Finite Group Databasebeta

← #15758650

Subgroups — #15758650

Order 3328.

1010 conjugacy classes of subgroups; only the 151 normal subgroups are shown.

normal subgroups only

This group has 1010 conjugacy classes of subgroups — too many to draw. Only its 151 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×C4×C22⋊Dic13C211yesmaximal, characteristic
2#13114746C211yesmaximal, characteristic
3C2×#11718130C212yesmaximal, complemented
4#13112714C212yesmaximal, complemented
5C13×#2848C211yesmaximal, characteristic
6C24×C4×C13C2211yescharacteristic
7C2×C13×C22⋊Q8C412yescomplemented
8C2×C13×C22⋊Q8C2211yescharacteristic
9C22×C22⋊Dic13—21no—
10C22×C4×Dic13—21no—
11C13×#385—21no—
12C13×#385—22no—
13C13×#380C412yescomplemented
14C13×#380C2211yescharacteristic
15C13×#379—21no—
16C4×C22⋊Dic13—24no—
17C2×#88071C2212yes—
18C2×C22⋊#1055—22no—
19C2×C22⋊#1055C2212yes—
20#11718130—24no—
21C25×C13D411yescharacteristic
22C22×Q8×C13C2×C411yescharacteristic
23C23×C4×C13—22no—
24C23×C4×C13—22no—
25C23×C4×C13—44no—
26C23×C4×C13C2×C412yes—
27C23×C4×C13D411yescharacteristic
28C23×C4×C13D412yes—
29C23×C4×C13C2311yescharacteristic
30C23×Dic13—22no—
31C13×C22⋊Q8—22no—
32C13×C22⋊Q8—22no—
33C13×C22⋊Q8—44no—
34C2×C13×C4⋊C4—22no—
35C2×C13×C4⋊C4—21no—
36C2×C13×C4⋊C4C2×C411yescharacteristic
37C2×C13×C4⋊C4C2×C412yes—
38C2×C13×C22⋊C4—22no—
39C2×C13×C22⋊C4—22no—
40C2×C13×C22⋊C4—21no—
41C2×C13×C22⋊C4—21no—
42C2×C22⋊Dic13—28no—
43C2×C22⋊Dic13—24no—
44C2×C4×Dic13—24no—
45C2×C4×Dic13—44no—
46C22×#1055—22no—
47C13×#95—22no—
48C13×#95—21no—
49#88071—22no—
50#88071D414yes—
51C22⋊#1055—22no—
52C22⋊#1055—22no—
53C22⋊#1055—44no—
54#9146—131nomaximal, Sylow
55C24×C13—24no—
56C24×C13—21no—
57C24×C13—21no—
58C24×C13—22no—
59C24×C13—22no—
60C24×C13—42no—
61C24×C13C22⋊C412yes—
62C24×C13C2×D411yescharacteristic
63C2×Q8×C13—22no—
64C2×Q8×C13—42no—
65C22×C4×C13—21no—
66C22×C4×C13—21no—
67C22×C4×C13—24no—
68C22×C4×C13—24no—
69C22×C4×C13—24no—
70C22×C4×C13—24no—
71C22×C4×C13—24no—
72C22×C4×C13—21no—
73C22×C4×C13—22no—
74C22×C4×C13—21no—
75C22×C4×C13—42no—
76C22×C4×C13—42no—
77C22×C4×C13—42no—
78C22×C4×C13—48no—
79C22×C4×C13—48no—
80C22×C4×C13C22⋊C412yes—
81C22×C4×C13C22×C411yescharacteristic
82C22×C4×C13C2×D412yes—
83C22×C4×C13C2×D411yescharacteristic
84C22×C4×C13#4112yes—
85C22×Dic13—28no—
86C22×Dic13—24no—
87C22×Dic13—44no—
88C22×Dic13—42no—
89C22×Dic13—42no—
90C13×C4⋊C4—22no—
91C13×C4⋊C4—42no—
92C13×C4⋊C4—44no—
93C13×C4⋊C4—42no—
94C13×C22⋊C4—44no—
95C13×C22⋊C4—44no—
96C13×C22⋊C4—41no—
97C13×C22⋊C4—41no—
98C13×C22⋊C4—42no—
99C22⋊Dic13—216no—
100C4×Dic13—48no—
101C2×#1055—44no—
102C2×#1055—42no—
103#2848D1311yescharacteristic
104C2×C4×C22⋊C4—131no—
105#1779—131no—
106C2×#328—132no—
107#1294—132no—
108C23×C13—22no—
109C23×C13—22no—
110C23×C13—24no—
111C23×C13—24no—
112C23×C13—22no—
113C23×C13—22no—
114C23×C13—22no—
115C23×C13—22no—
116C23×C13—22no—
117C23×C13—22no—
118C23×C13—48no—
119C23×C13—48no—
120C23×C13—42no—
121C23×C13—42no—
122C23×C13—42no—
123C23×C13—42no—
124C23×C13#10414yes—
125C23×C13C2×C22⋊C411yescharacteristic
126C23×C13#12011yescharacteristic
127C23×C13#12311yescharacteristic
128C23×C13#13512yes—
129C23×C13#13712yes—
130Q8×C13—82no—
131C2×C4×C13—24no—
132C2×C4×C13—24no—
133C2×C4×C13—22no—
134C2×C4×C13—22no—
135C2×C4×C13—22no—
136C2×C4×C13—22no—
137C2×C4×C13—42no—
138C2×C4×C13—42no—
139C2×C4×C13—48no—
140C2×C4×C13—48no—
141C2×C4×C13—41no—
142C2×C4×C13—41no—
143C2×C4×C13—42no—
144C2×C4×C13—42no—
145C2×C4×C13—42no—
146C2×C4×C13—42no—
147C2×C4×C13—42no—
148C2×C4×C13#9914yes—
149C2×C4×C13C4×D412yes—
150C2×C4×C13#12112yes—
151C2×Dic13—28no—
152C2×Dic13—44no—
153C2×Dic13—48no—
154C2×Dic13—48no—
155C2×Dic13—44no—
156#1055—82no—
157C24×C4C2×D1311yescharacteristic
158C2×C22⋊Q8Dic1312yescomplemented
159C2×C22⋊Q8C2×D1311yescharacteristic
160C22×C22⋊C4—261no—
161C22×C42—261no—
162C2×C22⋊C8—132no—
163C2×C22⋊C8—262no—
164#385—21no—
165#385—22no—
166#380Dic1312yescomplemented
167#380C2×D1311yescharacteristic
168#379—21no—
169C4×C22⋊C4—264no—
170C2×#95—132no—
171#328—264no—
172C22×C13—21no—
173C22×C13—21no—
174C22×C13—21no—
175C22×C13—21no—
176C22×C13—24no—
177C22×C13—24no—
178C22×C13—24no—
179C22×C13—24no—
180C22×C13—24no—
181C22×C13—48no—
182C22×C13—48no—
183C22×C13—42no—
184C22×C13—42no—
185C22×C13—42no—
186C22×C13—42no—
187C22×C13#38611yescharacteristic
188C22×C13C2×#9912yes—
189C22×C13#41611yescharacteristic
190C22×C13#41911yescharacteristic
191C22×C13C2×#10412yes—
192C22×C13#45212yes—
193C22×C13#48512yes—
194C4×C13—22no—
195C4×C13—24no—
196C4×C13—22no—
197C4×C13—81no—
198C4×C13—81no—
199C4×C13—82no—
200Dic13—48no—
201C25C22⋊D1311yescharacteristic
202C22×Q8C2×Dic1311yescharacteristic
203C23×C4—22no—
204C23×C4—22no—
205C23×C4—44no—
206C23×C4—262no—
207C23×C4C2×Dic1312yes—
208C23×C4C22⋊D1311yescharacteristic
209C23×C4C22⋊D1312yes—
210C23×C4C22×D1311yescharacteristic
211C22×C8—262no—
212C22⋊Q8—22no—
213C22⋊Q8—22no—
214C22⋊Q8—44no—
215C2×C4⋊C4—22no—
216C2×C4⋊C4—21no—
217C2×C4⋊C4C2×Dic1311yescharacteristic
218C2×C4⋊C4C2×Dic1312yes—
219C2×C22⋊C4—22no—
220C2×C22⋊C4—22no—
221C2×C22⋊C4—21no—
222C2×C22⋊C4—21no—
223C2×C22⋊C4—264no—
224C2×C22⋊C4—268no—
225C2×C42—264no—
226C2×C42—524no—
227C22⋊C8—262no—
228C22⋊C8—262no—
229C22⋊C8—524no—
230#95—22no—
231#95—21no—
232#95—134no—
233#95—262no—
234C2×C13—22no—
235C2×C13—22no—
236C2×C13—44no—
237C2×C13#150112yes—
238C2×C13#150812yes—
239C2×C13#187311yescharacteristic
240C2×C13#189611yescharacteristic
241C2×C13#189811yescharacteristic
242C24—24no—
243C24—21no—
244C24—21no—
245C24—22no—
246C24—22no—
247C24—42no—
248C24C22⋊Dic1312yes—
249C24C2×C22⋊D1311yescharacteristic
250C2×Q8—22no—
251C2×Q8—42no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—24no—
255C22×C4—24no—
256C22×C4—24no—
257C22×C4—24no—
258C22×C4—24no—
259C22×C4—22no—
260C22×C4—21no—
261C22×C4—21no—
262C22×C4—42no—
263C22×C4—42no—
264C22×C4—42no—
265C22×C4—48no—
266C22×C4—48no—
267C22×C4—268no—
268C22×C4—264no—
269C22×C4—524no—
270C22×C4—522no—
271C22×C4—522no—
272C22×C4C22⋊Dic1312yes—
273C22×C4D4×D1312yes—
274C22×C4#612912yes—
275C22×C4C22×Dic1311yescharacteristic
276C22×C4C2×C22⋊D1311yescharacteristic
277C2×C8—524no—
278C2×C8—522no—
279C4⋊C4—22no—
280C4⋊C4—42no—
281C4⋊C4—44no—
282C4⋊C4—42no—
283C22⋊C4—44no—
284C22⋊C4—44no—
285C22⋊C4—41no—
286C22⋊C4—41no—
287C22⋊C4—42no—
288C22⋊C4—2616no—
289C42—528no—
290C13#914611yescharacteristic, complemented, Sylow
291C23—22no—
292C23—22no—
293C23—24no—
294C23—24no—
295C23—22no—
296C23—22no—
297C23—22no—
298C23—22no—
299C23—22no—
300C23—22no—
301C23—48no—
302C23—48no—
303C23—42no—
304C23—42no—
305C23—42no—
306C23—42no—
307C23#8807714yes—
308C23#8818911yescharacteristic
309C23#8819111yescharacteristic
310C23#8819612yes—
311C23#8820412yes—
312C23C2×C22⋊Dic1311yescharacteristic
313Q8—82no—
314C2×C4—24no—
315C2×C4—24no—
316C2×C4—22no—
317C2×C4—22no—
318C2×C4—22no—
319C2×C4—22no—
320C2×C4—42no—
321C2×C4—42no—
322C2×C4—48no—
323C2×C4—48no—
324C2×C4—42no—
325C2×C4—42no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—42no—
329C2×C4—42no—
330C2×C4—42no—
331C2×C4—268no—
332C2×C4—524no—
333C2×C4—528no—
334C2×C4—528no—
335C2×C4—524no—
336C2×C4#8807414yes—
337C2×C4D4×Dic1312yes—
338C2×C4#8819312yes—
339C8—1042no—
340C22—24no—
341C22—21no—
342C22—21no—
343C22—21no—
344C22—21no—
345C22—24no—
346C22—24no—
347C22—24no—
348C22—24no—
349C22—48no—
350C22—48no—
351C22—42no—
352C22—42no—
353C22—42no—
354C22—42no—
355C22#1171870612yes—
356C22#1171870812yes—
357C22C2×#8807412yes—
358C22#1171888111yescharacteristic
359C22#1171888611yescharacteristic
360C22#1171889411yescharacteristic
361C22C2×#8807712yes—
362C4—22no—
363C4—24no—
364C4—22no—
365C4—81no—
366C4—81no—
367C4—82no—
368C4—528no—
369C2—22no—
370C2—22no—
371C2—44no—
372C2#1311332712yes—
373C2#1311335612yes—
374C2#1311514911yescharacteristic
375C2#1311528011yescharacteristic
376C2#1311529011yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic13
commutatorC22×C4×C13C22×C4
FrattiniC23×C4C22×D13
FittingC13×#2848C2
socleC23×C13C2×C22⋊C4
prime radicalC25×C13D4
cosocleC23×C4×C13C23
hypercenter#2848D13
hypocenterC13#9146
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C24×C4 ◁ #2848

Complements

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

NH ≅ G/Ntype
3. C2×#11718130C2semidirect
4. #13112714C2semidirect
7. C2×C13×C22⋊Q8C4semidirect
13. C13×#380C4semidirect
158. C2×C22⋊Q8Dic13semidirect
166. #380Dic13semidirect
290. C13#9146semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C22⋊Dic132
#131147462
C2×#117181302
#131127142
C13×#28482
#914613