Finite Group Databasebeta

← #15760376

Subgroups — #15760376

Order 3328.

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

normal subgroups only

This group has 526 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#13120217C211yesmaximal, characteristic
2#13117436C211yesmaximal, characteristic
3#13113356C211yesmaximal, characteristic
4#13113165C211yesmaximal, characteristic
5#13112722C211yesmaximal, characteristic
6#13112721C211yesmaximal, characteristic
7C13×#1508C211yesmaximal, characteristic
8C2×C13×C22⋊Q8C2211yescharacteristic
9C22×#6101C2211yescharacteristic
10C13×#407C2211yescharacteristic
11C4×C13×C22⋊C4C2211yescharacteristic
12#11718890C412yescomplemented
13C4×C22⋊Dic13C2211yescharacteristic
14C4×C22⋊Dic13C2211yescharacteristic
15#11718868C2211yescharacteristic
16#11718641C412yescomplemented
17#11718633—22no—
18#11718607—21no—
19#11718607—21no—
20#11718604—21no—
21#11718603—21no—
22#11718594—22no—
23#11718313—22no—
24C13×#328—22no—
25#11718130—22no—
26#11718061—22no—
27C22×Q8×C13C2×C411yescharacteristic
28C23×C4×C13C2311yescharacteristic
29C23×Dic13D411yescharacteristic
30C23×Dic13D411yescharacteristic
31C2×C13×M16—21no—
32C13×C22⋊Q8—21no—
33C13×C22⋊Q8—21no—
34C13×C22⋊Q8—21no—
35C13×C22⋊Q8—21no—
36C2×C13×C4⋊C4—21no—
37C2×C13×C4⋊C4C2×C411yescharacteristic
38C2×C13×C22⋊C4—21no—
39C2×C13×C22⋊C4—21no—
40C2×C42×C13—21no—
41C2×C22⋊Dic13—21no—
42C2×C22⋊Dic13—21no—
43C2×#6101—21no—
44C2×#6101—21no—
45C2×#6101—21no—
46C2×#6101—21no—
47C2×#6101—22no—
48C2×#6101—22no—
49C2×#6101—22no—
50C2×#6101C2×C412yes—
51C2×#6101D412yes—
52C2×C4×Dic13—21no—
53C2×C4×Dic13—21no—
54C2×#6099—21no—
55C13×C22⋊C8—21no—
56C13×C22⋊C8—21no—
57C13×#95D412yes—
58#88071—22no—
59#88071—24no—
60#88071—22no—
61#88071—22no—
62#88071C2×C412yes—
63#88071D412yes—
64C22⋊#1055—21no—
65C22⋊#1055—21no—
66#9412—131nomaximal, Sylow
67C24×C13C2×D411yescharacteristic
68C2×Q8×C13—21no—
69C2×Q8×C13—21no—
70C2×Q8×C13—81no—
71C22×C4×C13—21no—
72C22×C4×C13—21no—
73C22×C4×C13—22no—
74C22×C4×C13—81no—
75C22×C4×C13C22×C411yescharacteristic
76C22×C4×C13C2×D411yescharacteristic
77C22×C4×C13C2×D411yescharacteristic
78C22×C4×C13C2×D411yescharacteristic
79C22×C4×C13#4111yescharacteristic
80C22×C4×C13#4111yescharacteristic
81C22×Dic13—22no—
82C22×Dic13—21no—
83C22×Dic13—21no—
84C22×Dic13—21no—
85C22×Dic13—21no—
86C22×Dic13—22no—
87C22×Dic13—42no—
88C22×Dic13—81no—
89C22×Dic13C22⋊C412yes—
90C22×Dic13C22⋊C412yes—
91C13×M16—81no—
92C2×C8×C13—41no—
93C13×C4⋊C4—21no—
94C13×C4⋊C4—21no—
95C13×C4⋊C4—41no—
96C13×C4⋊C4—41no—
97C13×C22⋊C4—42no—
98C13×C22⋊C4—41no—
99C13×C22⋊C4—41no—
100C42×C13—81no—
101C22⋊Dic13—24no—
102C22⋊Dic13—42no—
103#6101—22no—
104#6101—22no—
105#6101—22no—
106#6101—22no—
107#6101—44no—
108#6101—82no—
109#6101—82no—
110C4×Dic13—81no—
111C4×Dic13—81no—
112#6099—81no—
113C2×#1055—41no—
114#2583—131no—
115#2313—131no—
116#1508—131no—
117#1508D1311yescharacteristic
118#1463—131no—
119#1297—131no—
120#1297—131no—
121C23×C13—22no—
122C23×C13—22no—
123C23×C13—41no—
124C23×C13C2×C22⋊C411yescharacteristic
125C23×C13#12011yescharacteristic
126C23×C13#12311yescharacteristic
127Q8×C13—81no—
128Q8×C13—81no—
129C2×C4×C13—41no—
130C2×C4×C13—41no—
131C2×C4×C13—41no—
132C2×C4×C13—41no—
133C2×C4×C13—41no—
134C2×C4×C13—41no—
135C2×C4×C13—42no—
136C2×C4×C13—42no—
137C2×C4×C13—42no—
138C2×C4×C13—41no—
139C2×C4×C13—41no—
140C2×C4×C13—42no—
141C2×C4×C13—42no—
142C2×C4×C13C4×D411yescharacteristic
143C2×C4×C13C4×D411yescharacteristic
144C2×C4×C13#12111yescharacteristic
145C2×C4×C13#12111yescharacteristic
146C2×Dic13—24no—
147C2×Dic13—22no—
148C2×Dic13—22no—
149C2×Dic13—22no—
150C2×Dic13—22no—
151C2×Dic13—42no—
152C2×Dic13—42no—
153C2×Dic13—42no—
154C2×Dic13—42no—
155C2×Dic13—42no—
156C2×Dic13—42no—
157C2×Dic13—42no—
158C2×Dic13—42no—
159C2×Dic13—42no—
160C2×Dic13—81no—
161C8×C13—81no—
162#1055—81no—
163C2×C22⋊Q8C2×D1311yescharacteristic
164C22×C4⋊C4—131no—
165#407—131no—
166#407C2×D1311yescharacteristic
167#398—132no—
168#395—132no—
169#389—262no—
170#387—262no—
171#387—262no—
172#385—261no—
173#385—261no—
174#381—261no—
175#380—261no—
176C4×C22⋊C4—131no—
177C4×C22⋊C4—131no—
178C4×C22⋊C4C2×D1311yescharacteristic
179#328—22no—
180#328—262no—
181#324—262no—
182C22×C13—21no—
183C22×C13—21no—
184C22×C13—21no—
185C22×C13—21no—
186C22×C13—21no—
187C22×C13—21no—
188C22×C13—21no—
189C22×C13—44no—
190C22×C13#38611yescharacteristic
191C22×C13#42112yes—
192C22×C13#45612yes—
193C4×C13—21no—
194C4×C13—21no—
195C4×C13—21no—
196C4×C13—21no—
197C4×C13—82no—
198C4×C13—81no—
199C4×C13—81no—
200Dic13—44no—
201Dic13—42no—
202Dic13—42no—
203Dic13—82no—
204C22×Q8C4×D1311yescharacteristic
205C23×C4—131no—
206C23×C4—131no—
207C23×C4C22×D1311yescharacteristic
208C2×M16—21no—
209C2×M16—261no—
210C22⋊Q8—21no—
211C22⋊Q8—21no—
212C22⋊Q8—21no—
213C22⋊Q8—21no—
214C2×C4⋊C4—21no—
215C2×C4⋊C4—132no—
216C2×C4⋊C4—132no—
217C2×C4⋊C4—261no—
218C2×C4⋊C4—261no—
219C2×C4⋊C4—261no—
220C2×C4⋊C4—261no—
221C2×C4⋊C4—262no—
222C2×C4⋊C4—262no—
223C2×C4⋊C4—262no—
224C2×C4⋊C4C4×D1311yescharacteristic
225C2×C22⋊C4—21no—
226C2×C22⋊C4—21no—
227C2×C22⋊C4—261no—
228C2×C22⋊C4—261no—
229C2×C42—21no—
230C2×C42—261no—
231C2×C42—261no—
232C22⋊C8—21no—
233C22⋊C8—21no—
234C22⋊C8—261no—
235C22⋊C8—261no—
236#95—132no—
237#95—132no—
238#95—262no—
239#95—262no—
240#95—262no—
241#95—264no—
242#95C22⋊D1312yes—
243C2×C13—22no—
244C2×C13—22no—
245C2×C13—41no—
246C2×C13#188611yescharacteristic
247C2×C13#189711yescharacteristic
248C2×C13#191311yescharacteristic
249C24D4×D1311yescharacteristic
250C2×Q8—21no—
251C2×Q8—21no—
252C2×Q8—81no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—22no—
256C22×C4—81no—
257C22×C4—132no—
258C22×C4—132no—
259C22×C4—262no—
260C22×C4—261no—
261C22×C4—261no—
262C22×C4—261no—
263C22×C4—261no—
264C22×C4—262no—
265C22×C4—522no—
266C22×C4—1041no—
267C22×C4C2×C4×D1311yescharacteristic
268C22×C4#612711yescharacteristic
269C22×C4D4×D1311yescharacteristic
270C22×C4D4×D1311yescharacteristic
271C22×C4#612911yescharacteristic
272C22×C4C2×C22⋊D1311yescharacteristic
273M16—81no—
274M16—1041no—
275C2×C8—41no—
276C2×C8—521no—
277C4⋊C4—21no—
278C4⋊C4—21no—
279C4⋊C4—41no—
280C4⋊C4—41no—
281C4⋊C4—262no—
282C4⋊C4—262no—
283C4⋊C4—262no—
284C4⋊C4—262no—
285C4⋊C4—524no—
286C4⋊C4—1042no—
287C4⋊C4—1042no—
288C22⋊C4—42no—
289C22⋊C4—41no—
290C22⋊C4—41no—
291C22⋊C4—264no—
292C22⋊C4—522no—
293C42—81no—
294C42—1041no—
295C42—1041no—
296C13#941211yescharacteristic, complemented, Sylow
297C23—22no—
298C23—22no—
299C23—41no—
300C23C22⋊C4×D1311yescharacteristic
301C23#8813711yescharacteristic
302C23#8819111yescharacteristic
303Q8—81no—
304Q8—81no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—42no—
312C2×C4—42no—
313C2×C4—42no—
314C2×C4—42no—
315C2×C4—42no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—264no—
319C2×C4—262no—
320C2×C4—262no—
321C2×C4—262no—
322C2×C4—262no—
323C2×C4—522no—
324C2×C4—522no—
325C2×C4—522no—
326C2×C4—522no—
327C2×C4—522no—
328C2×C4—522no—
329C2×C4—522no—
330C2×C4—522no—
331C2×C4—522no—
332C2×C4—1041no—
333C2×C4#8813511yescharacteristic
334C2×C4#8813811yescharacteristic
335C2×C4C4×C22⋊D1311yescharacteristic
336C2×C4#8819211yescharacteristic
337C8—81no—
338C8—1041no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—44no—
347C22#1171848212yes—
348C22#1171861711yescharacteristic
349C22#1171886612yes—
350C4—21no—
351C4—21no—
352C4—21no—
353C4—21no—
354C4—82no—
355C4—81no—
356C4—81no—
357C4—524no—
358C4—522no—
359C4—522no—
360C4—1042no—
361C2—22no—
362C2—22no—
363C2—41no—
364C2#1311522611yescharacteristic
365C2#1311528111yescharacteristic
366C2#1311537511yescharacteristic
subgroupG/H
centerC22#11718617
commutatorC22×C4×C13C22×C4
FrattiniC23×C4C22×D13
FittingC13×#1508C2
socleC22×C13#386
prime radicalC24×C13C2×D4
cosocleC23×C4×C13C23
hypercenter#1508D13
hypocenterC13#9412
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1508

Complements

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

NH ≅ G/Ntype
12. #11718890C4semidirect
16. #11718641C4semidirect
296. C13#9412semidirect

Maximal subgroups

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

subgroupindex
#131202172
#131174362
#131133562
#131131652
#131127222
#131127212
C13×#15082
#941213