Finite Group Databasebeta

← #26185518

Subgroups — #26185518

Order 12032.

610 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C8×#10625350C211yesmaximal, characteristic
2#20252053C212yesmaximal
3#20242167C214yesmaximal, complemented
4#20242158C212yesmaximal, complemented
5#20242150C212yesmaximal, complemented
6#20242147C211yesmaximal, characteristic, complemented
7#20242135C212yesmaximal, complemented
8C2×C47×#335C211yesmaximal, characteristic, complemented
9C4×#10625350C2211yescharacteristic
10C8×Dic94C411yescharacteristic
11C8×Dic94C411yescharacteristic
12C8×D188C411yescharacteristic
13C8×D188C411yescharacteristic
14C8×C22⋊D47C412yes—
15C8×C22⋊D47C412yes—
16#15689183—24no—
17#15689179C2214yes—
18#15689176C2211yescharacteristic
19#15689175C2214yes—
20#15689174C2212yes—
21#15689147C2212yes—
22#15689089—22no—
23#15689078—22no—
24C4×C8×D47C2212yes—
25#15688876C2212yes—
26#15688876C2212yes—
27#15688873C2214yes—
28#15688873C2214yes—
29C2×C4⋊C8×C47C2212yes—
30C2×C4×C8×C47C2211yescharacteristic
31C47×#335C2211yescharacteristic
32C47×#335C2211yescharacteristic
33C47×#335C2212yes—
34C2×#10625350D411yescharacteristic
35C2×#10625329—22no—
36C2×C8×D47C2×C412yes—
37C2×C8×D47C2×C412yes—
38C4×Dic94C2×C411yescharacteristic
39C4×Dic94Q811yescharacteristic
40C4×D188C2×C411yescharacteristic
41C4×D188Q811yescharacteristic
42C4×C22⋊D47C2×C412yes—
43C4×C22⋊D47Q812yes—
44#13093983D411yescharacteristic
45#13093981D412yes—
46C42×D47C2312yes—
47C4⋊(C47⋊C8)—22no—
48C4⋊(C47⋊C8)C2×C411yescharacteristic
49C4⋊(C47⋊C8)C2×C411yescharacteristic
50C4⋊(C47⋊C8)C2314yes—
51Dic47⋊C8C2×C412yes—
52Dic47⋊C8C2×C412yes—
53C22⋊(C47⋊C8)C2×C412yes—
54(C2×D47)⋊C8—24no—
55(C2×D47)⋊C8—24no—
56(C2×D47)⋊C8C2×C412yes—
57(C2×D47)⋊C8C2×C412yes—
58#13093934—24no—
59C4×C47⋊C8C2312yes—
60C8×Dic47—24no—
61C8×Dic47C2×C412yes—
62C8×Dic47C2×C412yes—
63C22×C8×C47—22no—
64C22×C8×C47C2×C411yescharacteristic
65C22×C8×C47C2×C411yescharacteristic
66C2×C42×C47C2311yescharacteristic
67C4⋊C8×C47—22no—
68C4⋊C8×C47C2312yes—
69C4⋊C8×C47C2312yes—
70C4×C8×C47C2×C411yescharacteristic
71C4×C8×C47C2×C411yescharacteristic
72C4×C8×C47C2311yescharacteristic
73C4×C8×C47C2311yescharacteristic
74C22×C4×C47C22×C411yescharacteristic
75C22×C4×C47C2×D411yescharacteristic
76C22×C4×C47C2×Q811yescharacteristic
77C2×C22⋊D47C4⋊C412yes—
78#10625350—22no—
79#10625350—22no—
80C2×D188C4⋊C411yescharacteristic
81C2×C4×D47C22×C412yes—
82C2×C4×D47C2×D412yes—
83C2×C4×D47C2×Q812yes—
84C2×Dic94C4⋊C411yescharacteristic
85C2×C8×C47—22no—
86C2×C8×C47—22no—
87C2×C8×C47—22no—
88C2×C8×C47—41no—
89C2×C8×C47—44no—
90C2×C8×C47C22×C411yescharacteristic
91C2×C8×C47C22×C411yescharacteristic
92C2×C8×C47C22×C411yescharacteristic
93C2×C8×C47C22×C411yescharacteristic
94C42×C47C22×C411yescharacteristic
95C42×C47C2×D411yescharacteristic
96C42×C47C2×Q811yescharacteristic
97C42×C47C2411yescharacteristic
98C22⋊Dic47C4⋊C412yes—
99(C2×D47)⋊C4C4⋊C412yes—
100(C2×D47)⋊C4C4⋊C412yes—
101C4⋊Dic47C4⋊C411yescharacteristic
102C4⋊Dic47C4⋊C411yescharacteristic
103Dic47⋊C4C4⋊C412yes—
104Dic47⋊C4C4⋊C412yes—
105C4×Dic47C22×C412yes—
106C4×Dic47C2×D412yes—
107C4×Dic47C2×Q812yes—
108#10625329—44no—
109C2×C47⋊C8—24no—
110C2×C47⋊C8C22×C412yes—
111C2×C47⋊C8C22×C412yes—
112C8×D47—24no—
113C8×D47—42no—
114C23×C47C2×C4⋊C411yescharacteristic
115C22×D47C2×C4⋊C412yes—
116C2×C4×C47—21no—
117C2×C4×C47—21no—
118C2×C4×C47—41no—
119C2×C4×C47C2×C4⋊C411yescharacteristic
120C2×C4×C47C2×C4⋊C411yescharacteristic
121C2×C4×C47C2×C4⋊C411yescharacteristic
122C2×C4×C47#13512yes—
123C2×C4×C47#13512yes—
124C2×C4×C47C23×C411yescharacteristic
125C2×C4×C47C22×D411yescharacteristic
126C2×C4×C47C22×Q811yescharacteristic
127C22⋊D47—24no—
128C2×Dic47C2×C4⋊C412yes—
129C2×Dic47C2×C4⋊C412yes—
130C2×Dic47C2×C4⋊C412yes—
131D188—22no—
132C4×D47—22no—
133C4×D47—22no—
134C4×D47—22no—
135C4×D47—22no—
136C4×D47—42no—
137Dic94—22no—
138C8×C47—21no—
139C8×C47—21no—
140C8×C47—21no—
141C8×C47—42no—
142C8×C47—42no—
143C8×C47#13112yes—
144C47⋊C8—22no—
145C47⋊C8—22no—
146C47⋊C8—44no—
147#17829—471nomaximal, Sylow
148C22×C47—21no—
149C22×C47—21no—
150C22×C47#42712yes—
151C22×C47C22×C4⋊C411yescharacteristic
152C2×D47—22no—
153C2×D47—22no—
154C2×D47—22no—
155C4×C47—21no—
156C4×C47—21no—
157C4×C47—21no—
158C4×C47#42712yes—
159C4×C47C2×#13111yescharacteristic
160C4×C47#56811yescharacteristic
161C4×C47C2×#13511yescharacteristic
162C4×C47C2×#13511yescharacteristic
163Dic47—22no—
164Dic47—22no—
165Dic47—22no—
166C8×#41—471no—
167#2925—472no—
168#1572—474no—
169#1570—472no—
170#1568—472no—
171#1567—471no—
172#1564—472no—
173C2×#335D4711yescharacteristic, complemented
174C2×C47—22no—
175C2×C47#290611yescharacteristic
176C2×C47C2×#42711yescharacteristic
177C2×C47#291611yescharacteristic
178D47—42no—
179C4×#41—471no—
180C8×Q8—471no—
181C8×Q8—471no—
182C8×D4—472no—
183C8×D4—472no—
184C8×D4—471no—
185C8×D4—471no—
186#433—944no—
187#432—474no—
188#431—471no—
189#431—472no—
190#431—474no—
191#423—472no—
192C2×C4⋊C8C2×D4712yes—
193#408—942no—
194#405—942no—
195C2×C4×C8—472no—
196C2×C4×C8C2×D4711yescharacteristic
197#335—472no—
198#335—472no—
199#335C2×D4711yescharacteristic
200#335C2×D4711yescharacteristic
201#335C2×D4712yes—
202#334—474no—
203#334—474no—
204C47#1782911yescharacteristic, complemented, Sylow
205C2×#41—471no—
206C2×M16—942no—
207C22×C8—22no—
208C22×C8—472no—
209C22×C8—472no—
210C22×C8C4×D4711yescharacteristic
211C22×C8C4×D4711yescharacteristic
212C4×Q8—471no—
213C4×Q8—471no—
214C4×D4—472no—
215C4×D4—472no—
216C4×D4—471no—
217C4×D4—471no—
218#117—471no—
219#117—472no—
220C2×C42—472no—
221C2×C42C22×D4711yescharacteristic
222C4⋊C8—22no—
223C4⋊C8—472no—
224C4⋊C8—472no—
225C4⋊C8—471no—
226C4⋊C8—471no—
227C4⋊C8—474no—
228C4⋊C8—942no—
229C4⋊C8C22×D4712yes—
230C4⋊C8C22×D4712yes—
231C22⋊C8—472no—
232C22⋊C8—472no—
233C22⋊C8—472no—
234C22⋊C8—944no—
235C22⋊C8—944no—
236#97—944no—
237C4×C8—472no—
238C4×C8—472no—
239C4×C8—472no—
240C4×C8—944no—
241C4×C8C4×D4711yescharacteristic
242C4×C8C4×D4711yescharacteristic
243C4×C8C22×D4711yescharacteristic
244C4×C8C22×D4711yescharacteristic
245#41—942no—
246#41—942no—
247C2×Q8—471no—
248C2×D4—472no—
249C2×D4—471no—
250C22×C4—472no—
251C22×C4—472no—
252C22×C4—472no—
253C22×C4C2×C4×D4711yescharacteristic
254C22×C4D4×D4711yescharacteristic
255C22×C4Q8×D4711yescharacteristic
256M16—1884no—
257C2×C8—22no—
258C2×C8—22no—
259C2×C8—22no—
260C2×C8—41no—
261C2×C8—44no—
262C2×C8—472no—
263C2×C8—472no—
264C2×C8—944no—
265C2×C8—944no—
266C2×C8—1882no—
267C2×C8C2×C4×D4711yescharacteristic
268C2×C8C2×C4×D4711yescharacteristic
269C2×C8C2×C4×D4711yescharacteristic
270C2×C8C2×C4×D4711yescharacteristic
271C4⋊C4—472no—
272C4⋊C4—472no—
273C4⋊C4—471no—
274C4⋊C4—471no—
275C22⋊C4—472no—
276C22⋊C4—472no—
277C22⋊C4—472no—
278C42—472no—
279C42—472no—
280C42—472no—
281C42C2×C4×D4711yescharacteristic
282C42D4×D4711yescharacteristic
283C42Q8×D4711yescharacteristic
284C42C23×D4711yescharacteristic
285C23—472no—
286C23C4⋊C4×D4711yescharacteristic
287Q8—942no—
288D4—944no—
289D4—942no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—41no—
293C2×C4—472no—
294C2×C4—472no—
295C2×C4—472no—
296C2×C4—942no—
297C2×C4—942no—
298C2×C4—942no—
299C2×C4—942no—
300C2×C4—1882no—
301C2×C4C4⋊C4×D4711yescharacteristic
302C2×C4C4⋊C4×D4711yescharacteristic
303C2×C4C4⋊C4×D4711yescharacteristic
304C2×C4#1309404312yes—
305C2×C4#1309404712yes—
306C2×C4C22×C4×D4711yescharacteristic
307C2×C4C2×D4×D4711yescharacteristic
308C2×C4C2×Q8×D4711yescharacteristic
309C8—21no—
310C8—21no—
311C8—21no—
312C8—42no—
313C8—42no—
314C8—942no—
315C8—942no—
316C8—1884no—
317C8#1309403012yes—
318C22—21no—
319C22—21no—
320C22—942no—
321C22—942no—
322C22—942no—
323C22#1568916012yes—
324C22C2×C4⋊C4×D4711yescharacteristic
325C4—21no—
326C4—21no—
327C4—21no—
328C4—942no—
329C4—942no—
330C4—942no—
331C4#1568916012yes—
332C4C2×#1309403011yescharacteristic
333C4#1568988911yescharacteristic
334C4C2×#1309404311yescharacteristic
335C4C2×#1309404711yescharacteristic
336C2—22no—
337C2—1882no—
338C2#2025195311yescharacteristic
339C2C2×#1568916011yescharacteristic
340C2#2025199611yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC42C23×D47
FittingC2×C47×#335C2
socleC22×C47C22×C4⋊C4
prime radicalC2×#10625350D4
cosocleC42×C47C24
hypercenterC2×#335D47
hypocenterC47#17829
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×#335

Complements

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

NH ≅ G/Ntype
3. #20242167C2semidirect
4. #20242158C2semidirect
5. #20242150C2semidirect
6. #20242147C2semidirect
7. #20242135C2semidirect
8. C2×C47×#335C2semidirect
173. C2×#335D47semidirect
204. C47#17829semidirect

Maximal subgroups

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

subgroupindex
C8×#106253502
#202520532
#202421672
#202421582
#202421502
#202421472
#202421352
C2×C47×#3352
#1782947