Finite Group Databasebeta

← #15765772

Subgroups — #15765772

Order 3328.

538 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718754C211yesmaximal, characteristic
2C2×#11718342C211yesmaximal, characteristic
3C2×#11718742C211yesmaximal, characteristic
4#13115796C211yesmaximal, characteristic
5#13115796C211yesmaximal, characteristic
6#13112663C211yesmaximal, characteristic
7C13×#1990C211yesmaximal, characteristic
8C2×C13×C4⋊Q8C2211yescharacteristic
9C2×#88123C2211yescharacteristic
10C2×#88123C2211yescharacteristic
11C2×C4×C8×C13C2211yescharacteristic
12C13×#384C2211yescharacteristic
13C2×#88075—22no—
14C2×#88056—22no—
15#11718754—22no—
16#11718754—22no—
17#11718742—22no—
18#11718742—22no—
19C2×#88050—22no—
20C2×C4×#1055C2211yescharacteristic
21C2×C4×#1055C2211yescharacteristic
22#11718342—22no—
23#11718342—22no—
24C13×#340—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—
55C4×C8×C13—21no—
56C4×C8×C13—21no—
57#88075—28no—
58#88056—28no—
59#88050—28no—
60C4×#1055—21no—
61C4×#1055—21no—
62C4×#1055—21no—
63C4×#1055—21no—
64#10319—131nomaximal, Sylow
65C2×Q8×C13—22no—
66C2×Q8×C13—41no—
67C2×Q8×C13—42no—
68C2×Q8×C13—42no—
69C22×C4×C13—41no—
70C22×C4×C13—41no—
71C22×C4×C13C2×D411yescharacteristic
72C22×C4×C13C2×D411yescharacteristic
73C22×C4×C13C2×D411yescharacteristic
74C22×Dic13—41no—
75C22×Dic13—41no—
76C2×Dic26—22no—
77C2×Dic26—22no—
78C2×Dic26—42no—
79C2×Dic26—42no—
80C2×Dic26—42no—
81C2×Dic26—42no—
82C2×Dic26—41no—
83C2×Dic26—41no—
84C2×C8×C13—22no—
85C2×C8×C13—22no—
86C2×C8×C13—22no—
87C13×C4⋊C4—22no—
88C13×C4⋊C4—22no—
89C13×C4⋊C4—41no—
90C13×C4⋊C4—41no—
91C13×C4⋊C4—42no—
92C13×C4⋊C4—42no—
93C13×C4⋊C4—42no—
94C42×C13C2×D411yescharacteristic
95C42×C13C2×D411yescharacteristic
96C42×C13C2×D411yescharacteristic
97C42×C13#4111yescharacteristic
98C4⋊Dic13—22no—
99C4⋊Dic13—22no—
100C4⋊Dic13—22no—
101C4⋊Dic13—22no—
102C4⋊Dic13—41no—
103C4⋊Dic13—41no—
104C4⋊Dic13—41no—
105C4⋊Dic13—41no—
106C2×#1055—22no—
107C2×#1055—22no—
108C2×#1055—22no—
109C2×#1055—22no—
110C2×#1055—22no—
111C2×#1055—22no—
112C2×#487—131no—
113C2×#487—131no—
114C2×#487—131no—
115#1990—131no—
116#1990—131no—
117#1990D1311yescharacteristic
118#1273—131no—
119C23×C13#12711yescharacteristic
120Q8×C13—44no—
121Q8×C13—82no—
122C2×C4×C13—42no—
123C2×C4×C13—81no—
124C2×C4×C13—81no—
125C2×C4×C13—81no—
126C2×C4×C13—81no—
127C2×C4×C13—81no—
128C2×C4×C13#12011yescharacteristic
129C2×C4×C13#12011yescharacteristic
130C2×C4×C13#12011yescharacteristic
131C2×C4×C13#12111yescharacteristic
132C2×C4×C13#12111yescharacteristic
133C2×C4×C13#12111yescharacteristic
134C2×C4×C13#13512yes—
135C2×C4×C13#13512yes—
136C2×C4×C13#13512yes—
137C2×C4×C13#13712yes—
138C2×C4×C13#13712yes—
139C2×C4×C13#13712yes—
140C2×Dic13—42no—
141C2×Dic13—42no—
142C2×Dic13—81no—
143C2×Dic13—81no—
144C2×Dic13—81no—
145C2×Dic13—81no—
146Dic26—44no—
147Dic26—44no—
148Dic26—82no—
149Dic26—82no—
150C8×C13—42no—
151#1055—42no—
152#1055—42no—
153C2×C4⋊Q8—131no—
154C2×C4⋊Q8—131no—
155C2×C4⋊Q8C2×D1311yescharacteristic
156#487—262no—
157#487—262no—
158#487—262no—
159#487—262no—
160#487—262no—
161#487—262no—
162C2×#103—262no—
163C2×#103—262no—
164C2×#103—262no—
165C2×C4×C8—131no—
166C2×C4×C8—131no—
167C2×C4×C8C2×D1311yescharacteristic
168#384C2×D1311yescharacteristic
169#340—22no—
170#340—262no—
171#340—262no—
172C22×C13#39211yescharacteristic
173C22×C13#49511yescharacteristic
174C22×C13#49511yescharacteristic
175C22×C13#49511yescharacteristic
176C22×C13#49711yescharacteristic
177C22×C13#49711yescharacteristic
178C22×C13#49711yescharacteristic
179C4×C13—82no—
180C4×C13—161no—
181C4×C13#45212yes—
182C4×C13#45212yes—
183C4×C13#45212yes—
184C4×C13#46412yes—
185C4×C13#46412yes—
186C4×C13#46412yes—
187Dic13—82no—
188Dic13—82no—
189C22×Q8—21no—
190C22×Q8—261no—
191C22×Q8—261no—
192C22×C8—132no—
193C22×C8—132no—
194C22×C8C22⋊D1312yes—
195C4⋊Q8—21no—
196C4⋊Q8—21no—
197C4⋊Q8—21no—
198C4⋊Q8—132no—
199C4⋊Q8—132no—
200C4⋊Q8—261no—
201C4⋊Q8—261no—
202C4⋊Q8—261no—
203C4⋊Q8—261no—
204C4⋊Q8—261no—
205C4⋊Q8—261no—
206C4⋊Q8D5212yes—
207C2×C4⋊C4—21no—
208C2×C4⋊C4—21no—
209C2×C4⋊C4—21no—
210C2×C4⋊C4—21no—
211C2×C4⋊C4—21no—
212C2×C4⋊C4—261no—
213C2×C4⋊C4—261no—
214C2×C4⋊C4—261no—
215C2×C4⋊C4—261no—
216C2×C42C22×D1311yescharacteristic
217#103—268no—
218#103—268no—
219#103—268no—
220C4×C8—21no—
221C4×C8—21no—
222C4×C8—261no—
223C4×C8—261no—
224C4×C8—261no—
225C4×C8—261no—
226C2×C13#171111yescharacteristic
227C2×C13#171811yescharacteristic
228C2×C13#171811yescharacteristic
229C2×C13#171811yescharacteristic
230C2×C13#201511yescharacteristic
231C2×C13#201511yescharacteristic
232C2×C13#201511yescharacteristic
233C2×Q8—22no—
234C2×Q8—41no—
235C2×Q8—42no—
236C2×Q8—42no—
237C2×Q8—262no—
238C2×Q8—262no—
239C2×Q8—521no—
240C2×Q8—521no—
241C2×Q8—522no—
242C2×Q8—522no—
243C2×Q8—522no—
244C2×Q8—522no—
245C22×C4—41no—
246C22×C4—41no—
247C22×C4—521no—
248C22×C4—521no—
249C22×C4D4×D1311yescharacteristic
250C22×C4D4×D1311yescharacteristic
251C22×C4C2×C22⋊D1311yescharacteristic
252C2×C8—22no—
253C2×C8—22no—
254C2×C8—22no—
255C2×C8—262no—
256C2×C8—262no—
257C2×C8—262no—
258C2×C8—262no—
259C2×C8—262no—
260C2×C8—262no—
261C4⋊C4—22no—
262C4⋊C4—22no—
263C4⋊C4—41no—
264C4⋊C4—41no—
265C4⋊C4—42no—
266C4⋊C4—42no—
267C4⋊C4—42no—
268C4⋊C4—262no—
269C4⋊C4—262no—
270C4⋊C4—262no—
271C4⋊C4—262no—
272C4⋊C4—521no—
273C4⋊C4—521no—
274C4⋊C4—521no—
275C4⋊C4—521no—
276C42C2×D5211yescharacteristic
277C42#612711yescharacteristic
278C42D4×D1311yescharacteristic
279C42D4×D1311yescharacteristic
280C13#1031911yescharacteristic, complemented, Sylow
281C23#8819411yescharacteristic
282Q8—44no—
283Q8—82no—
284Q8—524no—
285Q8—524no—
286Q8—1042no—
287Q8—1042no—
288C2×C4—42no—
289C2×C4—81no—
290C2×C4—81no—
291C2×C4—81no—
292C2×C4—81no—
293C2×C4—81no—
294C2×C4—522no—
295C2×C4—522no—
296C2×C4—1041no—
297C2×C4—1041no—
298C2×C4—1041no—
299C2×C4—1041no—
300C2×C4#8813611yescharacteristic
301C2×C4#8813611yescharacteristic
302C2×C4#8813811yescharacteristic
303C2×C4#8813811yescharacteristic
304C2×C4#8816612yes—
305C2×C4#8816912yes—
306C2×C4#8817012yes—
307C2×C4#8817212yes—
308C2×C4#8818411yescharacteristic
309C2×C4#8819111yescharacteristic
310C2×C4#8819612yes—
311C2×C4#8820412yes—
312C8—42no—
313C8—522no—
314C8—522no—
315C22#1171862111yescharacteristic
316C22#1171872011yescharacteristic
317C22#1171874711yescharacteristic
318C22#1171881611yescharacteristic
319C22#1171882811yescharacteristic
320C22#1171882911yescharacteristic
321C22#1171885111yescharacteristic
322C4—82no—
323C4—161no—
324C4—1042no—
325C4—1042no—
326C4#1171842812yes—
327C4#1171844412yes—
328C4#1171845912yes—
329C4#1171847112yes—
330C4#1171868912yes—
331C4#1171870812yes—
332C2#1311444711yescharacteristic
333C2#1311447911yescharacteristic
334C2#1311448011yescharacteristic
335C2#1311448111yescharacteristic
336C2#1311592911yescharacteristic
337C2#1311593111yescharacteristic
338C2#1311593211yescharacteristic
subgroupG/H
centerC23#88194
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#1990C2
socle, prime radicalC23×C13#127
hypercenter#1990D13
hypocenterC13#10319
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1990

Complements

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

NH ≅ G/Ntype
280. C13#10319semidirect

Maximal subgroups

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

subgroupindex
C2×#117187542
C2×#117183422
C2×#117187422
#131157962
#131126632
C13×#19902
#1031913