Finite Group Databasebeta

← #15778918

Subgroups — #15778918

Order 3328.

500 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 500 conjugacy classes of subgroups — too many to draw. Only its 123 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×#11718134C212yesmaximal
2#13114832C212yesmaximal, complemented
3#13112963C212yesmaximal, complemented
4C4×C13×#124C211yesmaximal, characteristic
5C2×C13×#124C2211yescharacteristic
6C2×C4×Q8×C13C2211yescharacteristic
7C2×C4×D4×C13C411yescharacteristic
8C13×#391C2211yescharacteristic
9C13×#390C411yescharacteristic
10C13×#388—22no—
11C13×#382C411yescharacteristic
12C4×C13×C22⋊C4—22no—
13C43×C13C411yescharacteristic
14C2×#88076C2214yes—
15#11718585—22no—
16#11718134—24no—
17#11718122—22no—
18C22×Q8×C13C2311yescharacteristic
19C22×D4×C13C2×C411yescharacteristic
20C23×C4×C13—21no—
21C13×#124—22no—
22C13×#124D412yes—
23C13×#124Q812yes—
24C4×Q8×C13—41no—
25C4×Q8×C13—41no—
26C4×D4×C13—41no—
27C4×D4×C13—41no—
28C2×C13×C4⋊C4C2×C411yescharacteristic
29C2×C13×C4⋊C4C2×C411yescharacteristic
30C2×C13×C4⋊C4D412yes—
31C2×C13×C22⋊C4—22no—
32C2×C13×C22⋊C4—22no—
33C2×C13×C22⋊C4—21no—
34C2×C42×C13—21no—
35C2×C42×C13—21no—
36C2×C42×C13C2×C411yescharacteristic
37C2×C42×C13C2×C411yescharacteristic
38C2×C42×C13C2×C411yescharacteristic
39C2×C42×C13D412yes—
40C2×#6099—24no—
41C13×#95—22no—
42C13×#95—22no—
43#88076—24no—
44#88076—24no—
45C4⋊#1055—42no—
46C4⋊#1055—42no—
47#12801—131nomaximal, Sylow
48C24×C13—21no—
49C2×Q8×C13—41no—
50C2×Q8×C13—41no—
51C2×Q8×C13C2×D411yescharacteristic
52C2×Q8×C13C2×Q811yescharacteristic
53C2×Q8×C13#4112yes—
54C2×D4×C13—21no—
55C2×D4×C13—41no—
56C2×D4×C13—41no—
57C2×D4×C13C4⋊C412yes—
58C22×C4×C13—21no—
59C22×C4×C13—21no—
60C22×C4×C13—21no—
61C22×C4×C13—44no—
62C22×C4×C13—41no—
63C22×C4×C13—41no—
64C22×C4×C13C22⋊C412yes—
65C22×C4×C13C22⋊C411yescharacteristic
66C22×C4×C13C22⋊C411yescharacteristic
67C22×C4×C13C22×C411yescharacteristic
68C22×C4×C13C2×D412yes—
69C13×C4⋊C4—41no—
70C13×C4⋊C4—42no—
71C13×C4⋊C4—41no—
72C13×C22⋊C4—24no—
73C13×C22⋊C4—24no—
74C13×C22⋊C4—44no—
75C13×C22⋊C4—42no—
76C42×C13—21no—
77C42×C13—21no—
78C42×C13—22no—
79C42×C13—22no—
80C42×C13—21no—
81C42×C13—41no—
82C42×C13—42no—
83C42×C13—42no—
84C42×C13C4⋊C412yes—
85#6099—44no—
86#6099—44no—
87C2×#1055—44no—
88C4×#124D1311yescharacteristic
89C2×#355—132no—
90#1801—132no—
91#1394—132no—
92C23×C13—22no—
93C23×C13—42no—
94C23×C13—42no—
95C23×C13—41no—
96C23×C13—41no—
97C23×C13C2×C22⋊C411yescharacteristic
98Q8×C13—41no—
99Q8×C13—41no—
100Q8×C13—42no—
101D4×C13—42no—
102D4×C13—42no—
103C2×C4×C13—22no—
104C2×C4×C13—21no—
105C2×C4×C13—22no—
106C2×C4×C13—21no—
107C2×C4×C13—22no—
108C2×C4×C13—22no—
109C2×C4×C13—22no—
110C2×C4×C13—21no—
111C2×C4×C13—22no—
112C2×C4×C13—41no—
113C2×C4×C13—41no—
114C2×C4×C13—41no—
115C2×C4×C13—41no—
116C2×C4×C13—41no—
117C2×C4×C13—42no—
118C2×C4×C13—42no—
119C2×C4×C13—41no—
120C2×C4×C13—82no—
121C2×C4×C13—82no—
122C2×C4×C13#9911yescharacteristic
123C2×C4×C13#9911yescharacteristic
124C2×C4×C13C2×C4⋊C411yescharacteristic
125C2×C4×C13#11711yescharacteristic
126C2×C4×C13#12112yes—
127C2×C4×C13C22⋊Q812yes—
128#1055—84no—
129C2×#124C2×D1311yescharacteristic
130C2×C4×Q8C2×D1311yescharacteristic
131C2×C4×D4Dic1311yescharacteristic
132#423—262no—
133C2×#101—134no—
134#391C2×D1311yescharacteristic
135#390Dic1311yescharacteristic
136#388—22no—
137#382Dic1311yescharacteristic
138C4×C22⋊C4—22no—
139C43Dic1311yescharacteristic
140#355—264no—
141#343—262no—
142C22×C13—21no—
143C22×C13—21no—
144C22×C13—44no—
145C22×C13—42no—
146C22×C13—82no—
147C22×C13—81no—
148C22×C13—81no—
149C22×C13#38011yescharacteristic
150C22×C13C2×#9911yescharacteristic
151C22×C13#41011yescharacteristic
152C4×C13—22no—
153C4×C13—21no—
154C4×C13—21no—
155C4×C13—22no—
156C4×C13—21no—
157C4×C13—42no—
158C4×C13—42no—
159C4×C13—41no—
160C4×C13—42no—
161C4×C13—81no—
162C4×C13#35512yescomplemented
163C22×Q8C22×D1311yescharacteristic
164C22×D4C2×Dic1311yescharacteristic
165C23×C4—21no—
166C2×M16—264no—
167#124—22no—
168#124Dic2612yes—
169#124D5212yes—
170C4×Q8—41no—
171C4×Q8—41no—
172C4×D4—41no—
173C4×D4—41no—
174C2×C4⋊C4C2×Dic1311yescharacteristic
175C2×C4⋊C4C2×Dic1311yescharacteristic
176C2×C4⋊C4C22⋊D1312yes—
177C2×C22⋊C4—22no—
178C2×C22⋊C4—21no—
179C2×C22⋊C4—22no—
180C2×C42—21no—
181C2×C42—21no—
182C2×C42C2×Dic1311yescharacteristic
183C2×C42C2×Dic1311yescharacteristic
184C2×C42C2×Dic1311yescharacteristic
185C2×C42C22⋊D1312yes—
186C4⋊C8—522no—
187C4⋊C8—522no—
188#101—264no—
189#101—264no—
190#95—22no—
191#95—22no—
192C2×C13—21no—
193C2×C13—21no—
194C2×C13—82no—
195C2×C13#179911yescharacteristic
196C2×C13C2×#35511yescharacteristic
197C2×C13#213211yescharacteristic
198C24—21no—
199C2×Q8—41no—
200C2×Q8—41no—
201C2×Q8C2×Dic2611yescharacteristic
202C2×Q8C2×D5211yescharacteristic
203C2×Q8#612712yes—
204C2×D4—21no—
205C2×D4—41no—
206C2×D4—41no—
207C2×D4C4⋊Dic1312yes—
208C22×C4—21no—
209C22×C4—21no—
210C22×C4—21no—
211C22×C4—44no—
212C22×C4—41no—
213C22×C4—41no—
214C22×C4C22⋊Dic1312yes—
215C22×C4C22⋊Dic1311yescharacteristic
216C22×C4C22⋊Dic1311yescharacteristic
217C22×C4C22×Dic1311yescharacteristic
218C22×C4C2×C22⋊D1312yes—
219M16—524no—
220M16—524no—
221C2×C8—524no—
222C4⋊C4—41no—
223C4⋊C4—42no—
224C4⋊C4—41no—
225C22⋊C4—24no—
226C22⋊C4—24no—
227C22⋊C4—42no—
228C22⋊C4—44no—
229C42—22no—
230C42—22no—
231C42—21no—
232C42—21no—
233C42—21no—
234C42—41no—
235C42—42no—
236C42—42no—
237C42C4⋊Dic1312yes—
238C13#1280111yescharacteristic, complemented, Sylow
239C23—22no—
240C23—42no—
241C23—42no—
242C23—41no—
243C23—41no—
244C23C2×C22⋊Dic1311yescharacteristic
245Q8—41no—
246Q8—41no—
247Q8—42no—
248D4—42no—
249D4—42no—
250C2×C4—21no—
251C2×C4—22no—
252C2×C4—21no—
253C2×C4—22no—
254C2×C4—22no—
255C2×C4—22no—
256C2×C4—22no—
257C2×C4—21no—
258C2×C4—22no—
259C2×C4—41no—
260C2×C4—41no—
261C2×C4—41no—
262C2×C4—41no—
263C2×C4—41no—
264C2×C4—42no—
265C2×C4—42no—
266C2×C4—41no—
267C2×C4—82no—
268C2×C4—82no—
269C2×C4#8807411yescharacteristic
270C2×C4#8807411yescharacteristic
271C2×C4#8817812yes—
272C2×C4C2×C4⋊Dic1311yescharacteristic
273C2×C4#8818011yescharacteristic
274C2×C4#8818412yes—
275C8—1044no—
276C22—21no—
277C22—21no—
278C22—44no—
279C22—42no—
280C22—82no—
281C22—81no—
282C22—81no—
283C22#1171887311yescharacteristic
284C22C2×#8807411yescharacteristic
285C22#1171890111yescharacteristic
286C4—21no—
287C4—22no—
288C4—22no—
289C4—21no—
290C4—21no—
291C4—42no—
292C4—42no—
293C4—41no—
294C4—42no—
295C4—81no—
296C4#1171813412yescomplemented
297C2—21no—
298C2—21no—
299C2—82no—
300C2#1311482411yescharacteristic
301C2C2×#1171813411yescharacteristic
302C2#1311652111yescharacteristic
subgroupG/H
centerC22C2×#88074
commutatorC22×C4×C13C22×C4
FrattiniC22×Q8C22×D13
FittingC4×C13×#124C2
socleC22×C13C2×#99
prime radicalC22×D4×C13C2×C4
cosocleC22×Q8×C13C23
hypercenterC4×#124D13
hypocenterC13#12801
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ C4×#124

Complements

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

NH ≅ G/Ntype
2. #13114832C2semidirect
3. #13112963C2semidirect
162. C4×C13#355semidirect
238. C13#12801semidirect
296. C4#11718134semidirect

Maximal subgroups

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

subgroupindex
C2×#117181342
#131148322
#131129632
C4×C13×#1242
#1280113