Finite Group Databasebeta

← #15763483

Subgroups — #15763483

Order 3328.

772 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 772 conjugacy classes of subgroups — too many to draw. Only its 121 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
1C2×#11718695C212yesmaximal, complemented
2C2×#11718129C212yesmaximal, complemented
3#13113105C211yesmaximal, characteristic, complemented
4#13112679C211yesmaximal, characteristic, complemented
5C13×#2656C211yesmaximal, characteristic
6C2×C13×#121—22no—
7C2×C13×#121C2212yes—
8C22×C4⋊Dic13C2211yescharacteristic
9C13×#399—22no—
10C13×#392—22no—
11C2×C13×#95C2211yescharacteristic
12C2×#88072—22no—
13C2×#88071—22no—
14C2×#88071C2211yescharacteristic
15C2×C22⋊#1055C2212yes—
16#11718695—24no—
17#11718695—24no—
18C2×#88048—22no—
19#11718129—24no—
20C22×D4×C13—22no—
21C22×D4×C13—22no—
22C22×D4×C13D412yes—
23C23×C4×C13D412yes—
24C23×C4×C13C2311yescharacteristic
25C23×Dic13—21no—
26C23×Dic13—21no—
27C13×#121—22no—
28C13×#121—22no—
29C13×#121—22no—
30C13×#121—22no—
31C13×#121—44no—
32C13×#121—44no—
33C2×C13×C4⋊C4—22no—
34C2×C13×C4⋊C4D412yes—
35C2×C13×C22⋊C4—24no—
36C2×C13×C22⋊C4—22no—
37C2×C4⋊Dic13—22no—
38C2×C4⋊Dic13—22no—
39C2×C4⋊Dic13—21no—
40C2×C4⋊Dic13D412yescomplemented
41C22×#1055—22no—
42C13×#95—22no—
43#88072—28no—
44#88071—22no—
45#88071—44no—
46C22⋊#1055—22no—
47C22⋊#1055D414yescomplemented
48#88048—28no—
49#9968—131nomaximal, Sylow
50C24×C13—22no—
51C24×C13C2×D411yescharacteristic
52C2×D4×C13—22no—
53C2×D4×C13—22no—
54C2×D4×C13—44no—
55C2×D4×C13—44no—
56C2×D4×C13—42no—
57C2×D4×C13—42no—
58C2×D4×C13—44no—
59C2×D4×C13—44no—
60C2×D4×C13—82no—
61C2×D4×C13—82no—
62C22×C4×C13—22no—
63C22×C4×C13—22no—
64C22×C4×C13—22no—
65C22×C4×C13—42no—
66C22×C4×C13—42no—
67C22×C4×C13—42no—
68C22×C4×C13SD1614yes—
69C22×C4×C13C2×D411yescharacteristic
70C22×C4×C13C2×D412yes—
71C22×C4×C13C2×D412yes—
72C22×C4×C13#4111yescharacteristic
73C22×Dic13—22no—
74C22×Dic13—22no—
75C22×Dic13—42no—
76C22×Dic13—41no—
77C22×Dic13—42no—
78C22×Dic13—42no—
79C22×Dic13—41no—
80C22×Dic13—41no—
81C22×Dic13—41no—
82C22×Dic13—42no—
83C13×C4⋊C4—22no—
84C13×C4⋊C4—22no—
85C13×C4⋊C4—44no—
86C13×C22⋊C4—48no—
87C13×C22⋊C4—42no—
88C13×C22⋊C4—42no—
89C4⋊Dic13—24no—
90C4⋊Dic13—42no—
91C2×#1055—24no—
92C2×#1055—44no—
93C2×#481—132no—
94#2656D1311yescharacteristic
95C2×#327—132no—
96#1445—131no—
97#1280—131no—
98C23×C13—21no—
99C23×C13—21no—
100C23×C13—22no—
101C23×C13—42no—
102C23×C13—44no—
103C23×C13—42no—
104C23×C13—42no—
105C23×C13—44no—
106C23×C13#12011yescharacteristic
107C23×C13#12111yescharacteristic
108C23×C13#12711yescharacteristic
109C23×C13C2×SD1612yes—
110C23×C13AGL(1,ℤ/8)12yes—
111D4×C13—44no—
112D4×C13—82no—
113D4×C13—88no—
114D4×C13—84no—
115D4×C13—82no—
116D4×C13—82no—
117C2×C4×C13—24no—
118C2×C4×C13—24no—
119C2×C4×C13—41no—
120C2×C4×C13—42no—
121C2×C4×C13—41no—
122C2×C4×C13—42no—
123C2×C4×C13—42no—
124C2×C4×C13—44no—
125C2×C4×C13—42no—
126C2×C4×C13—44no—
127C2×C4×C13—82no—
128C2×C4×C13#12012yes—
129C2×C4×C13#12112yes—
130C2×Dic13—44no—
131C2×Dic13—42no—
132C2×Dic13—44no—
133C2×Dic13—42no—
134C2×Dic13—82no—
135C2×Dic13—81no—
136C2×Dic13—82no—
137C2×Dic13—81no—
138C2×Dic13—81no—
139C2×Dic13—81no—
140#1055—44no—
141C2×#121—22no—
142C2×#121C2×D1312yes—
143C22×C4⋊C4—131no—
144#481—264no—
145#481—264no—
146C2×#106—262no—
147C2×#102—262no—
148C2×C22⋊C8—132no—
149#399—22no—
150#392—22no—
151C2×#95—131no—
152C2×#95—262no—
153C2×#95C2×D1311yescharacteristic
154#327—264no—
155C22×C13—22no—
156C22×C13—22no—
157C22×C13—22no—
158C22×C13—22no—
159C22×C13—21no—
160C22×C13—21no—
161C22×C13—21no—
162C22×C13—21no—
163C22×C13—84no—
164C22×C13—84no—
165C22×C13—82no—
166C22×C13—82no—
167C22×C13—82no—
168C22×C13#39211yescharacteristic
169C22×C13#45012yes—
170C22×C13#45311yescharacteristic
171C22×C13#45411yescharacteristic
172C22×C13#45812yes—
173C22×C13#46012yes—
174C22×C13#49211yescharacteristic
175C22×C13#49611yescharacteristic
176C4×C13—22no—
177C4×C13—22no—
178C4×C13—44no—
179C4×C13—82no—
180Dic13—82no—
181Dic13—82no—
182C22×D4—22no—
183C22×D4—22no—
184C22×D4C22⋊D1312yes—
185C23×C4—261no—
186C23×C4—261no—
187C23×C4C22⋊D1312yes—
188C23×C4C22×D1311yescharacteristic
189C22×C8—262no—
190#121—22no—
191#121—22no—
192#121—22no—
193#121—22no—
194#121—44no—
195#121—44no—
196C2×C4⋊C4—22no—
197C2×C4⋊C4—132no—
198C2×C4⋊C4—262no—
199C2×C4⋊C4—262no—
200C2×C4⋊C4—261no—
201C2×C4⋊C4C22⋊D1312yes—
202C2×C22⋊C4—24no—
203C2×C22⋊C4—22no—
204#106—268no—
205#102—268no—
206C22⋊C8—134no—
207C22⋊C8—262no—
208#95—22no—
209#95—262no—
210#95—524no—
211C2×C13—21no—
212C2×C13—22no—
213C2×C13—21no—
214C2×C13—162no—
215C2×C13#161312yes—
216C2×C13#161612yes—
217C2×C13#200611yescharacteristic
218C2×C13#201411yescharacteristic
219C2×C13#202211yescharacteristic
220C24—22no—
221C24C2×C22⋊D1311yescharacteristic
222C2×D4—22no—
223C2×D4—22no—
224C2×D4—44no—
225C2×D4—44no—
226C2×D4—44no—
227C2×D4—44no—
228C2×D4—42no—
229C2×D4—42no—
230C2×D4—82no—
231C2×D4—82no—
232C22×C4—22no—
233C22×C4—22no—
234C22×C4—22no—
235C22×C4—42no—
236C22×C4—42no—
237C22×C4—42no—
238C22×C4—262no—
239C22×C4—262no—
240C22×C4—522no—
241C22×C4—522no—
242C22×C4—521no—
243C22×C4—522no—
244C22×C4—522no—
245C22×C4—521no—
246C22×C4—521no—
247C22×C4—521no—
248C22×C4#610514yes—
249C22×C4D4×D1311yescharacteristic
250C22×C4D4×D1312yes—
251C22×C4#612911yescharacteristic
252C22×C4C2×C22⋊D1312yes—
253C2×C8—264no—
254C2×C8—524no—
255C4⋊C4—22no—
256C4⋊C4—22no—
257C4⋊C4—44no—
258C4⋊C4—264no—
259C4⋊C4—522no—
260C22⋊C4—48no—
261C22⋊C4—42no—
262C22⋊C4—42no—
263C13#996811yescharacteristic, complemented, Sylow
264C23—21no—
265C23—22no—
266C23—21no—
267C23—44no—
268C23—42no—
269C23—42no—
270C23—44no—
271C23—42no—
272C23#8818612yes—
273C23C2×#610512yes—
274C23#8819211yescharacteristic
275C23#8819411yescharacteristic
276C23#8820711yescharacteristic
277D4—44no—
278D4—82no—
279D4—88no—
280D4—82no—
281D4—84no—
282D4—82no—
283C2×C4—24no—
284C2×C4—24no—
285C2×C4—41no—
286C2×C4—42no—
287C2×C4—41no—
288C2×C4—42no—
289C2×C4—42no—
290C2×C4—44no—
291C2×C4—44no—
292C2×C4—42no—
293C2×C4—82no—
294C2×C4—524no—
295C2×C4—522no—
296C2×C4—524no—
297C2×C4—522no—
298C2×C4—1042no—
299C2×C4—1041no—
300C2×C4—1042no—
301C2×C4—1041no—
302C2×C4—1041no—
303C2×C4—1041no—
304C2×C4#8819112yes—
305C2×C4#8819312yes—
306C8—524no—
307C22—22no—
308C22—22no—
309C22—22no—
310C22—22no—
311C22—21no—
312C22—21no—
313C22—21no—
314C22—21no—
315C22—84no—
316C22—84no—
317C22—82no—
318C22—82no—
319C22—82no—
320C22#1171873511yescharacteristic
321C22#1171873612yes—
322C22#1171873711yescharacteristic
323C22#1171887912yes—
324C22#1171888411yescharacteristic
325C22#1171890211yescharacteristic
326C22#1171890412yes—
327C22#1171890611yescharacteristic
328C4—22no—
329C4—22no—
330C4—44no—
331C4—82no—
332C4—1042no—
333C4—1042no—
334C2—21no—
335C2—22no—
336C2—21no—
337C2—162no—
338C2#1311385612yes—
339C2#1311387312yes—
340C2#1311587811yescharacteristic
341C2#1311592411yescharacteristic
342C2#1311596511yescharacteristic
subgroupG/H
centerC23#88207
commutator, cosocleC23×C4×C13C23
FrattiniC23×C4C22×D13
Fitting, prime radicalC13×#2656C2
socleC23×C13#120
hypercenter#2656D13
hypocenterC13#9968
LCSG ▷ C23×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2656

Complements

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

NH ≅ G/Ntype
1. C2×#11718695C2semidirect
2. C2×#11718129C2semidirect
3. #13113105C2semidirect
4. #13112679C2semidirect
40. C2×C4⋊Dic13D4semidirect
47. C22⋊#1055D4semidirect
263. C13#9968semidirect

Maximal subgroups

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

subgroupindex
C2×#117186952
C2×#117181292
#131131052
#131126792
C13×#26562
#996813