Finite Group Databasebeta

← #15773756

Subgroups — #15773756

Order 3328.

340 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 340 conjugacy classes of subgroups — too many to draw. Only its 79 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#13120712C211yesmaximal, characteristic
2#13114832C211yesmaximal, characteristic
3#13112864C212yesmaximal
4#13112843C212yesmaximal
5C13×#1467C211yesmaximal, characteristic
6C2×C4×Q8×C13C2211yescharacteristic
7C2×#88124C411yescharacteristic
8C13×#432—21no—
9#11718890—21no—
10C2×#88076—21no—
11#11718647C411yescharacteristic
12#11718647C2211yescharacteristic
13#11718644C411yescharacteristic
14#11718644C2211yescharacteristic
15#11718643—21no—
16#11718598C411yescharacteristic
17#11718594—21no—
18#11718594—21no—
19#11718585—21no—
20C13×#324—21no—
21C13×#324C2212yes—
22#11718122C2212yes—
23C22×Q8×C13D411yescharacteristic
24C4×Q8×C13—41no—
25C4×Q8×C13—41no—
26C2×C13×C4⋊C4C2×C411yescharacteristic
27C2×C13×C4⋊C4D411yescharacteristic
28C2×C13×C4⋊C4C2311yescharacteristic
29C2×C42×C13C2×C411yescharacteristic
30C2×C42×C13D411yescharacteristic
31C2×C42×C13D411yescharacteristic
32C2×C4⋊Dic13C2×C411yescharacteristic
33C2×C4⋊Dic13C2×C411yescharacteristic
34C2×#6101—21no—
35C2×#6101—21no—
36C2×#6101—21no—
37C2×#6101—21no—
38C2×#6099—22no—
39#88124—41no—
40#88124—41no—
41C13×C4⋊C8—41no—
42C13×C22⋊C8—22no—
43C13×#97—41no—
44#88076—42no—
45#88071—21no—
46#88071—21no—
47#88071—21no—
48#88071—21no—
49#88071—21no—
50#88071—21no—
51#88071—21no—
52#88071—21no—
53#88071C2×C411yescharacteristic
54#88071C2×C411yescharacteristic
55C4⋊#1055—41no—
56C4⋊#1055—41no—
57#11835—131nomaximal, Sylow
58C2×Q8×C13—21no—
59C2×Q8×C13—21no—
60C2×Q8×C13—41no—
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—
72C22×Dic13—21no—
73C2×C8×C13—42no—
74C13×C4⋊C4—41no—
75C13×C4⋊C4—41no—
76C13×C4⋊C4—41no—
77C42×C13—21no—
78C42×C13—21no—
79C42×C13—21no—
80C42×C13—21no—
81C42×C13—21no—
82C42×C13—21no—
83C4⋊Dic13—41no—
84C4⋊Dic13—41no—
85#6101—42no—
86#6101—42no—
87#6101—41no—
88#6101—41no—
89#6101—41no—
90#6101—41no—
91#6099—42no—
92#6099—42no—
93C2×#1055—42no—
94#2634—131no—
95#1801—131no—
96#1467D1311yescharacteristic
97#1353—132no—
98#1346—132no—
99C23×C13C2×C22⋊C411yescharacteristic
100Q8×C13—42no—
101Q8×C13—42no—
102C2×C4×C13—21no—
103C2×C4×C13—21no—
104C2×C4×C13—21no—
105C2×C4×C13—21no—
106C2×C4×C13—21no—
107C2×C4×C13—21no—
108C2×C4×C13—21no—
109C2×C4×C13—21no—
110C2×C4×C13—21no—
111C2×C4×C13—21no—
112C2×C4×C13—21no—
113C2×C4×C13—41no—
114C2×C4×C13—41no—
115C2×C4×C13—41no—
116C2×C4×C13—41no—
117C2×C4×C13#9911yescharacteristic
118C2×C4×C13#9911yescharacteristic
119C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
120C2×C4×C13#13711yescharacteristic
121C2×Dic13—41no—
122C2×Dic13—41no—
123C2×Dic13—41no—
124C2×Dic13—41no—
125C2×Dic13—42no—
126C2×Dic13—41no—
127C2×Dic13—41no—
128C2×Dic13—41no—
129C2×Dic13—41no—
130C2×Dic13—41no—
131C2×Dic13—41no—
132C8×C13—82no—
133#1055—82no—
134C2×#125—131no—
135C2×C4×Q8C2×D1311yescharacteristic
136#432—21no—
137#423—261no—
138C2×#101—261no—
139#400—131no—
140#400—131no—
141#400—261no—
142#398—131no—
143#398—131no—
144#395—261no—
145#387—261no—
146#387—261no—
147#383—131no—
148#343—132no—
149#324—21no—
150#324C2×D1312yes—
151C22×C13—21no—
152C22×C13—21no—
153C22×C13C2×#9911yescharacteristic
154C22×C13#41711yescharacteristic
155C22×C13#42111yescharacteristic
156C4×C13—21no—
157C4×C13—21no—
158C4×C13—21no—
159C4×C13—21no—
160C4×C13—41no—
161C4×C13—41no—
162C4×C13—41no—
163C4×C13—41no—
164C4×C13—41no—
165Dic13—81no—
166Dic13—81no—
167Dic13—81no—
168Dic13—81no—
169C22×Q8D5211yescharacteristic
170C2×M16—262no—
171#125—521no—
172#125—521no—
173C4×Q8—41no—
174C4×Q8—41no—
175C2×C4⋊C4—131no—
176C2×C4⋊C4—131no—
177C2×C4⋊C4—261no—
178C2×C4⋊C4—261no—
179C2×C4⋊C4—261no—
180C2×C4⋊C4—261no—
181C2×C4⋊C4C4×D1311yescharacteristic
182C2×C4⋊C4C22⋊D1311yescharacteristic
183C2×C4⋊C4C22×D1311yescharacteristic
184C2×C42C4×D1311yescharacteristic
185C2×C42D5211yescharacteristic
186C2×C42C22⋊D1311yescharacteristic
187C4⋊C8—41no—
188C4⋊C8—521no—
189C4⋊C8—521no—
190#101—522no—
191C22⋊C8—22no—
192#97—41no—
193#95—131no—
194#95—131no—
195#95—261no—
196#95—261no—
197#95—261no—
198#95—261no—
199#95—261no—
200#95—261no—
201#95—261no—
202#95—261no—
203C2×C13—21no—
204C2×C13—21no—
205C2×C13#151311yescharacteristic
206C2×C13#212311yescharacteristic
207C2×C13#213311yescharacteristic
208C2×Q8—21no—
209C2×Q8—21no—
210C2×Q8—41no—
211C2×Q8—41no—
212C22×C4—261no—
213C22×C4—261no—
214C22×C4—261no—
215C22×C4—261no—
216C22×C4#610311yescharacteristic
217C22×C4#610311yescharacteristic
218C22×C4#610311yescharacteristic
219C22×C4#610311yescharacteristic
220C22×C4C2×C4×D1311yescharacteristic
221C22×C4C2×D5211yescharacteristic
222C22×C4C2×C22⋊D1311yescharacteristic
223M16—522no—
224M16—522no—
225C2×C8—42no—
226C2×C8—522no—
227C4⋊C4—41no—
228C4⋊C4—41no—
229C4⋊C4—41no—
230C4⋊C4—521no—
231C4⋊C4—521no—
232C4⋊C4—522no—
233C4⋊C4—522no—
234C4⋊C4—521no—
235C4⋊C4—521no—
236C4⋊C4—521no—
237C4⋊C4—521no—
238C42—21no—
239C42—21no—
240C42—21no—
241C42—21no—
242C42—21no—
243C42—21no—
244C13#1183511yescharacteristic, complemented, Sylow
245C23C2×#610311yescharacteristic
246Q8—42no—
247Q8—42no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—41no—
260C2×C4—41no—
261C2×C4—41no—
262C2×C4—41no—
263C2×C4—521no—
264C2×C4—521no—
265C2×C4—521no—
266C2×C4—521no—
267C2×C4—522no—
268C2×C4—521no—
269C2×C4—521no—
270C2×C4—521no—
271C2×C4—521no—
272C2×C4—521no—
273C2×C4—521no—
274C2×C4#8804611yescharacteristic
275C2×C4#8804611yescharacteristic
276C2×C4#8816211yescharacteristic
277C2×C4#8816311yescharacteristic
278C8—82no—
279C8—1042no—
280C22—21no—
281C22—21no—
282C22C2×#8804611yescharacteristic
283C22#1171879411yescharacteristic
284C22#1171880011yescharacteristic
285C4—21no—
286C4—21no—
287C4—21no—
288C4—21no—
289C4—41no—
290C4—41no—
291C4—41no—
292C4—41no—
293C4—41no—
294C4—1041no—
295C4—1041no—
296C4—1041no—
297C4—1041no—
298C2—21no—
299C2—21no—
300C2#1311338011yescharacteristic
301C2#1311648911yescharacteristic
302C2#1311652311yescharacteristic
subgroupG/H
centerC22C2×#88046
commutatorC22×C4×C13C22×C4
FrattiniC2×C4⋊C4C22×D13
FittingC13×#1467C2
socleC22×C13C2×#99
prime radicalC23×C13C2×C22⋊C4
cosocleC2×C13×C4⋊C4C23
hypercenter#1467D13
hypocenterC13#11835
LCSG ▷ C22×C4×C13 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #1467

Complements

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

NH ≅ G/Ntype
244. C13#11835semidirect

Maximal subgroups

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

subgroupindex
#131207122
#131148322
#131128642
#131128432
C13×#14672
#1183513