Finite Group Databasebeta

← #11781033

Subgroups — #11781033

Order 1152.

381 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 381 conjugacy classes of subgroups — too many to draw. Only its 88 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#10592779C211yesmaximal, characteristic, complemented
2C3×#5084C211yesmaximal, characteristic
3#10590365C211yesmaximal, characteristic
4#10590329C211yesmaximal, characteristic
5C3×#4546C211yesmaximal, characteristic, complemented
6#10589098C211yesmaximal, characteristic, complemented
7#10589094C211yesmaximal, characteristic, complemented
8#71132—31nomaximal
9#68496—31nomaximal
10C32×C4⋊Q8C2211yescharacteristic
11#64078C2211yescharacteristic
12C3×C4×D12C2211yescharacteristic
13C2×#3716—21no—
14C2×D3×C3⋊C8—21no—
15#63635—21no—
16#63635—21no—
17C4×C3⋊(C3⋊C8)C2211yescharacteristic
18C3×#809—21no—
19C3×#808—21no—
20C3×C4⋊(C3⋊C8)C2211yescharacteristic
21C3×C4⋊(C3⋊C8)C2211yescharacteristic
22C3×C4⋊(C3⋊C8)C2211yescharacteristic
23#63567—21no—
24(C2×D3)⋊(C3⋊C8)—21no—
25C3×#476—31no—
26#5084D311yescharacteristic
27#5080—31no—
28#5080—31no—
29#5080—61no—
30#5019—31no—
31D4×C3⋊C8—31no—
32#4841—31no—
33#4834—31no—
34C3×#333—31no—
35#4546D311yescharacteristic, complemented
36#4486—31no—
37#4482—31no—
38#4480—31no—
39#4480—31no—
40C2×C32×Q8—21no—
41C2×#634—21no—
42C2×C3×D12D411yescharacteristic
43C2×C3×C4×D3—21no—
44C32×C4⋊C4—21no—
45C32×C4⋊C4—21no—
46C32×C42C2311yescharacteristic
47C4⋊(C3⋊Dic3)—21no—
48C4⋊(C3⋊Dic3)—21no—
49C2×C3⋊(C3⋊C8)D411yescharacteristic
50C2×C3⋊(C3⋊C8)D411yescharacteristic
51C3×(C2×D3)⋊C4—21no—
52C3×C4⋊Dic3D411yescharacteristic
53C2×C3×C3⋊C8—21no—
54C2×C3×C3⋊C8—21no—
55C2×C3×C3⋊C8—21no—
56#3716—42no—
57D3×C3⋊C8—42no—
58#1671—91noSylow
59C3×C4⋊Q8—21no—
60C3×C4⋊Q8C2×D311yescharacteristic
61C3×C4⋊Q8C2×D311yescharacteristic
62C3×C4×D4—31no—
63C2×#214—61no—
64C22×C3⋊C8—61no—
65C2×#204—61no—
66C2×D3×C8—61no—
67C4×D12C2×D311yescharacteristic
68#869—31no—
69#869—31no—
70#869—61no—
71C3×#106—61no—
72C3×C4⋊C8—31no—
73C3×C4⋊C8—31no—
74C3×C4⋊C8—31no—
75C3×#102—61no—
76#830—61no—
77(C2×D3)⋊C8—61no—
78#816—61no—
79#810—61no—
80#809—21no—
81#808—21no—
82#808—61no—
83#808—61no—
84#808—61no—
85#808—61no—
86#808—62no—
87#808—62no—
88C4⋊(C3⋊C8)C2×D311yescharacteristic
89C4⋊(C3⋊C8)C2×D311yescharacteristic
90C4⋊(C3⋊C8)C2×D311yescharacteristic
91C4×C3⋊C8—31no—
92C4×C3⋊C8—31no—
93C4×C3⋊C8—61no—
94C22×C3×D3—21no—
95C32×Q8—81no—
96C2×C32×C4—41no—
97C2×C32×C4C2×D411yescharacteristic
98C2×C32×C4C2×D411yescharacteristic
99C2×C32×C4#4111yescharacteristic
100C2×C3⋊Dic3—41no—
101#634—41no—
102#634—41no—
103C2×C3×Dic3—21no—
104C3×D12—21no—
105C3×D12SD1612yes—
106C3×C4×D3—41no—
107C3×C4×D3—41no—
108C3⋊(C3⋊C8)—21no—
109C3⋊(C3⋊C8)SD1612yescomplemented
110C3×C3⋊C8—41no—
111C3×C3⋊C8—41no—
112C3×C3⋊C8—41no—
113#498—91no—
114#476—31no—
115#461—91no—
116C8×D4—91no—
117#334—91no—
118#333—31no—
119#332—91no—
120C2×C3×Q8—21no—
121C2×C3×Q8—21no—
122C2×C3×Q8—41no—
123C2×C3×D4—31no—
124C22×C3×C4—61no—
125C2×D12#6711yescharacteristic
126C2×C4×D3—21no—
127C2×Dic6—61no—
128C2×Dic6—61no—
129C2×Dic6—121no—
130C2×C3×C8—61no—
131C2×C3×C8—61no—
132C2×C3×C8—61no—
133C3×C4⋊C4—22no—
134C3×C4⋊C4—21no—
135C3×C4⋊C4—21no—
136C3×C4⋊C4—21no—
137C3×C4⋊C4—21no—
138C3×C4⋊C4—31no—
139C3×C4⋊C4—41no—
140C3×C22⋊C4—61no—
141C3×C42—21no—
142C3×C42C22×D311yescharacteristic
143C3×C42C22×D311yescharacteristic
144#214—122no—
145(C2×D3)⋊C4—21no—
146C4⋊Dic3—62no—
147C4⋊Dic3—61no—
148C4⋊Dic3—61no—
149C4⋊Dic3—61no—
150C4⋊Dic3—61no—
151C4⋊Dic3—121no—
152C4⋊Dic3#6711yescharacteristic
153C2×C3⋊C8—21no—
154C2×C3⋊C8—21no—
155C2×C3⋊C8—21no—
156C2×C3⋊C8—31no—
157C2×C3⋊C8—31no—
158C2×C3⋊C8—31no—
159C2×C3⋊C8—31no—
160C2×C3⋊C8—61no—
161C2×C3⋊C8—61no—
162C2×C3⋊C8—122no—
163#204—122no—
164D3×C8—122no—
165C22×C32#12111yescharacteristic
166C2×C3×D3—22no—
167C2×C3×D3—41no—
168C2×C3×D3—41no—
169C32×C4—21no—
170C32×C4—81no—
171C32×C4C2×SD1611yescharacteristic
172C32×C4C2×SD1611yescharacteristic
173C32×C4#13511yescharacteristic
174C32×C4#13711yescharacteristic
175C3⋊Dic3—81no—
176C3×Dic3—41no—
177C2×SD16—181no—
178C22×C8—181no—
179C4⋊Q8—91no—
180C4⋊Q8D3211yescharacteristic
181C4×D4—31no—
182#106—61no—
183#106—181no—
184#106—181no—
185C4⋊C8—31no—
186C4⋊C8—31no—
187C4⋊C8—31no—
188#103—181no—
189#102—61no—
190C22⋊C8—181no—
191C4×C8—91no—
192C23×C3—61no—
193C22×D3—21no—
194C3×Q8—81no—
195C3×Q8—81no—
196C3×Q8—82no—
197C3×D4—32no—
198C3×D4—61no—
199C2×C3×C4—21no—
200C2×C3×C4—21no—
201C2×C3×C4—21no—
202C2×C3×C4—42no—
203C2×C3×C4—41no—
204C2×C3×C4—41no—
205C2×C3×C4—61no—
206C2×C3×C4—121no—
207C2×C3×C4—121no—
208C2×C3×C4#23511yescharacteristic
209C2×C3×C4D3×D411yescharacteristic
210C2×C3×C4D3×D411yescharacteristic
211C2×C3×C4D3×D411yescharacteristic
212C2×C3×C4#23711yescharacteristic
213C2×C3×C4C2×#6711yescharacteristic
214C2×Dic3—21no—
215C2×Dic3—122no—
216C2×Dic3—121no—
217C2×Dic3—121no—
218D12—21no—
219D12#21512yes—
220C4×D3—41no—
221C4×D3—41no—
222Dic6—121no—
223Dic6—121no—
224Dic6—121no—
225Dic6—121no—
226Dic6—241no—
227Dic6—241no—
228C3×C8—121no—
229C3×C8—121no—
230C3×C8—121no—
231C3⋊C8—32no—
232C3⋊C8—32no—
233C3⋊C8—41no—
234C3⋊C8—41no—
235C3⋊C8—41no—
236C3⋊C8—62no—
237C3⋊C8—62no—
238C3⋊C8—61no—
239C3⋊C8—61no—
240C2×C32#46111yescharacteristic
241C2×C32#46511yescharacteristic
242C2×C32#47111yescharacteristic
243C3×D3—42no—
244C2×Q8—21no—
245C2×Q8—181no—
246C2×D4—31no—
247C22×C4—61no—
248SD16—362no—
249C2×C8—61no—
250C2×C8—61no—
251C2×C8—61no—
252C2×C8—91no—
253C2×C8—91no—
254C2×C8—362no—
255C4⋊C4—21no—
256C4⋊C4—21no—
257C4⋊C4—31no—
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#88411yescharacteristic
267C22×C3#93911yescharacteristic
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—82no—
279C3×C4—81no—
280C3×C4—81no—
281C3×C4—121no—
282C3×C4D3×SD1611yescharacteristic
283C3×C4D3×SD1611yescharacteristic
284C3×C4D3×SD1611yescharacteristic
285C3×C4#91511yescharacteristic
286C3×C4#91811yescharacteristic
287C3×C4#91911yescharacteristic
288C3×C4C2×#21511yescharacteristic
289C3×C4#95011yescharacteristic
290Dic3—41no—
291Dic3—242no—
292Dic3—241no—
293Dic3—241no—
294C32#167111yescharacteristic, complemented, Sylow
295C23—61no—
296Q8—81no—
297Q8—361no—
298Q8—361no—
299D4—32no—
300D4—61no—
301C2×C4—41no—
302C2×C4—61no—
303C2×C4—121no—
304C2×C4—121no—
305C2×C4—361no—
306C2×C4#380411yescharacteristic
307C2×C4D3×#6711yescharacteristic
308C2×C4#381111yescharacteristic
309C8—92no—
310C8—121no—
311C8—121no—
312C8—121no—
313C8—181no—
314C2×C3—21no—
315C2×C3—21no—
316C2×C3—21no—
317C2×C3—122no—
318C2×C3#474811yescharacteristic
319C2×C3#480711yescharacteristic
320C2×C3#481811yescharacteristic
321C2×C3#504811yescharacteristic
322C2×C3#516211yescharacteristic
323C2×C3#520011yescharacteristic
324D3—42no—
325C22—62no—
326C22—121no—
327C22—121no—
328C22#6397111yescharacteristic
329C4—21no—
330C4—81no—
331C4—121no—
332C4—721no—
333C4D3×#21511yescharacteristic
334C4#6394011yescharacteristic
335C4#6394911yescharacteristic
336C4#6395111yescharacteristic
337C3—21no—
338C3#6849611yescharacteristic, complemented
339C3#7113211yescharacteristic, complemented
340C2—122no—
341C2#1059150711yescharacteristic
342C2#1059156911yescharacteristic
343C2#1059158511yescharacteristic
subgroupG/H
centerC22#63971
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊Q8C22
socleC22×C32#121
prime radicalC2×C3×D12D4
hypercenterC4⋊Q8D32
hypocenterC32#1671
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. #10592779C2semidirect
5. C3×#4546C2semidirect
6. #10589098C2semidirect
7. #10589094C2semidirect
35. #4546D3semidirect
109. C3⋊(C3⋊C8)SD16semidirect
294. C32#1671semidirect
338. C3#68496semidirect
339. C3#71132semidirect

Maximal subgroups

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

subgroupindex
#105927792
C3×#50842
#105903652
#105903292
C3×#45462
#105890982
#105890942
#711323
#684963