Finite Group Databasebeta

← #15752221

Subgroups — #15752221

Order 3328.

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

normal subgroups only

This group has 394 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#13121867C211yesmaximal, characteristic
2#13116400C211yesmaximal, characteristic
3#13116399C211yesmaximal, characteristic
4#13116373C211yesmaximal, characteristic
5#13112661C211yesmaximal, characteristic
6#13112660C211yesmaximal, characteristic
7C13×#1271C211yesmaximal, characteristic
8C2×#88142—21no—
9C13×#389C2211yescharacteristic
10C2×#88058—21no—
11C2×#88056—21no—
12#11718645—21no—
13#11718642—21no—
14#11718640—21no—
15#11718596C2211yescharacteristic
16#11718590C2211yescharacteristic
17#11718589C2211yescharacteristic
18#11718317—21no—
19#11718315—21no—
20C13×#336C2211yescharacteristic
21C13×#336C2211yescharacteristic
22#11718143—21no—
23#11718143—21no—
24#11718121—21no—
25#11718121—21no—
26#11718116C2211yescharacteristic
27C22×Dic26—21no—
28C22×Dic26D411yescharacteristic
29C22×C8×C13—21no—
30C22×C8×C13—21no—
31C2×C13×C4⋊C4—21no—
32C2×C13×C4⋊C4D411yescharacteristic
33C2×C13×C4⋊C4D411yescharacteristic
34C2×C42×C13C2311yescharacteristic
35C2×C4⋊Dic13—21no—
36C2×C4⋊Dic13—21no—
37C2×C4⋊Dic13—21no—
38C2×C4⋊Dic13—21no—
39C2×C4⋊Dic13D411yescharacteristic
40C2×C4⋊Dic13D411yescharacteristic
41C2×C4⋊Dic13D411yescharacteristic
42C2×#6101—21no—
43C2×#6101—21no—
44C2×#6101—21no—
45C2×C4×Dic13—21no—
46C22×#1055—21no—
47#88142—42no—
48#88142—42no—
49C13×#95—21no—
50#88071—21no—
51#88071—21no—
52#88071—21no—
53#88071—21no—
54#88071—21no—
55#88071—21no—
56#88058—42no—
57#88056—42no—
58#7829—131nomaximal, Sylow
59C22×C4×C13—21no—
60C22×C4×C13—21no—
61C22×C4×C13C2×D411yescharacteristic
62C22×C4×C13C2×D411yescharacteristic
63C22×C4×C13C2×D411yescharacteristic
64C22×Dic13—21no—
65C22×Dic13—21no—
66C22×Dic13—21no—
67C22×Dic13—21no—
68C22×Dic13—41no—
69C2×Dic26—21no—
70C2×Dic26—41no—
71C2×Dic26—41no—
72C2×Dic26—42no—
73C2×Dic26—81no—
74C2×Dic26—81no—
75C2×Dic26SD1612yes—
76C2×C8×C13—22no—
77C2×C8×C13—41no—
78C2×C8×C13—41no—
79C2×C8×C13—41no—
80C2×C8×C13—41no—
81C2×C8×C13—41no—
82C13×C4⋊C4—21no—
83C13×C4⋊C4—41no—
84C13×C4⋊C4—41no—
85C13×C4⋊C4—41no—
86C13×C4⋊C4Q1612yes—
87C42×C13—41no—
88C4⋊Dic13—21no—
89C4⋊Dic13—42no—
90C4⋊Dic13—41no—
91C4⋊Dic13—41no—
92C4⋊Dic13—42no—
93C4⋊Dic13—42no—
94C4⋊Dic13—41no—
95C4⋊Dic13—41no—
96C4⋊Dic13Q1612yes—
97#6101—42no—
98#6101—41no—
99#6101—41no—
100#6101—81no—
101C4×Dic13—42no—
102C2×#1055—41no—
103C2×#1055—41no—
104C2×#1055—41no—
105#2734—131no—
106#2100—131no—
107#2100—131no—
108#2095—131no—
109#1272—131no—
110#1271—131no—
111#1271D1311yescharacteristic
112C23×C13#12011yescharacteristic
113C2×C4×C13—21no—
114C2×C4×C13—21no—
115C2×C4×C13—21no—
116C2×C4×C13—21no—
117C2×C4×C13—21no—
118C2×C4×C13—21no—
119C2×C4×C13—22no—
120C2×C4×C13—41no—
121C2×C4×C13—41no—
122C2×C4×C13—41no—
123C2×C4×C13—41no—
124C2×C4×C13—41no—
125C2×C4×C13C2×SD1611yescharacteristic
126C2×C4×C13C2×Q1611yescharacteristic
127C2×C4×C13C2×Q1611yescharacteristic
128C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
129C2×C4×C13#13711yescharacteristic
130C2×C4×C13#13711yescharacteristic
131C2×Dic13—22no—
132C2×Dic13—22no—
133C2×Dic13—41no—
134C2×Dic13—41no—
135C2×Dic13—41no—
136C2×Dic13—41no—
137C2×Dic13—41no—
138C2×Dic13—41no—
139C2×Dic13—41no—
140C2×Dic13—41no—
141C2×Dic13—41no—
142C2×Dic13—41no—
143C2×Dic13—81no—
144C2×Dic13—81no—
145C2×Dic13—81no—
146Dic26—42no—
147Dic26—81no—
148Dic26—84no—
149C8×C13—42no—
150C8×C13—81no—
151#1055—81no—
152C2×C4⋊Q8—261no—
153C2×#107—261no—
154C2×#103—261no—
155#398—261no—
156#395—261no—
157#395—261no—
158#391—131no—
159#389—131no—
160#389C2×D1311yescharacteristic
161#387—261no—
162#387—261no—
163#384—131no—
164#340—261no—
165#340—261no—
166#340—261no—
167#340—261no—
168#336—131no—
169#336C2×D1311yescharacteristic
170#336C2×D1311yescharacteristic
171C22×C13#45011yescharacteristic
172C22×C13#45111yescharacteristic
173C22×C13#45111yescharacteristic
174C22×C13#45311yescharacteristic
175C22×C13#45411yescharacteristic
176C22×C13#45411yescharacteristic
177C22×C13#45811yescharacteristic
178C4×C13—21no—
179C4×C13—21no—
180C4×C13—21no—
181C4×C13—21no—
182C4×C13—21no—
183C4×C13—21no—
184C4×C13—42no—
185C4×C13—81no—
186Dic13—42no—
187Dic13—42no—
188Dic13—81no—
189Dic13—81no—
190Dic13—161no—
191C22×Q8—131no—
192C22×Q8—261no—
193C22×C8—21no—
194C22×C8—21no—
195C22×C8—261no—
196C4⋊Q8—522no—
197C4⋊Q8—522no—
198C2×C4⋊C4—21no—
199C2×C4⋊C4—131no—
200C2×C4⋊C4—131no—
201C2×C4⋊C4—131no—
202C2×C4⋊C4—261no—
203C2×C4⋊C4—261no—
204C2×C4⋊C4—261no—
205C2×C4⋊C4—261no—
206C2×C4⋊C4—261no—
207C2×C4⋊C4—261no—
208C2×C4⋊C4—261no—
209C2×C4⋊C4D5211yescharacteristic
210C2×C4⋊C4D5211yescharacteristic
211C2×C42—261no—
212C2×C42C22×D1311yescharacteristic
213#107—522no—
214#103—522no—
215#95—21no—
216#95—261no—
217#95—261no—
218#95—261no—
219#95—261no—
220#95—261no—
221#95—261no—
222C2×C13#161311yescharacteristic
223C2×C13#161711yescharacteristic
224C2×C13#161711yescharacteristic
225C2×C13#163311yescharacteristic
226C2×C13#163711yescharacteristic
227C2×C13#163711yescharacteristic
228C2×C13#165711yescharacteristic
229C2×Q8—132no—
230C2×Q8—261no—
231C2×Q8—521no—
232C2×Q8—521no—
233C2×Q8—522no—
234C2×Q8—1041no—
235C2×Q8—1041no—
236C22×C4—21no—
237C22×C4—21no—
238C22×C4—261no—
239C22×C4—261no—
240C22×C4—261no—
241C22×C4—261no—
242C22×C4—521no—
243C22×C4C2×D5211yescharacteristic
244C22×C4D4×D1311yescharacteristic
245C22×C4D4×D1311yescharacteristic
246C2×C8—22no—
247C2×C8—41no—
248C2×C8—41no—
249C2×C8—41no—
250C2×C8—41no—
251C2×C8—41no—
252C2×C8—521no—
253C2×C8—521no—
254C2×C8—521no—
255C4⋊C4—21no—
256C4⋊C4—41no—
257C4⋊C4—41no—
258C4⋊C4—41no—
259C4⋊C4—132no—
260C4⋊C4—261no—
261C4⋊C4—521no—
262C4⋊C4—521no—
263C4⋊C4—521no—
264C4⋊C4—521no—
265C4⋊C4—522no—
266C4⋊C4—522no—
267C4⋊C4—522no—
268C4⋊C4—522no—
269C4⋊C4—521no—
270C4⋊C4—521no—
271C4⋊C4—1041no—
272C4⋊C4Dic5212yes—
273C42—41no—
274C42—522no—
275C13#782911yescharacteristic, complemented, Sylow
276C23#8813611yescharacteristic
277Q8—522no—
278Q8—1041no—
279Q8—1044no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—22no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—262no—
293C2×C4—262no—
294C2×C4—521no—
295C2×C4—521no—
296C2×C4—521no—
297C2×C4—521no—
298C2×C4—521no—
299C2×C4—521no—
300C2×C4—521no—
301C2×C4—521no—
302C2×C4—521no—
303C2×C4—521no—
304C2×C4—1041no—
305C2×C4—1041no—
306C2×C4—1041no—
307C2×C4C2×Dic5211yescharacteristic
308C2×C4#8816311yescharacteristic
309C2×C4#8816511yescharacteristic
310C2×C4SD16×D1311yescharacteristic
311C2×C4#8816911yescharacteristic
312C2×C4Q16×D1311yescharacteristic
313C8—42no—
314C8—81no—
315C8—1041no—
316C22#1171840011yescharacteristic
317C22#1171840311yescharacteristic
318C22#1171841411yescharacteristic
319C22#1171843711yescharacteristic
320C22#1171846911yescharacteristic
321C22#1171848311yescharacteristic
322C22#1171848811yescharacteristic
323C4—21no—
324C4—21no—
325C4—21no—
326C4—21no—
327C4—21no—
328C4—21no—
329C4—42no—
330C4—81no—
331C4—522no—
332C4—522no—
333C4—1041no—
334C4—1041no—
335C4—2081no—
336C2#1311385711yescharacteristic
337C2#1311387911yescharacteristic
338C2#1311388011yescharacteristic
339C2#1311397811yescharacteristic
340C2#1311400211yescharacteristic
341C2#1311400411yescharacteristic
342C2#1311413611yescharacteristic
subgroupG/H
centerC23#88136
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#1271C2
socle, prime radicalC23×C13#120
hypercenter#1271D13
hypocenterC13#7829
LCSG ▷ C2×C42×C13 ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1271

Complements

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

NH ≅ G/Ntype
275. C13#7829semidirect

Maximal subgroups

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

subgroupindex
#131218672
#131164002
#131163992
#131163732
#131126612
#131126602
C13×#12712
#782913