Finite Group Databasebeta

← #26112048

Subgroups — #26112048

Order 12032.

902 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 902 conjugacy classes of subgroups — too many to draw. Only its 139 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#20251675C211yesmaximal, characteristic
2#20243298C211yesmaximal, characteristic
3C2×#15688859C212yesmaximal, complemented
4#20241267C212yesmaximal, complemented
5C2×C47×#381C211yesmaximal, characteristic
6C2×#13094003C412yescomplemented
7C2×#13094003C2211yescharacteristic
8C2×C22⋊(C47⋊C8)—22no—
9C2×C22⋊(C47⋊C8)C2212yes—
10#15688996—22no—
11#15688996—21no—
12#15688983C412yescomplemented
13#15688983C2211yescharacteristic
14#15688979—21no—
15#15688859—24no—
16C24×C4×C47C2211yescharacteristic
17C22×C22⋊C4×C47—21no—
18C47×#381—24no—
19C2×#95×C47—21no—
20C2×#95×C47C2212yes—
21C22×Dic94C2×C411yescharacteristic
22C22×C47⋊C8—22no—
23#13094003—22no—
24#13094003—22no—
25#13094003—44no—
26C2×C4⋊Dic47C2×C411yescharacteristic
27C2×C4⋊Dic47C2×C412yes—
28C2×Dic47⋊C4—22no—
29C2×Dic47⋊C4—21no—
30C2×C22⋊Dic47—22no—
31C2×C22⋊Dic47—22no—
32C2×C22⋊Dic47—21no—
33C2×C22⋊Dic47—21no—
34C22⋊(C47⋊C8)—22no—
35C22⋊(C47⋊C8)—22no—
36C22⋊(C47⋊C8)—44no—
37C47⋊#95—22no—
38C47⋊#95—21no—
39C25×C47D411yescharacteristic
40C23×C4×C47—22no—
41C23×C4×C47—22no—
42C23×C4×C47—22no—
43C23×C4×C47—44no—
44C23×C4×C47C2×C412yes—
45C23×C4×C47D412yes—
46C23×C4×C47D411yescharacteristic
47C23×C4×C47C2311yescharacteristic
48C2×C22⋊C4×C47—24no—
49C2×C22⋊C4×C47—44no—
50#95×C47—24no—
51#95×C47—22no—
52#95×C47D414yes—
53C24×C47—24no—
54C24×C47—21no—
55C24×C47—21no—
56C24×C47—22no—
57C24×C47—22no—
58C24×C47—42no—
59C24×C47C22⋊C412yes—
60C24×C47C2×D411yescharacteristic
61C22×C4×C47—24no—
62C22×C4×C47—24no—
63C22×C4×C47—21no—
64C22×C4×C47—21no—
65C22×C4×C47—24no—
66C22×C4×C47—24no—
67C22×C4×C47—24no—
68C22×C4×C47—42no—
69C22×C4×C47—42no—
70C22×C4×C47—42no—
71C22×C4×C47—42no—
72C22×C4×C47—48no—
73C22×C4×C47—48no—
74C22×C4×C47—44no—
75C22×C4×C47—44no—
76C22×C4×C47—42no—
77C22×C4×C47—42no—
78C22×C4×C47C22⋊C412yes—
79C22×C4×C47C22×C411yescharacteristic
80C22×C4×C47C2×D411yescharacteristic
81C22×C4×C47C2×D412yes—
82C22×C4×C47#4112yes—
83C22×Dic47—21no—
84C22×Dic47—22no—
85C22×Dic47—21no—
86C2×Dic94—22no—
87C2×Dic94—42no—
88C22⋊C4×C47—48no—
89C22⋊Dic47—44no—
90C22⋊Dic47—44no—
91C22⋊Dic47—41no—
92C22⋊Dic47—41no—
93C22⋊Dic47—42no—
94C4⋊Dic47—22no—
95C4⋊Dic47—42no—
96Dic47⋊C4—44no—
97Dic47⋊C4—42no—
98C2×C47⋊C8—44no—
99C2×C47⋊C8—42no—
100C23×C47—22no—
101C23×C47—22no—
102C23×C47—24no—
103C23×C47—24no—
104C23×C47—22no—
105C23×C47—22no—
106C23×C47—22no—
107C23×C47—22no—
108C23×C47—22no—
109C23×C47—22no—
110C23×C47—48no—
111C23×C47—48no—
112C23×C47—42no—
113C23×C47—42no—
114C23×C47—42no—
115C23×C47—42no—
116C23×C47#9914yes—
117C23×C47C2×C22⋊C411yescharacteristic
118C23×C47#12011yescharacteristic
119C23×C47#12311yescharacteristic
120C23×C47#13512yes—
121C23×C47#13712yes—
122C2×C4×C47—22no—
123C2×C4×C47—22no—
124C2×C4×C47—22no—
125C2×C4×C47—22no—
126C2×C4×C47—22no—
127C2×C4×C47—42no—
128C2×C4×C47—42no—
129C2×C4×C47—48no—
130C2×C4×C47—48no—
131C2×C4×C47—42no—
132C2×C4×C47—42no—
133C2×C4×C47—44no—
134C2×C4×C47—44no—
135C2×C4×C47—44no—
136C2×C4×C47—84no—
137C2×C4×C47—84no—
138C2×C4×C47C4×D412yes—
139C2×C4×C47#12112yes—
140C2×Dic47—41no—
141C2×Dic47—41no—
142C2×Dic47—42no—
143C2×Dic47—42no—
144C2×Dic47—42no—
145C2×Dic47—42no—
146C2×Dic47—42no—
147Dic94—82no—
148C47⋊C8—82no—
149#9154—471nomaximal, Sylow
150C22×C47—21no—
151C22×C47—21no—
152C22×C47—21no—
153C22×C47—21no—
154C22×C47—24no—
155C22×C47—24no—
156C22×C47—24no—
157C22×C47—24no—
158C22×C47—24no—
159C22×C47—48no—
160C22×C47—48no—
161C22×C47—42no—
162C22×C47—42no—
163C22×C47—42no—
164C22×C47—42no—
165C22×C47#38611yescharacteristic
166C22×C47C2×#9912yes—
167C22×C47#41611yescharacteristic
168C22×C47#41911yescharacteristic
169C22×C47#42112yes—
170C22×C47#45212yes—
171C22×C47#48512yes—
172C4×C47—22no—
173C4×C47—22no—
174C4×C47—42no—
175C4×C47—84no—
176Dic47—81no—
177Dic47—81no—
178Dic47—82no—
179#2848—471no—
180C2×#381D4711yescharacteristic
181#1779—471no—
182C2×#328—472no—
183#1294—472no—
184C2×C47—22no—
185C2×C47—22no—
186C2×C47—44no—
187C2×C47#151112yes—
188C2×C47#151612yes—
189C2×C47#187311yescharacteristic
190C2×C47#189711yescharacteristic
191C2×C47#189811yescharacteristic
192C24×C4C2×D4711yescharacteristic
193C2×C22⋊Q8—471no—
194C2×C22⋊Q8—472no—
195C22×C22⋊C4—21no—
196C2×C22⋊C8—472no—
197C2×C22⋊C8—942no—
198#385—942no—
199#385—941no—
200#381—24no—
201#380—472no—
202#380—471no—
203#379—941no—
204C2×#95—21no—
205C2×#95C2×D4712yes—
206#328—944no—
207C47#915411yescharacteristic, complemented, Sylow
208C25C22⋊D4711yescharacteristic
209C22×Q8—471no—
210C23×C4—22no—
211C23×C4—22no—
212C23×C4—22no—
213C23×C4—44no—
214C23×C4C4×D4712yes—
215C23×C4D18812yes—
216C23×C4C22⋊D4711yescharacteristic
217C23×C4C22×D4711yescharacteristic
218C22×C8—942no—
219C22⋊Q8—942no—
220C22⋊Q8—942no—
221C22⋊Q8—1884no—
222C2×C4⋊C4—471no—
223C2×C4⋊C4—472no—
224C2×C4⋊C4—942no—
225C2×C4⋊C4—941no—
226C2×C22⋊C4—24no—
227C2×C22⋊C4—44no—
228C2×C22⋊C4—942no—
229C2×C22⋊C4—942no—
230C2×C22⋊C4—941no—
231C2×C22⋊C4—941no—
232C22⋊C8—942no—
233C22⋊C8—942no—
234C22⋊C8—1884no—
235#95—24no—
236#95—22no—
237#95—942no—
238#95—941no—
239#95C22⋊D4714yes—
240C24—24no—
241C24—21no—
242C24—21no—
243C24—22no—
244C24—22no—
245C24—42no—
246C24(C2×D47)⋊C412yes—
247C24C2×C22⋊D4711yescharacteristic
248C2×Q8—942no—
249C2×Q8—1882no—
250C22×C4—24no—
251C22×C4—24no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—24no—
255C22×C4—24no—
256C22×C4—24no—
257C22×C4—42no—
258C22×C4—42no—
259C22×C4—42no—
260C22×C4—42no—
261C22×C4—48no—
262C22×C4—48no—
263C22×C4—44no—
264C22×C4—44no—
265C22×C4—42no—
266C22×C4—42no—
267C22×C4—941no—
268C22×C4—942no—
269C22×C4—941no—
270C22×C4(C2×D47)⋊C412yes—
271C22×C4C2×C4×D4711yescharacteristic
272C22×C4C2×D18811yescharacteristic
273C22×C4#1062535012yes—
274C22×C4C2×C22⋊D4712yes—
275C2×C8—1884no—
276C2×C8—1882no—
277C4⋊C4—942no—
278C4⋊C4—1882no—
279C4⋊C4—1884no—
280C4⋊C4—1882no—
281C22⋊C4—48no—
282C22⋊C4—1884no—
283C22⋊C4—1884no—
284C22⋊C4—1881no—
285C22⋊C4—1881no—
286C22⋊C4—1882no—
287C23—22no—
288C23—22no—
289C23—24no—
290C23—24no—
291C23—22no—
292C23—22no—
293C23—22no—
294C23—22no—
295C23—22no—
296C23—22no—
297C23—48no—
298C23—48no—
299C23—42no—
300C23—42no—
301C23—42no—
302C23—42no—
303C23#1309393814yes—
304C23C2×(C2×D47)⋊C411yescharacteristic
305C23#1309399311yescharacteristic
306C23#1309400711yescharacteristic
307C23#1309404412yes—
308C23#1309405412yes—
309Q8—3762no—
310C2×C4—22no—
311C2×C4—22no—
312C2×C4—22no—
313C2×C4—22no—
314C2×C4—22no—
315C2×C4—42no—
316C2×C4—42no—
317C2×C4—48no—
318C2×C4—48no—
319C2×C4—42no—
320C2×C4—42no—
321C2×C4—44no—
322C2×C4—44no—
323C2×C4—44no—
324C2×C4—84no—
325C2×C4—84no—
326C2×C4—1881no—
327C2×C4—1881no—
328C2×C4—1882no—
329C2×C4—1882no—
330C2×C4—1882no—
331C2×C4—1882no—
332C2×C4—1882no—
333C2×C4C4×C22⋊D4712yes—
334C2×C4#1309399812yes—
335C8—3762no—
336C22—24no—
337C22—24no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—24no—
343C22—24no—
344C22—24no—
345C22—48no—
346C22—48no—
347C22—42no—
348C22—42no—
349C22—42no—
350C22—42no—
351C22#1568900211yescharacteristic
352C22C2×#1309393812yes—
353C22#1568911711yescharacteristic
354C22#1568913111yescharacteristic
355C22#1568914112yes—
356C22#1568928512yes—
357C22#1568946412yes—
358C4—22no—
359C4—22no—
360C4—42no—
361C4—84no—
362C4—3762no—
363C4—3761no—
364C4—3761no—
365C2—22no—
366C2—22no—
367C2—44no—
368C2#2024192012yes—
369C2#2024194212yes—
370C2#2024370011yescharacteristic
371C2#2024383611yescharacteristic
372C2#2024384111yescharacteristic
subgroupG/H
centerC23C2×(C2×D47)⋊C4
commutatorC22×C4×C47C22×C4
FrattiniC23×C4C22×D47
FittingC2×C47×#381C2
socleC23×C47C2×C22⋊C4
prime radicalC25×C47D4
cosocleC23×C4×C47C23
hypercenterC2×#381D47
hypocenterC47#9154
LCSG ▷ C22×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C24×C4 ◁ C2×#381

Complements

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

NH ≅ G/Ntype
3. C2×#15688859C2semidirect
4. #20241267C2semidirect
6. C2×#13094003C4semidirect
12. #15688983C4semidirect
207. C47#9154semidirect

Maximal subgroups

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

subgroupindex
#202516752
#202432982
C2×#156888592
#202412672
C2×C47×#3812
#915447