Finite Group Databasebeta

← #27206012

Subgroups — #27206012

Order 13184.

410 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#20268364C211yesmaximal, characteristic, complemented
2#20268357C211yesmaximal, characteristic
3#20268134C211yesmaximal, characteristic, complemented
4#20268131C211yesmaximal, characteristic, complemented
5#20268118C211yesmaximal, characteristic, complemented
6#20268113C211yesmaximal, characteristic, complemented
7#20268037C211yesmaximal, characteristic, complemented
8#20268022C211yesmaximal, characteristic, complemented
9#20268018C211yesmaximal, characteristic, complemented
10#20267943C211yesmaximal, characteristic, complemented
11#20267940C211yesmaximal, characteristic, complemented
12#20267931C211yesmaximal, characteristic, complemented
13#20267928C211yesmaximal, characteristic, complemented
14#20267759C211yesmaximal, characteristic, complemented
15#468×C103C211yesmaximal, characteristic, complemented
16C2×#13110105C2211yescharacteristic
17C2×Q8×D103C2211yescharacteristic, complemented
18C2×D4×D103C2211yescharacteristic
19C2×#13110094C2211yescharacteristic
20C2×#13110093C2211yescharacteristic
21C2×#13110092C2211yescharacteristic
22C22×C103⋊C8C2211yescharacteristic, complemented
23#15693020—21no—
24#15693017—21no—
25#15693007—21no—
26#15693007—21no—
27#15693006—21no—
28#15693003—21no—
29#15693001C2211yescharacteristic
30#15693000C2211yescharacteristic, complemented
31#15692997C2211yescharacteristic
32#15692996C2211yescharacteristic
33#15692995C2211yescharacteristic
34#15692992C2211yescharacteristic
35#15692991—21no—
36#15692989—21no—
37#15692979C2211yescharacteristic
38#15692979C2211yescharacteristic, complemented
39#15692955C2211yescharacteristic, complemented
40#15692952C2211yescharacteristic, complemented
41#15692952C2211yescharacteristic, complemented
42#15692946C2211yescharacteristic, complemented
43#15692945C2211yescharacteristic, complemented
44#15692944C2211yescharacteristic, complemented
45#15692943C2211yescharacteristic
46#15692942C2211yescharacteristic
47#15692941C2211yescharacteristic
48(C2×D103)⋊C8C2211yescharacteristic
49(C2×D103)⋊C8C2211yescharacteristic
50(C2×D103)⋊C8C2211yescharacteristic, complemented
51(C2×D103)⋊C8C2211yescharacteristic, complemented
52C2×SD16×C103C2211yescharacteristic
53C2×M16×C103C2211yescharacteristic, complemented
54C22⋊Q8×C103C2211yescharacteristic, complemented
55#121×C103C2211yescharacteristic
56#107×C103C2211yescharacteristic, complemented
57#103×C103C2211yescharacteristic, complemented
58#102×C103C2211yescharacteristic
59C23×D103—21no—
60#13110105—41no—
61#13110105—41no—
62C2×Dic206—21no—
63C2×Dic206D411yescharacteristic
64C2×Dic206C2311yescharacteristic
65Q8×D103—41no—
66Q8×D103—41no—
67C2×D412—21no—
68C2×D412D411yescharacteristic
69C2×D412C2311yescharacteristic
70C2×C22⋊D103—21no—
71C2×C22⋊D103—21no—
72C2×C22⋊D103—21no—
73C2×C22⋊D103D411yescharacteristic
74C2×C22⋊D103D411yescharacteristic
75D4×D103—41no—
76D4×D103—41no—
77C2×C4×D103—21no—
78C2×C4×D103C2311yescharacteristic
79C2×C4×D103C2311yescharacteristic
80#13110094—41no—
81#13110093—41no—
82#13110092—41no—
83C2×C103⋊C8—41no—
84C2×C103⋊C8C2311yescharacteristic
85C2×C103⋊C8C2311yescharacteristic
86C4⋊Dic103—21no—
87C4⋊Dic103C2311yescharacteristic
88C4⋊Dic103C2311yescharacteristic
89Dic103⋊C4—21no—
90Dic103⋊C4—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—
97(C2×D103)⋊C4—21no—
98(C2×D103)⋊C4—21no—
99C4×Dic103—21no—
100C4×Dic103—21no—
101C2×Q8×C103C2311yescharacteristic
102C2×D4×C103—21no—
103C2×D4×C103C2311yescharacteristic
104C22×C4×C103C2311yescharacteristic
105SD16×C103—41no—
106M16×C103—41no—
107C2×C8×C103C2311yescharacteristic
108C2×C8×C103C2311yescharacteristic
109C4⋊C4×C103—21no—
110C4⋊C4×C103C2311yescharacteristic
111C4⋊C4×C103C2311yescharacteristic
112C22⋊C4×C103—21no—
113C22⋊C4×C103—21no—
114C23×C103—21no—
115C23×C103C2×D411yescharacteristic
116C22×D103—21no—
117C22×D103—42no—
118C22×D103—81no—
119C22×D103—81no—
120C22×D103C2×D411yescharacteristic
121C22×D103C2×D411yescharacteristic
122Q8×C103—21no—
123Q8×C103—21no—
124D4×C103—21no—
125D4×C103—21no—
126D4×C103—81no—
127C2×C4×C103—21no—
128C2×C4×C103—21no—
129C2×C4×C103—21no—
130C2×C4×C103—21no—
131C2×C4×C103—21no—
132C2×C4×C103C2×D411yescharacteristic
133C2×C4×C103C2411yescharacteristic
134C22⋊D103—41no—
135C22⋊D103—41no—
136C22⋊D103—42no—
137C22⋊D103—81no—
138C22⋊D103—81no—
139C2×Dic103—21no—
140C2×Dic103—21no—
141C2×Dic103—21no—
142C2×Dic103C2×D411yescharacteristic
143C2×Dic103C2×D411yescharacteristic
144D412—21no—
145D412—21no—
146D412—41no—
147D412—81no—
148C4×D103—21no—
149C4×D103—21no—
150C4×D103—21no—
151C4×D103—21no—
152C4×D103—42no—
153Dic206—21no—
154Dic206—21no—
155Dic206—41no—
156Dic206—42no—
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×C103C22×D411yescharacteristic
168C2×D103—21no—
169C2×D103—21no—
170C2×D103—21no—
171C2×D103—21no—
172C2×D103—21no—
173C2×D103—21no—
174C2×D103—41no—
175C2×D103—41no—
176C2×D103—41no—
177C2×D103—84no—
178C4×C103—21no—
179C4×C103—41no—
180C4×C103—41no—
181C4×C103—41no—
182C4×C103H(5,𝔽2)11yescharacteristic
183C4×C103H(5,𝔽2)11yescharacteristic
184Dic103—21no—
185Dic103—21no—
186Dic103—41no—
187Dic103—41no—
188Dic103—41no—
189C2×C103—41no—
190C2×C103—81no—
191C2×C103#53411yescharacteristic
192C2×C103#57711yescharacteristic
193C2×C103#57711yescharacteristic
194D103—41no—
195D103—41no—
196D103—81no—
197#3200—1031nomaximal, Sylow
198C103#320011yescharacteristic, complemented, Sylow
199#536—1031no—
200#535—1031no—
201#485—1031no—
202#485—1031no—
203#482—1031no—
204#482—1031no—
205#468—1031no—
206#468D10311yescharacteristic, complemented
207#465—1031no—
208#465—1031no—
209#450—1031no—
210#450—1031no—
211#448—1031no—
212#448—1031no—
213#408—1031no—
214C2×#41—1031no—
215C22×Q8—1031no—
216C22×D4—1031no—
217C2×SD16—1031no—
218C2×SD16—1031no—
219C2×SD16—1031no—
220C2×SD16C2×D10311yescharacteristic
221C2×M16C2×D10311yescharacteristic, complemented
222C22×C8—1031no—
223C4⋊Q8—2061no—
224#127—2061no—
225#124—2061no—
226#124—2061no—
227#123—2061no—
228#123—2061no—
229C22⋊Q8—1031no—
230C22⋊Q8—1031no—
231C22⋊Q8—1031no—
232C22⋊Q8C2×D10311yescharacteristic, complemented
233#121—1031no—
234#121—1031no—
235#121—1031no—
236#121C2×D10311yescharacteristic
237#120—2061no—
238#120—2061no—
239#117—1031no—
240#117—1031no—
241#107—1031no—
242#107C2×D10311yescharacteristic, complemented
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
253C22⋊C8—1031no—
254C22⋊C8—1031no—
255C22⋊C8—1031no—
256C22⋊C8—1031no—
257C24—2061no—
258#41—4121no—
259#41—4121no—
260C2×Q8—1031no—
261C2×Q8—1031no—
262C2×Q8—4121no—
263C2×Q8—4121no—
264C2×Q8—2061no—
265C2×Q8C22×D10311yescharacteristic
266C2×D4—21no—
267C2×D4—1031no—
268C2×D4—1031no—
269C2×D4—1031no—
270C2×D4—1031no—
271C2×D4—4121no—
272C2×D4—4121no—
273C2×D4—2061no—
274C2×D4—2061no—
275C2×D4—2061no—
276C2×D4—2061no—
277C2×D4C22×D10311yescharacteristic
278C22×C4—1031no—
279C22×C4—1031no—
280C22×C4—2061no—
281C22×C4C22×D10311yescharacteristic
282SD16—41no—
283SD16—4121no—
284SD16—4121no—
285SD16—4121no—
286M16—41no—
287C2×C8—1031no—
288C2×C8—1031no—
289C2×C8—4121no—
290C2×C8C22×D10311yescharacteristic
291C2×C8C22×D10311yescharacteristic
292C4⋊C4—21no—
293C4⋊C4—1031no—
294C4⋊C4—1031no—
295C4⋊C4—2061no—
296C4⋊C4—2061no—
297C4⋊C4—2061no—
298C4⋊C4C22×D10311yescharacteristic
299C4⋊C4C22×D10311yescharacteristic
300C22⋊C4—21no—
301C22⋊C4—21no—
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—8241no—
314C23—8241no—
315C23—1031no—
316C23—1031no—
317C23—4122no—
318C23—2061no—
319C23D4×D10311yescharacteristic
320Q8—21no—
321Q8—21no—
322Q8—4121no—
323Q8—4122no—
324Q8—2061no—
325Q8—2061no—
326D4—21no—
327D4—21no—
328D4—81no—
329D4—8241no—
330D4—8241no—
331D4—8241no—
332D4—4121no—
333D4—4121no—
334D4—4121no—
335D4—4122no—
336D4—2061no—
337D4—2061no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—1031no—
344C2×C4—1031no—
345C2×C4—4122no—
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—8244no—
366C22—4121no—
367C22—4121no—
368C22—4121no—
369C22—2061no—
370C22—2061no—
371C22—2061no—
372C22—2061no—
373C22—2061no—
374C22—2061no—
375C22C2×D4×D10311yescharacteristic
376C4—21no—
377C4—41no—
378C4—41no—
379C4—41no—
380C4—4121no—
381C4—4121no—
382C4—4121no—
383C4—2061no—
384C4—2061no—
385C4#1569306611yescharacteristic
386C4#1569306711yescharacteristic
387C2—41no—
388C2—81no—
389C2—8241no—
390C2—4121no—
391C2—4121no—
392C2#2026834911yescharacteristic
393C2#2026860011yescharacteristic
394C2#2026860111yescharacteristic
subgroupG/H
centerC22C2×D4×D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
Fitting#468×C103C2
socleC22×C103C22×D4
prime radical#20268357C2
hypercenter#468D103
hypocenterC103#3200
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C22×C4 ◁ #468

Complements

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

NH ≅ G/Ntype
1. #20268364C2semidirect
3. #20268134C2semidirect
4. #20268131C2semidirect
5. #20268118C2semidirect
6. #20268113C2semidirect
7. #20268037C2semidirect
8. #20268022C2semidirect
9. #20268018C2semidirect
10. #20267943C2semidirect
11. #20267940C2semidirect
12. #20267931C2semidirect
13. #20267928C2semidirect
14. #20267759C2semidirect
15. #468×C103C2semidirect
17. C2×Q8×D103C22semidirect
22. C22×C103⋊C8C22semidirect
30. #15693000C22semidirect
38. #15692979C22semidirect
39. #15692955C22semidirect
40. #15692952C22semidirect
41. #15692952C22semidirect
42. #15692946C22semidirect
43. #15692945C22semidirect
44. #15692944C22semidirect
50. (C2×D103)⋊C8C22semidirect
51. (C2×D103)⋊C8C22semidirect
53. C2×M16×C103C22semidirect
54. C22⋊Q8×C103C22semidirect
56. #107×C103C22semidirect
57. #103×C103C22semidirect
198. C103#3200semidirect
206. #468D103semidirect
221. C2×M16C2×D103semidirect
232. C22⋊Q8C2×D103semidirect
242. #107C2×D103semidirect
248. #103C2×D103semidirect

Maximal subgroups

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

subgroupindex
#202683642
#202683572
#202681342
#202681312
#202681182
#202681132
#202680372
#202680222
#202680182
#202679432
#202679402
#202679312
#202679282
#202677592
#468×C1032
#3200103