Finite Group Databasebeta

← #15765714

Subgroups — #15765714

Order 3328.

618 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718739C211yesmaximal, characteristic
2C2×#11718753C211yesmaximal, characteristic
3#13115798C211yesmaximal, characteristic
4#13115797C211yesmaximal, characteristic
5#13115639C211yesmaximal, characteristic
6#13112663C211yesmaximal, characteristic
7C2×C13×#500C211yesmaximal, characteristic
8C2×C13×C4⋊Q8C2211yescharacteristic
9C2×C13×C4⋊Q8C2211yescharacteristic
10C22×#6107—22no—
11C2×#88123C2211yescharacteristic
12C13×#500—22no—
13C13×#500—22no—
14C2×C13×#107—22no—
15C2×C4×C8×C13C2211yescharacteristic
16C2×#88075—22no—
17#11718753—22no—
18#11718753—22no—
19#11718739—22no—
20#11718739—22no—
21C2×#88047—22no—
22#11718596C2211yescharacteristic
23C2×C4×#1055C2211yescharacteristic
24C2×C4×#1055C2211yescharacteristic
25#11718143—22no—
26#11718121—22no—
27C22×Q8×C13—21no—
28C22×Q8×C13—21no—
29C22×Dic26—21no—
30C22×C8×C13D412yes—
31C13×C4⋊Q8—21no—
32C13×C4⋊Q8—21no—
33C13×C4⋊Q8—21no—
34C13×C4⋊Q8—21no—
35C13×C4⋊Q8—21no—
36C13×C4⋊Q8—21no—
37C13×C4⋊Q8D412yes—
38C13×C4⋊Q8D412yes—
39C2×C13×C4⋊C4—21no—
40C2×C13×C4⋊C4—21no—
41C2×C13×C4⋊C4—21no—
42C2×C13×C4⋊C4—21no—
43C2×C42×C13C2311yescharacteristic
44C2×#6107—28no—
45C2×#6107—44no—
46C2×#6107—44no—
47C2×C4⋊Dic13—21no—
48C2×C4⋊Dic13—21no—
49C2×C4⋊Dic13—21no—
50C2×C4⋊Dic13—21no—
51C2×C4⋊Dic13—21no—
52C22×#1055D412yes—
53C22×#1055D412yes—
54#88123—21no—
55#88123—21no—
56#88123—21no—
57#88123D412yes—
58C13×#107—28no—
59C4×C8×C13—21no—
60C4×C8×C13—21no—
61#88075—44no—
62#88047—28no—
63C4×#1055—21no—
64C4×#1055—21no—
65C4×#1055—21no—
66C4×#1055—21no—
67#10309—131nomaximal, Sylow
68C2×Q8×C13—22no—
69C2×Q8×C13—22no—
70C2×Q8×C13—41no—
71C2×Q8×C13—41no—
72C2×Q8×C13—42no—
73C2×Q8×C13—42no—
74C2×Q8×C13—42no—
75C2×Q8×C13—42no—
76C22×C4×C13—41no—
77C22×C4×C13—41no—
78C22×C4×C13C2×D411yescharacteristic
79C22×C4×C13C2×D411yescharacteristic
80C22×C4×C13C2×D411yescharacteristic
81C22×Dic13—41no—
82C22×Dic13—41no—
83C2×Dic26—22no—
84C2×Dic26—42no—
85C2×Dic26—42no—
86C2×Dic26—41no—
87C2×C8×C13—22no—
88C2×C8×C13—22no—
89C2×C8×C13Q1614yescomplemented
90C13×C4⋊C4—22no—
91C13×C4⋊C4—22no—
92C13×C4⋊C4—22no—
93C13×C4⋊C4—22no—
94C13×C4⋊C4—41no—
95C13×C4⋊C4—41no—
96C13×C4⋊C4—41no—
97C13×C4⋊C4—41no—
98C42×C13C2×D411yescharacteristic
99C42×C13C2×D411yescharacteristic
100C42×C13C2×D411yescharacteristic
101C42×C13#4111yescharacteristic
102#6107—416no—
103C4⋊Dic13—22no—
104C4⋊Dic13—22no—
105C4⋊Dic13—41no—
106C4⋊Dic13—41no—
107C4⋊Dic13—42no—
108C4⋊Dic13—42no—
109C4⋊Dic13—42no—
110C2×#1055—22no—
111C2×#1055—22no—
112C2×#1055—22no—
113C2×#1055—22no—
114C2×#1055D814yes—
115C2×#1055Q1614yescomplemented
116C2×#500—131no—
117C2×#500D1311yescharacteristic
118C2×#494—131no—
119#1990—131no—
120#1990—131no—
121#1956—131no—
122#1273—131no—
123C23×C13#12711yescharacteristic
124Q8×C13—44no—
125Q8×C13—44no—
126Q8×C13—82no—
127Q8×C13—82no—
128C2×C4×C13—42no—
129C2×C4×C13—42no—
130C2×C4×C13—81no—
131C2×C4×C13—81no—
132C2×C4×C13—81no—
133C2×C4×C13—81no—
134C2×C4×C13#12011yescharacteristic
135C2×C4×C13#12011yescharacteristic
136C2×C4×C13#12011yescharacteristic
137C2×C4×C13#12111yescharacteristic
138C2×C4×C13#12111yescharacteristic
139C2×C4×C13#12111yescharacteristic
140C2×C4×C13C2×D812yes—
141C2×C4×C13C2×Q1612yes—
142C2×C4×C13C2×Q1612yes—
143C2×C4×C13AGL(1,ℤ/8)12yes—
144C2×C4×C13#13712yes—
145C2×C4×C13#13712yes—
146C2×Dic13—42no—
147C2×Dic13—81no—
148C2×Dic13—81no—
149C2×Dic13—81no—
150C2×Dic13—81no—
151C2×Dic13—81no—
152Dic26—44no—
153Dic26—82no—
154C8×C13—24no—
155#1055—24no—
156#1055—24no—
157C22×Q16—262no—
158C2×C4⋊Q8—131no—
159C2×C4⋊Q8C2×D1311yescharacteristic
160C2×C4⋊Q8C2×D1311yescharacteristic
161#500—22no—
162#500—22no—
163#500—262no—
164#500—262no—
165#494—262no—
166#494—262no—
167C2×#107—22no—
168C2×#107—262no—
169C2×#103—262no—
170C2×C4×C8—131no—
171C2×C4×C8—131no—
172C2×C4×C8C2×D1311yescharacteristic
173#384—131no—
174#340—262no—
175#340—262no—
176C22×C13#39211yescharacteristic
177C22×C13#49311yescharacteristic
178C22×C13#49411yescharacteristic
179C22×C13#49411yescharacteristic
180C22×C13#49611yescharacteristic
181C22×C13#49711yescharacteristic
182C22×C13#49711yescharacteristic
183C4×C13—82no—
184C4×C13—82no—
185C4×C13#44712yes—
186C4×C13#45112yes—
187C4×C13#45112yes—
188C4×C13#45912yes—
189C4×C13#46212yes—
190C4×C13#46212yes—
191Dic13—82no—
192Dic13—161no—
193C22×Q8—21no—
194C22×Q8—21no—
195C22×Q8—261no—
196C2×Q16—268no—
197C2×Q16—524no—
198C2×Q16—524no—
199C22×C8—132no—
200C22×C8—132no—
201C22×C8C22⋊D1312yes—
202C4⋊Q8—21no—
203C4⋊Q8—21no—
204C4⋊Q8—21no—
205C4⋊Q8—21no—
206C4⋊Q8—21no—
207C4⋊Q8—21no—
208C4⋊Q8—132no—
209C4⋊Q8—261no—
210C4⋊Q8—261no—
211C4⋊Q8—261no—
212C4⋊Q8C22⋊D1312yes—
213C4⋊Q8C22⋊D1312yes—
214C2×C4⋊C4—21no—
215C2×C4⋊C4—21no—
216C2×C4⋊C4—21no—
217C2×C4⋊C4—21no—
218C2×C4⋊C4—261no—
219C2×C4⋊C4—261no—
220C2×C4⋊C4—261no—
221C2×C4⋊C4—261no—
222C2×C4⋊C4—261no—
223C2×C42C22×D1311yescharacteristic
224#107—28no—
225#107—268no—
226#103—524no—
227C4×C8—21no—
228C4×C8—21no—
229C4×C8—261no—
230C4×C8—261no—
231C4×C8—261no—
232C4×C8—261no—
233C2×C13#171311yescharacteristic
234C2×C13#172211yescharacteristic
235C2×C13#172311yescharacteristic
236C2×C13#172311yescharacteristic
237C2×C13#201111yescharacteristic
238C2×C13#201611yescharacteristic
239C2×C13#201611yescharacteristic
240C2×Q8—22no—
241C2×Q8—22no—
242C2×Q8—41no—
243C2×Q8—41no—
244C2×Q8—42no—
245C2×Q8—42no—
246C2×Q8—42no—
247C2×Q8—42no—
248C2×Q8—262no—
249C2×Q8—521no—
250C2×Q8—522no—
251C2×Q8—522no—
252C22×C4—41no—
253C22×C4—41no—
254C22×C4—521no—
255C22×C4—521no—
256C22×C4D4×D1311yescharacteristic
257C22×C4D4×D1311yescharacteristic
258C22×C4C2×C22⋊D1311yescharacteristic
259Q16—5216no—
260C2×C8—22no—
261C2×C8—22no—
262C2×C8—134no—
263C2×C8—134no—
264C2×C8—262no—
265C2×C8—262no—
266C2×C8—262no—
267C2×C8—262no—
268C2×C8#610714yescomplemented
269C4⋊C4—22no—
270C4⋊C4—22no—
271C4⋊C4—22no—
272C4⋊C4—22no—
273C4⋊C4—41no—
274C4⋊C4—41no—
275C4⋊C4—41no—
276C4⋊C4—41no—
277C4⋊C4—262no—
278C4⋊C4—262no—
279C4⋊C4—521no—
280C4⋊C4—521no—
281C4⋊C4—522no—
282C4⋊C4—522no—
283C4⋊C4—522no—
284C42D4×D1311yescharacteristic
285C42#612911yescharacteristic
286C42C2×C22⋊D1311yescharacteristic
287C42C2×C22⋊D1311yescharacteristic
288C13#1030911yescharacteristic, complemented, Sylow
289C23#8819411yescharacteristic
290Q8—44no—
291Q8—44no—
292Q8—82no—
293Q8—82no—
294Q8—524no—
295Q8—1042no—
296C2×C4—42no—
297C2×C4—42no—
298C2×C4—81no—
299C2×C4—81no—
300C2×C4—81no—
301C2×C4—81no—
302C2×C4—522no—
303C2×C4—1041no—
304C2×C4—1041no—
305C2×C4—1041no—
306C2×C4—1041no—
307C2×C4—1041no—
308C2×C4D8×D1312yes—
309C2×C4#8816512yes—
310C2×C4Q16×D1312yes—
311C2×C4#8817212yes—
312C2×C4#8819111yescharacteristic
313C2×C4#8819111yescharacteristic
314C2×C4#8819211yescharacteristic
315C2×C4#8819311yescharacteristic
316C2×C4#8819311yescharacteristic
317C2×C4#8819612yes—
318C2×C4C2×#610712yes—
319C2×C4#8820711yescharacteristic
320C8—24no—
321C8—264no—
322C8—264no—
323C22#1171874711yescharacteristic
324C22#1171875311yescharacteristic
325C22#1171881211yescharacteristic
326C22#1171881511yescharacteristic
327C22#1171884211yescharacteristic
328C22#1171885111yescharacteristic
329C22#1171888411yescharacteristic
330C4—82no—
331C4—82no—
332C4—1042no—
333C4—2081no—
334C4#1171875112yes—
335C4#1171881112yes—
336C4#1171881712yes—
337C4#1171884312yes—
338C4#1171884712yes—
339C4#1171888912yes—
340C2#1311445311yescharacteristic
341C2#1311450611yescharacteristic
342C2#1311451211yescharacteristic
343C2#1311451411yescharacteristic
344C2#1311590511yescharacteristic
345C2#1311593411yescharacteristic
346C2#1311593611yescharacteristic
subgroupG/H
centerC23#88194
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC2×C13×#500C2
socle, prime radicalC23×C13#127
hypercenterC2×#500D13
hypocenterC13#10309
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#500

Complements

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

NH ≅ G/Ntype
89. C2×C8×C13Q16semidirect
115. C2×#1055Q16semidirect
268. C2×C8#6107semidirect
288. C13#10309semidirect

Maximal subgroups

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

subgroupindex
C2×#117187392
C2×#117187532
#131157982
#131157972
#131156392
#131126632
C2×C13×#5002
#1030913