Finite Group Databasebeta

← #27207001

Subgroups — #27207001

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#20268491C211yesmaximal, characteristic, complemented
2#20268434C211yesmaximal, characteristic, complemented
3#20268145C211yesmaximal, characteristic, complemented
4#20268125C211yesmaximal, characteristic, complemented
5#20268114C211yesmaximal, characteristic, complemented
6#20268092C211yesmaximal, characteristic, complemented
7#20268024C211yesmaximal, characteristic, complemented
8#20268017C211yesmaximal, characteristic, complemented
9#20267935C211yesmaximal, characteristic, complemented
10#20267923C211yesmaximal, characteristic, complemented
11C4×#13110090C211yesmaximal, characteristic, complemented
12#20267856C211yesmaximal, characteristic, complemented
13#20267786C211yesmaximal, characteristic, complemented
14#102×D103C211yesmaximal, characteristic, complemented
15#463×C103C211yesmaximal, characteristic, complemented
16C2×#13110106C2211yescharacteristic
17C2×D4×D103C2211yescharacteristic
18C2×#13110090C2211yescharacteristic
19C2×C8×D103C2211yescharacteristic
20C2×C8×D103C2211yescharacteristic, complemented
21#15693014—21no—
22#15693013C2211yescharacteristic, complemented
23#15693004—21no—
24#15693003—21no—
25#15692997C2211yescharacteristic
26#15692994—21no—
27#15692994—21no—
28#15692992C2211yescharacteristic
29#15692992C2211yescharacteristic
30#15692992C2211yescharacteristic, complemented
31#15692991—21no—
32C4×D412C2211yescharacteristic
33C4×D412C2211yescharacteristic
34C4×C22⋊D103—21no—
35#15692979C2211yescharacteristic, complemented
36C4⋊C4×D103C2211yescharacteristic
37C22⋊C4×D103—21no—
38#15692955C2211yescharacteristic, complemented
39#15692954C2211yescharacteristic, complemented
40#15692953C2211yescharacteristic, complemented
41#15692945C2211yescharacteristic, complemented
42#15692945C2211yescharacteristic, complemented
43#15692943C2211yescharacteristic
44#15692943C2211yescharacteristic
45#15692942C2211yescharacteristic
46#15692942C2211yescharacteristic
47#15692942C2211yescharacteristic, complemented
48#15692941C2211yescharacteristic
49(C2×D103)⋊C8C2211yescharacteristic
50(C2×D103)⋊C8C2211yescharacteristic, complemented
51C4×C103⋊C8C2211yescharacteristic, complemented
52C2×SD16×C103C2211yescharacteristic, complemented
53C2×D8×C103C2211yescharacteristic
54#124×C103C2211yescharacteristic
55C4×D4×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—
67C2×C22⋊D103—21no—
68C2×C22⋊D103—21no—
69D4×D103—22no—
70D4×D103—41no—
71C2×C4×D103—21no—
72C2×C4×D103—21no—
73C2×C4×D103—21no—
74C2×C4×D103C2311yescharacteristic
75C2×C4×D103C2311yescharacteristic
76#13110090—22no—
77C2×C103⋊C8C2311yescharacteristic
78C2×C103⋊C8C2311yescharacteristic
79C8×D103—41no—
80C8×D103—41no—
81C4⋊Dic103D411yescharacteristic
82C4⋊Dic103C2311yescharacteristic
83C4⋊Dic103C2311yescharacteristic
84C4⋊Dic103C2311yescharacteristic
85Dic103⋊C4—21no—
86Dic103⋊C4—21no—
87Dic103⋊C4—21no—
88Dic103⋊C4—21no—
89C22⋊Dic103—21no—
90C22⋊Dic103—21no—
91C22⋊Dic103—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×D4×C103C2311yescharacteristic
100C2×D4×C103C2311yescharacteristic
101C22×C4×C103—21no—
102SD16×C103—41no—
103D8×C103—41no—
104C2×C8×C103C2311yescharacteristic
105C2×C8×C103C2311yescharacteristic
106C4⋊C4×C103C2311yescharacteristic
107C22⋊C4×C103—21no—
108C22⋊C4×C103—21no—
109C22⋊C4×C103—21no—
110C42×C103C2311yescharacteristic
111C23×C103—21no—
112C23×C103—21no—
113C22×D103—21no—
114C22×D103—42no—
115C22×D103—42no—
116C22×D103—81no—
117C22×D103C2×D411yescharacteristic
118C22×D103C2×D411yescharacteristic
119Q8×C103—21no—
120Q8×C103—21no—
121D4×C103—21no—
122D4×C103—21no—
123D4×C103—21no—
124D4×C103—21no—
125C2×C4×C103—21no—
126C2×C4×C103—21no—
127C2×C4×C103—81no—
128C2×C4×C103C2×D411yescharacteristic
129C2×C4×C103C2×D411yescharacteristic
130C2×C4×C103C2411yescharacteristic
131C22⋊D103—42no—
132C22⋊D103—42no—
133C22⋊D103—81no—
134C22⋊D103—81no—
135C2×Dic103—21no—
136C2×Dic103—21no—
137C2×Dic103—21no—
138C2×Dic103C2×D411yescharacteristic
139C2×Dic103C2×D411yescharacteristic
140D412—22no—
141D412—21no—
142D412—42no—
143D412#4112yes—
144C4×D103—21no—
145C4×D103—21no—
146C4×D103—21no—
147C4×D103—21no—
148C4×D103—42no—
149C4×D103—81no—
150C4×D103—81no—
151C8×C103—21no—
152C8×C103—21no—
153C103⋊C8—21no—
154C103⋊C8—21no—
155C22×C103—41no—
156C22×C103—41no—
157C22×C103—41no—
158C22×C103—41no—
159C22×C103—41no—
160C22×C103—41no—
161C22×C103C22×D411yescharacteristic
162C2×D103—21no—
163C2×D103—21no—
164C2×D103—21no—
165C2×D103—22no—
166C2×D103—21no—
167C2×D103—21no—
168C2×D103—41no—
169C2×D103—41no—
170C2×D103—84no—
171C2×D103#13512yes—
172C4×C103—21no—
173C4×C103—21no—
174C4×C103—41no—
175C4×C103—41no—
176C4×C103C2×#4111yescharacteristic
177C4×C103H(5,𝔽2)11yescharacteristic
178Dic103—21no—
179Dic103—21no—
180Dic103—41no—
181Dic103—41no—
182Dic103—41no—
183C2×C103—81no—
184C2×C103—81no—
185C2×C103#54611yescharacteristic
186C2×C103C2×#13511yescharacteristic
187C2×C103#57611yescharacteristic
188D103—22no—
189D103—41no—
190D103—42no—
191#3297—1031nomaximal, Sylow
192C103#329711yescharacteristic, complemented, Sylow
193#553—1031no—
194#546—1031no—
195#488—1031no—
196#484—1031no—
197#482—1031no—
198#478—1031no—
199#466—1031no—
200#465—1031no—
201#463D10311yescharacteristic, complemented
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×SD16C2×D10311yescharacteristic, complemented
211C2×D8—1031no—
212C2×D8C2×D10311yescharacteristic
213C22×C8—1031no—
214C22×C8—1031no—
215#126—2061no—
216#125—1031no—
217#124C2×D10311yescharacteristic
218#123—2061no—
219#123—2061no—
220C22⋊Q8—1031no—
221#121—1031no—
222#121—1031no—
223#121—1031no—
224#121—2061no—
225#121—2061no—
226#120—2061no—
227C4×D4—1031no—
228C4×D4—1031no—
229C4×D4—2061no—
230C4×D4C2×D10311yescharacteristic, complemented
231#117—1031no—
232C2×C4⋊C4—1031no—
233C2×C22⋊C4—2061no—
234#107—1031no—
235#107—1031no—
236#106—1031no—
237C4⋊C8C2×D10311yescharacteristic, complemented
238#103—1031no—
239#103—1031no—
240#103C2×D10311yescharacteristic, complemented
241#102—1031no—
242#102—1031no—
243#102—1031no—
244#102—1031no—
245#102—1031no—
246#102—1031no—
247#102C2×D10311yescharacteristic
248C22⋊C8—1031no—
249C22⋊C8—1031no—
250C4×C8—1031no—
251C24—2061no—
252#41—4121no—
253#41—2062no—
254C2×Q8C22×D10311yescharacteristic
255C2×D4—1031no—
256C2×D4—1031no—
257C2×D4—4121no—
258C2×D4—2061no—
259C2×D4—2061no—
260C2×D4—2062no—
261C2×D4—2061no—
262C2×D4—2061no—
263C2×D4—2061no—
264C2×D4C22×D10311yescharacteristic
265C2×D4C22×D10311yescharacteristic
266C22×C4—21no—
267C22×C4—1031no—
268C22×C4—1031no—
269C22×C4—2061no—
270C22×C4—2061no—
271C22×C4—2061no—
272SD16—41no—
273D8—41no—
274D8—2062no—
275C2×C8—1031no—
276C2×C8—1031no—
277C2×C8—4121no—
278C2×C8—4121no—
279C2×C8C22×D10311yescharacteristic
280C2×C8C22×D10311yescharacteristic
281C4⋊C4—1031no—
282C4⋊C4—1031no—
283C4⋊C4—1031no—
284C4⋊C4—1031no—
285C4⋊C4—2061no—
286C4⋊C4—2061no—
287C4⋊C4—2061no—
288C4⋊C4—2061no—
289C4⋊C4C22×D10311yescharacteristic
290C22⋊C4—21no—
291C22⋊C4—21no—
292C22⋊C4—21no—
293C22⋊C4—1031no—
294C22⋊C4—1031no—
295C22⋊C4—2061no—
296C22⋊C4—2061no—
297C22⋊C4—2061no—
298C22⋊C4—2061no—
299C22⋊C4—2061no—
300C22⋊C4—2061no—
301C42—2061no—
302C42C22×D10311yescharacteristic
303C23—21no—
304C23—21no—
305C23—8241no—
306C23—1031no—
307C23—1031no—
308C23—4122no—
309C23—4122no—
310C23—2061no—
311Q8—21no—
312Q8—21no—
313D4—21no—
314D4—21no—
315D4—21no—
316D4—21no—
317D4—8241no—
318D4—8241no—
319D4—1032no—
320D4—4122no—
321D4—4122no—
322D4—4122no—
323D4—2062no—
324D4—2061no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—81no—
328C2×C4—8241no—
329C2×C4—8241no—
330C2×C4—1031no—
331C2×C4—1031no—
332C2×C4—4122no—
333C2×C4—2061no—
334C2×C4—2061no—
335C2×C4—2061no—
336C2×C4—2061no—
337C2×C4—2061no—
338C2×C4—2061no—
339C2×C4—2061no—
340C2×C4D4×D10311yescharacteristic
341C2×C4D4×D10311yescharacteristic
342C2×C4C23×D10311yescharacteristic
343C8—21no—
344C8—21no—
345C8—2061no—
346C8—2061no—
347C22—41no—
348C22—41no—
349C22—41no—
350C22—41no—
351C22—41no—
352C22—41no—
353C22—8244no—
354C22—1032no—
355C22—4121no—
356C22—4121no—
357C22—2061no—
358C22—2061no—
359C22—2062no—
360C22—2061no—
361C22—2061no—
362C22—2061no—
363C22C2×D4×D10311yescharacteristic
364C4—21no—
365C4—21no—
366C4—41no—
367C4—41no—
368C4—4121no—
369C4—4121no—
370C4—4121no—
371C4—2061no—
372C4—2061no—
373C4#41×D10311yescharacteristic
374C4#1569306611yescharacteristic
375C2—81no—
376C2—81no—
377C2—4122no—
378C2—4121no—
379C2—2062no—
380C2#2026843811yescharacteristic
381C2#135×D10311yescharacteristic
382C2#2026859511yescharacteristic
subgroupG/H
centerC22C2×D4×D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
Fitting#463×C103C2
socleC22×C103C22×D4
hypercenter#463D103
hypocenterC103#3297
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C42 ◁ #463

Complements

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

NH ≅ G/Ntype
1. #20268491C2semidirect
2. #20268434C2semidirect
3. #20268145C2semidirect
4. #20268125C2semidirect
5. #20268114C2semidirect
6. #20268092C2semidirect
7. #20268024C2semidirect
8. #20268017C2semidirect
9. #20267935C2semidirect
10. #20267923C2semidirect
11. C4×#13110090C2semidirect
12. #20267856C2semidirect
13. #20267786C2semidirect
14. #102×D103C2semidirect
15. #463×C103C2semidirect
20. C2×C8×D103C22semidirect
22. #15693013C22semidirect
30. #15692992C22semidirect
35. #15692979C22semidirect
38. #15692955C22semidirect
39. #15692954C22semidirect
40. #15692953C22semidirect
41. #15692945C22semidirect
42. #15692945C22semidirect
47. #15692942C22semidirect
50. (C2×D103)⋊C8C22semidirect
51. C4×C103⋊C8C22semidirect
52. C2×SD16×C103C22semidirect
55. C4×D4×C103C22semidirect
56. C4⋊C8×C103C22semidirect
57. #103×C103C22semidirect
192. C103#3297semidirect
201. #463D103semidirect
210. C2×SD16C2×D103semidirect
230. C4×D4C2×D103semidirect
237. C4⋊C8C2×D103semidirect
240. #103C2×D103semidirect

Maximal subgroups

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

subgroupindex
#202684912
#202684342
#202681452
#202681252
#202681142
#202680922
#202680242
#202680172
#202679352
#202679232
C4×#131100902
#202678562
#202677862
#102×D1032
#463×C1032
#3297103