Finite Group Databasebeta

← #26185505

Subgroups — #26185505

Order 12032.

610 conjugacy classes of subgroups.

The subgroup lattice has 334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C8×#10625350C211yesmaximal, characteristic
2#20252053C212yesmaximal
3#20242165C214yesmaximal, complemented
4#20242162C212yesmaximal, complemented
5#20242148C212yesmaximal, complemented
6#20242144C211yesmaximal, characteristic, complemented
7#20242133C212yesmaximal, complemented
8C2×C47×#334C211yesmaximal, 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#15688875C2214yes—
26#15688875C2214yes—
27#15688874C2212yes—
28#15688874C2212yes—
29C2×C4⋊C8×C47C2212yes—
30C2×C4×C8×C47C2211yescharacteristic
31C47×#334C2211yescharacteristic
32C47×#334C2211yescharacteristic
33C47×#334C2212yes—
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—24no—
79C2×D188C4⋊C411yescharacteristic
80C2×C4×D47C22×C412yes—
81C2×C4×D47C2×D412yes—
82C2×C4×D47C2×Q812yes—
83C2×Dic94C4⋊C411yescharacteristic
84C2×C8×C47—22no—
85C2×C8×C47—22no—
86C2×C8×C47—22no—
87C2×C8×C47—41no—
88C2×C8×C47—44no—
89C2×C8×C47C22×C411yescharacteristic
90C2×C8×C47C22×C411yescharacteristic
91C2×C8×C47C22×C411yescharacteristic
92C2×C8×C47C22×C411yescharacteristic
93C42×C47C22×C411yescharacteristic
94C42×C47C2×D411yescharacteristic
95C42×C47C2×Q811yescharacteristic
96C42×C47C2411yescharacteristic
97C22⋊Dic47C4⋊C412yes—
98(C2×D47)⋊C4C4⋊C412yes—
99(C2×D47)⋊C4C4⋊C412yes—
100C4⋊Dic47C4⋊C411yescharacteristic
101C4⋊Dic47C4⋊C411yescharacteristic
102Dic47⋊C4C4⋊C412yes—
103Dic47⋊C4C4⋊C412yes—
104C4×Dic47C22×C412yes—
105C4×Dic47C2×D412yes—
106C4×Dic47C2×Q812yes—
107#10625329—44no—
108C2×C47⋊C8—24no—
109C2×C47⋊C8C22×C412yes—
110C2×C47⋊C8C22×C412yes—
111C8×D47—24no—
112C8×D47—42no—
113C23×C47C2×C4⋊C411yescharacteristic
114C22×D47C2×C4⋊C412yes—
115C2×C4×C47—21no—
116C2×C4×C47—21no—
117C2×C4×C47—41no—
118C2×C4×C47C2×C4⋊C411yescharacteristic
119C2×C4×C47C2×C4⋊C411yescharacteristic
120C2×C4×C47C2×C4⋊C411yescharacteristic
121C2×C4×C47#13514yes—
122C2×C4×C47C23×C411yescharacteristic
123C2×C4×C47C22×D411yescharacteristic
124C2×C4×C47C22×Q811yescharacteristic
125C22⋊D47—24no—
126C2×Dic47C2×C4⋊C412yes—
127C2×Dic47C2×C4⋊C412yes—
128C2×Dic47C2×C4⋊C412yes—
129D188—22no—
130C4×D47—22no—
131C4×D47—22no—
132C4×D47—24no—
133C4×D47—42no—
134Dic94—22no—
135C8×C47—21no—
136C8×C47—21no—
137C8×C47—21no—
138C8×C47—42no—
139C8×C47—42no—
140C8×C47#13112yes—
141C47⋊C8—22no—
142C47⋊C8—22no—
143C47⋊C8—44no—
144#17827—471nomaximal, Sylow
145C22×C47—21no—
146C22×C47—21no—
147C22×C47#42712yes—
148C22×C47C22×C4⋊C411yescharacteristic
149C2×D47—22no—
150C2×D47—22no—
151C2×D47—22no—
152C4×C47—21no—
153C4×C47—21no—
154C4×C47—21no—
155C4×C47#42712yes—
156C4×C47C2×#13111yescharacteristic
157C4×C47#56811yescharacteristic
158C4×C47C2×#13512yes—
159Dic47—22no—
160Dic47—22no—
161Dic47—22no—
162C8×#41—471no—
163#2925—472no—
164#1572—474no—
165#1571—472no—
166#1568—472no—
167#1566—471no—
168#1564—472no—
169C2×#334D4711yescharacteristic, complemented
170C2×C47—22no—
171C2×C47#290611yescharacteristic
172C2×C47C2×#42711yescharacteristic
173C2×C47#291611yescharacteristic
174D47—42no—
175C4×#41—471no—
176C8×Q8—471no—
177C8×Q8—471no—
178C8×D4—472no—
179C8×D4—472no—
180C8×D4—471no—
181C8×D4—471no—
182#433—944no—
183#432—474no—
184#431—471no—
185#431—472no—
186#431—474no—
187#423—472no—
188C2×C4⋊C8C2×D4712yes—
189#408—942no—
190#405—942no—
191C2×C4×C8—472no—
192C2×C4×C8C2×D4711yescharacteristic
193#335—474no—
194#335—474no—
195#334—472no—
196#334—472no—
197#334C2×D4711yescharacteristic
198#334C2×D4711yescharacteristic
199#334C2×D4712yes—
200C47#1782711yescharacteristic, complemented, Sylow
201C2×#41—471no—
202C2×M16—942no—
203C22×C8—22no—
204C22×C8—472no—
205C22×C8—472no—
206C22×C8C4×D4711yescharacteristic
207C22×C8C4×D4711yescharacteristic
208C4×Q8—471no—
209C4×Q8—471no—
210C4×D4—472no—
211C4×D4—472no—
212C4×D4—471no—
213C4×D4—471no—
214#117—471no—
215#117—472no—
216C2×C42—472no—
217C2×C42C22×D4711yescharacteristic
218C4⋊C8—22no—
219C4⋊C8—472no—
220C4⋊C8—472no—
221C4⋊C8—471no—
222C4⋊C8—471no—
223C4⋊C8—474no—
224C4⋊C8—942no—
225C4⋊C8C22×D4712yes—
226C4⋊C8C22×D4712yes—
227C22⋊C8—472no—
228C22⋊C8—472no—
229C22⋊C8—472no—
230C22⋊C8—944no—
231C22⋊C8—944no—
232#97—944no—
233C4×C8—472no—
234C4×C8—472no—
235C4×C8—472no—
236C4×C8—944no—
237C4×C8C4×D4711yescharacteristic
238C4×C8C4×D4711yescharacteristic
239C4×C8C22×D4711yescharacteristic
240C4×C8C22×D4711yescharacteristic
241#41—944no—
242C2×Q8—471no—
243C2×D4—472no—
244C2×D4—471no—
245C22×C4—472no—
246C22×C4—472no—
247C22×C4—472no—
248C22×C4C2×C4×D4711yescharacteristic
249C22×C4D4×D4711yescharacteristic
250C22×C4Q8×D4711yescharacteristic
251M16—1884no—
252C2×C8—22no—
253C2×C8—22no—
254C2×C8—22no—
255C2×C8—41no—
256C2×C8—44no—
257C2×C8—472no—
258C2×C8—472no—
259C2×C8—944no—
260C2×C8—944no—
261C2×C8—1882no—
262C2×C8C2×C4×D4711yescharacteristic
263C2×C8C2×C4×D4711yescharacteristic
264C2×C8C2×C4×D4711yescharacteristic
265C2×C8C2×C4×D4711yescharacteristic
266C4⋊C4—472no—
267C4⋊C4—472no—
268C4⋊C4—471no—
269C4⋊C4—471no—
270C22⋊C4—472no—
271C22⋊C4—472no—
272C22⋊C4—472no—
273C42—472no—
274C42—472no—
275C42—472no—
276C42C2×C4×D4711yescharacteristic
277C42D4×D4711yescharacteristic
278C42Q8×D4711yescharacteristic
279C42C23×D4711yescharacteristic
280C23—472no—
281C23C4⋊C4×D4711yescharacteristic
282Q8—942no—
283D4—944no—
284D4—942no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—41no—
288C2×C4—472no—
289C2×C4—472no—
290C2×C4—472no—
291C2×C4—942no—
292C2×C4—942no—
293C2×C4—944no—
294C2×C4—1882no—
295C2×C4C4⋊C4×D4711yescharacteristic
296C2×C4C4⋊C4×D4711yescharacteristic
297C2×C4C4⋊C4×D4711yescharacteristic
298C2×C4#1309404514yes—
299C2×C4C22×C4×D4711yescharacteristic
300C2×C4C2×D4×D4711yescharacteristic
301C2×C4C2×Q8×D4711yescharacteristic
302C8—21no—
303C8—21no—
304C8—21no—
305C8—42no—
306C8—42no—
307C8—942no—
308C8—942no—
309C8—1884no—
310C8#1309403012yes—
311C22—21no—
312C22—21no—
313C22—942no—
314C22—942no—
315C22—942no—
316C22#1568915812yes—
317C22C2×C4⋊C4×D4711yescharacteristic
318C4—21no—
319C4—21no—
320C4—21no—
321C4—942no—
322C4—942no—
323C4—942no—
324C4#1568915812yes—
325C4C2×#1309403011yescharacteristic
326C4#1568988911yescharacteristic
327C4C2×#1309404512yes—
328C2—22no—
329C2—1882no—
330C2#2025195311yescharacteristic
331C2C2×#1568915811yescharacteristic
332C2#2025199611yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC42C23×D47
FittingC2×C47×#334C2
socleC22×C47C22×C4⋊C4
prime radicalC2×#10625350D4
cosocleC42×C47C24
hypercenterC2×#334D47
hypocenterC47#17827
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×#334

Complements

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

NH ≅ G/Ntype
3. #20242165C2semidirect
4. #20242162C2semidirect
5. #20242148C2semidirect
6. #20242144C2semidirect
7. #20242133C2semidirect
8. C2×C47×#334C2semidirect
169. C2×#334D47semidirect
200. C47#17827semidirect

Maximal subgroups

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

subgroupindex
C8×#106253502
#202520532
#202421652
#202421622
#202421482
#202421442
#202421332
C2×C47×#3342
#1782747