Finite Group Databasebeta

← #27183102

Subgroups — #27183102

Order 12928.

394 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20265832C211yesmaximal, characteristic, complemented
2#20265547C211yesmaximal, characteristic, complemented
3#20265518C211yesmaximal, characteristic, complemented
4#20265507C211yesmaximal, characteristic, complemented
5#20265474C211yesmaximal, characteristic, complemented
6#20265421C211yesmaximal, characteristic, complemented
7#20265404C211yesmaximal, characteristic, complemented
8#20265382C211yesmaximal, characteristic, complemented
9#20265320C211yesmaximal, characteristic, complemented
10#20265320C211yesmaximal, characteristic, complemented
11#20265287C211yesmaximal, characteristic, complemented
12#20265249C211yesmaximal, characteristic, complemented
13#20265176C211yesmaximal, characteristic, complemented
14#20265171C211yesmaximal, characteristic, complemented
15#553×C101C211yesmaximal, characteristic, complemented
16C2×#13108074C2211yescharacteristic
17C2×#13108074C2211yescharacteristic
18C2×#13108062C2211yescharacteristic
19C2×#13108062C2211yescharacteristic
20C2×#13108059C2211yescharacteristic
21C2×#13108058C2211yescharacteristic
22C22×#11717579C2211yescharacteristic
23#15692255C2211yescharacteristic
24#15692237—21no—
25#15692237—21no—
26#15692234C2211yescharacteristic
27#15692234C2211yescharacteristic
28#15692226—21no—
29C4×D404C2211yescharacteristic
30C4⋊C4×D101—21no—
31#15692188C2211yescharacteristic
32#15692186C2211yescharacteristic
33#15692186C2211yescharacteristic
34C4⋊#11717579C2211yescharacteristic
35#15692178C2211yescharacteristic
36#15692178C2211yescharacteristic
37#15692178C2211yescharacteristic
38#15692178C2211yescharacteristic
39#15692178C2211yescharacteristic
40#15692178C2211yescharacteristic
41#15692176C2211yescharacteristic
42#15692175C2211yescharacteristic
43#15692175C2211yescharacteristic
44#15692175C2211yescharacteristic
45C22⋊#11717579C2211yescharacteristic
46C22⋊#11717579C2211yescharacteristic
47#15692166C2211yescharacteristic
48#126×C101—21no—
49#125×C101C2211yescharacteristic
50#123×C101—21no—
51#121×C101—21no—
52#121×C101C2211yescharacteristic
53#121×C101C2211yescharacteristic
54C4×D4×C101—21no—
55C4×D4×C101C2211yescharacteristic
56C4×D4×C101C2211yescharacteristic
57#117×C101C2211yescharacteristic
58C2×C4⋊C4×C101C2211yescharacteristic
59#13108074—22no—
60#13108074—22no—
61#13108074—41no—
62#13108074—41no—
63C2×Dic202C2311yescharacteristic
64C2×Dic202C2311yescharacteristic
65C2×D404C2311yescharacteristic
66C2×C22⋊D101—21no—
67C2×C22⋊D101—21no—
68C2×C4×D101—21no—
69C2×C4×D101—21no—
70C2×C4×D101—21no—
71#13108062—41no—
72#13108062—41no—
73#13108059—22no—
74#13108058—41no—
75C2×#11717579—41no—
76C2×#11717579C2311yescharacteristic
77C2×#11717579C2311yescharacteristic
78C2×#11717579C2311yescharacteristic
79C2×#11717579C2311yescharacteristic
80C4⋊Dic101—21no—
81C4⋊Dic101—21no—
82C4⋊Dic101C2311yescharacteristic
83#13108053—21no—
84#13108053—21no—
85C22⋊Dic101—21no—
86C22⋊Dic101—21no—
87#13108051—21no—
88C2×D4×C101—21no—
89C2×D4×C101—21no—
90C2×D4×C101D411yescharacteristic
91C2×D4×C101C2311yescharacteristic
92C22×C4×C101—21no—
93C22×C4×C101—21no—
94C22×C4×C101C2311yescharacteristic
95C22×C4×C101C2311yescharacteristic
96C4⋊C4×C101—21no—
97C4⋊C4×C101—21no—
98C4⋊C4×C101—21no—
99C4⋊C4×C101D411yescharacteristic
100C4⋊C4×C101C2311yescharacteristic
101C4⋊C4×C101C2311yescharacteristic
102C4⋊C4×C101C2311yescharacteristic
103C22⋊C4×C101—21no—
104C22⋊C4×C101—21no—
105C22⋊C4×C101—21no—
106C22⋊C4×C101—21no—
107C22⋊C4×C101D411yescharacteristic
108C22⋊C4×C101D411yescharacteristic
109C42×C101—21no—
110C42×C101C2311yescharacteristic
111C23×C101—21no—
112C23×C101C2×D411yescharacteristic
113C23×C101C2×D411yescharacteristic
114C22×D101—21no—
115D4×C101—21no—
116D4×C101—21no—
117D4×C101—41no—
118D4×C101—42no—
119D4×C101—81no—
120C2×C4×C101—21no—
121C2×C4×C101—21no—
122C2×C4×C101—21no—
123C2×C4×C101—21no—
124C2×C4×C101—21no—
125C2×C4×C101—21no—
126C2×C4×C101—21no—
127C2×C4×C101—81no—
128C2×C4×C101—81no—
129C2×C4×C101C2×D411yescharacteristic
130C2×C4×C101C2×D411yescharacteristic
131C2×C4×C101C2×D411yescharacteristic
132C2×C4×C101C2×D411yescharacteristic
133C2×C4×C101C2411yescharacteristic
134C22⋊D101—42no—
135C22⋊D101—42no—
136C2×Dic101—21no—
137C2×Dic101—21no—
138C2×Dic101—21no—
139D404—21no—
140D404#4112yes—
141C4×D101—42no—
142C4×D101—42no—
143C4×D101—42no—
144Dic202—21no—
145Dic202—21no—
146Dic202—21no—
147Dic202—21no—
148#11717579—21no—
149#11717579—21no—
150#11717579—21no—
151#11717579—21no—
152C22×C101—21no—
153C22×C101—21no—
154C22×C101—21no—
155C22×C101—21no—
156C22×C101—21no—
157C22×C101—21no—
158C22×C101—41no—
159C22×C101—41no—
160C22×C101—41no—
161C22×C101C22×D411yescharacteristic
162C2×D101—22no—
163C2×D101—41no—
164C2×D101—41no—
165C4×C101—21no—
166C4×C101—21no—
167C4×C101—21no—
168C4×C101—21no—
169C4×C101—41no—
170C4×C101—41no—
171C4×C101—41no—
172C4×C101C2×#4111yescharacteristic
173C4×C101H(5,𝔽2)11yescharacteristic
174Dic101—41no—
175Dic101—41no—
176Dic101—41no—
177C2×C101—41no—
178C2×C101—41no—
179C2×C101—81no—
180C2×C101#54611yescharacteristic
181C2×C101#57511yescharacteristic
182C2×C101#57711yescharacteristic
183D101—42no—
184#3307—1011nomaximal, Sylow
185C101#330711yescharacteristic, complemented, Sylow
186#553D10111yescharacteristic, complemented
187#547—1011no—
188#491—1011no—
189#485—1011no—
190#483—1011no—
191#478—1011no—
192#468—1011no—
193#465—1011no—
194#461—1011no—
195#449—1011no—
196#449—1011no—
197#442—1011no—
198#435—1011no—
199#417—1011no—
200#416—1011no—
201C2×#41—1011no—
202C2×#41—1011no—
203C2×SD16—1011no—
204C2×SD16—1011no—
205C2×D8—1011no—
206C2×M16—1011no—
207C22×C8—1011no—
208C4⋊Q8—1011no—
209#126—21no—
210#125C2×D10111yescharacteristic
211#123—21no—
212#123—2021no—
213#123—2021no—
214C22⋊Q8—1011no—
215C22⋊Q8—1011no—
216#121—21no—
217#121—2021no—
218#121C2×D10111yescharacteristic
219#121C2×D10111yescharacteristic
220C4×D4—21no—
221C4×D4—1011no—
222C4×D4C2×D10111yescharacteristic
223C4×D4C2×D10111yescharacteristic
224#117C2×D10111yescharacteristic
225C2×C4⋊C4—2021no—
226C2×C4⋊C4C2×D10111yescharacteristic
227#107—1011no—
228#106—1011no—
229#106—1011no—
230C4⋊C8—1011no—
231#103—1011no—
232#103—1011no—
233#103—1011no—
234#103—1011no—
235#103—1011no—
236#103—1011no—
237#102—1011no—
238#102—1011no—
239#102—1011no—
240#102—1011no—
241C22⋊C8—1011no—
242C22⋊C8—1011no—
243#97—1011no—
244#41—4041no—
245#41—4041no—
246#41—2022no—
247#41—2022no—
248C2×Q8—1011no—
249C2×Q8—1011no—
250C2×D4—21no—
251C2×D4—21no—
252C2×D4—1011no—
253C2×D4—2021no—
254C2×D4—2021no—
255C2×D4C22⋊D10111yescharacteristic
256C2×D4C22×D10111yescharacteristic
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—2021no—
260C22×C4—2021no—
261C22×C4—2021no—
262C22×C4C22×D10111yescharacteristic
263C22×C4C22×D10111yescharacteristic
264SD16—4041no—
265SD16—4041no—
266D8—2022no—
267M16—4041no—
268C2×C8—1011no—
269C2×C8—1011no—
270C2×C8—1011no—
271C2×C8—1011no—
272C2×C8—4041no—
273C4⋊C4—21no—
274C4⋊C4—21no—
275C4⋊C4—21no—
276C4⋊C4—1011no—
277C4⋊C4—2021no—
278C4⋊C4—2021no—
279C4⋊C4—2021no—
280C4⋊C4—2021no—
281C4⋊C4C22⋊D10111yescharacteristic
282C4⋊C4C22×D10111yescharacteristic
283C4⋊C4C22×D10111yescharacteristic
284C4⋊C4C22×D10111yescharacteristic
285C22⋊C4—21no—
286C22⋊C4—21no—
287C22⋊C4—21no—
288C22⋊C4—21no—
289C22⋊C4—2021no—
290C22⋊C4—2021no—
291C22⋊C4—2021no—
292C22⋊C4C22⋊D10111yescharacteristic
293C22⋊C4C22⋊D10111yescharacteristic
294C42—21no—
295C42C22×D10111yescharacteristic
296C23—21no—
297C23—2021no—
298C23C2×C22⋊D10111yescharacteristic
299C23C2×C22⋊D10111yescharacteristic
300Q8—2021no—
301Q8—2021no—
302Q8—2021no—
303Q8—2021no—
304D4—21no—
305D4—21no—
306D4—41no—
307D4—42no—
308D4—81no—
309D4—1012no—
310D4—4042no—
311D4—4042no—
312D4—2021no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—81no—
321C2×C4—81no—
322C2×C4—4042no—
323C2×C4—4042no—
324C2×C4—4042no—
325C2×C4—2021no—
326C2×C4—2021no—
327C2×C4—2021no—
328C2×C4C2×C22⋊D10111yescharacteristic
329C2×C4C2×C22⋊D10111yescharacteristic
330C2×C4C2×C22⋊D10111yescharacteristic
331C2×C4C2×C22⋊D10111yescharacteristic
332C2×C4C23×D10111yescharacteristic
333C8—2021no—
334C8—2021no—
335C8—2021no—
336C8—2021no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—41no—
344C22—41no—
345C22—41no—
346C22—4041no—
347C22—4041no—
348C22—2022no—
349C22C22×C22⋊D10111yescharacteristic
350C4—21no—
351C4—21no—
352C4—21no—
353C4—21no—
354C4—41no—
355C4—41no—
356C4—41no—
357C4—4041no—
358C4—4041no—
359C4—4041no—
360C4#41×D10111yescharacteristic
361C4#1569230111yescharacteristic
362C2—41no—
363C2—41no—
364C2—81no—
365C2—4042no—
366C2#2026581511yescharacteristic
367C2#2026597511yescharacteristic
368C2#2026598811yescharacteristic
subgroupG/H
centerC22C22×C22⋊D101
commutator, cosocleC2×C4×C101C24
FrattiniC2×C4C23×D101
Fitting#553×C101C2
socleC22×C101C22×D4
hypercenter#553D101
hypocenterC101#3307
LCSG ▷ C2×C4×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C22 ◁ C4×D4 ◁ #553

Complements

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

NH ≅ G/Ntype
1. #20265832C2semidirect
2. #20265547C2semidirect
3. #20265518C2semidirect
4. #20265507C2semidirect
5. #20265474C2semidirect
6. #20265421C2semidirect
7. #20265404C2semidirect
8. #20265382C2semidirect
9. #20265320C2semidirect
10. #20265320C2semidirect
11. #20265287C2semidirect
12. #20265249C2semidirect
13. #20265176C2semidirect
14. #20265171C2semidirect
15. #553×C101C2semidirect
185. C101#3307semidirect
186. #553D101semidirect

Maximal subgroups

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

subgroupindex
#202658322
#202655472
#202655182
#202655072
#202654742
#202654212
#202654042
#202653822
#202653202
#202652872
#202652492
#202651762
#202651712
#553×C1012
#3307101