Finite Group Databasebeta

← #27206980

Subgroups — #27206980

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#20268480C211yesmaximal, characteristic, complemented
2#20268429C211yesmaximal, characteristic
3#20268147C211yesmaximal, characteristic, complemented
4#20268120C211yesmaximal, characteristic, complemented
5#20268115C211yesmaximal, characteristic, complemented
6#20268093C211yesmaximal, characteristic, complemented
7#20268031C211yesmaximal, characteristic, complemented
8#20268020C211yesmaximal, characteristic, complemented
9#20268016C211yesmaximal, characteristic, complemented
10#20267953C211yesmaximal, characteristic, complemented
11#20267943C211yesmaximal, characteristic, complemented
12#20267882C211yesmaximal, characteristic, complemented
13C8×C22⋊D103C211yesmaximal, characteristic, complemented
14#102×D103C211yesmaximal, characteristic, complemented
15#416×C103C211yesmaximal, characteristic, complemented
16C2×D4×D103C2211yescharacteristic
17C2×#13110095C2211yescharacteristic, complemented
18C2×#13110094C2211yescharacteristic
19C2×#13110093C2211yescharacteristic
20C2×C8×D103C2211yescharacteristic
21#15693014—21no—
22#15693013—21no—
23#15693012C2211yescharacteristic, complemented
24#15693010C2211yescharacteristic
25#15693004—21no—
26#15693003—21no—
27#15693001C2211yescharacteristic
28#15693000C2211yescharacteristic, complemented
29#15692997C2211yescharacteristic
30#15692995C2211yescharacteristic
31#15692993—21no—
32#15692989—21no—
33#15692986C2211yescharacteristic, complemented
34D4×Dic103C2211yescharacteristic
35C4×C22⋊D103C2211yescharacteristic
36#15692978—21no—
37C4⋊C4×D103C2211yescharacteristic
38C2×(C2×D103)⋊C4—21no—
39#15692954C2211yescharacteristic, complemented
40#15692953C2211yescharacteristic, complemented
41#15692952C2211yescharacteristic, complemented
42Dic103⋊C8C2211yescharacteristic, complemented
43#15692946C2211yescharacteristic, complemented
44#15692945C2211yescharacteristic, complemented
45#15692943C2211yescharacteristic
46#15692942C2211yescharacteristic
47#15692941C2211yescharacteristic
48#15692941C2211yescharacteristic
49C22⋊(C103⋊C8)C2211yescharacteristic, complemented
50(C2×D103)⋊C8C2211yescharacteristic
51C8×Dic103C2211yescharacteristic, complemented
52C2×#41×C103C2211yescharacteristic
53C22×C8×C103C2211yescharacteristic, complemented
54#117×C103C2211yescharacteristic, complemented
55#103×C103C2211yescharacteristic, complemented
56#103×C103C2211yescharacteristic, complemented
57#102×C103C2211yescharacteristic
58#102×C103C2211yescharacteristic
59C23×D103—21no—
60C2×Dic206C2311yescharacteristic
61C2×D412C2311yescharacteristic
62C2×C22⋊D103—21no—
63C2×C22⋊D103—21no—
64C2×C22⋊D103D411yescharacteristic
65D4×D103—22no—
66D4×D103—41no—
67C22×Dic103—21no—
68C2×C4×D103—21no—
69C2×C4×D103C2311yescharacteristic
70#13110095—41no—
71#13110094—41no—
72#13110093—22no—
73C2×C103⋊C8C2311yescharacteristic
74C2×C103⋊C8C2311yescharacteristic
75C8×D103—41no—
76C4⋊Dic103—21no—
77C4⋊Dic103—21no—
78C4⋊Dic103C2311yescharacteristic
79C4⋊Dic103C2311yescharacteristic
80Dic103⋊C4—21no—
81Dic103⋊C4—21no—
82Dic103⋊C4—21no—
83Dic103⋊C4—21no—
84Dic103⋊C4—21no—
85Dic103⋊C4D411yescharacteristic
86C22⋊Dic103—21no—
87C22⋊Dic103—21no—
88C22⋊Dic103D411yescharacteristic
89(C2×D103)⋊C4—21no—
90(C2×D103)⋊C4—21no—
91(C2×D103)⋊C4—21no—
92(C2×D103)⋊C4—21no—
93(C2×D103)⋊C4—21no—
94(C2×D103)⋊C4D411yescharacteristic
95C4×Dic103—21no—
96C4×Dic103C2311yescharacteristic
97#41×C103—22no—
98#41×C103—41no—
99C2×Q8×C103C2311yescharacteristic
100C2×D4×C103—21no—
101C2×D4×C103C2311yescharacteristic
102C22×C4×C103—21no—
103C22×C4×C103C2311yescharacteristic
104C2×C8×C103—41no—
105C2×C8×C103C2311yescharacteristic
106C2×C8×C103C2311yescharacteristic
107C4⋊C4×C103C2311yescharacteristic
108C4⋊C4×C103C2311yescharacteristic
109C22⋊C4×C103—21no—
110C42×C103—21no—
111C23×C103—21no—
112C23×C103C2×D411yescharacteristic
113C22×D103—21no—
114C22×D103—42no—
115C22×D103—42no—
116C22×D103—81no—
117C22×D103C2×D411yescharacteristic
118Q8×C103—21no—
119Q8×C103—21no—
120D4×C103—21no—
121D4×C103—42no—
122D4×C103#4112yes—
123C2×C4×C103—21no—
124C2×C4×C103—21no—
125C2×C4×C103—21no—
126C2×C4×C103—21no—
127C2×C4×C103—21no—
128C2×C4×C103—42no—
129C2×C4×C103C2×D411yescharacteristic
130C2×C4×C103C2411yescharacteristic
131C22⋊D103—22no—
132C22⋊D103—42no—
133C22⋊D103—81no—
134C2×Dic103—21no—
135C2×Dic103—21no—
136C2×Dic103—21no—
137C2×Dic103—81no—
138C2×Dic103C2×D411yescharacteristic
139C2×Dic103C2×D411yescharacteristic
140C2×Dic103C2×D411yescharacteristic
141D412—21no—
142D412—21no—
143C4×D103—21no—
144C4×D103—21no—
145C4×D103—42no—
146Dic206—21no—
147Dic206—21no—
148C8×C103—21no—
149C8×C103—21no—
150C103⋊C8—21no—
151C103⋊C8—21no—
152C22×C103—22no—
153C22×C103—21no—
154C22×C103—21no—
155C22×C103—21no—
156C22×C103—41no—
157C22×C103—41no—
158C22×C103C22×D411yescharacteristic
159C2×D103—21no—
160C2×D103—21no—
161C2×D103—41no—
162C2×D103—41no—
163C2×D103—41no—
164C2×D103—84no—
165C2×D103#13512yes—
166C4×C103—21no—
167C4×C103—41no—
168C4×C103—41no—
169C4×C103—41no—
170C4×C103C2×#4111yescharacteristic
171C4×C103H(5,𝔽2)11yescharacteristic
172Dic103—21no—
173Dic103—21no—
174Dic103—21no—
175Dic103—41no—
176Dic103—41no—
177Dic103—41no—
178C2×C103—42no—
179C2×C103—41no—
180C2×C103#54611yescharacteristic
181C2×C103C2×#13511yescharacteristic
182C2×C103#57711yescharacteristic
183D103—22no—
184D103—81no—
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#464—1031no—
196#452—1031no—
197#450—1031no—
198C4×SD16—1031no—
199C8×D4—1031no—
200#416D10311yescharacteristic, complemented
201C2×#102—1031no—
202C2×#41C2×D10311yescharacteristic
203C22×D4—1031no—
204C2×Q16—1031no—
205C2×SD16—1031no—
206C2×SD16—1031no—
207C22×C8—1031no—
208C22×C8C2×D10311yescharacteristic, complemented
209#126—2061no—
210#125—1031no—
211#125—2061no—
212#124—1031no—
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×Q8—1031no—
222C4×D4—1031no—
223C4×D4—1031no—
224#117—2061no—
225#117C2×D10311yescharacteristic, complemented
226C2×C4⋊C4—1031no—
227C2×C22⋊C4—2061no—
228#107—1031no—
229#106—1031no—
230#106—1031no—
231C4⋊C8—1031no—
232#103—1031no—
233#103—1031no—
234#103C2×D10311yescharacteristic, complemented
235#103C2×D10311yescharacteristic, complemented
236#102—1031no—
237#102—1031no—
238#102—1031no—
239#102—1031no—
240#102C2×D10311yescharacteristic
241#102C2×D10311yescharacteristic
242C22⋊C8—1031no—
243C22⋊C8—1031no—
244C4×C8—1031no—
245C24—2061no—
246#41—22no—
247#41—41no—
248C2×Q8—1031no—
249C2×Q8C22×D10311yescharacteristic
250C2×D4—21no—
251C2×D4—1031no—
252C2×D4—1031no—
253C2×D4—4121no—
254C2×D4—2061no—
255C2×D4—2061no—
256C2×D4—2062no—
257C2×D4C22×D10311yescharacteristic
258C22×C4—21no—
259C22×C4—1031no—
260C22×C4—2061no—
261C22×C4—2061no—
262C22×C4C22×D10311yescharacteristic
263Q16—4121no—
264SD16—4121no—
265SD16—2062no—
266C2×C8—41no—
267C2×C8—1031no—
268C2×C8—1031no—
269C2×C8—4121no—
270C2×C8C22×D10311yescharacteristic
271C2×C8C22×D10311yescharacteristic
272C4⋊C4—1031no—
273C4⋊C4—1031no—
274C4⋊C4—1031no—
275C4⋊C4—2061no—
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—1031no—
286C22⋊C4—1031no—
287C22⋊C4—2061no—
288C22⋊C4—2061no—
289C22⋊C4—2061no—
290C22⋊C4—2061no—
291C22⋊C4—2061no—
292C22⋊C4—2061no—
293C22⋊C4—2061no—
294C42—21no—
295C42—1031no—
296C42—2061no—
297C23—21no—
298C23—8241no—
299C23—1031no—
300C23—4122no—
301C23—4122no—
302C23—2061no—
303C23D4×D10311yescharacteristic
304Q8—21no—
305Q8—21no—
306Q8—2061no—
307Q8—2061no—
308D4—21no—
309D4—42no—
310D4—8241no—
311D4—4122no—
312D4—2062no—
313D4—2061no—
314D4—2061no—
315D4#1311010512yes—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—42no—
322C2×C4—8241no—
323C2×C4—1031no—
324C2×C4—1031no—
325C2×C4—1031no—
326C2×C4—4122no—
327C2×C4—2061no—
328C2×C4—2061no—
329C2×C4—2061no—
330C2×C4—2061no—
331C2×C4—2061no—
332C2×C4D4×D10311yescharacteristic
333C2×C4C23×D10311yescharacteristic
334C8—21no—
335C8—21no—
336C8—2061no—
337C8—2061no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—22no—
342C22—41no—
343C22—41no—
344C22—8244no—
345C22—1032no—
346C22—4121no—
347C22—4121no—
348C22—4121no—
349C22—2061no—
350C22—2061no—
351C22C2×D4×D10311yescharacteristic
352C4—21no—
353C4—41no—
354C4—41no—
355C4—41no—
356C4—4121no—
357C4—4121no—
358C4—4121no—
359C4—2061no—
360C4—2061no—
361C4—2061no—
362C4C2×#1311010511yescharacteristic
363C4#1569306611yescharacteristic
364C2—41no—
365C2—42no—
366C2—8241no—
367C2—2062no—
368C2#2026843111yescharacteristic
369C2#135×D10311yescharacteristic
370C2#2026859811yescharacteristic
subgroupG/H
centerC22C2×D4×D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
Fitting#416×C103C2
socleC22×C103C22×D4
prime radical#20268429C2
hypercenter#416D103
hypocenterC103#3296
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C22×C4 ◁ #416

Complements

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

NH ≅ G/Ntype
1. #20268480C2semidirect
3. #20268147C2semidirect
4. #20268120C2semidirect
5. #20268115C2semidirect
6. #20268093C2semidirect
7. #20268031C2semidirect
8. #20268020C2semidirect
9. #20268016C2semidirect
10. #20267953C2semidirect
11. #20267943C2semidirect
12. #20267882C2semidirect
13. C8×C22⋊D103C2semidirect
14. #102×D103C2semidirect
15. #416×C103C2semidirect
17. C2×#13110095C22semidirect
23. #15693012C22semidirect
28. #15693000C22semidirect
33. #15692986C22semidirect
39. #15692954C22semidirect
40. #15692953C22semidirect
41. #15692952C22semidirect
42. Dic103⋊C8C22semidirect
43. #15692946C22semidirect
44. #15692945C22semidirect
49. C22⋊(C103⋊C8)C22semidirect
51. C8×Dic103C22semidirect
53. C22×C8×C103C22semidirect
54. #117×C103C22semidirect
55. #103×C103C22semidirect
56. #103×C103C22semidirect
186. C103#3296semidirect
200. #416D103semidirect
208. C22×C8C2×D103semidirect
225. #117C2×D103semidirect
234. #103C2×D103semidirect
235. #103C2×D103semidirect

Maximal subgroups

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

subgroupindex
#202684802
#202684292
#202681472
#202681202
#202681152
#202680932
#202680312
#202680202
#202680162
#202679532
#202679432
#202678822
C8×C22⋊D1032
#102×D1032
#416×C1032
#3296103