Finite Group Databasebeta

← #26111698

Subgroups — #26111698

Order 12032.

480 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20252469C211yesmaximal, characteristic
2#20241783C211yesmaximal, characteristic
3#20241783C211yesmaximal, characteristic
4#20241712C211yesmaximal, characteristic
5#20241233C211yesmaximal, characteristic
6#20241219C211yesmaximal, characteristic
7C2×C47×#441C211yesmaximal, characteristic
8Q8×C47⋊C8—22no—
9Q8×C47⋊C8—22no—
10#15689176—22no—
11#15689176C2211yescharacteristic
12#15689176C2211yescharacteristic
13#15689176C2211yescharacteristic
14#15689176C2211yescharacteristic
15Q8⋊(C47⋊C8)—22no—
16Q8⋊(C47⋊C8)—22no—
17#15688849—22no—
18C22×Q16×C47C411yescharacteristic
19C2×C4×Q8×C47C2211yescharacteristic
20C2×C4×Q8×C47C2211yescharacteristic
21C47×#441—22no—
22C47×#441—22no—
23C2×#106×C47C411yescharacteristic
24C2×#103×C47C411yescharacteristic
25C2×#103×C47C411yescharacteristic
26C2×#97×C47C2211yescharacteristic
27C4⋊(C47⋊C8)—24no—
28C4⋊(C47⋊C8)—21no—
29C4⋊(C47⋊C8)—21no—
30C4⋊(C47⋊C8)—21no—
31C4⋊(C47⋊C8)—21no—
32C22⋊(C47⋊C8)—21no—
33C22⋊(C47⋊C8)—21no—
34C22⋊(C47⋊C8)—21no—
35C22⋊(C47⋊C8)D412yes—
36C4×C47⋊C8—24no—
37C4×C47⋊C8—21no—
38C4×C47⋊C8—21no—
39C4×C47⋊C8—21no—
40C4×C47⋊C8D412yes—
41C22×Q8×C47C2×C411yescharacteristic
42C22×Q8×C47C2×C411yescharacteristic
43C2×Q16×C47—22no—
44C2×Q16×C47—22no—
45C2×Q16×C47C814yescomplemented
46C22×C8×C47C2×C411yescharacteristic
47C22×C8×C47C2×C411yescharacteristic
48C4×Q8×C47—21no—
49C4×Q8×C47—21no—
50C4×Q8×C47—21no—
51C4×Q8×C47—21no—
52C4×Q8×C47—21no—
53C4×Q8×C47—21no—
54C4×Q8×C47D412yes—
55C4×Q8×C47D412yes—
56C2×C4⋊C4×C47—21no—
57C2×C4⋊C4×C47—21no—
58C2×C4⋊C4×C47C2×C411yescharacteristic
59C2×C4⋊C4×C47C2×C411yescharacteristic
60C2×C42×C47—21no—
61C2×C42×C47—21no—
62C2×C42×C47C2311yescharacteristic
63#106×C47—22no—
64#103×C47—22no—
65#103×C47—22no—
66#97×C47—21no—
67#97×C47—21no—
68C2×Q8×C47—21no—
69C2×Q8×C47—21no—
70C2×Q8×C47—21no—
71C2×Q8×C47—21no—
72C2×Q8×C47—21no—
73C2×Q8×C47—21no—
74C2×Q8×C47—21no—
75C2×Q8×C47—21no—
76C2×Q8×C47C22⋊C412yes—
77C2×Q8×C47C2×C812yes—
78C2×Q8×C47C2×C812yes—
79C2×Q8×C47M1612yes—
80C22×C4×C47—21no—
81C22×C4×C47—21no—
82C22×C4×C47—21no—
83C22×C4×C47—21no—
84C22×C4×C47C22×C411yescharacteristic
85C22×C4×C47C2×D411yescharacteristic
86C22×C4×C47#4111yescharacteristic
87Q16×C47—28no—
88C2×C8×C47—21no—
89C2×C8×C47—21no—
90C2×C8×C47—21no—
91C2×C8×C47—21no—
92C2×C8×C47—21no—
93C2×C8×C47C2×C812yes—
94C4⋊C4×C47—21no—
95C4⋊C4×C47—22no—
96C4⋊C4×C47—22no—
97C4⋊C4×C47—21no—
98C4⋊C4×C47—21no—
99C4⋊C4×C47—41no—
100C4⋊C4×C47—41no—
101C4⋊C4×C47C22⋊C412yes—
102C42×C47—22no—
103C42×C47—22no—
104C42×C47—41no—
105C42×C47—41no—
106C42×C47C2×D411yescharacteristic
107C42×C47C2×D411yescharacteristic
108C42×C47C2×D411yescharacteristic
109C42×C47#4111yescharacteristic
110C2×C47⋊C8—22no—
111C2×C47⋊C8—22no—
112C2×C47⋊C8—41no—
113C2×C47⋊C8—41no—
114C23×C47C4×D411yescharacteristic
115Q8×C47—22no—
116Q8×C47—22no—
117Q8×C47—22no—
118Q8×C47—22no—
119Q8×C47—22no—
120Q8×C47—41no—
121Q8×C47—41no—
122Q8×C47C22⋊C814yes—
123C2×C4×C47—22no—
124C2×C4×C47—22no—
125C2×C4×C47—22no—
126C2×C4×C47—22no—
127C2×C4×C47—22no—
128C2×C4×C47—41no—
129C2×C4×C47—41no—
130C2×C4×C47—41no—
131C2×C4×C47—41no—
132C2×C4×C47—41no—
133C2×C4×C47—81no—
134C2×C4×C47—81no—
135C2×C4×C47C2×C22⋊C411yescharacteristic
136C2×C4×C47C4×D411yescharacteristic
137C2×C4×C47#12011yescharacteristic
138C2×C4×C47#12111yescharacteristic
139C2×C4×C47#12111yescharacteristic
140C2×C4×C47#12311yescharacteristic
141C2×C4×C47C22×C811yescharacteristic
142C2×C4×C47C2×M1611yescharacteristic
143C2×C4×C47#13111yescharacteristic
144C2×C4×C47#13111yescharacteristic
145C8×C47—22no—
146C8×C47—41no—
147C47⋊C8—42no—
148C47⋊C8—42no—
149C47⋊C8—81no—
150C47⋊C8—81no—
151#9088—471nomaximal, Sylow
152C22×C47—21no—
153C22×C47—21no—
154C22×C47#38611yescharacteristic
155C22×C47C8×D411yescharacteristic
156C22×C47#43511yescharacteristic
157C4×C47—24no—
158C4×C47—21no—
159C4×C47—21no—
160C4×C47—21no—
161C4×C47—21no—
162C4×C47—42no—
163C4×C47—42no—
164C4×C47—81no—
165C4×C47C2×C22⋊C811yescharacteristic
166C4×C47#40811yescharacteristic
167C4×C47C8×D411yescharacteristic
168C4×C47#43511yescharacteristic
169#2982—471no—
170C2×#441D4711yescharacteristic
171#1479—471no—
172#1479—471no—
173#1461—471no—
174#1281—471no—
175#1275—471no—
176C2×C47—21no—
177C2×C47—21no—
178C2×C47#186911yescharacteristic
179C2×C47#190211yescharacteristic
180C2×C47#190511yescharacteristic
181C22×Q16Dic4711yescharacteristic
182C2×C4×Q8C2×D4711yescharacteristic
183C2×C4×Q8C2×D4711yescharacteristic
184C8×Q8—942no—
185C8×Q8—942no—
186#441—22no—
187#441—22no—
188#431—471no—
189#431—471no—
190#431—471no—
191#431—471no—
192#431—942no—
193C2×#106Dic4711yescharacteristic
194C2×#103Dic4711yescharacteristic
195C2×#103Dic4711yescharacteristic
196C2×#97C2×D4711yescharacteristic
197Q8⋊C8—942no—
198Q8⋊C8—942no—
199#324—942no—
200C47#908811yescharacteristic, complemented, Sylow
201C22×Q8C2×Dic4711yescharacteristic
202C22×Q8C2×Dic4711yescharacteristic
203C2×Q16—22no—
204C2×Q16—22no—
205C2×Q16C47⋊C814yescomplemented
206C22×C8C2×Dic4711yescharacteristic
207C22×C8C2×Dic4711yescharacteristic
208C4×Q8—21no—
209C4×Q8—21no—
210C4×Q8—21no—
211C4×Q8—21no—
212C4×Q8—21no—
213C4×Q8—21no—
214C4×Q8C22⋊D4712yes—
215C4×Q8C22⋊D4712yes—
216C2×C4⋊C4—21no—
217C2×C4⋊C4—21no—
218C2×C4⋊C4C2×Dic4711yescharacteristic
219C2×C4⋊C4C2×Dic4711yescharacteristic
220C2×C42—21no—
221C2×C42—21no—
222C2×C42C22×D4711yescharacteristic
223#106—22no—
224C4⋊C8—944no—
225C4⋊C8—941no—
226C4⋊C8—941no—
227C4⋊C8—941no—
228C4⋊C8—941no—
229#103—22no—
230#103—22no—
231C22⋊C8—472no—
232C22⋊C8—941no—
233C22⋊C8—941no—
234C22⋊C8—941no—
235#97—21no—
236#97—21no—
237C4×C8—472no—
238C4×C8—944no—
239C4×C8—941no—
240C4×C8—941no—
241C4×C8—941no—
242C2×Q8—21no—
243C2×Q8—21no—
244C2×Q8—21no—
245C2×Q8—21no—
246C2×Q8—21no—
247C2×Q8—21no—
248C2×Q8—21no—
249C2×Q8—21no—
250C2×Q8C2×C47⋊C812yes—
251C2×Q8C2×C47⋊C812yes—
252C2×Q8#1062532912yes—
253C2×Q8C22⋊Dic4712yes—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4D4×D4711yescharacteristic
259C22×C4#1062535211yescharacteristic
260C22×C4C22×Dic4711yescharacteristic
261Q16—28no—
262C2×C8—21no—
263C2×C8—21no—
264C2×C8—21no—
265C2×C8—21no—
266C2×C8—21no—
267C2×C8—942no—
268C2×C8—942no—
269C2×C8—1881no—
270C2×C8—1881no—
271C2×C8C2×C47⋊C812yes—
272C4⋊C4—21no—
273C4⋊C4—22no—
274C4⋊C4—22no—
275C4⋊C4—21no—
276C4⋊C4—21no—
277C4⋊C4—41no—
278C4⋊C4—41no—
279C4⋊C4C22⋊Dic4712yes—
280C42—22no—
281C42—22no—
282C42—41no—
283C42—41no—
284C42D4×D4711yescharacteristic
285C42#1062535211yescharacteristic
286C42C2×C22⋊D4711yescharacteristic
287C42C2×C22⋊D4711yescharacteristic
288C23D4×Dic4711yescharacteristic
289Q8—22no—
290Q8—22no—
291Q8—22no—
292Q8—22no—
293Q8—22no—
294Q8—41no—
295Q8—41no—
296Q8C22⋊(C47⋊C8)14yes—
297C2×C4—22no—
298C2×C4—22no—
299C2×C4—22no—
300C2×C4—22no—
301C2×C4—22no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—81no—
308C2×C4—81no—
309C2×C4C2×C22⋊Dic4711yescharacteristic
310C2×C4D4×Dic4711yescharacteristic
311C2×C4#1309399211yescharacteristic
312C2×C4#1309399611yescharacteristic
313C2×C4#1309399611yescharacteristic
314C2×C4#1309400511yescharacteristic
315C2×C4C22×C47⋊C811yescharacteristic
316C2×C4C2×#1062532911yescharacteristic
317C2×C4#1309403111yescharacteristic
318C2×C4#1309403111yescharacteristic
319C8—22no—
320C8—41no—
321C8—3761no—
322C8—3761no—
323C8—1882no—
324C8—1882no—
325C22—21no—
326C22—21no—
327C22#1568900311yescharacteristic
328C22D4×C47⋊C811yescharacteristic
329C22#1568919511yescharacteristic
330C4—21no—
331C4—21no—
332C4—21no—
333C4—21no—
334C4—24no—
335C4—42no—
336C4—42no—
337C4—81no—
338C4C2×C22⋊(C47⋊C8)11yescharacteristic
339C4#1568909011yescharacteristic
340C4D4×C47⋊C811yescharacteristic
341C4#1568919511yescharacteristic
342C2—21no—
343C2—21no—
344C2#2024368111yescharacteristic
345C2#2024386311yescharacteristic
346C2#2024388411yescharacteristic
subgroupG/H
centerC22#15689003
commutatorC2×C4×C47C22×C8
FrattiniC2×C42C22×D47
FittingC2×C47×#441C2
socleC22×C47#386
prime radicalC23×C47C4×D4
cosocleC2×C42×C47C23
hypercenterC2×#441D47
hypocenterC47#9088
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#441

Complements

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

NH ≅ G/Ntype
45. C2×Q16×C47C8semidirect
200. C47#9088semidirect
205. C2×Q16C47⋊C8semidirect

Maximal subgroups

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

subgroupindex
#202524692
#202417832
#202417122
#202412332
#202412192
C2×C47×#4412
#908847