Finite Group Databasebeta

← #26132795

Subgroups — #26132795

Order 12032.

404 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#108×D47C211yesmaximal, characteristic
2C2×#15688953C211yesmaximal, characteristic, complemented
3C2×#15688952C211yesmaximal, characteristic, complemented
4C2×(C2×D47)⋊C16C211yesmaximal, characteristic
5#20243423C211yesmaximal, characteristic
6#20241481C211yesmaximal, characteristic, complemented
7C47×#1381C211yesmaximal, characteristic, complemented
8C2×M16×D47—21no—
9C22×C8×D47C2211yescharacteristic
10C22×C47⋊C16C2211yescharacteristic
11C2×#13093960C2211yescharacteristic
12C2×#13093960C2211yescharacteristic
13C2×#13093959—21no—
14#108×D47—22no—
15#108×D47—22no—
16#15689086—21no—
17#15688953—22no—
18#15688952—22no—
19(C2×D47)⋊C16C412yes—
20(C2×D47)⋊C16C412yes—
21#15688887—21no—
22C22×C16×C47C2211yescharacteristic
23C2×#108×C47C2211yescharacteristic
24C2×#108×C47C2211yescharacteristic
25C22×C4×D47D411yescharacteristic
26C2×#10625329—21no—
27C2×#10625329—21no—
28C2×#10625324—41no—
29M16×D47—24no—
30M16×D47—42no—
31C22×C47⋊C8D411yescharacteristic
32C2×C8×D47—21no—
33C2×C8×D47—21no—
34C2×C8×D47—21no—
35C2×C8×D47—21no—
36C2×C8×D47—41no—
37C2×C8×D47C2×C411yescharacteristic
38C2×C8×D47C2×C411yescharacteristic
39C2×C8×D47Q811yescharacteristic
40C2×C8×D47Q811yescharacteristic
41C2×C47⋊C16—21no—
42C2×C47⋊C16—21no—
43C2×C47⋊C16C2×C412yes—
44#13093960—21no—
45#13093960—21no—
46#13093960—21no—
47#13093960D412yes—
48#13093959—24no—
49(C2×D47)⋊C8—41no—
50(C2×D47)⋊C8—41no—
51C2×M16×C47—21no—
52C2×M16×C47—21no—
53C22×C8×C47C2311yescharacteristic
54C2×C16×C47—21no—
55C2×C16×C47—21no—
56C2×C16×C47C2×C412yes—
57#108×C47—21no—
58#108×C47—21no—
59#108×C47—21no—
60#108×C47D412yes—
61C23×D47Q1611yescharacteristic
62C22×C4×C47C2×D411yescharacteristic
63C22×Dic47Q1611yescharacteristic
64C2×C4×D47—21no—
65C2×C4×D47—21no—
66C2×C4×D47—21no—
67C2×C4×D47—21no—
68C2×C4×D47C4⋊C411yescharacteristic
69C2×C4×D47C4⋊C411yescharacteristic
70C2×C4×D47D811yescharacteristic
71C2×C4×D47D811yescharacteristic
72M16×C47—22no—
73M16×C47—41no—
74M16×C47—41no—
75M16×C47—41no—
76C2×C8×C47—41no—
77C2×C8×C47—41no—
78C2×C8×C47C22×C411yescharacteristic
79C2×C8×C47C2×D411yescharacteristic
80C2×C8×C47C2×D411yescharacteristic
81C2×C8×C47C2×Q811yescharacteristic
82C2×C8×C47#4111yescharacteristic
83C2×C8×C47#4111yescharacteristic
84#10625329—22no—
85#10625329—41no—
86#10625329—41no—
87#10625329—41no—
88C2×C47⋊C8—21no—
89C2×C47⋊C8—21no—
90C2×C47⋊C8—41no—
91C2×C47⋊C8—41no—
92C2×C47⋊C8C4⋊C411yescharacteristic
93C2×C47⋊C8C4⋊C411yescharacteristic
94#10625324—44no—
95C8×D47—21no—
96C8×D47—21no—
97C8×D47—21no—
98C8×D47—21no—
99C8×D47—21no—
100C8×D47—21no—
101C8×D47—21no—
102C8×D47—21no—
103C8×D47—44no—
104C16×C47—22no—
105C47⋊C16—22no—
106C23×C47C2×Q1611yescharacteristic
107C22×D47—21no—
108C22×D47—21no—
109C22×D47—22no—
110C22×D47—41no—
111C22×D47#10711yescharacteristic
112C22×D47#10711yescharacteristic
113C2×C4×C47C2×C4⋊C411yescharacteristic
114C2×C4×C47#12011yescharacteristic
115C2×C4×C47#12311yescharacteristic
116C2×C4×C47C2×D811yescharacteristic
117C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
118C2×C4×C47#13711yescharacteristic
119C2×Dic47—21no—
120C2×Dic47—21no—
121C2×Dic47#10711yescharacteristic
122C2×Dic47#10711yescharacteristic
123C4×D47—21no—
124C4×D47—21no—
125C4×D47—21no—
126C4×D47—21no—
127C4×D47—21no—
128C4×D47—21no—
129C4×D47—21no—
130C4×D47—21no—
131C8×C47—42no—
132C8×C47—81no—
133C8×C47C4×D411yescharacteristic
134C8×C47C4×D411yescharacteristic
135C8×C47C22⋊Q811yescharacteristic
136C8×C47C22⋊Q811yescharacteristic
137C47⋊C8—21no—
138C47⋊C8—21no—
139C47⋊C8—42no—
140C47⋊C8—81no—
141#12922—471nomaximal, Sylow
142C22×C47—21no—
143C22×C47—21no—
144C22×C47C2×#10711yescharacteristic
145C22×C47#45111yescharacteristic
146C22×C47#48411yescharacteristic
147C2×D47—21no—
148C2×D47—21no—
149C2×D47—21no—
150C2×D47—21no—
151C2×D47—21no—
152C2×D47—42no—
153C2×D47—42no—
154C2×D47#36812yescomplemented
155C4×C47#38511yescharacteristic
156C4×C47#42811yescharacteristic
157C4×C47#44711yescharacteristic
158C4×C47#48011yescharacteristic
159Dic47—21no—
160Dic47—21no—
161C22×#108—471no—
162C2×#368—471no—
163C2×#368—471no—
164C2×C22⋊C16—471no—
165#1810—471no—
166#1381—471no—
167#1381D4711yescharacteristic, complemented
168C2×C47—21no—
169C2×C47—21no—
170C2×C47#185211yescharacteristic
171C2×C47C2×#36811yescharacteristic
172C2×C47#216111yescharacteristic
173D47—22no—
174D47—41no—
175C22×M16—941no—
176C23×C8—471no—
177C22×C16—471no—
178C22×C16C2×D4711yescharacteristic
179C2×#108—471no—
180C2×#108—471no—
181C2×#108—942no—
182C2×#108—941no—
183C2×#108—942no—
184C2×#108C2×D4711yescharacteristic
185C2×#108C2×D4711yescharacteristic
186#407—941no—
187#368—942no—
188#368—942no—
189C22⋊C16—472no—
190C22⋊C16—472no—
191#341—941no—
192C47#1292211yescharacteristic, complemented, Sylow
193C23×C4—471no—
194C2×M16—21no—
195C2×M16—21no—
196C2×M16—944no—
197C2×M16—941no—
198C2×M16—941no—
199C2×M16—1881no—
200C2×M16—1882no—
201C22×C8—471no—
202C22×C8—471no—
203C22×C8—471no—
204C22×C8—471no—
205C22×C8—471no—
206C22×C8—941no—
207C22×C8—941no—
208C22×C8—941no—
209C22×C8—941no—
210C22×C8—1881no—
211C22×C8C22×D4711yescharacteristic
212C2×C16—21no—
213C2×C16—21no—
214C2×C16—472no—
215C2×C16—941no—
216C2×C16—941no—
217C2×C16C4×D4712yes—
218#108—21no—
219#108—21no—
220#108—21no—
221#108—472no—
222#108—944no—
223#108—941no—
224#108—941no—
225#108—941no—
226#108D18812yes—
227C22⋊C8—1881no—
228C22⋊C8—1881no—
229C24—471no—
230C22×C4—471no—
231C22×C4—471no—
232C22×C4—471no—
233C22×C4—471no—
234C22×C4—471no—
235C22×C4—941no—
236C22×C4—941no—
237C22×C4—941no—
238C22×C4—941no—
239C22×C4D4×D4711yescharacteristic
240M16—22no—
241M16—41no—
242M16—41no—
243M16—41no—
244M16—942no—
245M16—1884no—
246M16—1881no—
247M16—1881no—
248M16—1881no—
249C2×C8—41no—
250C2×C8—41no—
251C2×C8—471no—
252C2×C8—471no—
253C2×C8—941no—
254C2×C8—941no—
255C2×C8—941no—
256C2×C8—941no—
257C2×C8—941no—
258C2×C8—941no—
259C2×C8—941no—
260C2×C8—941no—
261C2×C8—941no—
262C2×C8—941no—
263C2×C8—1884no—
264C2×C8—1881no—
265C2×C8—1881no—
266C2×C8C2×C4×D4711yescharacteristic
267C2×C8C2×D18811yescharacteristic
268C2×C8#1062535011yescharacteristic
269C2×C8D4×D4711yescharacteristic
270C2×C8#1062535211yescharacteristic
271C2×C8Q8×D4711yescharacteristic
272C16—22no—
273C16—942no—
274C23—471no—
275C23—471no—
276C23—942no—
277C23—941no—
278C23—941no—
279C23—1881no—
280C23Q16×D4711yescharacteristic
281C2×C4—471no—
282C2×C4—471no—
283C2×C4—941no—
284C2×C4—941no—
285C2×C4—941no—
286C2×C4—941no—
287C2×C4—941no—
288C2×C4—941no—
289C2×C4—941no—
290C2×C4—941no—
291C2×C4—941no—
292C2×C4—941no—
293C2×C4C4⋊C4×D4711yescharacteristic
294C2×C4#1309399411yescharacteristic
295C2×C4#1309400611yescharacteristic
296C2×C4D8×D4711yescharacteristic
297C2×C4#1309405111yescharacteristic
298C2×C4#1309405311yescharacteristic
299C8—42no—
300C8—81no—
301C8—941no—
302C8—941no—
303C8—3761no—
304C8—1882no—
305C8(C22⋊D47)⋊C411yescharacteristic
306C8C4×D18811yescharacteristic
307C8#1309400211yescharacteristic
308C8#1309400411yescharacteristic
309C22—21no—
310C22—21no—
311C22—472no—
312C22—941no—
313C22—941no—
314C22—941no—
315C22—941no—
316C22—941no—
317C22—1882no—
318C22—1882no—
319C22#107×D4711yescharacteristic
320C22#1568928011yescharacteristic
321C22#1568945711yescharacteristic
322C4—941no—
323C4—941no—
324C4#1568899711yescharacteristic
325C4#1568916211yescharacteristic
326C4#1568925811yescharacteristic
327C4#1568943511yescharacteristic
328C2—21no—
329C2—21no—
330C2—942no—
331C2—1881no—
332C2#2024357711yescharacteristic
333C2#368×D4711yescharacteristic
334C2#2024518111yescharacteristic
subgroupG/H
centerC2×C4D8×D47
commutatorC2×C8×C47C22×C4
FrattiniC22×C8C22×D47
FittingC47×#1381C2
socleC22×C47C2×#107
prime radicalC23×D47Q16
cosocleC22×C8×C47C23
hypercenter#1381D47
hypocenterC47#12922
LCSG ▷ C2×C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×C8 ◁ #1381

Complements

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

NH ≅ G/Ntype
2. C2×#15688953C2semidirect
3. C2×#15688952C2semidirect
6. #20241481C2semidirect
7. C47×#1381C2semidirect
154. C2×D47#368semidirect
167. #1381D47semidirect
192. C47#12922semidirect

Maximal subgroups

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

subgroupindex
C2×#108×D472
C2×#156889532
C2×#156889522
C2×(C2×D47)⋊C162
#202434232
#202414812
C47×#13812
#1292247