Finite Group Databasebeta

← #15772473

Subgroups — #15772473

Order 3328.

496 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 496 conjugacy classes of subgroups — too many to draw. Only its 83 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#13119303C211yesmaximal, characteristic
2#13113166C211yesmaximal, characteristic, complemented
3#13112781C212yesmaximal, complemented
4#13112767C212yesmaximal, complemented
5C2×C13×#324C211yesmaximal, characteristic, complemented
6C22×C13×C4⋊C4C2211yescharacteristic
7C2×#88184C411yescharacteristic
8C2×#88183—21no—
9C2×#88183—21no—
10C2×C13×C22⋊C8—21no—
11C4×C22⋊Dic13C411yescharacteristic
12#11718868—21no—
13#11718653—21no—
14#11718653—21no—
15#11718649C411yescharacteristic
16#11718649C2211yescharacteristic
17#11718637C411yescharacteristic
18#11718637C2211yescharacteristic
19C13×#324—21no—
20C13×#324C2212yes—
21#11718120—21no—
22#11718120C2212yes—
23C23×C4×C13C2×C411yescharacteristic
24C23×C4×C13D411yescharacteristic
25C23×C4×C13D411yescharacteristic
26C22×C22⋊D13—21no—
27C22×D52C2×C411yescharacteristic
28C22×C8×C13—41no—
29C2×C13×C4⋊C4—41no—
30C2×C13×C4⋊C4—41no—
31C2×C13×C4⋊C4C2×C411yescharacteristic
32C2×C13×C4⋊C4D411yescharacteristic
33C2×C13×C4⋊C4D411yescharacteristic
34C2×C13×C4⋊C4C2311yescharacteristic
35C2×C22⋊Dic13—21no—
36#88184—41no—
37#88184—41no—
38#88183—44no—
39#88183—44no—
40C2×#6103—21no—
41C2×#6103—21no—
42C2×#6103—21no—
43C2×#6103—21no—
44C2×#6103—21no—
45C2×C4⋊Dic13C2×C411yescharacteristic
46C2×#6101—21no—
47C2×#6101—21no—
48C2×#6101—21no—
49C2×#6101—21no—
50C2×C4×Dic13C2×C411yescharacteristic
51C2×C4×Dic13C2×C411yescharacteristic
52C2×#6099—41no—
53C13×C22⋊C8—22no—
54C13×C22⋊C8—41no—
55#88071—21no—
56C22⋊#1055—22no—
57C22⋊#1055—41no—
58#11549—131nomaximal, Sylow
59C24×C13C22⋊C411yescharacteristic
60C23×D13—21no—
61C22×C4×C13—21no—
62C22×C4×C13—21no—
63C22×C4×C13—21no—
64C22×C4×C13—21no—
65C22×C4×C13—21no—
66C22×C4×C13—21no—
67C22×C4×C13—22no—
68C22×C4×C13—41no—
69C22×C4×C13—42no—
70C22×C4×C13—42no—
71C22×C4×C13C22⋊C411yescharacteristic
72C22×C4×C13C22⋊C411yescharacteristic
73C22×C4×C13C22⋊C411yescharacteristic
74C22×C4×C13C22×C411yescharacteristic
75C22×C4×C13C2×D411yescharacteristic
76C22×C4×C13C2×D411yescharacteristic
77C2×C22⋊D13—42no—
78C2×C22⋊D13—42no—
79C2×C22⋊D13—41no—
80C2×C22⋊D13—41no—
81C22×Dic13—21no—
82C22×Dic13—21no—
83C22×Dic13—21no—
84C2×D52—22no—
85C2×D52—41no—
86C2×D52—41no—
87C2×C8×C13—42no—
88C2×C8×C13—82no—
89C13×C4⋊C4—41no—
90C13×C4⋊C4—41no—
91C13×C4⋊C4—41no—
92C13×C4⋊C4—41no—
93C22⋊Dic13—24no—
94#6103—42no—
95#6103—42no—
96#6103—42no—
97#6103—42no—
98#6103—42no—
99C4⋊Dic13—41no—
100#6101—42no—
101#6101—42no—
102#6101—42no—
103#6101—42no—
104C4×Dic13—22no—
105C4×Dic13—41no—
106#6099—82no—
107C2×#1055—42no—
108#2501—131no—
109#1463—131no—
110C2×#324D1311yescharacteristic, complemented
111#1325—132no—
112#1318—132no—
113C23×C13—22no—
114C23×C13—21no—
115C23×C13—21no—
116C23×C13—41no—
117C23×C13#9911yescharacteristic
118C23×C13#9911yescharacteristic
119C23×C13C2×C22⋊C411yescharacteristic
120C22×D13—41no—
121C22×D13—41no—
122C22×D13—41no—
123C22×D13—41no—
124C22×D13—41no—
125C22×D13—41no—
126C22×D13—41no—
127C2×C4×C13—21no—
128C2×C4×C13—21no—
129C2×C4×C13—21no—
130C2×C4×C13—21no—
131C2×C4×C13—21no—
132C2×C4×C13—21no—
133C2×C4×C13—21no—
134C2×C4×C13—21no—
135C2×C4×C13—21no—
136C2×C4×C13—42no—
137C2×C4×C13—42no—
138C2×C4×C13—42no—
139C2×C4×C13—42no—
140C2×C4×C13—41no—
141C2×C4×C13—41no—
142C2×C4×C13—41no—
143C2×C4×C13—41no—
144C2×C4×C13—81no—
145C2×C4×C13—81no—
146C2×C4×C13#13112yes—
147C22⋊D13—82no—
148C22⋊D13—82no—
149C2×Dic13—22no—
150C2×Dic13—22no—
151C2×Dic13—41no—
152C2×Dic13—41no—
153C2×Dic13—41no—
154C2×Dic13—41no—
155C2×Dic13—41no—
156C2×Dic13—41no—
157C2×Dic13—41no—
158D52—82no—
159C8×C13—82no—
160#1055—82no—
161C2×#123—261no—
162C2×#123—261no—
163C2×#121—131no—
164C22×C4⋊C4C2×D1311yescharacteristic
165#407—261no—
166C2×C22⋊C8—21no—
167#399—261no—
168#399—261no—
169#390—131no—
170#390—131no—
171#384—131no—
172#384—131no—
173C4×C22⋊C4—131no—
174#324—21no—
175#324—132no—
176#324—261no—
177#324C2×D1312yes—
178C22×C13—21no—
179C22×C13—21no—
180C22×C13—21no—
181C22×C13—21no—
182C22×C13—21no—
183C22×C13—21no—
184C22×C13—21no—
185C22×C13—42no—
186C22×C13—42no—
187C22×C13#35312yes—
188C22×C13#40811yescharacteristic
189C22×C13C2×#9911yescharacteristic
190C22×C13#41311yescharacteristic
191C2×D13—81no—
192C2×D13—81no—
193C2×D13—81no—
194C2×D13—81no—
195C2×D13—81no—
196C2×D13—81no—
197C2×D13—81no—
198C4×C13—22no—
199C4×C13—41no—
200C4×C13—41no—
201C4×C13—41no—
202C4×C13—41no—
203C4×C13—41no—
204Dic13—42no—
205Dic13—42no—
206Dic13—81no—
207C22×D4—131no—
208C22×D4—261no—
209C23×C4C4×D1311yescharacteristic
210C23×C4D5211yescharacteristic
211C23×C4C22⋊D1311yescharacteristic
212C2×M16—521no—
213C22×C8—41no—
214#123—524no—
215#123—524no—
216#121—521no—
217#121—521no—
218C2×C4⋊C4—41no—
219C2×C4⋊C4—41no—
220C2×C4⋊C4—131no—
221C2×C4⋊C4—261no—
222C2×C4⋊C4—261no—
223C2×C4⋊C4—261no—
224C2×C4⋊C4—261no—
225C2×C4⋊C4C4×D1311yescharacteristic
226C2×C4⋊C4D5211yescharacteristic
227C2×C4⋊C4C22⋊D1311yescharacteristic
228C2×C4⋊C4C22×D1311yescharacteristic
229C2×C22⋊C4—261no—
230C2×C22⋊C4—261no—
231C2×C22⋊C4—261no—
232C2×C22⋊C4—261no—
233C2×C22⋊C4—261no—
234C2×C22⋊C4—261no—
235C2×C42—131no—
236C2×C42—131no—
237C22⋊C8—22no—
238C22⋊C8—41no—
239C22⋊C8—262no—
240C22⋊C8—521no—
241#95—261no—
242C2×C13—21no—
243C2×C13—21no—
244C2×C13—22no—
245C2×C13—41no—
246C2×C13#146811yescharacteristic
247C2×C13C2×#35311yescharacteristic
248C2×C13#213311yescharacteristic
249D13—161no—
250C24—261no—
251C24#610311yescharacteristic
252C2×D4—262no—
253C2×D4—521no—
254C2×D4—521no—
255C2×D4—522no—
256C2×D4—522no—
257C2×D4—521no—
258C2×D4—521no—
259C22×C4—21no—
260C22×C4—21no—
261C22×C4—21no—
262C22×C4—21no—
263C22×C4—21no—
264C22×C4—21no—
265C22×C4—22no—
266C22×C4—41no—
267C22×C4—42no—
268C22×C4—42no—
269C22×C4—261no—
270C22×C4—261no—
271C22×C4—261no—
272C22×C4#610311yescharacteristic
273C22×C4#610311yescharacteristic
274C22×C4#610311yescharacteristic
275C22×C4C2×C4×D1311yescharacteristic
276C22×C4C2×D5211yescharacteristic
277C22×C4C2×C22⋊D1311yescharacteristic
278M16—1042no—
279C2×C8—42no—
280C2×C8—82no—
281C2×C8—522no—
282C4⋊C4—41no—
283C4⋊C4—41no—
284C4⋊C4—41no—
285C4⋊C4—41no—
286C4⋊C4—521no—
287C4⋊C4—522no—
288C4⋊C4—522no—
289C4⋊C4—522no—
290C4⋊C4—522no—
291C22⋊C4—264no—
292C22⋊C4—522no—
293C22⋊C4—522no—
294C22⋊C4—522no—
295C22⋊C4—522no—
296C22⋊C4—522no—
297C42—262no—
298C42—521no—
299C13#1154911yescharacteristic, complemented, Sylow
300C23—21no—
301C23—21no—
302C23—22no—
303C23—41no—
304C23—521no—
305C23—521no—
306C23—521no—
307C23—521no—
308C23—521no—
309C23—521no—
310C23—521no—
311C23#8804611yescharacteristic
312C23#8804611yescharacteristic
313C23C2×#610311yescharacteristic
314D4—1042no—
315D4—1042no—
316D4—1042no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—42no—
327C2×C4—42no—
328C2×C4—42no—
329C2×C4—42no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—81no—
335C2×C4—81no—
336C2×C4—262no—
337C2×C4—262no—
338C2×C4—521no—
339C2×C4—521no—
340C2×C4—521no—
341C2×C4—521no—
342C2×C4—521no—
343C2×C4—521no—
344C2×C4—521no—
345C2×C4#8815512yes—
346C8—82no—
347C8—1042no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—21no—
353C22—21no—
354C22—21no—
355C22—42no—
356C22—42no—
357C22—1041no—
358C22—1041no—
359C22—1041no—
360C22—1041no—
361C22—1041no—
362C22—1041no—
363C22—1041no—
364C22#1171806612yes—
365C22C2×#8804611yescharacteristic
366C22#1171877111yescharacteristic
367C22#1171879311yescharacteristic
368C4—22no—
369C4—41no—
370C4—41no—
371C4—41no—
372C4—41no—
373C4—41no—
374C4—522no—
375C4—522no—
376C4—1041no—
377C2—21no—
378C2—21no—
379C2—22no—
380C2—41no—
381C2—2081no—
382C2#1311318211yescharacteristic
383C2C2×#1171806611yescharacteristic
384C2#1311652311yescharacteristic
subgroupG/H
centerC22C2×#88046
commutatorC22×C4×C13C22×C4
FrattiniC2×C4⋊C4C22×D13
FittingC2×C13×#324C2
socleC22×C13C2×#99
prime radicalC2×#88184C4
cosocleC2×C13×C4⋊C4C23
hypercenterC2×#324D13
hypocenterC13#11549
LCSG ▷ C22×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
2. #13113166C2semidirect
3. #13112781C2semidirect
4. #13112767C2semidirect
5. C2×C13×#324C2semidirect
110. C2×#324D13semidirect
299. C13#11549semidirect

Maximal subgroups

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

subgroupindex
#131193032
#131131662
#131127812
#131127672
C2×C13×#3242
#1154913