Finite Group Databasebeta

← #26117594

Subgroups — #26117594

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×#15689491C211yesmaximal, characteristic
2#20251455C211yesmaximal, characteristic
3#20244362C211yesmaximal, characteristic
4C2×#15688865C211yesmaximal, characteristic
5C2×#15688864C211yesmaximal, characteristic
6#20241270C211yesmaximal, characteristic
7C2×C47×#501C211yesmaximal, characteristic
8C2×#13094016C2211yescharacteristic
9#15689491—22no—
10#15689491—22no—
11C2×#13093948—21no—
12C2×#13093948—21no—
13C2×#13093935C2211yescharacteristic
14C2×#13093935C2211yescharacteristic
15#15689062—21no—
16#15689061—21no—
17#15689056—22no—
18#15689054—21no—
19#15689053—21no—
20#15688989C2211yescharacteristic
21#15688885—22no—
22#15688865—22no—
23#15688864—22no—
24C2×C4⋊Q8×C47C2211yescharacteristic
25C2×#125×C47C2211yescharacteristic
26C47×#501—22no—
27C47×#501—22no—
28C2×#107×C47—21no—
29C2×#106×C47—21no—
30C2×#97×C47C2211yescharacteristic
31C22×C47⋊C8—21no—
32C22×C47⋊C8—21no—
33#13094016—21no—
34#13094016—21no—
35#13094016—21no—
36#13094016—21no—
37C2×C4⋊Dic47D411yescharacteristic
38C2×C4⋊Dic47D411yescharacteristic
39C2×C4⋊Dic47D412yes—
40C2×Dic47⋊C4—21no—
41C2×Dic47⋊C4—21no—
42C2×Dic47⋊C4—22no—
43#13093948—24no—
44#13093948—24no—
45#13093935—21no—
46#13093935—21no—
47#13093935—21no—
48#13093935D412yes—
49C47⋊#95—22no—
50C47⋊#95—22no—
51C47⋊#95—22no—
52C47⋊#95—21no—
53C47⋊#95—21no—
54C22×Q8×C47—21no—
55C22×C8×C47—21no—
56C4⋊Q8×C47—21no—
57C4⋊Q8×C47—21no—
58C4⋊Q8×C47—21no—
59C4⋊Q8×C47D412yes—
60#125×C47—21no—
61#125×C47—21no—
62#125×C47—21no—
63#125×C47—21no—
64C2×C4⋊C4×C47—21no—
65C2×C4⋊C4×C47—21no—
66C2×C4⋊C4×C47—21no—
67C2×C4⋊C4×C47—21no—
68C2×C4⋊C4×C47D411yescharacteristic
69C2×C4⋊C4×C47D411yescharacteristic
70C2×C42×C47C2311yescharacteristic
71#107×C47—24no—
72#106×C47—24no—
73#97×C47—21no—
74#97×C47D412yes—
75C2×Q8×C47—22no—
76C2×Q8×C47—44no—
77C2×Q8×C47—41no—
78C22×C4×C47—21no—
79C22×C4×C47—21no—
80C22×C4×C47—41no—
81C22×C4×C47C2×D411yescharacteristic
82C22×C4×C47C2×D411yescharacteristic
83C22×C4×C47C2×D411yescharacteristic
84C22×Dic47—22no—
85C22×Dic47—21no—
86C22×Dic47—21no—
87C2×C8×C47—24no—
88C2×C8×C47—22no—
89C4⋊C4×C47—21no—
90C4⋊C4×C47—22no—
91C4⋊C4×C47—21no—
92C4⋊C4×C47—22no—
93C4⋊C4×C47—21no—
94C4⋊C4×C47—21no—
95C4⋊C4×C47—41no—
96C4⋊C4×C47—41no—
97C4⋊C4×C47—41no—
98C4⋊C4×C47—41no—
99C4⋊C4×C47—41no—
100C4⋊C4×C47—41no—
101C42×C47C2×D411yescharacteristic
102C42×C47C2×D411yescharacteristic
103C42×C47C2×D411yescharacteristic
104C42×C47#4111yescharacteristic
105C4⋊Dic47—21no—
106C4⋊Dic47—21no—
107C4⋊Dic47—21no—
108C4⋊Dic47—21no—
109C4⋊Dic47—42no—
110Dic47⋊C4—41no—
111Dic47⋊C4—41no—
112Dic47⋊C4—41no—
113Dic47⋊C4—41no—
114Dic47⋊C4—82no—
115C2×C47⋊C8—22no—
116C2×C47⋊C8—22no—
117C2×C47⋊C8—42no—
118C2×C47⋊C8—41no—
119C2×C47⋊C8—41no—
120C23×C47#12011yescharacteristic
121Q8×C47—44no—
122Q8×C47—82no—
123C2×C4×C47—22no—
124C2×C4×C47—21no—
125C2×C4×C47—21no—
126C2×C4×C47—22no—
127C2×C4×C47—41no—
128C2×C4×C47—41no—
129C2×C4×C47—42no—
130C2×C4×C47—42no—
131C2×C4×C47—41no—
132C2×C4×C47—41no—
133C2×C4×C47—82no—
134C2×C4×C47#12011yescharacteristic
135C2×C4×C47#12011yescharacteristic
136C2×C4×C47#12111yescharacteristic
137C2×C4×C47#12111yescharacteristic
138C2×C4×C47#12111yescharacteristic
139C2×C4×C47#12711yescharacteristic
140C2×Dic47—41no—
141C2×Dic47—41no—
142C2×Dic47—42no—
143C2×Dic47—41no—
144C2×Dic47—42no—
145C2×Dic47—41no—
146C2×Dic47—42no—
147C2×Dic47—42no—
148C8×C47—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—81no—
164C4×C47—82no—
165C4×C47—81no—
166Dic47—82no—
167Dic47—81no—
168Dic47—81no—
169C2×#501D4711yescharacteristic
170C2×#491—471no—
171#2822—471no—
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⋊Q8C2×D4711yescharacteristic
182C2×#125—471no—
183C2×#125C2×D4711yescharacteristic
184#501—22no—
185#501—22no—
186#491—942no—
187#491—942no—
188C2×#107—21no—
189C2×#106—21no—
190C2×#103—941no—
191C2×#103—941no—
192C2×#97—471no—
193C2×#97—471no—
194C2×#97C2×D4711yescharacteristic
195#400—941no—
196#400—941no—
197#398—941no—
198#398—942no—
199#398—941no—
200#382—471no—
201#340—942no—
202#330—942no—
203#330—942no—
204C47#1008411yescharacteristic, complemented, Sylow
205C22×Q8—21no—
206C22×C8—21no—
207C22×C8—941no—
208C22×C8—941no—
209C4⋊Q8—21no—
210C4⋊Q8—21no—
211C4⋊Q8—21no—
212C4⋊Q8C22⋊D4712yes—
213#125—21no—
214#125—21no—
215#125—21no—
216#125—21no—
217#125—941no—
218#125—941no—
219#125—941no—
220#125—941no—
221C2×C4⋊C4—21no—
222C2×C4⋊C4—21no—
223C2×C4⋊C4—21no—
224C2×C4⋊C4—21no—
225C2×C4⋊C4—471no—
226C2×C4⋊C4—471no—
227C2×C4⋊C4—472no—
228C2×C4⋊C4—942no—
229C2×C4⋊C4—941no—
230C2×C4⋊C4—941no—
231C2×C4⋊C4C22⋊D4711yescharacteristic
232C2×C4⋊C4C22⋊D4711yescharacteristic
233C2×C42C22×D4711yescharacteristic
234#107—24no—
235#106—24no—
236#103—944no—
237#103—944no—
238#97—21no—
239#97—472no—
240#97—941no—
241#97—941no—
242#97—941no—
243#97C22⋊D4712yes—
244#95—942no—
245#95—942no—
246#95—942no—
247#95—941no—
248#95—941no—
249C2×Q8—22no—
250C2×Q8—44no—
251C2×Q8—41no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—41no—
255C22×C4—942no—
256C22×C4—941no—
257C22×C4—941no—
258C22×C4D4×D4711yescharacteristic
259C22×C4D4×D4711yescharacteristic
260C22×C4C2×C22⋊D4711yescharacteristic
261C2×C8—24no—
262C2×C8—22no—
263C2×C8—942no—
264C2×C8—942no—
265C2×C8—1882no—
266C2×C8—1881no—
267C2×C8—1881no—
268C4⋊C4—21no—
269C4⋊C4—22no—
270C4⋊C4—21no—
271C4⋊C4—22no—
272C4⋊C4—21no—
273C4⋊C4—21no—
274C4⋊C4—41no—
275C4⋊C4—41no—
276C4⋊C4—41no—
277C4⋊C4—41no—
278C4⋊C4—41no—
279C4⋊C4—41no—
280C4⋊C4—941no—
281C4⋊C4—941no—
282C4⋊C4—941no—
283C4⋊C4—941no—
284C4⋊C4—3762no—
285C4⋊C4—1882no—
286C4⋊C4—1881no—
287C4⋊C4—1881no—
288C4⋊C4—1881no—
289C4⋊C4—1881no—
290C42D4×D4711yescharacteristic
291C42#1062535211yescharacteristic
292C42C2×C22⋊D4711yescharacteristic
293C42C2×C22⋊D4711yescharacteristic
294C23#1309399211yescharacteristic
295Q8—44no—
296Q8—82no—
297C2×C4—22no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—22no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—42no—
304C2×C4—42no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—82no—
308C2×C4—1881no—
309C2×C4—1881no—
310C2×C4—1882no—
311C2×C4—1881no—
312C2×C4—1882no—
313C2×C4—1881no—
314C2×C4—1882no—
315C2×C4—1882no—
316C2×C4#1309399211yescharacteristic
317C2×C4#1309399311yescharacteristic
318C2×C4#1309399511yescharacteristic
319C2×C4#1309399611yescharacteristic
320C2×C4#1309399611yescharacteristic
321C2×C4#1309402011yescharacteristic
322C8—24no—
323C8—1882no—
324C8—1882no—
325C22#1568903111yescharacteristic
326C22#1568929412yes—
327C22#1568929911yescharacteristic
328C22#1568930411yescharacteristic
329C22#1568930512yes—
330C4—21no—
331C4—21no—
332C4—21no—
333C4—21no—
334C4—21no—
335C4—21no—
336C4—81no—
337C4—82no—
338C4—81no—
339C4—3762no—
340C4—3761no—
341C4—3761no—
342C2#2024271512yes—
343C2#2024272012yes—
344C2#2024440711yescharacteristic
345C2#2024442411yescharacteristic
346C2#2024443311yescharacteristic
subgroupG/H
centerC23#13093992
commutator, cosocleC2×C42×C47C23
FrattiniC2×C42C22×D47
FittingC2×C47×#501C2
socle, prime radicalC23×C47#120
hypercenterC2×#501D47
hypocenterC47#10084
LCSG ▷ C2×C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#501

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×#156894912
#202514552
#202443622
C2×#156888652
C2×#156888642
#202412702
C2×C47×#5012
#1008447