Finite Group Databasebeta

← #26107630

Subgroups — #26107630

Order 12032.

810 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 810 conjugacy classes of subgroups — too many to draw. Only its 143 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
1C22×#13094014C211yesmaximal, characteristic
2#20243454C212yesmaximal
3C2×#15688849C211yesmaximal, characteristic
4C2×#15688848C212yesmaximal
5C2×C47×#324C211yesmaximal, characteristic
6C2×#13094014—24no—
7C2×#13094014—24no—
8C2×#13094014—22no—
9C2×#13094014—22no—
10C22×C4⋊Dic47C411yescharacteristic
11C22×Dic47⋊C4C411yescharacteristic
12C22×Dic47⋊C4C411yescharacteristic
13C22×Dic47⋊C4C411yescharacteristic
14C22×Dic47⋊C4C2211yescharacteristic
15C22×C4×Dic47C2211yescharacteristic
16C2×C22⋊(C47⋊C8)C2212yes—
17#15688877—24no—
18#15688849—22no—
19#15688848—24no—
20C22×C4⋊C4×C47C2211yescharacteristic
21C2×C22⋊C8×C47C2212yes—
22C47×#324—22no—
23C23×Dic47C2×C411yescharacteristic
24C23×Dic47C2×C411yescharacteristic
25C23×Dic47C2×C411yescharacteristic
26C23×Dic47C2×C411yescharacteristic
27C22×C47⋊C8—22no—
28#13094014—216no—
29#13094014—216no—
30C2×C4⋊Dic47—22no—
31C2×C4⋊Dic47—22no—
32C2×C4⋊Dic47—22no—
33C2×Dic47⋊C4—22no—
34C2×Dic47⋊C4—22no—
35C2×Dic47⋊C4—22no—
36C2×Dic47⋊C4—22no—
37C2×Dic47⋊C4—21no—
38C2×Dic47⋊C4—21no—
39C2×Dic47⋊C4—22no—
40C2×Dic47⋊C4—22no—
41C2×Dic47⋊C4—22no—
42C2×Dic47⋊C4—22no—
43C2×Dic47⋊C4—22no—
44C2×Dic47⋊C4—22no—
45C2×Dic47⋊C4D414yes—
46C2×C4×Dic47—21no—
47C2×C4×Dic47—22no—
48C2×C4×Dic47—21no—
49C2×C4×Dic47D414yes—
50C22⋊(C47⋊C8)—22no—
51C22⋊(C47⋊C8)—22no—
52C23×C4×C47C2×C411yescharacteristic
53C23×C4×C47C2×C411yescharacteristic
54C23×C4×C47C2311yescharacteristic
55C22×C8×C47—22no—
56C2×C4⋊C4×C47—22no—
57C2×C4⋊C4×C47—22no—
58C2×C4⋊C4×C47D412yes—
59C2×C4⋊C4×C47D412yes—
60C22⋊C8×C47—22no—
61C22⋊C8×C47—22no—
62C24×C47C22×C411yescharacteristic
63C22×C4×C47—21no—
64C22×C4×C47—21no—
65C22×C4×C47—21no—
66C22×C4×C47—21no—
67C22×C4×C47—22no—
68C22×C4×C47—22no—
69C22×C4×C47—42no—
70C22×C4×C47—42no—
71C22×C4×C47C22⋊C412yes—
72C22×C4×C47C22⋊C412yes—
73C22×C4×C47C2×D412yes—
74C22×C4×C47C2×D411yescharacteristic
75C22×C4×C47C2×D412yes—
76C22×C4×C47C2×D411yescharacteristic
77C22×Dic47—21no—
78C22×Dic47—21no—
79C22×Dic47—24no—
80C22×Dic47—21no—
81C22×Dic47—21no—
82C22×Dic47—21no—
83C22×Dic47—21no—
84C22×Dic47—21no—
85C22×Dic47—21no—
86C22×Dic47—22no—
87C22×Dic47—22no—
88C22×Dic47—22no—
89C22×Dic47—22no—
90C22×Dic47—42no—
91C22×Dic47C22⋊C412yes—
92C22×Dic47C22⋊C412yes—
93C22×Dic47C22⋊C412yes—
94C22×Dic47C22⋊C412yes—
95C2×C8×C47—44no—
96C2×C8×C47—42no—
97C4⋊C4×C47—24no—
98C4⋊C4×C47—24no—
99C4⋊Dic47—28no—
100Dic47⋊C4—28no—
101Dic47⋊C4—28no—
102Dic47⋊C4—28no—
103Dic47⋊C4—24no—
104Dic47⋊C4—24no—
105C4×Dic47—24no—
106C4×Dic47—24no—
107C2×C47⋊C8—44no—
108C2×C47⋊C8—42no—
109C23×C47—22no—
110C23×C47—22no—
111C23×C47C2×C22⋊C411yescharacteristic
112C23×C47C2×C22⋊C411yescharacteristic
113C23×C47C2×C22⋊C411yescharacteristic
114C23×C47#13112yes—
115C23×C47#13112yes—
116C2×C4×C47—24no—
117C2×C4×C47—22no—
118C2×C4×C47—22no—
119C2×C4×C47—22no—
120C2×C4×C47—22no—
121C2×C4×C47—41no—
122C2×C4×C47—42no—
123C2×C4×C47—41no—
124C2×C4×C47—42no—
125C2×C4×C47—42no—
126C2×C4×C47—42no—
127C2×C4×C47—42no—
128C2×C4×C47—42no—
129C2×C4×C47#12012yes—
130C2×C4×C47#12012yes—
131C2×Dic47—24no—
132C2×Dic47—24no—
133C2×Dic47—22no—
134C2×Dic47—22no—
135C2×Dic47—22no—
136C2×Dic47—22no—
137C2×Dic47—22no—
138C2×Dic47—24no—
139C2×Dic47—24no—
140C2×Dic47—42no—
141C2×Dic47—42no—
142C2×Dic47—42no—
143C2×Dic47—41no—
144C2×Dic47—41no—
145C2×Dic47—41no—
146C2×Dic47—41no—
147C2×Dic47—42no—
148C2×Dic47—42no—
149C2×Dic47#10114yes—
150C8×C47—82no—
151C47⋊C8—82no—
152#8306—471nomaximal, Sylow
153C22×C47—24no—
154C22×C47—24no—
155C22×C47—21no—
156C22×C47—21no—
157C22×C47—21no—
158C22×C47—21no—
159C22×C47#37911yescharacteristic
160C22×C47#40812yes—
161C22×C47#40812yes—
162C22×C47#40811yescharacteristic
163C22×C47#40811yescharacteristic
164C22×C47#41012yes—
165C22×C47C2×#10112yes—
166C4×C47—22no—
167C4×C47—22no—
168C4×C47—42no—
169C4×C47—42no—
170Dic47—24no—
171Dic47—42no—
172Dic47—42no—
173Dic47—42no—
174C22×#125—471no—
175#1817—472no—
176C2×#324—472no—
177C2×#324—471no—
178C2×#324D4711yescharacteristic
179C2×C47—22no—
180C2×C47—21no—
181C2×C47—21no—
182C2×C47#147014yes—
183C2×C47#178011yescharacteristic
184C2×C47#178211yescharacteristic
185C2×C47#178411yescharacteristic
186C2×#125—944no—
187C2×#125—944no—
188C2×#125—942no—
189C2×#125—942no—
190C22×C4⋊C4—471no—
191C22×C4⋊C4—471no—
192C22×C4⋊C4—471no—
193C22×C4⋊C4—471no—
194C22×C4⋊C4—471no—
195C22×C4⋊C4C2×D4711yescharacteristic
196C22×C42—471no—
197C2×C22⋊C8—472no—
198C2×C22⋊C8C2×D4712yes—
199#336—944no—
200#324—22no—
201#324—944no—
202#324—942no—
203C47#830611yescharacteristic, complemented, Sylow
204C23×C4—471no—
205C23×C4—471no—
206C23×C4—471no—
207C23×C4—471no—
208C23×C4C4×D4711yescharacteristic
209C23×C4C4×D4711yescharacteristic
210C23×C4C22×D4711yescharacteristic
211C22×C8—22no—
212C22×C8—942no—
213#125—9416no—
214#125—9416no—
215C2×C4⋊C4—22no—
216C2×C4⋊C4—22no—
217C2×C4⋊C4—474no—
218C2×C4⋊C4—942no—
219C2×C4⋊C4—942no—
220C2×C4⋊C4—942no—
221C2×C4⋊C4—942no—
222C2×C4⋊C4—942no—
223C2×C4⋊C4—942no—
224C2×C4⋊C4—942no—
225C2×C4⋊C4—942no—
226C2×C4⋊C4—942no—
227C2×C4⋊C4—942no—
228C2×C4⋊C4—942no—
229C2×C4⋊C4—942no—
230C2×C4⋊C4—941no—
231C2×C4⋊C4—942no—
232C2×C4⋊C4—941no—
233C2×C4⋊C4D18812yes—
234C2×C4⋊C4C22⋊D4712yes—
235C2×C42—474no—
236C2×C42—941no—
237C2×C42—942no—
238C2×C42—941no—
239C22⋊C8—22no—
240C22⋊C8—22no—
241C22⋊C8—942no—
242C22⋊C8—942no—
243C24C2×C4×D4711yescharacteristic
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—22no—
249C22×C4—22no—
250C22×C4—42no—
251C22×C4—42no—
252C22×C4—472no—
253C22×C4—472no—
254C22×C4—472no—
255C22×C4—472no—
256C22×C4—944no—
257C22×C4—941no—
258C22×C4—941no—
259C22×C4—941no—
260C22×C4—941no—
261C22×C4—941no—
262C22×C4—941no—
263C22×C4—941no—
264C22×C4—941no—
265C22×C4—942no—
266C22×C4—942no—
267C22×C4—942no—
268C22×C4—942no—
269C22×C4—1882no—
270C22×C4(C2×D47)⋊C412yes—
271C22×C4(C2×D47)⋊C412yes—
272C22×C4C2×D18811yescharacteristic
273C22×C4D4×D4712yes—
274C22×C4D4×D4712yes—
275C22×C4C2×C22⋊D4711yescharacteristic
276C2×C8—44no—
277C2×C8—42no—
278C2×C8—1884no—
279C2×C8—1882no—
280C4⋊C4—24no—
281C4⋊C4—24no—
282C4⋊C4—948no—
283C4⋊C4—948no—
284C4⋊C4—948no—
285C4⋊C4—948no—
286C4⋊C4—944no—
287C4⋊C4—944no—
288C42—944no—
289C42—944no—
290C23—22no—
291C23—22no—
292C23C22⋊C4×D4711yescharacteristic
293C23C22⋊C4×D4711yescharacteristic
294C23C2×(C2×D47)⋊C411yescharacteristic
295C23#1309403012yes—
296C23#1309403212yes—
297C2×C4—24no—
298C2×C4—22no—
299C2×C4—22no—
300C2×C4—22no—
301C2×C4—22no—
302C2×C4—41no—
303C2×C4—42no—
304C2×C4—41no—
305C2×C4—42no—
306C2×C4—42no—
307C2×C4—42no—
308C2×C4—42no—
309C2×C4—42no—
310C2×C4—474no—
311C2×C4—944no—
312C2×C4—944no—
313C2×C4—942no—
314C2×C4—942no—
315C2×C4—942no—
316C2×C4—942no—
317C2×C4—942no—
318C2×C4—944no—
319C2×C4—944no—
320C2×C4—1882no—
321C2×C4—1882no—
322C2×C4—1882no—
323C2×C4—1881no—
324C2×C4—1881no—
325C2×C4—1881no—
326C2×C4—1881no—
327C2×C4—1882no—
328C2×C4—1882no—
329C2×C4#1309399212yes—
330C2×C4#1309399412yes—
331C8—82no—
332C8—3762no—
333C22—24no—
334C22—24no—
335C22—21no—
336C22—21no—
337C22—21no—
338C22—21no—
339C22#1568897811yescharacteristic
340C22#1568908812yes—
341C22#1568908812yes—
342C22#1568908911yescharacteristic
343C22#1568909111yescharacteristic
344C22#1568909512yes—
345C22#101×D4712yes—
346C4—22no—
347C4—22no—
348C4—42no—
349C4—42no—
350C4—944no—
351C4—1882no—
352C4—1882no—
353C4—1882no—
354C2—22no—
355C2—21no—
356C2—21no—
357C2#2024174214yes—
358C2#2024329911yescharacteristic
359C2#2024330411yescharacteristic
360C2#2024331011yescharacteristic
subgroupG/H
centerC23C22⋊C4×D47
commutator, prime radicalC24×C47C22×C4
FrattiniC23×C4C22×D47
FittingC2×C47×#324C2
socleC23×C47C2×C22⋊C4
cosocleC23×C4×C47C23
hypercenterC2×#324D47
hypocenterC47#8306
LCSG ▷ C24×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#324

Complements

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

NH ≅ G/Ntype
203. C47#8306semidirect

Maximal subgroups

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

subgroupindex
C22×#130940142
#202434542
C2×#156888492
C2×#156888482
C2×C47×#3242
#830647