Finite Group Databasebeta

← #15781604

Subgroups — #15781604

Order 3328.

420 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 93 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#13120046C211yesmaximal, characteristic
2#13114830C211yesmaximal, characteristic
3#101×Dic13C211yesmaximal, characteristic
4#13112963C211yesmaximal, characteristic
5#13112962C211yesmaximal, characteristic
6#13112962C211yesmaximal, characteristic
7C13×#1394C211yesmaximal, characteristic
8C2×Q8×Dic13C2211yescharacteristic
9C2×#88142C411yescharacteristic
10C2×C13×#101C2211yescharacteristic
11C2×C13×#101C2211yescharacteristic
12C13×#391C2211yescharacteristic
13#11718891C2211yescharacteristic
14C2×#88076C2211yescharacteristic
15C2×#88076C2211yescharacteristic
16#11718779—21no—
17M16×Dic13—21no—
18#11718637C411yescharacteristic
19#11718596C411yescharacteristic
20C4×#6101C411yescharacteristic
21#11718317—21no—
22#11718317—21no—
23#11718308—21no—
24#11718308—21no—
25#11718146—21no—
26#11718146—21no—
27C22×Q8×C13C2311yescharacteristic
28C22×Dic26—21no—
29C2×C13×M16—21no—
30C2×C13×M16—21no—
31C2×C13×C4⋊C4C2×C411yescharacteristic
32C2×C42×C13C2×C411yescharacteristic
33Q8×Dic13—41no—
34Q8×Dic13—41no—
35C2×C4⋊Dic13—21no—
36C2×C4⋊Dic13—21no—
37C2×C4⋊Dic13C2×C411yescharacteristic
38C2×C4⋊Dic13C2×C411yescharacteristic
39C2×C4⋊Dic13D411yescharacteristic
40C2×C4⋊Dic13D411yescharacteristic
41C2×#6101—21no—
42C2×#6101—21no—
43C2×#6101—21no—
44C2×#6101—21no—
45C2×C4×Dic13C2×C411yescharacteristic
46C2×C4×Dic13C2×C411yescharacteristic
47C2×C4×Dic13D411yescharacteristic
48C2×C4×Dic13D411yescharacteristic
49C2×#6099—21no—
50C2×#6099—21no—
51#88142—41no—
52#88142—41no—
53C13×#101—21no—
54C13×#101—21no—
55C13×#101—21no—
56C13×#101Q812yescomplemented
57C13×#95—21no—
58C13×#95—21no—
59#88076—21no—
60#88076—21no—
61#88076—21no—
62#88076Q812yescomplemented
63#88071—21no—
64#88071—21no—
65#88071—21no—
66#88055—41no—
67#88054—41no—
68#88054—41no—
69C8×Dic13—41no—
70#13302—131nomaximal, Sylow
71C2×Q8×C13—41no—
72C2×Q8×C13—41no—
73C2×Q8×C13C2×Q811yescharacteristic
74C2×Q8×C13C2×Q811yescharacteristic
75C2×Q8×C13#4111yescharacteristic
76C2×Q8×C13#4111yescharacteristic
77C22×C4×C13—21no—
78C22×C4×C13—21no—
79C22×C4×C13C22×C411yescharacteristic
80C22×C4×C13C2×D411yescharacteristic
81C22×C4×C13C2×D411yescharacteristic
82C22×Dic13—21no—
83C22×Dic13—21no—
84C22×Dic13C22⋊C411yescharacteristic
85C22×Dic13C22⋊C411yescharacteristic
86C22×Dic13C22⋊C411yescharacteristic
87C22×Dic13C22⋊C411yescharacteristic
88C2×Dic26—42no—
89C2×Dic26—81no—
90C2×Dic26—81no—
91C13×M16—22no—
92C13×M16—41no—
93C13×M16—41no—
94C13×M16—41no—
95C2×C8×C13—41no—
96C2×C8×C13—41no—
97C13×C4⋊C4—41no—
98C42×C13—41no—
99C4⋊Dic13—41no—
100C4⋊Dic13—41no—
101C4⋊Dic13—41no—
102C4⋊Dic13—41no—
103C4⋊Dic13—81no—
104C4⋊Dic13—81no—
105#6101—24no—
106#6101—41no—
107#6101—41no—
108#6101—81no—
109#6101—81no—
110C4×Dic13—21no—
111C4×Dic13—21no—
112C4×Dic13—21no—
113C4×Dic13—21no—
114C4×Dic13—21no—
115C4×Dic13—21no—
116C4×Dic13—41no—
117#6099—22no—
118#6099—41no—
119#6099—41no—
120#6099—41no—
121C2×#1055—41no—
122C2×#1055—41no—
123#2567—131no—
124#1801—131no—
125C4×#101—131no—
126#1394—131no—
127#1394—131no—
128#1394—131no—
129#1394D1311yescharacteristic
130C23×C13C2×C22⋊C411yescharacteristic
131Q8×C13—41no—
132Q8×C13—41no—
133Q8×C13—41no—
134Q8×C13—41no—
135C2×C4×C13—21no—
136C2×C4×C13—21no—
137C2×C4×C13—21no—
138C2×C4×C13—21no—
139C2×C4×C13—21no—
140C2×C4×C13—21no—
141C2×C4×C13—22no—
142C2×C4×C13—41no—
143C2×C4×C13—41no—
144C2×C4×C13—41no—
145C2×C4×C13—41no—
146C2×C4×C13—41no—
147C2×C4×C13C4×Q811yescharacteristic
148C2×C4×C13C4×Q811yescharacteristic
149C2×C4×C13C22⋊Q811yescharacteristic
150C2×C4×C13C22⋊Q811yescharacteristic
151C2×C4×C13#12411yescharacteristic
152C2×C4×C13C4⋊Q811yescharacteristic
153C2×Dic13—22no—
154C2×Dic13—22no—
155C2×Dic13—21no—
156C2×Dic13—21no—
157C2×Dic13—21no—
158C2×Dic13—41no—
159C2×Dic13—41no—
160C2×Dic13—41no—
161C2×Dic13—41no—
162C2×Dic13—41no—
163C2×Dic13—41no—
164C2×Dic13—41no—
165C2×Dic13—41no—
166C2×Dic13#9911yescharacteristic
167C2×Dic13#9911yescharacteristic
168Dic26—84no—
169C8×C13—42no—
170C8×C13—81no—
171#1055—42no—
172#1055—81no—
173C2×C4⋊Q8—131no—
174C2×C4×Q8—131no—
175#423—261no—
176C2×#101—131no—
177C2×#101—131no—
178C2×#101C2×D1311yescharacteristic
179C2×#101C2×D1311yescharacteristic
180C4×M16—261no—
181#395—261no—
182#395—261no—
183#391—131no—
184#391C2×D1311yescharacteristic
185#389—261no—
186#389—261no—
187#384—131no—
188#384—131no—
189C4×C4⋊C4—131no—
190#343—261no—
191#343—261no—
192C22×C13—21no—
193C22×C13—21no—
194C22×C13#39111yescharacteristic
195C22×C13C2×#9911yescharacteristic
196C22×C13#41011yescharacteristic
197C4×C13—21no—
198C4×C13—21no—
199C4×C13—21no—
200C4×C13—21no—
201C4×C13—21no—
202C4×C13—21no—
203C4×C13—42no—
204C4×C13—81no—
205Dic13—21no—
206Dic13—42no—
207Dic13—41no—
208Dic13—41no—
209Dic13—41no—
210Dic13—81no—
211Dic13#35612yes—
212C22×Q8—261no—
213C22×Q8C22×D1311yescharacteristic
214C2×M16—21no—
215C2×M16—21no—
216C2×M16—261no—
217C2×M16—261no—
218C4⋊Q8—521no—
219C4⋊Q8—521no—
220C4×Q8—521no—
221C4×Q8—521no—
222C2×C4⋊C4—131no—
223C2×C4⋊C4—131no—
224C2×C4⋊C4—131no—
225C2×C4⋊C4—131no—
226C2×C4⋊C4—261no—
227C2×C4⋊C4—261no—
228C2×C4⋊C4—261no—
229C2×C4⋊C4—261no—
230C2×C4⋊C4—261no—
231C2×C4⋊C4—261no—
232C2×C4⋊C4C4×D1311yescharacteristic
233C2×C42—131no—
234C2×C42—131no—
235C2×C42—131no—
236C2×C42—131no—
237C2×C42C4×D1311yescharacteristic
238C4⋊C8—521no—
239C4⋊C8—521no—
240#101—21no—
241#101—21no—
242#101—21no—
243#101—132no—
244#101—261no—
245#101—261no—
246#101—261no—
247#101Dic2612yescomplemented
248#97—521no—
249C4×C8—521no—
250#95—21no—
251#95—21no—
252#95—261no—
253#95—261no—
254#95—261no—
255C2×C13—21no—
256C2×C13—21no—
257C2×C13#199611yescharacteristic
258C2×C13C2×#35611yescharacteristic
259C2×C13#213411yescharacteristic
260C2×Q8—41no—
261C2×Q8—41no—
262C2×Q8—522no—
263C2×Q8—1041no—
264C2×Q8—1041no—
265C2×Q8C2×Dic2611yescharacteristic
266C2×Q8#612711yescharacteristic
267C2×Q8#612911yescharacteristic
268C2×Q8Q8×D1311yescharacteristic
269C22×C4—21no—
270C22×C4—21no—
271C22×C4—131no—
272C22×C4—131no—
273C22×C4—131no—
274C22×C4—131no—
275C22×C4—261no—
276C22×C4—261no—
277C22×C4C2×C4×D1311yescharacteristic
278C22×C4D4×D1311yescharacteristic
279C22×C4D4×D1311yescharacteristic
280M16—22no—
281M16—41no—
282M16—41no—
283M16—41no—
284M16—262no—
285M16—521no—
286M16—521no—
287M16—521no—
288C2×C8—41no—
289C2×C8—41no—
290C2×C8—521no—
291C2×C8—521no—
292C4⋊C4—41no—
293C4⋊C4—264no—
294C4⋊C4—521no—
295C4⋊C4—521no—
296C4⋊C4—521no—
297C4⋊C4—521no—
298C4⋊C4—521no—
299C4⋊C4—521no—
300C4⋊C4—1041no—
301C4⋊C4—1041no—
302C4⋊C4—1041no—
303C4⋊C4—1041no—
304C42—41no—
305C42—261no—
306C42—261no—
307C42—261no—
308C42—261no—
309C42—261no—
310C42—261no—
311C42—521no—
312C13#1330211yescharacteristic, complemented, Sylow
313C23C22⋊C4×D1311yescharacteristic
314Q8—41no—
315Q8—41no—
316Q8—41no—
317Q8—41no—
318Q8—1044no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—22no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—131no—
332C2×C4—131no—
333C2×C4—262no—
334C2×C4—262no—
335C2×C4—261no—
336C2×C4—261no—
337C2×C4—261no—
338C2×C4—521no—
339C2×C4—521no—
340C2×C4—521no—
341C2×C4—521no—
342C2×C4—521no—
343C2×C4—521no—
344C2×C4—521no—
345C2×C4—521no—
346C2×C4C4×Dic2611yescharacteristic
347C2×C4#8813211yescharacteristic
348C2×C4#8813911yescharacteristic
349C2×C4#8814111yescharacteristic
350C2×C4#8814211yescharacteristic
351C2×C4#8815011yescharacteristic
352C8—42no—
353C8—81no—
354C8—522no—
355C8—1041no—
356C22—21no—
357C22—21no—
358C22#1171830711yescharacteristic
359C22#1171840111yescharacteristic
360C22D13×#9911yescharacteristic
361C4—21no—
362C4—21no—
363C4—21no—
364C4—21no—
365C4—21no—
366C4—21no—
367C4—42no—
368C4—81no—
369C4—132no—
370C4—261no—
371C4—522no—
372C4—521no—
373C4—521no—
374C4—521no—
375C4—1041no—
376C2—21no—
377C2—21no—
378C2#1311581911yescharacteristic
379C2D13×#35611yescharacteristic
380C2#1311652611yescharacteristic
subgroupG/H
centerC22D13×#99
commutatorC22×C4×C13C22×C4
FrattiniC22×Q8C22×D13
FittingC13×#1394C2
socleC22×C13C2×#99
prime radicalC23×C13C2×C22⋊C4
cosocleC22×Q8×C13C23
hypercenter#1394D13
hypocenterC13#13302
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23 ◁ C22×Q8 ◁ #1394

Complements

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

NH ≅ G/Ntype
56. C13×#101Q8semidirect
62. #88076Q8semidirect
247. #101Dic26semidirect
312. C13#13302semidirect

Maximal subgroups

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

subgroupindex
#131200462
#131148302
#101×Dic132
#131129632
#131129622
C13×#13942
#1330213