Finite Group Databasebeta

← #15765766

Subgroups — #15765766

Order 3328.

602 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718341C211yesmaximal, characteristic
2C2×#11718753C211yesmaximal, characteristic
3C2×#11718754C211yesmaximal, characteristic
4#13115796C211yesmaximal, characteristic
5#13115796C211yesmaximal, characteristic
6#13112663C211yesmaximal, characteristic
7C13×#1990C211yesmaximal, characteristic
8C2×C13×C4⋊Q8C2211yescharacteristic
9C22×#6107—22no—
10C2×#88123C2211yescharacteristic
11C2×#88123C2211yescharacteristic
12C2×C4×C8×C13C2211yescharacteristic
13C13×#384C2211yescharacteristic
14C2×#88057—22no—
15#11718754—22no—
16#11718754—22no—
17#11718753—22no—
18#11718753—22no—
19C2×#88050—22no—
20C2×C4×#1055C2211yescharacteristic
21C2×C4×#1055C2211yescharacteristic
22#11718341—22no—
23#11718341—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×#6107—28no—
42C2×#6107—44no—
43C2×#6107—44no—
44C2×C4⋊Dic13—21no—
45C2×C4⋊Dic13—21no—
46C2×C4⋊Dic13—21no—
47C2×C4⋊Dic13—21no—
48C22×#1055D412yes—
49C22×#1055D412yes—
50#88123—21no—
51#88123—21no—
52#88123—21no—
53#88123—21no—
54#88123—21no—
55#88123—21no—
56#88123D412yes—
57#88123D412yes—
58C4×C8×C13—21no—
59C4×C8×C13—21no—
60#88057—28no—
61#88050—28no—
62C4×#1055—21no—
63C4×#1055—21no—
64C4×#1055—21no—
65C4×#1055—21no—
66#10318—131nomaximal, Sylow
67C2×Q8×C13—22no—
68C2×Q8×C13—41no—
69C2×Q8×C13—42no—
70C2×Q8×C13—42no—
71C22×C4×C13—41no—
72C22×C4×C13—41no—
73C22×C4×C13C2×D411yescharacteristic
74C22×C4×C13C2×D411yescharacteristic
75C22×C4×C13C2×D411yescharacteristic
76C22×Dic13—41no—
77C22×Dic13—41no—
78C2×Dic26—22no—
79C2×Dic26—22no—
80C2×Dic26—42no—
81C2×Dic26—42no—
82C2×Dic26—42no—
83C2×Dic26—42no—
84C2×Dic26—41no—
85C2×Dic26—41no—
86C2×C8×C13—22no—
87C2×C8×C13—22no—
88C2×C8×C13Q1614yescomplemented
89C13×C4⋊C4—22no—
90C13×C4⋊C4—22no—
91C13×C4⋊C4—41no—
92C13×C4⋊C4—41no—
93C13×C4⋊C4—42no—
94C13×C4⋊C4—42no—
95C13×C4⋊C4—42no—
96C42×C13C2×D411yescharacteristic
97C42×C13C2×D411yescharacteristic
98C42×C13C2×D411yescharacteristic
99C42×C13#4111yescharacteristic
100#6107—416no—
101C4⋊Dic13—22no—
102C4⋊Dic13—22no—
103C4⋊Dic13—22no—
104C4⋊Dic13—22no—
105C4⋊Dic13—41no—
106C4⋊Dic13—41no—
107C4⋊Dic13—41no—
108C4⋊Dic13—41no—
109C2×#1055—22no—
110C2×#1055—22no—
111C2×#1055—22no—
112C2×#1055—22no—
113C2×#1055—22no—
114C2×#1055SD1614yes—
115C2×#498—131no—
116C2×#494—131no—
117C2×#487—131no—
118#1990—131no—
119#1990—131no—
120#1990D1311yescharacteristic
121#1273—131no—
122C23×C13#12711yescharacteristic
123Q8×C13—44no—
124Q8×C13—82no—
125C2×C4×C13—42no—
126C2×C4×C13—81no—
127C2×C4×C13—81no—
128C2×C4×C13—81no—
129C2×C4×C13—81no—
130C2×C4×C13—81no—
131C2×C4×C13#12011yescharacteristic
132C2×C4×C13#12011yescharacteristic
133C2×C4×C13#12011yescharacteristic
134C2×C4×C13#12111yescharacteristic
135C2×C4×C13#12111yescharacteristic
136C2×C4×C13#12111yescharacteristic
137C2×C4×C13C2×SD1612yes—
138C2×C4×C13C2×Q1612yes—
139C2×C4×C13#13512yes—
140C2×C4×C13AGL(1,ℤ/8)12yes—
141C2×C4×C13#13712yes—
142C2×C4×C13#13712yes—
143C2×Dic13—42no—
144C2×Dic13—42no—
145C2×Dic13—81no—
146C2×Dic13—81no—
147C2×Dic13—81no—
148C2×Dic13—81no—
149Dic26—44no—
150Dic26—44no—
151Dic26—82no—
152Dic26—82no—
153C8×C13—24no—
154#1055—24no—
155#1055—42no—
156C22×Q16—262no—
157C2×C4⋊Q8—131no—
158C2×C4⋊Q8—131no—
159C2×C4⋊Q8C2×D1311yescharacteristic
160#498—262no—
161#498—262no—
162#494—262no—
163#494—262no—
164#487—262no—
165#487—262no—
166C2×#106—262no—
167C2×#103—262no—
168C2×C4×C8—131no—
169C2×C4×C8—131no—
170C2×C4×C8C2×D1311yescharacteristic
171#384C2×D1311yescharacteristic
172#340—22no—
173#340—262no—
174#340—262no—
175C22×C13#39211yescharacteristic
176C22×C13#49211yescharacteristic
177C22×C13#49411yescharacteristic
178C22×C13#49511yescharacteristic
179C22×C13#49611yescharacteristic
180C22×C13#49711yescharacteristic
181C22×C13#49711yescharacteristic
182C4×C13—82no—
183C4×C13—161no—
184C4×C13#45012yes—
185C4×C13#45112yes—
186C4×C13#45212yes—
187C4×C13#46012yes—
188C4×C13#46212yes—
189C4×C13#46412yes—
190Dic13—82no—
191Dic13—82no—
192C22×Q8—21no—
193C22×Q8—261no—
194C22×Q8—261no—
195C2×Q16—268no—
196C2×Q16—524no—
197C2×Q16—524no—
198C22×C8—132no—
199C22×C8—132no—
200C22×C8C22⋊D1312yes—
201C4⋊Q8—21no—
202C4⋊Q8—21no—
203C4⋊Q8—21no—
204C4⋊Q8—132no—
205C4⋊Q8—132no—
206C4⋊Q8—261no—
207C4⋊Q8—261no—
208C4⋊Q8—261no—
209C4⋊Q8—261no—
210C4⋊Q8—261no—
211C4⋊Q8—261no—
212C4⋊Q8D5212yes—
213C2×C4⋊C4—21no—
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×C42C22×D1311yescharacteristic
223#106—268no—
224#103—268no—
225C4×C8—21no—
226C4×C8—21no—
227C4×C8—261no—
228C4×C8—261no—
229C4×C8—261no—
230C4×C8—261no—
231C2×C13#170711yescharacteristic
232C2×C13#171611yescharacteristic
233C2×C13#172011yescharacteristic
234C2×C13#172311yescharacteristic
235C2×C13#201411yescharacteristic
236C2×C13#201511yescharacteristic
237C2×C13#201611yescharacteristic
238C2×Q8—22no—
239C2×Q8—41no—
240C2×Q8—42no—
241C2×Q8—42no—
242C2×Q8—262no—
243C2×Q8—262no—
244C2×Q8—521no—
245C2×Q8—521no—
246C2×Q8—522no—
247C2×Q8—522no—
248C2×Q8—522no—
249C2×Q8—522no—
250C22×C4—41no—
251C22×C4—41no—
252C22×C4—521no—
253C22×C4—521no—
254C22×C4D4×D1311yescharacteristic
255C22×C4D4×D1311yescharacteristic
256C22×C4C2×C22⋊D1311yescharacteristic
257Q16—5216no—
258C2×C8—22no—
259C2×C8—22no—
260C2×C8—134no—
261C2×C8—262no—
262C2×C8—262no—
263C2×C8—262no—
264C2×C8—262no—
265C2×C8—262no—
266C2×C8#610714yescomplemented
267C4⋊C4—22no—
268C4⋊C4—22no—
269C4⋊C4—41no—
270C4⋊C4—41no—
271C4⋊C4—42no—
272C4⋊C4—42no—
273C4⋊C4—42no—
274C4⋊C4—262no—
275C4⋊C4—262no—
276C4⋊C4—262no—
277C4⋊C4—262no—
278C4⋊C4—521no—
279C4⋊C4—521no—
280C4⋊C4—521no—
281C4⋊C4—521no—
282C42C2×D5211yescharacteristic
283C42#612711yescharacteristic
284C42D4×D1311yescharacteristic
285C42D4×D1311yescharacteristic
286C13#1031811yescharacteristic, complemented, Sylow
287C23#8819411yescharacteristic
288Q8—44no—
289Q8—82no—
290Q8—524no—
291Q8—524no—
292Q8—1042no—
293Q8—1042no—
294C2×C4—42no—
295C2×C4—81no—
296C2×C4—81no—
297C2×C4—81no—
298C2×C4—81no—
299C2×C4—81no—
300C2×C4—522no—
301C2×C4—522no—
302C2×C4—1041no—
303C2×C4—1041no—
304C2×C4—1041no—
305C2×C4—1041no—
306C2×C4#8813611yescharacteristic
307C2×C4#8813611yescharacteristic
308C2×C4#8813811yescharacteristic
309C2×C4#8813811yescharacteristic
310C2×C4#8816512yes—
311C2×C4SD16×D1312yes—
312C2×C4#8817012yes—
313C2×C4#8817212yes—
314C2×C4#8818411yescharacteristic
315C2×C4#8819111yescharacteristic
316C2×C4C2×#610712yes—
317C2×C4#8820512yes—
318C8—24no—
319C8—264no—
320C8—522no—
321C22#1171862111yescharacteristic
322C22#1171872111yescharacteristic
323C22#1171875311yescharacteristic
324C22#1171881511yescharacteristic
325C22#1171882911yescharacteristic
326C22#1171883611yescharacteristic
327C22#1171885111yescharacteristic
328C4—82no—
329C4—161no—
330C4—1042no—
331C4—1042no—
332C4#1171842312yes—
333C4#1171843712yes—
334C4#1171845912yes—
335C4#1171847112yes—
336C4#1171869212yes—
337C4#1171871112yes—
338C2#1311443111yescharacteristic
339C2#1311447111yescharacteristic
340C2#1311449811yescharacteristic
341C2#1311451411yescharacteristic
342C2#1311592511yescharacteristic
343C2#1311593111yescharacteristic
344C2#1311593511yescharacteristic
subgroupG/H
centerC23#88194
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#1990C2
socle, prime radicalC23×C13#127
hypercenter#1990D13
hypocenterC13#10318
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
88. C2×C8×C13Q16semidirect
266. C2×C8#6107semidirect
286. C13#10318semidirect

Maximal subgroups

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

subgroupindex
C2×#117183412
C2×#117187532
C2×#117187542
#131157962
#131126632
C13×#19902
#1031813