Finite Group Databasebeta

← #15763640

Subgroups — #15763640

Order 3328.

510 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 510 conjugacy classes of subgroups — too many to draw. Only its 89 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×#11718705C211yesmaximal, characteristic
2C2×#11718704C211yesmaximal, characteristic
3#13114914C211yesmaximal, characteristic
4#13113200C211yesmaximal, characteristic
5#13113200C211yesmaximal, characteristic
6#13112723C211yesmaximal, characteristic
7C13×#3195C211yesmaximal, characteristic
8C2×C13×C22⋊Q8C2211yescharacteristic
9C2×C13×C22⋊Q8C2211yescharacteristic
10C22×C4⋊Dic13C2211yescharacteristic
11C13×#483—21no—
12C13×#483—21no—
13C13×#470—22no—
14C13×#451—21no—
15C13×#451—21no—
16C13×#407C2211yescharacteristic
17C2×#88075—21no—
18C2×#88075—21no—
19#11718868C2211yescharacteristic
20C2×C22⋊#1055C2211yescharacteristic
21C2×C22⋊#1055C2211yescharacteristic
22#11718705—22no—
23#11718705—22no—
24#11718704—22no—
25#11718704—22no—
26C2×#88048—21no—
27C2×#88047—21no—
28#11718146—22no—
29#11718120—22no—
30#11718120—22no—
31C22×Q8×C13D411yescharacteristic
32C22×Q8×C13D411yescharacteristic
33C23×C4×C13C2311yescharacteristic
34C23×Dic13—21no—
35C2×C13×Q16—22no—
36C2×C13×M16D412yes—
37C13×C22⋊Q8—21no—
38C13×C22⋊Q8—21no—
39C13×C22⋊Q8—21no—
40C13×C22⋊Q8—21no—
41C13×C22⋊Q8—21no—
42C13×C22⋊Q8—21no—
43C13×C22⋊Q8—21no—
44C13×C22⋊Q8—21no—
45C2×C13×C4⋊C4—21no—
46C2×C13×C4⋊C4—21no—
47C2×C13×C4⋊C4D411yescharacteristic
48C2×C13×C4⋊C4D411yescharacteristic
49C2×C13×C22⋊C4—21no—
50C2×C13×C22⋊C4—21no—
51C2×C4⋊Dic13—21no—
52C2×C4⋊Dic13—21no—
53C2×C4⋊Dic13—21no—
54C2×C4⋊Dic13—21no—
55C2×C4⋊Dic13—21no—
56C2×C4⋊Dic13D412yes—
57C2×#6099—21no—
58C22×#1055—21no—
59C22×#1055—21no—
60C13×#106—22no—
61C13×#103—22no—
62C13×#103—22no—
63C13×C22⋊C8—21no—
64C13×C22⋊C8—21no—
65#88075—24no—
66#88075—24no—
67C22⋊#1055—21no—
68C22⋊#1055—21no—
69C22⋊#1055—21no—
70C22⋊#1055—21no—
71C22⋊#1055D412yes—
72C22⋊#1055D412yes—
73#88048—24no—
74#88047—24no—
75#9995—131nomaximal, Sylow
76C24×C13#4111yescharacteristic
77C2×Q8×C13—21no—
78C2×Q8×C13—21no—
79C2×Q8×C13—21no—
80C2×Q8×C13—21no—
81C2×Q8×C13—42no—
82C2×Q8×C13—42no—
83C22×C4×C13—21no—
84C22×C4×C13—21no—
85C22×C4×C13—21no—
86C22×C4×C13—21no—
87C22×C4×C13—42no—
88C22×C4×C13C2×D411yescharacteristic
89C22×C4×C13C2×D411yescharacteristic
90C22×C4×C13C2×D411yescharacteristic
91C22×C4×C13C2×D411yescharacteristic
92C22×C4×C13C2×D411yescharacteristic
93C22×C4×C13C2×D411yescharacteristic
94C22×Dic13—22no—
95C22×Dic13—41no—
96C22×Dic13—41no—
97C22×Dic13—82no—
98C13×Q16—82no—
99C13×M16—42no—
100C2×C8×C13—22no—
101C13×C4⋊C4—21no—
102C13×C4⋊C4—21no—
103C13×C4⋊C4—21no—
104C13×C4⋊C4—21no—
105C13×C4⋊C4—41no—
106C13×C4⋊C4—41no—
107C13×C4⋊C4—41no—
108C13×C4⋊C4—41no—
109C13×C22⋊C4—41no—
110C13×C22⋊C4—41no—
111C13×C22⋊C4—41no—
112C13×C22⋊C4—41no—
113C4⋊Dic13—22no—
114C4⋊Dic13—22no—
115C4⋊Dic13—41no—
116C4⋊Dic13—41no—
117#6099—42no—
118C2×#1055—22no—
119C2×#1055—22no—
120C2×#1055—42no—
121C2×#1055—42no—
122C2×#1055—41no—
123#3195D1311yescharacteristic
124C2×#484—131no—
125C2×#483—131no—
126#1821—131no—
127#1472—131no—
128#1472—131no—
129#1298—131no—
130C23×C13—22no—
131C23×C13—22no—
132C23×C13—41no—
133C23×C13#12111yescharacteristic
134C23×C13#12111yescharacteristic
135C23×C13#12111yescharacteristic
136Q8×C13—42no—
137Q8×C13—42no—
138Q8×C13—42no—
139Q8×C13—42no—
140C2×C4×C13—22no—
141C2×C4×C13—22no—
142C2×C4×C13—22no—
143C2×C4×C13—41no—
144C2×C4×C13—41no—
145C2×C4×C13—41no—
146C2×C4×C13—41no—
147C2×C4×C13—41no—
148C2×C4×C13—41no—
149C2×C4×C13—41no—
150C2×C4×C13—42no—
151C2×C4×C13—42no—
152C2×C4×C13—81no—
153C2×C4×C13—81no—
154C2×C4×C13#12011yescharacteristic
155C2×C4×C13#12011yescharacteristic
156C2×C4×C13#12011yescharacteristic
157C2×C4×C13#12711yescharacteristic
158C2×Dic13—42no—
159C2×Dic13—82no—
160C2×Dic13—82no—
161C2×Dic13—82no—
162C8×C13—42no—
163#1055—42no—
164#1055—42no—
165#1055—81no—
166C2×C22⋊Q8C2×D1311yescharacteristic
167C2×C22⋊Q8C2×D1311yescharacteristic
168C22×C4⋊C4—131no—
169#484—262no—
170#484—262no—
171#483—21no—
172#483—21no—
173#483—262no—
174#483—262no—
175#470—22no—
176#451—21no—
177#451—21no—
178C2×#107—261no—
179C2×#106—261no—
180C2×#103—261no—
181C2×#103—261no—
182#407—131no—
183#407C2×D1311yescharacteristic
184C2×C22⋊C8—131no—
185C2×C22⋊C8—131no—
186#343—262no—
187#324—262no—
188#324—262no—
189C22×C13—21no—
190C22×C13—21no—
191C22×C13—21no—
192C22×C13—21no—
193C22×C13—21no—
194C22×C13—21no—
195C22×C13—21no—
196C22×C13—44no—
197C22×C13#39211yescharacteristic
198C22×C13#47112yes—
199C22×C13#47312yes—
200C4×C13—21no—
201C4×C13—21no—
202C4×C13—21no—
203C4×C13—81no—
204C4×C13—81no—
205C4×C13—81no—
206C4×C13—81no—
207C4×C13#45812yes—
208Dic13—82no—
209C22×Q8C22⋊D1311yescharacteristic
210C22×Q8C22⋊D1311yescharacteristic
211C23×C4—261no—
212C23×C4C22×D1311yescharacteristic
213C2×Q16—22no—
214C2×M16—261no—
215C2×M16C22⋊D1312yes—
216C22×C8—261no—
217C22×C8—261no—
218C22⋊Q8—21no—
219C22⋊Q8—21no—
220C22⋊Q8—21no—
221C22⋊Q8—21no—
222C22⋊Q8—21no—
223C22⋊Q8—21no—
224C22⋊Q8—21no—
225C22⋊Q8—21no—
226C2×C4⋊C4—21no—
227C2×C4⋊C4—21no—
228C2×C4⋊C4—132no—
229C2×C4⋊C4—261no—
230C2×C4⋊C4—261no—
231C2×C4⋊C4—261no—
232C2×C4⋊C4—261no—
233C2×C4⋊C4—261no—
234C2×C4⋊C4C22⋊D1311yescharacteristic
235C2×C4⋊C4C22⋊D1311yescharacteristic
236C2×C22⋊C4—21no—
237C2×C22⋊C4—21no—
238#107—264no—
239#106—22no—
240#106—264no—
241#103—22no—
242#103—22no—
243#103—264no—
244#103—264no—
245C22⋊C8—21no—
246C22⋊C8—21no—
247C22⋊C8—132no—
248C22⋊C8—132no—
249C22⋊C8—261no—
250C22⋊C8—261no—
251C22⋊C8—261no—
252C22⋊C8—261no—
253C2×C13—22no—
254C2×C13—22no—
255C2×C13—41no—
256C2×C13#201911yescharacteristic
257C2×C13#202011yescharacteristic
258C2×C13#202211yescharacteristic
259C24#612911yescharacteristic
260C2×Q8—21no—
261C2×Q8—21no—
262C2×Q8—21no—
263C2×Q8—21no—
264C2×Q8—42no—
265C2×Q8—42no—
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—21no—
270C22×C4—42no—
271C22×C4—262no—
272C22×C4—521no—
273C22×C4—521no—
274C22×C4—1042no—
275C22×C4D4×D1311yescharacteristic
276C22×C4D4×D1311yescharacteristic
277C22×C4D4×D1311yescharacteristic
278C22×C4C2×C22⋊D1311yescharacteristic
279C22×C4C2×C22⋊D1311yescharacteristic
280C22×C4C2×C22⋊D1311yescharacteristic
281Q16—82no—
282M16—42no—
283M16—522no—
284C2×C8—22no—
285C2×C8—262no—
286C2×C8—262no—
287C2×C8—522no—
288C2×C8—522no—
289C2×C8—521no—
290C4⋊C4—21no—
291C4⋊C4—21no—
292C4⋊C4—21no—
293C4⋊C4—21no—
294C4⋊C4—41no—
295C4⋊C4—41no—
296C4⋊C4—41no—
297C4⋊C4—41no—
298C4⋊C4—262no—
299C4⋊C4—262no—
300C4⋊C4—521no—
301C4⋊C4—521no—
302C22⋊C4—41no—
303C22⋊C4—41no—
304C22⋊C4—41no—
305C22⋊C4—41no—
306C13#999511yescharacteristic, complemented, Sylow
307C23—22no—
308C23—22no—
309C23—41no—
310C23#8819211yescharacteristic
311C23#8819311yescharacteristic
312C23#8819311yescharacteristic
313Q8—42no—
314Q8—42no—
315Q8—42no—
316Q8—42no—
317C2×C4—22no—
318C2×C4—22no—
319C2×C4—22no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—42no—
324C2×C4—42no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—81no—
330C2×C4—81no—
331C2×C4—522no—
332C2×C4—1042no—
333C2×C4—1042no—
334C2×C4—1042no—
335C2×C4#8819111yescharacteristic
336C2×C4#8819111yescharacteristic
337C2×C4#8819411yescharacteristic
338C2×C4#8820711yescharacteristic
339C8—42no—
340C8—522no—
341C8—522no—
342C8—1041no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—21no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—44no—
351C22#1171886412yes—
352C22#1171886512yes—
353C22#1171888411yescharacteristic
354C4—21no—
355C4—21no—
356C4—21no—
357C4—81no—
358C4—81no—
359C4—81no—
360C4—81no—
361C4—1042no—
362C4#1171890412yes—
363C2—22no—
364C2—22no—
365C2—41no—
366C2#1311594711yescharacteristic
367C2#1311595411yescharacteristic
368C2#1311596511yescharacteristic
subgroupG/H
centerC22#11718884
commutator, cosocleC23×C4×C13C23
FrattiniC23×C4C22×D13
FittingC13×#3195C2
socleC22×C13#392
prime radicalC24×C13#41
hypercenter#3195D13
hypocenterC13#9995
LCSG ▷ C23×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3195

Complements

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

NH ≅ G/Ntype
306. C13#9995semidirect

Maximal subgroups

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

subgroupindex
C2×#117187052
C2×#117187042
#131149142
#131132002
#131127232
C13×#31952
#999513