Finite Group Databasebeta

← #15750009

Subgroups — #15750009

Order 3328.

376 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 376 conjugacy classes of subgroups — too many to draw. Only its 87 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#13115631C211yesmaximal, characteristic
2#13114824C211yesmaximal, characteristic
3C13×#1799C211yesmaximal, characteristic
4C2×C4×D4×C13C2211yescharacteristic
5C2×C13×#99—21no—
6C13×#380—21no—
7C2×#88074—21no—
8#11718873—21no—
9C2×C22⋊#1055—21no—
10C2×C22⋊#1055—21no—
11C2×C4⋊#1055C411yescharacteristic, complemented
12C2×C4×#1055C411yescharacteristic, complemented
13C13×#342C412yescomplemented
14#11718118C412yescomplemented
15C22×D4×C13D411yescharacteristic
16C23×C4×C13D411yescharacteristic
17C23×C4×C13D411yescharacteristic
18C4×D4×C13—41no—
19C4×D4×C13—41no—
20C2×C13×C4⋊C4—41no—
21C2×C13×C4⋊C4Q811yescharacteristic
22C2×C13×C22⋊C4—22no—
23C2×C13×C22⋊C4C2×C411yescharacteristic
24C2×C13×C22⋊C4C2×C411yescharacteristic
25C2×C42×C13C2×C411yescharacteristic
26C2×C22⋊Dic13—22no—
27C2×C4⋊Dic13—41no—
28C22×#1055—21no—
29C22×#1055—21no—
30C13×#99—41no—
31C13×#99—41no—
32C13×#95—41no—
33#88074—41no—
34#88074—41no—
35#88071—41no—
36C22⋊#1055—42no—
37C22⋊#1055—42no—
38C4⋊#1055—41no—
39C4×#1055—41no—
40#7237—131nomaximal, Sylow
41C24×C13C22⋊C411yescharacteristic
42C24×C13C22⋊C411yescharacteristic
43C2×D4×C13—41no—
44C2×D4×C13—41no—
45C2×D4×C13D811yescharacteristic
46C2×D4×C13SD1611yescharacteristic
47C2×D4×C13SD1611yescharacteristic
48C2×D4×C13Q1611yescharacteristic
49C22×C4×C13—21no—
50C22×C4×C13—21no—
51C22×C4×C13—21no—
52C22×C4×C13—21no—
53C22×C4×C13—41no—
54C22×C4×C13—41no—
55C22×C4×C13—41no—
56C22×C4×C13—41no—
57C22×C4×C13—42no—
58C22×C4×C13C4211yescharacteristic
59C22×C4×C13C22⋊C411yescharacteristic
60C22×C4×C13C4⋊C411yescharacteristic
61C22×C4×C13C4⋊C411yescharacteristic
62C22×C4×C13C4⋊C411yescharacteristic
63C22×Dic13—42no—
64C13×C4⋊C4—41no—
65C13×C4⋊C4—81no—
66C13×C4⋊C4—81no—
67C13×C22⋊C4—41no—
68C13×C22⋊C4—41no—
69C13×C22⋊C4—42no—
70C13×C22⋊C4—42no—
71C42×C13—21no—
72C42×C13—21no—
73C22⋊Dic13—42no—
74C22⋊Dic13—42no—
75C4⋊Dic13—81no—
76C4⋊Dic13—81no—
77C2×#1055—22no—
78C2×#1055—41no—
79C2×#1055—41no—
80C2×#1055—41no—
81C2×#1055—41no—
82C2×#1055—41no—
83#1954—131no—
84#1799—131no—
85#1799D1311yescharacteristic
86C23×C13—21no—
87C23×C13—21no—
88C23×C13—21no—
89C23×C13—21no—
90C23×C13—41no—
91C23×C13—41no—
92C23×C13—41no—
93C23×C13—41no—
94C23×C13#9511yescharacteristic
95C23×C13#10211yescharacteristic
96C23×C13#10211yescharacteristic
97C23×C13#10311yescharacteristic
98C23×C13#10311yescharacteristic
99D4×C13—41no—
100D4×C13—41no—
101D4×C13—41no—
102D4×C13—41no—
103C2×C4×C13—21no—
104C2×C4×C13—21no—
105C2×C4×C13—21no—
106C2×C4×C13—21no—
107C2×C4×C13—21no—
108C2×C4×C13—21no—
109C2×C4×C13—21no—
110C2×C4×C13—41no—
111C2×C4×C13—41no—
112C2×C4×C13—41no—
113C2×C4×C13—41no—
114C2×C4×C13—41no—
115C2×C4×C13—41no—
116C2×C4×C13—41no—
117C2×C4×C13—81no—
118C2×C4×C13—81no—
119C2×C4×C13—82no—
120C2×C4×C13—82no—
121C2×C4×C13—82no—
122C2×C4×C13#9911yescharacteristic
123C2×C4×C13#9911yescharacteristic
124C2×C4×C13#10611yescharacteristic
125C2×C4×C13#10711yescharacteristic
126C2×Dic13—82no—
127C2×Dic13—82no—
128C2×Dic13—82no—
129#1055—42no—
130#1055—81no—
131C2×C4×D4C2×D1311yescharacteristic
132C2×C4⋊C8—131no—
133C2×#99—21no—
134C2×#99—261no—
135C2×C22⋊C8—261no—
136C2×C22⋊C8—261no—
137C2×C4×C8—131no—
138#380—21no—
139#380—261no—
140#342—132no—
141#342Dic1312yescomplemented
142C22×C13—21no—
143C22×C13—21no—
144C22×C13—21no—
145C22×C13—21no—
146C22×C13—21no—
147C22×C13—21no—
148C22×C13—41no—
149C22×C13—41no—
150C22×C13—41no—
151C22×C13—41no—
152C22×C13—41no—
153C22×C13—41no—
154C22×C13—41no—
155C22×C13—41no—
156C22×C13—81no—
157C22×C13—81no—
158C22×C13H(3,ℤ/4)11yescharacteristic
159C22×C13#34011yescharacteristic
160C22×C13#34211yescharacteristic
161C4×C13—21no—
162C4×C13—21no—
163C4×C13—21no—
164C4×C13—41no—
165C4×C13—41no—
166C4×C13—41no—
167C4×C13—162no—
168C4×C13#35311yescharacteristic
169C4×C13#35411yescharacteristic
170Dic13—162no—
171C22×D4C22⋊D1311yescharacteristic
172C23×C4D5211yescharacteristic
173C23×C4C22⋊D1311yescharacteristic
174C22×C8—261no—
175C22×C8—261no—
176C4×D4—41no—
177C4×D4—41no—
178C2×C4⋊C4—41no—
179C2×C4⋊C4—521no—
180C2×C4⋊C4Dic2611yescharacteristic
181C2×C22⋊C4—22no—
182C2×C22⋊C4—262no—
183C2×C22⋊C4C4×D1311yescharacteristic
184C2×C22⋊C4C2×Dic1311yescharacteristic
185C2×C42C4×D1311yescharacteristic
186C4⋊C8—521no—
187#99—41no—
188#99—41no—
189#99—521no—
190#99—521no—
191C22⋊C8—522no—
192C22⋊C8—522no—
193C4×C8—521no—
194#95—41no—
195#95—521no—
196C2×C13—21no—
197C2×C13—21no—
198C2×C13—41no—
199C2×C13—41no—
200C2×C13—41no—
201C2×C13—41no—
202C2×C13#128911yescharacteristic
203C2×C13#139111yescharacteristic
204C2×C13#139311yescharacteristic
205C24#610311yescharacteristic
206C24C22⋊Dic1311yescharacteristic
207C2×D4—41no—
208C2×D4—41no—
209C2×D4#610411yescharacteristic
210C2×D4#610511yescharacteristic
211C2×D4#610611yescharacteristic
212C2×D4#610711yescharacteristic
213C22×C4—21no—
214C22×C4—21no—
215C22×C4—21no—
216C22×C4—21no—
217C22×C4—41no—
218C22×C4—41no—
219C22×C4—41no—
220C22×C4—41no—
221C22×C4—42no—
222C22×C4—522no—
223C22×C4C4×Dic1311yescharacteristic
224C22×C4#610111yescharacteristic
225C22×C4#610111yescharacteristic
226C22×C4C4⋊Dic1311yescharacteristic
227C22×C4#610311yescharacteristic
228C2×C8—262no—
229C2×C8—521no—
230C2×C8—521no—
231C2×C8—521no—
232C2×C8—521no—
233C2×C8—521no—
234C4⋊C4—41no—
235C4⋊C4—81no—
236C4⋊C4—81no—
237C4⋊C4—1041no—
238C4⋊C4—1041no—
239C22⋊C4—41no—
240C22⋊C4—41no—
241C22⋊C4—42no—
242C22⋊C4—42no—
243C22⋊C4—522no—
244C22⋊C4—522no—
245C42—21no—
246C42—21no—
247C13#723711yescharacteristic, complemented, Sylow
248C23—21no—
249C23—21no—
250C23—21no—
251C23—21no—
252C23—41no—
253C23—41no—
254C23—41no—
255C23—41no—
256C23#8804911yescharacteristic
257C23#8805011yescharacteristic
258C23#8807111yescharacteristic
259C23#8807211yescharacteristic
260C23#8807511yescharacteristic
261D4—41no—
262D4—41no—
263D4—41no—
264D4—41no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—81no—
280C2×C4—81no—
281C2×C4—82no—
282C2×C4—82no—
283C2×C4—82no—
284C2×C4—1042no—
285C2×C4—1042no—
286C2×C4—1042no—
287C2×C4#8804611yescharacteristic
288C2×C4#8804611yescharacteristic
289C2×C4#8804711yescharacteristic
290C2×C4#8804811yescharacteristic
291C8—522no—
292C8—1041no—
293C22—21no—
294C22—21no—
295C22—21no—
296C22—21no—
297C22—21no—
298C22—21no—
299C22—41no—
300C22—41no—
301C22—41no—
302C22—41no—
303C22—41no—
304C22—41no—
305C22—41no—
306C22—41no—
307C22—81no—
308C22—81no—
309C22#1171811911yescharacteristic
310C22#1171812111yescharacteristic
311C22#1171812311yescharacteristic
312C4—21no—
313C4—21no—
314C4—21no—
315C4—41no—
316C4—41no—
317C4—41no—
318C4—162no—
319C4—2082no—
320C4#1171806511yescharacteristic
321C4#1171806611yescharacteristic
322C2—21no—
323C2—21no—
324C2—41no—
325C2—41no—
326C2—41no—
327C2—41no—
328C2#1311270311yescharacteristic
329C2#1311295611yescharacteristic
330C2#1311296011yescharacteristic
subgroupG/H
centerC22#11718119
commutatorC22×C4×C13C42
FrattiniC2×C4×D4C2×D13
FittingC13×#1799C2
socleC22×C13#342
prime radicalC22×D4×C13D4
cosocleC2×C4×D4×C13C22
hypercenter#1799D13
hypocenterC13#7237
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #1799

Complements

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

NH ≅ G/Ntype
11. C2×C4⋊#1055C4semidirect
12. C2×C4×#1055C4semidirect
13. C13×#342C4semidirect
14. #11718118C4semidirect
141. #342Dic13semidirect
247. C13#7237semidirect

Maximal subgroups

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

subgroupindex
#131156312
#131148242
C13×#17992
#723713