Finite Group Databasebeta

← #15760639

Subgroups — #15760639

Order 3328.

904 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 904 conjugacy classes of subgroups — too many to draw. Only its 115 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
1#13117414C211yesmaximal, characteristic
2#13114757C211yesmaximal, characteristic
3#13113369C212yesmaximal, complemented
4#13112689C212yesmaximal, complemented
5C13×#2435C211yesmaximal, characteristic
6C23×D4×C13C2211yescharacteristic
7C2×C13×#124C412yescomplemented
8C2×C13×C22⋊Q8C2211yescharacteristic
9C22×C22⋊Dic13—21no—
10C13×#394—22no—
11C13×#390C412yescomplemented
12C13×#379—21no—
13C13×#379—21no—
14C4×C13×C22⋊C4C2211yescharacteristic
15#11718908—21no—
16#11718881—24no—
17C2×#88073—22no—
18#11718872C2212yes—
19#11718868C2212yes—
20#11718130—24no—
21C25×C13D411yescharacteristic
22C25×C13D411yescharacteristic
23C22×Q8×C13C2×C411yescharacteristic, complemented
24C22×D4×C13—22no—
25C22×D4×C13—22no—
26C22×D4×C13—44no—
27C22×D4×C13C2×C412yes—
28C22×D4×C13D412yes—
29C23×C4×C13C2311yescharacteristic
30C23×Dic13—22no—
31C13×#124—44no—
32C13×C22⋊Q8—22no—
33C13×C22⋊Q8—22no—
34C2×C13×C4⋊C4—21no—
35C2×C13×C4⋊C4C2×C411yescharacteristic, complemented
36C2×C13×C22⋊C4—22no—
37C2×C13×C22⋊C4—22no—
38C2×C13×C22⋊C4—21no—
39C2×C13×C22⋊C4—21no—
40C2×C13×C22⋊C4—22no—
41C2×C13×C22⋊C4—22no—
42C2×C42×C13C2×C412yescomplemented
43C2×C22⋊Dic13—22no—
44C2×C22⋊Dic13—22no—
45C2×C22⋊Dic13—22no—
46C2×C22⋊Dic13—22no—
47C2×C22⋊Dic13—44no—
48C2×#6099—22no—
49C13×#95—21no—
50#88073—44no—
51#88071—22no—
52#88071D414yes—
53C22⋊#1055—22no—
54C22⋊#1055—22no—
55#9459—131nomaximal, Sylow
56C24×C13—21no—
57C24×C13—24no—
58C24×C13—21no—
59C24×C13—21no—
60C24×C13—21no—
61C24×C13—42no—
62C24×C13—42no—
63C24×C13—42no—
64C24×C13—81no—
65C24×C13—81no—
66C24×C13C22⋊C412yes—
67C24×C13C22⋊C412yes—
68C24×C13C2×D411yescharacteristic
69C2×Q8×C13—22no—
70C2×Q8×C13—42no—
71C2×D4×C13—24no—
72C2×D4×C13—24no—
73C2×D4×C13—24no—
74C2×D4×C13—24no—
75C2×D4×C13—42no—
76C2×D4×C13—42no—
77C2×D4×C13—44no—
78C2×D4×C13—44no—
79C2×D4×C13—48no—
80C22×C4×C13—22no—
81C22×C4×C13—21no—
82C22×C4×C13—21no—
83C22×C4×C13—42no—
84C22×C4×C13C22×C411yescharacteristic
85C22×C4×C13C2×D412yes—
86C22×C4×C13C2×D411yescharacteristic
87C22×C4×C13#4112yes—
88C22×Dic13—24no—
89C22×Dic13—44no—
90C22×Dic13—82no—
91C22×Dic13—82no—
92C13×C4⋊C4—22no—
93C13×C4⋊C4—42no—
94C13×C22⋊C4—42no—
95C13×C22⋊C4—44no—
96C13×C22⋊C4—44no—
97C13×C22⋊C4—41no—
98C13×C22⋊C4—41no—
99C13×C22⋊C4—82no—
100C13×C22⋊C4—82no—
101C42×C13—42no—
102C22⋊Dic13—44no—
103C22⋊Dic13—44no—
104C22⋊Dic13—82no—
105C22⋊Dic13—82no—
106#6099—44no—
107C2×#1055—42no—
108#2435D1311yescharacteristic
109#2308—131no—
110#1783—131no—
111#1511—132no—
112#1284—132no—
113C23×C13—22no—
114C23×C13—22no—
115C23×C13—24no—
116C23×C13—22no—
117C23×C13—22no—
118C23×C13—22no—
119C23×C13—22no—
120C23×C13—22no—
121C23×C13—22no—
122C23×C13—22no—
123C23×C13—41no—
124C23×C13—42no—
125C23×C13—42no—
126C23×C13—42no—
127C23×C13—42no—
128C23×C13—42no—
129C23×C13—42no—
130C23×C13—42no—
131C23×C13—42no—
132C23×C13—42no—
133C23×C13—42no—
134C23×C13—81no—
135C23×C13—81no—
136C23×C13—81no—
137C23×C13—81no—
138C23×C13—88no—
139C23×C13—88no—
140C23×C13#9914yes—
141C23×C13C2×C22⋊C411yescharacteristic
142C23×C13#12011yescharacteristic
143C23×C13#12311yescharacteristic
144Q8×C13—82no—
145D4×C13—48no—
146D4×C13—48no—
147C2×C4×C13—22no—
148C2×C4×C13—22no—
149C2×C4×C13—42no—
150C2×C4×C13—42no—
151C2×C4×C13—42no—
152C2×C4×C13—42no—
153C2×C4×C13—42no—
154C2×C4×C13—41no—
155C2×C4×C13—41no—
156C2×C4×C13—42no—
157C2×C4×C13—42no—
158C2×C4×C13C4×D412yes—
159C2×C4×C13#12112yes—
160C2×Dic13—44no—
161C2×Dic13—44no—
162C2×Dic13—44no—
163C2×Dic13—88no—
164#1055—82no—
165C23×D4C2×D1311yescharacteristic
166C2×#124Dic1312yescomplemented
167C2×C22⋊Q8C2×D1311yescharacteristic
168C22×C22⋊C4—261no—
169C2×#100—262no—
170#407—132no—
171#394—22no—
172#390Dic1312yescomplemented
173#386—264no—
174#381—132no—
175#379—21no—
176#379—21no—
177#379—261no—
178C4×C22⋊C4C2×D1311yescharacteristic
179#328—264no—
180C22×C13—21no—
181C22×C13—21no—
182C22×C13—21no—
183C22×C13—21no—
184C22×C13—21no—
185C22×C13—21no—
186C22×C13—24no—
187C22×C13—21no—
188C22×C13—44no—
189C22×C13—44no—
190C22×C13—44no—
191C22×C13—44no—
192C22×C13—44no—
193C22×C13—42no—
194C22×C13—42no—
195C22×C13—42no—
196C22×C13—42no—
197C22×C13—42no—
198C22×C13—82no—
199C22×C13—82no—
200C22×C13—84no—
201C22×C13—84no—
202C22×C13—84no—
203C22×C13#38611yescharacteristic
204C22×C13C2×#9912yes—
205C22×C13#45512yes—
206C4×C13—22no—
207C4×C13—22no—
208C4×C13—82no—
209C4×C13—81no—
210C4×C13—81no—
211Dic13—84no—
212C25C22⋊D1311yescharacteristic
213C25C22⋊D1311yescharacteristic
214C22×Q8C2×Dic1311yescharacteristic, complemented
215C22×D4—22no—
216C22×D4—22no—
217C22×D4—44no—
218C22×D4C2×Dic1312yes—
219C22×D4C22⋊D1312yes—
220C23×C4—262no—
221C23×C4C22×D1311yescharacteristic
222C2×M16—262no—
223#124—44no—
224C22⋊Q8—22no—
225C22⋊Q8—22no—
226C2×C4⋊C4—21no—
227C2×C4⋊C4C2×Dic1311yescharacteristic, complemented
228C2×C22⋊C4—22no—
229C2×C22⋊C4—22no—
230C2×C22⋊C4—21no—
231C2×C22⋊C4—21no—
232C2×C22⋊C4—22no—
233C2×C22⋊C4—22no—
234C2×C22⋊C4—262no—
235C2×C22⋊C4—262no—
236C2×C22⋊C4—262no—
237C2×C22⋊C4—262no—
238C2×C22⋊C4—524no—
239C2×C42C2×Dic1312yescomplemented
240#100—524no—
241C22⋊C8—262no—
242C22⋊C8—262no—
243#95—21no—
244#95—134no—
245#95—262no—
246C2×C13—22no—
247C2×C13—22no—
248C2×C13—41no—
249C2×C13—44no—
250C2×C13—82no—
251C2×C13#188511yescharacteristic
252C2×C13#189811yescharacteristic
253C2×C13#191111yescharacteristic
254C24—21no—
255C24—24no—
256C24—21no—
257C24—21no—
258C24—21no—
259C24—42no—
260C24—42no—
261C24—42no—
262C24—81no—
263C24—81no—
264C24C22⋊Dic1312yes—
265C24C22⋊Dic1312yes—
266C24C2×C22⋊D1311yescharacteristic
267C2×Q8—22no—
268C2×Q8—42no—
269C2×D4—24no—
270C2×D4—24no—
271C2×D4—24no—
272C2×D4—24no—
273C2×D4—42no—
274C2×D4—42no—
275C2×D4—44no—
276C2×D4—44no—
277C2×D4—48no—
278C22×C4—22no—
279C22×C4—21no—
280C22×C4—21no—
281C22×C4—42no—
282C22×C4—264no—
283C22×C4—524no—
284C22×C4—1042no—
285C22×C4—1042no—
286C22×C4D4×D1312yes—
287C22×C4#612912yes—
288C22×C4C22×Dic1311yescharacteristic
289C22×C4C2×C22⋊D1311yescharacteristic
290M16—524no—
291C2×C8—522no—
292C4⋊C4—22no—
293C4⋊C4—42no—
294C22⋊C4—44no—
295C22⋊C4—42no—
296C22⋊C4—44no—
297C22⋊C4—41no—
298C22⋊C4—41no—
299C22⋊C4—82no—
300C22⋊C4—82no—
301C22⋊C4—524no—
302C22⋊C4—524no—
303C22⋊C4—1042no—
304C22⋊C4—1042no—
305C42—42no—
306C13#945911yescharacteristic, complemented, Sylow
307C23—22no—
308C23—22no—
309C23—24no—
310C23—22no—
311C23—22no—
312C23—22no—
313C23—22no—
314C23—22no—
315C23—22no—
316C23—22no—
317C23—41no—
318C23—42no—
319C23—42no—
320C23—42no—
321C23—42no—
322C23—42no—
323C23—42no—
324C23—42no—
325C23—42no—
326C23—42no—
327C23—42no—
328C23—81no—
329C23—81no—
330C23—81no—
331C23—81no—
332C23—88no—
333C23—88no—
334C23#8807414yes—
335C23#8818911yescharacteristic
336C23#8819111yescharacteristic
337C23C2×C22⋊Dic1311yescharacteristic
338Q8—82no—
339D4—48no—
340D4—48no—
341C2×C4—22no—
342C2×C4—22no—
343C2×C4—42no—
344C2×C4—42no—
345C2×C4—42no—
346C2×C4—42no—
347C2×C4—42no—
348C2×C4—42no—
349C2×C4—42no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—524no—
353C2×C4—524no—
354C2×C4—524no—
355C2×C4—1048no—
356C2×C4D4×Dic1312yes—
357C2×C4#8819312yes—
358C8—1042no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—21no—
363C22—21no—
364C22—21no—
365C22—24no—
366C22—21no—
367C22—44no—
368C22—44no—
369C22—44no—
370C22—44no—
371C22—44no—
372C22—42no—
373C22—42no—
374C22—42no—
375C22—42no—
376C22—42no—
377C22—82no—
378C22—82no—
379C22—84no—
380C22—84no—
381C22—84no—
382C22#1171872212yes—
383C22C2×#8807412yes—
384C22#1171888111yescharacteristic
385C4—22no—
386C4—22no—
387C4—82no—
388C4—81no—
389C4—81no—
390C4—1044no—
391C2—22no—
392C2—22no—
393C2—41no—
394C2—44no—
395C2—82no—
396C2#1311522511yescharacteristic
397C2#1311529011yescharacteristic
398C2#1311536911yescharacteristic
subgroupG/H
centerC22#11718881
commutatorC22×C4×C13C22×C4
FrattiniC23×C4C22×D13
FittingC13×#2435C2
socleC22×C13#386
prime radicalC23×D4×C13C22
cosocleC23×C4×C13C23
hypercenter#2435D13
hypocenterC13#9459
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2435

Complements

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

NH ≅ G/Ntype
3. #13113369C2semidirect
4. #13112689C2semidirect
7. C2×C13×#124C4semidirect
11. C13×#390C4semidirect
23. C22×Q8×C13C2×C4semidirect
35. C2×C13×C4⋊C4C2×C4semidirect
42. C2×C42×C13C2×C4semidirect
166. C2×#124Dic13semidirect
172. #390Dic13semidirect
214. C22×Q8C2×Dic13semidirect
227. C2×C4⋊C4C2×Dic13semidirect
239. C2×C42C2×Dic13semidirect
306. C13#9459semidirect

Maximal subgroups

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

subgroupindex
#131174142
#131147572
#131133692
#131126892
C13×#24352
#945913