Finite Group Databasebeta

← #15919559

Subgroups — #15919559

Order 3328.

1104 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719175C211yesmaximal, characteristic, complemented
2C2×#11718717C212yesmaximal, complemented
3#13115977C212yesmaximal, complemented
4#13115972C212yesmaximal, complemented
5#13115800C212yesmaximal, complemented
6#13115159C212yesmaximal
7#13115149C212yesmaximal, complemented
8C4×C22⋊#1055C211yesmaximal, characteristic, complemented
9C13×#2850C211yesmaximal, characteristic
10C2×C13×#124C2211yescharacteristic
11C2×C13×C22⋊Q8C2211yescharacteristic
12C2×C13×#121C2211yescharacteristic
13C22×C42×C13C2211yescharacteristic
14C2×#88180C2212yes—
15C2×#88178—22no—
16#11719175—28no—
17C2×#88124C2212yes—
18C2×#88123C2212yes—
19C2×C4×Dic26—22no—
20C13×#391C2211yescharacteristic
21C13×#390C2211yescharacteristic
22C13×#388—22no—
23C13×#386—22no—
24C13×#382C2211yescharacteristic
25C2×#88075C2214yes—
26C2×#88072C2214yes—
27C2×C22⋊#1055C2212yes—
28#11718717—28no—
29C2×C4×#1055C2212yes—
30#11718121C2214yes—
31#11718121C2214yes—
32#11718116C2212yes—
33C22×Q8×C13C2311yescharacteristic
34C22×D4×C13—21no—
35C22×D4×C13C2311yescharacteristic
36C23×C4×C13D412yes—
37C23×C4×C13C2311yescharacteristic
38C22×Dic26—22no—
39C13×#124—24no—
40C13×C22⋊Q8—24no—
41C13×#121—24no—
42C2×C13×C4⋊C4—21no—
43C2×C13×C4⋊C4C2311yescharacteristic
44C2×C13×C4⋊C4C2311yescharacteristic
45C2×C13×C22⋊C4—21no—
46C2×C13×C22⋊C4—22no—
47C2×C13×C22⋊C4—22no—
48C2×C13×C22⋊C4—21no—
49C2×C42×C13—24no—
50C2×C42×C13D412yes—
51C2×C42×C13C2311yescharacteristic
52C2×C42×C13C2311yescharacteristic
53C2×C22⋊Dic13—22no—
54#88180—28no—
55C2×C4⋊Dic13—22no—
56C2×C4⋊Dic13C2314yes—
57#88178—216no—
58C2×#6101—24no—
59C2×C4×Dic13—22no—
60C22×#1055C2314yes—
61#88124—24no—
62#88124D418yescomplemented
63#88123—28no—
64C4×Dic26—216no—
65C13×#95—22no—
66C13×#95—22no—
67#88075—28no—
68#88072—28no—
69C22⋊#1055—24no—
70C4×#1055—24no—
71#25906—131nomaximal, Sylow
72C24×C13—21no—
73C24×C13C2×D411yescharacteristic
74C2×Q8×C13—22no—
75C2×Q8×C13—22no—
76C2×Q8×C13—22no—
77C2×D4×C13—22no—
78C2×D4×C13—22no—
79C2×D4×C13—22no—
80C2×D4×C13—44no—
81C2×D4×C13—42no—
82C22×C4×C13—22no—
83C22×C4×C13—22no—
84C22×C4×C13—24no—
85C22×C4×C13—24no—
86C22×C4×C13—21no—
87C22×C4×C13—21no—
88C22×C4×C13—21no—
89C22×C4×C13—42no—
90C22×C4×C13C2×D412yes—
91C22×C4×C13C2×D411yescharacteristic
92C22×C4×C13C2×D412yes—
93C22×C4×C13#4114yes—
94C22×C4×C13C2411yescharacteristic
95C22×Dic13—24no—
96C2×Dic26—28no—
97C2×Dic26—44no—
98C2×Dic26—44no—
99C13×C4⋊C4—22no—
100C13×C4⋊C4—22no—
101C13×C4⋊C4—42no—
102C13×C22⋊C4—42no—
103C13×C22⋊C4—44no—
104C13×C22⋊C4—42no—
105C13×C22⋊C4—44no—
106C42×C13—24no—
107C42×C13—22no—
108C42×C13C2×D414yes—
109C22⋊Dic13—28no—
110C4⋊Dic13—28no—
111C4⋊Dic13—24no—
112C4⋊Dic13C2×D418yes—
113#6101—216no—
114C4×Dic13—28no—
115C2×#1055—24no—
116C2×#1055—24no—
117C2×#1055—24no—
118C2×#533—131no—
119C2×#488—132no—
120#2850D1311yescharacteristic
121#2024—132no—
122#2023—132no—
123#1991—132no—
124#1875—132no—
125#1873—132no—
126C4×C22⋊C8—131no—
127C23×C13—21no—
128C23×C13—21no—
129C23×C13—22no—
130C23×C13—22no—
131C23×C13—41no—
132C23×C13—41no—
133C23×C13—41no—
134C23×C13—42no—
135C23×C13—42no—
136C23×C13#12412yes—
137C23×C13C22×D411yescharacteristic
138Q8×C13—44no—
139D4×C13—44no—
140D4×C13—84no—
141C2×C4×C13—21no—
142C2×C4×C13—22no—
143C2×C4×C13—21no—
144C2×C4×C13—22no—
145C2×C4×C13—22no—
146C2×C4×C13—22no—
147C2×C4×C13—28no—
148C2×C4×C13—48no—
149C2×C4×C13—41no—
150C2×C4×C13—41no—
151C2×C4×C13—41no—
152C2×C4×C13—41no—
153C2×C4×C13—41no—
154C2×C4×C13—42no—
155C2×C4×C13—42no—
156C2×C4×C13#12014yes—
157C2×C4×C13#12412yes—
158C2×C4×C13#13514yes—
159C2×C4×C13C22×D412yes—
160C2×C4×C13C2×#4112yes—
161C2×C4×C132−1+412yes—
162C2×Dic13—28no—
163C2×Dic13—44no—
164C2×Dic13—44no—
165Dic26—416no—
166#1055—44no—
167#533—268no—
168C2×C4⋊Q8—132no—
169C2×#125—132no—
170C2×#124C2×D1311yescharacteristic
171C2×C22⋊Q8—262no—
172C2×C22⋊Q8C2×D1311yescharacteristic
173C2×#121C2×D1311yescharacteristic
174C2×C4×Q8—262no—
175C2×#117—132no—
176C22×C42C2×D1311yescharacteristic
177#488—268no—
178C2×#103—134no—
179C2×#102—134no—
180C2×C22⋊C8—132no—
181C2×C4×C8—132no—
182#391C2×D1311yescharacteristic
183#390C2×D1311yescharacteristic
184#388—22no—
185#386—22no—
186#382C2×D1311yescharacteristic
187#340—134no—
188#340—134no—
189#336—132no—
190C22×C13—22no—
191C22×C13—22no—
192C22×C13—22no—
193C22×C13—42no—
194C22×C13—42no—
195C22×C13—81no—
196C22×C13—81no—
197C22×C13—81no—
198C22×C13—82no—
199C22×C13—82no—
200C22×C13C2×#12011yescharacteristic
201C22×C13C2×#12411yescharacteristic
202C22×C13#53611yescharacteristic
203C22×C13C2×#13512yes—
204C22×C13#57512yes—
205C4×C13—22no—
206C4×C13—24no—
207C4×C13—24no—
208C4×C13—81no—
209C4×C13—81no—
210C4×C13—81no—
211C4×C13#54814yes—
212Dic13—48no—
213C22×Q8—262no—
214C22×Q8C22×D1311yescharacteristic
215C22×D4—21no—
216C22×D4C22×D1311yescharacteristic
217C23×C4C22⋊D1312yes—
218C23×C4C22×D1311yescharacteristic
219C22×C8—134no—
220C4⋊Q8—268no—
221#125—138no—
222#125—264no—
223#124—24no—
224C22⋊Q8—24no—
225C22⋊Q8—2616no—
226#121—24no—
227C4×Q8—2616no—
228#117—268no—
229C2×C4⋊C4—21no—
230C2×C4⋊C4—134no—
231C2×C4⋊C4—264no—
232C2×C4⋊C4—262no—
233C2×C4⋊C4C22×D1311yescharacteristic
234C2×C4⋊C4C22×D1311yescharacteristic
235C2×C22⋊C4—21no—
236C2×C22⋊C4—21no—
237C2×C22⋊C4—22no—
238C2×C22⋊C4—22no—
239C2×C22⋊C4—262no—
240C2×C42—24no—
241C2×C42—262no—
242C2×C42C22⋊D1312yes—
243C2×C42C22×D1311yescharacteristic
244C2×C42C22×D1311yescharacteristic
245#103—268no—
246#102—268no—
247C22⋊C8—264no—
248C4×C8—264no—
249#95—22no—
250#95—22no—
251C2×C13—42no—
252C2×C13—161no—
253C2×C13#243611yescharacteristic
254C2×C13#300212yes—
255C2×C13#313111yescharacteristic
256C2×C13#314011yescharacteristic
257C2×C13#323312yes—
258C24—21no—
259C24C2×C22⋊D1311yescharacteristic
260C2×Q8—22no—
261C2×Q8—22no—
262C2×Q8—22no—
263C2×Q8—268no—
264C2×Q8—524no—
265C2×Q8—524no—
266C2×D4—22no—
267C2×D4—22no—
268C2×D4—22no—
269C2×D4—44no—
270C2×D4—42no—
271C22×C4—22no—
272C22×C4—22no—
273C22×C4—24no—
274C22×C4—24no—
275C22×C4—21no—
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—42no—
279C22×C4—264no—
280C22×C4#612914yes—
281C22×C4C2×C22⋊D1311yescharacteristic
282C22×C4C2×C22⋊D1312yes—
283C22×C4C2×C22⋊D1312yes—
284C22×C4C23×D1311yescharacteristic
285C2×C8—264no—
286C2×C8—264no—
287C2×C8—264no—
288C4⋊C4—22no—
289C4⋊C4—22no—
290C4⋊C4—42no—
291C4⋊C4—138no—
292C4⋊C4—268no—
293C4⋊C4—2616no—
294C4⋊C4—264no—
295C22⋊C4—42no—
296C22⋊C4—42no—
297C22⋊C4—44no—
298C22⋊C4—44no—
299C22⋊C4—268no—
300C42—24no—
301C42—22no—
302C42—268no—
303C42D4×D1314yes—
304C13#2590611yescharacteristic, complemented, Sylow
305C23—21no—
306C23—22no—
307C23—22no—
308C23—21no—
309C23—41no—
310C23—41no—
311C23—42no—
312C23—42no—
313C23—41no—
314C23#8819012yes—
315C23C22×C22⋊D1311yescharacteristic
316Q8—44no—
317Q8—5216no—
318D4—44no—
319D4—84no—
320C2×C4—21no—
321C2×C4—22no—
322C2×C4—22no—
323C2×C4—22no—
324C2×C4—22no—
325C2×C4—21no—
326C2×C4—28no—
327C2×C4—48no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—42no—
333C2×C4—42no—
334C2×C4—41no—
335C2×C4—268no—
336C2×C4—524no—
337C2×C4—524no—
338C2×C4#8819012yes—
339C2×C4#8819114yes—
340C2×C4#8820414yes—
341C2×C4C2×D4×D1312yes—
342C2×C4C2×#612912yes—
343C2×C4#8825712yes—
344C8—524no—
345C22—22no—
346C22—22no—
347C22—22no—
348C22—42no—
349C22—42no—
350C22—81no—
351C22—81no—
352C22—81no—
353C22—82no—
354C22—82no—
355C22C2×#8819011yescharacteristic
356C22C2×#8819111yescharacteristic
357C22C2×#8820412yes—
358C22#1171952712yes—
359C22#1171953011yescharacteristic
360C4—22no—
361C4—24no—
362C4—24no—
363C4—81no—
364C4—81no—
365C4—81no—
366C4—528no—
367C4#1171930314yes—
368C2—42no—
369C2—161no—
370C2#1311849511yescharacteristic
371C2#1312405212yes—
372C2#1312515811yescharacteristic
373C2#1312522211yescharacteristic
374C2#1312601112yes—
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#2850C2
socleC23×C13C22×D4
prime radicalC2×C13×#121C22
hypercenter#2850D13
hypocenterC13#25906
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C22×C42 ◁ #2850

Complements

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

NH ≅ G/Ntype
1. C2×#11719175C2semidirect
2. C2×#11718717C2semidirect
3. #13115977C2semidirect
4. #13115972C2semidirect
5. #13115800C2semidirect
7. #13115149C2semidirect
8. C4×C22⋊#1055C2semidirect
62. #88124D4semidirect
304. C13#25906semidirect

Maximal subgroups

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

subgroupindex
C2×#117191752
C2×#117187172
#131159772
#131159722
#131158002
#131151592
#131151492
C4×C22⋊#10552
C13×#28502
#2590613