Finite Group Databasebeta

← #11781444

Subgroups — #11781444

Order 1152.

431 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 431 conjugacy classes of subgroups — too many to draw. Only its 94 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
1D4×C3⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
2C3×#5019C211yesmaximal, characteristic, complemented
3C3×#5015C211yesmaximal, characteristic
4#10590277C211yesmaximal, characteristic, complemented
5#10589100C211yesmaximal, characteristic, complemented
6#10589093C211yesmaximal, characteristic, complemented
7#10589090C211yesmaximal, characteristic, complemented
8#71039—31nomaximal
9#71007—31nomaximal
10C32×C4×D4C2211yescharacteristic
11C22×C3⋊(C3⋊C8)—21no—
12C2×C3×#214—21no—
13C2×C3×#213—21no—
14C3×#874C2211yescharacteristic
15C3×#869C2211yescharacteristic
16#63657—21no—
17C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
18C4×C3⋊(C3⋊C8)C2211yescharacteristic
19C3×#810—21no—
20C3×#809—21no—
21C3×C4⋊(C3⋊C8)C2211yescharacteristic
22C3×C4⋊(C3⋊C8)C2211yescharacteristic
23#63562—21no—
24#63562—21no—
25C3×#461—31no—
26C3×#459—31no—
27#5088—31no—
28#5070—31no—
29#5019D311yescharacteristic, complemented
30#5015D311yescharacteristic
31D4×C3⋊C8—31no—
32D4×C3⋊C8—31no—
33D4×C3⋊C8—61no—
34#4547—31no—
35#4544—31no—
36#4485—31no—
37#4482—31no—
38#4479—31no—
39#4479—31no—
40C2×C32×D4D411yescharacteristic
41C22×C32×C4—21no—
42C2×C3×D12—21no—
43C2×C3×D12—21no—
44C2×C3×D12—21no—
45C2×C3×Dic6—21no—
46C32×C4⋊C4D411yescharacteristic
47C32×C22⋊C4—21no—
48C32×C42C2311yescharacteristic
49C2×C3⋊(C3⋊C8)—21no—
50C2×C3⋊(C3⋊C8)—42no—
51C2×C3⋊(C3⋊C8)D411yescharacteristic
52C2×C3⋊(C3⋊C8)D411yescharacteristic
53C3×#214—42no—
54C3×#213—42no—
55C3×C4⋊Dic3—21no—
56C3×C4⋊Dic3—21no—
57C2×C3×C3⋊C8—21no—
58C2×C3×C3⋊C8—21no—
59#1681—91noSylow
60C2×C3×SD16—61no—
61C2×C3×D8—61no—
62C3×C4⋊Q8—31no—
63C3×#127—31no—
64C3×C4×D4—21no—
65C3×C4×D4C2×D311yescharacteristic
66C3×C4×D4C2×D311yescharacteristic
67C2×#214—21no—
68C2×#213—21no—
69C22×C3⋊C8—61no—
70C22×C3⋊C8—61no—
71C22×C3⋊C8—62no—
72#874C2×D311yescharacteristic
73#869C2×D311yescharacteristic
74C3×C4⋊C8—31no—
75C3×C4⋊C8—31no—
76C3×#103—61no—
77C3×#102—61no—
78#832—61no—
79#832—61no—
80#830—61no—
81#830—61no—
82#830—62no—
83#810—21no—
84#809—21no—
85#809—61no—
86#809—61no—
87C4⋊(C3⋊C8)—31no—
88C4⋊(C3⋊C8)—31no—
89C4⋊(C3⋊C8)—61no—
90C4⋊(C3⋊C8)C2×D311yescharacteristic
91C4⋊(C3⋊C8)C2×D311yescharacteristic
92C4×C3⋊C8—31no—
93C4×C3⋊C8—31no—
94C4×C3⋊C8—61no—
95C23×C32—21no—
96C22×C3×D3—41no—
97C32×D4—21no—
98C32×D4D812yes—
99C2×C32×C4—21no—
100C2×C32×C4—41no—
101C2×C32×C4—41no—
102C2×C32×C4C2×D411yescharacteristic
103C2×C32×C4C2×D411yescharacteristic
104C2×C32×C4#4111yescharacteristic
105C2×C3×Dic3—41no—
106C3×D12—41no—
107C3×D12—41no—
108C3×D12—41no—
109C3×D12—41no—
110C3×D12—81no—
111C3×Dic6—41no—
112C3×Dic6—41no—
113C3⋊(C3⋊C8)—21no—
114C3⋊(C3⋊C8)—21no—
115C3⋊(C3⋊C8)—41no—
116C3×C3⋊C8—41no—
117C3×C3⋊C8—41no—
118#486—91no—
119#461—31no—
120#459—31no—
121C8×D4—91no—
122#335—91no—
123#332—91no—
124#331—91no—
125C2×C3×Q8—61no—
126C2×C3×D4—21no—
127C2×C3×D4—61no—
128C2×C3×D4—61no—
129C2×C3×D4—61no—
130C2×C3×D4#6711yescharacteristic
131C2×C3×D4#6711yescharacteristic
132C22×C3×C4—22no—
133C22×C3×C4—21no—
134C22×C3×C4—21no—
135C2×D12—21no—
136C2×D12—21no—
137C2×D12—21no—
138C2×Dic6—21no—
139C3×SD16—122no—
140C3×D8—122no—
141C2×C3×C8—61no—
142C2×C3×C8—61no—
143C3×C4⋊C4—21no—
144C3×C4⋊C4—61no—
145C3×C4⋊C4—61no—
146C3×C4⋊C4#6711yescharacteristic
147C3×C4⋊C4#6711yescharacteristic
148C3×C22⋊C4—22no—
149C3×C22⋊C4—21no—
150C3×C22⋊C4—21no—
151C3×C42—21no—
152C3×C42C22×D311yescharacteristic
153C3×C42C22×D311yescharacteristic
154#214—42no—
155#213—42no—
156C4⋊Dic3—21no—
157C4⋊Dic3—21no—
158C2×C3⋊C8—21no—
159C2×C3⋊C8—21no—
160C2×C3⋊C8—31no—
161C2×C3⋊C8—31no—
162C2×C3⋊C8—31no—
163C2×C3⋊C8—31no—
164C2×C3⋊C8—61no—
165C2×C3⋊C8—61no—
166C2×C3⋊C8—62no—
167C2×C3⋊C8—61no—
168C2×C3⋊C8—61no—
169C2×C3⋊C8—124no—
170C2×C3⋊C8—122no—
171C2×C3⋊C8—122no—
172C22×C32—22no—
173C22×C32—41no—
174C22×C32—41no—
175C22×C32#12111yescharacteristic
176C2×C3×D3—81no—
177C2×C3×D3—81no—
178C2×C3×D3—81no—
179C32×C4—21no—
180C32×C4—41no—
181C32×C4C2×D811yescharacteristic
182C32×C4#13511yescharacteristic
183C32×C4#13511yescharacteristic
184C32×C4AGL(1,ℤ/8)11yescharacteristic
185C3×Dic3—81no—
186C2×SD16—61no—
187C2×D8—61no—
188C22×C8—181no—
189C4⋊Q8—31no—
190#127—31no—
191C4×D4D3211yescharacteristic
192C4⋊C8—31no—
193C4⋊C8—31no—
194C4⋊C8—91no—
195#103—61no—
196#102—61no—
197#102—181no—
198#102—181no—
199C22⋊C8—181no—
200C4×C8—91no—
201C23×C3—22no—
202C23×C3—21no—
203C23×C3—21no—
204C23×C3—121no—
205C22×D3—41no—
206C3×Q8—121no—
207C3×Q8—121no—
208C3×D4—22no—
209C3×D4—21no—
210C3×D4—21no—
211C3×D4—22no—
212C3×D4—121no—
213C3×D4—121no—
214C3×D4—121no—
215C3×D4—121no—
216C3×D4—241no—
217C3×D4#21312yes—
218C3×D4#21312yes—
219C2×C3×C4—22no—
220C2×C3×C4—21no—
221C2×C3×C4—21no—
222C2×C3×C4—21no—
223C2×C3×C4—21no—
224C2×C3×C4—21no—
225C2×C3×C4—42no—
226C2×C3×C4—42no—
227C2×C3×C4—41no—
228C2×C3×C4—41no—
229C2×C3×C4—41no—
230C2×C3×C4—41no—
231C2×C3×C4—121no—
232C2×C3×C4D3×D411yescharacteristic
233C2×C3×C4D3×D411yescharacteristic
234C2×C3×C4#23711yescharacteristic
235C2×C3×C4#23711yescharacteristic
236C2×C3×C4C2×#6711yescharacteristic
237C2×C3×C4C2×#6711yescharacteristic
238C2×Dic3—41no—
239D12—41no—
240D12—41no—
241D12—41no—
242D12—41no—
243D12—81no—
244Dic6—41no—
245Dic6—41no—
246C3×C8—121no—
247C3×C8—121no—
248C3⋊C8—41no—
249C3⋊C8—41no—
250C3⋊C8—62no—
251C3⋊C8—61no—
252C3⋊C8—61no—
253C3⋊C8—61no—
254C3⋊C8—61no—
255C3⋊C8—121no—
256C3⋊C8—122no—
257C3⋊C8—121no—
258C3⋊C8—121no—
259C2×C32—42no—
260C2×C32#46311yescharacteristic
261C2×C32#46611yescharacteristic
262C2×C32#47111yescharacteristic
263C3×D3—161no—
264C2×Q8—61no—
265C2×D4—61no—
266C2×D4—61no—
267C2×D4—61no—
268C2×D4#62511yescharacteristic
269C22×C4—21no—
270SD16—122no—
271D8—122no—
272C2×C8—61no—
273C2×C8—61no—
274C2×C8—91no—
275C2×C8—91no—
276C2×C8—181no—
277C2×C8—362no—
278C4⋊C4—61no—
279C4⋊C4—61no—
280C4⋊C4#62511yescharacteristic
281C22⋊C4—21no—
282C42C2×D3211yescharacteristic
283C22×C3—24no—
284C22×C3—22no—
285C22×C3—22no—
286C22×C3—21no—
287C22×C3—42no—
288C22×C3—42no—
289C22×C3—41no—
290C22×C3—41no—
291C22×C3—41no—
292C22×C3—41no—
293C22×C3—241no—
294C22×C3—241no—
295C22×C3—241no—
296C22×C3#93911yescharacteristic
297C22×C3#93911yescharacteristic
298C2×D3—81no—
299C2×D3—81no—
300C2×D3—81no—
301C3×C4—21no—
302C3×C4—21no—
303C3×C4—21no—
304C3×C4—21no—
305C3×C4—21no—
306C3×C4—21no—
307C3×C4—41no—
308C3×C4—42no—
309C3×C4—41no—
310C3×C4—41no—
311C3×C4—241no—
312C3×C4#91111yescharacteristic
313C3×C4#91211yescharacteristic
314C3×C4#91411yescharacteristic
315C3×C4#91611yescharacteristic
316C3×C4C2×#21311yescharacteristic
317C3×C4C2×#21311yescharacteristic
318C3×C4#95011yescharacteristic
319C3×C4#95011yescharacteristic
320Dic3—81no—
321C32#168111yescharacteristic, complemented, Sylow
322C23—21no—
323C23—121no—
324Q8—121no—
325Q8—121no—
326D4—21no—
327D4—121no—
328D4—121no—
329D4—121no—
330D4—121no—
331D4—241no—
332D4#371312yes—
333C2×C4—21no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—121no—
337C2×C4#380511yescharacteristic
338C2×C4C2×#62511yescharacteristic
339C2×C4#381111yescharacteristic
340C8—121no—
341C8—121no—
342C8—181no—
343C8—181no—
344C8—361no—
345C2×C3—21no—
346C2×C3—21no—
347C2×C3—21no—
348C2×C3—44no—
349C2×C3—42no—
350C2×C3—42no—
351C2×C3—481no—
352C2×C3#503811yescharacteristic
353C2×C3#503811yescharacteristic
354C2×C3#515311yescharacteristic
355C2×C3#516511yescharacteristic
356C2×C3#520011yescharacteristic
357C2×C3#520311yescharacteristic
358D3—161no—
359C22—22no—
360C22—41no—
361C22—41no—
362C22—241no—
363C22—241no—
364C22—241no—
365C22#6398011yescharacteristic
366C4—21no—
367C4—41no—
368C4—241no—
369C4C2×#371311yescharacteristic
370C4#6382211yescharacteristic
371C4#6393611yescharacteristic
372C4#6393711yescharacteristic
373C3—21no—
374C3#7100711yescharacteristic, complemented
375C3#7103911yescharacteristic, complemented
376C2—42no—
377C2—481no—
378C2#1059116611yescharacteristic
379C2#1059147611yescharacteristic
380C2#1059168111yescharacteristic
subgroupG/H
centerC22#63980
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4×D4C22
socleC22×C32#121
prime radicalC3×#5015C2
hypercenterC4×D4D32
hypocenterC32#1681
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. D4×C3⋊(C3⋊C8)C2semidirect
2. C3×#5019C2semidirect
4. #10590277C2semidirect
5. #10589100C2semidirect
6. #10589093C2semidirect
7. #10589090C2semidirect
29. #5019D3semidirect
321. C32#1681semidirect
374. C3#71007semidirect
375. C3#71039semidirect

Maximal subgroups

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

subgroupindex
D4×C3⋊(C3⋊C8)2
C3×#50192
C3×#50152
#105902772
#105891002
#105890932
#105890902
#710393
#710073