Finite Group Databasebeta

← #11781448

Subgroups — #11781448

Order 1152.

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

normal subgroups only

This group has 396 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
1C3×#5088C211yesmaximal, characteristic, complemented
2C3×#5083C211yesmaximal, characteristic, complemented
3#10590347C211yesmaximal, characteristic
4C3⋊C8×D12C211yesmaximal, characteristic, complemented
5#10589413C211yesmaximal, characteristic, complemented
6#10589099C211yesmaximal, characteristic, complemented
7#10589090C211yesmaximal, characteristic, complemented
8#71201—31nomaximal
9#71039—31nomaximal
10C32×C4⋊Q8C2211yescharacteristic
11C2×C3×#215—21no—
12C3×#874C2211yescharacteristic
13C3×C4×D12C2211yescharacteristic
14C2×#3713—21no—
15C2×D3×C3⋊C8—21no—
16C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
17C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
18C3×#835—21no—
19C3×#809—21no—
20C3×#809—21no—
21C3×C4⋊(C3⋊C8)C2211yescharacteristic
22C3×C4×C3⋊C8C2211yescharacteristic
23#63562—21no—
24(C2×D3)⋊(C3⋊C8)—21no—
25C3×#486—31no—
26C3×#461—31no—
27#5088D311yescharacteristic, complemented
28#5083D311yescharacteristic, complemented
29#5072—31no—
30#5015—31no—
31D4×C3⋊C8—31no—
32C8×D12—31no—
33#4547—31no—
34#4547—31no—
35#4547—61no—
36#4544—31no—
37#4485—31no—
38#4479—31no—
39#4458—31no—
40C2×C32×Q8—21no—
41C2×C3×D12—21no—
42C2×C3×D12—21no—
43C2×C3×D12—21no—
44C2×C3×D12D411yescharacteristic
45C2×C3×C4×D3—21no—
46C32×C4⋊C4—21no—
47C32×C4⋊C4—21no—
48C32×C42C2311yescharacteristic
49C2×C3⋊(C3⋊C8)—21no—
50C2×C3⋊(C3⋊C8)—21no—
51C3×#215—42no—
52C3×(C2×D3)⋊C4—21no—
53C3×C4⋊Dic3D411yescharacteristic
54C2×C3×C3⋊C8—21no—
55C2×C3×C3⋊C8D411yescharacteristic
56C2×C3×C3⋊C8D411yescharacteristic
57#3713—42no—
58D3×C3⋊C8—42no—
59#1681—91noSylow
60C2×C3×SD16—61no—
61C3×C4⋊Q8—21no—
62C3×C4⋊Q8C2×D311yescharacteristic
63C3×C4⋊Q8C2×D311yescharacteristic
64C3×#127—31no—
65C3×C4×D4—31no—
66C2×#215—21no—
67C2×#213—61no—
68C2×#213—61no—
69C22×C3⋊C8—61no—
70C2×D3×C8—61no—
71#874C2×D311yescharacteristic
72C4×D12C2×D311yescharacteristic
73C3×C4⋊C8—31no—
74C3×#103—61no—
75C3×#102—61no—
76C3×#102—61no—
77C3×C4×C8—31no—
78#835—21no—
79#832—61no—
80#830—61no—
81(C2×D3)⋊C8—61no—
82#809—21no—
83#809—21no—
84#809—61no—
85C4⋊(C3⋊C8)—31no—
86C4⋊(C3⋊C8)—31no—
87C4⋊(C3⋊C8)—31no—
88C4⋊(C3⋊C8)—31no—
89C4⋊(C3⋊C8)—61no—
90C4⋊(C3⋊C8)—61no—
91C4⋊(C3⋊C8)C2×D311yescharacteristic
92C4×C3⋊C8C2×D311yescharacteristic
93C22×C3×D3—21no—
94C22×C3×D3—41no—
95C32×Q8—41no—
96C32×Q8—41no—
97C2×C32×C4—41no—
98C2×C32×C4C2×D411yescharacteristic
99C2×C32×C4C2×D411yescharacteristic
100C2×C32×C4#4111yescharacteristic
101C2×C3×Dic3—21no—
102C3×D12—21no—
103C3×D12—41no—
104C3×D12—41no—
105C3×D12—41no—
106C3×D12—41no—
107C3×D12—81no—
108C3×D12D812yes—
109C3×C4×D3—41no—
110C3×C4×D3—41no—
111C3⋊(C3⋊C8)—41no—
112C3⋊(C3⋊C8)—41no—
113C3×C3⋊C8—21no—
114C3×C3⋊C8—21no—
115C3×C3⋊C8—41no—
116#486—31no—
117#461—31no—
118#459—91no—
119C8×D4—91no—
120#335—91no—
121#332—91no—
122#331—91no—
123C2×C3×Q8—21no—
124C2×C3×Q8—21no—
125C2×C3×Q8—41no—
126C2×C3×D4—31no—
127C2×C3×D4—61no—
128C2×C3×D4—61no—
129C2×C3×D4—61no—
130C22×C3×C4—61no—
131C2×D12—21no—
132C2×D12—21no—
133C2×D12—21no—
134C2×D12#6711yescharacteristic
135C2×C4×D3—21no—
136C3×SD16—122no—
137C2×C3×C8—31no—
138C2×C3×C8—31no—
139C2×C3×C8—61no—
140C3×C4⋊C4—22no—
141C3×C4⋊C4—21no—
142C3×C4⋊C4—21no—
143C3×C4⋊C4—21no—
144C3×C4⋊C4—21no—
145C3×C4⋊C4—31no—
146C3×C4⋊C4—41no—
147C3×C22⋊C4—61no—
148C3×C42—21no—
149C3×C42C22×D311yescharacteristic
150C3×C42C22×D311yescharacteristic
151#215—42no—
152#213—122no—
153#213—122no—
154(C2×D3)⋊C4—21no—
155C4⋊Dic3#6711yescharacteristic
156C2×C3⋊C8—21no—
157C2×C3⋊C8—61no—
158C2×C3⋊C8—61no—
159C2×C3⋊C8—61no—
160C2×C3⋊C8—61no—
161C2×C3⋊C8—121no—
162C2×C3⋊C8—121no—
163C2×C3⋊C8—122no—
164C2×C3⋊C8#6711yescharacteristic
165C2×C3⋊C8#6711yescharacteristic
166D3×C8—122no—
167C22×C32#12111yescharacteristic
168C2×C3×D3—22no—
169C2×C3×D3—41no—
170C2×C3×D3—41no—
171C2×C3×D3—81no—
172C2×C3×D3—81no—
173C2×C3×D3—81no—
174C32×C4—21no—
175C32×C4—81no—
176C32×C4C2×D811yescharacteristic
177C32×C4#13511yescharacteristic
178C32×C4#13511yescharacteristic
179C32×C4AGL(1,ℤ/8)11yescharacteristic
180C3×Dic3—41no—
181C2×SD16—61no—
182C2×D8—181no—
183C22×C8—181no—
184C4⋊Q8D3211yescharacteristic
185#127—31no—
186C4×D4—31no—
187C4⋊C8—31no—
188C4⋊C8—91no—
189C4⋊C8—91no—
190#103—61no—
191#102—61no—
192#102—61no—
193#102—181no—
194C22⋊C8—181no—
195C4×C8—31no—
196C23×C3—61no—
197C23×C3—121no—
198C22×D3—21no—
199C22×D3—41no—
200C3×Q8—41no—
201C3×Q8—41no—
202C3×Q8—41no—
203C3×Q8—41no—
204C3×Q8—81no—
205C3×Q8—81no—
206C3×D4—32no—
207C3×D4—61no—
208C3×D4—121no—
209C3×D4—121no—
210C3×D4—121no—
211C3×D4—121no—
212C3×D4—241no—
213C2×C3×C4—21no—
214C2×C3×C4—21no—
215C2×C3×C4—21no—
216C2×C3×C4—42no—
217C2×C3×C4—41no—
218C2×C3×C4—41no—
219C2×C3×C4—61no—
220C2×C3×C4—121no—
221C2×C3×C4—121no—
222C2×C3×C4D3×D411yescharacteristic
223C2×C3×C4D3×D411yescharacteristic
224C2×C3×C4#23711yescharacteristic
225C2×C3×C4#23711yescharacteristic
226C2×C3×C4C2×#6711yescharacteristic
227C2×C3×C4C2×#6711yescharacteristic
228C2×Dic3—21no—
229D12—21no—
230D12—41no—
231D12—41no—
232D12—41no—
233D12—41no—
234D12—81no—
235D12#21312yes—
236C4×D3—41no—
237C4×D3—41no—
238C3×C8—61no—
239C3×C8—61no—
240C3×C8—121no—
241C3⋊C8—21no—
242C3⋊C8—21no—
243C3⋊C8—41no—
244C3⋊C8—121no—
245C3⋊C8—121no—
246C3⋊C8—121no—
247C3⋊C8—121no—
248C3⋊C8—241no—
249C3⋊C8—241no—
250C2×C32#46311yescharacteristic
251C2×C32#46611yescharacteristic
252C2×C32#47111yescharacteristic
253C3×D3—42no—
254C3×D3—161no—
255C2×Q8—21no—
256C2×D4—31no—
257C2×D4—61no—
258C2×D4—61no—
259C2×D4—61no—
260C22×C4—61no—
261SD16—122no—
262D8—362no—
263C2×C8—31no—
264C2×C8—31no—
265C2×C8—61no—
266C2×C8—181no—
267C2×C8—181no—
268C2×C8—362no—
269C4⋊C4—21no—
270C4⋊C4—21no—
271C4⋊C4—31no—
272C22⋊C4—61no—
273C42C2×D3211yescharacteristic
274C22×C3—21no—
275C22×C3—62no—
276C22×C3—121no—
277C22×C3—121no—
278C22×C3—241no—
279C22×C3—241no—
280C22×C3—241no—
281C22×C3#93811yescharacteristic
282C22×C3#93911yescharacteristic
283C2×D3—22no—
284C2×D3—41no—
285C2×D3—41no—
286C2×D3—81no—
287C2×D3—81no—
288C2×D3—81no—
289C3×C4—21no—
290C3×C4—21no—
291C3×C4—21no—
292C3×C4—21no—
293C3×C4—21no—
294C3×C4—21no—
295C3×C4—41no—
296C3×C4—82no—
297C3×C4—81no—
298C3×C4—81no—
299C3×C4—121no—
300C3×C4D3×D811yescharacteristic
301C3×C4#91211yescharacteristic
302C3×C4#91411yescharacteristic
303C3×C4#91611yescharacteristic
304C3×C4C2×#21311yescharacteristic
305C3×C4#94911yescharacteristic
306C3×C4#95011yescharacteristic
307C3×C4#95011yescharacteristic
308Dic3—41no—
309C32#168111yescharacteristic, complemented, Sylow
310C23—61no—
311C23—121no—
312Q8—41no—
313Q8—41no—
314D4—32no—
315D4—61no—
316D4—121no—
317D4—121no—
318D4—121no—
319D4—121no—
320D4—241no—
321C2×C4—41no—
322C2×C4—61no—
323C2×C4—121no—
324C2×C4—121no—
325C2×C4#380511yescharacteristic
326C2×C4D3×#6711yescharacteristic
327C2×C4D3×#6711yescharacteristic
328C8—61no—
329C8—61no—
330C8—121no—
331C8—361no—
332C8—361no—
333C2×C3—21no—
334C2×C3—21no—
335C2×C3—21no—
336C2×C3—122no—
337C2×C3—481no—
338C2×C3#503811yescharacteristic
339C2×C3#505711yescharacteristic
340C2×C3#515711yescharacteristic
341C2×C3#516511yescharacteristic
342C2×C3#517711yescharacteristic
343C2×C3#520311yescharacteristic
344D3—42no—
345D3—161no—
346C22—62no—
347C22—121no—
348C22—121no—
349C22—241no—
350C22—241no—
351C22—241no—
352C22#6397011yescharacteristic
353C4—21no—
354C4—81no—
355C4—121no—
356C4D3×#21311yescharacteristic
357C4#6393311yescharacteristic
358C4#6393911yescharacteristic
359C4#6394711yescharacteristic
360C3—21no—
361C3#7103911yescharacteristic, complemented
362C3#7120111yescharacteristic, complemented
363C2—122no—
364C2—481no—
365C2#1059149811yescharacteristic
366C2#1059156711yescharacteristic
367C2#1059164211yescharacteristic
subgroupG/H
centerC22#63970
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊Q8C22
socleC22×C32#121
prime radical#10590347C2
hypercenterC4⋊Q8D32
hypocenterC32#1681
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. C3×#5088C2semidirect
2. C3×#5083C2semidirect
4. C3⋊C8×D12C2semidirect
5. #10589413C2semidirect
6. #10589099C2semidirect
7. #10589090C2semidirect
27. #5088D3semidirect
28. #5083D3semidirect
309. C32#1681semidirect
361. C3#71039semidirect
362. C3#71201semidirect

Maximal subgroups

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

subgroupindex
C3×#50882
C3×#50832
#105903472
C3⋊C8×D122
#105894132
#105890992
#105890902
#712013
#710393