Finite Group Databasebeta

← #15773685

Subgroups — #15773685

Order 3328.

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

normal subgroups only

This group has 582 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#13114824C211yesmaximal, characteristic, complemented
2#13113174C211yesmaximal, characteristic, complemented
3#13112860C212yesmaximal, complemented
4#13112833C212yesmaximal, complemented
5C13×#2397C211yesmaximal, characteristic
6C2×C4×D4×C13—21no—
7C2×C4×D4×C13—21no—
8C2×C4×D4×C13C411yescharacteristic, complemented
9C2×C4×D4×C13C2211yescharacteristic
10C13×#399—21no—
11C13×#399C411yescharacteristic, complemented
12C13×#399C2211yescharacteristic
13C13×#392—21no—
14C13×#392C411yescharacteristic, complemented
15C13×#392C2211yescharacteristic
16C13×#376C411yescharacteristic, complemented
17C2×#88074—21no—
18#11718873—21no—
19#11718868—21no—
20#11718120—21no—
21#11718118C2212yes—
22#11718117C2212yes—
23C22×D4×C13—21no—
24C22×D4×C13—21no—
25C22×D4×C13C2×C411yescharacteristic
26C22×D4×C13D411yescharacteristic
27C23×C4×C13—21no—
28C23×C4×C13D411yescharacteristic
29C23×C4×C13D411yescharacteristic
30C4×D4×C13—41no—
31C4×D4×C13—41no—
32C4×D4×C13—44no—
33C4×D4×C13—44no—
34C4×D4×C13—41no—
35C4×D4×C13—41no—
36C2×C13×C4⋊C4—21no—
37C2×C13×C4⋊C4—21no—
38C2×C13×C4⋊C4C2×C411yescharacteristic
39C2×C13×C4⋊C4D411yescharacteristic
40C2×C13×C22⋊C4—21no—
41C2×C13×C22⋊C4—21no—
42C2×C13×C22⋊C4—21no—
43C2×C13×C22⋊C4—21no—
44C2×C13×C22⋊C4—21no—
45C2×C13×C22⋊C4C2×C411yescharacteristic
46C2×C13×C22⋊C4C2311yescharacteristic
47C2×C42×C13—21no—
48C2×C42×C13C2×C411yescharacteristic
49C2×C22⋊Dic13—22no—
50C2×C4⋊Dic13—41no—
51C2×#6099—41no—
52C13×#95—21no—
53C13×#95C2×C411yescharacteristic
54C13×#95C2×C411yescharacteristic
55#88074—42no—
56#88071—41no—
57C22⋊#1055—22no—
58C22⋊#1055—41no—
59#11821—131nomaximal, Sylow
60C24×C13—21no—
61C24×C13C22⋊C411yescharacteristic
62C24×C13C2×D411yescharacteristic
63C2×D4×C13—21no—
64C2×D4×C13—21no—
65C2×D4×C13—41no—
66C2×D4×C13—41no—
67C2×D4×C13—41no—
68C2×D4×C13—42no—
69C2×D4×C13—42no—
70C2×D4×C13—42no—
71C2×D4×C13—42no—
72C2×D4×C13—42no—
73C2×D4×C13—41no—
74C2×D4×C13—41no—
75C2×D4×C13—42no—
76C22×C4×C13—21no—
77C22×C4×C13—21no—
78C22×C4×C13—21no—
79C22×C4×C13—21no—
80C22×C4×C13—21no—
81C22×C4×C13—21no—
82C22×C4×C13—21no—
83C22×C4×C13—42no—
84C22×C4×C13—42no—
85C22×C4×C13—42no—
86C22×C4×C13—42no—
87C22×C4×C13—41no—
88C22×C4×C13—41no—
89C22×C4×C13C22⋊C411yescharacteristic
90C22×C4×C13C22⋊C411yescharacteristic
91C22×C4×C13C22⋊C411yescharacteristic
92C22×C4×C13C22×C411yescharacteristic
93C22×C4×C13C2×D411yescharacteristic
94C22×Dic13—42no—
95C13×C4⋊C4—41no—
96C13×C4⋊C4—41no—
97C13×C4⋊C4—42no—
98C13×C4⋊C4—42no—
99C13×C22⋊C4—41no—
100C13×C22⋊C4—41no—
101C13×C22⋊C4—42no—
102C13×C22⋊C4—42no—
103C13×C22⋊C4—42no—
104C13×C22⋊C4—42no—
105C13×C22⋊C4—42no—
106C42×C13—24no—
107C42×C13—21no—
108C42×C13—21no—
109C22⋊Dic13—42no—
110C22⋊Dic13—42no—
111C4⋊Dic13—82no—
112#6099—82no—
113C2×#1055—42no—
114#2397D1311yescharacteristic
115#1799—131no—
116#1465—131no—
117#1352—132no—
118#1343—132no—
119C23×C13—21no—
120C23×C13—21no—
121C23×C13—22no—
122C23×C13—21no—
123C23×C13—21no—
124C23×C13—21no—
125C23×C13—41no—
126C23×C13—41no—
127C23×C13—41no—
128C23×C13—41no—
129C23×C13—41no—
130C23×C13—41no—
131C23×C13—41no—
132C23×C13—41no—
133C23×C13—41no—
134C23×C13—41no—
135C23×C13C2×C22⋊C411yescharacteristic
136C23×C13AGL(1,ℤ/8)11yescharacteristic
137C23×C13#13711yescharacteristic
138D4×C13—42no—
139D4×C13—42no—
140D4×C13—44no—
141D4×C13—44no—
142D4×C13—48no—
143D4×C13—42no—
144D4×C13—42no—
145C2×C4×C13—22no—
146C2×C4×C13—22no—
147C2×C4×C13—22no—
148C2×C4×C13—21no—
149C2×C4×C13—21no—
150C2×C4×C13—21no—
151C2×C4×C13—21no—
152C2×C4×C13—21no—
153C2×C4×C13—21no—
154C2×C4×C13—41no—
155C2×C4×C13—41no—
156C2×C4×C13—41no—
157C2×C4×C13—41no—
158C2×C4×C13—42no—
159C2×C4×C13—42no—
160C2×C4×C13—41no—
161C2×C4×C13—41no—
162C2×C4×C13—41no—
163C2×C4×C13—41no—
164C2×C4×C13—41no—
165C2×C4×C13—41no—
166C2×C4×C13—81no—
167C2×C4×C13—81no—
168C2×C4×C13—82no—
169C2×C4×C13—82no—
170C2×C4×C13#9911yescharacteristic
171C2×C4×C13#9911yescharacteristic
172C2×Dic13—82no—
173C2×Dic13—82no—
174C2×Dic13—82no—
175#1055—82no—
176C2×C4×D4—21no—
177C2×C4×D4—21no—
178C2×C4×D4Dic1311yescharacteristic, complemented
179C2×C4×D4C2×D1311yescharacteristic
180C2×#99—261no—
181#407—261no—
182#399—21no—
183#399Dic1311yescharacteristic, complemented
184#399C2×D1311yescharacteristic
185#392—21no—
186#392Dic1311yescharacteristic, complemented
187#392C2×D1311yescharacteristic
188#380—261no—
189#376Dic1311yescharacteristic, complemented
190#342—132no—
191#324—261no—
192#323—132no—
193C22×C13—21no—
194C22×C13—21no—
195C22×C13—21no—
196C22×C13—21no—
197C22×C13—41no—
198C22×C13—41no—
199C22×C13—42no—
200C22×C13—42no—
201C22×C13—42no—
202C22×C13—41no—
203C22×C13—41no—
204C22×C13—42no—
205C22×C13—41no—
206C22×C13—41no—
207C22×C13—41no—
208C22×C13—81no—
209C22×C13—81no—
210C22×C13—81no—
211C22×C13—81no—
212C22×C13—81no—
213C22×C13—81no—
214C22×C13C2×#9911yescharacteristic
215C22×C13#41711yescharacteristic
216C22×C13#42111yescharacteristic
217C4×C13—21no—
218C4×C13—42no—
219C4×C13—42no—
220C4×C13—41no—
221C4×C13—41no—
222C4×C13—41no—
223C4×C13—41no—
224C4×C13—81no—
225C4×C13#35312yes—
226Dic13—162no—
227C22×D4—21no—
228C22×D4—21no—
229C22×D4C2×Dic1311yescharacteristic
230C22×D4C22⋊D1311yescharacteristic
231C23×C4—21no—
232C23×C4C22⋊D1311yescharacteristic
233C23×C4C22⋊D1311yescharacteristic
234C2×M16—521no—
235C4×D4—41no—
236C4×D4—41no—
237C4×D4—44no—
238C4×D4—44no—
239C4×D4—41no—
240C4×D4—41no—
241C2×C4⋊C4—21no—
242C2×C4⋊C4—21no—
243C2×C4⋊C4—521no—
244C2×C4⋊C4C2×Dic1311yescharacteristic
245C2×C4⋊C4C22⋊D1311yescharacteristic
246C2×C22⋊C4—21no—
247C2×C22⋊C4—21no—
248C2×C22⋊C4—21no—
249C2×C22⋊C4—21no—
250C2×C22⋊C4—21no—
251C2×C22⋊C4—262no—
252C2×C22⋊C4C2×Dic1311yescharacteristic
253C2×C22⋊C4C22×D1311yescharacteristic
254C2×C42—21no—
255C2×C42C2×Dic1311yescharacteristic
256#99—522no—
257C22⋊C8—262no—
258C22⋊C8—521no—
259#95—21no—
260#95—521no—
261#95C2×Dic1311yescharacteristic
262#95C2×Dic1311yescharacteristic
263C2×C13—21no—
264C2×C13—21no—
265C2×C13—41no—
266C2×C13—41no—
267C2×C13—81no—
268C2×C13—82no—
269C2×C13#151311yescharacteristic
270C2×C13#212011yescharacteristic
271C2×C13C2×#35311yescharacteristic
272C24—21no—
273C24C22⋊Dic1311yescharacteristic
274C24C2×C22⋊D1311yescharacteristic
275C2×D4—21no—
276C2×D4—21no—
277C2×D4—41no—
278C2×D4—41no—
279C2×D4—41no—
280C2×D4—42no—
281C2×D4—42no—
282C2×D4—42no—
283C2×D4—42no—
284C2×D4—42no—
285C2×D4—41no—
286C2×D4—41no—
287C2×D4—42no—
288C22×C4—21no—
289C22×C4—21no—
290C22×C4—21no—
291C22×C4—21no—
292C22×C4—21no—
293C22×C4—21no—
294C22×C4—21no—
295C22×C4—42no—
296C22×C4—42no—
297C22×C4—42no—
298C22×C4—42no—
299C22×C4—41no—
300C22×C4—41no—
301C22×C4—522no—
302C22×C4C22⋊Dic1311yescharacteristic
303C22×C4C22⋊Dic1311yescharacteristic
304C22×C4C22⋊Dic1311yescharacteristic
305C22×C4C22×Dic1311yescharacteristic
306C22×C4C2×C22⋊D1311yescharacteristic
307M16—1042no—
308C2×C8—522no—
309C4⋊C4—41no—
310C4⋊C4—41no—
311C4⋊C4—42no—
312C4⋊C4—42no—
313C4⋊C4—1042no—
314C22⋊C4—41no—
315C22⋊C4—41no—
316C22⋊C4—42no—
317C22⋊C4—42no—
318C22⋊C4—42no—
319C22⋊C4—42no—
320C22⋊C4—42no—
321C22⋊C4—522no—
322C22⋊C4—522no—
323C42—24no—
324C42—21no—
325C42—21no—
326C13#1182111yescharacteristic, complemented, Sylow
327C23—21no—
328C23—21no—
329C23—22no—
330C23—21no—
331C23—21no—
332C23—21no—
333C23—41no—
334C23—41no—
335C23—41no—
336C23—41no—
337C23—41no—
338C23—41no—
339C23—41no—
340C23—41no—
341C23—41no—
342C23—41no—
343C23#8820311yescharacteristic
344C23#8820511yescharacteristic
345C23C2×C22⋊Dic1311yescharacteristic
346D4—42no—
347D4—42no—
348D4—42no—
349D4—44no—
350D4—44no—
351D4—48no—
352D4—42no—
353C2×C4—22no—
354C2×C4—22no—
355C2×C4—22no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—42no—
367C2×C4—42no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—81no—
375C2×C4—81no—
376C2×C4—82no—
377C2×C4—82no—
378C2×C4—1042no—
379C2×C4—1042no—
380C2×C4—1042no—
381C2×C4#8807411yescharacteristic
382C2×C4#8807411yescharacteristic
383C8—1042no—
384C22—21no—
385C22—21no—
386C22—21no—
387C22—21no—
388C22—41no—
389C22—41no—
390C22—42no—
391C22—42no—
392C22—42no—
393C22—41no—
394C22—41no—
395C22—41no—
396C22—42no—
397C22—41no—
398C22—41no—
399C22—81no—
400C22—81no—
401C22—81no—
402C22—81no—
403C22—81no—
404C22—81no—
405C22C2×#8807411yescharacteristic
406C22#1171889311yescharacteristic
407C22#1171889711yescharacteristic
408C4—21no—
409C4—42no—
410C4—42no—
411C4—41no—
412C4—41no—
413C4—41no—
414C4—41no—
415C4—81no—
416C4—2082no—
417C4#1171813712yes—
418C2—21no—
419C2—21no—
420C2—41no—
421C2—41no—
422C2—81no—
423C2—82no—
424C2#1311337911yescharacteristic
425C2#1311647711yescharacteristic
426C2C2×#1171813711yescharacteristic
subgroupG/H
centerC22C2×#88074
commutatorC22×C4×C13C22×C4
FrattiniC2×C22⋊C4C22×D13
Fitting, prime radicalC13×#2397C2
socleC22×C13C2×#99
cosocleC2×C13×C22⋊C4C23
hypercenter#2397D13
hypocenterC13#11821
LCSG ▷ C22×C4×C13 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #2397

Complements

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

NH ≅ G/Ntype
1. #13114824C2semidirect
2. #13113174C2semidirect
3. #13112860C2semidirect
4. #13112833C2semidirect
8. C2×C4×D4×C13C4semidirect
11. C13×#399C4semidirect
14. C13×#392C4semidirect
16. C13×#376C4semidirect
178. C2×C4×D4Dic13semidirect
183. #399Dic13semidirect
186. #392Dic13semidirect
189. #376Dic13semidirect
326. C13#11821semidirect

Maximal subgroups

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

subgroupindex
#131148242
#131131742
#131128602
#131128332
C13×#23972
#1182113