Finite Group Databasebeta

← #11780806

Subgroups — #11780806

Order 1152.

443 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 443 conjugacy classes of subgroups — too many to draw. Only its 96 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×#5007C211yesmaximal, characteristic, complemented
4#10590375C211yesmaximal, characteristic, complemented
5#10589098C211yesmaximal, characteristic, complemented
6#10589092C211yesmaximal, characteristic, complemented
7#10589090C211yesmaximal, characteristic, complemented
8#71100—31nomaximal
9#71004—31nomaximal
10C32×C4×D4C2211yescharacteristic
11C22×C3⋊(C3⋊C8)—21no—
12C2×C3×#213—21no—
13C3×#874C2211yescharacteristic
14C3×#869C2211yescharacteristic
15C2×#3715—21no—
16C2×#3715—21no—
17#63657—21no—
18C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
19C4×C3⋊(C3⋊C8)C2211yescharacteristic
20C3×#832—21no—
21C3×#809—21no—
22C3×#807—21no—
23C3×C4⋊(C3⋊C8)C2211yescharacteristic
24C3×C4⋊(C3⋊C8)C2211yescharacteristic
25C3×#474—31no—
26C3×#459—31no—
27#5085—31no—
28#5076—31no—
29#5015D311yescharacteristic
30D4×C3⋊C8—31no—
31D4×C3⋊C8—31no—
32D4×C3⋊C8—61no—
33#5007D311yescharacteristic, complemented
34#4547—31no—
35#4544—31no—
36#4486—31no—
37#4485—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#3715—42no—
59#3715—42no—
60#1665—91noSylow
61C2×C3×D8—61no—
62C3×C4⋊Q8—31no—
63C3×#127—31no—
64C3×C4×D4—21no—
65C3×C4×D4C2×D311yescharacteristic
66C3×C4×D4C2×D311yescharacteristic
67C2×#215—61no—
68C2×#215—61no—
69C2×#214—61no—
70C2×#214—61no—
71C2×#213—21no—
72C22×C3⋊C8—61no—
73C22×C3⋊C8—61no—
74C22×C3⋊C8—62no—
75#874C2×D311yescharacteristic
76#869C2×D311yescharacteristic
77C3×#107—61no—
78C3×C4⋊C8—31no—
79C3×C4⋊C8—31no—
80C3×#102—61no—
81C3×#102—61no—
82#832—21no—
83#830—61no—
84#830—61no—
85#830—62no—
86#809—21no—
87#807—21no—
88C4⋊(C3⋊C8)—31no—
89C4⋊(C3⋊C8)—31no—
90C4⋊(C3⋊C8)—61no—
91C4⋊(C3⋊C8)C2×D311yescharacteristic
92C4⋊(C3⋊C8)C2×D311yescharacteristic
93C4×C3⋊C8—31no—
94C4×C3⋊C8—31no—
95C4×C3⋊C8—61no—
96C23×C32—21no—
97C22×C3×D3—41no—
98C32×D4—21no—
99C32×D4SD1612yescomplemented
100C2×C32×C4—21no—
101C2×C32×C4—41no—
102C2×C32×C4—41no—
103C2×C32×C4C2×D411yescharacteristic
104C2×C32×C4C2×D411yescharacteristic
105C2×C32×C4#4111yescharacteristic
106C2×C3×Dic3—41no—
107C3×D12—41no—
108C3×D12—41no—
109C3×D12—41no—
110C3×D12—41no—
111C3×D12—81no—
112C3×Dic6—41no—
113C3×Dic6—41no—
114C3⋊(C3⋊C8)—21no—
115C3⋊(C3⋊C8)—41no—
116C3⋊(C3⋊C8)D812yescomplemented
117C3×C3⋊C8—41no—
118C3×C3⋊C8—41no—
119#492—91no—
120#474—31no—
121#459—31no—
122C8×D4—91no—
123#334—91no—
124#332—91no—
125#331—91no—
126C2×C3×Q8—61no—
127C2×C3×D4—21no—
128C2×C3×D4—61no—
129C2×C3×D4—61no—
130C2×C3×D4—61no—
131C2×C3×D4#6711yescharacteristic
132C2×C3×D4#6711yescharacteristic
133C22×C3×C4—22no—
134C22×C3×C4—21no—
135C22×C3×C4—21no—
136C2×D12—21no—
137C2×D12—21no—
138C2×D12—21no—
139C2×Dic6—21no—
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#215—122no—
155#215—122no—
156#214—122no—
157#214—122no—
158#213—42no—
159C4⋊Dic3—21no—
160C4⋊Dic3—21no—
161C2×C3⋊C8—21no—
162C2×C3⋊C8—21no—
163C2×C3⋊C8—31no—
164C2×C3⋊C8—31no—
165C2×C3⋊C8—31no—
166C2×C3⋊C8—31no—
167C2×C3⋊C8—61no—
168C2×C3⋊C8—61no—
169C2×C3⋊C8—62no—
170C2×C3⋊C8—61no—
171C2×C3⋊C8—61no—
172C2×C3⋊C8—122no—
173C2×C3⋊C8—122no—
174C2×C3⋊C8—124no—
175C22×C32—22no—
176C22×C32—41no—
177C22×C32—41no—
178C22×C32#12111yescharacteristic
179C2×C3×D3—81no—
180C2×C3×D3—81no—
181C2×C3×D3—81no—
182C32×C4—21no—
183C32×C4—41no—
184C32×C4C2×D811yescharacteristic
185C32×C4C2×SD1611yescharacteristic
186C32×C4#13511yescharacteristic
187C32×C4AGL(1,ℤ/8)11yescharacteristic
188C3×Dic3—81no—
189C2×SD16—181no—
190C2×SD16—181no—
191C2×D8—61no—
192C22×C8—181no—
193C4⋊Q8—31no—
194#127—31no—
195C4×D4D3211yescharacteristic
196#107—61no—
197C4⋊C8—31no—
198C4⋊C8—31no—
199C4⋊C8—91no—
200#102—61no—
201#102—61no—
202C22⋊C8—181no—
203C4×C8—91no—
204C23×C3—22no—
205C23×C3—21no—
206C23×C3—21no—
207C23×C3—121no—
208C22×D3—41no—
209C3×Q8—121no—
210C3×Q8—121no—
211C3×D4—22no—
212C3×D4—21no—
213C3×D4—21no—
214C3×D4—22no—
215C3×D4—121no—
216C3×D4—121no—
217C3×D4—121no—
218C3×D4—121no—
219C3×D4—241no—
220C3×D4#21412yescomplemented
221C3×D4#21512yescomplemented
222C2×C3×C4—22no—
223C2×C3×C4—21no—
224C2×C3×C4—21no—
225C2×C3×C4—21no—
226C2×C3×C4—21no—
227C2×C3×C4—21no—
228C2×C3×C4—42no—
229C2×C3×C4—42no—
230C2×C3×C4—41no—
231C2×C3×C4—41no—
232C2×C3×C4—41no—
233C2×C3×C4—41no—
234C2×C3×C4—121no—
235C2×C3×C4D3×D411yescharacteristic
236C2×C3×C4D3×D411yescharacteristic
237C2×C3×C4#23711yescharacteristic
238C2×C3×C4#23711yescharacteristic
239C2×C3×C4C2×#6711yescharacteristic
240C2×C3×C4C2×#6711yescharacteristic
241C2×Dic3—41no—
242D12—41no—
243D12—41no—
244D12—41no—
245D12—41no—
246D12—81no—
247Dic6—41no—
248Dic6—41no—
249C3×C8—121no—
250C3×C8—121no—
251C3⋊C8—32no—
252C3⋊C8—32no—
253C3⋊C8—41no—
254C3⋊C8—41no—
255C3⋊C8—62no—
256C3⋊C8—61no—
257C3⋊C8—61no—
258C3⋊C8—121no—
259C3⋊C8—122no—
260C3⋊C8—121no—
261C3⋊C8—121no—
262C2×C32—42no—
263C2×C32#45911yescharacteristic
264C2×C32#46511yescharacteristic
265C2×C32#47111yescharacteristic
266C3×D3—161no—
267C2×Q8—61no—
268C2×D4—61no—
269C2×D4—61no—
270C2×D4—61no—
271C2×D4#62511yescharacteristic
272C22×C4—21no—
273SD16—362no—
274SD16—362no—
275D8—122no—
276C2×C8—61no—
277C2×C8—61no—
278C2×C8—91no—
279C2×C8—91no—
280C2×C8—181no—
281C2×C8—362no—
282C4⋊C4—61no—
283C4⋊C4—61no—
284C4⋊C4#62511yescharacteristic
285C22⋊C4—21no—
286C42C2×D3211yescharacteristic
287C22×C3—24no—
288C22×C3—22no—
289C22×C3—22no—
290C22×C3—21no—
291C22×C3—42no—
292C22×C3—42no—
293C22×C3—41no—
294C22×C3—41no—
295C22×C3—41no—
296C22×C3—41no—
297C22×C3—241no—
298C22×C3—241no—
299C22×C3—241no—
300C22×C3#93911yescharacteristic
301C22×C3#93911yescharacteristic
302C2×D3—81no—
303C2×D3—81no—
304C2×D3—81no—
305C3×C4—21no—
306C3×C4—21no—
307C3×C4—21no—
308C3×C4—21no—
309C3×C4—21no—
310C3×C4—21no—
311C3×C4—41no—
312C3×C4—42no—
313C3×C4—41no—
314C3×C4—41no—
315C3×C4—241no—
316C3×C4D3×D811yescharacteristic
317C3×C4D3×D811yescharacteristic
318C3×C4#91111yescharacteristic
319C3×C4#91111yescharacteristic
320C3×C4C2×#21411yescharacteristic
321C3×C4C2×#21511yescharacteristic
322C3×C4#95011yescharacteristic
323C3×C4#95011yescharacteristic
324Dic3—81no—
325C32#166511yescharacteristic, complemented, Sylow
326C23—21no—
327C23—121no—
328Q8—121no—
329Q8—121no—
330D4—21no—
331D4—121no—
332D4—121no—
333D4—121no—
334D4—121no—
335D4—241no—
336D4#371512yescomplemented
337C2×C4—21no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—121no—
341C2×C4#380511yescharacteristic
342C2×C4C2×#62511yescharacteristic
343C2×C4#381111yescharacteristic
344C8—92no—
345C8—121no—
346C8—121no—
347C8—181no—
348C8—361no—
349C2×C3—21no—
350C2×C3—21no—
351C2×C3—21no—
352C2×C3—44no—
353C2×C3—42no—
354C2×C3—42no—
355C2×C3—481no—
356C2×C3#504111yescharacteristic
357C2×C3#504811yescharacteristic
358C2×C3#515011yescharacteristic
359C2×C3#515011yescharacteristic
360C2×C3#520011yescharacteristic
361C2×C3#520311yescharacteristic
362D3—161no—
363C22—22no—
364C22—41no—
365C22—41no—
366C22—241no—
367C22—241no—
368C22—241no—
369C22#6398011yescharacteristic
370C4—21no—
371C4—41no—
372C4—241no—
373C4#6382211yescharacteristic
374C4C2×#371511yescharacteristic
375C4#6392611yescharacteristic
376C4#6392711yescharacteristic
377C3—21no—
378C3#7100411yescharacteristic, complemented
379C3#7110011yescharacteristic, complemented
380C2—42no—
381C2—481no—
382C2#1059117911yescharacteristic
383C2#1059148611yescharacteristic
384C2#1059168111yescharacteristic
subgroupG/H
centerC22#63980
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4×D4C22
socleC22×C32#121
prime radicalC3×#5015C2
hypercenterC4×D4D32
hypocenterC32#1665
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×#5007C2semidirect
4. #10590375C2semidirect
5. #10589098C2semidirect
6. #10589092C2semidirect
7. #10589090C2semidirect
33. #5007D3semidirect
99. C32×D4SD16semidirect
116. C3⋊(C3⋊C8)D8semidirect
220. C3×D4#214semidirect
221. C3×D4#215semidirect
325. C32#1665semidirect
336. D4#3715semidirect
378. C3#71004semidirect
379. C3#71100semidirect

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×#50072
#105903752
#105890982
#105890922
#105890902
#711003
#710043