Finite Group Databasebeta

← #11781455

Subgroups — #11781455

Order 1152.

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

normal subgroups only

This group has 391 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
1C3×#4841C211yesmaximal, characteristic, complemented
2#10590347C211yesmaximal, characteristic
3#10590329C211yesmaximal, characteristic, complemented
4#10590277C211yesmaximal, characteristic, complemented
5#10589345C211yesmaximal, characteristic, complemented
6C3×#4485C211yesmaximal, characteristic, complemented
7#10589092C211yesmaximal, characteristic, complemented
8#71039—31nomaximal
9#68397—31nomaximal
10C2×C3×#204—21no—
11C3×#874C2211yescharacteristic
12C3×C4×D12C2211yescharacteristic
13C3×#869C2211yescharacteristic
14C2×#3713—21no—
15C2×D3×C3⋊C8—21no—
16C32×C4⋊C8C2211yescharacteristic
17C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
18C4×C3⋊(C3⋊C8)C2211yescharacteristic
19C3×#816—21no—
20C3×C4⋊(C3⋊C8)C2211yescharacteristic
21#63562—21no—
22#63562—21no—
23#63562—21no—
24(C2×D3)⋊(C3⋊C8)—21no—
25C3×#461—31no—
26#5088—31no—
27#5072—31no—
28#5070—31no—
29#5015—31no—
30D4×C3⋊C8—31no—
31#4841D311yescharacteristic, complemented
32#4834—31no—
33C3×#331—31no—
34#4547—31no—
35#4486—31no—
36#4485D311yescharacteristic, complemented
37#4479—31no—
38#4479—31no—
39#4479—61no—
40C2×C3×D12—21no—
41C2×C3×D12—21no—
42C2×C3×D12—21no—
43C2×C3×D12D411yescharacteristic
44C2×C3×C4×D3—21no—
45C2×C3×Dic6—21no—
46C2×C32×C8—21no—
47C32×C42C2311yescharacteristic
48C2×C3⋊(C3⋊C8)—21no—
49C2×C3⋊(C3⋊C8)D411yescharacteristic
50C2×C3⋊(C3⋊C8)D411yescharacteristic
51C3×(C2×D3)⋊C4—21no—
52C3×C4⋊Dic3—21no—
53C3×C4⋊Dic3—21no—
54C3×C4⋊Dic3D411yescharacteristic
55C2×C3×C3⋊C8—21no—
56C3×#204—42no—
57#3713—42no—
58D3×C3⋊C8—42no—
59#1681—91noSylow
60C2×C3×SD16—61no—
61C3×C4⋊Q8—31no—
62C3×#127—31no—
63C3×C4×D4—31no—
64C2×#213—61no—
65C2×#213—61no—
66C22×C3⋊C8—61no—
67C2×#204—21no—
68C2×D3×C8—61no—
69#874C2×D311yescharacteristic
70C4×D12C2×D311yescharacteristic
71#869C2×D311yescharacteristic
72C3×C4⋊C8—21no—
73C3×C4⋊C8—31no—
74C3×C4⋊C8C2×D311yescharacteristic
75C3×C4⋊C8C2×D311yescharacteristic
76C3×#103—61no—
77#832—61no—
78#832—61no—
79#832—61no—
80#830—61no—
81(C2×D3)⋊C8—61no—
82#816—21no—
83#809—61no—
84#809—61no—
85#809—61no—
86C4⋊(C3⋊C8)—31no—
87C4⋊(C3⋊C8)—31no—
88C4⋊(C3⋊C8)—61no—
89C4⋊(C3⋊C8)C2×D311yescharacteristic
90C4×C3⋊C8—31no—
91C4×C3⋊C8—31no—
92C4×C3⋊C8—61no—
93C22×C3×D3—21no—
94C22×C3×D3—41no—
95C2×C32×C4C2×D411yescharacteristic
96C2×C32×C4C2×D411yescharacteristic
97C2×C32×C4#4111yescharacteristic
98C2×C3×Dic3—21no—
99C2×C3×Dic3—41no—
100C3×D12—21no—
101C3×D12—41no—
102C3×D12—41no—
103C3×D12—41no—
104C3×D12—41no—
105C3×D12—81no—
106C3×D12D812yes—
107C3×C4×D3—41no—
108C3×C4×D3—41no—
109C3×Dic6—41no—
110C3×Dic6—41no—
111C32×C8—41no—
112C3⋊(C3⋊C8)—21no—
113C3⋊(C3⋊C8)—21no—
114C3⋊(C3⋊C8)—41no—
115C3×C3⋊C8—41no—
116#486—91no—
117#461—31no—
118#459—91no—
119C8×D4—91no—
120#335—91no—
121#332—91no—
122#331—31no—
123C2×C3×Q8—61no—
124C2×C3×D4—31no—
125C2×C3×D4—61no—
126C2×C3×D4—61no—
127C2×C3×D4—61no—
128C22×C3×C4—61no—
129C2×D12—21no—
130C2×D12—21no—
131C2×D12—21no—
132C2×D12#6711yescharacteristic
133C2×C4×D3—21no—
134C2×Dic6—21no—
135C3×SD16—122no—
136C2×C3×C8—21no—
137C2×C3×C8—21no—
138C2×C3×C8—41no—
139C2×C3×C8—61no—
140C3×C4⋊C4—31no—
141C3×C4⋊C4—61no—
142C3×C4⋊C4—61no—
143C3×C22⋊C4—61no—
144C3×C42—21no—
145C3×C42C22×D311yescharacteristic
146C3×C42C22×D311yescharacteristic
147#213—122no—
148#213—122no—
149(C2×D3)⋊C4—21no—
150C4⋊Dic3—21no—
151C4⋊Dic3—21no—
152C4⋊Dic3#6711yescharacteristic
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—61no—
161C2×C3⋊C8—61no—
162C2×C3⋊C8—121no—
163C2×C3⋊C8—122no—
164#204—42no—
165D3×C8—122no—
166C22×C32#12111yescharacteristic
167C2×C3×D3—22no—
168C2×C3×D3—41no—
169C2×C3×D3—41no—
170C2×C3×D3—81no—
171C2×C3×D3—81no—
172C2×C3×D3—81no—
173C32×C4—21no—
174C32×C4C2×D811yescharacteristic
175C32×C4#13511yescharacteristic
176C32×C4#13511yescharacteristic
177C32×C4AGL(1,ℤ/8)11yescharacteristic
178C3×Dic3—41no—
179C3×Dic3—81no—
180C2×SD16—61no—
181C2×D8—181no—
182C22×C8—181no—
183C4⋊Q8—31no—
184#127—31no—
185C4×D4—31no—
186C4⋊C8—31no—
187C4⋊C8—91no—
188C4⋊C8D3211yescharacteristic
189#103—61no—
190#102—181no—
191#102—181no—
192#102—181no—
193C22⋊C8—181no—
194C4×C8—91no—
195C23×C3—61no—
196C23×C3—121no—
197C22×D3—21no—
198C22×D3—41no—
199C3×Q8—121no—
200C3×Q8—121no—
201C3×D4—32no—
202C3×D4—61no—
203C3×D4—121no—
204C3×D4—121no—
205C3×D4—121no—
206C3×D4—121no—
207C3×D4—241no—
208C2×C3×C4—21no—
209C2×C3×C4—21no—
210C2×C3×C4—21no—
211C2×C3×C4—61no—
212C2×C3×C4—121no—
213C2×C3×C4—121no—
214C2×C3×C4—121no—
215C2×C3×C4#23511yescharacteristic
216C2×C3×C4D3×D411yescharacteristic
217C2×C3×C4D3×D411yescharacteristic
218C2×C3×C4D3×D411yescharacteristic
219C2×C3×C4#23711yescharacteristic
220C2×C3×C4C2×#6711yescharacteristic
221C2×Dic3—21no—
222C2×Dic3—41no—
223D12—21no—
224D12—41no—
225D12—41no—
226D12—41no—
227D12—41no—
228D12—81no—
229D12#21312yes—
230C4×D3—41no—
231C4×D3—41no—
232Dic6—41no—
233Dic6—41no—
234C3×C8—41no—
235C3×C8—41no—
236C3×C8—81no—
237C3×C8—121no—
238C3⋊C8—41no—
239C3⋊C8—62no—
240C3⋊C8—61no—
241C3⋊C8—61no—
242C3⋊C8—61no—
243C3⋊C8—61no—
244C3⋊C8—121no—
245C3⋊C8—121no—
246C3⋊C8—121no—
247C3⋊C8—241no—
248C2×C32#46311yescharacteristic
249C2×C32#46611yescharacteristic
250C2×C32#47111yescharacteristic
251C3×D3—42no—
252C3×D3—161no—
253C2×Q8—61no—
254C2×D4—31no—
255C2×D4—61no—
256C2×D4—61no—
257C2×D4—61no—
258C22×C4—61no—
259SD16—122no—
260D8—362no—
261C2×C8—21no—
262C2×C8—61no—
263C2×C8—91no—
264C2×C8—91no—
265C2×C8—181no—
266C2×C8—362no—
267C4⋊C4—31no—
268C4⋊C4—61no—
269C4⋊C4—61no—
270C22⋊C4—61no—
271C42C2×D3211yescharacteristic
272C22×C3—21no—
273C22×C3—62no—
274C22×C3—121no—
275C22×C3—121no—
276C22×C3—241no—
277C22×C3—241no—
278C22×C3—241no—
279C22×C3#88411yescharacteristic
280C22×C3#93911yescharacteristic
281C2×D3—22no—
282C2×D3—41no—
283C2×D3—41no—
284C2×D3—81no—
285C2×D3—81no—
286C2×D3—81no—
287C3×C4—21no—
288C3×C4—21no—
289C3×C4—21no—
290C3×C4—21no—
291C3×C4—21no—
292C3×C4—21no—
293C3×C4—41no—
294C3×C4—121no—
295C3×C4—241no—
296C3×C4D3×D811yescharacteristic
297C3×C4#91111yescharacteristic
298C3×C4#91411yescharacteristic
299C3×C4#91611yescharacteristic
300C3×C4#91611yescharacteristic
301C3×C4#91611yescharacteristic
302C3×C4C2×#21311yescharacteristic
303C3×C4#95011yescharacteristic
304Dic3—41no—
305Dic3—81no—
306C32#168111yescharacteristic, complemented, Sylow
307C23—61no—
308C23—121no—
309Q8—121no—
310Q8—121no—
311D4—32no—
312D4—61no—
313D4—121no—
314D4—121no—
315D4—121no—
316D4—121no—
317D4—241no—
318C2×C4—61no—
319C2×C4—121no—
320C2×C4—121no—
321C2×C4—121no—
322C2×C4#379511yescharacteristic
323C2×C4#380211yescharacteristic
324C2×C4D3×#6711yescharacteristic
325C8—41no—
326C8—121no—
327C8—181no—
328C8—181no—
329C8—361no—
330C2×C3—21no—
331C2×C3—21no—
332C2×C3—21no—
333C2×C3—122no—
334C2×C3—481no—
335C2×C3#474811yescharacteristic
336C2×C3#477511yescharacteristic
337C2×C3#478711yescharacteristic
338C2×C3#503811yescharacteristic
339C2×C3#516511yescharacteristic
340C2×C3#520311yescharacteristic
341D3—42no—
342D3—161no—
343C22—62no—
344C22—121no—
345C22—121no—
346C22—241no—
347C22—241no—
348C22—241no—
349C22#6388511yescharacteristic
350C4—21no—
351C4—121no—
352C4—241no—
353C4#6379811yescharacteristic
354C4#6380911yescharacteristic
355C4D3×#21311yescharacteristic
356C4#6394711yescharacteristic
357C3—21no—
358C3#6839711yescharacteristic, complemented
359C3#7103911yescharacteristic, complemented
360C2—122no—
361C2—481no—
362C2#1059049911yescharacteristic
363C2#1059075011yescharacteristic
364C2#1059097911yescharacteristic
subgroupG/H
centerC22#63885
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊C8C22
socleC22×C32#121
prime radical#10590347C2
hypercenterC4⋊C8D32
hypocenterC32#1681
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. C3×#4841C2semidirect
3. #10590329C2semidirect
4. #10590277C2semidirect
5. #10589345C2semidirect
6. C3×#4485C2semidirect
7. #10589092C2semidirect
31. #4841D3semidirect
36. #4485D3semidirect
306. C32#1681semidirect
358. C3#68397semidirect
359. C3#71039semidirect

Maximal subgroups

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

subgroupindex
C3×#48412
#105903472
#105903292
#105902772
#105893452
C3×#44852
#105890922
#710393
#683973