Finite Group Databasebeta

← #27205708

Subgroups — #27205708

Order 13184.

380 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20268325C211yesmaximal, characteristic, complemented
2#20268190C211yesmaximal, characteristic, complemented
3#20268173C211yesmaximal, characteristic, complemented
4#20268148C211yesmaximal, characteristic, complemented
5#20268145C211yesmaximal, characteristic, complemented
6#20268030C211yesmaximal, characteristic, complemented
7#20268025C211yesmaximal, characteristic
8#20268022C211yesmaximal, characteristic, complemented
9#20268018C211yesmaximal, characteristic, complemented
10C4×#13110095C211yesmaximal, characteristic, complemented
11C4×#13110092C211yesmaximal, characteristic, complemented
12C4×#13110093C211yesmaximal, characteristic, complemented
13C4×#13110090C211yesmaximal, characteristic, complemented
14C2×C4×C103⋊C8C211yesmaximal, characteristic, complemented
15#529×C103C211yesmaximal, characteristic, complemented
16C2×#13110095C2211yescharacteristic
17C2×#13110093C2211yescharacteristic
18C2×#13110092C2211yescharacteristic
19C2×#13110090C2211yescharacteristic
20C22×C103⋊C8C2211yescharacteristic
21C22×C103⋊C8C2211yescharacteristic
22#15693015—21no—
23#15693013C2211yescharacteristic
24#15693009C2211yescharacteristic
25#15693004—21no—
26#15693000C2211yescharacteristic
27#15692995C2211yescharacteristic
28C4×Dic206C2211yescharacteristic
29C4×D412C2211yescharacteristic
30C4×C22⋊D103—21no—
31#15692978—21no—
32#15692954C2211yescharacteristic
33#15692954C2211yescharacteristic
34#15692952C2211yescharacteristic
35#15692952C2211yescharacteristic
36#15692945C2211yescharacteristic
37#15692945C2211yescharacteristic
38#15692944C2211yescharacteristic
39#15692944C2211yescharacteristic
40#15692942C2211yescharacteristic
41#15692942C2211yescharacteristic
42#15692941C2211yescharacteristic
43#15692941C2211yescharacteristic
44C4×C103⋊C8C2211yescharacteristic
45C4×C103⋊C8C2211yescharacteristic
46C4×C103⋊C8C2211yescharacteristic
47C4×C103⋊C8C2211yescharacteristic
48#126×C103—21no—
49#125×C103C2211yescharacteristic
50#124×C103C2211yescharacteristic
51#123×C103—21no—
52C22⋊Q8×C103C2211yescharacteristic
53#121×C103C2211yescharacteristic
54C4×Q8×C103C2211yescharacteristic
55C4×D4×C103—21no—
56C4×D4×C103C2211yescharacteristic
57#117×C103—21no—
58C2×C42×C103C2211yescharacteristic
59C2×Dic206C2311yescharacteristic
60C2×D412C2311yescharacteristic
61C2×C22⋊D103—21no—
62C2×C4×D103—21no—
63#13110095—22no—
64#13110093—22no—
65#13110092—22no—
66#13110090—22no—
67C2×C103⋊C8—22no—
68C2×C103⋊C8—22no—
69C2×C103⋊C8C2311yescharacteristic
70C2×C103⋊C8C2311yescharacteristic
71C2×C103⋊C8C2311yescharacteristic
72C2×C103⋊C8C2311yescharacteristic
73C4⋊Dic103C2311yescharacteristic
74C4⋊Dic103C2311yescharacteristic
75Dic103⋊C4—21no—
76Dic103⋊C4—21no—
77Dic103⋊C4—21no—
78Dic103⋊C4—21no—
79C22⋊Dic103—21no—
80(C2×D103)⋊C4—21no—
81(C2×D103)⋊C4—21no—
82(C2×D103)⋊C4—21no—
83(C2×D103)⋊C4—21no—
84C4×Dic103—21no—
85C2×Q8×C103C2311yescharacteristic
86C2×D4×C103—21no—
87C2×D4×C103C2311yescharacteristic
88C22×C4×C103—21no—
89C22×C4×C103D411yescharacteristic
90C22×C4×C103D411yescharacteristic
91C22×C4×C103C2311yescharacteristic
92C4⋊C4×C103—21no—
93C4⋊C4×C103—21no—
94C4⋊C4×C103—21no—
95C4⋊C4×C103—21no—
96C4⋊C4×C103C2311yescharacteristic
97C4⋊C4×C103C2311yescharacteristic
98C22⋊C4×C103—21no—
99C22⋊C4×C103—21no—
100C22⋊C4×C103—21no—
101C22⋊C4×C103—21no—
102C22⋊C4×C103—21no—
103C42×C103—21no—
104C42×C103D411yescharacteristic
105C42×C103D411yescharacteristic
106C42×C103C2311yescharacteristic
107C42×C103C2311yescharacteristic
108C23×C103—21no—
109C23×C103C2×D411yescharacteristic
110C22×D103—21no—
111Q8×C103—21no—
112Q8×C103—21no—
113D4×C103—21no—
114D4×C103—21no—
115D4×C103—42no—
116C2×C4×C103—22no—
117C2×C4×C103—22no—
118C2×C4×C103—21no—
119C2×C4×C103—21no—
120C2×C4×C103—21no—
121C2×C4×C103—21no—
122C2×C4×C103—21no—
123C2×C4×C103—42no—
124C2×C4×C103C2×D411yescharacteristic
125C2×C4×C103C2×D411yescharacteristic
126C2×C4×C103C2×D411yescharacteristic
127C2×C4×C103C2×D411yescharacteristic
128C2×C4×C103C2×D411yescharacteristic
129C2×C4×C103C2411yescharacteristic
130C22⋊D103—42no—
131C2×Dic103—21no—
132C2×Dic103—21no—
133C2×Dic103—21no—
134D412—21no—
135D412—21no—
136C4×D103—42no—
137Dic206—21no—
138Dic206—21no—
139C103⋊C8—21no—
140C103⋊C8—21no—
141C103⋊C8#4112yes—
142C103⋊C8#4112yes—
143C22×C103—21no—
144C22×C103—21no—
145C22×C103—41no—
146C22×C103—41no—
147C22×C103—41no—
148C22×C103#13512yes—
149C22×C103C22×D411yescharacteristic
150C2×D103—41no—
151C2×D103—41no—
152C2×D103—41no—
153C4×C103—21no—
154C4×C103—21no—
155C4×C103—21no—
156C4×C103—21no—
157C4×C103—41no—
158C4×C103—41no—
159C4×C103—41no—
160C4×C103#13512yes—
161C4×C103C2×#4111yescharacteristic
162C4×C103C2×#4111yescharacteristic
163Dic103—41no—
164Dic103—41no—
165Dic103—41no—
166C2×C103—22no—
167C2×C103—81no—
168C2×C103#53211yescharacteristic
169C2×C103C2×#13511yescharacteristic
170C2×C103C2×#13511yescharacteristic
171D103—81no—
172#3168—1031nomaximal, Sylow
173C103#316811yescharacteristic, complemented, Sylow
174#529—1031no—
175#529D10311yescharacteristic, complemented
176#499—1031no—
177#495—1031no—
178#488—1031no—
179#488—1031no—
180#467—1031no—
181#466—1031no—
182#465—1031no—
183#465—1031no—
184C4×Q16—1031no—
185C4×SD16—1031no—
186C4×SD16—1031no—
187C4×D8—1031no—
188C2×C4×C8—1031no—
189C2×Q16—1031no—
190C2×SD16—1031no—
191C2×SD16—1031no—
192C2×D8—1031no—
193C22×C8—1031no—
194C22×C8—1031no—
195#126—21no—
196#126—2061no—
197#125—1031no—
198#125C2×D10311yescharacteristic
199#124—1031no—
200#124C2×D10311yescharacteristic
201#123—21no—
202#123—2061no—
203C22⋊Q8—1031no—
204C22⋊Q8C2×D10311yescharacteristic
205#121—1031no—
206#121C2×D10311yescharacteristic
207C4×Q8—1031no—
208C4×Q8C2×D10311yescharacteristic
209C4×D4—21no—
210C4×D4—1031no—
211C4×D4—2061no—
212C4×D4C2×D10311yescharacteristic
213#117—21no—
214#117—2061no—
215C2×C42C2×D10311yescharacteristic
216#107—1031no—
217#107—1031no—
218#106—1031no—
219#106—1031no—
220#103—1031no—
221#103—1031no—
222#103—1031no—
223#103—1031no—
224#102—1031no—
225#102—1031no—
226#102—1031no—
227#102—1031no—
228C4×C8—1031no—
229C4×C8—1031no—
230C4×C8—1031no—
231C4×C8—1031no—
232C2×Q8—1031no—
233C2×Q8C22×D10311yescharacteristic
234C2×D4—21no—
235C2×D4—1031no—
236C2×D4—2061no—
237C2×D4C22×D10311yescharacteristic
238C22×C4—21no—
239C22×C4—2061no—
240C22×C4C22⋊D10311yescharacteristic
241C22×C4C22⋊D10311yescharacteristic
242C22×C4C22×D10311yescharacteristic
243Q16—2062no—
244SD16—2062no—
245SD16—2062no—
246D8—2062no—
247C2×C8—1031no—
248C2×C8—1031no—
249C2×C8—1031no—
250C2×C8—1031no—
251C2×C8—2062no—
252C2×C8—2062no—
253C4⋊C4—21no—
254C4⋊C4—21no—
255C4⋊C4—21no—
256C4⋊C4—21no—
257C4⋊C4—1031no—
258C4⋊C4—1031no—
259C4⋊C4—2061no—
260C4⋊C4—2061no—
261C4⋊C4—2061no—
262C4⋊C4—2061no—
263C4⋊C4C22×D10311yescharacteristic
264C4⋊C4C22×D10311yescharacteristic
265C22⋊C4—21no—
266C22⋊C4—21no—
267C22⋊C4—21no—
268C22⋊C4—21no—
269C22⋊C4—21no—
270C22⋊C4—2061no—
271C22⋊C4—2061no—
272C22⋊C4—2061no—
273C22⋊C4—2061no—
274C22⋊C4—2061no—
275C42—21no—
276C42—2061no—
277C42C22⋊D10311yescharacteristic
278C42C22⋊D10311yescharacteristic
279C42C22×D10311yescharacteristic
280C42C22×D10311yescharacteristic
281C23—21no—
282C23—2061no—
283C23C2×C22⋊D10311yescharacteristic
284Q8—21no—
285Q8—21no—
286Q8—2061no—
287Q8—2061no—
288D4—21no—
289D4—21no—
290D4—42no—
291D4—4122no—
292D4—2061no—
293D4—2061no—
294C2×C4—22no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—22no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—42no—
302C2×C4—4122no—
303C2×C4—2061no—
304C2×C4—2061no—
305C2×C4—2061no—
306C2×C4C2×C22⋊D10311yescharacteristic
307C2×C4C2×C22⋊D10311yescharacteristic
308C2×C4C2×C22⋊D10311yescharacteristic
309C2×C4C2×C22⋊D10311yescharacteristic
310C2×C4C2×C22⋊D10311yescharacteristic
311C2×C4C23×D10311yescharacteristic
312C8—1032no—
313C8—1032no—
314C8—2061no—
315C8—2061no—
316C22—21no—
317C22—21no—
318C22—41no—
319C22—41no—
320C22—41no—
321C22—4121no—
322C22—4121no—
323C22—4121no—
324C22#1569304112yes—
325C22C22×C22⋊D10311yescharacteristic
326C4—21no—
327C4—21no—
328C4—21no—
329C4—21no—
330C4—41no—
331C4—41no—
332C4—41no—
333C4—4121no—
334C4—4121no—
335C4—4121no—
336C4#1569304112yes—
337C4#41×D10311yescharacteristic
338C4#41×D10311yescharacteristic
339C2—22no—
340C2—81no—
341C2—8241no—
342C2#2026833711yescharacteristic
343C2C2×#1569304111yescharacteristic
344C2C2×#1569304111yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
Fitting#529×C103C2
socleC22×C103C22×D4
prime radical#20268025C2
hypercenter#529D103
hypocenterC103#3168
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #529

Complements

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

NH ≅ G/Ntype
1. #20268325C2semidirect
2. #20268190C2semidirect
3. #20268173C2semidirect
4. #20268148C2semidirect
5. #20268145C2semidirect
6. #20268030C2semidirect
8. #20268022C2semidirect
9. #20268018C2semidirect
10. C4×#13110095C2semidirect
11. C4×#13110092C2semidirect
12. C4×#13110093C2semidirect
13. C4×#13110090C2semidirect
14. C2×C4×C103⋊C8C2semidirect
15. #529×C103C2semidirect
173. C103#3168semidirect
175. #529D103semidirect

Maximal subgroups

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

subgroupindex
#202683252
#202681902
#202681732
#202681482
#202681452
#202680302
#202680252
#202680222
#202680182
C4×#131100952
C4×#131100922
C4×#131100932
C4×#131100902
C2×C4×C103⋊C82
#529×C1032
#3168103