Finite Group Databasebeta

← #15751014

Subgroups — #15751014

Order 3328.

654 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 654 conjugacy classes of subgroups — too many to draw. Only its 117 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#13117323C211yesmaximal, characteristic
2#13114815C212yesmaximal, complemented
3#13112661C212yesmaximal, complemented
4#13112657C211yesmaximal, characteristic, complemented
5C13×#1270C211yesmaximal, characteristic, complemented
6C22×#6129C411yescharacteristic
7C2×#88146C411yescharacteristic
8C2×C42×D13C2211yescharacteristic
9C13×#390C2211yescharacteristic
10#11718882C411yescharacteristic
11C2×#88060—22no—
12C2×#88054—22no—
13#11718635C411yescharacteristic
14#11718617—22no—
15C22⋊C4×Dic13—22no—
16#11718590C2211yescharacteristic
17C13×#336C2212yes—
18#11718116C2212yes—
19C22×D4×C13C2×C411yescharacteristic
20C22×C22⋊D13—21no—
21C23×Dic13—21no—
22C2×#6129—22no—
23C2×#6129—42no—
24C2×#6129—42no—
25C2×#6129C814yescomplemented
26C22×C4×D13C2×C411yescharacteristic
27C22×C4×D13D412yes—
28C22×Dic26C2×C411yescharacteristic
29C22×C8×C13—22no—
30C2×C13×C4⋊C4C2×C411yescharacteristic
31C2×C13×C22⋊C4—22no—
32C2×C42×C13C2311yescharacteristic
33C2×C22⋊Dic13—22no—
34C2×#6103—21no—
35C2×C4⋊Dic13C2×C411yescharacteristic
36C2×C4×Dic13—21no—
37C2×C4×Dic13C2×C411yescharacteristic
38C2×C4×Dic13D412yes—
39C22×#1055—22no—
40#88146—42no—
41C42×D13—42no—
42#88071—22no—
43#88071—22no—
44#88060—44no—
45#88054—44no—
46#7597—131nomaximal, Sylow
47C24×C13—21no—
48C23×D13C22⋊C411yescharacteristic
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—24no—
57C2×C22⋊D13—42no—
58C2×C22⋊D13—42no—
59C22×Dic13—21no—
60C22×Dic13—24no—
61C22×Dic13—21no—
62C22×Dic13—42no—
63C22×Dic13—42no—
64C22×Dic13C22⋊C412yes—
65C22×Dic13C22⋊C411yescharacteristic
66#6129—48no—
67#6129—48no—
68C2×C4×D13—22no—
69C2×C4×D13—22no—
70C2×C4×D13—22no—
71C2×C4×D13—22no—
72C2×C4×D13—42no—
73C2×C4×D13—42no—
74C2×C4×D13C2×C812yes—
75C2×C4×D13M1612yes—
76C2×Dic26—21no—
77C2×Dic26—41no—
78C2×Dic26—41no—
79C2×Dic26C2×C812yes—
80C2×C8×C13—42no—
81C2×C8×C13—42no—
82C2×C8×C13—42no—
83C13×C4⋊C4—41no—
84C13×C22⋊C4—42no—
85C13×C22⋊C4—42no—
86C42×C13—41no—
87C22⋊Dic13—44no—
88#6103—42no—
89C4⋊Dic13—41no—
90C4×Dic13—24no—
91C4×Dic13—41no—
92C4×Dic13—42no—
93C2×#1055—42no—
94C2×#1055—42no—
95C2×#1055—42no—
96#2297—131no—
97#1797—132no—
98#1272—132no—
99#1270—131no—
100#1270D1311yescharacteristic, complemented
101C23×C13—22no—
102C23×C13—41no—
103C23×C13—41no—
104C23×C13—42no—
105C23×C13—42no—
106C23×C13C2×C22⋊C411yescharacteristic
107C22×D13—21no—
108C22×D13—21no—
109C22×D13—22no—
110C22×D13—22no—
111C22×D13C22⋊C812yes—
112D4×C13—42no—
113D4×C13—42no—
114C2×C4×C13—22no—
115C2×C4×C13—21no—
116C2×C4×C13—21no—
117C2×C4×C13—22no—
118C2×C4×C13—41no—
119C2×C4×C13—42no—
120C2×C4×C13C22×C811yescharacteristic
121C2×C4×C13C2×M1611yescharacteristic
122C2×C4×C13AGL(1,ℤ/8)12yes—
123C2×C4×C13#13712yes—
124C22⋊D13—48no—
125C2×Dic13—22no—
126C2×Dic13—22no—
127C2×Dic13—22no—
128C2×Dic13—22no—
129C2×Dic13—41no—
130C2×Dic13—41no—
131C2×Dic13—48no—
132C2×Dic13—41no—
133C2×Dic13—42no—
134C2×Dic13C22⋊C812yes—
135C2×Dic13#9912yes—
136C2×Dic13#10012yes—
137C4×D13—24no—
138C4×D13—24no—
139C4×D13—44no—
140C4×D13—44no—
141Dic26—42no—
142Dic26—42no—
143C8×C13—82no—
144#1055—82no—
145C22×#41—131no—
146C2×#117—131no—
147C22×C42—131no—
148C2×C4⋊C8—262no—
149C2×C22⋊C8—262no—
150#391—131no—
151#391—131no—
152#390—131no—
153#390C2×D1311yescharacteristic
154#386—262no—
155C4×C22⋊C4—262no—
156#336—132no—
157#336C2×D1312yes—
158C22×C13—42no—
159C22×C13—44no—
160C22×C13—81no—
161C22×C13—81no—
162C22×C13—82no—
163C22×C13C2×C22⋊C811yescharacteristic
164C22×C13C2×#9911yescharacteristic
165C22×C13C2×#10011yescharacteristic
166C22×C13#41712yes—
167C22×C13#42112yes—
168C2×D13—22no—
169C2×D13—24no—
170C2×D13—41no—
171C2×D13—41no—
172C2×D13—42no—
173C4×C13—21no—
174C4×C13—21no—
175C4×C13—22no—
176C4×C13—22no—
177C4×C13—81no—
178Dic13—42no—
179Dic13—42no—
180Dic13—81no—
181Dic13#32314yes—
182C2×#41—134no—
183C2×#41—262no—
184C2×#41—522no—
185C2×#41—522no—
186C22×Q8—131no—
187C22×D4—261no—
188C22×D4C4×D1311yescharacteristic
189C23×C4—131no—
190C23×C4—132no—
191C23×C4—261no—
192C22×C8—22no—
193C22×C8—262no—
194#117—522no—
195C2×C4⋊C4—131no—
196C2×C4⋊C4C4×D1311yescharacteristic
197C2×C22⋊C4—22no—
198C2×C22⋊C4—261no—
199C2×C22⋊C4—262no—
200C2×C42—132no—
201C2×C42—131no—
202C2×C42—261no—
203C2×C42—522no—
204C2×C42C22×D1311yescharacteristic
205C4⋊C8—524no—
206C22⋊C8—524no—
207#95—262no—
208#95—262no—
209C2×C13—82no—
210C2×C13C2×#32311yescharacteristic
211C2×C13#147712yes—
212C2×C13#151312yes—
213C2×C13#153611yescharacteristic
214C2×C13#156011yescharacteristic
215D13—42no—
216C24—21no—
217C24—131no—
218#41—528no—
219#41—528no—
220C2×Q8—132no—
221C2×Q8—261no—
222C2×Q8—521no—
223C2×Q8—521no—
224C2×D4—21no—
225C2×D4—41no—
226C2×D4—41no—
227C2×D4—264no—
228C2×D4—522no—
229C2×D4—522no—
230C2×D4C8×D1312yes—
231C22×C4—21no—
232C22×C4—131no—
233C22×C4—132no—
234C22×C4—132no—
235C22×C4—132no—
236C22×C4—262no—
237C22×C4—262no—
238C22×C4—264no—
239C22×C4—261no—
240C22×C4—262no—
241C22×C4—262no—
242C22×C4—261no—
243C22×C4—522no—
244C22×C4—522no—
245C22×C4—522no—
246C22×C4—522no—
247C22×C4C2×C4×D1311yescharacteristic
248C22×C4D4×D1312yes—
249C2×C8—42no—
250C2×C8—42no—
251C2×C8—42no—
252C2×C8—522no—
253C2×C8—522no—
254C2×C8—522no—
255C4⋊C4—41no—
256C4⋊C4—521no—
257C22⋊C4—42no—
258C22⋊C4—42no—
259C22⋊C4—522no—
260C22⋊C4—524no—
261C42—41no—
262C42—264no—
263C42—521no—
264C42—522no—
265C13#759711yescharacteristic, complemented, Sylow
266C23—22no—
267C23—41no—
268C23—41no—
269C23—42no—
270C23—42no—
271C23—132no—
272C23—261no—
273C23—261no—
274C23—262no—
275C23—262no—
276C23C22⋊C4×D1311yescharacteristic
277Q8—522no—
278Q8—522no—
279D4—42no—
280D4—42no—
281D4—528no—
282C2×C4—22no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—22no—
286C2×C4—41no—
287C2×C4—42no—
288C2×C4—132no—
289C2×C4—132no—
290C2×C4—132no—
291C2×C4—264no—
292C2×C4—264no—
293C2×C4—262no—
294C2×C4—262no—
295C2×C4—262no—
296C2×C4—262no—
297C2×C4—524no—
298C2×C4—524no—
299C2×C4—528no—
300C2×C4—521no—
301C2×C4—521no—
302C2×C4—521no—
303C2×C4—522no—
304C2×C4C2×C8×D1311yescharacteristic
305C2×C4M16×D1311yescharacteristic
306C2×C4#8816512yes—
307C2×C4#8816912yes—
308C8—82no—
309C8—1042no—
310C22—42no—
311C22—44no—
312C22—82no—
313C22—81no—
314C22—81no—
315C22—262no—
316C22—264no—
317C22—522no—
318C22—521no—
319C22—521no—
320C22D13×C22⋊C811yescharacteristic
321C22D13×#9911yescharacteristic
322C22D13×#10011yescharacteristic
323C22#1171843212yes—
324C22#1171848212yes—
325C4—22no—
326C4—22no—
327C4—21no—
328C4—21no—
329C4—81no—
330C4—134no—
331C4—522no—
332C4—522no—
333C4—1041no—
334C2—82no—
335C2—522no—
336C2D13×#32311yescharacteristic
337C2#1311322012yes—
338C2#1311337612yes—
339C2#1311346911yescharacteristic
340C2#1311356811yescharacteristic
subgroupG/H
centerC23C22⋊C4×D13
commutatorC2×C4×C13C22×C8
FrattiniC2×C42C22×D13
FittingC13×#1270C2
socleC23×C13C2×C22⋊C4
prime radicalC22×#6129C4
cosocleC2×C42×C13C23
hypercenter#1270D13
hypocenterC13#7597
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. #13114815C2semidirect
3. #13112661C2semidirect
4. #13112657C2semidirect
5. C13×#1270C2semidirect
25. C2×#6129C8semidirect
100. #1270D13semidirect
265. C13#7597semidirect

Maximal subgroups

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

subgroupindex
#131173232
#131148152
#131126612
#131126572
C13×#12702
#759713