Finite Group Databasebeta

← #27206979

Subgroups — #27206979

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#20268481C211yesmaximal, characteristic, complemented
2#20268145C211yesmaximal, characteristic, complemented
3#20268119C211yesmaximal, characteristic, complemented
4#20268112C211yesmaximal, characteristic, complemented
5#20268091C211yesmaximal, characteristic, complemented
6#20268030C211yesmaximal, characteristic, complemented
7#20268018C211yesmaximal, characteristic, complemented
8#20268010C211yesmaximal, characteristic, complemented
9#20267953C211yesmaximal, characteristic, complemented
10#20267942C211yesmaximal, characteristic, complemented
11C4×#13110093C211yesmaximal, characteristic, complemented
12D4×C103⋊C8C211yesmaximal, characteristic, complemented
13#20267787C211yesmaximal, characteristic, complemented
14C2×#15692942C211yesmaximal, characteristic, complemented
15#546×C103C211yesmaximal, characteristic
16C2×#13110095C2211yescharacteristic, complemented
17C2×#13110093C2211yescharacteristic
18C2×#13110093C2211yescharacteristic
19C22×C103⋊C8C2211yescharacteristic
20C22×C103⋊C8C2211yescharacteristic, complemented
21#15693014—21no—
22#15693013C2211yescharacteristic, complemented
23#15693011—21no—
24#15693002—21no—
25#15693000C2211yescharacteristic
26#15693000C2211yescharacteristic, complemented
27C4×Dic206C2211yescharacteristic, complemented
28#15692980C2211yescharacteristic, complemented
29#15692977—21no—
30C2×C4⋊Dic103C2211yescharacteristic
31#15692954C2211yescharacteristic, complemented
32#15692952C2211yescharacteristic, complemented
33#15692952C2211yescharacteristic, complemented
34C4⋊(C103⋊C8)C2211yescharacteristic, complemented
35#15692945C2211yescharacteristic, complemented
36#15692945C2211yescharacteristic, complemented
37#15692945C2211yescharacteristic, complemented
38#15692944C2211yescharacteristic, complemented
39#15692942C2211yescharacteristic
40#15692942C2211yescharacteristic
41#15692942C2211yescharacteristic
42#15692942C2211yescharacteristic
43#15692942C2211yescharacteristic
44#15692942C2211yescharacteristic
45C22⋊(C103⋊C8)C2211yescharacteristic
46C22⋊(C103⋊C8)C2211yescharacteristic, complemented
47C4×C103⋊C8C2211yescharacteristic, complemented
48C2×#41×C103C2211yescharacteristic
49C22×D4×C103C2211yescharacteristic
50#124×C103C2211yescharacteristic
51#123×C103—21no—
52C22⋊Q8×C103C2211yescharacteristic
53#121×C103—21no—
54#121×C103C2211yescharacteristic
55#120×C103—21no—
56C4×D4×C103C2211yescharacteristic
57C4×D4×C103C2211yescharacteristic
58C2×C22⋊C4×C103—21no—
59C2×Dic206C2311yescharacteristic
60C22×Dic103—21no—
61#13110095—41no—
62#13110093—22no—
63#13110093—41no—
64C2×C103⋊C8—41no—
65C2×C103⋊C8—41no—
66C2×C103⋊C8C2311yescharacteristic
67C2×C103⋊C8C2311yescharacteristic
68C2×C103⋊C8C2311yescharacteristic
69C2×C103⋊C8C2311yescharacteristic
70C4⋊Dic103—21no—
71C4⋊Dic103C2311yescharacteristic
72C4⋊Dic103C2311yescharacteristic
73C4⋊Dic103C2311yescharacteristic
74Dic103⋊C4—21no—
75Dic103⋊C4—21no—
76Dic103⋊C4—21no—
77Dic103⋊C4—21no—
78Dic103⋊C4—21no—
79C22⋊Dic103—21no—
80C22⋊Dic103—21no—
81C22⋊Dic103—21no—
82C4×Dic103—21no—
83C4×Dic103—21no—
84C24×C103—21no—
85#41×C103—22no—
86#41×C103—41no—
87C2×Q8×C103C2311yescharacteristic
88C2×D4×C103—22no—
89C2×D4×C103—21no—
90C2×D4×C103—21no—
91C2×D4×C103—21no—
92C2×D4×C103—41no—
93C2×D4×C103D411yescharacteristic
94C2×D4×C103C2311yescharacteristic
95C2×D4×C103C2311yescharacteristic
96C22×C4×C103—21no—
97C22×C4×C103—21no—
98C22×C4×C103C2311yescharacteristic
99C22×C4×C103C2311yescharacteristic
100C4⋊C4×C103—21no—
101C4⋊C4×C103D411yescharacteristic
102C4⋊C4×C103C2311yescharacteristic
103C22⋊C4×C103—21no—
104C22⋊C4×C103—21no—
105C22⋊C4×C103—21no—
106C22⋊C4×C103—21no—
107C22⋊C4×C103—21no—
108C22⋊C4×C103D411yescharacteristic
109C22⋊C4×C103D411yescharacteristic
110C42×C103C2311yescharacteristic
111C23×C103—21no—
112C23×C103—21no—
113C23×C103—42no—
114C23×C103—42no—
115C23×C103—81no—
116C23×C103C2×D411yescharacteristic
117C23×C103C2×D411yescharacteristic
118Q8×C103—21no—
119Q8×C103—21no—
120D4×C103—22no—
121D4×C103—21no—
122D4×C103—21no—
123D4×C103—21no—
124D4×C103—42no—
125D4×C103—42no—
126D4×C103—81no—
127D4×C103#4112yes—
128C2×C4×C103—21no—
129C2×C4×C103—21no—
130C2×C4×C103—21no—
131C2×C4×C103—21no—
132C2×C4×C103—21no—
133C2×C4×C103—21no—
134C2×C4×C103—42no—
135C2×C4×C103—81no—
136C2×C4×C103C2×D411yescharacteristic
137C2×C4×C103C2×D411yescharacteristic
138C2×C4×C103C2×D411yescharacteristic
139C2×C4×C103C2×D411yescharacteristic
140C2×C4×C103C2411yescharacteristic
141C2×Dic103—21no—
142C2×Dic103—21no—
143C2×Dic103—21no—
144C2×Dic103—21no—
145C2×Dic103—42no—
146Dic206—21no—
147Dic206—21no—
148C103⋊C8—21no—
149C103⋊C8—21no—
150C103⋊C8—21no—
151C103⋊C8—21no—
152C22×C103—21no—
153C22×C103—21no—
154C22×C103—21no—
155C22×C103—22no—
156C22×C103—21no—
157C22×C103—21no—
158C22×C103—41no—
159C22×C103—41no—
160C22×C103—41no—
161C22×C103—41no—
162C22×C103—41no—
163C22×C103—84no—
164C22×C103#13512yes—
165C22×C103C22×D411yescharacteristic
166C4×C103—21no—
167C4×C103—21no—
168C4×C103—21no—
169C4×C103—21no—
170C4×C103—41no—
171C4×C103—41no—
172C4×C103C2×#4111yescharacteristic
173C4×C103H(5,𝔽2)11yescharacteristic
174Dic103—41no—
175Dic103—41no—
176Dic103—41no—
177Dic103—41no—
178C2×C103—22no—
179C2×C103—41no—
180C2×C103—42no—
181C2×C103—81no—
182C2×C103#54611yescharacteristic
183C2×C103C2×#13511yescharacteristic
184C2×C103#57711yescharacteristic
185#3296—1031nomaximal, Sylow
186C103#329611yescharacteristic, complemented, Sylow
187#552—1031no—
188#546D10311yescharacteristic
189#488—1031no—
190#483—1031no—
191#482—1031no—
192#478—1031no—
193#467—1031no—
194#465—1031no—
195#464—1031no—
196#452—1031no—
197#450—1031no—
198C4×SD16—1031no—
199C8×D4—1031no—
200#416—1031no—
201C2×#102—1031no—
202C2×#41C2×D10311yescharacteristic
203C22×D4C2×D10311yescharacteristic
204C2×Q16—1031no—
205C2×SD16—1031no—
206C2×SD16—1031no—
207C22×C8—1031no—
208C22×C8—1031no—
209#126—2061no—
210#125—1031no—
211#125—2061no—
212#124C2×D10311yescharacteristic
213#123—21no—
214#123—2061no—
215C22⋊Q8—1031no—
216C22⋊Q8—1031no—
217C22⋊Q8C2×D10311yescharacteristic
218#121—21no—
219#121C2×D10311yescharacteristic
220#120—21no—
221C4×Q8—1031no—
222C4×D4C2×D10311yescharacteristic
223C4×D4C2×D10311yescharacteristic
224#117—1031no—
225#117—2061no—
226C2×C4⋊C4—1031no—
227C2×C22⋊C4—21no—
228#107—1031no—
229#106—1031no—
230#106—1031no—
231C4⋊C8—1031no—
232#103—1031no—
233#103—1031no—
234#103—1031no—
235#103—1031no—
236#102—1031no—
237#102—1031no—
238#102—1031no—
239#102—1031no—
240#102—1031no—
241#102—1031no—
242C22⋊C8—1031no—
243C22⋊C8—1031no—
244C4×C8—1031no—
245C24—21no—
246#41—22no—
247#41—41no—
248C2×Q8—1031no—
249C2×Q8C22×D10311yescharacteristic
250C2×D4—22no—
251C2×D4—21no—
252C2×D4—21no—
253C2×D4—21no—
254C2×D4—41no—
255C2×D4C22⋊D10311yescharacteristic
256C2×D4C22×D10311yescharacteristic
257C2×D4C22×D10311yescharacteristic
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—2061no—
261C22×C4C22×D10311yescharacteristic
262C22×C4C22×D10311yescharacteristic
263Q16—4121no—
264SD16—4121no—
265SD16—2062no—
266C2×C8—1031no—
267C2×C8—1031no—
268C2×C8—1031no—
269C2×C8—1031no—
270C2×C8—4121no—
271C2×C8—4121no—
272C4⋊C4—21no—
273C4⋊C4—1031no—
274C4⋊C4—1031no—
275C4⋊C4—1031no—
276C4⋊C4—2061no—
277C4⋊C4—2061no—
278C4⋊C4—2061no—
279C4⋊C4—2061no—
280C4⋊C4—2061no—
281C4⋊C4—2061no—
282C4⋊C4C22⋊D10311yescharacteristic
283C4⋊C4C22×D10311yescharacteristic
284C22⋊C4—21no—
285C22⋊C4—21no—
286C22⋊C4—21no—
287C22⋊C4—21no—
288C22⋊C4—21no—
289C22⋊C4—2061no—
290C22⋊C4—2061no—
291C22⋊C4—2061no—
292C22⋊C4C22⋊D10311yescharacteristic
293C22⋊C4C22⋊D10311yescharacteristic
294C42—2061no—
295C42—2061no—
296C42C22×D10311yescharacteristic
297C23—21no—
298C23—21no—
299C23—42no—
300C23—42no—
301C23—81no—
302C23C2×C22⋊D10311yescharacteristic
303C23C2×C22⋊D10311yescharacteristic
304Q8—21no—
305Q8—21no—
306Q8—2061no—
307Q8—2061no—
308D4—22no—
309D4—21no—
310D4—21no—
311D4—21no—
312D4—42no—
313D4—42no—
314D4—81no—
315D4#1311010412yes—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—42no—
323C2×C4—81no—
324C2×C4—4122no—
325C2×C4—2061no—
326C2×C4—2061no—
327C2×C4—2061no—
328C2×C4—2061no—
329C2×C4C2×C22⋊D10311yescharacteristic
330C2×C4C2×C22⋊D10311yescharacteristic
331C2×C4C2×C22⋊D10311yescharacteristic
332C2×C4C2×C22⋊D10311yescharacteristic
333C2×C4C23×D10311yescharacteristic
334C8—2061no—
335C8—2061no—
336C8—2061no—
337C8—2061no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—22no—
344C22—41no—
345C22—41no—
346C22—41no—
347C22—41no—
348C22—41no—
349C22—84no—
350C22#1569304112yes—
351C22C22×C22⋊D10311yescharacteristic
352C4—21no—
353C4—21no—
354C4—21no—
355C4—21no—
356C4—41no—
357C4—41no—
358C4—4121no—
359C4—4121no—
360C4—4121no—
361C4—4121no—
362C4C2×#1311010411yescharacteristic
363C4#1569306611yescharacteristic
364C2—22no—
365C2—41no—
366C2—42no—
367C2—81no—
368C2#2026843511yescharacteristic
369C2C2×#1569304111yescharacteristic
370C2#2026860211yescharacteristic
subgroupG/H
centerC22C22×C22⋊D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
Fitting, prime radical#546×C103C2
socleC22×C103C22×D4
hypercenter#546D103
hypocenterC103#3296
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C4×D4 ◁ #546

Complements

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

NH ≅ G/Ntype
1. #20268481C2semidirect
2. #20268145C2semidirect
3. #20268119C2semidirect
4. #20268112C2semidirect
5. #20268091C2semidirect
6. #20268030C2semidirect
7. #20268018C2semidirect
8. #20268010C2semidirect
9. #20267953C2semidirect
10. #20267942C2semidirect
11. C4×#13110093C2semidirect
12. D4×C103⋊C8C2semidirect
13. #20267787C2semidirect
14. C2×#15692942C2semidirect
16. C2×#13110095C22semidirect
20. C22×C103⋊C8C22semidirect
22. #15693013C22semidirect
26. #15693000C22semidirect
27. C4×Dic206C22semidirect
28. #15692980C22semidirect
31. #15692954C22semidirect
32. #15692952C22semidirect
33. #15692952C22semidirect
34. C4⋊(C103⋊C8)C22semidirect
35. #15692945C22semidirect
36. #15692945C22semidirect
37. #15692945C22semidirect
38. #15692944C22semidirect
46. C22⋊(C103⋊C8)C22semidirect
47. C4×C103⋊C8C22semidirect
186. C103#3296semidirect

Maximal subgroups

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

subgroupindex
#202684812
#202681452
#202681192
#202681122
#202680912
#202680302
#202680182
#202680102
#202679532
#202679422
C4×#131100932
D4×C103⋊C82
#202677872
C2×#156929422
#546×C1032
#3296103