Finite Group Databasebeta

← #11777052

Subgroups — #11777052

Order 1152.

355 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 355 conjugacy classes of subgroups — too many to draw. Only its 98 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#10592534C211yesmaximal, characteristic
2#10590297C211yesmaximal, characteristic
3#10590256C211yesmaximal, characteristic
4C3×#4480C211yesmaximal, characteristic, complemented
5C3×#4479C211yesmaximal, characteristic, complemented
6#10589099C211yesmaximal, characteristic, complemented
7#10589097C211yesmaximal, characteristic, complemented
8#68573—31nomaximal
9#68533—31nomaximal
10C42×C3⋊D3C2211yescharacteristic
11C32×C4⋊C8C2211yescharacteristic
12#63647—21no—
13#63642—21no—
14C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
15C3×C4⋊(C3⋊C8)C2211yescharacteristic
16C3×C4⋊(C3⋊C8)C2211yescharacteristic
17C3×C4×C3⋊C8C2211yescharacteristic
18C3×C4×C3⋊C8C2211yescharacteristic
19#63572C411yescharacteristic
20#63572C411yescharacteristic
21#63557—21no—
22#63557C411yescharacteristic
23#63557C411yescharacteristic
24#63553—21no—
25#4835—31no—
26#4835—31no—
27#4835—61no—
28#4833—31no—
29#4833—31no—
30#4685—31no—
31#4685—31no—
32C3×#335—31no—
33C3×#334—31no—
34#4480—31no—
35#4480D311yescharacteristic, complemented
36#4479—31no—
37#4479D311yescharacteristic, complemented
38#4458—31no—
39#4457—31no—
40C2×C4×C3⋊D3C2×C411yescharacteristic
41C2×C4×C3⋊D3D411yescharacteristic
42C2×C4×C3⋊D3Q811yescharacteristic
43C2×C32×C8—21no—
44C32×C42C2311yescharacteristic
45C4×C3⋊Dic3C2×C411yescharacteristic
46C4×C3⋊Dic3D411yescharacteristic
47C4×C3⋊Dic3Q811yescharacteristic
48C2×C3⋊(C3⋊C8)—21no—
49C2×C3×C3⋊C8—21no—
50C2×C3×C3⋊C8—21no—
51C2×C3×C3⋊C8C2×C411yescharacteristic
52C2×C3×C3⋊C8C2×C411yescharacteristic
53C2×C3×C3⋊C8C2×C411yescharacteristic
54C2×C3×C3⋊C8C2×C411yescharacteristic
55#1572—91noSylow
56C42×D3—31no—
57C42×D3—31no—
58C42×D3—61no—
59C3×C4⋊C8—21no—
60C3×C4⋊C8—31no—
61C3×C4⋊C8—31no—
62C3×C4⋊C8C2×D311yescharacteristic
63C3×C4⋊C8C2×D311yescharacteristic
64C3×C4×C8—31no—
65C3×C4×C8—31no—
66(C2×D3)⋊C8—31no—
67(C2×D3)⋊C8—31no—
68(C2×D3)⋊C8—31no—
69(C2×D3)⋊C8—31no—
70(C2×D3)⋊C8—61no—
71(C2×D3)⋊C8—61no—
72(C2×D3)⋊C8—61no—
73(C2×D3)⋊C8—61no—
74(C2×D3)⋊C8—62no—
75#815—61no—
76#815—61no—
77#815—62no—
78Dic3⋊C8—31no—
79Dic3⋊C8—31no—
80Dic3⋊C8—31no—
81Dic3⋊C8—31no—
82C8×Dic3—61no—
83C8×Dic3—61no—
84C4⋊(C3⋊C8)—31no—
85C4⋊(C3⋊C8)—31no—
86C4⋊(C3⋊C8)—61no—
87C4⋊(C3⋊C8)C2×D311yescharacteristic
88C4⋊(C3⋊C8)C2×D311yescharacteristic
89C4×C3⋊C8C2×D311yescharacteristic
90C4×C3⋊C8C2×D311yescharacteristic
91C22×C3⋊D3C4⋊C411yescharacteristic
92C2×C32×C4C22×C411yescharacteristic
93C2×C32×C4C2×D411yescharacteristic
94C2×C32×C4C2×Q811yescharacteristic
95C2×C3⋊Dic3C4⋊C411yescharacteristic
96C2×C3⋊Dic3C4⋊C411yescharacteristic
97C2×C3⋊Dic3C4⋊C411yescharacteristic
98C4×C3⋊D3—21no—
99C4×C3⋊D3—21no—
100C4×C3⋊D3—21no—
101C4×C3⋊D3—21no—
102C4×C3⋊D3—41no—
103C32×C8—41no—
104C3⋊(C3⋊C8)—41no—
105C3×C3⋊C8—21no—
106C3×C3⋊C8—21no—
107C3×C3⋊C8—21no—
108C3×C3⋊C8—21no—
109C3×C3⋊C8—41no—
110C3×C3⋊C8—41no—
111#432—91no—
112#431—91no—
113#431—91no—
114#335—31no—
115#335—91no—
116#334—31no—
117#334—91no—
118C2×C4×D3—31no—
119C2×C4×D3—31no—
120C2×C4×D3—31no—
121C2×C4×D3—31no—
122C2×C4×D3—31no—
123C2×C4×D3—31no—
124C2×C4×D3—61no—
125C2×C4×D3—61no—
126C2×C4×D3—61no—
127C2×C3×C8—22no—
128C2×C3×C8—21no—
129C2×C3×C8—21no—
130C2×C3×C8—31no—
131C2×C3×C8—31no—
132C2×C3×C8—31no—
133C2×C3×C8—31no—
134C2×C3×C8—61no—
135C2×C3×C8—61no—
136C3×C42—21no—
137C3×C42C22×D311yescharacteristic
138C3×C42C22×D311yescharacteristic
139C4×Dic3—31no—
140C4×Dic3—31no—
141C4×Dic3—31no—
142C4×Dic3—31no—
143C4×Dic3—31no—
144C4×Dic3—31no—
145C4×Dic3—61no—
146C4×Dic3—61no—
147C4×Dic3—61no—
148C2×C3⋊C8—21no—
149C2×C3⋊C8—21no—
150C2×C3⋊C8—62no—
151C2×C3⋊C8—61no—
152C2×C3⋊C8—61no—
153C2×C3⋊C8C4×D311yescharacteristic
154C2×C3⋊C8C4×D311yescharacteristic
155C2×C3⋊C8C4×D311yescharacteristic
156C2×C3⋊C8C4×D311yescharacteristic
157C22×C32C2×C4⋊C411yescharacteristic
158C2×C3⋊D3—21no—
159C2×C3⋊D3—21no—
160C2×C3⋊D3—21no—
161C32×C4—21no—
162C32×C4#13111yescharacteristic
163C32×C4#13111yescharacteristic
164C32×C4#13511yescharacteristic
165C32×C4#13511yescharacteristic
166C3⋊Dic3—21no—
167C3⋊Dic3—21no—
168C3⋊Dic3—21no—
169C2×C42—91no—
170C4⋊C8—31no—
171C4⋊C8—31no—
172C4⋊C8—91no—
173C4⋊C8—91no—
174C4⋊C8—91no—
175C4⋊C8D3211yescharacteristic
176C22⋊C8—91no—
177C22⋊C8—91no—
178C22⋊C8—181no—
179C22⋊C8—181no—
180#97—181no—
181C4×C8—31no—
182C4×C8—31no—
183C4×C8—181no—
184C22×D3—31no—
185C22×D3—31no—
186C22×D3—61no—
187C2×C3×C4—21no—
188C2×C3×C4—21no—
189C2×C3×C4—21no—
190C2×C3×C4C2×C4×D311yescharacteristic
191C2×C3×C4C2×C4×D311yescharacteristic
192C2×C3×C4D3×D411yescharacteristic
193C2×C3×C4D3×D411yescharacteristic
194C2×C3×C4D3×Q811yescharacteristic
195C2×C3×C4D3×Q811yescharacteristic
196C2×Dic3—31no—
197C2×Dic3—31no—
198C2×Dic3—31no—
199C2×Dic3—31no—
200C2×Dic3—31no—
201C2×Dic3—31no—
202C2×Dic3—61no—
203C2×Dic3—61no—
204C2×Dic3—61no—
205C4×D3—61no—
206C4×D3—61no—
207C4×D3—61no—
208C4×D3—61no—
209C4×D3—61no—
210C4×D3—61no—
211C4×D3—61no—
212C4×D3—61no—
213C4×D3—121no—
214C4×D3—121no—
215C4×D3—121no—
216C4×D3—121no—
217C4×D3—121no—
218C4×D3—121no—
219C4×D3—122no—
220C3×C8—42no—
221C3×C8—41no—
222C3×C8—41no—
223C3×C8—61no—
224C3×C8—61no—
225C3×C8—61no—
226C3×C8—61no—
227C3×C8—121no—
228C3×C8—121no—
229C3⋊C8—21no—
230C3⋊C8—21no—
231C3⋊C8—21no—
232C3⋊C8—21no—
233C3⋊C8—41no—
234C3⋊C8—41no—
235C3⋊C8—122no—
236C3⋊C8—121no—
237C3⋊C8—121no—
238C2×C32#42411yescharacteristic
239C2×C32#42711yescharacteristic
240C2×C32#43011yescharacteristic
241C3⋊D3—41no—
242C22×C4—91no—
243C22×C4—91no—
244C22×C4—91no—
245C2×C8—21no—
246C2×C8—31no—
247C2×C8—31no—
248C2×C8—31no—
249C2×C8—31no—
250C2×C8—61no—
251C2×C8—61no—
252C2×C8—181no—
253C42—91no—
254C42—91no—
255C42—91no—
256C42C2×D3211yescharacteristic
257C22×C3—21no—
258C22×C3D3×C4⋊C411yescharacteristic
259C22×C3D3×C4⋊C411yescharacteristic
260C2×D3—62no—
261C2×D3—61no—
262C2×D3—61no—
263C2×D3—61no—
264C2×D3—61no—
265C2×D3—61no—
266C2×D3—61no—
267C2×D3—121no—
268C2×D3—121no—
269C3×C4—21no—
270C3×C4—21no—
271C3×C4—21no—
272C3×C4—21no—
273C3×C4—21no—
274C3×C4—21no—
275C3×C4—41no—
276C3×C4#90111yescharacteristic
277C3×C4#90111yescharacteristic
278C3×C4#90711yescharacteristic
279C3×C4#90711yescharacteristic
280C3×C4#91211yescharacteristic
281C3×C4#91611yescharacteristic
282C3×C4#91611yescharacteristic
283C3×C4#91911yescharacteristic
284Dic3—61no—
285Dic3—61no—
286Dic3—61no—
287Dic3—61no—
288Dic3—61no—
289Dic3—61no—
290Dic3—121no—
291Dic3—121no—
292Dic3—121no—
293C32#157211yescharacteristic, complemented, Sylow
294C23—91no—
295C2×C4—91no—
296C2×C4—91no—
297C2×C4—91no—
298C2×C4—181no—
299C2×C4—181no—
300C2×C4—181no—
301C2×C4—181no—
302C2×C4—361no—
303C2×C4#379711yescharacteristic
304C2×C4C4×D3211yescharacteristic
305C2×C4#381111yescharacteristic
306C8—41no—
307C8—61no—
308C8—61no—
309C8—61no—
310C8—61no—
311C8—121no—
312C8—121no—
313C8—361no—
314C2×C3—21no—
315C2×C3—21no—
316C2×C3—21no—
317C2×C3#483911yescharacteristic
318C2×C3#483911yescharacteristic
319C2×C3#486011yescharacteristic
320C2×C3#488011yescharacteristic
321C2×C3#489311yescharacteristic
322C2×C3#489311yescharacteristic
323D3—122no—
324D3—121no—
325D3—121no—
326C22—181no—
327C22—181no—
328C22—181no—
329C22#6388311yescharacteristic
330C4—21no—
331C4—181no—
332C4—181no—
333C4—181no—
334C4#6380411yescharacteristic
335C4#6380411yescharacteristic
336C4#6393611yescharacteristic
337C4#6395011yescharacteristic
338C3—21no—
339C3#6853311yescharacteristic, complemented
340C3#6857311yescharacteristic, complemented
341C2—361no—
342C2#1059057411yescharacteristic
343C2#1059070211yescharacteristic
344C2#1059097411yescharacteristic
subgroupG/H
centerC2×C4#3811
commutatorC2×C32×C4C22×C4
FrattiniC42C2×D32
FittingC32×C4⋊C8C22
socleC22×C32C2×C4⋊C4
prime radicalC22×C3⋊D3C4⋊C4
cosocleC32×C42C23
hypercenterC4⋊C8D32
hypocenterC32#1572
LCSG ▷ C2×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
4. C3×#4480C2semidirect
5. C3×#4479C2semidirect
6. #10589099C2semidirect
7. #10589097C2semidirect
35. #4480D3semidirect
37. #4479D3semidirect
293. C32#1572semidirect
339. C3#68533semidirect
340. C3#68573semidirect

Maximal subgroups

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

subgroupindex
#105925342
#105902972
#105902562
C3×#44802
C3×#44792
#105890992
#105890972
#685733
#685333