Finite Group Databasebeta

← #11781499

Subgroups — #11781499

Order 1152.

383 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 383 conjugacy classes of subgroups — too many to draw. Only its 82 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#10592529C211yesmaximal, characteristic, complemented
2#10590388C211yesmaximal, characteristic, complemented
3#10590377C211yesmaximal, characteristic
4#10590277C211yesmaximal, characteristic
5C3×#4486C211yesmaximal, characteristic, complemented
6C3×#4485C211yesmaximal, characteristic
7#10589100C211yesmaximal, characteristic, complemented
8#68470—31nomaximal
9#68411—31nomaximal
10C4×#634C2211yescharacteristic
11C3×#874C2211yescharacteristic
12C3×#869C2211yescharacteristic
13C2×#3719—21no—
14C2×#3716—21no—
15C32×C4⋊C8C2211yescharacteristic
16#63641—21no—
17C8×C3⋊Dic3—21no—
18C4×C3⋊(C3⋊C8)C2211yescharacteristic
19C3×C4⋊(C3⋊C8)C2211yescharacteristic
20C3×C4⋊(C3⋊C8)C2211yescharacteristic
21#63566—21no—
22#63563—21no—
23#63562—21no—
24#63562—21no—
25#5090—31no—
26#5088—31no—
27#5075—31no—
28#5070—31no—
29#4849—31no—
30#4848—31no—
31#4830—31no—
32#4830—31no—
33#4830—61no—
34C3×#332—31no—
35C3×#331—31no—
36#4486D311yescharacteristic, complemented
37#4485D311yescharacteristic
38#4479—31no—
39#4479—31no—
40C2×#634D411yescharacteristic
41C2×C3×D12—21no—
42C2×C3×D12—21no—
43C2×C3×D12—21no—
44C2×C3×Dic6—21no—
45C2×C32×C8—21no—
46C32×C42C2311yescharacteristic
47C4⋊(C3⋊Dic3)D411yescharacteristic
48#3750—21no—
49C4×C3⋊Dic3—21no—
50C2×C3⋊(C3⋊C8)D411yescharacteristic
51C2×C3⋊(C3⋊C8)D411yescharacteristic
52C3×C4⋊Dic3—21no—
53C3×C4⋊Dic3—21no—
54C2×C3×C3⋊C8—21no—
55C2×C3×C3⋊C8—21no—
56#3719—42no—
57#3716—42no—
58#1682—91noSylow
59C3×C4⋊Q8—31no—
60C3×#127—31no—
61C2×#216—61no—
62C2×#214—61no—
63C2×Dic12—61no—
64C2×#204—61no—
65#874C2×D311yescharacteristic
66#869C2×D311yescharacteristic
67C4×Dic6—31no—
68C4×Dic6—31no—
69C4×Dic6—61no—
70C3×C4⋊C8—21no—
71C3×C4⋊C8—31no—
72C3×C4⋊C8—31no—
73C3×C4⋊C8C2×D311yescharacteristic
74C3×C4⋊C8C2×D311yescharacteristic
75#835—61no—
76#832—61no—
77#832—61no—
78#832—61no—
79#821—61no—
80#816—61no—
81Dic3⋊C8—61no—
82Dic3⋊C8—61no—
83Dic3⋊C8—62no—
84C8×Dic3—61no—
85C8×Dic3—61no—
86C8×Dic3—62no—
87#809—61no—
88#809—61no—
89C4⋊(C3⋊C8)C2×D311yescharacteristic
90C4⋊(C3⋊C8)C2×D311yescharacteristic
91C4×C3⋊C8—31no—
92C4×C3⋊C8—31no—
93C4×C3⋊C8—61no—
94C22×C3×D3—41no—
95C2×C32×C4C2×D411yescharacteristic
96C2×C32×C4C2×D411yescharacteristic
97C2×C32×C4#4111yescharacteristic
98C2×C3⋊Dic3—21no—
99C2×C3⋊Dic3—21no—
100#634—21no—
101#634D812yes—
102C2×C3×Dic3—41no—
103C3×D12—41no—
104C3×D12—41no—
105C3×D12—41no—
106C3×D12—41no—
107C3×D12—81no—
108C3×Dic6—41no—
109C3×Dic6—41no—
110C32×C8—41no—
111C3⋊(C3⋊C8)—21no—
112C3⋊(C3⋊C8)—21no—
113C3×C3⋊C8—41no—
114C3×C3⋊C8—41no—
115#486—91no—
116#462—91no—
117#460—91no—
118C8×Q8—91no—
119#335—91no—
120#332—31no—
121#331—31no—
122C2×C3×Q8—61no—
123C2×C3×D4—61no—
124C2×C3×D4—61no—
125C2×C3×D4—61no—
126C2×D12—21no—
127C2×D12—21no—
128C2×D12—21no—
129C2×Dic6—21no—
130C2×Dic6—31no—
131C2×Dic6—31no—
132C2×Dic6—61no—
133C2×C3×C8—22no—
134C2×C3×C8—21no—
135C2×C3×C8—21no—
136C2×C3×C8—61no—
137C2×C3×C8—61no—
138C3×C4⋊C4—61no—
139C3×C4⋊C4—61no—
140C3×C42—21no—
141C3×C42C22×D311yescharacteristic
142C3×C42C22×D311yescharacteristic
143#216—122no—
144#214—122no—
145C4⋊Dic3—21no—
146C4⋊Dic3—21no—
147C4⋊Dic3—31no—
148C4⋊Dic3—31no—
149C4⋊Dic3—61no—
150Dic3⋊C4—62no—
151Dic3⋊C4—61no—
152Dic3⋊C4—61no—
153C4×Dic3—62no—
154C4×Dic3—61no—
155C4×Dic3—61no—
156C2×C3⋊C8—21no—
157C2×C3⋊C8—21no—
158C2×C3⋊C8—31no—
159C2×C3⋊C8—31no—
160C2×C3⋊C8—31no—
161C2×C3⋊C8—31no—
162C2×C3⋊C8—61no—
163C2×C3⋊C8—61no—
164Dic12—122no—
165#204—122no—
166C22×C32#12111yescharacteristic
167C2×C3×D3—81no—
168C2×C3×D3—81no—
169C2×C3×D3—81no—
170C32×C4—21no—
171C32×C4C2×D811yescharacteristic
172C32×C4#13511yescharacteristic
173C32×C4#13511yescharacteristic
174C32×C4#13711yescharacteristic
175C3⋊Dic3—22no—
176C3⋊Dic3—41no—
177C3×Dic3—81no—
178C2×Q16—181no—
179C2×SD16—181no—
180C4⋊Q8—31no—
181#127—31no—
182C4×Q8—91no—
183C4⋊C8—31no—
184C4⋊C8—31no—
185C4⋊C8—181no—
186C4⋊C8D3211yescharacteristic
187#103—181no—
188#102—181no—
189#102—181no—
190#102—181no—
191C4×C8—91no—
192C4×C8—181no—
193C23×C3—121no—
194C22×D3—41no—
195C3×Q8—121no—
196C3×Q8—121no—
197C3×D4—121no—
198C3×D4—121no—
199C3×D4—121no—
200C3×D4—121no—
201C3×D4—241no—
202C2×C3×C4—21no—
203C2×C3×C4—21no—
204C2×C3×C4—21no—
205C2×C3×C4—121no—
206C2×C3×C4#23511yescharacteristic
207C2×C3×C4#23511yescharacteristic
208C2×C3×C4D3×D411yescharacteristic
209C2×C3×C4D3×D411yescharacteristic
210C2×C3×C4D3×D411yescharacteristic
211C2×C3×C4D3×D411yescharacteristic
212C2×Dic3—41no—
213C2×Dic3—62no—
214C2×Dic3—61no—
215C2×Dic3—61no—
216C2×Dic3—62no—
217C2×Dic3—61no—
218C2×Dic3—61no—
219D12—41no—
220D12—41no—
221D12—41no—
222D12—41no—
223D12—81no—
224Dic6—32no—
225Dic6—32no—
226Dic6—41no—
227Dic6—41no—
228Dic6—62no—
229Dic6—62no—
230Dic6—61no—
231Dic6—61no—
232C3×C8—42no—
233C3×C8—41no—
234C3×C8—41no—
235C3×C8—121no—
236C3×C8—121no—
237C3⋊C8—41no—
238C3⋊C8—41no—
239C3⋊C8—62no—
240C3⋊C8—61no—
241C3⋊C8—61no—
242C3⋊C8—61no—
243C3⋊C8—61no—
244C3⋊C8—121no—
245C2×C32#46411yescharacteristic
246C2×C32#46611yescharacteristic
247C2×C32#47111yescharacteristic
248C3×D3—161no—
249C2×Q8—61no—
250C2×Q8—91no—
251C2×D4—61no—
252C2×D4—61no—
253C2×D4—61no—
254Q16—362no—
255SD16—362no—
256C2×C8—21no—
257C2×C8—61no—
258C2×C8—61no—
259C2×C8—91no—
260C2×C8—91no—
261C4⋊C4—61no—
262C4⋊C4—61no—
263C4⋊C4—91no—
264C4⋊C4—181no—
265C42—181no—
266C42C2×D3211yescharacteristic
267C22×C3—21no—
268C22×C3—241no—
269C22×C3—241no—
270C22×C3—241no—
271C22×C3#88411yescharacteristic
272C22×C3#88411yescharacteristic
273C2×D3—81no—
274C2×D3—81no—
275C2×D3—81no—
276C3×C4—21no—
277C3×C4—21no—
278C3×C4—21no—
279C3×C4—21no—
280C3×C4—21no—
281C3×C4—21no—
282C3×C4—41no—
283C3×C4—241no—
284C3×C4D3×D811yescharacteristic
285C3×C4D3×D811yescharacteristic
286C3×C4#91211yescharacteristic
287C3×C4#91511yescharacteristic
288C3×C4#91611yescharacteristic
289C3×C4#91611yescharacteristic
290C3×C4#91611yescharacteristic
291C3×C4#91811yescharacteristic
292Dic3—64no—
293Dic3—62no—
294Dic3—62no—
295Dic3—81no—
296Dic3—122no—
297Dic3—121no—
298Dic3—121no—
299C32#168211yescharacteristic, complemented, Sylow
300C23—121no—
301Q8—92no—
302Q8—121no—
303Q8—121no—
304Q8—181no—
305D4—121no—
306D4—121no—
307D4—121no—
308D4—121no—
309D4—241no—
310C2×C4—121no—
311C2×C4—181no—
312C2×C4—181no—
313C2×C4#379811yescharacteristic
314C2×C4#380211yescharacteristic
315C2×C4#381111yescharacteristic
316C8—41no—
317C8—121no—
318C8—121no—
319C8—181no—
320C8—181no—
321C2×C3—21no—
322C2×C3—21no—
323C2×C3—21no—
324C2×C3—481no—
325C2×C3#474811yescharacteristic
326C2×C3#475411yescharacteristic
327C2×C3#476711yescharacteristic
328C2×C3#477511yescharacteristic
329C2×C3#477511yescharacteristic
330C2×C3#479811yescharacteristic
331D3—161no—
332C22—241no—
333C22—241no—
334C22—241no—
335C22#6391211yescharacteristic
336C4—21no—
337C4—182no—
338C4—241no—
339C4—361no—
340C4#6379711yescharacteristic
341C4#6380911yescharacteristic
342C4#6393611yescharacteristic
343C4#6395111yescharacteristic
344C3—21no—
345C3#6841111yescharacteristic, complemented
346C3#6847011yescharacteristic, complemented
347C2—481no—
348C2#1059053811yescharacteristic
349C2#1059083911yescharacteristic
350C2#1059099111yescharacteristic
subgroupG/H
centerC22#63912
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊C8C22
socleC22×C32#121
prime radicalC3×#874C22
hypercenterC4⋊C8D32
hypocenterC32#1682
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #10592529C2semidirect
2. #10590388C2semidirect
5. C3×#4486C2semidirect
7. #10589100C2semidirect
36. #4486D3semidirect
299. C32#1682semidirect
345. C3#68411semidirect
346. C3#68470semidirect

Maximal subgroups

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

subgroupindex
#105925292
#105903882
#105903772
#105902772
C3×#44862
C3×#44852
#105891002
#684703
#684113