Finite Group Databasebeta

← #15754281

Subgroups — #15754281

Order 3328.

874 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 874 conjugacy classes of subgroups — too many to draw. Only its 139 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
1C22×#88130C211yesmaximal, characteristic
2#13114904C211yesmaximal, characteristic, complemented
3C2×#11718061C212yesmaximal, complemented
4C2×#11718060C212yesmaximal
5C13×#1817C211yesmaximal, characteristic, complemented
6C22×C42×C13C2211yescharacteristic
7C22×#6103C411yescharacteristic
8C22×#6103C411yescharacteristic
9C22×#6103C2211yescharacteristic
10C22×#6101C411yescharacteristic
11C22×#6101C411yescharacteristic
12C22×#6101C2211yescharacteristic
13C2×#88130—22no—
14C2×#88130—22no—
15C2×#88130—24no—
16C2×#88130—24no—
17C2×C13×C22⋊C8C2212yes—
18C2×C22⋊#1055C2212yes—
19C13×#336—22no—
20#11718116—22no—
21#11718061—24no—
22#11718060—24no—
23C24×D13C2×C411yescharacteristic
24C23×C4×C13C2×C411yescharacteristic
25C23×C4×C13C2×C411yescharacteristic
26C23×C4×C13C2311yescharacteristic
27C23×Dic13C2×C411yescharacteristic
28C23×Dic13C2×C411yescharacteristic
29C23×Dic13C2×C411yescharacteristic
30C22×C8×C13—22no—
31C2×C42×C13—22no—
32C2×C42×C13—22no—
33C2×C42×C13D412yes—
34C2×C42×C13D412yes—
35C2×#6103—22no—
36C2×#6103—22no—
37C2×#6103—22no—
38C2×#6103—22no—
39C2×#6103—21no—
40C2×#6103—22no—
41C2×#6103—21no—
42C2×#6103—22no—
43C2×#6103—22no—
44C2×#6103D414yes—
45C2×#6101—22no—
46C2×#6101—22no—
47C2×#6101—21no—
48C2×#6101—22no—
49C2×#6101—21no—
50C2×#6101—22no—
51C2×#6101—22no—
52C2×#6101—22no—
53C2×#6101—22no—
54C2×#6101D414yes—
55C22×#1055—22no—
56#88130—216no—
57#88130—216no—
58C13×C22⋊C8—22no—
59C13×C22⋊C8—22no—
60C22⋊#1055—22no—
61C22⋊#1055—22no—
62#8309—131nomaximal, Sylow
63C24×C13C22×C411yescharacteristic
64C23×D13—21no—
65C23×D13—21no—
66C23×D13—22no—
67C23×D13—22no—
68C23×D13—42no—
69C23×D13—42no—
70C23×D13C22⋊C412yes—
71C22×C4×C13—21no—
72C22×C4×C13—21no—
73C22×C4×C13—21no—
74C22×C4×C13—21no—
75C22×C4×C13—22no—
76C22×C4×C13—22no—
77C22×C4×C13—42no—
78C22×C4×C13—42no—
79C22×C4×C13C22⋊C412yes—
80C22×C4×C13C22⋊C412yes—
81C22×C4×C13C2×D411yescharacteristic
82C22×C4×C13C2×D412yes—
83C22×C4×C13C2×D412yes—
84C22×C4×C13C2×D411yescharacteristic
85C22×Dic13—21no—
86C22×Dic13—21no—
87C22×Dic13—21no—
88C22×Dic13—21no—
89C22×Dic13—21no—
90C22×Dic13—21no—
91C22×Dic13—22no—
92C22×Dic13—22no—
93C22×Dic13—42no—
94C22×Dic13—42no—
95C22×Dic13C22⋊C412yes—
96C22×Dic13C22⋊C412yes—
97C22×Dic13C22⋊C412yes—
98C2×C8×C13—44no—
99C2×C8×C13—42no—
100C42×C13—24no—
101C42×C13—24no—
102#6103—28no—
103#6103—28no—
104#6103—24no—
105#6103—24no—
106#6101—28no—
107#6101—28no—
108#6101—24no—
109#6101—24no—
110C2×#1055—44no—
111C2×#1055—42no—
112C22×#126—131no—
113#1817—131no—
114#1817D1311yescharacteristic, complemented
115C2×#324—132no—
116C2×#323—132no—
117C23×C13—22no—
118C23×C13—22no—
119C23×C13C2×C22⋊C411yescharacteristic
120C23×C13C2×C22⋊C411yescharacteristic
121C23×C13C2×C22⋊C411yescharacteristic
122C23×C13#13112yes—
123C23×C13#13112yes—
124C22×D13—22no—
125C22×D13—24no—
126C22×D13—42no—
127C22×D13—42no—
128C22×D13—42no—
129C22×D13—41no—
130C22×D13—41no—
131C22×D13—42no—
132C22×D13—42no—
133C22×D13—42no—
134C22×D13—42no—
135C22×D13—84no—
136C22×D13—84no—
137C2×C4×C13—22no—
138C2×C4×C13—22no—
139C2×C4×C13—22no—
140C2×C4×C13—22no—
141C2×C4×C13—22no—
142C2×C4×C13—22no—
143C2×C4×C13—24no—
144C2×C4×C13—42no—
145C2×C4×C13—42no—
146C2×C4×C13—42no—
147C2×C4×C13—42no—
148C2×C4×C13—42no—
149C2×C4×C13—42no—
150C2×C4×C13#12012yes—
151C2×C4×C13#12012yes—
152C2×Dic13—22no—
153C2×Dic13—22no—
154C2×Dic13—22no—
155C2×Dic13—24no—
156C2×Dic13—42no—
157C2×Dic13—42no—
158C2×Dic13—41no—
159C2×Dic13—41no—
160C2×Dic13—42no—
161C2×Dic13—42no—
162C2×Dic13—42no—
163C2×Dic13—42no—
164C2×Dic13—42no—
165C8×C13—82no—
166#1055—82no—
167C2×#126—264no—
168C2×#126—264no—
169C2×#126—262no—
170C2×#126—262no—
171C22×C4⋊C4—131no—
172C22×C4⋊C4—131no—
173C22×C4⋊C4—131no—
174C22×C22⋊C4—131no—
175C22×C22⋊C4—131no—
176C22×C22⋊C4—131no—
177C22×C42C2×D1311yescharacteristic
178C2×C22⋊C8—132no—
179C2×C22⋊C8C2×D1312yes—
180#336—22no—
181#336—262no—
182#324—264no—
183#323—264no—
184C22×C13—24no—
185C22×C13—24no—
186C22×C13—21no—
187C22×C13—21no—
188C22×C13—21no—
189C22×C13—21no—
190C22×C13#37911yescharacteristic
191C22×C13#40811yescharacteristic
192C22×C13#40811yescharacteristic
193C22×C13#40812yes—
194C22×C13#40812yes—
195C22×C13#41012yes—
196C22×C13#41312yes—
197C2×D13—42no—
198C2×D13—42no—
199C2×D13—42no—
200C2×D13—84no—
201C2×D13—82no—
202C2×D13—82no—
203C2×D13—84no—
204C4×C13—22no—
205C4×C13—22no—
206C4×C13—42no—
207C4×C13—42no—
208Dic13—42no—
209Dic13—42no—
210Dic13—42no—
211C25—131no—
212C23×C4—131no—
213C23×C4—131no—
214C23×C4—131no—
215C23×C4C4×D1311yescharacteristic
216C23×C4C4×D1311yescharacteristic
217C23×C4C22×D1311yescharacteristic
218C22×C8—22no—
219C22×C8—262no—
220#126—2616no—
221#126—2616no—
222C2×C4⋊C4—134no—
223C2×C4⋊C4—262no—
224C2×C4⋊C4—262no—
225C2×C4⋊C4—262no—
226C2×C4⋊C4—262no—
227C2×C4⋊C4—262no—
228C2×C4⋊C4—262no—
229C2×C4⋊C4—261no—
230C2×C4⋊C4—262no—
231C2×C4⋊C4—261no—
232C2×C22⋊C4—134no—
233C2×C22⋊C4—262no—
234C2×C22⋊C4—262no—
235C2×C22⋊C4—262no—
236C2×C22⋊C4—262no—
237C2×C22⋊C4—262no—
238C2×C22⋊C4—262no—
239C2×C22⋊C4—261no—
240C2×C22⋊C4—262no—
241C2×C22⋊C4—261no—
242C2×C42—22no—
243C2×C42—22no—
244C2×C42D5212yes—
245C2×C42C22⋊D1312yes—
246C22⋊C8—22no—
247C22⋊C8—22no—
248C22⋊C8—262no—
249C22⋊C8—262no—
250C2×C13—22no—
251C2×C13—22no—
252C2×C13#147312yes—
253C2×C13#147312yes—
254C2×C13#178011yescharacteristic
255C2×C13#178211yescharacteristic
256C2×C13#178511yescharacteristic
257D13—82no—
258C24—132no—
259C24—261no—
260C24—261no—
261C24—262no—
262C24—262no—
263C24—522no—
264C24—522no—
265C24C2×C4×D1311yescharacteristic
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—21no—
270C22×C4—22no—
271C22×C4—22no—
272C22×C4—42no—
273C22×C4—42no—
274C22×C4—132no—
275C22×C4—132no—
276C22×C4—132no—
277C22×C4—261no—
278C22×C4—261no—
279C22×C4—261no—
280C22×C4—262no—
281C22×C4—262no—
282C22×C4—261no—
283C22×C4—261no—
284C22×C4—261no—
285C22×C4—522no—
286C22×C4—522no—
287C22×C4#610312yes—
288C22×C4#610312yes—
289C22×C4C2×D5211yescharacteristic
290C22×C4D4×D1312yes—
291C22×C4D4×D1312yes—
292C22×C4C2×C22⋊D1311yescharacteristic
293C2×C8—44no—
294C2×C8—42no—
295C2×C8—524no—
296C2×C8—522no—
297C4⋊C4—268no—
298C4⋊C4—268no—
299C4⋊C4—264no—
300C4⋊C4—264no—
301C22⋊C4—268no—
302C22⋊C4—268no—
303C22⋊C4—264no—
304C22⋊C4—264no—
305C42—24no—
306C42—24no—
307C13#830911yescharacteristic, complemented, Sylow
308C23—22no—
309C23—22no—
310C23—262no—
311C23—264no—
312C23—522no—
313C23—522no—
314C23—522no—
315C23—522no—
316C23—522no—
317C23—521no—
318C23—521no—
319C23—522no—
320C23—522no—
321C23—1044no—
322C23—1044no—
323C23C22⋊C4×D1311yescharacteristic
324C23C22⋊C4×D1311yescharacteristic
325C23#8815512yes—
326C23#8816112yes—
327C23C2×#610311yescharacteristic
328C2×C4—22no—
329C2×C4—22no—
330C2×C4—22no—
331C2×C4—22no—
332C2×C4—24no—
333C2×C4—22no—
334C2×C4—22no—
335C2×C4—42no—
336C2×C4—42no—
337C2×C4—42no—
338C2×C4—42no—
339C2×C4—42no—
340C2×C4—42no—
341C2×C4—262no—
342C2×C4—262no—
343C2×C4—262no—
344C2×C4—264no—
345C2×C4—522no—
346C2×C4—522no—
347C2×C4—522no—
348C2×C4—521no—
349C2×C4—521no—
350C2×C4—522no—
351C2×C4—522no—
352C2×C4—522no—
353C2×C4—522no—
354C2×C4#8813612yes—
355C2×C4#8819112yes—
356C8—82no—
357C8—1042no—
358C22—24no—
359C22—24no—
360C22—21no—
361C22—21no—
362C22—21no—
363C22—21no—
364C22—522no—
365C22—522no—
366C22—522no—
367C22—1044no—
368C22—1044no—
369C22—1042no—
370C22—1042no—
371C22#1171838812yes—
372C22#1171838812yes—
373C22#1171861611yescharacteristic
374C22#1171866712yes—
375C22#1171877111yescharacteristic
376C22#1171879011yescharacteristic
377C22#1171879312yes—
378C4—22no—
379C4—22no—
380C4—42no—
381C4—42no—
382C4—522no—
383C4—522no—
384C4—522no—
385C2—22no—
386C2—22no—
387C2—1042no—
388C2#1311320312yes—
389C2#1311320612yes—
390C2#1311474711yescharacteristic
391C2#1311475311yescharacteristic
392C2#1311476211yescharacteristic
subgroupG/H
centerC23C2×#6103
commutatorC24×C13C22×C4
FrattiniC23×C4C22×D13
FittingC13×#1817C2
socleC23×C13C2×C22⋊C4
prime radicalC24×D13C2×C4
cosocleC23×C4×C13C23
hypercenter#1817D13
hypocenterC13#8309
LCSG ▷ C24×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C22×C42 ◁ #1817

Complements

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

NH ≅ G/Ntype
2. #13114904C2semidirect
3. C2×#11718061C2semidirect
5. C13×#1817C2semidirect
114. #1817D13semidirect
307. C13#8309semidirect

Maximal subgroups

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

subgroupindex
C22×#881302
#131149042
C2×#117180612
C2×#117180602
C13×#18172
#830913