1211yescharacteristic
198C2×C3×C4#23511yescharacteristic
199C2×C3×C4#23511yescharacteristic
200C2×C3×C4D3×D411yescharacteristic
201C2×C3×C4D3×D411yescharacteristic
202C2×C3×C4C2×#6711yescharacteristic
203C2×Dic3—21no—
204C2×Dic3—41no—
205C2×Dic3—122no—
206C2×Dic3—121no—
207C2×Dic3—121no—
208D12—21no—
209D12—21no—
210C4×D3—41no—
211C4×D3—41no—
212Dic6—41no—
213Dic6—41no—
214Dic6—241no—
215Dic6—241no—
216Dic6—242no—
217C3×C8—41no—
218C3×C8—41no—
219C3×C8—61no—
220C3×C8—61no—
221C3×C8—81no—
222C3×C8—121no—
223C3⋊C8—21no—
224C3⋊C8—21no—
225C3⋊C8—41no—
226C3⋊C8—121no—
227C3⋊C8—121no—
228C3⋊C8—241no—
229C2×C32#46311yescharacteristic
230C2×C32#47011yescharacteristic
231C2×C32#47111yescharacteristic
232C3×D3—81no—
233C2×Q8—61no—
234C2×Q8—181no—
235C2×D4—31no—
236C22×C4—61no—
237M16—122no—
238C2×C8—21no—
239C2×C8—31no—
240C2×C8—31no—
241C2×C8—61no—
242C2×C8—181no—
243C4⋊C4—31no—
244C4⋊C4—61no—
245C4⋊C4—61no—
246C4⋊C4—181no—
247C4⋊C4—181no—
248C22⋊C4—61no—
249C42C2×D3211yescharacteristic
250C22×C3—21no—
251C22×C3—121no—
252C22×C3—121no—
253C22×C3—121no—
254C22×C3#88411yescharacteristic
255C22×C3#93011yescharacteristic
256C2×D3—41no—
257C2×D3—41no—
258C2×D3—41no—
259C3×C4—21no—
260C3×C4—21no—
261C3×C4—21no—
262C3×C4—21no—
263C3×C4—21no—
264C3×C4—21no—
265C3×C4—41no—
266C3×C4—121no—
267C3×C4—241no—
268C3×C4#90911yescharacteristic
269C3×C4#90911yescharacteristic
270C3×C4#91111yescharacteristic
271C3×C4#91511yescharacteristic
272C3×C4#91611yescharacteristic
273C3×C4#91811yescharacteristic
274C3×C4#93211yescharacteristic
275C3×C4#95011yescharacteristic
276Dic3—41no—
277Dic3—81no—
278Dic3—242no—
279Dic3—241no—
280Dic3—241no—
281C32#170311yescharacteristic, complemented, Sylow
282C23—61no—
283Q8—121no—
284Q8—121no—
285Q8—721no—
286D4—61no—
287D4—61no—
288C2×C4—61no—
289C2×C4—121no—
290C2×C4—121no—
291C2×C4—121no—
292C2×C4—361no—
293C2×C4#379811yescharacteristic
294C2×C4D3×D1211yescharacteristic
295C2×C4D3×#6711yescharacteristic
296C8—41no—
297C8—61no—
298C8—61no—
299C8—121no—
300C8—361no—
301C2×C3—21no—
302C2×C3—21no—
303C2×C3—21no—
304C2×C3—241no—
305C2×C3#475411yescharacteristic
306C2×C3#478711yescharacteristic
307C2×C3#481611yescharacteristic
308C2×C3#501611yescharacteristic
309C2×C3#513711yescharacteristic
310C2×C3#514111yescharacteristic
311D3—81no—
312C22—121no—
313C22—121no—
314C22—121no—
315C22#6390611yescharacteristic
316C4—21no—
317C4—121no—
318C4—241no—
319C4—721no—
320C4#6380011yescharacteristic
321C4#6380111yescharacteristic
322C4#6393211yescharacteristic
323C4#6394711yescharacteristic
324C3—21no—
325C3#6845511yescharacteristic, complemented
326C3#7087611yescharacteristic, complemented
327C2—241no—
328C2#1059053011yescharacteristic
329C2#1059084911yescharacteristic
330C2#1059099811yescharacteristic
subgroupG/H
centerC22#63906
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊C8C22
socleC22×C32#121
prime radicalC2×C3×D12D4
hypercenterC4⋊C8D32
hypocenterC32#1703
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
2. #10590287C2semidirect
5. #10589347C2semidirect
6. C3×#4482C2semidirect
7. #10589097C2semidirect
34. #4482D3semidirect
281. C32#1703semidirect
325. C3#68455semidirect
326. C3#70876semidirect

Maximal subgroups

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

subgroupindex
C3×#48382
#105902872
#105902692
#105902682
#105893472
C3×#44822
#105890972
#708763
#684553