Finite Group Databasebeta

← #15773959

Subgroups — #15773959

Order 3328.

440 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 440 conjugacy classes of subgroups — too many to draw. Only its 95 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#13119741C211yesmaximal, characteristic
2#13113160C211yesmaximal, characteristic, complemented
3#13112841C212yesmaximal, complemented
4#13112838C212yesmaximal
5C13×#1801C211yesmaximal, characteristic, complemented
6C2×C4×Q8×C13C2211yescharacteristic
7C2×#88200—21no—
8C2×C4×D52C411yescharacteristic
9C13×#423—21no—
10C2×C13×#101—21no—
11#11718652C411yescharacteristic
12#11718652C2211yescharacteristic
13#11718648—21no—
14#11718644C411yescharacteristic
15#11718644C2211yescharacteristic
16#11718601—21no—
17#11718601—21no—
18#11718597C411yescharacteristic
19#11718586—21no—
20C13×#343C2212yes—
21#11718120—21no—
22#11718120C2212yes—
23C22×Q8×C13D411yescharacteristic
24C22×D52C2×C411yescharacteristic
25C22×C4×D13—21no—
26C2×C13×M16—22no—
27C4×Q8×C13—41no—
28C4×Q8×C13—41no—
29C2×C13×C4⋊C4C2×C411yescharacteristic
30C2×C13×C4⋊C4D411yescharacteristic
31C2×C13×C4⋊C4C2311yescharacteristic
32C2×C42×C13C2×C411yescharacteristic
33C2×C42×C13D411yescharacteristic
34C2×C42×C13D411yescharacteristic
35#88200—42no—
36#88200—42no—
37C2×#6103—21no—
38C2×#6103—21no—
39C2×#6103—21no—
40C2×#6103—21no—
41C2×#6103—21no—
42C2×C4⋊Dic13—21no—
43C2×C4⋊Dic13C2×C411yescharacteristic
44C2×#6101—21no—
45C2×#6101—21no—
46C4×D52—41no—
47C4×D52—41no—
48C13×C4⋊C8—41no—
49C13×C4⋊C8—41no—
50C13×#101—42no—
51#88071—21no—
52#88071—21no—
53#88071—21no—
54#88071C2×C411yescharacteristic
55#88071C2×C411yescharacteristic
56C22⋊#1055—22no—
57C4⋊#1055—41no—
58C4×#1055—41no—
59#11879—131nomaximal, Sylow
60C23×D13—21no—
61C2×Q8×C13—41no—
62C2×Q8×C13—41no—
63C2×Q8×C13D812yes—
64C2×Q8×C13SD1612yes—
65C22×C4×C13C22⋊C411yescharacteristic
66C22×C4×C13C22⋊C411yescharacteristic
67C22×C4×C13C22⋊C411yescharacteristic
68C22×C4×C13C22⋊C411yescharacteristic
69C22×C4×C13C22×C411yescharacteristic
70C22×C4×C13C2×D411yescharacteristic
71C22×C4×C13C2×D411yescharacteristic
72C22×Dic13—21no—
73C22×Dic13—21no—
74C22×Dic13—21no—
75C2×D52—41no—
76C2×D52—42no—
77C2×C4×D13—42no—
78C2×C4×D13—42no—
79C2×C4×D13—42no—
80C13×M16—42no—
81C13×M16—42no—
82C2×C8×C13—42no—
83C13×C4⋊C4—41no—
84C13×C4⋊C4—41no—
85C13×C4⋊C4—41no—
86C42×C13—21no—
87C42×C13—21no—
88C42×C13—21no—
89C42×C13—21no—
90C42×C13—21no—
91C42×C13—21no—
92#6103—42no—
93#6103—42no—
94#6103—41no—
95#6103—41no—
96#6103—42no—
97#6103—41no—
98#6103—41no—
99C4⋊Dic13—42no—
100C4⋊Dic13—41no—
101#6101—42no—
102#6101—41no—
103#6101—41no—
104C2×#1055—42no—
105#2536—131no—
106#1801D1311yescharacteristic, complemented
107#1461—131no—
108#1346—132no—
109#1345—132no—
110C23×C13C2×C22⋊C411yescharacteristic
111C22×D13—22no—
112C22×D13—41no—
113C22×D13—41no—
114C22×D13—41no—
115C22×D13—41no—
116C22×D13—41no—
117C22×D13—41no—
118Q8×C13—42no—
119Q8×C13—42no—
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—21no—
129C2×C4×C13—41no—
130C2×C4×C13—41no—
131C2×C4×C13—41no—
132C2×C4×C13—41no—
133C2×C4×C13#9911yescharacteristic
134C2×C4×C13#9911yescharacteristic
135C2×C4×C13#10212yes—
136C2×C4×C13#10212yes—
137C2×C4×C13C2×D811yescharacteristic
138C2×C4×C13C2×SD1611yescharacteristic
139C2×Dic13—41no—
140C2×Dic13—41no—
141C2×Dic13—41no—
142C2×Dic13—41no—
143C2×Dic13—41no—
144C2×Dic13—41no—
145C2×Dic13—41no—
146C2×Dic13—41no—
147C2×Dic13—41no—
148D52—42no—
149D52—42no—
150C4×D13—84no—
151C8×C13—82no—
152#1055—82no—
153C2×C22⋊Q8—261no—
154C2×C4×Q8C2×D1311yescharacteristic
155C2×C4×D4—131no—
156#431—261no—
157#423—21no—
158C2×#101—21no—
159#398—131no—
160#398—131no—
161#394—131no—
162#394—131no—
163#388—261no—
164#388—261no—
165#382—131no—
166#380—261no—
167#343C2×D1312yes—
168#324—132no—
169#324—261no—
170C22×C13—21no—
171C22×C13—21no—
172C22×C13C2×#9911yescharacteristic
173C22×C13C2×#10211yescharacteristic
174C22×C13#42111yescharacteristic
175C2×D13—42no—
176C2×D13—42no—
177C2×D13—42no—
178C2×D13—81no—
179C2×D13—81no—
180C2×D13—81no—
181C2×D13—81no—
182C4×C13—21no—
183C4×C13—21no—
184C4×C13—21no—
185C4×C13—22no—
186C4×C13—22no—
187C4×C13—21no—
188C4×C13—41no—
189C4×C13—41no—
190C4×C13—41no—
191Dic13—81no—
192Dic13—81no—
193Dic13—81no—
194C22×Q8C22⋊D1311yescharacteristic
195C22×D4—131no—
196C23×C4—261no—
197C2×M16—22no—
198C22⋊Q8—522no—
199C22⋊Q8—522no—
200C4×Q8—41no—
201C4×Q8—41no—
202C4×D4—521no—
203C4×D4—521no—
204C2×C4⋊C4—131no—
205C2×C4⋊C4—261no—
206C2×C4⋊C4—261no—
207C2×C4⋊C4—261no—
208C2×C4⋊C4C4×D1311yescharacteristic
209C2×C4⋊C4D5211yescharacteristic
210C2×C4⋊C4C22×D1311yescharacteristic
211C2×C22⋊C4—261no—
212C2×C22⋊C4—261no—
213C2×C22⋊C4—261no—
214C2×C22⋊C4—261no—
215C2×C22⋊C4—261no—
216C2×C42C4×D1311yescharacteristic
217C2×C42D5211yescharacteristic
218C2×C42C22⋊D1311yescharacteristic
219C4⋊C8—41no—
220C4⋊C8—41no—
221C4⋊C8—521no—
222#101—42no—
223C22⋊C8—262no—
224C4×C8—521no—
225#95—131no—
226#95—131no—
227#95—261no—
228#95—261no—
229#95—261no—
230C2×C13—21no—
231C2×C13—21no—
232C2×C13#151911yescharacteristic
233C2×C13#212011yescharacteristic
234C2×C13#213311yescharacteristic
235D13—82no—
236C24—261no—
237C2×Q8—41no—
238C2×Q8—41no—
239C2×Q8#610412yes—
240C2×Q8#610612yes—
241C2×D4—521no—
242C2×D4—522no—
243C22×C4—261no—
244C22×C4—261no—
245C22×C4—261no—
246C22×C4—522no—
247C22×C4—522no—
248C22×C4—522no—
249C22×C4#610311yescharacteristic
250C22×C4#610311yescharacteristic
251C22×C4#610311yescharacteristic
252C22×C4#610311yescharacteristic
253C22×C4C2×C4×D1311yescharacteristic
254C22×C4C2×D5211yescharacteristic
255C22×C4C2×C22⋊D1311yescharacteristic
256M16—42no—
257M16—42no—
258C2×C8—42no—
259C2×C8—522no—
260C4⋊C4—41no—
261C4⋊C4—41no—
262C4⋊C4—41no—
263C4⋊C4—521no—
264C4⋊C4—521no—
265C4⋊C4—521no—
266C4⋊C4—522no—
267C4⋊C4—522no—
268C22⋊C4—522no—
269C22⋊C4—522no—
270C22⋊C4—521no—
271C22⋊C4—521no—
272C22⋊C4—521no—
273C22⋊C4—521no—
274C22⋊C4—522no—
275C42—21no—
276C42—21no—
277C42—21no—
278C42—21no—
279C42—21no—
280C42—21no—
281C13#1187911yescharacteristic, complemented, Sylow
282C23—262no—
283C23—521no—
284C23—521no—
285C23—521no—
286C23—521no—
287C23—521no—
288C23—521no—
289C23C2×#610311yescharacteristic
290Q8—42no—
291Q8—42no—
292D4—522no—
293D4—522no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—521no—
308C2×C4—521no—
309C2×C4—521no—
310C2×C4—521no—
311C2×C4—521no—
312C2×C4—521no—
313C2×C4—521no—
314C2×C4—521no—
315C2×C4—521no—
316C2×C4—1044no—
317C2×C4#8804611yescharacteristic
318C2×C4#8804611yescharacteristic
319C2×C4#8804912yes—
320C2×C4#8804912yes—
321C2×C4C2×#610411yescharacteristic
322C2×C4C2×#610611yescharacteristic
323C8—82no—
324C8—1042no—
325C22—21no—
326C22—21no—
327C22—522no—
328C22—522no—
329C22—522no—
330C22—1041no—
331C22—1041no—
332C22—1041no—
333C22—1041no—
334C22C2×#8804611yescharacteristic
335C22C2×#8804911yescharacteristic
336C22#1171866611yescharacteristic
337C4—21no—
338C4—22no—
339C4—21no—
340C4—22no—
341C4—21no—
342C4—21no—
343C4—41no—
344C4—41no—
345C4—41no—
346C4—1041no—
347C4—1041no—
348C4—1041no—
349C2—21no—
350C2—21no—
351C2—1042no—
352C2#1311340311yescharacteristic
353C2#1311647811yescharacteristic
354C2#1311652311yescharacteristic
subgroupG/H
centerC22C2×#88046
commutatorC22×C4×C13C22×C4
FrattiniC2×C4⋊C4C22×D13
FittingC13×#1801C2
socleC22×C13C2×#99
prime radicalC22×D52C2×C4
cosocleC2×C13×C4⋊C4C23
hypercenter#1801D13
hypocenterC13#11879
LCSG ▷ C22×C4×C13 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #1801

Complements

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

NH ≅ G/Ntype
2. #13113160C2semidirect
3. #13112841C2semidirect
5. C13×#1801C2semidirect
106. #1801D13semidirect
281. C13#11879semidirect

Maximal subgroups

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

subgroupindex
#131197412
#131131602
#131128412
#131128382
C13×#18012
#1187913