Finite Group Databasebeta

← #27205920

Subgroups — #27205920

Order 13184.

420 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20268301C211yesmaximal, characteristic
2C22⋊Q8×D103C211yesmaximal, characteristic, complemented
3#20268135C211yesmaximal, characteristic, complemented
4#20268131C211yesmaximal, characteristic, complemented
5#20268123C211yesmaximal, characteristic, complemented
6#20268103C211yesmaximal, characteristic, complemented
7#20268032C211yesmaximal, characteristic, complemented
8#20268030C211yesmaximal, characteristic, complemented
9#20268018C211yesmaximal, characteristic, complemented
10#20267954C211yesmaximal, characteristic, complemented
11#20267950C211yesmaximal, characteristic, complemented
12#20267948C211yesmaximal, characteristic, complemented
13#20267928C211yesmaximal, characteristic, complemented
14C2×(C2×D103)⋊C8C211yesmaximal, characteristic, complemented
15#465×C103C211yesmaximal, characteristic, complemented
16C2×#13110104C2211yescharacteristic
17C2×Q8×D103C2211yescharacteristic
18C22×C4×D103C2211yescharacteristic
19C2×Dic412C2211yescharacteristic, complemented
20C2×#13110095C2211yescharacteristic, complemented
21C2×#13110093C2211yescharacteristic, complemented
22C22×C103⋊C8C2211yescharacteristic
23#15693003—21no—
24#15693001C2211yescharacteristic
25#15693001C2211yescharacteristic
26#15693000C2211yescharacteristic
27#15693000C2211yescharacteristic
28#15692999—21no—
29#15692998—21no—
30#15692997C2211yescharacteristic
31#15692992C2211yescharacteristic
32#15692989—21no—
33D4×Dic103—21no—
34(C22⋊D103)⋊C4—21no—
35#15692979C2211yescharacteristic
36C4⋊C4×D103—21no—
37C4⋊C4×D103C2211yescharacteristic
38C22⋊C4×D103—21no—
39#15692955C2211yescharacteristic, complemented
40#15692954C2211yescharacteristic, complemented
41#15692952C2211yescharacteristic, complemented
42#15692946C2211yescharacteristic, complemented
43#15692946C2211yescharacteristic, complemented
44#15692945C2211yescharacteristic, complemented
45#15692944C2211yescharacteristic, complemented
46#15692944C2211yescharacteristic, complemented
47#15692942C2211yescharacteristic, complemented
48(C2×D103)⋊C8C2211yescharacteristic
49(C2×D103)⋊C8C2211yescharacteristic
50(C2×D103)⋊C8C2211yescharacteristic
51(C2×D103)⋊C8C2211yescharacteristic
52C2×SD16×C103C2211yescharacteristic, complemented
53C22×C8×C103C2211yescharacteristic
54C22⋊Q8×C103C2211yescharacteristic
55#121×C103C2211yescharacteristic
56#106×C103C2211yescharacteristic, complemented
57#103×C103C2211yescharacteristic, complemented
58#102×C103C2211yescharacteristic, complemented
59C23×D103D411yescharacteristic
60#13110104—41no—
61#13110104—41no—
62C2×Dic206—21no—
63C2×Dic206C2311yescharacteristic
64C2×Dic206C2311yescharacteristic
65Q8×D103—41no—
66Q8×D103—41no—
67C2×C22⋊D103—21no—
68C2×C22⋊D103—21no—
69C22×Dic103—21no—
70C22×Dic103D411yescharacteristic
71C2×C4×D103—21no—
72C2×C4×D103—21no—
73C2×C4×D103—41no—
74C2×C4×D103—41no—
75C2×C4×D103D411yescharacteristic
76C2×C4×D103D411yescharacteristic
77C2×C4×D103C2311yescharacteristic
78C2×C4×D103C2311yescharacteristic
79Dic412—41no—
80#13110095—41no—
81#13110093—41no—
82C2×C103⋊C8—41no—
83C2×C103⋊C8C2311yescharacteristic
84C2×C103⋊C8C2311yescharacteristic
85C4⋊Dic103—21no—
86C4⋊Dic103—21no—
87C4⋊Dic103C2311yescharacteristic
88C4⋊Dic103C2311yescharacteristic
89Dic103⋊C4—21no—
90Dic103⋊C4—21no—
91Dic103⋊C4—21no—
92Dic103⋊C4—21no—
93C22⋊Dic103—21no—
94C22⋊Dic103—21no—
95C22⋊Dic103—21no—
96(C2×D103)⋊C4—21no—
97(C2×D103)⋊C4—21no—
98(C2×D103)⋊C4—21no—
99(C2×D103)⋊C4—21no—
100C4×Dic103—21no—
101C2×Q8×C103C2311yescharacteristic
102C2×D4×C103—21no—
103C2×D4×C103C2311yescharacteristic
104C22×C4×C103C2311yescharacteristic
105SD16×C103—41no—
106C2×C8×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—22no—
117C22×D103—22no—
118C22×D103—41no—
119C22×D103C2×D411yescharacteristic
120C22×D103C2×D411yescharacteristic
121Q8×C103—21no—
122Q8×C103—21no—
123D4×C103—21no—
124D4×C103—21no—
125D4×C103—42no—
126C2×C4×C103—21no—
127C2×C4×C103—21no—
128C2×C4×C103—21no—
129C2×C4×C103—21no—
130C2×C4×C103—21no—
131C2×C4×C103C2×D411yescharacteristic
132C2×C4×C103C2411yescharacteristic
133C22⋊D103—42no—
134C22⋊D103—42no—
135C2×Dic103—21no—
136C2×Dic103—21no—
137C2×Dic103—21no—
138C2×Dic103—21no—
139C2×Dic103—41no—
140C2×Dic103—42no—
141C2×Dic103C2×D411yescharacteristic
142C2×Dic103C2×D411yescharacteristic
143C4×D103—21no—
144C4×D103—21no—
145C4×D103—21no—
146C4×D103—21no—
147C4×D103—41no—
148C4×D103—41no—
149C4×D103—42no—
150C4×D103—42no—
151Dic206—21no—
152Dic206—21no—
153Dic206—21no—
154Dic206—21no—
155Dic206—42no—
156C8×C103—21no—
157C8×C103—21no—
158C103⋊C8—21no—
159C103⋊C8—21no—
160C22×C103—21no—
161C22×C103—21no—
162C22×C103—41no—
163C22×C103—41no—
164C22×C103—41no—
165C22×C103#13712yes—
166C22×C103C22×D411yescharacteristic
167C2×D103—21no—
168C2×D103—21no—
169C2×D103—21no—
170C2×D103—21no—
171C2×D103—21no—
172C2×D103—44no—
173C2×D103#13512yes—
174C4×C103—21no—
175C4×C103—41no—
176C4×C103—41no—
177C4×C103—41no—
178C4×C103H(5,𝔽2)11yescharacteristic
179C4×C103H(5,𝔽2)11yescharacteristic
180Dic103—21no—
181Dic103—21no—
182Dic103—41no—
183Dic103—41no—
184Dic103—41no—
185Dic103—41no—
186C2×C103—22no—
187C2×C103—81no—
188C2×C103#53411yescharacteristic
189C2×C103C2×#13511yescharacteristic
190C2×C103C2×#13711yescharacteristic
191D103—22no—
192D103—41no—
193#3190—1031nomaximal, Sylow
194C103#319011yescharacteristic, complemented, Sylow
195#525—1031no—
196C2×C22⋊Q8—1031no—
197#485—1031no—
198#485—1031no—
199#483—1031no—
200#480—1031no—
201#467—1031no—
202#467—1031no—
203#465—1031no—
204#465D10311yescharacteristic, complemented
205#452—1031no—
206#452—1031no—
207#451—1031no—
208#448—1031no—
209C2×C22⋊C8—1031no—
210C2×#41—1031no—
211C22×Q8—1031no—
212C23×C4—1031no—
213C2×Q16—1031no—
214C2×Q16—1031no—
215C2×SD16—1031no—
216C2×SD16C2×D10311yescharacteristic, complemented
217C22×C8—1031no—
218C22×C8C2×D10311yescharacteristic
219#123—2061no—
220C22⋊Q8—1031no—
221C22⋊Q8—1031no—
222C22⋊Q8—1031no—
223C22⋊Q8—1031no—
224C22⋊Q8—1031no—
225C22⋊Q8—2061no—
226C22⋊Q8—2061no—
227C22⋊Q8C2×D10311yescharacteristic
228#121—1031no—
229#121C2×D10311yescharacteristic
230#120—2061no—
231C4×D4—2061no—
232C4×D4—2061no—
233#117—1031no—
234C2×C4⋊C4—1031no—
235C2×C4⋊C4—2061no—
236C2×C22⋊C4—2061no—
237#107—1031no—
238#107—1031no—
239#106—1031no—
240#106C2×D10311yescharacteristic, complemented
241#103—1031no—
242#103—1031no—
243#103—1031no—
244#103—1031no—
245#103—1031no—
246#103C2×D10311yescharacteristic, complemented
247#102—1031no—
248#102C2×D10311yescharacteristic, complemented
249C22⋊C8—1031no—
250C22⋊C8—1031no—
251C22⋊C8—1031no—
252C22⋊C8—1031no—
253C24—1031no—
254#41—4121no—
255#41—4121no—
256C2×Q8—1031no—
257C2×Q8—1031no—
258C2×Q8—4121no—
259C2×Q8—4121no—
260C2×Q8—2061no—
261C2×Q8C22×D10311yescharacteristic
262C2×D4—21no—
263C2×D4—2061no—
264C2×D4—2061no—
265C2×D4C22×D10311yescharacteristic
266C22×C4—1031no—
267C22×C4—1031no—
268C22×C4—1031no—
269C22×C4—1031no—
270C22×C4—1031no—
271C22×C4—4121no—
272C22×C4—4121no—
273C22×C4—2061no—
274C22×C4—2061no—
275C22×C4—2061no—
276C22×C4C22×D10311yescharacteristic
277Q16—4121no—
278Q16—4121no—
279SD16—41no—
280SD16—4121no—
281C2×C8—41no—
282C2×C8—1031no—
283C2×C8—1031no—
284C2×C8—4121no—
285C2×C8C22×D10311yescharacteristic
286C2×C8C22×D10311yescharacteristic
287C4⋊C4—21no—
288C4⋊C4—1031no—
289C4⋊C4—1031no—
290C4⋊C4—2061no—
291C4⋊C4—2061no—
292C4⋊C4—2061no—
293C4⋊C4—2061no—
294C4⋊C4—2061no—
295C4⋊C4—2061no—
296C4⋊C4C22×D10311yescharacteristic
297C4⋊C4C22×D10311yescharacteristic
298C22⋊C4—21no—
299C22⋊C4—21no—
300C22⋊C4—2061no—
301C22⋊C4—2061no—
302C22⋊C4—2061no—
303C22⋊C4—2061no—
304C22⋊C4—2061no—
305C22⋊C4—2061no—
306C22⋊C4—2061no—
307C42—2061no—
308C23—21no—
309C23—1031no—
310C23—1031no—
311C23—4121no—
312C23—2062no—
313C23—2062no—
314C23D4×D10311yescharacteristic
315Q8—21no—
316Q8—21no—
317Q8—4122no—
318Q8—2061no—
319Q8—2061no—
320Q8—2061no—
321Q8—2061no—
322D4—21no—
323D4—21no—
324D4—42no—
325D4—4122no—
326D4—4122no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—1031no—
333C2×C4—1031no—
334C2×C4—4121no—
335C2×C4—4121no—
336C2×C4—4122no—
337C2×C4—4122no—
338C2×C4—4122no—
339C2×C4—4121no—
340C2×C4—2061no—
341C2×C4—2061no—
342C2×C4—2061no—
343C2×C4—2061no—
344C2×C4—2061no—
345C2×C4—2061no—
346C2×C4—2061no—
347C2×C4—2061no—
348C2×C4D4×D10311yescharacteristic
349C2×C4C23×D10311yescharacteristic
350C8—21no—
351C8—21no—
352C8—2061no—
353C8—2061no—
354C22—21no—
355C22—21no—
356C22—41no—
357C22—41no—
358C22—41no—
359C22—1032no—
360C22—4124no—
361C22—2061no—
362C22—2061no—
363C22—2061no—
364C22—2061no—
365C22—2061no—
366C22#1569305012yes—
367C22C2×D4×D10311yescharacteristic
368C4—21no—
369C4—41no—
370C4—41no—
371C4—41no—
372C4—4121no—
373C4—4121no—
374C4—4121no—
375C4—4121no—
376C4—2061no—
377C4—2061no—
378C4#1569306611yescharacteristic
379C4#1569306711yescharacteristic
380C2—22no—
381C2—81no—
382C2—4121no—
383C2—2062no—
384C2#2026834911yescharacteristic
385C2#135×D10311yescharacteristic
386C2C2×#1569305011yescharacteristic
subgroupG/H
centerC22C2×D4×D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
Fitting#465×C103C2
socleC22×C103C22×D4
prime radical#20268301C2
hypercenter#465D103
hypocenterC103#3190
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
2. C22⋊Q8×D103C2semidirect
3. #20268135C2semidirect
4. #20268131C2semidirect
5. #20268123C2semidirect
6. #20268103C2semidirect
7. #20268032C2semidirect
8. #20268030C2semidirect
9. #20268018C2semidirect
10. #20267954C2semidirect
11. #20267950C2semidirect
12. #20267948C2semidirect
13. #20267928C2semidirect
14. C2×(C2×D103)⋊C8C2semidirect
15. #465×C103C2semidirect
19. C2×Dic412C22semidirect
20. C2×#13110095C22semidirect
21. C2×#13110093C22semidirect
39. #15692955C22semidirect
40. #15692954C22semidirect
41. #15692952C22semidirect
42. #15692946C22semidirect
43. #15692946C22semidirect
44. #15692945C22semidirect
45. #15692944C22semidirect
46. #15692944C22semidirect
47. #15692942C22semidirect
52. C2×SD16×C103C22semidirect
56. #106×C103C22semidirect
57. #103×C103C22semidirect
58. #102×C103C22semidirect
194. C103#3190semidirect
204. #465D103semidirect
216. C2×SD16C2×D103semidirect
240. #106C2×D103semidirect
246. #103C2×D103semidirect
248. #102C2×D103semidirect

Maximal subgroups

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

subgroupindex
#202683012
C22⋊Q8×D1032
#202681352
#202681312
#202681232
#202681032
#202680322
#202680302
#202680182
#202679542
#202679502
#202679482
#202679282
C2×(C2×D103)⋊C82
#465×C1032
#3190103