Finite Group Databasebeta

← #16791755

Subgroups — #16791755

Order 3328.

1486 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719059C211yesmaximal, characteristic
2C2×#11719060C211yesmaximal, characteristic
3C2×#11719060C211yesmaximal, characteristic
4C2×C4×C4⋊#261C211yesmaximal, characteristic
5#13130021C214yesmaximal
6#13130016C214yesmaximal
7#13130014C211yesmaximal, characteristic
8#13130014C211yesmaximal, characteristic
9C4×C4⋊C4×D13C211yesmaximal, characteristic
10C22×C4⋊#261C2211yescharacteristic
11C22×C4⋊#261C2211yescharacteristic
12C22×C4⋊#261C2214yes—
13C22×C4⋊#261C2211yescharacteristic
14C22×C4⋊#261C2211yescharacteristic
15C22×C4×#261C2212yes—
16C2×C4⋊C4×D13C2212yes—
17C2×C42×D13C2211yescharacteristic
18C2×C42×D13C2211yescharacteristic
19C2×C42×D13C2211yescharacteristic
20C2×(C2×#261)⋊C4C2212yes—
21C2×(C2×#261)⋊C4C2212yes—
22C2×(C2×#261)⋊C4C2214yes—
23C2×(C2×#261)⋊C4C2212yes—
24C2×(C2×#261)⋊C4C2214yes—
25C2×(C2×#261)⋊C4C2214yes—
26#11719060—24no—
27#11719060—24no—
28#11719059—24no—
29C4×C4⋊#261—24no—
30C4×C13×C4⋊C4C411yescharacteristic, complemented
31C4⋊C4×Dic13C412yescomplemented
32C4×C4⋊Dic13C411yescharacteristic, complemented
33C4×#6101C411yescharacteristic, complemented
34C4×#6101C411yescharacteristic, complemented
35D13×#95C2212yes—
36#11718310C412yescomplemented
37C23×#261C2312yes—
38C23×#261C2312yes—
39C23×#261C2312yes—
40C23×#261C2312yes—
41C22×C4×D13C2312yes—
42C22×C4×D13C2311yescharacteristic
43C22×C4×D13C2311yescharacteristic
44C22×C4×D13C2312yes—
45C22×C4×D13C2311yescharacteristic
46C2×C4⋊#261—22no—
47C2×C4⋊#261—22no—
48C2×C4⋊#261—22no—
49C2×C4⋊#261—22no—
50C2×C4⋊#261—28no—
51C2×C4⋊#261—22no—
52C2×C4⋊#261—22no—
53C2×C4⋊#261—22no—
54C2×C4⋊#261—22no—
55C2×C4⋊#261—28no—
56C2×C4⋊#261—22no—
57C2×C4⋊#261—22no—
58C2×C4⋊#261—44no—
59C2×C4⋊#261D414yes—
60C2×C4⋊#261Q814yes—
61C2×C4×#261—24no—
62C2×C4×#261—44no—
63C2×C13×C4⋊C4C2×C412yes—
64C2×C42×C13C2×C411yescharacteristic
65C2×C42×C13C2×C411yescharacteristic
66C2×C42×C13C2×C411yescharacteristic
67C2×C4⋊Dic13C2×C412yes—
68C2×#6101C2×C412yes—
69C2×#6101C2×C412yes—
70C2×C4×Dic13C2×C412yes—
71C2×C4×Dic13C2×C412yes—
72C2×C4×Dic13C2×C411yescharacteristic
73C2×C4×Dic13C2×C411yescharacteristic
74C2×C4×Dic13C2×C411yescharacteristic
75C2×C4×Dic13C2×C411yescharacteristic
76C2×C4×Dic13C2×C411yescharacteristic
77C4⋊C4×D13—24no—
78C4⋊C4×D13—24no—
79C42×D13—22no—
80C42×D13—22no—
81C42×D13—22no—
82C42×D13—22no—
83C42×D13D414yes—
84C42×D13Q814yes—
85(C2×#261)⋊C4—28no—
86(C2×#261)⋊C4—24no—
87(C2×#261)⋊C4—24no—
88(C2×#261)⋊C4—24no—
89(C2×#261)⋊C4—28no—
90(C2×#261)⋊C4—44no—
91C13×#95C2×C412yes—
92#88071C2×C412yes—
93#88071C2×C412yes—
94#88071C2×C412yes—
95#13909—131nomaximal, Sylow
96C23×D13C2411yescharacteristic
97C22×#261—22no—
98C22×#261—22no—
99C22×#261—24no—
100C22×#261—22no—
101C22×#261—22no—
102C22×#261—24no—
103C22×#261—24no—
104C22×#261—24no—
105C22×#261—22no—
106C22×#261—22no—
107C22×#261—22no—
108C22×#261—22no—
109C22×#261—24no—
110C22×#261—22no—
111C22×#261—22no—
112C22×#261—24no—
113C22×#261—24no—
114C22×#261—24no—
115C22×#261C2×D414yes—
116C22×#261C2×Q814yes—
117C22×C4×C13C22×C412yes—
118C22×C4×C13C22×C411yescharacteristic
119C22×C4×C13C22×C411yescharacteristic
120C22×C4×C13C22×C412yes—
121C22×C4×C13C22×C411yescharacteristic
122C22×Dic13C22×C412yes—
123C22×Dic13C22×C411yescharacteristic
124C22×Dic13C22×C411yescharacteristic
125C22×Dic13C22×C412yes—
126C22×Dic13C22×C411yescharacteristic
127C2×C4×D13—22no—
128C2×C4×D13—22no—
129C2×C4×D13—22no—
130C2×C4×D13—22no—
131C2×C4×D13—22no—
132C2×C4×D13—22no—
133C2×C4×D13—22no—
134C2×C4×D13—22no—
135C2×C4×D13—22no—
136C2×C4×D13—22no—
137C2×C4×D13—22no—
138C2×C4×D13—22no—
139C2×C4×D13—22no—
140C2×C4×D13—22no—
141C2×C4×D13C2×D412yes—
142C2×C4×D13C2×D412yes—
143C2×C4×D13C2×D412yes—
144C2×C4×D13C2×D412yes—
145C2×C4×D13C2×Q812yes—
146C2×C4×D13C2×Q812yes—
147C2×C4×D13C2×Q812yes—
148C2×C4×D13C2×Q812yes—
149C2×C4×D13#4114yes—
150C2×C4×D13#4114yes—
151C2×C4×D13#4112yes—
152C2×C4×D13#4112yes—
153C4⋊#261—28no—
154C4⋊#261—28no—
155C4⋊#261—416no—
156C4⋊#261—44no—
157C4⋊#261—44no—
158C4×#261—48no—
159C13×C4⋊C4—24no—
160C42×C13—22no—
161C42×C13—22no—
162C42×C13C4⋊C414yescomplemented
163C4⋊Dic13—24no—
164#6101—24no—
165#6101—24no—
166C4×Dic13—22no—
167C4×Dic13—22no—
168C4×Dic13—24no—
169C4×Dic13—24no—
170C4×Dic13C4⋊C414yescomplemented
171C4×Dic13C4⋊C414yescomplemented
172C4×Dic13C4⋊C414yescomplemented
173C2×#384—131no—
174C2×#382—131no—
175C2×#382—131no—
176C2×C4×C4⋊C4—131no—
177C2×C4×C4⋊C4—131no—
178#1441—134no—
179#1436—134no—
180C4⋊#95—131no—
181C4⋊#95—131no—
182C23×C13C23×C411yescharacteristic
183C22×D13C22×D411yescharacteristic
184C22×D13C22×D411yescharacteristic
185C22×D13C22×Q811yescharacteristic
186C22×D13C22×Q811yescharacteristic
187C22×D13C2×#4111yescharacteristic
188C22×D13C2×#4111yescharacteristic
189C22×D13C2×#4112yes—
190C22×D13C2×#4112yes—
191C22×D13H(5,𝔽2)12yes—
192C22×D132−1+412yes—
193C2×#261—24no—
194C2×#261—24no—
195C2×#261—28no—
196C2×#261—28no—
197C2×#261—42no—
198C2×#261—42no—
199C2×#261—42no—
200C2×#261—42no—
201C2×#261—44no—
202C2×#261—44no—
203C2×#261—42no—
204C2×#261—42no—
205C2×#261—42no—
206C2×#261—42no—
207C2×#261—42no—
208C2×#261—42no—
209C2×#261—44no—
210C2×#261—44no—
211C2×#261—44no—
212C2×#261—44no—
213C2×C4×C13—22no—
214C2×C4×C13—22no—
215C2×C4×C13—22no—
216C2×C4×C13—22no—
217C2×C4×C13—22no—
218C2×C4×C13—22no—
219C2×C4×C13—22no—
220C2×C4×C13C2×C4⋊C412yes—
221C2×C4×C13C2×C4⋊C412yes—
222C2×C4×C13C2×C4⋊C412yes—
223C2×C4×C13#11714yes—
224C2×C4×C13C4×D412yes—
225C2×C4×C13C4×Q812yes—
226C2×Dic13—22no—
227C2×Dic13—22no—
228C2×Dic13—22no—
229C2×Dic13—22no—
230C2×Dic13—22no—
231C2×Dic13—22no—
232C2×Dic13—22no—
233C2×Dic13C2×C4⋊C412yes—
234C2×Dic13C2×C4⋊C412yes—
235C2×Dic13C2×C4⋊C412yes—
236C2×Dic13#11714yes—
237C2×Dic13C4×D412yes—
238C2×Dic13C4×Q812yes—
239C4×D13—22no—
240C4×D13—22no—
241C4×D13—24no—
242C4×D13—22no—
243C4×D13—22no—
244C4×D13—24no—
245C4×D13—24no—
246C4×D13—24no—
247C4×D13—24no—
248C4×D13—24no—
249C4×D13—42no—
250C4×D13—42no—
251C4×D13—42no—
252C4×D13—42no—
253C4×D13#12114yes—
254C4×D13C22⋊Q814yes—
255C4×D13#12514yes—
256C4×D13C4⋊Q814yes—
257C22×C4⋊C4—131no—
258C22×C4⋊C4—131no—
259C22×C4⋊C4—132no—
260C22×C4⋊C4—131no—
261C22×C4⋊C4—131no—
262C22×C4⋊C4—134no—
263C22×C42—131no—
264C22×C42—131no—
265C22×C42—131no—
266C22×C42—132no—
267#384—264no—
268#382—264no—
269#382—264no—
270C4×C4⋊C4—132no—
271C4×C4⋊C4—131no—
272C4×C4⋊C4—131no—
273C4×C4⋊C4—131no—
274C4×C4⋊C4—132no—
275C4×C4⋊C4—264no—
276C4×C4⋊C4#26111yescharacteristic, complemented
277C2×#95—132no—
278C2×#95—134no—
279C2×#95—132no—
280C2×#95—134no—
281C2×#95—132no—
282C2×#95—132no—
283C2×#95—134no—
284C22×C13C22×C4⋊C411yescharacteristic
285C22×C13C2×#11712yes—
286C22×C13C2×C4×D411yescharacteristic
287C22×C13C2×C4×Q811yescharacteristic
288C22×C13#52012yes—
289C2×D13C2×#12111yescharacteristic
290C2×D13C2×C22⋊Q811yescharacteristic
291C2×D13C2×#12511yescharacteristic
292C2×D13C2×C4⋊Q811yescharacteristic
293C2×D13#53211yescharacteristic
294C2×D13#53211yescharacteristic
295C2×D13#53312yes—
296C2×D13#53511yescharacteristic
297C2×D13#53611yescharacteristic
298C2×D13#54412yes—
299C2×D13#54612yes—
300C2×D13#54812yes—
301C2×D13#55212yes—
302C2×D13#55312yes—
303C2×D13#55412yes—
304C2×D13#55612yes—
305C2×D13#55712yes—
306C2×D13#55912yes—
307#261—44no—
308#261—44no—
309#261—82no—
310#261—82no—
311C4×C13—22no—
312C4×C13—24no—
313C4×C13—22no—
314C4×C13—42no—
315C4×C13#38914yes—
316Dic13—22no—
317Dic13—24no—
318Dic13—22no—
319Dic13—42no—
320Dic13#38914yes—
321C23×C4—131no—
322C23×C4—132no—
323C23×C4—131no—
324C23×C4—131no—
325C23×C4—132no—
326C23×C4—132no—
327C23×C4—132no—
328C23×C4—132no—
329C23×C4—132no—
330C2×C4⋊C4—134no—
331C2×C4⋊C4—134no—
332C2×C4⋊C4—132no—
333C2×C4⋊C4—132no—
334C2×C4⋊C4—132no—
335C2×C4⋊C4—264no—
336C2×C4⋊C4—264no—
337C2×C4⋊C4—262no—
338C2×C4⋊C4—262no—
339C2×C4⋊C4—262no—
340C2×C4⋊C4—262no—
341C2×C4⋊C4—262no—
342C2×C4⋊C4—262no—
343C2×C4⋊C4—262no—
344C2×C4⋊C4—262no—
345C2×C4⋊C4—268no—
346C2×C4⋊C4—262no—
347C2×C4⋊C4—262no—
348C2×C4⋊C4—268no—
349C2×C4⋊C4—524no—
350C2×C4⋊C4C2×#26112yes—
351C2×C42—131no—
352C2×C42—131no—
353C2×C42—131no—
354C2×C42—134no—
355C2×C42—134no—
356C2×C42—132no—
357C2×C42—132no—
358C2×C42—131no—
359C2×C42—131no—
360C2×C42—262no—
361C2×C42—262no—
362C2×C42—262no—
363C2×C42—262no—
364C2×C42—264no—
365C2×C42—524no—
366C2×C42C2×#26111yescharacteristic
367C2×C42C2×#26111yescharacteristic
368C2×C42C2×#26111yescharacteristic
369#95—132no—
370#95—132no—
371#95—132no—
372#95—268no—
373#95—264no—
374#95—264no—
375#95—264no—
376#95—268no—
377#95—524no—
378#95C2×#26112yes—
379C2×C13#228511yescharacteristic
380C2×C13C2×#38911yescharacteristic
381C2×C13#231711yescharacteristic
382C2×C13#235212yes—
383C2×C13#235512yes—
384D13#254411yescharacteristic
385D13#254511yescharacteristic
386D13#255012yes—
387D13#256511yescharacteristic
388D13#256611yescharacteristic
389D13#257012yes—
390C24—131no—
391C22×C4—131no—
392C22×C4—132no—
393C22×C4—132no—
394C22×C4—132no—
395C22×C4—132no—
396C22×C4—132no—
397C22×C4—132no—
398C22×C4—131no—
399C22×C4—132no—
400C22×C4—131no—
401C22×C4—132no—
402C22×C4—132no—
403C22×C4—132no—
404C22×C4—132no—
405C22×C4—134no—
406C22×C4—134no—
407C22×C4—134no—
408C22×C4—134no—
409C22×C4—132no—
410C22×C4—262no—
411C22×C4—262no—
412C22×C4—262no—
413C22×C4—262no—
414C22×C4—262no—
415C22×C4—262no—
416C22×C4—262no—
417C22×C4—262no—
418C22×C4—262no—
419C22×C4—262no—
420C22×C4—262no—
421C22×C4—262no—
422C22×C4—262no—
423C22×C4—262no—
424C22×C4—262no—
425C22×C4—262no—
426C22×C4—264no—
427C22×C4—264no—
428C22×C4—264no—
429C22×C4—262no—
430C22×C4—262no—
431C22×C4—264no—
432C22×C4—262no—
433C22×C4—262no—
434C22×C4—262no—
435C22×C4—264no—
436C22×C4—264no—
437C22×C4—262no—
438C22×C4—264no—
439C22×C4—262no—
440C22×C4—262no—
441C22×C4—264no—
442C22×C4C22×#26112yes—
443C22×C4C22×#26111yescharacteristic
444C22×C4C22×#26111yescharacteristic
445C22×C4C22×#26112yes—
446C22×C4C22×#26111yescharacteristic
447C4⋊C4—24no—
448C4⋊C4—264no—
449C4⋊C4—264no—
450C4⋊C4—268no—
451C4⋊C4—268no—
452C4⋊C4—264no—
453C4⋊C4—524no—
454C4⋊C4—524no—
455C4⋊C4—5216no—
456C42—22no—
457C42—22no—
458C42—134no—
459C42—134no—
460C42—134no—
461C42—264no—
462C42—264no—
463C42—262no—
464C42—262no—
465C42—528no—
466C42C4⋊#26114yescomplemented
467C13#1390911yescharacteristic, complemented, Sylow
468C23—131no—
469C23—131no—
470C23—132no—
471C23—132no—
472C23—131no—
473C23—131no—
474C23—131no—
475C23—131no—
476C23—132no—
477C23—132no—
478C23C23×#26111yescharacteristic
479C2×C4—22no—
480C2×C4—22no—
481C2×C4—22no—
482C2×C4—22no—
483C2×C4—22no—
484C2×C4—22no—
485C2×C4—22no—
486C2×C4—132no—
487C2×C4—132no—
488C2×C4—132no—
489C2×C4—134no—
490C2×C4—134no—
491C2×C4—134no—
492C2×C4—134no—
493C2×C4—132no—
494C2×C4—132no—
495C2×C4—134no—
496C2×C4—262no—
497C2×C4—264no—
498C2×C4—262no—
499C2×C4—262no—
500C2×C4—264no—
501C2×C4—262no—
502C2×C4—264no—
503C2×C4—264no—
504C2×C4—264no—
505C2×C4—264no—
506C2×C4—262no—
507C2×C4—262no—
508C2×C4—262no—
509C2×C4—262no—
510C2×C4—264no—
511C2×C4—264no—
512C2×C4—268no—
513C2×C4—268no—
514C2×C4—262no—
515C2×C4—262no—
516C2×C4—262no—
517C2×C4—522no—
518C2×C4—522no—
519C2×C4—522no—
520C2×C4—522no—
521C2×C4—522no—
522C2×C4—522no—
523C2×C4—522no—
524C2×C4—522no—
525C2×C4—524no—
526C2×C4—524no—
527C2×C4—522no—
528C2×C4—522no—
529C2×C4—524no—
530C2×C4—522no—
531C2×C4—522no—
532C2×C4—522no—
533C2×C4—522no—
534C2×C4—524no—
535C2×C4—524no—
536C2×C4—524no—
537C2×C4C2×C4⋊#26112yes—
538C2×C4C2×C4⋊#26112yes—
539C2×C4C2×C4⋊#26112yes—
540C2×C4#8823714yes—
541C2×C4D4×#26112yes—
542C2×C4Q8×#26112yes—
543C22—131no—
544C22—131no—
545C22—132no—
546C22—131no—
547C22—131no—
548C22—131no—
549C22—131no—
550C22—131no—
551C22—131no—
552C22—132no—
553C22—132no—
554C22—132no—
555C22—132no—
556C22—132no—
557C22—132no—
558C22—132no—
559C22—132no—
560C22—132no—
561C22C22×C4⋊#26111yescharacteristic
562C22C2×#8823712yes—
563C22C2×D4×#26111yescharacteristic
564C22C2×Q8×#26111yescharacteristic
565C22#1171963112yes—
566C4—22no—
567C4—22no—
568C4—24no—
569C4—42no—
570C4—134no—
571C4—262no—
572C4—262no—
573C4—264no—
574C4—524no—
575C4—524no—
576C4—522no—
577C4—1042no—
578C4—1042no—
579C4#1171908314yes—
580C2—131no—
581C2—131no—
582C2—131no—
583C2—131no—
584C2—132no—
585C2—132no—
586C2#1313128511yescharacteristic
587C2C2×#1171908311yescharacteristic
588C2#1313131711yescharacteristic
589C2#1313135212yes—
590C2#1313135512yes—
subgroupG/H
center, FrattiniC23C23×#261
commutator, socleC23×C13C23×C4
FittingC4×C13×C4⋊C4C4
prime radical, cosocleC23×D13C24
hypercenterC4×C4⋊C4#261
hypocenterC13#13909
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
30. C4×C13×C4⋊C4C4semidirect
31. C4⋊C4×Dic13C4semidirect
32. C4×C4⋊Dic13C4semidirect
33. C4×#6101C4semidirect
34. C4×#6101C4semidirect
36. #11718310C4semidirect
162. C42×C13C4⋊C4semidirect
170. C4×Dic13C4⋊C4semidirect
171. C4×Dic13C4⋊C4semidirect
172. C4×Dic13C4⋊C4semidirect
276. C4×C4⋊C4#261semidirect
466. C42C4⋊#261semidirect
467. C13#13909semidirect

Maximal subgroups

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

subgroupindex
C2×#117190592
C2×#117190602
C2×C4×C4⋊#2612
#131300212
#131300162
#131300142
C4×C4⋊C4×D132
#1390913