Finite Group Databasebeta

← #15780414

Subgroups — #15780414

Order 3328.

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

normal subgroups only

This group has 818 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×#11718898C211yesmaximal, characteristic, complemented
2C2×#11718128C212yesmaximal, complemented
3#13114754C211yesmaximal, characteristic, complemented
4#13112954C212yesmaximal, complemented
5C13×#2404C211yesmaximal, characteristic
6C22×C13×#41C2211yescharacteristic
7C2×C13×#120C411yescharacteristic, complemented
8C2×C13×#120C2211yescharacteristic
9C22×C13×C22⋊C4C411yescharacteristic, complemented
10C22×#6099—21no—
11C13×#393—21no—
12C13×#392—21no—
13C13×#386—21no—
14C13×#386—21no—
15C13×#386C411yescharacteristic, complemented
16C13×#386C2211yescharacteristic
17C13×#381C411yescharacteristic, complemented
18#11718898—24no—
19C2×#88076—21no—
20C2×#88074—21no—
21C2×#88074C2212yes—
22C2×#88073C2212yes—
23#11718872—21no—
24#11718128—24no—
25C25×C13C2×C411yescharacteristic
26C2×C13×#41—22no—
27C2×C13×#41—22no—
28C2×C13×#41—41no—
29C2×C13×#41—41no—
30C2×C13×#41—42no—
31C22×Q8×C13D411yescharacteristic
32C22×D4×C13—21no—
33C22×D4×C13—21no—
34C22×D4×C13C2×C411yescharacteristic
35C22×D4×C13D411yescharacteristic
36C22×D4×C13C2311yescharacteristic
37C23×C4×C13C2×C411yescharacteristic
38C23×C4×C13C2×C411yescharacteristic
39C23×C4×C13D411yescharacteristic
40C23×C4×C13D411yescharacteristic
41C13×#120—22no—
42C13×#120—22no—
43C13×#120—42no—
44C2×C13×C22⋊C4—21no—
45C2×C13×C22⋊C4—21no—
46C2×C13×C22⋊C4—21no—
47C2×C13×C22⋊C4—21no—
48C2×C13×C22⋊C4—21no—
49C2×C13×C22⋊C4—21no—
50C2×C13×C22⋊C4—41no—
51C2×C13×C22⋊C4—41no—
52C2×C13×C22⋊C4C2×C411yescharacteristic
53C2×C13×C22⋊C4C2×C411yescharacteristic
54C2×C22⋊Dic13—22no—
55C2×#6099—24no—
56C2×#6099—22no—
57C2×#6099—42no—
58C2×#6099—41no—
59C22×#1055—41no—
60C13×#95—21no—
61C13×#95—21no—
62C13×#95—21no—
63C13×#95—21no—
64#88076—24no—
65#88074—22no—
66#88074—22no—
67#88074—42no—
68#88073—22no—
69#88073D414yescomplemented
70#88071—41no—
71#88071—41no—
72#13083—131nomaximal, Sylow
73C24×C13—21no—
74C24×C13—22no—
75C24×C13—41no—
76C24×C13—42no—
77C24×C13—41no—
78C24×C13—81no—
79C24×C13C22⋊C411yescharacteristic
80C24×C13C22×C411yescharacteristic
81C24×C13C2×D411yescharacteristic
82C13×#41—44no—
83C13×#41—44no—
84C13×#41—44no—
85C13×#41—44no—
86C2×Q8×C13—21no—
87C2×Q8×C13—21no—
88C2×Q8×C13—41no—
89C2×Q8×C13—41no—
90C2×D4×C13—22no—
91C2×D4×C13—22no—
92C2×D4×C13—22no—
93C2×D4×C13—22no—
94C2×D4×C13—41no—
95C2×D4×C13—41no—
96C2×D4×C13—41no—
97C2×D4×C13—41no—
98C2×D4×C13—42no—
99C2×D4×C13—42no—
100C2×D4×C13—42no—
101C2×D4×C13—42no—
102C2×D4×C13—81no—
103C2×D4×C13—81no—
104C2×D4×C13C2×D412yes—
105C2×D4×C13#4112yes—
106C22×C4×C13—22no—
107C22×C4×C13—21no—
108C22×C4×C13—21no—
109C22×C4×C13—21no—
110C22×C4×C13—21no—
111C22×C4×C13—22no—
112C22×C4×C13—22no—
113C22×C4×C13—21no—
114C22×C4×C13—21no—
115C22×C4×C13—21no—
116C22×C4×C13—21no—
117C22×C4×C13—21no—
118C22×C4×C13—21no—
119C22×C4×C13—21no—
120C22×C4×C13—41no—
121C22×C4×C13—41no—
122C22×C4×C13—41no—
123C22×C4×C13—81no—
124C22×C4×C13C22⋊C411yescharacteristic
125C22×C4×C13C22⋊C411yescharacteristic
126C22×C4×C13C22⋊C411yescharacteristic
127C22×C4×C13C2×D411yescharacteristic
128C22×Dic13—42no—
129C13×C22⋊C4—22no—
130C13×C22⋊C4—42no—
131C13×C22⋊C4—42no—
132C13×C22⋊C4—41no—
133C13×C22⋊C4—41no—
134C13×C22⋊C4—41no—
135C13×C22⋊C4—41no—
136C13×C22⋊C4—41no—
137C13×C22⋊C4—81no—
138C13×C22⋊C4—81no—
139C22⋊Dic13—42no—
140C22⋊Dic13—42no—
141#6099—24no—
142#6099—44no—
143#6099—42no—
144C2×#1055—44no—
145C2×#1055—42no—
146C2×#413—131no—
147#2404D1311yescharacteristic
148C2×AΣL(1,𝔽16)—132no—
149#1782—131no—
150#1390—132no—
151C23×C13—21no—
152C23×C13—21no—
153C23×C13—21no—
154C23×C13—21no—
155C23×C13—21no—
156C23×C13—21no—
157C23×C13—22no—
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—42no—
168C23×C13—41no—
169C23×C13—41no—
170C23×C13—41no—
171C23×C13—42no—
172C23×C13—82no—
173C23×C13—84no—
174C23×C13—84no—
175C23×C13—82no—
176C23×C13#9912yes—
177C23×C13C2×C22⋊C411yescharacteristic
178C23×C13C4×D412yes—
179C23×C13#12112yes—
180Q8×C13—42no—
181Q8×C13—42no—
182D4×C13—42no—
183D4×C13—42no—
184D4×C13—44no—
185D4×C13—44no—
186D4×C13—84no—
187D4×C13—84no—
188C2×C4×C13—22no—
189C2×C4×C13—22no—
190C2×C4×C13—22no—
191C2×C4×C13—22no—
192C2×C4×C13—21no—
193C2×C4×C13—21no—
194C2×C4×C13—21no—
195C2×C4×C13—21no—
196C2×C4×C13—21no—
197C2×C4×C13—21no—
198C2×C4×C13—21no—
199C2×C4×C13—21no—
200C2×C4×C13—21no—
201C2×C4×C13—21no—
202C2×C4×C13—42no—
203C2×C4×C13—42no—
204C2×C4×C13—42no—
205C2×C4×C13—42no—
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—41no—
213C2×C4×C13—41no—
214C2×C4×C13—41no—
215C2×C4×C13—82no—
216C2×C4×C13#9911yescharacteristic
217C2×C4×C13#9911yescharacteristic
218C2×C4×C13#12011yescharacteristic
219C2×C4×C13#12311yescharacteristic
220C2×Dic13—82no—
221C2×Dic13—82no—
222C2×Dic13—82no—
223#1055—44no—
224C22×#41C2×D1311yescharacteristic
225C22×M16—261no—
226C2×#120Dic1311yescharacteristic, complemented
227C2×#120C2×D1311yescharacteristic
228C22×C22⋊C4Dic1311yescharacteristic, complemented
229#413—264no—
230C2×#101—261no—
231C2×#100—132no—
232C2×#99—132no—
233C2×#99—261no—
234#393—21no—
235#392—21no—
236#386—21no—
237#386—21no—
238#386Dic1311yescharacteristic, complemented
239#386C2×D1311yescharacteristic
240#381—261no—
241#381Dic1311yescharacteristic, complemented
242AΣL(1,𝔽16)—264no—
243C22×C13—21no—
244C22×C13—21no—
245C22×C13—22no—
246C22×C13—22no—
247C22×C13—22no—
248C22×C13—42no—
249C22×C13—42no—
250C22×C13—42no—
251C22×C13—42no—
252C22×C13—42no—
253C22×C13—42no—
254C22×C13—41no—
255C22×C13—41no—
256C22×C13—41no—
257C22×C13—41no—
258C22×C13—41no—
259C22×C13—41no—
260C22×C13—42no—
261C22×C13—81no—
262C22×C13—81no—
263C22×C13—81no—
264C22×C13—81no—
265C22×C13—84no—
266C22×C13—84no—
267C22×C13—81no—
268C22×C13—81no—
269C22×C13#38611yescharacteristic
270C22×C13C2×#9911yescharacteristic
271C22×C13C2×#9911yescharacteristic
272C4×C13—21no—
273C4×C13—21no—
274C4×C13—21no—
275C4×C13—21no—
276C4×C13—41no—
277C4×C13—41no—
278C4×C13—81no—
279C4×C13—81no—
280C4×C13—81no—
281Dic13—162no—
282C25C2×Dic1311yescharacteristic
283C2×#41—22no—
284C2×#41—22no—
285C2×#41—41no—
286C2×#41—41no—
287C2×#41—42no—
288C22×Q8C22⋊D1311yescharacteristic
289C22×D4—21no—
290C22×D4—21no—
291C22×D4C2×Dic1311yescharacteristic
292C22×D4C22⋊D1311yescharacteristic
293C22×D4C22×D1311yescharacteristic
294C23×C4C2×Dic1311yescharacteristic
295C23×C4C2×Dic1311yescharacteristic
296C23×C4C22⋊D1311yescharacteristic
297C23×C4C22⋊D1311yescharacteristic
298C2×M16—264no—
299C2×M16—262no—
300C2×M16—522no—
301C2×M16—521no—
302C22×C8—521no—
303#120—22no—
304#120—22no—
305#120—42no—
306C2×C22⋊C4—21no—
307C2×C22⋊C4—21no—
308C2×C22⋊C4—21no—
309C2×C22⋊C4—21no—
310C2×C22⋊C4—21no—
311C2×C22⋊C4—21no—
312C2×C22⋊C4—41no—
313C2×C22⋊C4—41no—
314C2×C22⋊C4—262no—
315C2×C22⋊C4C2×Dic1311yescharacteristic
316C2×C22⋊C4C2×Dic1311yescharacteristic
317#101—264no—
318#100—134no—
319#100—262no—
320#99—262no—
321#99—262no—
322#99—522no—
323#95—21no—
324#95—21no—
325#95—21no—
326#95—21no—
327#95—521no—
328#95—521no—
329C2×C13—21no—
330C2×C13—21no—
331C2×C13—42no—
332C2×C13—42no—
333C2×C13—42no—
334C2×C13—82no—
335C2×C13#189811yescharacteristic
336C2×C13#212011yescharacteristic
337C2×C13#212211yescharacteristic
338C24—21no—
339C24—22no—
340C24—41no—
341C24—42no—
342C24—41no—
343C24—81no—
344C24C22⋊Dic1311yescharacteristic
345C24C22×Dic1311yescharacteristic
346C24C2×C22⋊D1311yescharacteristic
347#41—44no—
348#41—44no—
349#41—44no—
350#41—44no—
351C2×Q8—21no—
352C2×Q8—21no—
353C2×Q8—41no—
354C2×Q8—41no—
355C2×D4—22no—
356C2×D4—22no—
357C2×D4—22no—
358C2×D4—22no—
359C2×D4—41no—
360C2×D4—41no—
361C2×D4—41no—
362C2×D4—41no—
363C2×D4—42no—
364C2×D4—42no—
365C2×D4—42no—
366C2×D4—42no—
367C2×D4—81no—
368C2×D4—81no—
369C2×D4D4×D1312yes—
370C2×D4#612912yes—
371C22×C4—22no—
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—21no—
384C22×C4—21no—
385C22×C4—41no—
386C22×C4—41no—
387C22×C4—41no—
388C22×C4—81no—
389C22×C4—522no—
390C22×C4C22⋊Dic1311yescharacteristic
391C22×C4C22⋊Dic1311yescharacteristic
392C22×C4C22⋊Dic1311yescharacteristic
393C22×C4C2×C22⋊D1311yescharacteristic
394M16—264no—
395M16—524no—
396M16—522no—
397C2×C8—524no—
398C2×C8—522no—
399C22⋊C4—22no—
400C22⋊C4—42no—
401C22⋊C4—42no—
402C22⋊C4—41no—
403C22⋊C4—41no—
404C22⋊C4—41no—
405C22⋊C4—41no—
406C22⋊C4—41no—
407C22⋊C4—81no—
408C22⋊C4—81no—
409C22⋊C4—522no—
410C22⋊C4—522no—
411C13#1308311yescharacteristic, complemented, Sylow
412C23—21no—
413C23—21no—
414C23—21no—
415C23—21no—
416C23—21no—
417C23—21no—
418C23—22no—
419C23—41no—
420C23—41no—
421C23—41no—
422C23—41no—
423C23—41no—
424C23—41no—
425C23—41no—
426C23—41no—
427C23—41no—
428C23—42no—
429C23—42no—
430C23—41no—
431C23—41no—
432C23—41no—
433C23—82no—
434C23—84no—
435C23—84no—
436C23—82no—
437C23#8807412yes—
438C23D4×Dic1312yes—
439C23#8819312yes—
440C23C2×C22⋊Dic1311yescharacteristic
441Q8—42no—
442Q8—42no—
443D4—42no—
444D4—42no—
445D4—44no—
446D4—44no—
447D4—84no—
448D4—84no—
449C2×C4—22no—
450C2×C4—22no—
451C2×C4—22no—
452C2×C4—22no—
453C2×C4—21no—
454C2×C4—21no—
455C2×C4—21no—
456C2×C4—21no—
457C2×C4—21no—
458C2×C4—21no—
459C2×C4—21no—
460C2×C4—21no—
461C2×C4—21no—
462C2×C4—21no—
463C2×C4—42no—
464C2×C4—42no—
465C2×C4—42no—
466C2×C4—42no—
467C2×C4—41no—
468C2×C4—41no—
469C2×C4—41no—
470C2×C4—41no—
471C2×C4—41no—
472C2×C4—41no—
473C2×C4—41no—
474C2×C4—41no—
475C2×C4—41no—
476C2×C4—82no—
477C2×C4—1042no—
478C2×C4—1042no—
479C2×C4—1042no—
480C2×C4#8807411yescharacteristic
481C2×C4#8807411yescharacteristic
482C2×C4#8818911yescharacteristic
483C2×C4#8819111yescharacteristic
484C8—524no—
485C22—21no—
486C22—21no—
487C22—22no—
488C22—22no—
489C22—22no—
490C22—42no—
491C22—42no—
492C22—42no—
493C22—42no—
494C22—42no—
495C22—42no—
496C22—41no—
497C22—41no—
498C22—41no—
499C22—41no—
500C22—41no—
501C22—41no—
502C22—42no—
503C22—81no—
504C22—81no—
505C22—81no—
506C22—81no—
507C22—84no—
508C22—84no—
509C22—81no—
510C22—81no—
511C22C2×#8807411yescharacteristic
512C22C2×#8807411yescharacteristic
513C22#1171888111yescharacteristic
514C4—21no—
515C4—21no—
516C4—21no—
517C4—21no—
518C4—41no—
519C4—41no—
520C4—81no—
521C4—81no—
522C4—81no—
523C4—2082no—
524C2—21no—
525C2—21no—
526C2—42no—
527C2—42no—
528C2—42no—
529C2—82no—
530C2#1311529011yescharacteristic
531C2#1311647711yescharacteristic
532C2#1311648611yescharacteristic
subgroupG/H
centerC22C2×#88074
commutatorC24×C13C22×C4
FrattiniC22×D4C22×D13
Fitting, prime radicalC13×#2404C2
socleC22×C13C2×#99
cosocleC22×D4×C13C23
hypercenter#2404D13
hypocenterC13#13083
LCSG ▷ C24×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×#41 ◁ #2404

Complements

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

NH ≅ G/Ntype
1. C2×#11718898C2semidirect
2. C2×#11718128C2semidirect
3. #13114754C2semidirect
4. #13112954C2semidirect
7. C2×C13×#120C4semidirect
9. C22×C13×C22⋊C4C4semidirect
15. C13×#386C4semidirect
17. C13×#381C4semidirect
69. #88073D4semidirect
226. C2×#120Dic13semidirect
228. C22×C22⋊C4Dic13semidirect
238. #386Dic13semidirect
241. #381Dic13semidirect
411. C13#13083semidirect

Maximal subgroups

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

subgroupindex
C2×#117188982
C2×#117181282
#131147542
#131129542
C13×#24042
#1308313