Finite Group Databasebeta

← #27205934

Subgroups — #27205934

Order 13184.

424 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20268301C211yesmaximal, characteristic, complemented
2#20268298C211yesmaximal, characteristic, complemented
3#20268133C211yesmaximal, characteristic, complemented
4#20268131C211yesmaximal, characteristic, complemented
5#20268114C211yesmaximal, characteristic, complemented
6#20268112C211yesmaximal, characteristic, complemented
7#20268031C211yesmaximal, characteristic, complemented
8#20268024C211yesmaximal, characteristic, complemented
9#20268019C211yesmaximal, characteristic, complemented
10#20268017C211yesmaximal, characteristic, complemented
11#20267953C211yesmaximal, characteristic, complemented
12#20267950C211yesmaximal, characteristic, complemented
13#20267933C211yesmaximal, characteristic, complemented
14C22⋊C8×D103C211yesmaximal, characteristic, complemented
15#449×C103C211yesmaximal, characteristic, complemented
16C2×#13110104C2211yescharacteristic
17C22×C4×D103C2211yescharacteristic
18C2×#13110095C2211yescharacteristic, complemented
19C2×#13110093C2211yescharacteristic, complemented
20C2×C8×D103C2211yescharacteristic
21C2×C8×D103C2211yescharacteristic
22#15693003—21no—
23#15693002—21no—
24#15693001C2211yescharacteristic
25#15693000C2211yescharacteristic
26#15692997C2211yescharacteristic
27#15692997C2211yescharacteristic
28#15692992C2211yescharacteristic
29#15692992C2211yescharacteristic
30#15692992C2211yescharacteristic
31#15692989—21no—
32#15692989—21no—
33D4×Dic103—21no—
34C4×C22⋊D103—21no—
35C4×C22⋊D103—21no—
36(C22⋊D103)⋊C4—21no—
37#15692980C2211yescharacteristic
38#15692979C2211yescharacteristic
39#15692955C2211yescharacteristic, complemented
40#15692954C2211yescharacteristic, complemented
41#15692953C2211yescharacteristic, complemented
42#15692952C2211yescharacteristic, complemented
43#15692946C2211yescharacteristic, complemented
44#15692946C2211yescharacteristic, complemented
45#15692945C2211yescharacteristic, complemented
46#15692942C2211yescharacteristic, complemented
47#15692942C2211yescharacteristic, complemented
48#15692942C2211yescharacteristic, complemented
49C22⋊(C103⋊C8)C2211yescharacteristic
50(C2×D103)⋊C8C2211yescharacteristic
51(C2×D103)⋊C8C2211yescharacteristic
52C2×#41×C103C2211yescharacteristic
53C2×SD16×C103C2211yescharacteristic, complemented
54C2×D8×C103C2211yescharacteristic, complemented
55#121×C103C2211yescharacteristic
56#103×C103C2211yescharacteristic, complemented
57#102×C103C2211yescharacteristic, complemented
58C22⋊C8×C103C2211yescharacteristic
59C23×D103D411yescharacteristic
60#13110104—41no—
61#13110104—41no—
62C2×Dic206C2311yescharacteristic
63C2×C22⋊D103—21no—
64C2×C22⋊D103—21no—
65C2×C22⋊D103—21no—
66C2×C22⋊D103—21no—
67C22×Dic103—21no—
68C22×Dic103D411yescharacteristic
69C2×C4×D103—41no—
70C2×C4×D103—41no—
71C2×C4×D103D411yescharacteristic
72C2×C4×D103D411yescharacteristic
73C2×C4×D103C2311yescharacteristic
74C2×C4×D103C2311yescharacteristic
75#13110095—41no—
76#13110093—41no—
77C2×C103⋊C8C2311yescharacteristic
78C2×C103⋊C8C2311yescharacteristic
79C8×D103—41no—
80C8×D103—41no—
81C4⋊Dic103—21no—
82C4⋊Dic103C2311yescharacteristic
83C4⋊Dic103C2311yescharacteristic
84C4⋊Dic103C2311yescharacteristic
85Dic103⋊C4—21no—
86Dic103⋊C4—21no—
87Dic103⋊C4—21no—
88C22⋊Dic103—21no—
89C22⋊Dic103—21no—
90C22⋊Dic103—21no—
91C22⋊Dic103—21no—
92C22⋊Dic103—21no—
93(C2×D103)⋊C4—21no—
94(C2×D103)⋊C4—21no—
95(C2×D103)⋊C4—21no—
96(C2×D103)⋊C4—21no—
97C4×Dic103—21no—
98C4×Dic103—21no—
99#41×C103—41no—
100#41×C103—41no—
101C2×Q8×C103C2311yescharacteristic
102C2×D4×C103—21no—
103C2×D4×C103—21no—
104C2×D4×C103C2311yescharacteristic
105C2×D4×C103C2311yescharacteristic
106C22×C4×C103—21no—
107C22×C4×C103C2311yescharacteristic
108SD16×C103—41no—
109D8×C103—41no—
110C2×C8×C103C2311yescharacteristic
111C2×C8×C103C2311yescharacteristic
112C4⋊C4×C103C2311yescharacteristic
113C22⋊C4×C103—21no—
114C23×C103—21no—
115C23×C103—21no—
116C23×C103C2×D411yescharacteristic
117C22×D103—22no—
118C22×D103—41no—
119C22×D103—41no—
120C22×D103C2×D411yescharacteristic
121C22×D103C2×D411yescharacteristic
122Q8×C103—21no—
123Q8×C103—21no—
124D4×C103—21no—
125D4×C103—21no—
126D4×C103—21no—
127D4×C103—21no—
128D4×C103—42no—
129D4×C103—42no—
130C2×C4×C103—21no—
131C2×C4×C103—21no—
132C2×C4×C103—21no—
133C2×C4×C103—21no—
134C2×C4×C103—42no—
135C2×C4×C103C2×D411yescharacteristic
136C2×C4×C103C2411yescharacteristic
137C22⋊D103—42no—
138C22⋊D103—42no—
139C22⋊D103—42no—
140C22⋊D103—42no—
141C2×Dic103—21no—
142C2×Dic103—21no—
143C2×Dic103—21no—
144C2×Dic103—21no—
145C2×Dic103—41no—
146C2×Dic103—42no—
147C2×Dic103C2×D411yescharacteristic
148C2×Dic103C2×D411yescharacteristic
149C4×D103—21no—
150C4×D103—21no—
151C4×D103—21no—
152C4×D103—21no—
153C4×D103—41no—
154C4×D103—41no—
155Dic206—21no—
156Dic206—21no—
157C8×C103—21no—
158C8×C103—21no—
159C103⋊C8—21no—
160C103⋊C8—21no—
161C22×C103—21no—
162C22×C103—21no—
163C22×C103—21no—
164C22×C103—41no—
165C22×C103—41no—
166C22×C103—41no—
167C22×C103—41no—
168C22×C103—41no—
169C22×C103—41no—
170C22×C103C22×D411yescharacteristic
171C2×D103—21no—
172C2×D103—21no—
173C2×D103—21no—
174C2×D103—21no—
175C2×D103—21no—
176C2×D103—44no—
177C2×D103#13512yes—
178C4×C103—21no—
179C4×C103—41no—
180C4×C103—41no—
181C4×C103H(5,𝔽2)11yescharacteristic
182C4×C103H(5,𝔽2)11yescharacteristic
183Dic103—21no—
184Dic103—21no—
185Dic103—41no—
186Dic103—41no—
187Dic103—41no—
188Dic103—41no—
189C2×C103—41no—
190C2×C103—81no—
191C2×C103—81no—
192C2×C103#53411yescharacteristic
193C2×C103C2×#13511yescharacteristic
194C2×C103#57511yescharacteristic
195D103—22no—
196D103—41no—
197#3191—1031nomaximal, Sylow
198C103#319111yescharacteristic, complemented, Sylow
199#525—1031no—
200#525—1031no—
201#485—1031no—
202#485—1031no—
203#482—1031no—
204#482—1031no—
205#467—1031no—
206#466—1031no—
207#465—1031no—
208#465—1031no—
209#452—1031no—
210#452—1031no—
211#449—1031no—
212#449D10311yescharacteristic, complemented
213C2×C22⋊C8—1031no—
214C2×#41—1031no—
215C2×#41C2×D10311yescharacteristic
216C23×C4—1031no—
217C2×Q16—1031no—
218C2×SD16—1031no—
219C2×SD16C2×D10311yescharacteristic, complemented
220C2×D8C2×D10311yescharacteristic, complemented
221C22×C8—1031no—
222C22×C8—1031no—
223#123—2061no—
224#123—2061no—
225C22⋊Q8—1031no—
226C22⋊Q8—1031no—
227C22⋊Q8—1031no—
228C22⋊Q8—1031no—
229#121—1031no—
230#121—1031no—
231#121—1031no—
232#121C2×D10311yescharacteristic
233#120—2061no—
234#120—2061no—
235C4×D4—2061no—
236C4×D4—2061no—
237C4×D4—2061no—
238C4×D4—2061no—
239#117—1031no—
240#117—1031no—
241#107—1031no—
242#107—1031no—
243#106—1031no—
244#106—1031no—
245#103—1031no—
246#103—1031no—
247#103—1031no—
248#103C2×D10311yescharacteristic, complemented
249#102—1031no—
250#102—1031no—
251#102—1031no—
252#102C2×D10311yescharacteristic, complemented
253C22⋊C8—1031no—
254C22⋊C8—1031no—
255C22⋊C8—1031no—
256C22⋊C8C2×D10311yescharacteristic
257C24—1031no—
258#41—41no—
259#41—41no—
260#41—4121no—
261#41—4121no—
262C2×Q8—1031no—
263C2×Q8C22×D10311yescharacteristic
264C2×D4—21no—
265C2×D4—21no—
266C2×D4—2061no—
267C2×D4—2061no—
268C2×D4—2061no—
269C2×D4—2061no—
270C2×D4C22×D10311yescharacteristic
271C2×D4C22×D10311yescharacteristic
272C22×C4—21no—
273C22×C4—1031no—
274C22×C4—1031no—
275C22×C4—1031no—
276C22×C4—1031no—
277C22×C4—1031no—
278C22×C4—4121no—
279C22×C4—4121no—
280C22×C4—2061no—
281C22×C4C22×D10311yescharacteristic
282Q16—4121no—
283SD16—41no—
284SD16—4121no—
285D8—41no—
286C2×C8—1031no—
287C2×C8—1031no—
288C2×C8—4121no—
289C2×C8—4121no—
290C2×C8C22×D10311yescharacteristic
291C2×C8C22×D10311yescharacteristic
292C4⋊C4—1031no—
293C4⋊C4—1031no—
294C4⋊C4—1031no—
295C4⋊C4—2061no—
296C4⋊C4—2061no—
297C4⋊C4—2061no—
298C4⋊C4—2061no—
299C4⋊C4C22×D10311yescharacteristic
300C22⋊C4—21no—
301C22⋊C4—2061no—
302C22⋊C4—2061no—
303C22⋊C4—2061no—
304C22⋊C4—2061no—
305C22⋊C4—2061no—
306C22⋊C4—2061no—
307C22⋊C4—2061no—
308C22⋊C4—2061no—
309C22⋊C4—2061no—
310C42—2061no—
311C42—2061no—
312C23—21no—
313C23—21no—
314C23—1031no—
315C23—1031no—
316C23—4121no—
317C23—4121no—
318C23—2062no—
319C23D4×D10311yescharacteristic
320Q8—21no—
321Q8—21no—
322Q8—2061no—
323Q8—2061no—
324D4—21no—
325D4—21no—
326D4—21no—
327D4—21no—
328D4—42no—
329D4—42no—
330D4—4122no—
331D4—4122no—
332D4—4122no—
333D4—4122no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—42no—
339C2×C4—1031no—
340C2×C4—1031no—
341C2×C4—4121no—
342C2×C4—4121no—
343C2×C4—4122no—
344C2×C4—4121no—
345C2×C4—2061no—
346C2×C4—2061no—
347C2×C4—2061no—
348C2×C4—2061no—
349C2×C4—2061no—
350C2×C4—2061no—
351C2×C4—2061no—
352C2×C4—2061no—
353C2×C4D4×D10311yescharacteristic
354C2×C4C23×D10311yescharacteristic
355C8—21no—
356C8—21no—
357C8—2061no—
358C8—2061no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22—41no—
367C22—41no—
368C22—1032no—
369C22—4124no—
370C22—2061no—
371C22—2061no—
372C22—2061no—
373C22—2061no—
374C22—2061no—
375C22C2×D4×D10311yescharacteristic
376C4—21no—
377C4—41no—
378C4—41no—
379C4—4121no—
380C4—4121no—
381C4—4121no—
382C4—4121no—
383C4—2061no—
384C4—2061no—
385C4#1569306611yescharacteristic
386C4#1569306611yescharacteristic
387C2—41no—
388C2—81no—
389C2—81no—
390C2—4121no—
391C2—2062no—
392C2#2026835111yescharacteristic
393C2#135×D10311yescharacteristic
394C2#2026858711yescharacteristic
subgroupG/H
centerC22C2×D4×D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
Fitting#449×C103C2
socleC22×C103C22×D4
hypercenter#449D103
hypocenterC103#3191
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

Complements

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

NH ≅ G/Ntype
1. #20268301C2semidirect
2. #20268298C2semidirect
3. #20268133C2semidirect
4. #20268131C2semidirect
5. #20268114C2semidirect
6. #20268112C2semidirect
7. #20268031C2semidirect
8. #20268024C2semidirect
9. #20268019C2semidirect
10. #20268017C2semidirect
11. #20267953C2semidirect
12. #20267950C2semidirect
13. #20267933C2semidirect
14. C22⋊C8×D103C2semidirect
15. #449×C103C2semidirect
18. C2×#13110095C22semidirect
19. C2×#13110093C22semidirect
39. #15692955C22semidirect
40. #15692954C22semidirect
41. #15692953C22semidirect
42. #15692952C22semidirect
43. #15692946C22semidirect
44. #15692946C22semidirect
45. #15692945C22semidirect
46. #15692942C22semidirect
47. #15692942C22semidirect
48. #15692942C22semidirect
53. C2×SD16×C103C22semidirect
54. C2×D8×C103C22semidirect
56. #103×C103C22semidirect
57. #102×C103C22semidirect
198. C103#3191semidirect
212. #449D103semidirect
219. C2×SD16C2×D103semidirect
220. C2×D8C2×D103semidirect
248. #103C2×D103semidirect
252. #102C2×D103semidirect

Maximal subgroups

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

subgroupindex
#202683012
#202682982
#202681332
#202681312
#202681142
#202681122
#202680312
#202680242
#202680192
#202680172
#202679532
#202679502
#202679332
C22⋊C8×D1032
#449×C1032
#3191103