Finite Group Databasebeta

← #15750892

Subgroups — #15750892

Order 3328.

684 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 684 conjugacy classes of subgroups — too many to draw. Only its 143 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#13117400C211yesmaximal, characteristic
2#13114684C212yesmaximal, complemented
3#13112657C211yesmaximal, characteristic, complemented
4#13112656C212yesmaximal, complemented
5C13×#1270C211yesmaximal, characteristic, complemented
6C2×#88194C411yescharacteristic
7C2×D4×Dic13C411yescharacteristic
8C2×#88147C411yescharacteristic
9C2×#88135—22no—
10C13×#390C2211yescharacteristic
11C2×#88054—22no—
12C2×C8×Dic13—22no—
13#11718637C411yescharacteristic
14#11718618—22no—
15#11718600C2211yescharacteristic
16C42×Dic13C2211yescharacteristic
17C13×#336C2212yes—
18#11718116C2212yes—
19C22×D4×C13C2×C411yescharacteristic
20C22×C22⋊D13—22no—
21C23×Dic13—21no—
22C22×D52C2×C411yescharacteristic
23C22×C4×D13—21no—
24C22×C8×C13—22no—
25C2×C13×C4⋊C4C2×C411yescharacteristic
26C2×C13×C22⋊C4—22no—
27C2×C42×C13C2311yescharacteristic
28C2×C22⋊Dic13—21no—
29#88194—22no—
30#88194C814yescomplemented
31D4×Dic13—42no—
32C2×#6103—22no—
33C2×#6103—21no—
34C2×C4⋊Dic13C2×C411yescharacteristic
35C2×#6101—22no—
36C2×C4×Dic13C2×C411yescharacteristic
37C2×C4×Dic13C2×C411yescharacteristic
38C2×C4×Dic13D412yes—
39C2×C4×Dic13D412yes—
40C22×#1055—22no—
41#88147—42no—
42#88135—44no—
43#88135—44no—
44#88054—28no—
45C8×Dic13—44no—
46#7569—131nomaximal, Sylow
47C24×C13—21no—
48C23×D13—21no—
49C2×D4×C13—21no—
50C2×D4×C13—41no—
51C2×D4×C13—41no—
52C2×D4×C13C2×C812yes—
53C22×C4×C13—21no—
54C22×C4×C13C22×C411yescharacteristic
55C22×C4×C13C2×D412yes—
56C2×C22⋊D13—28no—
57C2×C22⋊D13—44no—
58C2×C22⋊D13—44no—
59C22×Dic13—21no—
60C22×Dic13—42no—
61C22×Dic13—44no—
62C22×Dic13C22⋊C411yescharacteristic
63C22×Dic13C22⋊C412yes—
64C22×Dic13C22⋊C411yescharacteristic
65C2×D52—21no—
66C2×D52—41no—
67C2×D52—41no—
68C2×D52C2×C812yes—
69C2×C4×D13—42no—
70C2×C4×D13—44no—
71C2×C8×C13—24no—
72C2×C8×C13—42no—
73C2×C8×C13—42no—
74C13×C4⋊C4—41no—
75C13×C22⋊C4—42no—
76C13×C22⋊C4—42no—
77C42×C13—41no—
78C22⋊Dic13—42no—
79#6103—42no—
80#6103—42no—
81#6103—42no—
82C4⋊Dic13—41no—
83#6101—44no—
84C4×Dic13—22no—
85C4×Dic13—24no—
86C4×Dic13C2×C812yes—
87C4×Dic13M1612yes—
88C4×Dic13D814yes—
89C4×Dic13SD1614yes—
90C2×#1055—24no—
91C2×#1055—42no—
92C2×#1055—42no—
93C4×#127—131no—
94C4×C4⋊C8—132no—
95#1270—131no—
96#1270—132no—
97#1270D1311yescharacteristic, complemented
98C23×C13—22no—
99C23×C13—41no—
100C23×C13—41no—
101C23×C13—42no—
102C23×C13—42no—
103C23×C13C2×C22⋊C411yescharacteristic
104C22×D13—22no—
105C22×D13—41no—
106C22×D13—41no—
107C22×D13—42no—
108C22×D13—42no—
109D4×C13—42no—
110D4×C13—42no—
111C2×C4×C13—22no—
112C2×C4×C13—21no—
113C2×C4×C13—21no—
114C2×C4×C13—22no—
115C2×C4×C13—41no—
116C2×C4×C13—42no—
117C2×C4×C13C22×C811yescharacteristic
118C2×C4×C13C2×M1611yescharacteristic
119C2×C4×C13C2×D812yes—
120C2×C4×C13C2×SD1612yes—
121C22⋊D13—416no—
122C2×Dic13—21no—
123C2×Dic13—22no—
124C2×Dic13—41no—
125C2×Dic13—42no—
126C2×Dic13—84no—
127C2×Dic13C22⋊C814yes—
128C2×Dic13#10012yes—
129C2×Dic13#10214yes—
130C2×Dic13#10214yes—
131C2×Dic13#10414yes—
132D52—42no—
133D52—42no—
134C4×D13—84no—
135C8×C13—44no—
136#1055—44no—
137C2×#127—131no—
138C2×C4×D4—131no—
139C2×C4×D4—131no—
140C2×C4×D4—262no—
141C2×C4⋊C8—262no—
142C2×C4×C8—262no—
143#390—131no—
144#390—262no—
145#390C2×D1311yescharacteristic
146#384—131no—
147C43—131no—
148#336—132no—
149#336C2×D1312yes—
150C22×C13—42no—
151C22×C13—44no—
152C22×C13—81no—
153C22×C13—82no—
154C22×C13—81no—
155C22×C13C2×C22⋊C811yescharacteristic
156C22×C13#41011yescharacteristic
157C22×C13C2×#10011yescharacteristic
158C22×C13C2×#10212yes—
159C22×C13C2×#10412yes—
160C2×D13—42no—
161C2×D13—44no—
162C2×D13—81no—
163C2×D13—82no—
164C2×D13—81no—
165C4×C13—21no—
166C4×C13—21no—
167C4×C13—22no—
168C4×C13—22no—
169C4×C13—81no—
170Dic13—41no—
171Dic13—81no—
172Dic13D4⋊C818yes—
173Dic13#33114yes—
174C22×D4—131no—
175C22×D4—262no—
176C22×D4C4×D1311yescharacteristic
177C23×C4—261no—
178C23×C4—261no—
179C22×C8—22no—
180C22×C8—262no—
181#127—134no—
182#127—262no—
183C4×D4—524no—
184C4×D4—524no—
185C4×D4—522no—
186C4×D4—522no—
187C2×C4⋊C4—131no—
188C2×C4⋊C4—262no—
189C2×C4⋊C4C4×D1311yescharacteristic
190C2×C22⋊C4—22no—
191C2×C22⋊C4—261no—
192C2×C22⋊C4—261no—
193C2×C22⋊C4—262no—
194C2×C42—131no—
195C2×C42—132no—
196C2×C42—131no—
197C2×C42—132no—
198C2×C42C22×D1311yescharacteristic
199C4⋊C8—268no—
200C4×C8—524no—
201C2×C13—82no—
202C2×C13#146011yescharacteristic
203C2×C13C2×D4⋊C812yes—
204C2×C13#150212yes—
205C2×C13#152511yescharacteristic
206C2×C13C2×#33111yescharacteristic
207D13—82no—
208C24—21no—
209C24—261no—
210C2×D4—21no—
211C2×D4—41no—
212C2×D4—41no—
213C2×D4—132no—
214C2×D4—268no—
215C2×D4—261no—
216C2×D4—521no—
217C2×D4—521no—
218C2×D4—524no—
219C2×D4—524no—
220C2×D4C8×D1312yes—
221C22×C4—21no—
222C22×C4—132no—
223C22×C4—131no—
224C22×C4—131no—
225C22×C4—261no—
226C22×C4—524no—
227C22×C4—522no—
228C22×C4—524no—
229C22×C4—522no—
230C22×C4C2×C4×D1311yescharacteristic
231C22×C4D4×D1312yes—
232C2×C8—24no—
233C2×C8—42no—
234C2×C8—42no—
235C2×C8—264no—
236C2×C8—522no—
237C2×C8—522no—
238C4⋊C4—41no—
239C4⋊C4—521no—
240C4⋊C4—524no—
241C22⋊C4—42no—
242C22⋊C4—42no—
243C22⋊C4—522no—
244C22⋊C4—522no—
245C22⋊C4—522no—
246C22⋊C4—522no—
247C42—41no—
248C42—132no—
249C42—132no—
250C42—134no—
251C42—134no—
252C42—264no—
253C42—262no—
254C13#756911yescharacteristic, complemented, Sylow
255C23—22no—
256C23—41no—
257C23—41no—
258C23—42no—
259C23—42no—
260C23—262no—
261C23—521no—
262C23—521no—
263C23—522no—
264C23—522no—
265C23C22⋊C4×D1311yescharacteristic
266D4—42no—
267D4—42no—
268D4—522no—
269D4—522no—
270D4—5216no—
271C2×C4—22no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—22no—
275C2×C4—41no—
276C2×C4—42no—
277C2×C4—132no—
278C2×C4—134no—
279C2×C4—134no—
280C2×C4—134no—
281C2×C4—134no—
282C2×C4—261no—
283C2×C4—262no—
284C2×C4—521no—
285C2×C4—522no—
286C2×C4—1044no—
287C2×C4—1044no—
288C2×C4C2×C8×D1311yescharacteristic
289C2×C4M16×D1311yescharacteristic
290C2×C4D8×D1312yes—
291C2×C4SD16×D1312yes—
292C8—44no—
293C8—524no—
294C22—42no—
295C22—44no—
296C22—81no—
297C22—81no—
298C22—82no—
299C22—522no—
300C22—524no—
301C22—1041no—
302C22—1041no—
303C22—1042no—
304C22D13×C22⋊C811yescharacteristic
305C22#1171840111yescharacteristic
306C22D13×#10011yescharacteristic
307C22D13×#10212yes—
308C22D13×#10412yes—
309C4—21no—
310C4—21no—
311C4—22no—
312C4—22no—
313C4—81no—
314C4—138no—
315C4—134no—
316C4—521no—
317C4—1041no—
318C2—82no—
319C2—1042no—
320C2#1311315511yescharacteristic
321C2D13×D4⋊C812yes—
322C2#1311332912yes—
323C2#1311342611yescharacteristic
324C2D13×#33111yescharacteristic
subgroupG/H
centerC23C22⋊C4×D13
commutatorC2×C4×C13C22×C8
FrattiniC2×C42C22×D13
FittingC13×#1270C2
socleC23×C13C2×C22⋊C4
prime radicalC2×#88194C4
cosocleC2×C42×C13C23
hypercenter#1270D13
hypocenterC13#7569
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1270

Complements

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

NH ≅ G/Ntype
2. #13114684C2semidirect
3. #13112657C2semidirect
4. #13112656C2semidirect
5. C13×#1270C2semidirect
30. #88194C8semidirect
97. #1270D13semidirect
254. C13#7569semidirect

Maximal subgroups

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

subgroupindex
#131174002
#131146842
#131126572
#131126562
C13×#12702
#756913