Finite Group Databasebeta

← #26132353

Subgroups — #26132353

Order 12032.

474 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689205C211yesmaximal, characteristic
2#20245143C211yesmaximal, characteristic, complemented
3C2×#15688937C211yesmaximal, characteristic
4C2×#15688935C211yesmaximal, characteristic
5#20243558C211yesmaximal, characteristic, complemented
6#20241496C211yesmaximal, characteristic, complemented
7C47×#1387C211yesmaximal, characteristic, complemented
8C22×D376C2211yescharacteristic
9C2×#13093986—21no—
10C2×#13093964C2211yescharacteristic
11#15689205—21no—
12#15689205—21no—
13#15689205C412yes—
14#15689205C412yes—
15C2×#13093960C2211yescharacteristic
16C2×#13093959—21no—
17#15689146—21no—
18C2×#13093944—21no—
19C2×C8×Dic47C2211yescharacteristic
20Dic47⋊C16—21no—
21Dic47⋊C16—21no—
22#15688937—22no—
23#15688935—22no—
24C2×M32×C47C2211yescharacteristic
25C2×#108×C47C2211yescharacteristic
26C2×#107×C47C2211yescharacteristic
27C22×D188—21no—
28C22×C4×D47—41no—
29C2×D376—21no—
30C2×D376—21no—
31C2×D376—21no—
32C2×D376C2×C412yes—
33C2×D376D412yes—
34C2×D376Q812yes—
35C2×#10625329—21no—
36C22×C47⋊C8D411yescharacteristic
37#13093986—22no—
38#13093986—22no—
39#13093986—41no—
40#13093986—41no—
41C2×(C2×D47)⋊C4—41no—
42C2×C4×Dic47D411yescharacteristic
43#13093964—21no—
44#13093964—21no—
45C2×C47⋊C16—21no—
46#13093960—21no—
47#13093960—21no—
48#13093959—42no—
49Dic47⋊C8—41no—
50Dic47⋊C8—41no—
51#13093944—22no—
52#13093944—22no—
53C8×Dic47C2×C411yescharacteristic
54C8×Dic47C2×C411yescharacteristic
55C8×Dic47D411yescharacteristic
56C8×Dic47D411yescharacteristic
57C2×M16×C47—21no—
58C22×C8×C47C2311yescharacteristic
59C2×C4⋊C4×C47—21no—
60M32×C47—21no—
61M32×C47—21no—
62C2×C16×C47—21no—
63#108×C47—21no—
64#108×C47—21no—
65#107×C47—21no—
66#107×C47C2×C412yes—
67C23×D47—41no—
68C22×C4×C47—41no—
69C22×C4×C47C2×D411yescharacteristic
70C22×Dic47SD1611yescharacteristic
71C22×Dic47SD1611yescharacteristic
72C2×D188—22no—
73C2×D188—22no—
74C2×D188—22no—
75C2×D188—41no—
76C2×D188—41no—
77C2×D188—41no—
78C2×C4×D47—42no—
79C2×C4×D47—42no—
80C2×C4×D47—84no—
81M16×C47—41no—
82M16×C47—41no—
83C2×C8×C47—41no—
84C2×C8×C47C22×C411yescharacteristic
85C2×C8×C47C2×D411yescharacteristic
86C2×C8×C47C2×D411yescharacteristic
87C2×C8×C47C2×Q811yescharacteristic
88C2×C8×C47#4111yescharacteristic
89C2×C8×C47#4111yescharacteristic
90C4⋊C4×C47—22no—
91C4⋊C4×C47—41no—
92(C2×D47)⋊C4—42no—
93(C2×D47)⋊C4—42no—
94C4×Dic47C22⋊C411yescharacteristic
95C4×Dic47C22⋊C411yescharacteristic
96C4×Dic47D811yescharacteristic
97C4×Dic47D811yescharacteristic
98#10625329—41no—
99#10625329—41no—
100C2×C47⋊C8—21no—
101C2×C47⋊C8—21no—
102C2×C47⋊C8—41no—
103C2×C47⋊C8C22⋊C411yescharacteristic
104C2×C47⋊C8C22⋊C411yescharacteristic
105D376—22no—
106D376—22no—
107D376—22no—
108D376C4⋊C414yes—
109C16×C47—41no—
110C47⋊C16—41no—
111C23×C47C2×SD1611yescharacteristic
112C22×D47—42no—
113C22×D47—42no—
114C22×D47—42no—
115C22×D47—82no—
116C22×D47—82no—
117C2×C4×C47—42no—
118C2×C4×C47—82no—
119C2×C4×C47C2×C22⋊C411yescharacteristic
120C2×C4×C47#12111yescharacteristic
121C2×C4×C47C22⋊Q811yescharacteristic
122C2×C4×C47C2×D811yescharacteristic
123C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
124C2×C4×C47#13711yescharacteristic
125C2×Dic47—22no—
126C2×Dic47—41no—
127C2×Dic47#10211yescharacteristic
128C2×Dic47#10211yescharacteristic
129C2×Dic47#10211yescharacteristic
130C2×Dic47#10211yescharacteristic
131D188—24no—
132D188—42no—
133D188—42no—
134D188—42no—
135C4×D47—84no—
136C4×D47—84no—
137C8×C47—81no—
138C8×C47C2×C4⋊C411yescharacteristic
139C8×C47#11711yescharacteristic
140C8×C47#12111yescharacteristic
141C8×C47C22⋊Q811yescharacteristic
142C47⋊C8—21no—
143C47⋊C8—21no—
144C47⋊C8—81no—
145#12818—471nomaximal, Sylow
146C22×C47—21no—
147C22×C47—21no—
148C22×C47C2×#10211yescharacteristic
149C22×C47#46111yescharacteristic
150C22×C47#47611yescharacteristic
151C2×D47—44no—
152C2×D47—84no—
153C2×D47—84no—
154C2×D47—82no—
155C2×D47—82no—
156C4×C47—82no—
157C4×C47#38011yescharacteristic
158C4×C47#41711yescharacteristic
159C4×C47#45911yescharacteristic
160C4×C47#47411yescharacteristic
161Dic47—21no—
162Dic47—21no—
163Dic47—21no—
164Dic47#36112yescomplemented
165C2×C4×D8—471no—
166#2150—471no—
167C2×#361—471no—
168C2×#361—471no—
169#1848—471no—
170#1387—471no—
171#1387D4711yescharacteristic, complemented
172C2×C47—21no—
173C2×C47—21no—
174C2×C47#180211yescharacteristic
175C2×C47C2×#36111yescharacteristic
176C2×C47#214811yescharacteristic
177D47—84no—
178C22×D8—471no—
179C2×C4×D4—941no—
180C2×M32—471no—
181C2×M32C2×D4711yescharacteristic
182C4×D8—472no—
183C4×D8—472no—
184C4×D8—941no—
185C4×D8—941no—
186C2×#108—471no—
187C2×#108—941no—
188C2×#108C2×D4711yescharacteristic
189C2×#107C2×D4711yescharacteristic
190#423—941no—
191C2×#102—941no—
192C2×C4×C8—471no—
193C4⋊C16—941no—
194C4⋊C16—941no—
195#361—942no—
196#361—942no—
197C47#1281811yescharacteristic, complemented, Sylow
198C22×D4—941no—
199C23×C4—1881no—
200C2×D8—472no—
201C2×D8—472no—
202C2×D8—472no—
203C2×D8—941no—
204C2×D8—941no—
205C2×D8—941no—
206C2×M16—21no—
207C2×M16—941no—
208C22×C8—471no—
209C22×C8C22×D4711yescharacteristic
210C4×D4—942no—
211C4×D4—942no—
212C4×D4—1881no—
213C4×D4—1881no—
214C2×C4⋊C4—21no—
215C2×C22⋊C4—1881no—
216C2×C42—471no—
217M32—21no—
218M32—21no—
219M32—941no—
220M32—941no—
221C2×C16—21no—
222C2×C16—941no—
223#108—21no—
224#108—21no—
225#108—941no—
226#108—941no—
227#108—1882no—
228#107—21no—
229#107C4×D4712yes—
230C4⋊C8—1881no—
231C4⋊C8—1881no—
232#102—942no—
233#102—942no—
234C4×C8—471no—
235C4×C8—471no—
236C4×C8—471no—
237C4×C8—471no—
238C24—1881no—
239C2×D4—942no—
240C2×D4—942no—
241C2×D4—942no—
242C2×D4—1881no—
243C2×D4—1881no—
244C2×D4—1881no—
245C22×C4—41no—
246C22×C4—471no—
247C22×C4—471no—
248C22×C4—3764no—
249C22×C4—1882no—
250C22×C4—1882no—
251C22×C4D4×D4711yescharacteristic
252D8—474no—
253D8—942no—
254D8—942no—
255D8—942no—
256M16—41no—
257M16—41no—
258M16—1881no—
259M16—1881no—
260C2×C8—41no—
261C2×C8—471no—
262C2×C8—471no—
263C2×C8—941no—
264C2×C8—941no—
265C2×C8—1881no—
266C2×C8C2×C4×D4711yescharacteristic
267C2×C8#1062535011yescharacteristic
268C2×C8#1062535011yescharacteristic
269C2×C8D4×D4711yescharacteristic
270C2×C8D4×D4711yescharacteristic
271C2×C8Q8×D4711yescharacteristic
272C4⋊C4—22no—
273C4⋊C4—41no—
274C22⋊C4—1882no—
275C22⋊C4—1882no—
276C42—471no—
277C42—471no—
278C42—471no—
279C42—471no—
280C16—41no—
281C16—1881no—
282C23—3762no—
283C23—3762no—
284C23—1882no—
285C23—1882no—
286C23—1882no—
287C23SD16×D4711yescharacteristic
288D4—944no—
289D4—1882no—
290D4—1882no—
291D4—1882no—
292C2×C4—42no—
293C2×C4—82no—
294C2×C4—471no—
295C2×C4—471no—
296C2×C4—471no—
297C2×C4—471no—
298C2×C4—942no—
299C2×C4—3764no—
300C2×C4—3764no—
301C2×C4—1881no—
302C2×C4C22⋊C4×D4711yescharacteristic
303C2×C4#1309399711yescharacteristic
304C2×C4#1309400211yescharacteristic
305C2×C4D8×D4711yescharacteristic
306C2×C4#1309405111yescharacteristic
307C2×C4#1309405611yescharacteristic
308C8—81no—
309C8—941no—
310C8—941no—
311C8—3761no—
312C8C4⋊C4×D4711yescharacteristic
313C8#1309398111yescharacteristic
314C8#1309399711yescharacteristic
315C8#1309400211yescharacteristic
316C22—21no—
317C22—21no—
318C22—3764no—
319C22—3764no—
320C22—3762no—
321C22—3762no—
322C22—1884no—
323C22#102×D4711yescharacteristic
324C22#1568932711yescharacteristic
325C22#1568941211yescharacteristic
326C4—82no—
327C4—472no—
328C4—941no—
329C4—941no—
330C4—941no—
331C4#1568898211yescharacteristic
332C4#1568912311yescharacteristic
333C4#1568931711yescharacteristic
334C4#1568940211yescharacteristic
335C2—21no—
336C2—21no—
337C2—3764no—
338C2#2024338711yescharacteristic
339C2#361×D4711yescharacteristic
340C2#2024513611yescharacteristic
subgroupG/H
centerC22#102×D47
commutatorC2×C8×C47C22×C4
FrattiniC22×C8C22×D47
FittingC47×#1387C2
socleC22×C47C2×#102
prime radicalC22×D376C22
cosocleC22×C8×C47C23
hypercenter#1387D47
hypocenterC47#12818
LCSG ▷ C2×C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #1387

Complements

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

NH ≅ G/Ntype
2. #20245143C2semidirect
5. #20243558C2semidirect
6. #20241496C2semidirect
7. C47×#1387C2semidirect
164. Dic47#361semidirect
171. #1387D47semidirect
197. C47#12818semidirect

Maximal subgroups

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

subgroupindex
C2×#156892052
#202451432
C2×#156889372
C2×#156889352
#202435582
#202414962
C47×#13872
#1281847