Finite Group Databasebeta

← #15763625

Subgroups — #15763625

Order 3328.

536 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 536 conjugacy classes of subgroups — too many to draw. Only its 89 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#13125638C211yesmaximal, characteristic
2C2×#11718629C211yesmaximal, characteristic
3#13114916C211yesmaximal, characteristic, complemented
4#13113200C211yesmaximal, characteristic, complemented
5#13113195C211yesmaximal, characteristic
6#13112724C211yesmaximal, characteristic, complemented
7C2×C13×#483C211yesmaximal, characteristic, complemented
8C2×C13×C22⋊Q8C2211yescharacteristic
9C22×C13×C4⋊C4C2211yescharacteristic
10C2×#88184C2211yescharacteristic
11C13×#483—22no—
12C13×#483—22no—
13C2×C13×#106—21no—
14C2×C13×#103—21no—
15C2×C13×C22⋊C8C2211yescharacteristic
16#11718888—21no—
17#11718868C2211yescharacteristic
18#11718868C2211yescharacteristic
19C2×C22⋊#1055C2211yescharacteristic
20#11718710—22no—
21#11718707—21no—
22#11718705—21no—
23#11718629—22no—
24#11718629—22no—
25#11718628—21no—
26C2×#88049—21no—
27C2×#88048—21no—
28#11718122—22no—
29#11718120—22no—
30#11718060—22no—
31C22×Q8×C13D411yescharacteristic
32C23×C4×C13—21no—
33C23×C4×C13C2311yescharacteristic
34C22×C22⋊D13—21no—
35C22×D52D411yescharacteristic
36C22×C8×C13—21no—
37C13×C22⋊Q8—21no—
38C13×C22⋊Q8—21no—
39C13×C22⋊Q8—21no—
40C13×C22⋊Q8—21no—
41C2×C13×C4⋊C4—21no—
42C2×C13×C4⋊C4—21no—
43C2×C13×C4⋊C4—21no—
44C2×C13×C4⋊C4—21no—
45C2×C13×C4⋊C4—21no—
46C2×C13×C4⋊C4—21no—
47C2×C13×C4⋊C4D411yescharacteristic
48C2×C13×C4⋊C4D412yes—
49C2×C13×C22⋊C4—21no—
50C2×#6106—22no—
51#88184—21no—
52#88184—21no—
53#88184—21no—
54#88184—21no—
55C2×#6103—21no—
56C2×C4⋊Dic13D411yescharacteristic
57C2×#6099—21no—
58C2×#6099D412yes—
59C22×#1055—21no—
60C13×#106—24no—
61C13×#103—24no—
62C13×C22⋊C8—21no—
63C13×C22⋊C8D412yes—
64#88075—22no—
65C22⋊#1055—21no—
66C22⋊#1055—21no—
67C22⋊#1055—21no—
68C22⋊#1055—21no—
69C22⋊#1055—21no—
70C22⋊#1055D412yes—
71#88049—22no—
72#88049—24no—
73#88048—24no—
74#88047—22no—
75#9993—131nomaximal, Sylow
76C24×C13#4111yescharacteristic
77C23×D13—21no—
78C2×Q8×C13—21no—
79C2×Q8×C13—21no—
80C2×Q8×C13—42no—
81C22×C4×C13—21no—
82C22×C4×C13—21no—
83C22×C4×C13—22no—
84C22×C4×C13—42no—
85C22×C4×C13—41no—
86C22×C4×C13—41no—
87C22×C4×C13—82no—
88C22×C4×C13C2×D411yescharacteristic
89C22×C4×C13C2×D411yescharacteristic
90C22×C4×C13C2×D411yescharacteristic
91C22×C4×C13C2×D411yescharacteristic
92C22×C4×C13C2×D411yescharacteristic
93C22×C4×C13C2×D411yescharacteristic
94C2×C22⋊D13—41no—
95C2×C22⋊D13—41no—
96C2×C22⋊D13—82no—
97C22×Dic13—21no—
98C2×D52—21no—
99C2×D52—21no—
100C2×D52—42no—
101C2×C8×C13—22no—
102C2×C8×C13—42no—
103C13×C4⋊C4—22no—
104C13×C4⋊C4—21no—
105C13×C4⋊C4—22no—
106C13×C4⋊C4—21no—
107C13×C4⋊C4—41no—
108C13×C4⋊C4—41no—
109C13×C4⋊C4—41no—
110C13×C4⋊C4—41no—
111C13×C22⋊C4—41no—
112C13×C22⋊C4—41no—
113#6106—82no—
114#6103—41no—
115#6103—41no—
116C4⋊Dic13—21no—
117C4⋊Dic13—21no—
118#6099—42no—
119#6099—42no—
120C2×#1055—22no—
121C2×#1055—22no—
122C2×#1055—42no—
123C2×#1055—41no—
124#3193—131no—
125C2×#481—131no—
126C2×#483D1311yescharacteristic, complemented
127#1821—131no—
128#1472—131no—
129#1471—131no—
130#1298—131no—
131C23×C13—22no—
132C23×C13—22no—
133C23×C13—41no—
134C23×C13#12111yescharacteristic
135C23×C13#12111yescharacteristic
136C23×C13#12111yescharacteristic
137C22×D13—41no—
138C22×D13—42no—
139C22×D13—81no—
140C22×D13—81no—
141Q8×C13—42no—
142Q8×C13—42no—
143C2×C4×C13—22no—
144C2×C4×C13—22no—
145C2×C4×C13—22no—
146C2×C4×C13—41no—
147C2×C4×C13—41no—
148C2×C4×C13—41no—
149C2×C4×C13—41no—
150C2×C4×C13—41no—
151C2×C4×C13—42no—
152C2×C4×C13—42no—
153C2×C4×C13—82no—
154C2×C4×C13—82no—
155C2×C4×C13—82no—
156C2×C4×C13—81no—
157C2×C4×C13#12011yescharacteristic
158C2×C4×C13#12011yescharacteristic
159C2×C4×C13#12011yescharacteristic
160C2×C4×C13#12711yescharacteristic
161C22⋊D13—82no—
162C22⋊D13—82no—
163C2×Dic13—41no—
164C2×Dic13—81no—
165D52—42no—
166D52—42no—
167C8×C13—42no—
168#1055—42no—
169#1055—42no—
170#1055—81no—
171C2×C22⋊Q8C2×D1311yescharacteristic
172C2×#121—131no—
173C22×C4⋊C4C2×D1311yescharacteristic
174#484—261no—
175#483—22no—
176#483—22no—
177#481—262no—
178#481—262no—
179#480—261no—
180#468—262no—
181#450—261no—
182#448—261no—
183C2×#106—21no—
184C2×#106—261no—
185C2×#103—21no—
186C2×#102—261no—
187#407—131no—
188#407—131no—
189C2×C22⋊C8—131no—
190C2×C22⋊C8C2×D1311yescharacteristic
191#343—262no—
192#324—262no—
193#323—262no—
194C22×C13—21no—
195C22×C13—21no—
196C22×C13—21no—
197C22×C13—21no—
198C22×C13—21no—
199C22×C13—21no—
200C22×C13—21no—
201C22×C13—44no—
202C22×C13#39211yescharacteristic
203C22×C13#47112yes—
204C22×C13#47112yes—
205C2×D13—81no—
206C2×D13—81no—
207C2×D13—81no—
208C2×D13—162no—
209C4×C13—21no—
210C4×C13—21no—
211C4×C13—21no—
212C4×C13—81no—
213C4×C13—82no—
214C4×C13—81no—
215C4×C13#45812yes—
216Dic13—81no—
217C22×Q8C22⋊D1311yescharacteristic
218C22×D4—131no—
219C22×D4—261no—
220C23×C4—21no—
221C23×C4C22×D1311yescharacteristic
222C2×SD16—262no—
223C2×M16—132no—
224C2×M16—261no—
225C22×C8—21no—
226C22×C8—261no—
227C22⋊Q8—21no—
228C22⋊Q8—21no—
229C22⋊Q8—21no—
230C22⋊Q8—21no—
231#121—261no—
232#121—261no—
233#121—261no—
234#121—261no—
235C2×C4⋊C4—21no—
236C2×C4⋊C4—21no—
237C2×C4⋊C4—21no—
238C2×C4⋊C4—21no—
239C2×C4⋊C4—21no—
240C2×C4⋊C4—21no—
241C2×C4⋊C4—131no—
242C2×C4⋊C4C22⋊D1312yes—
243C2×C4⋊C4C22⋊D1311yescharacteristic
244C2×C22⋊C4—21no—
245C2×C22⋊C4—261no—
246#107—262no—
247#106—24no—
248#106—264no—
249#103—24no—
250#103—262no—
251#102—264no—
252#102—262no—
253C22⋊C8—21no—
254C22⋊C8—132no—
255C22⋊C8—261no—
256C22⋊C8—261no—
257C22⋊C8—261no—
258C22⋊C8—261no—
259C22⋊C8—261no—
260C22⋊C8C22⋊D1312yes—
261C2×C13—22no—
262C2×C13—22no—
263C2×C13—41no—
264C2×C13#201911yescharacteristic
265C2×C13#201911yescharacteristic
266C2×C13#202211yescharacteristic
267D13—161no—
268C24—261no—
269C24#612911yescharacteristic
270C2×Q8—21no—
271C2×Q8—21no—
272C2×Q8—42no—
273C2×D4—261no—
274C2×D4—261no—
275C2×D4—522no—
276C2×D4—521no—
277C2×D4—521no—
278C2×D4—1042no—
279C22×C4—21no—
280C22×C4—21no—
281C22×C4—22no—
282C22×C4—42no—
283C22×C4—41no—
284C22×C4—41no—
285C22×C4—82no—
286C22×C4—261no—
287C22×C4D4×D1311yescharacteristic
288C22×C4D4×D1311yescharacteristic
289C22×C4D4×D1311yescharacteristic
290C22×C4C2×C22⋊D1311yescharacteristic
291C22×C4C2×C22⋊D1311yescharacteristic
292C22×C4C2×C22⋊D1311yescharacteristic
293SD16—1042no—
294M16—522no—
295M16—522no—
296C2×C8—22no—
297C2×C8—42no—
298C2×C8—262no—
299C2×C8—262no—
300C2×C8—522no—
301C2×C8—521no—
302C4⋊C4—22no—
303C4⋊C4—21no—
304C4⋊C4—22no—
305C4⋊C4—21no—
306C4⋊C4—41no—
307C4⋊C4—41no—
308C4⋊C4—41no—
309C4⋊C4—41no—
310C4⋊C4—261no—
311C4⋊C4—261no—
312C22⋊C4—41no—
313C22⋊C4—41no—
314C22⋊C4—521no—
315C22⋊C4—521no—
316C13#999311yescharacteristic, complemented, Sylow
317C23—22no—
318C23—22no—
319C23—41no—
320C23—521no—
321C23—522no—
322C23—1041no—
323C23—1041no—
324C23#8819211yescharacteristic
325C23#8819311yescharacteristic
326C23#8819311yescharacteristic
327Q8—42no—
328Q8—42no—
329D4—522no—
330D4—522no—
331D4—1042no—
332D4—1042no—
333C2×C4—22no—
334C2×C4—22no—
335C2×C4—22no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—42no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—42no—
343C2×C4—82no—
344C2×C4—82no—
345C2×C4—82no—
346C2×C4—81no—
347C2×C4—521no—
348C2×C4—1041no—
349C2×C4#8819111yescharacteristic
350C2×C4#8819111yescharacteristic
351C2×C4#8819411yescharacteristic
352C2×C4#8820711yescharacteristic
353C8—42no—
354C8—522no—
355C8—522no—
356C8—1041no—
357C22—21no—
358C22—21no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—21no—
363C22—21no—
364C22—44no—
365C22—1041no—
366C22—1041no—
367C22—1041no—
368C22—2082no—
369C22#1171883812yes—
370C22#1171886412yes—
371C22#1171888411yescharacteristic
372C4—21no—
373C4—21no—
374C4—21no—
375C4—81no—
376C4—82no—
377C4—81no—
378C4—1041no—
379C4#1171871412yes—
380C2—22no—
381C2—22no—
382C2—41no—
383C2—2081no—
384C2#1311594711yescharacteristic
385C2#1311594811yescharacteristic
386C2#1311596411yescharacteristic
subgroupG/H
centerC22#11718884
commutator, cosocleC23×C4×C13C23
FrattiniC23×C4C22×D13
FittingC2×C13×#483C2
socleC22×C13#392
prime radicalC2×#88184C22
hypercenterC2×#483D13
hypocenterC13#9993
LCSG ▷ C23×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#483

Complements

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

NH ≅ G/Ntype
3. #13114916C2semidirect
4. #13113200C2semidirect
6. #13112724C2semidirect
7. C2×C13×#483C2semidirect
126. C2×#483D13semidirect
316. C13#9993semidirect

Maximal subgroups

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

subgroupindex
#131256382
C2×#117186292
#131149162
#131132002
#131131952
#131127242
C2×C13×#4832
#999313