Finite Group Databasebeta

← #27181341

Subgroups — #27181341

Order 12928.

372 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20265787C211yesmaximal, characteristic, complemented
2#20265658C211yesmaximal, characteristic
3#20265507C211yesmaximal, characteristic, complemented
4#20265483C211yesmaximal, characteristic, complemented
5#20265480C211yesmaximal, characteristic, complemented
6#20265386C211yesmaximal, characteristic, complemented
7#20265381C211yesmaximal, characteristic, complemented
8#20265341C211yesmaximal, characteristic
9#20265337C211yesmaximal, characteristic
10#20265281C211yesmaximal, characteristic, complemented
11#20265276C211yesmaximal, characteristic, complemented
12#20265271C211yesmaximal, characteristic, complemented
13#20265262C211yesmaximal, characteristic, complemented
14#20265235C211yesmaximal, characteristic, complemented
15#484×C101C211yesmaximal, characteristic, complemented
16C2×#13108074C2211yescharacteristic
17C2×Dic404C2211yescharacteristic
18C2×#13108064C2211yescharacteristic
19C2×#13108063C2211yescharacteristic
20C2×#13108061C2211yescharacteristic
21#15692253C2211yescharacteristic
22#15692248—21no—
23#15692248—21no—
24#15692246—21no—
25#15692246C2211yescharacteristic
26#15692245—21no—
27#15692234C2211yescharacteristic
28Q8×Dic101C2211yescharacteristic
29#15692220C2211yescharacteristic
30#15692220C2211yescharacteristic
31#15692220C2211yescharacteristic
32#15692217C2211yescharacteristic
33#15692217C2211yescharacteristic
34C4×C22⋊D101—21no—
35C4×C22⋊D101—21no—
36#15692214C2211yescharacteristic
37#15692213—21no—
38C4⋊C4×D101—21no—
39#15692186C2211yescharacteristic
40#15692186C2211yescharacteristic
41#15692184C2211yescharacteristic
42#15692184C2211yescharacteristic
43#15692180C2211yescharacteristic
44#15692178C2211yescharacteristic
45#15692178C2211yescharacteristic
46#15692178C2211yescharacteristic
47#15692177C2211yescharacteristic
48#15692175C2211yescharacteristic
49C22⋊#11717579C2211yescharacteristic
50#15692165C2211yescharacteristic
51C8×Dic101C2211yescharacteristic
52C22⋊Q8×C101C2211yescharacteristic
53C2×C4⋊C4×C101C2211yescharacteristic
54#107×C101C2211yescharacteristic
55#107×C101C2211yescharacteristic
56#103×C101C2211yescharacteristic
57#103×C101C2211yescharacteristic
58C22⋊C8×C101C2211yescharacteristic
59#13108074—22no—
60#13108074—22no—
61C2×Dic202C2311yescharacteristic
62C2×Dic202C2311yescharacteristic
63C2×D404C2311yescharacteristic
64C2×C22⋊D101—21no—
65C2×C4×D101—21no—
66C2×C4×D101—21no—
67C2×C4×D101—21no—
68Dic404—22no—
69#13108064—22no—
70#13108063—22no—
71#13108061—22no—
72C2×#11717579C2311yescharacteristic
73C2×#11717579C2311yescharacteristic
74C4⋊Dic101—21no—
75C4⋊Dic101—21no—
76C4⋊Dic101D411yescharacteristic
77C4⋊Dic101D411yescharacteristic
78C4⋊Dic101C2311yescharacteristic
79#13108053—21no—
80#13108053—21no—
81#13108053—21no—
82#13108053—21no—
83#13108053—21no—
84#13108053—21no—
85#13108053—21no—
86C22⋊Dic101—21no—
87C22⋊Dic101D411yescharacteristic
88C22⋊Dic101D411yescharacteristic
89#13108051—21no—
90#13108051—21no—
91C4×Dic101—21no—
92C4×Dic101—21no—
93C4×Dic101—21no—
94C4×Dic101—21no—
95C4×Dic101C2311yescharacteristic
96C4×Dic101C2311yescharacteristic
97C2×Q8×C101C2311yescharacteristic
98C22×C4×C101—21no—
99C22×C4×C101C2311yescharacteristic
100C2×C8×C101C2311yescharacteristic
101C2×C8×C101C2311yescharacteristic
102C4⋊C4×C101—21no—
103C4⋊C4×C101—21no—
104C4⋊C4×C101C2311yescharacteristic
105C4⋊C4×C101C2311yescharacteristic
106C4⋊C4×C101C2311yescharacteristic
107C22⋊C4×C101—21no—
108C23×C101C2×D411yescharacteristic
109C22×D101—21no—
110Q8×C101—21no—
111Q8×C101—21no—
112C2×C4×C101—21no—
113C2×C4×C101—21no—
114C2×C4×C101—21no—
115C2×C4×C101—21no—
116C2×C4×C101—21no—
117C2×C4×C101—21no—
118C2×C4×C101—81no—
119C2×C4×C101C2×D411yescharacteristic
120C2×C4×C101C2411yescharacteristic
121C22⋊D101—24no—
122C2×Dic101—21no—
123C2×Dic101—21no—
124C2×Dic101—21no—
125C2×Dic101C2×D411yescharacteristic
126C2×Dic101C2×D411yescharacteristic
127C2×Dic101C2×D411yescharacteristic
128C2×Dic101C2×D411yescharacteristic
129D404—21no—
130D404#4112yes—
131C4×D101—24no—
132C4×D101—81no—
133C4×D101—81no—
134Dic202—21no—
135Dic202—21no—
136Dic202—21no—
137Dic202#4112yes—
138C8×C101—21no—
139C8×C101—21no—
140#11717579—21no—
141#11717579—21no—
142C22×C101—21no—
143C22×C101—21no—
144C22×C101—21no—
145C22×C101C22×D411yescharacteristic
146C2×D101—22no—
147C2×D101—41no—
148C2×D101—41no—
149C4×C101—21no—
150C4×C101—41no—
151C4×C101—41no—
152C4×C101—41no—
153C4×C101—41no—
154C4×C101C2×#4111yescharacteristic
155C4×C101C2×#4111yescharacteristic
156Dic101—22no—
157Dic101—21no—
158Dic101—21no—
159Dic101—21no—
160Dic101—21no—
161Dic101—41no—
162Dic101—41no—
163C2×C101—41no—
164C2×C101#52511yescharacteristic
165C2×C101#57711yescharacteristic
166C2×C101#57811yescharacteristic
167D101—42no—
168#3120—1011nomaximal, Sylow
169C101#312011yescharacteristic, complemented, Sylow
170#541—1011no—
171#520—1011no—
172#484D10111yescharacteristic, complemented
173#483—1011no—
174#479—1011no—
175#478—1011no—
176#462—1011no—
177#461—1011no—
178#452—1011no—
179#452—1011no—
180#441—1011no—
181#440—1011no—
182C4×Q16—1011no—
183C4×SD16—1011no—
184#433—1011no—
185C2×#41—1011no—
186C2×Q16—1011no—
187C2×Q16—1011no—
188C2×SD16—1011no—
189C2×SD16—1011no—
190C4⋊Q8—1011no—
191#126—2021no—
192#126—2021no—
193#125—1011no—
194#125—2021no—
195#125—2021no—
196C22⋊Q8—1011no—
197C22⋊Q8C2×D10111yescharacteristic
198C4×Q8—1011no—
199C4×Q8—1011no—
200C4×Q8—1011no—
201C4×Q8—1011no—
202C4×D4—1011no—
203C4×D4—1011no—
204C4×D4—2021no—
205C4×D4—2021no—
206#117—1011no—
207#117—2021no—
208C2×C4⋊C4—2021no—
209C2×C4⋊C4C2×D10111yescharacteristic
210#107C2×D10111yescharacteristic
211#107C2×D10111yescharacteristic
212#106—1011no—
213#106—1011no—
214C4⋊C8—1011no—
215C4⋊C8—1011no—
216#103—1011no—
217#103—1011no—
218#103—1011no—
219#103—1011no—
220#103C2×D10111yescharacteristic
221#103C2×D10111yescharacteristic
222#102—1011no—
223#102—1011no—
224C22⋊C8—1011no—
225C22⋊C8C2×D10111yescharacteristic
226#97—1011no—
227C4×C8—1011no—
228#41—2022no—
229#41—2022no—
230C2×Q8—1011no—
231C2×Q8—1011no—
232C2×Q8C22×D10111yescharacteristic
233C2×D4—1011no—
234C2×D4—2021no—
235C22×C4—21no—
236C22×C4—2021no—
237C22×C4—2021no—
238C22×C4—2021no—
239C22×C4C22×D10111yescharacteristic
240Q16—2022no—
241Q16—2022no—
242SD16—2022no—
243SD16—2022no—
244C2×C8—1011no—
245C2×C8—1011no—
246C2×C8C22×D10111yescharacteristic
247C2×C8C22×D10111yescharacteristic
248C4⋊C4—21no—
249C4⋊C4—21no—
250C4⋊C4—1011no—
251C4⋊C4—1011no—
252C4⋊C4—1011no—
253C4⋊C4—2021no—
254C4⋊C4—2021no—
255C4⋊C4—2021no—
256C4⋊C4—2021no—
257C4⋊C4—2021no—
258C4⋊C4—2021no—
259C4⋊C4—2021no—
260C4⋊C4—2021no—
261C4⋊C4—2021no—
262C4⋊C4C22×D10111yescharacteristic
263C4⋊C4C22×D10111yescharacteristic
264C4⋊C4C22×D10111yescharacteristic
265C22⋊C4—21no—
266C22⋊C4—1011no—
267C22⋊C4—1011no—
268C22⋊C4—2021no—
269C22⋊C4—2021no—
270C22⋊C4—2021no—
271C42—1011no—
272C42—1011no—
273C42—2021no—
274C42—2021no—
275C42—2021no—
276C42—2021no—
277C23—2021no—
278C23D4×D10111yescharacteristic
279Q8—21no—
280Q8—21no—
281Q8—1012no—
282Q8—2021no—
283Q8—2021no—
284Q8—2021no—
285D4—1012no—
286D4—2024no—
287D4—2021no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—81no—
295C2×C4—8081no—
296C2×C4—8081no—
297C2×C4—1011no—
298C2×C4—1011no—
299C2×C4—1011no—
300C2×C4—1011no—
301C2×C4—2024no—
302C2×C4—2021no—
303C2×C4—2021no—
304C2×C4—2021no—
305C2×C4D4×D10111yescharacteristic
306C2×C4C23×D10111yescharacteristic
307C8—21no—
308C8—21no—
309C8—2021no—
310C8—2021no—
311C22—21no—
312C22—21no—
313C22—21no—
314C22—4041no—
315C22—4041no—
316C22—2022no—
317C22C2×D4×D10111yescharacteristic
318C4—21no—
319C4—41no—
320C4—41no—
321C4—41no—
322C4—41no—
323C4—4041no—
324C4—4041no—
325C4—2021no—
326C4—2021no—
327C4—2021no—
328C4—2021no—
329C4—2022no—
330C4#41×D10111yescharacteristic
331C4#41×D10111yescharacteristic
332C2—41no—
333C2—4042no—
334C2#2026568511yescharacteristic
335C2#2026598711yescharacteristic
336C2#2026599011yescharacteristic
subgroupG/H
centerC22C2×D4×D101
commutator, cosocleC2×C4×C101C24
FrattiniC2×C4C23×D101
Fitting#484×C101C2
socleC22×C101C22×D4
prime radicalC2×#13108074C22
hypercenter#484D101
hypocenterC101#3120
LCSG ▷ C2×C4×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C22 ◁ C22×C4 ◁ #484

Complements

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

NH ≅ G/Ntype
1. #20265787C2semidirect
3. #20265507C2semidirect
4. #20265483C2semidirect
5. #20265480C2semidirect
6. #20265386C2semidirect
7. #20265381C2semidirect
10. #20265281C2semidirect
11. #20265276C2semidirect
12. #20265271C2semidirect
13. #20265262C2semidirect
14. #20265235C2semidirect
15. #484×C101C2semidirect
169. C101#3120semidirect
172. #484D101semidirect

Maximal subgroups

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

subgroupindex
#202657872
#202656582
#202655072
#202654832
#202654802
#202653862
#202653812
#202653412
#202653372
#202652812
#202652762
#202652712
#202652622
#202652352
#484×C1012
#3120101