Finite Group Databasebeta

← #15778914

Subgroups — #15778914

Order 3328.

524 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 524 conjugacy classes of subgroups — too many to draw. Only its 119 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
1C2×#11718133C212yesmaximal
2#13114824C212yesmaximal
3#13112961C212yesmaximal
4C13×#2326C211yesmaximal, characteristic
5C2×C13×#124C2211yescharacteristic
6C2×C4×Q8×C13C411yescharacteristic, complemented
7C2×C4×D4×C13C2211yescharacteristic
8C13×#391C411yescharacteristic, complemented
9C13×#390C2211yescharacteristic
10C13×#388—22no—
11C13×#385—22no—
12C13×#384C411yescharacteristic, complemented
13C13×#376C411yescharacteristic, complemented
14C2×#88074C2214yes—
15#11718873—22no—
16#11718133—24no—
17#11718118—22no—
18C22×Q8×C13C2×C411yescharacteristic
19C22×D4×C13C2311yescharacteristic
20C23×C4×C13D412yes—
21C13×#124—22no—
22C13×#124D412yes—
23C13×#124Q812yes—
24C4×Q8×C13—42no—
25C4×D4×C13—42no—
26C2×C13×C4⋊C4—21no—
27C2×C13×C4⋊C4—22no—
28C2×C13×C4⋊C4C2×C411yescharacteristic
29C2×C13×C4⋊C4C2×C411yescharacteristic
30C2×C13×C22⋊C4—22no—
31C2×C13×C22⋊C4—22no—
32C2×C13×C22⋊C4D412yes—
33C2×C42×C13—21no—
34C2×C42×C13C2×C411yescharacteristic
35C2×C42×C13C2×C411yescharacteristic
36C2×C42×C13C2×C411yescharacteristic
37C2×C22⋊Dic13—24no—
38C2×C4⋊Dic13—42no—
39C13×#95—21no—
40C13×#95—22no—
41C13×#95—21no—
42#88074—24no—
43#88074—24no—
44#88071—42no—
45#12800—131nomaximal, Sylow
46C24×C13C2×D412yes—
47C2×Q8×C13—21no—
48C2×Q8×C13—41no—
49C2×Q8×C13—41no—
50C2×Q8×C13C4⋊C412yescomplemented
51C2×D4×C13—41no—
52C2×D4×C13—41no—
53C2×D4×C13C2×D411yescharacteristic
54C2×D4×C13C2×Q811yescharacteristic
55C2×D4×C13#4112yes—
56C22×C4×C13—21no—
57C22×C4×C13—21no—
58C22×C4×C13—22no—
59C22×C4×C13—22no—
60C22×C4×C13—21no—
61C22×C4×C13—21no—
62C22×C4×C13—82no—
63C22×C4×C13C22⋊C411yescharacteristic
64C22×C4×C13C22⋊C412yes—
65C22×C4×C13C22⋊C411yescharacteristic
66C22×C4×C13C22×C411yescharacteristic
67C22×Dic13—44no—
68C13×C4⋊C4—41no—
69C13×C4⋊C4—41no—
70C13×C4⋊C4—42no—
71C13×C4⋊C4—82no—
72C13×C22⋊C4—24no—
73C13×C22⋊C4—24no—
74C13×C22⋊C4—42no—
75C13×C22⋊C4—82no—
76C42×C13—22no—
77C42×C13—21no—
78C42×C13—41no—
79C42×C13—42no—
80C42×C13C4⋊C412yescomplemented
81C22⋊Dic13—44no—
82C22⋊Dic13—44no—
83C4⋊Dic13—84no—
84#2326D1311yescharacteristic
85C2×#354—132no—
86#1799—132no—
87#1393—132no—
88C23×C13—22no—
89C23×C13—22no—
90C23×C13—42no—
91C23×C13—42no—
92C23×C13C2×C22⋊C411yescharacteristic
93C23×C13#12112yes—
94C23×C13C22⋊Q812yes—
95Q8×C13—42no—
96Q8×C13—42no—
97D4×C13—41no—
98D4×C13—41no—
99D4×C13—42no—
100C2×C4×C13—21no—
101C2×C4×C13—21no—
102C2×C4×C13—22no—
103C2×C4×C13—22no—
104C2×C4×C13—21no—
105C2×C4×C13—22no—
106C2×C4×C13—41no—
107C2×C4×C13—44no—
108C2×C4×C13—41no—
109C2×C4×C13—41no—
110C2×C4×C13—41no—
111C2×C4×C13—41no—
112C2×C4×C13—42no—
113C2×C4×C13—41no—
114C2×C4×C13—41no—
115C2×C4×C13—42no—
116C2×C4×C13—41no—
117C2×C4×C13—41no—
118C2×C4×C13—41no—
119C2×C4×C13—82no—
120C2×C4×C13#9912yes—
121C2×C4×C13C2×C4⋊C411yescharacteristic
122C2×C4×C13#11711yescharacteristic
123C2×Dic13—84no—
124C2×Dic13—84no—
125C2×Dic13—84no—
126C2×#124C2×D1311yescharacteristic
127C2×C4×Q8Dic1311yescharacteristic, complemented
128C2×C4×D4C2×D1311yescharacteristic
129C2×#99—134no—
130#391Dic1311yescharacteristic, complemented
131#390C2×D1311yescharacteristic
132#388—22no—
133#385—22no—
134#384Dic1311yescharacteristic, complemented
135#380—262no—
136#376Dic1311yescharacteristic, complemented
137#354—264no—
138#342—262no—
139C22×C13—21no—
140C22×C13—21no—
141C22×C13—22no—
142C22×C13—22no—
143C22×C13—42no—
144C22×C13—42no—
145C22×C13—42no—
146C22×C13—42no—
147C22×C13—82no—
148C22×C13#38011yescharacteristic
149C22×C13C2×#9911yescharacteristic
150C22×C13#41011yescharacteristic
151C4×C13—21no—
152C4×C13—21no—
153C4×C13—22no—
154C4×C13—42no—
155C4×C13—42no—
156C4×C13—42no—
157C4×C13—41no—
158C4×C13—81no—
159C4×C13—81no—
160Dic13—164no—
161C22×Q8C2×Dic1311yescharacteristic
162C22×D4C22×D1311yescharacteristic
163C23×C4C22⋊D1312yes—
164#124—22no—
165#124Dic2612yes—
166#124D5212yes—
167C4×Q8—42no—
168C4×D4—42no—
169C2×C4⋊C4—21no—
170C2×C4⋊C4—22no—
171C2×C4⋊C4—522no—
172C2×C4⋊C4C2×Dic1311yescharacteristic
173C2×C4⋊C4C2×Dic1311yescharacteristic
174C2×C22⋊C4—22no—
175C2×C22⋊C4—22no—
176C2×C22⋊C4—264no—
177C2×C22⋊C4C22⋊D1312yes—
178C2×C42—21no—
179C2×C42C2×Dic1311yescharacteristic
180C2×C42C2×Dic1311yescharacteristic
181C2×C42C2×Dic1311yescharacteristic
182#99—264no—
183#99—264no—
184#95—21no—
185#95—22no—
186#95—21no—
187#95—522no—
188C2×C13—21no—
189C2×C13—21no—
190C2×C13—42no—
191C2×C13—42no—
192C2×C13#179911yescharacteristic
193C2×C13#212711yescharacteristic
194C2×C13#212911yescharacteristic
195C24C2×C22⋊D1312yes—
196C2×Q8—21no—
197C2×Q8—41no—
198C2×Q8—41no—
199C2×Q8C4⋊Dic1312yescomplemented
200C2×D4—41no—
201C2×D4—41no—
202C2×D4C2×Dic2611yescharacteristic
203C2×D4C2×D5211yescharacteristic
204C2×D4#612712yes—
205C22×C4—21no—
206C22×C4—21no—
207C22×C4—22no—
208C22×C4—22no—
209C22×C4—21no—
210C22×C4—21no—
211C22×C4—82no—
212C22×C4—524no—
213C22×C4C22⋊Dic1311yescharacteristic
214C22×C4C22⋊Dic1312yes—
215C22×C4C22⋊Dic1311yescharacteristic
216C22×C4C22×Dic1311yescharacteristic
217C4⋊C4—41no—
218C4⋊C4—41no—
219C4⋊C4—42no—
220C4⋊C4—82no—
221C4⋊C4—1044no—
222C22⋊C4—24no—
223C22⋊C4—24no—
224C22⋊C4—42no—
225C22⋊C4—82no—
226C22⋊C4—524no—
227C22⋊C4—524no—
228C42—22no—
229C42—21no—
230C42—41no—
231C42—42no—
232C42C4⋊Dic1312yescomplemented
233C13#1280011yescharacteristic, complemented, Sylow
234C23—22no—
235C23—22no—
236C23—42no—
237C23—42no—
238C23#8817812yes—
239C23#8818412yes—
240C23C2×C22⋊Dic1311yescharacteristic
241Q8—42no—
242Q8—42no—
243D4—41no—
244D4—41no—
245D4—42no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—22no—
249C2×C4—22no—
250C2×C4—21no—
251C2×C4—22no—
252C2×C4—41no—
253C2×C4—44no—
254C2×C4—41no—
255C2×C4—41no—
256C2×C4—41no—
257C2×C4—41no—
258C2×C4—42no—
259C2×C4—41no—
260C2×C4—41no—
261C2×C4—42no—
262C2×C4—41no—
263C2×C4—41no—
264C2×C4—41no—
265C2×C4—82no—
266C2×C4—1044no—
267C2×C4—1044no—
268C2×C4—1044no—
269C2×C4#8807412yes—
270C2×C4C2×C4⋊Dic1311yescharacteristic
271C2×C4#8818011yescharacteristic
272C22—21no—
273C22—21no—
274C22—22no—
275C22—22no—
276C22—42no—
277C22—42no—
278C22—42no—
279C22—42no—
280C22—82no—
281C22#1171887311yescharacteristic
282C22C2×#8807411yescharacteristic
283C22#1171890111yescharacteristic
284C4—22no—
285C4—21no—
286C4—21no—
287C4—42no—
288C4—42no—
289C4—41no—
290C4—42no—
291C4—81no—
292C4—81no—
293C4—2084no—
294C2—21no—
295C2—21no—
296C2—42no—
297C2—42no—
298C2#1311482411yescharacteristic
299C2#1311650511yescharacteristic
300C2#1311651111yescharacteristic
subgroupG/H
centerC22C2×#88074
commutatorC22×C4×C13C22×C4
FrattiniC22×D4C22×D13
FittingC13×#2326C2
socleC22×C13C2×#99
prime radical, cosocleC22×D4×C13C23
hypercenter#2326D13
hypocenterC13#12800
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #2326

Complements

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

NH ≅ G/Ntype
6. C2×C4×Q8×C13C4semidirect
8. C13×#391C4semidirect
12. C13×#384C4semidirect
13. C13×#376C4semidirect
50. C2×Q8×C13C4⋊C4semidirect
80. C42×C13C4⋊C4semidirect
127. C2×C4×Q8Dic13semidirect
130. #391Dic13semidirect
134. #384Dic13semidirect
136. #376Dic13semidirect
199. C2×Q8C4⋊Dic13semidirect
232. C42C4⋊Dic13semidirect
233. C13#12800semidirect

Maximal subgroups

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

subgroupindex
C2×#117181332
#131148242
#131129612
C13×#23262
#1280013