Finite Group Databasebeta

← #16023061

Subgroups — #16023061

Order 3328.

2542 conjugacy classes of subgroups.

The subgroup lattice has 664 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719227C211yesmaximal, characteristic
2#13117790C214yesmaximal, complemented
3#13117782C214yesmaximal, complemented
4#13117764C214yesmaximal, complemented
5#13117760C214yesmaximal, complemented
6#13117446C211yesmaximal, characteristic, complemented
7#13117445C211yesmaximal, characteristic, complemented
8#13117444C211yesmaximal, characteristic, complemented
9#13117425C212yesmaximal
10#13117242C211yesmaximal, characteristic, complemented
11#13117240C212yesmaximal, complemented
12#13117238C212yesmaximal, complemented
13D13×#384C211yesmaximal, characteristic, complemented
14#13117190C212yesmaximal, complemented
15C13×#2314C211yesmaximal, characteristic, complemented
16C22×#6127C2211yescharacteristic
17C2×C13×#117C2211yescharacteristic
18C22×C4×Dic13C2211yescharacteristic
19#11719227C4116yescomplemented
20C2×#88147C2212yes—
21C2×#88146C2212yes—
22C2×C4⋊C4×D13C2212yes—
23C2×C4⋊C4×D13C2214yes—
24C2×#88141C2212yes—
25C2×#88135C2212yes—
26C2×#88135C2212yes—
27C2×#88131C2214yes—
28C2×#88126C2214yes—
29C2×#88126C2211yescharacteristic
30C2×#88126C2211yescharacteristic
31C2×C42×D13C2211yescharacteristic
32C2×C42×D13C2211yescharacteristic
33C13×#388C2214yes—
34C13×#387C2214yes—
35C13×#384C2211yescharacteristic
36C13×#382C2211yescharacteristic
37C13×#380C2212yes—
38C4×C13×C4⋊C4C2212yes—
39#11718873C2212yes—
40#11718651C2214yes—
41#11718648C2212yes—
42#11718648C2212yes—
43#11718642C2214yes—
44#11718639C2214yes—
45#11718637C2212yes—
46#11718637C2214yes—
47#11718637C2212yes—
48C4⋊C4×Dic13C2212yes—
49C4⋊C4×Dic13C2212yes—
50#11718618C2214yes—
51#11718617C2214yes—
52#11718612C2214yes—
53#11718603C2214yes—
54C4×#6103C2214yes—
55#11718597C2211yescharacteristic
56#11718596C2211yescharacteristic
57C4×C4⋊Dic13C2212yes—
58C4×#6101C2214yes—
59C4×#6101C2214yes—
60#11718331C2214yes—
61#11718328C2214yes—
62#11718328C2214yes—
63#11718327C2214yes—
64#11718326C2214yes—
65#11718316C2214yes—
66#11718311C2214yes—
67#11718311C2214yes—
68#11718310C2214yes—
69#11718310C2214yes—
70#11718310C2214yes—
71#11718307C2214yes—
72C23×C4×C13C2311yescharacteristic
73C22×C22⋊D13C2311yescharacteristic
74C22×C22⋊D13C2311yescharacteristic
75C23×Dic13C2312yes—
76C2×#6127—24no—
77C2×#6127—24no—
78C2×#6127C2×C418yes—
79C22×D52C2311yescharacteristic
80C22×C4×D13C2312yes—
81C22×C4×D13C2311yescharacteristic
82C22×C4×D13C2312yes—
83C22×C4×D13C2314yes—
84C22×C4×D13C2311yescharacteristic
85C22×Dic26C2311yescharacteristic
86C13×#117C2×C418yescomplemented
87C2×C13×C4⋊C4C2312yes—
88C2×C13×C4⋊C4C2312yes—
89C2×C13×C4⋊C4C2314yes—
90C2×C13×C4⋊C4C2312yes—
91C2×C13×C22⋊C4C2314yes—
92C2×C13×C22⋊C4C2312yes—
93C2×C42×C13C2314yes—
94C2×C42×C13C2311yescharacteristic
95C2×C42×C13C2311yescharacteristic
96C2×C22⋊Dic13C2314yes—
97C2×#6103C2314yes—
98C2×#6103C2314yes—
99C2×#6103C2314yes—
100C2×#6103C2312yes—
101C2×#6103C2312yes—
102C2×C4⋊Dic13C2312yes—
103C2×C4⋊Dic13C2312yes—
104C2×C4⋊Dic13C2314yes—
105C2×#6101C2314yes—
106C2×#6101C2314yes—
107C2×#6101C2314yes—
108C2×#6101C2314yes—
109C2×#6101C2314yes—
110C2×#6101C2312yes—
111C2×#6101C2312yes—
112C2×C4×Dic13C2×C418yescomplemented
113C2×C4×Dic13C2314yes—
114C2×C4×Dic13C2314yes—
115C2×C4×Dic13C2314yes—
116C2×C4×Dic13C2314yes—
117C2×C4×Dic13C2311yescharacteristic
118C2×C4×Dic13C2312yes—
119C2×C4×Dic13C2312yes—
120C2×C4×Dic13C2311yescharacteristic
121C2×C4×Dic13C2312yes—
122#88147C2×C4116yes—
123#88146—28no—
124C4⋊C4×D13—28no—
125C4⋊C4×D13—48no—
126#88141C2×C4116yescomplemented
127#88135C2×C4116yes—
128#88135C2×C4116yescomplemented
129#88131—48no—
130#88126—48no—
131#88126C2×C418yes—
132#88126C2×C418yescomplemented
133C42×D13C2×C418yes—
134C42×D13C2×C418yescomplemented
135C13×#95C2314yes—
136C13×#95C2314yes—
137C13×#95C2314yes—
138#88071C2314yes—
139#88071C2314yes—
140#88071C2314yes—
141#88071C2314yes—
142#88071C2314yes—
143#88071C2314yes—
144#88071C2314yes—
145#34188—131nomaximal, Sylow
146C24×C13C2411yescharacteristic
147C23×D13C2411yescharacteristic
148C23×D13C2411yescharacteristic
149C22×C4×C13—22no—
150C22×C4×C13—22no—
151C22×C4×C13C22×C414yes—
152C22×C4×C13C2414yes—
153C22×C4×C13C2414yes—
154C22×C4×C13C2411yescharacteristic
155C22×C4×C13C2412yes—
156C22×C4×C13C2412yes—
157C22×C4×C13C2411yescharacteristic
158C2×C22⋊D13—22no—
159C2×C22⋊D13—22no—
160C2×C22⋊D13—22no—
161C2×C22⋊D13—22no—
162C2×C22⋊D13C22×C414yes—
163C2×C22⋊D13C22×C414yes—
164C22×Dic13—24no—
165C22×Dic13—24no—
166C22×Dic13C22×C418yes—
167C22×Dic13C2414yes—
168C22×Dic13C2414yes—
169C22×Dic13C2411yescharacteristic
170C22×Dic13C2412yes—
171C22×Dic13C2411yescharacteristic
172C22×Dic13C2412yes—
173#6127—232no—
174C2×D52—22no—
175C2×D52—22no—
176C2×D52C22×C414yes—
177C2×C4×D13—22no—
178C2×C4×D13—22no—
179C2×C4×D13—24no—
180C2×C4×D13—24no—
181C2×C4×D13—24no—
182C2×C4×D13—24no—
183C2×C4×D13—28no—
184C2×C4×D13—44no—
185C2×C4×D13—44no—
186C2×C4×D13C22×C418yes—
187C2×C4×D13C22×C414yes—
188C2×C4×D13C22×C418yes—
189C2×C4×D13C22×C414yes—
190C2×C4×D13#4114yes—
191C2×C4×D13#4114yes—
192C2×Dic26—22no—
193C2×Dic26—22no—
194C2×Dic26C22×C414yes—
195C13×C4⋊C4—24no—
196C13×C4⋊C4—24no—
197C13×C4⋊C4—44no—
198C13×C4⋊C4C22×C418yes—
199C13×C22⋊C4—44no—
200C13×C22⋊C4C22×C418yes—
201C42×C13—44no—
202C42×C13C22×C414yes—
203C42×C13C22×C414yes—
204C22⋊Dic13—44no—
205#6103—28no—
206#6103—44no—
207#6103—44no—
208#6103C22×C418yes—
209#6103C22×C418yes—
210C4⋊Dic13—24no—
211C4⋊Dic13—24no—
212C4⋊Dic13—44no—
213#6101—28no—
214#6101—28no—
215#6101—28no—
216#6101—28no—
217#6101—28no—
218#6101C22×C418yes—
219#6101C22×C418yes—
220C4×Dic13—28no—
221C4×Dic13—44no—
222C4×Dic13—44no—
223C4×Dic13—44no—
224C4×Dic13C22×C414yes—
225C4×Dic13C22×C418yes—
226C4×Dic13C22×C418yes—
227C4×Dic13C22×C414yes—
228C4×Dic13C22×C418yes—
229C2×C4×#41—131no—
230#2355—134no—
231#2354—134no—
232#2352—134no—
233#2352—134no—
234#2314—131no—
235#2314—131no—
236#2314—131no—
237#2314D1311yescharacteristic, complemented
238#2311—132no—
239#2285—131no—
240#2285—132no—
241#2285—132no—
242C2×#384—131no—
243#2274—132no—
244C23×C13—21no—
245C23×C13—21no—
246C23×C13—22no—
247C23×C13—22no—
248C23×C13C23×C412yes—
249C23×C13C2511yescharacteristic
250C22×D13—22no—
251C22×D13—22no—
252C22×D13—21no—
253C22×D13—21no—
254C22×D13—22no—
255C22×D13—22no—
256C22×D13C23×C412yes—
257C22×D13C23×C412yes—
258C22×D13C2×#4112yes—
259C22×D13C2×#4112yes—
260C2×C4×C13—21no—
261C2×C4×C13—21no—
262C2×C4×C13—22no—
263C2×C4×C13—22no—
264C2×C4×C13—22no—
265C2×C4×C13—22no—
266C2×C4×C13—28no—
267C2×C4×C13—24no—
268C2×C4×C13—24no—
269C2×C4×C13—24no—
270C2×C4×C13—24no—
271C2×C4×C13—24no—
272C2×C4×C13—24no—
273C2×C4×C13C23×C412yes—
274C2×C4×C13C23×C414yes—
275C2×C4×C13C23×C414yes—
276C2×C4×C13C23×C412yes—
277C2×C4×C13C2×#4112yes—
278C2×C4×C13C2×#4112yes—
279C22⋊D13—28no—
280C22⋊D13—28no—
281C2×Dic13—21no—
282C2×Dic13—21no—
283C2×Dic13—22no—
284C2×Dic13—22no—
285C2×Dic13—216no—
286C2×Dic13—24no—
287C2×Dic13—24no—
288C2×Dic13—24no—
289C2×Dic13—24no—
290C2×Dic13—24no—
291C2×Dic13—24no—
292C2×Dic13C23×C414yes—
293C2×Dic13C23×C412yes—
294C2×Dic13C23×C412yes—
295C2×Dic13C23×C414yes—
296C2×Dic13C2×#4112yes—
297C2×Dic13C2×#4112yes—
298C2×Dic13H(5,𝔽2)14yes—
299C2×Dic132−1+414yes—
300D52—28no—
301C4×D13—28no—
302C4×D13—216no—
303C4×D13—216no—
304C4×D13—88no—
305C4×D13#117116yescomplemented
306Dic26—28no—
307C22×#41—131no—
308C4×#41—1316no—
309C2×C4×Q8—132no—
310C2×C4×D4—132no—
311C2×C4×D4—132no—
312C2×C4×D4—132no—
313C2×#117—132no—
314C2×#117—134no—
315C2×#117—131no—
316C2×#117—131no—
317C2×#117—134no—
318C2×#117C2×D1311yescharacteristic
319C22×C4⋊C4—132no—
320C22×C4⋊C4—134no—
321C22×C42—131no—
322C22×C42—131no—
323C22×C42—131no—
324#391—134no—
325#390—134no—
326#388—134no—
327#388—134no—
328#388—134no—
329#388C2×D1314yes—
330#387—134no—
331#387—134no—
332#387—134no—
333#387C2×D1314yes—
334#386—134no—
335#386—134no—
336#384—134no—
337#384—132no—
338#384—132no—
339#384—131no—
340#384C2×D1311yescharacteristic
341#382—131no—
342#382—134no—
343#382—134no—
344#382C2×D1311yescharacteristic
345#380—132no—
346#380—132no—
347#380—132no—
348#380—134no—
349#380—134no—
350#380—134no—
351#380C2×D1312yes—
352C4×C4⋊C4—132no—
353C4×C4⋊C4—132no—
354C4×C4⋊C4—132no—
355C4×C4⋊C4—134no—
356C4×C4⋊C4—134no—
357C4×C4⋊C4—134no—
358C4×C4⋊C4—134no—
359C4×C4⋊C4—134no—
360C4×C4⋊C4C2×D1312yes—
361C4×C22⋊C4—134no—
362C4×C22⋊C4—134no—
363C22×C13—22no—
364C22×C13—24no—
365C22×C13—41no—
366C22×C13—41no—
367C22×C13—42no—
368C22×C13C24×C411yescharacteristic
369C22×C13C22×#4111yescharacteristic
370C22×C13C22×#4111yescharacteristic
371C22×C13C2×H(5,𝔽2)12yes—
372C22×C13C2×2−1+412yes—
373C2×D13—24no—
374C2×D13—22no—
375C2×D13—22no—
376C2×D13—24no—
377C2×D13—22no—
378C2×D13—24no—
379C2×D13—41no—
380C2×D13—41no—
381C2×D13—42no—
382C2×D13C2×#11714yes—
383C4×C13—22no—
384C4×C13—24no—
385C4×C13—24no—
386C4×C13—44no—
387C4×C13—44no—
388C4×C13C2×#11714yes—
389Dic13—22no—
390Dic13—24no—
391Dic13—44no—
392Dic13—44no—
393Dic13C2×#11714yes—
394Dic13#52018yes—
395C2×#41—138no—
396C2×#41—264no—
397C2×#41—264no—
398C22×Q8—131no—
399C22×D4—131no—
400C22×D4—131no—
401C22×D4—131no—
402C23×C4—131no—
403C23×C4—132no—
404C23×C4—132no—
405C23×C4—132no—
406C23×C4—131no—
407C23×C4—134no—
408C23×C4C22×D1311yescharacteristic
409C4×Q8—1316no—
410C4×D4—1316no—
411C4×D4—1316no—
412C4×D4—1316no—
413#117—138no—
414#117—138no—
415#117—268no—
416#117—528no—
417#117—528no—
418#117C4×D1318yescomplemented
419C2×C4⋊C4—132no—
420C2×C4⋊C4—132no—
421C2×C4⋊C4—134no—
422C2×C4⋊C4—134no—
423C2×C4⋊C4—134no—
424C2×C4⋊C4—132no—
425C2×C4⋊C4—134no—
426C2×C4⋊C4—132no—
427C2×C4⋊C4—134no—
428C2×C4⋊C4—134no—
429C2×C4⋊C4—268no—
430C2×C4⋊C4—528no—
431C2×C4⋊C4C22×D1312yes—
432C2×C4⋊C4C22×D1312yes—
433C2×C4⋊C4C22×D1314yes—
434C2×C4⋊C4C22×D1312yes—
435C2×C22⋊C4—132no—
436C2×C22⋊C4—132no—
437C2×C22⋊C4—134no—
438C2×C22⋊C4—134no—
439C2×C22⋊C4—134no—
440C2×C22⋊C4—134no—
441C2×C22⋊C4C22×D1314yes—
442C2×C22⋊C4C22×D1312yes—
443C2×C42—138no—
444C2×C42—131no—
445C2×C42—132no—
446C2×C42—132no—
447C2×C42—132no—
448C2×C42—131no—
449C2×C42—138no—
450C2×C42—138no—
451C2×C42—134no—
452C2×C42—134no—
453C2×C42—134no—
454C2×C42—134no—
455C2×C42C22×D1314yes—
456C2×C42C22×D1311yescharacteristic
457C2×C42C22×D1311yescharacteristic
458#95—134no—
459#95—134no—
460#95—134no—
461#95—134no—
462#95—134no—
463#95—134no—
464#95—134no—
465#95C22×D1314yes—
466#95C22×D1314yes—
467#95C22×D1314yes—
468C2×C13—42no—
469C2×C13C22×#11711yescharacteristic
470C2×C13C2×#52012yes—
471C2×C13#350811yescharacteristic
472C2×C13#350911yescharacteristic
473C2×C13#351112yes—
474D13—24no—
475D13—42no—
476C24—131no—
477C24—131no—
478C24C23×D1311yescharacteristic
479#41—2632no—
480C2×Q8—134no—
481C2×Q8—262no—
482C2×Q8—262no—
483C2×D4—134no—
484C2×D4—134no—
485C2×D4—134no—
486C2×D4—262no—
487C2×D4—262no—
488C2×D4—262no—
489C2×D4—262no—
490C2×D4—262no—
491C2×D4—262no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—131no—
495C22×C4—132no—
496C22×C4—134no—
497C22×C4—134no—
498C22×C4—134no—
499C22×C4—138no—
500C22×C4—131no—
501C22×C4—132no—
502C22×C4—134no—
503C22×C4—138no—
504C22×C4—138no—
505C22×C4—134no—
506C22×C4—134no—
507C22×C4—264no—
508C22×C4—264no—
509C22×C4—264no—
510C22×C4—264no—
511C22×C4—268no—
512C22×C4—264no—
513C22×C4—264no—
514C22×C4—262no—
515C22×C4—262no—
516C22×C4—524no—
517C22×C4—524no—
518C22×C4C2×C4×D1314yes—
519C22×C4C23×D1314yes—
520C22×C4C23×D1314yes—
521C22×C4C23×D1311yescharacteristic
522C22×C4C23×D1312yes—
523C22×C4C23×D1312yes—
524C22×C4C23×D1311yescharacteristic
525C4⋊C4—24no—
526C4⋊C4—24no—
527C4⋊C4—44no—
528C4⋊C4—138no—
529C4⋊C4—138no—
530C4⋊C4—268no—
531C4⋊C4—268no—
532C4⋊C4—268no—
533C4⋊C4—268no—
534C4⋊C4—268no—
535C4⋊C4—264no—
536C4⋊C4—264no—
537C4⋊C4—524no—
538C4⋊C4C2×C4×D1318yes—
539C22⋊C4—44no—
540C22⋊C4—138no—
541C22⋊C4—138no—
542C22⋊C4—268no—
543C22⋊C4—524no—
544C22⋊C4—524no—
545C22⋊C4—524no—
546C22⋊C4C2×C4×D1318yes—
547C42—44no—
548C42—134no—
549C42—134no—
550C42—138no—
551C42—138no—
552C42—138no—
553C42—268no—
554C42—524no—
555C42—524no—
556C42—524no—
557C42C2×C4×D1314yes—
558C42C2×C4×D1314yes—
559C13#3418811yescharacteristic, complemented, Sylow
560C23—21no—
561C23—21no—
562C23—22no—
563C23—22no—
564C23—132no—
565C23—132no—
566C23—132no—
567C23—132no—
568C23—262no—
569C23—262no—
570C23—261no—
571C23—261no—
572C23—262no—
573C23—262no—
574C23C22×C4×D1312yes—
575C23C24×D1311yescharacteristic
576Q8—268no—
577D4—268no—
578D4—268no—
579D4—268no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—22no—
583C2×C4—22no—
584C2×C4—22no—
585C2×C4—22no—
586C2×C4—28no—
587C2×C4—24no—
588C2×C4—24no—
589C2×C4—24no—
590C2×C4—24no—
591C2×C4—24no—
592C2×C4—24no—
593C2×C4—134no—
594C2×C4—132no—
595C2×C4—132no—
596C2×C4—132no—
597C2×C4—134no—
598C2×C4—134no—
599C2×C4—1316no—
600C2×C4—134no—
601C2×C4—132no—
602C2×C4—2616no—
603C2×C4—2616no—
604C2×C4—2616no—
605C2×C4—261no—
606C2×C4—261no—
607C2×C4—262no—
608C2×C4—262no—
609C2×C4—268no—
610C2×C4—264no—
611C2×C4—264no—
612C2×C4—264no—
613C2×C4—264no—
614C2×C4—264no—
615C2×C4—264no—
616C2×C4—1048no—
617C2×C4C22×C4×D1312yes—
618C2×C4C22×C4×D1314yes—
619C2×C4C22×C4×D1314yes—
620C2×C4C22×C4×D1312yes—
621C2×C4#41×D1312yes—
622C2×C4#41×D1312yes—
623C22—22no—
624C22—24no—
625C22—41no—
626C22—41no—
627C22—42no—
628C22—134no—
629C22—262no—
630C22—262no—
631C22—264no—
632C22—264no—
633C22—262no—
634C22—264no—
635C22—521no—
636C22—521no—
637C22—522no—
638C22C23×C4×D1311yescharacteristic
639C22C2×#41×D1311yescharacteristic
640C22C2×#41×D1311yescharacteristic
641C22D13×H(5,𝔽2)12yes—
642C22D13×2−1+412yes—
643C4—22no—
644C4—24no—
645C4—24no—
646C4—44no—
647C4—44no—
648C4—134no—
649C4—138no—
650C4—262no—
651C4—264no—
652C4—524no—
653C4—524no—
654C4D13×#11714yes—
655C2—42no—
656C2—264no—
657C2—522no—
658C2C2×D13×#11711yescharacteristic
659C2D13×#52012yes—
660C2#1312870811yescharacteristic
661C2#1312871811yescharacteristic
662C2#1312874112yes—
subgroupG/H
center, FrattiniC23C24×D13
commutatorC22×C13C24×C4
FittingC13×#2314C2
socle, cosocleC23×C13C25
prime radicalC22×#6127C22
hypercenter#2314D13
hypocenterC13#34188
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ #2314

Complements

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

NH ≅ G/Ntype
2. #13117790C2semidirect
3. #13117782C2semidirect
4. #13117764C2semidirect
5. #13117760C2semidirect
6. #13117446C2semidirect
7. #13117445C2semidirect
8. #13117444C2semidirect
10. #13117242C2semidirect
11. #13117240C2semidirect
12. #13117238C2semidirect
13. D13×#384C2semidirect
14. #13117190C2semidirect
15. C13×#2314C2semidirect
19. #11719227C4semidirect
86. C13×#117C2×C4semidirect
112. C2×C4×Dic13C2×C4semidirect
126. #88141C2×C4semidirect
128. #88135C2×C4semidirect
132. #88126C2×C4semidirect
134. C42×D13C2×C4semidirect
237. #2314D13semidirect
305. C4×D13#117semidirect
418. #117C4×D13semidirect
559. C13#34188semidirect

Maximal subgroups

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

subgroupindex
C2×#117192272
#131177902
#131177822
#131177642
#131177602
#131174462
#131174452
#131174442
#131174252
#131172422
#131172402
#131172382
D13×#3842
#131171902
C13×#23142
#3418813