Finite Group Databasebeta

← #15773575

Subgroups — #15773575

Order 3328.

1068 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 1068 conjugacy classes of subgroups — too many to draw. Only its 95 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, complemented
2#13113163C211yesmaximal, characteristic, complemented
3#13112833C214yesmaximal, complemented
4C2×C13×#392C211yesmaximal, characteristic
5C23×D4×C13—21no—
6C23×D4×C13C411yescharacteristic, complemented
7C22×C13×C22⋊C4—21no—
8C22×C13×C22⋊C4C2211yescharacteristic
9C13×#392—21no—
10C13×#392—21no—
11C13×#392C412yescomplemented
12C13×#392C2212yes—
13C2×C13×#95C411yescharacteristic, complemented
14#11718908—21no—
15#11718868—21no—
16#11718118—21no—
17#11718118C2212yescomplemented
18#11718117—21no—
19#11718117C2212yescomplemented
20C25×C13—21no—
21C25×C13D411yescharacteristic
22C22×D4×C13—22no—
23C22×D4×C13—22no—
24C22×D4×C13—21no—
25C22×D4×C13—41no—
26C22×D4×C13—41no—
27C22×D4×C13—44no—
28C22×D4×C13—44no—
29C22×D4×C13—44no—
30C22×D4×C13—44no—
31C22×D4×C13C2×C412yes—
32C23×C4×C13—21no—
33C23×C4×C13C2×C411yescharacteristic
34C23×C4×C13D411yescharacteristic
35C2×C13×C22⋊C4—22no—
36C2×C13×C22⋊C4—22no—
37C2×C13×C22⋊C4—41no—
38C2×C13×C22⋊C4—41no—
39C2×C13×C22⋊C4—44no—
40C2×C13×C22⋊C4C2×C411yescharacteristic
41C2×C13×C22⋊C4D411yescharacteristic
42C2×C13×C22⋊C4D411yescharacteristic
43C2×C13×C22⋊C4C2311yescharacteristic
44C2×C22⋊Dic13—22no—
45C2×C22⋊Dic13—41no—
46C2×C22⋊Dic13—41no—
47C2×#6099—41no—
48C13×#95—21no—
49C13×#95C2×C412yes—
50C22⋊#1055—22no—
51C22⋊#1055—41no—
52#11796—131nomaximal, Sylow
53C24×C13—24no—
54C24×C13—22no—
55C24×C13—22no—
56C24×C13—21no—
57C24×C13—21no—
58C24×C13—41no—
59C24×C13—42no—
60C24×C13—42no—
61C24×C13—42no—
62C24×C13—42no—
63C24×C13—42no—
64C24×C13—42no—
65C24×C13—42no—
66C24×C13—41no—
67C24×C13—41no—
68C24×C13C22⋊C411yescharacteristic
69C24×C13C22⋊C411yescharacteristic
70C24×C13C2×D411yescharacteristic
71C2×D4×C13—42no—
72C2×D4×C13—44no—
73C2×D4×C13—44no—
74C2×D4×C13—42no—
75C2×D4×C13—44no—
76C2×D4×C13—44no—
77C2×D4×C13—44no—
78C2×D4×C13—44no—
79C2×D4×C13—44no—
80C2×D4×C13—432no—
81C2×D4×C13—48no—
82C2×D4×C13—44no—
83C2×D4×C13—44no—
84C2×D4×C13—44no—
85C22×C4×C13—24no—
86C22×C4×C13—21no—
87C22×C4×C13—21no—
88C22×C4×C13—21no—
89C22×C4×C13—22no—
90C22×C4×C13—21no—
91C22×C4×C13—42no—
92C22×C4×C13—42no—
93C22×C4×C13—42no—
94C22×C4×C13—42no—
95C22×C4×C13C22⋊C411yescharacteristic
96C22×C4×C13C22⋊C411yescharacteristic
97C22×C4×C13C22×C411yescharacteristic
98C22×C4×C13C2×D411yescharacteristic
99C22×Dic13—42no—
100C13×C22⋊C4—41no—
101C13×C22⋊C4—41no—
102C13×C22⋊C4—41no—
103C13×C22⋊C4—41no—
104C13×C22⋊C4—44no—
105C13×C22⋊C4—44no—
106C22⋊Dic13—42no—
107C22⋊Dic13—42no—
108C22⋊Dic13—82no—
109C22⋊Dic13—82no—
110#6099—82no—
111C2×#1055—42no—
112C2×#392D1311yescharacteristic
113#1819—131no—
114#1462—131no—
115#1343—134no—
116C23×C13—22no—
117C23×C13—22no—
118C23×C13—21no—
119C23×C13—21no—
120C23×C13—21no—
121C23×C13—21no—
122C23×C13—24no—
123C23×C13—21no—
124C23×C13—21no—
125C23×C13—21no—
126C23×C13—42no—
127C23×C13—42no—
128C23×C13—41no—
129C23×C13—41no—
130C23×C13—41no—
131C23×C13—41no—
132C23×C13—42no—
133C23×C13—48no—
134C23×C13—48no—
135C23×C13—42no—
136C23×C13—44no—
137C23×C13—42no—
138C23×C13—48no—
139C23×C13—42no—
140C23×C13—44no—
141C23×C13—42no—
142C23×C13—42no—
143C23×C13—42no—
144C23×C13—42no—
145C23×C13—81no—
146C23×C13—81no—
147C23×C13—84no—
148C23×C13—84no—
149C23×C13—84no—
150C23×C13—82no—
151C23×C13—82no—
152C23×C13—82no—
153C23×C13—82no—
154C23×C13#9911yescharacteristic
155C23×C13#9911yescharacteristic
156C23×C13C2×C22⋊C411yescharacteristic
157C23×C13AGL(1,ℤ/8)12yes—
158D4×C13—416no—
159D4×C13—416no—
160D4×C13—44no—
161D4×C13—48no—
162D4×C13—44no—
163C2×C4×C13—24no—
164C2×C4×C13—21no—
165C2×C4×C13—21no—
166C2×C4×C13—21no—
167C2×C4×C13—21no—
168C2×C4×C13—48no—
169C2×C4×C13—42no—
170C2×C4×C13—42no—
171C2×C4×C13—42no—
172C2×C4×C13—42no—
173C2×C4×C13—42no—
174C2×C4×C13—41no—
175C2×C4×C13—41no—
176C2×C4×C13—41no—
177C2×C4×C13—41no—
178C2×C4×C13—81no—
179C2×Dic13—82no—
180C2×Dic13—82no—
181C2×Dic13—82no—
182#1055—82no—
183C23×D4—21no—
184C23×D4Dic1311yescharacteristic, complemented
185C22×C22⋊C4—21no—
186C22×C22⋊C4C2×D1311yescharacteristic
187#407—261no—
188#392—21no—
189#392—21no—
190#392Dic1312yescomplemented
191#392C2×D1312yes—
192#379—261no—
193C2×#95Dic1311yescharacteristic, complemented
194#342—132no—
195#342—261no—
196#323—132no—
197#323—261no—
198C22×C13—24no—
199C22×C13—24no—
200C22×C13—21no—
201C22×C13—21no—
202C22×C13—21no—
203C22×C13—21no—
204C22×C13—21no—
205C22×C13—21no—
206C22×C13—22no—
207C22×C13—42no—
208C22×C13—42no—
209C22×C13—44no—
210C22×C13—44no—
211C22×C13—41no—
212C22×C13—41no—
213C22×C13—44no—
214C22×C13—41no—
215C22×C13—41no—
216C22×C13—41no—
217C22×C13—81no—
218C22×C13—84no—
219C22×C13—84no—
220C22×C13—81no—
221C22×C13—82no—
222C22×C13—82no—
223C22×C13—88no—
224C22×C13—88no—
225C22×C13—82no—
226C22×C13—82no—
227C22×C13AΣL(1,𝔽16)12yes—
228C22×C13#35312yes—
229C22×C13C2×#9911yescharacteristic
230C22×C13#41811yescharacteristic
231C22×C13#42111yescharacteristic
232C4×C13—44no—
233C4×C13—41no—
234C4×C13—41no—
235C4×C13—41no—
236C4×C13—41no—
237Dic13—162no—
238C25—21no—
239C25C22⋊D1311yescharacteristic
240C22×D4—22no—
241C22×D4—22no—
242C22×D4—21no—
243C22×D4—41no—
244C22×D4—41no—
245C22×D4—44no—
246C22×D4—44no—
247C22×D4—44no—
248C22×D4—44no—
249C22×D4C2×Dic1312yes—
250C23×C4—21no—
251C23×C4C2×Dic1311yescharacteristic
252C23×C4C22⋊D1311yescharacteristic
253C2×M16—521no—
254C2×C22⋊C4—22no—
255C2×C22⋊C4—22no—
256C2×C22⋊C4—41no—
257C2×C22⋊C4—41no—
258C2×C22⋊C4—44no—
259C2×C22⋊C4—262no—
260C2×C22⋊C4—521no—
261C2×C22⋊C4—521no—
262C2×C22⋊C4C2×Dic1311yescharacteristic
263C2×C22⋊C4C22⋊D1311yescharacteristic
264C2×C22⋊C4C22⋊D1311yescharacteristic
265C2×C22⋊C4C22×D1311yescharacteristic
266C22⋊C8—262no—
267C22⋊C8—521no—
268#95—21no—
269#95C2×Dic1312yes—
270C2×C13—21no—
271C2×C13—21no—
272C2×C13—22no—
273C2×C13—22no—
274C2×C13—42no—
275C2×C13—81no—
276C2×C13—84no—
277C2×C13#151011yescharacteristic
278C2×C13C2×AΣL(1,𝔽16)11yescharacteristic
279C2×C13C2×#35311yescharacteristic
280C24—24no—
281C24—22no—
282C24—22no—
283C24—21no—
284C24—21no—
285C24—41no—
286C24—42no—
287C24—42no—
288C24—42no—
289C24—42no—
290C24—42no—
291C24—42no—
292C24—42no—
293C24—41no—
294C24—41no—
295C24C22⋊Dic1311yescharacteristic
296C24C22⋊Dic1311yescharacteristic
297C24C2×C22⋊D1311yescharacteristic
298C2×D4—42no—
299C2×D4—44no—
300C2×D4—44no—
301C2×D4—42no—
302C2×D4—44no—
303C2×D4—44no—
304C2×D4—44no—
305C2×D4—44no—
306C2×D4—44no—
307C2×D4—48no—
308C2×D4—432no—
309C2×D4—44no—
310C2×D4—44no—
311C2×D4—44no—
312C22×C4—24no—
313C22×C4—21no—
314C22×C4—21no—
315C22×C4—21no—
316C22×C4—22no—
317C22×C4—21no—
318C22×C4—42no—
319C22×C4—42no—
320C22×C4—42no—
321C22×C4—42no—
322C22×C4—522no—
323C22×C4C22⋊Dic1311yescharacteristic
324C22×C4C22⋊Dic1311yescharacteristic
325C22×C4C22×Dic1311yescharacteristic
326C22×C4C2×C22⋊D1311yescharacteristic
327M16—1042no—
328C2×C8—522no—
329C22⋊C4—41no—
330C22⋊C4—41no—
331C22⋊C4—41no—
332C22⋊C4—41no—
333C22⋊C4—44no—
334C22⋊C4—44no—
335C22⋊C4—522no—
336C22⋊C4—522no—
337C22⋊C4—1042no—
338C22⋊C4—1042no—
339C13#1179611yescharacteristic, complemented, Sylow
340C23—21no—
341C23—22no—
342C23—21no—
343C23—22no—
344C23—21no—
345C23—21no—
346C23—24no—
347C23—21no—
348C23—21no—
349C23—21no—
350C23—42no—
351C23—42no—
352C23—41no—
353C23—41no—
354C23—41no—
355C23—41no—
356C23—42no—
357C23—48no—
358C23—48no—
359C23—42no—
360C23—44no—
361C23—42no—
362C23—48no—
363C23—42no—
364C23—42no—
365C23—42no—
366C23—44no—
367C23—42no—
368C23—42no—
369C23—81no—
370C23—81no—
371C23—84no—
372C23—84no—
373C23—84no—
374C23—82no—
375C23—82no—
376C23—82no—
377C23—82no—
378C23#8807411yescharacteristic
379C23#8807411yescharacteristic
380C23#8818612yes—
381C23C2×C22⋊Dic1311yescharacteristic
382D4—44no—
383D4—416no—
384D4—416no—
385D4—44no—
386D4—48no—
387C2×C4—24no—
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—21no—
391C2×C4—21no—
392C2×C4—48no—
393C2×C4—42no—
394C2×C4—42no—
395C2×C4—42no—
396C2×C4—42no—
397C2×C4—42no—
398C2×C4—41no—
399C2×C4—41no—
400C2×C4—41no—
401C2×C4—41no—
402C2×C4—81no—
403C2×C4—1042no—
404C2×C4—1042no—
405C2×C4—1042no—
406C8—1042no—
407C22—24no—
408C22—24no—
409C22—21no—
410C22—21no—
411C22—21no—
412C22—21no—
413C22—21no—
414C22—21no—
415C22—22no—
416C22—42no—
417C22—42no—
418C22—44no—
419C22—44no—
420C22—41no—
421C22—41no—
422C22—41no—
423C22—44no—
424C22—41no—
425C22—41no—
426C22—81no—
427C22—84no—
428C22—84no—
429C22—81no—
430C22—82no—
431C22—82no—
432C22—88no—
433C22—88no—
434C22—82no—
435C22—82no—
436C22#1171812812yes—
437C22#1171813712yes—
438C22#1171887611yescharacteristic
439C22C2×#8807411yescharacteristic
440C22#1171889711yescharacteristic
441C4—44no—
442C4—41no—
443C4—41no—
444C4—41no—
445C4—41no—
446C4—2082no—
447C2—21no—
448C2—21no—
449C2—22no—
450C2—22no—
451C2—42no—
452C2—81no—
453C2—84no—
454C2#1311336511yescharacteristic
455C2C2×#1171812811yescharacteristic
456C2C2×#1171813711yescharacteristic
subgroupG/H
centerC22C2×#88074
commutatorC22×C4×C13C22×C4
FrattiniC2×C22⋊C4C22×D13
Fitting, prime radicalC2×C13×#392C2
socleC22×C13C2×#99
cosocleC2×C13×C22⋊C4C23
hypercenterC2×#392D13
hypocenterC13#11796
LCSG ▷ C22×C4×C13 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C24 ◁ C22×C22⋊C4 ◁ C2×#392

Complements

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

NH ≅ G/Ntype
1. #13114910C2semidirect
2. #13113163C2semidirect
3. #13112833C2semidirect
6. C23×D4×C13C4semidirect
11. C13×#392C4semidirect
13. C2×C13×#95C4semidirect
17. #11718118C22semidirect
19. #11718117C22semidirect
184. C23×D4Dic13semidirect
190. #392Dic13semidirect
193. C2×#95Dic13semidirect
339. C13#11796semidirect

Maximal subgroups

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

subgroupindex
#131149102
#131131632
#131128332
C2×C13×#3922
#1179613