Finite Group Databasebeta

← #27206986

Subgroups — #27206986

Order 13184.

408 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20268482C211yesmaximal, characteristic, complemented
2#20268434C211yesmaximal, characteristic
3#20268145C211yesmaximal, characteristic, complemented
4#20268120C211yesmaximal, characteristic, complemented
5#20268113C211yesmaximal, characteristic, complemented
6#20268092C211yesmaximal, characteristic, complemented
7#20268029C211yesmaximal, characteristic, complemented
8#20268017C211yesmaximal, characteristic, complemented
9#20267952C211yesmaximal, characteristic, complemented
10#20267940C211yesmaximal, characteristic, complemented
11C4×#13110092C211yesmaximal, characteristic, complemented
12#20267856C211yesmaximal, characteristic, complemented
13#20267786C211yesmaximal, characteristic, complemented
14#102×D103C211yesmaximal, characteristic, complemented
15#464×C103C211yesmaximal, characteristic, complemented
16C2×#13110106C2211yescharacteristic
17C2×D4×D103C2211yescharacteristic
18C2×#13110092C2211yescharacteristic
19C2×C8×D103C2211yescharacteristic
20C2×C8×D103C2211yescharacteristic, complemented
21#15693015—21no—
22#15693013C2211yescharacteristic, complemented
23#15693011—21no—
24#15693006—21no—
25#15693003—21no—
26#15692997C2211yescharacteristic
27#15692997C2211yescharacteristic
28#15692997C2211yescharacteristic, complemented
29#15692994—21no—
30#15692992C2211yescharacteristic
31#15692991—21no—
32C4×D412C2211yescharacteristic
33C4×D412C2211yescharacteristic
34#15692979C2211yescharacteristic, complemented
35#15692978—21no—
36C4⋊C4×D103C2211yescharacteristic
37C22⋊C4×D103—21no—
38#15692955C2211yescharacteristic, complemented
39#15692953C2211yescharacteristic, complemented
40#15692952C2211yescharacteristic, complemented
41#15692945C2211yescharacteristic, complemented
42#15692945C2211yescharacteristic, complemented
43#15692945C2211yescharacteristic, complemented
44#15692943C2211yescharacteristic
45#15692943C2211yescharacteristic
46#15692942C2211yescharacteristic
47#15692942C2211yescharacteristic
48#15692941C2211yescharacteristic
49(C2×D103)⋊C8C2211yescharacteristic
50(C2×D103)⋊C8C2211yescharacteristic, complemented
51C4×C103⋊C8C2211yescharacteristic, complemented
52C2×Q16×C103C2211yescharacteristic, complemented
53C2×SD16×C103C2211yescharacteristic
54#124×C103C2211yescharacteristic
55C4×Q8×C103C2211yescharacteristic, complemented
56C4⋊C8×C103C2211yescharacteristic, complemented
57#103×C103C2211yescharacteristic, complemented
58#102×C103C2211yescharacteristic
59C23×D103—21no—
60#13110106—22no—
61#13110106—41no—
62C2×D412—21no—
63C2×D412D411yescharacteristic
64C2×D412C2311yescharacteristic
65C2×C22⋊D103—21no—
66C2×C22⋊D103—21no—
67D4×D103—22no—
68D4×D103—41no—
69C2×C4×D103—21no—
70C2×C4×D103—21no—
71C2×C4×D103—21no—
72C2×C4×D103C2311yescharacteristic
73C2×C4×D103C2311yescharacteristic
74#13110092—22no—
75C2×C103⋊C8C2311yescharacteristic
76C2×C103⋊C8C2311yescharacteristic
77C8×D103—41no—
78C8×D103—41no—
79C4⋊Dic103D411yescharacteristic
80C4⋊Dic103C2311yescharacteristic
81C4⋊Dic103C2311yescharacteristic
82C4⋊Dic103C2311yescharacteristic
83Dic103⋊C4—21no—
84Dic103⋊C4—21no—
85Dic103⋊C4—21no—
86Dic103⋊C4—21no—
87Dic103⋊C4—21no—
88Dic103⋊C4—21no—
89C22⋊Dic103—21no—
90(C2×D103)⋊C4—21no—
91(C2×D103)⋊C4—21no—
92(C2×D103)⋊C4—21no—
93(C2×D103)⋊C4—21no—
94(C2×D103)⋊C4—21no—
95(C2×D103)⋊C4D411yescharacteristic
96(C2×D103)⋊C4D411yescharacteristic
97C4×Dic103—21no—
98C2×Q8×C103C2311yescharacteristic
99C2×Q8×C103C2311yescharacteristic
100C2×D4×C103C2311yescharacteristic
101Q16×C103—41no—
102SD16×C103—41no—
103C2×C8×C103C2311yescharacteristic
104C2×C8×C103C2311yescharacteristic
105C4⋊C4×C103—21no—
106C4⋊C4×C103C2311yescharacteristic
107C22⋊C4×C103—21no—
108C22⋊C4×C103—21no—
109C42×C103—21no—
110C42×C103C2311yescharacteristic
111C23×C103—21no—
112C22×D103—21no—
113C22×D103—42no—
114C22×D103—42no—
115C22×D103—81no—
116C22×D103C2×D411yescharacteristic
117C22×D103C2×D411yescharacteristic
118Q8×C103—21no—
119Q8×C103—21no—
120Q8×C103—21no—
121Q8×C103—21no—
122D4×C103—21no—
123D4×C103—21no—
124C2×C4×C103—21no—
125C2×C4×C103—21no—
126C2×C4×C103—21no—
127C2×C4×C103C2×D411yescharacteristic
128C2×C4×C103C2×D411yescharacteristic
129C2×C4×C103C2411yescharacteristic
130C22⋊D103—42no—
131C22⋊D103—81no—
132C2×Dic103—21no—
133C2×Dic103—21no—
134C2×Dic103—21no—
135C2×Dic103C2×D411yescharacteristic
136C2×Dic103C2×D411yescharacteristic
137D412—22no—
138D412—21no—
139D412—42no—
140D412#4112yes—
141C4×D103—21no—
142C4×D103—21no—
143C4×D103—21no—
144C4×D103—21no—
145C4×D103—42no—
146C4×D103—42no—
147C4×D103—81no—
148C8×C103—21no—
149C8×C103—21no—
150C103⋊C8—21no—
151C103⋊C8—21no—
152C22×C103—41no—
153C22×C103—41no—
154C22×C103—41no—
155C22×C103C22×D411yescharacteristic
156C2×D103—21no—
157C2×D103—21no—
158C2×D103—21no—
159C2×D103—22no—
160C2×D103—21no—
161C2×D103—21no—
162C2×D103—41no—
163C2×D103—41no—
164C2×D103—84no—
165C2×D103#13512yes—
166C4×C103—21no—
167C4×C103—21no—
168C4×C103—41no—
169C4×C103—41no—
170C4×C103—41no—
171C4×C103C2×#4111yescharacteristic
172C4×C103H(5,𝔽2)11yescharacteristic
173Dic103—21no—
174Dic103—21no—
175Dic103—41no—
176Dic103—41no—
177Dic103—41no—
178C2×C103—81no—
179C2×C103#54611yescharacteristic
180C2×C103C2×#13511yescharacteristic
181C2×C103#57711yescharacteristic
182D103—22no—
183D103—41no—
184D103—42no—
185#3296—1031nomaximal, Sylow
186C103#329611yescharacteristic, complemented, Sylow
187#552—1031no—
188#546—1031no—
189#488—1031no—
190#483—1031no—
191#482—1031no—
192#478—1031no—
193#467—1031no—
194#465—1031no—
195#464D10311yescharacteristic, complemented
196#452—1031no—
197#450—1031no—
198C4×SD16—1031no—
199C8×D4—1031no—
200#416—1031no—
201C2×#102—1031no—
202C2×#41—1031no—
203C22×D4—1031no—
204C2×Q16C2×D10311yescharacteristic, complemented
205C2×SD16—1031no—
206C2×SD16C2×D10311yescharacteristic
207C22×C8—1031no—
208C22×C8—1031no—
209#126—2061no—
210#125—1031no—
211#125—2061no—
212#124C2×D10311yescharacteristic
213#123—2061no—
214#123—2061no—
215C22⋊Q8—1031no—
216C22⋊Q8—1031no—
217C22⋊Q8—1031no—
218#121—1031no—
219#121—2061no—
220#120—2061no—
221C4×Q8C2×D10311yescharacteristic, complemented
222C4×D4—1031no—
223C4×D4—1031no—
224#117—1031no—
225#117—2061no—
226C2×C4⋊C4—1031no—
227C2×C22⋊C4—2061no—
228#107—1031no—
229#106—1031no—
230#106—1031no—
231C4⋊C8C2×D10311yescharacteristic, complemented
232#103—1031no—
233#103—1031no—
234#103—1031no—
235#103C2×D10311yescharacteristic, complemented
236#102—1031no—
237#102—1031no—
238#102—1031no—
239#102—1031no—
240#102—1031no—
241#102C2×D10311yescharacteristic
242C22⋊C8—1031no—
243C22⋊C8—1031no—
244C4×C8—1031no—
245C24—2061no—
246#41—4121no—
247#41—2062no—
248C2×Q8C22×D10311yescharacteristic
249C2×Q8C22×D10311yescharacteristic
250C2×D4—1031no—
251C2×D4—1031no—
252C2×D4—4121no—
253C2×D4—2061no—
254C2×D4—2061no—
255C2×D4—2062no—
256C2×D4—2061no—
257C2×D4C22×D10311yescharacteristic
258C22×C4—1031no—
259C22×C4—1031no—
260C22×C4—2061no—
261C22×C4—2061no—
262C22×C4—2061no—
263Q16—41no—
264SD16—41no—
265SD16—2062no—
266C2×C8—1031no—
267C2×C8—1031no—
268C2×C8—4121no—
269C2×C8—4121no—
270C2×C8C22×D10311yescharacteristic
271C2×C8C22×D10311yescharacteristic
272C4⋊C4—21no—
273C4⋊C4—1031no—
274C4⋊C4—1031no—
275C4⋊C4—1031no—
276C4⋊C4—1031no—
277C4⋊C4—2061no—
278C4⋊C4—2061no—
279C4⋊C4—2061no—
280C4⋊C4—2061no—
281C4⋊C4—2061no—
282C4⋊C4—2061no—
283C4⋊C4C22×D10311yescharacteristic
284C22⋊C4—21no—
285C22⋊C4—21no—
286C22⋊C4—1031no—
287C22⋊C4—1031no—
288C22⋊C4—2061no—
289C22⋊C4—2061no—
290C22⋊C4—2061no—
291C22⋊C4—2061no—
292C22⋊C4—2061no—
293C22⋊C4—2061no—
294C42—21no—
295C42—2061no—
296C42C22×D10311yescharacteristic
297C23—21no—
298C23—8241no—
299C23—1031no—
300C23—1031no—
301C23—4122no—
302C23—4122no—
303C23—2061no—
304Q8—21no—
305Q8—21no—
306Q8—21no—
307Q8—21no—
308D4—21no—
309D4—21no—
310D4—8241no—
311D4—1032no—
312D4—4122no—
313D4—4122no—
314D4—2062no—
315D4—2061no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—8241no—
320C2×C4—1031no—
321C2×C4—1031no—
322C2×C4—4122no—
323C2×C4—4122no—
324C2×C4—2061no—
325C2×C4—2061no—
326C2×C4—2061no—
327C2×C4—2061no—
328C2×C4—2061no—
329C2×C4—2061no—
330C2×C4—2061no—
331C2×C4D4×D10311yescharacteristic
332C2×C4D4×D10311yescharacteristic
333C2×C4C23×D10311yescharacteristic
334C8—21no—
335C8—21no—
336C8—2061no—
337C8—2061no—
338C22—41no—
339C22—41no—
340C22—41no—
341C22—8244no—
342C22—1032no—
343C22—4121no—
344C22—4121no—
345C22—2061no—
346C22—2061no—
347C22—2062no—
348C22—2061no—
349C22—2061no—
350C22—2061no—
351C22C2×D4×D10311yescharacteristic
352C4—21no—
353C4—21no—
354C4—41no—
355C4—41no—
356C4—41no—
357C4—4121no—
358C4—4121no—
359C4—4121no—
360C4—2061no—
361C4—2061no—
362C4#41×D10311yescharacteristic
363C4#1569306611yescharacteristic
364C2—81no—
365C2—4122no—
366C2—4121no—
367C2—2062no—
368C2#2026843811yescharacteristic
369C2#135×D10311yescharacteristic
370C2#2026860011yescharacteristic
subgroupG/H
centerC22C2×D4×D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
Fitting#464×C103C2
socleC22×C103C22×D4
prime radical#20268434C2
hypercenter#464D103
hypocenterC103#3296
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C42 ◁ #464

Complements

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

NH ≅ G/Ntype
1. #20268482C2semidirect
3. #20268145C2semidirect
4. #20268120C2semidirect
5. #20268113C2semidirect
6. #20268092C2semidirect
7. #20268029C2semidirect
8. #20268017C2semidirect
9. #20267952C2semidirect
10. #20267940C2semidirect
11. C4×#13110092C2semidirect
12. #20267856C2semidirect
13. #20267786C2semidirect
14. #102×D103C2semidirect
15. #464×C103C2semidirect
20. C2×C8×D103C22semidirect
22. #15693013C22semidirect
28. #15692997C22semidirect
34. #15692979C22semidirect
38. #15692955C22semidirect
39. #15692953C22semidirect
40. #15692952C22semidirect
41. #15692945C22semidirect
42. #15692945C22semidirect
43. #15692945C22semidirect
50. (C2×D103)⋊C8C22semidirect
51. C4×C103⋊C8C22semidirect
52. C2×Q16×C103C22semidirect
55. C4×Q8×C103C22semidirect
56. C4⋊C8×C103C22semidirect
57. #103×C103C22semidirect
186. C103#3296semidirect
195. #464D103semidirect
204. C2×Q16C2×D103semidirect
221. C4×Q8C2×D103semidirect
231. C4⋊C8C2×D103semidirect
235. #103C2×D103semidirect

Maximal subgroups

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

subgroupindex
#202684822
#202684342
#202681452
#202681202
#202681132
#202680922
#202680292
#202680172
#202679522
#202679402
C4×#131100922
#202678562
#202677862
#102×D1032
#464×C1032
#3296103