Finite Group Databasebeta

← #26132512

Subgroups — #26132512

Order 12032.

416 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20251804C211yesmaximal, characteristic
2C2×#15688904C211yesmaximal, characteristic
3C2×#15688904C211yesmaximal, characteristic
4#20241475C211yesmaximal, characteristic, complemented
5#20241474C211yesmaximal, characteristic, complemented
6#20241473C211yesmaximal, characteristic, complemented
7C47×#1378C211yesmaximal, characteristic, complemented
8C22×#10625324C2211yescharacteristic
9C2×M16×D47C411yescharacteristic
10#117×D47C411yescharacteristic
11C2×#13093964C2211yescharacteristic
12C2×#13093964C2211yescharacteristic
13#15689081C411yescharacteristic
14#15689080—21no—
15#15689079C411yescharacteristic
16#15689078C2211yescharacteristic
17#15689077—21no—
18#15689075—21no—
19C4×#10625324—21no—
20#15688904—21no—
21#15688904—21no—
22#15688904—21no—
23#15688904—21no—
24C2×M32×C47C2211yescharacteristic
25C2×M32×C47C2211yescharacteristic
26C47×#405C2211yescharacteristic
27C22×C4×D47C2×C411yescharacteristic
28C2×#10625329C2×C411yescharacteristic
29C2×#10625324—21no—
30C2×#10625324—21no—
31C2×#10625324—21no—
32C2×#10625324—21no—
33C2×#10625324—21no—
34C2×#10625324D411yescharacteristic
35C2×#10625324D411yescharacteristic
36C2×#10625324D411yescharacteristic
37C2×#10625324D411yescharacteristic
38M16×D47—22no—
39M16×D47—22no—
40C22×C47⋊C8C2×C411yescharacteristic
41C2×C8×D47—21no—
42#13093983C2×C411yescharacteristic
43#13093982—21no—
44#13093981—21no—
45#13093980C812yes—
46C4⋊C4×D47—21no—
47C22⋊C4×D47C812yes—
48C42×D47—21no—
49#13093964—21no—
50#13093964—21no—
51#13093964—21no—
52#13093964—21no—
53C2×C47⋊C16—21no—
54C2×C47⋊C16—21no—
55#13093935—21no—
56#13093934—21no—
57#13093934—21no—
58C4×C47⋊C8—21no—
59C8×Dic47—21no—
60C8×Dic47—21no—
61C2×M16×C47C2×C411yescharacteristic
62C22×C8×C47C2311yescharacteristic
63#117×C47C2×C411yescharacteristic
64M32×C47—21no—
65M32×C47—21no—
66M32×C47—21no—
67M32×C47—21no—
68C2×C16×C47—21no—
69C2×C16×C47—21no—
70#97×C47—21no—
71C4×C8×C47—21no—
72C23×D47C2×C811yescharacteristic
73C22×C4×C47C22×C411yescharacteristic
74C22×Dic47C2×C811yescharacteristic
75C2×C4×D47—21no—
76C2×C4×D47—21no—
77C2×C4×D47—21no—
78C2×C4×D47—21no—
79C2×C4×D47—22no—
80C2×C4×D47C22⋊C411yescharacteristic
81C2×C4×D47C22⋊C411yescharacteristic
82C2×C4×D47M1611yescharacteristic
83C2×C4×D47M1611yescharacteristic
84M16×C47—21no—
85M16×C47M1612yes—
86C2×C8×C47—21no—
87C2×C8×C47C2×D411yescharacteristic
88C2×C8×C47C2×D411yescharacteristic
89C2×C8×C47#4111yescharacteristic
90C2×C8×C47#4111yescharacteristic
91C2×C8×C47#4111yescharacteristic
92C2×C8×C47#4111yescharacteristic
93C4⋊C4×C47—21no—
94C22⋊C4×C47C2×C812yes—
95C42×C47—21no—
96C22⋊Dic47C2×C812yes—
97(C2×D47)⋊C4—22no—
98C4⋊Dic47—21no—
99Dic47⋊C4—22no—
100C4×Dic47—21no—
101C4×Dic47—22no—
102#10625329—21no—
103#10625329M1612yes—
104C2×C47⋊C8—21no—
105C2×C47⋊C8—21no—
106C2×C47⋊C8—21no—
107C2×C47⋊C8C22⋊C411yescharacteristic
108C2×C47⋊C8C22⋊C411yescharacteristic
109#10625324—24no—
110#10625324—21no—
111#10625324—21no—
112#10625324—21no—
113#10625324—21no—
114#10625324—21no—
115#10625324—21no—
116#10625324—21no—
117#10625324—21no—
118C8×D47—24no—
119C16×C47—41no—
120C16×C47—41no—
121C47⋊C16—41no—
122C47⋊C16—41no—
123C23×C47C22×C811yescharacteristic
124C22×D47—21no—
125C22×D47—21no—
126C22×D47—81no—
127C22×D47C22⋊C811yescharacteristic
128C22×D47C22⋊C811yescharacteristic
129C2×C4×C47—22no—
130C2×C4×C47C2×C22⋊C411yescharacteristic
131C2×C4×C47#11711yescharacteristic
132C2×C4×C47#11711yescharacteristic
133C2×C4×C47C2×M1611yescharacteristic
134C2×C4×C47C2×M1611yescharacteristic
135C2×C4×C47C2×M1611yescharacteristic
136C2×Dic47—21no—
137C2×Dic47—21no—
138C2×Dic47—22no—
139C2×Dic47C22⋊C811yescharacteristic
140C2×Dic47C22⋊C811yescharacteristic
141C4×D47—21no—
142C4×D47—21no—
143C4×D47—21no—
144C4×D47—21no—
145C4×D47—21no—
146C4×D47—21no—
147C4×D47—21no—
148C4×D47—21no—
149C4×D47—82no—
150C8×C47—22no—
151C8×C47#12311yescharacteristic
152C8×C47#12311yescharacteristic
153C8×C47#12311yescharacteristic
154C8×C47#12311yescharacteristic
155C47⋊C8—21no—
156C47⋊C8—21no—
157C47⋊C8—22no—
158#12851—471nomaximal, Sylow
159C22×C47—41no—
160C22×C47C2×C22⋊C811yescharacteristic
161C22×C47#43111yescharacteristic
162C22×C47#43111yescharacteristic
163C2×D47—21no—
164C2×D47—21no—
165C2×D47—41no—
166C2×D47—41no—
167C2×D47—81no—
168C2×D47—81no—
169C4×C47—42no—
170C4×C47#38111yescharacteristic
171C4×C47#40711yescharacteristic
172C4×C47#43211yescharacteristic
173C4×C47#43211yescharacteristic
174Dic47—21no—
175Dic47—21no—
176Dic47—42no—
177#2873—471no—
178C2×#349—471no—
179C2×#349—471no—
180#1378—471no—
181#1378—471no—
182#1378—471no—
183#1378D4711yescharacteristic, complemented
184C2×C47—21no—
185C2×C47—21no—
186C2×C47—21no—
187C2×C47#181711yescharacteristic
188D47—41no—
189D47—41no—
190C22×M16—471no—
191C22×M16—471no—
192C2×#117—471no—
193C2×M32—471no—
194C2×M32—471no—
195C2×M32C2×D4711yescharacteristic
196C2×M32C2×D4711yescharacteristic
197#405—471no—
198#405—471no—
199#405—471no—
200#405—941no—
201#405—941no—
202#405C2×D4711yescharacteristic
203C4×M16—941no—
204C4×M16—941no—
205#349—941no—
206#349—941no—
207#349—941no—
208#349—941no—
209C47#1285111yescharacteristic, complemented, Sylow
210C23×C4—471no—
211C2×M16—471no—
212C2×M16—471no—
213C2×M16—471no—
214C2×M16—471no—
215C2×M16—471no—
216C2×M16—941no—
217C2×M16—942no—
218C2×M16—942no—
219C2×M16—941no—
220C2×M16—941no—
221C2×M16—941no—
222C2×M16—941no—
223C2×M16C4×D4711yescharacteristic
224C22×C8—471no—
225C22×C8—941no—
226C22×C8C22×D4711yescharacteristic
227#117—471no—
228#117—472no—
229#117—941no—
230#117—941no—
231#117C4×D4711yescharacteristic
232C2×C4⋊C4—941no—
233C2×C22⋊C4—472no—
234C2×C42—941no—
235M32—21no—
236M32—21no—
237M32—21no—
238M32—21no—
239M32—941no—
240M32—941no—
241M32—941no—
242M32—941no—
243C2×C16—21no—
244C2×C16—21no—
245C2×C16—941no—
246C2×C16—941no—
247#97—21no—
248#97—941no—
249#97—941no—
250#97—941no—
251C4×C8—21no—
252C4×C8—941no—
253C4×C8—941no—
254C4×C8—941no—
255C24—471no—
256C22×C4—471no—
257C22×C4—471no—
258C22×C4—471no—
259C22×C4—471no—
260C22×C4—471no—
261C22×C4—942no—
262C22×C4—941no—
263C22×C4—941no—
264C22×C4—941no—
265C22×C4—941no—
266C22×C4C2×C4×D4711yescharacteristic
267M16—21no—
268M16—472no—
269M16—944no—
270M16—941no—
271M16—941no—
272M16—941no—
273M16—941no—
274M16—941no—
275M16—941no—
276M16—941no—
277M16—941no—
278M16—941no—
279M16#1062532412yes—
280C2×C8—21no—
281C2×C8—471no—
282C2×C8—471no—
283C2×C8—944no—
284C2×C8—941no—
285C2×C8—941no—
286C2×C8—941no—
287C2×C8#1062535011yescharacteristic
288C2×C8#1062535011yescharacteristic
289C2×C8D4×D4711yescharacteristic
290C2×C8D4×D4711yescharacteristic
291C2×C8#1062535211yescharacteristic
292C2×C8#1062535411yescharacteristic
293C4⋊C4—21no—
294C4⋊C4—942no—
295C4⋊C4—941no—
296C22⋊C4—472no—
297C22⋊C4—942no—
298C22⋊C4C8×D4712yes—
299C42—21no—
300C42—942no—
301C42—941no—
302C16—41no—
303C16—41no—
304C16—1881no—
305C16—1881no—
306C23—471no—
307C23—471no—
308C23—941no—
309C23—941no—
310C23—3761no—
311C23C2×C8×D4711yescharacteristic
312C2×C4—22no—
313C2×C4—471no—
314C2×C4—471no—
315C2×C4—941no—
316C2×C4—941no—
317C2×C4—941no—
318C2×C4—941no—
319C2×C4—941no—
320C2×C4—941no—
321C2×C4—941no—
322C2×C4—941no—
323C2×C4—941no—
324C2×C4—941no—
325C2×C4—942no—
326C2×C4—3762no—
327C2×C4C22⋊C4×D4711yescharacteristic
328C2×C4#1309398111yescharacteristic
329C2×C4#1309398211yescharacteristic
330C2×C4M16×D4711yescharacteristic
331C2×C4M16×D4711yescharacteristic
332C2×C4C2×#1062532411yescharacteristic
333C8—22no—
334C8—941no—
335C8—941no—
336C8—942no—
337C8#1309400611yescharacteristic
338C8#1309400611yescharacteristic
339C8#1309400911yescharacteristic
340C8#1309400911yescharacteristic
341C22—41no—
342C22—941no—
343C22—941no—
344C22—3761no—
345C22—3761no—
346C22—1881no—
347C22—1881no—
348C22C22⋊C8×D4711yescharacteristic
349C22#1568917411yescharacteristic
350C22#1568917511yescharacteristic
351C4—42no—
352C4—941no—
353C4—941no—
354C4—1882no—
355C4#1568898511yescharacteristic
356C4#1568908511yescharacteristic
357C4#1568917811yescharacteristic
358C4#1568917911yescharacteristic
359C2—21no—
360C2—21no—
361C2—21no—
362C2—1881no—
363C2—1881no—
364C2#2024345511yescharacteristic
subgroupG/H
centerC4#15688985
commutatorC23×C47C22×C8
FrattiniC22×C8C22×D47
FittingC47×#1378C2
socleC2×C47#1817
prime radicalC23×D47C2×C8
cosocleC22×C8×C47C23
hypercenter#1378D47
hypocenterC47#12851
LCSG ▷ C23×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C4 ◁ C22×C8 ◁ #1378

Complements

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

NH ≅ G/Ntype
4. #20241475C2semidirect
5. #20241474C2semidirect
6. #20241473C2semidirect
7. C47×#1378C2semidirect
183. #1378D47semidirect
209. C47#12851semidirect

Maximal subgroups

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

subgroupindex
#202518042
C2×#156889042
#202414752
#202414742
#202414732
C47×#13782
#1285147