Finite Group Databasebeta

← #27180235

Subgroups — #27180235

Order 12928.

314 conjugacy classes of subgroups.

The subgroup lattice has 314 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20265731C211yesmaximal, characteristic
2#20265308C211yesmaximal, characteristic, complemented
3#20265307C211yesmaximal, characteristic, complemented
4#20265306C211yesmaximal, characteristic, complemented
5#20265306C211yesmaximal, characteristic, complemented
6#20265305C211yesmaximal, characteristic, complemented
7#20265305C211yesmaximal, characteristic, complemented
8#20265304C211yesmaximal, characteristic, complemented
9#20265239C211yesmaximal, characteristic
10#20265237C211yesmaximal, characteristic
11#20265237C211yesmaximal, characteristic
12#20265236C211yesmaximal, characteristic
13#20265233C211yesmaximal, characteristic
14#20265232C211yesmaximal, characteristic
15#446×C101C211yesmaximal, characteristic, complemented
16#15692254C411yescharacteristic
17#15692253C411yescharacteristic
18#15692245C411yescharacteristic
19#15692245C411yescharacteristic
20#15692235C411yescharacteristic
21#15692233C411yescharacteristic
22#15692233C411yescharacteristic
23#15692231C411yescharacteristic
24C4×Dic202C2211yescharacteristic
25C4×Dic202C2211yescharacteristic
26C4×Dic202C2211yescharacteristic
27#15692212C2211yescharacteristic
28#15692212C2211yescharacteristic
29C42×D101C2211yescharacteristic
30C4⋊#11717579C2211yescharacteristic
31C4⋊#11717579C2211yescharacteristic
32C4⋊#11717579C2211yescharacteristic
33#15692184C2211yescharacteristic
34#15692184C2211yescharacteristic
35#15692184C2211yescharacteristic
36#15692184C2211yescharacteristic
37#15692184C2211yescharacteristic
38#15692184C2211yescharacteristic
39#15692167C2211yescharacteristic
40#15692167C2211yescharacteristic
41#15692167C2211yescharacteristic
42#15692167C2211yescharacteristic
43#15692166C2211yescharacteristic
44#15692166C2211yescharacteristic
45#15692165C2211yescharacteristic
46#15692165C2211yescharacteristic
47#15692165C2211yescharacteristic
48#15692165C2211yescharacteristic
49C4×#11717579C2211yescharacteristic
50C8×Dic101C2211yescharacteristic
51C8×Dic101C2211yescharacteristic
52C4×Q8×C101C2211yescharacteristic
53C4⋊C8×C101C2211yescharacteristic
54C4⋊C8×C101C2211yescharacteristic
55C4⋊C8×C101C2211yescharacteristic
56#97×C101C2211yescharacteristic
57#97×C101C2211yescharacteristic
58C4×C8×C101C2211yescharacteristic
59C2×Dic202C2×C411yescharacteristic
60C2×Dic202C2×C411yescharacteristic
61C2×Dic202C2×C411yescharacteristic
62C2×C4×D101C2×C411yescharacteristic
63C2×C4×D101C2×C411yescharacteristic
64C2×C4×D101C2311yescharacteristic
65C2×#11717579C2311yescharacteristic
66C2×#11717579C2311yescharacteristic
67C2×#11717579C2311yescharacteristic
68C2×#11717579C2311yescharacteristic
69C4⋊Dic101C2×C411yescharacteristic
70C4⋊Dic101C2×C411yescharacteristic
71C4⋊Dic101C2×C411yescharacteristic
72#13108053C2×C411yescharacteristic
73#13108053C2×C411yescharacteristic
74#13108053C2×C411yescharacteristic
75#13108053C2×C411yescharacteristic
76#13108053C2×C411yescharacteristic
77#13108053C2×C411yescharacteristic
78#13108053C2×C411yescharacteristic
79#13108053C2×C411yescharacteristic
80#13108053C2×C411yescharacteristic
81#13108053C2×C411yescharacteristic
82#13108051C2×C411yescharacteristic
83#13108051C2×C411yescharacteristic
84#13108051C2×C411yescharacteristic
85#13108051C2×C411yescharacteristic
86C4×Dic101C2×C411yescharacteristic
87C4×Dic101C2×C411yescharacteristic
88C4×Dic101C2311yescharacteristic
89C4×Dic101C2311yescharacteristic
90C4×Dic101C2311yescharacteristic
91C2×Q8×C101C2×C411yescharacteristic
92C2×C8×C101C2311yescharacteristic
93C2×C8×C101C2311yescharacteristic
94C2×C8×C101C2311yescharacteristic
95C2×C8×C101C2311yescharacteristic
96C4⋊C4×C101C2×C411yescharacteristic
97C4⋊C4×C101C2×C411yescharacteristic
98C4⋊C4×C101C2×C411yescharacteristic
99C42×C101C2311yescharacteristic
100C42×C101C2311yescharacteristic
101C42×C101C2311yescharacteristic
102C22×D101C22×C411yescharacteristic
103Q8×C101—41no—
104C2×C4×C101C22×C411yescharacteristic
105C2×C4×C101C22×C411yescharacteristic
106C2×C4×C101C22×C411yescharacteristic
107C2×C4×C101C22×C411yescharacteristic
108C2×C4×C101C22×C411yescharacteristic
109C2×C4×C101C22×C411yescharacteristic
110C2×C4×C101C2411yescharacteristic
111C2×Dic101C22×C411yescharacteristic
112C2×Dic101C22×C411yescharacteristic
113C2×Dic101C22×C411yescharacteristic
114C2×Dic101C22×C411yescharacteristic
115C2×Dic101C22×C411yescharacteristic
116C2×Dic101C22×C411yescharacteristic
117C2×Dic101C22×C411yescharacteristic
118C4×D101—21no—
119C4×D101—21no—
120C4×D101—41no—
121C4×D101—41no—
122Dic202—41no—
123Dic202—41no—
124Dic202—41no—
125C8×C101—21no—
126C8×C101—21no—
127C8×C101—21no—
128C8×C101—21no—
129#11717579—21no—
130#11717579—21no—
131#11717579—21no—
132#11717579—21no—
133C22×C101C23×C411yescharacteristic
134C2×D101—21no—
135C2×D101—21no—
136C2×D101—21no—
137C4×C101—21no—
138C4×C101—21no—
139C4×C101—21no—
140C4×C101—21no—
141C4×C101—21no—
142C4×C101—21no—
143C4×C1012−1+411yescharacteristic
144C4×C1012−1+411yescharacteristic
145Dic101—21no—
146Dic101—21no—
147Dic101—21no—
148Dic101—21no—
149Dic101—21no—
150Dic101—21no—
151Dic101—21no—
152C2×C101#51911yescharacteristic
153C2×C101#56811yescharacteristic
154C2×C101#56811yescharacteristic
155D101—41no—
156#2987—1011nomaximal, Sylow
157C101#298711yescharacteristic, complemented, Sylow
158#533—1011no—
159#446—1011no—
160#446—1011no—
161#446—1011no—
162#446—1011no—
163#446—1011no—
164#446—1011no—
165#446—1011no—
166#446D10111yescharacteristic, complemented
167#433—1011no—
168#433—1011no—
169#433—1011no—
170#433—1011no—
171#432—1011no—
172#432—1011no—
173C4⋊Q8—1011no—
174C4⋊Q8—1011no—
175#125—1011no—
176#125—1011no—
177C22⋊Q8—1011no—
178C22⋊Q8—1011no—
179C22⋊Q8—1011no—
180C22⋊Q8—1011no—
181C4×Q8—1011no—
182C4×Q8—1011no—
183C4×Q8—1011no—
184C4×Q8C2×D10111yescharacteristic
185#117—1011no—
186#117—1011no—
187C2×C42—1011no—
188C4⋊C8—1011no—
189C4⋊C8—1011no—
190C4⋊C8—1011no—
191C4⋊C8—1011no—
192C4⋊C8—1011no—
193C4⋊C8—1011no—
194C4⋊C8—1011no—
195C4⋊C8—1011no—
196C4⋊C8—1011no—
197C4⋊C8C2×D10111yescharacteristic
198C4⋊C8C2×D10111yescharacteristic
199C4⋊C8C2×D10111yescharacteristic
200C22⋊C8—1011no—
201C22⋊C8—1011no—
202C22⋊C8—1011no—
203C22⋊C8—1011no—
204#97—1011no—
205#97—1011no—
206#97—1011no—
207#97—1011no—
208#97—1011no—
209#97—1011no—
210#97C2×D10111yescharacteristic
211#97C2×D10111yescharacteristic
212C4×C8—1011no—
213C4×C8—1011no—
214C4×C8—1011no—
215C4×C8C2×D10111yescharacteristic
216C2×Q8—1011no—
217C2×Q8—1011no—
218C2×Q8—1011no—
219C2×Q8C4×D10111yescharacteristic
220C22×C4—1011no—
221C22×C4—1011no—
222C22×C4—1011no—
223C2×C8—1011no—
224C2×C8—1011no—
225C2×C8—1011no—
226C2×C8—1011no—
227C2×C8C22×D10111yescharacteristic
228C2×C8C22×D10111yescharacteristic
229C2×C8C22×D10111yescharacteristic
230C2×C8C22×D10111yescharacteristic
231C4⋊C4—1011no—
232C4⋊C4—1011no—
233C4⋊C4—1011no—
234C4⋊C4—1011no—
235C4⋊C4—1011no—
236C4⋊C4—1011no—
237C4⋊C4—1011no—
238C4⋊C4—1011no—
239C4⋊C4—1011no—
240C4⋊C4—1011no—
241C4⋊C4—1011no—
242C4⋊C4—1011no—
243C4⋊C4—1011no—
244C4⋊C4C4×D10111yescharacteristic
245C4⋊C4C4×D10111yescharacteristic
246C4⋊C4C4×D10111yescharacteristic
247C22⋊C4—1011no—
248C22⋊C4—1011no—
249C22⋊C4—1011no—
250C22⋊C4—1011no—
251C42—1011no—
252C42—1011no—
253C42—1011no—
254C42—1011no—
255C42—1011no—
256C42C22×D10111yescharacteristic
257C42C22×D10111yescharacteristic
258C42C22×D10111yescharacteristic
259C23—1011no—
260Q8—41no—
261Q8—4041no—
262Q8—4041no—
263Q8—4041no—
264C2×C4—1011no—
265C2×C4—1011no—
266C2×C4—1011no—
267C2×C4—1011no—
268C2×C4—1011no—
269C2×C4—1011no—
270C2×C4—1011no—
271C2×C4—4041no—
272C2×C4—4041no—
273C2×C4—2021no—
274C2×C4—2021no—
275C2×C4C2×C4×D10111yescharacteristic
276C2×C4C2×C4×D10111yescharacteristic
277C2×C4C2×C4×D10111yescharacteristic
278C2×C4C2×C4×D10111yescharacteristic
279C2×C4C2×C4×D10111yescharacteristic
280C2×C4C2×C4×D10111yescharacteristic
281C2×C4C23×D10111yescharacteristic
282C8—21no—
283C8—21no—
284C8—21no—
285C8—21no—
286C8—2021no—
287C8—2021no—
288C8—2021no—
289C8—2021no—
290C22—2021no—
291C22—2021no—
292C22—2021no—
293C22C22×C4×D10111yescharacteristic
294C4—21no—
295C4—21no—
296C4—21no—
297C4—21no—
298C4—21no—
299C4—21no—
300C4—2021no—
301C4—2021no—
302C4—2021no—
303C4—2021no—
304C4—2021no—
305C4—2021no—
306C4—2021no—
307C4#1569230211yescharacteristic
308C4#1569230311yescharacteristic
309C2—4041no—
310C2#2026565311yescharacteristic
311C2#2026594211yescharacteristic
312C2#2026594311yescharacteristic
subgroupG/H
center, FrattiniC2×C4C23×D101
commutator, socleC22×C101C23×C4
Fitting#446×C101C2
prime radicalC22×D101C22×C4
cosocleC2×C4×C101C24
hypercenter#446D101
hypocenterC101#2987
LCSG ▷ C22×C101 ▷ C101
UCSC1 ◁ C2×C4 ◁ #446

Complements

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

NH ≅ G/Ntype
2. #20265308C2semidirect
3. #20265307C2semidirect
4. #20265306C2semidirect
5. #20265306C2semidirect
6. #20265305C2semidirect
7. #20265305C2semidirect
8. #20265304C2semidirect
15. #446×C101C2semidirect
157. C101#2987semidirect
166. #446D101semidirect

Maximal subgroups

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

subgroupindex
#202657312
#202653082
#202653072
#202653062
#202653052
#202653042
#202652392
#202652372
#202652362
#202652332
#202652322
#446×C1012
#2987101