Finite Group Databasebeta

← #15765742

Subgroups — #15765742

Order 3328.

554 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718739C211yesmaximal, characteristic
2C2×#11718754C211yesmaximal, characteristic
3C2×#11718342C211yesmaximal, characteristic
4#13115796C211yesmaximal, characteristic
5#13115796C211yesmaximal, characteristic
6#13112663C211yesmaximal, characteristic
7C13×#1956C211yesmaximal, characteristic
8C2×C13×C4⋊Q8C2211yescharacteristic
9C2×#88123C2211yescharacteristic
10C2×#88123C2211yescharacteristic
11C2×C13×#103—22no—
12C2×C4×C8×C13C2211yescharacteristic
13C13×#384C2211yescharacteristic
14C2×#88056—22no—
15#11718754—22no—
16#11718754—22no—
17#11718739—22no—
18#11718739—22no—
19C2×#88050—22no—
20C2×#88047—22no—
21C2×C4×#1055C2211yescharacteristic
22C2×C4×#1055C2211yescharacteristic
23#11718342—22no—
24#11718342—22no—
25#11718121—22no—
26#11718121—22no—
27C22×Q8×C13—21no—
28C22×Dic26—21no—
29C22×Dic26—21no—
30C22×C8×C13D412yes—
31C13×C4⋊Q8—21no—
32C13×C4⋊Q8—21no—
33C13×C4⋊Q8—21no—
34C13×C4⋊Q8D412yes—
35C2×C13×C4⋊C4—21no—
36C2×C13×C4⋊C4—21no—
37C2×C13×C4⋊C4—21no—
38C2×C13×C4⋊C4—21no—
39C2×C13×C4⋊C4—21no—
40C2×C42×C13C2311yescharacteristic
41C2×C4⋊Dic13—21no—
42C2×C4⋊Dic13—21no—
43C2×C4⋊Dic13—21no—
44C2×C4⋊Dic13—21no—
45C22×#1055D412yes—
46C22×#1055D412yes—
47#88123—21no—
48#88123—21no—
49#88123—21no—
50#88123—21no—
51#88123—21no—
52#88123—21no—
53#88123D412yes—
54#88123D412yes—
55C13×#103—44no—
56C4×C8×C13—21no—
57C4×C8×C13—21no—
58#88056—28no—
59#88050—28no—
60#88047—28no—
61C4×#1055—21no—
62C4×#1055—21no—
63C4×#1055—21no—
64C4×#1055—21no—
65#10313—131nomaximal, Sylow
66C2×Q8×C13—22no—
67C2×Q8×C13—41no—
68C2×Q8×C13—42no—
69C2×Q8×C13—42no—
70C22×C4×C13—41no—
71C22×C4×C13—41no—
72C22×C4×C13C2×D411yescharacteristic
73C22×C4×C13C2×D411yescharacteristic
74C22×C4×C13C2×D411yescharacteristic
75C22×Dic13—41no—
76C22×Dic13—41no—
77C2×Dic26—22no—
78C2×Dic26—22no—
79C2×Dic26—42no—
80C2×Dic26—42no—
81C2×Dic26—42no—
82C2×Dic26—42no—
83C2×Dic26—41no—
84C2×Dic26—41no—
85C2×C8×C13—22no—
86C2×C8×C13—22no—
87C2×C8×C13—22no—
88C13×C4⋊C4—22no—
89C13×C4⋊C4—22no—
90C13×C4⋊C4—41no—
91C13×C4⋊C4—41no—
92C13×C4⋊C4—42no—
93C13×C4⋊C4—42no—
94C13×C4⋊C4—42no—
95C42×C13C2×D411yescharacteristic
96C42×C13C2×D411yescharacteristic
97C42×C13C2×D411yescharacteristic
98C42×C13#4111yescharacteristic
99C4⋊Dic13—22no—
100C4⋊Dic13—22no—
101C4⋊Dic13—22no—
102C4⋊Dic13—22no—
103C4⋊Dic13—41no—
104C4⋊Dic13—41no—
105C4⋊Dic13—41no—
106C4⋊Dic13—41no—
107C2×#1055—22no—
108C2×#1055—22no—
109C2×#1055—22no—
110C2×#1055—22no—
111C2×#1055—22no—
112C2×#1055Q1614yes—
113C2×#500—131no—
114C2×#487—131no—
115C2×#487—131no—
116#1990—131no—
117#1990—131no—
118#1956D1311yescharacteristic
119#1273—131no—
120C23×C13#12711yescharacteristic
121Q8×C13—44no—
122Q8×C13—82no—
123C2×C4×C13—42no—
124C2×C4×C13—81no—
125C2×C4×C13—81no—
126C2×C4×C13—81no—
127C2×C4×C13—81no—
128C2×C4×C13—81no—
129C2×C4×C13#12011yescharacteristic
130C2×C4×C13#12011yescharacteristic
131C2×C4×C13#12011yescharacteristic
132C2×C4×C13#12111yescharacteristic
133C2×C4×C13#12111yescharacteristic
134C2×C4×C13#12111yescharacteristic
135C2×C4×C13C2×Q1612yes—
136C2×C4×C13#13512yes—
137C2×C4×C13#13512yes—
138C2×C4×C13AGL(1,ℤ/8)12yes—
139C2×C4×C13#13712yes—
140C2×C4×C13#13712yes—
141C2×Dic13—42no—
142C2×Dic13—42no—
143C2×Dic13—81no—
144C2×Dic13—81no—
145C2×Dic13—81no—
146C2×Dic13—81no—
147Dic26—44no—
148Dic26—44no—
149Dic26—82no—
150Dic26—82no—
151C8×C13—42no—
152#1055—24no—
153#1055—42no—
154C2×C4⋊Q8—131no—
155C2×C4⋊Q8—131no—
156C2×C4⋊Q8C2×D1311yescharacteristic
157#500—262no—
158#500—262no—
159#487—262no—
160#487—262no—
161#487—262no—
162#487—262no—
163C2×#107—262no—
164C2×#103—22no—
165C2×#103—262no—
166C2×#103—262no—
167C2×C4×C8—131no—
168C2×C4×C8—131no—
169C2×C4×C8C2×D1311yescharacteristic
170#384C2×D1311yescharacteristic
171#340—262no—
172#340—262no—
173C22×C13#39211yescharacteristic
174C22×C13#49411yescharacteristic
175C22×C13#49511yescharacteristic
176C22×C13#49511yescharacteristic
177C22×C13#49611yescharacteristic
178C22×C13#49711yescharacteristic
179C22×C13#49711yescharacteristic
180C4×C13—82no—
181C4×C13—161no—
182C4×C13#44912yes—
183C4×C13#45112yes—
184C4×C13#45212yes—
185C4×C13#46212yes—
186C4×C13#46312yes—
187C4×C13#46412yes—
188Dic13—82no—
189Dic13—82no—
190C22×Q8—21no—
191C22×Q8—261no—
192C22×Q8—261no—
193C22×C8—132no—
194C22×C8—132no—
195C22×C8C22⋊D1312yes—
196C4⋊Q8—21no—
197C4⋊Q8—21no—
198C4⋊Q8—21no—
199C4⋊Q8—132no—
200C4⋊Q8—132no—
201C4⋊Q8—261no—
202C4⋊Q8—261no—
203C4⋊Q8—261no—
204C4⋊Q8—261no—
205C4⋊Q8—261no—
206C4⋊Q8—261no—
207C4⋊Q8D5212yes—
208C2×C4⋊C4—21no—
209C2×C4⋊C4—21no—
210C2×C4⋊C4—21no—
211C2×C4⋊C4—21no—
212C2×C4⋊C4—21no—
213C2×C4⋊C4—261no—
214C2×C4⋊C4—261no—
215C2×C4⋊C4—261no—
216C2×C4⋊C4—261no—
217C2×C42C22×D1311yescharacteristic
218#107—268no—
219#103—44no—
220#103—268no—
221#103—268no—
222C4×C8—21no—
223C4×C8—21no—
224C4×C8—261no—
225C4×C8—261no—
226C4×C8—261no—
227C4×C8—261no—
228C2×C13#171011yescharacteristic
229C2×C13#171811yescharacteristic
230C2×C13#171911yescharacteristic
231C2×C13#172311yescharacteristic
232C2×C13#201211yescharacteristic
233C2×C13#201511yescharacteristic
234C2×C13#201611yescharacteristic
235C2×Q8—22no—
236C2×Q8—41no—
237C2×Q8—42no—
238C2×Q8—42no—
239C2×Q8—262no—
240C2×Q8—262no—
241C2×Q8—521no—
242C2×Q8—521no—
243C2×Q8—522no—
244C2×Q8—522no—
245C2×Q8—522no—
246C2×Q8—522no—
247C22×C4—41no—
248C22×C4—41no—
249C22×C4—521no—
250C22×C4—521no—
251C22×C4D4×D1311yescharacteristic
252C22×C4D4×D1311yescharacteristic
253C22×C4C2×C22⋊D1311yescharacteristic
254C2×C8—22no—
255C2×C8—22no—
256C2×C8—22no—
257C2×C8—134no—
258C2×C8—262no—
259C2×C8—262no—
260C2×C8—262no—
261C2×C8—262no—
262C2×C8—262no—
263C4⋊C4—22no—
264C4⋊C4—22no—
265C4⋊C4—41no—
266C4⋊C4—41no—
267C4⋊C4—42no—
268C4⋊C4—42no—
269C4⋊C4—42no—
270C4⋊C4—262no—
271C4⋊C4—262no—
272C4⋊C4—262no—
273C4⋊C4—262no—
274C4⋊C4—521no—
275C4⋊C4—521no—
276C4⋊C4—521no—
277C4⋊C4—521no—
278C42C2×D5211yescharacteristic
279C42#612711yescharacteristic
280C42D4×D1311yescharacteristic
281C42D4×D1311yescharacteristic
282C13#1031311yescharacteristic, complemented, Sylow
283C23#8819411yescharacteristic
284Q8—44no—
285Q8—82no—
286Q8—524no—
287Q8—524no—
288Q8—1042no—
289Q8—1042no—
290C2×C4—42no—
291C2×C4—81no—
292C2×C4—81no—
293C2×C4—81no—
294C2×C4—81no—
295C2×C4—81no—
296C2×C4—522no—
297C2×C4—522no—
298C2×C4—1041no—
299C2×C4—1041no—
300C2×C4—1041no—
301C2×C4—1041no—
302C2×C4#8813611yescharacteristic
303C2×C4#8813611yescharacteristic
304C2×C4#8813811yescharacteristic
305C2×C4#8813811yescharacteristic
306C2×C4#8816912yes—
307C2×C4#8817012yes—
308C2×C4Q16×D1312yes—
309C2×C4#8817212yes—
310C2×C4#8818411yescharacteristic
311C2×C4#8818612yes—
312C2×C4#8819111yescharacteristic
313C2×C4#8820412yes—
314C8—42no—
315C8—264no—
316C8—522no—
317C22#1171862111yescharacteristic
318C22#1171872011yescharacteristic
319C22#1171873511yescharacteristic
320C22#1171882811yescharacteristic
321C22#1171882911yescharacteristic
322C22#1171884211yescharacteristic
323C22#1171885111yescharacteristic
324C4—82no—
325C4—161no—
326C4—1042no—
327C4—1042no—
328C4#1171845412yes—
329C4#1171845912yes—
330C4#1171846912yes—
331C4#1171847112yes—
332C4#1171867712yes—
333C4#1171869812yes—
334C2#1311444411yescharacteristic
335C2#1311448311yescharacteristic
336C2#1311448711yescharacteristic
337C2#1311451111yescharacteristic
338C2#1311591211yescharacteristic
339C2#1311593111yescharacteristic
340C2#1311593711yescharacteristic
subgroupG/H
centerC23#88194
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#1956C2
socle, prime radicalC23×C13#127
hypercenter#1956D13
hypocenterC13#10313
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1956

Complements

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

NH ≅ G/Ntype
282. C13#10313semidirect

Maximal subgroups

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

subgroupindex
C2×#117187392
C2×#117187542
C2×#117183422
#131157962
#131126632
C13×#19562
#1031313