Finite Group Databasebeta

← #27205923

Subgroups — #27205923

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#20268298C211yesmaximal, characteristic
2C22⋊Q8×D103C211yesmaximal, characteristic, complemented
3#20268133C211yesmaximal, characteristic, complemented
4#20268129C211yesmaximal, characteristic, complemented
5#20268120C211yesmaximal, characteristic, complemented
6#20268103C211yesmaximal, characteristic, complemented
7#20268031C211yesmaximal, characteristic, complemented
8#20268029C211yesmaximal, characteristic, complemented
9#20268019C211yesmaximal, characteristic, complemented
10#20268017C211yesmaximal, characteristic, complemented
11#20267953C211yesmaximal, characteristic, complemented
12#20267945C211yesmaximal, characteristic, complemented
13#20267928C211yesmaximal, characteristic, complemented
14C22⋊C8×D103C211yesmaximal, characteristic, complemented
15#452×C103C211yesmaximal, characteristic, complemented
16C2×Q8×D103C2211yescharacteristic
17C22×C4×D103C2211yescharacteristic
18C2×#13110095C2211yescharacteristic, complemented
19C2×#13110093C2211yescharacteristic, complemented
20C2×C8×D103C2211yescharacteristic
21C2×C8×D103C2211yescharacteristic
22#15693002—21no—
23#15693001C2211yescharacteristic
24#15693000C2211yescharacteristic
25#15692999—21no—
26#15692998—21no—
27#15692997C2211yescharacteristic
28#15692997C2211yescharacteristic
29#15692997C2211yescharacteristic
30#15692992C2211yescharacteristic
31#15692992C2211yescharacteristic
32#15692989—21no—
33C4×C22⋊D103—21no—
34C4×C22⋊D103—21no—
35#15692980C2211yescharacteristic
36C4⋊C4×D103—21no—
37C4⋊C4×D103C2211yescharacteristic
38C22⋊C4×D103—21no—
39#15692955C2211yescharacteristic, complemented
40#15692954C2211yescharacteristic, complemented
41#15692953C2211yescharacteristic, complemented
42#15692952C2211yescharacteristic, complemented
43#15692946C2211yescharacteristic, complemented
44#15692946C2211yescharacteristic, complemented
45#15692945C2211yescharacteristic, complemented
46#15692945C2211yescharacteristic, complemented
47#15692945C2211yescharacteristic, complemented
48#15692942C2211yescharacteristic, complemented
49C22⋊(C103⋊C8)C2211yescharacteristic
50(C2×D103)⋊C8C2211yescharacteristic
51(C2×D103)⋊C8C2211yescharacteristic
52C2×#41×C103C2211yescharacteristic
53C2×Q16×C103C2211yescharacteristic, complemented
54C2×SD16×C103C2211yescharacteristic, complemented
55C22⋊Q8×C103C2211yescharacteristic
56#103×C103C2211yescharacteristic, complemented
57#102×C103C2211yescharacteristic, complemented
58C22⋊C8×C103C2211yescharacteristic
59C23×D103D411yescharacteristic
60C2×Dic206—21no—
61C2×Dic206C2311yescharacteristic
62Q8×D103—41no—
63Q8×D103—41no—
64C2×C22⋊D103—21no—
65C2×C22⋊D103—21no—
66C22×Dic103D411yescharacteristic
67C2×C4×D103—21no—
68C2×C4×D103—21no—
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—
88Dic103⋊C4—21no—
89Dic103⋊C4—21no—
90C22⋊Dic103—21no—
91C22⋊Dic103—21no—
92C22⋊Dic103—21no—
93C22⋊Dic103—21no—
94(C2×D103)⋊C4—21no—
95(C2×D103)⋊C4—21no—
96(C2×D103)⋊C4—21no—
97(C2×D103)⋊C4—21no—
98C4×Dic103—21no—
99#41×C103—41no—
100#41×C103—41no—
101C2×Q8×C103C2311yescharacteristic
102C2×Q8×C103C2311yescharacteristic
103C2×D4×C103—21no—
104C2×D4×C103C2311yescharacteristic
105C22×C4×C103—21no—
106C22×C4×C103C2311yescharacteristic
107Q16×C103—41no—
108SD16×C103—41no—
109C2×C8×C103C2311yescharacteristic
110C2×C8×C103C2311yescharacteristic
111C4⋊C4×C103—21no—
112C4⋊C4×C103C2311yescharacteristic
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—
123Q8×C103—21no—
124Q8×C103—21no—
125D4×C103—21no—
126D4×C103—21no—
127D4×C103—42no—
128C2×C4×C103—21no—
129C2×C4×C103—21no—
130C2×C4×C103—21no—
131C2×C4×C103—21no—
132C2×C4×C103—21no—
133C2×C4×C103—42no—
134C2×C4×C103C2×D411yescharacteristic
135C2×C4×C103C2411yescharacteristic
136C22⋊D103—42no—
137C22⋊D103—42no—
138C2×Dic103—21no—
139C2×Dic103—21no—
140C2×Dic103—21no—
141C2×Dic103—21no—
142C2×Dic103—41no—
143C2×Dic103C2×D411yescharacteristic
144C2×Dic103C2×D411yescharacteristic
145C4×D103—21no—
146C4×D103—21no—
147C4×D103—21no—
148C4×D103—21no—
149C4×D103—41no—
150C4×D103—41no—
151C4×D103—42no—
152C4×D103—42no—
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—21no—
163C22×C103—41no—
164C22×C103—41no—
165C22×C103—41no—
166C22×C103C22×D411yescharacteristic
167C2×D103—21no—
168C2×D103—21no—
169C2×D103—21no—
170C2×D103—21no—
171C2×D103—44no—
172C2×D103#13512yes—
173C2×D103#13712yes—
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—41no—
187C2×C103—81no—
188C2×C103#53411yescharacteristic
189C2×C103C2×#13511yescharacteristic
190C2×C103C2×#13711yescharacteristic
191D103—22no—
192D103—22no—
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#465—1031no—
205#452—1031no—
206#452D10311yescharacteristic, complemented
207#451—1031no—
208#448—1031no—
209C2×C22⋊C8—1031no—
210C2×#41C2×D10311yescharacteristic
211C22×Q8—1031no—
212C23×C4—1031no—
213C2×Q16—1031no—
214C2×Q16C2×D10311yescharacteristic, complemented
215C2×SD16—1031no—
216C2×SD16C2×D10311yescharacteristic, complemented
217C22×C8—1031no—
218C22×C8—1031no—
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#121—1031no—
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#106—1031no—
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⋊C8C2×D10311yescharacteristic
253C24—1031no—
254#41—41no—
255#41—41no—
256C2×Q8—1031no—
257C2×Q8—4121no—
258C2×Q8—4121no—
259C2×Q8—2061no—
260C2×Q8C22×D10311yescharacteristic
261C2×Q8C22×D10311yescharacteristic
262C2×D4—21no—
263C2×D4—2061no—
264C2×D4—2061no—
265C2×D4C22×D10311yescharacteristic
266C22×C4—21no—
267C22×C4—1031no—
268C22×C4—1031no—
269C22×C4—1031no—
270C22×C4—1031no—
271C22×C4—1031no—
272C22×C4—4121no—
273C22×C4—4121no—
274C22×C4—2061no—
275C22×C4—2061no—
276C22×C4C22×D10311yescharacteristic
277Q16—41no—
278Q16—4121no—
279SD16—41no—
280SD16—4121no—
281C2×C8—1031no—
282C2×C8—1031no—
283C2×C8—4121no—
284C2×C8—4121no—
285C2×C8C22×D10311yescharacteristic
286C2×C8C22×D10311yescharacteristic
287C4⋊C4—21no—
288C4⋊C4—1031no—
289C4⋊C4—1031no—
290C4⋊C4—1031no—
291C4⋊C4—2061no—
292C4⋊C4—2061no—
293C4⋊C4—2061no—
294C4⋊C4—2061no—
295C4⋊C4—2061no—
296C4⋊C4—2061no—
297C4⋊C4C22×D10311yescharacteristic
298C22⋊C4—21no—
299C22⋊C4—2061no—
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—21no—
318Q8—21no—
319Q8—4122no—
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—42no—
333C2×C4—1031no—
334C2×C4—1031no—
335C2×C4—4121no—
336C2×C4—4121no—
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—21no—
357C22—41no—
358C22—41no—
359C22—41no—
360C22—1032no—
361C22—1032no—
362C22—4124no—
363C22—2061no—
364C22—2061no—
365C22—2061no—
366C22—2061no—
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#1569306611yescharacteristic
380C2—41no—
381C2—81no—
382C2—2062no—
383C2—2062no—
384C2#2026835111yescharacteristic
385C2#135×D10311yescharacteristic
386C2#137×D10311yescharacteristic
subgroupG/H
centerC22C2×D4×D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
Fitting#452×C103C2
socleC22×C103C22×D4
prime radical#20268298C2
hypercenter#452D103
hypocenterC103#3190
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C22×C4 ◁ #452

Complements

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

NH ≅ G/Ntype
2. C22⋊Q8×D103C2semidirect
3. #20268133C2semidirect
4. #20268129C2semidirect
5. #20268120C2semidirect
6. #20268103C2semidirect
7. #20268031C2semidirect
8. #20268029C2semidirect
9. #20268019C2semidirect
10. #20268017C2semidirect
11. #20267953C2semidirect
12. #20267945C2semidirect
13. #20267928C2semidirect
14. C22⋊C8×D103C2semidirect
15. #452×C103C2semidirect
18. C2×#13110095C22semidirect
19. C2×#13110093C22semidirect
39. #15692955C22semidirect
40. #15692954C22semidirect
41. #15692953C22semidirect
42. #15692952C22semidirect
43. #15692946C22semidirect
44. #15692946C22semidirect
45. #15692945C22semidirect
46. #15692945C22semidirect
47. #15692945C22semidirect
48. #15692942C22semidirect
53. C2×Q16×C103C22semidirect
54. C2×SD16×C103C22semidirect
56. #103×C103C22semidirect
57. #102×C103C22semidirect
194. C103#3190semidirect
206. #452D103semidirect
214. C2×Q16C2×D103semidirect
216. C2×SD16C2×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
#202682982
C22⋊Q8×D1032
#202681332
#202681292
#202681202
#202681032
#202680312
#202680292
#202680192
#202680172
#202679532
#202679452
#202679282
C22⋊C8×D1032
#452×C1032
#3190103