Finite Group Databasebeta

← #16778474

Subgroups — #16778474

Order 3328.

594 conjugacy classes of subgroups; only the 116 normal subgroups are shown.

normal subgroups only

This group has 594 conjugacy classes of subgroups — too many to draw. Only its 116 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
1#13130562C211yesmaximal, characteristic
2#13130562C211yesmaximal, characteristic
3#13129654C214yesmaximal, complemented
4C2×#11718646C211yesmaximal, characteristic
5C22×C13×C4⋊C4C411yescharacteristic
6C22×C4⋊Dic13—21no—
7C22×C4⋊Dic13C411yescharacteristic
8C22×C4×Dic13C2211yescharacteristic
9C2×C22⋊#1057—21no—
10C2×C22⋊#1057—21no—
11C2×#88110—21no—
12C2×#88110—21no—
13C2×#88071—21no—
14#11718646—21no—
15#11718646—21no—
16#11718646C412yes—
17#11718646C2212yes—
18#11718290C2212yes—
19#11718290C2212yes—
20C23×C4×C13—21no—
21C23×C4×C13C2×C411yescharacteristic
22C23×Dic13—21no—
23C23×Dic13D411yescharacteristic
24C23×Dic13D411yescharacteristic
25C22×#1057—22no—
26C22×#1057—22no—
27C2×C13×C4⋊C4—21no—
28C2×C13×C4⋊C4—24no—
29C2×C13×C4⋊C4C2×C412yes—
30C2×C4⋊Dic13—21no—
31C2×C4⋊Dic13—22no—
32C2×C4⋊Dic13—22no—
33C2×C4⋊Dic13—44no—
34C2×C4⋊Dic13—42no—
35C2×C4⋊Dic13C2×C412yes—
36C2×C4×Dic13—42no—
37C2×C4×Dic13C2×C411yescharacteristic
38C2×C4×Dic13D411yescharacteristic
39C2×C4×Dic13D411yescharacteristic
40C2×C4×Dic13C2311yescharacteristic
41C22⋊#1057—24no—
42C22⋊#1057—24no—
43#88110—42no—
44#88110—42no—
45#88071—22no—
46#88071—22no—
47#7627—131nomaximal, Sylow
48C24×C13C22⋊C411yescharacteristic
49C22×C4×C13—22no—
50C22×C4×C13—22no—
51C22×C4×C13—22no—
52C22×C4×C13—24no—
53C22×C4×C13—22no—
54C22×C4×C13—42no—
55C22×C4×C13—42no—
56C22×C4×C13C22⋊C411yescharacteristic
57C22×C4×C13C22×C411yescharacteristic
58C22×Dic13—22no—
59C22×Dic13—22no—
60C22×Dic13—22no—
61C22×Dic13—22no—
62C22×Dic13—22no—
63C22×Dic13—41no—
64C22×Dic13—41no—
65C22×Dic13—42no—
66C22×Dic13—42no—
67C22×Dic13—42no—
68C22×Dic13C22⋊C411yescharacteristic
69C22×Dic13C22⋊C411yescharacteristic
70C22×Dic13C2×D411yescharacteristic
71C22×Dic13C2×D411yescharacteristic
72C2×#1057—24no—
73C2×#1057—24no—
74C2×#1057—42no—
75C2×#1057—42no—
76C2×#1057—42no—
77C2×#1057—42no—
78C13×C4⋊C4—24no—
79C13×C4⋊C4—22no—
80C13×C4⋊C4M1614yes—
81C4⋊Dic13—44no—
82C4⋊Dic13—42no—
83C4⋊Dic13—44no—
84C4⋊Dic13—42no—
85C4×Dic13—22no—
86C4×Dic13—22no—
87C4×Dic13—41no—
88C4×Dic13—41no—
89C2×#389—131no—
90#1749—131no—
91#1749—131no—
92#1271—134no—
93C23×C13—21no—
94C23×C13—21no—
95C23×C13—21no—
96C23×C13—21no—
97C23×C13#10112yes—
98C23×C13#10412yes—
99C23×C13#10412yes—
100C23×C13C2×C22⋊C411yescharacteristic
101C2×C4×C13—28no—
102C2×C4×C13—21no—
103C2×C4×C13—21no—
104C2×C4×C13—21no—
105C2×C4×C13—21no—
106C2×C4×C13—24no—
107C2×C4×C13—48no—
108C2×C4×C13—42no—
109C2×C4×C13—42no—
110C2×C4×C13#9912yes—
111C2×C4×C13C2×M1612yes—
112C2×Dic13—21no—
113C2×Dic13—21no—
114C2×Dic13—21no—
115C2×Dic13—21no—
116C2×Dic13—21no—
117C2×Dic13—21no—
118C2×Dic13—21no—
119C2×Dic13—21no—
120C2×Dic13—21no—
121C2×Dic13—21no—
122C2×Dic13—44no—
123C2×Dic13—44no—
124C2×Dic13—42no—
125C2×Dic13—42no—
126C2×Dic13—42no—
127C2×Dic13—84no—
128C2×Dic13AGL(1,ℤ/8)12yes—
129C2×Dic13#13712yes—
130#1057—44no—
131#1057—44no—
132C22×C4⋊C4—131no—
133C22×C4⋊C4—261no—
134C22×C4⋊C4#26111yescharacteristic
135C22×C42—131no—
136C2×C22⋊C8—261no—
137C2×C22⋊C8—261no—
138C2×#97—261no—
139C2×#97—261no—
140#389—132no—
141#389—132no—
142#389—261no—
143#389—261no—
144C2×#95—261no—
145#336—132no—
146#336—132no—
147C22×C13—22no—
148C22×C13—22no—
149C22×C13—22no—
150C22×C13—22no—
151C22×C13—22no—
152C22×C13—22no—
153C22×C13#33014yes—
154C22×C13#40711yescharacteristic
155C22×C13C2×#9911yescharacteristic
156C22×C13C2×#10111yescharacteristic
157C22×C13#41811yescharacteristic
158C22×C13#41911yescharacteristic
159C22×C13C2×#10411yescharacteristic
160C22×C13C2×#10411yescharacteristic
161C4×C13—22no—
162C4×C13—22no—
163C4×C13—44no—
164Dic13—22no—
165Dic13—22no—
166Dic13—41no—
167Dic13—41no—
168Dic13—82no—
169C23×C4—21no—
170C23×C4—131no—
171C23×C4—131no—
172C23×C4—261no—
173C23×C4C2×#26111yescharacteristic
174C22×C8—262no—
175C22×C8—262no—
176C2×C4⋊C4—21no—
177C2×C4⋊C4—24no—
178C2×C4⋊C4—132no—
179C2×C4⋊C4—262no—
180C2×C4⋊C4—262no—
181C2×C4⋊C4—261no—
182C2×C4⋊C4—524no—
183C2×C4⋊C4—522no—
184C2×C4⋊C4C2×#26112yes—
185C2×C42—131no—
186C2×C42—131no—
187C2×C42—131no—
188C2×C42—131no—
189C2×C42—522no—
190C22⋊C8—264no—
191C22⋊C8—264no—
192#97—522no—
193#97—522no—
194#95—262no—
195#95—262no—
196C2×C13—24no—
197C2×C13#146311yescharacteristic
198C2×C13#149011yescharacteristic
199C2×C13#149111yescharacteristic
200C2×C13#150711yescharacteristic
201C2×C13#150811yescharacteristic
202C2×C13C2×#33011yescharacteristic
203C2×C13#155611yescharacteristic
204C24C22⋊#26111yescharacteristic
205C22×C4—22no—
206C22×C4—22no—
207C22×C4—22no—
208C22×C4—24no—
209C22×C4—22no—
210C22×C4—42no—
211C22×C4—42no—
212C22×C4—131no—
213C22×C4—131no—
214C22×C4—131no—
215C22×C4—131no—
216C22×C4—262no—
217C22×C4—262no—
218C22×C4—262no—
219C22×C4—262no—
220C22×C4—262no—
221C22×C4—521no—
222C22×C4—521no—
223C22×C4—522no—
224C22×C4—522no—
225C22×C4—522no—
226C22×C4C22⋊#26111yescharacteristic
227C22×C4C22×#26111yescharacteristic
228C2×C8—264no—
229C2×C8—264no—
230C2×C8—522no—
231C2×C8—522no—
232C2×C8—522no—
233C2×C8—522no—
234C4⋊C4—24no—
235C4⋊C4—22no—
236C4⋊C4—522no—
237C4⋊C4—524no—
238C4⋊C4—524no—
239C4⋊C4—522no—
240C4⋊C4#612214yes—
241C42—262no—
242C42—262no—
243C42—521no—
244C42—521no—
245C13#762711yescharacteristic, complemented, Sylow
246C23—21no—
247C23—21no—
248C23—21no—
249C23—21no—
250C23#8811312yes—
251C23#8811612yes—
252C23#8811812yes—
253C23C2×C22⋊#26111yescharacteristic
254C2×C4—28no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—24no—
260C2×C4—48no—
261C2×C4—42no—
262C2×C4—42no—
263C2×C4—132no—
264C2×C4—132no—
265C2×C4—261no—
266C2×C4—261no—
267C2×C4—261no—
268C2×C4—261no—
269C2×C4—261no—
270C2×C4—261no—
271C2×C4—261no—
272C2×C4—261no—
273C2×C4—261no—
274C2×C4—261no—
275C2×C4—524no—
276C2×C4—524no—
277C2×C4—522no—
278C2×C4—522no—
279C2×C4—522no—
280C2×C4—1044no—
281C2×C4#8810712yes—
282C2×C4C2×#612212yes—
283C8—524no—
284C8—524no—
285C22—22no—
286C22—22no—
287C22—22no—
288C22—22no—
289C22—22no—
290C22—22no—
291C22#1171824214yes—
292C22C2×#8810711yescharacteristic
293C22C2×#8811311yescharacteristic
294C22#1171913811yescharacteristic
295C22C2×#8811611yescharacteristic
296C22#1171915311yescharacteristic
297C22C2×#8811811yescharacteristic
298C22#1171916911yescharacteristic
299C4—22no—
300C4—22no—
301C4—44no—
302C4—262no—
303C4—262no—
304C4—521no—
305C4—521no—
306C4—1042no—
307C2—24no—
308C2#1313008411yescharacteristic
309C2#1313017511yescharacteristic
310C2#1313017811yescharacteristic
311C2#1313023311yescharacteristic
312C2#1313023511yescharacteristic
313C2C2×#1171824211yescharacteristic
314C2#1313036511yescharacteristic
subgroupG/H
centerC23C2×C22⋊#261
commutatorC22×C4×C13C22×C4
FrattiniC22×C4C22×#261
FittingC22×C13×C4⋊C4C4
socleC23×C13C2×C22⋊C4
prime radicalC24×C13C22⋊C4
cosocleC2×C4×Dic13C23
hypercenterC22×C4⋊C4#261
hypocenterC13#7627
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. #13129654C2semidirect
245. C13#7627semidirect

Maximal subgroups

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

subgroupindex
#131305622
#131296542
C2×#117186462
#762713