Finite Group Databasebeta

← #11777205

Subgroups — #11777205

Order 1152.

411 conjugacy classes of subgroups; only the 108 normal subgroups are shown.

normal subgroups only

This group has 411 conjugacy classes of subgroups — too many to draw. Only its 108 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#10592529C211yesmaximal, characteristic, complemented
2C4×#3716C211yesmaximal, characteristic
3#10590329C211yesmaximal, characteristic
4C3×#4483C211yesmaximal, characteristic
5C3×#4480C211yesmaximal, characteristic, complemented
6#10589085C211yesmaximal, characteristic, complemented
7C3⋊C82C211yesmaximal, characteristic, complemented
8#68516—31nomaximal
9#68149—31nomaximal
10C4×#634C2211yescharacteristic
11C3×C4×D12C2211yescharacteristic
12C2×#3716C411yescharacteristic
13C2×D3×C3⋊C8—21no—
14C32×C4⋊C8C2211yescharacteristic
15#63641—21no—
16C8×C3⋊Dic3—21no—
17C4×C3⋊(C3⋊C8)C2211yescharacteristic
18C3×C4⋊(C3⋊C8)C2211yescharacteristic
19C3×C4×C3⋊C8C2211yescharacteristic
20C3×C4×C3⋊C8C2211yescharacteristic
21#63573C411yescharacteristic
22#63567C411yescharacteristic
23#63563C411yescharacteristic
24(C2×D3)⋊(C3⋊C8)—21no—
25C4×#214—31no—
26D4×C3⋊C8—31no—
27#4834—31no—
28#4830—31no—
29#4830—31no—
30#4830—61no—
31C4×#204—31no—
32C3×#334—31no—
33C3×D4⋊C8—31no—
34#4484—31no—
35#4483D311yescharacteristic
36#4480D311yescharacteristic, complemented
37#4456—31no—
38C8×C3⋊C8—31no—
39C8×C3⋊C8—31no—
40C2×#634C2×C411yescharacteristic
41C2×C3×D12C2×C411yescharacteristic
42C2×C3×C4×D3—21no—
43C2×C32×C8—21no—
44C32×C42C2311yescharacteristic
45C4⋊(C3⋊Dic3)C2×C411yescharacteristic
46#3750—21no—
47C4×C3⋊Dic3—21no—
48C2×C3⋊(C3⋊C8)D411yescharacteristic
49C2×C3⋊(C3⋊C8)D411yescharacteristic
50C3×(C2×D3)⋊C4—21no—
51C3×C4⋊Dic3C2×C411yescharacteristic
52C2×C3×C3⋊C8—21no—
53C2×C3×C3⋊C8—21no—
54C2×C3×C3⋊C8C2×C411yescharacteristic
55C2×C3×C3⋊C8C2×C411yescharacteristic
56#3716C814yescomplemented
57D3×C3⋊C8—42no—
58C8×SD16—91noSylow
59C3×C4×D4—31no—
60C2×#214—31no—
61C22×C3⋊C8—61no—
62C2×#204—31no—
63C2×D3×C8—61no—
64C4×D12C2×D311yescharacteristic
65C4×Dic6—31no—
66C4×Dic6—31no—
67C4×Dic6—61no—
68C3×C4⋊C8—21no—
69C3×C4⋊C8—31no—
70C3×C4⋊C8C2×D311yescharacteristic
71C3×C4⋊C8C2×D311yescharacteristic
72C3×C4×C8—31no—
73C3×C4×C8—31no—
74#832—31no—
75#830—61no—
76#821—31no—
77(C2×D3)⋊C8—61no—
78#817—31no—
79#816—31no—
80Dic3⋊C8—61no—
81Dic3⋊C8—61no—
82Dic3⋊C8—62no—
83C8×Dic3—61no—
84C8×Dic3—61no—
85C8×Dic3—62no—
86#810—31no—
87#808—31no—
88C4⋊(C3⋊C8)C2×D311yescharacteristic
89C4×C3⋊C8—31no—
90C4×C3⋊C8—31no—
91C4×C3⋊C8—61no—
92C4×C3⋊C8C2×D311yescharacteristic
93C4×C3⋊C8C2×D311yescharacteristic
94C22×C3×D3—21no—
95C2×C32×C4C22×C411yescharacteristic
96C2×C32×C4C2×D411yescharacteristic
97C2×C32×C4#4111yescharacteristic
98C2×C3⋊Dic3—21no—
99C2×C3⋊Dic3—21no—
100#634—21no—
101#634C2×C812yescomplemented
102C2×C3×Dic3—21no—
103C3×D12—21no—
104C3×D12C2×C812yes—
105C3×C4×D3—41no—
106C3×C4×D3—41no—
107C32×C8—41no—
108C3⋊(C3⋊C8)—21no—
109C3⋊(C3⋊C8)SD1612yescomplemented
110C3×C3⋊C8—22no—
111C3×C3⋊C8—21no—
112C3×C3⋊C8—41no—
113C3×C3⋊C8C2×C812yescomplemented
114C8×Q8—91no—
115C4×SD16—91no—
116C8×D4—91no—
117#334—31no—
118Q8⋊C8—91no—
119D4⋊C8—31no—
120C82—91no—
121C2×C3×D4—31no—
122C22×C3×C4—61no—
123C2×D12C4×D311yescharacteristic
124C2×C4×D3—21no—
125C2×Dic6—31no—
126C2×Dic6—31no—
127C2×Dic6—61no—
128C2×C3×C8—22no—
129C2×C3×C8—21no—
130C2×C3×C8—21no—
131C2×C3×C8—31no—
132C2×C3×C8—31no—
133C2×C3×C8—61no—
134C2×C3×C8—61no—
135C3×C4⋊C4—31no—
136C3×C22⋊C4—61no—
137C3×C42—21no—
138C3×C42C22×D311yescharacteristic
139C3×C42C22×D311yescharacteristic
140#214—34no—
141(C2×D3)⋊C4—21no—
142C4⋊Dic3—31no—
143C4⋊Dic3—31no—
144C4⋊Dic3—61no—
145C4⋊Dic3C4×D311yescharacteristic
146Dic3⋊C4—62no—
147Dic3⋊C4—61no—
148Dic3⋊C4—61no—
149C4×Dic3—62no—
150C4×Dic3—61no—
151C4×Dic3—61no—
152C2×C3⋊C8—21no—
153C2×C3⋊C8—21no—
154C2×C3⋊C8—31no—
155C2×C3⋊C8—31no—
156C2×C3⋊C8—31no—
157C2×C3⋊C8—31no—
158C2×C3⋊C8—61no—
159C2×C3⋊C8—61no—
160C2×C3⋊C8—122no—
161C2×C3⋊C8C4×D311yescharacteristic
162C2×C3⋊C8C4×D311yescharacteristic
163#204—34no—
164D3×C8—122no—
165C22×C32C4×D411yescharacteristic
166C2×C3×D3—22no—
167C2×C3×D3—41no—
168C2×C3×D3—41no—
169C32×C4—21no—
170C32×C4C22×C811yescharacteristic
171C32×C4#13111yescharacteristic
172C32×C4C2×SD1611yescharacteristic
173C32×C4#13511yescharacteristic
174C3⋊Dic3—22no—
175C3⋊Dic3—41no—
176C3×Dic3—41no—
177C2×SD16—91no—
178C22×C8—181no—
179C4×Q8—91no—
180C4×D4—31no—
181#106—91no—
182C4⋊C8—31no—
183C4⋊C8—181no—
184C4⋊C8D3211yescharacteristic
185#103—91no—
186#102—91no—
187C22⋊C8—181no—
188C4×C8—31no—
189C4×C8—31no—
190C4×C8—91no—
191C4×C8—181no—
192C23×C3—61no—
193C22×D3—21no—
194C3×D4—32no—
195C3×D4—61no—
196C2×C3×C4—21no—
197C2×C3×C4—21no—
198C2×C3×C4—21no—
199C2×C3×C4—61no—
200C2×C3×C4—121no—
201C2×C3×C4—121no—
202C2×C3×C4C2×C4×D311yescharacteristic
203C2×C3×C4C2×C4×D311yescharacteristic
204C2×C3×C4D3×D411yescharacteristic
205C2×C3×C4D3×D411yescharacteristic
206C2×C3×C4#23711yescharacteristic
207C2×C3×C4#23911yescharacteristic
208C2×Dic3—21no—
209C2×Dic3—62no—
210C2×Dic3—61no—
211C2×Dic3—61no—
212C2×Dic3—62no—
213C2×Dic3—61no—
214C2×Dic3—61no—
215D12—21no—
216D12D3×C812yes—
217C4×D3—41no—
218C4×D3—41no—
219Dic6—32no—
220Dic6—32no—
221Dic6—62no—
222Dic6—62no—
223Dic6—61no—
224Dic6—61no—
225C3×C8—32no—
226C3×C8—42no—
227C3×C8—41no—
228C3×C8—41no—
229C3×C8—62no—
230C3×C8—61no—
231C3×C8—121no—
232C3⋊C8—22no—
233C3⋊C8—21no—
234C3⋊C8—32no—
235C3⋊C8—32no—
236C3⋊C8—41no—
237C3⋊C8—62no—
238C3⋊C8—61no—
239C3⋊C8—61no—
240C3⋊C8—121no—
241C3⋊C8D3×C812yescomplemented
242C2×C32C8×D411yescharacteristic
243C2×C32C4×SD1611yescharacteristic
244C2×C32#44311yescharacteristic
245C3×D3—42no—
246C2×Q8—91no—
247C2×D4—31no—
248C22×C4—61no—
249SD16—94no—
250C2×C8—21no—
251C2×C8—31no—
252C2×C8—31no—
253C2×C8—61no—
254C2×C8—61no—
255C2×C8—91no—
256C2×C8—91no—
257C2×C8—362no—
258C4⋊C4—31no—
259C4⋊C4—91no—
260C4⋊C4—181no—
261C22⋊C4—61no—
262C42—181no—
263C42C2×D3211yescharacteristic
264C22×C3—21no—
265C22×C3—62no—
266C22×C3—121no—
267C22×C3—121no—
268C22×C3#67⋊C411yescharacteristic
269C22×C3#89311yescharacteristic
270C2×D3—22no—
271C2×D3—41no—
272C2×D3—41no—
273C3×C4—21no—
274C3×C4—21no—
275C3×C4—21no—
276C3×C4—21no—
277C3×C4—21no—
278C3×C4—21no—
279C3×C4—41no—
280C3×C4—121no—
281C3×C4C2×D3×C811yescharacteristic
282C3×C4C2×D3×C811yescharacteristic
283C3×C4#90711yescharacteristic
284C3×C4#90711yescharacteristic
285C3×C4#91211yescharacteristic
286C3×C4D3×SD1611yescharacteristic
287C3×C4D3×SD1611yescharacteristic
288C3×C4#91611yescharacteristic
289Dic3—41no—
290Dic3—64no—
291Dic3—62no—
292Dic3—62no—
293Dic3—122no—
294Dic3—121no—
295Dic3—121no—
296C32C8×SD1611yescharacteristic, complemented, Sylow
297C23—61no—
298Q8—92no—
299Q8—181no—
300D4—32no—
301D4—61no—
302C2×C4—61no—
303C2×C4—121no—
304C2×C4—121no—
305C2×C4—181no—
306C2×C4—181no—
307C2×C4#379611yescharacteristic
308C2×C4C4×D3211yescharacteristic
309C2×C4#381111yescharacteristic
310C8—32no—
311C8—41no—
312C8—62no—
313C8—61no—
314C8—92no—
315C8—121no—
316C8—181no—
317C2×C3—21no—
318C2×C3—21no—
319C2×C3—21no—
320C2×C3—122no—
321C2×C3#67⋊C811yescharacteristic
322C2×C3#475811yescharacteristic
323C2×C3#482411yescharacteristic
324C2×C3#483411yescharacteristic
325C2×C3#485211yescharacteristic
326C2×C3#489511yescharacteristic
327D3—42no—
328C22—62no—
329C22—121no—
330C22—121no—
331C22#6388111yescharacteristic
332C4—21no—
333C4—121no—
334C4—182no—
335C4—361no—
336C4D32×C811yescharacteristic
337C4#6380511yescharacteristic
338C4#6393611yescharacteristic
339C4#6394011yescharacteristic
340C3—21no—
341C3#6814911yescharacteristic, complemented
342C3#6851611yescharacteristic, complemented
343C2—122no—
344C2#1059046011yescharacteristic
345C2#1059090611yescharacteristic
346C2#1059097711yescharacteristic
subgroupG/H
centerC2×C4#3811
commutatorC32×C4C22×C8
FrattiniC42C2×D32
FittingC32×C4⋊C8C22
socleC22×C32C4×D4
prime radicalC2×C3×D12C2×C4
cosocleC32×C42C23
hypercenterC4⋊C8D32
hypocenterC32C8×SD16
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
1. #10592529C2semidirect
5. C3×#4480C2semidirect
6. #10589085C2semidirect
7. C3⋊C82C2semidirect
36. #4480D3semidirect
56. #3716C8semidirect
101. #634C2×C8semidirect
109. C3⋊(C3⋊C8)SD16semidirect
113. C3×C3⋊C8C2×C8semidirect
241. C3⋊C8D3×C8semidirect
296. C32C8×SD16semidirect
341. C3#68149semidirect
342. C3#68516semidirect

Maximal subgroups

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

subgroupindex
#105925292
C4×#37162
#105903292
C3×#44832
C3×#44802
#105890852
C3⋊C822
#685163
#681493