Finite Group Databasebeta

← #15757976

Subgroups — #15757976

Order 3328.

660 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 660 conjugacy classes of subgroups — too many to draw. Only its 143 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×#11718644C211yesmaximal, characteristic
2#13117454C211yesmaximal, characteristic
3#13114923C212yesmaximal
4#13112716C212yesmaximal
5C2×C13×#324C211yesmaximal, characteristic
6C22×C13×C4⋊C4C2211yescharacteristic
7C2×#88180—21no—
8C22×C4⋊Dic13C2211yescharacteristic
9C22×#6101—21no—
10C2×C13×C22⋊C8C2212yes—
11#11718873—21no—
12#11718873C2212yes—
13C2×#88071—21no—
14C2×#88071C2211yescharacteristic
15#11718646—24no—
16#11718644—22no—
17#11718644C414yescomplemented
18C13×#324—22no—
19#11718143—24no—
20C23×C4×C13D411yescharacteristic
21C23×C4×C13D411yescharacteristic
22C23×C4×C13C2311yescharacteristic
23C23×Dic13—21no—
24C23×Dic13—21no—
25C22×C8×C13—22no—
26C2×C13×C4⋊C4—22no—
27C2×C13×C4⋊C4—22no—
28C2×C13×C4⋊C4C2×C412yes—
29C2×C13×C4⋊C4D412yes—
30C2×C22⋊Dic13—22no—
31#88180—42no—
32#88180—42no—
33C2×C4⋊Dic13—22no—
34C2×C4⋊Dic13—22no—
35C2×C4⋊Dic13—22no—
36C2×C4⋊Dic13—21no—
37C2×C4⋊Dic13—22no—
38C2×C4⋊Dic13C2×C412yes—
39C2×C4⋊Dic13D414yes—
40C2×#6101—24no—
41C2×#6101—42no—
42C2×#6101—42no—
43C2×C4×Dic13—22no—
44C13×C22⋊C8—22no—
45C13×C22⋊C8—22no—
46#88071—22no—
47#88071—24no—
48#88071—21no—
49#88071—22no—
50#88071C2×C412yes—
51#9027—131nomaximal, Sylow
52C24×C13C2×D411yescharacteristic
53C22×C4×C13—21no—
54C22×C4×C13—21no—
55C22×C4×C13—21no—
56C22×C4×C13—21no—
57C22×C4×C13—21no—
58C22×C4×C13—21no—
59C22×C4×C13—42no—
60C22×C4×C13—42no—
61C22×C4×C13C22⋊C412yes—
62C22×C4×C13C22⋊C412yes—
63C22×C4×C13D812yes—
64C22×C4×C13SD1612yes—
65C22×C4×C13C22×C411yescharacteristic
66C22×C4×C13C2×D412yes—
67C22×C4×C13C2×D411yescharacteristic
68C22×C4×C13#4112yes—
69C22×Dic13—24no—
70C22×Dic13—22no—
71C22×Dic13—22no—
72C22×Dic13—24no—
73C22×Dic13—42no—
74C22×Dic13—41no—
75C22×Dic13—41no—
76C22×Dic13—41no—
77C22×Dic13—41no—
78C22×Dic13—41no—
79C22×Dic13—41no—
80C22×Dic13—41no—
81C22×Dic13—41no—
82C2×C8×C13—44no—
83C2×C8×C13—42no—
84C13×C4⋊C4—24no—
85C13×C4⋊C4—24no—
86C22⋊Dic13—42no—
87C22⋊Dic13—42no—
88C4⋊Dic13—24no—
89C4⋊Dic13—44no—
90C4⋊Dic13—42no—
91C4⋊Dic13—44no—
92C4⋊Dic13—82no—
93#6101—48no—
94C4×Dic13—44no—
95C2×#398—131no—
96#2316—131no—
97#1823—132no—
98C2×#324D1311yescharacteristic
99#1294—132no—
100C23×C13—22no—
101C23×C13—22no—
102C23×C13C2×C22⋊C411yescharacteristic
103C23×C13#12011yescharacteristic
104C23×C13#12311yescharacteristic
105C23×C13C2×D811yescharacteristic
106C23×C13C2×SD1611yescharacteristic
107C23×C13AGL(1,ℤ/8)11yescharacteristic
108C23×C13#13711yescharacteristic
109C2×C4×C13—22no—
110C2×C4×C13—22no—
111C2×C4×C13—22no—
112C2×C4×C13—22no—
113C2×C4×C13—24no—
114C2×C4×C13—22no—
115C2×C4×C13—22no—
116C2×C4×C13—22no—
117C2×C4×C13—41no—
118C2×C4×C13—41no—
119C2×C4×C13—42no—
120C2×C4×C13—42no—
121C2×C4×C13—42no—
122C2×C4×C13—81no—
123C2×C4×C13#10214yes—
124C2×C4×C13C4×D412yes—
125C2×C4×C13#12112yes—
126C2×Dic13—24no—
127C2×Dic13—44no—
128C2×Dic13—44no—
129C2×Dic13—42no—
130C2×Dic13—42no—
131C2×Dic13—42no—
132C2×Dic13—42no—
133C2×Dic13—42no—
134C2×Dic13—44no—
135C2×Dic13—44no—
136C2×Dic13—44no—
137C2×Dic13—81no—
138C2×Dic13—81no—
139C2×Dic13—81no—
140C2×Dic13—81no—
141C8×C13—82no—
142C2×#117—261no—
143C22×C4⋊C4—131no—
144C22×C4⋊C4—261no—
145C22×C4⋊C4C2×D1311yescharacteristic
146C2×C22⋊C8C2×D1312yes—
147#398—134no—
148#398—262no—
149#389—264no—
150#380—132no—
151#380—261no—
152C2×#95—131no—
153C2×#95—261no—
154#340—264no—
155#324—22no—
156C22×C13—22no—
157C22×C13—22no—
158C22×C13—22no—
159C22×C13—22no—
160C22×C13—21no—
161C22×C13—21no—
162C22×C13—21no—
163C22×C13—21no—
164C22×C13#38611yescharacteristic
165C22×C13C2×#10211yescharacteristic
166C22×C13#41711yescharacteristic
167C22×C13#44711yescharacteristic
168C22×C13#44811yescharacteristic
169C22×C13#45612yes—
170C22×C13#45812yes—
171C22×C13#48011yescharacteristic
172C22×C13#48111yescharacteristic
173C4×C13—24no—
174C4×C13—22no—
175C4×C13—22no—
176C4×C13—42no—
177Dic13—44no—
178Dic13—84no—
179Dic13—82no—
180C23×C4—261no—
181C23×C4—261no—
182C23×C4D5211yescharacteristic
183C23×C4D5211yescharacteristic
184C23×C4C22×D1311yescharacteristic
185C22×C8—22no—
186#117—522no—
187#117—522no—
188C2×C4⋊C4—22no—
189C2×C4⋊C4—22no—
190C2×C4⋊C4—132no—
191C2×C4⋊C4—134no—
192C2×C4⋊C4—262no—
193C2×C4⋊C4—262no—
194C2×C4⋊C4—262no—
195C2×C4⋊C4—264no—
196C2×C4⋊C4—261no—
197C2×C4⋊C4—262no—
198C2×C4⋊C4—522no—
199C2×C4⋊C4—522no—
200C2×C4⋊C4C4×D1312yes—
201C2×C4⋊C4C22⋊D1312yes—
202C2×C22⋊C4—262no—
203C2×C42—262no—
204C22⋊C8—22no—
205C22⋊C8—22no—
206#95—132no—
207#95—262no—
208#95—264no—
209#95—262no—
210#95—261no—
211C2×C13—21no—
212C2×C13—21no—
213C2×C13—21no—
214C2×C13—21no—
215C2×C13#161012yes—
216C2×C13#161112yes—
217C2×C13#187411yescharacteristic
218C2×C13#188611yescharacteristic
219C2×C13#189011yescharacteristic
220C24C2×D5211yescharacteristic
221C22×C4—21no—
222C22×C4—21no—
223C22×C4—21no—
224C22×C4—21no—
225C22×C4—21no—
226C22×C4—21no—
227C22×C4—42no—
228C22×C4—42no—
229C22×C4—264no—
230C22×C4—262no—
231C22×C4—264no—
232C22×C4—262no—
233C22×C4—522no—
234C22×C4—521no—
235C22×C4—521no—
236C22×C4—521no—
237C22×C4—521no—
238C22×C4—521no—
239C22×C4—521no—
240C22×C4—521no—
241C22×C4—521no—
242C22×C4#609512yes—
243C22×C4D10412yes—
244C22×C4#610312yes—
245C22×C4#610312yes—
246C22×C4C2×C4×D1311yescharacteristic
247C22×C4D4×D1312yes—
248C22×C4#612912yes—
249C22×C4C2×C22⋊D1311yescharacteristic
250C2×C8—44no—
251C2×C8—42no—
252C4⋊C4—24no—
253C4⋊C4—24no—
254C4⋊C4—264no—
255C4⋊C4—524no—
256C4⋊C4—524no—
257C4⋊C4—522no—
258C4⋊C4—528no—
259C4⋊C4—1042no—
260C22⋊C4—522no—
261C22⋊C4—522no—
262C42—524no—
263C13#902711yescharacteristic, complemented, Sylow
264C23—22no—
265C23—22no—
266C23#8813611yescharacteristic
267C23#8814011yescharacteristic
268C23C2×#609511yescharacteristic
269C23C2×D10411yescharacteristic
270C23#8816211yescharacteristic
271C23#8816311yescharacteristic
272C23C2×#610311yescharacteristic
273C2×C4—24no—
274C2×C4—22no—
275C2×C4—22no—
276C2×C4—22no—
277C2×C4—22no—
278C2×C4—22no—
279C2×C4—22no—
280C2×C4—22no—
281C2×C4—41no—
282C2×C4—42no—
283C2×C4—41no—
284C2×C4—42no—
285C2×C4—42no—
286C2×C4—81no—
287C2×C4—264no—
288C2×C4—522no—
289C2×C4—524no—
290C2×C4—524no—
291C2×C4—522no—
292C2×C4—524no—
293C2×C4—524no—
294C2×C4—522no—
295C2×C4—522no—
296C2×C4—522no—
297C2×C4—524no—
298C2×C4—1041no—
299C2×C4—1041no—
300C2×C4—1041no—
301C2×C4—1041no—
302C2×C4#8806114yes—
303C2×C4#8813512yes—
304C2×C4#8819312yes—
305C8—82no—
306C22—21no—
307C22—21no—
308C22—21no—
309C22—21no—
310C22—22no—
311C22—22no—
312C22—22no—
313C22—22no—
314C22#1171839311yescharacteristic
315C22#1171839611yescharacteristic
316C22#1171839711yescharacteristic
317C22#1171839911yescharacteristic
318C22#1171840312yes—
319C22#1171841312yes—
320C22#1171861911yescharacteristic
321C22C2×#8806111yescharacteristic
322C22#1171879411yescharacteristic
323C4—24no—
324C4—22no—
325C4—22no—
326C4—42no—
327C4—524no—
328C4—1042no—
329C4—1044no—
330C2—21no—
331C2—21no—
332C2—21no—
333C2—21no—
334C2#1311384112yes—
335C2#1311384612yes—
336C2#1311515111yescharacteristic
337C2#1311522711yescharacteristic
338C2#1311524711yescharacteristic
subgroupG/H
centerC23#88136
commutatorC22×C4×C13C22×C4
FrattiniC23×C4C22×D13
FittingC2×C13×#324C2
socleC23×C13#120
prime radicalC24×C13C2×D4
cosocleC23×C4×C13C23
hypercenterC2×#324D13
hypocenterC13#9027
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#324

Complements

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

NH ≅ G/Ntype
17. #11718644C4semidirect
263. C13#9027semidirect

Maximal subgroups

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

subgroupindex
C2×#117186442
#131174542
#131149232
#131127162
C2×C13×#3242
#902713