Finite Group Databasebeta

← #11781529

Subgroups — #11781529

Order 1152.

369 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 369 conjugacy classes of subgroups — too many to draw. Only its 86 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#10592778C211yesmaximal, characteristic, complemented
2C3×#5087C211yesmaximal, characteristic
3#10590329C211yesmaximal, characteristic
4#10590268C211yesmaximal, characteristic
5C3×#4547C211yesmaximal, characteristic, complemented
6#10589100C211yesmaximal, characteristic, complemented
7#10589096C211yesmaximal, characteristic, complemented
8#71103—31nomaximal
9#68447—31nomaximal
10C32×C4⋊Q8C2211yescharacteristic
11#64078C2211yescharacteristic
12C3×C4×D12C2211yescharacteristic
13C2×D3×C3⋊C8—21no—
14#63662—21no—
15#63662—21no—
16C4×C3⋊(C3⋊C8)C2211yescharacteristic
17C3×#809—21no—
18C3×#807—21no—
19C3×C4⋊(C3⋊C8)C2211yescharacteristic
20C3×C4⋊(C3⋊C8)C2211yescharacteristic
21C3×C4⋊(C3⋊C8)C2211yescharacteristic
22#63573—21no—
23#63563—21no—
24(C2×D3)⋊(C3⋊C8)—21no—
25C3×#474—31no—
26#5087D311yescharacteristic
27#5079—31no—
28#5079—31no—
29#5079—61no—
30D4×C3⋊C8—31no—
31#5008—31no—
32#4842—31no—
33#4834—31no—
34C3×#332—31no—
35#4547D311yescharacteristic, complemented
36#4481—31no—
37#4481—31no—
38#4479—31no—
39#4479—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—
56D3×C3⋊C8—42no—
57#1683—91noSylow
58C3×C4⋊Q8—21no—
59C3×C4⋊Q8C2×D311yescharacteristic
60C3×C4⋊Q8C2×D311yescharacteristic
61C3×C4×D4—31no—
62C22×C3⋊C8—61no—
63C2×D3×C8—61no—
64C4×D12C2×D311yescharacteristic
65#869—31no—
66#869—31no—
67#869—61no—
68C3×#107—61no—
69C3×C4⋊C8—31no—
70C3×C4⋊C8—31no—
71C3×C4⋊C8—31no—
72C3×#102—61no—
73#835—61no—
74#835—61no—
75#835—61no—
76#835—61no—
77#835—62no—
78#835—62no—
79#832—61no—
80#830—61no—
81#821—61no—
82(C2×D3)⋊C8—61no—
83#817—61no—
84#809—21no—
85#808—61no—
86#807—21no—
87C4⋊(C3⋊C8)C2×D311yescharacteristic
88C4⋊(C3⋊C8)C2×D311yescharacteristic
89C4⋊(C3⋊C8)C2×D311yescharacteristic
90C4×C3⋊C8—31no—
91C4×C3⋊C8—31no—
92C4×C3⋊C8—61no—
93C22×C3×D3—21no—
94C32×Q8—41no—
95C32×Q8—41no—
96C2×C32×C4—41no—
97C2×C32×C4C2×D411yescharacteristic
98C2×C32×C4C2×D411yescharacteristic
99C2×C32×C4#4111yescharacteristic
100C2×C3⋊Dic3—41no—
101#634—81no—
102C2×C3×Dic3—21no—
103C3×D12—21no—
104C3×D12Q1612yes—
105C3×C4×D3—41no—
106C3×C4×D3—41no—
107C3⋊(C3⋊C8)—21no—
108C3⋊(C3⋊C8)—21no—
109C3×C3⋊C8—41no—
110C3×C3⋊C8—41no—
111C3×C3⋊C8—41no—
112#487—91no—
113#476—91no—
114#474—31no—
115C8×D4—91no—
116#335—91no—
117#333—91no—
118#332—31no—
119C2×C3×Q8—22no—
120C2×C3×Q8—21no—
121C2×C3×Q8—21no—
122C2×C3×D4—31no—
123C22×C3×C4—61no—
124C2×D12#6711yescharacteristic
125C2×C4×D3—21no—
126C2×Dic6—61no—
127C2×Dic6—61no—
128C2×Dic6—121no—
129C2×C3×C8—61no—
130C2×C3×C8—61no—
131C2×C3×C8—61no—
132C3×C4⋊C4—21no—
133C3×C4⋊C4—21no—
134C3×C4⋊C4—21no—
135C3×C4⋊C4—21no—
136C3×C4⋊C4—31no—
137C3×C4⋊C4—41no—
138C3×C4⋊C4—41no—
139C3×C22⋊C4—61no—
140C3×C42—21no—
141C3×C42C22×D311yescharacteristic
142C3×C42C22×D311yescharacteristic
143(C2×D3)⋊C4—21no—
144C4⋊Dic3—62no—
145C4⋊Dic3—61no—
146C4⋊Dic3—61no—
147C4⋊Dic3—61no—
148C4⋊Dic3—61no—
149C4⋊Dic3—121no—
150C4⋊Dic3#6711yescharacteristic
151C2×C3⋊C8—21no—
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—
161D3×C8—122no—
162C22×C32#12111yescharacteristic
163C2×C3×D3—22no—
164C2×C3×D3—41no—
165C2×C3×D3—41no—
166C32×C4—21no—
167C32×C4—81no—
168C32×C4C2×Q1611yescharacteristic
169C32×C4#13511yescharacteristic
170C32×C4#13511yescharacteristic
171C32×C4AGL(1,ℤ/8)11yescharacteristic
172C3⋊Dic3—81no—
173C3×Dic3—41no—
174C22×C8—181no—
175C4⋊Q8—91no—
176C4⋊Q8D3211yescharacteristic
177C4×D4—31no—
178#107—61no—
179#106—181no—
180C4⋊C8—31no—
181C4⋊C8—31no—
182C4⋊C8—31no—
183#103—181no—
184#103—181no—
185#102—61no—
186#102—181no—
187C22⋊C8—181no—
188C4×C8—91no—
189C23×C3—61no—
190C22×D3—21no—
191C3×Q8—42no—
192C3×Q8—42no—
193C3×Q8—41no—
194C3×Q8—41no—
195C3×Q8—41no—
196C3×Q8—41no—
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#21612yes—
220C4×D3—41no—
221C4×D3—41no—
222Dic6—242no—
223Dic6—241no—
224Dic6—241no—
225C3×C8—121no—
226C3×C8—121no—
227C3×C8—121no—
228C3⋊C8—41no—
229C3⋊C8—41no—
230C3⋊C8—41no—
231C3⋊C8—61no—
232C3⋊C8—61no—
233C3⋊C8—61no—
234C3⋊C8—61no—
235C3⋊C8—121no—
236C3⋊C8—121no—
237C2×C32#46311yescharacteristic
238C2×C32#46711yescharacteristic
239C2×C32#47111yescharacteristic
240C3×D3—42no—
241C2×Q8—21no—
242C2×Q8—181no—
243C2×D4—31no—
244C22×C4—61no—
245C2×C8—61no—
246C2×C8—61no—
247C2×C8—61no—
248C2×C8—91no—
249C2×C8—91no—
250C2×C8—362no—
251C4⋊C4—21no—
252C4⋊C4—21no—
253C4⋊C4—31no—
254C4⋊C4—181no—
255C4⋊C4—181no—
256C22⋊C4—61no—
257C42C2×D3211yescharacteristic
258C22×C3—21no—
259C22×C3—62no—
260C22×C3—121no—
261C22×C3—121no—
262C22×C3#88411yescharacteristic
263C22×C3#93911yescharacteristic
264C2×D3—22no—
265C2×D3—41no—
266C2×D3—41no—
267C3×C4—22no—
268C3×C4—21no—
269C3×C4—21no—
270C3×C4—21no—
271C3×C4—21no—
272C3×C4—21no—
273C3×C4—21no—
274C3×C4—82no—
275C3×C4—81no—
276C3×C4—81no—
277C3×C4—121no—
278C3×C4#91111yescharacteristic
279C3×C4#91111yescharacteristic
280C3×C4#91211yescharacteristic
281C3×C4#91611yescharacteristic
282C3×C4#91611yescharacteristic
283C3×C4D3×Q1611yescharacteristic
284C3×C4C2×#21611yescharacteristic
285C3×C4#95011yescharacteristic
286Dic3—41no—
287Dic3—242no—
288Dic3—241no—
289Dic3—241no—
290C32#168311yescharacteristic, complemented, Sylow
291C23—61no—
292Q8—41no—
293Q8—41no—
294Q8—721no—
295D4—32no—
296D4—61no—
297C2×C4—41no—
298C2×C4—61no—
299C2×C4—121no—
300C2×C4—121no—
301C2×C4—361no—
302C2×C4#380411yescharacteristic
303C2×C4D3×#6711yescharacteristic
304C2×C4#381111yescharacteristic
305C8—121no—
306C8—121no—
307C8—121no—
308C8—181no—
309C8—181no—
310C2×C3—21no—
311C2×C3—21no—
312C2×C3—21no—
313C2×C3—122no—
314C2×C3#475411yescharacteristic
315C2×C3#478711yescharacteristic
316C2×C3#481311yescharacteristic
317C2×C3#505111yescharacteristic
318C2×C3#515311yescharacteristic
319C2×C3#520311yescharacteristic
320D3—42no—
321C22—62no—
322C22—121no—
323C22—121no—
324C22#6397111yescharacteristic
325C4—21no—
326C4—81no—
327C4—121no—
328C4—721no—
329C4#6392711yescharacteristic
330C4#6393611yescharacteristic
331C4D3×#21611yescharacteristic
332C4#6394711yescharacteristic
333C3—21no—
334C3#6844711yescharacteristic, complemented
335C3#7110311yescharacteristic, complemented
336C2—122no—
337C2#1059143411yescharacteristic
338C2#1059159611yescharacteristic
339C2#1059164311yescharacteristic
subgroupG/H
centerC22#63971
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊Q8C22
socleC22×C32#121
prime radicalC2×C3×D12D4
hypercenterC4⋊Q8D32
hypocenterC32#1683
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. #10592778C2semidirect
5. C3×#4547C2semidirect
6. #10589100C2semidirect
7. #10589096C2semidirect
35. #4547D3semidirect
290. C32#1683semidirect
334. C3#68447semidirect
335. C3#71103semidirect

Maximal subgroups

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

subgroupindex
#105927782
C3×#50872
#105903292
#105902682
C3×#45472
#105891002
#105890962
#711033
#684473