Finite Group Databasebeta

← #15780444

Subgroups — #15780444

Order 3328.

782 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 782 conjugacy classes of subgroups — too many to draw. Only its 111 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
1C2×#11718901C211yesmaximal, characteristic, complemented
2C2×#11718137C212yesmaximal, complemented
3#13114754C211yesmaximal, characteristic, complemented
4#13112961C212yesmaximal, complemented
5C13×#2431C211yesmaximal, characteristic
6C22×C13×#41C2211yescharacteristic
7C2×C13×#127C2211yescharacteristic
8C2×C13×#124C411yescharacteristic, complemented
9C2×C13×#121C411yescharacteristic, complemented
10C2×#88180—21no—
11C13×#392—21no—
12C13×#392—21no—
13C13×#391C411yescharacteristic, complemented
14C13×#390C2211yescharacteristic
15C13×#386—21no—
16C13×#386—21no—
17C4×C13×C22⋊C4C411yescharacteristic, complemented
18#11718901—24no—
19C2×#88074—21no—
20C2×#88074—21no—
21C2×#88074C2212yes—
22C2×#88074C2212yes—
23#11718872—21no—
24#11718137—24no—
25C2×C13×#41—22no—
26C2×C13×#41—22no—
27C2×C13×#41—41no—
28C2×C13×#41—41no—
29C2×C13×#41—42no—
30C22×Q8×C13C2×C411yescharacteristic
31C22×D4×C13—21no—
32C22×D4×C13—21no—
33C22×D4×C13—21no—
34C22×D4×C13C2×C411yescharacteristic
35C22×D4×C13D411yescharacteristic
36C22×D4×C13D411yescharacteristic
37C22×D4×C13C2311yescharacteristic
38C23×C4×C13C2×C411yescharacteristic
39C23×C4×C13D411yescharacteristic
40C23×C4×C13D411yescharacteristic
41C13×#127—22no—
42C13×#127—22no—
43C13×#124—42no—
44C13×#121—41no—
45C13×#121—41no—
46C2×C13×C4⋊C4C2×C411yescharacteristic
47C2×C13×C22⋊C4—21no—
48C2×C13×C22⋊C4—21no—
49C2×C13×C22⋊C4—21no—
50C2×C13×C22⋊C4—21no—
51C2×C13×C22⋊C4—21no—
52C2×C13×C22⋊C4—21no—
53C2×C42×C13C2×C411yescharacteristic
54C2×C42×C13C2×C411yescharacteristic
55C2×C22⋊Dic13—22no—
56C2×C22⋊Dic13—22no—
57#88180—24no—
58#88180—42no—
59C2×C4⋊Dic13—41no—
60C2×C4×Dic13—41no—
61C13×#95—21no—
62C13×#95—21no—
63C13×#95—21no—
64#88074—24no—
65#88074—22no—
66#88074—22no—
67#88074—22no—
68#88074—42no—
69#88074D414yescomplemented
70#88071—41no—
71#88071—41no—
72#13089—131nomaximal, Sylow
73C24×C13—21no—
74C24×C13C22⋊C411yescharacteristic
75C24×C13C2×D411yescharacteristic
76C24×C13C2×D411yescharacteristic
77C13×#41—44no—
78C13×#41—44no—
79C13×#41—44no—
80C13×#41—44no—
81C2×Q8×C13—22no—
82C2×Q8×C13—22no—
83C2×Q8×C13—41no—
84C2×D4×C13—21no—
85C2×D4×C13—22no—
86C2×D4×C13—21no—
87C2×D4×C13—22no—
88C2×D4×C13—22no—
89C2×D4×C13—41no—
90C2×D4×C13—41no—
91C2×D4×C13—41no—
92C2×D4×C13—41no—
93C2×D4×C13—41no—
94C2×D4×C13—41no—
95C2×D4×C13—41no—
96C2×D4×C13—42no—
97C2×D4×C13—42no—
98C2×D4×C13—42no—
99C2×D4×C13—41no—
100C2×D4×C13—42no—
101C2×D4×C13—41no—
102C2×D4×C13—81no—
103C2×D4×C13—81no—
104C2×D4×C13—81no—
105C2×D4×C13—81no—
106C2×D4×C13C2×D412yes—
107C2×D4×C13#4112yes—
108C22×C4×C13—21no—
109C22×C4×C13—21no—
110C22×C4×C13—21no—
111C22×C4×C13—21no—
112C22×C4×C13—22no—
113C22×C4×C13—21no—
114C22×C4×C13—22no—
115C22×C4×C13—21no—
116C22×C4×C13—21no—
117C22×C4×C13—21no—
118C22×C4×C13—21no—
119C22×C4×C13—22no—
120C22×C4×C13—21no—
121C22×C4×C13—21no—
122C22×C4×C13—41no—
123C22×C4×C13—41no—
124C22×C4×C13C22⋊C411yescharacteristic
125C22×C4×C13C22⋊C411yescharacteristic
126C22×C4×C13C22⋊C411yescharacteristic
127C22×C4×C13C22×C411yescharacteristic
128C22×Dic13—42no—
129C22×Dic13—42no—
130C13×C4⋊C4—41no—
131C13×C22⋊C4—42no—
132C13×C22⋊C4—42no—
133C13×C22⋊C4—41no—
134C13×C22⋊C4—41no—
135C13×C22⋊C4—42no—
136C13×C22⋊C4—81no—
137C13×C22⋊C4—81no—
138C42×C13—22no—
139C42×C13—41no—
140C22⋊Dic13—24no—
141C22⋊Dic13—42no—
142C22⋊Dic13—42no—
143C22⋊Dic13—42no—
144C4⋊Dic13—44no—
145C4×Dic13—44no—
146C2×#410—131no—
147#2431D1311yescharacteristic
148C2×#353—132no—
149#1782—131no—
150#1393—132no—
151C23×C13—21no—
152C23×C13—21no—
153C23×C13—21no—
154C23×C13—21no—
155C23×C13—21no—
156C23×C13—21no—
157C23×C13—21no—
158C23×C13—41no—
159C23×C13—41no—
160C23×C13—41no—
161C23×C13—41no—
162C23×C13—41no—
163C23×C13—41no—
164C23×C13—41no—
165C23×C13—41no—
166C23×C13—41no—
167C23×C13—41no—
168C23×C13—41no—
169C23×C13—41no—
170C23×C13—41no—
171C23×C13C2×C22⋊C411yescharacteristic
172C23×C13#12011yescharacteristic
173C23×C13#12112yes—
174C23×C13#12311yescharacteristic
175Q8×C13—44no—
176D4×C13—42no—
177D4×C13—42no—
178D4×C13—44no—
179D4×C13—42no—
180D4×C13—42no—
181D4×C13—82no—
182D4×C13—82no—
183D4×C13—84no—
184D4×C13—82no—
185D4×C13—84no—
186C2×C4×C13—22no—
187C2×C4×C13—22no—
188C2×C4×C13—22no—
189C2×C4×C13—22no—
190C2×C4×C13—21no—
191C2×C4×C13—21no—
192C2×C4×C13—21no—
193C2×C4×C13—21no—
194C2×C4×C13—21no—
195C2×C4×C13—21no—
196C2×C4×C13—22no—
197C2×C4×C13—21no—
198C2×C4×C13—21no—
199C2×C4×C13—21no—
200C2×C4×C13—42no—
201C2×C4×C13—42no—
202C2×C4×C13—42no—
203C2×C4×C13—42no—
204C2×C4×C13—41no—
205C2×C4×C13—41no—
206C2×C4×C13—41no—
207C2×C4×C13—41no—
208C2×C4×C13—41no—
209C2×C4×C13—41no—
210C2×C4×C13—41no—
211C2×C4×C13—41no—
212C2×C4×C13#9911yescharacteristic
213C2×C4×C13#9911yescharacteristic
214C2×C4×C13#9912yes—
215C2×C4×C13C4×D412yes—
216C2×Dic13—44no—
217C2×Dic13—82no—
218C2×Dic13—82no—
219C2×Dic13—82no—
220C2×Dic13—82no—
221C2×Dic13—82no—
222C22×#41C2×D1311yescharacteristic
223C2×#127C2×D1311yescharacteristic
224C2×#124Dic1311yescharacteristic, complemented
225C2×#121Dic1311yescharacteristic, complemented
226C2×#117—261no—
227#410—264no—
228C2×#99—132no—
229C2×#99—132no—
230C2×#99—261no—
231C2×#99—261no—
232#392—21no—
233#392—21no—
234#391Dic1311yescharacteristic, complemented
235#390C2×D1311yescharacteristic
236#386—21no—
237#386—21no—
238#381—261no—
239C4×C22⋊C4Dic1311yescharacteristic, complemented
240#353—264no—
241C22×C13—21no—
242C22×C13—21no—
243C22×C13—21no—
244C22×C13—22no—
245C22×C13—21no—
246C22×C13—41no—
247C22×C13—42no—
248C22×C13—41no—
249C22×C13—41no—
250C22×C13—41no—
251C22×C13—41no—
252C22×C13—41no—
253C22×C13—41no—
254C22×C13—41no—
255C22×C13—41no—
256C22×C13—81no—
257C22×C13—81no—
258C22×C13—81no—
259C22×C13—81no—
260C22×C13—81no—
261C22×C13—81no—
262C22×C13—81no—
263C22×C13—81no—
264C22×C13—81no—
265C22×C13—81no—
266C22×C13—81no—
267C22×C13#38611yescharacteristic
268C22×C13C2×#9911yescharacteristic
269C22×C13C2×#9911yescharacteristic
270C4×C13—21no—
271C4×C13—21no—
272C4×C13—22no—
273C4×C13—22no—
274C4×C13—42no—
275C4×C13—41no—
276C4×C13—81no—
277C4×C13—81no—
278Dic13—84no—
279Dic13—162no—
280C2×#41—22no—
281C2×#41—22no—
282C2×#41—41no—
283C2×#41—41no—
284C2×#41—42no—
285C22×Q8C2×Dic1311yescharacteristic
286C22×D4—21no—
287C22×D4—21no—
288C22×D4—21no—
289C22×D4C2×Dic1311yescharacteristic
290C22×D4C22⋊D1311yescharacteristic
291C22×D4C22⋊D1311yescharacteristic
292C22×D4C22×D1311yescharacteristic
293C23×C4C2×Dic1311yescharacteristic
294C23×C4C22⋊D1311yescharacteristic
295C23×C4C22⋊D1311yescharacteristic
296#127—22no—
297#127—22no—
298#124—42no—
299#121—41no—
300#121—41no—
301#117—264no—
302#117—522no—
303C2×C4⋊C4—521no—
304C2×C4⋊C4C2×Dic1311yescharacteristic
305C2×C22⋊C4—21no—
306C2×C22⋊C4—21no—
307C2×C22⋊C4—21no—
308C2×C22⋊C4—21no—
309C2×C22⋊C4—21no—
310C2×C22⋊C4—21no—
311C2×C22⋊C4—262no—
312C2×C22⋊C4—262no—
313C2×C42—521no—
314C2×C42C2×Dic1311yescharacteristic
315C2×C42C2×Dic1311yescharacteristic
316#99—134no—
317#99—264no—
318#99—262no—
319#99—262no—
320#99—262no—
321#99—522no—
322#95—21no—
323#95—21no—
324#95—21no—
325#95—521no—
326#95—521no—
327C2×C13—21no—
328C2×C13—21no—
329C2×C13—41no—
330C2×C13—42no—
331C2×C13—41no—
332C2×C13—81no—
333C2×C13—161no—
334C2×C13#189811yescharacteristic
335C2×C13#212611yescharacteristic
336C2×C13#212811yescharacteristic
337C24—21no—
338C24C22⋊Dic1311yescharacteristic
339C24C2×C22⋊D1311yescharacteristic
340C24C2×C22⋊D1311yescharacteristic
341#41—44no—
342#41—44no—
343#41—44no—
344#41—44no—
345C2×Q8—22no—
346C2×Q8—22no—
347C2×Q8—41no—
348C2×D4—21no—
349C2×D4—21no—
350C2×D4—22no—
351C2×D4—22no—
352C2×D4—22no—
353C2×D4—41no—
354C2×D4—41no—
355C2×D4—41no—
356C2×D4—41no—
357C2×D4—41no—
358C2×D4—41no—
359C2×D4—41no—
360C2×D4—42no—
361C2×D4—42no—
362C2×D4—42no—
363C2×D4—41no—
364C2×D4—41no—
365C2×D4—42no—
366C2×D4—81no—
367C2×D4—81no—
368C2×D4—81no—
369C2×D4—81no—
370C2×D4D4×D1312yes—
371C2×D4#612912yes—
372C22×C4—21no—
373C22×C4—21no—
374C22×C4—21no—
375C22×C4—21no—
376C22×C4—22no—
377C22×C4—22no—
378C22×C4—21no—
379C22×C4—21no—
380C22×C4—21no—
381C22×C4—21no—
382C22×C4—21no—
383C22×C4—22no—
384C22×C4—21no—
385C22×C4—21no—
386C22×C4—41no—
387C22×C4—41no—
388C22×C4—522no—
389C22×C4—522no—
390C22×C4C22⋊Dic1311yescharacteristic
391C22×C4C22⋊Dic1311yescharacteristic
392C22×C4C22⋊Dic1311yescharacteristic
393C22×C4C22×Dic1311yescharacteristic
394C4⋊C4—41no—
395C4⋊C4—524no—
396C22⋊C4—42no—
397C22⋊C4—42no—
398C22⋊C4—41no—
399C22⋊C4—41no—
400C22⋊C4—42no—
401C22⋊C4—81no—
402C22⋊C4—81no—
403C22⋊C4—264no—
404C22⋊C4—522no—
405C22⋊C4—522no—
406C22⋊C4—522no—
407C42—22no—
408C42—41no—
409C42—524no—
410C13#1308911yescharacteristic, complemented, Sylow
411C23—21no—
412C23—21no—
413C23—21no—
414C23—21no—
415C23—21no—
416C23—21no—
417C23—21no—
418C23—41no—
419C23—41no—
420C23—41no—
421C23—41no—
422C23—41no—
423C23—41no—
424C23—41no—
425C23—41no—
426C23—41no—
427C23—41no—
428C23—41no—
429C23—41no—
430C23—41no—
431C23#8818911yescharacteristic
432C23#8819111yescharacteristic
433C23#8819312yes—
434C23C2×C22⋊Dic1311yescharacteristic
435Q8—44no—
436D4—42no—
437D4—42no—
438D4—44no—
439D4—42no—
440D4—42no—
441D4—82no—
442D4—82no—
443D4—82no—
444D4—84no—
445D4—84no—
446C2×C4—22no—
447C2×C4—22no—
448C2×C4—22no—
449C2×C4—22no—
450C2×C4—21no—
451C2×C4—21no—
452C2×C4—21no—
453C2×C4—21no—
454C2×C4—21no—
455C2×C4—21no—
456C2×C4—22no—
457C2×C4—21no—
458C2×C4—21no—
459C2×C4—21no—
460C2×C4—42no—
461C2×C4—42no—
462C2×C4—42no—
463C2×C4—42no—
464C2×C4—41no—
465C2×C4—41no—
466C2×C4—41no—
467C2×C4—41no—
468C2×C4—41no—
469C2×C4—41no—
470C2×C4—41no—
471C2×C4—41no—
472C2×C4—524no—
473C2×C4—1042no—
474C2×C4—1042no—
475C2×C4—1042no—
476C2×C4—1042no—
477C2×C4—1042no—
478C2×C4#8807412yes—
479C2×C4#8807411yescharacteristic
480C2×C4#8807411yescharacteristic
481C2×C4D4×Dic1312yes—
482C22—21no—
483C22—21no—
484C22—21no—
485C22—21no—
486C22—22no—
487C22—41no—
488C22—41no—
489C22—42no—
490C22—41no—
491C22—41no—
492C22—41no—
493C22—41no—
494C22—41no—
495C22—41no—
496C22—41no—
497C22—81no—
498C22—81no—
499C22—81no—
500C22—81no—
501C22—81no—
502C22—81no—
503C22—81no—
504C22—81no—
505C22—81no—
506C22—81no—
507C22—81no—
508C22C2×#8807411yescharacteristic
509C22C2×#8807411yescharacteristic
510C22#1171888111yescharacteristic
511C4—21no—
512C4—21no—
513C4—22no—
514C4—22no—
515C4—42no—
516C4—41no—
517C4—81no—
518C4—81no—
519C4—1044no—
520C4—2082no—
521C2—21no—
522C2—21no—
523C2—41no—
524C2—42no—
525C2—41no—
526C2—81no—
527C2—161no—
528C2#1311529011yescharacteristic
529C2#1311650111yescharacteristic
530C2#1311650811yescharacteristic
subgroupG/H
centerC22C2×#88074
commutatorC22×C4×C13C22×C4
FrattiniC22×D4C22×D13
Fitting, prime radicalC13×#2431C2
socleC22×C13C2×#99
cosocleC22×D4×C13C23
hypercenter#2431D13
hypocenterC13#13089
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×#41 ◁ #2431

Complements

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

NH ≅ G/Ntype
1. C2×#11718901C2semidirect
2. C2×#11718137C2semidirect
3. #13114754C2semidirect
4. #13112961C2semidirect
8. C2×C13×#124C4semidirect
9. C2×C13×#121C4semidirect
13. C13×#391C4semidirect
17. C4×C13×C22⋊C4C4semidirect
69. #88074D4semidirect
224. C2×#124Dic13semidirect
225. C2×#121Dic13semidirect
234. #391Dic13semidirect
239. C4×C22⋊C4Dic13semidirect
410. C13#13089semidirect

Maximal subgroups

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

subgroupindex
C2×#117189012
C2×#117181372
#131147542
#131129612
C13×#24312
#1308913