Finite Group Databasebeta

← #15755452

Subgroups — #15755452

Order 3328.

694 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13113553C212yesmaximal, complemented
2#13113463C212yesmaximal, complemented
3#13113170C211yesmaximal, characteristic
4#13113170C211yesmaximal, characteristic
5C2×C13×#544C211yesmaximal, characteristic
6C13×#544—24no—
7C13×#544—24no—
8C2×C13×C4⋊Q8—21no—
9C2×C13×C4⋊Q8C411yescharacteristic
10C2×C13×C4⋊Q8C2211yescharacteristic
11C2×C13×#125—21no—
12C2×C13×#125C411yescharacteristic
13C2×C13×#125C2211yescharacteristic
14C2×C13×C22⋊Q8—21no—
15C2×C13×C22⋊Q8—21no—
16C2×C13×#117C411yescharacteristic
17C2×C13×#117C2211yescharacteristic
18C22×C13×C4⋊C4C411yescharacteristic
19#11718587C2212yes—
20#11718587C2212yes—
21#11718139—24no—
22#11718135—24no—
23#11718120—21no—
24#11718120—21no—
25#11718117—21no—
26#11718117—21no—
27C22×Q8×C13—21no—
28C22×Q8×C13—21no—
29C23×C4×C13—21no—
30C23×C4×C13C2×C411yescharacteristic
31C13×C4⋊Q8—28no—
32C13×C4⋊Q8—22no—
33C13×C4⋊Q8—22no—
34C13×C4⋊Q8—22no—
35C13×C4⋊Q8D414yes—
36C13×#125—28no—
37C13×#125—22no—
38C13×#125—22no—
39C13×#125—22no—
40C13×#125D414yes—
41C13×C22⋊Q8—28no—
42C13×C22⋊Q8—28no—
43C13×#117—22no—
44C13×#117—22no—
45C13×#117—22no—
46C13×#117—22no—
47C2×C13×C4⋊C4—21no—
48C2×C13×C4⋊C4—21no—
49C2×C13×C4⋊C4—21no—
50C2×C13×C4⋊C4—21no—
51C2×C13×C4⋊C4—21no—
52C2×C13×C4⋊C4—21no—
53C2×C13×C4⋊C4—21no—
54C2×C13×C4⋊C4—22no—
55C2×C13×C4⋊C4—22no—
56C2×C13×C4⋊C4C2×C411yescharacteristic
57C2×C13×C4⋊C4C2×C411yescharacteristic
58C2×C13×C4⋊C4C2×C411yescharacteristic
59C2×C13×C4⋊C4C2×C411yescharacteristic
60C2×C13×C4⋊C4D411yescharacteristic
61C2×C13×C4⋊C4D411yescharacteristic
62C2×C13×C22⋊C4—21no—
63C2×C13×C22⋊C4D411yescharacteristic
64C2×C13×C22⋊C4D411yescharacteristic
65C2×C42×C13—21no—
66C2×C42×C13C2×C411yescharacteristic
67C2×C42×C13C2311yescharacteristic
68C22⋊#1055—22no—
69C22⋊#1055—22no—
70C4⋊#1055—22no—
71C4⋊#1055—22no—
72#88043—22no—
73#88043—22no—
74#8525—131nomaximal, Sylow
75C24×C13C22⋊C411yescharacteristic
76C2×Q8×C13—24no—
77C2×Q8×C13—24no—
78C2×Q8×C13—82no—
79C2×Q8×C13—82no—
80C22×C4×C13—22no—
81C22×C4×C13—22no—
82C22×C4×C13—21no—
83C22×C4×C13—21no—
84C22×C4×C13—21no—
85C22×C4×C13—21no—
86C22×C4×C13—21no—
87C22×C4×C13—21no—
88C22×C4×C13—24no—
89C22×C4×C13—82no—
90C22×C4×C13C22⋊C411yescharacteristic
91C22×C4×C13C22⋊C411yescharacteristic
92C22×C4×C13C22⋊C411yescharacteristic
93C22×C4×C13C22×C411yescharacteristic
94C22×C4×C13C2×D411yescharacteristic
95C22×C4×C13C2×D411yescharacteristic
96C13×C4⋊C4—24no—
97C13×C4⋊C4—24no—
98C13×C4⋊C4—24no—
99C13×C4⋊C4—24no—
100C13×C4⋊C4—21no—
101C13×C4⋊C4—21no—
102C13×C4⋊C4—21no—
103C13×C4⋊C4—21no—
104C13×C4⋊C4—24no—
105C13×C4⋊C4—24no—
106C13×C4⋊C4—24no—
107C13×C4⋊C4—22no—
108C13×C4⋊C4—22no—
109C13×C4⋊C4C22⋊C412yes—
110C13×C4⋊C4C22⋊C412yes—
111C13×C4⋊C4C22⋊C412yes—
112C13×C4⋊C4C22⋊C412yes—
113C13×C22⋊C4—24no—
114C13×C22⋊C4—22no—
115C13×C22⋊C4—22no—
116C42×C13—24no—
117C42×C13—21no—
118C42×C13—21no—
119C42×C13C2×D412yes—
120C42×C13C2×D412yes—
121C2×#1055—42no—
122C2×#1055—42no—
123C2×#544D1311yescharacteristic
124#1556—132no—
125#1534—132no—
126#1464—131no—
127#1464—131no—
128C23×C13—21no—
129C23×C13—21no—
130C23×C13—41no—
131C23×C13—41no—
132C23×C13#10112yes—
133C23×C13C2×C22⋊C411yescharacteristic
134Q8×C13—84no—
135Q8×C13—84no—
136C2×C4×C13—24no—
137C2×C4×C13—24no—
138C2×C4×C13—21no—
139C2×C4×C13—21no—
140C2×C4×C13—21no—
141C2×C4×C13—21no—
142C2×C4×C13—21no—
143C2×C4×C13—22no—
144C2×C4×C13—21no—
145C2×C4×C13—22no—
146C2×C4×C13—22no—
147C2×C4×C13—22no—
148C2×C4×C13—41no—
149C2×C4×C13—41no—
150C2×C4×C13—42no—
151C2×C4×C13—42no—
152C2×C4×C13—42no—
153C2×C4×C13—42no—
154C2×C4×C13—41no—
155C2×C4×C13—41no—
156C2×C4×C13—84no—
157C2×C4×C13#10112yes—
158C2×C4×C13C2×C22⋊C411yescharacteristic
159C2×C4×C13C2×C22⋊C411yescharacteristic
160C2×C4×C13#12012yes—
161C2×C4×C13#12012yes—
162#1055—82no—
163#1055—82no—
164#544—24no—
165#544—24no—
166C2×C4⋊Q8—21no—
167C2×C4⋊Q8Dic1311yescharacteristic
168C2×C4⋊Q8C2×D1311yescharacteristic
169C2×#125—21no—
170C2×#125Dic1311yescharacteristic
171C2×#125C2×D1311yescharacteristic
172C2×C22⋊Q8—21no—
173C2×C22⋊Q8—21no—
174C2×#117Dic1311yescharacteristic
175C2×#117C2×D1311yescharacteristic
176C22×C4⋊C4Dic1311yescharacteristic
177#432—132no—
178#432—132no—
179#332—264no—
180#330—264no—
181#324—261no—
182#324—261no—
183#323—261no—
184#323—261no—
185C22×C13—21no—
186C22×C13—21no—
187C22×C13—22no—
188C22×C13—42no—
189C22×C13—42no—
190C22×C13—41no—
191C22×C13—41no—
192C22×C13#37911yescharacteristic
193C22×C13C2×#10111yescharacteristic
194C22×C13C2×#10111yescharacteristic
195C4×C13—22no—
196C4×C13—22no—
197C4×C13—22no—
198C4×C13—21no—
199C4×C13—21no—
200C4×C13—42no—
201C4×C13—42no—
202C4×C13—42no—
203C4×C13—41no—
204C4×C13—41no—
205C4×C13—42no—
206C22×Q8—21no—
207C22×Q8—21no—
208C23×C4—21no—
209C23×C4C2×Dic1311yescharacteristic
210C4⋊Q8—28no—
211C4⋊Q8—22no—
212C4⋊Q8—22no—
213C4⋊Q8—22no—
214C4⋊Q8C22⋊D1314yes—
215#125—28no—
216#125—22no—
217#125—22no—
218#125—22no—
219#125C22⋊D1314yes—
220C22⋊Q8—28no—
221C22⋊Q8—28no—
222#117—22no—
223#117—22no—
224#117—22no—
225#117—22no—
226C2×C4⋊C4—21no—
227C2×C4⋊C4—21no—
228C2×C4⋊C4—21no—
229C2×C4⋊C4—21no—
230C2×C4⋊C4—21no—
231C2×C4⋊C4—21no—
232C2×C4⋊C4—21no—
233C2×C4⋊C4—22no—
234C2×C4⋊C4—22no—
235C2×C4⋊C4C2×Dic1311yescharacteristic
236C2×C4⋊C4C2×Dic1311yescharacteristic
237C2×C4⋊C4C2×Dic1311yescharacteristic
238C2×C4⋊C4C2×Dic1311yescharacteristic
239C2×C4⋊C4C22⋊D1311yescharacteristic
240C2×C4⋊C4C22⋊D1311yescharacteristic
241C2×C22⋊C4—21no—
242C2×C22⋊C4C22⋊D1311yescharacteristic
243C2×C22⋊C4C22⋊D1311yescharacteristic
244C2×C42—21no—
245C2×C42C2×Dic1311yescharacteristic
246C2×C42C22×D1311yescharacteristic
247C4⋊C8—262no—
248C4⋊C8—262no—
249C22⋊C8—262no—
250C22⋊C8—262no—
251#97—262no—
252#97—262no—
253C2×C13—21no—
254C2×C13—21no—
255C2×C13—42no—
256C2×C13#178411yescharacteristic
257C2×C13#179511yescharacteristic
258C2×C13#179611yescharacteristic
259C24C22⋊Dic1311yescharacteristic
260C2×Q8—24no—
261C2×Q8—24no—
262C2×Q8—82no—
263C2×Q8—82no—
264C22×C4—22no—
265C22×C4—22no—
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—21no—
270C22×C4—21no—
271C22×C4—21no—
272C22×C4—24no—
273C22×C4—82no—
274C22×C4C22⋊Dic1311yescharacteristic
275C22×C4C22⋊Dic1311yescharacteristic
276C22×C4C22⋊Dic1311yescharacteristic
277C22×C4C22×Dic1311yescharacteristic
278C22×C4C2×C22⋊D1311yescharacteristic
279C22×C4C2×C22⋊D1311yescharacteristic
280C2×C8—522no—
281C2×C8—522no—
282C4⋊C4—24no—
283C4⋊C4—24no—
284C4⋊C4—24no—
285C4⋊C4—24no—
286C4⋊C4—21no—
287C4⋊C4—21no—
288C4⋊C4—21no—
289C4⋊C4—21no—
290C4⋊C4—24no—
291C4⋊C4—24no—
292C4⋊C4—24no—
293C4⋊C4—22no—
294C4⋊C4—22no—
295C4⋊C4C22⋊Dic1312yes—
296C4⋊C4C22⋊Dic1312yes—
297C4⋊C4C22⋊Dic1312yes—
298C4⋊C4C22⋊Dic1312yes—
299C22⋊C4—24no—
300C22⋊C4—22no—
301C22⋊C4—22no—
302C42—24no—
303C42—21no—
304C42—21no—
305C42C2×C22⋊D1312yes—
306C42C2×C22⋊D1312yes—
307C13#852511yescharacteristic, complemented, Sylow
308C23—21no—
309C23—21no—
310C23—41no—
311C23—41no—
312C23#8807612yes—
313C23C2×C22⋊Dic1311yescharacteristic
314Q8—84no—
315Q8—84no—
316C2×C4—24no—
317C2×C4—24no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—22no—
324C2×C4—21no—
325C2×C4—22no—
326C2×C4—22no—
327C2×C4—22no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—42no—
331C2×C4—42no—
332C2×C4—42no—
333C2×C4—42no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—84no—
337C2×C4#8807612yes—
338C2×C4C2×C22⋊Dic1311yescharacteristic
339C2×C4C2×C22⋊Dic1311yescharacteristic
340C2×C4#8820712yes—
341C2×C4#8820712yes—
342C8—1042no—
343C8—1042no—
344C22—21no—
345C22—21no—
346C22—22no—
347C22—42no—
348C22—42no—
349C22—41no—
350C22—41no—
351C22C2×#8807611yescharacteristic
352C22C2×#8807611yescharacteristic
353C22#1171890811yescharacteristic
354C4—22no—
355C4—21no—
356C4—21no—
357C4—22no—
358C4—22no—
359C4—42no—
360C4—42no—
361C4—42no—
362C4—41no—
363C4—41no—
364C4—42no—
365C2—21no—
366C2—21no—
367C2—42no—
368C2#1311476011yescharacteristic
369C2#1311480611yescharacteristic
370C2#1311481111yescharacteristic
subgroupG/H
centerC22#11718908
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC2×C13×#544C2
socleC22×C13#379
prime radicalC24×C13C22⋊C4
cosocleC2×C42×C13C23
hypercenterC2×#544D13
hypocenterC13#8525
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#544

Complements

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

NH ≅ G/Ntype
1. #13113553C2semidirect
2. #13113463C2semidirect
307. C13#8525semidirect

Maximal subgroups

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

subgroupindex
#131135532
#131134632
#131131702
C2×C13×#5442
#852513