Finite Group Databasebeta

← #26120781

Subgroups — #26120781

Order 12032.

374 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 374 conjugacy classes of subgroups — too many to draw. Only its 97 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#20251660C211yesmaximal, characteristic
2#20243556C211yesmaximal, characteristic
3#20243522C211yesmaximal, characteristic
4#20243521C211yesmaximal, characteristic
5#20241270C211yesmaximal, characteristic
6#20241270C211yesmaximal, characteristic
7C47×#1295C211yesmaximal, characteristic
8C2×#13093958—21no—
9C2×#13093956—21no—
10C2×#13093935C2211yescharacteristic
11#15689065—21no—
12#15689065—21no—
13#15689062—21no—
14#15689044—21no—
15#15689044—21no—
16#15689043—21no—
17#15688993C2211yescharacteristic
18#15688989C2211yescharacteristic
19#15688989C2211yescharacteristic
20#15688886—21no—
21#15688886—21no—
22#15688885—21no—
23#15688885—21no—
24C2×#97×C47C2211yescharacteristic
25C2×#97×C47C2211yescharacteristic
26C47×#382C2211yescharacteristic
27C22×Dic94—21no—
28C22×C47⋊C8—21no—
29C2×C4⋊Dic47—21no—
30C2×C4⋊Dic47—21no—
31C2×C4⋊Dic47—21no—
32C2×C4⋊Dic47—21no—
33C2×C4⋊Dic47D411yescharacteristic
34C2×C4⋊Dic47D411yescharacteristic
35C2×C4⋊Dic47D411yescharacteristic
36C2×C4⋊Dic47D411yescharacteristic
37C2×Dic47⋊C4—21no—
38C2×Dic47⋊C4—21no—
39#13093958—42no—
40#13093956—42no—
41#13093935—21no—
42#13093935Q812yescomplemented
43C47⋊#95—21no—
44C47⋊#95—21no—
45C47⋊#95—21no—
46C47⋊#95—21no—
47C47⋊#95—21no—
48C47⋊#95—21no—
49C47⋊#95—21no—
50C47⋊#95—21no—
51C22×C8×C47—21no—
52C22×C8×C47—21no—
53C2×C4⋊C4×C47D411yescharacteristic
54C2×C4⋊C4×C47D411yescharacteristic
55C2×C42×C47C2311yescharacteristic
56#97×C47—21no—
57#97×C47—21no—
58#97×C47Q812yescomplemented
59#97×C47Q812yescomplemented
60#95×C47—21no—
61#95×C47—21no—
62C22×C4×C47—21no—
63C22×C4×C47—21no—
64C22×C4×C47C2×D411yescharacteristic
65C22×C4×C47C2×D411yescharacteristic
66C22×C4×C47C2×D411yescharacteristic
67C22×Dic47—21no—
68C22×Dic47—21no—
69C22×Dic47—21no—
70C22×Dic47—21no—
71C22×Dic47—41no—
72C2×Dic94—81no—
73C2×Dic94—81no—
74C2×Dic94—81no—
75C2×C8×C47—22no—
76C2×C8×C47—22no—
77C2×C8×C47—22no—
78C2×C8×C47—22no—
79C2×C8×C47—41no—
80C2×C8×C47—41no—
81C4⋊C4×C47—41no—
82C4⋊C4×C47—41no—
83C42×C47C2×Q811yescharacteristic
84C42×C47C2×Q811yescharacteristic
85C42×C47C2×Q811yescharacteristic
86C42×C47#4111yescharacteristic
87C4⋊Dic47—41no—
88C4⋊Dic47—41no—
89C4⋊Dic47—41no—
90C4⋊Dic47—41no—
91C4⋊Dic47—41no—
92C4⋊Dic47—41no—
93C4⋊Dic47—42no—
94C4⋊Dic47—42no—
95C4⋊Dic47—81no—
96Dic47⋊C4—81no—
97Dic47⋊C4—81no—
98C2×C47⋊C8—22no—
99C2×C47⋊C8—41no—
100C2×C47⋊C8—41no—
101C23×C47#12011yescharacteristic
102C2×C4×C47—21no—
103C2×C4×C47—21no—
104C2×C4×C47—21no—
105C2×C4×C47—21no—
106C2×C4×C47—21no—
107C2×C4×C47—21no—
108C2×C4×C47—41no—
109C2×C4×C47—41no—
110C2×C4×C47—41no—
111C2×C4×C47—41no—
112C2×C4×C47—41no—
113C2×C4×C47—41no—
114C2×C4×C47C22⋊Q811yescharacteristic
115C2×C4×C47C22⋊Q811yescharacteristic
116C2×C4×C47C22⋊Q811yescharacteristic
117C2×C4×C47C4⋊Q811yescharacteristic
118C2×C4×C47C4⋊Q811yescharacteristic
119C2×C4×C47C4⋊Q811yescharacteristic
120C2×Dic47—41no—
121C2×Dic47—41no—
122C2×Dic47—41no—
123C2×Dic47—41no—
124C2×Dic47—41no—
125C2×Dic47—41no—
126C2×Dic47—41no—
127C2×Dic47—41no—
128C2×Dic47—41no—
129C2×Dic47—41no—
130C2×Dic47—41no—
131C2×Dic47—41no—
132C2×Dic47—81no—
133C2×Dic47—81no—
134C2×Dic47—81no—
135Dic94—84no—
136C8×C47—24no—
137C8×C47—42no—
138C47⋊C8—42no—
139#10584—471nomaximal, Sylow
140C22×C47#39511yescharacteristic
141C22×C47#45311yescharacteristic
142C22×C47#45411yescharacteristic
143C22×C47#45411yescharacteristic
144C22×C47#45511yescharacteristic
145C22×C47#45511yescharacteristic
146C22×C47#45611yescharacteristic
147C4×C47—21no—
148C4×C47—21no—
149C4×C47—21no—
150C4×C47—21no—
151C4×C47—21no—
152C4×C47—21no—
153C4×C47—81no—
154C4×C47—81no—
155Dic47—81no—
156Dic47—81no—
157Dic47—81no—
158Dic47—81no—
159Dic47—161no—
160#2844—471no—
161#1847—471no—
162#1836—471no—
163#1836—471no—
164#1295—471no—
165#1295—471no—
166#1295D4711yescharacteristic
167C2×C47#165711yescharacteristic
168C2×C47#165911yescharacteristic
169C2×C47#166411yescharacteristic
170C2×C47#166411yescharacteristic
171C2×C47#206011yescharacteristic
172C2×C47#206111yescharacteristic
173C2×C47#206111yescharacteristic
174C2×#107—941no—
175C2×#106—941no—
176C2×#97—471no—
177C2×#97C2×D4711yescharacteristic
178C2×#97C2×D4711yescharacteristic
179#400—941no—
180#400—941no—
181#400—941no—
182#395—941no—
183#395—941no—
184#395—941no—
185#384—471no—
186#382—471no—
187#382—471no—
188#382C2×D4711yescharacteristic
189#340—941no—
190#340—941no—
191#340—941no—
192#340—941no—
193C47#1058411yescharacteristic, complemented, Sylow
194C22×Q8—941no—
195C22×C8—21no—
196C22×C8—21no—
197C22×C8—941no—
198C2×C4⋊C4—471no—
199C2×C4⋊C4—471no—
200C2×C4⋊C4—471no—
201C2×C4⋊C4—471no—
202C2×C4⋊C4—941no—
203C2×C4⋊C4—941no—
204C2×C4⋊C4—941no—
205C2×C4⋊C4—941no—
206C2×C4⋊C4—941no—
207C2×C4⋊C4—941no—
208C2×C4⋊C4D18811yescharacteristic
209C2×C4⋊C4D18811yescharacteristic
210C2×C42C22×D4711yescharacteristic
211#107—1882no—
212#106—1882no—
213#97—21no—
214#97—21no—
215#97—472no—
216#97—941no—
217#97Dic9412yescomplemented
218#97Dic9412yescomplemented
219#95—21no—
220#95—21no—
221#95—941no—
222#95—941no—
223#95—941no—
224#95—941no—
225#95—941no—
226#95—941no—
227#95—941no—
228#95—941no—
229C2×Q8—3761no—
230C2×Q8—3761no—
231C2×Q8—3761no—
232C22×C4—21no—
233C22×C4—21no—
234C22×C4—941no—
235C22×C4—941no—
236C22×C4—941no—
237C22×C4—941no—
238C22×C4—1881no—
239C22×C4C2×D18811yescharacteristic
240C22×C4D4×D4711yescharacteristic
241C22×C4D4×D4711yescharacteristic
242C2×C8—22no—
243C2×C8—22no—
244C2×C8—22no—
245C2×C8—22no—
246C2×C8—41no—
247C2×C8—41no—
248C2×C8—942no—
249C2×C8—1881no—
250C2×C8—1881no—
251C4⋊C4—41no—
252C4⋊C4—41no—
253C4⋊C4—3761no—
254C4⋊C4—3761no—
255C4⋊C4—3761no—
256C4⋊C4—1881no—
257C4⋊C4—1881no—
258C4⋊C4—1882no—
259C4⋊C4—1882no—
260C4⋊C4—1881no—
261C4⋊C4—1881no—
262C4⋊C4—1881no—
263C4⋊C4—1881no—
264C42C2×Dic9411yescharacteristic
265C42C2×Dic9411yescharacteristic
266C42#1062535211yescharacteristic
267C42Q8×D4711yescharacteristic
268C23#1309399411yescharacteristic
269Q8—3764no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—3761no—
283C2×C4—3761no—
284C2×C4—3761no—
285C2×C4—1881no—
286C2×C4—1881no—
287C2×C4—1881no—
288C2×C4—1881no—
289C2×C4—1881no—
290C2×C4—1881no—
291C2×C4—1881no—
292C2×C4—1881no—
293C2×C4—1881no—
294C2×C4—1881no—
295C2×C4—1881no—
296C2×C4—1881no—
297C2×C4#1309400111yescharacteristic
298C2×C4#1309400111yescharacteristic
299C2×C4#1309400411yescharacteristic
300C2×C4#1309402311yescharacteristic
301C2×C4#1309402311yescharacteristic
302C2×C4#1309402411yescharacteristic
303C8—24no—
304C8—42no—
305C8—1882no—
306C22#1568904411yescharacteristic
307C22#1568929211yescharacteristic
308C22#1568929711yescharacteristic
309C22#1568929811yescharacteristic
310C22#1568930211yescharacteristic
311C22#1568930311yescharacteristic
312C22#1568930711yescharacteristic
313C4—21no—
314C4—21no—
315C4—21no—
316C4—21no—
317C4—21no—
318C4—21no—
319C4—81no—
320C4—81no—
321C4—3761no—
322C4—3761no—
323C4—3761no—
324C4—3761no—
325C4—7521no—
326C2#2024268811yescharacteristic
327C2#2024269611yescharacteristic
328C2#2024272311yescharacteristic
329C2#2024272511yescharacteristic
330C2#2024473211yescharacteristic
331C2#2024473711yescharacteristic
332C2#2024473911yescharacteristic
subgroupG/H
centerC23#13093994
commutator, cosocleC2×C42×C47C23
FrattiniC2×C42C22×D47
FittingC47×#1295C2
socle, prime radicalC23×C47#120
hypercenter#1295D47
hypocenterC47#10584
LCSG ▷ C2×C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1295

Complements

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

NH ≅ G/Ntype
42. #13093935Q8semidirect
58. #97×C47Q8semidirect
59. #97×C47Q8semidirect
193. C47#10584semidirect
217. #97Dic94semidirect
218. #97Dic94semidirect

Maximal subgroups

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

subgroupindex
#202516602
#202435562
#202435222
#202435212
#202412702
C47×#12952
#1058447