Finite Group Databasebeta

← #26125646

Subgroups — #26125646

Order 12032.

714 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 714 conjugacy classes of subgroups — too many to draw. Only its 99 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
1#20241715C212yesmaximal, complemented
2#20241318C212yesmaximal, complemented
3#20241316C212yesmaximal, complemented
4C47×#2308C211yesmaximal, characteristic
5#15689087—22no—
6#15688847—22no—
7#15688847C2214yes—
8C23×D4×C47C411yescharacteristic
9C22×C22⋊C4×C47C411yescharacteristic
10C22×C22⋊C4×C47C2211yescharacteristic
11C47×#386—22no—
12C47×#386—22no—
13C47×#381C411yescharacteristic
14C47×#381C2211yescharacteristic
15C47×#379C411yescharacteristic
16C47×#379C2211yescharacteristic
17C2×#10625329—42no—
18C22⋊(C47⋊C8)—24no—
19C22⋊(C47⋊C8)—42no—
20C25×C47C2×C411yescharacteristic
21C25×C47C2×C411yescharacteristic
22C22×D4×C47—21no—
23C22×D4×C47—21no—
24C22×D4×C47—22no—
25C22×D4×C47—22no—
26C22×D4×C47—41no—
27C22×D4×C47—41no—
28C22×D4×C47—42no—
29C23×C4×C47—21no—
30C23×C4×C47C2×C411yescharacteristic
31C23×C4×C47D412yes—
32C2×C22⋊C4×C47—21no—
33C2×C22⋊C4×C47—22no—
34C2×C22⋊C4×C47—22no—
35C2×C22⋊C4×C47—41no—
36C2×C22⋊C4×C47—41no—
37C2×C22⋊C4×C47—42no—
38C2×C22⋊C4×C47C2×C411yescharacteristic
39C2×C22⋊C4×C47C2×C411yescharacteristic
40C2×C22⋊C4×C47C2×C411yescharacteristic
41C2×C22⋊C4×C47D412yes—
42C2×C22⋊C4×C47C2311yescharacteristic
43#95×C47—22no—
44#95×C47—22no—
45C24×C47—21no—
46C24×C47—21no—
47C24×C47—22no—
48C24×C47—21no—
49C24×C47—21no—
50C24×C47—21no—
51C24×C47—21no—
52C24×C47—41no—
53C24×C47—41no—
54C24×C47—82no—
55C24×C47—82no—
56C24×C47C22⋊C411yescharacteristic
57C24×C47C22⋊C411yescharacteristic
58C24×C47M1612yescomplemented
59C24×C47C22×C411yescharacteristic
60C2×D4×C47—24no—
61C2×D4×C47—24no—
62C2×D4×C47—44no—
63C2×D4×C47—44no—
64C2×D4×C47—42no—
65C2×D4×C47—42no—
66C2×D4×C47—44no—
67C2×D4×C47—44no—
68C2×D4×C47—41no—
69C2×D4×C47—41no—
70C2×D4×C47—42no—
71C22×C4×C47—22no—
72C22×C4×C47—21no—
73C22×C4×C47—21no—
74C22×C4×C47—22no—
75C22×C4×C47—21no—
76C22×C4×C47—21no—
77C22×C4×C47—41no—
78C22×C4×C47—41no—
79C22×C4×C47—42no—
80C22×C4×C47—82no—
81C22×C4×C47—82no—
82C22×C4×C47C22⋊C412yes—
83C22×C4×C47M1612yescomplemented
84C22×C4×C47C2×D412yes—
85C22⋊C4×C47—41no—
86C22⋊C4×C47—42no—
87C22⋊C4×C47—41no—
88C22⋊C4×C47—42no—
89C22⋊C4×C47—41no—
90C22⋊C4×C47—41no—
91C22⋊C4×C47—82no—
92C22⋊C4×C47—82no—
93#10625329—84no—
94C2×C47⋊C8—44no—
95C23×C47—22no—
96C23×C47—22no—
97C23×C47—22no—
98C23×C47—22no—
99C23×C47—21no—
100C23×C47—21no—
101C23×C47—21no—
102C23×C47—21no—
103C23×C47—21no—
104C23×C47—21no—
105C23×C47—22no—
106C23×C47—42no—
107C23×C47—42no—
108C23×C47—42no—
109C23×C47—42no—
110C23×C47—42no—
111C23×C47—42no—
112C23×C47—42no—
113C23×C47—41no—
114C23×C47—41no—
115C23×C47—82no—
116C23×C47—82no—
117C23×C47—82no—
118C23×C47—84no—
119C23×C47—82no—
120C23×C47—82no—
121C23×C47—82no—
122C23×C47—84no—
123C23×C47—84no—
124C23×C47#9911yescharacteristic
125C23×C47#9911yescharacteristic
126C23×C47#10012yes—
127C23×C47C2×C22⋊C411yescharacteristic
128C23×C47C2×M1611yescharacteristic
129C23×C47C2×M1611yescharacteristic
130D4×C47—44no—
131D4×C47—44no—
132D4×C47—48no—
133C2×C4×C47—22no—
134C2×C4×C47—22no—
135C2×C4×C47—22no—
136C2×C4×C47—44no—
137C2×C4×C47—42no—
138C2×C4×C47—41no—
139C2×C4×C47—41no—
140C2×C4×C47—42no—
141C2×C4×C47—42no—
142C2×C4×C47—42no—
143C2×C4×C47—42no—
144C2×C4×C47—42no—
145C2×C4×C47—41no—
146C2×C4×C47—41no—
147C2×C4×C47—82no—
148C2×C4×C47—84no—
149C47⋊C8—84no—
150#11502—471nomaximal, Sylow
151C22×C47—22no—
152C22×C47—22no—
153C22×C47—22no—
154C22×C47—21no—
155C22×C47—21no—
156C22×C47—21no—
157C22×C47—21no—
158C22×C47—22no—
159C22×C47—42no—
160C22×C47—41no—
161C22×C47—41no—
162C22×C47—42no—
163C22×C47—42no—
164C22×C47—42no—
165C22×C47—42no—
166C22×C47—42no—
167C22×C47—42no—
168C22×C47—42no—
169C22×C47—42no—
170C22×C47—42no—
171C22×C47—82no—
172C22×C47—82no—
173C22×C47—82no—
174C22×C47—82no—
175C22×C47—82no—
176C22×C47—84no—
177C22×C47—84no—
178C22×C47—82no—
179C22×C47#40711yescharacteristic
180C22×C47C2×#9911yescharacteristic
181C22×C47C2×#10011yescharacteristic
182C4×C47—42no—
183C4×C47—42no—
184C4×C47—42no—
185C4×C47—81no—
186C4×C47—81no—
187#2308D4711yescharacteristic
188#1462—472no—
189#1317—472no—
190#1316—472no—
191C2×C47—21no—
192C2×C47—21no—
193C2×C47—41no—
194C2×C47—41no—
195C2×C47—42no—
196C2×C47—41no—
197C2×C47—41no—
198C2×C47—82no—
199C2×C47#146211yescharacteristic
200C2×C47#212112yes—
201C23×D4Dic4711yescharacteristic
202C22×C22⋊C4Dic4711yescharacteristic
203C22×C22⋊C4C2×D4711yescharacteristic
204#407—942no—
205#386—22no—
206#386—22no—
207#381Dic4711yescharacteristic
208#381C2×D4711yescharacteristic
209#379Dic4711yescharacteristic
210#379C2×D4711yescharacteristic
211#323—474no—
212#323—942no—
213C47#1150211yescharacteristic, complemented, Sylow
214C25C2×Dic4711yescharacteristic
215C25C2×Dic4711yescharacteristic
216C22×D4—22no—
217C22×D4—21no—
218C22×D4—21no—
219C22×D4—22no—
220C22×D4—41no—
221C22×D4—41no—
222C22×D4—42no—
223C23×C4—21no—
224C23×C4C2×Dic4711yescharacteristic
225C23×C4C22⋊D4712yes—
226C2×M16—1882no—
227C2×C22⋊C4—21no—
228C2×C22⋊C4—22no—
229C2×C22⋊C4—22no—
230C2×C22⋊C4—41no—
231C2×C22⋊C4—41no—
232C2×C22⋊C4—42no—
233C2×C22⋊C4C2×Dic4711yescharacteristic
234C2×C22⋊C4C2×Dic4711yescharacteristic
235C2×C22⋊C4C2×Dic4711yescharacteristic
236C2×C22⋊C4C22⋊D4712yes—
237C2×C22⋊C4C22×D4711yescharacteristic
238C22⋊C8—944no—
239C22⋊C8—1882no—
240#95—22no—
241#95—22no—
242C24—21no—
243C24—21no—
244C24—22no—
245C24—21no—
246C24—21no—
247C24—21no—
248C24—21no—
249C24—41no—
250C24—41no—
251C24—82no—
252C24—82no—
253C24#1062532912yescomplemented
254C24C22⋊Dic4711yescharacteristic
255C24C22⋊Dic4711yescharacteristic
256C24C22×Dic4711yescharacteristic
257C2×D4—24no—
258C2×D4—24no—
259C2×D4—44no—
260C2×D4—44no—
261C2×D4—42no—
262C2×D4—42no—
263C2×D4—44no—
264C2×D4—44no—
265C2×D4—41no—
266C2×D4—41no—
267C2×D4—42no—
268C22×C4—22no—
269C22×C4—21no—
270C22×C4—21no—
271C22×C4—22no—
272C22×C4—21no—
273C22×C4—21no—
274C22×C4—41no—
275C22×C4—41no—
276C22×C4—42no—
277C22×C4—82no—
278C22×C4—82no—
279C22×C4#1062532912yescomplemented
280C22×C4C22⋊Dic4712yes—
281C22×C4C2×C22⋊D4712yes—
282M16—3764no—
283C2×C8—1884no—
284C22⋊C4—41no—
285C22⋊C4—42no—
286C22⋊C4—41no—
287C22⋊C4—42no—
288C22⋊C4—41no—
289C22⋊C4—41no—
290C22⋊C4—82no—
291C22⋊C4—82no—
292C23—22no—
293C23—22no—
294C23—22no—
295C23—22no—
296C23—21no—
297C23—21no—
298C23—21no—
299C23—21no—
300C23—21no—
301C23—21no—
302C23—22no—
303C23—42no—
304C23—42no—
305C23—42no—
306C23—42no—
307C23—42no—
308C23—42no—
309C23—42no—
310C23—41no—
311C23—41no—
312C23—82no—
313C23—82no—
314C23—82no—
315C23—84no—
316C23—82no—
317C23—82no—
318C23—82no—
319C23—84no—
320C23—84no—
321C23#1309393911yescharacteristic
322C23#1309393911yescharacteristic
323C23#1309394112yes—
324C23C2×C22⋊Dic4711yescharacteristic
325C23C2×#1062532911yescharacteristic
326C23C2×#1062532911yescharacteristic
327D4—44no—
328D4—44no—
329D4—48no—
330C2×C4—22no—
331C2×C4—22no—
332C2×C4—22no—
333C2×C4—44no—
334C2×C4—42no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—42no—
338C2×C4—42no—
339C2×C4—42no—
340C2×C4—42no—
341C2×C4—42no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—82no—
345C2×C4—84no—
346C8—3764no—
347C22—22no—
348C22—22no—
349C22—22no—
350C22—21no—
351C22—21no—
352C22—21no—
353C22—21no—
354C22—22no—
355C22—42no—
356C22—41no—
357C22—41no—
358C22—42no—
359C22—42no—
360C22—42no—
361C22—42no—
362C22—42no—
363C22—42no—
364C22—42no—
365C22—42no—
366C22—42no—
367C22—82no—
368C22—82no—
369C22—82no—
370C22—82no—
371C22—82no—
372C22—84no—
373C22—84no—
374C22—82no—
375C22#1568908711yescharacteristic
376C22C2×#1309393911yescharacteristic
377C22C2×#1309394111yescharacteristic
378C4—42no—
379C4—42no—
380C4—42no—
381C4—81no—
382C4—81no—
383C2—21no—
384C2—21no—
385C2—41no—
386C2—41no—
387C2—41no—
388C2—41no—
389C2—42no—
390C2—82no—
391C2#2024171511yescharacteristic
392C2#2024503412yes—
subgroupG/H
centerC22C2×#13093939
commutatorC24×C47C22×C4
FrattiniC2×C22⋊C4C22×D47
FittingC47×#2308C2
socleC22×C47C2×#99
prime radicalC23×D4×C47C4
cosocleC2×C22⋊C4×C47C23
hypercenter#2308D47
hypocenterC47#11502
LCSG ▷ C24×C47 ▷ C22×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C24 ◁ C22×C22⋊C4 ◁ #2308

Complements

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

NH ≅ G/Ntype
1. #20241715C2semidirect
2. #20241318C2semidirect
3. #20241316C2semidirect
58. C24×C47M16semidirect
83. C22×C4×C47M16semidirect
213. C47#11502semidirect
253. C24#10625329semidirect
279. C22×C4#10625329semidirect

Maximal subgroups

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

subgroupindex
#202417152
#202413182
#202413162
C47×#23082
#1150247