Finite Group Databasebeta

← #16023246

Subgroups — #16023246

Order 3328.

3038 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88151C211yesmaximal, characteristic
2C2×#11719221C211yesmaximal, characteristic, complemented
3C2×D13×#117C211yesmaximal, characteristic
4#13117865C214yesmaximal, complemented
5#13117843C214yesmaximal, complemented
6#13117703C214yesmaximal, complemented
7#13117688C214yesmaximal
8#13117519C214yesmaximal, complemented
9#13117454C211yesmaximal, characteristic, complemented
10#13117420C211yesmaximal, characteristic, complemented
11C4×#88151C214yesmaximal, complemented
12#13117215C211yesmaximal, characteristic
13C13×#2274C211yesmaximal, characteristic, complemented
14C23×C4×D13C2211yescharacteristic
15C23×Dic26C2211yescharacteristic
16C2×C13×#117C2211yescharacteristic
17C2×C13×#117C2211yescharacteristic
18C22×C13×C4⋊C4C2211yescharacteristic
19C22×#6103C2212yes—
20C2×#88180C2211yescharacteristic
21C2×#88180C2211yescharacteristic
22C22×C4⋊Dic13C2212yes—
23D13×#117—28no—
24#11719221—28no—
25C2×#88151C4116yescomplemented
26C2×#88151C2212yes—
27C2×#88151C2212yes—
28C2×#88151C2212yes—
29C2×#88151C2212yes—
30C2×#88146C2212yes—
31C2×C4⋊C4×D13C2212yes—
32C2×#88141C2214yescomplemented
33C2×C22⋊C4×D13C2212yes—
34C2×#88131C2212yes—
35C2×#88131C2214yes—
36C2×#88126C2212yes—
37C2×C42×D13C2212yes—
38C2×C4×Dic26C2214yescomplemented
39C4×C13×C4⋊C4C2214yescomplemented
40C4×C13×C4⋊C4C2214yescomplemented
41C4×C13×C22⋊C4C2214yes—
42#11718873C2214yes—
43#11718648C2212yes—
44#11718648C2212yes—
45#11718646C2214yescomplemented
46#11718646C2214yescomplemented
47#11718635C2214yescomplemented
48#11718616C2212yes—
49#11718604C2212yes—
50#11718604C2214yes—
51#11718601C2218yes—
52C4×#6103C2212yes—
53C4×#6103C2212yes—
54C4×#6103C2218yes—
55C4×C4⋊Dic13C2218yescomplemented
56#11718590C2214yescomplemented
57#11718589C2218yescomplemented
58#11718331C2218yes—
59#11718329C2218yes—
60#11718314C2218yescomplemented
61#11718314C2218yescomplemented
62C24×D13C2311yescharacteristic
63C23×C4×C13C2312yes—
64C23×C4×C13C2311yescharacteristic
65C23×Dic13C2311yescharacteristic
66C23×Dic13C2312yes—
67C22×C4×D13—24no—
68C22×C4×D13—24no—
69C22×C4×D13C2×C418yes—
70C22×C4×D13C2314yes—
71C22×C4×D13C2311yescharacteristic
72C22×C4×D13C2311yescharacteristic
73C22×C4×D13C2311yescharacteristic
74C22×C4×D13C2311yescharacteristic
75C22×Dic26—24no—
76C22×Dic26—24no—
77C22×Dic26C2×C418yescomplemented
78C22×Dic26C2312yes—
79C22×Dic26C2312yes—
80C13×#117—24no—
81C13×#117D418yes—
82C2×C13×C4⋊C4C2×C418yescomplemented
83C2×C13×C4⋊C4C2312yes—
84C2×C13×C4⋊C4C2312yes—
85C2×C13×C4⋊C4C2312yes—
86C2×C13×C4⋊C4C2312yes—
87C2×C13×C22⋊C4C2312yes—
88C2×C13×C22⋊C4C2312yes—
89C2×C42×C13C2312yes—
90C2×C42×C13C2318yes—
91C2×C42×C13C2312yes—
92C2×C22⋊Dic13C2312yes—
93C2×C22⋊Dic13C2312yes—
94C2×#6103C2×C4116yes—
95C2×#6103C2314yes—
96C2×#6103C2314yes—
97C2×#6103C2314yes—
98C2×#6103C2314yes—
99C2×#6103C2314yes—
100#88180—24no—
101#88180—24no—
102C2×C4⋊Dic13C2×C4116yescomplemented
103C2×C4⋊Dic13C2312yes—
104C2×C4⋊Dic13C2312yes—
105C2×C4⋊Dic13C2318yes—
106C2×C4⋊Dic13C2314yes—
107C2×C4⋊Dic13C2314yes—
108C2×#6101C2318yes—
109C2×#6101C2314yes—
110C2×C4×Dic13C2318yes—
111C2×C4×Dic13C2312yes—
112C2×C4×Dic13C2314yes—
113C2×C4×Dic13C2312yes—
114#88151C2×C4116yes—
115#88151C2×C4116yes—
116#88151C2×C4116yescomplemented
117#88151C2×C4116yescomplemented
118#88146—28no—
119C4⋊C4×D13—28no—
120#88141—216no—
121C22⋊C4×D13—28no—
122#88131—216no—
123#88131—28no—
124#88126—28no—
125C42×D13—28no—
126C4×Dic26—216no—
127C13×#95C2318yes—
128#88071C2314yes—
129#88071C2314yes—
130#88071C2318yes—
131#88071C2318yes—
132#88071C2318yes—
133#34203—131nomaximal, Sylow
134C24×C13C2411yescharacteristic
135C23×D13—22no—
136C23×D13—22no—
137C23×D13—24no—
138C23×D13—42no—
139C23×D13C22×C414yes—
140C23×D13C2411yescharacteristic
141C23×D13C2411yescharacteristic
142C22×C4×C13—44no—
143C22×C4×C13C22×C418yes—
144C22×C4×C13C22×C414yes—
145C22×C4×C13C2×D414yes—
146C22×C4×C13#4114yes—
147C22×C4×C13C2414yes—
148C22×C4×C13C2414yes—
149C22×C4×C13C2414yes—
150C22×C4×C13C2411yescharacteristic
151C22×C4×C13C2411yescharacteristic
152C22×Dic13—24no—
153C22×Dic13—22no—
154C22×Dic13—24no—
155C22×Dic13—22no—
156C22×Dic13C22×C414yes—
157C22×Dic13C22×C418yes—
158C22×Dic13C2414yes—
159C22×Dic13C2414yes—
160C22×Dic13C2411yescharacteristic
161C22×Dic13C2414yes—
162C22×Dic13C2411yescharacteristic
163C2×C4×D13—232no—
164C2×C4×D13—22no—
165C2×C4×D13—22no—
166C2×C4×D13—22no—
167C2×C4×D13—22no—
168C2×C4×D13—22no—
169C2×C4×D13—22no—
170C2×C4×D13—22no—
171C2×C4×D13—22no—
172C2×C4×D13—28no—
173C2×C4×D13—28no—
174C2×C4×D13—44no—
175C2×C4×D13C22×C414yes—
176C2×C4×D13C22×C414yes—
177C2×C4×D13C22×C414yes—
178C2×C4×D13C22×C414yes—
179C2×Dic26—232no—
180C2×Dic26—24no—
181C2×Dic26—24no—
182C2×Dic26—24no—
183C2×Dic26—24no—
184C2×Dic26C22×C418yes—
185C2×Dic26C22×C418yes—
186C13×C4⋊C4—24no—
187C13×C4⋊C4C22×C418yes—
188C13×C4⋊C4C22×C418yes—
189C13×C4⋊C4C2×D418yes—
190C13×C22⋊C4—24no—
191C13×C22⋊C4C2×D418yes—
192C42×C13—24no—
193C42×C13—48no—
194C42×C13C2×D418yes—
195C22⋊Dic13—24no—
196C22⋊Dic13—24no—
197#6103—28no—
198#6103—28no—
199#6103—44no—
200#6103C22×C4116yes—
201#6103C22×C4116yes—
202C4⋊Dic13—24no—
203C4⋊Dic13—24no—
204C4⋊Dic13—48no—
205C4⋊Dic13C22×C4116yes—
206C4⋊Dic13C22×C4116yes—
207#6101—216no—
208#6101—28no—
209C4×Dic13—216no—
210C4×Dic13—24no—
211C4×Dic13—28no—
212C4×Dic13—24no—
213C22×C22⋊Q8—131no—
214C2×#519—131no—
215C22×#117—131no—
216#2362—134no—
217#2360—134no—
218#2344—134no—
219#2342—134no—
220#2323—134no—
221#2316—131no—
222#2310—131no—
223C4×C22⋊Q8—134no—
224#2280—131no—
225#2274D1311yescharacteristic, complemented
226C23×C13—22no—
227C23×C13—22no—
228C23×C13C23×C412yes—
229C23×C13C22×D412yes—
230C23×C13C2×#4112yes—
231C23×C13C2511yescharacteristic
232C22×D13—21no—
233C22×D13—21no—
234C22×D13—22no—
235C22×D13—28no—
236C22×D13—21no—
237C22×D13—21no—
238C22×D13—22no—
239C22×D13—22no—
240C22×D13—28no—
241C22×D13—44no—
242C22×D13—48no—
243C22×D13—48no—
244C22×D13C23×C412yes—
245C22×D13C23×C412yes—
246C22×D132−1+414yes—
247C2×C4×C13—24no—
248C2×C4×C13—28no—
249C2×C4×C13—24no—
250C2×C4×C13—24no—
251C2×C4×C13—24no—
252C2×C4×C13—24no—
253C2×C4×C13—48no—
254C2×C4×C13C4×D4116yes—
255C2×C4×C13C23×C418yes—
256C2×C4×C13C23×C412yes—
257C2×C4×C13C23×C412yes—
258C2×C4×C13C22×D418yes—
259C2×C4×C13C22×D412yes—
260C2×C4×C13C22×D412yes—
261C2×C4×C13C2×#4112yes—
262C2×C4×C13C2×#4112yes—
263C2×Dic13—216no—
264C2×Dic13—28no—
265C2×Dic13—21no—
266C2×Dic13—24no—
267C2×Dic13—21no—
268C2×Dic13—24no—
269C2×Dic13—21no—
270C2×Dic13—21no—
271C2×Dic13—24no—
272C2×Dic13—24no—
273C2×Dic13—24no—
274C2×Dic13—24no—
275C2×Dic13—24no—
276C2×Dic13—24no—
277C2×Dic13C23×C412yes—
278C2×Dic13C23×C412yes—
279C2×Dic13C23×C418yes—
280C4×D13—28no—
281C4×D13—28no—
282C4×D13—28no—
283C4×D13—28no—
284C4×D13—416no—
285Dic26—216no—
286Dic26—216no—
287C23×Q8—131no—
288C24×C4—131no—
289C2×C22⋊Q8—1316no—
290C2×C22⋊Q8—132no—
291C2×C22⋊Q8—132no—
292C2×C22⋊Q8—132no—
293C2×C22⋊Q8—132no—
294#519—268no—
295C2×C4×Q8—134no—
296C2×C4×Q8—134no—
297C2×#117—131no—
298C2×#117—131no—
299C2×#117—132no—
300C2×#117—134no—
301C2×#117—132no—
302C2×#117—132no—
303C2×#117—268no—
304C2×#117C2×D1311yescharacteristic
305C2×#117C2×D1311yescharacteristic
306C22×C4⋊C4—132no—
307C22×C4⋊C4—132no—
308C22×C4⋊C4C2×D1311yescharacteristic
309C22×C22⋊C4—132no—
310C22×C22⋊C4—132no—
311C22×C42—132no—
312#391—134no—
313#391—134no—
314#389—134no—
315#389—134no—
316#389—138no—
317#388—138no—
318#388—138no—
319#387—138no—
320#387—138no—
321#385—138no—
322#381—134no—
323#381—132no—
324#380—134no—
325#380—132no—
326#380—132no—
327#379—132no—
328C4×C4⋊C4—138no—
329C4×C4⋊C4C2×D1314yescomplemented
330C4×C4⋊C4C2×D1314yescomplemented
331C4×C22⋊C4—138no—
332C4×C22⋊C4—132no—
333C4×C22⋊C4—132no—
334C4×C22⋊C4C2×D1314yes—
335C22×C13—22no—
336C22×C13—22no—
337C22×C13—24no—
338C22×C13—24no—
339C22×C13C2×C4×D414yes—
340C22×C13C24×C411yescharacteristic
341C22×C13C23×D411yescharacteristic
342C22×C13C22×#4111yescharacteristic
343C22×C13C2×2−1+412yes—
344C22×C13#58512yes—
345C2×D13—22no—
346C2×D13—22no—
347C2×D13—24no—
348C2×D13—24no—
349C2×D13—22no—
350C2×D13—22no—
351C2×D13—22no—
352C2×D13—416no—
353C2×D13—42no—
354C2×D13—42no—
355C2×D13#51914yescomplemented
356C4×C13—28no—
357C4×C13—28no—
358C4×C13—44no—
359C4×C13C2×C4×D414yes—
360C4×C13C2×C4×D414yes—
361Dic13—28no—
362Dic13—22no—
363Dic13—22no—
364Dic13—44no—
365Dic13—44no—
366C25—131no—
367C22×Q8—138no—
368C22×Q8—132no—
369C22×Q8—132no—
370C22×Q8—264no—
371C22×Q8—264no—
372C23×C4—132no—
373C23×C4—131no—
374C23×C4—138no—
375C23×C4—131no—
376C23×C4—131no—
377C23×C4—131no—
378C23×C4—131no—
379C23×C4—134no—
380C23×C4—264no—
381C23×C4—264no—
382C23×C4C22×D1312yes—
383C23×C4C22×D1311yescharacteristic
384C22⋊Q8—1316no—
385C22⋊Q8—1316no—
386C22⋊Q8—1316no—
387C22⋊Q8—1316no—
388C4×Q8—2616no—
389C4×Q8—2616no—
390#117—24no—
391#117—264no—
392#117—264no—
393#117—268no—
394#117—268no—
395#117—2616no—
396#117—268no—
397#117D5218yes—
398C2×C4⋊C4—1316no—
399C2×C4⋊C4—134no—
400C2×C4⋊C4—134no—
401C2×C4⋊C4—134no—
402C2×C4⋊C4—132no—
403C2×C4⋊C4—138no—
404C2×C4⋊C4—132no—
405C2×C4⋊C4—138no—
406C2×C4⋊C4—268no—
407C2×C4⋊C4C4×D1318yescomplemented
408C2×C4⋊C4C22×D1312yes—
409C2×C4⋊C4C22×D1312yes—
410C2×C4⋊C4C22×D1312yes—
411C2×C4⋊C4C22×D1312yes—
412C2×C22⋊C4—1316no—
413C2×C22⋊C4—134no—
414C2×C22⋊C4—134no—
415C2×C22⋊C4—132no—
416C2×C22⋊C4—132no—
417C2×C22⋊C4—134no—
418C2×C22⋊C4—134no—
419C2×C22⋊C4—134no—
420C2×C22⋊C4—268no—
421C2×C22⋊C4C22×D1312yes—
422C2×C22⋊C4C22×D1312yes—
423C2×C42—134no—
424C2×C42—132no—
425C2×C42—132no—
426C2×C42—138no—
427C2×C42—268no—
428C2×C42C22×D1312yes—
429C2×C42C22×D1318yes—
430C2×C42C22×D1312yes—
431#95—134no—
432#95—134no—
433#95—138no—
434#95—138no—
435#95—138no—
436#95C22×D1318yes—
437C2×C13—24no—
438C2×C13C22×C4×D411yescharacteristic
439C2×C13C2×#51911yescharacteristic
440C2×C13#342811yescharacteristic
441C2×C13#348912yes—
442C2×C13#349512yes—
443D13—24no—
444D13—42no—
445C24—131no—
446C24—131no—
447C24—134no—
448C24—264no—
449C24—262no—
450C24—262no—
451C24—522no—
452C24C23×D1311yescharacteristic
453C2×Q8—138no—
454C2×Q8—138no—
455C2×Q8—2632no—
456C2×Q8—264no—
457C2×Q8—264no—
458C2×Q8—264no—
459C2×Q8—264no—
460C22×C4—44no—
461C22×C4—138no—
462C22×C4—134no—
463C22×C4—131no—
464C22×C4—134no—
465C22×C4—131no—
466C22×C4—134no—
467C22×C4—134no—
468C22×C4—134no—
469C22×C4—134no—
470C22×C4—134no—
471C22×C4—134no—
472C22×C4—268no—
473C22×C4—262no—
474C22×C4—264no—
475C22×C4—262no—
476C22×C4—264no—
477C22×C4—2632no—
478C22×C4—262no—
479C22×C4—262no—
480C22×C4—262no—
481C22×C4—262no—
482C22×C4—262no—
483C22×C4—262no—
484C22×C4—262no—
485C22×C4—262no—
486C22×C4—268no—
487C22×C4—524no—
488C22×C4C2×C4×D1318yes—
489C22×C4C2×C4×D1314yes—
490C22×C4C2×D5214yes—
491C22×C4#612714yes—
492C22×C4C23×D1314yes—
493C22×C4C23×D1314yes—
494C22×C4C23×D1314yes—
495C22×C4C23×D1311yescharacteristic
496C22×C4C23×D1311yescharacteristic
497C4⋊C4—24no—
498C4⋊C4—1316no—
499C4⋊C4—1316no—
500C4⋊C4—268no—
501C4⋊C4—264no—
502C4⋊C4—2616no—
503C4⋊C4—264no—
504C4⋊C4—528no—
505C4⋊C4C2×C4×D1318yes—
506C4⋊C4C2×C4×D1318yes—
507C4⋊C4C2×D5218yes—
508C22⋊C4—24no—
509C22⋊C4—1316no—
510C22⋊C4—1316no—
511C22⋊C4—268no—
512C22⋊C4—264no—
513C22⋊C4—264no—
514C22⋊C4—268no—
515C22⋊C4—524no—
516C22⋊C4C2×D5218yes—
517C42—24no—
518C42—48no—
519C42—268no—
520C42—264no—
521C42—2616no—
522C42—264no—
523C42C2×D5218yes—
524C13#3420311yescharacteristic, complemented, Sylow
525C23—22no—
526C23—22no—
527C23—132no—
528C23—134no—
529C23—132no—
530C23—268no—
531C23—261no—
532C23—261no—
533C23—262no—
534C23—268no—
535C23—261no—
536C23—261no—
537C23—262no—
538C23—262no—
539C23—524no—
540C23—528no—
541C23—528no—
542C23C22×C4×D1312yes—
543C23C22×D5212yes—
544C23C2×#612712yes—
545C23C24×D1311yescharacteristic
546Q8—2616no—
547Q8—2616no—
548C2×C4—24no—
549C2×C4—28no—
550C2×C4—24no—
551C2×C4—24no—
552C2×C4—24no—
553C2×C4—24no—
554C2×C4—48no—
555C2×C4—138no—
556C2×C4—132no—
557C2×C4—132no—
558C2×C4—268no—
559C2×C4—2616no—
560C2×C4—261no—
561C2×C4—264no—
562C2×C4—261no—
563C2×C4—261no—
564C2×C4—261no—
565C2×C4—264no—
566C2×C4—268no—
567C2×C4—268no—
568C2×C4—268no—
569C2×C4—268no—
570C2×C4—264no—
571C2×C4—264no—
572C2×C4—264no—
573C2×C4—264no—
574C2×C4—264no—
575C2×C4—264no—
576C2×C4—5216no—
577C2×C4C4×D52116yes—
578C2×C4C22×C4×D1318yes—
579C2×C4C22×C4×D1312yes—
580C2×C4C22×C4×D1312yes—
581C2×C4C22×D5218yes—
582C2×C4C22×D5212yes—
583C2×C4C22×D5212yes—
584C2×C4C2×#612712yes—
585C2×C4C2×#612712yes—
586C22—24no—
587C22—22no—
588C22—22no—
589C22—24no—
590C22—134no—
591C22—264no—
592C22—262no—
593C22—262no—
594C22—264no—
595C22—262no—
596C22—262no—
597C22—262no—
598C22—5216no—
599C22—522no—
600C22—522no—
601C22C2×C4×D5214yes—
602C22C23×C4×D1311yescharacteristic
603C22C23×D5211yescharacteristic
604C22C22×#612711yescharacteristic
605C22#1171965012yes—
606C22D13×2−1+412yes—
607C4—28no—
608C4—28no—
609C4—44no—
610C4—262no—
611C4—262no—
612C4—268no—
613C4—524no—
614C4—524no—
615C4C2×C4×D5214yes—
616C4C2×C4×D5214yes—
617C2—24no—
618C2—264no—
619C2—522no—
620C2C22×C4×D5211yescharacteristic
621C2D13×#51911yescharacteristic
622C2#1312803411yescharacteristic
623C2#1312851712yes—
624C2#1312858912yes—
subgroupG/H
center, FrattiniC23C24×D13
commutatorC22×C13C24×C4
FittingC13×#2274C2
socle, cosocleC23×C13C25
prime radicalC24×D13C23
hypercenter#2274D13
hypocenterC13#34203
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ #2274

Complements

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

NH ≅ G/Ntype
2. C2×#11719221C2semidirect
4. #13117865C2semidirect
5. #13117843C2semidirect
6. #13117703C2semidirect
8. #13117519C2semidirect
9. #13117454C2semidirect
10. #13117420C2semidirect
11. C4×#88151C2semidirect
13. C13×#2274C2semidirect
25. C2×#88151C4semidirect
32. C2×#88141C22semidirect
38. C2×C4×Dic26C22semidirect
39. C4×C13×C4⋊C4C22semidirect
40. C4×C13×C4⋊C4C22semidirect
45. #11718646C22semidirect
46. #11718646C22semidirect
47. #11718635C22semidirect
55. C4×C4⋊Dic13C22semidirect
56. #11718590C22semidirect
57. #11718589C22semidirect
60. #11718314C22semidirect
61. #11718314C22semidirect
77. C22×Dic26C2×C4semidirect
82. C2×C13×C4⋊C4C2×C4semidirect
102. C2×C4⋊Dic13C2×C4semidirect
116. #88151C2×C4semidirect
117. #88151C2×C4semidirect
225. #2274D13semidirect
329. C4×C4⋊C4C2×D13semidirect
330. C4×C4⋊C4C2×D13semidirect
355. C2×D13#519semidirect
407. C2×C4⋊C4C4×D13semidirect
524. C13#34203semidirect

Maximal subgroups

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

subgroupindex
C22×#881512
C2×#117192212
C2×D13×#1172
#131178652
#131178432
#131177032
#131176882
#131175192
#131174542
#131174202
C4×#881512
#131172152
C13×#22742
#3420313