Finite Group Databasebeta

← #27205385

Subgroups — #27205385

Order 13184.

418 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20268395C211yesmaximal, characteristic, complemented
2#20268263C211yesmaximal, characteristic, complemented
3#20268114C211yesmaximal, characteristic, complemented
4#20268113C211yesmaximal, characteristic, complemented
5#20268092C211yesmaximal, characteristic, complemented
6#20268091C211yesmaximal, characteristic, complemented
7#20267983C211yesmaximal, characteristic, complemented
8#20267923C211yesmaximal, characteristic, complemented
9#20267923C211yesmaximal, characteristic, complemented
10#20267903C211yesmaximal, characteristic, complemented
11#20267900C211yesmaximal, characteristic, complemented
12D8×Dic103C211yesmaximal, characteristic, complemented
13#20267871C211yesmaximal, characteristic, complemented
14#20267851C211yesmaximal, characteristic, complemented
15#459×C103C211yesmaximal, characteristic, complemented
16C2×D4×D103C2211yescharacteristic
17C2×#13110090C2211yescharacteristic
18C2×#13110090C2211yescharacteristic
19#15693013C2211yescharacteristic, complemented
20#15693002—21no—
21#15693002—21no—
22#15692993—21no—
23#15692993—21no—
24#15692992C2211yescharacteristic
25#15692992C2211yescharacteristic
26C4×D412C2211yescharacteristic
27D4×Dic103C2211yescharacteristic
28D4×Dic103C2211yescharacteristic, complemented
29D4×Dic103C2211yescharacteristic, complemented
30#15692983C2211yescharacteristic
31C4×C22⋊D103—21no—
32(C22⋊D103)⋊C4—21no—
33#15692979C2211yescharacteristic
34#15692978C2211yescharacteristic
35C2×(C2×D103)⋊C4—21no—
36C22⋊C4×D103—21no—
37#15692955C2211yescharacteristic, complemented
38#15692954C2211yescharacteristic, complemented
39#15692953C2211yescharacteristic, complemented
40#15692952C2211yescharacteristic, complemented
41C4⋊(C103⋊C8)C2211yescharacteristic, complemented
42#15692943C2211yescharacteristic
43#15692943C2211yescharacteristic
44#15692942C2211yescharacteristic
45#15692942C2211yescharacteristic
46#15692942C2211yescharacteristic, complemented
47#15692942C2211yescharacteristic, complemented
48(C2×D103)⋊C8C2211yescharacteristic
49(C2×D103)⋊C8C2211yescharacteristic
50#15692931C2211yescharacteristic, complemented
51C8×Dic103C2211yescharacteristic, complemented
52C2×D8×C103C2211yescharacteristic
53C2×D8×C103C2211yescharacteristic
54#127×C103C2211yescharacteristic, complemented
55C4×D4×C103C2211yescharacteristic
56C4⋊C8×C103C2211yescharacteristic, complemented
57#102×C103C2211yescharacteristic, complemented
58#102×C103C2211yescharacteristic, complemented
59C23×D103—21no—
60C2×D412C2311yescharacteristic
61C2×C22⋊D103—21no—
62C2×C22⋊D103—21no—
63C2×C22⋊D103—21no—
64D4×D103—22no—
65D4×D103—22no—
66C22×Dic103—21no—
67C22×Dic103—21no—
68C22×Dic103—21no—
69C2×C4×D103—21no—
70C2×C4×D103—21no—
71C2×C4×D103C2311yescharacteristic
72#13110090—22no—
73#13110090—22no—
74C2×C103⋊C8C2311yescharacteristic
75C2×C103⋊C8C2311yescharacteristic
76C4⋊Dic103C2311yescharacteristic
77C4⋊Dic103C2311yescharacteristic
78C4⋊Dic103C2311yescharacteristic
79Dic103⋊C4—21no—
80Dic103⋊C4—21no—
81Dic103⋊C4D411yescharacteristic
82Dic103⋊C4D411yescharacteristic
83C22⋊Dic103—21no—
84C22⋊Dic103—21no—
85C22⋊Dic103—21no—
86C22⋊Dic103—21no—
87C22⋊Dic103—21no—
88(C2×D103)⋊C4—21no—
89(C2×D103)⋊C4—21no—
90(C2×D103)⋊C4—21no—
91(C2×D103)⋊C4D411yescharacteristic
92(C2×D103)⋊C4D411yescharacteristic
93C4×Dic103—21no—
94C4×Dic103C2311yescharacteristic
95C2×D4×C103—21no—
96C2×D4×C103—21no—
97C2×D4×C103C2311yescharacteristic
98C2×D4×C103C2311yescharacteristic
99C2×D4×C103C2311yescharacteristic
100C22×C4×C103—21no—
101D8×C103—22no—
102D8×C103—22no—
103C2×C8×C103C2311yescharacteristic
104C2×C8×C103C2311yescharacteristic
105C4⋊C4×C103C2311yescharacteristic
106C22⋊C4×C103—21no—
107C42×C103C2311yescharacteristic
108C23×C103—21no—
109C23×C103—21no—
110C23×C103—21no—
111C22×D103—21no—
112C22×D103—24no—
113C22×D103—81no—
114C22×D103—81no—
115C22×D103C2×D411yescharacteristic
116D4×C103—21no—
117D4×C103—21no—
118D4×C103—21no—
119D4×C103—21no—
120D4×C103—21no—
121D4×C103—81no—
122D4×C103—81no—
123D4×C103#4112yes—
124C2×C4×C103—21no—
125C2×C4×C103—81no—
126C2×C4×C103C2×D411yescharacteristic
127C2×C4×C103C2×D411yescharacteristic
128C2×C4×C103C2411yescharacteristic
129C22⋊D103—24no—
130C22⋊D103—81no—
131C22⋊D103—81no—
132C2×Dic103—21no—
133C2×Dic103—21no—
134C2×Dic103—21no—
135C2×Dic103—81no—
136C2×Dic103—81no—
137C2×Dic103—81no—
138C2×Dic103C2×D411yescharacteristic
139C2×Dic103C2×D411yescharacteristic
140C2×Dic103C2×D411yescharacteristic
141D412—21no—
142D412#4112yes—
143C4×D103—21no—
144C4×D103—21no—
145C4×D103—81no—
146C4×D103—81no—
147C8×C103—21no—
148C8×C103—21no—
149C103⋊C8—21no—
150C103⋊C8—21no—
151C22×C103—22no—
152C22×C103—41no—
153C22×C103—41no—
154C22×C103—41no—
155C22×C103—41no—
156C22×C103—41no—
157C22×C103—41no—
158C22×C103—41no—
159C22×C103—41no—
160C22×C103C22×D411yescharacteristic
161C2×D103—21no—
162C2×D103—22no—
163C2×D103—21no—
164C2×D103—21no—
165C2×D103—41no—
166C2×D103—41no—
167C2×D103—84no—
168C4×C103—21no—
169C4×C103—21no—
170C4×C103—41no—
171C4×C103C2×#4111yescharacteristic
172C4×C103C2×#4111yescharacteristic
173Dic103—21no—
174Dic103—21no—
175Dic103—21no—
176Dic103—41no—
177Dic103—41no—
178Dic103—41no—
179C2×C103—42no—
180C2×C103—81no—
181C2×C103—81no—
182C2×C103#52511yescharacteristic
183C2×C103#57611yescharacteristic
184C2×C103#57611yescharacteristic
185D103—41no—
186D103—42no—
187#3122—1031nomaximal, Sylow
188C103#312211yescharacteristic, complemented, Sylow
189#540—1031no—
190#518—1031no—
191#482—1031no—
192#482—1031no—
193#478—1031no—
194#478—1031no—
195#459—1031no—
196#459D10311yescharacteristic, complemented
197#447—1031no—
198#447—1031no—
199#442—1031no—
200#442—1031no—
201C4×D8—1031no—
202C4×D8—1031no—
203#433—1031no—
204C22×D4—1031no—
205C2×D8—1031no—
206C2×D8—1031no—
207C2×D8C2×D10311yescharacteristic
208C2×D8C2×D10311yescharacteristic
209#127C2×D10311yescharacteristic, complemented
210#125—1031no—
211#123—2061no—
212#123—2061no—
213#121—1031no—
214#121—1031no—
215#121—2061no—
216#121—2061no—
217C4×D4—1031no—
218C4×D4—1031no—
219C4×D4—1031no—
220C4×D4—1031no—
221C4×D4—1031no—
222C4×D4—2061no—
223C4×D4—2061no—
224C4×D4C2×D10311yescharacteristic
225#117—1031no—
226#117—1031no—
227C2×C22⋊C4—2061no—
228C2×C22⋊C4—2061no—
229#107—1031no—
230#107—1031no—
231#106—1031no—
232#106—1031no—
233C4⋊C8—1031no—
234C4⋊C8C2×D10311yescharacteristic, complemented
235#102—1031no—
236#102—1031no—
237#102—1031no—
238#102—1031no—
239#102—1031no—
240#102—1031no—
241#102C2×D10311yescharacteristic, complemented
242#102C2×D10311yescharacteristic, complemented
243C22⋊C8—1031no—
244C22⋊C8—1031no—
245#97—1031no—
246C4×C8—1031no—
247C24—2061no—
248C2×D4—21no—
249C2×D4—21no—
250C2×D4—1031no—
251C2×D4—2061no—
252C2×D4—2062no—
253C2×D4—2061no—
254C2×D4—2061no—
255C2×D4—2062no—
256C2×D4C22×D10311yescharacteristic
257C2×D4C22×D10311yescharacteristic
258C2×D4C22×D10311yescharacteristic
259C22×C4—21no—
260C22×C4—1031no—
261C22×C4—2061no—
262C22×C4—2061no—
263C22×C4—2061no—
264C22×C4—2061no—
265C22×C4—2061no—
266D8—22no—
267D8—22no—
268D8—2062no—
269D8—2062no—
270C2×C8—1031no—
271C2×C8—1031no—
272C2×C8C22×D10311yescharacteristic
273C2×C8C22×D10311yescharacteristic
274C4⋊C4—1031no—
275C4⋊C4—1031no—
276C4⋊C4—1031no—
277C4⋊C4—1031no—
278C4⋊C4—1031no—
279C4⋊C4—2061no—
280C4⋊C4—2061no—
281C4⋊C4C22×D10311yescharacteristic
282C22⋊C4—21no—
283C22⋊C4—1031no—
284C22⋊C4—1031no—
285C22⋊C4—2061no—
286C22⋊C4—2061no—
287C22⋊C4—2061no—
288C22⋊C4—2061no—
289C22⋊C4—2061no—
290C22⋊C4—2061no—
291C22⋊C4—2061no—
292C22⋊C4—2061no—
293C42—1031no—
294C42—2061no—
295C42C22×D10311yescharacteristic
296C23—21no—
297C23—21no—
298C23—21no—
299C23—8241no—
300C23—8241no—
301C23—1031no—
302C23—2064no—
303C23—2061no—
304D4—21no—
305D4—21no—
306D4—21no—
307D4—21no—
308D4—21no—
309D4—81no—
310D4—81no—
311D4—8241no—
312D4—8241no—
313D4—1032no—
314D4—2064no—
315D4—2061no—
316D4#1311010412yes—
317C2×C4—21no—
318C2×C4—81no—
319C2×C4—8241no—
320C2×C4—8241no—
321C2×C4—8241no—
322C2×C4—8241no—
323C2×C4—8241no—
324C2×C4—1031no—
325C2×C4—1031no—
326C2×C4—1031no—
327C2×C4—2061no—
328C2×C4—2061no—
329C2×C4—2061no—
330C2×C4—2061no—
331C2×C4—2061no—
332C2×C4D4×D10311yescharacteristic
333C2×C4D4×D10311yescharacteristic
334C2×C4C23×D10311yescharacteristic
335C8—21no—
336C8—21no—
337C8—2061no—
338C8—2061no—
339C22—22no—
340C22—41no—
341C22—41no—
342C22—41no—
343C22—41no—
344C22—41no—
345C22—41no—
346C22—41no—
347C22—41no—
348C22—8244no—
349C22—4121no—
350C22—4121no—
351C22—2061no—
352C22—2062no—
353C22—2061no—
354C22—2061no—
355C22C2×D4×D10311yescharacteristic
356C4—21no—
357C4—21no—
358C4—41no—
359C4—4121no—
360C4—4121no—
361C4—4121no—
362C4—2061no—
363C4—2061no—
364C4—2061no—
365C4#41×D10311yescharacteristic
366C4C2×#1311010411yescharacteristic
367C2—42no—
368C2—81no—
369C2—81no—
370C2—4121no—
371C2—4122no—
372C2#2026830111yescharacteristic
373C2#2026859211yescharacteristic
374C2#2026859511yescharacteristic
subgroupG/H
centerC22C2×D4×D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
Fitting#459×C103C2
socleC22×C103C22×D4
hypercenter#459D103
hypocenterC103#3122
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. #20268395C2semidirect
2. #20268263C2semidirect
3. #20268114C2semidirect
4. #20268113C2semidirect
5. #20268092C2semidirect
6. #20268091C2semidirect
7. #20267983C2semidirect
8. #20267923C2semidirect
9. #20267923C2semidirect
10. #20267903C2semidirect
11. #20267900C2semidirect
12. D8×Dic103C2semidirect
13. #20267871C2semidirect
14. #20267851C2semidirect
15. #459×C103C2semidirect
19. #15693013C22semidirect
28. D4×Dic103C22semidirect
29. D4×Dic103C22semidirect
37. #15692955C22semidirect
38. #15692954C22semidirect
39. #15692953C22semidirect
40. #15692952C22semidirect
41. C4⋊(C103⋊C8)C22semidirect
46. #15692942C22semidirect
47. #15692942C22semidirect
50. #15692931C22semidirect
51. C8×Dic103C22semidirect
54. #127×C103C22semidirect
56. C4⋊C8×C103C22semidirect
57. #102×C103C22semidirect
58. #102×C103C22semidirect
188. C103#3122semidirect
196. #459D103semidirect
209. #127C2×D103semidirect
234. C4⋊C8C2×D103semidirect
241. #102C2×D103semidirect
242. #102C2×D103semidirect

Maximal subgroups

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

subgroupindex
#202683952
#202682632
#202681142
#202681132
#202680922
#202680912
#202679832
#202679232
#202679032
#202679002
D8×Dic1032
#202678712
#202678512
#459×C1032
#3122103