Finite Group Databasebeta

← #15872434

Subgroups — #15872434

Order 3328.

1066 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88144C211yesmaximal, characteristic
2C2×#11718380C211yesmaximal, characteristic
3#13117238C211yesmaximal, characteristic
4#13115803C214yesmaximal, complemented
5#13115792C214yesmaximal, complemented
6#13114926C211yesmaximal, characteristic
7#13114923C211yesmaximal, characteristic
8#13114920C211yesmaximal, characteristic
9C13×#1824C211yesmaximal, characteristic
10C22×C13×C4⋊C4C2211yescharacteristic
11C22×C4⋊Dic13—21no—
12C22×C4⋊Dic13C2211yescharacteristic
13C22×#6101—21no—
14C22×C4×Dic13C2211yescharacteristic
15C2×#88144—21no—
16C2×#88144—21no—
17C2×#88144—24no—
18C2×#88144C418yescomplemented
19C2×#88144C2212yes—
20C2×#88144C2212yes—
21C2×#88131—21no—
22C2×C13×C22⋊C8C2211yescharacteristic
23C13×#380C2211yescharacteristic
24#11718873C2211yescharacteristic
25C2×C22⋊#1055C2211yescharacteristic
26C2×#88055C2212yes—
27C2×#88054C2212yes—
28#11718637C2212yes—
29C4⋊C4×Dic13C2212yes—
30#11718603—21no—
31#11718380—24no—
32#11718311—21no—
33#11718310—21no—
34C13×#340C2214yes—
35#11718143C2214yes—
36#11718121C2214yes—
37#11718121C2214yes—
38C23×C4×C13—21no—
39C23×C4×C13C2311yescharacteristic
40C23×Dic13—21no—
41C23×Dic13D411yescharacteristic
42C23×Dic13D411yescharacteristic
43C22×C8×C13C2312yes—
44C2×C13×C4⋊C4—21no—
45C2×C13×C4⋊C4—22no—
46C2×C13×C4⋊C4C2×C414yes—
47C2×C13×C4⋊C4C2312yes—
48C2×C13×C4⋊C4C2312yes—
49C2×C13×C22⋊C4—21no—
50C2×C22⋊Dic13—21no—
51C2×C4⋊Dic13—21no—
52C2×C4⋊Dic13—22no—
53C2×C4⋊Dic13—28no—
54C2×C4⋊Dic13—22no—
55C2×C4⋊Dic13—22no—
56C2×C4⋊Dic13C2×C414yes—
57C2×C4⋊Dic13C2312yes—
58C2×C4⋊Dic13C2312yes—
59C2×#6101—28no—
60C2×#6101—22no—
61C2×#6101—22no—
62C2×#6101—22no—
63C2×#6101—22no—
64C2×C4×Dic13—22no—
65C2×C4×Dic13C2×C414yes—
66C2×C4×Dic13D411yescharacteristic
67C2×C4×Dic13D411yescharacteristic
68C2×C4×Dic13D414yes—
69C2×C4×Dic13C2311yescharacteristic
70C2×C4×Dic13C2311yescharacteristic
71C22×#1055C2312yes—
72#88144—28no—
73#88144—28no—
74#88144—24no—
75#88144—24no—
76#88144C2×C418yes—
77#88144C2×C418yes—
78#88131—44no—
79C13×C22⋊C8—22no—
80C13×#95—21no—
81#88071—21no—
82#88071—22no—
83C22⋊#1055—22no—
84#88055—24no—
85#88054—24no—
86#21838—131nomaximal, Sylow
87C24×C13C2×D411yescharacteristic
88C22×C4×C13—24no—
89C22×C4×C13—24no—
90C22×C4×C13—22no—
91C22×C4×C13—22no—
92C22×C4×C13—44no—
93C22×C4×C13C22×C412yes—
94C22×C4×C13C2×D411yescharacteristic
95C22×C4×C13C2×D412yes—
96C22×C4×C13C2411yescharacteristic
97C22×Dic13—22no—
98C22×Dic13—22no—
99C22×Dic13—24no—
100C22×Dic13—22no—
101C22×Dic13—22no—
102C22×Dic13—42no—
103C22×Dic13—42no—
104C22×Dic13—42no—
105C22×Dic13C22⋊C414yes—
106C22×Dic13C22⋊C414yes—
107C22×Dic13C2×D411yescharacteristic
108C22×Dic13C2×D411yescharacteristic
109C22×Dic13C2×D411yescharacteristic
110C22×Dic13C2×D411yescharacteristic
111C2×C8×C13—22no—
112C2×C8×C13—24no—
113C13×C4⋊C4—24no—
114C13×C4⋊C4—22no—
115C13×C4⋊C4—24no—
116C13×C4⋊C4C22×C414yes—
117C13×C22⋊C4—42no—
118C22⋊Dic13—42no—
119C4⋊Dic13—24no—
120C4⋊Dic13—22no—
121C4⋊Dic13—28no—
122C4⋊Dic13—28no—
123C4⋊Dic13—24no—
124C4⋊Dic13C22×C414yes—
125#6101—28no—
126#6101—28no—
127#6101—44no—
128#6101—44no—
129C4×Dic13—44no—
130C4×Dic13C22⋊C414yes—
131C4×Dic13C22⋊C414yes—
132C4×Dic13C22×C412yes—
133C4×Dic13C22×C412yes—
134C4×Dic13C2×D412yes—
135C4×Dic13C2×D412yes—
136C2×#1055—22no—
137C2×#1055—24no—
138C22×#125—131no—
139C2×#432—131no—
140#2285—131no—
141#1992—134no—
142#1989—134no—
143#1824—131no—
144#1824D1311yescharacteristic
145#1823—131no—
146#1823—131no—
147C23×C13—22no—
148C23×C13—22no—
149C23×C13C2×C22⋊C412yes—
150C23×C13AGL(1,ℤ/8)12yes—
151C23×C13#13712yes—
152C23×C13C22×D411yescharacteristic
153C2×C4×C13—22no—
154C2×C4×C13—24no—
155C2×C4×C13—24no—
156C2×C4×C13—24no—
157C2×C4×C13—48no—
158C2×C4×C13—44no—
159C2×C4×C13—42no—
160C2×C4×C13—42no—
161C2×C4×C13—42no—
162C2×C4×C13C2×C22⋊C412yes—
163C2×C4×C13C23×C411yescharacteristic
164C2×C4×C13C22×D411yescharacteristic
165C2×C4×C132−1+414yes—
166C2×Dic13—21no—
167C2×Dic13—21no—
168C2×Dic13—21no—
169C2×Dic13—21no—
170C2×Dic13—22no—
171C2×Dic13—22no—
172C2×Dic13—28no—
173C2×Dic13—24no—
174C2×Dic13—44no—
175C2×Dic13—42no—
176C2×Dic13—42no—
177C2×Dic13—48no—
178C2×Dic13—42no—
179C2×Dic13—42no—
180C2×Dic13—42no—
181C2×Dic13C2×C22⋊C412yes—
182C2×Dic13C2×C22⋊C412yes—
183C2×Dic13C2×C22⋊C412yes—
184C2×Dic13C2×C22⋊C412yes—
185C8×C13—42no—
186#1055—42no—
187C2×#125—138no—
188C2×#125—132no—
189C2×#125—132no—
190C2×#125—261no—
191C2×#125—261no—
192C2×#125—264no—
193C2×#117—261no—
194C22×C4⋊C4—131no—
195C22×C4⋊C4—261no—
196C22×C4⋊C4—261no—
197C22×C4⋊C4C2×D1311yescharacteristic
198C22×C42—131no—
199#432—264no—
200C2×C4⋊C8—132no—
201C2×C22⋊C8—131no—
202C2×C22⋊C8C2×D1311yescharacteristic
203C2×#97—132no—
204#384—132no—
205#382—261no—
206#380—131no—
207#380—261no—
208#380C2×D1311yescharacteristic
209C4×C4⋊C4—132no—
210C4×C4⋊C4—261no—
211#340—134no—
212#340—134no—
213#340—134no—
214#340C2×D1314yes—
215C22×C13—22no—
216C22×C13—22no—
217C22×C13—24no—
218C22×C13—24no—
219C22×C13#41714yes—
220C22×C13C22×C22⋊C411yescharacteristic
221C22×C13#53612yes—
222C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
223C22×C13C2×#13711yescharacteristic
224C22×C13#57512yes—
225C4×C13—22no—
226C4×C13—44no—
227C4×C13—82no—
228C4×C13#51912yes—
229C4×C13#53612yes—
230Dic13—22no—
231Dic13—22no—
232Dic13—22no—
233Dic13—22no—
234Dic13—44no—
235Dic13—82no—
236C23×C4—21no—
237C23×C4—131no—
238C23×C4—131no—
239C23×C4—261no—
240C23×C4C22×D1311yescharacteristic
241C22×C8—132no—
242C22×C8C22×D1312yes—
243#125—138no—
244#125—138no—
245#125—268no—
246#125—268no—
247#125—264no—
248#125—264no—
249#117—524no—
250C2×C4⋊C4—21no—
251C2×C4⋊C4—22no—
252C2×C4⋊C4—134no—
253C2×C4⋊C4—132no—
254C2×C4⋊C4—132no—
255C2×C4⋊C4—268no—
256C2×C4⋊C4—262no—
257C2×C4⋊C4—262no—
258C2×C4⋊C4—268no—
259C2×C4⋊C4—262no—
260C2×C4⋊C4—262no—
261C2×C4⋊C4—261no—
262C2×C4⋊C4—262no—
263C2×C4⋊C4—262no—
264C2×C4⋊C4—262no—
265C2×C4⋊C4C4×D1314yes—
266C2×C4⋊C4C22×D1312yes—
267C2×C4⋊C4C22×D1312yes—
268C2×C22⋊C4—21no—
269C2×C22⋊C4—261no—
270C2×C42—134no—
271C2×C42—131no—
272C2×C42—131no—
273C2×C42—134no—
274C2×C42—131no—
275C2×C42—131no—
276C2×C42—262no—
277C4⋊C8—264no—
278C22⋊C8—22no—
279C22⋊C8—262no—
280#97—264no—
281#95—21no—
282#95—262no—
283#95—261no—
284C2×C13—24no—
285C2×C13#231011yescharacteristic
286C2×C13C2×#41711yescharacteristic
287C2×C13#289611yescharacteristic
288C2×C13#323412yes—
289C2×C13#323612yes—
290C24D4×D1311yescharacteristic
291C22×C4—24no—
292C22×C4—24no—
293C22×C4—22no—
294C22×C4—22no—
295C22×C4—44no—
296C22×C4—134no—
297C22×C4—131no—
298C22×C4—131no—
299C22×C4—131no—
300C22×C4—131no—
301C22×C4—134no—
302C22×C4—262no—
303C22×C4—262no—
304C22×C4—264no—
305C22×C4—262no—
306C22×C4—262no—
307C22×C4—522no—
308C22×C4—522no—
309C22×C4—522no—
310C22×C4C2×C4×D1312yes—
311C22×C4D4×D1311yescharacteristic
312C22×C4D4×D1312yes—
313C22×C4C23×D1311yescharacteristic
314C2×C8—22no—
315C2×C8—24no—
316C2×C8—262no—
317C2×C8—264no—
318C4⋊C4—24no—
319C4⋊C4—22no—
320C4⋊C4—24no—
321C4⋊C4—134no—
322C4⋊C4—268no—
323C4⋊C4—268no—
324C4⋊C4—268no—
325C4⋊C4—268no—
326C4⋊C4—264no—
327C4⋊C4—262no—
328C4⋊C4—264no—
329C4⋊C4—524no—
330C4⋊C4—524no—
331C4⋊C4C2×C4×D1314yes—
332C22⋊C4—42no—
333C22⋊C4—522no—
334C42—134no—
335C42—134no—
336C42—132no—
337C42—132no—
338C42—132no—
339C42—132no—
340C42—524no—
341C13#2183811yescharacteristic, complemented, Sylow
342C23—22no—
343C23—22no—
344C23C22⋊C4×D1312yes—
345C23#8816812yes—
346C23#8817212yes—
347C23C2×D4×D1311yescharacteristic
348C2×C4—22no—
349C2×C4—24no—
350C2×C4—24no—
351C2×C4—24no—
352C2×C4—48no—
353C2×C4—44no—
354C2×C4—42no—
355C2×C4—42no—
356C2×C4—42no—
357C2×C4—132no—
358C2×C4—132no—
359C2×C4—132no—
360C2×C4—132no—
361C2×C4—261no—
362C2×C4—261no—
363C2×C4—261no—
364C2×C4—261no—
365C2×C4—262no—
366C2×C4—262no—
367C2×C4—268no—
368C2×C4—264no—
369C2×C4—524no—
370C2×C4—522no—
371C2×C4—522no—
372C2×C4—528no—
373C2×C4—522no—
374C2×C4—522no—
375C2×C4—522no—
376C2×C4C22⋊C4×D1312yes—
377C2×C4C22×C4×D1311yescharacteristic
378C2×C4C2×D4×D1311yescharacteristic
379C2×C4#8825714yes—
380C8—42no—
381C8—522no—
382C22—22no—
383C22—24no—
384C22—24no—
385C22—22no—
386C22#1171846414yes—
387C22C2×C22⋊C4×D1311yescharacteristic
388C22#1171935312yes—
389C22C2×#8816811yescharacteristic
390C22C2×#8817211yescharacteristic
391C22#1171947812yes—
392C4—22no—
393C4—44no—
394C4—82no—
395C4—262no—
396C4—262no—
397C4—262no—
398C4—262no—
399C4—524no—
400C4—1042no—
401C4#1171922112yes—
402C4#1171935312yes—
403C2—24no—
404C2#1311742111yescharacteristic
405C2C2×#1171846411yescharacteristic
406C2#1312335011yescharacteristic
407C2#1312602512yes—
408C2#1312604112yes—
subgroupG/H
centerC23C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#1824C2
socleC23×C13C22×D4
prime radicalC24×C13C2×D4
cosocleC22×C4×C13C24
hypercenter#1824D13
hypocenterC13#21838
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1824

Complements

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

NH ≅ G/Ntype
4. #13115803C2semidirect
5. #13115792C2semidirect
18. C2×#88144C4semidirect
341. C13#21838semidirect

Maximal subgroups

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

subgroupindex
C22×#881442
C2×#117183802
#131172382
#131158032
#131157922
#131149262
#131149232
#131149202
C13×#18242
#2183813