Finite Group Databasebeta

← #15860578

Subgroups — #15860578

Order 3328.

1606 conjugacy classes of subgroups.

The subgroup lattice has 630 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719251C211yesmaximal, characteristic
2C2×#11718401C212yesmaximal
3#13117191C212yesmaximal, complemented
4#99×Dic13C212yesmaximal, complemented
5C4×#88046C212yesmaximal, complemented
6C4×#88074C211yesmaximal, characteristic, complemented
7#13114623C212yesmaximal, complemented
8#13114567C212yesmaximal, complemented
9C4×C13×#99C211yesmaximal, characteristic, complemented
10C22×#6129C2211yescharacteristic
11C2×C4×D4×C13C2211yescharacteristic
12C2×D4×Dic13C2211yescharacteristic
13C2×C4×C22⋊D13C411yescharacteristic, complemented
14C2×C4×C22⋊D13C2211yescharacteristic
15C22×#6101C411yescharacteristic, complemented
16C22×#6101C2211yescharacteristic
17#11719251—24no—
18#11719251—24no—
19C2×C4⋊C4×D13C411yescharacteristic, complemented
20C2×#88141C411yescharacteristic, complemented
21C2×#88135C411yescharacteristic, complemented
22C2×#88135C2211yescharacteristic
23C2×#88131C411yescharacteristic, complemented
24C2×#88131C2211yescharacteristic
25C2×#88131C2214yes—
26C2×#88126C411yescharacteristic, complemented
27C2×C4×Dic26C411yescharacteristic, complemented
28C2×C13×#99C2212yes—
29C4×C13×C22⋊C4C2212yes—
30C2×#88074C2212yes—
31C4×C22⋊Dic13C2212yes—
32C2×#88046C2214yes—
33C22⋊C4×Dic13C2214yes—
34C4×#6101—24no—
35#11718401C4116yescomplemented
36#11718310—24no—
37C13×#342C2212yes—
38#11718119C2214yes—
39#11718118C2212yes—
40C22×D4×C13C2311yescharacteristic
41C23×C4×C13C2×C411yescharacteristic
42C23×C4×C13C2311yescharacteristic
43C22×C22⋊D13C2×C411yescharacteristic
44C22×C22⋊D13C2311yescharacteristic
45C23×Dic13C2×C411yescharacteristic
46C23×Dic13C2×C411yescharacteristic
47C23×Dic13C2311yescharacteristic
48C23×Dic13C2311yescharacteristic
49C2×#6129—24no—
50C2×#6129—24no—
51C2×#6129C2×C418yes—
52C22×C4×D13C2×C411yescharacteristic
53C22×C4×D13C2×C411yescharacteristic
54C22×C4×D13C2×C411yescharacteristic
55C22×Dic26C2×C411yescharacteristic
56C4×D4×C13—22no—
57C4×D4×C13—22no—
58C2×C13×C4⋊C4C2×C411yescharacteristic
59C2×C13×C22⋊C4C2×C411yescharacteristic
60C2×C13×C22⋊C4C2311yescharacteristic
61C2×C13×C22⋊C4C2314yes—
62C2×C42×C13—22no—
63C2×C42×C13C2×C411yescharacteristic
64C2×C22⋊Dic13C2×C411yescharacteristic
65C2×C22⋊Dic13C2311yescharacteristic
66C2×C22⋊Dic13C2314yes—
67D4×Dic13—24no—
68C4×C22⋊D13—22no—
69C4×C22⋊D13—22no—
70C4×C22⋊D13—22no—
71C4×C22⋊D13—22no—
72C2×#6103C2×C411yescharacteristic
73C2×#6103C2×C411yescharacteristic
74C2×C4⋊Dic13C2×C411yescharacteristic
75C2×#6101—24no—
76C2×#6101—22no—
77C2×#6101—22no—
78C2×#6101C2×C411yescharacteristic
79C2×#6101C2×C411yescharacteristic
80C2×#6101C2×C411yescharacteristic
81C2×#6101C2×C411yescharacteristic
82C2×#6101C2×C411yescharacteristic
83C2×#6101C2×C411yescharacteristic
84C2×#6101C2×C411yescharacteristic
85C2×#6101C2×C411yescharacteristic
86C2×#6101D414yes—
87C2×#6101D414yes—
88C2×C4×Dic13—24no—
89C2×C4×Dic13—22no—
90C2×C4×Dic13—24no—
91C2×C4×Dic13C2×C411yescharacteristic
92C2×C4×Dic13C2×C411yescharacteristic
93C2×C4×Dic13C2×C411yescharacteristic
94C2×C4×Dic13C2×C411yescharacteristic
95C2×C4×Dic13C2×C411yescharacteristic
96C4⋊C4×D13—24no—
97#88141—24no—
98#88135—24no—
99#88135—24no—
100#88131—24no—
101#88131—28no—
102#88131—24no—
103#88131C2×C4116yescomplemented
104#88126—22no—
105#88126—22no—
106C4×Dic26—22no—
107C4×Dic26—22no—
108C13×#99C2×C418yescomplemented
109C13×#95—22no—
110#88074C2×C418yescomplemented
111#88071—22no—
112#88071—24no—
113#88046C2×C4116yescomplemented
114#20393—131nomaximal, Sylow
115C24×C13C22×C411yescharacteristic
116C24×C13C2411yescharacteristic
117C23×D13C22×C411yescharacteristic
118C2×D4×C13—22no—
119C2×D4×C13—22no—
120C2×D4×C13C22×C414yes—
121C22×C4×C13—24no—
122C22×C4×C13—21no—
123C22×C4×C13—21no—
124C22×C4×C13—81no—
125C22×C4×C13—81no—
126C22×C4×C13C22×C411yescharacteristic
127C22×C4×C13C22×C411yescharacteristic
128C22×C4×C13C22×C411yescharacteristic
129C22×C4×C13C22×C411yescharacteristic
130C22×C4×C13C22×C411yescharacteristic
131C22×C4×C13C2×D412yes—
132C22×C4×C13C2×D412yes—
133C2×C22⋊D13—22no—
134C2×C22⋊D13—22no—
135C2×C22⋊D13—22no—
136C2×C22⋊D13—22no—
137C2×C22⋊D13C4214yescomplemented
138C2×C22⋊D13C22×C414yes—
139C22×Dic13—22no—
140C22×Dic13—22no—
141C22×Dic13—24no—
142C22×Dic13—22no—
143C22×Dic13—81no—
144C22×Dic13—81no—
145C22×Dic13C4214yescomplemented
146C22×Dic13C22×C411yescharacteristic
147C22×Dic13C22×C411yescharacteristic
148C22×Dic13C22×C411yescharacteristic
149C22×Dic13C22×C411yescharacteristic
150C22×Dic13C22×C411yescharacteristic
151C22×Dic13C22×C411yescharacteristic
152C22×Dic13C22×C411yescharacteristic
153C22×Dic13C22×C414yes—
154C22×Dic13C2×D414yes—
155C22×Dic13C2×D414yes—
156C22×Dic13#4114yes—
157#6129—216no—
158#6129—216no—
159C2×C4×D13—22no—
160C2×C4×D13—22no—
161C2×C4×D13—22no—
162C2×C4×D13—22no—
163C2×C4×D13—81no—
164C2×C4×D13—81no—
165C2×C4×D13C4214yescomplemented
166C2×Dic26—22no—
167C2×Dic26—22no—
168C2×Dic26C4214yescomplemented
169C13×C4⋊C4—22no—
170C13×C22⋊C4—22no—
171C13×C22⋊C4—24no—
172C13×C22⋊C4—22no—
173C13×C22⋊C4C22×C418yes—
174C42×C13—21no—
175C42×C13—21no—
176C42×C13—82no—
177C22⋊Dic13—22no—
178C22⋊Dic13—24no—
179C22⋊Dic13—22no—
180C22⋊Dic13C22×C418yes—
181#6103—21no—
182#6103—21no—
183#6103—22no—
184C4⋊Dic13—22no—
185#6101—21no—
186#6101—21no—
187#6101—22no—
188#6101—22no—
189#6101—22no—
190#6101—216no—
191#6101C22⋊C412yes—
192#6101C22⋊C412yes—
193#6101C22⋊C412yes—
194#6101C22⋊C412yes—
195#6101C22⋊C414yes—
196#6101C22⋊C414yes—
197C4×Dic13—22no—
198C4×Dic13—22no—
199C4×Dic13—22no—
200C4×Dic13—22no—
201C4×Dic13—22no—
202C4×Dic13—216no—
203C4×Dic13—84no—
204C4×Dic13—82no—
205C2×#520—131no—
206C2×#410—132no—
207#2274—132no—
208C4×#99—132no—
209C4×#99—132no—
210C4×#99—132no—
211C4×#99—131no—
212C4×#99D1311yescharacteristic, complemented
213#1740—132no—
214C23×C13—21no—
215C23×C13—21no—
216C23×C13—41no—
217C23×C13—41no—
218C23×C13—41no—
219C23×C13—41no—
220C23×C13C2×C4212yes—
221C23×C13C23×C411yescharacteristic
222C23×C13C23×C412yes—
223C23×C13C22×D412yes—
224C23×C13C2×#4112yes—
225C22×D13—21no—
226C22×D13—21no—
227C22×D13—41no—
228C22×D13—41no—
229C22×D13C2×C4212yes—
230D4×C13—28no—
231C2×C4×C13—21no—
232C2×C4×C13—21no—
233C2×C4×C13—21no—
234C2×C4×C13—21no—
235C2×C4×C13—28no—
236C2×C4×C13—42no—
237C2×C4×C13—42no—
238C2×C4×C13—41no—
239C2×C4×C13—41no—
240C2×C4×C13—44no—
241C2×C4×C13—44no—
242C2×C4×C13—41no—
243C2×C4×C13—41no—
244C2×C4×C13—81no—
245C2×C4×C13—81no—
246C2×C4×C13C2×C4212yes—
247C2×C4×C13C2×C22⋊C412yes—
248C2×C4×C13C2×C22⋊C411yescharacteristic
249C2×C4×C13C2×C22⋊C411yescharacteristic
250C22⋊D13—28no—
251C22⋊D13—28no—
252C2×Dic13—21no—
253C2×Dic13—21no—
254C2×Dic13—28no—
255C2×Dic13—21no—
256C2×Dic13—21no—
257C2×Dic13—28no—
258C2×Dic13—44no—
259C2×Dic13—41no—
260C2×Dic13—41no—
261C2×Dic13—44no—
262C2×Dic13—44no—
263C2×Dic13—41no—
264C2×Dic13—41no—
265C2×Dic13—82no—
266C2×Dic13C2×C4212yes—
267C2×Dic13C2×C4212yes—
268C2×Dic13C2×C4212yes—
269C2×Dic13C2×C22⋊C412yes—
270C2×Dic13C2×C22⋊C412yes—
271C2×Dic13C2×C22⋊C412yes—
272C2×Dic13C2×C22⋊C412yes—
273C2×Dic13#11712yes—
274C2×Dic13#11712yes—
275C2×Dic13C4×D418yes—
276C2×Dic13C4×D418yes—
277C4×D13—28no—
278C4×D13—82no—
279C4×D13—82no—
280Dic26—28no—
281C22×#41—131no—
282#520—264no—
283#520—264no—
284C2×C4×Q8—131no—
285C2×C4×Q8—131no—
286C2×C4×D4—131no—
287C2×C4×D4—131no—
288C2×C4×D4—131no—
289C2×C4×D4—131no—
290C2×C4×D4—131no—
291C2×C4×D4C2×D1311yescharacteristic
292C2×#117—131no—
293C2×#117—131no—
294C2×#117—131no—
295C2×#117—134no—
296C22×C4⋊C4—131no—
297C22×C4⋊C4—131no—
298C22×C4⋊C4—131no—
299#410—1316no—
300C2×#99—132no—
301C2×#99—134no—
302C2×#99C2×D1312yes—
303C4×C4⋊C4—264no—
304C4×C4⋊C4—264no—
305C4×C22⋊C4—132no—
306C4×C22⋊C4—134no—
307C4×C22⋊C4C2×D1312yes—
308#342—132no—
309#342—134no—
310#342C2×D1312yes—
311C22×C13—22no—
312C22×C13—21no—
313C22×C13—22no—
314C22×C13—21no—
315C22×C13—22no—
316C22×C13—42no—
317C22×C13—42no—
318C22×C13—42no—
319C22×C13—42no—
320C22×C13—41no—
321C22×C13—41no—
322C22×C13C22×C4211yescharacteristic
323C22×C13C22×C22⋊C411yescharacteristic
324C22×C13C2×#11711yescharacteristic
325C22×C13C2×C4×D414yes—
326C2×D13—22no—
327C2×D13—42no—
328C2×D13—41no—
329C2×D13—41no—
330C2×D13—42no—
331C4×C13—22no—
332C4×C13—21no—
333C4×C13—21no—
334C4×C13—22no—
335C4×C13—48no—
336C4×C13—41no—
337C4×C13—41no—
338Dic13—22no—
339Dic13—22no—
340Dic13—22no—
341Dic13—48no—
342Dic13—41no—
343Dic13—41no—
344Dic13C4×C22⋊C414yes—
345Dic13C4×C22⋊C414yes—
346C2×#41—138no—
347C2×#41—264no—
348C2×#41—264no—
349C22×Q8—131no—
350C22×D4—131no—
351C22×D4—131no—
352C22×D4C22×D1311yescharacteristic
353C23×C4—131no—
354C23×C4—131no—
355C23×C4—131no—
356C23×C4—131no—
357C23×C4—131no—
358C23×C4—131no—
359C23×C4—131no—
360C23×C4C4×D1311yescharacteristic
361C23×C4C22×D1311yescharacteristic
362C4×Q8—262no—
363C4×Q8—262no—
364C4×Q8—264no—
365C4×D4—22no—
366C4×D4—22no—
367C4×D4—264no—
368C4×D4—264no—
369C4×D4—262no—
370C4×D4—262no—
371C4×D4—264no—
372C4×D4—262no—
373C4×D4—262no—
374#117—1316no—
375#117—262no—
376#117—262no—
377#117—264no—
378#117—264no—
379#117—268no—
380C2×C4⋊C4—131no—
381C2×C4⋊C4—131no—
382C2×C4⋊C4—131no—
383C2×C4⋊C4—131no—
384C2×C4⋊C4—134no—
385C2×C4⋊C4—134no—
386C2×C4⋊C4—131no—
387C2×C4⋊C4—131no—
388C2×C4⋊C4—131no—
389C2×C4⋊C4—131no—
390C2×C4⋊C4—131no—
391C2×C4⋊C4—264no—
392C2×C4⋊C4—262no—
393C2×C4⋊C4—262no—
394C2×C4⋊C4—264no—
395C2×C4⋊C4C4×D1311yescharacteristic
396C2×C22⋊C4—134no—
397C2×C22⋊C4—131no—
398C2×C22⋊C4—131no—
399C2×C22⋊C4—131no—
400C2×C22⋊C4—131no—
401C2×C22⋊C4C4×D1311yescharacteristic
402C2×C22⋊C4C22×D1311yescharacteristic
403C2×C22⋊C4C22×D1314yes—
404C2×C42—22no—
405C2×C42—131no—
406C2×C42—131no—
407C2×C42—131no—
408C2×C42—131no—
409C2×C42—131no—
410C2×C42—264no—
411C2×C42—264no—
412C2×C42—262no—
413C2×C42C4×D1311yescharacteristic
414#99—138no—
415#99—1316no—
416#99C4×D1318yescomplemented
417#95—22no—
418#95—264no—
419#95—262no—
420C2×C13—24no—
421C2×C13—21no—
422C2×C13—21no—
423C2×C13—42no—
424C2×C13C2×C4×C22⋊C411yescharacteristic
425C2×C13#288311yescharacteristic
426C2×C13#288411yescharacteristic
427D13—42no—
428C24—131no—
429C24C2×C4×D1311yescharacteristic
430C24C23×D1311yescharacteristic
431#41—2616no—
432#41—2616no—
433C2×Q8—134no—
434C2×Q8—262no—
435C2×Q8—262no—
436C2×D4—22no—
437C2×D4—22no—
438C2×D4—134no—
439C2×D4—134no—
440C2×D4—262no—
441C2×D4—262no—
442C2×D4—262no—
443C2×D4—262no—
444C2×D4C2×C4×D1314yes—
445C22×C4—24no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—81no—
449C22×C4—81no—
450C22×C4—131no—
451C22×C4—131no—
452C22×C4—134no—
453C22×C4—134no—
454C22×C4—134no—
455C22×C4—134no—
456C22×C4—131no—
457C22×C4—131no—
458C22×C4—131no—
459C22×C4—134no—
460C22×C4—134no—
461C22×C4—131no—
462C22×C4—131no—
463C22×C4—262no—
464C22×C4—262no—
465C22×C4—262no—
466C22×C4—262no—
467C22×C4—262no—
468C22×C4—262no—
469C22×C4—264no—
470C22×C4—262no—
471C22×C4—1041no—
472C22×C4—1041no—
473C22×C4—1041no—
474C22×C4—1041no—
475C22×C4C2×C4×D1311yescharacteristic
476C22×C4C2×C4×D1311yescharacteristic
477C22×C4C2×C4×D1311yescharacteristic
478C22×C4C2×C4×D1311yescharacteristic
479C22×C4C2×C4×D1311yescharacteristic
480C22×C4D4×D1312yes—
481C22×C4D4×D1312yes—
482C4⋊C4—22no—
483C4⋊C4—132no—
484C4⋊C4—132no—
485C4⋊C4—134no—
486C4⋊C4—132no—
487C4⋊C4—132no—
488C4⋊C4—134no—
489C4⋊C4—262no—
490C4⋊C4—262no—
491C4⋊C4—262no—
492C4⋊C4—262no—
493C4⋊C4—2616no—
494C4⋊C4—261no—
495C4⋊C4—261no—
496C22⋊C4—22no—
497C22⋊C4—24no—
498C22⋊C4—22no—
499C22⋊C4—138no—
500C22⋊C4—262no—
501C22⋊C4—262no—
502C22⋊C4—262no—
503C22⋊C4—264no—
504C22⋊C4—261no—
505C22⋊C4—261no—
506C22⋊C4C2×C4×D1318yes—
507C42—21no—
508C42—21no—
509C42—82no—
510C42—262no—
511C42—262no—
512C42—262no—
513C42—262no—
514C42—2616no—
515C42—262no—
516C42—1042no—
517C42—1044no—
518C13#2039311yescharacteristic, complemented, Sylow
519C23—21no—
520C23—21no—
521C23—41no—
522C23—41no—
523C23—41no—
524C23—41no—
525C23—132no—
526C23—261no—
527C23—261no—
528C23—521no—
529C23—521no—
530C23C42×D1312yes—
531C23C22×C4×D1311yescharacteristic
532C23C22×C4×D1312yes—
533C23C2×D4×D1312yes—
534C23#41×D1312yes—
535Q8—268no—
536D4—28no—
537D4—268no—
538D4—268no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—28no—
544C2×C4—42no—
545C2×C4—42no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—44no—
549C2×C4—44no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—81no—
553C2×C4—81no—
554C2×C4—132no—
555C2×C4—132no—
556C2×C4—132no—
557C2×C4—132no—
558C2×C4—132no—
559C2×C4—132no—
560C2×C4—138no—
561C2×C4—138no—
562C2×C4—132no—
563C2×C4—132no—
564C2×C4—132no—
565C2×C4—268no—
566C2×C4—268no—
567C2×C4—261no—
568C2×C4—261no—
569C2×C4—261no—
570C2×C4—261no—
571C2×C4—268no—
572C2×C4—524no—
573C2×C4—521no—
574C2×C4—521no—
575C2×C4—524no—
576C2×C4—524no—
577C2×C4—521no—
578C2×C4—521no—
579C2×C4—1042no—
580C2×C4—1042no—
581C2×C4—1042no—
582C2×C4C42×D1312yes—
583C2×C4C22⋊C4×D1311yescharacteristic
584C2×C4C22⋊C4×D1311yescharacteristic
585C2×C4C22⋊C4×D1312yes—
586C22—22no—
587C22—21no—
588C22—22no—
589C22—21no—
590C22—22no—
591C22—42no—
592C22—42no—
593C22—42no—
594C22—42no—
595C22—41no—
596C22—41no—
597C22—262no—
598C22—522no—
599C22—522no—
600C22—521no—
601C22—521no—
602C22C2×C42×D1311yescharacteristic
603C22C2×C22⋊C4×D1311yescharacteristic
604C22D13×#11711yescharacteristic
605C22C4×D4×D1314yes—
606C4—21no—
607C4—21no—
608C4—22no—
609C4—22no—
610C4—48no—
611C4—41no—
612C4—41no—
613C4—134no—
614C4—134no—
615C4—262no—
616C4—262no—
617C4—262no—
618C4—528no—
619C4—521no—
620C4—521no—
621C2—24no—
622C2—21no—
623C2—21no—
624C2—42no—
625C2—522no—
626C2C4×C22⋊C4×D1311yescharacteristic
627C2#1312329411yescharacteristic
628C2#1312329811yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D13
commutatorC22×C13C22×C42
FrattiniC24C23×D13
FittingC4×C13×#99C2
socleC22×C13C22×C22⋊C4
prime radicalC22×#6129C22
cosocleC24×C13C24
hypercenterC4×#99D13
hypocenterC13#20393
LCSG ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ C4×#99

Complements

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

NH ≅ G/Ntype
3. #13117191C2semidirect
4. #99×Dic13C2semidirect
5. C4×#88046C2semidirect
6. C4×#88074C2semidirect
7. #13114623C2semidirect
8. #13114567C2semidirect
9. C4×C13×#99C2semidirect
13. C2×C4×C22⋊D13C4semidirect
15. C22×#6101C4semidirect
19. C2×C4⋊C4×D13C4semidirect
20. C2×#88141C4semidirect
21. C2×#88135C4semidirect
23. C2×#88131C4semidirect
26. C2×#88126C4semidirect
27. C2×C4×Dic26C4semidirect
35. #11718401C4semidirect
103. #88131C2×C4semidirect
108. C13×#99C2×C4semidirect
110. #88074C2×C4semidirect
113. #88046C2×C4semidirect
137. C2×C22⋊D13C42semidirect
145. C22×Dic13C42semidirect
165. C2×C4×D13C42semidirect
168. C2×Dic26C42semidirect
212. C4×#99D13semidirect
416. #99C4×D13semidirect
518. C13#20393semidirect

Maximal subgroups

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

subgroupindex
C2×#117192512
C2×#117184012
#131171912
#99×Dic132
C4×#880462
C4×#880742
#131146232
#131145672
C4×C13×#992
#2039313