Finite Group Databasebeta

← #15773580

Subgroups — #15773580

Order 3328.

572 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 572 conjugacy classes of subgroups — too many to draw. Only its 87 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
1C2×#11718614C211yesmaximal, characteristic
2#13114910C211yesmaximal, characteristic
3#13112837C214yesmaximal, complemented
4C13×#1462C211yesmaximal, characteristic
5C22×C13×C22⋊C4C2211yescharacteristic
6C22×C22⋊Dic13—21no—
7C22×C4⋊Dic13C411yescharacteristic, complemented
8C13×#407—21no—
9#11718908—21no—
10C2×#88071—21no—
11C2×#88071C411yescharacteristic, complemented
12#11718614—21no—
13#11718614—21no—
14#11718614C412yescomplemented
15#11718614C2212yes—
16C13×#323—21no—
17C13×#323C2212yes—
18#11718118—21no—
19#11718118C2212yes—
20C25×C13D411yescharacteristic
21C23×C4×C13C2×C411yescharacteristic
22C23×C4×C13D411yescharacteristic
23C23×Dic13—21no—
24C23×Dic13—21no—
25C2×C13×M16—41no—
26C2×C13×C22⋊C4—41no—
27C2×C13×C22⋊C4—41no—
28C2×C13×C22⋊C4C2×C411yescharacteristic
29C2×C13×C22⋊C4D411yescharacteristic
30C2×C13×C22⋊C4D411yescharacteristic
31C2×C13×C22⋊C4C2311yescharacteristic
32C2×C22⋊Dic13—22no—
33C2×C22⋊Dic13—22no—
34C2×C22⋊Dic13—22no—
35C2×C22⋊Dic13—44no—
36C2×C22⋊Dic13—41no—
37C2×C22⋊Dic13—41no—
38C2×C4⋊Dic13—21no—
39C2×C4⋊Dic13—41no—
40C2×C4⋊Dic13—41no—
41C2×C4⋊Dic13C2×C412yes—
42C13×C22⋊C8—22no—
43C13×C22⋊C8—41no—
44#88071—22no—
45#88071—21no—
46#88071—22no—
47#88071C2×C412yes—
48#11797—131nomaximal, Sylow
49C24×C13—22no—
50C24×C13—21no—
51C24×C13—21no—
52C24×C13—41no—
53C24×C13—42no—
54C24×C13—42no—
55C24×C13C22⋊C411yescharacteristic
56C24×C13C22⋊C411yescharacteristic
57C24×C13C2×D411yescharacteristic
58C22×C4×C13—21no—
59C22×C4×C13—21no—
60C22×C4×C13—21no—
61C22×C4×C13—21no—
62C22×C4×C13—42no—
63C22×C4×C13—42no—
64C22×C4×C13C22⋊C411yescharacteristic
65C22×C4×C13C22⋊C411yescharacteristic
66C22×C4×C13C22×C411yescharacteristic
67C22×C4×C13C2×D411yescharacteristic
68C22×Dic13—22no—
69C22×Dic13—22no—
70C22×Dic13—42no—
71C22×Dic13—42no—
72C22×Dic13—42no—
73C22×Dic13—42no—
74C22×Dic13—42no—
75C22×Dic13—41no—
76C22×Dic13—41no—
77C22×Dic13—42no—
78C13×M16—82no—
79C2×C8×C13—42no—
80C13×C22⋊C4—41no—
81C13×C22⋊C4—41no—
82C13×C22⋊C4—41no—
83C13×C22⋊C4—41no—
84C22⋊Dic13—44no—
85C22⋊Dic13—44no—
86C22⋊Dic13—42no—
87C22⋊Dic13—42no—
88C22⋊Dic13—82no—
89C22⋊Dic13—82no—
90C4⋊Dic13—42no—
91C4⋊Dic13—42no—
92C2×#397—131no—
93#1819—131no—
94#1462D1311yescharacteristic
95#1344—134no—
96C23×C13—22no—
97C23×C13—22no—
98C23×C13—21no—
99C23×C13—21no—
100C23×C13—21no—
101C23×C13—21no—
102C23×C13—21no—
103C23×C13—21no—
104C23×C13—21no—
105C23×C13—42no—
106C23×C13—42no—
107C23×C13—41no—
108C23×C13—41no—
109C23×C13—41no—
110C23×C13—41no—
111C23×C13—48no—
112C23×C13—42no—
113C23×C13—42no—
114C23×C13—81no—
115C23×C13—81no—
116C23×C13—84no—
117C23×C13#9911yescharacteristic
118C23×C13#9911yescharacteristic
119C23×C13C2×C22⋊C411yescharacteristic
120C23×C13AGL(1,ℤ/8)12yes—
121C2×C4×C13—21no—
122C2×C4×C13—21no—
123C2×C4×C13—21no—
124C2×C4×C13—21no—
125C2×C4×C13—42no—
126C2×C4×C13—42no—
127C2×C4×C13—42no—
128C2×C4×C13—41no—
129C2×C4×C13—41no—
130C2×C4×C13—41no—
131C2×C4×C13—41no—
132C2×C4×C13—81no—
133C2×Dic13—42no—
134C2×Dic13—42no—
135C2×Dic13—42no—
136C2×Dic13—42no—
137C2×Dic13—42no—
138C2×Dic13—42no—
139C2×Dic13—84no—
140C2×Dic13—82no—
141C2×Dic13—82no—
142C2×Dic13—82no—
143C2×Dic13—82no—
144C2×Dic13—82no—
145C8×C13—82no—
146C22×C4⋊C4—131no—
147C22×C22⋊C4—261no—
148C22×C22⋊C4C2×D1311yescharacteristic
149#407—21no—
150#397—132no—
151#397—132no—
152#397—261no—
153#397—261no—
154#379—261no—
155C2×#95—131no—
156C2×#95—261no—
157#342—132no—
158#342—261no—
159#323—21no—
160#323C2×D1312yes—
161C22×C13—24no—
162C22×C13—24no—
163C22×C13—21no—
164C22×C13—21no—
165C22×C13—21no—
166C22×C13—21no—
167C22×C13—21no—
168C22×C13—21no—
169C22×C13—22no—
170C22×C13—42no—
171C22×C13—42no—
172C22×C13—41no—
173C22×C13—41no—
174C22×C13—41no—
175C22×C13—41no—
176C22×C13—41no—
177C22×C13—81no—
178C22×C13—84no—
179C22×C13—84no—
180C22×C13—81no—
181C22×C13#35212yes—
182C22×C13#35412yes—
183C22×C13C2×#9911yescharacteristic
184C22×C13#41811yescharacteristic
185C22×C13#42111yescharacteristic
186C4×C13—41no—
187C4×C13—41no—
188C4×C13—41no—
189C4×C13—41no—
190Dic13—82no—
191Dic13—82no—
192Dic13—162no—
193C25D5211yescharacteristic
194C23×C4—261no—
195C23×C4—261no—
196C23×C4C4×D1311yescharacteristic
197C23×C4C22⋊D1311yescharacteristic
198C2×M16—41no—
199C2×C4⋊C4—132no—
200C2×C4⋊C4—261no—
201C2×C4⋊C4—521no—
202C2×C4⋊C4—521no—
203C2×C22⋊C4—41no—
204C2×C22⋊C4—41no—
205C2×C22⋊C4—262no—
206C2×C22⋊C4—262no—
207C2×C22⋊C4—262no—
208C2×C22⋊C4—524no—
209C2×C22⋊C4—521no—
210C2×C22⋊C4—521no—
211C2×C22⋊C4C4×D1311yescharacteristic
212C2×C22⋊C4D5211yescharacteristic
213C2×C22⋊C4C22⋊D1311yescharacteristic
214C2×C22⋊C4C22×D1311yescharacteristic
215C22⋊C8—22no—
216C22⋊C8—41no—
217#95—132no—
218#95—261no—
219#95—262no—
220#95—262no—
221C2×C13—21no—
222C2×C13—22no—
223C2×C13—22no—
224C2×C13—21no—
225C2×C13—42no—
226C2×C13—81no—
227C2×C13#151011yescharacteristic
228C2×C13C2×#35211yescharacteristic
229C2×C13C2×#35411yescharacteristic
230C24—22no—
231C24—21no—
232C24—21no—
233C24—41no—
234C24—42no—
235C24—42no—
236C24#610311yescharacteristic
237C24#610311yescharacteristic
238C24C2×D5211yescharacteristic
239C22×C4—21no—
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—42no—
244C22×C4—42no—
245C22×C4—262no—
246C22×C4—262no—
247C22×C4—522no—
248C22×C4—522no—
249C22×C4—522no—
250C22×C4—522no—
251C22×C4—522no—
252C22×C4—521no—
253C22×C4—521no—
254C22×C4—522no—
255C22×C4#610311yescharacteristic
256C22×C4#610311yescharacteristic
257C22×C4C2×C4×D1311yescharacteristic
258C22×C4C2×C22⋊D1311yescharacteristic
259M16—82no—
260C2×C8—42no—
261C4⋊C4—522no—
262C4⋊C4—522no—
263C22⋊C4—41no—
264C22⋊C4—41no—
265C22⋊C4—41no—
266C22⋊C4—41no—
267C22⋊C4—524no—
268C22⋊C4—524no—
269C22⋊C4—522no—
270C22⋊C4—522no—
271C22⋊C4—1042no—
272C22⋊C4—1042no—
273C13#1179711yescharacteristic, complemented, Sylow
274C23—21no—
275C23—21no—
276C23—22no—
277C23—22no—
278C23—21no—
279C23—21no—
280C23—21no—
281C23—21no—
282C23—21no—
283C23—42no—
284C23—42no—
285C23—41no—
286C23—41no—
287C23—41no—
288C23—41no—
289C23—48no—
290C23—42no—
291C23—42no—
292C23—81no—
293C23—81no—
294C23—84no—
295C23#8804611yescharacteristic
296C23#8804611yescharacteristic
297C23#8816212yes—
298C23C2×#610311yescharacteristic
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—42no—
304C2×C4—42no—
305C2×C4—42no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—81no—
311C2×C4—522no—
312C2×C4—522no—
313C2×C4—522no—
314C2×C4—522no—
315C2×C4—522no—
316C2×C4—522no—
317C2×C4—1044no—
318C2×C4—1042no—
319C2×C4—1042no—
320C2×C4—1042no—
321C2×C4—1042no—
322C2×C4—1042no—
323C8—82no—
324C22—24no—
325C22—24no—
326C22—21no—
327C22—21no—
328C22—21no—
329C22—21no—
330C22—21no—
331C22—21no—
332C22—22no—
333C22—42no—
334C22—42no—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—41no—
339C22—41no—
340C22—81no—
341C22—84no—
342C22—84no—
343C22—81no—
344C22#1171806512yes—
345C22#1171806812yes—
346C22C2×#8804611yescharacteristic
347C22#1171879211yescharacteristic
348C22#1171880011yescharacteristic
349C4—41no—
350C4—41no—
351C4—41no—
352C4—41no—
353C4—1042no—
354C4—1042no—
355C4—2082no—
356C2—21no—
357C2—21no—
358C2—22no—
359C2—22no—
360C2—42no—
361C2—81no—
362C2#1311336611yescharacteristic
363C2C2×#1171806811yescharacteristic
364C2C2×#1171806511yescharacteristic
subgroupG/H
centerC22C2×#88046
commutatorC22×C4×C13C22×C4
FrattiniC2×C22⋊C4C22×D13
FittingC13×#1462C2
socleC22×C13C2×#99
prime radicalC25×C13D4
cosocleC2×C13×C22⋊C4C23
hypercenter#1462D13
hypocenterC13#11797
LCSG ▷ C22×C4×C13 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C24 ◁ C22×C22⋊C4 ◁ #1462

Complements

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

NH ≅ G/Ntype
3. #13112837C2semidirect
7. C22×C4⋊Dic13C4semidirect
11. C2×#88071C4semidirect
14. #11718614C4semidirect
273. C13#11797semidirect

Maximal subgroups

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

subgroupindex
C2×#117186142
#131149102
#131128372
C13×#14622
#1179713