Finite Group Databasebeta

← #26119998

Subgroups — #26119998

Order 12032.

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

normal subgroups only

This group has 374 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
1#20253193C211yesmaximal, characteristic
2#20242143C211yesmaximal, characteristic
3#20242079C211yesmaximal, characteristic
4#20241842C211yesmaximal, characteristic
5C2×Q8⋊(C47⋊C8)C211yesmaximal, characteristic
6#20241262C211yesmaximal, characteristic
7C47×#1801C211yesmaximal, characteristic
8#15689680C2211yescharacteristic
9#15689430—22no—
10#15689418—21no—
11#15689408—21no—
12#15689163—21no—
13#15689147C2211yescharacteristic
14C2×C4⋊(C47⋊C8)C2211yescharacteristic
15#15689132—21no—
16C2×C4×C47⋊C8C2211yescharacteristic
17#15688873—22no—
18#15688871—21no—
19#15688868—21no—
20Q8⋊(C47⋊C8)—21no—
21Q8⋊(C47⋊C8)—21no—
22#15688853—21no—
23#15688853—21no—
24C2×C4×Q8×C47C2211yescharacteristic
25C47×#423C2211yescharacteristic
26C47×#423C2211yescharacteristic
27C2×#101×C47—21no—
28C47×#343—21no—
29C2×#10625329—21no—
30C22×C47⋊C8—21no—
31C22×C47⋊C8—21no—
32#13094024D411yescharacteristic
33#13094024D411yescharacteristic
34#13094016—21no—
35#13094003—21no—
36#13094003—21no—
37C4×Dic94—21no—
38C4×Dic94—21no—
39#13093983—21no—
40#13093957—22no—
41#13093955—22no—
42C4⋊(C47⋊C8)—21no—
43C4⋊(C47⋊C8)—21no—
44C4⋊(C47⋊C8)—21no—
45C4⋊(C47⋊C8)D412yes—
46#13093948—22no—
47#13093948—22no—
48C4×C47⋊C8—21no—
49C4×C47⋊C8D411yescharacteristic
50C4×C47⋊C8D411yescharacteristic
51C22×Q8×C47D411yescharacteristic
52C2×M16×C47—21no—
53C2×M16×C47—21no—
54C4×Q8×C47—21no—
55C4×Q8×C47—21no—
56C4×Q8×C47—21no—
57C4×Q8×C47—21no—
58C2×C4⋊C4×C47—21no—
59C2×C4⋊C4×C47D411yescharacteristic
60C2×C42×C47—21no—
61C2×C42×C47C2311yescharacteristic
62C4⋊C8×C47—21no—
63C4⋊C8×C47—21no—
64C4⋊C8×C47—21no—
65C4⋊C8×C47—21no—
66#101×C47—42no—
67C2×Q8×C47—21no—
68C2×Q8×C47—21no—
69C2×Q8×C47—21no—
70C2×Q8×C47—21no—
71C2×Q8×C47—21no—
72C2×Q8×C47SD1612yes—
73C22×C4×C47—21no—
74C22×C4×C47—21no—
75C22×C4×C47C2×D411yescharacteristic
76C22×C4×C47#4111yescharacteristic
77C22×C4×C47#4111yescharacteristic
78C2×Dic94—21no—
79C2×Dic94—21no—
80M16×C47—41no—
81M16×C47—41no—
82M16×C47—41no—
83M16×C47—41no—
84C2×C8×C47—41no—
85C2×C8×C47—41no—
86C4⋊C4×C47—21no—
87C4⋊C4×C47—21no—
88C4⋊C4×C47—41no—
89C4⋊C4×C47—41no—
90C42×C47—41no—
91C42×C47—41no—
92C42×C47C2×D411yescharacteristic
93C42×C47C2×D411yescharacteristic
94C42×C47C2×D411yescharacteristic
95C42×C47#4111yescharacteristic
96C22⋊Dic47—41no—
97C4⋊Dic47—21no—
98C4⋊Dic47—21no—
99C4⋊Dic47—21no—
100C4⋊Dic47—21no—
101Dic47⋊C4—41no—
102Dic47⋊C4—41no—
103C4×Dic47—41no—
104#10625329—41no—
105#10625329—41no—
106C2×C47⋊C8—21no—
107C2×C47⋊C8—22no—
108C2×C47⋊C8—21no—
109C2×C47⋊C8—42no—
110C2×C47⋊C8—41no—
111C2×C47⋊C8—81no—
112C23×C47#12311yescharacteristic
113Q8×C47—22no—
114Q8×C47—22no—
115Q8×C47—41no—
116Q8×C47—41no—
117C2×C4×C47—21no—
118C2×C4×C47—21no—
119C2×C4×C47—22no—
120C2×C4×C47—41no—
121C2×C4×C47—41no—
122C2×C4×C47—41no—
123C2×C4×C47—41no—
124C2×C4×C47—81no—
125C2×C4×C47#12011yescharacteristic
126C2×C4×C47#12111yescharacteristic
127C2×C4×C47#12111yescharacteristic
128C2×C4×C47#12111yescharacteristic
129C2×C4×C47#12311yescharacteristic
130C2×C4×C47#12411yescharacteristic
131C2×C4×C47C2×SD1611yescharacteristic
132C2×C4×C47#13511yescharacteristic
133C2×C4×C47#13711yescharacteristic
134C2×C4×C47#13711yescharacteristic
135C2×Dic47—41no—
136C2×Dic47—41no—
137Dic94—41no—
138Dic94—41no—
139Dic94—81no—
140C8×C47—81no—
141C8×C47—81no—
142C47⋊C8—22no—
143C47⋊C8—41no—
144C47⋊C8—42no—
145C47⋊C8—81no—
146#10462—471nomaximal, Sylow
147C22×C47—21no—
148C22×C47—21no—
149C22×C47#39411yescharacteristic
150C22×C47#48311yescharacteristic
151C22×C47#48511yescharacteristic
152C4×C47—21no—
153C4×C47—21no—
154C4×C47—21no—
155C4×C47—42no—
156C4×C47—81no—
157C4×C47#44811yescharacteristic
158C4×C47#45211yescharacteristic
159C4×C47#46511yescharacteristic
160C4×C47#47011yescharacteristic
161C4×C47#47111yescharacteristic
162C4×C47#47311yescharacteristic
163Dic47—81no—
164Dic47—81no—
165#3078—471no—
166#1801D4711yescharacteristic
167#1566—471no—
168#1550—471no—
169#1493—471no—
170C2×Q8⋊C8—471no—
171#1292—471no—
172C2×C47—21no—
173C2×C47—21no—
174C2×C47#203511yescharacteristic
175C2×C47#205011yescharacteristic
176C2×C47#205211yescharacteristic
177#533—471no—
178C2×C4×Q8C2×D4711yescharacteristic
179#479—942no—
180#477—941no—
181#475—941no—
182#428—941no—
183#423—471no—
184#423C2×D4711yescharacteristic
185#423C2×D4711yescharacteristic
186C2×C4⋊C8—471no—
187#419—941no—
188C2×#101—21no—
189C2×C4×C8—471no—
190#343—21no—
191#334—942no—
192#333—941no—
193#332—941no—
194Q8⋊C8—941no—
195Q8⋊C8—941no—
196Q8⋊C8—941no—
197Q8⋊C8—941no—
198C47#1046211yescharacteristic, complemented, Sylow
199C22×Q8C22⋊D4711yescharacteristic
200C2×M16—21no—
201C2×M16—21no—
202C2×M16—941no—
203C22×C8—941no—
204C22×C8—941no—
205C4⋊Q8—471no—
206C4⋊Q8—471no—
207#125—941no—
208C22⋊Q8—941no—
209C22⋊Q8—941no—
210C4×Q8—21no—
211C4×Q8—21no—
212C4×Q8—21no—
213C4×Q8—21no—
214C4×Q8—941no—
215C4×Q8—941no—
216#117—941no—
217C2×C4⋊C4—21no—
218C2×C4⋊C4C22⋊D4711yescharacteristic
219C2×C42—21no—
220C2×C42C22×D4711yescharacteristic
221#107—942no—
222#106—942no—
223C4⋊C8—21no—
224C4⋊C8—21no—
225C4⋊C8—21no—
226C4⋊C8—21no—
227C4⋊C8—472no—
228C4⋊C8—941no—
229C4⋊C8—941no—
230C4⋊C8—941no—
231#103—942no—
232#103—942no—
233#101—42no—
234C4×C8—471no—
235C4×C8—471no—
236C4×C8—941no—
237C2×Q8—21no—
238C2×Q8—21no—
239C2×Q8—21no—
240C2×Q8—21no—
241C2×Q8—21no—
242C2×Q8—941no—
243C2×Q8—941no—
244C2×Q8#1062533512yes—
245C22×C4—21no—
246C22×C4—21no—
247C22×C4#1062535011yescharacteristic
248C22×C4#1062535011yescharacteristic
249C22×C4C2×C22⋊D4711yescharacteristic
250M16—41no—
251M16—41no—
252M16—41no—
253M16—41no—
254M16—1881no—
255M16—1881no—
256C2×C8—41no—
257C2×C8—41no—
258C2×C8—941no—
259C2×C8—942no—
260C2×C8—941no—
261C2×C8—3761no—
262C2×C8—1882no—
263C2×C8—1881no—
264C4⋊C4—21no—
265C4⋊C4—21no—
266C4⋊C4—41no—
267C4⋊C4—41no—
268C4⋊C4—941no—
269C4⋊C4—941no—
270C4⋊C4—941no—
271C4⋊C4—941no—
272C4⋊C4—1881no—
273C4⋊C4—1881no—
274C22⋊C4—1881no—
275C42—41no—
276C42—41no—
277C42—1881no—
278C42D4×D4711yescharacteristic
279C42D4×D4711yescharacteristic
280C42D4×D4711yescharacteristic
281C42#1062535211yescharacteristic
282C23#1309400711yescharacteristic
283Q8—22no—
284Q8—22no—
285Q8—41no—
286Q8—41no—
287Q8—3761no—
288Q8—1881no—
289Q8—1881no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—22no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—81no—
298C2×C4—1881no—
299C2×C4—1881no—
300C2×C4#1309399211yescharacteristic
301C2×C4#1309399611yescharacteristic
302C2×C4#1309399711yescharacteristic
303C2×C4#1309399711yescharacteristic
304C2×C4#1309400611yescharacteristic
305C2×C4#1309401011yescharacteristic
306C2×C4C2×#1062533511yescharacteristic
307C2×C4#1309404411yescharacteristic
308C2×C4#1309405411yescharacteristic
309C2×C4#1309405511yescharacteristic
310C8—81no—
311C8—81no—
312C8—942no—
313C8—3761no—
314C8—1881no—
315C8—1882no—
316C22—21no—
317C22—21no—
318C22#1568903811yescharacteristic
319C22#1568945311yescharacteristic
320C22#1568946411yescharacteristic
321C4—21no—
322C4—21no—
323C4—21no—
324C4—42no—
325C4—81no—
326C4—3761no—
327C4—3761no—
328C4#1568926111yescharacteristic
329C4#1568928311yescharacteristic
330C4#1568935011yescharacteristic
331C4#1568937911yescharacteristic
332C4#1568938911yescharacteristic
333C4#1568939711yescharacteristic
334C2—21no—
335C2—21no—
336C2#2024458411yescharacteristic
337C2#2024467311yescharacteristic
338C2#2024468711yescharacteristic
subgroupG/H
centerC22#15689038
commutator, cosocleC2×C42×C47C23
FrattiniC2×C42C22×D47
FittingC47×#1801C2
socleC22×C47#394
prime radicalC23×C47#123
hypercenter#1801D47
hypocenterC47#10462
LCSG ▷ C2×C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1801

Complements

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

NH ≅ G/Ntype
198. C47#10462semidirect

Maximal subgroups

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

subgroupindex
#202531932
#202421432
#202420792
#202418422
C2×Q8⋊(C47⋊C8)2
#202412622
C47×#18012
#1046247