Finite Group Databasebeta

← #15760296

Subgroups — #15760296

Order 3328.

470 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 470 conjugacy classes of subgroups — too many to draw. Only its 117 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#13123916C211yesmaximal, characteristic
2#13120052C211yesmaximal, characteristic
3#13114829C211yesmaximal, characteristic
4#13113521C211yesmaximal, characteristic
5#13112738C211yesmaximal, characteristic
6#13112737C211yesmaximal, characteristic
7C13×#1549C211yesmaximal, characteristic
8C2×C13×C4⋊Q8C2211yescharacteristic
9C2×C4×Dic26C2211yescharacteristic
10C13×#431C2211yescharacteristic
11C13×#423C2211yescharacteristic
12#11718891—22no—
13C2×#88064—21no—
14#11718643C414yes—
15#11718638—21no—
16#11718635—21no—
17C4×C4⋊Dic13C2211yescharacteristic
18#11718586C2211yescharacteristic
19#11718585C2211yescharacteristic
20#11718491—22no—
21#11718379—22no—
22C8×Dic26—22no—
23C13×#332—22no—
24#11718146—21no—
25#11718139—22no—
26C22×Q8×C13—21no—
27C22×Dic26D411yescharacteristic
28C2×C13×M16—21no—
29C13×C4⋊Q8—21no—
30C13×C4⋊Q8—21no—
31C13×C4⋊Q8—21no—
32C13×C4⋊Q8—21no—
33C2×C13×C4⋊C4—21no—
34C2×C13×C4⋊C4C2×C412yes—
35C2×C42×C13C2311yescharacteristic
36C2×C4⋊Dic13—21no—
37C2×C4⋊Dic13D411yescharacteristic
38C2×#6101C2×C412yes—
39C2×C4×Dic13—21no—
40C2×C4×Dic13D412yes—
41C2×#6099—21no—
42C4×Dic26—21no—
43C4×Dic26—21no—
44C4×Dic26—21no—
45C4×Dic26—21no—
46C13×C4⋊C8—21no—
47C13×C4⋊C8—21no—
48C13×C4⋊C8D412yes—
49C13×C22⋊C8—21no—
50C4×C8×C13—21no—
51#88071—24no—
52#88071—24no—
53#88071C2×C412yes—
54C22⋊#1055—21no—
55#88064—42no—
56#88054—24no—
57C8×Dic13—24no—
58C4⋊#1055—21no—
59C4⋊#1055—21no—
60C4⋊#1055D412yes—
61C4×#1055—21no—
62#9396—131nomaximal, Sylow
63C2×Q8×C13—44no—
64C2×Q8×C13—41no—
65C2×Q8×C13—41no—
66C22×C4×C13—22no—
67C22×C4×C13C22×C411yescharacteristic
68C22×C4×C13C2×D411yescharacteristic
69C22×C4×C13C2×D411yescharacteristic
70C22×Dic13—22no—
71C22×Dic13C22⋊C412yes—
72C22×Dic13C22⋊C412yes—
73C2×Dic26—21no—
74C2×Dic26—21no—
75C2×Dic26—21no—
76C2×Dic26—21no—
77C2×Dic26SD1612yes—
78C2×Dic26Q1612yes—
79C13×M16—41no—
80C13×M16—41no—
81C2×C8×C13—22no—
82C2×C8×C13—41no—
83C13×C4⋊C4—22no—
84C13×C4⋊C4—22no—
85C13×C4⋊C4—41no—
86C13×C4⋊C4—41no—
87C42×C13C2×D411yescharacteristic
88C42×C13C2×D411yescharacteristic
89C42×C13#4111yescharacteristic
90C42×C13#4111yescharacteristic
91C4⋊Dic13—21no—
92C4⋊Dic13—21no—
93C4⋊Dic13—42no—
94#6101—22no—
95#6101—22no—
96C4×Dic13—22no—
97C4×Dic13—22no—
98C4×Dic13—41no—
99C4×Dic13—41no—
100#6099—41no—
101#6099—41no—
102C2×#1055—22no—
103C2×#1055—41no—
104#2982—131no—
105#2568—131no—
106#1801—131no—
107#1549—131no—
108#1549D1311yescharacteristic
109#1303—131no—
110#1303—131no—
111C23×C13C2×C22⋊C411yescharacteristic
112Q8×C13—82no—
113Q8×C13—82no—
114C2×C4×C13—22no—
115C2×C4×C13—41no—
116C2×C4×C13—44no—
117C2×C4×C13—42no—
118C2×C4×C13C4×D411yescharacteristic
119C2×C4×C13C4×D411yescharacteristic
120C2×C4×C13#12011yescharacteristic
121C2×C4×C13#12111yescharacteristic
122C2×C4×C13#12111yescharacteristic
123C2×C4×C13#12311yescharacteristic
124C2×C4×C13C2×SD1611yescharacteristic
125C2×C4×C13C2×Q1611yescharacteristic
126C2×C4×C13#13511yescharacteristic
127C2×C4×C13#13511yescharacteristic
128C2×Dic13—22no—
129C2×Dic13—22no—
130C2×Dic13—22no—
131C2×Dic13—42no—
132C2×Dic13—42no—
133C2×Dic13—42no—
134C2×Dic13—42no—
135C2×Dic13#10314yes—
136Dic26—22no—
137Dic26—22no—
138Dic26—22no—
139Dic26—22no—
140C8×C13—42no—
141C8×C13—81no—
142#1055—42no—
143#1055—81no—
144C2×C4⋊Q8C2×D1311yescharacteristic
145C2×C4×Q8—131no—
146C8×Q8—262no—
147C8×Q8—262no—
148#431—131no—
149#431—262no—
150#431C2×D1311yescharacteristic
151#423—131no—
152#423C2×D1311yescharacteristic
153C2×#101—261no—
154#400—134no—
155#391—262no—
156#391—261no—
157#382—261no—
158C4×C4⋊C4—131no—
159#343—261no—
160#332—22no—
161#332—262no—
162C22×C13—21no—
163C22×C13—21no—
164C22×C13#38611yescharacteristic
165C22×C13C2×#10311yescharacteristic
166C22×C13#41611yescharacteristic
167C4×C13—21no—
168C4×C13—21no—
169C4×C13—21no—
170C4×C13—82no—
171C4×C13#45412yes—
172C4×C13#46511yescharacteristic
173C4×C13#46511yescharacteristic
174C4×C13#46711yescharacteristic
175C4×C13#46711yescharacteristic
176Dic13—24no—
177Dic13—42no—
178Dic13—82no—
179C22×Q8—21no—
180C22×Q8—131no—
181C2×M16—21no—
182C2×M16—261no—
183C4⋊Q8—21no—
184C4⋊Q8—21no—
185C4⋊Q8—21no—
186C4⋊Q8—21no—
187C4×Q8—261no—
188C4×Q8—261no—
189C4×Q8—261no—
190C4×Q8—261no—
191C2×C4⋊C4—21no—
192C2×C4⋊C4—132no—
193C2×C4⋊C4—131no—
194C2×C4⋊C4—261no—
195C2×C4⋊C4C4×D1312yes—
196C2×C42—132no—
197C2×C42—261no—
198C2×C42C22×D1311yescharacteristic
199C4⋊C8—21no—
200C4⋊C8—21no—
201C4⋊C8—132no—
202C4⋊C8—264no—
203C4⋊C8—261no—
204C4⋊C8—261no—
205C4⋊C8C22⋊D1312yes—
206#101—522no—
207C22⋊C8—21no—
208C22⋊C8—261no—
209C4×C8—21no—
210C4×C8—264no—
211C4×C8—261no—
212#95—132no—
213#95—264no—
214#95—264no—
215C2×C13—21no—
216C2×C13—21no—
217C2×C13#188811yescharacteristic
218C2×C13#189211yescharacteristic
219C2×C13#191511yescharacteristic
220C2×Q8—44no—
221C2×Q8—41no—
222C2×Q8—41no—
223C2×Q8—132no—
224C2×Q8—132no—
225C2×Q8—261no—
226C2×Q8—261no—
227C2×Q8—261no—
228C2×Q8—261no—
229C22×C4—22no—
230C22×C4—132no—
231C22×C4—132no—
232C22×C4—262no—
233C22×C4C2×C4×D1311yescharacteristic
234C22×C4D4×D1311yescharacteristic
235C22×C4D4×D1311yescharacteristic
236M16—41no—
237M16—41no—
238M16—521no—
239M16—521no—
240C2×C8—22no—
241C2×C8—41no—
242C2×C8—262no—
243C2×C8—521no—
244C4⋊C4—22no—
245C4⋊C4—22no—
246C4⋊C4—41no—
247C4⋊C4—41no—
248C4⋊C4—262no—
249C4⋊C4—261no—
250C4⋊C4—262no—
251C4⋊C4—261no—
252C4⋊C4—522no—
253C42—262no—
254C42—262no—
255C42—521no—
256C42—521no—
257C42#612711yescharacteristic
258C42D4×D1311yescharacteristic
259C42#612911yescharacteristic
260C42C2×C22⋊D1311yescharacteristic
261C13#939611yescharacteristic, complemented, Sylow
262C23C22⋊C4×D1311yescharacteristic
263Q8—82no—
264Q8—82no—
265Q8—262no—
266Q8—262no—
267Q8—262no—
268Q8—262no—
269C2×C4—22no—
270C2×C4—41no—
271C2×C4—44no—
272C2×C4—42no—
273C2×C4—134no—
274C2×C4—262no—
275C2×C4—262no—
276C2×C4—262no—
277C2×C4—522no—
278C2×C4—522no—
279C2×C4—522no—
280C2×C4—522no—
281C2×C4#8813511yescharacteristic
282C2×C4#8813711yescharacteristic
283C2×C4#8813811yescharacteristic
284C2×C4SD16×D1311yescharacteristic
285C2×C4#8817011yescharacteristic
286C2×C4Q16×D1311yescharacteristic
287C2×C4#8817311yescharacteristic
288C2×C4C4×C22⋊D1311yescharacteristic
289C2×C4#8819111yescharacteristic
290C2×C4#8819211yescharacteristic
291C8—42no—
292C8—81no—
293C8—522no—
294C8—1041no—
295C22—21no—
296C22—21no—
297C22D13×#10311yescharacteristic
298C22#1171846511yescharacteristic
299C22#1171861711yescharacteristic
300C4—21no—
301C4—21no—
302C4—21no—
303C4—82no—
304C4—264no—
305C4—522no—
306C4—1042no—
307C4#1171846811yescharacteristic
308C4#1171847411yescharacteristic
309C4#1171883211yescharacteristic
310C4#1171884911yescharacteristic
311C4#1171886212yes—
312C2—21no—
313C2—21no—
314C2#1311523611yescharacteristic
315C2#1311525611yescharacteristic
316C2#1311538511yescharacteristic
subgroupG/H
centerC22#11718617
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#1549C2
socleC22×C13#386
prime radicalC23×C13C2×C22⋊C4
cosocleC2×C42×C13C23
hypercenter#1549D13
hypocenterC13#9396
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1549

Complements

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

NH ≅ G/Ntype
261. C13#9396semidirect

Maximal subgroups

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

subgroupindex
#131239162
#131200522
#131148292
#131135212
#131127382
#131127372
C13×#15492
#939613