Finite Group Databasebeta

← #11781027

Subgroups — #11781027

Order 1152.

381 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 381 conjugacy classes of subgroups — too many to draw. Only its 100 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#10592379C211yesmaximal, characteristic, complemented
2C3×C8×D12C211yesmaximal, characteristic
3#10590365C211yesmaximal, characteristic
4#10590268C211yesmaximal, characteristic
5C3×#4457C211yesmaximal, characteristic, complemented
6#10589096C211yesmaximal, characteristic, complemented
7#10589094C211yesmaximal, characteristic, complemented
8#70851—31nomaximal
9#68537—31nomaximal
10#64078C2211yescharacteristic
11#64078C2211yescharacteristic
12C2×C3×D3×C8—21no—
13C3×C4×D12C2211yescharacteristic
14C2×#3716—21no—
15C32×C4×C8C2211yescharacteristic
16#63644—21no—
17#63644—21no—
18C3×(C2×D3)⋊C8—21no—
19C3×C4⋊(C3⋊C8)C2211yescharacteristic
20C3×C4⋊(C3⋊C8)C2211yescharacteristic
21C3×C4⋊(C3⋊C8)C2211yescharacteristic
22#63573—21no—
23#63567—21no—
24#63563—21no—
25C3×C8×D4—31no—
26#5019—31no—
27#5008—31no—
28#4842—31no—
29#4841—31no—
30C8×D12D311yescharacteristic
31#4680—31no—
32#4680—31no—
33#4680—61no—
34C3×#334—31no—
35#4486—31no—
36#4482—31no—
37#4481—31no—
38#4481—31no—
39#4457D311yescharacteristic, complemented
40C2×#634—21no—
41C2×#634—21no—
42C2×C3×D12D411yescharacteristic
43C2×C3×C4×D3—21no—
44C2×C32×C8D411yescharacteristic
45C2×C32×C8D411yescharacteristic
46C32×C42C2311yescharacteristic
47C4⋊(C3⋊Dic3)—21no—
48C4⋊(C3⋊Dic3)—21no—
49C4⋊(C3⋊Dic3)—21no—
50C4⋊(C3⋊Dic3)—21no—
51C3×(C2×D3)⋊C4—21no—
52C3×C4⋊Dic3D411yescharacteristic
53C2×C3×C3⋊C8—21no—
54C2×C3×C3⋊C8—21no—
55C2×C3×C3⋊C8—21no—
56C3×D3×C8—42no—
57#3716—42no—
58#1671—91noSylow
59C22×C3×C8—61no—
60C3×C4×D4—31no—
61C2×#214—61no—
62C2×#204—61no—
63C2×D3×C8—21no—
64C4×D12C2×D311yescharacteristic
65#869—31no—
66#869—31no—
67#869—31no—
68#869—31no—
69#869—61no—
70#869—61no—
71C3×C4⋊C8—31no—
72C3×C4⋊C8—31no—
73C3×C4⋊C8—31no—
74C3×C22⋊C8—61no—
75C3×C4×C8—21no—
76C3×C4×C8C2×D311yescharacteristic
77C3×C4×C8C2×D311yescharacteristic
78#832—61no—
79#821—61no—
80(C2×D3)⋊C8—21no—
81#817—62no—
82#817—62no—
83#817—61no—
84#817—61no—
85#817—61no—
86#817—61no—
87#817—61no—
88#816—61no—
89#810—61no—
90#808—61no—
91C4⋊(C3⋊C8)C2×D311yescharacteristic
92C4⋊(C3⋊C8)C2×D311yescharacteristic
93C4⋊(C3⋊C8)C2×D311yescharacteristic
94C22×C3×D3—21no—
95C2×C32×C4C2×D411yescharacteristic
96C2×C32×C4C2×D411yescharacteristic
97C2×C32×C4#4111yescharacteristic
98C2×C3⋊Dic3—41no—
99C2×C3⋊Dic3—41no—
100#634—41no—
101#634—41no—
102#634—81no—
103C2×C3×Dic3—21no—
104C3×D12—21no—
105C3×D12SD1612yes—
106C3×C4×D3—41no—
107C3×C4×D3—41no—
108C32×C8—21no—
109C32×C8SD1612yescomplemented
110C3×C3⋊C8—41no—
111C3×C3⋊C8—41no—
112C3×C3⋊C8—41no—
113#498—91no—
114#476—91no—
115#461—91no—
116C8×D4—31no—
117#334—31no—
118#333—91no—
119#332—91no—
120C2×C3×D4—31no—
121C22×C3×C4—61no—
122C2×D12D1211yescharacteristic
123C2×C4×D3—21no—
124C2×Dic6—61no—
125C2×Dic6—61no—
126C2×Dic6—61no—
127C2×Dic6—61no—
128C2×Dic6—121no—
129C2×Dic6—121no—
130C2×C3×C8—21no—
131C2×C3×C8—21no—
132C2×C3×C8—61no—
133C2×C3×C8—61no—
134C2×C3×C8—61no—
135C2×C3×C8—122no—
136C2×C3×C8D1211yescharacteristic
137C2×C3×C8D1211yescharacteristic
138C2×C3×C8#6711yescharacteristic
139C2×C3×C8#6711yescharacteristic
140C3×C4⋊C4—31no—
141C3×C22⋊C4—61no—
142C3×C42—21no—
143C3×C42C22×D311yescharacteristic
144C3×C42C22×D311yescharacteristic
145#214—122no—
146(C2×D3)⋊C4—21no—
147C4⋊Dic3—62no—
148C4⋊Dic3—62no—
149C4⋊Dic3—61no—
150C4⋊Dic3—61no—
151C4⋊Dic3—61no—
152C4⋊Dic3—61no—
153C4⋊Dic3—61no—
154C4⋊Dic3—61no—
155C4⋊Dic3—61no—
156C4⋊Dic3—61no—
157C4⋊Dic3—121no—
158C4⋊Dic3—121no—
159C4⋊Dic3D1211yescharacteristic
160C2×C3⋊C8—21no—
161C2×C3⋊C8—21no—
162C2×C3⋊C8—21no—
163#204—122no—
164D3×C8—42no—
165C22×C32#12111yescharacteristic
166C2×C3×D3—22no—
167C2×C3×D3—41no—
168C2×C3×D3—41no—
169C32×C4—21no—
170C32×C4C2×SD1611yescharacteristic
171C32×C4C2×SD1611yescharacteristic
172C32×C4#13511yescharacteristic
173C32×C4#13711yescharacteristic
174C3⋊Dic3—81no—
175C3⋊Dic3—81no—
176C3×Dic3—41no—
177C2×SD16—181no—
178C22×C8—61no—
179C4⋊Q8—91no—
180C4⋊Q8—91no—
181C4×D4—31no—
182#106—181no—
183#106—181no—
184#106—181no—
185C4⋊C8—31no—
186C4⋊C8—31no—
187C4⋊C8—31no—
188#103—181no—
189#102—181no—
190C22⋊C8—61no—
191C4×C8D3211yescharacteristic
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×D1211yescharacteristic
203C2×C3×C4C2×D1211yescharacteristic
204C2×C3×C4#23511yescharacteristic
205C2×C3×C4D3×D411yescharacteristic
206C2×C3×C4#23911yescharacteristic
207C2×C3×C4C2×#6711yescharacteristic
208C2×Dic3—21no—
209C2×Dic3—122no—
210C2×Dic3—122no—
211C2×Dic3—121no—
212C2×Dic3—121no—
213C2×Dic3—121no—
214C2×Dic3—121no—
215D12—21no—
216D12#20412yes—
217C4×D3—41no—
218C4×D3—41no—
219Dic6—121no—
220Dic6—121no—
221Dic6—121no—
222Dic6—121no—
223Dic6—241no—
224Dic6—241no—
225Dic6—242no—
226Dic6—241no—
227Dic6—241no—
228C3×C8—22no—
229C3×C8—21no—
230C3×C8—21no—
231C3×C8—22no—
232C3×C8—121no—
233C3×C8—121no—
234C3×C8—121no—
235C3×C8#20412yescomplemented
236C3×C8#21412yescomplemented
237C3⋊C8—41no—
238C3⋊C8—41no—
239C3⋊C8—41no—
240C2×C32#46111yescharacteristic
241C2×C32#46511yescharacteristic
242C2×C32#47111yescharacteristic
243C3×D3—42no—
244C2×Q8—181no—
245C2×Q8—181no—
246C2×D4—31no—
247C22×C4—61no—
248SD16—362no—
249C2×C8—61no—
250C2×C8—61no—
251C2×C8—61no—
252C2×C8—122no—
253C2×C8#62611yescharacteristic
254C2×C8#62611yescharacteristic
255C4⋊C4—31no—
256C4⋊C4—181no—
257C4⋊C4—181no—
258C4⋊C4—181no—
259C4⋊C4—181no—
260C22⋊C4—61no—
261C42C2×D3211yescharacteristic
262C22×C3—21no—
263C22×C3—62no—
264C22×C3—121no—
265C22×C3—121no—
266C22×C3#89511yescharacteristic
267C22×C3#93011yescharacteristic
268C2×D3—22no—
269C2×D3—41no—
270C2×D3—41no—
271C3×C4—22no—
272C3×C4—21no—
273C3×C4—21no—
274C3×C4—21no—
275C3×C4—21no—
276C3×C4—21no—
277C3×C4—21no—
278C3×C4—121no—
279C3×C4C2×#20411yescharacteristic
280C3×C4C2×#20411yescharacteristic
281C3×C4#90411yescharacteristic
282C3×C4#90911yescharacteristic
283C3×C4D3×SD1611yescharacteristic
284C3×C4#91611yescharacteristic
285C3×C4C2×#21411yescharacteristic
286C3×C4#95111yescharacteristic
287Dic3—41no—
288Dic3—242no—
289Dic3—242no—
290Dic3—241no—
291Dic3—241no—
292Dic3—241no—
293Dic3—241no—
294C32#167111yescharacteristic, complemented, Sylow
295C23—61no—
296Q8—361no—
297Q8—361no—
298Q8—721no—
299D4—32no—
300D4—61no—
301C2×C4—61no—
302C2×C4—121no—
303C2×C4—121no—
304C2×C4—361no—
305C2×C4—361no—
306C2×C4#379911yescharacteristic
307C2×C4D3×D1211yescharacteristic
308C2×C4C2×#62611yescharacteristic
309C8—21no—
310C8—121no—
311C8—121no—
312C8—121no—
313C8#371612yescomplemented
314C2×C3—21no—
315C2×C3—21no—
316C2×C3—21no—
317C2×C3—122no—
318C2×C3#484111yescharacteristic
319C2×C3#486411yescharacteristic
320C2×C3#489811yescharacteristic
321C2×C3#501911yescharacteristic
322C2×C3#511411yescharacteristic
323C2×C3#514111yescharacteristic
324D3—42no—
325C22—62no—
326C22—121no—
327C22—121no—
328C22#6390911yescharacteristic
329C4—21no—
330C4—121no—
331C4—721no—
332C4—721no—
333C4D3×#20411yescharacteristic
334C4#6380611yescharacteristic
335C4C2×#371611yescharacteristic
336C4#6383111yescharacteristic
337C3—21no—
338C3#6853711yescharacteristic, complemented
339C3#7085111yescharacteristic, complemented
340C2—122no—
341C2#1059036511yescharacteristic
342C2#1059083011yescharacteristic
343C2#1059093111yescharacteristic
subgroupG/H
centerC22#63909
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4×C8C22
socleC22×C32#121
prime radicalC2×C3×D12D4
hypercenterC4×C8D32
hypocenterC32#1671
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
1. #10592379C2semidirect
5. C3×#4457C2semidirect
6. #10589096C2semidirect
7. #10589094C2semidirect
39. #4457D3semidirect
109. C32×C8SD16semidirect
235. C3×C8#204semidirect
236. C3×C8#214semidirect
294. C32#1671semidirect
313. C8#3716semidirect
338. C3#68537semidirect
339. C3#70851semidirect

Maximal subgroups

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

subgroupindex
#105923792
C3×C8×D122
#105903652
#105902682
C3×#44572
#105890962
#105890942
#708513
#685373