Finite Group Databasebeta

← #15773231

Subgroups — #15773231

Order 3328.

452 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 452 conjugacy classes of subgroups — too many to draw. Only its 107 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#13120649C211yesmaximal, characteristic
2C2×#11718122C211yesmaximal, characteristic
3#13112867C212yesmaximal, complemented
4#13112864C212yesmaximal, complemented
5C2×C13×#324C211yesmaximal, characteristic
6C22×C13×C4⋊C4C2211yescharacteristic
7C2×#88178C411yescharacteristic
8C22×#6099—21no—
9C2×C13×C22⋊C8—21no—
10#11718873C411yescharacteristic
11#11718872—21no—
12#11718871—21no—
13#11718647C411yescharacteristic
14#11718647C2211yescharacteristic
15#11718645—21no—
16#11718645—21no—
17#11718640C411yescharacteristic
18#11718640C2211yescharacteristic
19C13×#324—21no—
20C13×#324C2212yes—
21#11718122—21no—
22#11718122C2212yes—
23C23×C4×C13C2×C411yescharacteristic
24C23×C4×C13D411yescharacteristic
25C23×C4×C13D411yescharacteristic
26C22×Dic26C2×C411yescharacteristic
27C22×C8×C13—41no—
28C2×C13×C4⋊C4—41no—
29C2×C13×C4⋊C4—41no—
30C2×C13×C4⋊C4C2×C411yescharacteristic
31C2×C13×C4⋊C4D411yescharacteristic
32C2×C13×C4⋊C4D411yescharacteristic
33C2×C13×C4⋊C4C2311yescharacteristic
34C2×C22⋊Dic13—21no—
35C2×C22⋊Dic13—21no—
36C2×C4⋊Dic13—21no—
37C2×C4⋊Dic13C2×C411yescharacteristic
38#88178—41no—
39#88178—41no—
40C2×#6101—21no—
41C2×#6101—21no—
42C2×#6101—21no—
43C2×#6099—24no—
44C2×#6099—22no—
45C2×#6099—41no—
46C2×#6099—42no—
47C22×#1055—41no—
48C13×C22⋊C8—22no—
49C13×C22⋊C8—41no—
50#88071—21no—
51#88071—21no—
52#88071—21no—
53#88071—21no—
54#88071—21no—
55#88071—21no—
56#88071C2×C411yescharacteristic
57#88071C2×C411yescharacteristic
58#11722—131nomaximal, Sylow
59C24×C13C22⋊C411yescharacteristic
60C22×C4×C13—21no—
61C22×C4×C13—21no—
62C22×C4×C13—22no—
63C22×C4×C13—21no—
64C22×C4×C13—21no—
65C22×C4×C13—21no—
66C22×C4×C13—21no—
67C22×C4×C13—81no—
68C22×C4×C13—81no—
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
77C22×Dic13—21no—
78C22×Dic13—21no—
79C22×Dic13—21no—
80C22×Dic13—21no—
81C2×Dic26—41no—
82C2×Dic26—81no—
83C2×C8×C13—42no—
84C2×C8×C13—82no—
85C13×C4⋊C4—41no—
86C13×C4⋊C4—41no—
87C13×C4⋊C4—41no—
88C13×C4⋊C4—41no—
89C22⋊Dic13—41no—
90C22⋊Dic13—41no—
91C22⋊Dic13—42no—
92C4⋊Dic13—41no—
93C4⋊Dic13—81no—
94#6101—42no—
95#6101—81no—
96#6101—81no—
97#6099—24no—
98#6099—44no—
99#6099—42no—
100C2×#1055—44no—
101C2×#1055—42no—
102#2627—131no—
103C2×#343—131no—
104C2×#324D1311yescharacteristic
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
114C2×C4×C13—22no—
115C2×C4×C13—22no—
116C2×C4×C13—22no—
117C2×C4×C13—22no—
118C2×C4×C13—21no—
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—42no—
127C2×C4×C13—41no—
128C2×C4×C13—41no—
129C2×C4×C13—41no—
130C2×C4×C13—41no—
131C2×C4×C13—81no—
132C2×C4×C13—81no—
133C2×C4×C13—81no—
134C2×C4×C13#10312yes—
135C2×C4×C13C2×SD1611yescharacteristic
136C2×C4×C13C2×Q1611yescharacteristic
137C2×Dic13—41no—
138C2×Dic13—41no—
139C2×Dic13—41no—
140C2×Dic13—41no—
141C2×Dic13—41no—
142C2×Dic13—41no—
143C2×Dic13—42no—
144C2×Dic13—41no—
145C2×Dic13—41no—
146C2×Dic13—41no—
147C2×Dic13—41no—
148Dic26—82no—
149C8×C13—82no—
150#1055—44no—
151C22×M16—261no—
152C2×C22⋊Q8—131no—
153C22×C4⋊C4C2×D1311yescharacteristic
154C2×C22⋊C8—21no—
155#400—131no—
156#400—131no—
157#398—261no—
158#398—261no—
159#395—131no—
160#395—131no—
161#385—261no—
162#381—261no—
163#380—131no—
164#343—132no—
165#343—261no—
166#324—21no—
167#324C2×D1312yes—
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—
188Dic13—81no—
189Dic13—81no—
190Dic13—81no—
191Dic13—81no—
192C22×Q8—131no—
193C23×C4C4×D1311yescharacteristic
194C23×C4D5211yescharacteristic
195C23×C4C22⋊D1311yescharacteristic
196C2×M16—264no—
197C2×M16—262no—
198C2×M16—521no—
199C2×M16—522no—
200C22×C8—41no—
201C22×C8—521no—
202C22⋊Q8—521no—
203C22⋊Q8—521no—
204C2×C4⋊C4—41no—
205C2×C4⋊C4—41no—
206C2×C4⋊C4—131no—
207C2×C4⋊C4—261no—
208C2×C4⋊C4—261no—
209C2×C4⋊C4—261no—
210C2×C4⋊C4—261no—
211C2×C4⋊C4C4×D1311yescharacteristic
212C2×C4⋊C4D5211yescharacteristic
213C2×C4⋊C4C22⋊D1311yescharacteristic
214C2×C4⋊C4C22×D1311yescharacteristic
215C2×C22⋊C4—261no—
216C2×C22⋊C4—261no—
217C22⋊C8—22no—
218C22⋊C8—41no—
219#95—131no—
220#95—131no—
221#95—261no—
222#95—261no—
223#95—261no—
224#95—261no—
225#95—261no—
226#95—261no—
227C2×C13—21no—
228C2×C13—22no—
229C2×C13—22no—
230C2×C13—21no—
231C2×C13C2×#32811yescharacteristic
232C2×C13#212111yescharacteristic
233C2×C13#213311yescharacteristic
234C24#610311yescharacteristic
235C2×Q8—521no—
236C2×Q8—1041no—
237C22×C4—22no—
238C22×C4—21no—
239C22×C4—21no—
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—21no—
244C22×C4—81no—
245C22×C4—81no—
246C22×C4—261no—
247C22×C4—261no—
248C22×C4—261no—
249C22×C4—261no—
250C22×C4#609512yes—
251C22×C4Dic5212yes—
252C22×C4#610311yescharacteristic
253C22×C4#610311yescharacteristic
254C22×C4#610311yescharacteristic
255C22×C4C2×C4×D1311yescharacteristic
256C22×C4C2×D5211yescharacteristic
257C22×C4C2×C22⋊D1311yescharacteristic
258M16—264no—
259M16—524no—
260M16—522no—
261C2×C8—42no—
262C2×C8—82no—
263C2×C8—524no—
264C2×C8—522no—
265C4⋊C4—41no—
266C4⋊C4—41no—
267C4⋊C4—41no—
268C4⋊C4—41no—
269C4⋊C4—521no—
270C4⋊C4—522no—
271C4⋊C4—1041no—
272C4⋊C4—1041no—
273C4⋊C4—1041no—
274C22⋊C4—522no—
275C22⋊C4—521no—
276C22⋊C4—521no—
277C13#1172211yescharacteristic, complemented, Sylow
278C23—41no—
279C23—41no—
280C23#8804611yescharacteristic
281C23#8804611yescharacteristic
282C23#8805612yes—
283C23#8806512yes—
284C23C2×#610311yescharacteristic
285Q8—1042no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—22no—
289C2×C4—22no—
290C2×C4—22no—
291C2×C4—22no—
292C2×C4—21no—
293C2×C4—21no—
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—81no—
304C2×C4—81no—
305C2×C4—81no—
306C2×C4—521no—
307C2×C4—521no—
308C2×C4—521no—
309C2×C4—521no—
310C2×C4—521no—
311C2×C4—521no—
312C2×C4—522no—
313C2×C4—521no—
314C2×C4—521no—
315C2×C4—521no—
316C2×C4—521no—
317C2×C4#8805612yes—
318C2×C4C2×#609511yescharacteristic
319C2×C4C2×Dic5211yescharacteristic
320C8—82no—
321C8—524no—
322C22—21no—
323C22—21no—
324C22—21no—
325C22—21no—
326C22—21no—
327C22—21no—
328C22—42no—
329C22—42no—
330C22#1171805912yes—
331C22#1171805912yes—
332C22C2×#8804611yescharacteristic
333C22C2×#8805611yescharacteristic
334C22C2×#8806511yescharacteristic
335C4—21no—
336C4—21no—
337C4—22no—
338C4—41no—
339C4—41no—
340C4—41no—
341C4—41no—
342C4—1041no—
343C4—1041no—
344C4—1041no—
345C4—1041no—
346C2—21no—
347C2—21no—
348C2—22no—
349C2—22no—
350C2C2×#1171805911yescharacteristic
351C2#1311648011yescharacteristic
352C2#1311652311yescharacteristic
subgroupG/H
centerC22C2×#88046
commutatorC22×C4×C13C22×C4
FrattiniC2×C4⋊C4C22×D13
FittingC2×C13×#324C2
socleC22×C13C2×#99
prime radicalC24×C13C22⋊C4
cosocleC2×C13×C4⋊C4C23
hypercenterC2×#324D13
hypocenterC13#11722
LCSG ▷ C22×C4×C13 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C24 ◁ C22×C4⋊C4 ◁ C2×#324

Complements

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

NH ≅ G/Ntype
3. #13112867C2semidirect
4. #13112864C2semidirect
277. C13#11722semidirect

Maximal subgroups

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

subgroupindex
#131206492
C2×#117181222
#131128672
#131128642
C2×C13×#3242
#1172213