Finite Group Databasebeta

← #15773822

Subgroups — #15773822

Order 3328.

572 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 572 conjugacy classes of subgroups — too many to draw. Only its 91 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
2C2×#11718120C211yesmaximal, characteristic, complemented
3#13112866C212yesmaximal, complemented
4#13112839C212yesmaximal, complemented
5C13×#2406C211yesmaximal, characteristic
6C22×C13×#41C411yescharacteristic
7C2×C13×#123—21no—
8C22×C13×C4⋊C4C2211yescharacteristic
9C13×#395C411yescharacteristic
10C13×#395C2211yescharacteristic
11C13×#394C411yescharacteristic
12C13×#394C2211yescharacteristic
13C13×#386—21no—
14C13×#385—21no—
15C13×#385—21no—
16C13×#381C411yescharacteristic
17#11718868—21no—
18C2×C22⋊#1055—21no—
19#11718122—21no—
20#11718122C2212yes—
21#11718120—21no—
22#11718120C2212yes—
23C2×C13×#41—41no—
24C2×C13×#41—41no—
25C2×C13×#41—44no—
26C22×Q8×C13C2×C411yescharacteristic
27C22×D4×C13—21no—
28C22×D4×C13C2×C411yescharacteristic
29C23×C4×C13—21no—
30C23×C4×C13C2×C411yescharacteristic
31C23×C4×C13D411yescharacteristic
32C23×C4×C13D411yescharacteristic
33C13×#123—44no—
34C2×C13×C4⋊C4—21no—
35C2×C13×C4⋊C4—21no—
36C2×C13×C4⋊C4—41no—
37C2×C13×C4⋊C4—41no—
38C2×C13×C4⋊C4C2×C411yescharacteristic
39C2×C13×C4⋊C4D411yescharacteristic
40C2×C13×C4⋊C4D411yescharacteristic
41C2×C13×C4⋊C4C2311yescharacteristic
42C2×C13×C22⋊C4—21no—
43C2×C13×C22⋊C4—21no—
44C2×C13×C22⋊C4—21no—
45C2×C13×C22⋊C4—21no—
46C2×C13×C22⋊C4—21no—
47C2×#6099—22no—
48C22×#1055—41no—
49C13×#95—21no—
50C13×#95—21no—
51C13×#95—21no—
52C13×#95C2×C411yescharacteristic
53C13×#95C2×C411yescharacteristic
54C22⋊#1055—22no—
55C22⋊#1055—41no—
56C22⋊#1055—41no—
57C22⋊#1055—41no—
58#11848—131nomaximal, Sylow
59C24×C13—21no—
60C24×C13C22⋊C411yescharacteristic
61C13×#41—44no—
62C13×#41—44no—
63C13×#41—44no—
64C13×#41—44no—
65C2×Q8×C13—42no—
66C2×Q8×C13—41no—
67C2×D4×C13—24no—
68C2×D4×C13—41no—
69C2×D4×C13—42no—
70C2×D4×C13—41no—
71C2×D4×C13—41no—
72C2×D4×C13—42no—
73C22×C4×C13—21no—
74C22×C4×C13—21no—
75C22×C4×C13—21no—
76C22×C4×C13—21no—
77C22×C4×C13—21no—
78C22×C4×C13—21no—
79C22×C4×C13—21no—
80C22×C4×C13—22no—
81C22×C4×C13—21no—
82C22×C4×C13—21no—
83C22×C4×C13—41no—
84C22×C4×C13—42no—
85C22×C4×C13—42no—
86C22×C4×C13—42no—
87C22×C4×C13—42no—
88C22×C4×C13—42no—
89C22×C4×C13C22⋊C411yescharacteristic
90C22×C4×C13C22⋊C411yescharacteristic
91C22×C4×C13C22⋊C411yescharacteristic
92C22×C4×C13C22×C411yescharacteristic
93C22×C4×C13C2×D411yescharacteristic
94C22×C4×C13C2×D411yescharacteristic
95C13×C4⋊C4—41no—
96C13×C4⋊C4—41no—
97C13×C4⋊C4—41no—
98C13×C4⋊C4—41no—
99C13×C4⋊C4—42no—
100C13×C4⋊C4—42no—
101C13×C22⋊C4—42no—
102C13×C22⋊C4—42no—
103C13×C22⋊C4—42no—
104C13×C22⋊C4—42no—
105C13×C22⋊C4—42no—
106#6099—42no—
107#6099—42no—
108C2×#1055—42no—
109C2×#1055—42no—
110C2×#1055—82no—
111#2406D1311yescharacteristic
112#1821—131no—
113C2×#324—131no—
114#1354—132no—
115#1345—132no—
116C23×C13—22no—
117C23×C13—21no—
118C23×C13—21no—
119C23×C13—22no—
120C23×C13—41no—
121C23×C13—41no—
122C23×C13—41no—
123C23×C13—41no—
124C23×C13—41no—
125C23×C13—41no—
126C23×C13—41no—
127C23×C13#9911yescharacteristic
128C23×C13#9911yescharacteristic
129C23×C13C2×C22⋊C411yescharacteristic
130Q8×C13—42no—
131Q8×C13—42no—
132D4×C13—44no—
133D4×C13—42no—
134D4×C13—44no—
135D4×C13—42no—
136C2×C4×C13—21no—
137C2×C4×C13—21no—
138C2×C4×C13—22no—
139C2×C4×C13—21no—
140C2×C4×C13—21no—
141C2×C4×C13—21no—
142C2×C4×C13—21no—
143C2×C4×C13—21no—
144C2×C4×C13—21no—
145C2×C4×C13—21no—
146C2×C4×C13—42no—
147C2×C4×C13—42no—
148C2×C4×C13—41no—
149C2×C4×C13—42no—
150C2×C4×C13—48no—
151C2×C4×C13—42no—
152C2×C4×C13—42no—
153C2×C4×C13—41no—
154C2×C4×C13—41no—
155C2×C4×C13—41no—
156C2×C4×C13—41no—
157C2×C4×C13—41no—
158C2×C4×C13—41no—
159C2×C4×C13—41no—
160C2×C4×C13—41no—
161C2×C4×C13—41no—
162C2×C4×C13—41no—
163C2×C4×C13—41no—
164C2×C4×C13—81no—
165C2×C4×C13#13512yes—
166#1055—82no—
167#1055—82no—
168C22×#41Dic1311yescharacteristic
169C2×#123—21no—
170C22×C4⋊C4C2×D1311yescharacteristic
171#407—261no—
172C2×C22⋊C8—261no—
173#395Dic1311yescharacteristic
174#395C2×D1311yescharacteristic
175#394Dic1311yescharacteristic
176#394C2×D1311yescharacteristic
177#386—21no—
178#385—21no—
179#385—21no—
180#381Dic1311yescharacteristic
181#343—132no—
182#343—261no—
183#324—132no—
184#324—261no—
185C22×C13—21no—
186C22×C13—21no—
187C22×C13—21no—
188C22×C13—21no—
189C22×C13—21no—
190C22×C13—21no—
191C22×C13—21no—
192C22×C13—42no—
193C22×C13—42no—
194C22×C13—42no—
195C22×C13—42no—
196C22×C13—42no—
197C22×C13—81no—
198C22×C13—81no—
199C22×C13—81no—
200C22×C13—81no—
201C22×C13AΣL(1,𝔽16)12yes—
202C22×C13C2×#9911yescharacteristic
203C22×C13#41611yescharacteristic
204C22×C13#42111yescharacteristic
205C4×C13—22no—
206C4×C13—41no—
207C4×C13—41no—
208C4×C13—42no—
209C4×C13—41no—
210C4×C13—41no—
211C4×C13—41no—
212C4×C13—81no—
213C4×C13—81no—
214C2×#41—41no—
215C2×#41—41no—
216C2×#41—44no—
217C22×Q8C2×Dic1311yescharacteristic
218C22×D4—21no—
219C22×D4C2×Dic1311yescharacteristic
220C23×C4—21no—
221C23×C4C2×Dic1311yescharacteristic
222C23×C4C22⋊D1311yescharacteristic
223C23×C4C22⋊D1311yescharacteristic
224C2×M16—262no—
225C22×C8—521no—
226#123—44no—
227C2×C4⋊C4—21no—
228C2×C4⋊C4—21no—
229C2×C4⋊C4—41no—
230C2×C4⋊C4—41no—
231C2×C4⋊C4C2×Dic1311yescharacteristic
232C2×C4⋊C4C22⋊D1311yescharacteristic
233C2×C4⋊C4C22⋊D1311yescharacteristic
234C2×C4⋊C4C22×D1311yescharacteristic
235C2×C22⋊C4—21no—
236C2×C22⋊C4—21no—
237C2×C22⋊C4—21no—
238C2×C22⋊C4—21no—
239C2×C22⋊C4—21no—
240C22⋊C8—262no—
241C22⋊C8—521no—
242C22⋊C8—521no—
243C22⋊C8—521no—
244#95—21no—
245#95—21no—
246#95—21no—
247#95C2×Dic1311yescharacteristic
248#95C2×Dic1311yescharacteristic
249C2×C13—21no—
250C2×C13—21no—
251C2×C13—22no—
252C2×C13—41no—
253C2×C13—82no—
254C2×C13#151611yescharacteristic
255C2×C13C2×AΣL(1,𝔽16)11yescharacteristic
256C2×C13#213311yescharacteristic
257C24—21no—
258C24C22⋊Dic1311yescharacteristic
259#41—44no—
260#41—44no—
261#41—44no—
262#41—44no—
263C2×Q8—42no—
264C2×Q8—41no—
265C2×D4—24no—
266C2×D4—41no—
267C2×D4—42no—
268C2×D4—41no—
269C2×D4—41no—
270C2×D4—42no—
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—21no—
274C22×C4—21no—
275C22×C4—21no—
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—22no—
279C22×C4—21no—
280C22×C4—21no—
281C22×C4—41no—
282C22×C4—42no—
283C22×C4—42no—
284C22×C4—42no—
285C22×C4—42no—
286C22×C4—42no—
287C22×C4C22⋊Dic1311yescharacteristic
288C22×C4C22⋊Dic1311yescharacteristic
289C22×C4C22⋊Dic1311yescharacteristic
290C22×C4C22×Dic1311yescharacteristic
291C22×C4C2×C22⋊D1311yescharacteristic
292C22×C4C2×C22⋊D1311yescharacteristic
293M16—522no—
294M16—522no—
295C2×C8—522no—
296C2×C8—522no—
297C2×C8—1042no—
298C4⋊C4—41no—
299C4⋊C4—41no—
300C4⋊C4—41no—
301C4⋊C4—41no—
302C4⋊C4—42no—
303C4⋊C4—42no—
304C22⋊C4—42no—
305C22⋊C4—42no—
306C22⋊C4—42no—
307C22⋊C4—42no—
308C22⋊C4—42no—
309C13#1184811yescharacteristic, complemented, Sylow
310C23—21no—
311C23—22no—
312C23—21no—
313C23—22no—
314C23—41no—
315C23—41no—
316C23—41no—
317C23—41no—
318C23—41no—
319C23—41no—
320C23—41no—
321C23#8807411yescharacteristic
322C23#8807411yescharacteristic
323C23C2×C22⋊Dic1311yescharacteristic
324Q8—42no—
325Q8—42no—
326D4—44no—
327D4—42no—
328D4—42no—
329D4—44no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—22no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—42no—
341C2×C4—42no—
342C2×C4—41no—
343C2×C4—42no—
344C2×C4—48no—
345C2×C4—41no—
346C2×C4—42no—
347C2×C4—42no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—81no—
359C2×C4#8820412yes—
360C8—1042no—
361C8—1042no—
362C22—21no—
363C22—21no—
364C22—21no—
365C22—21no—
366C22—21no—
367C22—21no—
368C22—21no—
369C22—42no—
370C22—42no—
371C22—42no—
372C22—42no—
373C22—42no—
374C22—81no—
375C22—81no—
376C22—81no—
377C22—81no—
378C22#1171812812yes—
379C22C2×#8807411yescharacteristic
380C22#1171889411yescharacteristic
381C22#1171889711yescharacteristic
382C4—22no—
383C4—41no—
384C4—41no—
385C4—41no—
386C4—42no—
387C4—41no—
388C4—41no—
389C4—81no—
390C4—81no—
391C2—21no—
392C2—21no—
393C2—22no—
394C2—41no—
395C2—82no—
396C2#1311339211yescharacteristic
397C2C2×#1171812811yescharacteristic
398C2#1311652511yescharacteristic
subgroupG/H
centerC22C2×#88074
commutatorC22×C4×C13C22×C4
FrattiniC2×C4⋊C4C22×D13
FittingC13×#2406C2
socleC22×C13C2×#99
prime radicalC22×C13×#41C4
cosocleC2×C13×C4⋊C4C23
hypercenter#2406D13
hypocenterC13#11848
LCSG ▷ C22×C4×C13 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C24 ◁ C22×C4⋊C4 ◁ #2406

Complements

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

NH ≅ G/Ntype
1. #13114916C2semidirect
2. C2×#11718120C2semidirect
3. #13112866C2semidirect
4. #13112839C2semidirect
309. C13#11848semidirect

Maximal subgroups

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

subgroupindex
#131149162
C2×#117181202
#131128662
#131128392
C13×#24062
#1184813