Finite Group Databasebeta

← #15773423

Subgroups — #15773423

Order 3328.

428 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 428 conjugacy classes of subgroups — too many to draw. Only its 83 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#13120413C211yesmaximal, characteristic
2#13113170C211yesmaximal, characteristic
3#13112865C212yesmaximal, complemented
4#13112841C212yesmaximal, complemented
5C13×#1742C211yesmaximal, characteristic
6C22×C13×M16—21no—
7C2×C13×#117C2211yescharacteristic
8C2×C4×Dic26C411yescharacteristic
9#11718871—21no—
10#11718644C2211yescharacteristic
11#11718640C2211yescharacteristic
12#11718639—21no—
13#11718614C411yescharacteristic
14#11718608C411yescharacteristic
15#11718605—21no—
16#11718598C411yescharacteristic
17#11718594—21no—
18#11718587—21no—
19C13×#343—21no—
20C13×#343C2212yes—
21#11718120C2212yes—
22#11718117—21no—
23C23×C4×C13D411yescharacteristic
24C22×Dic26C2×C411yescharacteristic
25C2×C13×M16—24no—
26C2×C13×M16—22no—
27C2×C13×M16—41no—
28C2×C13×M16—42no—
29C22×C8×C13—41no—
30C13×#117—41no—
31C13×#117—41no—
32C2×C13×C4⋊C4D411yescharacteristic
33C2×C13×C4⋊C4C2311yescharacteristic
34C2×C13×C22⋊C4C2×C411yescharacteristic
35C2×C13×C22⋊C4D411yescharacteristic
36C2×C42×C13C2×C411yescharacteristic
37C2×C42×C13D411yescharacteristic
38C2×C22⋊Dic13—21no—
39C2×C22⋊Dic13—21no—
40C2×C4⋊Dic13C2×C411yescharacteristic
41C2×#6101—21no—
42C2×#6101—21no—
43C2×#6101—21no—
44C2×C4×Dic13—21no—
45C4×Dic26—41no—
46C4×Dic26—41no—
47#88071—21no—
48#88071—21no—
49#88071—21no—
50#88071—21no—
51#88071—21no—
52#88071—21no—
53#88071C2×C411yescharacteristic
54#88071C2×C411yescharacteristic
55C22⋊#1055—22no—
56C4⋊#1055—41no—
57#88043—41no—
58#11763—131nomaximal, Sylow
59C24×C13C22⋊C411yescharacteristic
60C22×C4×C13—22no—
61C22×C4×C13—21no—
62C22×C4×C13—21no—
63C22×C4×C13—21no—
64C22×C4×C13—21no—
65C22×C4×C13C22⋊C411yescharacteristic
66C22×C4×C13C22⋊C411yescharacteristic
67C22×C4×C13C22⋊C411yescharacteristic
68C22×C4×C13C22×C411yescharacteristic
69C22×C4×C13C2×D411yescharacteristic
70C22×C4×C13C2×D411yescharacteristic
71C22×Dic13—21no—
72C22×Dic13—21no—
73C22×Dic13—21no—
74C22×Dic13—21no—
75C2×Dic26—41no—
76C2×Dic26—42no—
77C13×M16—24no—
78C13×M16—44no—
79C13×M16—42no—
80C2×C8×C13—44no—
81C2×C8×C13—42no—
82C13×C4⋊C4—41no—
83C13×C4⋊C4—41no—
84C13×C22⋊C4—41no—
85C13×C22⋊C4—41no—
86C42×C13—21no—
87C42×C13—21no—
88C42×C13—21no—
89C42×C13—21no—
90C22⋊Dic13—42no—
91C22⋊Dic13—42no—
92C4⋊Dic13—41no—
93#6101—42no—
94#6101—41no—
95#6101—41no—
96#6101—41no—
97#6101—41no—
98C4×Dic13—42no—
99C2×#1055—42no—
100#2599—131no—
101#1742D1311yescharacteristic
102#1464—131no—
103#1354—132no—
104#1346—132no—
105C23×C13—21no—
106C23×C13—21no—
107C23×C13—41no—
108C23×C13—41no—
109C23×C13#10412yes—
110C23×C13C2×C22⋊C411yescharacteristic
111C2×C4×C13—22no—
112C2×C4×C13—22no—
113C2×C4×C13—22no—
114C2×C4×C13—22no—
115C2×C4×C13—21no—
116C2×C4×C13—21no—
117C2×C4×C13—21no—
118C2×C4×C13—21no—
119C2×C4×C13—21no—
120C2×C4×C13—21no—
121C2×C4×C13—21no—
122C2×C4×C13—21no—
123C2×C4×C13—41no—
124C2×C4×C13—41no—
125C2×C4×C13—41no—
126C2×C4×C13—41no—
127C2×C4×C13#9911yescharacteristic
128C2×C4×C13#9911yescharacteristic
129C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
130C2×C4×C13#13711yescharacteristic
131C2×Dic13—22no—
132C2×Dic13—41no—
133C2×Dic13—41no—
134C2×Dic13—41no—
135C2×Dic13—41no—
136C2×Dic13—41no—
137C2×Dic13—41no—
138C2×Dic13—41no—
139C2×Dic13—41no—
140C2×Dic13—41no—
141C2×Dic13—41no—
142C2×Dic13—41no—
143Dic26—42no—
144Dic26—42no—
145C8×C13—44no—
146#1055—82no—
147C22×M16—21no—
148C2×C4×Q8—131no—
149C2×#117C2×D1311yescharacteristic
150#432—261no—
151#398—131no—
152#397—131no—
153#395—131no—
154#393—131no—
155#388—261no—
156#387—261no—
157#387—261no—
158#385—261no—
159#383—131no—
160#343—21no—
161#343C2×D1312yes—
162#324—132no—
163#323—261no—
164C22×C13—21no—
165C22×C13—21no—
166C22×C13—22no—
167C22×C13—42no—
168C22×C13—41no—
169C22×C13—41no—
170C22×C13—81no—
171C22×C13C2×#9911yescharacteristic
172C22×C13#41711yescharacteristic
173C22×C13C2×#10411yescharacteristic
174C4×C13—21no—
175C4×C13—21no—
176C4×C13—21no—
177C4×C13—21no—
178C4×C13—41no—
179C4×C13—41no—
180C4×C13—41no—
181C4×C13—41no—
182Dic13—42no—
183Dic13—81no—
184Dic13—81no—
185Dic13—81no—
186C22×Q8—131no—
187C23×C4C22⋊D1311yescharacteristic
188C2×M16—24no—
189C2×M16—22no—
190C2×M16—41no—
191C2×M16—42no—
192C22×C8—41no—
193C4×Q8—521no—
194C4×Q8—521no—
195#117—41no—
196#117—41no—
197C2×C4⋊C4—131no—
198C2×C4⋊C4—261no—
199C2×C4⋊C4—261no—
200C2×C4⋊C4—261no—
201C2×C4⋊C4C22⋊D1311yescharacteristic
202C2×C4⋊C4C22×D1311yescharacteristic
203C2×C22⋊C4—261no—
204C2×C22⋊C4—261no—
205C2×C22⋊C4C4×D1311yescharacteristic
206C2×C22⋊C4D5211yescharacteristic
207C2×C42—261no—
208C2×C42C4×D1311yescharacteristic
209C2×C42D5211yescharacteristic
210C4⋊C8—521no—
211C22⋊C8—262no—
212#97—521no—
213#95—131no—
214#95—131no—
215#95—261no—
216#95—261no—
217#95—261no—
218#95—261no—
219#95—261no—
220#95—261no—
221C2×C13—21no—
222C2×C13—21no—
223C2×C13—42no—
224C2×C13#150411yescharacteristic
225C2×C13#212011yescharacteristic
226C2×C13#213511yescharacteristic
227C24#610311yescharacteristic
228C2×Q8—521no—
229C2×Q8—522no—
230C22×C4—22no—
231C22×C4—21no—
232C22×C4—21no—
233C22×C4—21no—
234C22×C4—21no—
235C22×C4—261no—
236C22×C4—261no—
237C22×C4—261no—
238C22×C4—261no—
239C22×C4#610311yescharacteristic
240C22×C4#610311yescharacteristic
241C22×C4#610311yescharacteristic
242C22×C4C2×C4×D1311yescharacteristic
243C22×C4C2×D5211yescharacteristic
244C22×C4C2×C22⋊D1311yescharacteristic
245M16—24no—
246M16—44no—
247M16—42no—
248C2×C8—44no—
249C2×C8—42no—
250C2×C8—522no—
251C4⋊C4—41no—
252C4⋊C4—41no—
253C4⋊C4—521no—
254C4⋊C4—522no—
255C4⋊C4—521no—
256C4⋊C4—521no—
257C4⋊C4—521no—
258C4⋊C4—521no—
259C22⋊C4—41no—
260C22⋊C4—41no—
261C22⋊C4—522no—
262C22⋊C4—522no—
263C42—21no—
264C42—21no—
265C42—21no—
266C42—21no—
267C42—522no—
268C13#1176311yescharacteristic, complemented, Sylow
269C23—21no—
270C23—21no—
271C23—41no—
272C23—41no—
273C23#8804512yes—
274C23C2×#610311yescharacteristic
275Q8—522no—
276Q8—522no—
277C2×C4—22no—
278C2×C4—22no—
279C2×C4—22no—
280C2×C4—22no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—262no—
294C2×C4—521no—
295C2×C4—521no—
296C2×C4—521no—
297C2×C4—521no—
298C2×C4—521no—
299C2×C4—521no—
300C2×C4—521no—
301C2×C4—521no—
302C2×C4—521no—
303C2×C4—521no—
304C2×C4—521no—
305C2×C4#8804611yescharacteristic
306C2×C4#8804611yescharacteristic
307C2×C4#8818611yescharacteristic
308C2×C4#8819611yescharacteristic
309C8—44no—
310C8—1042no—
311C22—21no—
312C22—21no—
313C22—22no—
314C22—42no—
315C22—41no—
316C22—41no—
317C22—81no—
318C22C2×#8804511yescharacteristic
319C22C2×#8804611yescharacteristic
320C22#1171862711yescharacteristic
321C4—21no—
322C4—21no—
323C4—21no—
324C4—21no—
325C4—41no—
326C4—41no—
327C4—41no—
328C4—41no—
329C4—522no—
330C4—1041no—
331C4—1041no—
332C4—1041no—
333C2—21no—
334C2—21no—
335C2—42no—
336C2#1311333811yescharacteristic
337C2#1311647811yescharacteristic
338C2#1311653011yescharacteristic
subgroupG/H
centerC22C2×#88046
commutatorC22×C4×C13C22×C4
FrattiniC2×C4⋊C4C22×D13
FittingC13×#1742C2
socleC22×C13C2×#99
prime radicalC24×C13C22⋊C4
cosocleC2×C13×C4⋊C4C23
hypercenter#1742D13
hypocenterC13#11763
LCSG ▷ C22×C4×C13 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#117 ◁ #1742

Complements

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

NH ≅ G/Ntype
3. #13112865C2semidirect
4. #13112841C2semidirect
268. C13#11763semidirect

Maximal subgroups

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

subgroupindex
#131204132
#131131702
#131128652
#131128412
C13×#17422
#1176313