Finite Group Databasebeta

← #16780365

Subgroups — #16780365

Order 3328.

698 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13130562C212yesmaximal
2C2×#11718286C212yesmaximal
3#13129674C212yesmaximal
4C2×#11718310C211yesmaximal, characteristic
5C22×#6101C411yescharacteristic
6C22×#6101C2211yescharacteristic
7C22×C4×Dic13C411yescharacteristic
8C22×C4×Dic13C411yescharacteristic
9C22×C4×Dic13C2211yescharacteristic
10C2×C22⋊#1057C2214yes—
11C2×#88110—22no—
12C2×C13×#95C411yescharacteristic
13C2×#88071C2211yescharacteristic
14#11718310—22no—
15#11718310—22no—
16#11718290—22no—
17#11718286C418yescomplemented
18C23×C4×C13C2×C411yescharacteristic
19C23×C4×C13C2×C411yescharacteristic
20C23×C4×C13C2×C411yescharacteristic
21C23×Dic13C2×C411yescharacteristic
22C23×Dic13C2×C411yescharacteristic
23C23×Dic13C2×C411yescharacteristic
24C23×Dic13C2311yescharacteristic
25C22×#1057—24no—
26C2×#6101—22no—
27C2×#6101—22no—
28C2×#6101—22no—
29C2×#6101—22no—
30C2×#6101—22no—
31C2×#6101C2×C414yes—
32C2×C4×Dic13—22no—
33C2×C4×Dic13—21no—
34C2×C4×Dic13—21no—
35C2×C4×Dic13—22no—
36C2×C4×Dic13—21no—
37C2×C4×Dic13—21no—
38C2×C4×Dic13—42no—
39C2×C4×Dic13—42no—
40C2×C4×Dic13D412yes—
41C2×C4×Dic13D412yes—
42C22⋊#1057—24no—
43C22⋊#1057C2×C418yes—
44#88110—44no—
45C13×#95—22no—
46#88071—22no—
47#8153—131nomaximal, Sylow
48C24×C13C22×C411yescharacteristic
49C22×C4×C13—21no—
50C22×C4×C13—21no—
51C22×C4×C13—21no—
52C22×C4×C13—21no—
53C22×C4×C13—21no—
54C22×C4×C13—21no—
55C22×C4×C13—41no—
56C22×C4×C13—41no—
57C22×C4×C13—41no—
58C22×C4×C13—41no—
59C22×C4×C13—41no—
60C22×C4×C13—41no—
61C22×C4×C13C4212yes—
62C22×C4×C13C22⋊C412yes—
63C22×C4×C13M1612yes—
64C22×Dic13—21no—
65C22×Dic13—21no—
66C22×Dic13—21no—
67C22×Dic13—21no—
68C22×Dic13—21no—
69C22×Dic13—21no—
70C22×Dic13—22no—
71C22×Dic13—22no—
72C22×Dic13—21no—
73C22×Dic13—21no—
74C22×Dic13—41no—
75C22×Dic13—41no—
76C22×Dic13—41no—
77C22×Dic13—41no—
78C22×Dic13C4212yes—
79C22×Dic13C22⋊C411yescharacteristic
80C22×Dic13C22⋊C411yescharacteristic
81C22×Dic13M1612yes—
82C22×Dic13M1612yes—
83C22×Dic13M1612yes—
84C22×Dic13C22×C412yes—
85C22×Dic13C2×D412yes—
86C22×Dic13#4112yes—
87C2×#1057—28no—
88C2×#1057—44no—
89C2×#1057—44no—
90#6101—28no—
91#6101—28no—
92C4×Dic13—24no—
93C4×Dic13—24no—
94C4×Dic13—24no—
95C4×Dic13—42no—
96C4×Dic13—42no—
97C4×Dic13—42no—
98C2×C4×C4⋊C4—131no—
99#1749—132no—
100C2×#324—132no—
101#1280—132no—
102C23×C13—21no—
103C23×C13—21no—
104C23×C13—21no—
105C23×C13—21no—
106C23×C13C2×C4211yescharacteristic
107C23×C13C2×C22⋊C411yescharacteristic
108C23×C13#11711yescharacteristic
109C23×C13C2×M1611yescharacteristic
110C23×C13C2×M1611yescharacteristic
111C23×C13C2×M1611yescharacteristic
112C23×C13C2×M1611yescharacteristic
113C2×C4×C13—22no—
114C2×C4×C13—22no—
115C2×C4×C13—22no—
116C2×C4×C13—22no—
117C2×C4×C13—22no—
118C2×C4×C13—42no—
119C2×C4×C13—42no—
120C2×C4×C13—42no—
121C2×C4×C13—42no—
122C2×C4×C13—41no—
123C2×C4×C13—41no—
124C2×C4×C13—41no—
125C2×C4×C13—41no—
126C2×C4×C13—42no—
127C2×C4×C13—42no—
128C2×Dic13—24no—
129C2×Dic13—24no—
130C2×Dic13—22no—
131C2×Dic13—22no—
132C2×Dic13—21no—
133C2×Dic13—21no—
134C2×Dic13—22no—
135C2×Dic13—22no—
136C2×Dic13—22no—
137C2×Dic13—21no—
138C2×Dic13—22no—
139C2×Dic13—21no—
140C2×Dic13—22no—
141C2×Dic13—22no—
142C2×Dic13—22no—
143C2×Dic13—42no—
144C2×Dic13—42no—
145C2×Dic13—42no—
146C2×Dic13—41no—
147C2×Dic13—41no—
148C2×Dic13—42no—
149C2×Dic13#9714yescomplemented
150C2×Dic13#9912yes—
151C2×Dic13#10112yes—
152C2×Dic13C4×D414yes—
153#1057—48no—
154C22×C4⋊C4—131no—
155C22×C4⋊C4—131no—
156C22×C42—131no—
157C22×C42—131no—
158C22×C42—131no—
159C2×C22⋊C8—134no—
160C2×#97—262no—
161C4×C4⋊C4—262no—
162C4×C4⋊C4—262no—
163C2×#95—131no—
164C2×#95#26111yescharacteristic
165#336—262no—
166#324—138no—
167C22×C13—21no—
168C22×C13—21no—
169C22×C13—21no—
170C22×C13—21no—
171C22×C13—21no—
172C22×C13—21no—
173C22×C13—21no—
174C22×C13—21no—
175C22×C13—21no—
176C22×C13—21no—
177C22×C13—21no—
178C22×C13—21no—
179C22×C13C4×C22⋊C411yescharacteristic
180C22×C13C2×#9711yescharacteristic
181C22×C13C4×M1611yescharacteristic
182C22×C13#40711yescharacteristic
183C22×C13#40711yescharacteristic
184C22×C13C2×#9911yescharacteristic
185C22×C13#41011yescharacteristic
186C22×C13C2×#10111yescharacteristic
187C22×C13#41311yescharacteristic
188C22×C13#43211yescharacteristic
189C22×C13#43211yescharacteristic
190C4×C13—42no—
191C4×C13—42no—
192C4×C13—42no—
193Dic13—22no—
194Dic13—22no—
195Dic13—24no—
196Dic13—24no—
197Dic13—42no—
198C23×C4—131no—
199C23×C4—131no—
200C23×C4—131no—
201C23×C4—131no—
202C23×C4C2×#26111yescharacteristic
203C23×C4C2×#26111yescharacteristic
204C23×C4C2×#26111yescharacteristic
205C22×C8—264no—
206C2×C4⋊C4—134no—
207C2×C4⋊C4—262no—
208C2×C4⋊C4—262no—
209C2×C4⋊C4—262no—
210C2×C4⋊C4—262no—
211C2×C4⋊C4—262no—
212C2×C42—132no—
213C2×C42—132no—
214C2×C42—261no—
215C2×C42—261no—
216C2×C42—262no—
217C2×C42—262no—
218C2×C42—261no—
219C2×C42—261no—
220C2×C42—522no—
221C2×C42—522no—
222C22⋊C8—138no—
223C22⋊C8—264no—
224#97—524no—
225#95—22no—
226#95—262no—
227C2×C13—21no—
228C2×C13—21no—
229C2×C13—21no—
230C2×C13—21no—
231C2×C13#146311yescharacteristic
232C2×C13#146411yescharacteristic
233C2×C13#146511yescharacteristic
234C2×C13#146711yescharacteristic
235C2×C13#174911yescharacteristic
236C2×C13C4×#9911yescharacteristic
237C2×C13C4×#10111yescharacteristic
238C24C22×#26111yescharacteristic
239C22×C4—21no—
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—41no—
246C22×C4—41no—
247C22×C4—41no—
248C22×C4—41no—
249C22×C4—41no—
250C22×C4—41no—
251C22×C4—132no—
252C22×C4—132no—
253C22×C4—132no—
254C22×C4—132no—
255C22×C4—131no—
256C22×C4—131no—
257C22×C4—132no—
258C22×C4—132no—
259C22×C4—132no—
260C22×C4—262no—
261C22×C4—262no—
262C22×C4—261no—
263C22×C4—261no—
264C22×C4—261no—
265C22×C4—261no—
266C22×C4—261no—
267C22×C4—261no—
268C22×C4—261no—
269C22×C4—261no—
270C22×C4—521no—
271C22×C4—521no—
272C22×C4—521no—
273C22×C4—521no—
274C22×C4#611812yes—
275C22×C4C4×#26112yes—
276C22×C4C22⋊#26112yes—
277C2×C8—268no—
278C2×C8—524no—
279C2×C8—524no—
280C4⋊C4—268no—
281C4⋊C4—268no—
282C42—264no—
283C42—264no—
284C42—264no—
285C42—522no—
286C42—522no—
287C42—522no—
288C13#815311yescharacteristic, complemented, Sylow
289C23—21no—
290C23—21no—
291C23—21no—
292C23—21no—
293C23C2×#611811yescharacteristic
294C23D13⋊M1611yescharacteristic
295C23D13⋊M1611yescharacteristic
296C23D13⋊M1611yescharacteristic
297C23C2×C4×#26111yescharacteristic
298C23#8823711yescharacteristic
299C23C2×C22⋊#26111yescharacteristic
300C2×C4—22no—
301C2×C4—22no—
302C2×C4—22no—
303C2×C4—22no—
304C2×C4—22no—
305C2×C4—42no—
306C2×C4—42no—
307C2×C4—42no—
308C2×C4—42no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—42no—
314C2×C4—42no—
315C2×C4—134no—
316C2×C4—134no—
317C2×C4—132no—
318C2×C4—132no—
319C2×C4—264no—
320C2×C4—264no—
321C2×C4—262no—
322C2×C4—262no—
323C2×C4—262no—
324C2×C4—262no—
325C2×C4—262no—
326C2×C4—261no—
327C2×C4—261no—
328C2×C4—262no—
329C2×C4—262no—
330C2×C4—261no—
331C2×C4—262no—
332C2×C4—261no—
333C2×C4—262no—
334C2×C4—522no—
335C2×C4—522no—
336C2×C4—522no—
337C2×C4—521no—
338C2×C4—521no—
339C2×C4—522no—
340C8—528no—
341C22—21no—
342C22—21no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—21no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—21no—
353C22#1171904711yescharacteristic
354C22C4×#611811yescharacteristic
355C22#1171905411yescharacteristic
356C22#1171905511yescharacteristic
357C22#1171912611yescharacteristic
358C22#1171912711yescharacteristic
359C22C4×C22⋊#26111yescharacteristic
360C22D13⋊#9911yescharacteristic
361C22#1171914211yescharacteristic
362C22#1171914811yescharacteristic
363C22D13⋊#10111yescharacteristic
364C4—42no—
365C4—42no—
366C4—42no—
367C4—264no—
368C4—264no—
369C4—262no—
370C4—262no—
371C4—522no—
372C2—21no—
373C2—21no—
374C2—21no—
375C2—21no—
376C2#1313008511yescharacteristic
377C2#1313008811yescharacteristic
378C2#1313009411yescharacteristic
379C2#1313010011yescharacteristic
380C2#1313056311yescharacteristic
381C2#1313058311yescharacteristic
382C2#1313058911yescharacteristic
subgroupG/H
centerC23C2×C22⋊#261
commutatorC23×C13C2×C42
FrattiniC24C22×#261
FittingC2×C13×#95C4
socleC23×C13C2×C22⋊C4
prime radicalC24×C13C22×C4
cosocleC23×Dic13C23
hypercenterC2×#95#261
hypocenterC13#8153
LCSG ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#95

Complements

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

NH ≅ G/Ntype
17. #11718286C4semidirect
149. C2×Dic13#97semidirect
288. C13#8153semidirect

Maximal subgroups

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

subgroupindex
#131305622
C2×#117182862
#131296742
C2×#117183102
#815313