Finite Group Databasebeta

← #16782170

Subgroups — #16782170

Order 3328.

588 conjugacy classes of subgroups; only the 108 normal subgroups are shown.

normal subgroups only

This group has 588 conjugacy classes of subgroups — too many to draw. Only its 108 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#13130728C211yesmaximal, characteristic
2#13130012C211yesmaximal, characteristic
3#13129709C212yesmaximal
4#13129709C212yesmaximal
5#13117240C211yesmaximal, characteristic
6C2×#88126—21no—
7C2×C42×D13C2211yescharacteristic
8C2×(C2×#261)⋊C4—21no—
9C2×(C2×#261)⋊C4—21no—
10C2×(C2×#261)⋊C4C2212yes—
11C2×#88111C2212yes—
12C4×C13×C4⋊C4C411yescharacteristic, complemented
13#11718648C2211yescharacteristic
14#11718648C2211yescharacteristic
15#11718637C411yescharacteristic, complemented
16#11718637C411yescharacteristic, complemented
17C4×C4⋊Dic13C411yescharacteristic, complemented
18C4×#6101—21no—
19#11718328—21no—
20#11718311—21no—
21#11718290—21no—
22#11718290—21no—
23C23×#261—22no—
24C22×C4×D13D411yescharacteristic
25C22×C4×D13D411yescharacteristic
26C22×C4×D13C2311yescharacteristic
27C22×#1057—22no—
28C2×C13×C4⋊C4C2×C411yescharacteristic
29C2×C13×C4⋊C4C2×C411yescharacteristic
30C2×C42×C13—21no—
31C2×C42×C13C2×C411yescharacteristic
32C2×#6103—21no—
33C2×#6103—21no—
34C2×C4⋊Dic13C2×C411yescharacteristic
35C2×C4⋊Dic13C2×C411yescharacteristic
36C2×#6101—21no—
37C2×#6101—21no—
38C2×#6101—21no—
39C2×#6101—21no—
40C2×C4×Dic13—21no—
41C2×C4×Dic13C2×C411yescharacteristic
42C2×C4×Dic13D411yescharacteristic
43C2×C4×Dic13D411yescharacteristic
44#88126—44no—
45C42×D13—24no—
46(C2×#261)⋊C4—24no—
47(C2×#261)⋊C4—24no—
48(C2×#261)⋊C4—42no—
49#88111—24no—
50C13×#95—21no—
51#88071—21no—
52#88071—21no—
53#88071—21no—
54#8717—131nomaximal, Sylow
55C23×D13C2×D411yescharacteristic
56C22×#261—24no—
57C22×#261—42no—
58C22×#261—42no—
59C22×#261—42no—
60C22×#261—42no—
61C22×#261—42no—
62C22×#261—42no—
63C22×C4×C13—21no—
64C22×C4×C13—21no—
65C22×C4×C13C22⋊C411yescharacteristic
66C22×C4×C13C22⋊C411yescharacteristic
67C22×C4×C13C22×C411yescharacteristic
68C22×Dic13—21no—
69C22×Dic13—21no—
70C22×Dic13C22⋊C411yescharacteristic
71C22×Dic13C22⋊C411yescharacteristic
72C22×Dic13C2×D411yescharacteristic
73C2×C4×D13—22no—
74C2×C4×D13—22no—
75C2×C4×D13—22no—
76C2×C4×D13—22no—
77C2×C4×D13—41no—
78C2×C4×D13—41no—
79C2×C4×D13—41no—
80C2×C4×D13SD1612yes—
81C2×C4×D13Q1612yes—
82C2×C4×D13#4114yes—
83C2×#1057—42no—
84C2×#1057—42no—
85C2×#1057—42no—
86C13×C4⋊C4—41no—
87C13×C4⋊C4—41no—
88C42×C13—22no—
89C42×C13—42no—
90#6103—42no—
91#6103—42no—
92C4⋊Dic13—41no—
93C4⋊Dic13—41no—
94#6101—42no—
95#6101—42no—
96#6101—42no—
97#6101—42no—
98C4×Dic13—22no—
99C4×Dic13—22no—
100C4×Dic13—22no—
101C4×Dic13—42no—
102#2285—131no—
103#1817—131no—
104#1434—131no—
105#1294—132no—
106#1294—132no—
107C23×C13C2×C22⋊C411yescharacteristic
108C22×D13—21no—
109C22×D13—21no—
110C22×D13—21no—
111C22×D13—21no—
112C22×D13#12312yes—
113C22×D13C2×SD1611yescharacteristic
114C22×D13C2×Q1611yescharacteristic
115C22×D13AGL(1,ℤ/8)12yes—
116C2×#261—44no—
117C2×#261—44no—
118C2×#261—44no—
119C2×#261—82no—
120C2×#261—82no—
121C2×#261—82no—
122C2×#261—82no—
123C2×C4×C13—21no—
124C2×C4×C13—21no—
125C2×C4×C13—21no—
126C2×C4×C13—21no—
127C2×C4×C13—21no—
128C2×C4×C13—21no—
129C2×C4×C13—21no—
130C2×C4×C13—41no—
131C2×C4×C13—41no—
132C2×C4×C13—41no—
133C2×C4×C13—41no—
134C2×C4×C13—41no—
135C2×C4×C13—41no—
136C2×C4×C13#10312yes—
137C2×C4×C13#11712yes—
138C2×Dic13—21no—
139C2×Dic13—21no—
140C2×Dic13—21no—
141C2×Dic13—21no—
142C2×Dic13—21no—
143C2×Dic13—21no—
144C2×Dic13—41no—
145C2×Dic13—41no—
146C2×Dic13—41no—
147C2×Dic13—41no—
148C2×Dic13—41no—
149C2×Dic13—41no—
150C2×Dic13#10312yes—
151C2×Dic13#10412yes—
152C2×Dic13#12312yes—
153C4×D13—24no—
154C4×D13—24no—
155C4×D13—44no—
156C4×D13—44no—
157#1057—82no—
158C2×#117—261no—
159C22×C42—131no—
160C2×C22⋊C8—132no—
161#384—131no—
162#384—131no—
163#382—261no—
164#380—131no—
165#380—131no—
166#380—261no—
167C4×C4⋊C4—131no—
168C4×C4⋊C4—261no—
169C4×C4⋊C4#26111yescharacteristic, complemented
170C2×#95—132no—
171C2×#95—261no—
172C2×#95—261no—
173#336—261no—
174#336—261no—
175C22×C13#38111yescharacteristic
176C22×C13#41011yescharacteristic
177C22×C13#41011yescharacteristic
178C22×C13C2×#10311yescharacteristic
179C22×C13#41811yescharacteristic
180C22×C13C2×#10411yescharacteristic
181C22×C13#42111yescharacteristic
182C2×D13—22no—
183C2×D13—22no—
184C2×D13—21no—
185C2×D13—21no—
186C2×D13—22no—
187C2×D13—22no—
188C2×D13—21no—
189C2×D13—21no—
190C2×D13#48112yes—
191C2×D13#48412yes—
192#261—84no—
193C4×C13—22no—
194C4×C13—22no—
195C4×C13—41no—
196C4×C13—81no—
197C4×C13—81no—
198Dic13—22no—
199Dic13—22no—
200Dic13—22no—
201Dic13—81no—
202Dic13—81no—
203C23×C4—131no—
204C23×C4—131no—
205C23×C4—131no—
206C23×C4—262no—
207C22×C8—262no—
208#117—524no—
209C2×C4⋊C4—131no—
210C2×C4⋊C4—131no—
211C2×C4⋊C4—261no—
212C2×C4⋊C4—261no—
213C2×C4⋊C4—261no—
214C2×C4⋊C4—261no—
215C2×C4⋊C4C2×#26111yescharacteristic
216C2×C4⋊C4C2×#26111yescharacteristic
217C2×C22⋊C4—261no—
218C2×C22⋊C4—261no—
219C2×C42—21no—
220C2×C42—131no—
221C2×C42—131no—
222C2×C42—131no—
223C2×C42—264no—
224C2×C42—261no—
225C2×C42C2×#26111yescharacteristic
226C22⋊C8—264no—
227#95—21no—
228#95—261no—
229#95—261no—
230#95—264no—
231#95—264no—
232#95—261no—
233#95—522no—
234C2×C13#150311yescharacteristic
235C2×C13#150511yescharacteristic
236C2×C13#151411yescharacteristic
237C2×C13#151811yescharacteristic
238C2×C13#182011yescharacteristic
239C2×C13#182411yescharacteristic
240C2×C13#182611yescharacteristic
241D13—22no—
242D13—22no—
243C24—131no—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—131no—
247C22×C4—131no—
248C22×C4—131no—
249C22×C4—132no—
250C22×C4—132no—
251C22×C4—134no—
252C22×C4—262no—
253C22×C4—262no—
254C22×C4—262no—
255C22×C4—262no—
256C22×C4—264no—
257C22×C4—261no—
258C22×C4—261no—
259C22×C4—521no—
260C22×C4—521no—
261C22×C4—521no—
262C22×C4—522no—
263C22×C4—522no—
264C22×C4—522no—
265C22×C4—522no—
266C22×C4—522no—
267C22×C4—522no—
268C22×C4C22⋊#26111yescharacteristic
269C22×C4C22⋊#26111yescharacteristic
270C22×C4C22×#26111yescharacteristic
271C2×C8—522no—
272C2×C8—522no—
273C2×C8—522no—
274C4⋊C4—41no—
275C4⋊C4—41no—
276C4⋊C4—521no—
277C4⋊C4—521no—
278C4⋊C4—522no—
279C4⋊C4—522no—
280C4⋊C4—522no—
281C4⋊C4—522no—
282C22⋊C4—522no—
283C22⋊C4—522no—
284C42—22no—
285C42—42no—
286C42—262no—
287C42—262no—
288C42—262no—
289C42—522no—
290C13#871711yescharacteristic, complemented, Sylow
291C23—132no—
292C23—132no—
293C23—131no—
294C23—131no—
295C23—261no—
296C23—261no—
297C23—261no—
298C23—261no—
299C23C2×C22⋊#26111yescharacteristic
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—132no—
314C2×C4—132no—
315C2×C4—132no—
316C2×C4—264no—
317C2×C4—264no—
318C2×C4—261no—
319C2×C4—261no—
320C2×C4—261no—
321C2×C4—261no—
322C2×C4—261no—
323C2×C4—261no—
324C2×C4—524no—
325C2×C4—524no—
326C2×C4—524no—
327C2×C4—524no—
328C2×C4—524no—
329C2×C4—521no—
330C2×C4—521no—
331C2×C4—521no—
332C2×C4—521no—
333C2×C4—521no—
334C2×C4—521no—
335C2×C4—1042no—
336C2×C4—1042no—
337C2×C4—1042no—
338C2×C4—1042no—
339C2×C4#8811712yes—
340C2×C4#8823712yes—
341C8—1042no—
342C22—132no—
343C22—132no—
344C22—262no—
345C22—261no—
346C22—261no—
347C22—261no—
348C22—261no—
349C22—262no—
350C22—262no—
351C22—262no—
352C22#1171911611yescharacteristic
353C22#1171911611yescharacteristic
354C22#1171913511yescharacteristic
355C22#1171913811yescharacteristic
356C22C2×#8811711yescharacteristic
357C22D13⋊#10411yescharacteristic
358C22#1171916611yescharacteristic
359C4—22no—
360C4—22no—
361C4—41no—
362C4—81no—
363C4—81no—
364C4—262no—
365C4—262no—
366C4—262no—
367C4—1044no—
368C4—1041no—
369C4—1041no—
370C2—262no—
371C2—262no—
372C2#1313021811yescharacteristic
373C2#1313022611yescharacteristic
374C2#1313025511yescharacteristic
375C2#1313026911yescharacteristic
376C2#1313073311yescharacteristic
377C2#1313074011yescharacteristic
378C2#1313074411yescharacteristic
subgroupG/H
centerC23C2×C22⋊#261
commutatorC22×C4×C13C22×C4
FrattiniC22×C4C22×#261
FittingC4×C13×C4⋊C4C4
socleC23×C13C2×C22⋊C4
prime radicalC23×D13C2×D4
cosocleC22×C4×D13C23
hypercenterC4×C4⋊C4#261
hypocenterC13#8717
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
12. C4×C13×C4⋊C4C4semidirect
15. #11718637C4semidirect
16. #11718637C4semidirect
17. C4×C4⋊Dic13C4semidirect
169. C4×C4⋊C4#261semidirect
290. C13#8717semidirect

Maximal subgroups

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

subgroupindex
#131307282
#131300122
#131297092
#131172402
#871713