Finite Group Databasebeta

← #15766088

Subgroups — #15766088

Order 3328.

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

normal subgroups only

This group has 422 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#13120055C211yesmaximal, characteristic
2#13113408C211yesmaximal, characteristic
3C2×#11718130C211yesmaximal, characteristic
4#13112714C211yesmaximal, characteristic
5#13112703C211yesmaximal, characteristic
6#13112684C211yesmaximal, characteristic
7C13×#1996C211yesmaximal, characteristic
8C2×C13×C22⋊Q8C2211yescharacteristic
9C13×#380C2211yescharacteristic
10C4×C13×C22⋊C4C2211yescharacteristic
11#11718873C2211yescharacteristic
12C2×#88071C2211yescharacteristic
13C2×C22⋊#1055C2211yescharacteristic
14C2×C22⋊#1055C2211yescharacteristic
15#11718607—21no—
16#11718603—21no—
17#11718594—21no—
18#11718594—21no—
19#11718321—21no—
20#11718318—21no—
21C13×#342—21no—
22C13×#342—21no—
23#11718130—21no—
24#11718130—21no—
25#11718130—21no—
26#11718130—21no—
27C22×Q8×C13Q811yescharacteristic
28C23×C4×C13C2311yescharacteristic
29C23×Dic13—21no—
30C13×C22⋊Q8—21no—
31C13×C22⋊Q8—21no—
32C13×C22⋊Q8—21no—
33C13×C22⋊Q8—21no—
34C2×C13×C4⋊C4—21no—
35C2×C13×C4⋊C4—21no—
36C2×C13×C4⋊C4Q811yescharacteristic
37C2×C13×C22⋊C4—21no—
38C2×C13×C22⋊C4—21no—
39C2×C13×C22⋊C4D411yescharacteristic
40C2×C13×C22⋊C4D411yescharacteristic
41C2×C42×C13—21no—
42C2×C22⋊Dic13—21no—
43C2×C4⋊Dic13—21no—
44C2×#6101—21no—
45C2×#6101—21no—
46C2×#6101—21no—
47C2×#6101—21no—
48C22×#1055—21no—
49C22×#1055—21no—
50C13×#95—21no—
51C13×#95—21no—
52#88071—21no—
53#88071—21no—
54#88071—21no—
55#88071—21no—
56#88071—21no—
57#88071D411yescharacteristic
58#88071D411yescharacteristic
59#88071D411yescharacteristic
60#88071D411yescharacteristic
61C22⋊#1055—21no—
62C22⋊#1055—21no—
63C22⋊#1055—21no—
64C22⋊#1055—21no—
65#10377—131nomaximal, Sylow
66C24×C13C2×D411yescharacteristic
67C2×Q8×C13—21no—
68C2×Q8×C13—21no—
69C2×Q8×C13—81no—
70C22×C4×C13—21no—
71C22×C4×C13—21no—
72C22×C4×C13—21no—
73C22×C4×C13—21no—
74C22×C4×C13—41no—
75C22×C4×C13—81no—
76C22×C4×C13C2×D411yescharacteristic
77C22×C4×C13C2×D411yescharacteristic
78C22×C4×C13C2×Q811yescharacteristic
79C22×C4×C13#4111yescharacteristic
80C22×C4×C13#4111yescharacteristic
81C22×C4×C13#4111yescharacteristic
82C22×Dic13—21no—
83C22×Dic13—21no—
84C22×Dic13—21no—
85C22×Dic13—21no—
86C22×Dic13—42no—
87C22×Dic13—41no—
88C22×Dic13—41no—
89C22×Dic13—81no—
90C13×C4⋊C4—21no—
91C13×C4⋊C4—21no—
92C13×C4⋊C4—41no—
93C13×C4⋊C4—41no—
94C13×C4⋊C4—81no—
95C13×C22⋊C4—21no—
96C13×C22⋊C4—21no—
97C13×C22⋊C4—21no—
98C13×C22⋊C4—21no—
99C13×C22⋊C4—41no—
100C13×C22⋊C4—41no—
101C13×C22⋊C4—41no—
102C13×C22⋊C4—41no—
103C42×C13—81no—
104C22⋊Dic13—41no—
105C22⋊Dic13—41no—
106C4⋊Dic13—81no—
107#6101—42no—
108#6101—42no—
109#6101—81no—
110#6101—81no—
111C2×#1055—41no—
112C2×#1055—41no—
113C2×#1055—81no—
114C2×#1055—81no—
115#2569—131no—
116#1996D1311yescharacteristic
117#1520—131no—
118C2×#328—131no—
119#1294—131no—
120#1289—131no—
121#1282—131no—
122C23×C13—41no—
123C23×C13—41no—
124C23×C13#12011yescharacteristic
125C23×C13C22⋊Q811yescharacteristic
126C23×C13#12411yescharacteristic
127C23×C13#13511yescharacteristic
128C23×C13#13511yescharacteristic
129C23×C13#13711yescharacteristic
130C23×C13#13711yescharacteristic
131Q8×C13—81no—
132Q8×C13—81no—
133C2×C4×C13—41no—
134C2×C4×C13—41no—
135C2×C4×C13—41no—
136C2×C4×C13—41no—
137C2×C4×C13—41no—
138C2×C4×C13—41no—
139C2×C4×C13—41no—
140C2×C4×C13—41no—
141C2×C4×C13—41no—
142C2×C4×C13—41no—
143C2×C4×C13—41no—
144C2×C4×C13—41no—
145C2×C4×C13—41no—
146C2×C4×C13—41no—
147C2×C4×C13—81no—
148C2×C4×C13—81no—
149C2×C4×C13—81no—
150C2×C4×C13—81no—
151C2×C4×C13—81no—
152C2×C4×C13C22⋊Q811yescharacteristic
153C2×C4×C13C22⋊Q811yescharacteristic
154C2×C4×C13#12411yescharacteristic
155C2×C4×C13#12411yescharacteristic
156C2×Dic13—22no—
157C2×Dic13—41no—
158C2×Dic13—41no—
159C2×Dic13—41no—
160C2×Dic13—41no—
161C2×Dic13—41no—
162C2×Dic13—41no—
163C2×Dic13—41no—
164C2×Dic13—41no—
165C2×Dic13—41no—
166C2×Dic13—41no—
167C2×Dic13—41no—
168C2×Dic13—82no—
169C2×Dic13—82no—
170#1055—81no—
171#1055—81no—
172C2×C22⋊Q8C2×D1311yescharacteristic
173C2×C22⋊C8—131no—
174C2×C22⋊C8—131no—
175#400—261no—
176#398—261no—
177#387—261no—
178#387—261no—
179#385—261no—
180#380—131no—
181#380—261no—
182#380C2×D1311yescharacteristic
183C4×C22⋊C4C2×D1311yescharacteristic
184C2×#95—131no—
185#342—21no—
186#342—21no—
187#328—261no—
188#328—261no—
189#328—261no—
190#328—261no—
191C22×C13—21no—
192C22×C13—21no—
193C22×C13—21no—
194C22×C13—21no—
195C22×C13—21no—
196C22×C13—21no—
197C22×C13—41no—
198C22×C13—41no—
199C22×C13—41no—
200C22×C13—41no—
201C22×C13#39311yescharacteristic
202C22×C13#45211yescharacteristic
203C22×C13#45211yescharacteristic
204C22×C13#47911yescharacteristic
205C22×C13#47911yescharacteristic
206C22×C13#48811yescharacteristic
207C22×C13#49111yescharacteristic
208C4×C13—21no—
209C4×C13—21no—
210C4×C13—21no—
211C4×C13—21no—
212C4×C13—81no—
213C4×C13—81no—
214C4×C13—81no—
215C4×C13—81no—
216C4×C13—161no—
217Dic13—42no—
218Dic13—81no—
219Dic13—81no—
220Dic13—81no—
221C22×Q8Dic2611yescharacteristic
222C23×C4—261no—
223C23×C4C22×D1311yescharacteristic
224C22×C8—261no—
225C22×C8—261no—
226C22⋊Q8—21no—
227C22⋊Q8—21no—
228C22⋊Q8—21no—
229C22⋊Q8—21no—
230C2×C4⋊C4—21no—
231C2×C4⋊C4—21no—
232C2×C4⋊C4—261no—
233C2×C4⋊C4—261no—
234C2×C4⋊C4—261no—
235C2×C4⋊C4—261no—
236C2×C4⋊C4—261no—
237C2×C4⋊C4Dic2611yescharacteristic
238C2×C22⋊C4—21no—
239C2×C22⋊C4—21no—
240C2×C22⋊C4—261no—
241C2×C22⋊C4C22⋊D1311yescharacteristic
242C2×C22⋊C4C22⋊D1311yescharacteristic
243C2×C42—21no—
244C22⋊C8—261no—
245C22⋊C8—261no—
246C22⋊C8—261no—
247C22⋊C8—261no—
248#95—21no—
249#95—21no—
250#95—131no—
251#95—131no—
252#95—131no—
253#95—131no—
254#95—261no—
255#95—261no—
256#95—261no—
257#95—261no—
258#95—261no—
259C2×C13—21no—
260C2×C13—21no—
261C2×C13—21no—
262C2×C13—21no—
263C2×C13—21no—
264C2×C13—21no—
265C2×C13#202611yescharacteristic
266C2×C13#203111yescharacteristic
267C2×C13#203211yescharacteristic
268C24C2×C22⋊D1311yescharacteristic
269C2×Q8—21no—
270C2×Q8—21no—
271C2×Q8—81no—
272C22×C4—21no—
273C22×C4—21no—
274C22×C4—21no—
275C22×C4—21no—
276C22×C4—41no—
277C22×C4—81no—
278C22×C4—261no—
279C22×C4—261no—
280C22×C4—261no—
281C22×C4—261no—
282C22×C4—522no—
283C22×C4—521no—
284C22×C4—521no—
285C22×C4—1041no—
286C22×C4C2×Dic2611yescharacteristic
287C22×C4#612711yescharacteristic
288C22×C4D4×D1311yescharacteristic
289C22×C4D4×D1311yescharacteristic
290C22×C4#612911yescharacteristic
291C22×C4#612911yescharacteristic
292C2×C8—521no—
293C2×C8—521no—
294C2×C8—1041no—
295C2×C8—1041no—
296C4⋊C4—21no—
297C4⋊C4—21no—
298C4⋊C4—41no—
299C4⋊C4—41no—
300C4⋊C4—81no—
301C4⋊C4—522no—
302C4⋊C4—522no—
303C4⋊C4—1041no—
304C4⋊C4—1041no—
305C4⋊C4—1041no—
306C22⋊C4—21no—
307C22⋊C4—21no—
308C22⋊C4—21no—
309C22⋊C4—21no—
310C22⋊C4—41no—
311C22⋊C4—41no—
312C22⋊C4—41no—
313C22⋊C4—41no—
314C22⋊C4—521no—
315C22⋊C4—521no—
316C42—81no—
317C13#1037711yescharacteristic, complemented, Sylow
318C23—41no—
319C23—41no—
320C23#8817811yescharacteristic
321C23#8819011yescharacteristic
322C23#8819111yescharacteristic
323C23#8819611yescharacteristic
324C23#8819611yescharacteristic
325C23#8820411yescharacteristic
326C23#8820411yescharacteristic
327Q8—81no—
328Q8—81no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—81no—
344C2×C4—81no—
345C2×C4—81no—
346C2×C4—81no—
347C2×C4—81no—
348C2×C4—262no—
349C2×C4—521no—
350C2×C4—521no—
351C2×C4—521no—
352C2×C4—521no—
353C2×C4—521no—
354C2×C4—521no—
355C2×C4—521no—
356C2×C4—521no—
357C2×C4—521no—
358C2×C4—521no—
359C2×C4—521no—
360C2×C4—1042no—
361C2×C4—1042no—
362C2×C4#8813211yescharacteristic
363C2×C4#8813211yescharacteristic
364C2×C4#8813911yescharacteristic
365C2×C4#8813911yescharacteristic
366C8—1041no—
367C8—1041no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—41no—
375C22—41no—
376C22—41no—
377C22—41no—
378C22#1171860811yescharacteristic
379C22#1171868311yescharacteristic
380C22#1171868311yescharacteristic
381C22#1171870811yescharacteristic
382C22#1171870811yescharacteristic
383C22#1171871711yescharacteristic
384C22#1171874311yescharacteristic
385C4—21no—
386C4—21no—
387C4—21no—
388C4—21no—
389C4—81no—
390C4—81no—
391C4—81no—
392C4—81no—
393C4—161no—
394C4—522no—
395C4—1041no—
396C4—1041no—
397C4—1041no—
398C2—21no—
399C2—21no—
400C2—21no—
401C2—21no—
402C2—21no—
403C2—21no—
404C2#1311598711yescharacteristic
405C2#1311601011yescharacteristic
406C2#1311601311yescharacteristic
subgroupG/H
centerC22#11718608
commutator, cosocleC23×C4×C13C23
FrattiniC23×C4C22×D13
FittingC13×#1996C2
socleC22×C13#393
prime radicalC24×C13C2×D4
hypercenter#1996D13
hypocenterC13#10377
LCSG ▷ C23×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1996

Complements

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

NH ≅ G/Ntype
317. C13#10377semidirect

Maximal subgroups

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

subgroupindex
#131200552
#131134082
C2×#117181302
#131127142
#131127032
#131126842
C13×#19962
#1037713