Finite Group Databasebeta

← #27205390

Subgroups — #27205390

Order 13184.

394 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20268401C211yesmaximal, characteristic, complemented
2#20268266C211yesmaximal, characteristic
3#20268133C211yesmaximal, characteristic, complemented
4#20268129C211yesmaximal, characteristic, complemented
5#20268093C211yesmaximal, characteristic, complemented
6#20268089C211yesmaximal, characteristic, complemented
7#20267994C211yesmaximal, characteristic, complemented
8#20267994C211yesmaximal, characteristic, complemented
9#20267942C211yesmaximal, characteristic
10#20267892C211yesmaximal, characteristic, complemented
11#20267888C211yesmaximal, characteristic, complemented
12#20267882C211yesmaximal, characteristic, complemented
13SD16×Dic103C211yesmaximal, characteristic, complemented
14#20267849C211yesmaximal, characteristic, complemented
15#450×C103C211yesmaximal, characteristic
16C2×#13110093C2211yescharacteristic
17C2×#13110093C2211yescharacteristic
18#15693019C2211yescharacteristic, complemented
19#15693014—21no—
20#15693014—21no—
21#15693012—21no—
22#15693012C2211yescharacteristic, complemented
23#15693011—21no—
24#15693000C2211yescharacteristic
25Q8×Dic103C2211yescharacteristic, complemented
26#15692986C2211yescharacteristic, complemented
27D4×Dic103—21no—
28D4×Dic103—21no—
29D4×Dic103C2211yescharacteristic
30D4×Dic103C2211yescharacteristic
31D4×Dic103C2211yescharacteristic
32D4×Dic103C2211yescharacteristic
33#15692980C2211yescharacteristic
34#15692980C2211yescharacteristic
35C2×C22⋊Dic103—21no—
36C2×C22⋊Dic103—21no—
37#15692955C2211yescharacteristic, complemented
38#15692954C2211yescharacteristic, complemented
39#15692953C2211yescharacteristic, complemented
40#15692952C2211yescharacteristic, complemented
41Dic103⋊C8C2211yescharacteristic, complemented
42Dic103⋊C8C2211yescharacteristic, complemented
43#15692946C2211yescharacteristic, complemented
44#15692946C2211yescharacteristic, complemented
45#15692945C2211yescharacteristic, complemented
46#15692945C2211yescharacteristic, complemented
47#15692942C2211yescharacteristic
48#15692942C2211yescharacteristic
49C22⋊(C103⋊C8)C2211yescharacteristic
50#15692931C2211yescharacteristic, complemented
51C8×Dic103C2211yescharacteristic, complemented
52C22×D4×C103C2211yescharacteristic
53C2×SD16×C103C2211yescharacteristic
54C2×SD16×C103C2211yescharacteristic
55C22⋊Q8×C103C2211yescharacteristic
56#102×C103C2211yescharacteristic
57#102×C103C2211yescharacteristic
58C22⋊C8×C103C2211yescharacteristic
59C2×Dic206C2311yescharacteristic
60C22×Dic103—21no—
61C22×Dic103—21no—
62C22×Dic103—21no—
63C22×Dic103—21no—
64#13110093—22no—
65#13110093—22no—
66C2×C103⋊C8C2311yescharacteristic
67C2×C103⋊C8C2311yescharacteristic
68C4⋊Dic103—21no—
69C4⋊Dic103—21no—
70C4⋊Dic103D411yescharacteristic
71C4⋊Dic103D411yescharacteristic
72C4⋊Dic103C2311yescharacteristic
73C4⋊Dic103C2311yescharacteristic
74C4⋊Dic103C2311yescharacteristic
75Dic103⋊C4—21no—
76Dic103⋊C4—21no—
77Dic103⋊C4—21no—
78Dic103⋊C4—21no—
79Dic103⋊C4—21no—
80C22⋊Dic103—21no—
81C22⋊Dic103—21no—
82C22⋊Dic103—21no—
83C22⋊Dic103—21no—
84C22⋊Dic103—21no—
85C22⋊Dic103—21no—
86C22⋊Dic103D411yescharacteristic
87C22⋊Dic103D411yescharacteristic
88C4×Dic103—21no—
89C4×Dic103—21no—
90C4×Dic103—21no—
91C4×Dic103C2311yescharacteristic
92C4×Dic103C2311yescharacteristic
93C24×C103—21no—
94C2×Q8×C103C2311yescharacteristic
95C2×D4×C103—22no—
96C2×D4×C103—22no—
97C2×D4×C103—21no—
98C2×D4×C103C2311yescharacteristic
99C2×D4×C103C2311yescharacteristic
100C22×C4×C103C2311yescharacteristic
101SD16×C103—22no—
102SD16×C103—22no—
103C2×C8×C103C2311yescharacteristic
104C2×C8×C103C2311yescharacteristic
105C4⋊C4×C103—21no—
106C4⋊C4×C103C2311yescharacteristic
107C22⋊C4×C103—21no—
108C23×C103—24no—
109C23×C103—21no—
110C23×C103—21no—
111C23×C103—81no—
112C23×C103—81no—
113C23×C103C2×D411yescharacteristic
114Q8×C103—21no—
115Q8×C103—21no—
116D4×C103—24no—
117D4×C103—21no—
118D4×C103—21no—
119D4×C103#4112yes—
120D4×C103#4112yes—
121C2×C4×C103—21no—
122C2×C4×C103—21no—
123C2×C4×C103—21no—
124C2×C4×C103—21no—
125C2×C4×C103C2×D411yescharacteristic
126C2×C4×C103C2411yescharacteristic
127C2×Dic103—21no—
128C2×Dic103—21no—
129C2×Dic103—21no—
130C2×Dic103—21no—
131C2×Dic103—81no—
132C2×Dic103—81no—
133C2×Dic103—81no—
134C2×Dic103—81no—
135C2×Dic103C2×D411yescharacteristic
136C2×Dic103C2×D411yescharacteristic
137C2×Dic103C2×D411yescharacteristic
138C2×Dic103C2×D411yescharacteristic
139Dic206—21no—
140Dic206—21no—
141C8×C103—21no—
142C8×C103—21no—
143C103⋊C8—21no—
144C103⋊C8—21no—
145C22×C103—21no—
146C22×C103—22no—
147C22×C103—22no—
148C22×C103—21no—
149C22×C103—21no—
150C22×C103—41no—
151C22×C103—41no—
152C22×C103—41no—
153C22×C103—41no—
154C22×C103—84no—
155C22×C103C22×D411yescharacteristic
156C4×C103—21no—
157C4×C103—41no—
158C4×C103—41no—
159C4×C103C2×#4111yescharacteristic
160C4×C103C2×#4111yescharacteristic
161Dic103—21no—
162Dic103—21no—
163Dic103—21no—
164Dic103—21no—
165Dic103—41no—
166Dic103—41no—
167Dic103—41no—
168Dic103—41no—
169C2×C103—41no—
170C2×C103—42no—
171C2×C103—42no—
172C2×C103#52511yescharacteristic
173C2×C103#57711yescharacteristic
174C2×C103#57711yescharacteristic
175#3123—1031nomaximal, Sylow
176C103#312311yescharacteristic, complemented, Sylow
177#541—1031no—
178#518—1031no—
179#485—1031no—
180#485—1031no—
181#478—1031no—
182#478—1031no—
183#461—1031no—
184#461—1031no—
185#450—1031no—
186#450D10311yescharacteristic
187#440—1031no—
188#440—1031no—
189C4×SD16—1031no—
190C4×SD16—1031no—
191#433—1031no—
192C22×D4C2×D10311yescharacteristic
193C2×SD16—1031no—
194C2×SD16—1031no—
195C2×SD16C2×D10311yescharacteristic
196C2×SD16C2×D10311yescharacteristic
197C4⋊Q8—1031no—
198#126—2061no—
199#126—2061no—
200#125—1031no—
201#125—2061no—
202#125—2061no—
203C22⋊Q8—1031no—
204C22⋊Q8C2×D10311yescharacteristic
205C4×Q8—1031no—
206C4×Q8—1031no—
207C4×D4—1031no—
208C4×D4—1031no—
209C4×D4—1031no—
210C4×D4—1031no—
211C4×D4—2061no—
212C4×D4—2061no—
213#117—1031no—
214#117—1031no—
215C2×C22⋊C4—2061no—
216C2×C22⋊C4—2061no—
217#107—1031no—
218#107—1031no—
219#106—1031no—
220#106—1031no—
221C4⋊C8—1031no—
222C4⋊C8—1031no—
223#103—1031no—
224#103—1031no—
225#103—1031no—
226#103—1031no—
227#102—1031no—
228#102—1031no—
229#102C2×D10311yescharacteristic
230#102C2×D10311yescharacteristic
231C22⋊C8—1031no—
232C22⋊C8C2×D10311yescharacteristic
233#97—1031no—
234C4×C8—1031no—
235C24—21no—
236C2×Q8—1031no—
237C2×Q8C22×D10311yescharacteristic
238C2×D4—22no—
239C2×D4—22no—
240C2×D4—21no—
241C2×D4C22×D10311yescharacteristic
242C2×D4C22×D10311yescharacteristic
243C22×C4—2061no—
244C22×C4—2061no—
245C22×C4—2061no—
246C22×C4—2061no—
247C22×C4C22×D10311yescharacteristic
248SD16—22no—
249SD16—22no—
250SD16—2062no—
251SD16—2062no—
252C2×C8—1031no—
253C2×C8—1031no—
254C2×C8C22×D10311yescharacteristic
255C2×C8C22×D10311yescharacteristic
256C4⋊C4—21no—
257C4⋊C4—1031no—
258C4⋊C4—1031no—
259C4⋊C4—1031no—
260C4⋊C4—1031no—
261C4⋊C4—1031no—
262C4⋊C4—2061no—
263C4⋊C4—2061no—
264C4⋊C4—2061no—
265C4⋊C4—2061no—
266C4⋊C4—2061no—
267C4⋊C4—2061no—
268C4⋊C4—2061no—
269C4⋊C4C22×D10311yescharacteristic
270C22⋊C4—21no—
271C22⋊C4—1031no—
272C22⋊C4—1031no—
273C22⋊C4—2061no—
274C22⋊C4—2061no—
275C22⋊C4—2061no—
276C22⋊C4—2061no—
277C22⋊C4—2061no—
278C22⋊C4—2061no—
279C42—1031no—
280C42—1031no—
281C42—2061no—
282C42—2061no—
283C42—2061no—
284C23—24no—
285C23—21no—
286C23—21no—
287C23—81no—
288C23—81no—
289C23D4×D10311yescharacteristic
290Q8—21no—
291Q8—21no—
292Q8—2061no—
293Q8—2061no—
294D4—24no—
295D4—21no—
296D4—21no—
297D4#1311010412yes—
298D4#1311010412yes—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—8241no—
304C2×C4—8241no—
305C2×C4—8241no—
306C2×C4—8241no—
307C2×C4—1031no—
308C2×C4—1031no—
309C2×C4—1031no—
310C2×C4—1031no—
311C2×C4—2061no—
312C2×C4—2061no—
313C2×C4—2061no—
314C2×C4—2061no—
315C2×C4D4×D10311yescharacteristic
316C2×C4C23×D10311yescharacteristic
317C8—21no—
318C8—21no—
319C8—2061no—
320C8—2061no—
321C22—21no—
322C22—22no—
323C22—22no—
324C22—21no—
325C22—21no—
326C22—41no—
327C22—41no—
328C22—41no—
329C22—41no—
330C22—84no—
331C22C2×D4×D10311yescharacteristic
332C4—21no—
333C4—41no—
334C4—41no—
335C4—4121no—
336C4—4121no—
337C4—4121no—
338C4—4121no—
339C4—2061no—
340C4—2061no—
341C4—2061no—
342C4—2061no—
343C4C2×#1311010411yescharacteristic
344C4C2×#1311010411yescharacteristic
345C2—41no—
346C2—42no—
347C2—42no—
348C2#2026829711yescharacteristic
349C2#2026859711yescharacteristic
350C2#2026860111yescharacteristic
subgroupG/H
centerC22C2×D4×D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
Fitting#450×C103C2
socleC22×C103C22×D4
prime radicalC22×D4×C103C22
hypercenter#450D103
hypocenterC103#3123
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C22×C4 ◁ #450

Complements

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

NH ≅ G/Ntype
1. #20268401C2semidirect
3. #20268133C2semidirect
4. #20268129C2semidirect
5. #20268093C2semidirect
6. #20268089C2semidirect
7. #20267994C2semidirect
8. #20267994C2semidirect
10. #20267892C2semidirect
11. #20267888C2semidirect
12. #20267882C2semidirect
13. SD16×Dic103C2semidirect
14. #20267849C2semidirect
18. #15693019C22semidirect
22. #15693012C22semidirect
25. Q8×Dic103C22semidirect
26. #15692986C22semidirect
37. #15692955C22semidirect
38. #15692954C22semidirect
39. #15692953C22semidirect
40. #15692952C22semidirect
41. Dic103⋊C8C22semidirect
42. Dic103⋊C8C22semidirect
43. #15692946C22semidirect
44. #15692946C22semidirect
45. #15692945C22semidirect
46. #15692945C22semidirect
50. #15692931C22semidirect
51. C8×Dic103C22semidirect
176. C103#3123semidirect

Maximal subgroups

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

subgroupindex
#202684012
#202682662
#202681332
#202681292
#202680932
#202680892
#202679942
#202679422
#202678922
#202678882
#202678822
SD16×Dic1032
#202678492
#450×C1032
#3123103