Finite Group Databasebeta

← #15891038

Subgroups — #15891038

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
1C2×#11719205C211yesmaximal, characteristic
2#13123425C212yesmaximal
3#13116186C214yesmaximal, complemented
4#13116181C214yesmaximal, complemented
5C2×#11718122C211yesmaximal, characteristic
6#13114546C212yesmaximal
7C13×#2317C211yesmaximal, characteristic
8C2×C13×#117C2211yescharacteristic
9C2×C13×#117C2211yescharacteristic
10C22×C13×C4⋊C4C2211yescharacteristic
11C2×#88180C2212yes—
12C2×#88178—22no—
13C22×#6099C2212yes—
14#11719205—22no—
15#11719205—24no—
16#11719205C2214yes—
17C2×#88144—22no—
18C2×#88142—22no—
19C13×#389—22no—
20C13×#385—22no—
21C13×#384C2212yes—
22C13×#382C2212yes—
23#11718659—24no—
24#11718656—22no—
25#11718656—22no—
26#11718625C2214yes—
27#11718625C2214yes—
28#11718122C2214yes—
29#11718115C2218yes—
30C23×C4×C13D412yes—
31C23×C4×C13C2311yescharacteristic
32C22×Dic26—22no—
33C13×#117—22no—
34C13×#117—22no—
35C13×#117—22no—
36C13×#117Q814yescomplemented
37C2×C13×C4⋊C4—21no—
38C2×C13×C4⋊C4—22no—
39C2×C13×C4⋊C4—22no—
40C2×C13×C4⋊C4—24no—
41C2×C13×C4⋊C4D412yes—
42C2×C13×C4⋊C4C2311yescharacteristic
43C2×C13×C4⋊C4C2311yescharacteristic
44C2×C13×C4⋊C4C2312yes—
45C2×C13×C22⋊C4—21no—
46C2×C13×C22⋊C4—21no—
47C2×C42×C13—21no—
48C2×C42×C13C2312yes—
49C2×C22⋊Dic13—22no—
50#88180—22no—
51#88180—22no—
52#88180D414yes—
53#88180C2314yes—
54C2×C4⋊Dic13—22no—
55C2×C4⋊Dic13D412yes—
56C2×C4⋊Dic13D412yes—
57#88178—28no—
58#88178—28no—
59C2×#6101—24no—
60C2×C4×Dic13—22no—
61C2×#6099—22no—
62C2×#6099—24no—
63C2×#6099Q818yescomplemented
64C2×#6099C2314yes—
65C22×#1055—22no—
66#88144—28no—
67#88144—28no—
68#88142—28no—
69#88142—28no—
70C13×#95—24no—
71#88048—24no—
72#88048—24no—
73#88047—24no—
74#88047—24no—
75#23561—131nomaximal, Sylow
76C24×C13C2×D411yescharacteristic
77C22×C4×C13—22no—
78C22×C4×C13—22no—
79C22×C4×C13—22no—
80C22×C4×C13—21no—
81C22×C4×C13—21no—
82C22×C4×C13—82no—
83C22×C4×C13C2×D412yes—
84C22×C4×C13C2×D412yes—
85C22×C4×C13C2×D414yes—
86C22×C4×C13C2×D411yescharacteristic
87C22×C4×C13C2×Q812yes—
88C22×C4×C13C2×Q814yes—
89C22×C4×C13#4112yes—
90C22×C4×C13C2411yescharacteristic
91C22×Dic13—22no—
92C22×Dic13—22no—
93C2×Dic26—28no—
94C2×Dic26—84no—
95C13×C4⋊C4—24no—
96C13×C4⋊C4—24no—
97C13×C4⋊C4—24no—
98C13×C4⋊C4—22no—
99C13×C4⋊C4—22no—
100C13×C4⋊C4—84no—
101C13×C22⋊C4—24no—
102C13×C22⋊C4—41no—
103C13×C22⋊C4—41no—
104C42×C13—22no—
105C42×C13—42no—
106C42×C13C2×Q814yescomplemented
107C22⋊Dic13—24no—
108C22⋊Dic13—24no—
109C4⋊Dic13—28no—
110C4⋊Dic13—22no—
111C4⋊Dic13—22no—
112C4⋊Dic13C2×D414yes—
113C4⋊Dic13C2×D414yes—
114#6101—216no—
115C4×Dic13—24no—
116C4×Dic13—24no—
117#6099—28no—
118#6099—24no—
119#6099C2×Q818yescomplemented
120C2×#1055—28no—
121C2×#1055—24no—
122C2×#544—131no—
123#2911—132no—
124#2317D1311yescharacteristic
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
136C2×C4×C13—24no—
137C2×C4×C13—24no—
138C2×C4×C13—42no—
139C2×C4×C13—44no—
140C2×C4×C13—42no—
141C2×C4×C13—44no—
142C2×C4×C13—42no—
143C2×C4×C13—42no—
144C2×C4×C13—41no—
145C2×C4×C13—41no—
146C2×C4×C13—82no—
147C2×C4×C13#12012yes—
148C2×C4×C13C22⋊Q814yes—
149C2×C4×C13C22⋊Q814yes—
150C2×C4×C13C22⋊Q812yes—
151C2×C4×C13C4⋊Q814yes—
152C2×C4×C13C4⋊Q814yes—
153C2×C4×C13C4⋊Q812yes—
154C2×C4×C13C22×D412yes—
155C2×C4×C13C22×Q812yes—
156C2×C4×C13C22×Q811yescharacteristic
157C2×C4×C13C2×#4111yescharacteristic
158C2×Dic13—24no—
159C2×Dic13—24no—
160C2×Dic13—44no—
161C2×Dic13—44no—
162Dic26—88no—
163#1055—28no—
164C22×M16—132no—
165#544—134no—
166#544—264no—
167#544—262no—
168C2×C4⋊Q8—262no—
169C2×#125—262no—
170C2×C22⋊Q8—262no—
171C2×#117—132no—
172C2×#117C2×D1311yescharacteristic
173C2×#117C2×D1311yescharacteristic
174C22×C4⋊C4C2×D1311yescharacteristic
175#428—134no—
176#428—134no—
177#428—262no—
178#428—262no—
179#427—264no—
180#389—22no—
181#385—22no—
182#384C2×D1312yes—
183#382C2×D1312yes—
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—81no—
202C4×C13—81no—
203C4×C13#39514yes—
204C4×C13C2×C22⋊Q812yes—
205C4×C13C2×C4⋊Q812yes—
206Dic13—44no—
207Dic13—44no—
208C22×Q8—262no—
209C23×C4C22⋊D1312yes—
210C23×C4C22×D1311yescharacteristic
211C2×M16—138no—
212C2×M16—134no—
213C2×M16—264no—
214C2×M16—262no—
215C22×C8—262no—
216C4⋊Q8—268no—
217C4⋊Q8—268no—
218#125—268no—
219#125—268no—
220C22⋊Q8—268no—
221C22⋊Q8—268no—
222#117—22no—
223#117—22no—
224#117—22no—
225#117—134no—
226#117—134no—
227#117—262no—
228#117—262no—
229#117Dic2614yescomplemented
230C2×C4⋊C4—22no—
231C2×C4⋊C4—22no—
232C2×C4⋊C4—21no—
233C2×C4⋊C4—24no—
234C2×C4⋊C4—132no—
235C2×C4⋊C4—132no—
236C2×C4⋊C4—262no—
237C2×C4⋊C4—264no—
238C2×C4⋊C4C22⋊D1312yes—
239C2×C4⋊C4C22×D1311yescharacteristic
240C2×C4⋊C4C22×D1311yescharacteristic
241C2×C4⋊C4C22×D1312yes—
242C2×C22⋊C4—21no—
243C2×C22⋊C4—21no—
244C2×C22⋊C4—262no—
245C2×C42—21no—
246C2×C42—262no—
247C2×C42C22×D1312yes—
248#107—264no—
249#107—264no—
250#106—264no—
251#106—264no—
252#95—24no—
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—268no—
262C2×Q8—1044no—
263C22×C4—22no—
264C22×C4—22no—
265C22×C4—22no—
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—82no—
269C22×C4—262no—
270C22×C4—262no—
271C22×C4C2×Dic2612yes—
272C22×C4#612712yes—
273C22×C4D4×D1312yes—
274C22×C4D4×D1312yes—
275C22×C4Q8×D1314yes—
276C22×C4C2×C22⋊D1314yes—
277C22×C4C2×C22⋊D1311yescharacteristic
278C22×C4C23×D1311yescharacteristic
279M16—138no—
280M16—268no—
281M16—264no—
282C2×C8—268no—
283C2×C8—264no—
284C4⋊C4—24no—
285C4⋊C4—24no—
286C4⋊C4—24no—
287C4⋊C4—22no—
288C4⋊C4—22no—
289C4⋊C4—84no—
290C4⋊C4—134no—
291C4⋊C4—134no—
292C4⋊C4—268no—
293C4⋊C4—2616no—
294C4⋊C4—262no—
295C4⋊C4—262no—
296C22⋊C4—24no—
297C22⋊C4—41no—
298C22⋊C4—41no—
299C22⋊C4—264no—
300C22⋊C4—264no—
301C42—22no—
302C42—42no—
303C42—264no—
304C42—264no—
305C42C2×Dic2614yescomplemented
306C13#2356111yescharacteristic, complemented, Sylow
307C23—41no—
308C23—41no—
309C23#8817812yes—
310C23#8819111yescharacteristic
311C23#8819111yescharacteristic
312C23#8819812yes—
313C23C22×C22⋊D1311yescharacteristic
314Q8—1048no—
315C2×C4—24no—
316C2×C4—24no—
317C2×C4—42no—
318C2×C4—44no—
319C2×C4—42no—
320C2×C4—44no—
321C2×C4—42no—
322C2×C4—42no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—82no—
326C2×C4—264no—
327C2×C4—264no—
328C2×C4—524no—
329C2×C4—524no—
330C2×C4#8814214yes—
331C2×C4#8814214yes—
332C2×C4#8815014yes—
333C2×C4#8815014yes—
334C2×C4#8817812yes—
335C2×C4#8819112yes—
336C2×C4#8819812yes—
337C2×C4C22×Dic2611yescharacteristic
338C2×C4C2×#612711yescharacteristic
339C2×C4C2×D4×D1312yes—
340C2×C4C2×Q8×D1312yes—
341C8—268no—
342C22—21no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—21no—
347C22—21no—
348C22—42no—
349C22—42no—
350C22#1171864012yes—
351C22#1171864012yes—
352C22C2×#8817811yescharacteristic
353C22C2×#8819111yescharacteristic
354C22C2×#8819811yescharacteristic
355C4—44no—
356C4—44no—
357C4—81no—
358C4—81no—
359C4—524no—
360C4—524no—
361C4#1171864014yes—
362C4C2×#8814212yes—
363C4C2×#8815012yes—
364C2—21no—
365C2—21no—
366C2—22no—
367C2—22no—
368C2C2×#1171864011yescharacteristic
369C2#1312419211yescharacteristic
370C2#1312419911yescharacteristic
subgroupG/H
centerC22C2×#88191
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#2317C2
socleC22×C13C2×#120
prime radicalC24×C13C2×D4
hypercenter#2317D13
hypocenterC13#23561
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2317

Complements

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

NH ≅ G/Ntype
3. #13116186C2semidirect
4. #13116181C2semidirect
36. C13×#117Q8semidirect
63. C2×#6099Q8semidirect
106. C42×C13C2×Q8semidirect
119. #6099C2×Q8semidirect
229. #117Dic26semidirect
305. C42C2×Dic26semidirect
306. C13#23561semidirect

Maximal subgroups

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

subgroupindex
C2×#117192052
#131234252
#131161862
#131161812
C2×#117181222
#131145462
C13×#23172
#2356113