Finite Group Databasebeta

← #15756258

Subgroups — #15756258

Order 3328.

830 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 830 conjugacy classes of subgroups — too many to draw. Only its 139 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718873C211yesmaximal, characteristic
2#13114746C211yesmaximal, characteristic
3#13112678C214yesmaximal, complemented
4C13×#1779C211yesmaximal, characteristic
5C24×C4×C13C2211yescharacteristic
6C22×C22⋊Dic13C412yes—
7C22×C4⋊Dic13C411yescharacteristic
8C22×C4⋊Dic13C411yescharacteristic
9C2×C13×C22⋊C8—21no—
10C2×C13×C22⋊C8—21no—
11C2×C13×C22⋊C8C2212yes—
12#11718873—21no—
13#11718873—21no—
14#11718873—21no—
15#11718873—21no—
16C2×#88071C2212yes—
17C2×C22⋊#1055—21no—
18C2×C22⋊#1055—21no—
19C2×C22⋊#1055C2212yes—
20C25×C13C2×C411yescharacteristic
21C23×C4×C13—24no—
22C23×C4×C13—42no—
23C23×C4×C13—42no—
24C23×C4×C13C2×C411yescharacteristic
25C23×C4×C13D411yescharacteristic
26C23×C4×C13D411yescharacteristic
27C23×C4×C13D411yescharacteristic
28C23×C4×C13D411yescharacteristic
29C23×C4×C13C2311yescharacteristic
30C23×Dic13C2×C412yes—
31C23×Dic13C2×C412yes—
32C22×C8×C13—22no—
33C2×C22⋊Dic13—22no—
34C2×C22⋊Dic13—22no—
35C2×C22⋊Dic13—44no—
36C2×C4⋊Dic13—21no—
37C2×C4⋊Dic13—21no—
38C2×C4⋊Dic13—21no—
39C2×C4⋊Dic13—21no—
40C2×C4⋊Dic13—42no—
41C2×C4⋊Dic13—42no—
42C22×#1055—22no—
43C13×C22⋊C8—24no—
44C13×C22⋊C8—42no—
45C13×C22⋊C8—42no—
46#88071—22no—
47#88071—22no—
48C22⋊#1055—24no—
49C22⋊#1055—42no—
50C22⋊#1055—42no—
51#8704—131nomaximal, Sylow
52C24×C13—22no—
53C24×C13—22no—
54C24×C13—22no—
55C24×C13—22no—
56C24×C13—22no—
57C24×C13—41no—
58C24×C13—41no—
59C24×C13C22⋊C411yescharacteristic
60C24×C13C22⋊C411yescharacteristic
61C24×C13C22×C411yescharacteristic
62C22×C4×C13—22no—
63C22×C4×C13—22no—
64C22×C4×C13—22no—
65C22×C4×C13—22no—
66C22×C4×C13—22no—
67C22×C4×C13—22no—
68C22×C4×C13—22no—
69C22×C4×C13—22no—
70C22×C4×C13—22no—
71C22×C4×C13—22no—
72C22×C4×C13—22no—
73C22×C4×C13—41no—
74C22×C4×C13—41no—
75C22×C4×C13—41no—
76C22×C4×C13—41no—
77C22×C4×C13—41no—
78C22×C4×C13—41no—
79C22×C4×C13—416no—
80C22×C4×C13C22⋊C411yescharacteristic
81C22×C4×C13C22⋊C411yescharacteristic
82C22×C4×C13C2×D411yescharacteristic
83C22×C4×C13C2×D411yescharacteristic
84C22×C4×C13#4114yes—
85C22×Dic13—22no—
86C22×Dic13—22no—
87C22×Dic13—24no—
88C22×Dic13—24no—
89C22×Dic13—42no—
90C22×Dic13—42no—
91C22×Dic13—42no—
92C22×Dic13—42no—
93C2×C8×C13—42no—
94C2×C8×C13—42no—
95C2×C8×C13—42no—
96C22⋊Dic13—44no—
97C22⋊Dic13—44no—
98C4⋊Dic13—42no—
99C4⋊Dic13—42no—
100C4⋊Dic13—42no—
101C4⋊Dic13—42no—
102C2×#1055—42no—
103C2×#1055—42no—
104C2×#1055—42no—
105C2×#380—131no—
106#1779—131no—
107#1779D1311yescharacteristic
108#1280—134no—
109C23×C13—21no—
110C23×C13—21no—
111C23×C13—21no—
112C23×C13—21no—
113C23×C13—28no—
114C23×C13—21no—
115C23×C13—21no—
116C23×C13—21no—
117C23×C13—21no—
118C23×C13—21no—
119C23×C13—21no—
120C23×C13—21no—
121C23×C13—21no—
122C23×C13—21no—
123C23×C13—21no—
124C23×C13—21no—
125C23×C13—21no—
126C23×C13—44no—
127C23×C13—44no—
128C23×C13—44no—
129C23×C13—44no—
130C23×C13—44no—
131C23×C13—44no—
132C23×C13#10012yes—
133C23×C13#10112yes—
134C23×C13C2×C22⋊C411yescharacteristic
135C23×C13#11712yes—
136C23×C13#13112yes—
137C23×C13#13112yes—
138C2×C4×C13—28no—
139C2×C4×C13—21no—
140C2×C4×C13—21no—
141C2×C4×C13—21no—
142C2×C4×C13—21no—
143C2×C4×C13—21no—
144C2×C4×C13—21no—
145C2×C4×C13—21no—
146C2×C4×C13—21no—
147C2×C4×C13—44no—
148C2×C4×C13—44no—
149C2×C4×C13—44no—
150C2×C4×C13—44no—
151C2×C4×C13—44no—
152C2×C4×C13#9912yes—
153C2×C4×C13#9912yes—
154C2×C4×C13#12312yes—
155C2×C4×C13#12312yes—
156C2×Dic13—42no—
157C2×Dic13—42no—
158C2×Dic13—42no—
159C2×Dic13—42no—
160C2×Dic13—42no—
161C2×Dic13—42no—
162C2×Dic13—84no—
163C2×Dic13—84no—
164C8×C13—82no—
165#1055—82no—
166C24×C4C2×D1311yescharacteristic
167C22×C4⋊C4—131no—
168C22×C4⋊C4—131no—
169C22×C22⋊C4—132no—
170C2×C22⋊C8—21no—
171C2×C22⋊C8—21no—
172C2×C22⋊C8—132no—
173C2×C22⋊C8—261no—
174C2×C22⋊C8—261no—
175C2×C22⋊C8C2×D1312yes—
176#380—261no—
177#380—261no—
178#380—261no—
179#380—261no—
180C2×#95—132no—
181C22×C13—22no—
182C22×C13—22no—
183C22×C13—22no—
184C22×C13—22no—
185C22×C13—22no—
186C22×C13—22no—
187C22×C13—22no—
188C22×C13—22no—
189C22×C13—22no—
190C22×C13—22no—
191C22×C13—22no—
192C22×C13—22no—
193C22×C13—416no—
194C22×C13—41no—
195C22×C13—41no—
196C22×C13—41no—
197C22×C13—41no—
198C22×C13—41no—
199C22×C13—41no—
200C22×C13—41no—
201C22×C13—41no—
202C22×C13#38111yescharacteristic
203C22×C13#40811yescharacteristic
204C22×C13#40811yescharacteristic
205C22×C13C2×#9911yescharacteristic
206C22×C13C2×#9911yescharacteristic
207C22×C13C2×#10011yescharacteristic
208C22×C13C2×#10111yescharacteristic
209C22×C13#43314yes—
210C4×C13—22no—
211C4×C13—22no—
212C4×C13—22no—
213C4×C13—22no—
214Dic13—82no—
215Dic13—82no—
216C25C4×D1311yescharacteristic
217C23×C4—24no—
218C23×C4—42no—
219C23×C4—42no—
220C23×C4—132no—
221C23×C4—132no—
222C23×C4C4×D1311yescharacteristic
223C23×C4D5211yescharacteristic
224C23×C4D5211yescharacteristic
225C23×C4C22⋊D1311yescharacteristic
226C23×C4C22⋊D1311yescharacteristic
227C23×C4C22×D1311yescharacteristic
228C22×C8—22no—
229C22×C8—262no—
230C2×C4⋊C4—261no—
231C2×C4⋊C4—261no—
232C2×C4⋊C4—261no—
233C2×C4⋊C4—261no—
234C2×C4⋊C4—522no—
235C2×C4⋊C4—522no—
236C2×C22⋊C4—262no—
237C2×C22⋊C4—262no—
238C2×C22⋊C4—524no—
239C22⋊C8—24no—
240C22⋊C8—42no—
241C22⋊C8—42no—
242C22⋊C8—264no—
243C22⋊C8—522no—
244C22⋊C8—522no—
245#95—262no—
246#95—262no—
247C2×C13—24no—
248C2×C13—42no—
249C2×C13—42no—
250C2×C13#147111yescharacteristic
251C2×C13#147111yescharacteristic
252C2×C13#147211yescharacteristic
253C2×C13#147211yescharacteristic
254C2×C13#181811yescharacteristic
255C2×C13#181911yescharacteristic
256C2×C13#182111yescharacteristic
257C24—22no—
258C24—22no—
259C24—22no—
260C24—22no—
261C24—22no—
262C24—41no—
263C24—41no—
264C24#610311yescharacteristic
265C24#610311yescharacteristic
266C24C2×C4×D1311yescharacteristic
267C22×C4—22no—
268C22×C4—22no—
269C22×C4—22no—
270C22×C4—22no—
271C22×C4—22no—
272C22×C4—22no—
273C22×C4—22no—
274C22×C4—22no—
275C22×C4—22no—
276C22×C4—22no—
277C22×C4—22no—
278C22×C4—41no—
279C22×C4—41no—
280C22×C4—41no—
281C22×C4—41no—
282C22×C4—41no—
283C22×C4—41no—
284C22×C4—416no—
285C22×C4—262no—
286C22×C4—262no—
287C22×C4—264no—
288C22×C4—264no—
289C22×C4—522no—
290C22×C4—522no—
291C22×C4—522no—
292C22×C4—522no—
293C22×C4#610311yescharacteristic
294C22×C4#610311yescharacteristic
295C22×C4C2×D5211yescharacteristic
296C22×C4#612914yes—
297C22×C4C2×C22⋊D1311yescharacteristic
298C2×C8—42no—
299C2×C8—42no—
300C2×C8—42no—
301C2×C8—522no—
302C2×C8—522no—
303C2×C8—522no—
304C4⋊C4—522no—
305C4⋊C4—522no—
306C4⋊C4—522no—
307C4⋊C4—522no—
308C22⋊C4—524no—
309C22⋊C4—524no—
310C13#870411yescharacteristic, complemented, Sylow
311C23—21no—
312C23—21no—
313C23—21no—
314C23—21no—
315C23—28no—
316C23—21no—
317C23—21no—
318C23—21no—
319C23—21no—
320C23—21no—
321C23—21no—
322C23—21no—
323C23—21no—
324C23—21no—
325C23—21no—
326C23—21no—
327C23—21no—
328C23—44no—
329C23—44no—
330C23—44no—
331C23—44no—
332C23—44no—
333C23—44no—
334C23#8806312yes—
335C23#8806412yes—
336C23#8813112yes—
337C23#8815512yes—
338C23#8816112yes—
339C23C2×#610311yescharacteristic
340C2×C4—28no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—44no—
350C2×C4—44no—
351C2×C4—44no—
352C2×C4—44no—
353C2×C4—44no—
354C2×C4—522no—
355C2×C4—522no—
356C2×C4—522no—
357C2×C4—522no—
358C2×C4—522no—
359C2×C4—522no—
360C2×C4—1044no—
361C2×C4—1044no—
362C2×C4#8804612yes—
363C2×C4#8804612yes—
364C2×C4#8814012yes—
365C2×C4#8818912yes—
366C8—82no—
367C8—1042no—
368C22—22no—
369C22—22no—
370C22—22no—
371C22—22no—
372C22—22no—
373C22—22no—
374C22—22no—
375C22—22no—
376C22—22no—
377C22—22no—
378C22—22no—
379C22—22no—
380C22—416no—
381C22—41no—
382C22—41no—
383C22—41no—
384C22—41no—
385C22—41no—
386C22—41no—
387C22—41no—
388C22—41no—
389C22#1171838114yes—
390C22#1171860411yescharacteristic
391C22C2×#8804611yescharacteristic
392C22C2×#8804611yescharacteristic
393C22#1171877111yescharacteristic
394C22#1171879011yescharacteristic
395C22C2×#8806311yescharacteristic
396C22C2×#8806411yescharacteristic
397C4—22no—
398C4—22no—
399C4—22no—
400C4—22no—
401C4—1042no—
402C4—1042no—
403C2—24no—
404C2—42no—
405C2—42no—
406C2#1311319511yescharacteristic
407C2#1311319711yescharacteristic
408C2#1311319911yescharacteristic
409C2#1311320111yescharacteristic
410C2#1311490511yescharacteristic
411C2#1311490811yescharacteristic
412C2#1311491411yescharacteristic
subgroupG/H
centerC23C2×#6103
commutatorC24×C13C22×C4
FrattiniC23×C4C22×D13
FittingC13×#1779C2
socleC23×C13C2×C22⋊C4
prime radicalC25×C13C2×C4
cosocleC23×C4×C13C23
hypercenter#1779D13
hypocenterC13#8704
LCSG ▷ C24×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C24×C4 ◁ #1779

Complements

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

NH ≅ G/Ntype
3. #13112678C2semidirect
310. C13#8704semidirect

Maximal subgroups

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

subgroupindex
C2×#117188732
#131147462
#131126782
C13×#17792
#870413