Finite Group Databasebeta

← #15760084

Subgroups — #15760084

Order 3328.

500 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 500 conjugacy classes of subgroups — too many to draw. Only its 93 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#13124780C211yesmaximal, characteristic
2#13117727C211yesmaximal, characteristic
3#13115822C211yesmaximal, characteristic
4#13114933C211yesmaximal, characteristic
5#13112743C211yesmaximal, characteristic
6#13112722C211yesmaximal, characteristic
7C13×#1508C211yesmaximal, characteristic
8C2×C13×C22⋊Q8C2211yescharacteristic
9C2×#88180C2211yescharacteristic
10C13×#407C2211yescharacteristic
11C4×C13×C22⋊C4C2211yescharacteristic
12#11718886C412yescomplemented
13#11718873C2211yescharacteristic
14C4×C22⋊Dic13C2211yescharacteristic
15#11718868C2211yescharacteristic
16#11718706—22no—
17#11718705—21no—
18#11718704—21no—
19#11718625C412yescomplemented
20#11718606—22no—
21C4×C4⋊Dic13—21no—
22#11718589—21no—
23#11718312—21no—
24#11718310—21no—
25C13×#328—21no—
26C13×#328—21no—
27#11718147—22no—
28#11718118—22no—
29C22×Q8×C13C2×C411yescharacteristic
30C23×C4×C13C2311yescharacteristic
31C2×C13×M16—21no—
32C13×C22⋊Q8—21no—
33C13×C22⋊Q8—21no—
34C13×C22⋊Q8—21no—
35C13×C22⋊Q8—21no—
36C2×C13×C4⋊C4—21no—
37C2×C13×C4⋊C4C2×C411yescharacteristic
38C2×C13×C22⋊C4—21no—
39C2×C13×C22⋊C4—21no—
40C2×C42×C13—21no—
41C2×C22⋊Dic13—21no—
42C2×C22⋊Dic13—21no—
43C2×C22⋊Dic13D412yes—
44#88180—21no—
45#88180—21no—
46#88180C2×C412yes—
47#88180D412yes—
48C2×C4⋊Dic13—21no—
49C2×C4⋊Dic13D411yescharacteristic
50C2×C4⋊Dic13D411yescharacteristic
51C2×#6101—22no—
52C2×C4×Dic13—21no—
53C2×C4×Dic13—21no—
54C2×C4×Dic13—22no—
55C2×#6099C2×C412yes—
56C13×C22⋊C8—21no—
57C13×C22⋊C8—21no—
58C13×#95D411yescharacteristic
59C13×#95D411yescharacteristic
60#88075—22no—
61#88075—22no—
62#88071—22no—
63#88071—22no—
64#88071—21no—
65#88071—21no—
66C22⋊#1055—21no—
67C22⋊#1055—21no—
68#88048—22no—
69#88047—22no—
70#9362—131nomaximal, Sylow
71C24×C13C2×D411yescharacteristic
72C2×Q8×C13—21no—
73C2×Q8×C13—21no—
74C2×Q8×C13—42no—
75C22×C4×C13—21no—
76C22×C4×C13—21no—
77C22×C4×C13—21no—
78C22×C4×C13—21no—
79C22×C4×C13—42no—
80C22×C4×C13C22×C411yescharacteristic
81C22×C4×C13C2×D411yescharacteristic
82C22×C4×C13C2×D411yescharacteristic
83C22×C4×C13C2×D411yescharacteristic
84C22×C4×C13#4111yescharacteristic
85C22×C4×C13#4111yescharacteristic
86C22×Dic13—21no—
87C22×Dic13—21no—
88C22×Dic13—22no—
89C22×Dic13—41no—
90C13×M16—42no—
91C2×C8×C13—41no—
92C13×C4⋊C4—21no—
93C13×C4⋊C4—21no—
94C13×C4⋊C4—41no—
95C13×C4⋊C4—41no—
96C13×C22⋊C4—42no—
97C13×C22⋊C4—41no—
98C13×C22⋊C4—41no—
99C42×C13—42no—
100C22⋊Dic13—22no—
101C22⋊Dic13—22no—
102C22⋊Dic13—22no—
103C22⋊Dic13—41no—
104C22⋊Dic13—42no—
105C4⋊Dic13—21no—
106C4⋊Dic13—21no—
107C4⋊Dic13—42no—
108C4⋊Dic13C22⋊C412yes—
109C4⋊Dic13C22⋊C412yes—
110#6101—44no—
111C4×Dic13—22no—
112C4×Dic13—22no—
113C4×Dic13—42no—
114C4×Dic13—82no—
115#6099—42no—
116C2×#1055—22no—
117#3095—131no—
118#2347—131no—
119#1996—131no—
120#1826—131no—
121#1508D1311yescharacteristic
122#1305—131no—
123#1297—131no—
124C23×C13—21no—
125C23×C13—21no—
126C23×C13—41no—
127C23×C13—41no—
128C23×C13C4×D411yescharacteristic
129C23×C13#12011yescharacteristic
130C23×C13#12111yescharacteristic
131Q8×C13—42no—
132Q8×C13—81no—
133C2×C4×C13—22no—
134C2×C4×C13—22no—
135C2×C4×C13—22no—
136C2×C4×C13—22no—
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×C13C2×C22⋊C411yescharacteristic
150C2×C4×C13C4×D411yescharacteristic
151C2×C4×C13#12111yescharacteristic
152C2×C4×C13#12311yescharacteristic
153C2×Dic13—22no—
154C2×Dic13—22no—
155C2×Dic13—42no—
156C2×Dic13—41no—
157C2×Dic13—41no—
158C2×Dic13—42no—
159C2×Dic13—42no—
160C2×Dic13—42no—
161C2×Dic13—42no—
162C2×Dic13—81no—
163C2×Dic13—81no—
164C8×C13—81no—
165#1055—42no—
166C2×C22⋊Q8C2×D1311yescharacteristic
167C2×#117—131no—
168#485—262no—
169#484—261no—
170#483—261no—
171#428—132no—
172#419—132no—
173#407—131no—
174#407C2×D1311yescharacteristic
175#389—261no—
176#388—262no—
177#383—261no—
178#380—131no—
179C4×C4⋊C4—261no—
180C4×C4⋊C4—261no—
181C4×C22⋊C4—131no—
182C4×C22⋊C4C2×D1311yescharacteristic
183#342—262no—
184#339—262no—
185#328—21no—
186#328—21no—
187C22×C13—21no—
188C22×C13—21no—
189C22×C13—21no—
190C22×C13—21no—
191C22×C13—21no—
192C22×C13—21no—
193C22×C13—21no—
194C22×C13—21no—
195C22×C13—81no—
196C22×C13—81no—
197C22×C13#38611yescharacteristic
198C22×C13#45511yescharacteristic
199C22×C13#45611yescharacteristic
200C4×C13—21no—
201C4×C13—21no—
202C4×C13—21no—
203C4×C13—42no—
204C4×C13—81no—
205C4×C13—81no—
206C4×C13—81no—
207C4×C13#41012yes—
208Dic13—42no—
209Dic13—42no—
210Dic13—82no—
211Dic13—82no—
212C22×Q8C4×D1311yescharacteristic
213C23×C4C22×D1311yescharacteristic
214C2×M16—21no—
215C2×M16—132no—
216C22⋊Q8—21no—
217C22⋊Q8—21no—
218C22⋊Q8—21no—
219C22⋊Q8—21no—
220#117—132no—
221#117—132no—
222#117—261no—
223#117—261no—
224C2×C4⋊C4—21no—
225C2×C4⋊C4—131no—
226C2×C4⋊C4—131no—
227C2×C4⋊C4—262no—
228C2×C4⋊C4—261no—
229C2×C4⋊C4C4×D1311yescharacteristic
230C2×C22⋊C4—21no—
231C2×C22⋊C4—21no—
232C2×C22⋊C4—132no—
233C2×C22⋊C4—261no—
234C2×C22⋊C4—261no—
235C2×C42—21no—
236C2×C42—261no—
237C2×C42—261no—
238C2×C42—262no—
239#107—262no—
240#106—262no—
241#103—262no—
242#103—262no—
243C22⋊C8—21no—
244C22⋊C8—21no—
245C22⋊C8—261no—
246C22⋊C8—261no—
247#95—262no—
248#95—262no—
249#95—261no—
250#95—261no—
251#95C22⋊D1311yescharacteristic
252#95C22⋊D1311yescharacteristic
253C2×C13—21no—
254C2×C13—21no—
255C2×C13—41no—
256C2×C13—41no—
257C2×C13#188211yescharacteristic
258C2×C13#189911yescharacteristic
259C2×C13#190611yescharacteristic
260C24D4×D1311yescharacteristic
261C2×Q8—21no—
262C2×Q8—21no—
263C2×Q8—42no—
264C22×C4—21no—
265C22×C4—21no—
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—42no—
269C22×C4—261no—
270C22×C4—261no—
271C22×C4—262no—
272C22×C4—521no—
273C22×C4C2×C4×D1311yescharacteristic
274C22×C4#612711yescharacteristic
275C22×C4D4×D1311yescharacteristic
276C22×C4D4×D1311yescharacteristic
277C22×C4#612911yescharacteristic
278C22×C4C2×C22⋊D1311yescharacteristic
279M16—42no—
280M16—522no—
281C2×C8—41no—
282C2×C8—262no—
283C4⋊C4—21no—
284C4⋊C4—21no—
285C4⋊C4—41no—
286C4⋊C4—41no—
287C4⋊C4—132no—
288C4⋊C4—132no—
289C4⋊C4—261no—
290C4⋊C4—261no—
291C4⋊C4—524no—
292C4⋊C4—522no—
293C22⋊C4—42no—
294C22⋊C4—41no—
295C22⋊C4—41no—
296C22⋊C4—262no—
297C22⋊C4—262no—
298C22⋊C4—262no—
299C22⋊C4—521no—
300C22⋊C4—522no—
301C42—42no—
302C42—262no—
303C42—262no—
304C42—522no—
305C42—1042no—
306C13#936211yescharacteristic, complemented, Sylow
307C23—21no—
308C23—21no—
309C23—41no—
310C23—41no—
311C23#8813511yescharacteristic
312C23#8813811yescharacteristic
313C23#8819111yescharacteristic
314Q8—42no—
315Q8—81no—
316C2×C4—22no—
317C2×C4—22no—
318C2×C4—22no—
319C2×C4—22no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—81no—
331C2×C4—81no—
332C2×C4—262no—
333C2×C4—262no—
334C2×C4—522no—
335C2×C4—521no—
336C2×C4—521no—
337C2×C4—522no—
338C2×C4—522no—
339C2×C4—522no—
340C2×C4—522no—
341C2×C4—1041no—
342C2×C4—1041no—
343C2×C4C22⋊C4×D1311yescharacteristic
344C2×C4#8813711yescharacteristic
345C2×C4C4×C22⋊D1311yescharacteristic
346C2×C4#8819211yescharacteristic
347C8—81no—
348C8—522no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—21no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—81no—
358C22—81no—
359C22#1171861711yescharacteristic
360C22#1171886311yescharacteristic
361C22#1171886611yescharacteristic
362C4—21no—
363C4—21no—
364C4—21no—
365C4—42no—
366C4—81no—
367C4—81no—
368C4—81no—
369C4—522no—
370C4—522no—
371C4—1042no—
372C4—1042no—
373C4#1171840112yes—
374C2—21no—
375C2—21no—
376C2—41no—
377C2—41no—
378C2#1311520211yescharacteristic
379C2#1311529111yescharacteristic
380C2#1311534011yescharacteristic
subgroupG/H
centerC22#11718617
commutatorC22×C4×C13C22×C4
FrattiniC23×C4C22×D13
FittingC13×#1508C2
socleC22×C13#386
prime radicalC24×C13C2×D4
cosocleC23×C4×C13C23
hypercenter#1508D13
hypocenterC13#9362
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1508

Complements

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

NH ≅ G/Ntype
12. #11718886C4semidirect
19. #11718625C4semidirect
306. C13#9362semidirect

Maximal subgroups

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

subgroupindex
#131247802
#131177272
#131158222
#131149332
#131127432
#131127222
C13×#15082
#936213