Finite Group Databasebeta

← #27206988

Subgroups — #27206988

Order 13184.

420 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20268437C211yesmaximal, characteristic, complemented
2#20268148C211yesmaximal, characteristic, complemented
3#20268126C211yesmaximal, characteristic, complemented
4#20268115C211yesmaximal, characteristic, complemented
5#20268088C211yesmaximal, characteristic, complemented
6#20268025C211yesmaximal, characteristic, complemented
7#20268018C211yesmaximal, characteristic, complemented
8#20268006C211yesmaximal, characteristic, complemented
9#20267934C211yesmaximal, characteristic, complemented
10#20267924C211yesmaximal, characteristic, complemented
11C4×#13110090C211yesmaximal, characteristic, complemented
12D4×C103⋊C8C211yesmaximal, characteristic, complemented
13#20267785C211yesmaximal, characteristic, complemented
14C2×#15692941C211yesmaximal, characteristic, complemented
15#553×C103C211yesmaximal, characteristic, complemented
16C2×#13110105C2211yescharacteristic
17C22×D412C2211yescharacteristic
18C2×#13110093C2211yescharacteristic, complemented
19C2×#13110090C2211yescharacteristic
20C2×#13110090C2211yescharacteristic
21C22×C103⋊C8C2211yescharacteristic
22C22×C103⋊C8C2211yescharacteristic, complemented
23#15693009C2211yescharacteristic
24#15693006—21no—
25#15693000C2211yescharacteristic
26#15692995C2211yescharacteristic
27#15692994—21no—
28#15692989—21no—
29C4×D412C2211yescharacteristic
30C22⋊C4×D103—21no—
31#15692954C2211yescharacteristic, complemented
32#15692954C2211yescharacteristic, complemented
33#15692952C2211yescharacteristic, complemented
34C4⋊(C103⋊C8)C2211yescharacteristic, complemented
35#15692944C2211yescharacteristic, complemented
36#15692944C2211yescharacteristic, complemented
37#15692944C2211yescharacteristic, complemented
38#15692942C2211yescharacteristic, complemented
39#15692941C2211yescharacteristic
40#15692941C2211yescharacteristic
41#15692941C2211yescharacteristic
42#15692941C2211yescharacteristic
43#15692941C2211yescharacteristic
44#15692941C2211yescharacteristic
45C22⋊(C103⋊C8)C2211yescharacteristic
46C22⋊(C103⋊C8)C2211yescharacteristic, complemented
47C4×C103⋊C8C2211yescharacteristic, complemented
48#126×C103—21no—
49#125×C103C2211yescharacteristic, complemented
50#123×C103—21no—
51#121×C103—21no—
52#121×C103C2211yescharacteristic
53#121×C103C2211yescharacteristic, complemented
54C4×D4×C103—21no—
55C4×D4×C103C2211yescharacteristic
56C4×D4×C103C2211yescharacteristic, complemented
57#117×C103C2211yescharacteristic, complemented
58C2×C4⋊C4×C103C2211yescharacteristic
59C23×D103—21no—
60#13110105—22no—
61#13110105—41no—
62C2×Dic206C2311yescharacteristic
63C2×D412—22no—
64C2×D412—21no—
65C2×D412—41no—
66C2×D412C2311yescharacteristic
67C2×D412C2311yescharacteristic
68C2×C22⋊D103—21no—
69C2×C22⋊D103—21no—
70C2×C4×D103—21no—
71C2×C4×D103—21no—
72#13110093—41no—
73#13110090—22no—
74#13110090—41no—
75C2×C103⋊C8—41no—
76C2×C103⋊C8—41no—
77C2×C103⋊C8C2311yescharacteristic
78C2×C103⋊C8C2311yescharacteristic
79C2×C103⋊C8C2311yescharacteristic
80C2×C103⋊C8C2311yescharacteristic
81C4⋊Dic103C2311yescharacteristic
82Dic103⋊C4—21no—
83C22⋊Dic103—21no—
84(C2×D103)⋊C4—21no—
85(C2×D103)⋊C4—21no—
86(C2×D103)⋊C4—21no—
87(C2×D103)⋊C4—21no—
88C2×D4×C103—21no—
89C2×D4×C103—21no—
90C2×D4×C103D411yescharacteristic
91C2×D4×C103C2311yescharacteristic
92C22×C4×C103—21no—
93C22×C4×C103—21no—
94C22×C4×C103C2311yescharacteristic
95C22×C4×C103C2311yescharacteristic
96C4⋊C4×C103—21no—
97C4⋊C4×C103—21no—
98C4⋊C4×C103—21no—
99C4⋊C4×C103D411yescharacteristic
100C4⋊C4×C103C2311yescharacteristic
101C4⋊C4×C103C2311yescharacteristic
102C4⋊C4×C103C2311yescharacteristic
103C22⋊C4×C103—21no—
104C22⋊C4×C103—21no—
105C22⋊C4×C103—21no—
106C22⋊C4×C103—21no—
107C22⋊C4×C103D411yescharacteristic
108C22⋊C4×C103D411yescharacteristic
109C42×C103—21no—
110C42×C103C2311yescharacteristic
111C23×C103—21no—
112C23×C103C2×D411yescharacteristic
113C23×C103C2×D411yescharacteristic
114C22×D103—21no—
115C22×D103—21no—
116C22×D103—42no—
117C22×D103—42no—
118C22×D103—81no—
119D4×C103—22no—
120D4×C103—21no—
121D4×C103—21no—
122D4×C103—42no—
123D4×C103—81no—
124C2×C4×C103—21no—
125C2×C4×C103—21no—
126C2×C4×C103—21no—
127C2×C4×C103—21no—
128C2×C4×C103—21no—
129C2×C4×C103—21no—
130C2×C4×C103—21no—
131C2×C4×C103—81no—
132C2×C4×C103—81no—
133C2×C4×C103C2×D411yescharacteristic
134C2×C4×C103C2×D411yescharacteristic
135C2×C4×C103C2×D411yescharacteristic
136C2×C4×C103C2×D411yescharacteristic
137C2×C4×C103C2411yescharacteristic
138C22⋊D103—42no—
139C22⋊D103—81no—
140C2×Dic103—21no—
141C2×Dic103—21no—
142D412—21no—
143D412—21no—
144D412—21no—
145D412—42no—
146D412#4112yes—
147C4×D103—42no—
148C4×D103—81no—
149Dic206—21no—
150Dic206—21no—
151C103⋊C8—21no—
152C103⋊C8—21no—
153C103⋊C8—21no—
154C103⋊C8—21no—
155C22×C103—21no—
156C22×C103—21no—
157C22×C103—21no—
158C22×C103—21no—
159C22×C103—21no—
160C22×C103—41no—
161C22×C103—41no—
162C22×C103—41no—
163C22×C103#13512yes—
164C22×C103C22×D411yescharacteristic
165C2×D103—22no—
166C2×D103—41no—
167C2×D103—41no—
168C2×D103—41no—
169C2×D103—41no—
170C2×D103—41no—
171C2×D103—84no—
172C4×C103—21no—
173C4×C103—21no—
174C4×C103—21no—
175C4×C103—21no—
176C4×C103—41no—
177C4×C103—41no—
178C4×C103—41no—
179C4×C103C2×#4111yescharacteristic
180C4×C103H(5,𝔽2)11yescharacteristic
181Dic103—41no—
182Dic103—41no—
183C2×C103—22no—
184C2×C103—41no—
185C2×C103—81no—
186C2×C103#54611yescharacteristic
187C2×C103C2×#13511yescharacteristic
188C2×C103#57611yescharacteristic
189D103—42no—
190D103—81no—
191#3297—1031nomaximal, Sylow
192C103#329711yescharacteristic, complemented, Sylow
193#553D10311yescharacteristic, complemented
194#546—1031no—
195#488—1031no—
196#484—1031no—
197#482—1031no—
198#478—1031no—
199#466—1031no—
200#465—1031no—
201#463—1031no—
202#449—1031no—
203#447—1031no—
204C4×D8—1031no—
205C8×D4—1031no—
206#416—1031no—
207C2×#102—1031no—
208C2×#41—1031no—
209C22×D4—1031no—
210C2×SD16—1031no—
211C2×D8—1031no—
212C2×D8—1031no—
213C22×C8—1031no—
214C22×C8—1031no—
215#126—21no—
216#125C2×D10311yescharacteristic, complemented
217#124—1031no—
218#123—21no—
219#123—2061no—
220C22⋊Q8—1031no—
221#121—21no—
222#121—1031no—
223#121—2061no—
224#121C2×D10311yescharacteristic
225#121C2×D10311yescharacteristic, complemented
226#120—2061no—
227C4×D4—21no—
228C4×D4—1031no—
229C4×D4C2×D10311yescharacteristic
230C4×D4C2×D10311yescharacteristic, complemented
231#117C2×D10311yescharacteristic, complemented
232C2×C4⋊C4C2×D10311yescharacteristic
233C2×C22⋊C4—2061no—
234#107—1031no—
235#107—1031no—
236#106—1031no—
237C4⋊C8—1031no—
238#103—1031no—
239#103—1031no—
240#103—1031no—
241#102—1031no—
242#102—1031no—
243#102—1031no—
244#102—1031no—
245#102—1031no—
246#102—1031no—
247#102—1031no—
248C22⋊C8—1031no—
249C22⋊C8—1031no—
250C4×C8—1031no—
251C24—2061no—
252#41—4121no—
253#41—2062no—
254C2×Q8—1031no—
255C2×D4—21no—
256C2×D4—21no—
257C2×D4—1031no—
258C2×D4—1031no—
259C2×D4—4121no—
260C2×D4—2062no—
261C2×D4—2061no—
262C2×D4—2061no—
263C2×D4—2061no—
264C2×D4C22⋊D10311yescharacteristic
265C2×D4C22×D10311yescharacteristic
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—2061no—
269C22×C4—2061no—
270C22×C4C22×D10311yescharacteristic
271C22×C4C22×D10311yescharacteristic
272SD16—4121no—
273D8—4121no—
274D8—2062no—
275C2×C8—1031no—
276C2×C8—1031no—
277C2×C8—1031no—
278C2×C8—1031no—
279C2×C8—4121no—
280C2×C8—4121no—
281C4⋊C4—21no—
282C4⋊C4—21no—
283C4⋊C4—21no—
284C4⋊C4—1031no—
285C4⋊C4—2061no—
286C4⋊C4C22⋊D10311yescharacteristic
287C4⋊C4C22×D10311yescharacteristic
288C4⋊C4C22×D10311yescharacteristic
289C4⋊C4C22×D10311yescharacteristic
290C22⋊C4—21no—
291C22⋊C4—21no—
292C22⋊C4—21no—
293C22⋊C4—21no—
294C22⋊C4—2061no—
295C22⋊C4—2061no—
296C22⋊C4—2061no—
297C22⋊C4—2061no—
298C22⋊C4—2061no—
299C22⋊C4C22⋊D10311yescharacteristic
300C22⋊C4C22⋊D10311yescharacteristic
301C42—21no—
302C42C22×D10311yescharacteristic
303C23—21no—
304C23—8241no—
305C23—4122no—
306C23—4122no—
307C23—2061no—
308C23—2061no—
309C23C2×C22⋊D10311yescharacteristic
310C23C2×C22⋊D10311yescharacteristic
311Q8—2061no—
312Q8—2061no—
313D4—22no—
314D4—21no—
315D4—21no—
316D4—42no—
317D4—81no—
318D4—8241no—
319D4—1032no—
320D4—4122no—
321D4—4122no—
322D4—2061no—
323D4—2061no—
324D4—2061no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—81no—
333C2×C4—81no—
334C2×C4—8241no—
335C2×C4—4122no—
336C2×C4—2061no—
337C2×C4—2061no—
338C2×C4C2×C22⋊D10311yescharacteristic
339C2×C4C2×C22⋊D10311yescharacteristic
340C2×C4C2×C22⋊D10311yescharacteristic
341C2×C4C2×C22⋊D10311yescharacteristic
342C2×C4C23×D10311yescharacteristic
343C8—2061no—
344C8—2061no—
345C8—2061no—
346C8—2061no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—41no—
353C22—41no—
354C22—41no—
355C22—8244no—
356C22—4121no—
357C22—4121no—
358C22—4121no—
359C22—4121no—
360C22—4121no—
361C22—2062no—
362C22#1569304112yes—
363C22C22×C22⋊D10311yescharacteristic
364C4—21no—
365C4—21no—
366C4—21no—
367C4—21no—
368C4—41no—
369C4—41no—
370C4—41no—
371C4—4121no—
372C4—4121no—
373C4#41×D10311yescharacteristic
374C4#1569306711yescharacteristic
375C2—22no—
376C2—41no—
377C2—81no—
378C2—8241no—
379C2—4122no—
380C2#2026842911yescharacteristic
381C2C2×#1569304111yescharacteristic
382C2#2026859411yescharacteristic
subgroupG/H
centerC22C22×C22⋊D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
Fitting#553×C103C2
socleC22×C103C22×D4
hypercenter#553D103
hypocenterC103#3297
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C4×D4 ◁ #553

Complements

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

NH ≅ G/Ntype
1. #20268437C2semidirect
2. #20268148C2semidirect
3. #20268126C2semidirect
4. #20268115C2semidirect
5. #20268088C2semidirect
6. #20268025C2semidirect
7. #20268018C2semidirect
8. #20268006C2semidirect
9. #20267934C2semidirect
10. #20267924C2semidirect
11. C4×#13110090C2semidirect
12. D4×C103⋊C8C2semidirect
13. #20267785C2semidirect
14. C2×#15692941C2semidirect
15. #553×C103C2semidirect
18. C2×#13110093C22semidirect
22. C22×C103⋊C8C22semidirect
31. #15692954C22semidirect
32. #15692954C22semidirect
33. #15692952C22semidirect
34. C4⋊(C103⋊C8)C22semidirect
35. #15692944C22semidirect
36. #15692944C22semidirect
37. #15692944C22semidirect
38. #15692942C22semidirect
46. C22⋊(C103⋊C8)C22semidirect
47. C4×C103⋊C8C22semidirect
49. #125×C103C22semidirect
53. #121×C103C22semidirect
56. C4×D4×C103C22semidirect
57. #117×C103C22semidirect
192. C103#3297semidirect
193. #553D103semidirect
216. #125C2×D103semidirect
225. #121C2×D103semidirect
230. C4×D4C2×D103semidirect
231. #117C2×D103semidirect

Maximal subgroups

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

subgroupindex
#202684372
#202681482
#202681262
#202681152
#202680882
#202680252
#202680182
#202680062
#202679342
#202679242
C4×#131100902
D4×C103⋊C82
#202677852
C2×#156929412
#553×C1032
#3297103