Finite Group Databasebeta

← #15773823

Subgroups — #15773823

Order 3328.

572 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 572 conjugacy classes of subgroups — too many to draw. Only its 83 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#13118171C211yesmaximal, characteristic
2#13114916C211yesmaximal, characteristic, complemented
3#13112867C212yesmaximal, complemented
4#13112840C212yesmaximal, complemented
5C2×C13×#324C211yesmaximal, characteristic, complemented
6C22×#6127C411yescharacteristic
7C22×C13×C4⋊C4C2211yescharacteristic
8C2×#88183—21no—
9C2×C13×C22⋊C8—21no—
10#11718874—21no—
11#11718872C411yescharacteristic
12#11718868—21no—
13#11718652C411yescharacteristic
14#11718652C2211yescharacteristic
15#11718650—21no—
16#11718650—21no—
17#11718640C411yescharacteristic
18#11718640C2211yescharacteristic
19C13×#324—21no—
20C13×#324C2212yes—
21#11718122—21no—
22#11718122C2212yes—
23C23×C4×C13C2×C411yescharacteristic
24C23×C4×C13D411yescharacteristic
25C23×C4×C13D411yescharacteristic
26C22×C22⋊D13—21no—
27C2×#6127—41no—
28C2×#6127—41no—
29C2×#6127—44no—
30C22×D52C2×C411yescharacteristic
31C22×C4×D13—21no—
32C22×Dic26C2×C411yescharacteristic
33C22×C8×C13—41no—
34C2×C13×C4⋊C4—41no—
35C2×C13×C4⋊C4—41no—
36C2×C13×C4⋊C4C2×C411yescharacteristic
37C2×C13×C4⋊C4D411yescharacteristic
38C2×C13×C4⋊C4D411yescharacteristic
39C2×C13×C4⋊C4C2311yescharacteristic
40C2×C22⋊Dic13—21no—
41#88183—44no—
42C2×#6103—21no—
43C2×#6103—21no—
44C2×#6103—21no—
45C2×#6103—21no—
46C2×#6101—21no—
47C2×#6101—21no—
48C2×#6099—22no—
49C13×C22⋊C8—22no—
50C13×C22⋊C8—41no—
51#88071—21no—
52#88071—21no—
53#88071—21no—
54#88071C2×C411yescharacteristic
55#88071C2×C411yescharacteristic
56C22⋊#1055—41no—
57C22⋊#1055—41no—
58#11848—131nomaximal, Sylow
59C24×C13C22⋊C411yescharacteristic
60C23×D13—21no—
61C22×C4×C13—21no—
62C22×C4×C13—21no—
63C22×C4×C13—21no—
64C22×C4×C13—21no—
65C22×C4×C13—21no—
66C22×C4×C13—21no—
67C22×C4×C13—22no—
68C22×C4×C13—41no—
69C22×C4×C13—42no—
70C22×C4×C13—42no—
71C22×C4×C13C22⋊C411yescharacteristic
72C22×C4×C13C22⋊C411yescharacteristic
73C22×C4×C13C22⋊C411yescharacteristic
74C22×C4×C13C22×C411yescharacteristic
75C22×C4×C13C2×D411yescharacteristic
76C22×C4×C13C2×D411yescharacteristic
77C2×C22⋊D13—24no—
78C2×C22⋊D13—42no—
79C2×C22⋊D13—41no—
80C2×C22⋊D13—41no—
81C22×Dic13—21no—
82C22×Dic13—21no—
83C22×Dic13—21no—
84#6127—44no—
85#6127—44no—
86#6127—44no—
87#6127—44no—
88C2×D52—41no—
89C2×D52—42no—
90C2×C4×D13—42no—
91C2×C4×D13—42no—
92C2×C4×D13—42no—
93C2×Dic26—41no—
94C2×Dic26—42no—
95C2×C8×C13—42no—
96C2×C8×C13—82no—
97C13×C4⋊C4—41no—
98C13×C4⋊C4—41no—
99C13×C4⋊C4—41no—
100C13×C4⋊C4—41no—
101C22⋊Dic13—42no—
102#6103—42no—
103#6103—42no—
104#6103—42no—
105#6103—42no—
106#6101—42no—
107#6101—42no—
108#6099—42no—
109#6099—42no—
110C2×#1055—42no—
111#2406—131no—
112#1821—131no—
113C2×#324D1311yescharacteristic, complemented
114#1354—132no—
115#1345—132no—
116C23×C13—22no—
117C23×C13—21no—
118C23×C13—21no—
119C23×C13—41no—
120C23×C13#9911yescharacteristic
121C23×C13#9911yescharacteristic
122C23×C13C2×C22⋊C411yescharacteristic
123C22×D13—22no—
124C22×D13—41no—
125C22×D13—41no—
126C22×D13—41no—
127C22×D13—41no—
128C22×D13—41no—
129C22×D13—41no—
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—42no—
140C2×C4×C13—42no—
141C2×C4×C13—42no—
142C2×C4×C13—42no—
143C2×C4×C13—42no—
144C2×C4×C13—41no—
145C2×C4×C13—41no—
146C2×C4×C13—41no—
147C2×C4×C13—41no—
148C2×C4×C13—81no—
149C2×C4×C13#13512yes—
150C22⋊D13—44no—
151C22⋊D13—44no—
152C2×Dic13—22no—
153C2×Dic13—41no—
154C2×Dic13—41no—
155C2×Dic13—41no—
156C2×Dic13—41no—
157C2×Dic13—41no—
158C2×Dic13—41no—
159C2×Dic13—41no—
160C2×Dic13—41no—
161D52—42no—
162D52—42no—
163C4×D13—48no—
164Dic26—42no—
165Dic26—42no—
166C8×C13—82no—
167#1055—82no—
168C22×#41—131no—
169C2×#123—261no—
170C22×C4⋊C4C2×D1311yescharacteristic
171#407—261no—
172C2×C22⋊C8—21no—
173#395—131no—
174#395—131no—
175#394—131no—
176#394—131no—
177#386—261no—
178#385—261no—
179#385—261no—
180#381—131no—
181#343—132no—
182#343—261no—
183#324—21no—
184#324C2×D1312yes—
185C22×C13—21no—
186C22×C13—21no—
187C22×C13—21no—
188C22×C13—21no—
189C22×C13—21no—
190C22×C13—21no—
191C22×C13—21no—
192C22×C13—42no—
193C22×C13—42no—
194C22×C13AΣL(1,𝔽16)12yes—
195C22×C13C2×#9911yescharacteristic
196C22×C13#41611yescharacteristic
197C22×C13#42111yescharacteristic
198C2×D13—42no—
199C2×D13—42no—
200C2×D13—42no—
201C2×D13—81no—
202C2×D13—81no—
203C2×D13—81no—
204C2×D13—81no—
205C4×C13—22no—
206C4×C13—41no—
207C4×C13—41no—
208C4×C13—41no—
209C4×C13—41no—
210C4×C13—41no—
211Dic13—42no—
212Dic13—81no—
213Dic13—81no—
214C2×#41—521no—
215C2×#41—521no—
216C2×#41—524no—
217C22×Q8—131no—
218C22×D4—131no—
219C22×D4—261no—
220C23×C4—261no—
221C23×C4C4×D1311yescharacteristic
222C23×C4D5211yescharacteristic
223C23×C4C22⋊D1311yescharacteristic
224C2×M16—262no—
225C22×C8—41no—
226#123—524no—
227C2×C4⋊C4—41no—
228C2×C4⋊C4—41no—
229C2×C4⋊C4—261no—
230C2×C4⋊C4—261no—
231C2×C4⋊C4C4×D1311yescharacteristic
232C2×C4⋊C4D5211yescharacteristic
233C2×C4⋊C4C22⋊D1311yescharacteristic
234C2×C4⋊C4C22×D1311yescharacteristic
235C2×C22⋊C4—261no—
236C2×C22⋊C4—261no—
237C2×C22⋊C4—261no—
238C2×C22⋊C4—261no—
239C2×C22⋊C4—261no—
240C22⋊C8—22no—
241C22⋊C8—41no—
242C22⋊C8—521no—
243C22⋊C8—521no—
244#95—131no—
245#95—131no—
246#95—261no—
247#95—261no—
248#95—261no—
249C2×C13—21no—
250C2×C13—21no—
251C2×C13—22no—
252C2×C13—41no—
253C2×C13#151611yescharacteristic
254C2×C13C2×AΣL(1,𝔽16)11yescharacteristic
255C2×C13#213311yescharacteristic
256D13—82no—
257C24—261no—
258C24#610311yescharacteristic
259#41—524no—
260#41—524no—
261#41—524no—
262#41—524no—
263C2×Q8—521no—
264C2×Q8—522no—
265C2×D4—264no—
266C2×D4—521no—
267C2×D4—522no—
268C2×D4—522no—
269C2×D4—521no—
270C2×D4—521no—
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—21no—
274C22×C4—21no—
275C22×C4—21no—
276C22×C4—21no—
277C22×C4—22no—
278C22×C4—41no—
279C22×C4—42no—
280C22×C4—42no—
281C22×C4—261no—
282C22×C4—261no—
283C22×C4—261no—
284C22×C4—522no—
285C22×C4—522no—
286C22×C4—522no—
287C22×C4#610311yescharacteristic
288C22×C4#610311yescharacteristic
289C22×C4#610311yescharacteristic
290C22×C4C2×C4×D1311yescharacteristic
291C22×C4C2×D5211yescharacteristic
292C22×C4C2×C22⋊D1311yescharacteristic
293M16—522no—
294M16—522no—
295C2×C8—42no—
296C2×C8—82no—
297C2×C8—522no—
298C4⋊C4—41no—
299C4⋊C4—41no—
300C4⋊C4—41no—
301C4⋊C4—41no—
302C4⋊C4—522no—
303C4⋊C4—522no—
304C22⋊C4—522no—
305C22⋊C4—522no—
306C22⋊C4—522no—
307C22⋊C4—522no—
308C22⋊C4—522no—
309C13#1184811yescharacteristic, complemented, Sylow
310C23—21no—
311C23—21no—
312C23—22no—
313C23—41no—
314C23—262no—
315C23—521no—
316C23—521no—
317C23—521no—
318C23—521no—
319C23—521no—
320C23—521no—
321C23#8804611yescharacteristic
322C23#8804611yescharacteristic
323C23C2×#610311yescharacteristic
324Q8—522no—
325Q8—522no—
326D4—522no—
327D4—522no—
328D4—524no—
329D4—524no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—42no—
340C2×C4—42no—
341C2×C4—42no—
342C2×C4—42no—
343C2×C4—42no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—81no—
349C2×C4—262no—
350C2×C4—528no—
351C2×C4—521no—
352C2×C4—521no—
353C2×C4—521no—
354C2×C4—521no—
355C2×C4—521no—
356C2×C4—521no—
357C2×C4—521no—
358C2×C4—521no—
359C2×C4#8815812yes—
360C8—82no—
361C8—1042no—
362C22—21no—
363C22—21no—
364C22—21no—
365C22—21no—
366C22—21no—
367C22—21no—
368C22—21no—
369C22—42no—
370C22—42no—
371C22—522no—
372C22—522no—
373C22—522no—
374C22—1041no—
375C22—1041no—
376C22—1041no—
377C22—1041no—
378C22#1171806312yes—
379C22C2×#8804611yescharacteristic
380C22#1171877411yescharacteristic
381C22#1171880011yescharacteristic
382C4—22no—
383C4—41no—
384C4—41no—
385C4—41no—
386C4—41no—
387C4—41no—
388C4—522no—
389C4—1041no—
390C4—1041no—
391C2—21no—
392C2—21no—
393C2—22no—
394C2—41no—
395C2—1042no—
396C2#1311339311yescharacteristic
397C2C2×#1171806311yescharacteristic
398C2#1311652311yescharacteristic
subgroupG/H
centerC22C2×#88046
commutatorC22×C4×C13C22×C4
FrattiniC2×C4⋊C4C22×D13
FittingC2×C13×#324C2
socleC22×C13C2×#99
prime radicalC22×#6127C4
cosocleC2×C13×C4⋊C4C23
hypercenterC2×#324D13
hypocenterC13#11848
LCSG ▷ C22×C4×C13 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C24 ◁ C22×C4⋊C4 ◁ C2×#324

Complements

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

NH ≅ G/Ntype
2. #13114916C2semidirect
3. #13112867C2semidirect
4. #13112840C2semidirect
5. C2×C13×#324C2semidirect
113. C2×#324D13semidirect
309. C13#11848semidirect

Maximal subgroups

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

subgroupindex
#131181712
#131149162
#131128672
#131128402
C2×C13×#3242
#1184813