Finite Group Databasebeta

← #26106894

Subgroups — #26106894

Order 12032.

610 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#13093989C211yesmaximal, characteristic
2#20243243C211yesmaximal, characteristic
3C4×#13093934C211yesmaximal, characteristic
4C2×#15688855C211yesmaximal, characteristic
5C2×#15688853C211yesmaximal, characteristic
6#20241229C211yesmaximal, characteristic
7C47×#1279C211yesmaximal, characteristic
8C2×C4×Dic94C2211yescharacteristic
9C2×#13093989C412yes—
10C2×C4⋊(C47⋊C8)C2211yescharacteristic
11C2×#13093934—22no—
12C2×#13093934—21no—
13C2×C4×C47⋊C8C2211yescharacteristic
14C4⋊C4×Dic47C412yes—
15C4×Dic47⋊C4—21no—
16#15688974—22no—
17C42×Dic47—21no—
18C42×Dic47C2211yescharacteristic
19#15688877—21no—
20#15688855C414yescomplemented
21#15688853C414yescomplemented
22C2×C4⋊C8×C47C2211yescharacteristic
23C2×C4×C8×C47C2211yescharacteristic
24C4×C4⋊C4×C47C2211yescharacteristic
25C22×Dic94C2×C411yescharacteristic
26C22×C47⋊C8—21no—
27C22×C47⋊C8—21no—
28C4×Dic94—21no—
29C4×Dic94—21no—
30C4×Dic94C2×C412yes—
31C4×Dic94C2×C412yes—
32#13093989—24no—
33#13093989—24no—
34C2×C4⋊Dic47C2×C411yescharacteristic
35C2×Dic47⋊C4—21no—
36C2×Dic47⋊C4—22no—
37C2×C4×Dic47—21no—
38C2×C4×Dic47—22no—
39C2×C4×Dic47—22no—
40C2×C4×Dic47C2×C412yes—
41C2×C4×Dic47D411yescharacteristic
42C2×C4×Dic47D412yes—
43C2×C4×Dic47D411yescharacteristic
44C4⋊(C47⋊C8)—21no—
45C4⋊(C47⋊C8)C2×C412yes—
46#13093934—28no—
47#13093934—42no—
48C4×C47⋊C8—21no—
49C4×C47⋊C8C2×C412yes—
50C47⋊#95—22no—
51C22×C8×C47—21no—
52C22×C8×C47—21no—
53C2×C4⋊C4×C47C2×C412yes—
54C2×C42×C47—21no—
55C2×C42×C47C2311yescharacteristic
56C4⋊C8×C47—21no—
57C4⋊C8×C47C2×C412yes—
58C4×C8×C47—21no—
59C4×C8×C47C2×C412yes—
60#95×C47—21no—
61C22×C4×C47—22no—
62C22×C4×C47C22×C411yescharacteristic
63C22×C4×C47C2×D411yescharacteristic
64C22×C4×C47C2×D411yescharacteristic
65C22×Dic47—21no—
66C22×Dic47—21no—
67C22×Dic47C22⋊C412yes—
68C22×Dic47C22⋊C412yes—
69C2×Dic94—21no—
70C2×Dic94—22no—
71C2×Dic94C4212yes—
72C2×Dic94M1614yes—
73C2×C8×C47—24no—
74C2×C8×C47—22no—
75C2×C8×C47—22no—
76C2×C8×C47—41no—
77C2×C8×C47—41no—
78C4⋊C4×C47—22no—
79C4⋊C4×C47M1614yes—
80C42×C47—41no—
81C42×C47—41no—
82C42×C47C22×C411yescharacteristic
83C42×C47C22×C411yescharacteristic
84C42×C47#4111yescharacteristic
85C42×C47#4111yescharacteristic
86C4⋊Dic47—21no—
87C4⋊Dic47C4212yes—
88Dic47⋊C4—28no—
89Dic47⋊C4—22no—
90Dic47⋊C4—22no—
91C4×Dic47—28no—
92C4×Dic47—22no—
93C4×Dic47—22no—
94C4×Dic47—22no—
95C4×Dic47—22no—
96C4×Dic47—21no—
97C4×Dic47—21no—
98C4×Dic47—21no—
99C4×Dic47—21no—
100C4×Dic47—24no—
101C4×Dic47—44no—
102C2×C47⋊C8—24no—
103C2×C47⋊C8—22no—
104C2×C47⋊C8—22no—
105C2×C47⋊C8—41no—
106C2×C47⋊C8—41no—
107C23×C47C2×C22⋊C411yescharacteristic
108C2×C4×C47—22no—
109C2×C4×C47—24no—
110C2×C4×C47—42no—
111C2×C4×C47—42no—
112C2×C4×C47C2×C4211yescharacteristic
113C2×C4×C47#11711yescharacteristic
114C2×C4×C47C4×D411yescharacteristic
115C2×C4×C47C4×D411yescharacteristic
116C2×C4×C47C4×D411yescharacteristic
117C2×C4×C47C4×D411yescharacteristic
118C2×C4×C47C2×M1612yes—
119C2×C4×C47C2×M1612yes—
120C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
121C2×C4×C47#13711yescharacteristic
122C2×C4×C47#13711yescharacteristic
123C2×C4×C47#13711yescharacteristic
124C2×Dic47—22no—
125C2×Dic47—22no—
126C2×Dic47—24no—
127C2×Dic47—22no—
128C2×Dic47—22no—
129C2×Dic47—22no—
130C2×Dic47—22no—
131C2×Dic47—22no—
132C2×Dic47—42no—
133C2×Dic47#10414yes—
134Dic94—22no—
135Dic94—24no—
136Dic94#9714yescomplemented
137C8×C47—24no—
138C8×C47—42no—
139C47⋊C8—24no—
140C47⋊C8—42no—
141#8173—471nomaximal, Sylow
142C22×C47C4×C22⋊C411yescharacteristic
143C22×C47#40712yes—
144C22×C47#41711yescharacteristic
145C22×C47#41911yescharacteristic
146C22×C47C2×#10412yes—
147C4×C47—21no—
148C4×C47—21no—
149C4×C47—44no—
150C4×C47C2×#9711yescharacteristic
151C4×C47C4×M1611yescharacteristic
152C4×C47#43212yes—
153C4×C47#44011yescharacteristic
154C4×C47#44011yescharacteristic
155C4×C47#44111yescharacteristic
156C4×C47#44111yescharacteristic
157Dic47—24no—
158Dic47—24no—
159Dic47—42no—
160Dic47—42no—
161C42×Q8—471no—
162#1767—471no—
163C4×#97—471no—
164C2×Q8⋊C8—471no—
165C2×Q8⋊C8—471no—
166#1279—471no—
167#1279D4711yescharacteristic
168C2×C47#148912yes—
169C2×C47#149112yes—
170C2×C47#174911yescharacteristic
171C2×C47C4×#10411yescharacteristic
172C2×C47#176311yescharacteristic
173C2×C4×Q8—472no—
174C2×C4×Q8—471no—
175C2×C4⋊C8—471no—
176C2×C4⋊C8C2×D4711yescharacteristic
177C2×#97—942no—
178C2×#97—941no—
179C2×C4×C8—471no—
180C2×C4×C8C2×D4711yescharacteristic
181C4×C4⋊C4—472no—
182C4×C4⋊C4—942no—
183C4×C4⋊C4—941no—
184C4×C4⋊C4C2×D4711yescharacteristic
185C43—471no—
186C43—941no—
187#336—941no—
188Q8⋊C8—474no—
189Q8⋊C8—474no—
190C47#817311yescharacteristic, complemented, Sylow
191C22×Q8—471no—
192C22×C8—21no—
193C22×C8—21no—
194C22×C8—941no—
195C22×C8—941no—
196C4×Q8—472no—
197C4×Q8—472no—
198C4×Q8—944no—
199C4×Q8—944no—
200C4×Q8—941no—
201C4×Q8—941no—
202C2×C4⋊C4—471no—
203C2×C4⋊C4—942no—
204C2×C4⋊C4—941no—
205C2×C4⋊C4C4×D4712yes—
206C2×C42—21no—
207C2×C42—472no—
208C2×C42—472no—
209C2×C42—471no—
210C2×C42—471no—
211C2×C42—942no—
212C2×C42—941no—
213C2×C42—942no—
214C2×C42C22×D4711yescharacteristic
215C4⋊C8—21no—
216C4⋊C8—472no—
217C4⋊C8—941no—
218C4⋊C8C4×D4712yes—
219#97—948no—
220#97—1882no—
221C4×C8—21no—
222C4×C8—472no—
223C4×C8—941no—
224C4×C8C4×D4712yes—
225#95—21no—
226#95—942no—
227C2×Q8—472no—
228C2×Q8—474no—
229C2×Q8—941no—
230C2×Q8—942no—
231C22×C4—22no—
232C22×C4—472no—
233C22×C4—472no—
234C22×C4—941no—
235C22×C4—941no—
236C22×C4C2×C4×D4711yescharacteristic
237C22×C4D4×D4711yescharacteristic
238C22×C4D4×D4711yescharacteristic
239C2×C8—24no—
240C2×C8—22no—
241C2×C8—22no—
242C2×C8—41no—
243C2×C8—41no—
244C2×C8—944no—
245C2×C8—942no—
246C2×C8—942no—
247C2×C8—1881no—
248C2×C8—1881no—
249C4⋊C4—22no—
250C4⋊C4—472no—
251C4⋊C4—948no—
252C4⋊C4—941no—
253C4⋊C4—942no—
254C4⋊C4—942no—
255C4⋊C4#1062532414yes—
256C42—41no—
257C42—41no—
258C42—944no—
259C42—948no—
260C42—942no—
261C42—942no—
262C42—942no—
263C42—942no—
264C42—941no—
265C42—941no—
266C42—941no—
267C42—941no—
268C42—1884no—
269C42C2×C4×D4711yescharacteristic
270C42C2×C4×D4711yescharacteristic
271C42#1062535211yescharacteristic
272C42#1062535411yescharacteristic
273C23C22⋊C4×D4711yescharacteristic
274Q8—474no—
275Q8—942no—
276Q8—944no—
277C2×C4—22no—
278C2×C4—24no—
279C2×C4—42no—
280C2×C4—42no—
281C2×C4—474no—
282C2×C4—942no—
283C2×C4—942no—
284C2×C4—944no—
285C2×C4—942no—
286C2×C4—942no—
287C2×C4—942no—
288C2×C4—942no—
289C2×C4—942no—
290C2×C4—1882no—
291C2×C4C42×D4711yescharacteristic
292C2×C4#1309398211yescharacteristic
293C2×C4(C22⋊D47)⋊C411yescharacteristic
294C2×C4(C22⋊D47)⋊C411yescharacteristic
295C2×C4#1309398611yescharacteristic
296C2×C4#1309398611yescharacteristic
297C2×C4M16×D4712yes—
298C2×C4C2×#1062532412yes—
299C2×C4#1309404811yescharacteristic
300C2×C4#1309405311yescharacteristic
301C2×C4#1309405311yescharacteristic
302C2×C4#1309405611yescharacteristic
303C8—24no—
304C8—42no—
305C8—944no—
306C8—1882no—
307C22#1568897011yescharacteristic
308C22#1568908512yes—
309C22#1568912111yescharacteristic
310C22#1568913011yescharacteristic
311C22#104×D4712yes—
312C4—21no—
313C4—21no—
314C4—44no—
315C4—944no—
316C4—944no—
317C4—1882no—
318C4—1882no—
319C4#97×D4711yescharacteristic
320C4C4×#1062532411yescharacteristic
321C4#1568917912yes—
322C4#1568922011yescharacteristic
323C4#1568922211yescharacteristic
324C4#1568922711yescharacteristic
325C4#1568922911yescharacteristic
326C2#2024182412yes—
327C2#2024183312yes—
328C2#2024314911yescharacteristic
329C2#2024319211yescharacteristic
330C2#2024321711yescharacteristic
subgroupG/H
centerC22×C4D4×D47
commutatorC2×C4×C47C2×C42
FrattiniC2×C42C22×D47
FittingC47×#1279C2
socle, prime radicalC23×C47C2×C22⋊C4
cosocleC2×C42×C47C23
hypercenter#1279D47
hypocenterC47#8173
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ #1279

Complements

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

NH ≅ G/Ntype
20. #15688855C4semidirect
21. #15688853C4semidirect
136. Dic94#97semidirect
190. C47#8173semidirect

Maximal subgroups

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

subgroupindex
C4×#130939892
#202432432
C4×#130939342
C2×#156888552
C2×#156888532
#202412292
C47×#12792
#817347