Finite Group Databasebeta

← #15758966

Subgroups — #15758966

Order 3328.

560 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 560 conjugacy classes of subgroups — too many to draw. Only its 113 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#13120652C211yesmaximal, characteristic
2#13117453C211yesmaximal, characteristic
3#13113409C211yesmaximal, characteristic
4#13113407C211yesmaximal, characteristic
5C2×#11718061C211yesmaximal, characteristic
6#13112703C211yesmaximal, characteristic
7C13×#1289C211yesmaximal, characteristic
8C2×#88178C2211yescharacteristic
9C22×#6101C2211yescharacteristic
10C2×#88131—21no—
11C2×C13×C22⋊C8C2211yescharacteristic
12C13×#380C2211yescharacteristic
13C13×#380C2211yescharacteristic
14#11718873C2211yescharacteristic
15C2×C22⋊#1055C2211yescharacteristic
16#11718644—22no—
17#11718633—22no—
18#11718611—21no—
19#11718604—21no—
20#11718603—21no—
21#11718320C412yescomplemented
22#11718317C412yescomplemented
23#11718308—22no—
24#11718061—22no—
25#11718059—22no—
26#11718044—22no—
27C23×C4×C13C2311yescharacteristic
28C23×Dic13D411yescharacteristic
29C23×Dic13D411yescharacteristic
30C22×Dic26C2×C411yescharacteristic
31C22×C8×C13—21no—
32C2×C13×C4⋊C4—21no—
33C2×C13×C4⋊C4—21no—
34C2×C13×C22⋊C4—21no—
35C2×C13×C22⋊C4—21no—
36C2×C22⋊Dic13—21no—
37C2×C22⋊Dic13—21no—
38C2×C4⋊Dic13—21no—
39C2×C4⋊Dic13—22no—
40C2×C4⋊Dic13C2×C411yescharacteristic
41#88178—21no—
42#88178—21no—
43#88178—21no—
44#88178—21no—
45C2×#6101—21no—
46C2×#6101—21no—
47C2×#6101—21no—
48C2×#6101—21no—
49C2×#6101—22no—
50C2×#6101—21no—
51C2×#6101—22no—
52C2×#6101C2×C412yes—
53C2×#6101D412yes—
54C2×C4×Dic13—22no—
55C22×#1055—21no—
56#88131—42no—
57#88131—42no—
58C13×C22⋊C8—21no—
59C13×C22⋊C8—21no—
60C13×#95C2×C412yes—
61C13×#95D412yes—
62#88071—22no—
63#88071—22no—
64#88071—22no—
65#88071—22no—
66#88071D412yes—
67C22⋊#1055—21no—
68C22⋊#1055—21no—
69#9200—131nomaximal, Sylow
70C24×C13C2×D411yescharacteristic
71C22×C4×C13—22no—
72C22×C4×C13—22no—
73C22×C4×C13—81no—
74C22×C4×C13C22×C411yescharacteristic
75C22×C4×C13C2×D411yescharacteristic
76C22×C4×C13C2×D411yescharacteristic
77C22×C4×C13C2×D411yescharacteristic
78C22×C4×C13#4111yescharacteristic
79C22×C4×C13#4111yescharacteristic
80C22×Dic13—21no—
81C22×Dic13—21no—
82C22×Dic13—21no—
83C22×Dic13—21no—
84C22×Dic13—21no—
85C22×Dic13—21no—
86C22×Dic13—21no—
87C22×Dic13—21no—
88C22×Dic13—22no—
89C22×Dic13—81no—
90C22×Dic13C22⋊C412yes—
91C22×Dic13C22⋊C412yes—
92C22×Dic13SD1612yes—
93C22×Dic13Q1612yes—
94C2×Dic26—21no—
95C2×Dic26—21no—
96C2×Dic26—81no—
97C2×C8×C13—41no—
98C2×C8×C13—81no—
99C13×C4⋊C4—81no—
100C13×C4⋊C4—81no—
101C13×C22⋊C4—41no—
102C13×C22⋊C4—41no—
103C13×C22⋊C4—41no—
104C13×C22⋊C4—41no—
105C22⋊Dic13—41no—
106C22⋊Dic13—41no—
107C22⋊Dic13—41no—
108C22⋊Dic13—41no—
109C4⋊Dic13—21no—
110C4⋊Dic13—21no—
111C4⋊Dic13—82no—
112C4⋊Dic13—81no—
113#6101—22no—
114#6101—22no—
115#6101—22no—
116#6101—22no—
117#6101—44no—
118#6101—41no—
119#6101—41no—
120#6101—82no—
121C4×Dic13—44no—
122C2×#1055—41no—
123C2×#1055—81no—
124#2627—131no—
125#2316—131no—
126#1520—131no—
127#1520—131no—
128C2×#324—131no—
129#1289—131no—
130#1289D1311yescharacteristic
131C23×C13—41no—
132C23×C13—41no—
133C23×C13C2×C22⋊C411yescharacteristic
134C23×C13#12011yescharacteristic
135C23×C13#12311yescharacteristic
136C23×C13C2×SD1611yescharacteristic
137C23×C13C2×Q1611yescharacteristic
138C23×C13AGL(1,ℤ/8)11yescharacteristic
139C23×C13#13711yescharacteristic
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—42no—
147C2×C4×C13—42no—
148C2×C4×C13—42no—
149C2×C4×C13—42no—
150C2×C4×C13—42no—
151C2×C4×C13—42no—
152C2×C4×C13C4×D411yescharacteristic
153C2×C4×C13C4×D411yescharacteristic
154C2×C4×C13#12111yescharacteristic
155C2×C4×C13#12111yescharacteristic
156C2×Dic13—22no—
157C2×Dic13—22no—
158C2×Dic13—22no—
159C2×Dic13—22no—
160C2×Dic13—22no—
161C2×Dic13—22no—
162C2×Dic13—22no—
163C2×Dic13—42no—
164C2×Dic13—42no—
165C2×Dic13—42no—
166C2×Dic13—42no—
167C2×Dic13—42no—
168C2×Dic13—42no—
169C2×Dic13—41no—
170C2×Dic13—41no—
171C2×Dic13—42no—
172C2×Dic13—81no—
173C2×Dic13#10314yes—
174Dic26—81no—
175Dic26—81no—
176C8×C13—81no—
177#1055—81no—
178C2×C22⋊Q8—131no—
179C2×#117—261no—
180C22×C4⋊C4—131no—
181C2×C22⋊C8—131no—
182C2×C22⋊C8C2×D1311yescharacteristic
183#400—132no—
184#398—262no—
185#395—132no—
186#389—262no—
187#389—262no—
188#385—261no—
189#381—261no—
190#380—131no—
191#380—261no—
192#380C2×D1311yescharacteristic
193#380C2×D1311yescharacteristic
194#328—262no—
195#328—262no—
196#324—262no—
197C22×C13—21no—
198C22×C13—21no—
199C22×C13—21no—
200C22×C13—21no—
201C22×C13—21no—
202C22×C13—21no—
203C22×C13—41no—
204C22×C13—41no—
205C22×C13—41no—
206C22×C13—41no—
207C22×C13#38611yescharacteristic
208C22×C13C2×#10311yescharacteristic
209C22×C13#41711yescharacteristic
210C22×C13#45011yescharacteristic
211C22×C13#45111yescharacteristic
212C22×C13#48311yescharacteristic
213C22×C13#48411yescharacteristic
214C4×C13—21no—
215C4×C13—21no—
216C4×C13—21no—
217C4×C13—21no—
218C4×C13—82no—
219C4×C13—82no—
220Dic13—24no—
221Dic13—42no—
222Dic13—82no—
223Dic13—81no—
224Dic13—81no—
225C22×Q8—131no—
226C23×C4—131no—
227C23×C4—131no—
228C23×C4C22×D1311yescharacteristic
229C22×C8—21no—
230C22×C8—261no—
231C22⋊Q8—261no—
232C22⋊Q8—261no—
233C22⋊Q8—261no—
234C22⋊Q8—261no—
235#117—522no—
236#117—522no—
237C2×C4⋊C4—21no—
238C2×C4⋊C4—21no—
239C2×C4⋊C4—132no—
240C2×C4⋊C4—132no—
241C2×C4⋊C4—131no—
242C2×C4⋊C4—261no—
243C2×C4⋊C4—261no—
244C2×C4⋊C4—261no—
245C2×C4⋊C4—261no—
246C2×C4⋊C4—262no—
247C2×C4⋊C4—261no—
248C2×C4⋊C4—262no—
249C2×C4⋊C4—262no—
250C2×C4⋊C4—261no—
251C2×C22⋊C4—21no—
252C2×C22⋊C4—21no—
253C2×C22⋊C4—261no—
254C2×C22⋊C4—261no—
255C2×C42—262no—
256C22⋊C8—21no—
257C22⋊C8—21no—
258C22⋊C8—261no—
259C22⋊C8—261no—
260#95—132no—
261#95—262no—
262#95—262no—
263#95—262no—
264#95—262no—
265#95C4×D1312yes—
266#95D5212yes—
267C2×C13—21no—
268C2×C13—21no—
269C2×C13—21no—
270C2×C13—21no—
271C2×C13—21no—
272C2×C13—21no—
273C2×C13#187211yescharacteristic
274C2×C13#191211yescharacteristic
275C2×C13#191311yescharacteristic
276C24D4×D1311yescharacteristic
277C2×Q8—261no—
278C2×Q8—261no—
279C2×Q8—1041no—
280C22×C4—22no—
281C22×C4—22no—
282C22×C4—81no—
283C22×C4—132no—
284C22×C4—132no—
285C22×C4—132no—
286C22×C4—132no—
287C22×C4—261no—
288C22×C4—261no—
289C22×C4—261no—
290C22×C4—261no—
291C22×C4—261no—
292C22×C4—261no—
293C22×C4—261no—
294C22×C4—261no—
295C22×C4—262no—
296C22×C4—1041no—
297C22×C4C2×C4×D1311yescharacteristic
298C22×C4C2×D5211yescharacteristic
299C22×C4#612711yescharacteristic
300C22×C4D4×D1311yescharacteristic
301C22×C4D4×D1311yescharacteristic
302C22×C4#613111yescharacteristic
303C2×C8—41no—
304C2×C8—81no—
305C2×C8—521no—
306C2×C8—1041no—
307C4⋊C4—81no—
308C4⋊C4—81no—
309C4⋊C4—262no—
310C4⋊C4—262no—
311C4⋊C4—262no—
312C4⋊C4—262no—
313C4⋊C4—261no—
314C4⋊C4—261no—
315C4⋊C4—524no—
316C4⋊C4—521no—
317C4⋊C4—521no—
318C4⋊C4—1042no—
319C4⋊C4—1041no—
320C4⋊C4—1042no—
321C22⋊C4—41no—
322C22⋊C4—41no—
323C22⋊C4—41no—
324C22⋊C4—41no—
325C22⋊C4—521no—
326C22⋊C4—521no—
327C22⋊C4—521no—
328C22⋊C4—521no—
329C42—524no—
330C13#920011yescharacteristic, complemented, Sylow
331C23—41no—
332C23—41no—
333C23C22⋊C4×D1311yescharacteristic
334C23#8813611yescharacteristic
335C23#8814811yescharacteristic
336C23#8816511yescharacteristic
337C23SD16×D1311yescharacteristic
338C23#8816911yescharacteristic
339C23Q16×D1311yescharacteristic
340Q8—1041no—
341Q8—1041no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—42no—
349C2×C4—42no—
350C2×C4—42no—
351C2×C4—42no—
352C2×C4—42no—
353C2×C4—42no—
354C2×C4—134no—
355C2×C4—262no—
356C2×C4—262no—
357C2×C4—262no—
358C2×C4—262no—
359C2×C4—262no—
360C2×C4—262no—
361C2×C4—262no—
362C2×C4—522no—
363C2×C4—522no—
364C2×C4—522no—
365C2×C4—522no—
366C2×C4—522no—
367C2×C4—522no—
368C2×C4—522no—
369C2×C4—521no—
370C2×C4—521no—
371C2×C4—1041no—
372C2×C4C4×D5211yescharacteristic
373C2×C4#8813811yescharacteristic
374C2×C4#8814711yescharacteristic
375C2×C4#8814911yescharacteristic
376C8—81no—
377C8—1041no—
378C22—21no—
379C22—21no—
380C22—21no—
381C22—21no—
382C22—21no—
383C22—21no—
384C22—41no—
385C22—41no—
386C22—41no—
387C22—41no—
388C22#1171832611yescharacteristic
389C22#1171843211yescharacteristic
390C22#1171843711yescharacteristic
391C22D13×#10311yescharacteristic
392C22#1171846911yescharacteristic
393C22#1171852311yescharacteristic
394C22#1171854511yescharacteristic
395C4—21no—
396C4—21no—
397C4—21no—
398C4—21no—
399C4—82no—
400C4—82no—
401C4—264no—
402C4—522no—
403C4—1042no—
404C4—1041no—
405C4—1041no—
406C2—21no—
407C2—21no—
408C2—21no—
409C2—21no—
410C2—21no—
411C2—21no—
412C2#1311514211yescharacteristic
413C2#1311537211yescharacteristic
414C2#1311537711yescharacteristic
subgroupG/H
centerC22#11718326
commutatorC22×C4×C13C22×C4
FrattiniC23×C4C22×D13
FittingC13×#1289C2
socleC22×C13#386
prime radicalC24×C13C2×D4
cosocleC23×C4×C13C23
hypercenter#1289D13
hypocenterC13#9200
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1289

Complements

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

NH ≅ G/Ntype
21. #11718320C4semidirect
22. #11718317C4semidirect
330. C13#9200semidirect

Maximal subgroups

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

subgroupindex
#131206522
#131174532
#131134092
#131134072
C2×#117180612
#131127032
C13×#12892
#920013