Finite Group Databasebeta

← #15763698

Subgroups — #15763698

Order 3328.

500 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 500 conjugacy classes of subgroups — too many to draw. Only its 101 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#13124875C211yesmaximal, characteristic
2#13124641C211yesmaximal, characteristic
3#13113399C211yesmaximal, characteristic
4#13113265C211yesmaximal, characteristic
5#13113231C211yesmaximal, characteristic
6#13112694C211yesmaximal, characteristic
7C13×#2581C211yesmaximal, characteristic
8C2×C4×Q8×C13C2211yescharacteristic
9C2×C4×Q8×C13C2211yescharacteristic
10#11719175C2211yescharacteristic
11C13×#400—21no—
12C13×#395—21no—
13C13×#391—21no—
14C13×#389—21no—
15C13×#387—22no—
16C13×#382C2211yescharacteristic
17#11718889—21no—
18#11718886—21no—
19#11718692—21no—
20C4×#6107—22no—
21#11718683—22no—
22#11718682—21no—
23#11718682—21no—
24#11718681—21no—
25#11718631—21no—
26#11718625—21no—
27#11718586C2211yescharacteristic
28#11718586C2211yescharacteristic
29#11718585C2211yescharacteristic
30Q8⋊#1055—22no—
31Q8⋊#1055—22no—
32#11718044—22no—
33C22×Q8×C13D411yescharacteristic
34C22×Q8×C13D411yescharacteristic
35C4×Q8×C13—21no—
36C4×Q8×C13—21no—
37C4×Q8×C13—21no—
38C4×Q8×C13—21no—
39C4×Q8×C13—21no—
40C4×Q8×C13—21no—
41C4×Q8×C13—21no—
42C4×Q8×C13—21no—
43C2×C13×C4⋊C4—22no—
44C2×C13×C4⋊C4—21no—
45C2×C13×C4⋊C4—21no—
46C2×C13×C4⋊C4—21no—
47C2×C13×C4⋊C4D411yescharacteristic
48C2×C13×C4⋊C4D411yescharacteristic
49C2×C42×C13—21no—
50C2×C42×C13—21no—
51C2×C42×C13C2311yescharacteristic
52C2×#6107—22no—
53#88180—21no—
54#88178—21no—
55#88178—21no—
56C2×#6099—21no—
57#88124—21no—
58#88123D411yescharacteristic
59#88123D411yescharacteristic
60C4×Dic26—21no—
61C4×Dic26—21no—
62C13×#95—22no—
63C13×#95—22no—
64C13×#95—22no—
65C13×#95—21no—
66C13×#95D412yes—
67#88075—22no—
68#88075—22no—
69#88075—22no—
70C22⋊#1055—21no—
71C22⋊#1055—21no—
72#88050—22no—
73#88048—22no—
74#88047—22no—
75#88047—22no—
76C4⋊#1055—21no—
77C4⋊#1055—21no—
78C4⋊#1055—21no—
79C4⋊#1055D412yes—
80C4×#1055—21no—
81C4×#1055D412yes—
82#10003—131nomaximal, Sylow
83C2×Q8×C13—21no—
84C2×Q8×C13—21no—
85C2×Q8×C13—21no—
86C2×Q8×C13—21no—
87C2×Q8×C13—21no—
88C2×Q8×C13—21no—
89C2×Q8×C13—21no—
90C2×Q8×C13—42no—
91C2×Q8×C13Q1612yescomplemented
92C22×C4×C13—21no—
93C22×C4×C13—21no—
94C22×C4×C13—22no—
95C22×C4×C13—21no—
96C22×C4×C13—21no—
97C22×C4×C13C2×D411yescharacteristic
98C22×C4×C13C2×D411yescharacteristic
99C22×C4×C13C2×D411yescharacteristic
100C2×Dic26—21no—
101C2×Dic26—21no—
102C13×C4⋊C4—21no—
103C13×C4⋊C4—21no—
104C13×C4⋊C4—21no—
105C13×C4⋊C4—21no—
106C13×C4⋊C4—44no—
107C13×C4⋊C4—41no—
108C13×C4⋊C4—41no—
109C13×C4⋊C4—41no—
110C13×C4⋊C4—41no—
111C13×C4⋊C4—41no—
112C13×C4⋊C4—41no—
113C42×C13—41no—
114C42×C13—41no—
115C42×C13—41no—
116C42×C13—41no—
117C42×C13C2×D411yescharacteristic
118C42×C13C2×D411yescharacteristic
119C42×C13C2×D411yescharacteristic
120C42×C13#4111yescharacteristic
121C22⋊Dic13—41no—
122#6107—44no—
123C4⋊Dic13—21no—
124C4⋊Dic13—21no—
125C4⋊Dic13—21no—
126C4⋊Dic13—21no—
127#6101—41no—
128#6101—41no—
129C4×Dic13—41no—
130#6099—41no—
131#6099—41no—
132C2×#1055—22no—
133C2×#1055—22no—
134C2×#1055—41no—
135#3104—131no—
136#3078—131no—
137#2581D1311yescharacteristic
138#1518—131no—
139#1487—131no—
140#1479—131no—
141#1286—131no—
142C23×C13#12011yescharacteristic
143Q8×C13—22no—
144Q8×C13—22no—
145Q8×C13—22no—
146Q8×C13—22no—
147Q8×C13—41no—
148Q8×C13—41no—
149Q8×C13—41no—
150Q8×C13—41no—
151C2×C4×C13—22no—
152C2×C4×C13—22no—
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—42no—
160C2×C4×C13—42no—
161C2×C4×C13—42no—
162C2×C4×C13—42no—
163C2×C4×C13—41no—
164C2×C4×C13—41no—
165C2×C4×C13—42no—
166C2×C4×C13#12011yescharacteristic
167C2×C4×C13#12011yescharacteristic
168C2×C4×C13#12111yescharacteristic
169C2×C4×C13#12111yescharacteristic
170C2×C4×C13#12111yescharacteristic
171C2×C4×C13#12711yescharacteristic
172C2×C4×C13C2×Q1611yescharacteristic
173C2×C4×C13#13511yescharacteristic
174C2×C4×C13#13711yescharacteristic
175C2×C4×C13#13711yescharacteristic
176C2×Dic13—41no—
177C2×Dic13—41no—
178Dic26—42no—
179Dic26—81no—
180#1055—42no—
181#1055—42no—
182#1055—81no—
183#533—131no—
184C2×C4×Q8C2×D1311yescharacteristic
185C2×C4×Q8C2×D1311yescharacteristic
186#484—261no—
187#479—262no—
188#477—261no—
189#477—261no—
190#475—261no—
191#462—261no—
192#451—261no—
193C4×Q16—262no—
194#431—131no—
195#431—131no—
196#428—261no—
197#423—131no—
198#419—261no—
199#400—21no—
200#395—21no—
201#391—21no—
202#389—21no—
203#387—22no—
204#382C2×D1311yescharacteristic
205#328—262no—
206Q8⋊C8—262no—
207Q8⋊C8—262no—
208C22×C13—21no—
209C22×C13—21no—
210C22×C13#39211yescharacteristic
211C22×C13#45111yescharacteristic
212C22×C13#45211yescharacteristic
213C4×C13—21no—
214C4×C13—21no—
215C4×C13—21no—
216C4×C13—21no—
217C4×C13—42no—
218C4×C13—42no—
219C4×C13—82no—
220C4×C13—81no—
221C4×C13—81no—
222C4×C13#45111yescharacteristic
223C4×C13#45211yescharacteristic
224C4×C13#46711yescharacteristic
225C4×C13#47011yescharacteristic
226Dic13—81no—
227Dic13—81no—
228C22×Q8C22⋊D1311yescharacteristic
229C22×Q8C22⋊D1311yescharacteristic
230C2×Q16—262no—
231C2×M16—261no—
232C4⋊Q8—131no—
233C4⋊Q8—131no—
234#125—261no—
235C22⋊Q8—261no—
236C22⋊Q8—261no—
237C4×Q8—21no—
238C4×Q8—21no—
239C4×Q8—21no—
240C4×Q8—21no—
241C4×Q8—21no—
242C4×Q8—21no—
243C4×Q8—21no—
244C4×Q8—21no—
245C4×Q8—261no—
246C4×Q8—261no—
247#117—261no—
248C2×C4⋊C4—22no—
249C2×C4⋊C4—21no—
250C2×C4⋊C4—21no—
251C2×C4⋊C4—21no—
252C2×C4⋊C4C22⋊D1311yescharacteristic
253C2×C4⋊C4C22⋊D1311yescharacteristic
254C2×C42—21no—
255C2×C42—21no—
256C2×C42C22×D1311yescharacteristic
257#107—262no—
258#107—262no—
259#106—262no—
260C4⋊C8—132no—
261C4⋊C8—261no—
262C4⋊C8—261no—
263C4⋊C8—261no—
264#103—262no—
265#103—262no—
266#103—262no—
267#103—262no—
268C22⋊C8—261no—
269C22⋊C8—261no—
270C4×C8—132no—
271C4×C8—261no—
272#95—22no—
273#95—22no—
274#95—22no—
275#95—21no—
276#95C22⋊D1312yes—
277C2×C13—21no—
278C2×C13—21no—
279C2×C13#200111yescharacteristic
280C2×C13#200911yescharacteristic
281C2×C13#201011yescharacteristic
282C2×Q8—21no—
283C2×Q8—21no—
284C2×Q8—21no—
285C2×Q8—21no—
286C2×Q8—21no—
287C2×Q8—21no—
288C2×Q8—21no—
289C2×Q8—42no—
290C2×Q8—261no—
291C2×Q8—261no—
292C2×Q8#610712yescomplemented
293C22×C4—21no—
294C22×C4—21no—
295C22×C4—22no—
296C22×C4—21no—
297C22×C4—21no—
298C22×C4C2×C22⋊D1311yescharacteristic
299C22×C4C2×C22⋊D1311yescharacteristic
300C22×C4C2×C22⋊D1311yescharacteristic
301Q16—524no—
302M16—521no—
303M16—521no—
304C2×C8—262no—
305C2×C8—262no—
306C2×C8—521no—
307C4⋊C4—21no—
308C4⋊C4—21no—
309C4⋊C4—21no—
310C4⋊C4—21no—
311C4⋊C4—44no—
312C4⋊C4—41no—
313C4⋊C4—41no—
314C4⋊C4—41no—
315C4⋊C4—41no—
316C4⋊C4—41no—
317C4⋊C4—41no—
318C4⋊C4—261no—
319C4⋊C4—261no—
320C4⋊C4—261no—
321C4⋊C4—261no—
322C4⋊C4—521no—
323C4⋊C4—521no—
324C22⋊C4—521no—
325C42—41no—
326C42—41no—
327C42—41no—
328C42—41no—
329C42—521no—
330C42D4×D1311yescharacteristic
331C42D4×D1311yescharacteristic
332C42D4×D1311yescharacteristic
333C42#612911yescharacteristic
334C13#1000311yescharacteristic, complemented, Sylow
335C23#8820711yescharacteristic
336Q8—22no—
337Q8—22no—
338Q8—22no—
339Q8—22no—
340Q8—41no—
341Q8—41no—
342Q8—41no—
343Q8—41no—
344Q8—522no—
345Q8—1041no—
346C2×C4—22no—
347C2×C4—22no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—42no—
355C2×C4—42no—
356C2×C4—42no—
357C2×C4—42no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—42no—
361C2×C4—521no—
362C2×C4—521no—
363C2×C4#8819111yescharacteristic
364C2×C4#8819111yescharacteristic
365C2×C4#8819211yescharacteristic
366C2×C4#8819311yescharacteristic
367C2×C4#8819311yescharacteristic
368C2×C4#8819411yescharacteristic
369C2×C4#8819611yescharacteristic
370C2×C4C2×#610711yescharacteristic
371C2×C4#8820411yescharacteristic
372C2×C4#8820511yescharacteristic
373C8—522no—
374C8—522no—
375C8—1041no—
376C22—21no—
377C22—21no—
378C22#1171888411yescharacteristic
379C22#1171888911yescharacteristic
380C22#1171890011yescharacteristic
381C4—21no—
382C4—21no—
383C4—21no—
384C4—21no—
385C4—42no—
386C4—42no—
387C4—82no—
388C4—81no—
389C4—81no—
390C4—1041no—
391C4—1041no—
392C4#1171870811yescharacteristic
393C4#1171871111yescharacteristic
394C4#1171871211yescharacteristic
395C4#1171871311yescharacteristic
396C2—21no—
397C2—21no—
398C2#1311584411yescharacteristic
399C2#1311589611yescharacteristic
400C2#1311590111yescharacteristic
subgroupG/H
centerC22#11718884
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#2581C2
socleC22×C13#392
prime radicalC23×C13#120
hypercenter#2581D13
hypocenterC13#10003
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2581

Complements

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

NH ≅ G/Ntype
91. C2×Q8×C13Q16semidirect
292. C2×Q8#6107semidirect
334. C13#10003semidirect

Maximal subgroups

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

subgroupindex
#131248752
#131246412
#131133992
#131132652
#131132312
#131126942
C13×#25812
#1000313