Finite Group Databasebeta

← #15766264

Subgroups — #15766264

Order 3328.

620 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 620 conjugacy classes of subgroups — too many to draw. Only its 117 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#13115144C212yesmaximal
2C2×#11718130C212yesmaximal
3#13113100C211yesmaximal, characteristic
4#13112679C211yesmaximal, characteristic
5C13×#2659C211yesmaximal, characteristic
6C2×C13×C22⋊Q8C2212yes—
7C22×C4⋊Dic13C2211yescharacteristic
8C22×#6101—21no—
9C13×#398—22no—
10C13×#395—22no—
11C13×#380—21no—
12C13×#380—21no—
13C2×C13×#95C2211yescharacteristic
14C2×#88075—22no—
15C2×#88071—21no—
16C2×#88071C2211yescharacteristic
17C2×C22⋊#1055C2212yes—
18#11718130—24no—
19#11718121—22no—
20C22×Q8×C13D412yes—
21C23×C4×C13D411yescharacteristic
22C23×C4×C13D411yescharacteristic
23C23×C4×C13C2311yescharacteristic
24C23×Dic13—21no—
25C23×Dic13—21no—
26C13×C22⋊Q8—22no—
27C13×C22⋊Q8—22no—
28C13×C22⋊Q8—22no—
29C13×C22⋊Q8—22no—
30C2×C13×C4⋊C4—22no—
31C2×C13×C4⋊C4—21no—
32C2×C13×C4⋊C4—21no—
33C2×C13×C4⋊C4—21no—
34C2×C13×C4⋊C4—21no—
35C2×C13×C4⋊C4D412yes—
36C2×C13×C22⋊C4—22no—
37C2×C4⋊Dic13—22no—
38C2×C4⋊Dic13—42no—
39C2×#6101—42no—
40C2×#6101—42no—
41C2×#6101—42no—
42C22×#1055—22no—
43C13×#95—22no—
44C13×#95—22no—
45C13×#95—22no—
46#88075—44no—
47#88071—21no—
48#88071—42no—
49#88071D412yes—
50C22⋊#1055—22no—
51C22⋊#1055—22no—
52#10406—131nomaximal, Sylow
53C24×C13C2×D411yescharacteristic
54C2×Q8×C13—22no—
55C2×Q8×C13—22no—
56C2×Q8×C13—42no—
57C2×Q8×C13—42no—
58C22×C4×C13—21no—
59C22×C4×C13—21no—
60C22×C4×C13—21no—
61C22×C4×C13—21no—
62C22×C4×C13—22no—
63C22×C4×C13—22no—
64C22×C4×C13—41no—
65C22×C4×C13—41no—
66C22×C4×C13—41no—
67C22×C4×C13—41no—
68C22×C4×C13—41no—
69C22×C4×C13—41no—
70C22×C4×C13SD1612yes—
71C22×C4×C13Q1612yes—
72C22×C4×C13C2×D411yescharacteristic
73C22×C4×C13C2×D412yes—
74C22×C4×C13#4112yes—
75C22×C4×C13#4111yescharacteristic
76C22×Dic13—22no—
77C22×Dic13—22no—
78C22×Dic13—22no—
79C22×Dic13—22no—
80C22×Dic13—41no—
81C22×Dic13—41no—
82C22×Dic13—41no—
83C22×Dic13—41no—
84C22×Dic13—41no—
85C22×Dic13—41no—
86C22×Dic13—41no—
87C22×Dic13—41no—
88C22×Dic13—41no—
89C22×Dic13—41no—
90C13×C4⋊C4—22no—
91C13×C4⋊C4—22no—
92C13×C4⋊C4—42no—
93C13×C4⋊C4—42no—
94C13×C4⋊C4—81no—
95C13×C4⋊C4—81no—
96C13×C4⋊C4—81no—
97C13×C4⋊C4—81no—
98C13×C22⋊C4—42no—
99C13×C22⋊C4—42no—
100C4⋊Dic13—24no—
101C4⋊Dic13—42no—
102#6101—48no—
103C2×#1055—42no—
104C2×#1055—42no—
105C2×#1055—42no—
106#2659D1311yescharacteristic
107#1872—132no—
108C2×#328—132no—
109#1444—131no—
110#1280—131no—
111C23×C13—21no—
112C23×C13—21no—
113C23×C13—21no—
114C23×C13—21no—
115C23×C13#12011yescharacteristic
116C23×C13#12111yescharacteristic
117C23×C13#12411yescharacteristic
118C23×C13C2×SD1611yescharacteristic
119C23×C13C2×Q1611yescharacteristic
120C23×C13#13711yescharacteristic
121C23×C13#13711yescharacteristic
122Q8×C13—44no—
123Q8×C13—82no—
124C2×C4×C13—22no—
125C2×C4×C13—22no—
126C2×C4×C13—22no—
127C2×C4×C13—22no—
128C2×C4×C13—41no—
129C2×C4×C13—42no—
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—42no—
139C2×C4×C13—42no—
140C2×C4×C13—42no—
141C2×C4×C13—42no—
142C2×C4×C13—42no—
143C2×C4×C13—81no—
144C2×C4×C13—81no—
145C2×C4×C13#12112yes—
146C2×C4×C13#12312yes—
147C2×Dic13—24no—
148C2×Dic13—42no—
149C2×Dic13—42no—
150C2×Dic13—42no—
151C2×Dic13—42no—
152C2×Dic13—42no—
153C2×Dic13—42no—
154C2×Dic13—42no—
155C2×Dic13—42no—
156C2×Dic13—42no—
157C2×Dic13—81no—
158C2×Dic13—81no—
159C2×Dic13—81no—
160C2×Dic13—81no—
161#1055—82no—
162C2×C22⋊Q8C2×D1312yes—
163C22×C4⋊C4—131no—
164C22×C4⋊C4—261no—
165C2×#103—262no—
166C2×C22⋊C8—132no—
167#398—22no—
168#395—22no—
169#380—21no—
170#380—21no—
171C2×#95—131no—
172C2×#95—261no—
173C2×#95C2×D1311yescharacteristic
174#340—262no—
175#328—264no—
176C22×C13—21no—
177C22×C13—21no—
178C22×C13—21no—
179C22×C13—21no—
180C22×C13—21no—
181C22×C13—21no—
182C22×C13—21no—
183C22×C13—21no—
184C22×C13—21no—
185C22×C13—21no—
186C22×C13—21no—
187C22×C13—21no—
188C22×C13#39411yescharacteristic
189C22×C13#44811yescharacteristic
190C22×C13#45111yescharacteristic
191C22×C13#45311yescharacteristic
192C22×C13#45611yescharacteristic
193C22×C13B(4,𝔽2)11yescharacteristic
194C22×C13#45811yescharacteristic
195C22×C13#46111yescharacteristic
196C22×C13#46211yescharacteristic
197C22×C13#48711yescharacteristic
198C22×C13#49111yescharacteristic
199C4×C13—22no—
200C4×C13—22no—
201C4×C13—42no—
202C4×C13—42no—
203C4×C13—82no—
204C4×C13—82no—
205Dic13—44no—
206Dic13—82no—
207C22×Q8C22⋊D1312yes—
208C23×C4—261no—
209C23×C4—261no—
210C23×C4C22⋊D1311yescharacteristic
211C23×C4C22⋊D1311yescharacteristic
212C23×C4C22×D1311yescharacteristic
213C22×C8—262no—
214C22⋊Q8—22no—
215C22⋊Q8—22no—
216C22⋊Q8—22no—
217C22⋊Q8—22no—
218C2×C4⋊C4—22no—
219C2×C4⋊C4—21no—
220C2×C4⋊C4—21no—
221C2×C4⋊C4—21no—
222C2×C4⋊C4—21no—
223C2×C4⋊C4—262no—
224C2×C4⋊C4—522no—
225C2×C4⋊C4—522no—
226C2×C4⋊C4—522no—
227C2×C4⋊C4—522no—
228C2×C4⋊C4C22⋊D1312yes—
229C2×C22⋊C4—22no—
230#103—524no—
231C22⋊C8—262no—
232C22⋊C8—262no—
233#95—22no—
234#95—22no—
235#95—22no—
236#95—132no—
237#95—261no—
238#95—522no—
239C2×C13—21no—
240C2×C13—21no—
241C2×C13—21no—
242C2×C13—21no—
243C2×C13#159611yescharacteristic
244C2×C13#160511yescharacteristic
245C2×C13#161111yescharacteristic
246C2×C13#161411yescharacteristic
247C2×C13#203911yescharacteristic
248C2×C13#204311yescharacteristic
249C2×C13#204411yescharacteristic
250C24C2×C22⋊D1311yescharacteristic
251C2×Q8—22no—
252C2×Q8—22no—
253C2×Q8—42no—
254C2×Q8—42no—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—22no—
260C22×C4—22no—
261C22×C4—41no—
262C22×C4—41no—
263C22×C4—41no—
264C22×C4—41no—
265C22×C4—41no—
266C22×C4—41no—
267C22×C4—262no—
268C22×C4—262no—
269C22×C4—262no—
270C22×C4—262no—
271C22×C4—521no—
272C22×C4—521no—
273C22×C4—521no—
274C22×C4—521no—
275C22×C4—521no—
276C22×C4—521no—
277C22×C4—521no—
278C22×C4—521no—
279C22×C4—521no—
280C22×C4—521no—
281C22×C4#610612yes—
282C22×C4#610712yes—
283C22×C4D4×D1311yescharacteristic
284C22×C4#612911yescharacteristic
285C22×C4#612912yes—
286C22×C4C2×C22⋊D1312yes—
287C2×C8—522no—
288C2×C8—522no—
289C2×C8—522no—
290C4⋊C4—22no—
291C4⋊C4—22no—
292C4⋊C4—42no—
293C4⋊C4—42no—
294C4⋊C4—81no—
295C4⋊C4—81no—
296C4⋊C4—81no—
297C4⋊C4—81no—
298C4⋊C4—264no—
299C4⋊C4—522no—
300C4⋊C4—528no—
301C22⋊C4—42no—
302C22⋊C4—42no—
303C13#1040611yescharacteristic, complemented, Sylow
304C23—21no—
305C23—21no—
306C23—21no—
307C23—21no—
308C23#8819011yescharacteristic
309C23#8819211yescharacteristic
310C23C2×#610611yescharacteristic
311C23#8819611yescharacteristic
312C23#8819611yescharacteristic
313C23C2×#610711yescharacteristic
314C23#8820711yescharacteristic
315Q8—44no—
316Q8—82no—
317C2×C4—22no—
318C2×C4—22no—
319C2×C4—22no—
320C2×C4—22no—
321C2×C4—41no—
322C2×C4—42no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—42no—
329C2×C4—42no—
330C2×C4—42no—
331C2×C4—42no—
332C2×C4—42no—
333C2×C4—42no—
334C2×C4—42no—
335C2×C4—42no—
336C2×C4—81no—
337C2×C4—81no—
338C2×C4—264no—
339C2×C4—522no—
340C2×C4—522no—
341C2×C4—522no—
342C2×C4—522no—
343C2×C4—522no—
344C2×C4—522no—
345C2×C4—522no—
346C2×C4—522no—
347C2×C4—522no—
348C2×C4—1041no—
349C2×C4—1041no—
350C2×C4—1041no—
351C2×C4—1041no—
352C2×C4#8818912yes—
353C2×C4#8819312yes—
354C8—1042no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—21no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—21no—
363C22—21no—
364C22—21no—
365C22—21no—
366C22—21no—
367C22#1171874211yescharacteristic
368C22#1171874311yescharacteristic
369C22#1171874411yescharacteristic
370C22#1171875111yescharacteristic
371C22#1171888311yescharacteristic
372C22#1171888811yescharacteristic
373C22#1171888911yescharacteristic
374C22#1171890211yescharacteristic
375C22#1171890411yescharacteristic
376C22#1171890511yescharacteristic
377C22#1171890711yescharacteristic
378C4—22no—
379C4—22no—
380C4—42no—
381C4—42no—
382C4—82no—
383C4—82no—
384C4—524no—
385C4—1042no—
386C2—21no—
387C2—21no—
388C2—21no—
389C2—21no—
390C2#1311375911yescharacteristic
391C2#1311381011yescharacteristic
392C2#1311384411yescharacteristic
393C2#1311386111yescharacteristic
394C2#1311605711yescharacteristic
395C2#1311607911yescharacteristic
396C2#1311608411yescharacteristic
subgroupG/H
centerC23#88207
commutator, cosocleC23×C4×C13C23
FrattiniC23×C4C22×D13
FittingC13×#2659C2
socleC23×C13#120
prime radicalC24×C13C2×D4
hypercenter#2659D13
hypocenterC13#10406
LCSG ▷ C23×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2659

Complements

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

NH ≅ G/Ntype
303. C13#10406semidirect

Maximal subgroups

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

subgroupindex
#131151442
C2×#117181302
#131131002
#131126792
C13×#26592
#1040613