Finite Group Databasebeta

← #15773230

Subgroups — #15773230

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
1C2×#11718122C211yesmaximal, characteristic
2C2×#11718120C211yesmaximal, characteristic
3#13112866C212yesmaximal, complemented
4#13112863C212yesmaximal, complemented
5C13×#2627C211yesmaximal, characteristic
6C2×C13×C22⋊Q8C411yescharacteristic
7C22×C13×C4⋊C4C2211yescharacteristic
8C22×#6099—21no—
9C13×#400C411yescharacteristic
10C13×#400C2211yescharacteristic
11C13×#398—21no—
12C13×#398—21no—
13C13×#395C411yescharacteristic
14C13×#395C2211yescharacteristic
15C13×#385—21no—
16C13×#381—21no—
17C13×#380C411yescharacteristic
18C2×C22⋊#1055—21no—
19#11718122—21no—
20#11718122C2212yes—
21#11718120—21no—
22#11718120C2212yes—
23C22×Q8×C13C2×C411yescharacteristic
24C23×C4×C13C2×C411yescharacteristic
25C23×C4×C13D411yescharacteristic
26C23×C4×C13D411yescharacteristic
27C13×C22⋊Q8—41no—
28C13×C22⋊Q8—41no—
29C2×C13×C4⋊C4—21no—
30C2×C13×C4⋊C4—21no—
31C2×C13×C4⋊C4—21no—
32C2×C13×C4⋊C4—21no—
33C2×C13×C4⋊C4—41no—
34C2×C13×C4⋊C4—41no—
35C2×C13×C4⋊C4C2×C411yescharacteristic
36C2×C13×C4⋊C4C2×C411yescharacteristic
37C2×C13×C4⋊C4D411yescharacteristic
38C2×C13×C4⋊C4D411yescharacteristic
39C2×C13×C4⋊C4C2311yescharacteristic
40C2×C13×C22⋊C4—21no—
41C2×C13×C22⋊C4—21no—
42C2×#6099—24no—
43C2×#6099—22no—
44C2×#6099—41no—
45C2×#6099—42no—
46C22×#1055—41no—
47C22×#1055—41no—
48C13×#95—21no—
49C13×#95—21no—
50C13×#95—21no—
51C13×#95—21no—
52C13×#95—21no—
53C13×#95—21no—
54C13×#95C2×C411yescharacteristic
55C13×#95C2×C411yescharacteristic
56C22⋊#1055—22no—
57C22⋊#1055—41no—
58#11722—131nomaximal, Sylow
59C24×C13C22⋊C411yescharacteristic
60C2×Q8×C13—41no—
61C2×Q8×C13—81no—
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×C13—21no—
70C22×C4×C13—21no—
71C22×C4×C13—21no—
72C22×C4×C13—21no—
73C22×C4×C13—81no—
74C22×C4×C13—81no—
75C22×C4×C13C22⋊C411yescharacteristic
76C22×C4×C13C22⋊C411yescharacteristic
77C22×C4×C13C22⋊C411yescharacteristic
78C22×C4×C13SD1612yes—
79C22×C4×C13Q1612yes—
80C22×C4×C13C22×C411yescharacteristic
81C22×C4×C13C2×D411yescharacteristic
82C22×C4×C13C2×D411yescharacteristic
83C13×C4⋊C4—41no—
84C13×C4⋊C4—41no—
85C13×C4⋊C4—41no—
86C13×C4⋊C4—41no—
87C13×C4⋊C4—41no—
88C13×C4⋊C4—42no—
89C13×C4⋊C4—81no—
90C13×C4⋊C4—81no—
91C13×C4⋊C4—81no—
92C13×C22⋊C4—41no—
93C13×C22⋊C4—41no—
94C13×C22⋊C4—42no—
95#6099—24no—
96#6099—44no—
97#6099—42no—
98C2×#1055—44no—
99C2×#1055—42no—
100C2×#1055—42no—
101C2×#1055—82no—
102#2627D1311yescharacteristic
103C2×#343—131no—
104C2×#324—131no—
105#1354—132no—
106#1353—132no—
107C23×C13—41no—
108C23×C13—41no—
109C23×C13#9911yescharacteristic
110C23×C13#9911yescharacteristic
111C23×C13#10312yes—
112C23×C13#10412yes—
113C23×C13C2×C22⋊C411yescharacteristic
114Q8×C13—82no—
115C2×C4×C13—22no—
116C2×C4×C13—22no—
117C2×C4×C13—22no—
118C2×C4×C13—22no—
119C2×C4×C13—21no—
120C2×C4×C13—21no—
121C2×C4×C13—21no—
122C2×C4×C13—21no—
123C2×C4×C13—21no—
124C2×C4×C13—21no—
125C2×C4×C13—21no—
126C2×C4×C13—21no—
127C2×C4×C13—42no—
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—42no—
139C2×C4×C13—41no—
140C2×C4×C13—41no—
141C2×C4×C13—41no—
142C2×C4×C13—41no—
143C2×C4×C13—81no—
144C2×C4×C13—81no—
145C2×C4×C13—81no—
146C2×C4×C13#10312yes—
147C2×C4×C13C2×SD1611yescharacteristic
148C2×C4×C13C2×Q1611yescharacteristic
149#1055—44no—
150#1055—82no—
151C22×M16—261no—
152C2×C22⋊Q8Dic1311yescharacteristic
153C22×C4⋊C4C2×D1311yescharacteristic
154C2×C22⋊C8—261no—
155#400Dic1311yescharacteristic
156#400C2×D1311yescharacteristic
157#398—21no—
158#398—21no—
159#395Dic1311yescharacteristic
160#395C2×D1311yescharacteristic
161#385—21no—
162#381—21no—
163#380Dic1311yescharacteristic
164#343—132no—
165#343—261no—
166#324—132no—
167#324—261no—
168C22×C13—21no—
169C22×C13—21no—
170C22×C13—21no—
171C22×C13—21no—
172C22×C13—21no—
173C22×C13—21no—
174C22×C13—42no—
175C22×C13—42no—
176C22×C13#32812yes—
177C22×C13#32812yes—
178C22×C13C2×#9911yescharacteristic
179C22×C13C2×#10311yescharacteristic
180C22×C13C2×#10411yescharacteristic
181C4×C13—21no—
182C4×C13—22no—
183C4×C13—21no—
184C4×C13—41no—
185C4×C13—41no—
186C4×C13—41no—
187C4×C13—41no—
188C4×C13—81no—
189C4×C13—81no—
190C4×C13—81no—
191C4×C13—81no—
192C22×Q8C2×Dic1311yescharacteristic
193C23×C4C2×Dic1311yescharacteristic
194C23×C4C22⋊D1311yescharacteristic
195C23×C4C22⋊D1311yescharacteristic
196C2×M16—264no—
197C2×M16—262no—
198C2×M16—521no—
199C2×M16—522no—
200C22×C8—521no—
201C22×C8—521no—
202C22⋊Q8—41no—
203C22⋊Q8—41no—
204C2×C4⋊C4—21no—
205C2×C4⋊C4—21no—
206C2×C4⋊C4—21no—
207C2×C4⋊C4—21no—
208C2×C4⋊C4—41no—
209C2×C4⋊C4—41no—
210C2×C4⋊C4C2×Dic1311yescharacteristic
211C2×C4⋊C4C2×Dic1311yescharacteristic
212C2×C4⋊C4C22⋊D1311yescharacteristic
213C2×C4⋊C4C22⋊D1311yescharacteristic
214C2×C4⋊C4C22×D1311yescharacteristic
215C2×C22⋊C4—21no—
216C2×C22⋊C4—21no—
217C22⋊C8—262no—
218C22⋊C8—521no—
219#95—21no—
220#95—21no—
221#95—21no—
222#95—21no—
223#95—21no—
224#95—21no—
225#95C2×Dic1311yescharacteristic
226#95C2×Dic1311yescharacteristic
227C2×C13—21no—
228C2×C13—22no—
229C2×C13—22no—
230C2×C13—21no—
231C2×C13C2×#32811yescharacteristic
232C2×C13#212111yescharacteristic
233C2×C13#213311yescharacteristic
234C24C22⋊Dic1311yescharacteristic
235C2×Q8—41no—
236C2×Q8—81no—
237C22×C4—21no—
238C22×C4—21no—
239C22×C4—22no—
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—81no—
249C22×C4—81no—
250C22×C4#610612yes—
251C22×C4#610712yes—
252C22×C4C22⋊Dic1311yescharacteristic
253C22×C4C22⋊Dic1311yescharacteristic
254C22×C4C22⋊Dic1311yescharacteristic
255C22×C4C22×Dic1311yescharacteristic
256C22×C4C2×C22⋊D1311yescharacteristic
257C22×C4C2×C22⋊D1311yescharacteristic
258M16—264no—
259M16—524no—
260M16—522no—
261C2×C8—522no—
262C2×C8—524no—
263C2×C8—522no—
264C2×C8—1042no—
265C4⋊C4—41no—
266C4⋊C4—41no—
267C4⋊C4—41no—
268C4⋊C4—41no—
269C4⋊C4—41no—
270C4⋊C4—42no—
271C4⋊C4—81no—
272C4⋊C4—81no—
273C4⋊C4—81no—
274C22⋊C4—41no—
275C22⋊C4—41no—
276C22⋊C4—42no—
277C13#1172211yescharacteristic, complemented, Sylow
278C23—41no—
279C23—41no—
280C23#8807411yescharacteristic
281C23#8807411yescharacteristic
282C23#8807512yes—
283C23#8807712yes—
284C23C2×C22⋊Dic1311yescharacteristic
285Q8—82no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—22no—
291C2×C4—22no—
292C2×C4—22no—
293C2×C4—22no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—42no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—42no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—81no—
315C2×C4—81no—
316C2×C4—81no—
317C2×C4#8807512yes—
318C2×C4C2×#610611yescharacteristic
319C2×C4C2×#610711yescharacteristic
320C8—524no—
321C8—1042no—
322C22—21no—
323C22—21no—
324C22—21no—
325C22—21no—
326C22—21no—
327C22—21no—
328C22—42no—
329C22—42no—
330C22#1171813012yes—
331C22#1171813012yes—
332C22C2×#8807411yescharacteristic
333C22C2×#8807511yescharacteristic
334C22C2×#8807711yescharacteristic
335C4—21no—
336C4—22no—
337C4—21no—
338C4—41no—
339C4—41no—
340C4—41no—
341C4—41no—
342C4—81no—
343C4—81no—
344C4—81no—
345C4—81no—
346C2—21no—
347C2—21no—
348C2—22no—
349C2—22no—
350C2C2×#1171813011yescharacteristic
351C2#1311648211yescharacteristic
352C2#1311652511yescharacteristic
subgroupG/H
centerC22C2×#88074
commutatorC22×C4×C13C22×C4
FrattiniC2×C4⋊C4C22×D13
FittingC13×#2627C2
socleC22×C13C2×#99
prime radicalC24×C13C22⋊C4
cosocleC2×C13×C4⋊C4C23
hypercenter#2627D13
hypocenterC13#11722
LCSG ▷ C22×C4×C13 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C24 ◁ C22×C4⋊C4 ◁ #2627

Complements

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

NH ≅ G/Ntype
3. #13112866C2semidirect
4. #13112863C2semidirect
277. C13#11722semidirect

Maximal subgroups

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

subgroupindex
C2×#117181222
C2×#117181202
#131128662
#131128632
C13×#26272
#1172213