Finite Group Databasebeta

← #15772079

Subgroups — #15772079

Order 3328.

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

normal subgroups only

This group has 454 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#13117460C211yesmaximal, characteristic
2C2×#11718120C211yesmaximal, characteristic
3#13112781C212yesmaximal, complemented
4#13112779C212yesmaximal, complemented
5C2×C13×#324C211yesmaximal, characteristic
6C22×C13×C4⋊C4C2211yescharacteristic
7C2×#88180C411yescharacteristic
8C2×#88180C411yescharacteristic
9C2×C13×C22⋊C8—21no—
10#11718871—21no—
11#11718871—21no—
12C2×C22⋊#1055—21no—
13#11718638C411yescharacteristic
14#11718638C2211yescharacteristic
15#11718637C411yescharacteristic
16#11718637C2211yescharacteristic
17#11718634—21no—
18#11718634—21no—
19C13×#324—21no—
20C13×#324C2212yes—
21#11718120—21no—
22#11718120C2212yes—
23C23×C4×C13C2×C411yescharacteristic
24C23×C4×C13D411yescharacteristic
25C23×C4×C13D411yescharacteristic
26C22×C8×C13—41no—
27C2×C13×C4⋊C4—41no—
28C2×C13×C4⋊C4—41no—
29C2×C13×C4⋊C4C2×C411yescharacteristic
30C2×C13×C4⋊C4D411yescharacteristic
31C2×C13×C4⋊C4D411yescharacteristic
32C2×C13×C4⋊C4C2311yescharacteristic
33C2×C22⋊Dic13—21no—
34C2×C22⋊Dic13—21no—
35#88180—22no—
36#88180—41no—
37#88180—41no—
38#88180C814yescomplemented
39C2×C4⋊Dic13—21no—
40C2×C4⋊Dic13C2×C411yescharacteristic
41C2×C4⋊Dic13C2×C411yescharacteristic
42C2×#6101—21no—
43C2×#6101—21no—
44C2×#6101—21no—
45C2×#6101—21no—
46C2×C4×Dic13—21no—
47C2×C4×Dic13C2×C411yescharacteristic
48C2×C4×Dic13C2×C411yescharacteristic
49C22×#1055—41no—
50C13×C22⋊C8—22no—
51C13×C22⋊C8—41no—
52#88071—21no—
53#88071—21no—
54#88071—21no—
55#88071—21no—
56C22⋊#1055—22no—
57C22⋊#1055—41no—
58#11448—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×C13C2×C812yes—
73C22×C4×C13M1612yes—
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×C8×C13—42no—
82C2×C8×C13—82no—
83C13×C4⋊C4—41no—
84C13×C4⋊C4—41no—
85C13×C4⋊C4—41no—
86C13×C4⋊C4—41no—
87C22⋊Dic13—24no—
88C22⋊Dic13—41no—
89C22⋊Dic13—41no—
90C4⋊Dic13—24no—
91C4⋊Dic13—41no—
92C4⋊Dic13—41no—
93#6101—81no—
94#6101—81no—
95#6101—81no—
96#6101—81no—
97C4×Dic13—21no—
98C4×Dic13—21no—
99C4×Dic13—42no—
100C4×Dic13C2×C812yescomplemented
101C4×Dic13C2×C812yescomplemented
102C2×#1055—42no—
103C2×#1055—82no—
104#2317—131no—
105C2×#324—131no—
106C2×#324D1311yescharacteristic
107#1325—132no—
108#1324—132no—
109C23×C13—41no—
110C23×C13—41no—
111C23×C13C22⋊C812yes—
112C23×C13#9911yescharacteristic
113C23×C13#9911yescharacteristic
114C23×C13#10112yes—
115C23×C13C2×C22⋊C411yescharacteristic
116C2×C4×C13—22no—
117C2×C4×C13—22no—
118C2×C4×C13—22no—
119C2×C4×C13—22no—
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—21no—
128C2×C4×C13—42no—
129C2×C4×C13—42no—
130C2×C4×C13—41no—
131C2×C4×C13—41no—
132C2×C4×C13—41no—
133C2×C4×C13—41no—
134C2×C4×C13—81no—
135C2×C4×C13—81no—
136C2×C4×C13C22⋊C812yes—
137C2×C4×C13C22×C811yescharacteristic
138C2×C4×C13C2×M1611yescharacteristic
139C2×Dic13—22no—
140C2×Dic13—22no—
141C2×Dic13—41no—
142C2×Dic13—41no—
143C2×Dic13—41no—
144C2×Dic13—41no—
145C2×Dic13—41no—
146C2×Dic13—41no—
147C2×Dic13—42no—
148C2×Dic13—41no—
149C2×Dic13—41no—
150C8×C13—82no—
151#1055—82no—
152C2×#117—131no—
153C2×#117—131no—
154C22×C4⋊C4C2×D1311yescharacteristic
155C2×C22⋊C8—21no—
156C2×C22⋊C8—261no—
157#389—261no—
158#389—261no—
159#385—261no—
160#385—261no—
161#384—131no—
162#384—131no—
163#382—131no—
164#382—131no—
165#324—21no—
166#324—132no—
167#324—261no—
168#324C2×D1312yes—
169C22×C13—21no—
170C22×C13—21no—
171C22×C13—21no—
172C22×C13—21no—
173C22×C13—21no—
174C22×C13—21no—
175C22×C13—42no—
176C22×C13—42no—
177C22×C13#32412yes—
178C22×C13#32412yes—
179C22×C13C2×C22⋊C811yescharacteristic
180C22×C13C2×#9911yescharacteristic
181C22×C13C2×#10111yescharacteristic
182C4×C13—22no—
183C4×C13—21no—
184C4×C13—21no—
185C4×C13—41no—
186C4×C13—41no—
187C4×C13—41no—
188C4×C13—41no—
189Dic13—42no—
190Dic13—42no—
191Dic13—81no—
192Dic13—81no—
193C23×C4C4×D1311yescharacteristic
194C23×C4D5211yescharacteristic
195C23×C4C22⋊D1311yescharacteristic
196C22×C8—41no—
197C22×C8—521no—
198#117—134no—
199#117—262no—
200#117—521no—
201#117—521no—
202C2×C4⋊C4—41no—
203C2×C4⋊C4—41no—
204C2×C4⋊C4—131no—
205C2×C4⋊C4—131no—
206C2×C4⋊C4—261no—
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—
217C2×C42—131no—
218C2×C42—131no—
219C2×C42—261no—
220C22⋊C8—22no—
221C22⋊C8—41no—
222C22⋊C8—262no—
223C22⋊C8—521no—
224#95—261no—
225#95—261no—
226#95—261no—
227#95—261no—
228C2×C13—21no—
229C2×C13—22no—
230C2×C13—22no—
231C2×C13—21no—
232C2×C13C2×#32411yescharacteristic
233C2×C13#212711yescharacteristic
234C2×C13#213311yescharacteristic
235C24#610311yescharacteristic
236C22×C4—22no—
237C22×C4—21no—
238C22×C4—21no—
239C22×C4—21no—
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—81no—
244C22×C4—81no—
245C22×C4—261no—
246C22×C4—261no—
247C22×C4—261no—
248C22×C4—261no—
249C22×C4C8×D1312yes—
250C22×C4#609412yes—
251C22×C4#610311yescharacteristic
252C22×C4#610311yescharacteristic
253C22×C4#610311yescharacteristic
254C22×C4C2×C4×D1311yescharacteristic
255C22×C4C2×D5211yescharacteristic
256C22×C4C2×C22⋊D1311yescharacteristic
257C2×C8—42no—
258C2×C8—82no—
259C2×C8—522no—
260C2×C8—1042no—
261C4⋊C4—41no—
262C4⋊C4—41no—
263C4⋊C4—41no—
264C4⋊C4—41no—
265C4⋊C4—264no—
266C4⋊C4—521no—
267C4⋊C4—521no—
268C4⋊C4—1041no—
269C4⋊C4—1041no—
270C4⋊C4—1041no—
271C4⋊C4—1041no—
272C22⋊C4—264no—
273C22⋊C4—521no—
274C22⋊C4—521no—
275C42—132no—
276C42—132no—
277C42—261no—
278C42—261no—
279C42—522no—
280C13#1144811yescharacteristic, complemented, Sylow
281C23—41no—
282C23—41no—
283C23#8804611yescharacteristic
284C23#8804611yescharacteristic
285C23#8806012yes—
286C23#8806412yes—
287C23C2×#610311yescharacteristic
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—21no—
299C2×C4—21no—
300C2×C4—42no—
301C2×C4—42no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—81no—
307C2×C4—81no—
308C2×C4—262no—
309C2×C4—262no—
310C2×C4—521no—
311C2×C4—521no—
312C2×C4—521no—
313C2×C4—521no—
314C2×C4—521no—
315C2×C4—521no—
316C2×C4—522no—
317C2×C4—521no—
318C2×C4—521no—
319C2×C4#8806012yes—
320C2×C4C2×C8×D1311yescharacteristic
321C2×C4C2×#609411yescharacteristic
322C8—82no—
323C8—1042no—
324C22—21no—
325C22—21no—
326C22—21no—
327C22—21no—
328C22—21no—
329C22—21no—
330C22—42no—
331C22—42no—
332C22#1171806112yes—
333C22#1171806112yes—
334C22C2×#8804611yescharacteristic
335C22C2×#8806011yescharacteristic
336C22C2×#8806411yescharacteristic
337C4—21no—
338C4—21no—
339C4—22no—
340C4—41no—
341C4—41no—
342C4—41no—
343C4—41no—
344C4—522no—
345C4—522no—
346C4—1041no—
347C4—1041no—
348C2—21no—
349C2—21no—
350C2—22no—
351C2—22no—
352C2C2×#1171806111yescharacteristic
353C2#1311650311yescharacteristic
354C2#1311652311yescharacteristic
subgroupG/H
centerC22C2×#88046
commutatorC2×C4×C13C22×C8
FrattiniC2×C4⋊C4C22×D13
FittingC2×C13×#324C2
socleC22×C13C2×#99
prime radicalC24×C13C22⋊C4
cosocleC2×C13×C4⋊C4C23
hypercenterC2×#324D13
hypocenterC13#11448
LCSG ▷ C2×C4×C13 ▷ C22×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. #13112781C2semidirect
4. #13112779C2semidirect
38. #88180C8semidirect
100. C4×Dic13C2×C8semidirect
101. C4×Dic13C2×C8semidirect
280. C13#11448semidirect

Maximal subgroups

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

subgroupindex
#131174602
C2×#117181202
#131127812
#131127792
C2×C13×#3242
#1144813