Finite Group Databasebeta

← #27180301

Subgroups — #27180301

Order 12928.

346 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20265714C211yesmaximal, characteristic
2#20265308C211yesmaximal, characteristic, complemented
3#20265256C211yesmaximal, characteristic, complemented
4#20265254C211yesmaximal, characteristic, complemented
5#20265250C211yesmaximal, characteristic, complemented
6#20265250C211yesmaximal, characteristic, complemented
7#20265247C211yesmaximal, characteristic, complemented
8#20265247C211yesmaximal, characteristic, complemented
9#20265239C211yesmaximal, characteristic, complemented
10#20265236C211yesmaximal, characteristic, complemented
11#20265232C211yesmaximal, characteristic, complemented
12#20265202C211yesmaximal, characteristic, complemented
13#20265202C211yesmaximal, characteristic, complemented
14#20265199C211yesmaximal, characteristic, complemented
15#446×C101C211yesmaximal, characteristic, complemented
16C2×#13108057C2211yescharacteristic
17C2×#13108057C2211yescharacteristic
18C2×#13108057C2211yescharacteristic
19C2×#13108057C2211yescharacteristic
20C2×C8×D101C2211yescharacteristic
21C2×C8×D101C2211yescharacteristic
22#15692250C411yescharacteristic
23#15692250C411yescharacteristic
24#15692246C411yescharacteristic
25#15692244C411yescharacteristic
26#15692240C411yescharacteristic
27#15692240C411yescharacteristic
28#15692231C411yescharacteristic
29#15692230C411yescharacteristic
30C4×D404C2211yescharacteristic
31C4×D404C2211yescharacteristic
32C4×D404C2211yescharacteristic
33#15692212C2211yescharacteristic
34#15692212C2211yescharacteristic
35C42×D101C2211yescharacteristic
36C4⋊#11717579C2211yescharacteristic
37C4⋊#11717579C2211yescharacteristic
38C4⋊#11717579C2211yescharacteristic
39#15692184C2211yescharacteristic
40#15692184C2211yescharacteristic
41#15692184C2211yescharacteristic
42#15692184C2211yescharacteristic
43#15692167C2211yescharacteristic
44#15692167C2211yescharacteristic
45#15692167C2211yescharacteristic
46#15692167C2211yescharacteristic
47#15692167C2211yescharacteristic
48#15692167C2211yescharacteristic
49#15692166C2211yescharacteristic
50#15692166C2211yescharacteristic
51C4×#11717579C2211yescharacteristic
52C4×Q8×C101C2211yescharacteristic
53C4⋊C8×C101C2211yescharacteristic
54C4⋊C8×C101C2211yescharacteristic
55C4⋊C8×C101C2211yescharacteristic
56#97×C101C2211yescharacteristic
57#97×C101C2211yescharacteristic
58C4×C8×C101C2211yescharacteristic
59C2×D404C2×C411yescharacteristic
60C2×D404C2×C411yescharacteristic
61C2×D404C2×C411yescharacteristic
62C2×C4×D101C2×C411yescharacteristic
63C2×C4×D101C2×C411yescharacteristic
64C2×C4×D101C2311yescharacteristic
65C2×C4×D101C2311yescharacteristic
66C2×C4×D101C2311yescharacteristic
67#13108057—41no—
68#13108057—41no—
69#13108057—41no—
70#13108057—41no—
71C2×#11717579C2311yescharacteristic
72C2×#11717579C2311yescharacteristic
73C2×#11717579C2311yescharacteristic
74C2×#11717579C2311yescharacteristic
75C8×D101—41no—
76C8×D101—41no—
77C4⋊Dic101C2×C411yescharacteristic
78C4⋊Dic101C2×C411yescharacteristic
79C4⋊Dic101C2×C411yescharacteristic
80#13108053C2×C411yescharacteristic
81#13108053C2×C411yescharacteristic
82#13108053C2×C411yescharacteristic
83#13108053C2×C411yescharacteristic
84#13108051C2×C411yescharacteristic
85#13108051C2×C411yescharacteristic
86#13108051C2×C411yescharacteristic
87#13108051C2×C411yescharacteristic
88#13108051C2×C411yescharacteristic
89#13108051C2×C411yescharacteristic
90#13108051C2×C411yescharacteristic
91#13108051C2×C411yescharacteristic
92#13108051C2×C411yescharacteristic
93#13108051C2×C411yescharacteristic
94C4×Dic101C2×C411yescharacteristic
95C4×Dic101C2×C411yescharacteristic
96C4×Dic101C2311yescharacteristic
97C2×Q8×C101C2×C411yescharacteristic
98C2×C8×C101C2311yescharacteristic
99C2×C8×C101C2311yescharacteristic
100C2×C8×C101C2311yescharacteristic
101C2×C8×C101C2311yescharacteristic
102C4⋊C4×C101C2×C411yescharacteristic
103C4⋊C4×C101C2×C411yescharacteristic
104C4⋊C4×C101C2×C411yescharacteristic
105C42×C101C2311yescharacteristic
106C42×C101C2311yescharacteristic
107C42×C101C2311yescharacteristic
108C22×D101C22×C411yescharacteristic
109C22×D101C22×C411yescharacteristic
110C22×D101C22×C411yescharacteristic
111Q8×C101—41no—
112C2×C4×C101C22×C411yescharacteristic
113C2×C4×C101C22×C411yescharacteristic
114C2×C4×C101C22×C411yescharacteristic
115C2×C4×C101C22×C411yescharacteristic
116C2×C4×C101C22×C411yescharacteristic
117C2×C4×C101C22×C411yescharacteristic
118C2×C4×C101C2411yescharacteristic
119C2×Dic101C22×C411yescharacteristic
120C2×Dic101C22×C411yescharacteristic
121C2×Dic101C22×C411yescharacteristic
122C2×Dic101C22×C411yescharacteristic
123C2×Dic101C22×C411yescharacteristic
124D404—41no—
125D404—41no—
126D404—41no—
127C4×D101—21no—
128C4×D101—21no—
129C4×D101—21no—
130C4×D101—21no—
131C4×D101—21no—
132C4×D101—21no—
133C4×D101—41no—
134C4×D101—41no—
135C8×C101—21no—
136C8×C101—21no—
137C8×C101—21no—
138C8×C101—21no—
139#11717579—21no—
140#11717579—21no—
141#11717579—21no—
142#11717579—21no—
143C22×C101C23×C411yescharacteristic
144C2×D101—21no—
145C2×D101—21no—
146C2×D101—21no—
147C2×D101—21no—
148C2×D101—21no—
149C2×D101—21no—
150C2×D101—21no—
151C2×D101—21no—
152C2×D101—21no—
153C4×C101—21no—
154C4×C101—21no—
155C4×C101—21no—
156C4×C101—21no—
157C4×C101—21no—
158C4×C101—21no—
159C4×C101H(5,𝔽2)11yescharacteristic
160C4×C1012−1+411yescharacteristic
161Dic101—21no—
162Dic101—21no—
163Dic101—21no—
164Dic101—21no—
165Dic101—21no—
166C2×C101#52011yescharacteristic
167C2×C101#56811yescharacteristic
168C2×C101#56811yescharacteristic
169D101—41no—
170D101—41no—
171D101—41no—
172#2995—1011nomaximal, Sylow
173C101#299511yescharacteristic, complemented, Sylow
174#529—1011no—
175#446—1011no—
176#446D10111yescharacteristic, complemented
177#436—1011no—
178#436—1011no—
179#435—1011no—
180#435—1011no—
181#435—1011no—
182#435—1011no—
183#433—1011no—
184#433—1011no—
185#432—1011no—
186#424—1011no—
187#424—1011no—
188#423—1011no—
189C2×M16—1011no—
190C2×M16—1011no—
191C2×M16—1011no—
192C2×M16—1011no—
193C22×C8—1011no—
194C22×C8—1011no—
195#126—1011no—
196#126—1011no—
197#125—1011no—
198#124—1011no—
199#123—1011no—
200#123—1011no—
201C22⋊Q8—1011no—
202#121—1011no—
203C4×Q8C2×D10111yescharacteristic
204C4×D4—1011no—
205C4×D4—1011no—
206C4×D4—1011no—
207#117—1011no—
208#117—1011no—
209C2×C42—1011no—
210C4⋊C8—1011no—
211C4⋊C8—1011no—
212C4⋊C8—1011no—
213C4⋊C8—1011no—
214C4⋊C8—1011no—
215C4⋊C8—1011no—
216C4⋊C8—1011no—
217C4⋊C8C2×D10111yescharacteristic
218C4⋊C8C2×D10111yescharacteristic
219C4⋊C8C2×D10111yescharacteristic
220C22⋊C8—1011no—
221C22⋊C8—1011no—
222C22⋊C8—1011no—
223C22⋊C8—1011no—
224C22⋊C8—1011no—
225C22⋊C8—1011no—
226#97—1011no—
227#97—1011no—
228#97C2×D10111yescharacteristic
229#97C2×D10111yescharacteristic
230C4×C8—1011no—
231C4×C8C2×D10111yescharacteristic
232C2×Q8C4×D10111yescharacteristic
233C2×D4—1011no—
234C2×D4—1011no—
235C2×D4—1011no—
236C22×C4—1011no—
237C22×C4—1011no—
238C22×C4—1011no—
239C22×C4—1011no—
240C22×C4—1011no—
241M16—4041no—
242M16—4041no—
243M16—4041no—
244M16—4041no—
245C2×C8—1011no—
246C2×C8—1011no—
247C2×C8—1011no—
248C2×C8—1011no—
249C2×C8—4041no—
250C2×C8—4041no—
251C2×C8C22×D10111yescharacteristic
252C2×C8C22×D10111yescharacteristic
253C2×C8C22×D10111yescharacteristic
254C2×C8C22×D10111yescharacteristic
255C4⋊C4—1011no—
256C4⋊C4—1011no—
257C4⋊C4—1011no—
258C4⋊C4—1011no—
259C4⋊C4—1011no—
260C4⋊C4—1011no—
261C4⋊C4—1011no—
262C4⋊C4C4×D10111yescharacteristic
263C4⋊C4C4×D10111yescharacteristic
264C4⋊C4C4×D10111yescharacteristic
265C22⋊C4—1011no—
266C22⋊C4—1011no—
267C22⋊C4—1011no—
268C22⋊C4—1011no—
269C22⋊C4—1011no—
270C22⋊C4—1011no—
271C22⋊C4—1011no—
272C22⋊C4—1011no—
273C22⋊C4—1011no—
274C22⋊C4—1011no—
275C42—1011no—
276C42—1011no—
277C42—1011no—
278C42C22×D10111yescharacteristic
279C42C22×D10111yescharacteristic
280C42C22×D10111yescharacteristic
281C23—1011no—
282C23—1011no—
283C23—1011no—
284Q8—41no—
285D4—4041no—
286D4—4041no—
287D4—4041no—
288C2×C4—1011no—
289C2×C4—1011no—
290C2×C4—1011no—
291C2×C4—1011no—
292C2×C4—1011no—
293C2×C4—4041no—
294C2×C4—4041no—
295C2×C4—2021no—
296C2×C4—2021no—
297C2×C4—2021no—
298C2×C4—2021no—
299C2×C4—2021no—
300C2×C4—2021no—
301C2×C4C2×C4×D10111yescharacteristic
302C2×C4C2×C4×D10111yescharacteristic
303C2×C4C2×C4×D10111yescharacteristic
304C2×C4C2×C4×D10111yescharacteristic
305C2×C4C2×C4×D10111yescharacteristic
306C2×C4C2×C4×D10111yescharacteristic
307C2×C4C23×D10111yescharacteristic
308C8—21no—
309C8—21no—
310C8—21no—
311C8—21no—
312C8—2021no—
313C8—2021no—
314C8—2021no—
315C8—2021no—
316C22—2021no—
317C22—2021no—
318C22—2021no—
319C22—2021no—
320C22—2021no—
321C22—2021no—
322C22—2021no—
323C22—2021no—
324C22—2021no—
325C22C22×C4×D10111yescharacteristic
326C4—21no—
327C4—21no—
328C4—21no—
329C4—21no—
330C4—21no—
331C4—21no—
332C4—2021no—
333C4—2021no—
334C4—2021no—
335C4—2021no—
336C4—2021no—
337C4#1569230111yescharacteristic
338C4#1569230311yescharacteristic
339C2—4041no—
340C2—4041no—
341C2—4041no—
342C2#2026565911yescharacteristic
343C2#2026594211yescharacteristic
344C2#2026594311yescharacteristic
subgroupG/H
center, FrattiniC2×C4C23×D101
commutator, socleC22×C101C23×C4
Fitting#446×C101C2
prime radical#15692230C4
cosocleC2×C4×C101C24
hypercenter#446D101
hypocenterC101#2995
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. #20265256C2semidirect
4. #20265254C2semidirect
5. #20265250C2semidirect
6. #20265250C2semidirect
7. #20265247C2semidirect
8. #20265247C2semidirect
9. #20265239C2semidirect
10. #20265236C2semidirect
11. #20265232C2semidirect
12. #20265202C2semidirect
13. #20265202C2semidirect
14. #20265199C2semidirect
15. #446×C101C2semidirect
173. C101#2995semidirect
176. #446D101semidirect

Maximal subgroups

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

subgroupindex
#202657142
#202653082
#202652562
#202652542
#202652502
#202652472
#202652392
#202652362
#202652322
#202652022
#202651992
#446×C1012
#2995101