Finite Group Databasebeta

← #15773641

Subgroups — #15773641

Order 3328.

496 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 496 conjugacy classes of subgroups — too many to draw. Only its 87 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
2#13113163C211yesmaximal, characteristic
3#13112860C212yesmaximal, complemented
4#13112857C212yesmaximal, complemented
5C13×#2626C211yesmaximal, characteristic
6C2×C13×C22⋊Q8C411yescharacteristic, complemented
7C22×C13×C22⋊C4C2211yescharacteristic
8C13×#399C411yescharacteristic, complemented
9C13×#399C2211yescharacteristic
10C13×#396—21no—
11C13×#396—21no—
12C13×#393C411yescharacteristic, complemented
13C13×#393C2211yescharacteristic
14C13×#385—21no—
15C13×#380C411yescharacteristic, complemented
16C13×#379—21no—
17#11718908—21no—
18#11718868—21no—
19#11718118—21no—
20#11718118C2212yes—
21#11718117—21no—
22#11718117C2212yes—
23C25×C13D411yescharacteristic
24C22×Q8×C13C2×C411yescharacteristic
25C23×C4×C13C2×C411yescharacteristic
26C23×C4×C13D411yescharacteristic
27C13×C22⋊Q8—41no—
28C13×C22⋊Q8—41no—
29C2×C13×C4⋊C4—21no—
30C2×C13×C4⋊C4—21no—
31C2×C13×C4⋊C4—21no—
32C2×C13×C4⋊C4—21no—
33C2×C13×C4⋊C4C2×C411yescharacteristic
34C2×C13×C22⋊C4—21no—
35C2×C13×C22⋊C4—21no—
36C2×C13×C22⋊C4—21no—
37C2×C13×C22⋊C4—21no—
38C2×C13×C22⋊C4—21no—
39C2×C13×C22⋊C4—21no—
40C2×C13×C22⋊C4—41no—
41C2×C13×C22⋊C4—41no—
42C2×C13×C22⋊C4C2×C411yescharacteristic
43C2×C13×C22⋊C4D411yescharacteristic
44C2×C13×C22⋊C4D411yescharacteristic
45C2×C13×C22⋊C4C2311yescharacteristic
46C2×C22⋊Dic13—22no—
47C2×C22⋊Dic13—41no—
48C2×C22⋊Dic13—41no—
49C2×#6099—41no—
50C13×#95—21no—
51C13×#95—21no—
52C13×#95C2×C411yescharacteristic
53C13×#95C2×C411yescharacteristic
54C22⋊#1055—22no—
55C22⋊#1055—41no—
56#11811—131nomaximal, Sylow
57C24×C13—21no—
58C24×C13—21no—
59C24×C13—22no—
60C24×C13—41no—
61C24×C13—81no—
62C24×C13—81no—
63C24×C13C22⋊C411yescharacteristic
64C24×C13C22⋊C411yescharacteristic
65C24×C13C2×D411yescharacteristic
66C2×Q8×C13—41no—
67C2×Q8×C13—81no—
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—21no—
75C22×C4×C13—21no—
76C22×C4×C13—81no—
77C22×C4×C13—81no—
78C22×C4×C13C22⋊C411yescharacteristic
79C22×C4×C13C22⋊C411yescharacteristic
80C22×C4×C13C22×C411yescharacteristic
81C22×C4×C13C2×D411yescharacteristic
82C22×Dic13—42no—
83C13×C4⋊C4—41no—
84C13×C4⋊C4—42no—
85C13×C4⋊C4—81no—
86C13×C4⋊C4—81no—
87C13×C4⋊C4—81no—
88C13×C22⋊C4—41no—
89C13×C22⋊C4—41no—
90C13×C22⋊C4—41no—
91C13×C22⋊C4—41no—
92C13×C22⋊C4—42no—
93C13×C22⋊C4—41no—
94C13×C22⋊C4—41no—
95C13×C22⋊C4—81no—
96C13×C22⋊C4—81no—
97C13×C22⋊C4—81no—
98C13×C22⋊C4—81no—
99C22⋊Dic13—42no—
100C22⋊Dic13—42no—
101C22⋊Dic13—82no—
102C22⋊Dic13—82no—
103#6099—82no—
104C2×#1055—42no—
105#2626D1311yescharacteristic
106#1819—131no—
107#1462—131no—
108#1352—132no—
109#1351—132no—
110C23×C13—21no—
111C23×C13—21no—
112C23×C13—21no—
113C23×C13—21no—
114C23×C13—21no—
115C23×C13—21no—
116C23×C13—21no—
117C23×C13—41no—
118C23×C13—41no—
119C23×C13—42no—
120C23×C13—42no—
121C23×C13—41no—
122C23×C13—41no—
123C23×C13—41no—
124C23×C13—41no—
125C23×C13—42no—
126C23×C13—42no—
127C23×C13—81no—
128C23×C13—81no—
129C23×C13—84no—
130C23×C13—84no—
131C23×C13#9911yescharacteristic
132C23×C13#9911yescharacteristic
133C23×C13C2×C22⋊C411yescharacteristic
134C23×C13#13712yes—
135Q8×C13—82no—
136C2×C4×C13—21no—
137C2×C4×C13—21no—
138C2×C4×C13—21no—
139C2×C4×C13—21no—
140C2×C4×C13—42no—
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—41no—
157C2×C4×C13—81no—
158C2×C4×C13—81no—
159C2×C4×C13—81no—
160C2×Dic13—82no—
161C2×Dic13—82no—
162C2×Dic13—82no—
163#1055—82no—
164C2×C22⋊Q8Dic1311yescharacteristic, complemented
165C22×C22⋊C4C2×D1311yescharacteristic
166#407—261no—
167#399Dic1311yescharacteristic, complemented
168#399C2×D1311yescharacteristic
169#396—21no—
170#396—21no—
171#393Dic1311yescharacteristic, complemented
172#393C2×D1311yescharacteristic
173#385—21no—
174#380Dic1311yescharacteristic, complemented
175#379—21no—
176#379—261no—
177#342—132no—
178#342—261no—
179#323—132no—
180#323—261no—
181C22×C13—21no—
182C22×C13—21no—
183C22×C13—21no—
184C22×C13—21no—
185C22×C13—21no—
186C22×C13—21no—
187C22×C13—22no—
188C22×C13—21no—
189C22×C13—21no—
190C22×C13—42no—
191C22×C13—42no—
192C22×C13—42no—
193C22×C13—42no—
194C22×C13—41no—
195C22×C13—41no—
196C22×C13—41no—
197C22×C13—41no—
198C22×C13—41no—
199C22×C13—81no—
200C22×C13—81no—
201C22×C13—84no—
202C22×C13—84no—
203C22×C13C2×#9911yescharacteristic
204C22×C13#41911yescharacteristic
205C22×C13#42111yescharacteristic
206C4×C13—41no—
207C4×C13—41no—
208C4×C13—41no—
209C4×C13—41no—
210C4×C13—81no—
211C4×C13—81no—
212C4×C13—81no—
213C4×C13—81no—
214Dic13—162no—
215C25C22⋊D1311yescharacteristic
216C22×Q8C2×Dic1311yescharacteristic
217C23×C4C2×Dic1311yescharacteristic
218C23×C4C22⋊D1311yescharacteristic
219C2×M16—521no—
220C22⋊Q8—41no—
221C22⋊Q8—41no—
222C2×C4⋊C4—21no—
223C2×C4⋊C4—21no—
224C2×C4⋊C4—21no—
225C2×C4⋊C4—21no—
226C2×C4⋊C4C2×Dic1311yescharacteristic
227C2×C22⋊C4—21no—
228C2×C22⋊C4—21no—
229C2×C22⋊C4—21no—
230C2×C22⋊C4—21no—
231C2×C22⋊C4—21no—
232C2×C22⋊C4—21no—
233C2×C22⋊C4—41no—
234C2×C22⋊C4—41no—
235C2×C22⋊C4—262no—
236C2×C22⋊C4—521no—
237C2×C22⋊C4—521no—
238C2×C22⋊C4C2×Dic1311yescharacteristic
239C2×C22⋊C4C22⋊D1311yescharacteristic
240C2×C22⋊C4C22⋊D1311yescharacteristic
241C2×C22⋊C4C22×D1311yescharacteristic
242C22⋊C8—262no—
243C22⋊C8—521no—
244#95—21no—
245#95—21no—
246#95C2×Dic1311yescharacteristic
247#95C2×Dic1311yescharacteristic
248C2×C13—21no—
249C2×C13—21no—
250C2×C13—42no—
251C2×C13—41no—
252C2×C13—41no—
253C2×C13—81no—
254C2×C13#151111yescharacteristic
255C2×C13#212111yescharacteristic
256C2×C13#212711yescharacteristic
257C24—21no—
258C24—21no—
259C24—22no—
260C24—41no—
261C24—81no—
262C24—81no—
263C24C22⋊Dic1311yescharacteristic
264C24C22⋊Dic1311yescharacteristic
265C24C2×C22⋊D1311yescharacteristic
266C2×Q8—41no—
267C2×Q8—81no—
268C22×C4—21no—
269C22×C4—21no—
270C22×C4—21no—
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—21no—
274C22×C4—21no—
275C22×C4—21no—
276C22×C4—81no—
277C22×C4—81no—
278C22×C4—522no—
279C22×C4C22⋊Dic1311yescharacteristic
280C22×C4C22⋊Dic1311yescharacteristic
281C22×C4C22×Dic1311yescharacteristic
282C22×C4C2×C22⋊D1311yescharacteristic
283M16—1042no—
284C2×C8—522no—
285C4⋊C4—41no—
286C4⋊C4—42no—
287C4⋊C4—81no—
288C4⋊C4—81no—
289C4⋊C4—81no—
290C22⋊C4—41no—
291C22⋊C4—41no—
292C22⋊C4—41no—
293C22⋊C4—41no—
294C22⋊C4—42no—
295C22⋊C4—41no—
296C22⋊C4—41no—
297C22⋊C4—81no—
298C22⋊C4—81no—
299C22⋊C4—81no—
300C22⋊C4—81no—
301C22⋊C4—522no—
302C22⋊C4—522no—
303C22⋊C4—1042no—
304C22⋊C4—1042no—
305C13#1181111yescharacteristic, complemented, Sylow
306C23—21no—
307C23—21no—
308C23—21no—
309C23—21no—
310C23—21no—
311C23—21no—
312C23—21no—
313C23—41no—
314C23—41no—
315C23—42no—
316C23—42no—
317C23—41no—
318C23—41no—
319C23—41no—
320C23—41no—
321C23—42no—
322C23—42no—
323C23—81no—
324C23—81no—
325C23—84no—
326C23—84no—
327C23#8807411yescharacteristic
328C23#8807411yescharacteristic
329C23#8819612yes—
330C23C2×C22⋊Dic1311yescharacteristic
331Q8—82no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—42no—
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—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—81no—
354C2×C4—81no—
355C2×C4—81no—
356C2×C4—1042no—
357C2×C4—1042no—
358C2×C4—1042no—
359C8—1042no—
360C22—21no—
361C22—21no—
362C22—22no—
363C22—21no—
364C22—21no—
365C22—21no—
366C22—21no—
367C22—21no—
368C22—21no—
369C22—42no—
370C22—42no—
371C22—42no—
372C22—42no—
373C22—41no—
374C22—41no—
375C22—41no—
376C22—41no—
377C22—41no—
378C22—81no—
379C22—81no—
380C22—84no—
381C22—84no—
382C22C2×#8807411yescharacteristic
383C22#1171888611yescharacteristic
384C22#1171889711yescharacteristic
385C4—41no—
386C4—41no—
387C4—41no—
388C4—41no—
389C4—81no—
390C4—81no—
391C4—81no—
392C4—81no—
393C4—2082no—
394C2—21no—
395C2—21no—
396C2—42no—
397C2—41no—
398C2—41no—
399C2—81no—
400C2#1311336911yescharacteristic
401C2#1311648211yescharacteristic
402C2#1311650511yescharacteristic
subgroupG/H
centerC22C2×#88074
commutatorC22×C4×C13C22×C4
FrattiniC2×C22⋊C4C22×D13
FittingC13×#2626C2
socleC22×C13C2×#99
prime radicalC25×C13D4
cosocleC2×C13×C22⋊C4C23
hypercenter#2626D13
hypocenterC13#11811
LCSG ▷ C22×C4×C13 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C24 ◁ C22×C22⋊C4 ◁ #2626

Complements

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

NH ≅ G/Ntype
3. #13112860C2semidirect
4. #13112857C2semidirect
6. C2×C13×C22⋊Q8C4semidirect
8. C13×#399C4semidirect
12. C13×#393C4semidirect
15. C13×#380C4semidirect
164. C2×C22⋊Q8Dic13semidirect
167. #399Dic13semidirect
171. #393Dic13semidirect
174. #380Dic13semidirect
305. C13#11811semidirect

Maximal subgroups

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

subgroupindex
#131149102
#131131632
#131128602
#131128572
C13×#26262
#1181113