Finite Group Databasebeta

← #27181396

Subgroups — #27181396

Order 12928.

384 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20265798C211yesmaximal, characteristic, complemented
2#20265657C211yesmaximal, characteristic, complemented
3#20265513C211yesmaximal, characteristic, complemented
4#20265491C211yesmaximal, characteristic, complemented
5#20265473C211yesmaximal, characteristic, complemented
6#20265458C211yesmaximal, characteristic, complemented
7#20265400C211yesmaximal, characteristic, complemented
8#20265393C211yesmaximal, characteristic, complemented
9#20265341C211yesmaximal, characteristic, complemented
10#20265324C211yesmaximal, characteristic
11#20265279C211yesmaximal, characteristic, complemented
12#20265279C211yesmaximal, characteristic, complemented
13C4×Dic404C211yesmaximal, characteristic, complemented
14C4×D808C211yesmaximal, characteristic, complemented
15#433×C101C211yesmaximal, characteristic, complemented
16C2×#13108074C2211yescharacteristic
17C2×Dic404C2211yescharacteristic
18C2×#13108063C2211yescharacteristic
19C2×#13108063C2211yescharacteristic
20C2×D808C2211yescharacteristic
21#15692255C2211yescharacteristic
22#15692250—21no—
23#15692243C2211yescharacteristic
24#15692241—21no—
25#15692237—21no—
26#15692234C2211yescharacteristic
27#15692233—21no—
28#15692229C2211yescharacteristic
29C4×Dic202C2211yescharacteristic
30C4×Dic202C2211yescharacteristic
31C4×Dic202C2211yescharacteristic
32C4×D404C2211yescharacteristic
33C4×D404C2211yescharacteristic
34C4×D404C2211yescharacteristic
35#15692215—21no—
36#15692215—21no—
37#15692213—21no—
38C2×C4⋊Dic101C2211yescharacteristic
39C4⋊C4×D101—21no—
40#15692189C2211yescharacteristic
41#15692189C2211yescharacteristic
42#15692189C2211yescharacteristic
43#15692189C2211yescharacteristic
44#15692180C2211yescharacteristic
45#15692180C2211yescharacteristic
46#15692180C2211yescharacteristic
47#15692180C2211yescharacteristic
48#15692177C2211yescharacteristic
49#15692177C2211yescharacteristic
50#15692177C2211yescharacteristic
51#15692177C2211yescharacteristic
52#117×C101C2211yescharacteristic
53C4⋊C8×C101C2211yescharacteristic
54C4⋊C8×C101C2211yescharacteristic
55C22⋊C8×C101C2211yescharacteristic
56C22⋊C8×C101C2211yescharacteristic
57#97×C101C2211yescharacteristic
58C4×C8×C101C2211yescharacteristic
59#13108074—22no—
60#13108074—22no—
61C2×Dic202—21no—
62C2×Dic202C2311yescharacteristic
63C2×Dic202C2311yescharacteristic
64C2×D404C2311yescharacteristic
65C2×D404C2311yescharacteristic
66C2×C22⋊D101—21no—
67C2×C22⋊D101—21no—
68C22×Dic101—21no—
69C2×C4×D101—21no—
70C2×C4×D101—21no—
71C2×C4×D101—21no—
72C2×C4×D101—21no—
73Dic404—22no—
74#13108063—22no—
75#13108063—22no—
76D808—22no—
77C4⋊Dic101—21no—
78C4⋊Dic101—21no—
79C4⋊Dic101C2311yescharacteristic
80C4⋊Dic101C2311yescharacteristic
81C4⋊Dic101C2311yescharacteristic
82C4⋊Dic101C2311yescharacteristic
83#13108053—21no—
84#13108053—21no—
85#13108053—21no—
86#13108053—21no—
87C22⋊Dic101—21no—
88#13108051—21no—
89#13108051—21no—
90#13108051—21no—
91#13108051—21no—
92#13108051—21no—
93#13108051—21no—
94C4×Dic101—21no—
95C4×Dic101—21no—
96C4×Dic101—21no—
97C22×C4×C101C2311yescharacteristic
98C2×C8×C101C2311yescharacteristic
99C2×C8×C101C2311yescharacteristic
100C2×C8×C101C2311yescharacteristic
101C2×C8×C101C2311yescharacteristic
102C4⋊C4×C101D411yescharacteristic
103C4⋊C4×C101D411yescharacteristic
104C22⋊C4×C101D411yescharacteristic
105C22⋊C4×C101D411yescharacteristic
106C42×C101C2311yescharacteristic
107C42×C101C2311yescharacteristic
108C23×C101C2×D411yescharacteristic
109C22×D101—21no—
110C22×D101—21no—
111C2×C4×C101—21no—
112C2×C4×C101—21no—
113C2×C4×C101C2×D411yescharacteristic
114C2×C4×C101C2×D411yescharacteristic
115C2×C4×C101C2×D411yescharacteristic
116C2×C4×C101C2×D411yescharacteristic
117C2×C4×C101C2×D411yescharacteristic
118C2×C4×C101C2411yescharacteristic
119C22⋊D101—24no—
120C22⋊D101—81no—
121C2×Dic101—21no—
122C2×Dic101—21no—
123C2×Dic101—21no—
124C2×Dic101—21no—
125C2×Dic101—21no—
126C2×Dic101—21no—
127C2×Dic101—81no—
128D404—21no—
129D404—21no—
130D404—21no—
131D404#4112yes—
132C4×D101—24no—
133C4×D101—81no—
134C4×D101—81no—
135C4×D101—81no—
136Dic202—21no—
137Dic202—21no—
138Dic202—21no—
139Dic202—81no—
140Dic202#4112yes—
141C8×C101—21no—
142C8×C101—21no—
143C8×C101—21no—
144C8×C101—21no—
145C22×C101—21no—
146C22×C101—21no—
147C22×C101—21no—
148C22×C101C22×D411yescharacteristic
149C2×D101—22no—
150C2×D101—41no—
151C2×D101—41no—
152C2×D101—41no—
153C2×D101—41no—
154C2×D101—41no—
155C4×C101—21no—
156C4×C101—21no—
157C4×C101—21no—
158C4×C101—21no—
159C4×C101—21no—
160C4×C101C2×#4111yescharacteristic
161C4×C101C2×#4111yescharacteristic
162Dic101—22no—
163Dic101—41no—
164Dic101—41no—
165Dic101—41no—
166Dic101—41no—
167Dic101—41no—
168C2×C101—41no—
169C2×C101#52511yescharacteristic
170C2×C101#57611yescharacteristic
171C2×C101#57811yescharacteristic
172D101—42no—
173D101—81no—
174#3124—1011nomaximal, Sylow
175C101#312411yescharacteristic, complemented, Sylow
176#542—1011no—
177#520—1011no—
178#484—1011no—
179#480—1011no—
180#477—1011no—
181#474—1011no—
182#464—1011no—
183#463—1011no—
184#452—1011no—
185#449—1011no—
186#440—1011no—
187#440—1011no—
188C4×Q16—1011no—
189C4×D8—1011no—
190#433D10111yescharacteristic, complemented
191C2×#41—1011no—
192C2×Q16—1011no—
193C2×SD16—1011no—
194C2×SD16—1011no—
195C2×D8—1011no—
196C4⋊Q8—1011no—
197#126—2021no—
198#124—1011no—
199#124—2021no—
200#123—2021no—
201C22⋊Q8—1011no—
202C22⋊Q8—2021no—
203#121—1011no—
204C4×Q8—1011no—
205C4×Q8—1011no—
206C4×Q8—1011no—
207C4×D4—1011no—
208C4×D4—1011no—
209C4×D4—1011no—
210C4×D4—2021no—
211C4×D4—2021no—
212#117—2021no—
213#117C2×D10111yescharacteristic
214C2×C4⋊C4—1011no—
215C2×C4⋊C4—2021no—
216#107—1011no—
217#107—1011no—
218#107—1011no—
219#107—1011no—
220C4⋊C8C2×D10111yescharacteristic
221C4⋊C8C2×D10111yescharacteristic
222#103—1011no—
223#103—1011no—
224#103—1011no—
225#103—1011no—
226#102—1011no—
227#102—1011no—
228#102—1011no—
229#102—1011no—
230C22⋊C8C2×D10111yescharacteristic
231C22⋊C8C2×D10111yescharacteristic
232#97C2×D10111yescharacteristic
233C4×C8C2×D10111yescharacteristic
234#41—2022no—
235#41—2022no—
236C2×Q8—1011no—
237C2×Q8—1011no—
238C2×Q8—2021no—
239C2×D4—1011no—
240C2×D4—1011no—
241C2×D4—2021no—
242C2×D4—2021no—
243C22×C4—2021no—
244C22×C4—2021no—
245C22×C4—2021no—
246C22×C4—2021no—
247C22×C4—2021no—
248C22×C4C22×D10111yescharacteristic
249Q16—2022no—
250SD16—2022no—
251SD16—2022no—
252D8—2022no—
253C2×C8C22×D10111yescharacteristic
254C2×C8C22×D10111yescharacteristic
255C2×C8C22×D10111yescharacteristic
256C2×C8C22×D10111yescharacteristic
257C4⋊C4—1011no—
258C4⋊C4—1011no—
259C4⋊C4—1011no—
260C4⋊C4—1011no—
261C4⋊C4—2021no—
262C4⋊C4—2021no—
263C4⋊C4—2021no—
264C4⋊C4—2021no—
265C4⋊C4—2021no—
266C4⋊C4—2021no—
267C4⋊C4D40411yescharacteristic
268C4⋊C4D40411yescharacteristic
269C22⋊C4—2021no—
270C22⋊C4—2021no—
271C22⋊C4—2021no—
272C22⋊C4—2021no—
273C22⋊C4—2021no—
274C22⋊C4—2021no—
275C22⋊C4—2021no—
276C22⋊C4D40411yescharacteristic
277C22⋊C4D40411yescharacteristic
278C42—2021no—
279C42—2021no—
280C42—2021no—
281C42C22×D10111yescharacteristic
282C42C22×D10111yescharacteristic
283C23—2021no—
284C23—2021no—
285C23C2×D40411yescharacteristic
286Q8—8081no—
287Q8—1012no—
288Q8—2021no—
289Q8—2021no—
290Q8—2021no—
291D4—8081no—
292D4—1012no—
293D4—2024no—
294D4—2021no—
295D4—2021no—
296D4—2021no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—8081no—
300C2×C4—8081no—
301C2×C4—8081no—
302C2×C4—8081no—
303C2×C4—2024no—
304C2×C4—2021no—
305C2×C4—2021no—
306C2×C4—2021no—
307C2×C4—2021no—
308C2×C4—2021no—
309C2×C4—2021no—
310C2×C4C2×D40411yescharacteristic
311C2×C4C2×D40411yescharacteristic
312C2×C4C2×D40411yescharacteristic
313C2×C4C2×D40411yescharacteristic
314C2×C4C2×D40411yescharacteristic
315C2×C4C23×D10111yescharacteristic
316C8—21no—
317C8—21no—
318C8—21no—
319C8—21no—
320C22—21no—
321C22—21no—
322C22—21no—
323C22—4041no—
324C22—4041no—
325C22—4041no—
326C22—4041no—
327C22—4041no—
328C22—2022no—
329C22C22×D40411yescharacteristic
330C4—21no—
331C4—21no—
332C4—21no—
333C4—21no—
334C4—21no—
335C4—4041no—
336C4—4041no—
337C4—4041no—
338C4—4041no—
339C4—4041no—
340C4—2022no—
341C4#41×D10111yescharacteristic
342C4#41×D10111yescharacteristic
343C2—41no—
344C2—8081no—
345C2—4042no—
346C2#2026568911yescharacteristic
347C2#2026598211yescharacteristic
348C2#2026599411yescharacteristic
subgroupG/H
centerC22C22×D404
commutator, cosocleC2×C4×C101C24
FrattiniC2×C4C23×D101
Fitting#433×C101C2
socleC22×C101C22×D4
prime radical#20265324C2
hypercenter#433D101
hypocenterC101#3124
LCSG ▷ C2×C4×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
1. #20265798C2semidirect
2. #20265657C2semidirect
3. #20265513C2semidirect
4. #20265491C2semidirect
5. #20265473C2semidirect
6. #20265458C2semidirect
7. #20265400C2semidirect
8. #20265393C2semidirect
9. #20265341C2semidirect
11. #20265279C2semidirect
12. #20265279C2semidirect
13. C4×Dic404C2semidirect
14. C4×D808C2semidirect
15. #433×C101C2semidirect
175. C101#3124semidirect
190. #433D101semidirect

Maximal subgroups

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

subgroupindex
#202657982
#202656572
#202655132
#202654912
#202654732
#202654582
#202654002
#202653932
#202653412
#202653242
#202652792
C4×Dic4042
C4×D8082
#433×C1012
#3124101