Finite Group Databasebeta

← #27183075

Subgroups — #27183075

Order 12928.

408 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20265891C211yesmaximal, characteristic, complemented
2#20265846C211yesmaximal, characteristic, complemented
3#20265522C211yesmaximal, characteristic, complemented
4#20265502C211yesmaximal, characteristic, complemented
5#20265500C211yesmaximal, characteristic, complemented
6#20265470C211yesmaximal, characteristic, complemented
7#20265411C211yesmaximal, characteristic, complemented
8#20265410C211yesmaximal, characteristic, complemented
9#20265370C211yesmaximal, characteristic, complemented
10#20265321C211yesmaximal, characteristic, complemented
11SD16×Dic101C211yesmaximal, characteristic, complemented
12#20265240C211yesmaximal, characteristic, complemented
13#20265173C211yesmaximal, characteristic, complemented
14#20265172C211yesmaximal, characteristic, complemented
15#449×C101C211yesmaximal, characteristic, complemented
16C2×#13108075C2211yescharacteristic
17C2×#13108059C2211yescharacteristic
18C22×#11717579C2211yescharacteristic
19C2×C8×D101C2211yescharacteristic
20#15692254C2211yescharacteristic
21#15692251—21no—
22#15692251C2211yescharacteristic
23#15692242—21no—
24#15692241—21no—
25#15692229—21no—
26#15692229C2211yescharacteristic
27#15692227—21no—
28#15692226—21no—
29#15692226C2211yescharacteristic
30#15692226C2211yescharacteristic
31Q8×Dic101C2211yescharacteristic
32D4×Dic101C2211yescharacteristic
33C4×C22⋊D101—21no—
34C4×C22⋊D101C2211yescharacteristic
35#15692214C2211yescharacteristic
36#15692213C2211yescharacteristic
37#15692211—21no—
38#15692189C2211yescharacteristic
39#15692188C2211yescharacteristic
40#15692187C2211yescharacteristic
41#15692184C2211yescharacteristic
42#15692179C2211yescharacteristic
43#15692179C2211yescharacteristic
44#15692177C2211yescharacteristic
45#15692177C2211yescharacteristic
46#15692176C2211yescharacteristic
47#15692176C2211yescharacteristic
48#15692176C2211yescharacteristic
49#15692175C2211yescharacteristic
50#15692167C2211yescharacteristic
51C8×Dic101C2211yescharacteristic
52C2×#41×C101C2211yescharacteristic
53C2×SD16×C101C2211yescharacteristic
54C2×D8×C101C2211yescharacteristic
55#121×C101C2211yescharacteristic
56#103×C101C2211yescharacteristic
57#102×C101C2211yescharacteristic
58C22⋊C8×C101C2211yescharacteristic
59#13108075—22no—
60#13108075—41no—
61C2×Dic202—21no—
62C2×D404—21no—
63C2×D404C2311yescharacteristic
64C2×C22⋊D101—21no—
65C2×C22⋊D101—21no—
66C2×C22⋊D101—21no—
67C2×C22⋊D101—21no—
68C2×C22⋊D101—21no—
69C2×C22⋊D101D411yescharacteristic
70C22×Dic101—21no—
71C2×C4×D101—21no—
72C2×C4×D101C2311yescharacteristic
73#13108059—41no—
74C2×#11717579—41no—
75C2×#11717579C2311yescharacteristic
76C2×#11717579C2311yescharacteristic
77C8×D101—41no—
78C4⋊Dic101—21no—
79C4⋊Dic101C2311yescharacteristic
80C4⋊Dic101C2311yescharacteristic
81C4⋊Dic101C2311yescharacteristic
82#13108053—21no—
83#13108053D411yescharacteristic
84C22⋊Dic101—21no—
85C22⋊Dic101—21no—
86C22⋊Dic101—21no—
87C22⋊Dic101—21no—
88C22⋊Dic101D411yescharacteristic
89#13108051—21no—
90#13108051—21no—
91#13108051D411yescharacteristic
92C4×Dic101—21no—
93C4×Dic101—21no—
94C4×Dic101—21no—
95C4×Dic101C2311yescharacteristic
96#41×C101—22no—
97#41×C101—41no—
98C2×Q8×C101C2311yescharacteristic
99C2×D4×C101—21no—
100C2×D4×C101—21no—
101C2×D4×C101C2311yescharacteristic
102C2×D4×C101C2311yescharacteristic
103C22×C4×C101—21no—
104C22×C4×C101C2311yescharacteristic
105SD16×C101—22no—
106D8×C101—41no—
107C2×C8×C101C2311yescharacteristic
108C2×C8×C101C2311yescharacteristic
109C4⋊C4×C101C2311yescharacteristic
110C22⋊C4×C101—21no—
111C23×C101—21no—
112C23×C101—21no—
113C23×C101C2×D411yescharacteristic
114C22×D101—21no—
115C22×D101C2×D411yescharacteristic
116Q8×C101—21no—
117Q8×C101#4112yes—
118D4×C101—21no—
119D4×C101—21no—
120D4×C101—21no—
121D4×C101—21no—
122D4×C101—42no—
123D4×C101—81no—
124C2×C4×C101—21no—
125C2×C4×C101—21no—
126C2×C4×C101—21no—
127C2×C4×C101—21no—
128C2×C4×C101—42no—
129C2×C4×C101C2×D411yescharacteristic
130C2×C4×C101C2411yescharacteristic
131C22⋊D101—22no—
132C22⋊D101—42no—
133C22⋊D101—81no—
134C22⋊D101—81no—
135C22⋊D101—81no—
136C22⋊D101—81no—
137C2×Dic101—21no—
138C2×Dic101—21no—
139C2×Dic101—21no—
140C2×Dic101—42no—
141C2×Dic101C2×D411yescharacteristic
142C2×Dic101C2×D411yescharacteristic
143C2×Dic101C2×D411yescharacteristic
144D404—21no—
145D404—21no—
146D404—42no—
147C4×D101—21no—
148C4×D101—21no—
149C4×D101—42no—
150Dic202—81no—
151C8×C101—21no—
152C8×C101—21no—
153#11717579—21no—
154#11717579—21no—
155C22×C101—21no—
156C22×C101—21no—
157C22×C101—21no—
158C22×C101—41no—
159C22×C101—41no—
160C22×C101—41no—
161C22×C101—41no—
162C22×C101—41no—
163C22×C101—41no—
164C22×C101C22×D411yescharacteristic
165C2×D101—21no—
166C2×D101—21no—
167C2×D101—21no—
168C2×D101—41no—
169C2×D101—41no—
170C2×D101—41no—
171C4×C101—22no—
172C4×C101—21no—
173C4×C101—41no—
174C4×C101C2×#4111yescharacteristic
175C4×C101H(5,𝔽2)11yescharacteristic
176Dic101—21no—
177Dic101—21no—
178Dic101—41no—
179Dic101—41no—
180Dic101—41no—
181Dic101#13512yes—
182C2×C101—41no—
183C2×C101—81no—
184C2×C101—81no—
185C2×C101#54611yescharacteristic
186C2×C101C2×#13511yescharacteristic
187C2×C101#57611yescharacteristic
188D101—41no—
189D101—81no—
190#3305—1011nomaximal, Sylow
191C101#330511yescharacteristic, complemented, Sylow
192#555—1011no—
193#550—1011no—
194#486—1011no—
195#482—1011no—
196#482—1011no—
197#477—1011no—
198#466—1011no—
199#466—1011no—
200#459—1011no—
201#449—1011no—
202#449D10111yescharacteristic, complemented
203C4×SD16—1011no—
204C8×D4—1011no—
205#416—1011no—
206#416—1011no—
207C2×#41—1011no—
208C2×#41C2×D10111yescharacteristic
209C2×SD16C2×D10111yescharacteristic
210C2×D8—1011no—
211C2×D8C2×D10111yescharacteristic
212C22×C8—1011no—
213C22×C8—1011no—
214C4⋊Q8—1011no—
215#127—1011no—
216#127—2021no—
217#124—2021no—
218#124—2021no—
219#121—1011no—
220#121—1011no—
221#121—1011no—
222#121—2021no—
223#121—2021no—
224#121—2021no—
225#121C2×D10111yescharacteristic
226C4×Q8—1011no—
227C4×D4—1011no—
228C4×D4—1011no—
229C4×D4—2021no—
230#117—1011no—
231#117—1011no—
232#117—2021no—
233#107—1011no—
234#107—1011no—
235#106—1011no—
236C4⋊C8—1011no—
237#103—1011no—
238#103—1011no—
239#103C2×D10111yescharacteristic
240#102—1011no—
241#102—1011no—
242#102—1011no—
243#102—1011no—
244#102—1011no—
245#102—1011no—
246#102C2×D10111yescharacteristic
247C22⋊C8—1011no—
248C22⋊C8C2×D10111yescharacteristic
249C4×C8—1011no—
250#41—22no—
251#41—41no—
252#41—4041no—
253#41—2022no—
254C2×Q8—2021no—
255C2×Q8C22×D10111yescharacteristic
256C2×D4—21no—
257C2×D4—21no—
258C2×D4—1011no—
259C2×D4—1011no—
260C2×D4—2021no—
261C2×D4—2021no—
262C2×D4—2021no—
263C2×D4—2021no—
264C2×D4—2021no—
265C2×D4—2021no—
266C2×D4C22×D10111yescharacteristic
267C2×D4C22×D10111yescharacteristic
268C22×C4—21no—
269C22×C4—1011no—
270C22×C4—2021no—
271C22×C4—2021no—
272C22×C4C22×D10111yescharacteristic
273SD16—22no—
274D8—41no—
275D8—4041no—
276C2×C8—1011no—
277C2×C8—1011no—
278C2×C8—4041no—
279C2×C8—4041no—
280C2×C8C22×D10111yescharacteristic
281C2×C8C22×D10111yescharacteristic
282C4⋊C4—1011no—
283C4⋊C4—1011no—
284C4⋊C4—1011no—
285C4⋊C4—1011no—
286C4⋊C4—2021no—
287C4⋊C4—2021no—
288C4⋊C4C22×D10111yescharacteristic
289C22⋊C4—21no—
290C22⋊C4—1011no—
291C22⋊C4—1011no—
292C22⋊C4—2021no—
293C22⋊C4—2021no—
294C22⋊C4—2021no—
295C22⋊C4—2021no—
296C22⋊C4—2021no—
297C22⋊C4—2021no—
298C42—1011no—
299C42—2021no—
300C42—2021no—
301C42—2021no—
302C23—21no—
303C23—21no—
304C23—1011no—
305C23—2021no—
306C23D4×D10111yescharacteristic
307Q8—21no—
308Q8—8081no—
309Q8#1310807312yes—
310D4—21no—
311D4—21no—
312D4—21no—
313D4—21no—
314D4—42no—
315D4—81no—
316D4—8081no—
317D4—8081no—
318D4—8081no—
319D4—8081no—
320D4—4042no—
321D4—4042no—
322D4—2022no—
323D4—2021no—
324D4—2021no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—42no—
330C2×C4—1011no—
331C2×C4—1011no—
332C2×C4—1011no—
333C2×C4—4042no—
334C2×C4—4042no—
335C2×C4—2021no—
336C2×C4—2021no—
337C2×C4—2021no—
338C2×C4—2021no—
339C2×C4—2021no—
340C2×C4D4×D10111yescharacteristic
341C2×C4C23×D10111yescharacteristic
342C8—21no—
343C8—21no—
344C8—2021no—
345C8—2021no—
346C22—21no—
347C22—21no—
348C22—21no—
349C22—41no—
350C22—41no—
351C22—41no—
352C22—41no—
353C22—41no—
354C22—41no—
355C22—4041no—
356C22—4041no—
357C22—4041no—
358C22—2021no—
359C22—2021no—
360C22—2021no—
361C22C2×D4×D10111yescharacteristic
362C4—21no—
363C4—22no—
364C4—41no—
365C4—1012no—
366C4—4041no—
367C4—4041no—
368C4—4041no—
369C4—2021no—
370C4—2021no—
371C4C2×#1310807311yescharacteristic
372C4#1569230011yescharacteristic
373C2—41no—
374C2—81no—
375C2—81no—
376C2—8081no—
377C2—4041no—
378C2#2026581411yescharacteristic
379C2#135×D10111yescharacteristic
380C2#2026598111yescharacteristic
subgroupG/H
centerC22C2×D4×D101
commutator, cosocleC2×C4×C101C24
FrattiniC2×C4C23×D101
Fitting#449×C101C2
socleC22×C101C22×D4
hypercenter#449D101
hypocenterC101#3305
LCSG ▷ C2×C4×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

Complements

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

NH ≅ G/Ntype
1. #20265891C2semidirect
2. #20265846C2semidirect
3. #20265522C2semidirect
4. #20265502C2semidirect
5. #20265500C2semidirect
6. #20265470C2semidirect
7. #20265411C2semidirect
8. #20265410C2semidirect
9. #20265370C2semidirect
10. #20265321C2semidirect
11. SD16×Dic101C2semidirect
12. #20265240C2semidirect
13. #20265173C2semidirect
14. #20265172C2semidirect
15. #449×C101C2semidirect
191. C101#3305semidirect
202. #449D101semidirect

Maximal subgroups

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

subgroupindex
#202658912
#202658462
#202655222
#202655022
#202655002
#202654702
#202654112
#202654102
#202653702
#202653212
SD16×Dic1012
#202652402
#202651732
#202651722
#449×C1012
#3305101