Finite Group Databasebeta

← #15767322

Subgroups — #15767322

Order 3328.

604 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 604 conjugacy classes of subgroups — too many to draw. Only its 119 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#13120950C211yesmaximal, characteristic
2#13115024C212yesmaximal
3#13112715C212yesmaximal
4#13112679C211yesmaximal, characteristic
5C13×#1444C211yesmaximal, characteristic
6C22×C13×C4⋊C4—21no—
7C22×C13×C4⋊C4C2211yescharacteristic
8C2×#88178—21no—
9C2×C13×#95—21no—
10C2×C13×#95C2211yescharacteristic
11C2×C13×#95C2211yescharacteristic
12#11718873—21no—
13#11718873C2212yes—
14C2×C22⋊#1055C2212yes—
15C2×#88047—22no—
16#11718322—22no—
17#11718317—22no—
18#11718121—22no—
19C23×C4×C13—21no—
20C23×C4×C13—21no—
21C23×C4×C13D411yescharacteristic
22C23×C4×C13D411yescharacteristic
23C23×C4×C13C2311yescharacteristic
24C22×Dic26—21no—
25C2×C13×C4⋊C4—22no—
26C2×C13×C4⋊C4—42no—
27C2×C13×C4⋊C4—42no—
28C2×C13×C4⋊C4—42no—
29C2×C13×C4⋊C4—42no—
30C2×C22⋊Dic13—22no—
31C2×C4⋊Dic13—21no—
32C2×C4⋊Dic13—21no—
33C2×C4⋊Dic13—21no—
34C2×C4⋊Dic13D412yes—
35C2×C4⋊Dic13D412yes—
36#88178—42no—
37#88178—42no—
38C2×#6101—22no—
39C22×#1055—22no—
40C13×#95—22no—
41C13×#95—21no—
42C13×#95—42no—
43C13×#95Q812yescomplemented
44#88071—22no—
45#88071—22no—
46C22⋊#1055—22no—
47C22⋊#1055Q814yescomplemented
48#88047—44no—
49#10567—131nomaximal, Sylow
50C24×C13C2×D411yescharacteristic
51C22×C4×C13—22no—
52C22×C4×C13—22no—
53C22×C4×C13—21no—
54C22×C4×C13—21no—
55C22×C4×C13—22no—
56C22×C4×C13—21no—
57C22×C4×C13—21no—
58C22×C4×C13—22no—
59C22×C4×C13—41no—
60C22×C4×C13—41no—
61C22×C4×C13—41no—
62C22×C4×C13—41no—
63C22×C4×C13—41no—
64C22×C4×C13—41no—
65C22×C4×C13—41no—
66C22×C4×C13—41no—
67C22×C4×C13—41no—
68C22×C4×C13—41no—
69C22×C4×C13—41no—
70C22×C4×C13—41no—
71C22×C4×C13—41no—
72C22×C4×C13—41no—
73C22×C4×C13—41no—
74C22×C4×C13—41no—
75C22×C4×C13D812yes—
76C22×C4×C13Q1612yes—
77C22×C4×C13C2×D412yes—
78C22×C4×C13C2×Q811yescharacteristic
79C22×C4×C13C2×Q812yes—
80C22×C4×C13#4111yescharacteristic
81C22×Dic13—22no—
82C22×Dic13—22no—
83C2×Dic26—42no—
84C2×Dic26—81no—
85C2×Dic26—81no—
86C13×C4⋊C4—24no—
87C13×C4⋊C4—42no—
88C13×C4⋊C4—48no—
89C22⋊Dic13—42no—
90C22⋊Dic13—42no—
91C4⋊Dic13—42no—
92C4⋊Dic13—42no—
93C4⋊Dic13—42no—
94C4⋊Dic13—81no—
95C4⋊Dic13—81no—
96#6101—44no—
97C2×#1055—24no—
98C2×#1055—42no—
99C2×#1055—42no—
100#2659—131no—
101#1852—132no—
102#1444D1311yescharacteristic
103#1294—132no—
104#1280—131no—
105C23×C13—21no—
106C23×C13—21no—
107C23×C13—21no—
108C23×C13—21no—
109C23×C13#12011yescharacteristic
110C23×C13C22⋊Q811yescharacteristic
111C23×C13C4⋊Q811yescharacteristic
112C23×C13C2×D811yescharacteristic
113C23×C13C2×Q1611yescharacteristic
114C23×C13AGL(1,ℤ/8)11yescharacteristic
115C23×C13#13711yescharacteristic
116C2×C4×C13—22no—
117C2×C4×C13—22no—
118C2×C4×C13—24no—
119C2×C4×C13—22no—
120C2×C4×C13—22no—
121C2×C4×C13—42no—
122C2×C4×C13—41no—
123C2×C4×C13—41no—
124C2×C4×C13—42no—
125C2×C4×C13—42no—
126C2×C4×C13—42no—
127C2×C4×C13—42no—
128C2×C4×C13—42no—
129C2×C4×C13—41no—
130C2×C4×C13—41no—
131C2×C4×C13—41no—
132C2×C4×C13—41no—
133C2×C4×C13—42no—
134C2×C4×C13—42no—
135C2×C4×C13—42no—
136C2×C4×C13—42no—
137C2×C4×C13—42no—
138C2×C4×C13—42no—
139C2×C4×C13—81no—
140C2×C4×C13—81no—
141C2×C4×C13—81no—
142C2×C4×C13—81no—
143C2×C4×C13—81no—
144C2×C4×C13—81no—
145C2×C4×C13C22⋊Q812yes—
146C2×C4×C13C4⋊Q812yes—
147C2×Dic13—42no—
148C2×Dic13—42no—
149C2×Dic13—42no—
150C2×Dic13—42no—
151C2×Dic13—42no—
152C2×Dic13—42no—
153Dic26—84no—
154#1055—44no—
155C2×C22⋊Q8—261no—
156C22×C4⋊C4—21no—
157C22×C4⋊C4C2×D1311yescharacteristic
158C2×#107—262no—
159C2×C22⋊C8—132no—
160#398—262no—
161#395—262no—
162#380—132no—
163#380—261no—
164C2×#95—21no—
165C2×#95C2×D1311yescharacteristic
166C2×#95C2×D1311yescharacteristic
167#340—262no—
168C22×C13—21no—
169C22×C13—21no—
170C22×C13—21no—
171C22×C13—21no—
172C22×C13—21no—
173C22×C13—21no—
174C22×C13—21no—
175C22×C13—21no—
176C22×C13—21no—
177C22×C13—21no—
178C22×C13—21no—
179C22×C13—21no—
180C22×C13#39511yescharacteristic
181C22×C13#44711yescharacteristic
182C22×C13#45111yescharacteristic
183C22×C13#45311yescharacteristic
184C22×C13#45611yescharacteristic
185C22×C13B(4,𝔽2)11yescharacteristic
186C22×C13#45811yescharacteristic
187C22×C13#47411yescharacteristic
188C22×C13#47711yescharacteristic
189C22×C13#50011yescharacteristic
190C22×C13#50111yescharacteristic
191C4×C13—22no—
192C4×C13—22no—
193C4×C13—44no—
194C4×C13—42no—
195C4×C13—42no—
196C4×C13—82no—
197Dic13—82no—
198Dic13—82no—
199C22×Q8—261no—
200C23×C4—21no—
201C23×C4—21no—
202C23×C4C22⋊D1311yescharacteristic
203C23×C4C22⋊D1311yescharacteristic
204C23×C4C22×D1311yescharacteristic
205C22×C8—262no—
206C22⋊Q8—522no—
207C22⋊Q8—522no—
208C2×C4⋊C4—22no—
209C2×C4⋊C4—42no—
210C2×C4⋊C4—42no—
211C2×C4⋊C4—42no—
212C2×C4⋊C4—42no—
213C2×C4⋊C4—132no—
214C2×C4⋊C4—132no—
215C2×C4⋊C4—262no—
216C2×C4⋊C4—261no—
217C2×C4⋊C4—261no—
218C2×C4⋊C4—261no—
219C2×C22⋊C4—262no—
220#107—524no—
221C22⋊C8—134no—
222C22⋊C8—262no—
223#95—21no—
224#95—22no—
225#95—42no—
226#95—262no—
227#95—262no—
228#95Dic2612yescomplemented
229C2×C13—21no—
230C2×C13—21no—
231C2×C13—21no—
232C2×C13—21no—
233C2×C13#159511yescharacteristic
234C2×C13#160511yescharacteristic
235C2×C13#161011yescharacteristic
236C2×C13#161411yescharacteristic
237C2×C13#205711yescharacteristic
238C2×C13#206011yescharacteristic
239C2×C13#206211yescharacteristic
240C24C2×C22⋊D1311yescharacteristic
241C2×Q8—522no—
242C2×Q8—1041no—
243C2×Q8—1041no—
244C22×C4—22no—
245C22×C4—22no—
246C22×C4—22no—
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—21no—
251C22×C4—22no—
252C22×C4—41no—
253C22×C4—41no—
254C22×C4—41no—
255C22×C4—41no—
256C22×C4—41no—
257C22×C4—41no—
258C22×C4—41no—
259C22×C4—41no—
260C22×C4—41no—
261C22×C4—41no—
262C22×C4—41no—
263C22×C4—41no—
264C22×C4—41no—
265C22×C4—41no—
266C22×C4—41no—
267C22×C4—41no—
268C22×C4—262no—
269C22×C4—262no—
270C22×C4#610412yes—
271C22×C4#610712yes—
272C22×C4C2×Dic2611yescharacteristic
273C22×C4#612711yescharacteristic
274C22×C4D4×D1312yes—
275C22×C4Q8×D1312yes—
276C2×C8—264no—
277C2×C8—522no—
278C2×C8—522no—
279C4⋊C4—24no—
280C4⋊C4—42no—
281C4⋊C4—48no—
282C4⋊C4—522no—
283C4⋊C4—522no—
284C4⋊C4—524no—
285C4⋊C4—522no—
286C4⋊C4—1041no—
287C4⋊C4—1041no—
288C22⋊C4—522no—
289C22⋊C4—522no—
290C13#1056711yescharacteristic, complemented, Sylow
291C23—21no—
292C23—21no—
293C23—21no—
294C23—21no—
295C23#8817811yescharacteristic
296C23C2×#610411yescharacteristic
297C23#8819111yescharacteristic
298C23C2×#610711yescharacteristic
299C23#8819811yescharacteristic
300C23#8820311yescharacteristic
301C23#8820511yescharacteristic
302Q8—1044no—
303C2×C4—22no—
304C2×C4—22no—
305C2×C4—24no—
306C2×C4—22no—
307C2×C4—22no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—42no—
311C2×C4—42no—
312C2×C4—42no—
313C2×C4—42no—
314C2×C4—42no—
315C2×C4—42no—
316C2×C4—42no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—42no—
322C2×C4—42no—
323C2×C4—42no—
324C2×C4—42no—
325C2×C4—42no—
326C2×C4—81no—
327C2×C4—81no—
328C2×C4—81no—
329C2×C4—81no—
330C2×C4—81no—
331C2×C4—81no—
332C2×C4—522no—
333C2×C4—522no—
334C2×C4—522no—
335C2×C4—522no—
336C2×C4—522no—
337C2×C4—522no—
338C2×C4#8814212yes—
339C2×C4#8815012yes—
340C8—524no—
341C22—21no—
342C22—21no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—21no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—21no—
353C22#1171864011yescharacteristic
354C22#1171866811yescharacteristic
355C22#1171868211yescharacteristic
356C22#1171869311yescharacteristic
357C22#1171869711yescharacteristic
358C22#1171871111yescharacteristic
359C22#1171871411yescharacteristic
360C22#1171872611yescharacteristic
361C22#1171873811yescharacteristic
362C22#1171873911yescharacteristic
363C22#1171875611yescharacteristic
364C4—22no—
365C4—22no—
366C4—44no—
367C4—42no—
368C4—42no—
369C4—82no—
370C4—1042no—
371C4—1042no—
372C2—21no—
373C2—21no—
374C2—21no—
375C2—21no—
376C2#1311375311yescharacteristic
377C2#1311380911yescharacteristic
378C2#1311383811yescharacteristic
379C2#1311386011yescharacteristic
380C2#1311616411yescharacteristic
381C2#1311618111yescharacteristic
382C2#1311618911yescharacteristic
subgroupG/H
centerC23#88191
commutator, cosocleC23×C4×C13C23
FrattiniC23×C4C22×D13
FittingC13×#1444C2
socleC23×C13#120
prime radicalC24×C13C2×D4
hypercenter#1444D13
hypocenterC13#10567
LCSG ▷ C23×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1444

Complements

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

NH ≅ G/Ntype
43. C13×#95Q8semidirect
47. C22⋊#1055Q8semidirect
228. #95Dic26semidirect
290. C13#10567semidirect

Maximal subgroups

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

subgroupindex
#131209502
#131150242
#131127152
#131126792
C13×#14442
#1056713