Finite Group Databasebeta

← #15773510

Subgroups — #15773510

Order 3328.

482 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 482 conjugacy classes of subgroups — too many to draw. Only its 95 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
1C4×#88076C211yesmaximal, characteristic, complemented
2#13113180C211yesmaximal, characteristic, complemented
3#13112839C214yesmaximal, complemented
4C13×#2548C211yesmaximal, characteristic
5C2×C13×#127C411yescharacteristic
6C2×C13×#124—21no—
7C2×C4×Q8×C13C2211yescharacteristic
8C13×#394C412yes—
9C13×#394C2212yes—
10C13×#390—21no—
11C13×#390—21no—
12C13×#390—21no—
13C4×C13×C4⋊C4C411yescharacteristic
14C2×#88076—21no—
15#11718587—21no—
16C4×#6099—21no—
17#11718122C2212yes—
18#11718120—21no—
19#11718120C2212yes—
20C22×Q8×C13D411yescharacteristic
21C22×D4×C13—21no—
22C22×D4×C13—21no—
23C22×D4×C13C2×C412yes—
24C13×#127—41no—
25C13×#127—41no—
26C13×#124—44no—
27C4×Q8×C13—41no—
28C4×Q8×C13—41no—
29C2×C13×C4⋊C4—21no—
30C2×C13×C4⋊C4C2×C411yescharacteristic
31C2×C13×C4⋊C4D411yescharacteristic
32C2×C13×C4⋊C4C2311yescharacteristic
33C2×C13×C22⋊C4—22no—
34C2×C13×C22⋊C4—22no—
35C2×C13×C22⋊C4—22no—
36C2×C13×C22⋊C4—22no—
37C2×C42×C13—21no—
38C2×C42×C13C2×C411yescharacteristic
39C2×C42×C13D411yescharacteristic
40C2×C42×C13D411yescharacteristic
41C2×#6099—22no—
42C13×#95C2×C412yes—
43#88076—24no—
44C22⋊#1055—22no—
45C4⋊#1055—41no—
46#88043—41no—
47#88043—41no—
48C4×#1055—41no—
49#11781—131nomaximal, Sylow
50C24×C13—22no—
51C2×Q8×C13—22no—
52C2×Q8×C13—22no—
53C2×Q8×C13—41no—
54C2×D4×C13—42no—
55C2×D4×C13—42no—
56C2×D4×C13—42no—
57C2×D4×C13—42no—
58C2×D4×C13—42no—
59C2×D4×C13—41no—
60C2×D4×C13—41no—
61C2×D4×C13—42no—
62C2×D4×C13—82no—
63C22×C4×C13—22no—
64C22×C4×C13C22⋊C411yescharacteristic
65C22×C4×C13C22⋊C411yescharacteristic
66C22×C4×C13C22⋊C411yescharacteristic
67C22×C4×C13C22⋊C411yescharacteristic
68C22×C4×C13C22×C411yescharacteristic
69C22×C4×C13C2×D411yescharacteristic
70C22×C4×C13C2×D411yescharacteristic
71C13×C4⋊C4—41no—
72C13×C4⋊C4—41no—
73C13×C4⋊C4—41no—
74C13×C4⋊C4—42no—
75C13×C22⋊C4—44no—
76C13×C22⋊C4—44no—
77C13×C22⋊C4—82no—
78C13×C22⋊C4—82no—
79C42×C13—21no—
80C42×C13—21no—
81C42×C13—21no—
82C42×C13—21no—
83C42×C13—21no—
84C42×C13—21no—
85C42×C13—42no—
86#6099—24no—
87#6099—42no—
88C2×#1055—42no—
89C2×#1055—42no—
90#2548D1311yescharacteristic
91C4×#101—131no—
92#1467—131no—
93#1345—134no—
94C23×C13—42no—
95C23×C13—42no—
96C23×C13—42no—
97C23×C13—42no—
98C23×C13—42no—
99C23×C13—42no—
100C23×C13—42no—
101C23×C13C2×C22⋊C411yescharacteristic
102Q8×C13—44no—
103D4×C13—82no—
104D4×C13—84no—
105D4×C13—84no—
106D4×C13—82no—
107C2×C4×C13—21no—
108C2×C4×C13—21no—
109C2×C4×C13—21no—
110C2×C4×C13—21no—
111C2×C4×C13—22no—
112C2×C4×C13—21no—
113C2×C4×C13—21no—
114C2×C4×C13—21no—
115C2×C4×C13—21no—
116C2×C4×C13—21no—
117C2×C4×C13—21no—
118C2×C4×C13—41no—
119C2×C4×C13—41no—
120C2×C4×C13—41no—
121C2×C4×C13—42no—
122C2×C4×C13—42no—
123C2×C4×C13—42no—
124C2×C4×C13#9911yescharacteristic
125C2×C4×C13#9911yescharacteristic
126C2×C4×C13#10412yes—
127C2×C4×C13AGL(1,ℤ/8)12yes—
128#1055—44no—
129#1055—82no—
130C2×#127Dic1311yescharacteristic
131C2×#124—21no—
132C2×C4×Q8C2×D1311yescharacteristic
133#432—261no—
134C2×#101—261no—
135C4×M16—261no—
136#394Dic1312yes—
137#394C2×D1312yes—
138#390—21no—
139#390—21no—
140#390—21no—
141C4×C4⋊C4Dic1311yescharacteristic
142#343—132no—
143#324—132no—
144#324—261no—
145C22×C13—21no—
146C22×C13—21no—
147C22×C13—82no—
148C22×C13—82no—
149C22×C13—82no—
150C22×C13—82no—
151C22×C13—82no—
152C22×C13—82no—
153C22×C13—82no—
154C22×C13C2×#9911yescharacteristic
155C22×C13#41811yescharacteristic
156C22×C13C2×#10411yescharacteristic
157C4×C13—21no—
158C4×C13—22no—
159C4×C13—22no—
160C4×C13—41no—
161C4×C13—41no—
162C4×C13—41no—
163C4×C13—41no—
164C4×C13—82no—
165C4×C13#35512yes—
166C22×Q8C22⋊D1311yescharacteristic
167C22×D4—21no—
168C22×D4—21no—
169C22×D4C2×Dic1312yes—
170C2×M16—262no—
171#127—41no—
172#127—41no—
173#124—44no—
174C4×Q8—41no—
175C4×Q8—41no—
176C2×C4⋊C4—21no—
177C2×C4⋊C4C2×Dic1311yescharacteristic
178C2×C4⋊C4C22⋊D1311yescharacteristic
179C2×C4⋊C4C22×D1311yescharacteristic
180C2×C22⋊C4—22no—
181C2×C22⋊C4—22no—
182C2×C22⋊C4—22no—
183C2×C22⋊C4—22no—
184C2×C42—21no—
185C2×C42C2×Dic1311yescharacteristic
186C2×C42C22⋊D1311yescharacteristic
187C2×C42C22⋊D1311yescharacteristic
188C4⋊C8—521no—
189#101—264no—
190C22⋊C8—262no—
191#97—521no—
192#97—521no—
193C4×C8—521no—
194#95C2×Dic1312yes—
195C2×C13—21no—
196C2×C13—21no—
197C2×C13—162no—
198C2×C13#150711yescharacteristic
199C2×C13#212211yescharacteristic
200C2×C13C2×#35511yescharacteristic
201C24—22no—
202C2×Q8—22no—
203C2×Q8—22no—
204C2×Q8—41no—
205C2×D4—42no—
206C2×D4—42no—
207C2×D4—42no—
208C2×D4—42no—
209C2×D4—42no—
210C2×D4—41no—
211C2×D4—41no—
212C2×D4—42no—
213C2×D4—82no—
214C22×C4—22no—
215C22×C4C22⋊Dic1311yescharacteristic
216C22×C4C22⋊Dic1311yescharacteristic
217C22×C4C22⋊Dic1311yescharacteristic
218C22×C4C22⋊Dic1311yescharacteristic
219C22×C4C22×Dic1311yescharacteristic
220C22×C4C2×C22⋊D1311yescharacteristic
221C22×C4C2×C22⋊D1311yescharacteristic
222M16—264no—
223M16—522no—
224C2×C8—522no—
225C2×C8—522no—
226C4⋊C4—41no—
227C4⋊C4—41no—
228C4⋊C4—41no—
229C4⋊C4—42no—
230C22⋊C4—44no—
231C22⋊C4—44no—
232C22⋊C4—82no—
233C22⋊C4—82no—
234C42—21no—
235C42—21no—
236C42—21no—
237C42—21no—
238C42—21no—
239C42—21no—
240C42—42no—
241C13#1178111yescharacteristic, complemented, Sylow
242C23—42no—
243C23—42no—
244C23—42no—
245C23—42no—
246C23—42no—
247C23—42no—
248C23—42no—
249C23C2×C22⋊Dic1311yescharacteristic
250Q8—44no—
251D4—84no—
252D4—82no—
253D4—84no—
254D4—82no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—22no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—42no—
270C2×C4—42no—
271C2×C4—42no—
272C2×C4#8807411yescharacteristic
273C2×C4#8807411yescharacteristic
274C2×C4#8807712yes—
275C2×C4#8818612yes—
276C8—524no—
277C8—1042no—
278C22—21no—
279C22—21no—
280C22—82no—
281C22—82no—
282C22—82no—
283C22—82no—
284C22—82no—
285C22—82no—
286C22—82no—
287C22#1171887611yescharacteristic
288C22C2×#8807411yescharacteristic
289C22C2×#8807711yescharacteristic
290C4—22no—
291C4—22no—
292C4—21no—
293C4—41no—
294C4—41no—
295C4—41no—
296C4—41no—
297C4—82no—
298C4#1171813412yes—
299C2—21no—
300C2—21no—
301C2—162no—
302C2#1311335211yescharacteristic
303C2#1311648611yescharacteristic
304C2C2×#1171813411yescharacteristic
subgroupG/H
centerC22C2×#88074
commutatorC22×C4×C13C22×C4
FrattiniC2×C4⋊C4C22×D13
FittingC13×#2548C2
socleC22×C13C2×#99
prime radicalC2×C13×#127C4
cosocleC2×C13×C4⋊C4C23
hypercenter#2548D13
hypocenterC13#11781
LCSG ▷ C22×C4×C13 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #2548

Complements

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

NH ≅ G/Ntype
1. C4×#88076C2semidirect
2. #13113180C2semidirect
3. #13112839C2semidirect
241. C13#11781semidirect

Maximal subgroups

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

subgroupindex
C4×#880762
#131131802
#131128392
C13×#25482
#1178113