Finite Group Databasebeta

← #15751409

Subgroups — #15751409

Order 3328.

410 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 410 conjugacy classes of subgroups — too many to draw. Only its 103 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#13123219C211yesmaximal, characteristic
2#13114688C211yesmaximal, characteristic
3#13114684C211yesmaximal, characteristic
4#13112661C211yesmaximal, characteristic
5#13112661C211yesmaximal, characteristic
6#13112659C211yesmaximal, characteristic
7C13×#1271C211yesmaximal, characteristic
8C13×#389C2211yescharacteristic
9C2×#88055—21no—
10C2×#88054—21no—
11C2×#88054—21no—
12C2×C8×Dic13—21no—
13#11718646C411yescharacteristic
14#11718642—21no—
15#11718639—21no—
16#11718635C411yescharacteristic
17#11718635C411yescharacteristic
18#11718634C411yescharacteristic
19C42×Dic13C2211yescharacteristic
20#11718590C2211yescharacteristic
21#11718315—21no—
22#11718312—21no—
23C13×#336C2211yescharacteristic
24C13×#336C2211yescharacteristic
25#11718116C2211yescharacteristic
26#11718116C2211yescharacteristic
27C22×Dic26C2×C411yescharacteristic
28C22×C8×C13—21no—
29C22×C8×C13—21no—
30C2×C13×C4⋊C4—21no—
31C2×C13×C4⋊C4C2×C411yescharacteristic
32C2×C13×C4⋊C4C2×C411yescharacteristic
33C2×C42×C13C2311yescharacteristic
34C2×C4⋊Dic13—21no—
35C2×C4⋊Dic13C2×C411yescharacteristic
36C2×#6101—21no—
37C2×C4×Dic13C2×C411yescharacteristic
38C2×C4×Dic13C2×C411yescharacteristic
39C2×C4×Dic13D411yescharacteristic
40C2×C4×Dic13D411yescharacteristic
41C2×C4×Dic13D411yescharacteristic
42C2×C4×Dic13D411yescharacteristic
43C22×#1055—21no—
44C22×#1055—21no—
45C13×#95—21no—
46#88071—21no—
47#88071—21no—
48#88071—21no—
49#88071—21no—
50#88071—21no—
51#88071—21no—
52#88071—21no—
53#88071—21no—
54#88055—42no—
55#88054—24no—
56#88054—24no—
57C8×Dic13—42no—
58#7689—131nomaximal, Sylow
59C22×C4×C13—21no—
60C22×C4×C13—21no—
61C22×C4×C13C22×C411yescharacteristic
62C22×C4×C13C2×D411yescharacteristic
63C22×C4×C13C2×D411yescharacteristic
64C22×Dic13—21no—
65C22×Dic13—21no—
66C22×Dic13C22⋊C411yescharacteristic
67C22×Dic13C22⋊C411yescharacteristic
68C22×Dic13C22⋊C411yescharacteristic
69C22×Dic13C22⋊C411yescharacteristic
70C2×Dic26—21no—
71C2×Dic26—21no—
72C2×Dic26—41no—
73C2×Dic26—41no—
74C2×C8×C13—22no—
75C2×C8×C13—22no—
76C2×C8×C13—41no—
77C2×C8×C13—41no—
78C2×C8×C13—41no—
79C2×C8×C13—41no—
80C13×C4⋊C4—21no—
81C13×C4⋊C4—21no—
82C13×C4⋊C4—41no—
83C13×C4⋊C4—41no—
84C13×C4⋊C4—41no—
85C42×C13—41no—
86C4⋊Dic13—42no—
87C4⋊Dic13—41no—
88#6101—42no—
89C4×Dic13—21no—
90C4×Dic13—21no—
91C4×Dic13—21no—
92C4×Dic13—21no—
93C4×Dic13—22no—
94C4×Dic13—22no—
95C4×Dic13—41no—
96C4×Dic13SD1612yes—
97C4×Dic13Q1612yes—
98C2×#1055—22no—
99C2×#1055—22no—
100C2×#1055—41no—
101C2×#1055—41no—
102C2×#1055—41no—
103C2×#1055—41no—
104#2863—131no—
105#1767—131no—
106C4×C4⋊C8—131no—
107#1272—131no—
108#1272—131no—
109#1271—131no—
110#1271D1311yescharacteristic
111C23×C13C2×C22⋊C411yescharacteristic
112C2×C4×C13—21no—
113C2×C4×C13—21no—
114C2×C4×C13—21no—
115C2×C4×C13—21no—
116C2×C4×C13—21no—
117C2×C4×C13—21no—
118C2×C4×C13—41no—
119C2×C4×C13—41no—
120C2×C4×C13—41no—
121C2×C4×C13—41no—
122C2×C4×C13—41no—
123C2×C4×C13—41no—
124C2×C4×C13#13111yescharacteristic
125C2×C4×C13#13111yescharacteristic
126C2×C4×C13C2×SD1611yescharacteristic
127C2×C4×C13C2×Q1611yescharacteristic
128C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
129C2×C4×C13#13711yescharacteristic
130C2×Dic13—21no—
131C2×Dic13—21no—
132C2×Dic13—21no—
133C2×Dic13—21no—
134C2×Dic13—21no—
135C2×Dic13—21no—
136C2×Dic13—21no—
137C2×Dic13—21no—
138C2×Dic13—41no—
139C2×Dic13—41no—
140C2×Dic13—41no—
141C2×Dic13—41no—
142C2×Dic13—41no—
143C2×Dic13—41no—
144C2×Dic13#10312yes—
145C2×Dic13#10312yes—
146C2×Dic13#10412yes—
147C2×Dic13#10412yes—
148Dic26—81no—
149Dic26—81no—
150C8×C13—42no—
151C8×C13—42no—
152#1055—42no—
153#1055—42no—
154C2×C4⋊C8—261no—
155C2×C4⋊C8—261no—
156C2×#97—261no—
157C2×C4×C8—261no—
158#391—131no—
159#391—131no—
160#391—131no—
161#389—131no—
162#389—131no—
163#389C2×D1311yescharacteristic
164#387—261no—
165#387—261no—
166#387—261no—
167#383—261no—
168C43—131no—
169#336—131no—
170#336—131no—
171#336C2×D1311yescharacteristic
172#336C2×D1311yescharacteristic
173C22×C13#40811yescharacteristic
174C22×C13#41011yescharacteristic
175C22×C13#41311yescharacteristic
176C22×C13C2×#10311yescharacteristic
177C22×C13#41711yescharacteristic
178C22×C13C2×#10411yescharacteristic
179C22×C13C2×#10411yescharacteristic
180C4×C13—21no—
181C4×C13—21no—
182C4×C13—21no—
183C4×C13—21no—
184C4×C13—21no—
185C4×C13—21no—
186C4×C13—81no—
187C4×C13—81no—
188Dic13—22no—
189Dic13—22no—
190Dic13—22no—
191Dic13—22no—
192Dic13—81no—
193Dic13—81no—
194C22×Q8—131no—
195C22×C8—21no—
196C22×C8—21no—
197C22×C8—261no—
198C22×C8—261no—
199C2×C4⋊C4—21no—
200C2×C4⋊C4—131no—
201C2×C4⋊C4—261no—
202C2×C4⋊C4—261no—
203C2×C4⋊C4C4×D1311yescharacteristic
204C2×C4⋊C4C4×D1311yescharacteristic
205C2×C42—131no—
206C2×C42—131no—
207C2×C42—131no—
208C2×C42—131no—
209C2×C42—131no—
210C2×C42—131no—
211C2×C42C22×D1311yescharacteristic
212C4⋊C8—264no—
213C4⋊C8—264no—
214#97—522no—
215C4×C8—522no—
216#95—21no—
217#95—261no—
218#95—261no—
219#95—261no—
220#95—261no—
221#95—261no—
222#95—261no—
223#95—261no—
224#95—261no—
225C2×C13#147311yescharacteristic
226C2×C13#148311yescharacteristic
227C2×C13#149311yescharacteristic
228C2×C13#150311yescharacteristic
229C2×C13#150911yescharacteristic
230C2×C13#152411yescharacteristic
231C2×C13#155011yescharacteristic
232C2×Q8—261no—
233C2×Q8—261no—
234C2×Q8—521no—
235C2×Q8—521no—
236C22×C4—21no—
237C22×C4—21no—
238C22×C4—131no—
239C22×C4—131no—
240C22×C4—131no—
241C22×C4—131no—
242C22×C4—261no—
243C22×C4—261no—
244C22×C4C2×C4×D1311yescharacteristic
245C22×C4D4×D1311yescharacteristic
246C22×C4D4×D1311yescharacteristic
247C2×C8—22no—
248C2×C8—22no—
249C2×C8—41no—
250C2×C8—41no—
251C2×C8—41no—
252C2×C8—41no—
253C2×C8—262no—
254C2×C8—262no—
255C2×C8—521no—
256C2×C8—521no—
257C2×C8—521no—
258C2×C8—521no—
259C4⋊C4—21no—
260C4⋊C4—21no—
261C4⋊C4—41no—
262C4⋊C4—41no—
263C4⋊C4—41no—
264C4⋊C4—521no—
265C4⋊C4—522no—
266C4⋊C4—522no—
267C42—41no—
268C42—132no—
269C42—132no—
270C42—262no—
271C42—262no—
272C42—261no—
273C42—261no—
274C42—261no—
275C42—261no—
276C42—521no—
277C13#768911yescharacteristic, complemented, Sylow
278C23C22⋊C4×D1311yescharacteristic
279Q8—1041no—
280Q8—1041no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—132no—
294C2×C4—132no—
295C2×C4—132no—
296C2×C4—132no—
297C2×C4—261no—
298C2×C4—261no—
299C2×C4—261no—
300C2×C4—261no—
301C2×C4—261no—
302C2×C4—261no—
303C2×C4—261no—
304C2×C4—261no—
305C2×C4—521no—
306C2×C4—521no—
307C2×C4—521no—
308C2×C4—521no—
309C2×C4—521no—
310C2×C4—521no—
311C2×C4#8815511yescharacteristic
312C2×C4#8816111yescharacteristic
313C2×C4#8816511yescharacteristic
314C2×C4SD16×D1311yescharacteristic
315C2×C4#8816911yescharacteristic
316C2×C4Q16×D1311yescharacteristic
317C8—42no—
318C8—42no—
319C8—522no—
320C8—522no—
321C22#1171838811yescharacteristic
322C22#1171840111yescharacteristic
323C22#1171841211yescharacteristic
324C22#1171843211yescharacteristic
325C22D13×#10311yescharacteristic
326C22D13×#10411yescharacteristic
327C22D13×#10411yescharacteristic
328C4—21no—
329C4—21no—
330C4—21no—
331C4—21no—
332C4—21no—
333C4—21no—
334C4—81no—
335C4—81no—
336C4—262no—
337C4—262no—
338C4—262no—
339C4—262no—
340C4—1041no—
341C4—1041no—
342C2#1311320411yescharacteristic
343C2#1311324611yescharacteristic
344C2#1311328911yescharacteristic
345C2#1311333311yescharacteristic
346C2#1311335811yescharacteristic
347C2#1311342311yescharacteristic
348C2#1311352511yescharacteristic
subgroupG/H
centerC23C22⋊C4×D13
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#1271C2
socle, prime radicalC23×C13C2×C22⋊C4
cosocleC2×C42×C13C23
hypercenter#1271D13
hypocenterC13#7689
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1271

Complements

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

NH ≅ G/Ntype
277. C13#7689semidirect

Maximal subgroups

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

subgroupindex
#131232192
#131146882
#131146842
#131126612
#131126592
C13×#12712
#768913