Finite Group Databasebeta

← #15773601

Subgroups — #15773601

Order 3328.

758 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 758 conjugacy classes of subgroups — too many to draw. Only its 95 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#13114916C211yesmaximal, characteristic, complemented
2#13113166C211yesmaximal, characteristic, complemented
3#13112839C214yesmaximal, complemented
4C2×C13×#394C211yesmaximal, characteristic
5C23×D4×C13C411yescharacteristic
6C22×C13×C4⋊C4C2211yescharacteristic
7C22×C13×C22⋊C4—21no—
8C22×C13×C22⋊C4—21no—
9C13×#394—21no—
10C13×#394—21no—
11C13×#394C412yes—
12C13×#394C2212yes—
13C2×C13×#95C411yescharacteristic
14#11718868—21no—
15#11718868—21no—
16#11718122—21no—
17#11718122C2212yescomplemented
18#11718120—21no—
19#11718120C2212yescomplemented
20C25×C13—21no—
21C22×D4×C13—21no—
22C22×D4×C13—41no—
23C22×D4×C13—41no—
24C22×D4×C13—44no—
25C22×D4×C13C2×C412yes—
26C23×C4×C13—21no—
27C23×C4×C13C2×C411yescharacteristic
28C23×C4×C13D411yescharacteristic
29C23×C4×C13D411yescharacteristic
30C2×C13×C4⋊C4—41no—
31C2×C13×C4⋊C4—41no—
32C2×C13×C4⋊C4C2×C411yescharacteristic
33C2×C13×C4⋊C4D411yescharacteristic
34C2×C13×C4⋊C4D411yescharacteristic
35C2×C13×C4⋊C4C2311yescharacteristic
36C2×C13×C22⋊C4—22no—
37C2×C13×C22⋊C4—22no—
38C2×C13×C22⋊C4—22no—
39C2×C13×C22⋊C4—22no—
40C2×C13×C22⋊C4—44no—
41C2×C13×C22⋊C4—44no—
42C2×#6099—22no—
43C2×#6099—41no—
44C13×#95—21no—
45C13×#95C2×C412yes—
46C22⋊#1055—22no—
47C22⋊#1055—41no—
48C22⋊#1055—41no—
49C22⋊#1055—41no—
50#11802—131nomaximal, Sylow
51C24×C13—24no—
52C24×C13—22no—
53C24×C13—42no—
54C24×C13—42no—
55C24×C13—42no—
56C24×C13—42no—
57C24×C13—42no—
58C24×C13—41no—
59C24×C13—41no—
60C24×C13C22⋊C411yescharacteristic
61C2×D4×C13—42no—
62C2×D4×C13—42no—
63C2×D4×C13—44no—
64C2×D4×C13—44no—
65C2×D4×C13—48no—
66C2×D4×C13—44no—
67C2×D4×C13—44no—
68C22×C4×C13—21no—
69C22×C4×C13—21no—
70C22×C4×C13—21no—
71C22×C4×C13—21no—
72C22×C4×C13—21no—
73C22×C4×C13—21no—
74C22×C4×C13—22no—
75C22×C4×C13—22no—
76C22×C4×C13—41no—
77C22×C4×C13—42no—
78C22×C4×C13—42no—
79C22×C4×C13—42no—
80C22×C4×C13—42no—
81C22×C4×C13—42no—
82C22×C4×C13C22⋊C411yescharacteristic
83C22×C4×C13C22⋊C411yescharacteristic
84C22×C4×C13C22⋊C411yescharacteristic
85C22×C4×C13C22×C411yescharacteristic
86C22×C4×C13C2×D411yescharacteristic
87C22×C4×C13C2×D411yescharacteristic
88C13×C4⋊C4—41no—
89C13×C4⋊C4—41no—
90C13×C4⋊C4—41no—
91C13×C4⋊C4—41no—
92C13×C22⋊C4—44no—
93C13×C22⋊C4—44no—
94C13×C22⋊C4—44no—
95C13×C22⋊C4—44no—
96#6099—42no—
97#6099—42no—
98#6099—82no—
99C2×#1055—42no—
100C2×#1055—42no—
101C2×#394D1311yescharacteristic
102#1821—131no—
103#1463—131no—
104#1345—134no—
105C23×C13—22no—
106C23×C13—22no—
107C23×C13—21no—
108C23×C13—21no—
109C23×C13—24no—
110C23×C13—42no—
111C23×C13—44no—
112C23×C13—48no—
113C23×C13—48no—
114C23×C13—42no—
115C23×C13—42no—
116C23×C13—44no—
117C23×C13—42no—
118C23×C13—42no—
119C23×C13—42no—
120C23×C13—84no—
121C23×C13—84no—
122C23×C13—82no—
123C23×C13—82no—
124C23×C13—82no—
125C23×C13—82no—
126C23×C13#9911yescharacteristic
127C23×C13#9911yescharacteristic
128C23×C13C2×C22⋊C411yescharacteristic
129D4×C13—44no—
130D4×C13—48no—
131D4×C13—44no—
132C2×C4×C13—21no—
133C2×C4×C13—21no—
134C2×C4×C13—21no—
135C2×C4×C13—21no—
136C2×C4×C13—21no—
137C2×C4×C13—21no—
138C2×C4×C13—21no—
139C2×C4×C13—21no—
140C2×C4×C13—21no—
141C2×C4×C13—42no—
142C2×C4×C13—42no—
143C2×C4×C13—42no—
144C2×C4×C13—42no—
145C2×C4×C13—42no—
146C2×C4×C13—41no—
147C2×C4×C13—41no—
148C2×C4×C13—41no—
149C2×C4×C13—41no—
150C2×C4×C13—42no—
151C2×C4×C13—42no—
152C2×C4×C13—42no—
153C2×C4×C13—81no—
154C2×C4×C13—84no—
155C2×C4×C13AGL(1,ℤ/8)12yes—
156#1055—82no—
157#1055—82no—
158C23×D4Dic1311yescharacteristic
159C22×C4⋊C4C2×D1311yescharacteristic
160C22×C22⋊C4—21no—
161C22×C22⋊C4—21no—
162#407—261no—
163#407—261no—
164#394—21no—
165#394—21no—
166#394Dic1312yes—
167#394C2×D1312yes—
168C2×#95Dic1311yescharacteristic
169#343—132no—
170#343—261no—
171#324—132no—
172#324—261no—
173C22×C13—24no—
174C22×C13—24no—
175C22×C13—21no—
176C22×C13—21no—
177C22×C13—21no—
178C22×C13—21no—
179C22×C13—21no—
180C22×C13—21no—
181C22×C13—44no—
182C22×C13—44no—
183C22×C13—44no—
184C22×C13—82no—
185C22×C13—82no—
186C22×C13—88no—
187C22×C13—88no—
188C22×C13—82no—
189C22×C13—82no—
190C22×C13AΣL(1,𝔽16)12yes—
191C22×C13#35512yes—
192C22×C13C2×#9911yescharacteristic
193C22×C13#41811yescharacteristic
194C22×C13#42111yescharacteristic
195C4×C13—22no—
196C4×C13—41no—
197C4×C13—41no—
198C4×C13—41no—
199C4×C13—41no—
200C4×C13—41no—
201C4×C13—82no—
202C25—21no—
203C22×D4—21no—
204C22×D4—41no—
205C22×D4—41no—
206C22×D4—44no—
207C22×D4C2×Dic1312yes—
208C23×C4—21no—
209C23×C4C2×Dic1311yescharacteristic
210C23×C4C22⋊D1311yescharacteristic
211C23×C4C22⋊D1311yescharacteristic
212C2×M16—262no—
213C2×M16—521no—
214C2×C4⋊C4—41no—
215C2×C4⋊C4—41no—
216C2×C4⋊C4C2×Dic1311yescharacteristic
217C2×C4⋊C4C22⋊D1311yescharacteristic
218C2×C4⋊C4C22⋊D1311yescharacteristic
219C2×C4⋊C4C22×D1311yescharacteristic
220C2×C22⋊C4—22no—
221C2×C22⋊C4—22no—
222C2×C22⋊C4—22no—
223C2×C22⋊C4—22no—
224C2×C22⋊C4—44no—
225C2×C22⋊C4—44no—
226C22⋊C8—262no—
227C22⋊C8—521no—
228C22⋊C8—521no—
229C22⋊C8—521no—
230#95—21no—
231#95C2×Dic1312yes—
232C2×C13—21no—
233C2×C13—21no—
234C2×C13—22no—
235C2×C13—22no—
236C2×C13—84no—
237C2×C13#151011yescharacteristic
238C2×C13C2×AΣL(1,𝔽16)11yescharacteristic
239C2×C13C2×#35511yescharacteristic
240C24—24no—
241C24—22no—
242C24—42no—
243C24—42no—
244C24—42no—
245C24—42no—
246C24—42no—
247C24—41no—
248C24—41no—
249C24C22⋊Dic1311yescharacteristic
250C2×D4—42no—
251C2×D4—42no—
252C2×D4—44no—
253C2×D4—44no—
254C2×D4—48no—
255C2×D4—44no—
256C2×D4—44no—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—21no—
261C22×C4—21no—
262C22×C4—21no—
263C22×C4—22no—
264C22×C4—22no—
265C22×C4—41no—
266C22×C4—42no—
267C22×C4—42no—
268C22×C4—42no—
269C22×C4—42no—
270C22×C4—42no—
271C22×C4C22⋊Dic1311yescharacteristic
272C22×C4C22⋊Dic1311yescharacteristic
273C22×C4C22⋊Dic1311yescharacteristic
274C22×C4C22×Dic1311yescharacteristic
275C22×C4C2×C22⋊D1311yescharacteristic
276C22×C4C2×C22⋊D1311yescharacteristic
277M16—522no—
278M16—522no—
279M16—1042no—
280C2×C8—522no—
281C2×C8—522no—
282C4⋊C4—41no—
283C4⋊C4—41no—
284C4⋊C4—41no—
285C4⋊C4—41no—
286C22⋊C4—44no—
287C22⋊C4—44no—
288C22⋊C4—44no—
289C22⋊C4—44no—
290C13#1180211yescharacteristic, complemented, Sylow
291C23—21no—
292C23—22no—
293C23—21no—
294C23—22no—
295C23—24no—
296C23—42no—
297C23—44no—
298C23—48no—
299C23—48no—
300C23—42no—
301C23—42no—
302C23—42no—
303C23—42no—
304C23—44no—
305C23—42no—
306C23—84no—
307C23—84no—
308C23—82no—
309C23—82no—
310C23—82no—
311C23—82no—
312C23#8807411yescharacteristic
313C23#8807411yescharacteristic
314C23C2×C22⋊Dic1311yescharacteristic
315D4—44no—
316D4—44no—
317D4—48no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—42no—
328C2×C4—42no—
329C2×C4—42no—
330C2×C4—42no—
331C2×C4—42no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—42no—
337C2×C4—42no—
338C2×C4—42no—
339C2×C4—81no—
340C2×C4—84no—
341C2×C4#8818612yes—
342C8—1042no—
343C8—1042no—
344C22—24no—
345C22—24no—
346C22—21no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—44no—
353C22—44no—
354C22—44no—
355C22—82no—
356C22—82no—
357C22—88no—
358C22—88no—
359C22—82no—
360C22—82no—
361C22#1171812812yes—
362C22#1171813412yes—
363C22#1171887611yescharacteristic
364C22C2×#8807411yescharacteristic
365C22#1171889711yescharacteristic
366C4—22no—
367C4—41no—
368C4—41no—
369C4—41no—
370C4—41no—
371C4—41no—
372C4—82no—
373C2—21no—
374C2—21no—
375C2—22no—
376C2—22no—
377C2—84no—
378C2#1311336511yescharacteristic
379C2C2×#1171812811yescharacteristic
380C2C2×#1171813411yescharacteristic
subgroupG/H
centerC22C2×#88074
commutatorC22×C4×C13C22×C4
FrattiniC2×C4⋊C4C22×D13
FittingC2×C13×#394C2
socleC22×C13C2×#99
prime radicalC23×D4×C13C4
cosocleC2×C13×C4⋊C4C23
hypercenterC2×#394D13
hypocenterC13#11802
LCSG ▷ C22×C4×C13 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C24 ◁ C22×C4⋊C4 ◁ C2×#394

Complements

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

NH ≅ G/Ntype
1. #13114916C2semidirect
2. #13113166C2semidirect
3. #13112839C2semidirect
17. #11718122C22semidirect
19. #11718120C22semidirect
290. C13#11802semidirect

Maximal subgroups

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

subgroupindex
#131149162
#131131662
#131128392
C2×C13×#3942
#1180213