Finite Group Databasebeta

← #11780810

Subgroups — #11780810

Order 1152.

408 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 408 conjugacy classes of subgroups — too many to draw. Only its 92 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×#5087C211yesmaximal, characteristic, complemented
2C3×#5085C211yesmaximal, characteristic, complemented
3#10590347C211yesmaximal, characteristic
4C3⋊C8×D12C211yesmaximal, characteristic, complemented
5#10589413C211yesmaximal, characteristic, complemented
6#10589097C211yesmaximal, characteristic, complemented
7#10589090C211yesmaximal, characteristic, complemented
8#71267—31nomaximal
9#71100—31nomaximal
10C32×C4⋊Q8C2211yescharacteristic
11C2×C3×#215—21no—
12C2×C3×#215—21no—
13C3×#874C2211yescharacteristic
14C3×C4×D12C2211yescharacteristic
15C2×#3713—21no—
16C2×D3×C3⋊C8—21no—
17C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
18C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
19C3×#809—21no—
20C3×#807—21no—
21C3×C4⋊(C3⋊C8)C2211yescharacteristic
22C3×C4×C3⋊C8C2211yescharacteristic
23#63562—21no—
24(C2×D3)⋊(C3⋊C8)—21no—
25C3×#492—31no—
26C3×#474—31no—
27#5087D311yescharacteristic, complemented
28#5085D311yescharacteristic, 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#4480—31no—
39#4457—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×#215—42no—
53C3×(C2×D3)⋊C4—21no—
54C3×C4⋊Dic3D411yescharacteristic
55C2×C3×C3⋊C8—21no—
56C2×C3×C3⋊C8D411yescharacteristic
57C2×C3×C3⋊C8D411yescharacteristic
58#3713—42no—
59D3×C3⋊C8—42no—
60#1665—91noSylow
61C2×C3×SD16—61no—
62C2×C3×SD16—61no—
63C3×C4⋊Q8—21no—
64C3×C4⋊Q8C2×D311yescharacteristic
65C3×C4⋊Q8C2×D311yescharacteristic
66C3×#127—31no—
67C3×C4×D4—31no—
68C2×#215—21no—
69C2×#215—21no—
70C2×#213—61no—
71C2×#213—61no—
72C22×C3⋊C8—61no—
73C2×D3×C8—61no—
74#874C2×D311yescharacteristic
75C4×D12C2×D311yescharacteristic
76C3×#107—61no—
77C3×C4⋊C8—31no—
78C3×#102—61no—
79C3×C4×C8—31no—
80#832—61no—
81#830—61no—
82(C2×D3)⋊C8—61no—
83#809—21no—
84#809—61no—
85#807—21no—
86C4⋊(C3⋊C8)—31no—
87C4⋊(C3⋊C8)—31no—
88C4⋊(C3⋊C8)—31no—
89C4⋊(C3⋊C8)—31no—
90C4⋊(C3⋊C8)—61no—
91C4⋊(C3⋊C8)—61no—
92C4⋊(C3⋊C8)C2×D311yescharacteristic
93C4×C3⋊C8C2×D311yescharacteristic
94C22×C3×D3—21no—
95C22×C3×D3—41no—
96C32×Q8—41no—
97C32×Q8—41no—
98C2×C32×C4—41no—
99C2×C32×C4C2×D411yescharacteristic
100C2×C32×C4C2×D411yescharacteristic
101C2×C32×C4#4111yescharacteristic
102C2×C3×Dic3—21no—
103C3×D12—21no—
104C3×D12—41no—
105C3×D12—41no—
106C3×D12—41no—
107C3×D12—41no—
108C3×D12—81no—
109C3×D12SD1612yescomplemented
110C3×C4×D3—41no—
111C3×C4×D3—41no—
112C3⋊(C3⋊C8)—41no—
113C3⋊(C3⋊C8)—41no—
114C3×C3⋊C8—21no—
115C3×C3⋊C8—41no—
116C3×C3⋊C8D812yescomplemented
117#492—31no—
118#474—31no—
119#459—91no—
120C8×D4—91no—
121#334—91no—
122#332—91no—
123#331—91no—
124C2×C3×Q8—21no—
125C2×C3×Q8—21no—
126C2×C3×Q8—41no—
127C2×C3×D4—31no—
128C2×C3×D4—61no—
129C2×C3×D4—61no—
130C2×C3×D4—61no—
131C22×C3×C4—61no—
132C2×D12—21no—
133C2×D12—21no—
134C2×D12—21no—
135C2×D12#6711yescharacteristic
136C2×C4×D3—21no—
137C3×SD16—122no—
138C3×SD16—122no—
139C2×C3×C8—31no—
140C2×C3×C8—31no—
141C2×C3×C8—61no—
142C3×C4⋊C4—22no—
143C3×C4⋊C4—21no—
144C3×C4⋊C4—21no—
145C3×C4⋊C4—21no—
146C3×C4⋊C4—21no—
147C3×C4⋊C4—31no—
148C3×C4⋊C4—41no—
149C3×C22⋊C4—61no—
150C3×C42—21no—
151C3×C42C22×D311yescharacteristic
152C3×C42C22×D311yescharacteristic
153#215—42no—
154#215—42no—
155#213—122no—
156#213—122no—
157(C2×D3)⋊C4—21no—
158C4⋊Dic3#6711yescharacteristic
159C2×C3⋊C8—21no—
160C2×C3⋊C8—61no—
161C2×C3⋊C8—61no—
162C2×C3⋊C8—61no—
163C2×C3⋊C8—61no—
164C2×C3⋊C8—121no—
165C2×C3⋊C8—121no—
166C2×C3⋊C8—122no—
167C2×C3⋊C8#6711yescharacteristic
168C2×C3⋊C8#6711yescharacteristic
169D3×C8—122no—
170C22×C32#12111yescharacteristic
171C2×C3×D3—22no—
172C2×C3×D3—41no—
173C2×C3×D3—41no—
174C2×C3×D3—81no—
175C2×C3×D3—81no—
176C2×C3×D3—81no—
177C32×C4—21no—
178C32×C4—81no—
179C32×C4C2×D811yescharacteristic
180C32×C4C2×SD1611yescharacteristic
181C32×C4#13511yescharacteristic
182C32×C4AGL(1,ℤ/8)11yescharacteristic
183C3×Dic3—41no—
184C2×SD16—61no—
185C2×SD16—61no—
186C2×D8—181no—
187C22×C8—181no—
188C4⋊Q8D3211yescharacteristic
189#127—31no—
190C4×D4—31no—
191#107—61no—
192C4⋊C8—31no—
193C4⋊C8—91no—
194C4⋊C8—91no—
195#102—61no—
196#102—181no—
197C22⋊C8—181no—
198C4×C8—31no—
199C23×C3—61no—
200C23×C3—121no—
201C22×D3—21no—
202C22×D3—41no—
203C3×Q8—41no—
204C3×Q8—41no—
205C3×Q8—41no—
206C3×Q8—41no—
207C3×Q8—81no—
208C3×Q8—81no—
209C3×D4—32no—
210C3×D4—61no—
211C3×D4—121no—
212C3×D4—121no—
213C3×D4—121no—
214C3×D4—121no—
215C3×D4—241no—
216C2×C3×C4—21no—
217C2×C3×C4—21no—
218C2×C3×C4—21no—
219C2×C3×C4—42no—
220C2×C3×C4—41no—
221C2×C3×C4—41no—
222C2×C3×C4—61no—
223C2×C3×C4—121no—
224C2×C3×C4—121no—
225C2×C3×C4D3×D411yescharacteristic
226C2×C3×C4D3×D411yescharacteristic
227C2×C3×C4#23711yescharacteristic
228C2×C3×C4#23711yescharacteristic
229C2×C3×C4C2×#6711yescharacteristic
230C2×C3×C4C2×#6711yescharacteristic
231C2×Dic3—21no—
232D12—21no—
233D12—41no—
234D12—41no—
235D12—41no—
236D12—41no—
237D12—81no—
238D12#21512yescomplemented
239C4×D3—41no—
240C4×D3—41no—
241C3×C8—32no—
242C3×C8—61no—
243C3×C8—121no—
244C3⋊C8—21no—
245C3⋊C8—41no—
246C3⋊C8—121no—
247C3⋊C8—121no—
248C3⋊C8—121no—
249C3⋊C8—121no—
250C3⋊C8—241no—
251C3⋊C8—241no—
252C3⋊C8#21312yescomplemented
253C2×C32#45911yescharacteristic
254C2×C32#46511yescharacteristic
255C2×C32#47111yescharacteristic
256C3×D3—42no—
257C3×D3—161no—
258C2×Q8—21no—
259C2×D4—31no—
260C2×D4—61no—
261C2×D4—61no—
262C2×D4—61no—
263C22×C4—61no—
264SD16—122no—
265SD16—122no—
266D8—362no—
267C2×C8—31no—
268C2×C8—31no—
269C2×C8—61no—
270C2×C8—181no—
271C2×C8—181no—
272C2×C8—362no—
273C4⋊C4—21no—
274C4⋊C4—21no—
275C4⋊C4—31no—
276C22⋊C4—61no—
277C42C2×D3211yescharacteristic
278C22×C3—21no—
279C22×C3—62no—
280C22×C3—121no—
281C22×C3—121no—
282C22×C3—241no—
283C22×C3—241no—
284C22×C3—241no—
285C22×C3#93811yescharacteristic
286C22×C3#93911yescharacteristic
287C2×D3—22no—
288C2×D3—41no—
289C2×D3—41no—
290C2×D3—81no—
291C2×D3—81no—
292C2×D3—81no—
293C3×C4—21no—
294C3×C4—21no—
295C3×C4—21no—
296C3×C4—21no—
297C3×C4—21no—
298C3×C4—21no—
299C3×C4—41no—
300C3×C4—82no—
301C3×C4—81no—
302C3×C4—81no—
303C3×C4—121no—
304C3×C4D3×D811yescharacteristic
305C3×C4#91111yescharacteristic
306C3×C4D3×SD1611yescharacteristic
307C3×C4#91611yescharacteristic
308C3×C4C2×#21311yescharacteristic
309C3×C4#93211yescharacteristic
310C3×C4C2×#21511yescharacteristic
311C3×C4#95011yescharacteristic
312Dic3—41no—
313C32#166511yescharacteristic, complemented, Sylow
314C23—61no—
315C23—121no—
316Q8—41no—
317Q8—41no—
318D4—32no—
319D4—61no—
320D4—121no—
321D4—121no—
322D4—121no—
323D4—121no—
324D4—241no—
325C2×C4—41no—
326C2×C4—61no—
327C2×C4—121no—
328C2×C4—121no—
329C2×C4#380511yescharacteristic
330C2×C4D3×#6711yescharacteristic
331C2×C4D3×#6711yescharacteristic
332C8—32no—
333C8—61no—
334C8—121no—
335C8—361no—
336C8—361no—
337C2×C3—21no—
338C2×C3—21no—
339C2×C3—21no—
340C2×C3—122no—
341C2×C3—481no—
342C2×C3#504811yescharacteristic
343C2×C3#507211yescharacteristic
344C2×C3#515011yescharacteristic
345C2×C3#517111yescharacteristic
346C2×C3#517711yescharacteristic
347C2×C3#520311yescharacteristic
348D3—42no—
349D3—161no—
350C22—62no—
351C22—121no—
352C22—121no—
353C22—241no—
354C22—241no—
355C22—241no—
356C22#6397011yescharacteristic
357C4—21no—
358C4—81no—
359C4—121no—
360C4D3×#21311yescharacteristic
361C4#6393211yescharacteristic
362C4D3×#21511yescharacteristic
363C4#6394711yescharacteristic
364C3—21no—
365C3#7110011yescharacteristic, complemented
366C3#7126711yescharacteristic, complemented
367C2—122no—
368C2—481no—
369C2#1059142811yescharacteristic
370C2#1059163411yescharacteristic
371C2#1059164211yescharacteristic
subgroupG/H
centerC22#63970
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊Q8C22
socleC22×C32#121
prime radical#10590347C2
hypercenterC4⋊Q8D32
hypocenterC32#1665
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×#5087C2semidirect
2. C3×#5085C2semidirect
4. C3⋊C8×D12C2semidirect
5. #10589413C2semidirect
6. #10589097C2semidirect
7. #10589090C2semidirect
27. #5087D3semidirect
28. #5085D3semidirect
109. C3×D12SD16semidirect
116. C3×C3⋊C8D8semidirect
238. D12#215semidirect
252. C3⋊C8#213semidirect
313. C32#1665semidirect
365. C3#71100semidirect
366. C3#71267semidirect

Maximal subgroups

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

subgroupindex
C3×#50872
C3×#50852
#105903472
C3⋊C8×D122
#105894132
#105890972
#105890902
#712673
#711003