Finite Group Databasebeta

← #11898386

Subgroups — #11898386

Order 1152.

771 conjugacy classes of subgroups; only the 158 normal subgroups are shown.

normal subgroups only

This group has 771 conjugacy classes of subgroups — too many to draw. Only its 158 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#10593863C212yesmaximal, complemented
2#10592529C211yesmaximal, characteristic, complemented
3C3×#4841C212yesmaximal, complemented
4#10590867C212yesmaximal
5#10590796C214yesmaximal, complemented
6#10590790C212yesmaximal, complemented
7#10590387C211yesmaximal, characteristic, complemented
8C4×#3713C211yesmaximal, characteristic
9#80421—32nomaximal
10C4×#634C2211yescharacteristic
11C2×C3×#204C2214yes—
12C3×C4×D12C2212yes—
13C3×#869C2212yes—
14#63863C2214yes—
15#63858—24no—
16#63857—22no—
17#63843C2214yes—
18#63841—22no—
19C2×#3718C2212yes—
20C2×#3718C2212yes—
21C2×#3713C2211yescharacteristic
22C32×C4⋊C8C2211yescharacteristic
23#63641C2212yes—
24C8×C3⋊Dic3C2212yes—
25C4×C3⋊(C3⋊C8)C2211yescharacteristic
26C3×#816C2214yes—
27#63576C2211yescharacteristic
28#63562C2212yes—
29#5732—32no—
30#5542—32no—
31C3×#461—32no—
32#5168—34no—
33#5166—34no—
34#5092—32no—
35C4×#213—32no—
36#4841D312yescomplemented
37#4830—32no—
38#4830—61no—
39#4798—34no—
40#4790—34no—
41C2×#634D411yescharacteristic
42C2×C3×D12C2312yes—
43C2×C3×C4×D3—22no—
44C2×C3×Dic6C2314yes—
45C2×C32×C8C2312yes—
46C32×C42C2311yescharacteristic
47C4⋊(C3⋊Dic3)D411yescharacteristic
48#3750D412yes—
49C4×C3⋊Dic3C2312yes—
50C2×C3⋊(C3⋊C8)C2311yescharacteristic
51C2×C3⋊(C3⋊C8)C2311yescharacteristic
52C3×(C2×D3)⋊C4—22no—
53C3×C4⋊Dic3—22no—
54C3×C4⋊Dic3—22no—
55C3×C4⋊Dic3C2312yes—
56C3×#204—44no—
57Dic3⋊Dic3—24no—
58(C2×D3)⋊Dic3—24no—
59(C2×D3)⋊Dic3—24no—
60Dic32—24no—
61#3718—24no—
62#3718—42no—
63#3713—22no—
64#3393—91noSylow
65C2×C3×SD16—34no—
66C3×C4⋊Q8—32no—
67C3×C4×D4—32no—
68#947—34no—
69Q8×Dic3—34no—
70C2×#216—34no—
71C2×#216—34no—
72#936—34no—
73C2×#213—32no—
74#926—62no—
75#924—62no—
76C2×#204C2×D314yes—
77#898—64no—
78#897—62no—
79#892—62no—
80#887—34no—
81#879—64no—
82C4×D12C2×D312yes—
83#869C2×D312yes—
84C4×Dic6—32no—
85C4×Dic6—61no—
86C3×C4⋊C8—21no—
87C3×C4⋊C8C2×D312yes—
88C3×#103—34no—
89#832—32no—
90#816C2×D314yes—
91Dic3⋊C8—34no—
92Dic3⋊C8—62no—
93C8×Dic3—34no—
94C8×Dic3—62no—
95#809—32no—
96#807—32no—
97C4×C3⋊C8—32no—
98C4×C3⋊C8—61no—
99C22×C3×D3—22no—
100C2×C32×C4C2×D411yescharacteristic
101C2×C32×C4C2×D411yescharacteristic
102C2×C32×C4C2411yescharacteristic
103C2×C3⋊Dic3C2×D412yes—
104C2×C3⋊Dic3C2×D412yes—
105#634—22no—
106C2×C3×Dic3—22no—
107C2×C3×Dic3—24no—
108C3×D12—22no—
109C3×D12—22no—
110C3×C4×D3—44no—
111C3×Dic6—24no—
112C3×Dic6—24no—
113C32×C8—22no—
114C3⋊(C3⋊C8)—21no—
115C3⋊(C3⋊C8)#4112yes—
116#556—92no—
117#495—92no—
118#494—91no—
119#464—94no—
120#461—32no—
121C8×Q8—91no—
122C4×Q16—92no—
123C4×D8—91no—
124C2×C3×Q8—34no—
125C2×C3×D4—32no—
126C22×C3×C4—62no—
127C2×D12C22×D312yes—
128C2×C4×D3—22no—
129C2×Dic6—32no—
130C2×Dic6—61no—
131C2×Dic6C22×D314yes—
132C3×SD16—124no—
133C2×C3×C8—22no—
134C2×C3×C8C22×D314yes—
135C3×C4⋊C4—32no—
136C3×C4⋊C4—62no—
137C3×C4⋊C4—62no—
138C3×C22⋊C4—62no—
139C3×C42—21no—
140C3×C42C22×D312yes—
141#217—64no—
142#217—64no—
143#216—68no—
144#216—124no—
145#213—64no—
146(C2×D3)⋊C4—22no—
147(C2×D3)⋊C4—64no—
148(C2×D3)⋊C4—64no—
149C4⋊Dic3—22no—
150C4⋊Dic3—22no—
151C4⋊Dic3—32no—
152C4⋊Dic3—61no—
153C4⋊Dic3—64no—
154C4⋊Dic3C22×D312yes—
155Dic3⋊C4—34no—
156Dic3⋊C4—62no—
157Dic3⋊C4—64no—
158C4×Dic3—34no—
159C4×Dic3—62no—
160C4×Dic3—64no—
161C4×Dic3—64no—
162C2×C3⋊C8—32no—
163C2×C3⋊C8—32no—
164C2×C3⋊C8—61no—
165C2×C3⋊C8—61no—
166#204—44no—
167C22×C32C22×D411yescharacteristic
168C2×C3×D3—42no—
169C2×C3×D3—42no—
170C2×C3×D3—42no—
171C32×C4—21no—
172C32×C4#13512yes—
173C32×C4C2×#4111yescharacteristic
174C32×C4H(5,𝔽2)11yescharacteristic
175C3⋊Dic3—22no—
176C3⋊Dic3—22no—
177C3×Dic3—44no—
178C3×Dic3—42no—
179C2×Q16—92no—
180C2×Q16—92no—
181C2×SD16—34no—
182C2×D8—91no—
183C4⋊Q8—32no—
184#126—184no—
185#124—94no—
186C22⋊Q8—182no—
187C4×Q8—91no—
188C4×Q8—94no—
189C4×D4—32no—
190#117—182no—
191#107—91no—
192C4⋊C8—92no—
193C4⋊C8D3211yescharacteristic
194#103—34no—
195#102—92no—
196C4×C8—92no—
197C4×C8—91no—
198C23×C3—62no—
199C22×D3—22no—
200C3×Q8—64no—
201C3×Q8—64no—
202C3×D4—62no—
203C3×D4—62no—
204C2×C3×C4—21no—
205C2×C3×C4—21no—
206C2×C3×C4—21no—
207C2×C3×C4—62no—
208C2×C3×C4—64no—
209C2×C3×C4—124no—
210C2×C3×C4D3×D412yes—
211C2×C3×C4D3×D412yes—
212C2×C3×C4C23×D312yes—
213C2×Dic3—22no—
214C2×Dic3—24no—
215C2×Dic3—34no—
216C2×Dic3—34no—
217C2×Dic3—62no—
218C2×Dic3—62no—
219D12—22no—
220D12—22no—
221C4×D3—44no—
222Dic6—24no—
223Dic6—24no—
224Dic6—64no—
225Dic6—64no—
226C3×C8—24no—
227C3×C8—42no—
228C3⋊C8—34no—
229C3⋊C8—62no—
230C3⋊C8—62no—
231C3⋊C8—121no—
232C2×C32#55011yescharacteristic
233C2×C32C2×#13511yescharacteristic
234C2×C32#57811yescharacteristic
235C3×D3—82no—
236C2×Q8—34no—
237C2×Q8—91no—
238C2×D4—32no—
239C22×C4—62no—
240Q16—184no—
241Q16—362no—
242SD16—124no—
243D8—182no—
244C2×C8—91no—
245C2×C8—91no—
246C2×C8C2×D3212yes—
247C4⋊C4—32no—
248C4⋊C4—62no—
249C4⋊C4—62no—
250C4⋊C4—91no—
251C4⋊C4—92no—
252C4⋊C4—184no—
253C22⋊C4—62no—
254C22⋊C4—184no—
255C22⋊C4—184no—
256C42—92no—
257C42—184no—
258C42C2×D3211yescharacteristic
259C22×C3—21no—
260C22×C3—122no—
261C22×C3—122no—
262C22×C3—122no—
263C22×C3C2×D3×D412yes—
264C2×D3—42no—
265C2×D3—42no—
266C2×D3—42no—
267C3×C4—22no—
268C3×C4—21no—
269C3×C4—21no—
270C3×C4—22no—
271C3×C4—41no—
272C3×C4—122no—
273C3×C4—124no—
274C3×C4#91614yes—
275C3×C4#100412yes—
276C3×C4D3×#4112yes—
277Dic3—42no—
278Dic3—44no—
279Dic3—64no—
280Dic3—64no—
281Dic3—64no—
282Dic3—122no—
283C32#339311yescharacteristic, complemented, Sylow
284C23—62no—
285Q8—64no—
286Q8—64no—
287Q8—182no—
288D4—62no—
289D4—62no—
290C2×C4—62no—
291C2×C4—64no—
292C2×C4—92no—
293C2×C4—92no—
294C2×C4—124no—
295C2×C4#380211yescharacteristic
296C2×C4#380211yescharacteristic
297C2×C4C22×D3211yescharacteristic
298C8—22no—
299C8—92no—
300C8—181no—
301C2×C3—21no—
302C2×C3—21no—
303C2×C3—21no—
304C2×C3—242no—
305C2×C3#559912yes—
306C2×C3C2×#91612yes—
307C2×C3#577912yes—
308D3—82no—
309C22—122no—
310C22—122no—
311C22—122no—
312C22C2×#380211yescharacteristic
313C4—21no—
314C4—122no—
315C4—124no—
316C4—182no—
317C4—182no—
318C4#6380912yes—
319C4#6431311yescharacteristic
320C4#6431911yescharacteristic
321C3—21no—
322C3#8042112yescomplemented
323C2—242no—
324C2#1059452711yescharacteristic
325C2C2×#6380911yescharacteristic
326C2#1059472311yescharacteristic
subgroupG/H
centerC22C2×#3802
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊C8C22
socleC22×C32C22×D4
prime radicalC2×#3713C22
hypercenterC4⋊C8D32
hypocenterC32#3393
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
1. #10593863C2semidirect
2. #10592529C2semidirect
3. C3×#4841C2semidirect
5. #10590796C2semidirect
6. #10590790C2semidirect
7. #10590387C2semidirect
36. #4841D3semidirect
283. C32#3393semidirect
322. C3#80421semidirect

Maximal subgroups

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

subgroupindex
#105938632
#105925292
C3×#48412
#105908672
#105907962
#105907902
#105903872
C4×#37132
#804213