Finite Group Databasebeta

← #26134657

Subgroups — #26134657

Order 12032.

474 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13093967C211yesmaximal, characteristic
2C2×#15688950C211yesmaximal, characteristic, complemented
3C2×#15688927C211yesmaximal, characteristic, complemented
4C2×#15688923C211yesmaximal, characteristic
5C2×C4×C47⋊C16C211yesmaximal, characteristic, complemented
6#20244254C211yesmaximal, characteristic
7C47×#1969C211yesmaximal, characteristic, complemented
8C22×D376C2211yescharacteristic
9C2×#13093967—22no—
10C2×#13093967—22no—
11C2×#13093967C414yescomplemented
12C22×C47⋊C16C2211yescharacteristic
13C22×C47⋊C16C2211yescharacteristic
14C2×#13093958C2211yescharacteristic
15C2×#13093946—21no—
16#15689025—21no—
17#15688950—22no—
18#15688927—22no—
19#15688923—22no—
20C4×C47⋊C16—22no—
21C22×Q16×C47C2211yescharacteristic
22C2×#107×C47C2211yescharacteristic
23C2×#103×C47—21no—
24C2×C4×C8×C47C2211yescharacteristic
25C47×#391—21no—
26C22×D188—21no—
27C2×D376—21no—
28C2×D376—21no—
29C2×D376—21no—
30C2×D376—21no—
31C2×D376—21no—
32C2×D376C2×C412yes—
33C2×C4⋊Dic47—21no—
34C2×(C2×D47)⋊C4—42no—
35#13093967—28no—
36C2×C47⋊C16—21no—
37C2×C47⋊C16—21no—
38C2×C47⋊C16C2×C412yes—
39C2×C47⋊C16D412yes—
40C2×C47⋊C16D412yes—
41C2×C47⋊C16D412yes—
42#13093958—21no—
43#13093958—21no—
44#13093946—42no—
45C22×Q8×C47—21no—
46C2×Q16×C47—21no—
47C2×Q16×C47—21no—
48C2×Q16×C47—21no—
49C2×Q16×C47—21no—
50C2×Q16×C47—21no—
51C2×Q16×C47C2×C412yes—
52C22×C8×C47D411yescharacteristic
53C22×C8×C47C2311yescharacteristic
54C2×C4⋊C4×C47—21no—
55C2×C42×C47D411yescharacteristic
56#107×C47—21no—
57#107×C47—21no—
58#103×C47—42no—
59C4×C8×C47—21no—
60C4×C8×C47—21no—
61#95×C47—42no—
62C23×D47—41no—
63C2×Q8×C47—22no—
64C2×Q8×C47—41no—
65C2×Q8×C47—41no—
66C2×Q8×C47—41no—
67C2×Q8×C47—41no—
68C2×Q8×C47—41no—
69C22×C4×C47—41no—
70C22×C4×C47—41no—
71C22×C4×C47D812yes—
72C22×C4×C47C2×D411yescharacteristic
73C22×Dic47—41no—
74C2×D188—22no—
75C2×D188—41no—
76C2×D188—41no—
77C2×D188—41no—
78C2×D188—41no—
79C2×D188—41no—
80Q16×C47—22no—
81Q16×C47—22no—
82Q16×C47—41no—
83Q16×C47—41no—
84C2×C8×C47—21no—
85C2×C8×C47—21no—
86C2×C8×C47D812yes—
87C2×C8×C47C22×C411yescharacteristic
88C2×C8×C47C2×D411yescharacteristic
89C2×C8×C47C2×D411yescharacteristic
90C2×C8×C47C2×D411yescharacteristic
91C2×C8×C47#4111yescharacteristic
92C2×C8×C47#4111yescharacteristic
93C4⋊C4×C47—41no—
94C4⋊C4×C47—41no—
95C42×C47—21no—
96C42×C47—21no—
97(C2×D47)⋊C4—84no—
98C4⋊Dic47—41no—
99C4⋊Dic47—41no—
100D376—22no—
101D376—22no—
102D376—41no—
103D376—41no—
104C47⋊C16—22no—
105C47⋊C16C22⋊C414yescomplemented
106C23×C47C2×D811yescharacteristic
107C22×D47—42no—
108C22×D47—81no—
109C22×D47—81no—
110C22×D47—82no—
111C22×D47—82no—
112Q8×C47—42no—
113Q8×C47—42no—
114Q8×C47—81no—
115Q8×C47—81no—
116C2×C4×C47—22no—
117C2×C4×C47—22no—
118C2×C4×C47—42no—
119C2×C4×C47—81no—
120C2×C4×C47—81no—
121C2×C4×C47—81no—
122C2×C4×C47—82no—
123C2×C4×C47SD3214yescomplemented
124C2×C4×C47C4×D411yescharacteristic
125C2×C4×C47#12111yescharacteristic
126C2×C4×C47#12711yescharacteristic
127C2×C4×C47C2×D811yescharacteristic
128C2×C4×C47#13511yescharacteristic
129C2×C4×C47#13511yescharacteristic
130C2×Dic47—81no—
131C2×Dic47—82no—
132D188—42no—
133D188—42no—
134D188—81no—
135D188—81no—
136C8×C47—22no—
137C8×C47C2×C22⋊C411yescharacteristic
138C8×C47C4×D411yescharacteristic
139C8×C47#12111yescharacteristic
140C8×C47#12411yescharacteristic
141#13237—471nomaximal, Sylow
142C22×C47C4×D811yescharacteristic
143C22×C47#46611yescharacteristic
144C22×C47#49311yescharacteristic
145C22×C47C2×SD3212yes—
146C22×C47#50812yes—
147C2×D47—84no—
148C2×D47—82no—
149C2×D47—162no—
150C2×D47—161no—
151C2×D47—161no—
152C4×C47—24no—
153C4×C47—82no—
154C4×C47—161no—
155C4×C47#39011yescharacteristic
156C4×C47C4×D811yescharacteristic
157C4×C47#46611yescharacteristic
158C4×C47#49511yescharacteristic
159Dic47—161no—
160C22×SD32—471no—
161C2×#367—471no—
162C2×#358—471no—
163C2×#357—471no—
164C2×C4×C16—471no—
165#1970—471no—
166#1969D4711yescharacteristic, complemented
167C2×C47#197011yescharacteristic
168C2×C47C4×SD3212yes—
169C2×C47#221712yes—
170C2×C47#224811yescharacteristic
171C2×C47#224911yescharacteristic
172D47—162no—
173C22×Q16C2×D4711yescharacteristic
174C22×D8—471no—
175C2×SD32—474no—
176C2×SD32—942no—
177C2×SD32—942no—
178C22×C16—471no—
179C22×C16—471no—
180C2×#107—471no—
181C2×#107C2×D4711yescharacteristic
182C2×#103—21no—
183C2×#102—941no—
184C2×C4×C8C2×D4711yescharacteristic
185#391—21no—
186#390—941no—
187#367—942no—
188#358—942no—
189#357—942no—
190C4×C16—942no—
191C47#1323711yescharacteristic, complemented, Sylow
192C22×Q8—21no—
193C22×D4—941no—
194C2×Q16—21no—
195C2×Q16—21no—
196C2×Q16—21no—
197C2×Q16—21no—
198C2×Q16—21no—
199C2×Q16C4×D4712yes—
200C2×D8—472no—
201C2×D8—941no—
202C2×D8—941no—
203C2×D8—941no—
204C2×D8—941no—
205C2×D8—941no—
206C22×C8C22⋊D4711yescharacteristic
207C22×C8C22×D4711yescharacteristic
208C2×C4⋊C4—21no—
209C2×C4⋊C4—941no—
210C2×C22⋊C4—1882no—
211C2×C42C22⋊D4711yescharacteristic
212SD32—948no—
213C2×C16—472no—
214C2×C16—472no—
215C2×C16—472no—
216C2×C16—472no—
217C2×C16—941no—
218C2×C16—941no—
219#107—21no—
220#107—21no—
221#107—941no—
222#107—941no—
223#103—42no—
224#102—1882no—
225C4×C8—21no—
226C4×C8—21no—
227#95—42no—
228C24—1881no—
229C2×Q8—22no—
230C2×Q8—41no—
231C2×Q8—41no—
232C2×Q8—41no—
233C2×Q8—41no—
234C2×Q8—41no—
235C2×D4—942no—
236C2×D4—1881no—
237C2×D4—1881no—
238C2×D4—1881no—
239C2×D4—1881no—
240C2×D4—1881no—
241C22×C4—41no—
242C22×C4—41no—
243C22×C4—1881no—
244C22×C4#1062533412yes—
245C22×C4C2×C22⋊D4711yescharacteristic
246Q16—22no—
247Q16—22no—
248Q16—41no—
249Q16—41no—
250D8—942no—
251D8—942no—
252D8—1881no—
253D8—1881no—
254C2×C8—21no—
255C2×C8—21no—
256C2×C8#1062533412yes—
257C2×C8C2×C4×D4711yescharacteristic
258C2×C8#1062535011yescharacteristic
259C2×C8D4×D4711yescharacteristic
260C2×C8D4×D4711yescharacteristic
261C2×C8D4×D4711yescharacteristic
262C2×C8#1062535211yescharacteristic
263C4⋊C4—41no—
264C4⋊C4—41no—
265C4⋊C4—1881no—
266C4⋊C4—1881no—
267C22⋊C4—3764no—
268C42—21no—
269C42—21no—
270C16—474no—
271C16—942no—
272C23—3761no—
273C23—3762no—
274C23—3762no—
275C23—3761no—
276C23—1882no—
277C23C2×#1062533411yescharacteristic
278Q8—42no—
279Q8—42no—
280Q8—81no—
281Q8—81no—
282D4—3761no—
283D4—3761no—
284D4—1882no—
285D4—1882no—
286C2×C4—22no—
287C2×C4—22no—
288C2×C4—42no—
289C2×C4—81no—
290C2×C4—81no—
291C2×C4—81no—
292C2×C4—82no—
293C2×C4—3761no—
294C2×C4—3762no—
295C2×C4#1309396714yescomplemented
296C2×C4C4×C22⋊D4711yescharacteristic
297C2×C4#1309399611yescharacteristic
298C2×C4#1309402011yescharacteristic
299C2×C4C2×#1062533411yescharacteristic
300C2×C4#1309404411yescharacteristic
301C2×C4#1309404411yescharacteristic
302C8—22no—
303C8C22⋊C4×D4711yescharacteristic
304C8(C22⋊D47)⋊C411yescharacteristic
305C8#1309399711yescharacteristic
306C8#1309401011yescharacteristic
307C22—3762no—
308C22—3764no—
309C22—7521no—
310C22—7521no—
311C22—7522no—
312C22C4×#1062533411yescharacteristic
313C22#1568935711yescharacteristic
314C22#1568949911yescharacteristic
315C22C2×#1309396712yes—
316C22#1568955312yes—
317C4—24no—
318C4—82no—
319C4—161no—
320C4—7521no—
321C4#1568902311yescharacteristic
322C4C4×#1062533411yescharacteristic
323C4#1568935711yescharacteristic
324C4#1568950511yescharacteristic
325C2—7522no—
326C2#2024425311yescharacteristic
327C2C4×#1309396712yes—
328C2#2024548612yes—
329C2#2024564511yescharacteristic
330C2#2024564711yescharacteristic
subgroupG/H
centerC23C2×#10625334
commutatorC2×C8×C47C22×C4
FrattiniC22×C8C22×D47
FittingC47×#1969C2
socleC23×C47C2×D8
prime radicalC22×D376C22
cosocleC22×C8×C47C23
hypercenter#1969D47
hypocenterC47#13237
LCSG ▷ C2×C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×C8 ◁ #1969

Complements

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

NH ≅ G/Ntype
2. C2×#15688950C2semidirect
3. C2×#15688927C2semidirect
5. C2×C4×C47⋊C16C2semidirect
7. C47×#1969C2semidirect
11. C2×#13093967C4semidirect
105. C47⋊C16C22⋊C4semidirect
123. C2×C4×C47SD32semidirect
166. #1969D47semidirect
191. C47#13237semidirect
295. C2×C4#13093967semidirect

Maximal subgroups

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

subgroupindex
C22×#130939672
C2×#156889502
C2×#156889272
C2×#156889232
C2×C4×C47⋊C162
#202442542
C47×#19692
#1323747