Finite Group Databasebeta

← #27181688

Subgroups — #27181688

Order 12928.

412 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20265731C211yesmaximal, characteristic, complemented
2#20265724C211yesmaximal, characteristic
3#20265574C211yesmaximal, characteristic, complemented
4#20265548C211yesmaximal, characteristic, complemented
5#20265526C211yesmaximal, characteristic, complemented
6#20265522C211yesmaximal, characteristic, complemented
7#20265409C211yesmaximal, characteristic, complemented
8#20265407C211yesmaximal, characteristic, complemented
9#20265405C211yesmaximal, characteristic, complemented
10#20265403C211yesmaximal, characteristic, complemented
11C4×#13108063C211yesmaximal, characteristic, complemented
12C4×#13108061C211yesmaximal, characteristic, complemented
13C4×#13108062C211yesmaximal, characteristic, complemented
14C4×C8×D101C211yesmaximal, characteristic, complemented
15C4×SD16×C101C211yesmaximal, characteristic, complemented
16C2×#13108074—21no—
17C2×#13108063C2211yescharacteristic
18C2×#13108062C2211yescharacteristic
19C2×#13108061C2211yescharacteristic
20C2×C8×D101C2211yescharacteristic
21C2×C8×D101C2211yescharacteristic
22#15692254C2211yescharacteristic
23#15692254C2211yescharacteristic
24#15692253C2211yescharacteristic
25#15692251C2211yescharacteristic
26#15692245—21no—
27#15692241—21no—
28#15692235C2211yescharacteristic
29#15692233—21no—
30#15692231C2211yescharacteristic
31#15692230C2211yescharacteristic
32#15692228—21no—
33#15692226C2211yescharacteristic
34C4×Dic202—21no—
35C4×Dic202C2211yescharacteristic
36C4×D404C2211yescharacteristic
37C4×C22⋊D101—21no—
38#15692212—21no—
39C42×D101C2211yescharacteristic
40#15692187C2211yescharacteristic
41#15692186C2211yescharacteristic
42#15692186C2211yescharacteristic
43#15692180C2211yescharacteristic
44#15692179C2211yescharacteristic
45#15692178C2211yescharacteristic
46#15692177C2211yescharacteristic
47#15692176C2211yescharacteristic
48#15692175C2211yescharacteristic
49C4×#11717579C2211yescharacteristic
50C8×Dic101C2211yescharacteristic
51C8×Dic101C2211yescharacteristic
52C2×SD16×C101C2211yescharacteristic
53C4×Q8×C101C2211yescharacteristic
54C4×D4×C101C2211yescharacteristic
55#106×C101C2211yescharacteristic
56#103×C101C2211yescharacteristic
57#102×C101C2211yescharacteristic
58C4×C8×C101C2211yescharacteristic
59#13108074—44no—
60C2×Dic202—21no—
61C2×Dic202—21no—
62C2×Dic202C2311yescharacteristic
63C2×D404—21no—
64C2×D404C2311yescharacteristic
65C2×C22⋊D101—21no—
66C2×C22⋊D101—21no—
67C2×C22⋊D101—21no—
68C2×C4×D101—21no—
69C2×C4×D101D411yescharacteristic
70C2×C4×D101D411yescharacteristic
71C2×C4×D101C2311yescharacteristic
72#13108063—22no—
73#13108062—22no—
74#13108061—22no—
75C2×#11717579C2311yescharacteristic
76C2×#11717579C2311yescharacteristic
77C8×D101—22no—
78C8×D101—22no—
79C4⋊Dic101—21no—
80C4⋊Dic101C2311yescharacteristic
81C4⋊Dic101C2311yescharacteristic
82#13108053—21no—
83#13108053—21no—
84#13108053—21no—
85#13108053—21no—
86#13108053—21no—
87#13108053—21no—
88C22⋊Dic101—21no—
89#13108051—21no—
90#13108051—21no—
91#13108051—21no—
92#13108051—21no—
93C4×Dic101—21no—
94C4×Dic101D411yescharacteristic
95C4×Dic101D411yescharacteristic
96C4×Dic101C2311yescharacteristic
97C2×Q8×C101C2311yescharacteristic
98C2×D4×C101C2311yescharacteristic
99C22×C4×C101—21no—
100SD16×C101—22no—
101C2×C8×C101C2311yescharacteristic
102C2×C8×C101C2311yescharacteristic
103C4⋊C4×C101—21no—
104C4⋊C4×C101C2311yescharacteristic
105C4⋊C4×C101C2311yescharacteristic
106C22⋊C4×C101—21no—
107C42×C101—21no—
108C42×C101C2311yescharacteristic
109C23×C101—21no—
110C22×D101—21no—
111C22×D101C2×D411yescharacteristic
112Q8×C101—21no—
113Q8×C101—21no—
114D4×C101—21no—
115D4×C101—21no—
116C2×C4×C101—21no—
117C2×C4×C101—21no—
118C2×C4×C101—21no—
119C2×C4×C101—42no—
120C2×C4×C101C2×D411yescharacteristic
121C2×C4×C101C2×D411yescharacteristic
122C2×C4×C101C2411yescharacteristic
123C22⋊D101—42no—
124C22⋊D101—42no—
125C22⋊D101—42no—
126C2×Dic101—21no—
127C2×Dic101—21no—
128C2×Dic101—21no—
129C2×Dic101C2×D411yescharacteristic
130C2×Dic101C2×D411yescharacteristic
131C2×Dic101C2×D411yescharacteristic
132D404—21no—
133D404—21no—
134D404—42no—
135C4×D101—21no—
136C4×D101—21no—
137C4×D101—22no—
138C4×D101—42no—
139C4×D101SD1614yescomplemented
140Dic202—21no—
141Dic202—21no—
142Dic202—42no—
143Dic202—42no—
144C8×C101—21no—
145C8×C101#4112yescomplemented
146#11717579—21no—
147#11717579#4112yescomplemented
148C22×C101—41no—
149C22×C101—41no—
150C22×C101—41no—
151C22×C101C22×D411yescharacteristic
152C2×D101—21no—
153C2×D101—21no—
154C2×D101—41no—
155C2×D101—41no—
156C2×D101—41no—
157C2×D101C2×SD1612yes—
158C4×C101—21no—
159C4×C101—41no—
160C4×C101—41no—
161C4×C101—41no—
162C4×C101C2×SD1612yes—
163C4×C101C2×#4111yescharacteristic
164C4×C101C2×#4111yescharacteristic
165Dic101—21no—
166Dic101—41no—
167Dic101—41no—
168Dic101—41no—
169Dic101C2×SD1612yes—
170Dic101#13512yes—
171C2×C101—81no—
172C2×C101#53211yescharacteristic
173C2×C101C22×SD1611yescharacteristic
174C2×C101C2×#13511yescharacteristic
175D101—22no—
176D101—81no—
177#3167—1011nomaximal, Sylow
178C101#316711yescharacteristic, complemented, Sylow
179#533—1011no—
180#532—1011no—
181#498—1011no—
182#492—1011no—
183#487—1011no—
184#486—1011no—
185#465—1011no—
186#465—1011no—
187#465—1011no—
188#465—1011no—
189C4×SD16—1011no—
190C4×SD16—1011no—
191C4×SD16—1011no—
192C4×SD16D10111yescharacteristic, complemented
193C2×C4×C8—1011no—
194C2×#41—2021no—
195C2×SD16—1011no—
196C2×SD16—1011no—
197C2×SD16—1011no—
198C2×SD16C2×D10111yescharacteristic
199C22×C8—1011no—
200C22×C8—1011no—
201C4⋊Q8—1011no—
202C4⋊Q8—1011no—
203C4⋊Q8—1011no—
204#127—1011no—
205#125—2021no—
206#124—2021no—
207C22⋊Q8—1011no—
208C22⋊Q8—1011no—
209C22⋊Q8—2021no—
210#121—1011no—
211#121—1011no—
212#121—2021no—
213C4×Q8—1011no—
214C4×Q8—2021no—
215C4×Q8C2×D10111yescharacteristic
216C4×D4—1011no—
217C4×D4—2021no—
218C4×D4C2×D10111yescharacteristic
219#117—2021no—
220C2×C42—1011no—
221#106—1011no—
222#106—1011no—
223#106—1011no—
224#106C2×D10111yescharacteristic
225#103—1011no—
226#103—1011no—
227#103—1011no—
228#103C2×D10111yescharacteristic
229#102—1011no—
230#102—1011no—
231#102—1011no—
232#102C2×D10111yescharacteristic
233C4×C8—1011no—
234C4×C8—1011no—
235C4×C8—1011no—
236C4×C8C2×D10111yescharacteristic
237#41—4044no—
238C2×Q8—1011no—
239C2×Q8—2021no—
240C2×Q8—2021no—
241C2×Q8C22×D10111yescharacteristic
242C2×D4—1011no—
243C2×D4—2021no—
244C2×D4—2021no—
245C2×D4—2021no—
246C2×D4—2021no—
247C2×D4C22×D10111yescharacteristic
248C22×C4—21no—
249C22×C4—1011no—
250C22×C4—1011no—
251C22×C4—1011no—
252C22×C4—2021no—
253SD16—22no—
254SD16—2022no—
255SD16—2022no—
256SD16—2022no—
257C2×C8—1011no—
258C2×C8—1011no—
259C2×C8—2022no—
260C2×C8—2022no—
261C2×C8C22×D10111yescharacteristic
262C2×C8C22×D10111yescharacteristic
263C4⋊C4—21no—
264C4⋊C4—1011no—
265C4⋊C4—1011no—
266C4⋊C4—2021no—
267C4⋊C4—2021no—
268C4⋊C4—2021no—
269C4⋊C4—2021no—
270C4⋊C4—2021no—
271C4⋊C4—2021no—
272C4⋊C4—2021no—
273C4⋊C4C22×D10111yescharacteristic
274C4⋊C4C22×D10111yescharacteristic
275C22⋊C4—21no—
276C22⋊C4—2021no—
277C22⋊C4—2021no—
278C22⋊C4—2021no—
279C22⋊C4—2021no—
280C22⋊C4—2021no—
281C42—21no—
282C42—1011no—
283C42—1011no—
284C42—1011no—
285C42—2021no—
286C42C22×D10111yescharacteristic
287C23—21no—
288C23—1011no—
289C23—2021no—
290Q8—21no—
291Q8—21no—
292Q8—4042no—
293Q8—4042no—
294Q8—2021no—
295Q8—2021no—
296D4—21no—
297D4—21no—
298D4—4042no—
299D4—4042no—
300D4—4042no—
301D4—4042no—
302D4—2021no—
303D4—2021no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—42no—
308C2×C4—1011no—
309C2×C4—1011no—
310C2×C4—1014no—
311C2×C4—1011no—
312C2×C4—4042no—
313C2×C4—2022no—
314C2×C4—2021no—
315C2×C4—2021no—
316C2×C4—2021no—
317C2×C4—2021no—
318C2×C4—2021no—
319C2×C4D4×D10111yescharacteristic
320C2×C4D4×D10111yescharacteristic
321C2×C4C23×D10111yescharacteristic
322C8—21no—
323C8—1012no—
324C8—2021no—
325C8#1310807412yescomplemented
326C22—41no—
327C22—41no—
328C22—41no—
329C22—1012no—
330C22—4041no—
331C22—4041no—
332C22—4041no—
333C22—2021no—
334C22—2021no—
335C22C2×D4×D10111yescharacteristic
336C4—21no—
337C4—41no—
338C4—41no—
339C4—41no—
340C4—1012no—
341C4—1012no—
342C4—4041no—
343C4—4041no—
344C4—4041no—
345C4—2021no—
346C4SD16×D10112yes—
347C4#41×D10111yescharacteristic
348C4C2×#1310807411yescharacteristic
349C2—81no—
350C2—8081no—
351C2—2022no—
352C2#2026572411yescharacteristic
353C2C2×SD16×D10111yescharacteristic
354C2#135×D10111yescharacteristic
subgroupG/H
centerC2×C4D4×D101
commutator, cosocleC2×C4×C101C24
FrattiniC2×C4C23×D101
FittingC4×SD16×C101C2
socleC22×C101C22×D4
prime radical#20265724C2
hypercenterC4×SD16D101
hypocenterC101#3167
LCSG ▷ C2×C4×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×SD16

Complements

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

NH ≅ G/Ntype
1. #20265731C2semidirect
3. #20265574C2semidirect
4. #20265548C2semidirect
5. #20265526C2semidirect
6. #20265522C2semidirect
7. #20265409C2semidirect
8. #20265407C2semidirect
9. #20265405C2semidirect
10. #20265403C2semidirect
11. C4×#13108063C2semidirect
12. C4×#13108061C2semidirect
13. C4×#13108062C2semidirect
14. C4×C8×D101C2semidirect
15. C4×SD16×C101C2semidirect
139. C4×D101SD16semidirect
145. C8×C101#41semidirect
147. #11717579#41semidirect
178. C101#3167semidirect
192. C4×SD16D101semidirect
325. C8#13108074semidirect

Maximal subgroups

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

subgroupindex
#202657312
#202657242
#202655742
#202655482
#202655262
#202655222
#202654092
#202654072
#202654052
#202654032
C4×#131080632
C4×#131080612
C4×#131080622
C4×C8×D1012
C4×SD16×C1012
#3167101