Finite Group Databasebeta

← #15761003

Subgroups — #15761003

Order 3328.

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

normal subgroups only

This group has 396 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#13123931C211yesmaximal, characteristic
2#13113566C211yesmaximal, characteristic
3#13113265C211yesmaximal, characteristic
4#13113180C211yesmaximal, characteristic
5#13112746C211yesmaximal, characteristic
6#13112699C211yesmaximal, characteristic
7C13×#3113C211yesmaximal, characteristic
8C13×#533C2211yescharacteristic
9C2×C4×Q8×C13C2211yescharacteristic
10C13×#483C412yes—
11C13×#475—21no—
12C13×#462—21no—
13C13×#451C412yes—
14C13×#441—22no—
15C13×#432C2211yescharacteristic
16#11718685—21no—
17#11718685—22no—
18Q8×#1055—21no—
19#11718661—22no—
20#11718587C2211yescharacteristic
21#11718587C2211yescharacteristic
22#11718586C2211yescharacteristic
23#11718585C2211yescharacteristic
24#11718139—21no—
25#11718138—21no—
26Q8⋊#1055—21no—
27Q8⋊#1055—21no—
28#11718120—22no—
29C22×Q8×C13C2×C411yescharacteristic
30C2×C13×Q16—22no—
31C13×C4⋊Q8D411yescharacteristic
32C13×C4⋊Q8D411yescharacteristic
33C13×#125—21no—
34C13×C22⋊Q8—21no—
35C13×C22⋊Q8C2×C412yes—
36C4×Q8×C13—21no—
37C4×Q8×C13—21no—
38C4×Q8×C13—21no—
39C4×Q8×C13—21no—
40C4×Q8×C13—21no—
41C4×Q8×C13D412yes—
42C13×#117—21no—
43C2×C13×C4⋊C4—21no—
44C2×C13×C4⋊C4C2×C411yescharacteristic
45C2×C42×C13—21no—
46C2×C42×C13C2311yescharacteristic
47C2×#6099—21no—
48C13×#106—22no—
49C13×C4⋊C8—21no—
50C13×#103—22no—
51C13×#103—22no—
52C13×C22⋊C8C2×C412yes—
53C13×#97—21no—
54C22⋊#1055—21no—
55C22⋊#1055—21no—
56C22⋊#1055D412yes—
57C4⋊#1055—22no—
58C4⋊#1055—22no—
59C4⋊#1055—21no—
60C4⋊#1055—21no—
61C4⋊#1055—21no—
62C4⋊#1055—21no—
63C4⋊#1055—21no—
64#88043—22no—
65#88043—21no—
66#88043—21no—
67C4×#1055—22no—
68C4×#1055D411yescharacteristic
69C4×#1055D411yescharacteristic
70#9528—131nomaximal, Sylow
71C2×Q8×C13—21no—
72C2×Q8×C13—21no—
73C2×Q8×C13—21no—
74C2×Q8×C13—42no—
75C2×Q8×C13C22⋊C412yes—
76C22×C4×C13—21no—
77C22×C4×C13—21no—
78C22×C4×C13C22×C411yescharacteristic
79C22×C4×C13C2×D411yescharacteristic
80C22×C4×C13#4111yescharacteristic
81C13×Q16—44no—
82C2×C8×C13—22no—
83C13×C4⋊C4—22no—
84C13×C4⋊C4—21no—
85C13×C4⋊C4—21no—
86C13×C4⋊C4—21no—
87C13×C4⋊C4—22no—
88C13×C4⋊C4—21no—
89C13×C4⋊C4—21no—
90C13×C4⋊C4—41no—
91C13×C4⋊C4—41no—
92C13×C4⋊C4C22⋊C412yes—
93C13×C22⋊C4—22no—
94C42×C13—22no—
95C42×C13—41no—
96C42×C13—41no—
97C42×C13C2×D411yescharacteristic
98C42×C13C2×D411yescharacteristic
99C42×C13C2×D411yescharacteristic
100C42×C13#4111yescharacteristic
101#6099—81no—
102C2×#1055—21no—
103C2×#1055—21no—
104C2×#1055—22no—
105C2×#1055—41no—
106C2×#1055—41no—
107#3113D1311yescharacteristic
108#2985—131no—
109#1559—131no—
110#1487—131no—
111#1467—131no—
112#1307—131no—
113#1287—131no—
114C23×C13C4×D411yescharacteristic
115Q8×C13—22no—
116Q8×C13—22no—
117Q8×C13—41no—
118Q8×C13—41no—
119Q8×C13—42no—
120Q8×C13—41no—
121Q8×C13—41no—
122C2×C4×C13—21no—
123C2×C4×C13—21no—
124C2×C4×C13—22no—
125C2×C4×C13—22no—
126C2×C4×C13—22no—
127C2×C4×C13—41no—
128C2×C4×C13—41no—
129C2×C4×C13—41no—
130C2×C4×C13—41no—
131C2×C4×C13—41no—
132C2×C4×C13—81no—
133C2×C4×C13C2×C22⋊C411yescharacteristic
134C2×C4×C13C4×D411yescharacteristic
135C2×C4×C13#12011yescharacteristic
136C2×C4×C13#12111yescharacteristic
137C2×C4×C13#12111yescharacteristic
138C2×C4×C13#12311yescharacteristic
139C8×C13—42no—
140#1055—41no—
141#1055—41no—
142#1055—42no—
143#1055—81no—
144#1055—81no—
145#533C2×D1311yescharacteristic
146C2×C4×Q8C2×D1311yescharacteristic
147#483Dic1312yes—
148#475—21no—
149#462—21no—
150#451Dic1312yes—
151#446—261no—
152#446—262no—
153C8×Q8—261no—
154#441—22no—
155#433—262no—
156#432—131no—
157#432—131no—
158#432C2×D1311yescharacteristic
159#431—131no—
160#423—131no—
161#333—261no—
162#332—261no—
163Q8⋊C8—261no—
164Q8⋊C8—261no—
165#324—262no—
166C22×C13—21no—
167C22×C13—21no—
168C22×C13—21no—
169C22×C13#38611yescharacteristic
170C4×C13—21no—
171C4×C13—21no—
172C4×C13—21no—
173C4×C13—21no—
174C4×C13—21no—
175C4×C13—42no—
176C4×C13—42no—
177C4×C13—42no—
178C4×C13—81no—
179C4×C13#47111yescharacteristic
180C4×C13#47311yescharacteristic
181C22×Q8C2×Dic1311yescharacteristic
182C2×Q16—22no—
183C2×M16—261no—
184C4⋊Q8C22⋊D1311yescharacteristic
185C4⋊Q8C22⋊D1311yescharacteristic
186#125—21no—
187C22⋊Q8—21no—
188C22⋊Q8C2×Dic1312yes—
189C4×Q8—21no—
190C4×Q8—21no—
191C4×Q8—21no—
192C4×Q8—21no—
193C4×Q8—21no—
194C4×Q8C22⋊D1312yes—
195#117—21no—
196C2×C4⋊C4—21no—
197C2×C4⋊C4C2×Dic1311yescharacteristic
198C2×C42—21no—
199C2×C42C22×D1311yescharacteristic
200#106—22no—
201C4⋊C8—21no—
202C4⋊C8—262no—
203C4⋊C8—262no—
204C4⋊C8—261no—
205C4⋊C8—261no—
206C4⋊C8—261no—
207C4⋊C8—261no—
208C4⋊C8—261no—
209#103—22no—
210#103—22no—
211C22⋊C8—132no—
212C22⋊C8—261no—
213C22⋊C8—261no—
214C22⋊C8C2×Dic1312yes—
215#97—21no—
216#97—262no—
217#97—261no—
218#97—261no—
219C4×C8—131no—
220C4×C8—131no—
221C4×C8—262no—
222C2×C13—41no—
223C2×C13#189111yescharacteristic
224C2×C13#190511yescharacteristic
225C2×C13#190811yescharacteristic
226C2×Q8—21no—
227C2×Q8—21no—
228C2×Q8—21no—
229C2×Q8—42no—
230C2×Q8C22⋊Dic1312yes—
231C22×C4—21no—
232C22×C4—21no—
233C22×C4D4×D1311yescharacteristic
234C22×C4#612911yescharacteristic
235C22×C4C22×Dic1311yescharacteristic
236Q16—44no—
237M16—1041no—
238C2×C8—22no—
239C2×C8—261no—
240C2×C8—261no—
241C2×C8—262no—
242C2×C8—521no—
243C2×C8—521no—
244C4⋊C4—22no—
245C4⋊C4—22no—
246C4⋊C4—21no—
247C4⋊C4—21no—
248C4⋊C4—21no—
249C4⋊C4—21no—
250C4⋊C4—21no—
251C4⋊C4—41no—
252C4⋊C4—41no—
253C4⋊C4C22⋊Dic1312yes—
254C22⋊C4—22no—
255C42—22no—
256C42—41no—
257C42—41no—
258C42D4×D1311yescharacteristic
259C42#612911yescharacteristic
260C42C2×C22⋊D1311yescharacteristic
261C42C2×C22⋊D1311yescharacteristic
262C13#952811yescharacteristic, complemented, Sylow
263C23D4×Dic1311yescharacteristic
264Q8—22no—
265Q8—22no—
266Q8—42no—
267Q8—41no—
268Q8—41no—
269Q8—41no—
270Q8—41no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—22no—
274C2×C4—22no—
275C2×C4—22no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—81no—
282C2×C4D4×Dic1311yescharacteristic
283C2×C4#8818911yescharacteristic
284C2×C4#8819111yescharacteristic
285C2×C4#8819311yescharacteristic
286C2×C4#8819311yescharacteristic
287C2×C4C2×C22⋊Dic1311yescharacteristic
288C8—42no—
289C8—521no—
290C8—521no—
291C8—522no—
292C8—1041no—
293C8—1041no—
294C22—21no—
295C22—21no—
296C22—21no—
297C22#1171888111yescharacteristic
298C4—21no—
299C4—21no—
300C4—21no—
301C4—21no—
302C4—21no—
303C4—42no—
304C4—42no—
305C4—42no—
306C4—81no—
307C4#1171886411yescharacteristic
308C4#1171886511yescharacteristic
309C2—41no—
310C2#1311525511yescharacteristic
311C2#1311533211yescharacteristic
312C2#1311535311yescharacteristic
subgroupG/H
centerC22#11718881
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#3113C2
socleC22×C13#386
prime radicalC23×C13C4×D4
cosocleC2×C42×C13C23
hypercenter#3113D13
hypocenterC13#9528
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3113

Complements

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

NH ≅ G/Ntype
262. C13#9528semidirect

Maximal subgroups

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

subgroupindex
#131239312
#131135662
#131132652
#131131802
#131127462
#131126992
C13×#31132
#952813