Finite Group Databasebeta

← #15754527

Subgroups — #15754527

Order 3328.

1074 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13114780C212yesmaximal, complemented
2C4×#88074C211yesmaximal, characteristic, complemented
3#13113356C212yesmaximal, complemented
4#13113174C211yesmaximal, characteristic, complemented
5C2×C13×#547C211yesmaximal, characteristic
6C22×C13×#41C411yescharacteristic, complemented
7C22×C13×#41C2211yescharacteristic
8C13×#547—24no—
9C13×#547—24no—
10C2×C13×C4⋊Q8C411yescharacteristic, complemented
11C2×C13×#123—21no—
12C2×C13×#123—21no—
13C2×C13×C22⋊Q8C411yescharacteristic, complemented
14C2×C13×C22⋊Q8C2211yescharacteristic
15C2×C13×#121—21no—
16C2×C4×D4×C13C411yescharacteristic, complemented
17C2×C4×D4×C13C2211yescharacteristic
18C22×C13×C4⋊C4—21no—
19C2×#88077—24no—
20C2×#88074—21no—
21C4×C22⋊Dic13C2212yes—
22#11718868C2212yes—
23#11718130—24no—
24#11718120—21no—
25#11718118—21no—
26#11718117—21no—
27C2×C13×#41—22no—
28C2×C13×#41—22no—
29C2×C13×#41—22no—
30C2×C13×#41—44no—
31C2×C13×#41—44no—
32C2×C13×#41D414yes—
33C22×Q8×C13C2×C411yescharacteristic
34C22×Q8×C13C2×C411yescharacteristic
35C22×D4×C13—21no—
36C22×D4×C13—21no—
37C22×D4×C13C2×C411yescharacteristic
38C22×D4×C13D411yescharacteristic
39C23×C4×C13—21no—
40C23×C4×C13—21no—
41C23×C4×C13—21no—
42C23×C4×C13C2×C411yescharacteristic
43C23×C4×C13C2311yescharacteristic
44C13×C4⋊Q8—22no—
45C13×C4⋊Q8—22no—
46C13×#123—28no—
47C13×#123—28no—
48C13×C22⋊Q8—22no—
49C13×C22⋊Q8—22no—
50C13×C22⋊Q8—22no—
51C13×C22⋊Q8D414yes—
52C13×#121—28no—
53C4×D4×C13—22no—
54C4×D4×C13—22no—
55C4×D4×C13—22no—
56C4×D4×C13—22no—
57C2×C13×C4⋊C4—28no—
58C2×C13×C4⋊C4—21no—
59C2×C13×C4⋊C4—21no—
60C2×C13×C4⋊C4—21no—
61C2×C13×C4⋊C4—21no—
62C2×C13×C4⋊C4C2×C411yescharacteristic
63C2×C13×C4⋊C4D411yescharacteristic
64C2×C13×C22⋊C4—21no—
65C2×C13×C22⋊C4—21no—
66C2×C13×C22⋊C4—21no—
67C2×C13×C22⋊C4D411yescharacteristic
68C2×C13×C22⋊C4D411yescharacteristic
69C2×C42×C13C2×C411yescharacteristic
70C2×C22⋊Dic13—22no—
71C2×C4×Dic13—22no—
72C2×#6099—22no—
73#88077—48no—
74#88074—24no—
75#88071—22no—
76C22⋊#1055—22no—
77C22⋊#1055—22no—
78#8364—131nomaximal, Sylow
79C24×C13—21no—
80C24×C13C22⋊C411yescharacteristic
81C24×C13C2×D411yescharacteristic
82C13×#41—28no—
83C13×#41—44no—
84C13×#41—48no—
85C13×#41—48no—
86C13×#41—44no—
87C13×#41—44no—
88C2×Q8×C13—21no—
89C2×Q8×C13—21no—
90C2×Q8×C13—42no—
91C2×Q8×C13—42no—
92C2×Q8×C13C22⋊C412yes—
93C2×Q8×C13C22⋊C412yes—
94C2×D4×C13—24no—
95C2×D4×C13—24no—
96C2×D4×C13—22no—
97C2×D4×C13—24no—
98C2×D4×C13—22no—
99C2×D4×C13—21no—
100C2×D4×C13—41no—
101C2×D4×C13—44no—
102C2×D4×C13—44no—
103C2×D4×C13C22⋊C412yes—
104C22×C4×C13—24no—
105C22×C4×C13—24no—
106C22×C4×C13—21no—
107C22×C4×C13—21no—
108C22×C4×C13—21no—
109C22×C4×C13—21no—
110C22×C4×C13—21no—
111C22×C4×C13—24no—
112C22×C4×C13—42no—
113C22×C4×C13—42no—
114C22×C4×C13—42no—
115C22×C4×C13—44no—
116C22×C4×C13—44no—
117C22×C4×C13—42no—
118C22×C4×C13C22⋊C411yescharacteristic
119C22×C4×C13C22⋊C411yescharacteristic
120C22×C4×C13C22⋊C411yescharacteristic
121C22×C4×C13C22×C411yescharacteristic
122C22×C4×C13C2×D412yes—
123C22×C4×C13C2×D412yes—
124C22×C4×C13C2×D411yescharacteristic
125C22×Dic13—42no—
126C13×C4⋊C4—24no—
127C13×C4⋊C4—24no—
128C13×C4⋊C4—24no—
129C13×C4⋊C4—21no—
130C13×C4⋊C4—22no—
131C13×C4⋊C4—24no—
132C13×C4⋊C4C22⋊C412yes—
133C13×C22⋊C4—24no—
134C13×C22⋊C4—24no—
135C13×C22⋊C4—24no—
136C13×C22⋊C4—22no—
137C13×C22⋊C4—22no—
138C42×C13—21no—
139C42×C13—21no—
140C22⋊Dic13—24no—
141C22⋊Dic13—42no—
142C4×Dic13—44no—
143#6099—44no—
144C2×#1055—42no—
145C2×#547D1311yescharacteristic
146#1789—132no—
147C4×#99—131no—
148#1508—132no—
149#1465—131no—
150C23×C13—24no—
151C23×C13—22no—
152C23×C13—21no—
153C23×C13—21no—
154C23×C13—21no—
155C23×C13—21no—
156C23×C13—21no—
157C23×C13—41no—
158C23×C13—41no—
159C23×C13—42no—
160C23×C13—41no—
161C23×C13—41no—
162C23×C13—41no—
163C23×C13—41no—
164C23×C13C2×C22⋊C411yescharacteristic
165C23×C13#12012yes—
166Q8×C13—24no—
167Q8×C13—42no—
168Q8×C13—42no—
169Q8×C13—42no—
170D4×C13—24no—
171D4×C13—22no—
172D4×C13—44no—
173D4×C13—48no—
174D4×C13—48no—
175D4×C13#9914yescomplemented
176C2×C4×C13—21no—
177C2×C4×C13—21no—
178C2×C4×C13—24no—
179C2×C4×C13—22no—
180C2×C4×C13—21no—
181C2×C4×C13—22no—
182C2×C4×C13—21no—
183C2×C4×C13—22no—
184C2×C4×C13—22no—
185C2×C4×C13—41no—
186C2×C4×C13—42no—
187C2×C4×C13—48no—
188C2×C4×C13—48no—
189C2×C4×C13—42no—
190C2×C4×C13—42no—
191C2×C4×C13—42no—
192C2×C4×C13—48no—
193C2×C4×C13—41no—
194C2×C4×C13—41no—
195C2×C4×C13—42no—
196C2×C4×C13—41no—
197C2×C4×C13—41no—
198C2×C4×C13#10412yescomplemented
199C2×C4×C13C2×C22⋊C411yescharacteristic
200C2×C4×C13C2×C22⋊C411yescharacteristic
201C2×C4×C13#12012yes—
202C2×Dic13—44no—
203C2×Dic13—82no—
204C2×Dic13—82no—
205#1055—82no—
206C22×#41Dic1311yescharacteristic, complemented
207C22×#41C2×D1311yescharacteristic
208#547—24no—
209#547—24no—
210C2×C4⋊Q8Dic1311yescharacteristic, complemented
211C2×#123—21no—
212C2×#123—21no—
213C2×C22⋊Q8Dic1311yescharacteristic, complemented
214C2×C22⋊Q8C2×D1311yescharacteristic
215C2×#121—21no—
216C2×C4×D4Dic1311yescharacteristic, complemented
217C2×C4×D4C2×D1311yescharacteristic
218C22×C4⋊C4—21no—
219C2×#104—264no—
220C2×#99—261no—
221#407—132no—
222C4×C22⋊C4—132no—
223#342—261no—
224#328—264no—
225#324—261no—
226#323—261no—
227C22×C13—21no—
228C22×C13—21no—
229C22×C13—22no—
230C22×C13—22no—
231C22×C13—24no—
232C22×C13—22no—
233C22×C13—44no—
234C22×C13—44no—
235C22×C13—42no—
236C22×C13—42no—
237C22×C13—41no—
238C22×C13—41no—
239C22×C13—41no—
240C22×C13—81no—
241C22×C13—81no—
242C22×C13—81no—
243C22×C13—81no—
244C22×C13#37911yescharacteristic
245C22×C13C2×#10411yescharacteristic
246C22×C13#42111yescharacteristic
247C4×C13—22no—
248C4×C13—21no—
249C4×C13—22no—
250C4×C13—41no—
251C4×C13—41no—
252C4×C13—42no—
253C4×C13—42no—
254C4×C13—42no—
255C4×C13C2×#9912yes—
256Dic13—84no—
257C2×#41—22no—
258C2×#41—22no—
259C2×#41—22no—
260C2×#41—44no—
261C2×#41—44no—
262C2×#41C22⋊D1314yes—
263C22×Q8C2×Dic1311yescharacteristic
264C22×Q8C2×Dic1311yescharacteristic
265C22×D4—21no—
266C22×D4—21no—
267C22×D4C2×Dic1311yescharacteristic
268C22×D4C22⋊D1311yescharacteristic
269C23×C4—21no—
270C23×C4—21no—
271C23×C4—21no—
272C23×C4C2×Dic1311yescharacteristic
273C23×C4C22×D1311yescharacteristic
274C2×M16—262no—
275C4⋊Q8—22no—
276C4⋊Q8—22no—
277#123—28no—
278#123—28no—
279C22⋊Q8—22no—
280C22⋊Q8—22no—
281C22⋊Q8—22no—
282C22⋊Q8C22⋊D1314yes—
283#121—28no—
284C4×D4—22no—
285C4×D4—22no—
286C4×D4—22no—
287C4×D4—22no—
288C2×C4⋊C4—28no—
289C2×C4⋊C4—21no—
290C2×C4⋊C4—21no—
291C2×C4⋊C4—21no—
292C2×C4⋊C4—21no—
293C2×C4⋊C4C2×Dic1311yescharacteristic
294C2×C4⋊C4C22⋊D1311yescharacteristic
295C2×C22⋊C4—21no—
296C2×C22⋊C4—21no—
297C2×C22⋊C4—21no—
298C2×C22⋊C4—262no—
299C2×C22⋊C4C22⋊D1311yescharacteristic
300C2×C22⋊C4C22⋊D1311yescharacteristic
301C2×C42—262no—
302C2×C42C2×Dic1311yescharacteristic
303#104—528no—
304#99—264no—
305C22⋊C8—262no—
306C22⋊C8—262no—
307#95—262no—
308C2×C13—21no—
309C2×C13—21no—
310C2×C13—42no—
311C2×C13—44no—
312C2×C13—81no—
313C2×C13#178111yescharacteristic
314C2×C13#178911yescharacteristic
315C2×C13#179611yescharacteristic
316C24—21no—
317C24C22⋊Dic1311yescharacteristic
318C24C2×C22⋊D1311yescharacteristic
319#41—28no—
320#41—44no—
321#41—48no—
322#41—48no—
323#41—44no—
324#41—44no—
325C2×Q8—21no—
326C2×Q8—21no—
327C2×Q8—42no—
328C2×Q8—42no—
329C2×Q8C22⋊Dic1312yes—
330C2×Q8C22⋊Dic1312yes—
331C2×D4—24no—
332C2×D4—24no—
333C2×D4—22no—
334C2×D4—24no—
335C2×D4—22no—
336C2×D4—21no—
337C2×D4—41no—
338C2×D4—44no—
339C2×D4—44no—
340C2×D4C22⋊Dic1312yes—
341C22×C4—24no—
342C22×C4—24no—
343C22×C4—21no—
344C22×C4—21no—
345C22×C4—21no—
346C22×C4—21no—
347C22×C4—21no—
348C22×C4—24no—
349C22×C4—42no—
350C22×C4—42no—
351C22×C4—42no—
352C22×C4—44no—
353C22×C4—44no—
354C22×C4—42no—
355C22×C4—522no—
356C22×C4C22⋊Dic1311yescharacteristic
357C22×C4C22⋊Dic1311yescharacteristic
358C22×C4C22⋊Dic1311yescharacteristic
359C22×C4C22×Dic1311yescharacteristic
360C22×C4C2×C22⋊D1312yes—
361C22×C4C2×C22⋊D1312yes—
362C22×C4C2×C22⋊D1311yescharacteristic
363M16—524no—
364C2×C8—522no—
365C4⋊C4—24no—
366C4⋊C4—24no—
367C4⋊C4—24no—
368C4⋊C4—21no—
369C4⋊C4—22no—
370C4⋊C4—24no—
371C4⋊C4C22⋊Dic1312yes—
372C22⋊C4—24no—
373C22⋊C4—24no—
374C22⋊C4—24no—
375C22⋊C4—22no—
376C22⋊C4—22no—
377C22⋊C4—264no—
378C22⋊C4—522no—
379C42—21no—
380C42—21no—
381C42—524no—
382C13#836411yescharacteristic, complemented, Sylow
383C23—24no—
384C23—22no—
385C23—21no—
386C23—21no—
387C23—21no—
388C23—21no—
389C23—21no—
390C23—41no—
391C23—41no—
392C23—42no—
393C23—41no—
394C23—41no—
395C23—41no—
396C23—41no—
397C23C2×C22⋊Dic1311yescharacteristic
398C23#8820712yes—
399Q8—24no—
400Q8—42no—
401Q8—42no—
402Q8—42no—
403D4—24no—
404D4—22no—
405D4—44no—
406D4—48no—
407D4—48no—
408D4#8807414yescomplemented
409C2×C4—21no—
410C2×C4—21no—
411C2×C4—24no—
412C2×C4—22no—
413C2×C4—21no—
414C2×C4—22no—
415C2×C4—21no—
416C2×C4—22no—
417C2×C4—22no—
418C2×C4—41no—
419C2×C4—42no—
420C2×C4—48no—
421C2×C4—48no—
422C2×C4—42no—
423C2×C4—42no—
424C2×C4—42no—
425C2×C4—48no—
426C2×C4—41no—
427C2×C4—41no—
428C2×C4—42no—
429C2×C4—41no—
430C2×C4—41no—
431C2×C4—524no—
432C2×C4—1042no—
433C2×C4—1042no—
434C2×C4#8807712yescomplemented
435C2×C4C2×C22⋊Dic1311yescharacteristic
436C2×C4C2×C22⋊Dic1311yescharacteristic
437C2×C4#8820712yes—
438C8—1042no—
439C22—21no—
440C22—21no—
441C22—22no—
442C22—24no—
443C22—22no—
444C22—22no—
445C22—44no—
446C22—44no—
447C22—42no—
448C22—42no—
449C22—41no—
450C22—41no—
451C22—41no—
452C22—81no—
453C22—81no—
454C22—81no—
455C22—81no—
456C22C2×#8807711yescharacteristic
457C22#1171889711yescharacteristic
458C22#1171890811yescharacteristic
459C4—22no—
460C4—21no—
461C4—22no—
462C4—41no—
463C4—42no—
464C4—42no—
465C4—42no—
466C4—41no—
467C4—1044no—
468C4C2×#8807412yes—
469C2—21no—
470C2—21no—
471C2—42no—
472C2—44no—
473C2—81no—
474C2#1311475111yescharacteristic
475C2#1311478011yescharacteristic
476C2#1311481111yescharacteristic
subgroupG/H
centerC22#11718908
commutatorC22×C4×C13C22×C4
FrattiniC23×C4C22×D13
Fitting, prime radicalC2×C13×#547C2
socleC22×C13#379
cosocleC23×C4×C13C23
hypercenterC2×#547D13
hypocenterC13#8364
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#547

Complements

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

NH ≅ G/Ntype
1. #13114780C2semidirect
2. C4×#88074C2semidirect
3. #13113356C2semidirect
4. #13113174C2semidirect
6. C22×C13×#41C4semidirect
10. C2×C13×C4⋊Q8C4semidirect
13. C2×C13×C22⋊Q8C4semidirect
16. C2×C4×D4×C13C4semidirect
175. D4×C13#99semidirect
198. C2×C4×C13#104semidirect
206. C22×#41Dic13semidirect
210. C2×C4⋊Q8Dic13semidirect
213. C2×C22⋊Q8Dic13semidirect
216. C2×C4×D4Dic13semidirect
382. C13#8364semidirect
408. D4#88074semidirect
434. C2×C4#88077semidirect

Maximal subgroups

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

subgroupindex
#131147802
C4×#880742
#131133562
#131131742
C2×C13×#5472
#836413