Finite Group Databasebeta

← #16778270

Subgroups — #16778270

Order 3328.

684 conjugacy classes of subgroups; only the 146 normal subgroups are shown.

normal subgroups only

This group has 684 conjugacy classes of subgroups — too many to draw. Only its 146 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×#88112C212yesmaximal, complemented
2#13129653C212yesmaximal, complemented
3#13129652C212yesmaximal, complemented
4C4×#88194C211yesmaximal, characteristic
5C2×C4×D4×C13C411yescharacteristic
6C2×#88194C411yescharacteristic
7C2×C4×C22⋊D13—22no—
8C2×C4×D52C411yescharacteristic
9C2×#88112—22no—
10C2×C4×#1057—22no—
11#11718882C2211yescharacteristic
12#11718649C2211yescharacteristic
13#11718637C411yescharacteristic
14#11718618—22no—
15C42×Dic13C2211yescharacteristic
16#11718290C2214yes—
17C22×D4×C13C2×C411yescharacteristic
18C23×C4×C13—21no—
19C22×C22⋊D13—22no—
20C22×D52C2×C411yescharacteristic
21C22×C4×D13—21no—
22C22×#1057—24no—
23C4×D4×C13—42no—
24C2×C13×C4⋊C4C2×C411yescharacteristic
25C2×C13×C22⋊C4—21no—
26C2×C42×C13C2×C411yescharacteristic
27C2×C22⋊Dic13—22no—
28#88194—22no—
29#88194C814yescomplemented
30C4×C22⋊D13—44no—
31C4×C22⋊D13—44no—
32C2×#6103—21no—
33C2×#6103—22no—
34C2×C4⋊Dic13C2×C411yescharacteristic
35C2×#6101—22no—
36C2×C4×Dic13C2×C411yescharacteristic
37C2×C4×Dic13D412yes—
38C2×C4×Dic13D412yes—
39C2×C4×Dic13C2311yescharacteristic
40C4×D52—42no—
41#88112—28no—
42C4×#1057—44no—
43#7569—131nomaximal, Sylow
44C24×C13—21no—
45C23×D13—21no—
46C2×D4×C13—21no—
47C2×D4×C13—41no—
48C2×D4×C13—41no—
49C2×D4×C13C2×C812yes—
50C22×C4×C13—21no—
51C22×C4×C13—42no—
52C22×C4×C13—44no—
53C22×C4×C13C22⋊C411yescharacteristic
54C22×C4×C13C22⋊C411yescharacteristic
55C22×C4×C13C22×C411yescharacteristic
56C2×C22⋊D13—28no—
57C2×C22⋊D13—44no—
58C2×C22⋊D13—44no—
59C22×Dic13—21no—
60C22×Dic13C22⋊C412yes—
61C22×Dic13C2×D412yes—
62C2×D52—21no—
63C2×D52—41no—
64C2×D52—41no—
65C2×D52C2×C812yes—
66C2×C4×D13—42no—
67C2×C4×D13—44no—
68C2×#1057—28no—
69C2×#1057—44no—
70C2×#1057—44no—
71C13×C4⋊C4—41no—
72C13×C22⋊C4—42no—
73C42×C13—22no—
74C22⋊Dic13—42no—
75C22⋊Dic13—42no—
76#6103—42no—
77#6103—42no—
78#6103—42no—
79C4⋊Dic13—41no—
80#6101—44no—
81C4×Dic13—24no—
82C4×Dic13—41no—
83C4×Dic13C2×C812yes—
84C4×Dic13M1612yes—
85C4×Dic13D814yes—
86C4×Dic13SD1614yes—
87C4×#127—131no—
88C4×C4⋊C8—132no—
89#1270—132no—
90#1270—132no—
91C23×C13—22no—
92C23×C13—41no—
93C23×C13—41no—
94C23×C13—42no—
95C23×C13—42no—
96C23×C13C2×C22⋊C411yescharacteristic
97C22×D13—22no—
98C22×D13—41no—
99C22×D13—41no—
100C22×D13—42no—
101C22×D13—42no—
102D4×C13—42no—
103D4×C13—42no—
104C2×C4×C13—21no—
105C2×C4×C13—21no—
106C2×C4×C13—21no—
107C2×C4×C13—22no—
108C2×C4×C13—41no—
109C2×C4×C13—42no—
110C2×C4×C13—84no—
111C2×C4×C13#10012yes—
112C2×C4×C13#10214yes—
113C2×C4×C13C22×C811yescharacteristic
114C2×C4×C13C2×M1611yescharacteristic
115C22⋊D13—416no—
116C2×Dic13—22no—
117C2×Dic13—22no—
118C2×Dic13—41no—
119C2×Dic13—42no—
120C2×Dic13C22⋊C814yes—
121C2×Dic13#10214yes—
122C2×Dic13#10414yes—
123C2×Dic13C2×D812yes—
124C2×Dic13C2×SD1612yes—
125D52—42no—
126D52—42no—
127C4×D13—84no—
128#1057—48no—
129C2×#127—131no—
130C2×C4×D4—131no—
131C2×C4×D4—262no—
132C2×C4×D4#26111yescharacteristic
133C2×C4⋊C8—262no—
134C2×C4×C8—262no—
135#390—131no—
136#390—131no—
137#390—262no—
138#384—131no—
139C43—131no—
140#336—134no—
141C22×C13—42no—
142C22×C13—44no—
143C22×C13—81no—
144C22×C13—82no—
145C22×C13—81no—
146C22×C13C2×C22⋊C811yescharacteristic
147C22×C13#41011yescharacteristic
148C22×C13C2×#10011yescharacteristic
149C22×C13C2×#10212yes—
150C22×C13C2×#10412yes—
151C2×D13—42no—
152C2×D13—44no—
153C2×D13—81no—
154C2×D13—82no—
155C2×D13—81no—
156C4×C13—21no—
157C4×C13—21no—
158C4×C13—41no—
159C4×C13—81no—
160C4×C13#33114yes—
161Dic13—22no—
162Dic13—22no—
163Dic13—81no—
164Dic13D4⋊C818yes—
165C22×D4—131no—
166C22×D4—262no—
167C22×D4C2×#26111yescharacteristic
168C23×C4—21no—
169C23×C4—261no—
170C22×C8—264no—
171#127—134no—
172#127—262no—
173C4×D4—42no—
174C4×D4—522no—
175C4×D4—524no—
176C4×D4—524no—
177C2×C4⋊C4—131no—
178C2×C4⋊C4—262no—
179C2×C4⋊C4C2×#26111yescharacteristic
180C2×C22⋊C4—21no—
181C2×C22⋊C4—262no—
182C2×C22⋊C4—262no—
183C2×C22⋊C4—261no—
184C2×C42—132no—
185C2×C42—131no—
186C2×C42—132no—
187C2×C42—131no—
188C2×C42C2×#26111yescharacteristic
189C4⋊C8—268no—
190C4×C8—524no—
191C2×C13—82no—
192C2×C13#146011yescharacteristic
193C2×C13C2×D4⋊C812yes—
194C2×C13#150212yes—
195C2×C13#152511yescharacteristic
196C2×C13C2×#33111yescharacteristic
197D13—82no—
198C24—21no—
199C24—261no—
200C2×D4—21no—
201C2×D4—41no—
202C2×D4—41no—
203C2×D4—132no—
204C2×D4—268no—
205C2×D4—261no—
206C2×D4—521no—
207C2×D4—521no—
208C2×D4—524no—
209C2×D4—524no—
210C2×D4D13⋊C812yes—
211C22×C4—21no—
212C22×C4—44no—
213C22×C4—42no—
214C22×C4—132no—
215C22×C4—132no—
216C22×C4—261no—
217C22×C4—524no—
218C22×C4—522no—
219C22×C4C22⋊#26111yescharacteristic
220C22×C4C22⋊#26111yescharacteristic
221C22×C4C22×#26111yescharacteristic
222C2×C8—268no—
223C2×C8—524no—
224C2×C8—524no—
225C4⋊C4—41no—
226C4⋊C4—521no—
227C4⋊C4—524no—
228C22⋊C4—42no—
229C22⋊C4—522no—
230C22⋊C4—522no—
231C22⋊C4—522no—
232C22⋊C4—522no—
233C22⋊C4—522no—
234C42—22no—
235C42—134no—
236C42—134no—
237C42—132no—
238C42—132no—
239C42—264no—
240C42—521no—
241C13#756911yescharacteristic, complemented, Sylow
242C23—22no—
243C23—41no—
244C23—41no—
245C23—42no—
246C23—42no—
247C23—262no—
248C23—521no—
249C23—521no—
250C23—522no—
251C23—522no—
252C23C2×C22⋊#26111yescharacteristic
253D4—42no—
254D4—42no—
255D4—522no—
256D4—522no—
257D4—5216no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—22no—
262C2×C4—41no—
263C2×C4—42no—
264C2×C4—84no—
265C2×C4—134no—
266C2×C4—134no—
267C2×C4—134no—
268C2×C4—132no—
269C2×C4—132no—
270C2×C4—262no—
271C2×C4—262no—
272C2×C4—521no—
273C2×C4—522no—
274C2×C4—1044no—
275C2×C4#8811514yes—
276C2×C4#8812112yes—
277C2×C4C2×D13⋊C811yescharacteristic
278C2×C4D13⋊M1611yescharacteristic
279C8—528no—
280C22—42no—
281C22—44no—
282C22—81no—
283C22—81no—
284C22—82no—
285C22—522no—
286C22—524no—
287C22—1041no—
288C22—1041no—
289C22—1042no—
290C22#1171911611yescharacteristic
291C22D13⋊(C22⋊C8)11yescharacteristic
292C22C2×#8811512yes—
293C22D13⋊#10412yes—
294C22C2×#8812111yescharacteristic
295C4—21no—
296C4—21no—
297C4—41no—
298C4—81no—
299C4—138no—
300C4—262no—
301C4—262no—
302C4—1041no—
303C4#1171829714yes—
304C2—82no—
305C2—1042no—
306C2#1313007511yescharacteristic
307C2D13⋊(D4⋊C8)12yes—
308C2#1313021512yes—
309C2#1313029011yescharacteristic
310C2C2×#1171829711yescharacteristic
subgroupG/H
centerC22×C4C22⋊#261
commutatorC2×C4×C13C22×C8
FrattiniC22×C4C22×#261
FittingC2×C4×D4×C13C4
socleC23×C13C2×C22⋊C4
prime radicalC2×#88194C4
cosocleC2×C4×Dic13C23
hypercenterC2×C4×D4#261
hypocenterC13#7569
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
1. C4×#88112C2semidirect
2. #13129653C2semidirect
3. #13129652C2semidirect
29. #88194C8semidirect
241. C13#7569semidirect

Maximal subgroups

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

subgroupindex
C4×#881122
#131296532
#131296522
C4×#881942
#756913