Finite Group Databasebeta

← #16778613

Subgroups — #16778613

Order 3328.

568 conjugacy classes of subgroups; only the 126 normal subgroups are shown.

normal subgroups only

This group has 568 conjugacy classes of subgroups — too many to draw. Only its 126 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#13130691C211yesmaximal, characteristic
2#13130497C211yesmaximal, characteristic
3#13129656C214yesmaximal, complemented
4#13123183C211yesmaximal, characteristic
5C22×D13⋊C8—21no—
6C2×C13×C4⋊Q8C411yescharacteristic
7C2×#88200C412yes—
8C2×C42×D13C2211yescharacteristic
9C2×#88111—21no—
10C2×C4⋊#1057—21no—
11#11718891C2212yes—
12#11718648—21no—
13#11718648—21no—
14#11718634—21no—
15#11718634—21no—
16#11718596C411yescharacteristic
17#11718290—21no—
18#11718290C2212yes—
19#11718290C2212yes—
20C22×Q8×C13C2×C412yes—
21C22×C4×D13C2×C411yescharacteristic
22C22×C4×D13D411yescharacteristic
23C22×C4×D13D411yescharacteristic
24C22×#1057—22no—
25C22×#1057—22no—
26C2×D13⋊C8—24no—
27C2×D13⋊C8—42no—
28C2×D13⋊C8—42no—
29C13×C4⋊Q8—42no—
30C2×C13×C4⋊C4—21no—
31C2×C13×C4⋊C4—21no—
32C2×C42×C13C2×C411yescharacteristic
33#88200—44no—
34C2×#6103—22no—
35C2×C4⋊Dic13—21no—
36C2×C4⋊Dic13—21no—
37C2×C4⋊Dic13C2×C412yes—
38C2×#6101—22no—
39C2×C4×Dic13D411yescharacteristic
40C2×C4×Dic13D411yescharacteristic
41C2×C4×Dic13C2311yescharacteristic
42C42×D13—42no—
43#88111—42no—
44C4⋊#1057—42no—
45#88071—22no—
46#88071—22no—
47#7667—131nomaximal, Sylow
48C23×D13C22⋊C411yescharacteristic
49C2×Q8×C13—24no—
50C2×Q8×C13—42no—
51C2×Q8×C13—42no—
52C22×C4×C13—22no—
53C22×C4×C13C22⋊C411yescharacteristic
54C22×C4×C13C22⋊C411yescharacteristic
55C22×C4×C13C22×C411yescharacteristic
56C22×Dic13—22no—
57C22×Dic13C22⋊C411yescharacteristic
58C22×Dic13C2×D411yescharacteristic
59C22×Dic13C2×D411yescharacteristic
60C2×C4×D13—22no—
61C2×C4×D13—22no—
62C2×C4×D13—22no—
63C2×C4×D13—22no—
64C2×C4×D13—41no—
65C2×C4×D13—41no—
66C2×C4×D13—41no—
67C2×C4×D13SD1612yes—
68C2×C4×D13SD1612yes—
69C2×C4×D13Q1612yes—
70C2×C4×D13Q1612yes—
71C2×#1057—24no—
72C2×#1057—42no—
73C2×#1057—42no—
74C2×#1057—42no—
75C2×#1057—42no—
76C2×#1057—42no—
77D13⋊C8—48no—
78C13×C4⋊C4—42no—
79C13×C4⋊C4—42no—
80C42×C13—22no—
81#6103—44no—
82C4⋊Dic13—42no—
83C4⋊Dic13—42no—
84C4⋊Dic13—42no—
85#6101—44no—
86C4×Dic13—22no—
87C4×Dic13—41no—
88C4×Dic13—41no—
89#2857—131no—
90#1797—131no—
91C2×#336—131no—
92#1272—134no—
93C23×C13C2×C22⋊C411yescharacteristic
94C22×D13—21no—
95C22×D13—21no—
96C22×D13—21no—
97C22×D13—21no—
98C22×D13#10012yes—
99C22×D13#10312yes—
100C22×D13#10312yes—
101Q8×C13—84no—
102C2×C4×C13—21no—
103C2×C4×C13—21no—
104C2×C4×C13—21no—
105C2×C4×C13—21no—
106C2×C4×C13—42no—
107C2×C4×C13—42no—
108C2×C4×C13—42no—
109C2×C4×C13#9912yes—
110C2×C4×C13#10312yes—
111C2×C4×C13#10312yes—
112C2×C4×C13#10412yes—
113C2×C4×C13#13112yes—
114C2×Dic13—21no—
115C2×Dic13—21no—
116C2×Dic13—21no—
117C2×Dic13—21no—
118C2×Dic13—21no—
119C2×Dic13—21no—
120C2×Dic13—21no—
121C2×Dic13—42no—
122C2×Dic13—42no—
123C2×Dic13—42no—
124C2×Dic13C2×SD1611yescharacteristic
125C2×Dic13C2×SD1611yescharacteristic
126C2×Dic13C2×Q1611yescharacteristic
127C2×Dic13C2×Q1611yescharacteristic
128C4×D13—24no—
129C4×D13—24no—
130C4×D13—42no—
131C4×D13—42no—
132C4×D13—44no—
133#1057—44no—
134#1057—82no—
135C23×C8—261no—
136C2×C4⋊Q8#26111yescharacteristic
137C2×C22⋊Q8—132no—
138C22×C42—131no—
139C2×C4⋊C8—261no—
140C2×C22⋊C8—261no—
141#391—132no—
142#389—261no—
143#389—261no—
144#384—131no—
145#380—261no—
146#380—261no—
147#336—132no—
148#336—132no—
149#336—261no—
150C22×C13#40811yescharacteristic
151C22×C13C2×#9911yescharacteristic
152C22×C13C2×#10011yescharacteristic
153C22×C13C2×#10311yescharacteristic
154C22×C13C2×#10311yescharacteristic
155C22×C13C2×#10411yescharacteristic
156C22×C13#42111yescharacteristic
157C2×D13—22no—
158C2×D13—22no—
159C2×D13—22no—
160C2×D13—22no—
161C2×D13—22no—
162C2×D13—22no—
163C2×D13#33314yes—
164C4×C13—22no—
165C4×C13—22no—
166C4×C13—82no—
167C4×C13#32814yes—
168Dic13—21no—
169Dic13—21no—
170Dic13—21no—
171Dic13—21no—
172Dic13—41no—
173Dic13—82no—
174C22×Q8C2×#26112yes—
175C23×C4—131no—
176C23×C4—131no—
177C23×C4—131no—
178C22×C8—262no—
179C22×C8—264no—
180C22×C8—262no—
181C22×C8—522no—
182C22×C8—522no—
183C4⋊Q8—42no—
184C22⋊Q8—524no—
185C2×C4⋊C4—21no—
186C2×C4⋊C4—21no—
187C2×C4⋊C4—132no—
188C2×C4⋊C4—262no—
189C2×C4⋊C4—261no—
190C2×C4⋊C4—261no—
191C2×C22⋊C4—262no—
192C2×C42—131no—
193C2×C42—131no—
194C2×C42—131no—
195C2×C42—522no—
196C2×C42C2×#26111yescharacteristic
197C4⋊C8—522no—
198C22⋊C8—522no—
199#95—262no—
200#95—262no—
201C2×C13#147111yescharacteristic
202C2×C13#148111yescharacteristic
203C2×C13#149311yescharacteristic
204C2×C13C2×#32811yescharacteristic
205C2×C13#152011yescharacteristic
206C2×C13#153011yescharacteristic
207C2×C13C2×#33311yescharacteristic
208D13—24no—
209C24—131no—
210C2×Q8—24no—
211C2×Q8—42no—
212C2×Q8—42no—
213C22×C4—22no—
214C22×C4—131no—
215C22×C4—131no—
216C22×C4—132no—
217C22×C4—132no—
218C22×C4—132no—
219C22×C4—132no—
220C22×C4—131no—
221C22×C4—262no—
222C22×C4—262no—
223C22×C4—262no—
224C22×C4—262no—
225C22×C4—262no—
226C22×C4—521no—
227C22×C4—521no—
228C22×C4—521no—
229C22×C4C22⋊#26111yescharacteristic
230C22×C4C22⋊#26111yescharacteristic
231C22×C4C22×#26111yescharacteristic
232C2×C8—264no—
233C2×C8—522no—
234C2×C8—528no—
235C2×C8—522no—
236C2×C8—522no—
237C2×C8—522no—
238C2×C8—522no—
239C4⋊C4—42no—
240C4⋊C4—42no—
241C4⋊C4—522no—
242C4⋊C4—522no—
243C4⋊C4—524no—
244C4⋊C4—522no—
245C22⋊C4—524no—
246C42—22no—
247C42—262no—
248C42—521no—
249C42—521no—
250C13#766711yescharacteristic, complemented, Sylow
251C23—132no—
252C23—132no—
253C23—132no—
254C23—261no—
255C23—261no—
256C23—261no—
257C23—261no—
258C23C2×C22⋊#26111yescharacteristic
259Q8—84no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—42no—
265C2×C4—42no—
266C2×C4—42no—
267C2×C4—131no—
268C2×C4—131no—
269C2×C4—131no—
270C2×C4—131no—
271C2×C4—261no—
272C2×C4—261no—
273C2×C4—261no—
274C2×C4—261no—
275C2×C4—264no—
276C2×C4—264no—
277C2×C4—261no—
278C2×C4—261no—
279C2×C4—261no—
280C2×C4—522no—
281C2×C4—522no—
282C2×C4—524no—
283C2×C4—522no—
284C2×C4—522no—
285C2×C4—522no—
286C2×C4#8811712yes—
287C2×C4#8811712yes—
288C2×C4#8811812yes—
289C2×C4#8811912yes—
290C2×C4#8823812yes—
291C8—524no—
292C8—1042no—
293C22—134no—
294C22—262no—
295C22—262no—
296C22—262no—
297C22—262no—
298C22—262no—
299C22—262no—
300C22#1171914711yescharacteristic
301C22D13⋊#10011yescharacteristic
302C22C2×#8811711yescharacteristic
303C22C2×#8811711yescharacteristic
304C22C2×#8811811yescharacteristic
305C22#1171915511yescharacteristic
306C22C2×#8811911yescharacteristic
307C4—22no—
308C4—22no—
309C4—82no—
310C4—261no—
311C4—261no—
312C4—261no—
313C4—261no—
314C4—521no—
315C4—1042no—
316C4#1171829814yes—
317C2—264no—
318C2#1313011111yescharacteristic
319C2#1313014511yescharacteristic
320C2#1313018511yescharacteristic
321C2C2×#1171829811yescharacteristic
322C2#1313027611yescharacteristic
323C2#1313030711yescharacteristic
324C2D13⋊#33311yescharacteristic
subgroupG/H
centerC23C2×C22⋊#261
commutatorC22×C4×C13C22×C4
FrattiniC22×C4C22×#261
FittingC2×C13×C4⋊Q8C4
socleC23×C13C2×C22⋊C4
prime radicalC23×D13C22⋊C4
cosocleC2×C4×Dic13C23
hypercenterC2×C4⋊Q8#261
hypocenterC13#7667
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4⋊Q8

Complements

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

NH ≅ G/Ntype
3. #13129656C2semidirect
250. C13#7667semidirect

Maximal subgroups

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

subgroupindex
#131306912
#131304972
#131296562
#131231832
#766713