Finite Group Databasebeta

← #15765374

Subgroups — #15765374

Order 3328.

500 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 500 conjugacy classes of subgroups — too many to draw. Only its 105 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#13125781C211yesmaximal, characteristic
2#13120048C211yesmaximal, characteristic
3#13113518C211yesmaximal, characteristic
4#13113335C211yesmaximal, characteristic
5#13113231C211yesmaximal, characteristic
6#13112737C211yesmaximal, characteristic
7C13×#3078C211yesmaximal, characteristic
8C13×#533C2211yescharacteristic
9C2×C4×Q8×C13C2211yescharacteristic
10C2×#88123C2211yescharacteristic
11C13×#479—22no—
12C13×#477—21no—
13C13×#475—21no—
14C13×#428—21no—
15C13×#423C2211yescharacteristic
16C13×#419—21no—
17#11718891—21no—
18#11718754—21no—
19#11718753—21no—
20#11718711—22no—
21#11718692—22no—
22#11718647—22no—
23#11718638—21no—
24C4×C4⋊Dic13C2211yescharacteristic
25#11718590—22no—
26#11718586C2211yescharacteristic
27#11718586C2211yescharacteristic
28#11718130—22no—
29Q8⋊#1055—22no—
30#11718073—22no—
31C22×Q8×C13D411yescharacteristic
32C22×Dic26D412yes—
33C2×C13×M16—21no—
34C13×C4⋊Q8D411yescharacteristic
35C13×C4⋊Q8D411yescharacteristic
36C13×#125—21no—
37C13×C22⋊Q8—21no—
38C13×C22⋊Q8—21no—
39C4×Q8×C13—21no—
40C4×Q8×C13—21no—
41C4×Q8×C13—21no—
42C4×Q8×C13—21no—
43C4×Q8×C13—21no—
44C4×Q8×C13—21no—
45C13×#117—21no—
46C2×C13×C4⋊C4—21no—
47C2×C13×C4⋊C4D411yescharacteristic
48C2×C42×C13—21no—
49C2×C42×C13C2311yescharacteristic
50C2×#6107—24no—
51C2×C4⋊Dic13—21no—
52C2×C4⋊Dic13—21no—
53C2×C4⋊Dic13—21no—
54C2×C4×Dic13—21no—
55#88123—21no—
56#88123—21no—
57#88123—21no—
58#88123—21no—
59C13×#107—22no—
60C13×#106—22no—
61C13×C4⋊C8—21no—
62C13×C4⋊C8D412yes—
63C13×#103—22no—
64C13×#103—22no—
65#88071—24no—
66#88071—24no—
67#88071D412yes—
68C22⋊#1055—21no—
69C22⋊#1055—21no—
70#88050—24no—
71C4⋊#1055—21no—
72C4⋊#1055D412yes—
73C4×#1055—21no—
74C4×#1055—21no—
75#10252—131nomaximal, Sylow
76C2×Q8×C13—21no—
77C2×Q8×C13—21no—
78C2×Q8×C13—21no—
79C2×Q8×C13—21no—
80C2×Q8×C13—21no—
81C2×Q8×C13—21no—
82C2×Q8×C13—21no—
83C2×Q8×C13Q1612yescomplemented
84C22×C4×C13—21no—
85C22×C4×C13—21no—
86C22×C4×C13C2×D411yescharacteristic
87C22×C4×C13C2×D411yescharacteristic
88C22×C4×C13C2×D411yescharacteristic
89C22×Dic13—22no—
90C22×Dic13—22no—
91C2×Dic26—22no—
92C2×Dic26—22no—
93C2×Dic26—44no—
94C13×M16—41no—
95C13×M16—41no—
96C2×C8×C13—22no—
97C13×C4⋊C4—21no—
98C13×C4⋊C4—21no—
99C13×C4⋊C4—21no—
100C13×C4⋊C4—21no—
101C13×C4⋊C4—21no—
102C13×C4⋊C4—21no—
103C13×C4⋊C4—41no—
104C13×C4⋊C4—41no—
105C13×C4⋊C4—41no—
106C13×C4⋊C4—41no—
107C13×C22⋊C4—41no—
108C42×C13—41no—
109C42×C13—41no—
110C42×C13—41no—
111C42×C13C2×D411yescharacteristic
112C42×C13C2×D411yescharacteristic
113C42×C13C2×D411yescharacteristic
114C42×C13#4111yescharacteristic
115#6107—84no—
116C4⋊Dic13—42no—
117C4⋊Dic13—41no—
118C4⋊Dic13—41no—
119C4⋊Dic13—41no—
120C4⋊Dic13—41no—
121C4×Dic13—41no—
122C4×Dic13—41no—
123C2×#1055—22no—
124C2×#1055—41no—
125#3209—131no—
126#3078D1311yescharacteristic
127#2568—131no—
128#1548—131no—
129#1503—131no—
130#1479—131no—
131#1303—131no—
132C23×C13#12011yescharacteristic
133Q8×C13—22no—
134Q8×C13—22no—
135Q8×C13—41no—
136Q8×C13—41no—
137Q8×C13—42no—
138Q8×C13—81no—
139C2×C4×C13—22no—
140C2×C4×C13—22no—
141C2×C4×C13—41no—
142C2×C4×C13—41no—
143C2×C4×C13—41no—
144C2×C4×C13—42no—
145C2×C4×C13—41no—
146C2×C4×C13—41no—
147C2×C4×C13—41no—
148C2×C4×C13#12011yescharacteristic
149C2×C4×C13#12011yescharacteristic
150C2×C4×C13#12111yescharacteristic
151C2×C4×C13#12111yescharacteristic
152C2×C4×C13#12111yescharacteristic
153C2×C4×C13#12711yescharacteristic
154C2×C4×C13C2×Q1611yescharacteristic
155C2×C4×C13#13511yescharacteristic
156C2×C4×C13#13711yescharacteristic
157C2×C4×C13#13711yescharacteristic
158C2×Dic13—42no—
159C2×Dic13—44no—
160C2×Dic13—42no—
161C2×Dic13—42no—
162C2×Dic13—42no—
163Dic26—44no—
164Dic26—82no—
165C8×C13—42no—
166#1055—42no—
167#1055—81no—
168#533C2×D1311yescharacteristic
169C2×C4⋊Q8—131no—
170C2×C4×Q8C2×D1311yescharacteristic
171#494—261no—
172#487—261no—
173#479—22no—
174#477—21no—
175#475—21no—
176#462—262no—
177#451—262no—
178#431—131no—
179#431—131no—
180#428—21no—
181#423C2×D1311yescharacteristic
182#419—21no—
183#400—262no—
184#391—262no—
185#391—261no—
186#382—261no—
187C4×C4⋊C4—131no—
188#333—262no—
189#328—262no—
190Q8⋊C8—262no—
191C22×C13—21no—
192C22×C13—21no—
193C22×C13#39211yescharacteristic
194C22×C13#45111yescharacteristic
195C22×C13#45211yescharacteristic
196C4×C13—21no—
197C4×C13—21no—
198C4×C13—21no—
199C4×C13—42no—
200C4×C13—81no—
201C4×C13—81no—
202C4×C13—81no—
203C4×C13#45111yescharacteristic
204C4×C13#45211yescharacteristic
205C4×C13#45512yes—
206C4×C13#46711yescharacteristic
207C4×C13#47011yescharacteristic
208Dic13—82no—
209Dic13—82no—
210C22×Q8—132no—
211C22×Q8C22⋊D1311yescharacteristic
212C2×Q16—264no—
213C2×M16—21no—
214C4⋊Q8—261no—
215C4⋊Q8—261no—
216C4⋊Q8—261no—
217C4⋊Q8—261no—
218C4⋊Q8C22⋊D1311yescharacteristic
219C4⋊Q8C22⋊D1311yescharacteristic
220#125—21no—
221C22⋊Q8—21no—
222C22⋊Q8—21no—
223C4×Q8—21no—
224C4×Q8—21no—
225C4×Q8—21no—
226C4×Q8—21no—
227C4×Q8—21no—
228C4×Q8—21no—
229#117—21no—
230C2×C4⋊C4—21no—
231C2×C4⋊C4—261no—
232C2×C4⋊C4—261no—
233C2×C4⋊C4—261no—
234C2×C4⋊C4C22⋊D1311yescharacteristic
235C2×C42—21no—
236C2×C42—261no—
237C2×C42C22×D1311yescharacteristic
238#107—22no—
239#106—22no—
240C4⋊C8—21no—
241C4⋊C8—132no—
242C4⋊C8—261no—
243C4⋊C8C22⋊D1312yes—
244#103—22no—
245#103—22no—
246#103—264no—
247C22⋊C8—261no—
248C22⋊C8—261no—
249C4×C8—261no—
250C4×C8—261no—
251#95—132no—
252#95—264no—
253#95—264no—
254C2×C13—21no—
255C2×C13—21no—
256C2×C13#200111yescharacteristic
257C2×C13#200411yescharacteristic
258C2×C13#200911yescharacteristic
259C2×Q8—21no—
260C2×Q8—21no—
261C2×Q8—21no—
262C2×Q8—21no—
263C2×Q8—21no—
264C2×Q8—21no—
265C2×Q8—21no—
266C2×Q8—262no—
267C2×Q8—262no—
268C2×Q8—524no—
269C2×Q8#610712yescomplemented
270C22×C4—21no—
271C22×C4—21no—
272C22×C4—262no—
273C22×C4—262no—
274C22×C4D4×D1311yescharacteristic
275C22×C4D4×D1311yescharacteristic
276C22×C4C2×C22⋊D1311yescharacteristic
277Q16—1044no—
278M16—41no—
279M16—41no—
280C2×C8—22no—
281C2×C8—262no—
282C2×C8—521no—
283C4⋊C4—21no—
284C4⋊C4—21no—
285C4⋊C4—21no—
286C4⋊C4—21no—
287C4⋊C4—21no—
288C4⋊C4—21no—
289C4⋊C4—41no—
290C4⋊C4—41no—
291C4⋊C4—41no—
292C4⋊C4—41no—
293C4⋊C4—522no—
294C4⋊C4—521no—
295C4⋊C4—521no—
296C4⋊C4—521no—
297C4⋊C4—521no—
298C22⋊C4—41no—
299C42—41no—
300C42—41no—
301C42—41no—
302C42—521no—
303C42—521no—
304C42D4×D1311yescharacteristic
305C42#612911yescharacteristic
306C42C2×C22⋊D1311yescharacteristic
307C42C2×C22⋊D1311yescharacteristic
308C13#1025211yescharacteristic, complemented, Sylow
309C23#8819111yescharacteristic
310Q8—22no—
311Q8—22no—
312Q8—41no—
313Q8—41no—
314Q8—42no—
315Q8—81no—
316Q8—524no—
317Q8—1042no—
318C2×C4—22no—
319C2×C4—22no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—42no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—522no—
328C2×C4—522no—
329C2×C4—524no—
330C2×C4—522no—
331C2×C4—522no—
332C2×C4#8819111yescharacteristic
333C2×C4#8819211yescharacteristic
334C2×C4#8819311yescharacteristic
335C2×C4#8819311yescharacteristic
336C2×C4#8819411yescharacteristic
337C2×C4#8819611yescharacteristic
338C2×C4C2×#610711yescharacteristic
339C2×C4#8820411yescharacteristic
340C2×C4#8820511yescharacteristic
341C2×C4#8820711yescharacteristic
342C8—42no—
343C8—522no—
344C8—1041no—
345C22—21no—
346C22—21no—
347C22#1171870811yescharacteristic
348C22#1171871111yescharacteristic
349C22#1171888411yescharacteristic
350C4—21no—
351C4—21no—
352C4—21no—
353C4—42no—
354C4—81no—
355C4—81no—
356C4—81no—
357C4—1042no—
358C4—1042no—
359C4#1171871211yescharacteristic
360C4#1171871311yescharacteristic
361C4#1171886312yes—
362C4#1171888911yescharacteristic
363C4#1171890011yescharacteristic
364C2—21no—
365C2—21no—
366C2#1311584411yescharacteristic
367C2#1311586211yescharacteristic
368C2#1311589311yescharacteristic
subgroupG/H
centerC22#11718884
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#3078C2
socleC22×C13#392
prime radicalC23×C13#120
hypercenter#3078D13
hypocenterC13#10252
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3078

Complements

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

NH ≅ G/Ntype
83. C2×Q8×C13Q16semidirect
269. C2×Q8#6107semidirect
308. C13#10252semidirect

Maximal subgroups

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

subgroupindex
#131257812
#131200482
#131135182
#131133352
#131132312
#131127372
C13×#30782
#1025213