Finite Group Databasebeta

← #11781256

Subgroups — #11781256

Order 1152.

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

normal subgroups only

This group has 419 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×#5015C211yesmaximal, characteristic
3C3×#5008C211yesmaximal, characteristic, complemented
4#10590277C211yesmaximal, characteristic, complemented
5#10589098C211yesmaximal, characteristic, complemented
6#10589095C211yesmaximal, characteristic, complemented
7#10589090C211yesmaximal, characteristic, complemented
8#71134—31nomaximal
9#71006—31nomaximal
10C32×C4×D4C2211yescharacteristic
11C22×C3⋊(C3⋊C8)—21no—
12C2×C3×#213—21no—
13C3×#874C2211yescharacteristic
14C3×#869C2211yescharacteristic
15#63657—21no—
16C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
17C4×C3⋊(C3⋊C8)C2211yescharacteristic
18C3×#832—21no—
19C3×#809—21no—
20C3×#808—21no—
21C3×C4⋊(C3⋊C8)C2211yescharacteristic
22C3×C4⋊(C3⋊C8)C2211yescharacteristic
23#63562—21no—
24#63562—21no—
25C3×#476—31no—
26C3×#459—31no—
27#5088—31no—
28#5070—31no—
29#5015D311yescharacteristic
30D4×C3⋊C8—31no—
31D4×C3⋊C8—31no—
32D4×C3⋊C8—61no—
33#5008D311yescharacteristic, complemented
34#4546—31no—
35#4544—31no—
36#4485—31no—
37#4481—31no—
38#4480—31no—
39#4480—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×#213—42no—
54C3×C4⋊Dic3—21no—
55C3×C4⋊Dic3—21no—
56C2×C3×C3⋊C8—21no—
57C2×C3×C3⋊C8—21no—
58#1677—91noSylow
59C2×C3×D8—61no—
60C3×C4⋊Q8—31no—
61C3×#127—31no—
62C3×C4×D4—21no—
63C3×C4×D4C2×D311yescharacteristic
64C3×C4×D4C2×D311yescharacteristic
65C2×#213—21no—
66C22×C3⋊C8—61no—
67C22×C3⋊C8—61no—
68C22×C3⋊C8—62no—
69#874C2×D311yescharacteristic
70#869C2×D311yescharacteristic
71C3×#106—61no—
72C3×C4⋊C8—31no—
73C3×C4⋊C8—31no—
74C3×#102—61no—
75C3×#102—61no—
76#832—21no—
77#832—61no—
78#832—61no—
79#830—61no—
80#830—61no—
81#830—62no—
82#809—21no—
83#809—61no—
84#809—61no—
85#808—21no—
86C4⋊(C3⋊C8)—31no—
87C4⋊(C3⋊C8)—31no—
88C4⋊(C3⋊C8)—61no—
89C4⋊(C3⋊C8)C2×D311yescharacteristic
90C4⋊(C3⋊C8)C2×D311yescharacteristic
91C4×C3⋊C8—31no—
92C4×C3⋊C8—31no—
93C4×C3⋊C8—61no—
94C23×C32—21no—
95C22×C3×D3—41no—
96C32×D4—21no—
97C32×D4SD1612yes—
98C2×C32×C4—21no—
99C2×C32×C4—41no—
100C2×C32×C4—41no—
101C2×C32×C4C2×D411yescharacteristic
102C2×C32×C4C2×D411yescharacteristic
103C2×C32×C4#4111yescharacteristic
104C2×C3×Dic3—41no—
105C3×D12—41no—
106C3×D12—41no—
107C3×D12—41no—
108C3×D12—41no—
109C3×D12—81no—
110C3×Dic6—81no—
111C3⋊(C3⋊C8)—21no—
112C3⋊(C3⋊C8)—21no—
113C3⋊(C3⋊C8)—41no—
114C3×C3⋊C8—41no—
115C3×C3⋊C8—41no—
116#486—91no—
117#476—31no—
118#459—31no—
119C8×D4—91no—
120#334—91no—
121#333—91no—
122#331—91no—
123C2×C3×Q8—61no—
124C2×C3×D4—21no—
125C2×C3×D4—61no—
126C2×C3×D4—61no—
127C2×C3×D4—61no—
128C2×C3×D4#6711yescharacteristic
129C2×C3×D4#6711yescharacteristic
130C22×C3×C4—22no—
131C22×C3×C4—21no—
132C22×C3×C4—21no—
133C2×D12—21no—
134C2×D12—21no—
135C2×D12—21no—
136C2×Dic6—21no—
137C3×D8—122no—
138C2×C3×C8—61no—
139C2×C3×C8—61no—
140C3×C4⋊C4—21no—
141C3×C4⋊C4—61no—
142C3×C4⋊C4—61no—
143C3×C4⋊C4#6711yescharacteristic
144C3×C4⋊C4#6711yescharacteristic
145C3×C22⋊C4—22no—
146C3×C22⋊C4—21no—
147C3×C22⋊C4—21no—
148C3×C42—21no—
149C3×C42C22×D311yescharacteristic
150C3×C42C22×D311yescharacteristic
151#213—42no—
152C4⋊Dic3—21no—
153C4⋊Dic3—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—62no—
163C2×C3⋊C8—61no—
164C2×C3⋊C8—61no—
165C2×C3⋊C8—124no—
166C2×C3⋊C8—122no—
167C2×C3⋊C8—122no—
168C22×C32—22no—
169C22×C32—41no—
170C22×C32—41no—
171C22×C32#12111yescharacteristic
172C2×C3×D3—81no—
173C2×C3×D3—81no—
174C2×C3×D3—81no—
175C32×C4—21no—
176C32×C4—41no—
177C32×C4C2×SD1611yescharacteristic
178C32×C4#13511yescharacteristic
179C32×C4#13511yescharacteristic
180C32×C4AGL(1,ℤ/8)11yescharacteristic
181C3×Dic3—81no—
182C2×D8—61no—
183C22×C8—181no—
184C4⋊Q8—31no—
185#127—31no—
186C4×D4D3211yescharacteristic
187#106—61no—
188C4⋊C8—31no—
189C4⋊C8—31no—
190C4⋊C8—91no—
191#102—61no—
192#102—61no—
193#102—181no—
194#102—181no—
195C22⋊C8—181no—
196C4×C8—91no—
197C23×C3—22no—
198C23×C3—21no—
199C23×C3—21no—
200C23×C3—121no—
201C22×D3—41no—
202C3×Q8—241no—
203C3×D4—22no—
204C3×D4—21no—
205C3×D4—21no—
206C3×D4—22no—
207C3×D4—121no—
208C3×D4—121no—
209C3×D4—121no—
210C3×D4—121no—
211C3×D4—241no—
212C3×D4#21412yes—
213C3×D4#21512yes—
214C2×C3×C4—22no—
215C2×C3×C4—21no—
216C2×C3×C4—21no—
217C2×C3×C4—21no—
218C2×C3×C4—21no—
219C2×C3×C4—21no—
220C2×C3×C4—42no—
221C2×C3×C4—42no—
222C2×C3×C4—41no—
223C2×C3×C4—41no—
224C2×C3×C4—41no—
225C2×C3×C4—41no—
226C2×C3×C4—121no—
227C2×C3×C4D3×D411yescharacteristic
228C2×C3×C4D3×D411yescharacteristic
229C2×C3×C4#23711yescharacteristic
230C2×C3×C4#23711yescharacteristic
231C2×C3×C4C2×#6711yescharacteristic
232C2×C3×C4C2×#6711yescharacteristic
233C2×Dic3—41no—
234D12—41no—
235D12—41no—
236D12—41no—
237D12—41no—
238D12—81no—
239Dic6—81no—
240C3×C8—121no—
241C3×C8—121no—
242C3⋊C8—41no—
243C3⋊C8—41no—
244C3⋊C8—62no—
245C3⋊C8—61no—
246C3⋊C8—61no—
247C3⋊C8—61no—
248C3⋊C8—61no—
249C3⋊C8—121no—
250C3⋊C8—122no—
251C3⋊C8—121no—
252C3⋊C8—121no—
253C2×C32—42no—
254C2×C32#46311yescharacteristic
255C2×C32#46511yescharacteristic
256C2×C32#47211yescharacteristic
257C3×D3—161no—
258C2×Q8—61no—
259C2×D4—61no—
260C2×D4—61no—
261C2×D4—61no—
262C2×D4#62511yescharacteristic
263C22×C4—21no—
264D8—122no—
265C2×C8—61no—
266C2×C8—61no—
267C2×C8—91no—
268C2×C8—91no—
269C2×C8—181no—
270C2×C8—362no—
271C4⋊C4—61no—
272C4⋊C4—61no—
273C4⋊C4#62511yescharacteristic
274C22⋊C4—21no—
275C42C2×D3211yescharacteristic
276C22×C3—24no—
277C22×C3—22no—
278C22×C3—22no—
279C22×C3—21no—
280C22×C3—42no—
281C22×C3—42no—
282C22×C3—41no—
283C22×C3—41no—
284C22×C3—41no—
285C22×C3—41no—
286C22×C3—241no—
287C22×C3—241no—
288C22×C3—241no—
289C22×C3#93911yescharacteristic
290C22×C3#93911yescharacteristic
291C2×D3—81no—
292C2×D3—81no—
293C2×D3—81no—
294C3×C4—21no—
295C3×C4—21no—
296C3×C4—21no—
297C3×C4—21no—
298C3×C4—21no—
299C3×C4—21no—
300C3×C4—41no—
301C3×C4—42no—
302C3×C4—41no—
303C3×C4—41no—
304C3×C4—241no—
305C3×C4#91111yescharacteristic
306C3×C4#91211yescharacteristic
307C3×C4#91411yescharacteristic
308C3×C4#91611yescharacteristic
309C3×C4C2×#21411yescharacteristic
310C3×C4C2×#21511yescharacteristic
311C3×C4#95011yescharacteristic
312C3×C4#95011yescharacteristic
313Dic3—81no—
314C32#167711yescharacteristic, complemented, Sylow
315C23—21no—
316C23—121no—
317Q8—241no—
318D4—21no—
319D4—121no—
320D4—121no—
321D4—121no—
322D4—121no—
323D4—241no—
324D4#371512yes—
325C2×C4—21no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—121no—
329C2×C4#380511yescharacteristic
330C2×C4C2×#62511yescharacteristic
331C2×C4#381111yescharacteristic
332C8—121no—
333C8—121no—
334C8—181no—
335C8—181no—
336C8—361no—
337C2×C3—21no—
338C2×C3—21no—
339C2×C3—21no—
340C2×C3—44no—
341C2×C3—42no—
342C2×C3—42no—
343C2×C3—481no—
344C2×C3#504111yescharacteristic
345C2×C3#504811yescharacteristic
346C2×C3#515311yescharacteristic
347C2×C3#516511yescharacteristic
348C2×C3#519911yescharacteristic
349C2×C3#519911yescharacteristic
350D3—161no—
351C22—22no—
352C22—41no—
353C22—41no—
354C22—241no—
355C22—241no—
356C22—241no—
357C22#6398011yescharacteristic
358C4—21no—
359C4—41no—
360C4—241no—
361C4#6382211yescharacteristic
362C4C2×#371511yescharacteristic
363C4#6393611yescharacteristic
364C4#6393711yescharacteristic
365C3—21no—
366C3#7100611yescharacteristic, complemented
367C3#7113411yescharacteristic, complemented
368C2—42no—
369C2—481no—
370C2#1059117911yescharacteristic
371C2#1059147611yescharacteristic
372C2#1059167811yescharacteristic
subgroupG/H
centerC22#63980
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4×D4C22
socleC22×C32#121
prime radicalC3×#5015C2
hypercenterC4×D4D32
hypocenterC32#1677
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
3. C3×#5008C2semidirect
4. #10590277C2semidirect
5. #10589098C2semidirect
6. #10589095C2semidirect
7. #10589090C2semidirect
33. #5008D3semidirect
314. C32#1677semidirect
366. C3#71006semidirect
367. C3#71134semidirect

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×#50152
C3×#50082
#105902772
#105890982
#105890952
#105890902
#711343
#710063