Finite Group Databasebeta

← #15773725

Subgroups — #15773725

Order 3328.

416 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 91 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#13114832C211yesmaximal, characteristic, complemented
2#13113180C211yesmaximal, characteristic, complemented
3#13112863C212yesmaximal, complemented
4#13112839C212yesmaximal
5C13×#2398C211yesmaximal, characteristic
6C2×C4×Q8×C13C2211yescharacteristic
7C2×C4×D4×C13C411yescharacteristic
8C13×#400C411yescharacteristic
9C13×#400C2211yescharacteristic
10C13×#397—21no—
11C13×#394C411yescharacteristic
12C13×#394C2211yescharacteristic
13C13×#393—21no—
14C4×C13×C22⋊C4—21no—
15C4×C13×C22⋊C4—21no—
16C13×#376C411yescharacteristic
17C2×#88076—21no—
18#11718587—21no—
19#11718585—21no—
20#11718122C2212yes—
21#11718120—21no—
22#11718120C2212yes—
23C22×Q8×C13D411yescharacteristic
24C22×D4×C13C2×C411yescharacteristic
25C23×C4×C13—21no—
26C4×Q8×C13—41no—
27C4×Q8×C13—41no—
28C4×D4×C13—41no—
29C4×D4×C13—41no—
30C2×C13×C4⋊C4C2×C411yescharacteristic
31C2×C13×C4⋊C4C2×C411yescharacteristic
32C2×C13×C4⋊C4D411yescharacteristic
33C2×C13×C4⋊C4C2311yescharacteristic
34C2×C13×C22⋊C4—21no—
35C2×C13×C22⋊C4—21no—
36C2×C13×C22⋊C4—21no—
37C2×C13×C22⋊C4—21no—
38C2×C13×C22⋊C4—21no—
39C2×C42×C13—21no—
40C2×C42×C13C2×C411yescharacteristic
41C2×C42×C13D411yescharacteristic
42C2×C42×C13D411yescharacteristic
43C2×#6099—22no—
44C13×#95—21no—
45C13×#95—21no—
46C13×#95—21no—
47C13×#95—21no—
48C13×#95—21no—
49C13×#95C2×C411yescharacteristic
50C13×#95C2×C411yescharacteristic
51#88076—42no—
52C22⋊#1055—22no—
53C4⋊#1055—41no—
54C4⋊#1055—41no—
55C4⋊#1055—41no—
56#88043—41no—
57#11829—131nomaximal, Sylow
58C24×C13—21no—
59C2×Q8×C13—21no—
60C2×Q8×C13—21no—
61C2×Q8×C13—41no—
62C2×Q8×C13—41no—
63C2×D4×C13—41no—
64C2×D4×C13—42no—
65C22×C4×C13—21no—
66C22×C4×C13—21no—
67C22×C4×C13—21no—
68C22×C4×C13—42no—
69C22×C4×C13—42no—
70C22×C4×C13—41no—
71C22×C4×C13—41no—
72C22×C4×C13C22⋊C411yescharacteristic
73C22×C4×C13C22⋊C411yescharacteristic
74C22×C4×C13C22⋊C411yescharacteristic
75C22×C4×C13C22⋊C411yescharacteristic
76C22×C4×C13C22×C411yescharacteristic
77C22×C4×C13C2×D411yescharacteristic
78C22×C4×C13C2×D411yescharacteristic
79C13×C4⋊C4—41no—
80C13×C4⋊C4—41no—
81C13×C4⋊C4—41no—
82C13×C4⋊C4—41no—
83C13×C22⋊C4—42no—
84C13×C22⋊C4—42no—
85C13×C22⋊C4—42no—
86C13×C22⋊C4—42no—
87C13×C22⋊C4—41no—
88C13×C22⋊C4—41no—
89C42×C13—21no—
90C42×C13—21no—
91C42×C13—21no—
92C42×C13—21no—
93C42×C13—21no—
94C42×C13—21no—
95C42×C13—42no—
96#6099—42no—
97#6099—42no—
98C2×#1055—42no—
99C2×#1055—42no—
100#2398D1311yescharacteristic
101#1801—131no—
102#1467—131no—
103#1353—132no—
104#1345—132no—
105C23×C13—22no—
106C23×C13—41no—
107C23×C13—41no—
108C23×C13—41no—
109C23×C13—41no—
110C23×C13—41no—
111C23×C13—41no—
112C23×C13C2×C22⋊C411yescharacteristic
113Q8×C13—42no—
114Q8×C13—42no—
115D4×C13—42no—
116D4×C13—42no—
117C2×C4×C13—21no—
118C2×C4×C13—21no—
119C2×C4×C13—22no—
120C2×C4×C13—21no—
121C2×C4×C13—21no—
122C2×C4×C13—21no—
123C2×C4×C13—21no—
124C2×C4×C13—21no—
125C2×C4×C13—21no—
126C2×C4×C13—21no—
127C2×C4×C13—21no—
128C2×C4×C13—21no—
129C2×C4×C13—41no—
130C2×C4×C13—41no—
131C2×C4×C13—41no—
132C2×C4×C13—41no—
133C2×C4×C13—41no—
134C2×C4×C13—41no—
135C2×C4×C13—41no—
136C2×C4×C13—41no—
137C2×C4×C13—41no—
138C2×C4×C13—41no—
139C2×C4×C13—41no—
140C2×C4×C13—41no—
141C2×C4×C13—82no—
142C2×C4×C13—82no—
143C2×C4×C13#9911yescharacteristic
144C2×C4×C13#9911yescharacteristic
145C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
146C2×C4×C13#13711yescharacteristic
147#1055—82no—
148#1055—82no—
149C2×C4×Q8C2×D1311yescharacteristic
150C2×C4×D4Dic1311yescharacteristic
151#432—261no—
152#423—261no—
153C2×#101—261no—
154#400Dic1311yescharacteristic
155#400C2×D1311yescharacteristic
156#397—21no—
157#394Dic1311yescharacteristic
158#394C2×D1311yescharacteristic
159#393—21no—
160C4×C22⋊C4—21no—
161C4×C22⋊C4—21no—
162#376Dic1311yescharacteristic
163#343—132no—
164#324—132no—
165#324—261no—
166C22×C13—21no—
167C22×C13—21no—
168C22×C13—42no—
169C22×C13—42no—
170C22×C13—42no—
171C22×C13—81no—
172C22×C13—81no—
173C22×C13—81no—
174C22×C13—81no—
175C22×C13C2×#9911yescharacteristic
176C22×C13#41711yescharacteristic
177C22×C13#42111yescharacteristic
178C4×C13—21no—
179C4×C13—21no—
180C4×C13—21no—
181C4×C13—41no—
182C4×C13—41no—
183C4×C13—41no—
184C4×C13—41no—
185C4×C13—41no—
186C4×C13—81no—
187C4×C13—81no—
188C4×C13—81no—
189C4×C13#35512yes—
190C22×Q8C22⋊D1311yescharacteristic
191C22×D4C2×Dic1311yescharacteristic
192C23×C4—21no—
193C2×M16—262no—
194C4×Q8—41no—
195C4×Q8—41no—
196C4×D4—41no—
197C4×D4—41no—
198C2×C4⋊C4C2×Dic1311yescharacteristic
199C2×C4⋊C4C2×Dic1311yescharacteristic
200C2×C4⋊C4C22⋊D1311yescharacteristic
201C2×C4⋊C4C22×D1311yescharacteristic
202C2×C22⋊C4—21no—
203C2×C22⋊C4—21no—
204C2×C22⋊C4—21no—
205C2×C22⋊C4—21no—
206C2×C22⋊C4—21no—
207C2×C42—21no—
208C2×C42C2×Dic1311yescharacteristic
209C2×C42C22⋊D1311yescharacteristic
210C2×C42C22⋊D1311yescharacteristic
211C4⋊C8—521no—
212C4⋊C8—521no—
213C4⋊C8—521no—
214#101—522no—
215C22⋊C8—262no—
216#97—521no—
217#95—21no—
218#95—21no—
219#95—21no—
220#95—21no—
221#95—21no—
222#95C2×Dic1311yescharacteristic
223#95C2×Dic1311yescharacteristic
224C2×C13—21no—
225C2×C13—21no—
226C2×C13—82no—
227C2×C13#151311yescharacteristic
228C2×C13#212011yescharacteristic
229C2×C13C2×#35511yescharacteristic
230C24—21no—
231C2×Q8—21no—
232C2×Q8—21no—
233C2×Q8—41no—
234C2×Q8—41no—
235C2×D4—41no—
236C2×D4—42no—
237C22×C4—21no—
238C22×C4—21no—
239C22×C4—21no—
240C22×C4—42no—
241C22×C4—42no—
242C22×C4—41no—
243C22×C4—41no—
244C22×C4C22⋊Dic1311yescharacteristic
245C22×C4C22⋊Dic1311yescharacteristic
246C22×C4C22⋊Dic1311yescharacteristic
247C22×C4C22⋊Dic1311yescharacteristic
248C22×C4C22×Dic1311yescharacteristic
249C22×C4C2×C22⋊D1311yescharacteristic
250C22×C4C2×C22⋊D1311yescharacteristic
251M16—522no—
252M16—522no—
253C2×C8—522no—
254C2×C8—522no—
255C4⋊C4—41no—
256C4⋊C4—41no—
257C4⋊C4—41no—
258C4⋊C4—41no—
259C22⋊C4—42no—
260C22⋊C4—42no—
261C22⋊C4—42no—
262C22⋊C4—42no—
263C22⋊C4—41no—
264C22⋊C4—41no—
265C42—21no—
266C42—21no—
267C42—21no—
268C42—21no—
269C42—21no—
270C42—21no—
271C42—42no—
272C13#1182911yescharacteristic, complemented, Sylow
273C23—22no—
274C23—41no—
275C23—41no—
276C23—41no—
277C23—41no—
278C23—41no—
279C23—41no—
280C23C2×C22⋊Dic1311yescharacteristic
281Q8—42no—
282Q8—42no—
283D4—42no—
284D4—42no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—22no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—82no—
310C2×C4—82no—
311C2×C4#8807411yescharacteristic
312C2×C4#8807411yescharacteristic
313C2×C4#8820311yescharacteristic
314C2×C4#8820511yescharacteristic
315C8—1042no—
316C8—1042no—
317C22—21no—
318C22—21no—
319C22—42no—
320C22—42no—
321C22—42no—
322C22—81no—
323C22—81no—
324C22—81no—
325C22—81no—
326C22C2×#8807411yescharacteristic
327C22#1171889311yescharacteristic
328C22#1171889711yescharacteristic
329C4—21no—
330C4—21no—
331C4—21no—
332C4—41no—
333C4—41no—
334C4—41no—
335C4—41no—
336C4—41no—
337C4—81no—
338C4—81no—
339C4—81no—
340C4#1171813412yes—
341C2—21no—
342C2—21no—
343C2—82no—
344C2#1311337911yescharacteristic
345C2#1311647711yescharacteristic
346C2C2×#1171813411yescharacteristic
subgroupG/H
centerC22C2×#88074
commutatorC22×C4×C13C22×C4
FrattiniC2×C4⋊C4C22×D13
FittingC13×#2398C2
socleC22×C13C2×#99
prime radicalC22×D4×C13C2×C4
cosocleC2×C13×C4⋊C4C23
hypercenter#2398D13
hypocenterC13#11829
LCSG ▷ C22×C4×C13 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #2398

Complements

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

NH ≅ G/Ntype
1. #13114832C2semidirect
2. #13113180C2semidirect
3. #13112863C2semidirect
272. C13#11829semidirect

Maximal subgroups

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

subgroupindex
#131148322
#131131802
#131128632
#131128392
C13×#23982
#1182913