Finite Group Databasebeta

← #15751453

Subgroups — #15751453

Order 3328.

532 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 532 conjugacy classes of subgroups — too many to draw. Only its 107 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#13123167C211yesmaximal, characteristic
2#13114598C211yesmaximal, characteristic, complemented
3#13112658C212yesmaximal, complemented
4#13112656C212yesmaximal, complemented
5C13×#1797C211yesmaximal, characteristic, complemented
6C22×C42×C13C2211yescharacteristic
7C2×#88184C411yescharacteristic
8C2×#88183—21no—
9C2×C13×C4⋊C8—21no—
10C2×C13×C22⋊C8—21no—
11#11718874—21no—
12#11718873C411yescharacteristic
13C2×C22⋊#1055—21no—
14#11718601—21no—
15#11718601—21no—
16#11718600C411yescharacteristic
17#11718600C2211yescharacteristic
18#11718589C411yescharacteristic
19#11718589C2211yescharacteristic
20C2×#88043—21no—
21C13×#336C2212yes—
22#11718116C2212yes—
23C23×C4×C13C2×C411yescharacteristic
24C23×C4×C13D411yescharacteristic
25C23×C4×C13D411yescharacteristic
26C22×C22⋊D13—21no—
27C22×D52C2×C411yescharacteristic
28C22×C8×C13—22no—
29C2×C42×C13—42no—
30C2×C42×C13C2×C411yescharacteristic
31C2×C42×C13D411yescharacteristic
32C2×C42×C13D411yescharacteristic
33C2×C42×C13C2311yescharacteristic
34C2×C22⋊Dic13—21no—
35#88184—42no—
36#88183—44no—
37C2×#6103—21no—
38C2×#6103—21no—
39C2×#6103—21no—
40C2×#6103—21no—
41C2×#6103—21no—
42C2×C4⋊Dic13C2×C411yescharacteristic
43C2×C4⋊Dic13C2×C411yescharacteristic
44C2×C4⋊Dic13C2×C411yescharacteristic
45C2×#6101—21no—
46C2×#6101—21no—
47C22×#1055—22no—
48C13×C4⋊C8—42no—
49C13×C22⋊C8—42no—
50#88071—21no—
51#88071—21no—
52#88071—21no—
53C22⋊#1055—24no—
54#88043—42no—
55#7698—131nomaximal, Sylow
56C24×C13C22⋊C411yescharacteristic
57C23×D13—21no—
58C22×C4×C13—22no—
59C22×C4×C13—22no—
60C22×C4×C13—22no—
61C22×C4×C13—21no—
62C22×C4×C13—22no—
63C22×C4×C13—21no—
64C22×C4×C13—41no—
65C22×C4×C13—41no—
66C22×C4×C13—41no—
67C22×C4×C13—41no—
68C22×C4×C13C22⋊C411yescharacteristic
69C22×C4×C13C22⋊C411yescharacteristic
70C22×C4×C13C22⋊C411yescharacteristic
71C22×C4×C13C22×C411yescharacteristic
72C22×C4×C13C2×D411yescharacteristic
73C22×C4×C13C2×D411yescharacteristic
74C2×C22⋊D13—42no—
75C2×C22⋊D13—42no—
76C2×C22⋊D13—42no—
77C22×Dic13—21no—
78C22×Dic13—21no—
79C22×Dic13—21no—
80C2×D52—22no—
81C2×D52—41no—
82C2×D52—41no—
83C2×C8×C13—42no—
84C2×C8×C13—42no—
85C2×C8×C13—42no—
86C42×C13—22no—
87C42×C13—22no—
88C42×C13—41no—
89C42×C13—41no—
90C22⋊Dic13—42no—
91#6103—42no—
92#6103—42no—
93#6103—42no—
94#6103—41no—
95#6103—42no—
96#6103—41no—
97C4⋊Dic13—22no—
98C4⋊Dic13—41no—
99C4⋊Dic13—41no—
100#6101—42no—
101#6101—42no—
102C2×#1055—24no—
103C2×#1055—42no—
104C2×#1055—42no—
105#2854—131no—
106#1797D1311yescharacteristic, complemented
107#1749—131no—
108#1271—132no—
109#1270—132no—
110C23×C13—21no—
111C23×C13—21no—
112C23×C13—21no—
113C23×C13—21no—
114C23×C13—21no—
115C23×C13—21no—
116C23×C13#10412yes—
117C23×C13C2×C22⋊C411yescharacteristic
118C22×D13—41no—
119C22×D13—41no—
120C22×D13—41no—
121C22×D13—41no—
122C22×D13—41no—
123C22×D13—41no—
124C22×D13—41no—
125C2×C4×C13—21no—
126C2×C4×C13—21no—
127C2×C4×C13—21no—
128C2×C4×C13—21no—
129C2×C4×C13—21no—
130C2×C4×C13—21no—
131C2×C4×C13—21no—
132C2×C4×C13—21no—
133C2×C4×C13—21no—
134C2×C4×C13—21no—
135C2×C4×C13—21no—
136C2×C4×C13—21no—
137C2×C4×C13—21no—
138C2×C4×C13—21no—
139C2×C4×C13—44no—
140C2×C4×C13—44no—
141C2×C4×C13—42no—
142C2×C4×C13—42no—
143C2×C4×C13#9912yes—
144C2×C4×C13#13112yes—
145C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
146C2×C4×C13AGL(1,ℤ/8)12yes—
147C2×C4×C13#13711yescharacteristic
148C22⋊D13—84no—
149C2×Dic13—41no—
150C2×Dic13—41no—
151C2×Dic13—41no—
152C2×Dic13—41no—
153C2×Dic13—41no—
154C2×Dic13—41no—
155C2×Dic13—41no—
156C2×Dic13—41no—
157C2×Dic13—41no—
158D52—82no—
159C8×C13—82no—
160#1055—44no—
161C2×#123—261no—
162C2×#121—131no—
163C22×C42C2×D1311yescharacteristic
164C2×C4⋊C8—21no—
165C2×C22⋊C8—21no—
166C2×C22⋊C8—261no—
167C2×#97—261no—
168#390—131no—
169#390—131no—
170#389—131no—
171#389—131no—
172#388—261no—
173#388—261no—
174#386—261no—
175#380—131no—
176#336—132no—
177#336C2×D1312yes—
178C22×C13—22no—
179C22×C13—22no—
180C22×C13—22no—
181C22×C13—41no—
182C22×C13—41no—
183C22×C13—41no—
184C22×C13—41no—
185C22×C13#40811yescharacteristic
186C22×C13C2×#9911yescharacteristic
187C22×C13#41311yescharacteristic
188C22×C13#41711yescharacteristic
189C22×C13#41811yescharacteristic
190C22×C13C2×#10411yescharacteristic
191C22×C13#42111yescharacteristic
192C2×D13—81no—
193C2×D13—81no—
194C2×D13—81no—
195C2×D13—81no—
196C2×D13—81no—
197C2×D13—81no—
198C2×D13—81no—
199C4×C13—22no—
200C4×C13—22no—
201C4×C13—22no—
202C4×C13—21no—
203C4×C13—21no—
204C4×C13—41no—
205C4×C13—41no—
206Dic13—81no—
207Dic13—81no—
208Dic13—81no—
209C22×D4—131no—
210C22×D4—261no—
211C23×C4C4×D1311yescharacteristic
212C23×C4D5211yescharacteristic
213C23×C4C22⋊D1311yescharacteristic
214C22×C8—22no—
215C22×C8—262no—
216#123—524no—
217#121—522no—
218C2×C4⋊C4—131no—
219C2×C4⋊C4—131no—
220C2×C4⋊C4—131no—
221C2×C4⋊C4—261no—
222C2×C4⋊C4—261no—
223C2×C22⋊C4—261no—
224C2×C22⋊C4—261no—
225C2×C22⋊C4—261no—
226C2×C22⋊C4—261no—
227C2×C22⋊C4—261no—
228C2×C22⋊C4—261no—
229C2×C42—42no—
230C2×C42C4×D1311yescharacteristic
231C2×C42D5211yescharacteristic
232C2×C42C22⋊D1311yescharacteristic
233C2×C42C22×D1311yescharacteristic
234C4⋊C8—42no—
235C22⋊C8—42no—
236C22⋊C8—264no—
237#97—522no—
238#95—261no—
239#95—261no—
240#95—261no—
241C2×C13—42no—
242C2×C13#146811yescharacteristic
243C2×C13#148311yescharacteristic
244C2×C13#149611yescharacteristic
245C2×C13#150711yescharacteristic
246C2×C13#151311yescharacteristic
247C2×C13#153211yescharacteristic
248C2×C13#155711yescharacteristic
249D13—161no—
250C24—261no—
251C24#610311yescharacteristic
252C2×D4—262no—
253C2×D4—521no—
254C2×D4—521no—
255C2×D4—522no—
256C2×D4—522no—
257C2×D4—522no—
258C22×C4—22no—
259C22×C4—22no—
260C22×C4—22no—
261C22×C4—21no—
262C22×C4—21no—
263C22×C4—22no—
264C22×C4—41no—
265C22×C4—41no—
266C22×C4—41no—
267C22×C4—41no—
268C22×C4—261no—
269C22×C4—261no—
270C22×C4—261no—
271C22×C4#610311yescharacteristic
272C22×C4#610311yescharacteristic
273C22×C4#610311yescharacteristic
274C22×C4C2×C4×D1311yescharacteristic
275C22×C4C2×D5211yescharacteristic
276C22×C4C2×C22⋊D1311yescharacteristic
277C2×C8—42no—
278C2×C8—42no—
279C2×C8—42no—
280C2×C8—264no—
281C2×C8—522no—
282C2×C8—522no—
283C4⋊C4—262no—
284C4⋊C4—521no—
285C4⋊C4—521no—
286C4⋊C4—522no—
287C4⋊C4—522no—
288C22⋊C4—522no—
289C22⋊C4—522no—
290C22⋊C4—522no—
291C22⋊C4—522no—
292C22⋊C4—521no—
293C22⋊C4—521no—
294C22⋊C4—522no—
295C42—22no—
296C42—22no—
297C42—41no—
298C42—41no—
299C13#769811yescharacteristic, complemented, Sylow
300C23—21no—
301C23—21no—
302C23—21no—
303C23—21no—
304C23—21no—
305C23—21no—
306C23—521no—
307C23—521no—
308C23—521no—
309C23—521no—
310C23—521no—
311C23—521no—
312C23—521no—
313C23#8806512yes—
314C23C2×#610311yescharacteristic
315D4—1042no—
316D4—1044no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—44no—
332C2×C4—44no—
333C2×C4—42no—
334C2×C4—42no—
335C2×C4—521no—
336C2×C4—521no—
337C2×C4—521no—
338C2×C4—521no—
339C2×C4—521no—
340C2×C4—521no—
341C2×C4—521no—
342C2×C4—521no—
343C2×C4—521no—
344C2×C4#8804612yes—
345C2×C4#8815512yes—
346C2×C4#8816212yes—
347C2×C4#8818611yescharacteristic
348C2×C4#8819611yescharacteristic
349C8—82no—
350C8—524no—
351C22—22no—
352C22—22no—
353C22—22no—
354C22—41no—
355C22—41no—
356C22—41no—
357C22—41no—
358C22—1041no—
359C22—1041no—
360C22—1041no—
361C22—1041no—
362C22—1041no—
363C22—1041no—
364C22—1041no—
365C22C2×#8804611yescharacteristic
366C22#1171862711yescharacteristic
367C22#1171866611yescharacteristic
368C22#1171877111yescharacteristic
369C22#1171879211yescharacteristic
370C22#1171879311yescharacteristic
371C22C2×#8806511yescharacteristic
372C4—22no—
373C4—21no—
374C4—21no—
375C4—22no—
376C4—22no—
377C4—41no—
378C4—41no—
379C4—1041no—
380C4—1041no—
381C4—1041no—
382C2—42no—
383C2—2081no—
384C2#1311318211yescharacteristic
385C2#1311324711yescharacteristic
386C2#1311330611yescharacteristic
387C2#1311335311yescharacteristic
388C2#1311337711yescharacteristic
389C2#1311345711yescharacteristic
390C2#1311355611yescharacteristic
subgroupG/H
centerC23C2×#6103
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#1797C2
socleC23×C13C2×C22⋊C4
prime radicalC2×#88184C4
cosocleC2×C42×C13C23
hypercenter#1797D13
hypocenterC13#7698
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C22×C42 ◁ #1797

Complements

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

NH ≅ G/Ntype
2. #13114598C2semidirect
3. #13112658C2semidirect
4. #13112656C2semidirect
5. C13×#1797C2semidirect
106. #1797D13semidirect
299. C13#7698semidirect

Maximal subgroups

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

subgroupindex
#131231672
#131145982
#131126582
#131126562
C13×#17972
#769813