Finite Group Databasebeta

← #15781609

Subgroups — #15781609

Order 3328.

396 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 396 conjugacy classes of subgroups — too many to draw. Only its 99 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#13120023C211yesmaximal, characteristic
2C4×#88076C211yesmaximal, characteristic
3#13112962C212yesmaximal
4#13112962C212yesmaximal
5C13×#1801C211yesmaximal, characteristic
6C2×C4×Q8×C13C2211yescharacteristic
7C2×#88124C411yescharacteristic
8C13×#423—21no—
9C2×C13×#101C2212yes—
10#11718891C2211yescharacteristic
11#11718891C2211yescharacteristic
12C2×#88076C2212yes—
13#11718645—21no—
14#11718645—21no—
15#11718638C411yescharacteristic
16#11718637C411yescharacteristic
17C4×C4⋊Dic13C411yescharacteristic
18#11718594—21no—
19#11718594—21no—
20C4×#6099—21no—
21C13×#343—21no—
22#11718122—21no—
23C22×Q8×C13C2311yescharacteristic
24C2×C13×M16—22no—
25C4×Q8×C13—41no—
26C4×Q8×C13—41no—
27C2×C13×C4⋊C4C2×C411yescharacteristic
28C2×C13×C4⋊C4D411yescharacteristic
29C2×C13×C4⋊C4D411yescharacteristic
30C2×C42×C13C2×C411yescharacteristic
31C2×C42×C13D411yescharacteristic
32C2×C42×C13D411yescharacteristic
33C2×C4⋊Dic13—21no—
34C2×C4⋊Dic13C2×C411yescharacteristic
35C2×C4⋊Dic13C2×C411yescharacteristic
36C2×#6101—21no—
37C2×#6101—21no—
38C2×#6101—21no—
39C2×#6101—21no—
40C2×C4×Dic13C2×C411yescharacteristic
41C2×C4×Dic13C2×C411yescharacteristic
42C2×#6099—22no—
43#88124—41no—
44#88124—41no—
45C13×C4⋊C8—41no—
46C13×C4⋊C8—41no—
47C13×#101—24no—
48#88076—22no—
49#88076Q814yes—
50#88071—21no—
51#88071—21no—
52#88071—21no—
53#88071—21no—
54#88071—21no—
55#88071—21no—
56#88071—21no—
57#88043—41no—
58C4×#1055—41no—
59#13303—131nomaximal, Sylow
60C2×Q8×C13—41no—
61C2×Q8×C13—41no—
62C2×Q8×C13C2×Q812yes—
63C2×Q8×C13#4112yes—
64C22×C4×C13C22⋊C411yescharacteristic
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—
75C13×M16—42no—
76C13×M16—42no—
77C2×C8×C13—42no—
78C13×C4⋊C4—41no—
79C13×C4⋊C4—41no—
80C13×C4⋊C4—41no—
81C42×C13—21no—
82C42×C13—21no—
83C42×C13—21no—
84C42×C13—21no—
85C42×C13—21no—
86C42×C13—21no—
87C4⋊Dic13—42no—
88C4⋊Dic13—41no—
89C4⋊Dic13—41no—
90#6101—42no—
91#6101—42no—
92#6101—42no—
93#6101—41no—
94#6101—41no—
95C4×Dic13—41no—
96C4×Dic13—41no—
97#6099—24no—
98#6099—42no—
99C2×#1055—42no—
100#2565—131no—
101#1801D1311yescharacteristic
102C4×#101—131no—
103#1394—132no—
104#1394—132no—
105C23×C13C2×C22⋊C411yescharacteristic
106Q8×C13—42no—
107Q8×C13—42no—
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—21no—
116C2×C4×C13—21no—
117C2×C4×C13—41no—
118C2×C4×C13—41no—
119C2×C4×C13—41no—
120C2×C4×C13—41no—
121C2×C4×C13#9911yescharacteristic
122C2×C4×C13#9911yescharacteristic
123C2×C4×C13C4×Q812yes—
124C2×C4×C13C22⋊Q812yes—
125C2×C4×C13#12411yescharacteristic
126C2×C4×C13C4⋊Q811yescharacteristic
127C2×Dic13—22no—
128C2×Dic13—41no—
129C2×Dic13—41no—
130C2×Dic13—41no—
131C2×Dic13—41no—
132C2×Dic13—41no—
133C2×Dic13—41no—
134C2×Dic13—42no—
135C2×Dic13—41no—
136C2×Dic13—41no—
137C2×Dic13—41no—
138C8×C13—82no—
139#1055—44no—
140C2×#125—131no—
141C2×C4×Q8C2×D1311yescharacteristic
142#423—21no—
143C2×#101—132no—
144C2×#101C2×D1312yes—
145C4×M16—261no—
146#398—261no—
147#398—261no—
148#391—131no—
149#391—131no—
150#387—261no—
151#387—261no—
152#384—131no—
153#382—131no—
154C4×C4⋊C4—131no—
155#343—21no—
156#343—261no—
157C22×C13—21no—
158C22×C13—21no—
159C22×C13#39111yescharacteristic
160C22×C13C2×#9911yescharacteristic
161C22×C13#41011yescharacteristic
162C4×C13—21no—
163C4×C13—21no—
164C4×C13—22no—
165C4×C13—21no—
166C4×C13—22no—
167C4×C13—21no—
168C4×C13—41no—
169C4×C13—41no—
170C4×C13—41no—
171Dic13—42no—
172Dic13—81no—
173Dic13—81no—
174Dic13—81no—
175C22×Q8C22×D1311yescharacteristic
176C2×M16—22no—
177C2×M16—262no—
178#125—521no—
179#125—521no—
180C4×Q8—41no—
181C4×Q8—41no—
182C2×C4⋊C4—131no—
183C2×C4⋊C4—131no—
184C2×C4⋊C4—261no—
185C2×C4⋊C4—261no—
186C2×C4⋊C4—261no—
187C2×C4⋊C4—261no—
188C2×C4⋊C4—261no—
189C2×C4⋊C4C4×D1311yescharacteristic
190C2×C4⋊C4D5211yescharacteristic
191C2×C4⋊C4C22⋊D1311yescharacteristic
192C2×C42—131no—
193C2×C42—131no—
194C2×C42C4×D1311yescharacteristic
195C2×C42D5211yescharacteristic
196C2×C42C22⋊D1311yescharacteristic
197C4⋊C8—41no—
198C4⋊C8—41no—
199#101—24no—
200#101—134no—
201#101—262no—
202#97—521no—
203C4×C8—521no—
204#95—261no—
205#95—261no—
206#95—261no—
207#95—261no—
208#95—261no—
209#95—261no—
210#95—261no—
211C2×C13—21no—
212C2×C13—21no—
213C2×C13#199611yescharacteristic
214C2×C13#213211yescharacteristic
215C2×C13#213311yescharacteristic
216C2×Q8—41no—
217C2×Q8—41no—
218C2×Q8#612912yes—
219C2×Q8Q8×D1312yes—
220C22×C4—261no—
221C22×C4—261no—
222C22×C4—261no—
223C22×C4—261no—
224C22×C4#610311yescharacteristic
225C22×C4#610311yescharacteristic
226C22×C4#610311yescharacteristic
227C22×C4#610311yescharacteristic
228C22×C4C2×C4×D1311yescharacteristic
229C22×C4C2×D5211yescharacteristic
230C22×C4C2×C22⋊D1311yescharacteristic
231M16—42no—
232M16—42no—
233M16—264no—
234M16—522no—
235C2×C8—42no—
236C2×C8—522no—
237C4⋊C4—41no—
238C4⋊C4—41no—
239C4⋊C4—41no—
240C4⋊C4—521no—
241C4⋊C4—521no—
242C4⋊C4—522no—
243C4⋊C4—522no—
244C4⋊C4—522no—
245C4⋊C4—522no—
246C4⋊C4—521no—
247C4⋊C4—521no—
248C42—21no—
249C42—21no—
250C42—21no—
251C42—21no—
252C42—21no—
253C42—21no—
254C42—521no—
255C42—521no—
256C13#1330311yescharacteristic, complemented, Sylow
257C23C2×#610311yescharacteristic
258Q8—42no—
259Q8—42no—
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—521no—
275C2×C4—521no—
276C2×C4—521no—
277C2×C4—521no—
278C2×C4—521no—
279C2×C4—521no—
280C2×C4—522no—
281C2×C4—521no—
282C2×C4—521no—
283C2×C4—521no—
284C2×C4#8804611yescharacteristic
285C2×C4#8804611yescharacteristic
286C2×C4#8814112yes—
287C2×C4#8815112yes—
288C2×C4#8819011yescharacteristic
289C2×C4#8819811yescharacteristic
290C8—82no—
291C8—524no—
292C22—21no—
293C22—21no—
294C22C2×#8804611yescharacteristic
295C22#1171863511yescharacteristic
296C22#1171866711yescharacteristic
297C4—21no—
298C4—21no—
299C4—21no—
300C4—22no—
301C4—22no—
302C4—21no—
303C4—41no—
304C4—41no—
305C4—41no—
306C4—522no—
307C4—1041no—
308C4—1041no—
309C4—1041no—
310C2—21no—
311C2—21no—
312C2#1311582011yescharacteristic
313C2#1311651911yescharacteristic
314C2#1311652311yescharacteristic
subgroupG/H
centerC22C2×#88046
commutatorC22×C4×C13C22×C4
FrattiniC22×Q8C22×D13
FittingC13×#1801C2
socleC22×C13C2×#99
prime radicalC23×C13C2×C22⋊C4
cosocleC22×Q8×C13C23
hypercenter#1801D13
hypocenterC13#13303
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #1801

Complements

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

NH ≅ G/Ntype
256. C13#13303semidirect

Maximal subgroups

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

subgroupindex
#131200232
C4×#880762
#131129622
C13×#18012
#1330313