Finite Group Databasebeta

← #16778359

Subgroups — #16778359

Order 3328.

482 conjugacy classes of subgroups; only the 108 normal subgroups are shown.

normal subgroups only

This group has 482 conjugacy classes of subgroups — too many to draw. Only its 108 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#13130763C211yesmaximal, characteristic, complemented
2#13130751C211yesmaximal, characteristic, complemented
3#13129655C212yesmaximal, complemented
4#13129653C212yesmaximal
5#13117297C211yesmaximal, characteristic
6C2×C4×D52C411yescharacteristic
7C2×#88126—21no—
8C2×C4⋊#1057—21no—
9C4×C13×C4⋊C4C411yescharacteristic
10#11718649C411yescharacteristic
11#11718649C2211yescharacteristic
12#11718634C411yescharacteristic
13#11718634C2211yescharacteristic
14C4×#6103—21no—
15C42×Dic13C2211yescharacteristic
16#11718330—21no—
17#11718330—21no—
18#11718290—21no—
19#11718290—21no—
20#11718290—21no—
21#11718290C2212yes—
22#11718290C2212yes—
23C22×D52C2×C411yescharacteristic
24C22×C4×D13—21no—
25C22×#1057—22no—
26C22×#1057—22no—
27C2×C13×C4⋊C4C2×C411yescharacteristic
28C2×C13×C4⋊C4C2×C411yescharacteristic
29C2×C42×C13—21no—
30C2×C42×C13C2×C411yescharacteristic
31C2×#6103—21no—
32C2×#6103—21no—
33C2×#6103—21no—
34C2×#6103—21no—
35C2×#6103—21no—
36C2×C4⋊Dic13C2×C411yescharacteristic
37C2×#6101—21no—
38C2×#6101—21no—
39C2×C4×Dic13C2×C411yescharacteristic
40C2×C4×Dic13D411yescharacteristic
41C2×C4×Dic13D411yescharacteristic
42C2×C4×Dic13D411yescharacteristic
43C2×C4×Dic13D411yescharacteristic
44C2×C4×Dic13C2311yescharacteristic
45C4×D52—22no—
46C4×D52C814yescomplemented
47#88126—44no—
48C4⋊#1057—42no—
49C13×#95—21no—
50#88071—21no—
51#88071—21no—
52#7594—131nomaximal, Sylow
53C23×D13—21no—
54C22×C4×C13—21no—
55C22×C4×C13—21no—
56C22×C4×C13C22⋊C411yescharacteristic
57C22×C4×C13C22⋊C411yescharacteristic
58C22×C4×C13C22×C411yescharacteristic
59C22×Dic13—21no—
60C22×Dic13C22⋊C411yescharacteristic
61C22×Dic13C22⋊C411yescharacteristic
62C22×Dic13C2×D411yescharacteristic
63C22×Dic13C2×D411yescharacteristic
64C2×D52—21no—
65C2×D52—41no—
66C2×D52—41no—
67C2×D52C2×C812yes—
68C2×C4×D13—24no—
69C2×C4×D13—42no—
70C2×C4×D13—42no—
71C2×#1057—42no—
72C2×#1057—42no—
73C2×#1057—42no—
74C2×#1057—42no—
75C2×#1057—42no—
76C2×#1057—42no—
77C13×C4⋊C4—41no—
78C13×C4⋊C4—41no—
79C42×C13—42no—
80C42×C13C2×C812yes—
81C42×C13M1612yes—
82#6103—24no—
83#6103—42no—
84#6103—42no—
85#6103—42no—
86#6103—41no—
87#6103—41no—
88C4⋊Dic13—21no—
89C4⋊Dic13C2×C812yes—
90#6101—42no—
91#6101—42no—
92C4×Dic13—21no—
93C4×Dic13—22no—
94C4×Dic13—21no—
95C4×Dic13—41no—
96C4×Dic13—41no—
97C4×Dic13—41no—
98C4×Dic13—41no—
99#2293—131no—
100#1839—131no—
101#1831—131no—
102#1271—132no—
103#1270—132no—
104C23×C13C2×C22⋊C411yescharacteristic
105C22×D13—22no—
106C22×D13—41no—
107C22×D13—41no—
108C22×D13—41no—
109C22×D13—41no—
110C22×D13—41no—
111C22×D13—41no—
112C2×C4×C13—21no—
113C2×C4×C13—21no—
114C2×C4×C13—21no—
115C2×C4×C13—21no—
116C2×C4×C13—21no—
117C2×C4×C13—21no—
118C2×C4×C13—41no—
119C2×C4×C13—41no—
120C2×C4×C13—41no—
121C2×C4×C13—41no—
122C2×C4×C13—41no—
123C2×C4×C13—41no—
124C2×C4×C13C22⋊C812yes—
125C2×C4×C13C22⋊C812yes—
126C2×C4×C13C22×C811yescharacteristic
127C2×C4×C13C2×M1611yescharacteristic
128C2×Dic13—21no—
129C2×Dic13—21no—
130C2×Dic13—21no—
131C2×Dic13—21no—
132C2×Dic13—22no—
133C2×Dic13—21no—
134C2×Dic13—21no—
135C2×Dic13—21no—
136C2×Dic13—21no—
137C2×Dic13—21no—
138C2×Dic13—21no—
139C2×Dic13—41no—
140C2×Dic13—41no—
141C2×Dic13AGL(1,ℤ/8)11yescharacteristic
142C2×Dic13AGL(1,ℤ/8)12yes—
143C2×Dic13#13711yescharacteristic
144D52—42no—
145D52—42no—
146C4×D13—48no—
147#1057—82no—
148#1057—82no—
149C2×C4×D4—131no—
150C2×#117—261no—
151C2×C4⋊C8—261no—
152#390—131no—
153#390—131no—
154#389—131no—
155#389—131no—
156#388—261no—
157#388—261no—
158C4×C4⋊C4#26111yescharacteristic
159C4×C22⋊C4—261no—
160C43—131no—
161#336—132no—
162#336—132no—
163#336—261no—
164#336—261no—
165#336—261no—
166C22×C13C2×C22⋊C811yescharacteristic
167C22×C13#41011yescharacteristic
168C22×C13#41311yescharacteristic
169C22×C13#41711yescharacteristic
170C22×C13#41811yescharacteristic
171C22×C13#42111yescharacteristic
172C22×C13#42111yescharacteristic
173C2×D13—42no—
174C2×D13—42no—
175C2×D13—42no—
176C2×D13—81no—
177C2×D13—81no—
178C2×D13—81no—
179C2×D13—81no—
180C4×C13—21no—
181C4×C13—21no—
182C4×C13—22no—
183C4×C13—22no—
184C4×C13—81no—
185C4×C13—81no—
186Dic13—21no—
187Dic13—21no—
188Dic13—22no—
189Dic13—41no—
190Dic13—42no—
191Dic13—41no—
192C22×D4—131no—
193C23×C4—261no—
194C22×C8—262no—
195C22×C8—262no—
196C4×D4—134no—
197C4×D4—262no—
198#117—524no—
199C2×C4⋊C4—131no—
200C2×C4⋊C4—261no—
201C2×C4⋊C4—261no—
202C2×C4⋊C4C2×#26111yescharacteristic
203C2×C4⋊C4C2×#26111yescharacteristic
204C2×C22⋊C4—261no—
205C2×C22⋊C4—261no—
206C2×C22⋊C4—261no—
207C2×C22⋊C4—261no—
208C2×C22⋊C4—261no—
209C2×C42—21no—
210C2×C42—131no—
211C2×C42—131no—
212C2×C42—131no—
213C2×C42—131no—
214C2×C42—131no—
215C2×C42—131no—
216C2×C42C2×#26111yescharacteristic
217C4⋊C8—522no—
218#95—21no—
219#95—261no—
220#95—261no—
221C2×C13#145811yescharacteristic
222C2×C13#147711yescharacteristic
223C2×C13#147811yescharacteristic
224C2×C13#151211yescharacteristic
225C2×C13#151411yescharacteristic
226C2×C13#153511yescharacteristic
227C2×C13#155711yescharacteristic
228D13—82no—
229C24—261no—
230C2×D4—132no—
231C2×D4—261no—
232C2×D4—521no—
233C2×D4—521no—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—131no—
237C22×C4—131no—
238C22×C4—131no—
239C22×C4—131no—
240C22×C4—261no—
241C22×C4—264no—
242C22×C4—522no—
243C22×C4—522no—
244C22×C4C22⋊#26111yescharacteristic
245C22×C4C22⋊#26111yescharacteristic
246C22×C4C22×#26111yescharacteristic
247C2×C8—522no—
248C2×C8—522no—
249C2×C8—522no—
250C2×C8—522no—
251C2×C8—522no—
252C2×C8—522no—
253C4⋊C4—41no—
254C4⋊C4—41no—
255C4⋊C4—132no—
256C4⋊C4—261no—
257C4⋊C4—522no—
258C4⋊C4—522no—
259C22⋊C4—264no—
260C22⋊C4—522no—
261C22⋊C4—521no—
262C22⋊C4—521no—
263C22⋊C4—522no—
264C22⋊C4—522no—
265C42—42no—
266C42—261no—
267C42—262no—
268C42—261no—
269C42—521no—
270C42—521no—
271C42—521no—
272C42—521no—
273C42D13⋊C812yes—
274C42#611812yes—
275C13#759411yescharacteristic, complemented, Sylow
276C23—262no—
277C23—521no—
278C23—521no—
279C23—521no—
280C23—521no—
281C23—521no—
282C23—521no—
283C23C2×C22⋊#26111yescharacteristic
284D4—522no—
285D4—522no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—132no—
299C2×C4—131no—
300C2×C4—131no—
301C2×C4—261no—
302C2×C4—261no—
303C2×C4—261no—
304C2×C4—261no—
305C2×C4—262no—
306C2×C4—261no—
307C2×C4—261no—
308C2×C4—261no—
309C2×C4—261no—
310C2×C4—261no—
311C2×C4—261no—
312C2×C4—528no—
313C2×C4—521no—
314C2×C4—521no—
315C2×C4#8811112yes—
316C2×C4#8811112yes—
317C2×C4C2×D13⋊C811yescharacteristic
318C2×C4C2×#611811yescharacteristic
319C8—1042no—
320C8—1042no—
321C22—522no—
322C22—522no—
323C22—522no—
324C22—1041no—
325C22—1041no—
326C22—1041no—
327C22—1041no—
328C22#1171911611yescharacteristic
329C22C2×#8811111yescharacteristic
330C22#1171913211yescharacteristic
331C22#1171913811yescharacteristic
332C22#1171915511yescharacteristic
333C22#1171916411yescharacteristic
334C22#1171916611yescharacteristic
335C4—21no—
336C4—21no—
337C4—22no—
338C4—22no—
339C4—81no—
340C4—81no—
341C4—261no—
342C4—261no—
343C4—262no—
344C4—521no—
345C4—521no—
346C4—522no—
347C2—1042no—
348C2#1313006911yescharacteristic
349C2#1313013311yescharacteristic
350C2#1313013711yescharacteristic
351C2#1313024911yescharacteristic
352C2#1313025511yescharacteristic
353C2#1313032211yescharacteristic
354C2#1313036711yescharacteristic
subgroupG/H
centerC23C2×C22⋊#261
commutatorC2×C4×C13C22×C8
FrattiniC22×C4C22×#261
FittingC4×C13×C4⋊C4C4
socleC23×C13C2×C22⋊C4
prime radicalC22×D52C2×C4
cosocleC2×C4×Dic13C23
hypercenterC4×C4⋊C4#261
hypocenterC13#7594
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. #13130763C2semidirect
2. #13130751C2semidirect
3. #13129655C2semidirect
46. C4×D52C8semidirect
275. C13#7594semidirect

Maximal subgroups

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

subgroupindex
#131307632
#131307512
#131296552
#131296532
#131172972
#759413