Finite Group Databasebeta

← #15773225

Subgroups — #15773225

Order 3328.

452 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 452 conjugacy classes of subgroups — too many to draw. Only its 115 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#13114575C211yesmaximal, characteristic
2#13113150C211yesmaximal, characteristic
3#13112866C212yesmaximal, complemented
4#13112863C212yesmaximal, complemented
5C13×#2396C211yesmaximal, characteristic
6C2×C4×Q8×C13C411yescharacteristic
7C2×C13×#117C2211yescharacteristic
8C22×#6099—21no—
9C13×#400C2211yescharacteristic
10C13×#399C411yescharacteristic
11C13×#398—21no—
12C13×#396—21no—
13C13×#395C2211yescharacteristic
14C13×#393C411yescharacteristic
15C4×C13×C4⋊C4—21no—
16C4×C13×C4⋊C4C411yescharacteristic
17C4×C13×C22⋊C4—21no—
18#11718586—21no—
19#11718122—21no—
20#11718122C2212yes—
21#11718120C2212yes—
22#11718117—21no—
23C22×Q8×C13C2×C411yescharacteristic
24C23×C4×C13D411yescharacteristic
25C4×Q8×C13—41no—
26C4×Q8×C13—41no—
27C13×#117—41no—
28C13×#117—41no—
29C2×C13×C4⋊C4—21no—
30C2×C13×C4⋊C4—21no—
31C2×C13×C4⋊C4—21no—
32C2×C13×C4⋊C4—21no—
33C2×C13×C4⋊C4C2×C411yescharacteristic
34C2×C13×C4⋊C4D411yescharacteristic
35C2×C13×C4⋊C4C2311yescharacteristic
36C2×C13×C22⋊C4—21no—
37C2×C13×C22⋊C4—21no—
38C2×C13×C22⋊C4C2×C411yescharacteristic
39C2×C13×C22⋊C4D411yescharacteristic
40C2×C42×C13—21no—
41C2×C42×C13—21no—
42C2×C42×C13C2×C411yescharacteristic
43C2×C42×C13D411yescharacteristic
44C2×#6099—24no—
45C2×#6099—22no—
46C2×#6099—41no—
47C2×#6099—42no—
48C22×#1055—41no—
49C13×#95—21no—
50C13×#95—21no—
51C13×#95—21no—
52C13×#95—21no—
53C13×#95C2×C411yescharacteristic
54C13×#95C2×C411yescharacteristic
55C22⋊#1055—22no—
56C4⋊#1055—41no—
57C4×#1055—41no—
58#11721—131nomaximal, Sylow
59C24×C13C22⋊C411yescharacteristic
60C2×Q8×C13—42no—
61C2×Q8×C13—41no—
62C22×C4×C13—21no—
63C22×C4×C13—21no—
64C22×C4×C13—22no—
65C22×C4×C13—21no—
66C22×C4×C13—21no—
67C22×C4×C13—21no—
68C22×C4×C13—21no—
69C22×C4×C13C22⋊C411yescharacteristic
70C22×C4×C13C22⋊C411yescharacteristic
71C22×C4×C13C22⋊C411yescharacteristic
72C22×C4×C13SD1612yes—
73C22×C4×C13Q1612yes—
74C22×C4×C13C22×C411yescharacteristic
75C22×C4×C13C2×D411yescharacteristic
76C22×C4×C13C2×D411yescharacteristic
77C13×C4⋊C4—41no—
78C13×C4⋊C4—41no—
79C13×C4⋊C4—41no—
80C13×C4⋊C4—42no—
81C13×C4⋊C4—42no—
82C13×C4⋊C4—42no—
83C13×C4⋊C4—42no—
84C13×C22⋊C4—41no—
85C13×C22⋊C4—41no—
86C13×C22⋊C4—42no—
87C13×C22⋊C4—42no—
88C42×C13—21no—
89C42×C13—21no—
90C42×C13—21no—
91C42×C13—21no—
92C42×C13—41no—
93C42×C13—41no—
94C42×C13—42no—
95#6099—24no—
96#6099—44no—
97#6099—42no—
98C2×#1055—42no—
99C2×#1055—44no—
100C2×#1055—42no—
101#2396D1311yescharacteristic
102#1742—131no—
103#1458—131no—
104#1354—132no—
105#1353—132no—
106C23×C13—21no—
107C23×C13—21no—
108C23×C13—41no—
109C23×C13—41no—
110C23×C13#10312yes—
111C23×C13C2×C22⋊C411yescharacteristic
112Q8×C13—42no—
113Q8×C13—42no—
114C2×C4×C13—21no—
115C2×C4×C13—21no—
116C2×C4×C13—22no—
117C2×C4×C13—22no—
118C2×C4×C13—22no—
119C2×C4×C13—22no—
120C2×C4×C13—22no—
121C2×C4×C13—22no—
122C2×C4×C13—21no—
123C2×C4×C13—21no—
124C2×C4×C13—21no—
125C2×C4×C13—21no—
126C2×C4×C13—41no—
127C2×C4×C13—41no—
128C2×C4×C13—41no—
129C2×C4×C13—41no—
130C2×C4×C13—41no—
131C2×C4×C13—41no—
132C2×C4×C13—41no—
133C2×C4×C13—41no—
134C2×C4×C13—41no—
135C2×C4×C13—41no—
136C2×C4×C13—41no—
137C2×C4×C13—41no—
138C2×C4×C13—41no—
139C2×C4×C13—41no—
140C2×C4×C13#9911yescharacteristic
141C2×C4×C13#9911yescharacteristic
142C2×C4×C13#10312yes—
143C2×C4×C13#10412yes—
144C2×C4×C13C2×SD1611yescharacteristic
145C2×C4×C13C2×Q1611yescharacteristic
146#1055—44no—
147#1055—82no—
148C22×M16—261no—
149C2×C4×Q8Dic1311yescharacteristic
150C2×#117C2×D1311yescharacteristic
151#431—261no—
152#400C2×D1311yescharacteristic
153#399Dic1311yescharacteristic
154#398—21no—
155#396—21no—
156#395C2×D1311yescharacteristic
157#393Dic1311yescharacteristic
158C4×C4⋊C4—21no—
159C4×C4⋊C4Dic1311yescharacteristic
160C4×C22⋊C4—21no—
161#343—132no—
162#343—261no—
163#324—132no—
164#323—261no—
165C22×C13—21no—
166C22×C13—21no—
167C22×C13—22no—
168C22×C13—42no—
169C22×C13—41no—
170C22×C13—41no—
171C22×C13—81no—
172C22×C13C2×#9911yescharacteristic
173C22×C13C2×#10311yescharacteristic
174C22×C13C2×#10411yescharacteristic
175C4×C13—21no—
176C4×C13—21no—
177C4×C13—42no—
178C4×C13—41no—
179C4×C13—42no—
180C4×C13—41no—
181C4×C13—41no—
182C4×C13—41no—
183C4×C13—81no—
184C4×C13—81no—
185C4×C13#32812yes—
186C4×C13#32812yes—
187C22×Q8C2×Dic1311yescharacteristic
188C23×C4C22⋊D1311yescharacteristic
189C2×M16—264no—
190C2×M16—262no—
191C2×M16—521no—
192C2×M16—522no—
193C22×C8—521no—
194C4×Q8—41no—
195C4×Q8—41no—
196#117—41no—
197#117—41no—
198C2×C4⋊C4—21no—
199C2×C4⋊C4—21no—
200C2×C4⋊C4—21no—
201C2×C4⋊C4—21no—
202C2×C4⋊C4C2×Dic1311yescharacteristic
203C2×C4⋊C4C22⋊D1311yescharacteristic
204C2×C4⋊C4C22×D1311yescharacteristic
205C2×C22⋊C4—21no—
206C2×C22⋊C4—21no—
207C2×C22⋊C4C2×Dic1311yescharacteristic
208C2×C22⋊C4C22⋊D1311yescharacteristic
209C2×C42—21no—
210C2×C42—21no—
211C2×C42C2×Dic1311yescharacteristic
212C2×C42C22⋊D1311yescharacteristic
213C4⋊C8—521no—
214C22⋊C8—262no—
215C4×C8—521no—
216#95—21no—
217#95—21no—
218#95—21no—
219#95—21no—
220#95C2×Dic1311yescharacteristic
221#95C2×Dic1311yescharacteristic
222C2×C13—21no—
223C2×C13—21no—
224C2×C13—42no—
225C2×C13C2×#32811yescharacteristic
226C2×C13#212011yescharacteristic
227C2×C13#213211yescharacteristic
228C24C22⋊Dic1311yescharacteristic
229C2×Q8—42no—
230C2×Q8—41no—
231C22×C4—21no—
232C22×C4—21no—
233C22×C4—22no—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—21no—
238C22×C4#610612yes—
239C22×C4#610712yes—
240C22×C4C22⋊Dic1311yescharacteristic
241C22×C4C22⋊Dic1311yescharacteristic
242C22×C4C22⋊Dic1311yescharacteristic
243C22×C4C22×Dic1311yescharacteristic
244C22×C4C2×C22⋊D1311yescharacteristic
245C22×C4C2×C22⋊D1311yescharacteristic
246M16—264no—
247M16—524no—
248M16—522no—
249C2×C8—522no—
250C2×C8—524no—
251C2×C8—522no—
252C4⋊C4—41no—
253C4⋊C4—41no—
254C4⋊C4—41no—
255C4⋊C4—42no—
256C4⋊C4—42no—
257C4⋊C4—42no—
258C4⋊C4—42no—
259C22⋊C4—41no—
260C22⋊C4—41no—
261C22⋊C4—42no—
262C22⋊C4—42no—
263C42—21no—
264C42—21no—
265C42—21no—
266C42—21no—
267C42—41no—
268C42—41no—
269C42—42no—
270C13#1172111yescharacteristic, complemented, Sylow
271C23—21no—
272C23—21no—
273C23—41no—
274C23—41no—
275C23#8807512yes—
276C23C2×C22⋊Dic1311yescharacteristic
277Q8—42no—
278Q8—42no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—22no—
282C2×C4—22no—
283C2×C4—22no—
284C2×C4—22no—
285C2×C4—22no—
286C2×C4—22no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4#8807411yescharacteristic
306C2×C4#8807411yescharacteristic
307C2×C4#8807512yes—
308C2×C4#8807712yes—
309C2×C4C2×#610611yescharacteristic
310C2×C4C2×#610711yescharacteristic
311C8—524no—
312C8—1042no—
313C22—21no—
314C22—21no—
315C22—22no—
316C22—42no—
317C22—41no—
318C22—41no—
319C22—81no—
320C22C2×#8807411yescharacteristic
321C22C2×#8807511yescharacteristic
322C22C2×#8807711yescharacteristic
323C4—21no—
324C4—21no—
325C4—42no—
326C4—41no—
327C4—42no—
328C4—41no—
329C4—41no—
330C4—41no—
331C4—81no—
332C4—81no—
333C4#1171813012yes—
334C4#1171813012yes—
335C2—21no—
336C2—21no—
337C2—42no—
338C2C2×#1171813011yescharacteristic
339C2#1311647711yescharacteristic
340C2#1311652111yescharacteristic
subgroupG/H
centerC2×C4#88074
commutatorC22×C4×C13C22×C4
FrattiniC2×C4⋊C4C22×D13
FittingC13×#2396C2
socleC22×C13C2×#99
prime radicalC24×C13C22⋊C4
cosocleC2×C13×C4⋊C4C23
hypercenter#2396D13
hypocenterC13#11721
LCSG ▷ C22×C4×C13 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#117 ◁ #2396

Complements

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

NH ≅ G/Ntype
3. #13112866C2semidirect
4. #13112863C2semidirect
270. C13#11721semidirect

Maximal subgroups

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

subgroupindex
#131145752
#131131502
#131128662
#131128632
C13×#23962
#1172113