Finite Group Databasebeta

← #15783340

Subgroups — #15783340

Order 3328.

304 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 304 conjugacy classes of subgroups — too many to draw. Only its 75 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#13116531C211yesmaximal, characteristic
2#13116525C211yesmaximal, characteristic
3#13113009C212yesmaximal, complemented
4#13113005C212yesmaximal, complemented
5C13×#3223C211yesmaximal, characteristic
6C13×#541C411yescharacteristic
7C13×#536C2211yescharacteristic
8C13×#497C411yescharacteristic
9C13×#494C2211yescharacteristic
10C13×#491C2211yescharacteristic
11C13×#488C411yescharacteristic
12C13×#464—21no—
13C13×#462—21no—
14C13×#452—21no—
15C13×#451—21no—
16C13×#433C411yescharacteristic
17#11718898—21no—
18C2×#88076—21no—
19#11718140—21no—
20#11718140C2212yes—
21#11718140C2212yes—
22#11718134—21no—
23C2×C13×#41D411yescharacteristic
24C22×Q8×C13D411yescharacteristic
25C2×C13×Q16—21no—
26C2×C13×Q16—21no—
27C2×C13×Q16—21no—
28C2×C13×SD16—21no—
29C13×C4⋊Q8C2×C411yescharacteristic
30C13×C4⋊Q8D411yescharacteristic
31C13×C4⋊Q8C2311yescharacteristic
32C13×#126—41no—
33C13×#125—41no—
34C13×#125C2×C411yescharacteristic
35C13×#124C2×C411yescharacteristic
36C13×#124D411yescharacteristic
37C13×#123—41no—
38C13×C22⋊Q8—21no—
39C13×C22⋊Q8—41no—
40C4×Q8×C13—21no—
41C13×#117C2×C411yescharacteristic
42C2×#6099—41no—
43C2×#6099—41no—
44C13×C4⋊C8—21no—
45C13×#103—21no—
46C13×#103—21no—
47C13×#103—21no—
48C13×#102—21no—
49C13×C22⋊C8—21no—
50C13×#97C2×C411yescharacteristic
51C4×C8×C13C2×C411yescharacteristic
52#88076—22no—
53#88076—22no—
54#88076—41no—
55#88073—41no—
56#13612—131nomaximal, Sylow
57C13×#41—81no—
58C2×Q8×C13—21no—
59C2×Q8×C13—21no—
60C2×Q8×C13—81no—
61C2×Q8×C13C22⋊C411yescharacteristic
62C2×Q8×C13C2×D411yescharacteristic
63C2×Q8×C13C2×D411yescharacteristic
64C2×D4×C13—21no—
65C2×D4×C13C22⋊C411yescharacteristic
66C22×C4×C13—21no—
67C22×C4×C13—21no—
68C22×C4×C13C22⋊C411yescharacteristic
69C13×Q16—81no—
70C13×Q16—81no—
71C13×Q16—81no—
72C13×SD16—81no—
73C2×C8×C13—21no—
74C2×C8×C13—21no—
75C13×C4⋊C4—21no—
76C13×C4⋊C4—21no—
77C13×C4⋊C4—41no—
78C13×C4⋊C4—41no—
79C13×C4⋊C4—41no—
80C13×C4⋊C4—41no—
81C13×C4⋊C4—41no—
82C13×C4⋊C4—41no—
83C13×C22⋊C4—21no—
84C13×C22⋊C4—41no—
85C13×C22⋊C4—41no—
86C13×C22⋊C4—41no—
87C42×C13—41no—
88C42×C13C22⋊C411yescharacteristic
89C42×C13C22×C411yescharacteristic
90#6099—42no—
91#6099—42no—
92#6099—81no—
93#6099—81no—
94C2×#1055—81no—
95C2×#1055—81no—
96#3223D1311yescharacteristic
97#2135—131no—
98#2133—131no—
99#1413—132no—
100#1411—132no—
101C23×C13—21no—
102C23×C13#9911yescharacteristic
103Q8×C13—41no—
104Q8×C13—41no—
105Q8×C13—41no—
106Q8×C13—41no—
107Q8×C13—41no—
108Q8×C13—81no—
109D4×C13—41no—
110D4×C13—81no—
111C2×C4×C13—21no—
112C2×C4×C13—21no—
113C2×C4×C13—21no—
114C2×C4×C13—21no—
115C2×C4×C13—21no—
116C2×C4×C13—41no—
117C2×C4×C13—41no—
118C2×C4×C13—41no—
119C2×C4×C13—41no—
120C2×C4×C13—41no—
121C2×C4×C13—41no—
122C2×C4×C13—41no—
123C2×C4×C13#9911yescharacteristic
124C2×C4×C13C2×C22⋊C411yescharacteristic
125C8×C13—41no—
126C8×C13—41no—
127#1055—82no—
128#1055—82no—
129#541Dic1311yescharacteristic
130#536C2×D1311yescharacteristic
131#497Dic1311yescharacteristic
132#494C2×D1311yescharacteristic
133#491C2×D1311yescharacteristic
134#488Dic1311yescharacteristic
135#464—21no—
136#462—21no—
137#452—21no—
138#451—21no—
139#433Dic1311yescharacteristic
140#413—261no—
141C2×#101—261no—
142#356—132no—
143#356—132no—
144#356—261no—
145#355—261no—
146C22×C13—21no—
147C22×C13—41no—
148C22×C13—41no—
149C22×C13—81no—
150C22×C13C2×#9911yescharacteristic
151C4×C13—21no—
152C4×C13—21no—
153C4×C13—41no—
154C4×C13—41no—
155C4×C13—41no—
156C4×C13—41no—
157C4×C13—41no—
158C4×C13—81no—
159C4×C13—81no—
160C2×#41C22⋊D1311yescharacteristic
161C22×Q8C22⋊D1311yescharacteristic
162C2×Q16—21no—
163C2×Q16—21no—
164C2×Q16—21no—
165C2×SD16—21no—
166C2×M16—521no—
167C2×M16—521no—
168C4⋊Q8C2×Dic1311yescharacteristic
169C4⋊Q8C22⋊D1311yescharacteristic
170C4⋊Q8C22×D1311yescharacteristic
171#126—41no—
172#125—41no—
173#125C2×Dic1311yescharacteristic
174#124C2×Dic1311yescharacteristic
175#124C22⋊D1311yescharacteristic
176#123—41no—
177C22⋊Q8—21no—
178C22⋊Q8—41no—
179C4×Q8—21no—
180#117C2×Dic1311yescharacteristic
181C4⋊C8—21no—
182#103—21no—
183#103—21no—
184#103—21no—
185#102—21no—
186#101—262no—
187#101—262no—
188#101—521no—
189#100—521no—
190C22⋊C8—21no—
191#97C2×Dic1311yescharacteristic
192C4×C8C2×Dic1311yescharacteristic
193C2×C13—21no—
194C2×C13—41no—
195C2×C13—81no—
196C2×C13#212711yescharacteristic
197#41—81no—
198C2×Q8—21no—
199C2×Q8—21no—
200C2×Q8—81no—
201C2×Q8C22⋊Dic1311yescharacteristic
202C2×Q8C2×C22⋊D1311yescharacteristic
203C2×Q8C2×C22⋊D1311yescharacteristic
204C2×D4—21no—
205C2×D4C22⋊Dic1311yescharacteristic
206C22×C4—21no—
207C22×C4—21no—
208C22×C4C22⋊Dic1311yescharacteristic
209Q16—81no—
210Q16—81no—
211Q16—81no—
212SD16—81no—
213M16—522no—
214M16—522no—
215M16—1041no—
216M16—1041no—
217C2×C8—21no—
218C2×C8—21no—
219C2×C8—1041no—
220C2×C8—1041no—
221C4⋊C4—21no—
222C4⋊C4—21no—
223C4⋊C4—41no—
224C4⋊C4—41no—
225C4⋊C4—41no—
226C4⋊C4—41no—
227C4⋊C4—41no—
228C4⋊C4—41no—
229C22⋊C4—21no—
230C22⋊C4—41no—
231C22⋊C4—41no—
232C22⋊C4—41no—
233C42—41no—
234C42C22⋊Dic1311yescharacteristic
235C42C22×Dic1311yescharacteristic
236C13#1361211yescharacteristic, complemented, Sylow
237C23—21no—
238C23#8807411yescharacteristic
239Q8—41no—
240Q8—41no—
241Q8—41no—
242Q8—41no—
243Q8—41no—
244Q8—81no—
245D4—41no—
246D4—81no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—41no—
253C2×C4—41no—
254C2×C4—41no—
255C2×C4—41no—
256C2×C4—41no—
257C2×C4—41no—
258C2×C4—41no—
259C2×C4#8807411yescharacteristic
260C2×C4C2×C22⋊Dic1311yescharacteristic
261C8—41no—
262C8—41no—
263C8—1042no—
264C8—1042no—
265C22—21no—
266C22—41no—
267C22—41no—
268C22—81no—
269C22C2×#8807411yescharacteristic
270C4—21no—
271C4—21no—
272C4—41no—
273C4—41no—
274C4—41no—
275C4—41no—
276C4—41no—
277C4—81no—
278C4—81no—
279C2—21no—
280C2—41no—
281C2—81no—
282C2#1311650511yescharacteristic
subgroupG/H
centerC2#13116505
commutatorC42×C13C22×C4
FrattiniC4⋊Q8C22×D13
FittingC13×#3223C2
socleC2×C13#2127
prime radicalC2×C13×#41D4
cosocleC13×C4⋊Q8C23
hypercenter#3223D13
hypocenterC13#13612
LCSG ▷ C42×C13 ▷ C2×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C22 ◁ C22×C4 ◁ #536 ◁ #3223

Complements

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

NH ≅ G/Ntype
3. #13113009C2semidirect
4. #13113005C2semidirect
236. C13#13612semidirect

Maximal subgroups

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

subgroupindex
#131165312
#131165252
#131130092
#131130052
C13×#32232
#1361213