Finite Group Databasebeta

← #27183125

Subgroups — #27183125

Order 12928.

420 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20265836C211yesmaximal, characteristic, complemented
2#20265831C211yesmaximal, characteristic, complemented
3#20265537C211yesmaximal, characteristic, complemented
4#20265513C211yesmaximal, characteristic, complemented
5#20265491C211yesmaximal, characteristic, complemented
6#20265473C211yesmaximal, characteristic, complemented
7#20265423C211yesmaximal, characteristic, complemented
8#20265413C211yesmaximal, characteristic, complemented
9#20265393C211yesmaximal, characteristic, complemented
10#20265324C211yesmaximal, characteristic, complemented
11#20265318C211yesmaximal, characteristic, complemented
12#20265279C211yesmaximal, characteristic, complemented
13#20265179C211yesmaximal, characteristic, complemented
14C2×#15692180C211yesmaximal, characteristic, complemented
15#435×C101C211yesmaximal, characteristic, complemented
16C2×#13108074C2211yescharacteristic
17C2×#13108073—21no—
18C22×Dic202C2211yescharacteristic
19C2×#13108063C2211yescharacteristic
20C2×#13108063C2211yescharacteristic
21C2×D808C2211yescharacteristic
22#15692255C2211yescharacteristic
23#15692243C2211yescharacteristic
24#15692241—21no—
25#15692239—21no—
26#15692239—21no—
27#15692235—21no—
28#15692234C2211yescharacteristic
29#15692233—21no—
30#15692229C2211yescharacteristic
31#15692229C2211yescharacteristic
32#15692229C2211yescharacteristic
33#15692227—21no—
34C4×Dic202C2211yescharacteristic
35C4×D404C2211yescharacteristic
36#15692215—21no—
37C2×C4⋊Dic101C2211yescharacteristic
38C2×C4⋊Dic101C2211yescharacteristic
39#15692189C2211yescharacteristic
40#15692189C2211yescharacteristic
41#15692189C2211yescharacteristic
42#15692180C2211yescharacteristic
43#15692180C2211yescharacteristic
44#15692180C2211yescharacteristic
45#15692180C2211yescharacteristic
46#15692180C2211yescharacteristic
47#15692180C2211yescharacteristic
48#15692177C2211yescharacteristic
49#15692177C2211yescharacteristic
50#15692177C2211yescharacteristic
51#15692177C2211yescharacteristic
52C2×M16×C101C2211yescharacteristic
53C22×C8×C101C2211yescharacteristic
54C4×D4×C101C2211yescharacteristic
55C4⋊C8×C101C2211yescharacteristic
56C22⋊C8×C101C2211yescharacteristic
57C22⋊C8×C101C2211yescharacteristic
58#97×C101C2211yescharacteristic
59#13108074—22no—
60#13108074—41no—
61#13108073—44no—
62C2×Dic202—22no—
63C2×Dic202—21no—
64C2×Dic202—21no—
65C2×Dic202—41no—
66C2×Dic202C2311yescharacteristic
67C2×Dic202C2311yescharacteristic
68C2×D404C2311yescharacteristic
69C2×D404C2311yescharacteristic
70C2×C22⋊D101—21no—
71C2×C22⋊D101—21no—
72C2×C22⋊D101—21no—
73C2×C22⋊D101—21no—
74C22×Dic101—21no—
75C22×Dic101—21no—
76C22×Dic101—21no—
77C2×C4×D101—21no—
78C2×C4×D101—21no—
79#13108063—22no—
80#13108063—41no—
81D808—41no—
82C4⋊Dic101—21no—
83C4⋊Dic101—21no—
84C4⋊Dic101—21no—
85C4⋊Dic101C2311yescharacteristic
86C4⋊Dic101C2311yescharacteristic
87C4⋊Dic101C2311yescharacteristic
88C4⋊Dic101C2311yescharacteristic
89#13108053—21no—
90#13108053—21no—
91C22⋊Dic101—21no—
92#13108051—21no—
93#13108051—21no—
94#13108051—21no—
95#13108051—21no—
96#13108051—21no—
97#13108051—21no—
98C4×Dic101—21no—
99C2×D4×C101D411yescharacteristic
100C22×C4×C101C2311yescharacteristic
101C22×C4×C101C2311yescharacteristic
102M16×C101—41no—
103C2×C8×C101—41no—
104C2×C8×C101C2311yescharacteristic
105C2×C8×C101C2311yescharacteristic
106C2×C8×C101C2311yescharacteristic
107C2×C8×C101C2311yescharacteristic
108C4⋊C4×C101D411yescharacteristic
109C22⋊C4×C101D411yescharacteristic
110C22⋊C4×C101D411yescharacteristic
111C42×C101C2311yescharacteristic
112C23×C101C2×D411yescharacteristic
113C23×C101C2×D411yescharacteristic
114C22×D101—21no—
115C22×D101—21no—
116D4×C101—22no—
117C2×C4×C101—21no—
118C2×C4×C101—21no—
119C2×C4×C101—21no—
120C2×C4×C101—21no—
121C2×C4×C101C2×D411yescharacteristic
122C2×C4×C101C2×D411yescharacteristic
123C2×C4×C101C2×D411yescharacteristic
124C2×C4×C101C2×D411yescharacteristic
125C2×C4×C101C2411yescharacteristic
126C22⋊D101—42no—
127C22⋊D101—42no—
128C22⋊D101—42no—
129C22⋊D101—42no—
130C2×Dic101—21no—
131C2×Dic101—21no—
132C2×Dic101—21no—
133C2×Dic101—21no—
134C2×Dic101—21no—
135C2×Dic101—21no—
136C2×Dic101—42no—
137C2×Dic101—42no—
138C2×Dic101—42no—
139D404—21no—
140D404—21no—
141D404—21no—
142D404—21no—
143C4×D101—42no—
144C4×D101—42no—
145Dic202—21no—
146Dic202—21no—
147Dic202—21no—
148Dic202—42no—
149Dic202—42no—
150Dic202#4112yescomplemented
151C8×C101—21no—
152C8×C101—21no—
153C8×C101—21no—
154C8×C101—21no—
155C22×C101—21no—
156C22×C101—21no—
157C22×C101—21no—
158C22×C101—21no—
159C22×C101—21no—
160C22×C101AGL(1,ℤ/8)12yes—
161C22×C101C22×D411yescharacteristic
162C2×D101—41no—
163C2×D101—41no—
164C2×D101—41no—
165C2×D101—41no—
166C2×D101—41no—
167C2×D101—41no—
168C4×C101—21no—
169C4×C101—21no—
170C4×C101—21no—
171C4×C101—21no—
172C4×C101C2×#4111yescharacteristic
173C4×C101H(5,𝔽2)11yescharacteristic
174Dic101—22no—
175Dic101—41no—
176Dic101—41no—
177Dic101—41no—
178Dic101—41no—
179Dic101—41no—
180C2×C101—22no—
181C2×C101—41no—
182C2×C101#54611yescharacteristic
183C2×C101C2×AGL(1,ℤ/8)11yescharacteristic
184C2×C101#57811yescharacteristic
185D101—81no—
186D101—81no—
187#3308—1011nomaximal, Sylow
188C101#330811yescharacteristic, complemented, Sylow
189#548—1011no—
190#547—1011no—
191#489—1011no—
192#484—1011no—
193#480—1011no—
194#477—1011no—
195#468—1011no—
196#466—1011no—
197#463—1011no—
198#449—1011no—
199#448—1011no—
200#440—1011no—
201#435D10111yescharacteristic, complemented
202#417—1011no—
203C2×#103—1011no—
204C2×#41—1011no—
205C2×#41—2021no—
206C22×Q8—1011no—
207C2×SD16—1011no—
208C2×SD16—1011no—
209C2×D8—1011no—
210C2×M16C2×D10111yescharacteristic
211C22×C8C2×D10111yescharacteristic
212C4⋊Q8—1011no—
213#124—1011no—
214#124—2021no—
215#123—2021no—
216#123—2021no—
217C22⋊Q8—1011no—
218C22⋊Q8—2021no—
219C22⋊Q8—2021no—
220#121—1011no—
221#121—1011no—
222#121—1011no—
223#121—2021no—
224C4×Q8—1011no—
225C4×D4—1011no—
226C4×D4—2021no—
227C4×D4C2×D10111yescharacteristic
228C2×C4⋊C4—1011no—
229C2×C4⋊C4—1011no—
230#107—1011no—
231#107—1011no—
232#107—1011no—
233C4⋊C8C2×D10111yescharacteristic
234#103—1011no—
235#103—1011no—
236#103—1011no—
237#103—1011no—
238#103—1011no—
239#103—1011no—
240#102—1011no—
241#102—1011no—
242#102—1011no—
243#102—1011no—
244C22⋊C8C2×D10111yescharacteristic
245C22⋊C8C2×D10111yescharacteristic
246#97C2×D10111yescharacteristic
247#41—4041no—
248#41—4044no—
249#41—2022no—
250C2×Q8—1011no—
251C2×Q8—1011no—
252C2×Q8—4041no—
253C2×Q8—2022no—
254C2×Q8—2021no—
255C2×Q8—2021no—
256C2×D4—1011no—
257C2×D4—1011no—
258C2×D4—2021no—
259C2×D4—2021no—
260C2×D4—2021no—
261C2×D4—2021no—
262C2×D4D40411yescharacteristic
263C22×C4—2021no—
264C22×C4—2021no—
265C22×C4—2021no—
266C22×C4—2021no—
267C22×C4—2021no—
268C22×C4C22×D10111yescharacteristic
269C22×C4C22×D10111yescharacteristic
270SD16—4041no—
271SD16—2022no—
272D8—4041no—
273M16—41no—
274C2×C8—41no—
275C2×C8C22×D10111yescharacteristic
276C2×C8C22×D10111yescharacteristic
277C2×C8C22×D10111yescharacteristic
278C2×C8C22×D10111yescharacteristic
279C4⋊C4—1011no—
280C4⋊C4—1011no—
281C4⋊C4—1011no—
282C4⋊C4—1011no—
283C4⋊C4—2021no—
284C4⋊C4—2021no—
285C4⋊C4—2021no—
286C4⋊C4—2021no—
287C4⋊C4—2021no—
288C4⋊C4D40411yescharacteristic
289C22⋊C4—2021no—
290C22⋊C4—2021no—
291C22⋊C4—2021no—
292C22⋊C4—2021no—
293C22⋊C4—2021no—
294C22⋊C4—2021no—
295C22⋊C4—2021no—
296C22⋊C4D40411yescharacteristic
297C22⋊C4D40411yescharacteristic
298C42—2021no—
299C42C22×D10111yescharacteristic
300C23—2021no—
301C23—2021no—
302C23C2×D40411yescharacteristic
303C23C2×D40411yescharacteristic
304Q8—1012no—
305Q8—4042no—
306Q8—4042no—
307Q8—2021no—
308Q8—2021no—
309Q8—2021no—
310D4—22no—
311D4—4042no—
312D4—4042no—
313D4—4042no—
314D4—4042no—
315D4—2021no—
316D4—2021no—
317D4—2021no—
318D4—2021no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—4042no—
324C2×C4—4042no—
325C2×C4—4042no—
326C2×C4—4042no—
327C2×C4—4042no—
328C2×C4—2021no—
329C2×C4—2021no—
330C2×C4—2021no—
331C2×C4—2021no—
332C2×C4—2021no—
333C2×C4—2021no—
334C2×C4C2×D40411yescharacteristic
335C2×C4C2×D40411yescharacteristic
336C2×C4C2×D40411yescharacteristic
337C2×C4C2×D40411yescharacteristic
338C2×C4C23×D10111yescharacteristic
339C8—21no—
340C8—21no—
341C8—21no—
342C8—21no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—21no—
347C22—21no—
348C22—4041no—
349C22—4041no—
350C22—4041no—
351C22—4041no—
352C22—4041no—
353C22—4041no—
354C22#1569228312yes—
355C22C22×D40411yescharacteristic
356C4—21no—
357C4—21no—
358C4—21no—
359C4—21no—
360C4—4041no—
361C4—4041no—
362C4—4041no—
363C4—4041no—
364C4—4041no—
365C4—2022no—
366C4#41×D10111yescharacteristic
367C4#1569230011yescharacteristic
368C2—22no—
369C2—41no—
370C2—8081no—
371C2—8081no—
372C2#2026582211yescharacteristic
373C2C2×#1569228311yescharacteristic
374C2#2026599411yescharacteristic
subgroupG/H
centerC22C22×D404
commutator, cosocleC2×C4×C101C24
FrattiniC2×C4C23×D101
Fitting#435×C101C2
socleC22×C101C22×D4
hypercenter#435D101
hypocenterC101#3308
LCSG ▷ C2×C4×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C22 ◁ C4×D4 ◁ #435

Complements

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

NH ≅ G/Ntype
1. #20265836C2semidirect
2. #20265831C2semidirect
3. #20265537C2semidirect
4. #20265513C2semidirect
5. #20265491C2semidirect
6. #20265473C2semidirect
7. #20265423C2semidirect
8. #20265413C2semidirect
9. #20265393C2semidirect
10. #20265324C2semidirect
11. #20265318C2semidirect
12. #20265279C2semidirect
13. #20265179C2semidirect
14. C2×#15692180C2semidirect
15. #435×C101C2semidirect
150. Dic202#41semidirect
188. C101#3308semidirect
201. #435D101semidirect

Maximal subgroups

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

subgroupindex
#202658362
#202658312
#202655372
#202655132
#202654912
#202654732
#202654232
#202654132
#202653932
#202653242
#202653182
#202652792
#202651792
C2×#156921802
#435×C1012
#3308101