Finite Group Databasebeta

← #15773582

Subgroups — #15773582

Order 3328.

486 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 486 conjugacy classes of subgroups — too many to draw. Only its 79 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#13118072C211yesmaximal, characteristic
2#13113170C211yesmaximal, characteristic, complemented
3#13112835C212yesmaximal, complemented
4#13112832C212yesmaximal
5C13×#1820C211yesmaximal, characteristic, complemented
6C2×C13×#117C2211yescharacteristic
7C2×C4×C22⋊D13—21no—
8C2×C4×D52C411yescharacteristic, complemented
9C13×#381—21no—
10#11718655—21no—
11#11718652C411yescharacteristic, complemented
12#11718644C411yescharacteristic, complemented
13#11718622—21no—
14#11718621C2211yescharacteristic
15#11718614C2211yescharacteristic
16C4×#6103—21no—
17C4×C4⋊Dic13C411yescharacteristic, complemented
18#11718587—21no—
19C13×#342—21no—
20C13×#342C2212yes—
21#11718120—21no—
22#11718117C2212yes—
23C23×C4×C13D411yescharacteristic
24C22×C22⋊D13—21no—
25C22×D52C2×C411yescharacteristic
26C22×C4×D13—21no—
27C13×#117—41no—
28C13×#117—41no—
29C2×C13×C4⋊C4C2×C411yescharacteristic
30C2×C13×C4⋊C4D411yescharacteristic
31C2×C13×C22⋊C4—22no—
32C2×C13×C22⋊C4D411yescharacteristic
33C2×C13×C22⋊C4C2311yescharacteristic
34C2×C42×C13C2×C411yescharacteristic
35C2×C42×C13D411yescharacteristic
36C2×C22⋊Dic13—21no—
37C4×C22⋊D13—44no—
38C2×#6103—21no—
39C2×#6103—21no—
40C2×#6103—21no—
41C2×#6103—21no—
42C2×C4⋊Dic13—21no—
43C2×C4⋊Dic13C2×C411yescharacteristic
44C2×#6101—21no—
45C2×C4×Dic13—21no—
46C4×D52—41no—
47C4×D52—41no—
48C13×#95—41no—
49C13×#95—41no—
50#88071—21no—
51#88071—21no—
52#88071C2×C411yescharacteristic
53#88071C2×C411yescharacteristic
54C22⋊#1055—22no—
55C4⋊#1055—41no—
56#88043—41no—
57#11798—131nomaximal, Sylow
58C24×C13C2×D411yescharacteristic
59C23×D13—21no—
60C22×C4×C13—22no—
61C22×C4×C13—21no—
62C22×C4×C13—21no—
63C22×C4×C13—41no—
64C22×C4×C13—42no—
65C22×C4×C13C22⋊C411yescharacteristic
66C22×C4×C13C22⋊C411yescharacteristic
67C22×C4×C13C22⋊C411yescharacteristic
68C22×C4×C13C22⋊C411yescharacteristic
69C22×C4×C13C22×C411yescharacteristic
70C22×C4×C13C2×D411yescharacteristic
71C2×C22⋊D13—42no—
72C2×C22⋊D13—42no—
73C2×C22⋊D13—42no—
74C22×Dic13—21no—
75C22×Dic13—21no—
76C22×Dic13—21no—
77C2×D52—41no—
78C2×D52—42no—
79C2×C4×D13—42no—
80C2×C4×D13—42no—
81C2×C4×D13—41no—
82C2×C4×D13—41no—
83C13×C4⋊C4—41no—
84C13×C4⋊C4—41no—
85C13×C22⋊C4—41no—
86C13×C22⋊C4—41no—
87C13×C22⋊C4—42no—
88C13×C22⋊C4—42no—
89C42×C13—21no—
90C42×C13—21no—
91C42×C13—21no—
92C42×C13—21no—
93C22⋊Dic13—42no—
94#6103—42no—
95#6103—42no—
96#6103—42no—
97#6103—42no—
98C4⋊Dic13—42no—
99C4⋊Dic13—41no—
100#6101—42no—
101C4×Dic13—42no—
102C2×#1055—42no—
103#2392—131no—
104#1820D1311yescharacteristic, complemented
105#1464—131no—
106#1344—132no—
107#1343—132no—
108C23×C13—21no—
109C23×C13—21no—
110C23×C13—41no—
111C23×C13—41no—
112C23×C13C2×C22⋊C411yescharacteristic
113C23×C13AGL(1,ℤ/8)12yes—
114C22×D13—22no—
115C22×D13—41no—
116C22×D13—41no—
117C22×D13—41no—
118C22×D13—41no—
119C22×D13—41no—
120C22×D13—41no—
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—21no—
130C2×C4×C13—42no—
131C2×C4×C13—42no—
132C2×C4×C13—41no—
133C2×C4×C13—41no—
134C2×C4×C13—41no—
135C2×C4×C13—41no—
136C2×C4×C13—82no—
137C2×C4×C13—82no—
138C2×C4×C13—82no—
139C2×C4×C13#9911yescharacteristic
140C2×C4×C13#9911yescharacteristic
141C22⋊D13—48no—
142C2×Dic13—22no—
143C2×Dic13—41no—
144C2×Dic13—41no—
145C2×Dic13—41no—
146C2×Dic13—41no—
147C2×Dic13—41no—
148C2×Dic13—41no—
149C2×Dic13—41no—
150C2×Dic13—41no—
151D52—42no—
152D52—42no—
153C4×D13—82no—
154C4×D13—82no—
155#1055—82no—
156C2×C4×D4—131no—
157C2×C4×D4—261no—
158C2×#117C2×D1311yescharacteristic
159#432—261no—
160#398—131no—
161#397—131no—
162#396—261no—
163#394—131no—
164#394—261no—
165#392—131no—
166#381—21no—
167C4×C4⋊C4—131no—
168C4×C22⋊C4—261no—
169#342—21no—
170#342C2×D1312yes—
171#324—261no—
172#323—132no—
173C22×C13—21no—
174C22×C13—21no—
175C22×C13—22no—
176C22×C13—42no—
177C22×C13—41no—
178C22×C13—41no—
179C22×C13—81no—
180C22×C13C2×#9911yescharacteristic
181C22×C13#41811yescharacteristic
182C22×C13#42111yescharacteristic
183C2×D13—42no—
184C2×D13—42no—
185C2×D13—42no—
186C2×D13—81no—
187C2×D13—81no—
188C2×D13—81no—
189C2×D13—81no—
190C4×C13—21no—
191C4×C13—21no—
192C4×C13—41no—
193C4×C13—41no—
194C4×C13—41no—
195C4×C13—41no—
196C4×C13—41no—
197C4×C13—162no—
198Dic13—42no—
199Dic13—81no—
200Dic13—81no—
201C22×D4—131no—
202C22×D4—261no—
203C23×C4—261no—
204C23×C4C22⋊D1311yescharacteristic
205C4×D4—521no—
206C4×D4—521no—
207C4×D4—524no—
208#117—41no—
209#117—41no—
210C2×C4⋊C4—131no—
211C2×C4⋊C4—261no—
212C2×C4⋊C4—261no—
213C2×C4⋊C4C4×D1311yescharacteristic
214C2×C4⋊C4D5211yescharacteristic
215C2×C22⋊C4—22no—
216C2×C22⋊C4—261no—
217C2×C22⋊C4—261no—
218C2×C22⋊C4—261no—
219C2×C22⋊C4—261no—
220C2×C22⋊C4—261no—
221C2×C22⋊C4C22⋊D1311yescharacteristic
222C2×C22⋊C4C22×D1311yescharacteristic
223C2×C42—261no—
224C2×C42C4×D1311yescharacteristic
225C2×C42D5211yescharacteristic
226C4⋊C8—521no—
227C22⋊C8—262no—
228#97—521no—
229#95—41no—
230#95—41no—
231#95—131no—
232#95—131no—
233#95—261no—
234#95—261no—
235C2×C13—21no—
236C2×C13—21no—
237C2×C13—42no—
238C2×C13#151011yescharacteristic
239C2×C13#212011yescharacteristic
240C2×C13#212611yescharacteristic
241D13—82no—
242C24—261no—
243C24C2×C22⋊D1311yescharacteristic
244C2×D4—521no—
245C2×D4—522no—
246C2×D4—522no—
247C2×D4—522no—
248C2×D4—522no—
249C22×C4—22no—
250C22×C4—21no—
251C22×C4—21no—
252C22×C4—41no—
253C22×C4—42no—
254C22×C4—261no—
255C22×C4—261no—
256C22×C4—261no—
257C22×C4—522no—
258C22×C4—522no—
259C22×C4—521no—
260C22×C4—521no—
261C22×C4#610311yescharacteristic
262C22×C4#610311yescharacteristic
263C22×C4#610311yescharacteristic
264C22×C4#610311yescharacteristic
265C22×C4C2×C4×D1311yescharacteristic
266C22×C4C2×D5211yescharacteristic
267C2×C8—522no—
268C4⋊C4—41no—
269C4⋊C4—41no—
270C4⋊C4—521no—
271C4⋊C4—522no—
272C4⋊C4—522no—
273C22⋊C4—41no—
274C22⋊C4—41no—
275C22⋊C4—42no—
276C22⋊C4—42no—
277C22⋊C4—522no—
278C22⋊C4—522no—
279C22⋊C4—522no—
280C22⋊C4—522no—
281C22⋊C4—522no—
282C42—21no—
283C42—21no—
284C42—21no—
285C42—21no—
286C42—522no—
287C13#1179811yescharacteristic, complemented, Sylow
288C23—21no—
289C23—21no—
290C23—41no—
291C23—41no—
292C23—262no—
293C23—521no—
294C23—521no—
295C23—521no—
296C23—521no—
297C23—521no—
298C23—521no—
299C23C2×#610311yescharacteristic
300C23#8820312yes—
301D4—522no—
302D4—522no—
303D4—528no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—42no—
314C2×C4—42no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—82no—
320C2×C4—82no—
321C2×C4—82no—
322C2×C4—262no—
323C2×C4—521no—
324C2×C4—521no—
325C2×C4—521no—
326C2×C4—521no—
327C2×C4—521no—
328C2×C4—521no—
329C2×C4—521no—
330C2×C4—521no—
331C2×C4—1042no—
332C2×C4—1042no—
333C2×C4#8804611yescharacteristic
334C2×C4#8804611yescharacteristic
335C8—1042no—
336C22—21no—
337C22—21no—
338C22—22no—
339C22—42no—
340C22—41no—
341C22—41no—
342C22—81no—
343C22—522no—
344C22—522no—
345C22—522no—
346C22—1041no—
347C22—1041no—
348C22—1041no—
349C22—1041no—
350C22C2×#8804611yescharacteristic
351C22#1171866211yescharacteristic
352C22#1171866611yescharacteristic
353C4—21no—
354C4—21no—
355C4—41no—
356C4—41no—
357C4—41no—
358C4—41no—
359C4—41no—
360C4—162no—
361C4—522no—
362C4—1041no—
363C4—1041no—
364C2—21no—
365C2—21no—
366C2—42no—
367C2—1042no—
368C2#1311336411yescharacteristic
369C2#1311647511yescharacteristic
370C2#1311649911yescharacteristic
subgroupG/H
centerC22C2×#88046
commutatorC22×C4×C13C22×C4
FrattiniC2×C22⋊C4C22×D13
FittingC13×#1820C2
socleC22×C13C2×#99
prime radical#11718621C22
cosocleC2×C13×C22⋊C4C23
hypercenter#1820D13
hypocenterC13#11798
LCSG ▷ C22×C4×C13 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#117 ◁ #1820

Complements

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

NH ≅ G/Ntype
2. #13113170C2semidirect
3. #13112835C2semidirect
5. C13×#1820C2semidirect
8. C2×C4×D52C4semidirect
11. #11718652C4semidirect
12. #11718644C4semidirect
17. C4×C4⋊Dic13C4semidirect
104. #1820D13semidirect
287. C13#11798semidirect

Maximal subgroups

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

subgroupindex
#131180722
#131131702
#131128352
#131128322
C13×#18202
#1179813