Finite Group Databasebeta

← C2×D13⋊#99 #13131429

Subgroups — C2×D13⋊#99 #13131429

Order 1664.

1112 conjugacy classes of subgroups; only the 210 normal subgroups are shown.

normal subgroups only

This group has 1112 conjugacy classes of subgroups — too many to draw. Only its 210 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D4×D13C211yesmaximal, characteristic
2C22×C22⋊#261C212yesmaximal, complemented
3C2×#88119C212yesmaximal, complemented
4D13⋊#99C218yesmaximal, direct product factor
5C2×#88107C212yesmaximal, complemented
6C24×D13C411yescharacteristic, complemented
7C24×D13C2211yescharacteristic
8C23×#261—22no—
9C22×D4×C13C411yescharacteristic, complemented
10C22×C22⋊D13C411yescharacteristic, complemented
11C22×C22⋊D13C2211yescharacteristic
12C2×D4×D13—22no—
13C2×D4×D13—22no—
14C2×D4×D13—24no—
15C2×D4×D13C414yescomplemented
16C2×D4×D13C2214yes—
17C22×D52C2211yescharacteristic
18C22×C4×D13C411yescharacteristic, complemented
19C2×C22⋊#261—24no—
20C2×C22⋊#261—22no—
21C2×C22⋊#261C2214yescomplemented
22C2×C22⋊#261C2218yescomplemented
23#88119C2218yescomplemented
24#88107C2218yescomplemented
25C24×C13C2×C411yescharacteristic
26C24×C13C2×C411yescharacteristic, complemented
27C23×D13—22no—
28C23×D13—21no—
29C23×D13—21no—
30C23×D13—44no—
31C23×D13—44no—
32C23×D13C2×C411yescharacteristic
33C23×D13C2×C412yes—
34C23×D13C2×C414yescomplemented
35C23×D13C2×C411yescharacteristic, complemented
36C23×D13D412yes—
37C23×D13D414yes—
38C23×D13D412yes—
39C23×D13C2311yescharacteristic
40C23×D13C2312yes—
41C22×#261—24no—
42C22×#261—28no—
43C22×#261—48no—
44C2×D4×C13—22no—
45C2×D4×C13—22no—
46C2×D4×C13C2×C414yescomplemented
47C22×C4×C13C2×C411yescharacteristic, complemented
48C2×C22⋊D13—22no—
49C2×C22⋊D13—22no—
50C2×C22⋊D13—22no—
51C2×C22⋊D13—22no—
52C2×C22⋊D13C2×C412yescomplemented
53C2×C22⋊D13C2×C414yescomplemented
54C2×C22⋊D13C2312yes—
55C22×Dic13C2×C411yescharacteristic, complemented
56D4×D13—28no—
57D4×D13—28no—
58D4×D13—28no—
59D4×D13—28no—
60C2×D52—22no—
61C2×D52—22no—
62C2×D52C2×C412yescomplemented
63C2×D52C2312yes—
64C2×C4×D13—21no—
65C2×C4×D13—22no—
66C2×C4×D13—21no—
67C2×C4×D13C2×C414yescomplemented
68C22⋊#261—24no—
69C22⋊#261—28no—
70C22⋊#261C2318yescomplemented
71C22×#99—131nomaximal, Sylow
72C23×C13—21no—
73C23×C13—21no—
74C23×C13—42no—
75C23×C13—42no—
76C23×C13C22⋊C412yes—
77C23×C13C22⋊C412yes—
78C23×C13C22×C411yescharacteristic
79C23×C13C22×C412yes—
80C23×C13C22×C412yescomplemented
81C22×D13—28no—
82C22×D13—24no—
83C22×D13—21no—
84C22×D13—21no—
85C22×D13—24no—
86C22×D13—24no—
87C22×D13—44no—
88C22×D13—48no—
89C22×D13—44no—
90C22×D13—44no—
91C22×D13—42no—
92C22×D13—44no—
93C22×D13—48no—
94C22×D13—48no—
95C22×D13—44no—
96C22×D13—42no—
97C22×D13C22⋊C411yescharacteristic
98C22×D13C22⋊C412yes—
99C22×D13C22⋊C414yes—
100C22×D13C22⋊C414yes—
101C22×D13C22⋊C411yescharacteristic
102C22×D13C22×C412yes—
103C22×D13C22×C411yescharacteristic
104C22×D13C22×C412yescomplemented
105C22×D13C2×D412yes—
106C22×D13C2×D414yes—
107C22×D13C2×D412yes—
108C22×D13C2×D414yes—
109C22×D13C2411yescharacteristic
110C2×#261—28no—
111C2×#261—48no—
112C2×#261—416no—
113D4×C13—28no—
114C2×C4×C13—21no—
115C2×C4×C13—21no—
116C2×C4×C13C22×C412yescomplemented
117C22⋊D13—28no—
118C22⋊D13—24no—
119C22⋊D13—24no—
120C2×Dic13—21no—
121C2×Dic13—21no—
122C2×Dic13C22×C412yescomplemented
123D52—24no—
124D52—24no—
125C4×D13—24no—
126C4×D13—24no—
127C23×D4—131no—
128C22×C22⋊C4—132no—
129C2×#99—132no—
130C2×#99—138no—
131C2×#99—132no—
132C22×C13—22no—
133C22×C13—24no—
134C22×C13—22no—
135C22×C13—42no—
136C22×C13—42no—
137C22×C13—42no—
138C22×C13—42no—
139C22×C13—42no—
140C22×C13C2×C22⋊C411yescharacteristic
141C22×C13C2×C22⋊C414yes—
142C22×C13C2×C22⋊C411yescharacteristic
143C22×C13C23×C411yescharacteristic
144C2×D13—24no—
145C2×D13—22no—
146C2×D13—28no—
147C2×D13—24no—
148C2×D13—24no—
149C2×D13—28no—
150C2×D13—22no—
151C2×D13—44no—
152C2×D13—41no—
153C2×D13—44no—
154C2×D13—42no—
155C2×D13—41no—
156C2×D13—48no—
157C2×D13—42no—
158C2×D13—42no—
159C2×D13—48no—
160C2×D13—42no—
161C2×D13#9914yescomplemented
162C2×D13C2×C22⋊C412yes—
163C2×D13C2×C22⋊C412yes—
164C2×D13C2×C22⋊C412yes—
165C2×D13C22×D412yes—
166#261—48no—
167C4×C13—22no—
168Dic13—22no—
169C25—131no—
170C25—131no—
171C22×D4—131no—
172C22×D4—131no—
173C22×D4—134no—
174C22×D4—134no—
175C22×D4—131no—
176C22×D4—262no—
177C22×D4—264no—
178C22×D4—262no—
179C22×D4#26111yescharacteristic, complemented
180C23×C4—131no—
181C23×C4—262no—
182C2×C22⋊C4—134no—
183C2×C22⋊C4—138no—
184C2×C22⋊C4—264no—
185C2×C22⋊C4—262no—
186#99—138no—
187#99—138no—
188C2×C13—21no—
189C2×C13—21no—
190C2×C13—24no—
191C2×C13—42no—
192C2×C13C2×#9912yescomplemented
193C2×C13C22×C22⋊C411yescharacteristic
194D13—22no—
195D13—22no—
196D13—22no—
197D13—42no—
198D13C2×#9914yescomplemented
199C24—132no—
200C24—131no—
201C24—134no—
202C24—132no—
203C24—132no—
204C24—131no—
205C24—132no—
206C24—131no—
207C24—134no—
208C24—262no—
209C24—261no—
210C24—261no—
211C24—524no—
212C24—524no—
213C24C2×#26111yescharacteristic
214C24C2×#26111yescharacteristic, complemented
215C2×D4—22no—
216C2×D4—22no—
217C2×D4—134no—
218C2×D4—132no—
219C2×D4—132no—
220C2×D4—132no—
221C2×D4—132no—
222C2×D4—262no—
223C2×D4—262no—
224C2×D4—268no—
225C2×D4—268no—
226C2×D4—268no—
227C2×D4—268no—
228C2×D4—262no—
229C2×D4—262no—
230C2×D4—262no—
231C2×D4—262no—
232C2×D4C2×#26114yescomplemented
233C22×C4—131no—
234C22×C4—134no—
235C22×C4—262no—
236C22×C4—261no—
237C22×C4—261no—
238C22×C4—268no—
239C22×C4—264no—
240C22×C4—528no—
241C22×C4C2×#26111yescharacteristic, complemented
242C22⋊C4—138no—
243C22⋊C4—268no—
244C22⋊C4—264no—
245C13C22×#9911yescharacteristic, complemented, Sylow
246C23—21no—
247C23—21no—
248C23—42no—
249C23—42no—
250C23—131no—
251C23—134no—
252C23—132no—
253C23—134no—
254C23—132no—
255C23—131no—
256C23—132no—
257C23—134no—
258C23—132no—
259C23—134no—
260C23—131no—
261C23—131no—
262C23—132no—
263C23—268no—
264C23—264no—
265C23—264no—
266C23—264no—
267C23—261no—
268C23—261no—
269C23—522no—
270C23—524no—
271C23—522no—
272C23—524no—
273C23—528no—
274C23—524no—
275C23—524no—
276C23—528no—
277C23—528no—
278C23—524no—
279C23C22⋊#26112yes—
280C23C22⋊#26112yes—
281C23C22×#26111yescharacteristic
282C23C22×#26112yes—
283C23C22×#26112yescomplemented
284D4—28no—
285D4—264no—
286D4—264no—
287D4—264no—
288D4—264no—
289D4—268no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—132no—
293C2×C4—264no—
294C2×C4—264no—
295C2×C4—261no—
296C2×C4—261no—
297C2×C4—268no—
298C2×C4—5216no—
299C2×C4—528no—
300C2×C4C22×#26112yescomplemented
301C22—22no—
302C22—24no—
303C22—22no—
304C22—42no—
305C22—42no—
306C22—42no—
307C22—42no—
308C22—42no—
309C22—132no—
310C22—134no—
311C22—132no—
312C22—132no—
313C22—132no—
314C22—268no—
315C22—268no—
316C22—264no—
317C22—264no—
318C22—264no—
319C22—262no—
320C22—262no—
321C22—522no—
322C22—521no—
323C22—521no—
324C22—524no—
325C22—524no—
326C22—522no—
327C22—522no—
328C22—528no—
329C22—528no—
330C22—522no—
331C22C2×C22⋊#26111yescharacteristic
332C22C2×C22⋊#26114yes—
333C22C2×C22⋊#26111yescharacteristic
334C22C23×#26111yescharacteristic
335C4—22no—
336C4—262no—
337C4—528no—
338C2—21no—
339C2—21no—
340C2—24no—
341C2—42no—
342C2—134no—
343C2—262no—
344C2—262no—
345C2—262no—
346C2—522no—
347C2D13⋊#9912yesdirect product factor
348C2C22×C22⋊#26111yescharacteristic
subgroupG/H
centerC22C2×C22⋊#261
commutatorC22×C13C23×C4
FrattiniC22C23×#261
FittingC22×D4×C13C4
socleC22×C13C2×C22⋊C4
prime radicalC22×D4×D13C2
cosocleC22×D13C24
hypercenterC22×D4#261
hypocenterC13C22×#99
LCSG ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C24 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. C22×C22⋊#261C2semidirect
3. C2×#88119C2semidirect
4. D13⋊#99C2direct (N × H)
5. C2×#88107C2semidirect
6. C24×D13C4semidirect
9. C22×D4×C13C4semidirect
10. C22×C22⋊D13C4semidirect
15. C2×D4×D13C4semidirect
18. C22×C4×D13C4semidirect
21. C2×C22⋊#261C22semidirect
22. C2×C22⋊#261C22semidirect
23. #88119C22semidirect
24. #88107C22semidirect
26. C24×C13C2×C4semidirect
34. C23×D13C2×C4semidirect
35. C23×D13C2×C4semidirect
46. C2×D4×C13C2×C4semidirect
47. C22×C4×C13C2×C4semidirect
52. C2×C22⋊D13C2×C4semidirect
53. C2×C22⋊D13C2×C4semidirect
55. C22×Dic13C2×C4semidirect
62. C2×D52C2×C4semidirect
67. C2×C4×D13C2×C4semidirect
70. C22⋊#261C23semidirect
80. C23×C13C22×C4semidirect
104. C22×D13C22×C4semidirect
116. C2×C4×C13C22×C4semidirect
122. C2×Dic13C22×C4semidirect
161. C2×D13#99semidirect
179. C22×D4#261semidirect
192. C2×C13C2×#99semidirect
198. D13C2×#99semidirect
214. C24C2×#261semidirect
232. C2×D4C2×#261semidirect
241. C22×C4C2×#261semidirect
245. C13C22×#99semidirect
283. C23C22×#261semidirect
300. C2×C4C22×#261semidirect
347. C2D13⋊#99direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D4×D132
C22×C22⋊#2612
C2×#881192
D13⋊#992
C2×#881072
C22×#9913