Finite Group Databasebeta

← #15767295

Subgroups — #15767295

Order 3328.

438 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 438 conjugacy classes of subgroups — too many to draw. Only its 81 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#13115305C211yesmaximal, characteristic
2#13115270C211yesmaximal, characteristic
3#13115040C211yesmaximal, characteristic
4#13113408C211yesmaximal, characteristic
5#13113200C211yesmaximal, characteristic
6#13112741C211yesmaximal, characteristic
7C13×#3195C211yesmaximal, characteristic
8C2×C13×C22⋊Q8C2211yescharacteristic
9C2×C13×C22⋊Q8C2211yescharacteristic
10C22×#6099C2211yescharacteristic
11C13×#483—21no—
12C13×#483—21no—
13C13×#470—21no—
14C13×#470—21no—
15C13×#451—21no—
16C13×#451—21no—
17C13×#407C2211yescharacteristic
18C2×#88076—21no—
19C2×#88075—21no—
20#11718873C2211yescharacteristic
21#11718868C2211yescharacteristic
22C2×C22⋊#1055C2211yescharacteristic
23C2×#88062—21no—
24#11718150—21no—
25#11718130—22no—
26#11718122—21no—
27#11718121—21no—
28#11718120—22no—
29C22×Q8×C13D411yescharacteristic
30C22×Q8×C13D411yescharacteristic
31C23×C4×C13C2311yescharacteristic
32C2×C13×Q16—21no—
33C2×C13×Q16—21no—
34C2×C13×M16D411yescharacteristic
35C2×C13×M16D411yescharacteristic
36C13×C22⋊Q8—21no—
37C13×C22⋊Q8—21no—
38C13×C22⋊Q8—21no—
39C13×C22⋊Q8—21no—
40C13×C22⋊Q8—21no—
41C13×C22⋊Q8—21no—
42C13×C22⋊Q8—21no—
43C13×C22⋊Q8—21no—
44C2×C13×C4⋊C4—21no—
45C2×C13×C4⋊C4—21no—
46C2×C13×C4⋊C4D411yescharacteristic
47C2×C13×C4⋊C4D411yescharacteristic
48C2×C13×C22⋊C4—21no—
49C2×C13×C22⋊C4—21no—
50C2×C22⋊Dic13—21no—
51C2×C4⋊Dic13—21no—
52C2×#6099—21no—
53C2×#6099—21no—
54C2×#6099—21no—
55C2×#6099—42no—
56C22×#1055—21no—
57C22×#1055—21no—
58C13×#106—21no—
59C13×#106—21no—
60C13×#103—21no—
61C13×#103—21no—
62C13×#103—21no—
63C13×#103—21no—
64C13×C22⋊C8—21no—
65C13×C22⋊C8—21no—
66#88076—42no—
67#88075—42no—
68#88071—21no—
69C22⋊#1055—21no—
70C22⋊#1055—21no—
71C22⋊#1055—21no—
72C22⋊#1055D412yes—
73#88062—42no—
74#10563—131nomaximal, Sylow
75C24×C13#4111yescharacteristic
76C2×Q8×C13—21no—
77C2×Q8×C13—21no—
78C2×Q8×C13—21no—
79C2×Q8×C13—21no—
80C2×Q8×C13—41no—
81C2×Q8×C13—41no—
82C2×Q8×C13—41no—
83C2×Q8×C13—41no—
84C22×C4×C13—21no—
85C22×C4×C13—21no—
86C22×C4×C13—21no—
87C22×C4×C13—21no—
88C22×C4×C13—41no—
89C22×C4×C13—41no—
90C22×C4×C13C2×D411yescharacteristic
91C22×C4×C13C2×D411yescharacteristic
92C22×C4×C13C2×D411yescharacteristic
93C22×C4×C13C2×D411yescharacteristic
94C22×C4×C13#4111yescharacteristic
95C22×C4×C13#4111yescharacteristic
96C22×Dic13—41no—
97C13×Q16—81no—
98C13×Q16—81no—
99C13×M16—41no—
100C13×M16—41no—
101C2×C8×C13—21no—
102C2×C8×C13—21no—
103C13×C4⋊C4—21no—
104C13×C4⋊C4—21no—
105C13×C4⋊C4—21no—
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—
113C13×C22⋊C4—41no—
114C13×C22⋊C4—41no—
115C22⋊Dic13—81no—
116C4⋊Dic13—41no—
117C4⋊Dic13—41no—
118#6099—22no—
119#6099—22no—
120#6099—41no—
121#6099—41no—
122#6099—41no—
123#6099—41no—
124C2×#1055—22no—
125C2×#1055—22no—
126C2×#1055—41no—
127C2×#1055—41no—
128C2×#1055—41no—
129C2×#1055—41no—
130C2×#1055—41no—
131#3195D1311yescharacteristic
132#1901—131no—
133#1894—131no—
134#1855—131no—
135#1520—131no—
136#1472—131no—
137#1305—131no—
138C23×C13—21no—
139C23×C13—21no—
140C23×C13—41no—
141C23×C13—41no—
142C23×C13#12111yescharacteristic
143C23×C13#12311yescharacteristic
144C23×C13#12411yescharacteristic
145Q8×C13—42no—
146Q8×C13—41no—
147Q8×C13—41no—
148Q8×C13—41no—
149Q8×C13—41no—
150Q8×C13—81no—
151C2×C4×C13—21no—
152C2×C4×C13—21no—
153C2×C4×C13—21no—
154C2×C4×C13—21no—
155C2×C4×C13—21no—
156C2×C4×C13—21no—
157C2×C4×C13—41no—
158C2×C4×C13—41no—
159C2×C4×C13—41no—
160C2×C4×C13—42no—
161C2×C4×C13—41no—
162C2×C4×C13—41no—
163C2×C4×C13—41no—
164C2×C4×C13—41no—
165C2×C4×C13—41no—
166C2×C4×C13—41no—
167C2×C4×C13—81no—
168C2×C4×C13—81no—
169C2×C4×C13#12011yescharacteristic
170C2×C4×C13#12111yescharacteristic
171C2×C4×C13#12111yescharacteristic
172C2×C4×C13#12311yescharacteristic
173C2×Dic13—81no—
174C2×Dic13—81no—
175C2×Dic13—81no—
176C8×C13—41no—
177C8×C13—41no—
178#1055—42no—
179#1055—42no—
180#1055—81no—
181C22×M16—131no—
182C2×C22⋊Q8C2×D1311yescharacteristic
183C2×C22⋊Q8C2×D1311yescharacteristic
184#483—21no—
185#483—21no—
186#470—21no—
187#470—21no—
188#451—21no—
189#451—21no—
190C2×#108—261no—
191C2×#103—261no—
192C2×#101—261no—
193#407—131no—
194#407C2×D1311yescharacteristic
195C2×C22⋊C8—131no—
196#380—131no—
197#343—261no—
198#341—261no—
199#340—261no—
200#328—262no—
201#324—262no—
202C22×C13—21no—
203C22×C13—21no—
204C22×C13—21no—
205C22×C13—21no—
206C22×C13—21no—
207C22×C13—21no—
208C22×C13—21no—
209C22×C13—21no—
210C22×C13—81no—
211C22×C13—81no—
212C22×C13#39411yescharacteristic
213C22×C13#47111yescharacteristic
214C22×C13#47311yescharacteristic
215C4×C13—21no—
216C4×C13—21no—
217C4×C13—21no—
218C4×C13—81no—
219C4×C13—81no—
220C4×C13—81no—
221C4×C13—81no—
222C4×C13B(4,𝔽2)11yescharacteristic
223C4×C13#45811yescharacteristic
224Dic13—161no—
225C22×Q8C22⋊D1311yescharacteristic
226C22×Q8C22⋊D1311yescharacteristic
227C23×C4C22×D1311yescharacteristic
228C2×Q16—21no—
229C2×Q16—21no—
230C2×M16—261no—
231C2×M16—261no—
232C2×M16—261no—
233C2×M16—522no—
234C2×M16C22⋊D1311yescharacteristic
235C2×M16C22⋊D1311yescharacteristic
236C22×C8—261no—
237C22×C8—261no—
238C22⋊Q8—21no—
239C22⋊Q8—21no—
240C22⋊Q8—21no—
241C22⋊Q8—21no—
242C22⋊Q8—21no—
243C22⋊Q8—21no—
244C22⋊Q8—21no—
245C22⋊Q8—21no—
246C2×C4⋊C4—21no—
247C2×C4⋊C4—21no—
248C2×C4⋊C4—261no—
249C2×C4⋊C4C22⋊D1311yescharacteristic
250C2×C4⋊C4C22⋊D1311yescharacteristic
251C2×C22⋊C4—21no—
252C2×C22⋊C4—21no—
253C2×C22⋊C4—261no—
254#108—522no—
255#106—21no—
256#106—21no—
257#103—21no—
258#103—21no—
259#103—21no—
260#103—21no—
261#103—522no—
262#101—522no—
263C22⋊C8—21no—
264C22⋊C8—21no—
265C22⋊C8—132no—
266C22⋊C8—261no—
267C22⋊C8—261no—
268C22⋊C8—261no—
269#95—261no—
270C2×C13—21no—
271C2×C13—21no—
272C2×C13—41no—
273C2×C13—41no—
274C2×C13#204411yescharacteristic
275C2×C13#204911yescharacteristic
276C2×C13#205211yescharacteristic
277C24#612911yescharacteristic
278C2×Q8—21no—
279C2×Q8—21no—
280C2×Q8—21no—
281C2×Q8—21no—
282C2×Q8—41no—
283C2×Q8—41no—
284C2×Q8—41no—
285C2×Q8—41no—
286C22×C4—21no—
287C22×C4—21no—
288C22×C4—21no—
289C22×C4—21no—
290C22×C4—41no—
291C22×C4—41no—
292C22×C4—521no—
293C22×C4D4×D1311yescharacteristic
294C22×C4#612911yescharacteristic
295C22×C4#612911yescharacteristic
296C22×C4C2×C22⋊D1311yescharacteristic
297C22×C4C2×C22⋊D1311yescharacteristic
298C22×C4C2×C22⋊D1311yescharacteristic
299Q16—81no—
300Q16—81no—
301M16—41no—
302M16—41no—
303M16—262no—
304M16—262no—
305M16—521no—
306M16—521no—
307M16—521no—
308M16—521no—
309C2×C8—21no—
310C2×C8—21no—
311C2×C8—262no—
312C2×C8—262no—
313C2×C8—521no—
314C2×C8—521no—
315C2×C8—521no—
316C2×C8—521no—
317C2×C8—521no—
318C4⋊C4—21no—
319C4⋊C4—21no—
320C4⋊C4—21no—
321C4⋊C4—21no—
322C4⋊C4—41no—
323C4⋊C4—41no—
324C4⋊C4—41no—
325C4⋊C4—41no—
326C4⋊C4—521no—
327C4⋊C4—521no—
328C22⋊C4—41no—
329C22⋊C4—41no—
330C22⋊C4—41no—
331C22⋊C4—41no—
332C22⋊C4—1041no—
333C13#1056311yescharacteristic, complemented, Sylow
334C23—21no—
335C23—21no—
336C23—41no—
337C23—41no—
338C23#8818911yescharacteristic
339C23#8819011yescharacteristic
340C23#8819311yescharacteristic
341Q8—42no—
342Q8—41no—
343Q8—41no—
344Q8—41no—
345Q8—41no—
346Q8—81no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—42no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—81no—
364C2×C4—81no—
365C2×C4—1041no—
366C2×C4—1041no—
367C2×C4—1041no—
368C2×C4#8818911yescharacteristic
369C2×C4#8819211yescharacteristic
370C2×C4#8819311yescharacteristic
371C2×C4#8820711yescharacteristic
372C8—41no—
373C8—41no—
374C8—522no—
375C8—522no—
376C8—1041no—
377C22—21no—
378C22—21no—
379C22—21no—
380C22—21no—
381C22—21no—
382C22—21no—
383C22—21no—
384C22—21no—
385C22—81no—
386C22—81no—
387C22#1171886411yescharacteristic
388C22#1171886511yescharacteristic
389C22#1171888311yescharacteristic
390C4—21no—
391C4—21no—
392C4—21no—
393C4—81no—
394C4—81no—
395C4—81no—
396C4—81no—
397C4—2081no—
398C4#1171890411yescharacteristic
399C4#1171890511yescharacteristic
400C2—21no—
401C2—21no—
402C2—41no—
403C2—41no—
404C2#1311608411yescharacteristic
405C2#1311611311yescharacteristic
406C2#1311613211yescharacteristic
subgroupG/H
centerC22#11718883
commutator, cosocleC23×C4×C13C23
FrattiniC23×C4C22×D13
FittingC13×#3195C2
socleC22×C13#394
prime radicalC24×C13#41
hypercenter#3195D13
hypocenterC13#10563
LCSG ▷ C23×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3195

Complements

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

NH ≅ G/Ntype
333. C13#10563semidirect

Maximal subgroups

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

subgroupindex
#131153052
#131152702
#131150402
#131134082
#131132002
#131127412
C13×#31952
#1056313