Finite Group Databasebeta

← #15773306

Subgroups — #15773306

Order 3328.

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

normal subgroups only

This group has 400 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#13120696C211yesmaximal, characteristic
2#13113160C211yesmaximal, characteristic, complemented
3#13112865C212yesmaximal, complemented
4#13112838C212yesmaximal
5C4×C13×#101C211yesmaximal, characteristic, complemented
6C2×C4×Q8×C13C2211yescharacteristic
7C2×#88129C411yescharacteristic
8C2×C13×#101—21no—
9C4×C13×M16—21no—
10#11718892—21no—
11#11718653—21no—
12#11718652C411yescharacteristic
13#11718652C2211yescharacteristic
14#11718640C411yescharacteristic
15#11718640C2211yescharacteristic
16#11718601—21no—
17#11718601—21no—
18#11718598C411yescharacteristic
19#11718586—21no—
20C13×#343C2212yes—
21#11718120—21no—
22#11718120C2212yes—
23C22×Q8×C13D411yescharacteristic
24C22×D52C2×C411yescharacteristic
25C22×Dic26C2×C411yescharacteristic
26C2×C13×M16—22no—
27C4×Q8×C13—41no—
28C4×Q8×C13—41no—
29C2×C13×C4⋊C4C2×C411yescharacteristic
30C2×C13×C4⋊C4D411yescharacteristic
31C2×C13×C4⋊C4C2311yescharacteristic
32C2×C42×C13C2×C411yescharacteristic
33C2×C42×C13D411yescharacteristic
34C2×C42×C13D411yescharacteristic
35C2×#6103—21no—
36C2×#6103—21no—
37C2×#6103—21no—
38C2×#6103—21no—
39C2×#6103—21no—
40C2×#6103—21no—
41C2×#6101—21no—
42C2×#6101—21no—
43#88129—41no—
44#88129—41no—
45C13×#101—24no—
46C13×#97—41no—
47C4×C8×C13—41no—
48#88071—21no—
49#88071—21no—
50#88071—21no—
51#88071—21no—
52#88071C2×C411yescharacteristic
53#88071C2×C411yescharacteristic
54C22⋊#1055—22no—
55C4⋊#1055—41no—
56C4×#1055—41no—
57#11738—131nomaximal, Sylow
58C23×D13—21no—
59C2×Q8×C13—22no—
60C2×Q8×C13—22no—
61C2×Q8×C13—41no—
62C22×C4×C13C22⋊C411yescharacteristic
63C22×C4×C13C22⋊C411yescharacteristic
64C22×C4×C13C22⋊C411yescharacteristic
65C22×C4×C13C22⋊C411yescharacteristic
66C22×C4×C13C22×C411yescharacteristic
67C22×C4×C13C2×D411yescharacteristic
68C22×C4×C13C2×D411yescharacteristic
69C22×Dic13—21no—
70C22×Dic13—21no—
71C22×Dic13—21no—
72C2×D52—41no—
73C2×D52—81no—
74C2×Dic26—41no—
75C2×Dic26—81no—
76C13×M16—24no—
77C13×M16—42no—
78C2×C8×C13—42no—
79C13×C4⋊C4—41no—
80C13×C4⋊C4—41no—
81C13×C4⋊C4—41no—
82C42×C13—21no—
83C42×C13—21no—
84C42×C13—21no—
85C42×C13—21no—
86C42×C13—21no—
87C42×C13—21no—
88#6103—42no—
89#6103—41no—
90#6103—41no—
91#6103—42no—
92#6103—42no—
93#6103—81no—
94#6103—81no—
95#6101—81no—
96#6101—81no—
97C2×#1055—42no—
98#2632—131no—
99C4×#101D1311yescharacteristic, complemented
100#1461—131no—
101#1354—132no—
102#1345—132no—
103C23×C13C2×C22⋊C411yescharacteristic
104C22×D13—41no—
105C22×D13—41no—
106C22×D13—41no—
107C22×D13—41no—
108C22×D13—41no—
109C22×D13—41no—
110C22×D13—41no—
111Q8×C13—44no—
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—21no—
119C2×C4×C13—21no—
120C2×C4×C13—21no—
121C2×C4×C13—21no—
122C2×C4×C13—41no—
123C2×C4×C13—41no—
124C2×C4×C13—41no—
125C2×C4×C13—41no—
126C2×C4×C13#9911yescharacteristic
127C2×C4×C13#9911yescharacteristic
128C2×C4×C13#10412yes—
129C2×C4×C13#13512yes—
130C2×Dic13—41no—
131C2×Dic13—41no—
132C2×Dic13—41no—
133C2×Dic13—41no—
134C2×Dic13—41no—
135C2×Dic13—41no—
136C2×Dic13—41no—
137C2×Dic13—41no—
138C2×Dic13—41no—
139D52—82no—
140Dic26—82no—
141C8×C13—44no—
142#1055—82no—
143C2×#124—131no—
144C2×C4×Q8C2×D1311yescharacteristic
145#431—261no—
146C2×#101—21no—
147C4×M16—21no—
148#399—261no—
149#395—131no—
150#395—131no—
151#394—131no—
152#394—131no—
153#393—261no—
154#388—261no—
155#388—261no—
156#383—131no—
157#343C2×D1312yes—
158#324—132no—
159#324—261no—
160C22×C13—21no—
161C22×C13—21no—
162C22×C13C2×#9911yescharacteristic
163C22×C13#41611yescharacteristic
164C22×C13C2×#10411yescharacteristic
165C2×D13—81no—
166C2×D13—81no—
167C2×D13—81no—
168C2×D13—81no—
169C2×D13—81no—
170C2×D13—81no—
171C2×D13—81no—
172C4×C13—21no—
173C4×C13—21no—
174C4×C13—22no—
175C4×C13—22no—
176C4×C13—41no—
177C4×C13—41no—
178C4×C13—41no—
179C4×C13—41no—
180Dic13—81no—
181Dic13—81no—
182Dic13—81no—
183C22×Q8—131no—
184C22×Q8C22⋊D1311yescharacteristic
185C22×D4—131no—
186C2×M16—22no—
187#124—521no—
188#124—521no—
189C4×Q8—41no—
190C4×Q8—41no—
191C2×C4⋊C4—261no—
192C2×C4⋊C4—261no—
193C2×C4⋊C4C4×D1311yescharacteristic
194C2×C4⋊C4D5211yescharacteristic
195C2×C4⋊C4C22×D1311yescharacteristic
196C2×C22⋊C4—261no—
197C2×C22⋊C4—261no—
198C2×C22⋊C4—261no—
199C2×C22⋊C4—261no—
200C2×C22⋊C4—261no—
201C2×C22⋊C4—261no—
202C2×C42C4×D1311yescharacteristic
203C2×C42D5211yescharacteristic
204C2×C42C22⋊D1311yescharacteristic
205C4⋊C8—521no—
206#101—24no—
207C22⋊C8—262no—
208#97—41no—
209C4×C8—41no—
210C4×C8—521no—
211#95—131no—
212#95—131no—
213#95—261no—
214#95—261no—
215#95—261no—
216#95—261no—
217C2×C13—21no—
218C2×C13—21no—
219C2×C13#150111yescharacteristic
220C2×C13#212211yescharacteristic
221C2×C13#213311yescharacteristic
222D13—161no—
223C24—261no—
224C2×Q8—22no—
225C2×Q8—22no—
226C2×Q8—41no—
227C2×Q8—521no—
228C2×Q8—1041no—
229C2×D4—521no—
230C2×D4—1041no—
231C22×C4—261no—
232C22×C4—261no—
233C22×C4—261no—
234C22×C4#610311yescharacteristic
235C22×C4#610311yescharacteristic
236C22×C4#610311yescharacteristic
237C22×C4#610311yescharacteristic
238C22×C4C2×C4×D1311yescharacteristic
239C22×C4C2×D5211yescharacteristic
240C22×C4C2×C22⋊D1311yescharacteristic
241M16—24no—
242M16—42no—
243C2×C8—42no—
244C2×C8—522no—
245C4⋊C4—41no—
246C4⋊C4—41no—
247C4⋊C4—41no—
248C4⋊C4—1041no—
249C4⋊C4—1041no—
250C22⋊C4—522no—
251C22⋊C4—522no—
252C22⋊C4—522no—
253C22⋊C4—521no—
254C22⋊C4—521no—
255C22⋊C4—1041no—
256C22⋊C4—1041no—
257C42—21no—
258C42—21no—
259C42—21no—
260C42—21no—
261C42—21no—
262C42—21no—
263C13#1173811yescharacteristic, complemented, Sylow
264C23—521no—
265C23—521no—
266C23—521no—
267C23—521no—
268C23—521no—
269C23—521no—
270C23—521no—
271C23C2×#610311yescharacteristic
272Q8—44no—
273Q8—1042no—
274D4—1042no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—521no—
290C2×C4—521no—
291C2×C4—521no—
292C2×C4—521no—
293C2×C4—521no—
294C2×C4—521no—
295C2×C4—521no—
296C2×C4—521no—
297C2×C4—521no—
298C2×C4#8804512yes—
299C2×C4#8804611yescharacteristic
300C2×C4#8804611yescharacteristic
301C2×C4#8820412yes—
302C8—44no—
303C8—1042no—
304C22—21no—
305C22—21no—
306C22—1041no—
307C22—1041no—
308C22—1041no—
309C22—1041no—
310C22—1041no—
311C22—1041no—
312C22—1041no—
313C22C2×#8804511yescharacteristic
314C22C2×#8804611yescharacteristic
315C22#1171866311yescharacteristic
316C4—21no—
317C4—21no—
318C4—22no—
319C4—22no—
320C4—41no—
321C4—41no—
322C4—41no—
323C4—41no—
324C4—1041no—
325C4—1041no—
326C4—1041no—
327C2—21no—
328C2—21no—
329C2—2081no—
330C2#1311332511yescharacteristic
331C2#1311648711yescharacteristic
332C2#1311652311yescharacteristic
subgroupG/H
centerC22C2×#88046
commutatorC22×C4×C13C22×C4
FrattiniC2×C4⋊C4C22×D13
FittingC4×C13×#101C2
socleC22×C13C2×#99
prime radicalC22×D52C2×C4
cosocleC2×C13×C4⋊C4C23
hypercenterC4×#101D13
hypocenterC13#11738
LCSG ▷ C22×C4×C13 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ C4×#101

Complements

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

NH ≅ G/Ntype
2. #13113160C2semidirect
3. #13112865C2semidirect
5. C4×C13×#101C2semidirect
99. C4×#101D13semidirect
263. C13#11738semidirect

Maximal subgroups

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

subgroupindex
#131206962
#131131602
#131128652
#131128382
C4×C13×#1012
#1173813