Finite Group Databasebeta

← #16778685

Subgroups — #16778685

Order 3328.

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

normal subgroups only

This group has 562 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
1C4×#88111C211yesmaximal, characteristic
2#13130500C211yesmaximal, characteristic
3#13129656C214yesmaximal, complemented
4#13123183C211yesmaximal, characteristic
5C22×#6118—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×#6118—24no—
27C2×#6118—42no—
28C2×#6118—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—24no—
44C4×#1057—42no—
45#88071—22no—
46#88071—22no—
47#7687—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—22no—
65C2×C4×D13—22no—
66C2×C4×D13—41no—
67C2×C4×D13—41no—
68C2×C4×D13SD1612yes—
69C2×C4×D13Q1612yes—
70C2×#1057—24no—
71C2×#1057—24no—
72C2×#1057—42no—
73C2×#1057—42no—
74C2×#1057—42no—
75C2×#1057—42no—
76#6118—48no—
77C13×C4⋊C4—42no—
78C13×C4⋊C4—42no—
79C42×C13—22no—
80#6103—44no—
81C4⋊Dic13—42no—
82C4⋊Dic13—42no—
83C4⋊Dic13—42no—
84#6101—44no—
85C4×Dic13—22no—
86C4×Dic13—41no—
87C4×Dic13—41no—
88#2857—131no—
89C4×C22⋊C8—131no—
90#1728—131no—
91#1272—134no—
92C23×C13C2×C22⋊C411yescharacteristic
93C22×D13—21no—
94C22×D13—21no—
95C22×D13—21no—
96C22×D13—21no—
97C22×D13—21no—
98C22×D13—21no—
99C22×D13#10312yes—
100Q8×C13—84no—
101C2×C4×C13—21no—
102C2×C4×C13—21no—
103C2×C4×C13—21no—
104C2×C4×C13—21no—
105C2×C4×C13—42no—
106C2×C4×C13—42no—
107C2×C4×C13—42no—
108C2×C4×C13#9912yes—
109C2×C4×C13#10312yes—
110C2×C4×C13#10412yes—
111C2×C4×C13#10412yes—
112C2×C4×C13#13112yes—
113C2×Dic13—21no—
114C2×Dic13—21no—
115C2×Dic13—21no—
116C2×Dic13—21no—
117C2×Dic13—21no—
118C2×Dic13—21no—
119C2×Dic13—42no—
120C2×Dic13—42no—
121C2×Dic13—42no—
122C2×Dic13#10012yes—
123C2×Dic13C2×SD1611yescharacteristic
124C2×Dic13C2×Q1611yescharacteristic
125C2×Dic13#13712yes—
126C4×D13—24no—
127C4×D13—24no—
128C4×D13—44no—
129C4×D13—44no—
130#1057—44no—
131#1057—44no—
132C22×M16—261no—
133C2×C4⋊Q8#26111yescharacteristic
134C2×C22⋊Q8—132no—
135C22×C42—131no—
136C2×C22⋊C8—261no—
137C2×C4×C8—261no—
138#391—132no—
139#389—261no—
140#389—261no—
141#384—131no—
142#380—261no—
143#380—261no—
144#336—132no—
145#336—132no—
146#336—261no—
147C22×C13#40811yescharacteristic
148C22×C13C2×#9911yescharacteristic
149C22×C13C2×#10011yescharacteristic
150C22×C13C2×#10311yescharacteristic
151C22×C13#41911yescharacteristic
152C22×C13C2×#10411yescharacteristic
153C22×C13C2×#10411yescharacteristic
154C2×D13—22no—
155C2×D13—22no—
156C2×D13—22no—
157C2×D13—41no—
158C2×D13—41no—
159C2×D13—41no—
160C2×D13—41no—
161C4×C13—22no—
162C4×C13—22no—
163C4×C13—82no—
164C4×C13#32814yes—
165Dic13—22no—
166Dic13—21no—
167Dic13—21no—
168Dic13—22no—
169Dic13—82no—
170C22×Q8C2×#26112yes—
171C23×C4—131no—
172C23×C4—131no—
173C23×C4—131no—
174C2×M16—264no—
175C2×M16—522no—
176C2×M16—522no—
177C22×C8—262no—
178C22×C8—262no—
179C4⋊Q8—42no—
180C22⋊Q8—524no—
181C2×C4⋊C4—21no—
182C2×C4⋊C4—21no—
183C2×C4⋊C4—132no—
184C2×C4⋊C4—262no—
185C2×C4⋊C4—261no—
186C2×C4⋊C4—261no—
187C2×C22⋊C4—262no—
188C2×C42—131no—
189C2×C42—131no—
190C2×C42—131no—
191C2×C42—522no—
192C2×C42C2×#26111yescharacteristic
193C22⋊C8—264no—
194C4×C8—522no—
195#95—262no—
196#95—262no—
197C2×C13#147111yescharacteristic
198C2×C13#148511yescharacteristic
199C2×C13#149311yescharacteristic
200C2×C13C2×#32811yescharacteristic
201C2×C13#150811yescharacteristic
202C2×C13#152511yescharacteristic
203C2×C13#154811yescharacteristic
204D13—42no—
205C24—131no—
206C2×Q8—24no—
207C2×Q8—42no—
208C2×Q8—42no—
209C22×C4—22no—
210C22×C4—131no—
211C22×C4—131no—
212C22×C4—131no—
213C22×C4—132no—
214C22×C4—132no—
215C22×C4—262no—
216C22×C4—262no—
217C22×C4—262no—
218C22×C4—262no—
219C22×C4—262no—
220C22×C4—262no—
221C22×C4—262no—
222C22×C4—521no—
223C22×C4—521no—
224C22×C4C22⋊#26111yescharacteristic
225C22×C4C22⋊#26111yescharacteristic
226C22×C4C22×#26111yescharacteristic
227M16—528no—
228C2×C8—264no—
229C2×C8—264no—
230C2×C8—522no—
231C2×C8—522no—
232C2×C8—522no—
233C2×C8—522no—
234C4⋊C4—42no—
235C4⋊C4—42no—
236C4⋊C4—522no—
237C4⋊C4—524no—
238C4⋊C4—522no—
239C4⋊C4—522no—
240C22⋊C4—524no—
241C42—22no—
242C42—262no—
243C42—521no—
244C42—521no—
245C13#768711yescharacteristic, complemented, Sylow
246C23—132no—
247C23—261no—
248C23—261no—
249C23—261no—
250C23—261no—
251C23—261no—
252C23—261no—
253C23C2×C22⋊#26111yescharacteristic
254Q8—84no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—42no—
260C2×C4—42no—
261C2×C4—42no—
262C2×C4—132no—
263C2×C4—131no—
264C2×C4—131no—
265C2×C4—132no—
266C2×C4—261no—
267C2×C4—261no—
268C2×C4—261no—
269C2×C4—261no—
270C2×C4—261no—
271C2×C4—261no—
272C2×C4—264no—
273C2×C4—264no—
274C2×C4—524no—
275C2×C4—524no—
276C2×C4—522no—
277C2×C4—522no—
278C2×C4—522no—
279C2×C4#8811712yes—
280C2×C4#8811812yes—
281C2×C4#8811812yes—
282C2×C4#8811912yes—
283C2×C4#8823812yes—
284C8—524no—
285C8—524no—
286C22—262no—
287C22—262no—
288C22—262no—
289C22—521no—
290C22—521no—
291C22—521no—
292C22—521no—
293C22#1171914711yescharacteristic
294C22D13⋊#10011yescharacteristic
295C22C2×#8811711yescharacteristic
296C22#1171915311yescharacteristic
297C22C2×#8811811yescharacteristic
298C22C2×#8811811yescharacteristic
299C22C2×#8811911yescharacteristic
300C4—22no—
301C4—22no—
302C4—82no—
303C4—262no—
304C4—261no—
305C4—261no—
306C4—262no—
307C4—1042no—
308C4#1171829814yes—
309C2—522no—
310C2#1313011111yescharacteristic
311C2#1313015911yescharacteristic
312C2#1313018511yescharacteristic
313C2C2×#1171829811yescharacteristic
314C2#1313023611yescharacteristic
315C2#1313029211yescharacteristic
316C2#1313035011yescharacteristic
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#7687
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
245. C13#7687semidirect

Maximal subgroups

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

subgroupindex
C4×#881112
#131305002
#131296562
#131231832
#768713