Finite Group Databasebeta

← #15773787

Subgroups — #15773787

Order 3328.

506 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 506 conjugacy classes of subgroups — too many to draw. Only its 91 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#13114910C211yesmaximal, characteristic
2C2×#11718117C211yesmaximal, characteristic
3#13112860C212yesmaximal, complemented
4#13112836C212yesmaximal, complemented
5C13×#2482C211yesmaximal, characteristic
6C2×C13×#117C411yescharacteristic, complemented
7C22×C13×C22⋊C4C2211yescharacteristic
8C13×#399C411yescharacteristic, complemented
9C13×#399C2211yescharacteristic
10C13×#397C411yescharacteristic, complemented
11C13×#397C2211yescharacteristic
12C13×#388—21no—
13C13×#388—21no—
14C13×#385—21no—
15C13×#381C411yescharacteristic, complemented
16C13×#379—21no—
17#11718908—21no—
18C2×C22⋊#1055—21no—
19#11718118—21no—
20#11718118C2212yes—
21#11718117—21no—
22#11718117C2212yes—
23C25×C13D411yescharacteristic
24C23×C4×C13C2×C411yescharacteristic
25C23×C4×C13D411yescharacteristic
26C13×#117—41no—
27C13×#117—41no—
28C2×C13×C4⋊C4—21no—
29C2×C13×C4⋊C4—21no—
30C2×C13×C4⋊C4C2×C411yescharacteristic
31C2×C13×C4⋊C4C2×C411yescharacteristic
32C2×C13×C22⋊C4—21no—
33C2×C13×C22⋊C4—21no—
34C2×C13×C22⋊C4—21no—
35C2×C13×C22⋊C4—21no—
36C2×C13×C22⋊C4—21no—
37C2×C13×C22⋊C4—21no—
38C2×C13×C22⋊C4—41no—
39C2×C13×C22⋊C4—41no—
40C2×C13×C22⋊C4C2×C411yescharacteristic
41C2×C13×C22⋊C4D411yescharacteristic
42C2×C13×C22⋊C4D411yescharacteristic
43C2×C13×C22⋊C4C2311yescharacteristic
44C2×C42×C13—21no—
45C2×C22⋊Dic13—22no—
46C2×C22⋊Dic13—41no—
47C2×C22⋊Dic13—41no—
48C22×#1055—41no—
49C13×#95—21no—
50C13×#95—21no—
51C13×#95—21no—
52C13×#95C2×C411yescharacteristic
53C13×#95C2×C411yescharacteristic
54C22⋊#1055—22no—
55C22⋊#1055—41no—
56#11841—131nomaximal, Sylow
57C24×C13—21no—
58C24×C13—21no—
59C24×C13—22no—
60C24×C13—41no—
61C24×C13—42no—
62C24×C13—81no—
63C24×C13C22⋊C411yescharacteristic
64C24×C13C22⋊C411yescharacteristic
65C24×C13C2×D411yescharacteristic
66C22×C4×C13—21no—
67C22×C4×C13—21no—
68C22×C4×C13—21no—
69C22×C4×C13—21no—
70C22×C4×C13—21no—
71C22×C4×C13—21no—
72C22×C4×C13—21no—
73C22×C4×C13—21no—
74C22×C4×C13—42no—
75C22×C4×C13—81no—
76C22×C4×C13C22⋊C411yescharacteristic
77C22×C4×C13C22⋊C411yescharacteristic
78C22×C4×C13C22×C411yescharacteristic
79C22×C4×C13C2×D411yescharacteristic
80C22×Dic13—42no—
81C13×C4⋊C4—41no—
82C13×C4⋊C4—41no—
83C13×C4⋊C4—81no—
84C13×C4⋊C4—81no—
85C13×C22⋊C4—41no—
86C13×C22⋊C4—41no—
87C13×C22⋊C4—41no—
88C13×C22⋊C4—41no—
89C13×C22⋊C4—42no—
90C13×C22⋊C4—42no—
91C13×C22⋊C4—41no—
92C13×C22⋊C4—41no—
93C13×C22⋊C4—42no—
94C13×C22⋊C4—81no—
95C13×C22⋊C4—81no—
96C42×C13—42no—
97C22⋊Dic13—42no—
98C22⋊Dic13—42no—
99C22⋊Dic13—82no—
100C22⋊Dic13—82no—
101C2×#1055—42no—
102C2×#1055—82no—
103#2482D1311yescharacteristic
104#1819—131no—
105C2×#323—131no—
106#1352—132no—
107#1344—132no—
108C23×C13—22no—
109C23×C13—21no—
110C23×C13—21no—
111C23×C13—21no—
112C23×C13—21no—
113C23×C13—21no—
114C23×C13—21no—
115C23×C13—21no—
116C23×C13—41no—
117C23×C13—42no—
118C23×C13—42no—
119C23×C13—41no—
120C23×C13—41no—
121C23×C13—41no—
122C23×C13—41no—
123C23×C13—42no—
124C23×C13—42no—
125C23×C13—81no—
126C23×C13—81no—
127C23×C13—84no—
128C23×C13—84no—
129C23×C13#9911yescharacteristic
130C23×C13#9911yescharacteristic
131C23×C13C2×C22⋊C411yescharacteristic
132C23×C13#13512yes—
133C2×C4×C13—21no—
134C2×C4×C13—21no—
135C2×C4×C13—21no—
136C2×C4×C13—21no—
137C2×C4×C13—42no—
138C2×C4×C13—42no—
139C2×C4×C13—42no—
140C2×C4×C13—41no—
141C2×C4×C13—41no—
142C2×C4×C13—41no—
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—41no—
151C2×C4×C13—41no—
152C2×C4×C13—41no—
153C2×C4×C13—41no—
154C2×C4×C13—41no—
155C2×C4×C13—41no—
156C2×C4×C13—81no—
157C2×Dic13—82no—
158C2×Dic13—82no—
159C2×Dic13—82no—
160#1055—82no—
161C2×#117Dic1311yescharacteristic, complemented
162C22×C22⋊C4C2×D1311yescharacteristic
163C2×C22⋊C8—261no—
164#399Dic1311yescharacteristic, complemented
165#399C2×D1311yescharacteristic
166#397Dic1311yescharacteristic, complemented
167#397C2×D1311yescharacteristic
168#388—21no—
169#388—21no—
170#385—21no—
171#381Dic1311yescharacteristic, complemented
172#379—21no—
173#379—261no—
174#342—132no—
175#342—261no—
176#323—132no—
177#323—261no—
178C22×C13—21no—
179C22×C13—21no—
180C22×C13—21no—
181C22×C13—21no—
182C22×C13—21no—
183C22×C13—21no—
184C22×C13—22no—
185C22×C13—21no—
186C22×C13—42no—
187C22×C13—42no—
188C22×C13—42no—
189C22×C13—42no—
190C22×C13—41no—
191C22×C13—41no—
192C22×C13—41no—
193C22×C13—41no—
194C22×C13—41no—
195C22×C13—81no—
196C22×C13—84no—
197C22×C13—81no—
198C22×C13—84no—
199C22×C13#35212yes—
200C22×C13C2×#9911yescharacteristic
201C22×C13#41611yescharacteristic
202C22×C13#42111yescharacteristic
203C4×C13—41no—
204C4×C13—41no—
205C4×C13—41no—
206C4×C13—41no—
207C4×C13—81no—
208C4×C13—81no—
209C4×C13—81no—
210C4×C13—81no—
211Dic13—162no—
212C25C22⋊D1311yescharacteristic
213C23×C4C2×Dic1311yescharacteristic
214C23×C4C22⋊D1311yescharacteristic
215C22×C8—521no—
216#117—41no—
217#117—41no—
218C2×C4⋊C4—21no—
219C2×C4⋊C4—21no—
220C2×C4⋊C4C2×Dic1311yescharacteristic
221C2×C4⋊C4C2×Dic1311yescharacteristic
222C2×C22⋊C4—21no—
223C2×C22⋊C4—21no—
224C2×C22⋊C4—21no—
225C2×C22⋊C4—21no—
226C2×C22⋊C4—21no—
227C2×C22⋊C4—21no—
228C2×C22⋊C4—41no—
229C2×C22⋊C4—41no—
230C2×C22⋊C4—262no—
231C2×C22⋊C4—521no—
232C2×C22⋊C4—521no—
233C2×C22⋊C4C2×Dic1311yescharacteristic
234C2×C22⋊C4C22⋊D1311yescharacteristic
235C2×C22⋊C4C22⋊D1311yescharacteristic
236C2×C22⋊C4C22×D1311yescharacteristic
237C2×C42—21no—
238C22⋊C8—262no—
239C22⋊C8—521no—
240#95—21no—
241#95—21no—
242#95—21no—
243#95C2×Dic1311yescharacteristic
244#95C2×Dic1311yescharacteristic
245C2×C13—21no—
246C2×C13—21no—
247C2×C13—22no—
248C2×C13—42no—
249C2×C13—41no—
250C2×C13—81no—
251C2×C13#151611yescharacteristic
252C2×C13C2×#35211yescharacteristic
253C2×C13#212711yescharacteristic
254C24—21no—
255C24—21no—
256C24—22no—
257C24—41no—
258C24—42no—
259C24—81no—
260C24C22⋊Dic1311yescharacteristic
261C24C22⋊Dic1311yescharacteristic
262C24C2×C22⋊D1311yescharacteristic
263C22×C4—21no—
264C22×C4—21no—
265C22×C4—21no—
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—21no—
270C22×C4—21no—
271C22×C4—42no—
272C22×C4—81no—
273C22×C4—522no—
274C22×C4C22⋊Dic1311yescharacteristic
275C22×C4C22⋊Dic1311yescharacteristic
276C22×C4C22×Dic1311yescharacteristic
277C22×C4C2×C22⋊D1311yescharacteristic
278C2×C8—522no—
279C2×C8—1042no—
280C4⋊C4—41no—
281C4⋊C4—41no—
282C4⋊C4—81no—
283C4⋊C4—81no—
284C22⋊C4—41no—
285C22⋊C4—41no—
286C22⋊C4—41no—
287C22⋊C4—41no—
288C22⋊C4—42no—
289C22⋊C4—42no—
290C22⋊C4—41no—
291C22⋊C4—41no—
292C22⋊C4—42no—
293C22⋊C4—81no—
294C22⋊C4—81no—
295C22⋊C4—522no—
296C22⋊C4—522no—
297C22⋊C4—1042no—
298C22⋊C4—1042no—
299C42—42no—
300C13#1184111yescharacteristic, complemented, Sylow
301C23—21no—
302C23—21no—
303C23—21no—
304C23—22no—
305C23—21no—
306C23—21no—
307C23—21no—
308C23—21no—
309C23—41no—
310C23—42no—
311C23—42no—
312C23—41no—
313C23—41no—
314C23—41no—
315C23—41no—
316C23—42no—
317C23—42no—
318C23—81no—
319C23—81no—
320C23—84no—
321C23—84no—
322C23#8807411yescharacteristic
323C23#8807411yescharacteristic
324C23#8820412yes—
325C23C2×C22⋊Dic1311yescharacteristic
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—42no—
331C2×C4—42no—
332C2×C4—42no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—81no—
350C2×C4—1042no—
351C2×C4—1042no—
352C2×C4—1042no—
353C8—1042no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—22no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—42no—
363C22—42no—
364C22—42no—
365C22—42no—
366C22—41no—
367C22—41no—
368C22—41no—
369C22—41no—
370C22—41no—
371C22—81no—
372C22—84no—
373C22—81no—
374C22—84no—
375C22#1171813112yes—
376C22C2×#8807411yescharacteristic
377C22#1171889411yescharacteristic
378C22#1171889711yescharacteristic
379C4—41no—
380C4—41no—
381C4—41no—
382C4—41no—
383C4—81no—
384C4—81no—
385C4—81no—
386C4—81no—
387C4—2082no—
388C2—21no—
389C2—21no—
390C2—22no—
391C2—42no—
392C2—41no—
393C2—81no—
394C2#1311339211yescharacteristic
395C2C2×#1171813111yescharacteristic
396C2#1311650511yescharacteristic
subgroupG/H
centerC22C2×#88074
commutatorC22×C4×C13C22×C4
FrattiniC2×C22⋊C4C22×D13
FittingC13×#2482C2
socleC22×C13C2×#99
prime radicalC25×C13D4
cosocleC2×C13×C22⋊C4C23
hypercenter#2482D13
hypocenterC13#11841
LCSG ▷ C22×C4×C13 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C24 ◁ C22×C22⋊C4 ◁ #2482

Complements

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

NH ≅ G/Ntype
3. #13112860C2semidirect
4. #13112836C2semidirect
6. C2×C13×#117C4semidirect
8. C13×#399C4semidirect
10. C13×#397C4semidirect
15. C13×#381C4semidirect
161. C2×#117Dic13semidirect
164. #399Dic13semidirect
166. #397Dic13semidirect
171. #381Dic13semidirect
300. C13#11841semidirect

Maximal subgroups

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

subgroupindex
#131149102
C2×#117181172
#131128602
#131128362
C13×#24822
#1184113