Finite Group Databasebeta

← #27206994

Subgroups — #27206994

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#20268487C211yesmaximal, characteristic, complemented
2#20268145C211yesmaximal, characteristic, complemented
3#20268124C211yesmaximal, characteristic, complemented
4#20268112C211yesmaximal, characteristic, complemented
5#20268091C211yesmaximal, characteristic, complemented
6#20268025C211yesmaximal, characteristic, complemented
7#20268022C211yesmaximal, characteristic, complemented
8#20268003C211yesmaximal, characteristic, complemented
9#20267936C211yesmaximal, characteristic, complemented
10#20267925C211yesmaximal, characteristic, complemented
11C4×#13110090C211yesmaximal, characteristic, complemented
12D4×C103⋊C8C211yesmaximal, characteristic, complemented
13#20267787C211yesmaximal, characteristic, complemented
14C2×#15692942C211yesmaximal, characteristic, complemented
15#546×C103C211yesmaximal, characteristic, complemented
16C2×#13110092C2211yescharacteristic, complemented
17C2×#13110090C2211yescharacteristic
18C2×#13110090C2211yescharacteristic
19C22×C103⋊C8C2211yescharacteristic
20C22×C103⋊C8C2211yescharacteristic, complemented
21#15693016—21no—
22#15693013C2211yescharacteristic, complemented
23#15693003—21no—
24#15692995C2211yescharacteristic
25#15692995C2211yescharacteristic, complemented
26#15692993—21no—
27C4×D412C2211yescharacteristic, complemented
28(C22⋊D103)⋊C4—21no—
29#15692980C2211yescharacteristic, complemented
30C2×C4⋊Dic103C2211yescharacteristic
31#15692954C2211yescharacteristic, complemented
32#15692954C2211yescharacteristic, complemented
33#15692952C2211yescharacteristic, complemented
34C4⋊(C103⋊C8)C2211yescharacteristic, complemented
35#15692945C2211yescharacteristic, complemented
36#15692945C2211yescharacteristic, complemented
37#15692945C2211yescharacteristic, complemented
38#15692942C2211yescharacteristic
39#15692942C2211yescharacteristic
40#15692942C2211yescharacteristic
41#15692942C2211yescharacteristic
42#15692942C2211yescharacteristic
43#15692942C2211yescharacteristic
44#15692941C2211yescharacteristic, complemented
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×D412C2311yescharacteristic
60C2×C22⋊D103—21no—
61C2×C22⋊D103—21no—
62C22×Dic103—21no—
63C2×C4×D103—21no—
64#13110092—41no—
65#13110090—22no—
66#13110090—41no—
67C2×C103⋊C8—41no—
68C2×C103⋊C8—41no—
69C2×C103⋊C8C2311yescharacteristic
70C2×C103⋊C8C2311yescharacteristic
71C2×C103⋊C8C2311yescharacteristic
72C2×C103⋊C8C2311yescharacteristic
73C4⋊Dic103—21no—
74C4⋊Dic103C2311yescharacteristic
75C4⋊Dic103C2311yescharacteristic
76C4⋊Dic103C2311yescharacteristic
77Dic103⋊C4—21no—
78Dic103⋊C4—21no—
79C22⋊Dic103—21no—
80(C2×D103)⋊C4—21no—
81(C2×D103)⋊C4—21no—
82(C2×D103)⋊C4—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
118C22×D103—21no—
119Q8×C103—21no—
120Q8×C103—21no—
121D4×C103—22no—
122D4×C103—21no—
123D4×C103—21no—
124D4×C103—21no—
125D4×C103—42no—
126D4×C103—42no—
127D4×C103—81no—
128D4×C103#4112yes—
129C2×C4×C103—21no—
130C2×C4×C103—21no—
131C2×C4×C103—21no—
132C2×C4×C103—21no—
133C2×C4×C103—21no—
134C2×C4×C103—21no—
135C2×C4×C103—42no—
136C2×C4×C103—81no—
137C2×C4×C103C2×D411yescharacteristic
138C2×C4×C103C2×D411yescharacteristic
139C2×C4×C103C2×D411yescharacteristic
140C2×C4×C103C2×D411yescharacteristic
141C2×C4×C103C2411yescharacteristic
142C22⋊D103—42no—
143C22⋊D103—81no—
144C2×Dic103—21no—
145C2×Dic103—21no—
146C2×Dic103—21no—
147C2×Dic103—81no—
148D412—21no—
149D412—21no—
150C4×D103—81no—
151C103⋊C8—21no—
152C103⋊C8—21no—
153C103⋊C8—21no—
154C103⋊C8—21no—
155C22×C103—21no—
156C22×C103—21no—
157C22×C103—21no—
158C22×C103—22no—
159C22×C103—21no—
160C22×C103—21no—
161C22×C103—41no—
162C22×C103—41no—
163C22×C103—41no—
164C22×C103—41no—
165C22×C103—41no—
166C22×C103—84no—
167C22×C103#13512yes—
168C22×C103C22×D411yescharacteristic
169C2×D103—41no—
170C2×D103—41no—
171C2×D103—41no—
172C4×C103—21no—
173C4×C103—21no—
174C4×C103—21no—
175C4×C103—21no—
176C4×C103—41no—
177C4×C103—41no—
178C4×C103C2×#4111yescharacteristic
179C4×C103H(5,𝔽2)11yescharacteristic
180Dic103—41no—
181Dic103—41no—
182Dic103—41no—
183C2×C103—22no—
184C2×C103—41no—
185C2×C103—42no—
186C2×C103—81no—
187C2×C103#54611yescharacteristic
188C2×C103C2×#13511yescharacteristic
189C2×C103#57611yescharacteristic
190D103—81no—
191#3297—1031nomaximal, Sylow
192C103#329711yescharacteristic, complemented, Sylow
193#553—1031no—
194#546D10311yescharacteristic, complemented
195#488—1031no—
196#484—1031no—
197#482—1031no—
198#478—1031no—
199#466—1031no—
200#465—1031no—
201#463—1031no—
202#449—1031no—
203#447—1031no—
204C4×D8—1031no—
205C8×D4—1031no—
206#416—1031no—
207C2×#102—1031no—
208C2×#41C2×D10311yescharacteristic
209C22×D4C2×D10311yescharacteristic
210C2×SD16—1031no—
211C2×D8—1031no—
212C2×D8—1031no—
213C22×C8—1031no—
214C22×C8—1031no—
215#126—2061no—
216#125—1031no—
217#124C2×D10311yescharacteristic
218#123—21no—
219#123—2061no—
220C22⋊Q8C2×D10311yescharacteristic
221#121—21no—
222#121—1031no—
223#121—1031no—
224#121—2061no—
225#121C2×D10311yescharacteristic
226#120—21no—
227C4×D4—1031no—
228C4×D4—2061no—
229C4×D4C2×D10311yescharacteristic
230C4×D4C2×D10311yescharacteristic
231#117—1031no—
232C2×C4⋊C4—1031no—
233C2×C22⋊C4—21no—
234#107—1031no—
235#107—1031no—
236#106—1031no—
237C4⋊C8—1031no—
238#103—1031no—
239#103—1031no—
240#103—1031no—
241#102—1031no—
242#102—1031no—
243#102—1031no—
244#102—1031no—
245#102—1031no—
246#102—1031no—
247#102—1031no—
248C22⋊C8—1031no—
249C22⋊C8—1031no—
250C4×C8—1031no—
251C24—21no—
252#41—22no—
253#41—41no—
254C2×Q8C22×D10311yescharacteristic
255C2×D4—22no—
256C2×D4—21no—
257C2×D4—21no—
258C2×D4—21no—
259C2×D4—41no—
260C2×D4—1031no—
261C2×D4—2061no—
262C2×D4—2061no—
263C2×D4C22⋊D10311yescharacteristic
264C2×D4C22×D10311yescharacteristic
265C2×D4C22×D10311yescharacteristic
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—2061no—
269C22×C4—2061no—
270C22×C4C22×D10311yescharacteristic
271C22×C4C22×D10311yescharacteristic
272SD16—4121no—
273D8—4121no—
274D8—2062no—
275C2×C8—1031no—
276C2×C8—1031no—
277C2×C8—1031no—
278C2×C8—1031no—
279C2×C8—4121no—
280C2×C8—4121no—
281C4⋊C4—21no—
282C4⋊C4—1031no—
283C4⋊C4—1031no—
284C4⋊C4—1031no—
285C4⋊C4—2061no—
286C4⋊C4—2061no—
287C4⋊C4—2061no—
288C4⋊C4C22⋊D10311yescharacteristic
289C4⋊C4C22×D10311yescharacteristic
290C22⋊C4—21no—
291C22⋊C4—21no—
292C22⋊C4—21no—
293C22⋊C4—21no—
294C22⋊C4—21no—
295C22⋊C4—2061no—
296C22⋊C4—2061no—
297C22⋊C4—2061no—
298C22⋊C4—2061no—
299C22⋊C4C22⋊D10311yescharacteristic
300C22⋊C4C22⋊D10311yescharacteristic
301C42—2061no—
302C42C22×D10311yescharacteristic
303C23—21no—
304C23—21no—
305C23—42no—
306C23—42no—
307C23—81no—
308C23—2061no—
309C23C2×C22⋊D10311yescharacteristic
310C23C2×C22⋊D10311yescharacteristic
311Q8—21no—
312Q8—21no—
313D4—22no—
314D4—21no—
315D4—21no—
316D4—21no—
317D4—42no—
318D4—42no—
319D4—81no—
320D4—8241no—
321D4—4122no—
322D4—2061no—
323D4—2061no—
324D4#1311010412yes—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—42no—
332C2×C4—81no—
333C2×C4—8241no—
334C2×C4—8241no—
335C2×C4—2061no—
336C2×C4—2061no—
337C2×C4—2061no—
338C2×C4C2×C22⋊D10311yescharacteristic
339C2×C4C2×C22⋊D10311yescharacteristic
340C2×C4C2×C22⋊D10311yescharacteristic
341C2×C4C2×C22⋊D10311yescharacteristic
342C2×C4C23×D10311yescharacteristic
343C8—2061no—
344C8—2061no—
345C8—2061no—
346C8—2061no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—22no—
353C22—41no—
354C22—41no—
355C22—41no—
356C22—41no—
357C22—41no—
358C22—84no—
359C22—4121no—
360C22—4121no—
361C22—4121no—
362C22#1569304112yes—
363C22C22×C22⋊D10311yescharacteristic
364C4—21no—
365C4—21no—
366C4—21no—
367C4—21no—
368C4—41no—
369C4—41no—
370C4—4121no—
371C4—4121no—
372C4—4121no—
373C4C2×#1311010411yescharacteristic
374C4#1569306611yescharacteristic
375C2—22no—
376C2—41no—
377C2—42no—
378C2—81no—
379C2—8241no—
380C2#2026843511yescharacteristic
381C2C2×#1569304111yescharacteristic
382C2#2026859411yescharacteristic
subgroupG/H
centerC22C22×C22⋊D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
Fitting#546×C103C2
socleC22×C103C22×D4
hypercenter#546D103
hypocenterC103#3297
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. #20268487C2semidirect
2. #20268145C2semidirect
3. #20268124C2semidirect
4. #20268112C2semidirect
5. #20268091C2semidirect
6. #20268025C2semidirect
7. #20268022C2semidirect
8. #20268003C2semidirect
9. #20267936C2semidirect
10. #20267925C2semidirect
11. C4×#13110090C2semidirect
12. D4×C103⋊C8C2semidirect
13. #20267787C2semidirect
14. C2×#15692942C2semidirect
15. #546×C103C2semidirect
16. C2×#13110092C22semidirect
20. C22×C103⋊C8C22semidirect
22. #15693013C22semidirect
25. #15692995C22semidirect
27. C4×D412C22semidirect
29. #15692980C22semidirect
31. #15692954C22semidirect
32. #15692954C22semidirect
33. #15692952C22semidirect
34. C4⋊(C103⋊C8)C22semidirect
35. #15692945C22semidirect
36. #15692945C22semidirect
37. #15692945C22semidirect
44. #15692941C22semidirect
46. C22⋊(C103⋊C8)C22semidirect
47. C4×C103⋊C8C22semidirect
192. C103#3297semidirect
194. #546D103semidirect

Maximal subgroups

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

subgroupindex
#202684872
#202681452
#202681242
#202681122
#202680912
#202680252
#202680222
#202680032
#202679362
#202679252
C4×#131100902
D4×C103⋊C82
#202677872
C2×#156929422
#546×C1032
#3297103