Finite Group Databasebeta

← #15891034

Subgroups — #15891034

Order 3328.

1074 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13123425C212yesmaximal
2#13117460C211yesmaximal, characteristic
3#13116183C214yesmaximal, complemented
4#13116178C214yesmaximal, complemented
5C2×#11718122C211yesmaximal, characteristic
6#13114545C212yesmaximal
7C2×C13×#544C211yesmaximal, characteristic
8C13×#544—24no—
9C13×#544—22no—
10C13×#544C2214yes—
11C2×C13×C4⋊Q8—22no—
12C2×C13×#125—22no—
13C2×C13×C22⋊Q8—22no—
14C2×C13×#117C2212yes—
15C22×C13×C4⋊C4C2211yescharacteristic
16C2×#88180C2211yescharacteristic
17C2×#88180C2211yescharacteristic
18C22×#6099C2212yes—
19#11718871—22no—
20#11718659—24no—
21#11718656C2214yes—
22#11718656C2214yes—
23#11718638C2212yes—
24#11718637C2212yes—
25#11718634—22no—
26#11718625—22no—
27#11718625—22no—
28#11718124C2218yes—
29#11718122C2214yes—
30C22×Q8×C13—22no—
31C23×C4×C13D412yes—
32C23×C4×C13C2311yescharacteristic
33C13×C4⋊Q8—28no—
34C13×C4⋊Q8—28no—
35C13×#125—28no—
36C13×#125—28no—
37C13×C22⋊Q8—28no—
38C13×C22⋊Q8—28no—
39C13×#117—22no—
40C13×#117—22no—
41C13×#117D414yes—
42C13×#117C2314yes—
43C2×C13×C4⋊C4—22no—
44C2×C13×C4⋊C4—24no—
45C2×C13×C4⋊C4—22no—
46C2×C13×C4⋊C4—22no—
47C2×C13×C4⋊C4D412yes—
48C2×C13×C4⋊C4D412yes—
49C2×C13×C4⋊C4D412yes—
50C2×C13×C4⋊C4C2312yes—
51C2×C13×C22⋊C4—22no—
52C2×C42×C13—22no—
53C2×C22⋊Dic13—21no—
54C2×C22⋊Dic13—21no—
55#88180—22no—
56#88180—22no—
57#88180—22no—
58#88180Q814yescomplemented
59C2×C4⋊Dic13—21no—
60C2×C4⋊Dic13C2311yescharacteristic
61C2×C4⋊Dic13C2311yescharacteristic
62C2×#6101—24no—
63C2×C4×Dic13—21no—
64C2×C4×Dic13C2312yes—
65C2×#6099—22no—
66C2×#6099—24no—
67C2×#6099Q818yescomplemented
68C2×#6099C2314yes—
69C22×#1055—22no—
70#88071—24no—
71#88048—24no—
72#88048—24no—
73#88047—24no—
74#88047—24no—
75#23561—131nomaximal, Sylow
76C24×C13C2×D411yescharacteristic
77C2×Q8×C13—28no—
78C2×Q8×C13—84no—
79C22×C4×C13—22no—
80C22×C4×C13—22no—
81C22×C4×C13—22no—
82C22×C4×C13—22no—
83C22×C4×C13—82no—
84C22×C4×C13C2×D414yes—
85C22×C4×C13C2×D411yescharacteristic
86C22×C4×C13C2×D412yes—
87C22×C4×C13C2×D412yes—
88C22×C4×C13C2×Q814yes—
89C22×C4×C13C2×Q812yes—
90C22×C4×C13#4112yes—
91C22×C4×C13C2411yescharacteristic
92C22×Dic13—22no—
93C22×Dic13—21no—
94C22×Dic13—21no—
95C13×C4⋊C4—28no—
96C13×C4⋊C4—216no—
97C13×C4⋊C4—24no—
98C13×C4⋊C4—22no—
99C13×C4⋊C4—22no—
100C13×C4⋊C4—24no—
101C13×C4⋊C4C2×D414yes—
102C13×C4⋊C4C2×D414yes—
103C13×C22⋊C4—24no—
104C13×C22⋊C4—24no—
105C42×C13—24no—
106C42×C13—24no—
107C22⋊Dic13—24no—
108C22⋊Dic13—41no—
109C22⋊Dic13—41no—
110C4⋊Dic13—24no—
111C4⋊Dic13—22no—
112C4⋊Dic13—22no—
113#6101—84no—
114C4×Dic13—22no—
115C4×Dic13—42no—
116C4×Dic13C2×Q814yescomplemented
117#6099—28no—
118#6099—24no—
119#6099C2×Q818yescomplemented
120C2×#1055—28no—
121C2×#1055—24no—
122C2×#544D1311yescharacteristic
123#2911—132no—
124#2317—131no—
125#2061—134no—
126#2060—134no—
127C2×#343—131no—
128#1733—132no—
129C23×C13—41no—
130C23×C13—41no—
131C23×C13#12011yescharacteristic
132C23×C13#12011yescharacteristic
133C23×C13C22⋊Q812yes—
134C23×C13C4⋊Q812yes—
135C23×C13C22×D411yescharacteristic
136Q8×C13—88no—
137C2×C4×C13—24no—
138C2×C4×C13—24no—
139C2×C4×C13—24no—
140C2×C4×C13—44no—
141C2×C4×C13—44no—
142C2×C4×C13—44no—
143C2×C4×C13—44no—
144C2×C4×C13—82no—
145C2×C4×C13#12012yes—
146C2×C4×C13C22⋊Q814yes—
147C2×C4×C13C22⋊Q814yes—
148C2×C4×C13C22⋊Q812yes—
149C2×C4×C13C4⋊Q814yes—
150C2×C4×C13C4⋊Q814yes—
151C2×C4×C13C4⋊Q812yes—
152C2×C4×C13C22×D412yes—
153C2×C4×C13C22×Q812yes—
154C2×C4×C13C22×Q811yescharacteristic
155C2×C4×C13C2×#4111yescharacteristic
156C2×Dic13—24no—
157C2×Dic13—42no—
158C2×Dic13—42no—
159C2×Dic13—42no—
160C2×Dic13—42no—
161C2×Dic13—41no—
162C2×Dic13—41no—
163#1055—28no—
164C22×M16—132no—
165#544—24no—
166#544—22no—
167#544C2×D1314yes—
168C2×C4⋊Q8—22no—
169C2×#125—22no—
170C2×C22⋊Q8—22no—
171C2×#117—131no—
172C2×#117—131no—
173C2×#117C2×D1312yes—
174C22×C4⋊C4C2×D1311yescharacteristic
175#428—134no—
176#428—134no—
177#428—262no—
178#428—262no—
179#427—264no—
180#389—262no—
181#385—262no—
182#384—132no—
183#382—132no—
184#343—134no—
185#339—138no—
186C22×C13—21no—
187C22×C13—21no—
188C22×C13—21no—
189C22×C13—21no—
190C22×C13—21no—
191C22×C13—21no—
192C22×C13—42no—
193C22×C13—42no—
194C22×C13#39512yes—
195C22×C13#39512yes—
196C22×C13C2×#12011yescharacteristic
197C22×C13C2×C22⋊Q811yescharacteristic
198C22×C13C2×C4⋊Q811yescharacteristic
199C4×C13—44no—
200C4×C13—44no—
201C4×C13—44no—
202C4×C13#39514yes—
203C4×C13C2×C22⋊Q812yes—
204C4×C13C2×C4⋊Q812yes—
205Dic13—44no—
206Dic13—81no—
207Dic13—81no—
208C22×Q8—22no—
209C23×C4C22⋊D1312yes—
210C23×C4C22×D1311yescharacteristic
211C2×M16—138no—
212C2×M16—134no—
213C2×M16—264no—
214C2×M16—262no—
215C22×C8—262no—
216C4⋊Q8—28no—
217C4⋊Q8—28no—
218#125—28no—
219#125—28no—
220C22⋊Q8—28no—
221C22⋊Q8—28no—
222#117—22no—
223#117—22no—
224#117—134no—
225#117—262no—
226#117—262no—
227#117—262no—
228#117C22⋊D1314yes—
229#117C22×D1314yes—
230C2×C4⋊C4—22no—
231C2×C4⋊C4—24no—
232C2×C4⋊C4—22no—
233C2×C4⋊C4—22no—
234C2×C4⋊C4—131no—
235C2×C4⋊C4—131no—
236C2×C4⋊C4—261no—
237C2×C4⋊C4—264no—
238C2×C4⋊C4C22⋊D1312yes—
239C2×C4⋊C4C22⋊D1312yes—
240C2×C4⋊C4C22⋊D1312yes—
241C2×C4⋊C4C22×D1312yes—
242C2×C22⋊C4—22no—
243C2×C22⋊C4—261no—
244C2×C22⋊C4—261no—
245C2×C42—22no—
246C2×C42—132no—
247C2×C42—261no—
248#107—264no—
249#107—264no—
250#106—264no—
251#106—264no—
252#95—264no—
253C2×C13—21no—
254C2×C13—21no—
255C2×C13—22no—
256C2×C13—22no—
257C2×C13C2×#39511yescharacteristic
258C2×C13#301911yescharacteristic
259C2×C13#302011yescharacteristic
260C24C2×C22⋊D1311yescharacteristic
261C2×Q8—28no—
262C2×Q8—84no—
263C22×C4—22no—
264C22×C4—22no—
265C22×C4—22no—
266C22×C4—22no—
267C22×C4—82no—
268C22×C4—262no—
269C22×C4—261no—
270C22×C4—261no—
271C22×C4Q8×D1312yes—
272C22×C4Q8×D1314yes—
273C22×C4#613112yes—
274C22×C4C2×C22⋊D1314yes—
275C22×C4C2×C22⋊D1311yescharacteristic
276C22×C4C2×C22⋊D1312yes—
277C22×C4C2×C22⋊D1312yes—
278C22×C4C23×D1311yescharacteristic
279M16—138no—
280M16—268no—
281M16—264no—
282C2×C8—268no—
283C2×C8—264no—
284C4⋊C4—28no—
285C4⋊C4—216no—
286C4⋊C4—24no—
287C4⋊C4—22no—
288C4⋊C4—22no—
289C4⋊C4—24no—
290C4⋊C4—264no—
291C4⋊C4—262no—
292C4⋊C4—262no—
293C4⋊C4—1044no—
294C4⋊C4C2×C22⋊D1314yes—
295C4⋊C4C2×C22⋊D1314yes—
296C22⋊C4—24no—
297C22⋊C4—24no—
298C22⋊C4—264no—
299C22⋊C4—521no—
300C22⋊C4—521no—
301C42—24no—
302C42—24no—
303C42—134no—
304C42—262no—
305C42—522no—
306C13#2356111yescharacteristic, complemented, Sylow
307C23—41no—
308C23—41no—
309C23#8819812yes—
310C23#8820012yes—
311C23#8820711yescharacteristic
312C23#8820711yescharacteristic
313C23C22×C22⋊D1311yescharacteristic
314Q8—88no—
315C2×C4—24no—
316C2×C4—24no—
317C2×C4—24no—
318C2×C4—44no—
319C2×C4—44no—
320C2×C4—44no—
321C2×C4—44no—
322C2×C4—82no—
323C2×C4—264no—
324C2×C4—522no—
325C2×C4—522no—
326C2×C4—522no—
327C2×C4—522no—
328C2×C4—521no—
329C2×C4—521no—
330C2×C4#8819814yes—
331C2×C4#8819814yes—
332C2×C4#8819812yes—
333C2×C4#8820014yes—
334C2×C4#8820014yes—
335C2×C4#8820012yes—
336C2×C4#8820712yes—
337C2×C4C2×Q8×D1311yescharacteristic
338C2×C4C2×Q8×D1312yes—
339C2×C4C2×#613111yescharacteristic
340C2×C4C22×C22⋊D1312yes—
341C8—268no—
342C22—21no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—21no—
347C22—21no—
348C22—42no—
349C22—42no—
350C22#1171889012yes—
351C22#1171889012yes—
352C22C2×#8819811yescharacteristic
353C22C2×#8820011yescharacteristic
354C22C2×#8820711yescharacteristic
355C4—44no—
356C4—44no—
357C4—44no—
358C4—524no—
359C4—1041no—
360C4—1041no—
361C4#1171889014yes—
362C4C2×#8819812yes—
363C4C2×#8820012yes—
364C2—21no—
365C2—21no—
366C2—22no—
367C2—22no—
368C2C2×#1171889011yescharacteristic
369C2#1312419311yescharacteristic
370C2#1312420011yescharacteristic
subgroupG/H
centerC22C2×#88207
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC2×C13×#544C2
socleC22×C13C2×#120
prime radicalC24×C13C2×D4
hypercenterC2×#544D13
hypocenterC13#23561
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#544

Complements

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

NH ≅ G/Ntype
3. #13116183C2semidirect
4. #13116178C2semidirect
58. #88180Q8semidirect
67. C2×#6099Q8semidirect
116. C4×Dic13C2×Q8semidirect
119. #6099C2×Q8semidirect
306. C13#23561semidirect

Maximal subgroups

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

subgroupindex
#131234252
#131174602
#131161832
#131161782
C2×#117181222
#131145452
C2×C13×#5442
#2356113