Finite Group Databasebeta

← #15773438

Subgroups — #15773438

Order 3328.

488 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 488 conjugacy classes of subgroups — too many to draw. Only its 87 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#13120316C211yesmaximal, characteristic
2#13113166C211yesmaximal, characteristic, complemented
3#13112862C212yesmaximal, complemented
4#13112838C212yesmaximal, complemented
5C2×C13×#343C211yesmaximal, characteristic, complemented
6C22×C13×M16—21no—
7C22×C13×C4⋊C4C2211yescharacteristic
8C2×#88184C411yescharacteristic
9#11718874—21no—
10#11718874—21no—
11C4×C22⋊Dic13C411yescharacteristic
12#11718868—21no—
13#11718652C411yescharacteristic
14#11718652C2211yescharacteristic
15#11718651—21no—
16#11718651—21no—
17#11718647C411yescharacteristic
18#11718647C2211yescharacteristic
19C13×#343—21no—
20C13×#343C2212yes—
21#11718120—21no—
22#11718120C2212yes—
23C23×C4×C13C2×C411yescharacteristic
24C23×C4×C13D411yescharacteristic
25C23×C4×C13D411yescharacteristic
26C22×C22⋊D13—21no—
27C22×D52C2×C411yescharacteristic
28C2×C13×M16—24no—
29C2×C13×M16—22no—
30C2×C13×M16—41no—
31C2×C13×M16—42no—
32C22×C8×C13—41no—
33C2×C13×C4⋊C4—41no—
34C2×C13×C4⋊C4—41no—
35C2×C13×C4⋊C4C2×C411yescharacteristic
36C2×C13×C4⋊C4D411yescharacteristic
37C2×C13×C4⋊C4D411yescharacteristic
38C2×C13×C4⋊C4C2311yescharacteristic
39C2×C22⋊Dic13—21no—
40#88184—41no—
41#88184—41no—
42C2×#6103—21no—
43C2×#6103—21no—
44C2×#6103—21no—
45C2×#6103—21no—
46C2×#6103—21no—
47C2×C4⋊Dic13C2×C411yescharacteristic
48C2×C4×Dic13—21no—
49C2×#6099—41no—
50#88071—21no—
51#88071—21no—
52#88071—21no—
53#88071—21no—
54#88071C2×C411yescharacteristic
55#88071C2×C411yescharacteristic
56C22⋊#1055—22no—
57C22⋊#1055—41no—
58#11766—131nomaximal, Sylow
59C24×C13C22⋊C411yescharacteristic
60C23×D13—21no—
61C22×C4×C13—21no—
62C22×C4×C13—21no—
63C22×C4×C13—22no—
64C22×C4×C13—21no—
65C22×C4×C13—21no—
66C22×C4×C13—21no—
67C22×C4×C13—21no—
68C22×C4×C13—21no—
69C22×C4×C13—21no—
70C22×C4×C13—81no—
71C22×C4×C13—81no—
72C22×C4×C13C22⋊C411yescharacteristic
73C22×C4×C13C22⋊C411yescharacteristic
74C22×C4×C13C22⋊C411yescharacteristic
75C22×C4×C13C22×C411yescharacteristic
76C22×C4×C13C2×D411yescharacteristic
77C22×C4×C13C2×D411yescharacteristic
78C2×C22⋊D13—42no—
79C2×C22⋊D13—42no—
80C2×C22⋊D13—41no—
81C2×C22⋊D13—41no—
82C22×Dic13—21no—
83C22×Dic13—21no—
84C22×Dic13—21no—
85C2×D52—41no—
86C2×D52—81no—
87C13×M16—24no—
88C13×M16—44no—
89C13×M16—42no—
90C2×C8×C13—44no—
91C2×C8×C13—42no—
92C13×C4⋊C4—41no—
93C13×C4⋊C4—41no—
94C13×C4⋊C4—41no—
95C13×C4⋊C4—41no—
96C22⋊Dic13—42no—
97#6103—42no—
98#6103—42no—
99#6103—41no—
100#6103—41no—
101#6103—81no—
102#6103—81no—
103C4⋊Dic13—41no—
104C4×Dic13—81no—
105#6099—82no—
106C2×#1055—42no—
107#2591—131no—
108C2×#343D1311yescharacteristic, complemented
109#1463—131no—
110#1353—132no—
111#1345—132no—
112C23×C13—22no—
113C23×C13—21no—
114C23×C13—21no—
115C23×C13—41no—
116C23×C13#9911yescharacteristic
117C23×C13#9911yescharacteristic
118C23×C13C2×C22⋊C411yescharacteristic
119C22×D13—41no—
120C22×D13—41no—
121C22×D13—41no—
122C22×D13—41no—
123C22×D13—41no—
124C22×D13—41no—
125C22×D13—41no—
126C2×C4×C13—22no—
127C2×C4×C13—22no—
128C2×C4×C13—22no—
129C2×C4×C13—22no—
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—42no—
139C2×C4×C13—41no—
140C2×C4×C13—41no—
141C2×C4×C13—41no—
142C2×C4×C13—41no—
143C2×C4×C13—81no—
144C2×C4×C13—81no—
145C2×C4×C13—81no—
146C2×C4×C13#10412yes—
147C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
148C2×C4×C13#13711yescharacteristic
149C22⋊D13—82no—
150C22⋊D13—82no—
151C2×Dic13—41no—
152C2×Dic13—41no—
153C2×Dic13—41no—
154C2×Dic13—41no—
155C2×Dic13—41no—
156C2×Dic13—41no—
157C2×Dic13—41no—
158C2×Dic13—41no—
159C2×Dic13—41no—
160D52—82no—
161C8×C13—44no—
162#1055—82no—
163C22×M16—21no—
164C2×#121—131no—
165C22×C4⋊C4C2×D1311yescharacteristic
166#407—261no—
167#400—131no—
168#400—131no—
169#394—131no—
170#394—131no—
171#388—261no—
172#388—261no—
173#386—261no—
174#386—261no—
175C4×C22⋊C4—131no—
176#343—21no—
177#343C2×D1312yes—
178#324—132no—
179#324—261no—
180C22×C13—21no—
181C22×C13—21no—
182C22×C13—21no—
183C22×C13—21no—
184C22×C13—21no—
185C22×C13—21no—
186C22×C13—21no—
187C22×C13—42no—
188C22×C13—42no—
189C22×C13#35512yes—
190C22×C13C2×#9911yescharacteristic
191C22×C13#41711yescharacteristic
192C22×C13C2×#10411yescharacteristic
193C2×D13—81no—
194C2×D13—81no—
195C2×D13—81no—
196C2×D13—81no—
197C2×D13—81no—
198C2×D13—81no—
199C2×D13—81no—
200C4×C13—21no—
201C4×C13—22no—
202C4×C13—21no—
203C4×C13—41no—
204C4×C13—41no—
205C4×C13—41no—
206C4×C13—41no—
207Dic13—81no—
208Dic13—81no—
209Dic13—81no—
210C22×D4—131no—
211C22×D4—261no—
212C23×C4C4×D1311yescharacteristic
213C23×C4D5211yescharacteristic
214C23×C4C22⋊D1311yescharacteristic
215C2×M16—24no—
216C2×M16—22no—
217C2×M16—41no—
218C2×M16—42no—
219C2×M16—521no—
220C22×C8—41no—
221#121—521no—
222#121—521no—
223C2×C4⋊C4—41no—
224C2×C4⋊C4—41no—
225C2×C4⋊C4—131no—
226C2×C4⋊C4C4×D1311yescharacteristic
227C2×C4⋊C4D5211yescharacteristic
228C2×C4⋊C4C22⋊D1311yescharacteristic
229C2×C4⋊C4C22×D1311yescharacteristic
230C2×C22⋊C4—261no—
231C2×C22⋊C4—261no—
232C2×C22⋊C4—261no—
233C2×C22⋊C4—261no—
234C2×C22⋊C4—261no—
235C2×C22⋊C4—261no—
236C2×C42—261no—
237C22⋊C8—262no—
238C22⋊C8—521no—
239#95—131no—
240#95—131no—
241#95—261no—
242#95—261no—
243#95—261no—
244#95—261no—
245C2×C13—21no—
246C2×C13—21no—
247C2×C13—22no—
248C2×C13—41no—
249C2×C13#150411yescharacteristic
250C2×C13#212111yescharacteristic
251C2×C13C2×#35511yescharacteristic
252D13—161no—
253C24—261no—
254C24#610311yescharacteristic
255C2×D4—521no—
256C2×D4—522no—
257C2×D4—522no—
258C2×D4—521no—
259C2×D4—521no—
260C2×D4—1041no—
261C22×C4—21no—
262C22×C4—21no—
263C22×C4—21no—
264C22×C4—21no—
265C22×C4—22no—
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—21no—
270C22×C4—81no—
271C22×C4—81no—
272C22×C4—261no—
273C22×C4—261no—
274C22×C4—261no—
275C22×C4#610311yescharacteristic
276C22×C4#610311yescharacteristic
277C22×C4#610311yescharacteristic
278C22×C4C2×C4×D1311yescharacteristic
279C22×C4C2×D5211yescharacteristic
280C22×C4C2×C22⋊D1311yescharacteristic
281M16—24no—
282M16—44no—
283M16—42no—
284M16—1042no—
285C2×C8—44no—
286C2×C8—42no—
287C2×C8—522no—
288C4⋊C4—41no—
289C4⋊C4—41no—
290C4⋊C4—41no—
291C4⋊C4—41no—
292C4⋊C4—521no—
293C22⋊C4—522no—
294C22⋊C4—522no—
295C22⋊C4—521no—
296C22⋊C4—521no—
297C22⋊C4—522no—
298C22⋊C4—1041no—
299C22⋊C4—1041no—
300C42—1041no—
301C13#1176611yescharacteristic, complemented, Sylow
302C23—22no—
303C23—21no—
304C23—21no—
305C23—41no—
306C23—521no—
307C23—521no—
308C23—521no—
309C23—521no—
310C23—521no—
311C23—521no—
312C23—521no—
313C23#8804611yescharacteristic
314C23#8804611yescharacteristic
315C23C2×#610311yescharacteristic
316D4—1042no—
317D4—1042no—
318D4—1042no—
319C2×C4—22no—
320C2×C4—22no—
321C2×C4—22no—
322C2×C4—22no—
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—42no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—81no—
337C2×C4—81no—
338C2×C4—81no—
339C2×C4—521no—
340C2×C4—521no—
341C2×C4—521no—
342C2×C4—521no—
343C2×C4—521no—
344C2×C4—521no—
345C2×C4—521no—
346C2×C4—521no—
347C2×C4—521no—
348C2×C4#8804512yes—
349C2×C4#8818611yescharacteristic
350C2×C4#8819611yescharacteristic
351C8—44no—
352C8—1042no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—21no—
359C22—21no—
360C22—42no—
361C22—42no—
362C22—1041no—
363C22—1041no—
364C22—1041no—
365C22—1041no—
366C22—1041no—
367C22—1041no—
368C22—1041no—
369C22#1171806912yes—
370C22C2×#8804511yescharacteristic
371C22C2×#8804611yescharacteristic
372C22#1171862711yescharacteristic
373C4—21no—
374C4—21no—
375C4—22no—
376C4—41no—
377C4—41no—
378C4—41no—
379C4—41no—
380C4—1041no—
381C4—1041no—
382C4—1041no—
383C2—21no—
384C2—21no—
385C2—22no—
386C2—41no—
387C2—2081no—
388C2#1311333811yescharacteristic
389C2#1311648311yescharacteristic
390C2C2×#1171806911yescharacteristic
subgroupG/H
centerC22C2×#88046
commutatorC22×C4×C13C22×C4
FrattiniC2×C4⋊C4C22×D13
FittingC2×C13×#343C2
socleC22×C13C2×#99
prime radicalC2×#88184C4
cosocleC2×C13×C4⋊C4C23
hypercenterC2×#343D13
hypocenterC13#11766
LCSG ▷ C22×C4×C13 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C24 ◁ C22×C4⋊C4 ◁ C2×#343

Complements

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

NH ≅ G/Ntype
2. #13113166C2semidirect
3. #13112862C2semidirect
4. #13112838C2semidirect
5. C2×C13×#343C2semidirect
108. C2×#343D13semidirect
301. C13#11766semidirect

Maximal subgroups

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

subgroupindex
#131203162
#131131662
#131128622
#131128382
C2×C13×#3432
#1176613