Finite Group Databasebeta

← #15765349

Subgroups — #15765349

Order 3328.

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

normal subgroups only

This group has 604 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#13125784C211yesmaximal, characteristic, complemented
2#13124633C211yesmaximal, characteristic
3#13113517C211yesmaximal, characteristic, complemented
4#13113334C211yesmaximal, characteristic, complemented
5#13113227C211yesmaximal, characteristic
6#13112739C211yesmaximal, characteristic, complemented
7C13×#2542C211yesmaximal, characteristic
8C2×C13×C4⋊Q8C2211yescharacteristic
9C2×C13×C22⋊Q8—22no—
10C2×C4×D4×C13C2211yescharacteristic
11#11719175C2211yescharacteristic
12C13×#399—22no—
13C13×#390—21no—
14C13×#384—21no—
15C4×C13×C4⋊C4C2211yescharacteristic
16#11718889—22no—
17#11718876—21no—
18#11718753—21no—
19#11718751—22no—
20#11718742—21no—
21#11718670—22no—
22#11718669—21no—
23#11718668—21no—
24#11718625—21no—
25#11718586C2211yescharacteristic
26#11718586C2211yescharacteristic
27#11718585C2211yescharacteristic
28#11718138—22no—
29D4⋊#1055—22no—
30#11718044—22no—
31C22×Q8×C13D412yes—
32C22×D4×C13D411yescharacteristic
33C23×C4×C13—21no—
34C13×C4⋊Q8—21no—
35C13×C4⋊Q8—21no—
36C13×C4⋊Q8—21no—
37C13×C4⋊Q8—21no—
38C13×C22⋊Q8—48no—
39C4×D4×C13—21no—
40C4×D4×C13—21no—
41C4×D4×C13—21no—
42C4×D4×C13—21no—
43C2×C13×C4⋊C4—21no—
44C2×C13×C4⋊C4—24no—
45C2×C13×C4⋊C4—21no—
46C2×C13×C4⋊C4—21no—
47C2×C13×C4⋊C4D411yescharacteristic
48C2×C13×C22⋊C4—24no—
49C2×C13×C22⋊C4—21no—
50C2×C42×C13—21no—
51C2×C42×C13C2311yescharacteristic
52C2×#6107—24no—
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×#95D412yes—
63#88075—24no—
64#88072—22no—
65#88072—22no—
66C22⋊#1055—21no—
67C22⋊#1055—21no—
68#88048—22no—
69#88047—22no—
70C4⋊#1055—21no—
71C4⋊#1055—21no—
72C4⋊#1055D412yes—
73C4⋊#1055D412yes—
74C4×#1055—21no—
75C4×#1055—21no—
76#10248—131nomaximal, Sylow
77C24×C13—21no—
78C2×Q8×C13—22no—
79C2×Q8×C13—22no—
80C2×Q8×C13—44no—
81C2×D4×C13—21no—
82C2×D4×C13—21no—
83C2×D4×C13—21no—
84C2×D4×C13—21no—
85C2×D4×C13—21no—
86C2×D4×C13Q1612yescomplemented
87C22×C4×C13—22no—
88C22×C4×C13—22no—
89C22×C4×C13—21no—
90C22×C4×C13—44no—
91C22×C4×C13—41no—
92C22×C4×C13—41no—
93C22×C4×C13C2×D411yescharacteristic
94C22×C4×C13C2×D411yescharacteristic
95C22×C4×C13C2×D411yescharacteristic
96C2×Dic26—21no—
97C2×Dic26—21no—
98C13×C4⋊C4—24no—
99C13×C4⋊C4—21no—
100C13×C4⋊C4—21no—
101C13×C4⋊C4—48no—
102C13×C4⋊C4—41no—
103C13×C4⋊C4—41no—
104C13×C4⋊C4—41no—
105C13×C4⋊C4—41no—
106C13×C22⋊C4—48no—
107C13×C22⋊C4—41no—
108C13×C22⋊C4—41no—
109C42×C13—41no—
110C42×C13—41no—
111C42×C13C2×D411yescharacteristic
112C42×C13C2×D411yescharacteristic
113C42×C13C2×D411yescharacteristic
114C42×C13#4111yescharacteristic
115C22⋊Dic13—41no—
116#6107—84no—
117C4⋊Dic13—21no—
118C4⋊Dic13—21no—
119C4⋊Dic13—21no—
120C4⋊Dic13—21no—
121#6101—41no—
122#6101—41no—
123C4×Dic13—41no—
124#6099—41no—
125#6099—41no—
126C2×#1055—22no—
127C2×#1055—22no—
128C2×#1055—41no—
129#3209—131no—
130#3077—131no—
131#2542D1311yescharacteristic
132#1548—131no—
133#1503—131no—
134#1478—131no—
135#1303—131no—
136C23×C13—22no—
137C23×C13—42no—
138C23×C13—42no—
139C23×C13—41no—
140C23×C13—41no—
141C23×C13#12011yescharacteristic
142Q8×C13—44no—
143Q8×C13—82no—
144D4×C13—22no—
145D4×C13—22no—
146D4×C13—41no—
147D4×C13—41no—
148C2×C4×C13—22no—
149C2×C4×C13—24no—
150C2×C4×C13—41no—
151C2×C4×C13—42no—
152C2×C4×C13—42no—
153C2×C4×C13—44no—
154C2×C4×C13—42no—
155C2×C4×C13—41no—
156C2×C4×C13—42no—
157C2×C4×C13—82no—
158C2×C4×C13—82no—
159C2×C4×C13#12011yescharacteristic
160C2×C4×C13#12011yescharacteristic
161C2×C4×C13#12111yescharacteristic
162C2×C4×C13#12111yescharacteristic
163C2×C4×C13#12111yescharacteristic
164C2×C4×C13#12711yescharacteristic
165C2×C4×C13C2×Q1611yescharacteristic
166C2×C4×C13#13511yescharacteristic
167C2×C4×C13#13711yescharacteristic
168C2×C4×C13#13711yescharacteristic
169C2×Dic13—41no—
170C2×Dic13—41no—
171Dic26—42no—
172Dic26—81no—
173#1055—42no—
174#1055—42no—
175#1055—81no—
176#533—131no—
177C2×C4⋊Q8C2×D1311yescharacteristic
178C2×C22⋊Q8—22no—
179C2×C4×D4C2×D1311yescharacteristic
180#494—261no—
181#487—261no—
182#478—262no—
183#476—261no—
184#474—261no—
185#462—262no—
186#451—262no—
187#431—131no—
188#431—131no—
189#428—261no—
190#423—131no—
191#418—261no—
192#399—22no—
193#390—21no—
194#384—21no—
195C4×C4⋊C4C2×D1311yescharacteristic
196#333—262no—
197#328—262no—
198D4⋊C8—262no—
199C22×C13—21no—
200C22×C13—21no—
201C22×C13—44no—
202C22×C13—42no—
203C22×C13—82no—
204C22×C13—81no—
205C22×C13—81no—
206C22×C13#39211yescharacteristic
207C22×C13#45111yescharacteristic
208C22×C13#45211yescharacteristic
209C4×C13—21no—
210C4×C13—21no—
211C4×C13—21no—
212C4×C13—44no—
213C4×C13—81no—
214C4×C13—82no—
215C4×C13#45111yescharacteristic
216C4×C13#45211yescharacteristic
217C4×C13#45312yes—
218C4×C13#46711yescharacteristic
219C4×C13#47011yescharacteristic
220Dic13—81no—
221Dic13—81no—
222C22×Q8C22⋊D1312yes—
223C22×D4C22⋊D1311yescharacteristic
224C23×C4—21no—
225C2×Q16—264no—
226C2×M16—261no—
227C4⋊Q8—21no—
228C4⋊Q8—21no—
229C4⋊Q8—21no—
230C4⋊Q8—21no—
231C4⋊Q8—131no—
232C4⋊Q8—131no—
233#125—261no—
234C22⋊Q8—48no—
235C22⋊Q8—261no—
236C22⋊Q8—261no—
237C4×Q8—261no—
238C4×Q8—261no—
239C4×D4—21no—
240C4×D4—21no—
241C4×D4—21no—
242C4×D4—21no—
243#117—261no—
244C2×C4⋊C4—21no—
245C2×C4⋊C4—24no—
246C2×C4⋊C4—21no—
247C2×C4⋊C4—21no—
248C2×C4⋊C4C22⋊D1311yescharacteristic
249C2×C22⋊C4—24no—
250C2×C22⋊C4—21no—
251C2×C42—21no—
252C2×C42C22×D1311yescharacteristic
253#107—262no—
254#106—262no—
255C4⋊C8—132no—
256C4⋊C8—132no—
257C4⋊C8—261no—
258C4⋊C8—261no—
259#103—264no—
260#102—262no—
261#102—262no—
262C22⋊C8—261no—
263C22⋊C8—261no—
264C4×C8—261no—
265C4×C8—261no—
266#95C22⋊D1312yes—
267C2×C13—21no—
268C2×C13—21no—
269C2×C13—82no—
270C2×C13#200111yescharacteristic
271C2×C13#200211yescharacteristic
272C2×C13#200911yescharacteristic
273C24—21no—
274C2×Q8—22no—
275C2×Q8—22no—
276C2×Q8—44no—
277C2×Q8—261no—
278C2×Q8—261no—
279C2×D4—21no—
280C2×D4—21no—
281C2×D4—21no—
282C2×D4—21no—
283C2×D4—21no—
284C2×D4#610712yescomplemented
285C22×C4—22no—
286C22×C4—22no—
287C22×C4—21no—
288C22×C4—44no—
289C22×C4—41no—
290C22×C4—41no—
291C22×C4C2×C22⋊D1311yescharacteristic
292C22×C4C2×C22⋊D1311yescharacteristic
293C22×C4C2×C22⋊D1311yescharacteristic
294Q16—1044no—
295M16—521no—
296M16—521no—
297C2×C8—262no—
298C2×C8—262no—
299C2×C8—521no—
300C4⋊C4—24no—
301C4⋊C4—21no—
302C4⋊C4—21no—
303C4⋊C4—48no—
304C4⋊C4—41no—
305C4⋊C4—41no—
306C4⋊C4—41no—
307C4⋊C4—41no—
308C4⋊C4—261no—
309C4⋊C4—261no—
310C4⋊C4—261no—
311C4⋊C4—261no—
312C4⋊C4—521no—
313C4⋊C4—521no—
314C22⋊C4—48no—
315C22⋊C4—41no—
316C22⋊C4—41no—
317C22⋊C4—521no—
318C42—41no—
319C42—41no—
320C42—521no—
321C42D4×D1311yescharacteristic
322C42D4×D1311yescharacteristic
323C42D4×D1311yescharacteristic
324C42#612911yescharacteristic
325C13#1024811yescharacteristic, complemented, Sylow
326C23—22no—
327C23—42no—
328C23—42no—
329C23—41no—
330C23—41no—
331C23#8820711yescharacteristic
332Q8—44no—
333Q8—82no—
334Q8—522no—
335Q8—1041no—
336D4—22no—
337D4—22no—
338D4—41no—
339D4—41no—
340C2×C4—22no—
341C2×C4—24no—
342C2×C4—41no—
343C2×C4—42no—
344C2×C4—42no—
345C2×C4—44no—
346C2×C4—42no—
347C2×C4—41no—
348C2×C4—42no—
349C2×C4—82no—
350C2×C4—82no—
351C2×C4—521no—
352C2×C4—521no—
353C2×C4#8819111yescharacteristic
354C2×C4#8819111yescharacteristic
355C2×C4#8819211yescharacteristic
356C2×C4#8819311yescharacteristic
357C2×C4#8819311yescharacteristic
358C2×C4#8819411yescharacteristic
359C2×C4#8819611yescharacteristic
360C2×C4C2×#610711yescharacteristic
361C2×C4#8820411yescharacteristic
362C2×C4#8820511yescharacteristic
363C8—522no—
364C8—522no—
365C8—1041no—
366C22—21no—
367C22—21no—
368C22—44no—
369C22—42no—
370C22—82no—
371C22—81no—
372C22—81no—
373C22#1171888411yescharacteristic
374C22#1171888911yescharacteristic
375C22#1171890011yescharacteristic
376C4—21no—
377C4—21no—
378C4—21no—
379C4—44no—
380C4—81no—
381C4—82no—
382C4—1041no—
383C4—1041no—
384C4#1171870811yescharacteristic
385C4#1171871111yescharacteristic
386C4#1171871211yescharacteristic
387C4#1171871311yescharacteristic
388C4#1171873812yes—
389C2—21no—
390C2—21no—
391C2—82no—
392C2#1311584411yescharacteristic
393C2#1311585111yescharacteristic
394C2#1311589611yescharacteristic
subgroupG/H
centerC22#11718884
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#2542C2
socleC22×C13#392
prime radicalC22×D4×C13D4
hypercenter#2542D13
hypocenterC13#10248
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2542

Complements

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

NH ≅ G/Ntype
1. #13125784C2semidirect
3. #13113517C2semidirect
4. #13113334C2semidirect
6. #13112739C2semidirect
86. C2×D4×C13Q16semidirect
284. C2×D4#6107semidirect
325. C13#10248semidirect

Maximal subgroups

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

subgroupindex
#131257842
#131246332
#131135172
#131133342
#131132272
#131127392
C13×#25422
#1024813