Finite Group Databasebeta

← #27205896

Subgroups — #27205896

Order 13184.

468 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22⋊Q8×D103C211yesmaximal, characteristic, complemented
2#121×D103C211yesmaximal, characteristic
3#20268123C211yesmaximal, characteristic, complemented
4#20268120C211yesmaximal, characteristic, complemented
5#20268111C211yesmaximal, characteristic, complemented
6#20268108C211yesmaximal, characteristic, complemented
7#20268022C211yesmaximal, characteristic, complemented
8#20268020C211yesmaximal, characteristic, complemented
9#20268018C211yesmaximal, characteristic, complemented
10#20267943C211yesmaximal, characteristic, complemented
11#20267940C211yesmaximal, characteristic, complemented
12#20267931C211yesmaximal, characteristic, complemented
13#20267928C211yesmaximal, characteristic, complemented
14C2×(C2×D103)⋊C8C211yesmaximal, characteristic, complemented
15#465×C103C211yesmaximal, characteristic, complemented
16C2×Q8×D103C2211yescharacteristic, complemented
17C2×D4×D103—21no—
18C2×D4×D103C2211yescharacteristic
19C22×C4×D103C2211yescharacteristic
20C2×#13110094C2211yescharacteristic, complemented
21C2×#13110093C2211yescharacteristic, complemented
22C2×#13110092C2211yescharacteristic, complemented
23C22×C103⋊C8C2211yescharacteristic, complemented
24#15693001C2211yescharacteristic
25#15693000C2211yescharacteristic, complemented
26#15692999—21no—
27#15692998—21no—
28#15692997C2211yescharacteristic
29#15692996C2211yescharacteristic
30#15692995C2211yescharacteristic
31#15692994—21no—
32#15692993—21no—
33#15692992C2211yescharacteristic
34C4⋊C4×D103—21no—
35C4⋊C4×D103C2211yescharacteristic
36C4⋊C4×D103C2211yescharacteristic, complemented
37C22⋊C4×D103—21no—
38C22⋊C4×D103—21no—
39#15692953C2211yescharacteristic, complemented
40#15692952C2211yescharacteristic, complemented
41#15692952C2211yescharacteristic, complemented
42#15692946C2211yescharacteristic, complemented
43#15692945C2211yescharacteristic, complemented
44#15692944C2211yescharacteristic, complemented
45#15692943C2211yescharacteristic, complemented
46#15692942C2211yescharacteristic, complemented
47#15692941C2211yescharacteristic, complemented
48(C2×D103)⋊C8C2211yescharacteristic
49(C2×D103)⋊C8C2211yescharacteristic
50(C2×D103)⋊C8C2211yescharacteristic, complemented
51(C2×D103)⋊C8C2211yescharacteristic, complemented
52C2×SD16×C103C2211yescharacteristic, complemented
53C22×C8×C103C2211yescharacteristic, complemented
54C22⋊Q8×C103C2211yescharacteristic, complemented
55#121×C103C2211yescharacteristic
56#106×C103C2211yescharacteristic, complemented
57#103×C103C2211yescharacteristic, complemented
58#102×C103C2211yescharacteristic, complemented
59C23×D103—21no—
60C23×D103D411yescharacteristic
61C2×Dic206—21no—
62C2×Dic206C2311yescharacteristic
63Q8×D103—41no—
64Q8×D103—41no—
65C2×D412—21no—
66C2×D412C2311yescharacteristic
67C2×C22⋊D103—21no—
68C2×C22⋊D103—21no—
69C2×C22⋊D103—21no—
70D4×D103—41no—
71D4×D103—41no—
72D4×D103—44no—
73C22×Dic103D411yescharacteristic
74C2×C4×D103—21no—
75C2×C4×D103—21no—
76C2×C4×D103—21no—
77C2×C4×D103—41no—
78C2×C4×D103—41no—
79C2×C4×D103D411yescharacteristic
80C2×C4×D103D411yescharacteristic
81C2×C4×D103C2311yescharacteristic
82C2×C4×D103C2311yescharacteristic
83#13110094—41no—
84#13110093—41no—
85#13110092—41no—
86C2×C103⋊C8—41no—
87C2×C103⋊C8C2311yescharacteristic
88C2×C103⋊C8C2311yescharacteristic
89C4⋊Dic103—21no—
90C4⋊Dic103C2311yescharacteristic
91C4⋊Dic103C2311yescharacteristic
92Dic103⋊C4—21no—
93Dic103⋊C4—21no—
94Dic103⋊C4—21no—
95Dic103⋊C4—21no—
96C22⋊Dic103—21no—
97C22⋊Dic103—21no—
98(C2×D103)⋊C4—21no—
99(C2×D103)⋊C4—21no—
100(C2×D103)⋊C4—21no—
101(C2×D103)⋊C4—21no—
102C2×Q8×C103C2311yescharacteristic
103C2×D4×C103—21no—
104C2×D4×C103C2311yescharacteristic
105C22×C4×C103C2311yescharacteristic
106SD16×C103—41no—
107C2×C8×C103—41no—
108C2×C8×C103C2311yescharacteristic
109C2×C8×C103C2311yescharacteristic
110C4⋊C4×C103—21no—
111C4⋊C4×C103C2311yescharacteristic
112C4⋊C4×C103C2311yescharacteristic
113C22⋊C4×C103—21no—
114C22⋊C4×C103—21no—
115C23×C103—21no—
116C23×C103C2×D411yescharacteristic
117C22×D103—21no—
118C22×D103—41no—
119C22×D103—41no—
120C22×D103—42no—
121C22×D103—42no—
122C22×D103—42no—
123C22×D103SD1614yescomplemented
124C22×D103C2×D411yescharacteristic
125C22×D103C2×D411yescharacteristic
126Q8×C103—21no—
127Q8×C103—21no—
128D4×C103—21no—
129D4×C103—21no—
130D4×C103—42no—
131C2×C4×C103—21no—
132C2×C4×C103—21no—
133C2×C4×C103—21no—
134C2×C4×C103—21no—
135C2×C4×C103—21no—
136C2×C4×C103C2×D411yescharacteristic
137C2×C4×C103C2411yescharacteristic
138C22⋊D103—42no—
139C22⋊D103—42no—
140C22⋊D103—42no—
141C2×Dic103—21no—
142C2×Dic103—21no—
143C2×Dic103—21no—
144C2×Dic103—41no—
145C2×Dic103C2×D411yescharacteristic
146C2×Dic103C2×D411yescharacteristic
147D412—21no—
148D412—21no—
149D412—42no—
150C4×D103—21no—
151C4×D103—21no—
152C4×D103—21no—
153C4×D103—21no—
154C4×D103—41no—
155C4×D103—41no—
156C4×D103—42no—
157C4×D103—42no—
158C4×D103—42no—
159Dic206—21no—
160Dic206—21no—
161Dic206—42no—
162C8×C103—21no—
163C8×C103—21no—
164C103⋊C8—21no—
165C103⋊C8—21no—
166C22×C103—21no—
167C22×C103—21no—
168C22×C103—41no—
169C22×C103—41no—
170C22×C103—41no—
171C22×C103C2×SD1612yes—
172C22×C103C22×D411yescharacteristic
173C2×D103—21no—
174C2×D103—21no—
175C2×D103—21no—
176C2×D103—21no—
177C2×D103—44no—
178C2×D103—41no—
179C2×D103—41no—
180C2×D103—41no—
181C2×D103—84no—
182C2×D103C2×SD1612yes—
183C2×D103C2×SD1612yes—
184C4×C103—21no—
185C4×C103—41no—
186C4×C103—41no—
187C4×C103—41no—
188C4×C103H(5,𝔽2)11yescharacteristic
189C4×C103H(5,𝔽2)11yescharacteristic
190Dic103—21no—
191Dic103—21no—
192Dic103—41no—
193Dic103—41no—
194Dic103—41no—
195C2×C103—22no—
196C2×C103—81no—
197C2×C103#53411yescharacteristic
198C2×C103C22×SD1611yescharacteristic
199C2×C103#57511yescharacteristic
200D103—22no—
201D103—22no—
202D103—81no—
203#3187—1031nomaximal, Sylow
204C103#318711yescharacteristic, complemented, Sylow
205C2×C22⋊Q8—1031no—
206C2×#121—1031no—
207#483—1031no—
208#483—1031no—
209#481—1031no—
210#481—1031no—
211#465—1031no—
212#465—1031no—
213#465—1031no—
214#465D10311yescharacteristic, complemented
215#450—1031no—
216#450—1031no—
217#448—1031no—
218#448—1031no—
219C2×C22⋊C8—1031no—
220C22×Q8—1031no—
221C22×D4—1031no—
222C22×D4—2061no—
223C23×C4—1031no—
224C2×SD16—1031no—
225C2×SD16—1031no—
226C2×SD16—1031no—
227C2×SD16C2×D10311yescharacteristic, complemented
228C22×C8—1031no—
229C22×C8C2×D10311yescharacteristic, complemented
230C22⋊Q8—1031no—
231C22⋊Q8—1031no—
232C22⋊Q8—1031no—
233C22⋊Q8—2061no—
234C22⋊Q8—2061no—
235C22⋊Q8C2×D10311yescharacteristic, complemented
236#121—1031no—
237#121—1031no—
238#121—1031no—
239#121—2061no—
240#121—2061no—
241#121C2×D10311yescharacteristic
242C2×C4⋊C4—1031no—
243C2×C4⋊C4—1031no—
244C2×C4⋊C4—2061no—
245C2×C22⋊C4—2061no—
246C2×C22⋊C4—2061no—
247#106—1031no—
248#106—1031no—
249#106—1031no—
250#106C2×D10311yescharacteristic, complemented
251#103—1031no—
252#103—1031no—
253#103—1031no—
254#103C2×D10311yescharacteristic, complemented
255#102—1031no—
256#102—1031no—
257#102—1031no—
258#102C2×D10311yescharacteristic, complemented
259C22⋊C8—1031no—
260C22⋊C8—1031no—
261C22⋊C8—1031no—
262C22⋊C8—1031no—
263C24—1031no—
264C24—2061no—
265C2×Q8—1031no—
266C2×Q8—4121no—
267C2×Q8—4121no—
268C2×Q8—2061no—
269C2×Q8C22×D10311yescharacteristic
270C2×D4—21no—
271C2×D4—1031no—
272C2×D4—4124no—
273C2×D4—4121no—
274C2×D4—4121no—
275C2×D4—2061no—
276C2×D4—2061no—
277C2×D4—2061no—
278C2×D4—2061no—
279C2×D4C22×D10311yescharacteristic
280C22×C4—1031no—
281C22×C4—1031no—
282C22×C4—1031no—
283C22×C4—1031no—
284C22×C4—1031no—
285C22×C4—4121no—
286C22×C4—4121no—
287C22×C4—2061no—
288C22×C4—2061no—
289C22×C4—2061no—
290C22×C4C22×D10311yescharacteristic
291SD16—41no—
292SD16—4121no—
293SD16—4121no—
294SD16—4121no—
295C2×C8—41no—
296C2×C8—1031no—
297C2×C8—1031no—
298C2×C8—4121no—
299C2×C8C22×D10311yescharacteristic
300C2×C8C22×D10311yescharacteristic
301C4⋊C4—21no—
302C4⋊C4—1031no—
303C4⋊C4—1031no—
304C4⋊C4—2061no—
305C4⋊C4—2061no—
306C4⋊C4—2061no—
307C4⋊C4—2061no—
308C4⋊C4—2061no—
309C4⋊C4C22×D10311yescharacteristic
310C4⋊C4C22×D10311yescharacteristic
311C22⋊C4—21no—
312C22⋊C4—21no—
313C22⋊C4—2061no—
314C22⋊C4—2061no—
315C22⋊C4—2061no—
316C22⋊C4—2061no—
317C22⋊C4—2061no—
318C22⋊C4—2061no—
319C23—21no—
320C23—1034no—
321C23—1031no—
322C23—1031no—
323C23—4121no—
324C23—4121no—
325C23—4122no—
326C23—4122no—
327C23—4122no—
328C23—2061no—
329C23D4×D10311yescharacteristic
330Q8—21no—
331Q8—21no—
332Q8—4122no—
333Q8—2061no—
334Q8—2061no—
335D4—21no—
336D4—21no—
337D4—42no—
338D4—4122no—
339D4—4122no—
340D4—4122no—
341D4—4122no—
342D4—2061no—
343D4—2061no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—1031no—
350C2×C4—1031no—
351C2×C4—4121no—
352C2×C4—4121no—
353C2×C4—4122no—
354C2×C4—4122no—
355C2×C4—4122no—
356C2×C4—4121no—
357C2×C4—2061no—
358C2×C4—2061no—
359C2×C4—2061no—
360C2×C4—2061no—
361C2×C4—2061no—
362C2×C4—2061no—
363C2×C4—2061no—
364C2×C4D4×D10311yescharacteristic
365C2×C4C23×D10311yescharacteristic
366C8—21no—
367C8—21no—
368C8—2061no—
369C8—2061no—
370C22—21no—
371C22—21no—
372C22—41no—
373C22—41no—
374C22—41no—
375C22—8244no—
376C22—1032no—
377C22—1032no—
378C22—4124no—
379C22—4121no—
380C22—4121no—
381C22—4121no—
382C22—2061no—
383C22—2061no—
384C22—2061no—
385C22—2061no—
386C22SD16×D10312yes—
387C22C2×D4×D10311yescharacteristic
388C4—21no—
389C4—41no—
390C4—41no—
391C4—41no—
392C4—4121no—
393C4—4121no—
394C4—4121no—
395C4—2061no—
396C4—2061no—
397C4#1569306611yescharacteristic
398C4#1569306711yescharacteristic
399C2—22no—
400C2—81no—
401C2—8241no—
402C2—2062no—
403C2—2062no—
404C2#2026834911yescharacteristic
405C2C2×SD16×D10311yescharacteristic
406C2#2026858811yescharacteristic
subgroupG/H
centerC22C2×D4×D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
Fitting#465×C103C2
socleC22×C103C22×D4
prime radical#121×D103C2
hypercenter#465D103
hypocenterC103#3187
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C22×C4 ◁ #465

Complements

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

NH ≅ G/Ntype
1. C22⋊Q8×D103C2semidirect
3. #20268123C2semidirect
4. #20268120C2semidirect
5. #20268111C2semidirect
6. #20268108C2semidirect
7. #20268022C2semidirect
8. #20268020C2semidirect
9. #20268018C2semidirect
10. #20267943C2semidirect
11. #20267940C2semidirect
12. #20267931C2semidirect
13. #20267928C2semidirect
14. C2×(C2×D103)⋊C8C2semidirect
15. #465×C103C2semidirect
16. C2×Q8×D103C22semidirect
20. C2×#13110094C22semidirect
21. C2×#13110093C22semidirect
22. C2×#13110092C22semidirect
23. C22×C103⋊C8C22semidirect
25. #15693000C22semidirect
36. C4⋊C4×D103C22semidirect
39. #15692953C22semidirect
40. #15692952C22semidirect
41. #15692952C22semidirect
42. #15692946C22semidirect
43. #15692945C22semidirect
44. #15692944C22semidirect
45. #15692943C22semidirect
46. #15692942C22semidirect
47. #15692941C22semidirect
50. (C2×D103)⋊C8C22semidirect
51. (C2×D103)⋊C8C22semidirect
52. C2×SD16×C103C22semidirect
53. C22×C8×C103C22semidirect
54. C22⋊Q8×C103C22semidirect
56. #106×C103C22semidirect
57. #103×C103C22semidirect
58. #102×C103C22semidirect
123. C22×D103SD16semidirect
204. C103#3187semidirect
214. #465D103semidirect
227. C2×SD16C2×D103semidirect
229. C22×C8C2×D103semidirect
235. C22⋊Q8C2×D103semidirect
250. #106C2×D103semidirect
254. #103C2×D103semidirect
258. #102C2×D103semidirect

Maximal subgroups

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

subgroupindex
C22⋊Q8×D1032
#121×D1032
#202681232
#202681202
#202681112
#202681082
#202680222
#202680202
#202680182
#202679432
#202679402
#202679312
#202679282
C2×(C2×D103)⋊C82
#465×C1032
#3187103