Finite Group Databasebeta

← #11780862

Subgroups — #11780862

Order 1152.

395 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 395 conjugacy classes of subgroups — too many to draw. Only its 84 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#10590377C211yesmaximal, characteristic
3#10590375C211yesmaximal, characteristic
4#10590307C211yesmaximal, characteristic, complemented
5C3×#4485C211yesmaximal, characteristic
6C3×#4482C211yesmaximal, characteristic, complemented
7#10589098C211yesmaximal, characteristic, complemented
8#68464—31nomaximal
9#68408—31nomaximal
10C4×#634C2211yescharacteristic
11C3×#874C2211yescharacteristic
12C3×#869C2211yescharacteristic
13C2×#3716—21no—
14C2×#3715—21no—
15C2×#3715—21no—
16C32×C4⋊C8C2211yescharacteristic
17#63641—21no—
18C8×C3⋊Dic3—21no—
19C4×C3⋊(C3⋊C8)C2211yescharacteristic
20C3×C4⋊(C3⋊C8)C2211yescharacteristic
21C3×C4⋊(C3⋊C8)C2211yescharacteristic
22#63573—21no—
23#63567—21no—
24#63563—21no—
25#5094—31no—
26#5085—31no—
27#5076—31no—
28#5075—31no—
29#4851—31no—
30#4848—31no—
31#4830—31no—
32#4830—31no—
33#4830—61no—
34C3×#332—31no—
35C3×#331—31no—
36#4485D311yescharacteristic
37#4482D311yescharacteristic, complemented
38#4480—31no—
39#4480—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#3716—42no—
57#3715—42no—
58#3715—42no—
59#1666—91noSylow
60C3×C4⋊Q8—31no—
61C3×#127—31no—
62C2×#215—61no—
63C2×#215—61no—
64C2×#214—61no—
65C2×#214—61no—
66C2×#214—61no—
67C2×#204—61no—
68#874C2×D311yescharacteristic
69#869C2×D311yescharacteristic
70C4×Dic6—31no—
71C4×Dic6—31no—
72C4×Dic6—61no—
73C3×C4⋊C8—21no—
74C3×C4⋊C8—31no—
75C3×C4⋊C8—31no—
76C3×C4⋊C8C2×D311yescharacteristic
77C3×C4⋊C8C2×D311yescharacteristic
78#832—61no—
79#821—61no—
80#817—61no—
81#816—61no—
82Dic3⋊C8—61no—
83Dic3⋊C8—61no—
84Dic3⋊C8—62no—
85C8×Dic3—61no—
86C8×Dic3—61no—
87C8×Dic3—62no—
88#810—61no—
89#808—61no—
90C4⋊(C3⋊C8)C2×D311yescharacteristic
91C4⋊(C3⋊C8)C2×D311yescharacteristic
92C4×C3⋊C8—31no—
93C4×C3⋊C8—31no—
94C4×C3⋊C8—61no—
95C22×C3×D3—41no—
96C2×C32×C4C2×D411yescharacteristic
97C2×C32×C4C2×D411yescharacteristic
98C2×C32×C4#4111yescharacteristic
99C2×C3⋊Dic3—21no—
100C2×C3⋊Dic3—21no—
101#634—21no—
102#634SD1612yescomplemented
103C2×C3×Dic3—41no—
104C3×D12—41no—
105C3×D12—41no—
106C3×D12—41no—
107C3×D12—41no—
108C3×D12—81no—
109C3×Dic6—41no—
110C3×Dic6—41no—
111C32×C8—41no—
112C3⋊(C3⋊C8)—21no—
113C3⋊(C3⋊C8)SD1612yescomplemented
114C3×C3⋊C8—41no—
115C3×C3⋊C8—41no—
116#492—91no—
117#475—91no—
118#460—91no—
119C8×Q8—91no—
120#334—91no—
121#332—31no—
122#331—31no—
123C2×C3×Q8—61no—
124C2×C3×D4—61no—
125C2×C3×D4—61no—
126C2×C3×D4—61no—
127C2×D12—21no—
128C2×D12—21no—
129C2×D12—21no—
130C2×Dic6—21no—
131C2×Dic6—31no—
132C2×Dic6—31no—
133C2×Dic6—61no—
134C2×C3×C8—22no—
135C2×C3×C8—21no—
136C2×C3×C8—21no—
137C2×C3×C8—61no—
138C2×C3×C8—61no—
139C3×C4⋊C4—61no—
140C3×C4⋊C4—61no—
141C3×C42—21no—
142C3×C42C22×D311yescharacteristic
143C3×C42C22×D311yescharacteristic
144#215—122no—
145#215—122no—
146#214—122no—
147#214—122no—
148#214—122no—
149C4⋊Dic3—21no—
150C4⋊Dic3—21no—
151C4⋊Dic3—31no—
152C4⋊Dic3—31no—
153C4⋊Dic3—61no—
154Dic3⋊C4—62no—
155Dic3⋊C4—61no—
156Dic3⋊C4—61no—
157C4×Dic3—62no—
158C4×Dic3—61no—
159C4×Dic3—61no—
160C2×C3⋊C8—21no—
161C2×C3⋊C8—21no—
162C2×C3⋊C8—31no—
163C2×C3⋊C8—31no—
164C2×C3⋊C8—31no—
165C2×C3⋊C8—31no—
166C2×C3⋊C8—61no—
167C2×C3⋊C8—61no—
168#204—122no—
169C22×C32#12111yescharacteristic
170C2×C3×D3—81no—
171C2×C3×D3—81no—
172C2×C3×D3—81no—
173C32×C4—21no—
174C32×C4C2×SD1611yescharacteristic
175C32×C4C2×SD1611yescharacteristic
176C32×C4#13511yescharacteristic
177C32×C4AGL(1,ℤ/8)11yescharacteristic
178C3⋊Dic3—22no—
179C3⋊Dic3—41no—
180C3×Dic3—81no—
181C2×SD16—181no—
182C2×SD16—181no—
183C2×SD16—181no—
184C4⋊Q8—31no—
185#127—31no—
186C4×Q8—91no—
187#106—181no—
188C4⋊C8—31no—
189C4⋊C8—31no—
190C4⋊C8—181no—
191C4⋊C8D3211yescharacteristic
192#103—181no—
193#102—181no—
194C4×C8—91no—
195C4×C8—181no—
196C23×C3—121no—
197C22×D3—41no—
198C3×Q8—121no—
199C3×Q8—121no—
200C3×D4—121no—
201C3×D4—121no—
202C3×D4—121no—
203C3×D4—121no—
204C3×D4—241no—
205C2×C3×C4—21no—
206C2×C3×C4—21no—
207C2×C3×C4—21no—
208C2×C3×C4—121no—
209C2×C3×C4#23511yescharacteristic
210C2×C3×C4#23511yescharacteristic
211C2×C3×C4D3×D411yescharacteristic
212C2×C3×C4D3×D411yescharacteristic
213C2×C3×C4D3×D411yescharacteristic
214C2×C3×C4D3×D411yescharacteristic
215C2×Dic3—41no—
216C2×Dic3—62no—
217C2×Dic3—61no—
218C2×Dic3—61no—
219C2×Dic3—62no—
220C2×Dic3—61no—
221C2×Dic3—61no—
222D12—41no—
223D12—41no—
224D12—41no—
225D12—41no—
226D12—81no—
227Dic6—32no—
228Dic6—32no—
229Dic6—41no—
230Dic6—41no—
231Dic6—62no—
232Dic6—62no—
233Dic6—61no—
234Dic6—61no—
235C3×C8—42no—
236C3×C8—41no—
237C3×C8—41no—
238C3×C8—121no—
239C3×C8—121no—
240C3⋊C8—32no—
241C3⋊C8—32no—
242C3⋊C8—41no—
243C3⋊C8—41no—
244C3⋊C8—62no—
245C3⋊C8—61no—
246C3⋊C8—61no—
247C3⋊C8—121no—
248C2×C32#46011yescharacteristic
249C2×C32#46511yescharacteristic
250C2×C32#47111yescharacteristic
251C3×D3—161no—
252C2×Q8—61no—
253C2×Q8—91no—
254C2×D4—61no—
255C2×D4—61no—
256C2×D4—61no—
257SD16—362no—
258SD16—362no—
259SD16—362no—
260C2×C8—21no—
261C2×C8—61no—
262C2×C8—61no—
263C2×C8—91no—
264C2×C8—91no—
265C4⋊C4—61no—
266C4⋊C4—61no—
267C4⋊C4—91no—
268C4⋊C4—181no—
269C42—181no—
270C42C2×D3211yescharacteristic
271C22×C3—21no—
272C22×C3—241no—
273C22×C3—241no—
274C22×C3—241no—
275C22×C3#88411yescharacteristic
276C22×C3#88411yescharacteristic
277C2×D3—81no—
278C2×D3—81no—
279C2×D3—81no—
280C3×C4—21no—
281C3×C4—21no—
282C3×C4—21no—
283C3×C4—21no—
284C3×C4—21no—
285C3×C4—21no—
286C3×C4—41no—
287C3×C4—241no—
288C3×C4#91111yescharacteristic
289C3×C4#91111yescharacteristic
290C3×C4#91211yescharacteristic
291C3×C4D3×SD1611yescharacteristic
292C3×C4D3×SD1611yescharacteristic
293C3×C4D3×SD1611yescharacteristic
294C3×C4D3×SD1611yescharacteristic
295C3×C4#91911yescharacteristic
296Dic3—64no—
297Dic3—62no—
298Dic3—62no—
299Dic3—81no—
300Dic3—122no—
301Dic3—121no—
302Dic3—121no—
303C32#166611yescharacteristic, complemented, Sylow
304C23—121no—
305Q8—92no—
306Q8—121no—
307Q8—121no—
308Q8—181no—
309D4—121no—
310D4—121no—
311D4—121no—
312D4—121no—
313D4—241no—
314C2×C4—121no—
315C2×C4—181no—
316C2×C4—181no—
317C2×C4#379811yescharacteristic
318C2×C4#380211yescharacteristic
319C2×C4#381111yescharacteristic
320C8—41no—
321C8—92no—
322C8—121no—
323C8—121no—
324C8—181no—
325C2×C3—21no—
326C2×C3—21no—
327C2×C3—21no—
328C2×C3—481no—
329C2×C3#474811yescharacteristic
330C2×C3#475411yescharacteristic
331C2×C3#476211yescharacteristic
332C2×C3#476211yescharacteristic
333C2×C3#477811yescharacteristic
334C2×C3#480711yescharacteristic
335D3—161no—
336C22—241no—
337C22—241no—
338C22—241no—
339C22#6391211yescharacteristic
340C4—21no—
341C4—182no—
342C4—241no—
343C4—361no—
344C4#6379611yescharacteristic
345C4#6381011yescharacteristic
346C4#6392711yescharacteristic
347C4#6394011yescharacteristic
348C3—21no—
349C3#6840811yescharacteristic, complemented
350C3#6846411yescharacteristic, complemented
351C2—481no—
352C2#1059055311yescharacteristic
353C2#1059084111yescharacteristic
354C2#1059099111yescharacteristic
subgroupG/H
centerC22#63912
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊C8C22
socleC22×C32#121
prime radicalC3×#874C22
hypercenterC4⋊C8D32
hypocenterC32#1666
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
4. #10590307C2semidirect
6. C3×#4482C2semidirect
7. #10589098C2semidirect
37. #4482D3semidirect
102. #634SD16semidirect
113. C3⋊(C3⋊C8)SD16semidirect
303. C32#1666semidirect
349. C3#68408semidirect
350. C3#68464semidirect

Maximal subgroups

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

subgroupindex
#105925292
#105903772
#105903752
#105903072
C3×#44852
C3×#44822
#105890982
#684643
#684083