Finite Group Databasebeta

← #15773800

Subgroups — #15773800

Order 3328.

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

normal subgroups only

This group has 432 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#13120523C211yesmaximal, characteristic
2#13113150C211yesmaximal, characteristic, complemented
3#13112856C212yesmaximal, complemented
4#13112832C212yesmaximal
5C13×#1820C211yesmaximal, characteristic, complemented
6C2×C13×#117C2211yescharacteristic
7C2×#88129C411yescharacteristic, complemented
8C13×#381—21no—
9#11718874—21no—
10#11718652C411yescharacteristic, complemented
11#11718651—21no—
12#11718640C411yescharacteristic, complemented
13#11718621C2211yescharacteristic
14#11718618—21no—
15#11718608C2211yescharacteristic
16#11718601—21no—
17#11718593C411yescharacteristic, complemented
18#11718586—21no—
19C13×#342—21no—
20C13×#342C2212yes—
21#11718120—21no—
22#11718117C2212yes—
23C23×C4×C13D411yescharacteristic
24C22×C22⋊D13—21no—
25C22×D52C2×C411yescharacteristic
26C22×Dic26C2×C411yescharacteristic
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—
37C2×#6103—21no—
38C2×#6103—21no—
39C2×#6103—21no—
40C2×#6103—21no—
41C2×#6103—21no—
42C2×#6101—21no—
43C2×C4×Dic13—21no—
44#88129—41no—
45#88129—41no—
46C13×#95—41no—
47C13×#95—41no—
48#88071—21no—
49#88071—21no—
50#88071—21no—
51#88071C2×C411yescharacteristic
52#88071C2×C411yescharacteristic
53C22⋊#1055—22no—
54C4⋊#1055—41no—
55C4×#1055—41no—
56#11844—131nomaximal, Sylow
57C24×C13C2×D411yescharacteristic
58C23×D13—21no—
59C22×C4×C13—22no—
60C22×C4×C13—21no—
61C22×C4×C13—21no—
62C22×C4×C13—41no—
63C22×C4×C13—42no—
64C22×C4×C13C22⋊C411yescharacteristic
65C22×C4×C13C22⋊C411yescharacteristic
66C22×C4×C13C22⋊C411yescharacteristic
67C22×C4×C13C22⋊C411yescharacteristic
68C22×C4×C13C22×C411yescharacteristic
69C22×C4×C13C2×D411yescharacteristic
70C2×C22⋊D13—42no—
71C2×C22⋊D13—42no—
72C2×C22⋊D13—81no—
73C22×Dic13—21no—
74C22×Dic13—21no—
75C22×Dic13—21no—
76C2×D52—41no—
77C2×D52—81no—
78C2×Dic26—41no—
79C2×Dic26—81no—
80C13×C4⋊C4—41no—
81C13×C4⋊C4—41no—
82C13×C22⋊C4—41no—
83C13×C22⋊C4—41no—
84C13×C22⋊C4—42no—
85C13×C22⋊C4—42no—
86C42×C13—21no—
87C42×C13—21no—
88C42×C13—21no—
89C42×C13—21no—
90C22⋊Dic13—81no—
91#6103—42no—
92#6103—42no—
93#6103—42no—
94#6103—41no—
95#6103—41no—
96#6103—81no—
97#6101—81no—
98C4×Dic13—42no—
99C2×#1055—42no—
100#2610—131no—
101#1820D1311yescharacteristic, complemented
102#1458—131no—
103#1351—132no—
104#1343—132no—
105C23×C13—21no—
106C23×C13—21no—
107C23×C13—41no—
108C23×C13—41no—
109C23×C13C2×C22⋊C411yescharacteristic
110C23×C13#13512yes—
111C22×D13—41no—
112C22×D13—41no—
113C22×D13—41no—
114C22×D13—41no—
115C22×D13—41no—
116C22×D13—41no—
117C22×D13—41no—
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—21no—
127C2×C4×C13—42no—
128C2×C4×C13—42no—
129C2×C4×C13—41no—
130C2×C4×C13—41no—
131C2×C4×C13—41no—
132C2×C4×C13—41no—
133C2×C4×C13—82no—
134C2×C4×C13—82no—
135C2×C4×C13—82no—
136C2×C4×C13#9911yescharacteristic
137C2×C4×C13#9911yescharacteristic
138C22⋊D13—84no—
139C2×Dic13—22no—
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—82no—
149Dic26—82no—
150#1055—82no—
151C2×#124—131no—
152C2×#117C2×D1311yescharacteristic
153#431—261no—
154#395—131no—
155#394—131no—
156#393—131no—
157#392—131no—
158#390—261no—
159#388—261no—
160#388—261no—
161#386—261no—
162#381—21no—
163#376—131no—
164#342—21no—
165#342C2×D1312yes—
166#324—261no—
167#323—132no—
168C22×C13—21no—
169C22×C13—21no—
170C22×C13—22no—
171C22×C13—42no—
172C22×C13—41no—
173C22×C13—41no—
174C22×C13—81no—
175C22×C13C2×#9911yescharacteristic
176C22×C13#41611yescharacteristic
177C22×C13#42111yescharacteristic
178C2×D13—81no—
179C2×D13—81no—
180C2×D13—81no—
181C2×D13—81no—
182C2×D13—81no—
183C2×D13—81no—
184C2×D13—81no—
185C4×C13—21no—
186C4×C13—21no—
187C4×C13—41no—
188C4×C13—41no—
189C4×C13—41no—
190C4×C13—41no—
191C4×C13—41no—
192C4×C13—162no—
193Dic13—42no—
194Dic13—81no—
195Dic13—81no—
196C22×Q8—131no—
197C22×D4—131no—
198C22×D4—261no—
199C23×C4C22⋊D1311yescharacteristic
200#124—521no—
201#124—521no—
202#117—41no—
203#117—41no—
204C2×C4⋊C4—261no—
205C2×C4⋊C4C4×D1311yescharacteristic
206C2×C4⋊C4D5211yescharacteristic
207C2×C22⋊C4—22no—
208C2×C22⋊C4—261no—
209C2×C22⋊C4—261no—
210C2×C22⋊C4—261no—
211C2×C22⋊C4—261no—
212C2×C22⋊C4—261no—
213C2×C22⋊C4—261no—
214C2×C22⋊C4C22⋊D1311yescharacteristic
215C2×C22⋊C4C22×D1311yescharacteristic
216C2×C42—261no—
217C2×C42C4×D1311yescharacteristic
218C2×C42D5211yescharacteristic
219C4⋊C8—521no—
220C22⋊C8—262no—
221C4×C8—521no—
222#95—41no—
223#95—41no—
224#95—131no—
225#95—131no—
226#95—261no—
227#95—261no—
228#95—261no—
229C2×C13—21no—
230C2×C13—21no—
231C2×C13—42no—
232C2×C13#151611yescharacteristic
233C2×C13#212211yescharacteristic
234C2×C13#212611yescharacteristic
235D13—161no—
236C24—261no—
237C24C2×C22⋊D1311yescharacteristic
238C2×Q8—521no—
239C2×Q8—1041no—
240C2×D4—521no—
241C2×D4—522no—
242C2×D4—522no—
243C2×D4—1041no—
244C2×D4—1041no—
245C22×C4—22no—
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—41no—
249C22×C4—42no—
250C22×C4—261no—
251C22×C4—261no—
252C22×C4—261no—
253C22×C4#610311yescharacteristic
254C22×C4#610311yescharacteristic
255C22×C4#610311yescharacteristic
256C22×C4#610311yescharacteristic
257C22×C4C2×C4×D1311yescharacteristic
258C22×C4C2×D5211yescharacteristic
259C2×C8—522no—
260C4⋊C4—41no—
261C4⋊C4—41no—
262C4⋊C4—1041no—
263C22⋊C4—41no—
264C22⋊C4—41no—
265C22⋊C4—42no—
266C22⋊C4—42no—
267C22⋊C4—522no—
268C22⋊C4—522no—
269C22⋊C4—522no—
270C22⋊C4—521no—
271C22⋊C4—521no—
272C22⋊C4—1041no—
273C22⋊C4—1041no—
274C42—21no—
275C42—21no—
276C42—21no—
277C42—21no—
278C42—522no—
279C13#1184411yescharacteristic, complemented, Sylow
280C23—21no—
281C23—21no—
282C23—41no—
283C23—41no—
284C23—521no—
285C23—521no—
286C23—521no—
287C23—521no—
288C23—521no—
289C23—521no—
290C23—521no—
291C23C2×#610311yescharacteristic
292C23#8820412yes—
293Q8—1042no—
294D4—1042no—
295D4—1044no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—42no—
306C2×C4—42no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—82no—
312C2×C4—82no—
313C2×C4—82no—
314C2×C4—262no—
315C2×C4—521no—
316C2×C4—521no—
317C2×C4—521no—
318C2×C4—521no—
319C2×C4—521no—
320C2×C4—521no—
321C2×C4—521no—
322C2×C4—521no—
323C2×C4#8804611yescharacteristic
324C2×C4#8804611yescharacteristic
325C8—1042no—
326C22—21no—
327C22—21no—
328C22—22no—
329C22—42no—
330C22—41no—
331C22—41no—
332C22—81no—
333C22—1041no—
334C22—1041no—
335C22—1041no—
336C22—1041no—
337C22—1041no—
338C22—1041no—
339C22—1041no—
340C22C2×#8804611yescharacteristic
341C22#1171866311yescharacteristic
342C22#1171866611yescharacteristic
343C4—21no—
344C4—21no—
345C4—41no—
346C4—41no—
347C4—41no—
348C4—41no—
349C4—41no—
350C4—162no—
351C4—522no—
352C4—1041no—
353C4—1041no—
354C2—21no—
355C2—21no—
356C2—42no—
357C2—2081no—
358C2#1311339011yescharacteristic
359C2#1311648511yescharacteristic
360C2#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#11844
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. #13113150C2semidirect
3. #13112856C2semidirect
5. C13×#1820C2semidirect
7. C2×#88129C4semidirect
10. #11718652C4semidirect
12. #11718640C4semidirect
17. #11718593C4semidirect
101. #1820D13semidirect
279. C13#11844semidirect

Maximal subgroups

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

subgroupindex
#131205232
#131131502
#131128562
#131128322
C13×#18202
#1184413