Finite Group Databasebeta

← #15772215

Subgroups — #15772215

Order 3328.

392 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 392 conjugacy classes of subgroups — too many to draw. Only its 103 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#13117552C211yesmaximal, characteristic
2#13113160C211yesmaximal, characteristic
3#13112779C212yesmaximal
4#13112769C212yesmaximal
5C13×#1461C211yesmaximal, characteristic
6C2×C4×Q8×C13C2211yescharacteristic
7C2×#88198C411yescharacteristic
8C2×C4×Dic26C411yescharacteristic
9C13×#431—21no—
10#11718891C411yescharacteristic
11#11718639—21no—
12#11718639—21no—
13#11718638C2211yescharacteristic
14#11718635C2211yescharacteristic
15#11718594—21no—
16#11718594—21no—
17#11718593C411yescharacteristic
18#11718586—21no—
19C13×#324—21no—
20C13×#324C2212yes—
21#11718120—21no—
22#11718120C2212yes—
23C22×Q8×C13C2×C411yescharacteristic
24C22×Dic26C2×C411yescharacteristic
25C4×Q8×C13—41no—
26C4×Q8×C13—41no—
27C2×C13×C4⋊C4D411yescharacteristic
28C2×C13×C4⋊C4D411yescharacteristic
29C2×C13×C4⋊C4C2311yescharacteristic
30C2×C42×C13C2×C411yescharacteristic
31C2×C42×C13D411yescharacteristic
32C2×C42×C13D411yescharacteristic
33#88198—22no—
34#88198C814yescomplemented
35C2×C4⋊Dic13C2×C411yescharacteristic
36C2×#6101—21no—
37C2×#6101—21no—
38C2×#6101—21no—
39C2×C4×Dic13—21no—
40C2×C4×Dic13C2×C411yescharacteristic
41C2×C4×Dic13C2×C411yescharacteristic
42C4×Dic26—41no—
43C4×Dic26—41no—
44C13×C4⋊C8—41no—
45C13×C22⋊C8—22no—
46C4×C8×C13—41no—
47#88071—21no—
48#88071—21no—
49#88071—21no—
50#88071—21no—
51#88071—21no—
52#88071—21no—
53#88071—21no—
54#88071—21no—
55C22⋊#1055—22no—
56C4⋊#1055—41no—
57C4×#1055—41no—
58#11482—131nomaximal, Sylow
59C2×Q8×C13—41no—
60C2×Q8×C13—41no—
61C2×Q8×C13C2×C812yes—
62C2×Q8×C13M1612yes—
63C22×C4×C13C22⋊C411yescharacteristic
64C22×C4×C13C22⋊C411yescharacteristic
65C22×C4×C13C22⋊C411yescharacteristic
66C22×C4×C13C22⋊C411yescharacteristic
67C22×C4×C13C22×C411yescharacteristic
68C22×C4×C13C2×D411yescharacteristic
69C22×C4×C13C2×D411yescharacteristic
70C22×Dic13—21no—
71C22×Dic13—21no—
72C22×Dic13—21no—
73C22×Dic13—21no—
74C2×Dic26—21no—
75C2×Dic26—41no—
76C2×Dic26—41no—
77C2×Dic26C2×C812yes—
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—
88C4⋊Dic13—41no—
89#6101—24no—
90#6101—24no—
91#6101—41no—
92#6101—41no—
93C4×Dic13—21no—
94C4×Dic13—42no—
95C4×Dic13—41no—
96C4×Dic13C2×C812yes—
97C2×#1055—42no—
98#2327—131no—
99#1461—131no—
100#1461D1311yescharacteristic
101#1324—132no—
102#1319—132no—
103C23×C13C2×C22⋊C411yescharacteristic
104Q8×C13—42no—
105Q8×C13—42no—
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—21no—
114C2×C4×C13—21no—
115C2×C4×C13—41no—
116C2×C4×C13—41no—
117C2×C4×C13—41no—
118C2×C4×C13—41no—
119C2×C4×C13C22⋊C812yes—
120C2×C4×C13C22⋊C812yes—
121C2×C4×C13#9911yescharacteristic
122C2×C4×C13#9911yescharacteristic
123C2×C4×C13C22×C811yescharacteristic
124C2×C4×C13C2×M1611yescharacteristic
125C2×Dic13—22no—
126C2×Dic13—22no—
127C2×Dic13—41no—
128C2×Dic13—41no—
129C2×Dic13—41no—
130C2×Dic13—41no—
131C2×Dic13—41no—
132C2×Dic13—41no—
133C2×Dic13—42no—
134C2×Dic13—41no—
135C2×Dic13—41no—
136Dic26—42no—
137Dic26—42no—
138C8×C13—82no—
139#1055—82no—
140C2×C4⋊Q8—131no—
141C2×C4×Q8—131no—
142C2×C4×Q8C2×D1311yescharacteristic
143#431—21no—
144#431—261no—
145#391—131no—
146#391—131no—
147#387—261no—
148#387—261no—
149#387—261no—
150#387—261no—
151#382—131no—
152#376—131no—
153#324—21no—
154#324—132no—
155#324—261no—
156#324C2×D1312yes—
157C22×C13—21no—
158C22×C13—21no—
159C22×C13C2×C22⋊C811yescharacteristic
160C22×C13C2×#9911yescharacteristic
161C22×C13#41311yescharacteristic
162C4×C13—21no—
163C4×C13—21no—
164C4×C13—21no—
165C4×C13—21no—
166C4×C13—22no—
167C4×C13—22no—
168C4×C13—41no—
169C4×C13—41no—
170C4×C13—41no—
171Dic13—42no—
172Dic13—42no—
173Dic13—81no—
174Dic13—81no—
175C22×Q8—131no—
176C22×Q8C4×D1311yescharacteristic
177C4⋊Q8—134no—
178C4⋊Q8—262no—
179C4×Q8—41no—
180C4×Q8—41no—
181C4×Q8—521no—
182C4×Q8—521no—
183C2×C4⋊C4—131no—
184C2×C4⋊C4—261no—
185C2×C4⋊C4—261no—
186C2×C4⋊C4—261no—
187C2×C4⋊C4D5211yescharacteristic
188C2×C4⋊C4C22⋊D1311yescharacteristic
189C2×C4⋊C4C22×D1311yescharacteristic
190C2×C42—131no—
191C2×C42—131no—
192C2×C42—261no—
193C2×C42C4×D1311yescharacteristic
194C2×C42D5211yescharacteristic
195C2×C42C22⋊D1311yescharacteristic
196C4⋊C8—41no—
197C4⋊C8—521no—
198C22⋊C8—22no—
199C22⋊C8—262no—
200C4×C8—41no—
201C4×C8—521no—
202#95—261no—
203#95—261no—
204#95—261no—
205#95—261no—
206#95—261no—
207#95—261no—
208#95—261no—
209#95—261no—
210C2×C13—21no—
211C2×C13—21no—
212C2×C13#145911yescharacteristic
213C2×C13#212911yescharacteristic
214C2×C13#213311yescharacteristic
215C2×Q8—41no—
216C2×Q8—41no—
217C2×Q8—132no—
218C2×Q8—261no—
219C2×Q8—521no—
220C2×Q8—521no—
221C2×Q8C8×D1312yes—
222C2×Q8#609412yes—
223C22×C4—261no—
224C22×C4—261no—
225C22×C4—261no—
226C22×C4—261no—
227C22×C4#610311yescharacteristic
228C22×C4#610311yescharacteristic
229C22×C4#610311yescharacteristic
230C22×C4#610311yescharacteristic
231C22×C4C2×C4×D1311yescharacteristic
232C22×C4C2×D5211yescharacteristic
233C22×C4C2×C22⋊D1311yescharacteristic
234C2×C8—42no—
235C2×C8—522no—
236C4⋊C4—41no—
237C4⋊C4—41no—
238C4⋊C4—41no—
239C4⋊C4—264no—
240C4⋊C4—264no—
241C4⋊C4—521no—
242C4⋊C4—521no—
243C4⋊C4—521no—
244C42—21no—
245C42—21no—
246C42—21no—
247C42—21no—
248C42—21no—
249C42—21no—
250C42—132no—
251C42—261no—
252C42—521no—
253C42—522no—
254C13#1148211yescharacteristic, complemented, Sylow
255C23C2×#610311yescharacteristic
256Q8—42no—
257Q8—42no—
258Q8—522no—
259Q8—522no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—262no—
274C2×C4—262no—
275C2×C4—521no—
276C2×C4—521no—
277C2×C4—521no—
278C2×C4—521no—
279C2×C4—521no—
280C2×C4—521no—
281C2×C4—522no—
282C2×C4—521no—
283C2×C4—521no—
284C2×C4#8804611yescharacteristic
285C2×C4#8804611yescharacteristic
286C2×C4#8806012yes—
287C2×C4#8806012yes—
288C2×C4C2×C8×D1311yescharacteristic
289C2×C4C2×#609411yescharacteristic
290C8—82no—
291C8—1042no—
292C22—21no—
293C22—21no—
294C22C2×#8804611yescharacteristic
295C22C2×#8806011yescharacteristic
296C22#1171879311yescharacteristic
297C4—21no—
298C4—21no—
299C4—22no—
300C4—22no—
301C4—21no—
302C4—21no—
303C4—41no—
304C4—41no—
305C4—41no—
306C4—522no—
307C4—522no—
308C4—1041no—
309C4—1041no—
310C2—21no—
311C2—21no—
312C2#1311315211yescharacteristic
313C2#1311651011yescharacteristic
314C2#1311652311yescharacteristic
subgroupG/H
centerC22C2×#88046
commutatorC2×C4×C13C22×C8
FrattiniC2×C4⋊C4C22×D13
FittingC13×#1461C2
socleC22×C13C2×#99
prime radicalC23×C13C2×C22⋊C4
cosocleC2×C13×C4⋊C4C23
hypercenter#1461D13
hypocenterC13#11482
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #1461

Complements

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

NH ≅ G/Ntype
34. #88198C8semidirect
254. C13#11482semidirect

Maximal subgroups

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

subgroupindex
#131175522
#131131602
#131127792
#131127692
C13×#14612
#1148213