Finite Group Databasebeta

← #27179523

Subgroups — #27179523

Order 12928.

418 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20265071C211yesmaximal, characteristic
2#20265071C211yesmaximal, characteristic
3#20265070C211yesmaximal, characteristic
4#20265070C211yesmaximal, characteristic
5#20265065C211yesmaximal, characteristic
6#20265065C211yesmaximal, characteristic
7#20265064C211yesmaximal, characteristic, complemented
8#20265063C211yesmaximal, characteristic, complemented
9#20265062C211yesmaximal, characteristic, complemented
10#20265061C211yesmaximal, characteristic, complemented
11#20265060C211yesmaximal, characteristic, complemented
12#20265059C211yesmaximal, characteristic, complemented
13#20265058C211yesmaximal, characteristic, complemented
14C42×Dic101C211yesmaximal, characteristic, complemented
15#388×C101C211yesmaximal, characteristic
16C2×C4⋊Dic101C2211yescharacteristic
17C2×C4⋊Dic101C2211yescharacteristic
18C2×#13108053C2211yescharacteristic
19C2×#13108053C2211yescharacteristic
20C2×#13108053C2211yescharacteristic
21C2×#13108053C2211yescharacteristic
22C2×C22⋊Dic101C2211yescharacteristic
23C2×C22⋊Dic101C2211yescharacteristic
24C2×C22⋊Dic101C2211yescharacteristic
25C2×C22⋊Dic101C2211yescharacteristic
26C2×C4×Dic101C2211yescharacteristic
27C2×C4×Dic101C2211yescharacteristic
28C2×C4×Dic101C2211yescharacteristic
29C2×C4×Dic101C2211yescharacteristic
30C2×C4×Dic101C2211yescharacteristic
31C2×C4×Dic101C2211yescharacteristic
32#15692162C2211yescharacteristic
33#15692162C2211yescharacteristic
34#15692162C2211yescharacteristic
35#15692162C2211yescharacteristic
36#15692162C2211yescharacteristic
37#15692162C2211yescharacteristic
38#15692162C2211yescharacteristic
39#15692162C2211yescharacteristic
40#15692162C2211yescharacteristic
41#15692162C2211yescharacteristic
42#15692162C2211yescharacteristic
43#15692162C2211yescharacteristic
44C2×C4⋊C4×C101C2211yescharacteristic
45C2×C22⋊C4×C101C2211yescharacteristic
46C2×C22⋊C4×C101C2211yescharacteristic
47C2×C22⋊C4×C101C2211yescharacteristic
48C2×C42×C101C2211yescharacteristic
49#95×C101C2211yescharacteristic
50#95×C101C2211yescharacteristic
51C22×Dic101C2311yescharacteristic
52C22×Dic101C2311yescharacteristic
53C22×Dic101C2311yescharacteristic
54C22×Dic101C2311yescharacteristic
55C22×Dic101C2311yescharacteristic
56C22×Dic101C2311yescharacteristic
57C22×Dic101C2311yescharacteristic
58C22×Dic101C2311yescharacteristic
59C4⋊Dic101—22no—
60C4⋊Dic101—22no—
61#13108053—22no—
62#13108053—22no—
63#13108053—22no—
64#13108053—22no—
65C22⋊Dic101—22no—
66C22⋊Dic101—22no—
67C22⋊Dic101—22no—
68C22⋊Dic101—22no—
69C4×Dic101—22no—
70C4×Dic101—22no—
71C4×Dic101—22no—
72C4×Dic101—22no—
73C4×Dic101—22no—
74C4×Dic101—22no—
75C24×C101C2311yescharacteristic
76C22×C4×C101C2311yescharacteristic
77C22×C4×C101C2311yescharacteristic
78C22×C4×C101C2311yescharacteristic
79C22×C4×C101C2311yescharacteristic
80C22×C4×C101C2311yescharacteristic
81C22×C4×C101C2311yescharacteristic
82C4⋊C4×C101—22no—
83C22⋊C4×C101—22no—
84C22⋊C4×C101—22no—
85C22⋊C4×C101—22no—
86C42×C101—22no—
87C23×C101—21no—
88C23×C101—21no—
89C23×C101—21no—
90C23×C101—21no—
91C23×C101—21no—
92C23×C101—21no—
93C23×C101—21no—
94C23×C101C2411yescharacteristic
95C2×C4×C101—21no—
96C2×C4×C101—21no—
97C2×C4×C101—21no—
98C2×C4×C101—21no—
99C2×C4×C101—21no—
100C2×C4×C101—21no—
101C2×C4×C101—21no—
102C2×C4×C101—21no—
103C2×C4×C101—21no—
104C2×C4×C101—21no—
105C2×C4×C101—21no—
106C2×C4×C101—21no—
107C2×C4×C101—21no—
108C2×C4×C101—21no—
109C2×C4×C101—21no—
110C2×C4×C101#4112yes—
111C2×C4×C101#4112yes—
112C2×C4×C101#4112yes—
113C2×Dic101—21no—
114C2×Dic101—21no—
115C2×Dic101—21no—
116C2×Dic101—21no—
117C2×Dic101—21no—
118C2×Dic101—21no—
119C2×Dic101—21no—
120C2×Dic101—21no—
121C2×Dic101—21no—
122C2×Dic101—21no—
123C2×Dic101—21no—
124C2×Dic101—21no—
125C2×Dic101—21no—
126C2×Dic101—21no—
127C2×Dic101—21no—
128C2×Dic101—21no—
129C2×Dic101—21no—
130C2×Dic101—21no—
131C2×Dic101—21no—
132C2×Dic101—21no—
133C2×Dic101#4112yes—
134C2×Dic101#4112yes—
135C2×Dic101#4112yes—
136C2×Dic101#4112yes—
137C22×C101—41no—
138C22×C101—41no—
139C22×C101—41no—
140C22×C101—41no—
141C22×C101—41no—
142C22×C101—41no—
143C22×C101—41no—
144C22×C101C2×#4111yescharacteristic
145C22×C101C2×#4111yescharacteristic
146C22×C101C2×#4111yescharacteristic
147C22×C101C2×#4111yescharacteristic
148C22×C101C2×#4111yescharacteristic
149C22×C101C2×#4111yescharacteristic
150C22×C101C2×#4111yescharacteristic
151C4×C101—22no—
152C4×C101—22no—
153C4×C101—22no—
154C4×C101—41no—
155C4×C101—41no—
156C4×C101—41no—
157Dic101—22no—
158Dic101—22no—
159Dic101—22no—
160Dic101—22no—
161Dic101—41no—
162Dic101—41no—
163Dic101—41no—
164Dic101—41no—
165C2×C101—81no—
166C2×C101#52911yescharacteristic
167C2×C101#52911yescharacteristic
168C2×C101#52911yescharacteristic
169C2×C101#52911yescharacteristic
170C2×C101#52911yescharacteristic
171C2×C101#52911yescharacteristic
172C2×C101#52911yescharacteristic
173#2866—1011nomaximal, Sylow
174C101#286611yescharacteristic, complemented, Sylow
175#388—1011no—
176#388—1011no—
177#388—1011no—
178#388—1011no—
179#388—1011no—
180#388—1011no—
181#388D10111yescharacteristic
182#387—1011no—
183#387—1011no—
184#387—1011no—
185#387—1011no—
186#387—1011no—
187#387—1011no—
188#387—1011no—
189C43—1011no—
190C2×C4⋊C4—1011no—
191C2×C4⋊C4—1011no—
192C2×C4⋊C4—1011no—
193C2×C4⋊C4—1011no—
194C2×C4⋊C4—1011no—
195C2×C4⋊C4—1011no—
196C2×C4⋊C4C2×D10111yescharacteristic
197C2×C22⋊C4—1011no—
198C2×C22⋊C4—1011no—
199C2×C22⋊C4—1011no—
200C2×C22⋊C4—1011no—
201C2×C22⋊C4C2×D10111yescharacteristic
202C2×C22⋊C4C2×D10111yescharacteristic
203C2×C22⋊C4C2×D10111yescharacteristic
204C2×C42—1011no—
205C2×C42—1011no—
206C2×C42—1011no—
207C2×C42—1011no—
208C2×C42—1011no—
209C2×C42—1011no—
210C2×C42C2×D10111yescharacteristic
211#95—1011no—
212#95—1011no—
213#95—1011no—
214#95—1011no—
215#95—1011no—
216#95—1011no—
217#95—1011no—
218#95—1011no—
219#95—1011no—
220#95—1011no—
221#95—1011no—
222#95—1011no—
223#95C2×D10111yescharacteristic
224#95C2×D10111yescharacteristic
225C24C22×D10111yescharacteristic
226C22×C4—1011no—
227C22×C4—1011no—
228C22×C4—1011no—
229C22×C4—1011no—
230C22×C4—1011no—
231C22×C4—1011no—
232C22×C4—1011no—
233C22×C4—1011no—
234C22×C4C22×D10111yescharacteristic
235C22×C4C22×D10111yescharacteristic
236C22×C4C22×D10111yescharacteristic
237C22×C4C22×D10111yescharacteristic
238C22×C4C22×D10111yescharacteristic
239C22×C4C22×D10111yescharacteristic
240C4⋊C4—22no—
241C4⋊C4—2022no—
242C4⋊C4—2022no—
243C4⋊C4—2022no—
244C4⋊C4—2022no—
245C4⋊C4—2022no—
246C4⋊C4—2022no—
247C22⋊C4—22no—
248C22⋊C4—22no—
249C22⋊C4—22no—
250C22⋊C4—2022no—
251C22⋊C4—2022no—
252C22⋊C4—2022no—
253C22⋊C4—2022no—
254C42—22no—
255C42—2022no—
256C42—2022no—
257C42—2022no—
258C42—2022no—
259C42—2022no—
260C42—2022no—
261C23—21no—
262C23—21no—
263C23—21no—
264C23—21no—
265C23—21no—
266C23—21no—
267C23—21no—
268C23C23×D10111yescharacteristic
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—1012no—
285C2×C4—1012no—
286C2×C4—1012no—
287C2×C4—1012no—
288C2×C4—2021no—
289C2×C4—2021no—
290C2×C4—2021no—
291C2×C4—2021no—
292C2×C4—2021no—
293C2×C4—2021no—
294C2×C4—2021no—
295C2×C4—2021no—
296C2×C4—2021no—
297C2×C4—2021no—
298C2×C4—2021no—
299C2×C4—2021no—
300C2×C4—2021no—
301C2×C4—2021no—
302C2×C4—2021no—
303C2×C4—2021no—
304C2×C4—2021no—
305C2×C4—2021no—
306C2×C4—2021no—
307C2×C4—2021no—
308C2×C4#1310807312yes—
309C2×C4#1310807312yes—
310C2×C4#1310807412yes—
311C22—41no—
312C22—41no—
313C22—41no—
314C22—41no—
315C22—41no—
316C22—41no—
317C22—41no—
318C22#41×D10111yescharacteristic
319C22#41×D10111yescharacteristic
320C22#41×D10111yescharacteristic
321C22#41×D10111yescharacteristic
322C22C2×#1310807311yescharacteristic
323C22C2×#1310807311yescharacteristic
324C22C2×#1310807411yescharacteristic
325C4—22no—
326C4—22no—
327C4—22no—
328C4—41no—
329C4—41no—
330C4—41no—
331C4—4041no—
332C4—4041no—
333C4—4041no—
334C4—4041no—
335C4—2022no—
336C4—2022no—
337C4—2022no—
338C4—2022no—
339C2—81no—
340C2#2026570411yescharacteristic
341C2#2026570511yescharacteristic
342C2#2026570611yescharacteristic
343C2#2026570711yescharacteristic
344C2#2026570811yescharacteristic
345C2#2026570911yescharacteristic
346C2#2026571011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D101
commutator, socle, cosocleC23×C101C24
Fitting#388×C101C2
prime radicalC24×C101C23
hypercenter#388D101
hypocenterC101#2866
LCSG ▷ C23×C101 ▷ C101
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
7. #20265064C2semidirect
8. #20265063C2semidirect
9. #20265062C2semidirect
10. #20265061C2semidirect
11. #20265060C2semidirect
12. #20265059C2semidirect
13. #20265058C2semidirect
14. C42×Dic101C2semidirect
174. C101#2866semidirect

Maximal subgroups

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

subgroupindex
#202650712
#202650702
#202650652
#202650642
#202650632
#202650622
#202650612
#202650602
#202650592
#202650582
C42×Dic1012
#388×C1012
#2866101