Finite Group Databasebeta

← #11780808

Subgroups — #11780808

Order 1152.

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

normal subgroups only

This group has 447 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
1#10592784C211yesmaximal, characteristic, complemented
2C3×#5087C211yesmaximal, characteristic, complemented
3#10590349C211yesmaximal, characteristic
4#10590329C211yesmaximal, characteristic, complemented
5C3×#4547C211yesmaximal, characteristic, complemented
6#10589098C211yesmaximal, characteristic, complemented
7#10589091C211yesmaximal, characteristic, complemented
8#71100—31nomaximal
9#68440—31nomaximal
10C32×C4⋊Q8C2211yescharacteristic
11C2×#3755—21no—
12C2×#3755—21no—
13#64083C2211yescharacteristic
14C3×C4×D12C2211yescharacteristic
15C2×#3714—21no—
16C2×D3×C3⋊C8—21no—
17C4×C3⋊(C3⋊C8)C2211yescharacteristic
18C3×#809—21no—
19C3×#807—21no—
20C3×C4⋊(C3⋊C8)C2211yescharacteristic
21C3×C4⋊(C3⋊C8)C2211yescharacteristic
22C3×C4⋊(C3⋊C8)C2211yescharacteristic
23#63564—21no—
24(C2×D3)⋊(C3⋊C8)—21no—
25C3×#474—31no—
26#5087D311yescharacteristic, complemented
27#5085—31no—
28#5085—31no—
29#5085—61no—
30#5015—31no—
31D4×C3⋊C8—31no—
32#4843—31no—
33#4834—31no—
34C3×#332—31no—
35#4547D311yescharacteristic, complemented
36#4485—31no—
37#4485—31no—
38#4480—31no—
39#4480—31no—
40C2×C32×Q8—21no—
41C2×C4⋊(C3⋊D3)—21no—
42C2×C4⋊(C3⋊D3)—21no—
43C2×C4⋊(C3⋊D3)—21no—
44C2×C3×D12D411yescharacteristic
45C2×C3×C4×D3—21no—
46C32×C4⋊C4—21no—
47C32×C4⋊C4—21no—
48C32×C42C2311yescharacteristic
49#3755—42no—
50#3755—42no—
51C2×C3⋊(C3⋊C8)D411yescharacteristic
52C2×C3⋊(C3⋊C8)D411yescharacteristic
53C3×(C2×D3)⋊C4—21no—
54C3×C4⋊Dic3D411yescharacteristic
55C2×C3×C3⋊C8—21no—
56C2×C3×C3⋊C8—21no—
57C2×C3×C3⋊C8—21no—
58#3714—42no—
59D3×C3⋊C8—42no—
60#1665—91noSylow
61C3×C4⋊Q8—21no—
62C3×C4⋊Q8C2×D311yescharacteristic
63C3×C4⋊Q8C2×D311yescharacteristic
64C3×C4×D4—31no—
65C2×#215—61no—
66C2×#215—61no—
67C2×#215—61no—
68C2×#215—61no—
69C2×#215—62no—
70C2×#215—62no—
71C2×#213—61no—
72C22×C3⋊C8—61no—
73C2×D24—61no—
74C2×D3×C8—61no—
75#874—31no—
76#874—31no—
77#874—61no—
78C4×D12C2×D311yescharacteristic
79C3×#107—61no—
80C3×C4⋊C8—31no—
81C3×C4⋊C8—31no—
82C3×C4⋊C8—31no—
83C3×#102—61no—
84#830—61no—
85#821—61no—
86(C2×D3)⋊C8—61no—
87#809—21no—
88#809—61no—
89#807—21no—
90C4⋊(C3⋊C8)C2×D311yescharacteristic
91C4⋊(C3⋊C8)C2×D311yescharacteristic
92C4⋊(C3⋊C8)C2×D311yescharacteristic
93C4×C3⋊C8—31no—
94C4×C3⋊C8—31no—
95C4×C3⋊C8—61no—
96C22×C3⋊D3—41no—
97C22×C3×D3—21no—
98C32×Q8—41no—
99C32×Q8—41no—
100C2×C32×C4—41no—
101C2×C32×C4C2×D411yescharacteristic
102C2×C32×C4C2×D411yescharacteristic
103C2×C32×C4#4111yescharacteristic
104C4⋊(C3⋊D3)—41no—
105C4⋊(C3⋊D3)—41no—
106C4⋊(C3⋊D3)—41no—
107C4⋊(C3⋊D3)—41no—
108C4⋊(C3⋊D3)—81no—
109C2×C3×Dic3—21no—
110C3×D12—21no—
111C3×D12SD1612yescomplemented
112C3×C4×D3—41no—
113C3×C4×D3—41no—
114C3⋊(C3⋊C8)—21no—
115C3⋊(C3⋊C8)D812yescomplemented
116C3×C3⋊C8—41no—
117C3×C3⋊C8—41no—
118C3×C3⋊C8—41no—
119#492—91no—
120#474—31no—
121#459—91no—
122C8×D4—91no—
123#334—91no—
124#332—31no—
125#331—91no—
126C2×C3×Q8—22no—
127C2×C3×Q8—21no—
128C2×C3×Q8—21no—
129C2×C3×D4—31no—
130C22×C3×C4—61no—
131C2×D12—62no—
132C2×D12—61no—
133C2×D12—61no—
134C2×D12—61no—
135C2×D12—61no—
136C2×D12—61no—
137C2×D12—61no—
138C2×D12—121no—
139C2×D12—121no—
140C2×D12#6711yescharacteristic
141C2×C4×D3—21no—
142C2×C3×C8—61no—
143C2×C3×C8—61no—
144C2×C3×C8—61no—
145C3×C4⋊C4—21no—
146C3×C4⋊C4—21no—
147C3×C4⋊C4—21no—
148C3×C4⋊C4—21no—
149C3×C4⋊C4—31no—
150C3×C4⋊C4—41no—
151C3×C4⋊C4—41no—
152C3×C22⋊C4—61no—
153C3×C42—21no—
154C3×C42C22×D311yescharacteristic
155C3×C42C22×D311yescharacteristic
156#215—122no—
157#215—122no—
158#215—124no—
159#215—124no—
160#215—122no—
161#215—122no—
162#213—122no—
163(C2×D3)⋊C4—21no—
164C4⋊Dic3#6711yescharacteristic
165C2×C3⋊C8—21no—
166C2×C3⋊C8—21no—
167C2×C3⋊C8—21no—
168C2×C3⋊C8—31no—
169C2×C3⋊C8—31no—
170C2×C3⋊C8—31no—
171C2×C3⋊C8—31no—
172C2×C3⋊C8—61no—
173C2×C3⋊C8—61no—
174C2×C3⋊C8—122no—
175D24—122no—
176D3×C8—122no—
177C22×C32#12111yescharacteristic
178C2×C3⋊D3—81no—
179C2×C3⋊D3—81no—
180C2×C3⋊D3—81no—
181C2×C3×D3—22no—
182C2×C3×D3—41no—
183C2×C3×D3—41no—
184C32×C4—21no—
185C32×C4—81no—
186C32×C4C2×D811yescharacteristic
187C32×C4C2×SD1611yescharacteristic
188C32×C4#13511yescharacteristic
189C32×C4AGL(1,ℤ/8)11yescharacteristic
190C3×Dic3—41no—
191C2×SD16—181no—
192C2×SD16—181no—
193C2×D8—181no—
194C22×C8—181no—
195C4⋊Q8D3211yescharacteristic
196#127—91no—
197C4×D4—31no—
198#107—61no—
199C4⋊C8—31no—
200C4⋊C8—31no—
201C4⋊C8—31no—
202#102—61no—
203#102—181no—
204C22⋊C8—181no—
205C4×C8—91no—
206C23×C3—61no—
207C22×D3—21no—
208C22×D3—122no—
209C22×D3—121no—
210C22×D3—121no—
211C3×Q8—42no—
212C3×Q8—42no—
213C3×Q8—41no—
214C3×Q8—41no—
215C3×Q8—41no—
216C3×Q8—41no—
217C3×D4—32no—
218C3×D4—61no—
219C2×C3×C4—21no—
220C2×C3×C4—21no—
221C2×C3×C4—21no—
222C2×C3×C4—42no—
223C2×C3×C4—41no—
224C2×C3×C4—41no—
225C2×C3×C4—61no—
226C2×C3×C4—121no—
227C2×C3×C4—121no—
228C2×C3×C4#23511yescharacteristic
229C2×C3×C4D3×D411yescharacteristic
230C2×C3×C4D3×D411yescharacteristic
231C2×C3×C4D3×D411yescharacteristic
232C2×C3×C4#23711yescharacteristic
233C2×C3×C4C2×#6711yescharacteristic
234C2×Dic3—21no—
235D12—21no—
236D12—122no—
237D12—122no—
238D12—121no—
239D12—121no—
240D12—121no—
241D12—121no—
242D12—121no—
243D12—121no—
244D12—121no—
245D12—121no—
246D12—241no—
247D12—241no—
248D12—241no—
249D12—241no—
250D12—242no—
251D12#21512yescomplemented
252C4×D3—41no—
253C4×D3—41no—
254C3×C8—121no—
255C3×C8—121no—
256C3×C8—121no—
257C3⋊C8—32no—
258C3⋊C8—32no—
259C3⋊C8—41no—
260C3⋊C8—41no—
261C3⋊C8—41no—
262C3⋊C8—62no—
263C3⋊C8—62no—
264C3⋊C8—61no—
265C3⋊C8—61no—
266C2×C32#45911yescharacteristic
267C2×C32#46511yescharacteristic
268C2×C32#47111yescharacteristic
269C3⋊D3—161no—
270C3×D3—42no—
271C2×Q8—21no—
272C2×D4—31no—
273C2×D4—181no—
274C2×D4—181no—
275C2×D4—181no—
276C22×C4—61no—
277SD16—362no—
278SD16—362no—
279D8—362no—
280C2×C8—61no—
281C2×C8—61no—
282C2×C8—61no—
283C2×C8—91no—
284C2×C8—91no—
285C2×C8—362no—
286C4⋊C4—21no—
287C4⋊C4—21no—
288C4⋊C4—31no—
289C22⋊C4—61no—
290C42C2×D3211yescharacteristic
291C22×C3—21no—
292C22×C3—62no—
293C22×C3—121no—
294C22×C3—121no—
295C22×C3#88411yescharacteristic
296C22×C3#93911yescharacteristic
297C2×D3—22no—
298C2×D3—41no—
299C2×D3—41no—
300C2×D3—242no—
301C2×D3—242no—
302C2×D3—242no—
303C2×D3—241no—
304C2×D3—241no—
305C2×D3—241no—
306C2×D3—241no—
307C2×D3—241no—
308C2×D3—241no—
309C3×C4—22no—
310C3×C4—21no—
311C3×C4—21no—
312C3×C4—21no—
313C3×C4—21no—
314C3×C4—21no—
315C3×C4—21no—
316C3×C4—82no—
317C3×C4—81no—
318C3×C4—81no—
319C3×C4—121no—
320C3×C4D3×D811yescharacteristic
321C3×C4D3×D811yescharacteristic
322C3×C4#91111yescharacteristic
323C3×C4D3×SD1611yescharacteristic
324C3×C4#91411yescharacteristic
325C3×C4#91911yescharacteristic
326C3×C4C2×#21511yescharacteristic
327C3×C4#95011yescharacteristic
328Dic3—41no—
329C32#166511yescharacteristic, complemented, Sylow
330C23—61no—
331C23—361no—
332Q8—41no—
333Q8—41no—
334D4—32no—
335D4—61no—
336D4—361no—
337D4—361no—
338D4—361no—
339D4—361no—
340D4—721no—
341C2×C4—41no—
342C2×C4—61no—
343C2×C4—121no—
344C2×C4—121no—
345C2×C4#380411yescharacteristic
346C2×C4D3×#6711yescharacteristic
347C2×C4#381111yescharacteristic
348C8—92no—
349C8—121no—
350C8—121no—
351C8—121no—
352C8—181no—
353C2×C3—21no—
354C2×C3—21no—
355C2×C3—21no—
356C2×C3—122no—
357C2×C3#475411yescharacteristic
358C2×C3#478611yescharacteristic
359C2×C3#480711yescharacteristic
360C2×C3#504811yescharacteristic
361C2×C3#515011yescharacteristic
362C2×C3#520311yescharacteristic
363D3—42no—
364D3—482no—
365D3—481no—
366D3—481no—
367C22—62no—
368C22—121no—
369C22—121no—
370C22—721no—
371C22—721no—
372C22—721no—
373C22#6397111yescharacteristic
374C4—21no—
375C4—81no—
376C4—121no—
377C4#6392611yescharacteristic
378C4#6393711yescharacteristic
379C4D3×#21511yescharacteristic
380C4#6394911yescharacteristic
381C3—21no—
382C3#6844011yescharacteristic, complemented
383C3#7110011yescharacteristic, complemented
384C2—122no—
385C2—1441no—
386C2#1059143311yescharacteristic
387C2#1059158511yescharacteristic
388C2#1059164311yescharacteristic
subgroupG/H
centerC22#63971
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊Q8C22
socleC22×C32#121
prime radical#10590349C2
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. #10592784C2semidirect
2. C3×#5087C2semidirect
4. #10590329C2semidirect
5. C3×#4547C2semidirect
6. #10589098C2semidirect
7. #10589091C2semidirect
26. #5087D3semidirect
35. #4547D3semidirect
111. C3×D12SD16semidirect
115. C3⋊(C3⋊C8)D8semidirect
251. D12#215semidirect
329. C32#1665semidirect
382. C3#68440semidirect
383. C3#71100semidirect

Maximal subgroups

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

subgroupindex
#105927842
C3×#50872
#105903492
#105903292
C3×#45472
#105890982
#105890912
#711003
#684403