Finite Group Databasebeta

← #11782448

Subgroups — #11782448

Order 1152.

507 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 507 conjugacy classes of subgroups — too many to draw. Only its 110 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#10592769C211yesmaximal, characteristic, complemented
2C3×#5076C211yesmaximal, characteristic, complemented
3C3×#5073C211yesmaximal, characteristic
4#10590369C211yesmaximal, characteristic, complemented
5#10590311C211yesmaximal, characteristic, complemented
6#10590277C211yesmaximal, characteristic, complemented
7C3⋊C82C211yesmaximal, characteristic, complemented
8#71274—31nomaximal
9#71255—31nomaximal
10C32×#127C2211yescharacteristic
11#64078C2211yescharacteristic
12C2×C3×#214—22no—
13C2×C3×#213—22no—
14C3×#874C2211yescharacteristic
15C3×#869C2211yescharacteristic
16C2×#3716—22no—
17#63659—22no—
18C4×C3⋊(C3⋊C8)C2211yescharacteristic
19C3×C4×C3⋊C8C2211yescharacteristic
20C3×C4×C3⋊C8C2211yescharacteristic
21#63575—22no—
22#63562—22no—
23C3×#493—31no—
24C3×#492—31no—
25#5088—31no—
26#5078—31no—
27#5076—31no—
28#5076D311yescharacteristic, complemented
29#5073D311yescharacteristic
30#5070—31no—
31#5070—31no—
32#5070—31no—
33#5070—61no—
34#4693—31no—
35#4682—31no—
36C8×C3⋊C8—31no—
37C8×C3⋊C8—31no—
38C2×C32×D4—21no—
39C2×C32×D4—21no—
40C2×C32×D4—21no—
41C2×#634—21no—
42C2×C3×D12—21no—
43C2×C3×D12—21no—
44C2×C3×D12—21no—
45C2×C3×Dic6—21no—
46C32×C42C2311yescharacteristic
47C4⋊(C3⋊Dic3)—21no—
48C4⋊(C3⋊Dic3)—21no—
49C2×C3⋊(C3⋊C8)D412yes—
50C3×#214—44no—
51C3×#213—44no—
52C3×C4⋊Dic3—21no—
53C3×C4⋊Dic3—21no—
54C2×C3×C3⋊C8D412yes—
55C2×C3×C3⋊C8D412yes—
56#3716—44no—
57#1706—91noSylow
58C2×C3×SD16—62no—
59C2×C3×D8—62no—
60C3×C4⋊Q8—31no—
61C3×#127—21no—
62C3×#127—31no—
63C3×#127C2×D311yescharacteristic
64C3×#127C2×D311yescharacteristic
65C2×#214—22no—
66C2×#214—62no—
67C2×#213—22no—
68C2×#204—62no—
69#874C2×D311yescharacteristic
70#869—31no—
71#869—31no—
72#869—61no—
73#869C2×D311yescharacteristic
74C3×C4×C8—31no—
75C3×C4×C8—31no—
76#832—62no—
77#832—62no—
78#832—62no—
79#832—64no—
80#818—62no—
81#809—62no—
82#807—62no—
83C4×C3⋊C8—31no—
84C4×C3⋊C8—31no—
85C4×C3⋊C8—61no—
86C4×C3⋊C8C2×D311yescharacteristic
87C4×C3⋊C8C2×D311yescharacteristic
88C23×C32—41no—
89C22×C3×D3—41no—
90C32×D4—42no—
91C32×D4—42no—
92C32×D4—42no—
93C2×C32×C4C2×D411yescharacteristic
94C2×C32×C4C2×D411yescharacteristic
95C2×C32×C4C2×D411yescharacteristic
96C2×C3⋊Dic3—41no—
97#634—42no—
98C2×C3×Dic3—41no—
99C3×D12—42no—
100C3×D12—42no—
101C3×D12—42no—
102C3×Dic6—42no—
103C3⋊(C3⋊C8)—22no—
104C3×C3⋊C8D814yescomplemented
105C3×C3⋊C8SD1614yescomplemented
106#500—91no—
107#493—31no—
108#492—31no—
109#492—91no—
110#486—91no—
111#486—91no—
112C82—91no—
113C2×C3×Q8—61no—
114C2×C3×D4—22no—
115C2×C3×D4—21no—
116C2×C3×D4—21no—
117C2×C3×D4—21no—
118C2×C3×D4—21no—
119C2×C3×D4—21no—
120C2×C3×D4—21no—
121C2×C3×D4—41no—
122C2×C3×D4—41no—
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—61no—
131C2×Dic6—61no—
132C2×Dic6—121no—
133C3×SD16—124no—
134C3×D8—124no—
135C2×C3×C8—32no—
136C2×C3×C8—32no—
137C3×C4⋊C4—61no—
138C3×C4⋊C4—61no—
139C3×C42—21no—
140C3×C42C22×D311yescharacteristic
141C3×C42C22×D311yescharacteristic
142#214—44no—
143#214—124no—
144#213—44no—
145C4⋊Dic3—21no—
146C4⋊Dic3—21no—
147C4⋊Dic3—62no—
148C4⋊Dic3—61no—
149C4⋊Dic3—61no—
150C4⋊Dic3—61no—
151C4⋊Dic3—61no—
152C4⋊Dic3—121no—
153C2×C3⋊C8—32no—
154C2×C3⋊C8—32no—
155C2×C3⋊C8—62no—
156C2×C3⋊C8#6712yes—
157C2×C3⋊C8#6712yes—
158#204—124no—
159C22×C32—81no—
160C22×C32—81no—
161C22×C32—81no—
162C22×C32#12711yescharacteristic
163C2×C3×D3—81no—
164C2×C3×D3—81no—
165C2×C3×D3—81no—
166C32×C4C2×D812yes—
167C32×C4C2×SD1612yes—
168C32×C4#13512yes—
169C3⋊Dic3—81no—
170C3×Dic3—81no—
171C2×SD16—62no—
172C2×SD16—182no—
173C2×D8—62no—
174C4⋊Q8—31no—
175C4⋊Q8—91no—
176#127—31no—
177#127D3211yescharacteristic
178#107—182no—
179#102—182no—
180#102—182no—
181C4×C8—31no—
182C4×C8—31no—
183C4×C8—91no—
184C23×C3—42no—
185C23×C3—41no—
186C23×C3—41no—
187C23×C3—121no—
188C22×D3—41no—
189C3×Q8—122no—
190C3×D4—44no—
191C3×D4—42no—
192C3×D4—42no—
193C3×D4—42no—
194C3×D4—42no—
195C3×D4—42no—
196C3×D4—42no—
197C3×D4—82no—
198C3×D4—82no—
199C3×D4—122no—
200C3×D4—122no—
201C3×D4—122no—
202C2×C3×C4—21no—
203C2×C3×C4—21no—
204C2×C3×C4—21no—
205C2×C3×C4—121no—
206C2×C3×C4D3×D411yescharacteristic
207C2×C3×C4D3×D411yescharacteristic
208C2×C3×C4D3×D411yescharacteristic
209C2×C3×C4D3×D411yescharacteristic
210C2×C3×C4C2×#6711yescharacteristic
211C2×C3×C4C2×#6711yescharacteristic
212C2×Dic3—41no—
213C2×Dic3—122no—
214C2×Dic3—121no—
215C2×Dic3—121no—
216D12—42no—
217D12—42no—
218D12—42no—
219Dic6—42no—
220Dic6—122no—
221Dic6—122no—
222Dic6—242no—
223C3×C8—34no—
224C3×C8—34no—
225C3⋊C8—62no—
226C3⋊C8—62no—
227C3⋊C8—122no—
228C3⋊C8#21314yescomplemented
229C3⋊C8#21414yescomplemented
230C2×C32—161no—
231C2×C32#49211yescharacteristic
232C2×C32#49311yescharacteristic
233C2×C32#49511yescharacteristic
234C3×D3—161no—
235C2×Q8—61no—
236C2×Q8—181no—
237C2×D4—21no—
238C2×D4—21no—
239C2×D4—21no—
240C2×D4—61no—
241C2×D4—61no—
242C2×D4—61no—
243SD16—124no—
244SD16—364no—
245D8—124no—
246C2×C8—32no—
247C2×C8—32no—
248C2×C8—92no—
249C4⋊C4—61no—
250C4⋊C4—61no—
251C4⋊C4—181no—
252C4⋊C4—181no—
253C42C2×D3211yescharacteristic
254C22×C3—21no—
255C22×C3—82no—
256C22×C3—82no—
257C22×C3—82no—
258C22×C3—81no—
259C22×C3—81no—
260C22×C3—81no—
261C22×C3—81no—
262C22×C3—81no—
263C22×C3—81no—
264C22×C3—241no—
265C22×C3—241no—
266C22×C3—241no—
267C22×C3#94011yescharacteristic
268C22×C3#94011yescharacteristic
269C2×D3—81no—
270C2×D3—81no—
271C2×D3—81no—
272C3×C4—22no—
273C3×C4—22no—
274C3×C4—22no—
275C3×C4—241no—
276C3×C4D3×D812yes—
277C3×C4#91212yes—
278C3×C4D3×SD1612yes—
279C3×C4#91612yes—
280C3×C4C2×#21312yes—
281C3×C4C2×#21412yes—
282Dic3—81no—
283Dic3—242no—
284Dic3—241no—
285Dic3—241no—
286C32#170611yescharacteristic, complemented, Sylow
287C23—41no—
288C23—121no—
289Q8—122no—
290Q8—362no—
291D4—42no—
292D4—42no—
293D4—42no—
294D4—122no—
295D4—122no—
296D4—122no—
297C2×C4—121no—
298C2×C4—361no—
299C2×C4D3×#6711yescharacteristic
300C2×C4D3×#6711yescharacteristic
301C2×C4#381111yescharacteristic
302C8—34no—
303C8—34no—
304C8—182no—
305C2×C3—21no—
306C2×C3—21no—
307C2×C3—21no—
308C2×C3—162no—
309C2×C3—161no—
310C2×C3—161no—
311C2×C3—481no—
312C2×C3#507311yescharacteristic
313C2×C3#507611yescharacteristic
314C2×C3#515111yescharacteristic
315C2×C3#515511yescharacteristic
316C2×C3#516811yescharacteristic
317C2×C3#517511yescharacteristic
318D3—161no—
319C22—81no—
320C22—81no—
321C22—81no—
322C22—241no—
323C22—241no—
324C22—241no—
325C22#6397911yescharacteristic
326C4—241no—
327C4—721no—
328C4D3×#21312yes—
329C4D3×#21412yes—
330C4#6393612yes—
331C3—21no—
332C3#7125511yescharacteristic, complemented
333C3#7127411yescharacteristic, complemented
334C2—161no—
335C2—481no—
336C2#1059147411yescharacteristic
337C2#1059148211yescharacteristic
338C2#1059149011yescharacteristic
subgroupG/H
centerC22#63979
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×#127C22
socleC22×C32#127
prime radicalC3×#5073C2
hypercenter#127D32
hypocenterC32#1706
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #127

Complements

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

NH ≅ G/Ntype
1. #10592769C2semidirect
2. C3×#5076C2semidirect
4. #10590369C2semidirect
5. #10590311C2semidirect
6. #10590277C2semidirect
7. C3⋊C82C2semidirect
28. #5076D3semidirect
104. C3×C3⋊C8D8semidirect
105. C3×C3⋊C8SD16semidirect
228. C3⋊C8#213semidirect
229. C3⋊C8#214semidirect
286. C32#1706semidirect
332. C3#71255semidirect
333. C3#71274semidirect

Maximal subgroups

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

subgroupindex
#105927692
C3×#50762
C3×#50732
#105903692
#105903112
#105902772
C3⋊C822
#712743
#712553