Finite Group Databasebeta

← #26110395

Subgroups — #26110395

Order 12032.

380 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 93 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#20252524C211yesmaximal, characteristic
2#20242171C211yesmaximal, characteristic, complemented
3#20241872C211yesmaximal, characteristic
4#20241799C211yesmaximal, characteristic
5#20241281C211yesmaximal, characteristic, complemented
6#20241238C211yesmaximal, characteristic, complemented
7C47×#1843C211yesmaximal, characteristic, complemented
8#15689657C2211yescharacteristic
9#15689252—21no—
10#15689194—21no—
11#15689193—21no—
12C8×C22⋊D47—21no—
13#15689183—21no—
14#15689180C2211yescharacteristic
15#15689176C2211yescharacteristic
16#15689148—21no—
17C4×#10625329C2211yescharacteristic
18#15688875—21no—
19#15688873—21no—
20#15688859C411yescharacteristic
21#15688859C411yescharacteristic
22#15688856C411yescharacteristic
23#15688856C411yescharacteristic
24#15688853—21no—
25#15688850—21no—
26C2×C4⋊C8×C47—21no—
27C2×C4⋊C8×C47—21no—
28C2×C4⋊C8×C47C2211yescharacteristic
29C2×C4⋊C8×C47C2211yescharacteristic
30C47×#376C2211yescharacteristic
31C2×#10625329—21no—
32C2×#10625324—21no—
33C2×C8×D47—21no—
34#13094018—21no—
35#13094016Q811yescharacteristic
36#13094012Q811yescharacteristic
37#13094007—21no—
38#13094003C2×C411yescharacteristic
39#13093998C2×C411yescharacteristic
40C4×Dic94D411yescharacteristic
41C4×D188D411yescharacteristic
42C4×C22⋊D47—21no—
43#13093981—21no—
44C4⋊(C47⋊C8)—21no—
45C4⋊(C47⋊C8)D411yescharacteristic
46C4⋊(C47⋊C8)D411yescharacteristic
47Dic47⋊C8—21no—
48Dic47⋊C8—21no—
49C22⋊(C47⋊C8)—21no—
50C22⋊(C47⋊C8)C2×C411yescharacteristic
51C22⋊(C47⋊C8)C2×C411yescharacteristic
52(C2×D47)⋊C8—21no—
53(C2×D47)⋊C8—21no—
54#13093935—21no—
55#13093935—21no—
56#13093934—21no—
57C4×C47⋊C8—21no—
58C4×C47⋊C8—21no—
59C8×Dic47—21no—
60C22×C8×C47—21no—
61C22×C8×C47D411yescharacteristic
62C22×C8×C47D411yescharacteristic
63C2×C42×C47—21no—
64C2×C42×C47C2311yescharacteristic
65C4⋊C8×C47—21no—
66C4⋊C8×C47—21no—
67C4⋊C8×C47—21no—
68C4⋊C8×C47—21no—
69C4⋊C8×C47—42no—
70C4⋊C8×C47—42no—
71#95×C47—21no—
72#95×C47C2×C411yescharacteristic
73#95×C47C2×C411yescharacteristic
74C22×C4×C47—21no—
75C22×C4×C47—21no—
76C22×C4×C47C22×C411yescharacteristic
77C22×C4×C47C2×D411yescharacteristic
78C22×C4×C47#4111yescharacteristic
79C2×C22⋊D47—21no—
80C2×D188C4⋊C411yescharacteristic
81C2×C4×D47—21no—
82C2×Dic94C4⋊C411yescharacteristic
83C2×C8×C47—21no—
84C2×C8×C47—21no—
85C2×C8×C47—41no—
86C2×C8×C47—41no—
87C2×C8×C47—41no—
88C2×C8×C47—41no—
89C2×C8×C47—41no—
90C42×C47—22no—
91C42×C47—22no—
92C42×C47C2×D411yescharacteristic
93C42×C47C2×D411yescharacteristic
94C42×C47C2×Q811yescharacteristic
95C42×C47#4111yescharacteristic
96C22⋊Dic47—21no—
97(C2×D47)⋊C4—21no—
98(C2×D47)⋊C4—21no—
99(C2×D47)⋊C4—21no—
100(C2×D47)⋊C4—21no—
101C4⋊Dic47C4⋊C411yescharacteristic
102C4⋊Dic47C4⋊C411yescharacteristic
103Dic47⋊C4—21no—
104Dic47⋊C4—21no—
105Dic47⋊C4—21no—
106Dic47⋊C4—21no—
107C4×Dic47—21no—
108#10625329—22no—
109#10625329—41no—
110C2×C47⋊C8—21no—
111C2×C47⋊C8—21no—
112C2×C47⋊C8—21no—
113C2×C47⋊C8—21no—
114C2×C47⋊C8—41no—
115#10625324—81no—
116C8×D47—81no—
117C23×C47C4×D411yescharacteristic
118C22×D47—21no—
119C2×C4×C47—21no—
120C2×C4×C47—21no—
121C2×C4×C47—21no—
122C2×C4×C47—21no—
123C2×C4×C47—22no—
124C2×C4×C47—22no—
125C2×C4×C47—41no—
126C2×C4×C47—41no—
127C2×C4×C47—41no—
128C2×C4×C47—41no—
129C2×C4×C47—41no—
130C2×C4×C47C2×C4⋊C411yescharacteristic
131C2×C4×C47C4×D411yescharacteristic
132C2×C4×C47#12011yescharacteristic
133C2×C4×C47C22⋊Q811yescharacteristic
134C2×C4×C47C22⋊Q811yescharacteristic
135C2×C4×C47#12311yescharacteristic
136C22⋊D47—41no—
137C22⋊D47—41no—
138C2×Dic47—21no—
139C2×Dic47—21no—
140C2×Dic47—21no—
141D188—41no—
142C4×D47—41no—
143C4×D47—41no—
144Dic94—41no—
145C8×C47—41no—
146C8×C47—41no—
147C8×C47—81no—
148C47⋊C8—41no—
149C47⋊C8—41no—
150C47⋊C8—42no—
151C47⋊C8—41no—
152C47⋊C8—41no—
153#8876—471nomaximal, Sylow
154C22×C47—21no—
155C22×C47—21no—
156C22×C47#38511yescharacteristic
157C22×C47#44311yescharacteristic
158C22×C47#44411yescharacteristic
159C2×D47—41no—
160C2×D47—41no—
161C2×D47—41no—
162C4×C47—21no—
163C4×C47—21no—
164C4×C47—21no—
165C4×C47—21no—
166C4×C47—21no—
167C4×C47—42no—
168C4×C47—42no—
169C4×C47#45311yescharacteristic
170C4×C47#45611yescharacteristic
171Dic47—41no—
172Dic47—41no—
173Dic47—41no—
174#2992—471no—
175#1843D4711yescharacteristic, complemented
176#1573—471no—
177#1500—471no—
178#1483—471no—
179#1300—471no—
180#1283—471no—
181C2×C47—21no—
182C2×C47—21no—
183C2×C47#185911yescharacteristic
184C2×C47#186611yescharacteristic
185C2×C47#186811yescharacteristic
186D47—81no—
187#529—471no—
188#446—941no—
189#435—941no—
190#435—941no—
191C8×D4—941no—
192#433—941no—
193#432—471no—
194#431—471no—
195#424—941no—
196C2×C4⋊C8—21no—
197C2×C4⋊C8—21no—
198C2×C4⋊C8C2×D4711yescharacteristic
199C2×C4⋊C8C2×D4711yescharacteristic
200C4×M16—471no—
201#376C2×D4711yescharacteristic
202#335—941no—
203#334—941no—
204#328—471no—
205#328—471no—
206#327—471no—
207#327—471no—
208Q8⋊C8—941no—
209D4⋊C8—941no—
210C47#887611yescharacteristic, complemented, Sylow
211C2×M16—941no—
212C2×M16—941no—
213C22×C8—21no—
214C22×C8—941no—
215C22×C8C22⋊D4711yescharacteristic
216C22×C8C22⋊D4711yescharacteristic
217#126—941no—
218#125—471no—
219#124—471no—
220#123—941no—
221C22⋊Q8—471no—
222#121—471no—
223C4×Q8—471no—
224C4×D4—471no—
225C4×D4—941no—
226#117—941no—
227C2×C42—21no—
228C2×C42C22×D4711yescharacteristic
229C4⋊C8—21no—
230C4⋊C8—21no—
231C4⋊C8—21no—
232C4⋊C8—21no—
233C4⋊C8—42no—
234C4⋊C8—42no—
235C4⋊C8—471no—
236C4⋊C8—471no—
237C4⋊C8—941no—
238C4⋊C8—941no—
239C4⋊C8—941no—
240C22⋊C8—471no—
241C22⋊C8—471no—
242C22⋊C8—941no—
243C22⋊C8—941no—
244C22⋊C8—941no—
245#97—941no—
246#97—941no—
247#97—941no—
248C4×C8—941no—
249C4×C8—941no—
250C4×C8—941no—
251#95—21no—
252#95C4×D4711yescharacteristic
253#95C4×D4711yescharacteristic
254C2×Q8—471no—
255C2×D4—471no—
256C2×D4—941no—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—941no—
260C22×C4C2×C4×D4711yescharacteristic
261C22×C4#1062535011yescharacteristic
262C22×C4C2×C22⋊D4711yescharacteristic
263M16—942no—
264M16—3761no—
265M16—1881no—
266C2×C8—21no—
267C2×C8—21no—
268C2×C8—41no—
269C2×C8—41no—
270C2×C8—41no—
271C2×C8—41no—
272C2×C8—41no—
273C2×C8—941no—
274C2×C8—941no—
275C2×C8—941no—
276C2×C8—941no—
277C2×C8—3761no—
278C2×C8—1881no—
279C4⋊C4—471no—
280C4⋊C4—471no—
281C4⋊C4—941no—
282C4⋊C4—941no—
283C4⋊C4—941no—
284C4⋊C4—941no—
285C22⋊C4—941no—
286C22⋊C4—941no—
287C22⋊C4—941no—
288C22⋊C4—941no—
289C22⋊C4—941no—
290C42—22no—
291C42—22no—
292C42—941no—
293C42D4×D4711yescharacteristic
294C42D4×D4711yescharacteristic
295C42Q8×D4711yescharacteristic
296C42#1062535411yescharacteristic
297C23—941no—
298C23C4×C22⋊D4711yescharacteristic
299Q8—1881no—
300D4—1881no—
301D4—1881no—
302D4—1881no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—22no—
308C2×C4—22no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—941no—
315C2×C4—941no—
316C2×C4—941no—
317C2×C4—1881no—
318C2×C4—1881no—
319C2×C4C4⋊C4×D4711yescharacteristic
320C2×C4#1309398611yescharacteristic
321C2×C4#1309399211yescharacteristic
322C2×C4#1309400011yescharacteristic
323C2×C4#1309400211yescharacteristic
324C2×C4#1309400911yescharacteristic
325C8—41no—
326C8—41no—
327C8—81no—
328C8—1881no—
329C8—1881no—
330C8—1882no—
331C8—1881no—
332C8—1881no—
333C22—21no—
334C22—21no—
335C22—1881no—
336C22—1881no—
337C22—1881no—
338C22#1568899411yescharacteristic
339C22#1568923811yescharacteristic
340C22#1568924311yescharacteristic
341C4—21no—
342C4—21no—
343C4—21no—
344C4—21no—
345C4—21no—
346C4—42no—
347C4—42no—
348C4—1881no—
349C4—1881no—
350C4—1881no—
351C4#1568929011yescharacteristic
352C4#1568930511yescharacteristic
353C2—21no—
354C2—21no—
355C2—3761no—
356C2#2024361311yescharacteristic
357C2#2024366211yescharacteristic
358C2#2024367211yescharacteristic
subgroupG/H
centerC2×C4#13093992
commutatorC22×C4×C47C22×C4
FrattiniC2×C42C22×D47
FittingC47×#1843C2
socleC22×C47#385
prime radical#13093998C2×C4
cosocleC2×C42×C47C23
hypercenter#1843D47
hypocenterC47#8876
LCSG ▷ C22×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1843

Complements

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

NH ≅ G/Ntype
2. #20242171C2semidirect
5. #20241281C2semidirect
6. #20241238C2semidirect
7. C47×#1843C2semidirect
175. #1843D47semidirect
210. C47#8876semidirect

Maximal subgroups

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

subgroupindex
#202525242
#202421712
#202418722
#202417992
#202412812
#202412382
C47×#18432
#887647