Finite Group Databasebeta

← #26117596

Subgroups — #26117596

Order 12032.

484 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 97 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
1C2×#15689533C211yesmaximal, characteristic
2C2×#15689493C211yesmaximal, characteristic
3#20244360C211yesmaximal, characteristic
4C2×#15688865C211yesmaximal, characteristic
5C2×#15688865C211yesmaximal, characteristic
6#20241269C211yesmaximal, characteristic
7C47×#2822C211yesmaximal, characteristic
8C2×#13094024C2211yescharacteristic
9#15689533—22no—
10#15689533—22no—
11#15689493—22no—
12#15689493—22no—
13C2×#13093957—21no—
14C2×#13093955—21no—
15C2×#13093947—21no—
16C2×#13093947—21no—
17C2×#13093935C2211yescharacteristic
18C2×#13093935C2211yescharacteristic
19C2×#13093935C2211yescharacteristic
20#15688885—22no—
21#15688865—22no—
22#15688865—22no—
23C2×#125×C47C2211yescharacteristic
24C2×#125×C47C2211yescharacteristic
25C47×#400—21no—
26C47×#400—21no—
27C47×#398—22no—
28C47×#398—21no—
29C47×#398—21no—
30C47×#382C2211yescharacteristic
31C22×Dic94—21no—
32C22×C47⋊C8—21no—
33C22×C47⋊C8—21no—
34C22×C47⋊C8—21no—
35#13094024—21no—
36#13094024—21no—
37#13094024—21no—
38#13094024D412yes—
39C2×C4⋊Dic47—21no—
40C2×C4⋊Dic47—21no—
41#13093957—24no—
42#13093955—24no—
43#13093947—24no—
44#13093947—24no—
45#13093935—21no—
46#13093935—21no—
47#13093935—21no—
48#13093935—21no—
49#13093935D412yes—
50#13093935D412yes—
51#125×C47—21no—
52#125×C47—21no—
53#125×C47—21no—
54#125×C47—21no—
55#125×C47—21no—
56#125×C47—21no—
57#125×C47—21no—
58#125×C47—21no—
59C2×C4⋊C4×C47—21no—
60C2×C4⋊C4×C47—21no—
61C2×C4⋊C4×C47—21no—
62C2×C4⋊C4×C47—21no—
63C2×C4⋊C4×C47—22no—
64C2×C4⋊C4×C47D411yescharacteristic
65C2×C4⋊C4×C47D411yescharacteristic
66C2×C4⋊C4×C47D411yescharacteristic
67C2×C4⋊C4×C47D411yescharacteristic
68C2×C4⋊C4×C47D412yes—
69C2×C42×C47C2311yescharacteristic
70#95×C47—22no—
71#95×C47—22no—
72#95×C47—22no—
73#95×C47—21no—
74#95×C47—21no—
75C22×C4×C47—21no—
76C22×C4×C47—21no—
77C22×C4×C47—21no—
78C22×C4×C47—21no—
79C22×C4×C47—22no—
80C22×C4×C47C2×D411yescharacteristic
81C22×C4×C47C2×D411yescharacteristic
82C22×C4×C47C2×D411yescharacteristic
83C22×Dic47—41no—
84C2×Dic94—22no—
85C2×Dic94—44no—
86C2×Dic94—41no—
87C4⋊C4×C47—21no—
88C4⋊C4×C47—21no—
89C4⋊C4×C47—21no—
90C4⋊C4×C47—21no—
91C4⋊C4×C47—21no—
92C4⋊C4×C47—21no—
93C4⋊C4×C47—21no—
94C4⋊C4×C47—21no—
95C4⋊C4×C47—42no—
96C4⋊C4×C47—41no—
97C4⋊C4×C47—41no—
98C4⋊C4×C47—41no—
99C4⋊C4×C47—41no—
100C4⋊C4×C47—41no—
101C4⋊C4×C47—41no—
102C4⋊C4×C47—41no—
103C4⋊C4×C47—41no—
104C4⋊C4×C47—82no—
105C42×C47C2×D411yescharacteristic
106C42×C47C2×D411yescharacteristic
107C42×C47C2×D411yescharacteristic
108C42×C47#4111yescharacteristic
109C4⋊Dic47—22no—
110C4⋊Dic47—22no—
111C4⋊Dic47—41no—
112C4⋊Dic47—41no—
113C2×C47⋊C8—24no—
114C2×C47⋊C8—22no—
115C2×C47⋊C8—22no—
116C2×C47⋊C8—22no—
117C2×C47⋊C8—42no—
118C2×C47⋊C8—41no—
119C2×C47⋊C8—41no—
120C23×C47#12011yescharacteristic
121C2×C4×C47—22no—
122C2×C4×C47—21no—
123C2×C4×C47—22no—
124C2×C4×C47—21no—
125C2×C4×C47—41no—
126C2×C4×C47—41no—
127C2×C4×C47—41no—
128C2×C4×C47—41no—
129C2×C4×C47—42no—
130C2×C4×C47—42no—
131C2×C4×C47—42no—
132C2×C4×C47—41no—
133C2×C4×C47—41no—
134C2×C4×C47—42no—
135C2×C4×C47—42no—
136C2×C4×C47—41no—
137C2×C4×C47—41no—
138C2×C4×C47#12011yescharacteristic
139C2×C4×C47#12011yescharacteristic
140C2×C4×C47#12111yescharacteristic
141C2×C4×C47#12111yescharacteristic
142C2×C4×C47#12111yescharacteristic
143C2×C4×C47#12711yescharacteristic
144C2×Dic47—42no—
145C2×Dic47—82no—
146Dic94—44no—
147Dic94—82no—
148C47⋊C8—24no—
149C47⋊C8—42no—
150C47⋊C8—42no—
151#10084—471nomaximal, Sylow
152C22×C47#39211yescharacteristic
153C22×C47#45412yes—
154C22×C47#45511yescharacteristic
155C22×C47#45611yescharacteristic
156C22×C47#45612yes—
157C4×C47—21no—
158C4×C47—21no—
159C4×C47—21no—
160C4×C47—21no—
161C4×C47—21no—
162C4×C47—21no—
163C4×C47—82no—
164C4×C47—81no—
165C4×C47—81no—
166C4×C47—81no—
167C4×C47—81no—
168Dic47—82no—
169C2×#501—471no—
170C2×#491—471no—
171#2822D4711yescharacteristic
172#1993—471no—
173C2×#330—471no—
174C2×#330—471no—
175#1295—471no—
176C2×C47#166312yes—
177C2×C47#166412yes—
178C2×C47#200311yescharacteristic
179C2×C47#200511yescharacteristic
180C2×C47#200711yescharacteristic
181C2×C4⋊Q8—471no—
182C2×#125C2×D4711yescharacteristic
183C2×#125C2×D4711yescharacteristic
184#501—942no—
185#501—942no—
186#491—942no—
187#491—942no—
188C2×#107—941no—
189C2×#106—941no—
190C2×#103—941no—
191C2×#103—941no—
192C2×#97—471no—
193C2×#97—471no—
194C2×#97—471no—
195#400—21no—
196#400—21no—
197#398—22no—
198#398—21no—
199#398—21no—
200#382C2×D4711yescharacteristic
201#340—942no—
202#330—942no—
203#330—942no—
204C47#1008411yescharacteristic, complemented, Sylow
205C22×Q8—941no—
206C22×C8—941no—
207C22×C8—941no—
208C22×C8—941no—
209C4⋊Q8—472no—
210C4⋊Q8—941no—
211C4⋊Q8—941no—
212C4⋊Q8—941no—
213#125—21no—
214#125—21no—
215#125—21no—
216#125—21no—
217#125—21no—
218#125—21no—
219#125—21no—
220#125—21no—
221C2×C4⋊C4—21no—
222C2×C4⋊C4—21no—
223C2×C4⋊C4—21no—
224C2×C4⋊C4—21no—
225C2×C4⋊C4—22no—
226C2×C4⋊C4—941no—
227C2×C4⋊C4—941no—
228C2×C4⋊C4C22⋊D4711yescharacteristic
229C2×C4⋊C4C22⋊D4711yescharacteristic
230C2×C4⋊C4C22⋊D4711yescharacteristic
231C2×C4⋊C4C22⋊D4711yescharacteristic
232C2×C4⋊C4C22⋊D4712yes—
233C2×C42C22×D4711yescharacteristic
234#107—944no—
235#106—944no—
236#103—944no—
237#103—944no—
238#97—472no—
239#97—472no—
240#97—941no—
241#97—941no—
242#97—941no—
243#97—941no—
244#95—22no—
245#95—22no—
246#95—22no—
247#95—21no—
248#95—21no—
249C2×Q8—942no—
250C2×Q8—1884no—
251C2×Q8—1881no—
252C22×C4—22no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—1881no—
258C22×C4C2×C22⋊D4711yescharacteristic
259C22×C4C2×C22⋊D4711yescharacteristic
260C22×C4C2×C22⋊D4711yescharacteristic
261C2×C8—944no—
262C2×C8—942no—
263C2×C8—942no—
264C2×C8—942no—
265C2×C8—1882no—
266C2×C8—1881no—
267C2×C8—1881no—
268C4⋊C4—21no—
269C4⋊C4—21no—
270C4⋊C4—21no—
271C4⋊C4—21no—
272C4⋊C4—21no—
273C4⋊C4—21no—
274C4⋊C4—21no—
275C4⋊C4—21no—
276C4⋊C4—42no—
277C4⋊C4—41no—
278C4⋊C4—41no—
279C4⋊C4—41no—
280C4⋊C4—41no—
281C4⋊C4—41no—
282C4⋊C4—41no—
283C4⋊C4—41no—
284C4⋊C4—41no—
285C4⋊C4—82no—
286C4⋊C4—942no—
287C4⋊C4—942no—
288C4⋊C4—1881no—
289C4⋊C4—1881no—
290C42D4×D4711yescharacteristic
291C42D4×D4711yescharacteristic
292C42D4×D4711yescharacteristic
293C42#1062535211yescharacteristic
294C23#1309399311yescharacteristic
295Q8—3762no—
296Q8—1884no—
297C2×C4—22no—
298C2×C4—21no—
299C2×C4—22no—
300C2×C4—21no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—42no—
306C2×C4—42no—
307C2×C4—42no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—42no—
311C2×C4—42no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—3762no—
315C2×C4—1882no—
316C2×C4#1309399211yescharacteristic
317C2×C4#1309399211yescharacteristic
318C2×C4#1309399511yescharacteristic
319C2×C4#1309399611yescharacteristic
320C2×C4#1309399611yescharacteristic
321C2×C4#1309402011yescharacteristic
322C8—944no—
323C8—1882no—
324C8—1882no—
325C22#1568903111yescharacteristic
326C22#1568929612yes—
327C22#1568930111yescharacteristic
328C22#1568930611yescharacteristic
329C22#1568930612yes—
330C4—21no—
331C4—21no—
332C4—21no—
333C4—21no—
334C4—21no—
335C4—21no—
336C4—82no—
337C4—81no—
338C4—81no—
339C4—81no—
340C4—81no—
341C4—3762no—
342C2#2024271612yes—
343C2#2024272212yes—
344C2#2024440811yescharacteristic
345C2#2024442211yescharacteristic
346C2#2024443511yescharacteristic
subgroupG/H
centerC23#13093993
commutator, cosocleC2×C42×C47C23
FrattiniC2×C42C22×D47
FittingC47×#2822C2
socle, prime radicalC23×C47#120
hypercenter#2822D47
hypocenterC47#10084
LCSG ▷ C2×C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2822

Complements

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

NH ≅ G/Ntype
204. C47#10084semidirect

Maximal subgroups

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

subgroupindex
C2×#156895332
C2×#156894932
#202443602
C2×#156888652
#202412692
C47×#28222
#1008447