Finite Group Databasebeta

← #15879592

Subgroups — #15879592

Order 3328.

1066 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719284C211yesmaximal, characteristic
2#13117793C211yesmaximal, characteristic, complemented
3#13115809C211yesmaximal, characteristic, complemented
4#13115805C211yesmaximal, characteristic, complemented
5#13115801C211yesmaximal, characteristic, complemented
6#13115791C211yesmaximal, characteristic, complemented
7#13115791C211yesmaximal, characteristic, complemented
8#13115787C211yesmaximal, characteristic, complemented
9#13114847C211yesmaximal, characteristic
10#13114847C211yesmaximal, characteristic
11#13114837C211yesmaximal, characteristic
12#13114662C211yesmaximal, characteristic
13#13114662C211yesmaximal, characteristic
14C4×#88061C211yesmaximal, characteristic
15C2×C13×#446C211yesmaximal, characteristic, complemented
16C2×C4×Q8×C13C2211yescharacteristic
17C2×#88200—21no—
18#11719284—24no—
19#11719284C418yescomplemented
20C2×#88150—21no—
21C2×#88150—21no—
22C2×C4⋊C4×D13—21no—
23C2×C4×D52C2211yescharacteristic
24C2×C4×D52C2211yescharacteristic
25C2×C4×D52C2211yescharacteristic
26C2×#88124C2211yescharacteristic
27C2×#88124C2211yescharacteristic
28C2×#88123C2211yescharacteristic
29C13×#446—24no—
30C2×C13×C4⋊C8C2211yescharacteristic
31C2×C13×C4⋊C8C2211yescharacteristic
32C2×C13×C4⋊C8C2211yescharacteristic
33C2×C13×#97C2211yescharacteristic
34C2×C13×#97C2211yescharacteristic
35C2×C4×C8×C13C2211yescharacteristic
36#11718891—21no—
37C2×#88061C2211yescharacteristic
38C2×#88061C2211yescharacteristic
39C2×#88061C2211yescharacteristic
40C2×#88061C2211yescharacteristic
41#11718642—21no—
42#11718642—21no—
43C4⋊C4×Dic13—21no—
44#11718597C2211yescharacteristic
45#11718597C2211yescharacteristic
46#11718596C2211yescharacteristic
47C4×C4⋊Dic13C2211yescharacteristic
48C4×C4⋊Dic13C2211yescharacteristic
49C4×C4⋊Dic13C2211yescharacteristic
50#11718143C2211yescharacteristic
51#11718143C2211yescharacteristic
52#11718143C2211yescharacteristic
53#11718143C2211yescharacteristic
54#11718143C2211yescharacteristic
55#11718143C2211yescharacteristic
56#11718143C2211yescharacteristic
57#11718143C2211yescharacteristic
58#11718143C2211yescharacteristic
59#11718143C2211yescharacteristic
60#11718143C2211yescharacteristic
61#11718143C2211yescharacteristic
62C22×Q8×C13D411yescharacteristic
63C22×D52C2311yescharacteristic
64C22×C4×D13—21no—
65C22×C4×D13—21no—
66C22×C4×D13—21no—
67C22×Dic26—21no—
68C22×C8×C13C2311yescharacteristic
69C22×C8×C13C2311yescharacteristic
70C22×C8×C13C2311yescharacteristic
71C22×C8×C13C2311yescharacteristic
72C4×Q8×C13C2×C414yes—
73C4×Q8×C13D414yes—
74C2×C13×C4⋊C4D411yescharacteristic
75C2×C13×C4⋊C4D411yescharacteristic
76C2×C13×C4⋊C4D411yescharacteristic
77C2×C42×C13C2311yescharacteristic
78C2×C42×C13C2311yescharacteristic
79C2×C42×C13C2311yescharacteristic
80#88200—28no—
81C2×#6103—21no—
82C2×#6103—21no—
83C2×#6103—21no—
84C2×C4⋊Dic13—21no—
85C2×C4⋊Dic13—21no—
86C2×C4⋊Dic13—21no—
87C2×C4⋊Dic13C2311yescharacteristic
88C2×C4⋊Dic13C2311yescharacteristic
89C2×C4⋊Dic13C2311yescharacteristic
90C2×C4⋊Dic13C2311yescharacteristic
91C2×C4⋊Dic13C2311yescharacteristic
92C2×C4⋊Dic13C2311yescharacteristic
93C2×C4⋊Dic13C2311yescharacteristic
94C2×#6101—21no—
95C2×#6101—21no—
96C2×#6101—21no—
97C2×#6101—21no—
98C2×C4×Dic13—21no—
99C2×C4×Dic13—21no—
100C2×C4×Dic13—21no—
101#88150—28no—
102#88150—28no—
103C4⋊C4×D13—28no—
104C4×D52—22no—
105C4×D52—22no—
106C4×D52—22no—
107C4×D52C2×C414yes—
108C4×D52C2×C414yes—
109C4×D52C2×C414yes—
110#88124—22no—
111#88124—22no—
112#88124C2×C414yes—
113#88124C2×C414yes—
114#88123—22no—
115#88123C2×C414yes—
116C13×C4⋊C8—22no—
117C13×C4⋊C8—22no—
118C13×C4⋊C8—22no—
119C13×#97—22no—
120C13×#97—22no—
121C4×C8×C13—22no—
122#88071—21no—
123#88071—21no—
124#88071—21no—
125#88071—21no—
126#88071—21no—
127#88071—21no—
128#88071—21no—
129#88061—22no—
130#88061—22no—
131#88061—22no—
132#88061Q814yescomplemented
133#22526—131nomaximal, Sylow
134C23×D13—21no—
135C2×Q8×C13—41no—
136C2×Q8×C13—41no—
137C2×Q8×C13C22⋊C414yes—
138C22×C4×C13C2×D411yescharacteristic
139C22×C4×C13C2×D411yescharacteristic
140C22×C4×C13C2×D411yescharacteristic
141C22×C4×C13C2×D411yescharacteristic
142C22×C4×C13C2×D411yescharacteristic
143C22×C4×C13C2×D411yescharacteristic
144C22×C4×C13C2411yescharacteristic
145C22×Dic13—21no—
146C22×Dic13—21no—
147C22×Dic13—21no—
148C22×Dic13—21no—
149C22×Dic13—21no—
150C22×Dic13—21no—
151C22×Dic13—21no—
152C2×D52—21no—
153C2×D52—21no—
154C2×D52—21no—
155C2×D52C22×C412yes—
156C2×D52C2×Q812yes—
157C2×D52#4112yes—
158C2×C4×D13—24no—
159C2×C4×D13—24no—
160C2×C4×D13—24no—
161C2×C4×D13—42no—
162C2×C4×D13—42no—
163C2×C4×D13—81no—
164C2×C4×D13—81no—
165C2×C4×D13—81no—
166C2×C4×D13—81no—
167C2×Dic26—24no—
168C2×Dic26—81no—
169C2×Dic26—81no—
170C2×C8×C13—21no—
171C2×C8×C13—21no—
172C2×C8×C13—21no—
173C2×C8×C13—21no—
174C2×C8×C13—21no—
175C2×C8×C13—21no—
176C2×C8×C13—21no—
177C2×C8×C13—21no—
178C2×C8×C13—21no—
179C2×C8×C13—21no—
180C2×C8×C13—21no—
181C2×C8×C13C2×Q812yes—
182C13×C4⋊C4C22⋊C414yes—
183C13×C4⋊C4C22⋊C414yes—
184C13×C4⋊C4C22⋊C414yes—
185C42×C13C22×C412yes—
186C42×C13C22×C412yes—
187C42×C13C22×C412yes—
188C42×C13C2×D412yes—
189C42×C13C2×D412yes—
190C42×C13C2×D412yes—
191#6103—24no—
192#6103—24no—
193#6103—24no—
194C4⋊Dic13—24no—
195C4⋊Dic13—21no—
196C4⋊Dic13—21no—
197C4⋊Dic13—21no—
198C4⋊Dic13—21no—
199C4⋊Dic13—21no—
200C4⋊Dic13—21no—
201C4⋊Dic13—21no—
202C4⋊Dic13—21no—
203C4⋊Dic13—21no—
204C4⋊Dic13—21no—
205C4⋊Dic13—42no—
206C4⋊Dic13—81no—
207C4⋊Dic13C22×C412yes—
208C4⋊Dic13C22×C412yes—
209C4⋊Dic13C22×C412yes—
210C4⋊Dic13C2×Q812yes—
211#6101—24no—
212#6101—24no—
213#6101—24no—
214#6101—24no—
215C4×Dic13—42no—
216C4×Dic13—81no—
217C4×Dic13—81no—
218C2×#554—131no—
219C2×#446D1311yescharacteristic, complemented
220#2355—131no—
221#1993—131no—
222#1992—131no—
223#1991—131no—
224#1989—131no—
225#1989—131no—
226#1988—131no—
227#1804—131no—
228#1804—131no—
229#1802—131no—
230#1762—131no—
231#1762—131no—
232C4×#102—131no—
233C23×C13C22×D411yescharacteristic
234C22×D13—22no—
235C22×D13—22no—
236C22×D13—22no—
237C22×D13—41no—
238C22×D13—41no—
239C22×D13—41no—
240C22×D13—41no—
241Q8×C13—44no—
242C2×C4×C13—21no—
243C2×C4×C13—21no—
244C2×C4×C13—21no—
245C2×C4×C13—21no—
246C2×C4×C13—21no—
247C2×C4×C13—21no—
248C2×C4×C13—21no—
249C2×C4×C13—21no—
250C2×C4×C13—21no—
251C2×C4×C13—21no—
252C2×C4×C13—21no—
253C2×C4×C13—21no—
254C2×C4×C13C2×C22⋊C412yes—
255C2×C4×C13C2×C22⋊C412yes—
256C2×C4×C13C2×C22⋊C412yes—
257C2×C4×C13C2×C22⋊C412yes—
258C2×C4×C13C2×C22⋊C412yes—
259C2×C4×C13C2×C22⋊C412yes—
260C2×C4×C13C23×C411yescharacteristic
261C2×C4×C13C22×D411yescharacteristic
262C2×C4×C13C22×Q811yescharacteristic
263C2×C4×C13C2×#4111yescharacteristic
264C2×C4×C132−1+411yescharacteristic
265C2×C4×C132−1+411yescharacteristic
266C2×Dic13—22no—
267C2×Dic13—22no—
268C2×Dic13—22no—
269C2×Dic13—22no—
270C2×Dic13—41no—
271C2×Dic13—41no—
272C2×Dic13—41no—
273C2×Dic13—41no—
274C2×Dic13—41no—
275C2×Dic13—41no—
276C2×Dic13—41no—
277C2×Dic13—41no—
278C2×Dic13—41no—
279C2×Dic13—41no—
280C2×Dic13—41no—
281C2×Dic13—41no—
282C2×Dic13—41no—
283C2×Dic13—41no—
284C2×Dic13—41no—
285C2×Dic13—41no—
286C2×Dic13—41no—
287D52—22no—
288D52—22no—
289D52—22no—
290D52C4×Q814yes—
291C4×D13—48no—
292C4×D13—84no—
293C4×D13—84no—
294Dic26—84no—
295C8×C13—22no—
296C8×C13—41no—
297C8×C13—41no—
298C8×C13—41no—
299#554—138no—
300#554—264no—
301C2×C4⋊Q8—131no—
302C2×#125—131no—
303C2×#125—131no—
304C2×C22⋊Q8—261no—
305C2×C22⋊Q8—261no—
306C2×C22⋊Q8—261no—
307C2×C4×Q8C2×D1311yescharacteristic
308C2×C4×D4—131no—
309C2×C4×D4—131no—
310C2×C4×D4—131no—
311C22×C4⋊C4—261no—
312#446—24no—
313C2×C4⋊C8C2×D1311yescharacteristic
314C2×C4⋊C8C2×D1311yescharacteristic
315C2×C4⋊C8C2×D1311yescharacteristic
316C2×#102—131no—
317C2×#102—131no—
318C2×#102—131no—
319C2×#102—131no—
320C2×#97C2×D1311yescharacteristic
321C2×#97C2×D1311yescharacteristic
322C2×C4×C8C2×D1311yescharacteristic
323#391—261no—
324#387—261no—
325#387—261no—
326#384—131no—
327#382—131no—
328#382—131no—
329C4×C4⋊C4—131no—
330C4×C4⋊C4—131no—
331C4×C4⋊C4—131no—
332C4×C4⋊C4—261no—
333#340—131no—
334#340—131no—
335#340—131no—
336#340—131no—
337#340—131no—
338#340—131no—
339#340—131no—
340#340—131no—
341#340—131no—
342#340—131no—
343#340—131no—
344#340—131no—
345C22×C13C22×C22⋊C411yescharacteristic
346C22×C13#54811yescharacteristic
347C22×C13D4×Q811yescharacteristic
348C22×C13#57511yescharacteristic
349C22×C13#57511yescharacteristic
350C22×C13#57611yescharacteristic
351C22×C13#57711yescharacteristic
352C2×D13—24no—
353C2×D13—42no—
354C2×D13—42no—
355C2×D13—42no—
356C2×D13—42no—
357C2×D13—42no—
358C2×D13—42no—
359C4×C13—22no—
360C4×C13—22no—
361C4×C13—22no—
362C4×C13—22no—
363C4×C13—22no—
364C4×C13—22no—
365C4×C13C2×C4×Q811yescharacteristic
366C4×C13#51911yescharacteristic
367C4×C13#54811yescharacteristic
368C4×C13D4×Q811yescharacteristic
369Dic13—42no—
370Dic13—42no—
371Dic13—42no—
372Dic13—42no—
373Dic13—81no—
374Dic13—81no—
375Dic13—81no—
376C22×Q8—261no—
377C22×Q8D5211yescharacteristic
378C22×D4—131no—
379C23×C4—261no—
380C23×C4—261no—
381C23×C4—261no—
382C22×C8C22×D1311yescharacteristic
383C22×C8C22×D1311yescharacteristic
384C22×C8C22×D1311yescharacteristic
385C22×C8C22×D1311yescharacteristic
386C4⋊Q8—134no—
387C4⋊Q8—262no—
388#125—134no—
389#125—134no—
390#125—262no—
391#125—262no—
392C22⋊Q8—268no—
393C22⋊Q8—268no—
394C22⋊Q8—268no—
395C4×Q8C4×D1314yes—
396C4×Q8C22⋊D1314yes—
397C4×D4—134no—
398C4×D4—134no—
399C4×D4—134no—
400C4×D4—262no—
401C4×D4—262no—
402C4×D4—262no—
403C2×C4⋊C4—131no—
404C2×C4⋊C4—131no—
405C2×C4⋊C4—131no—
406C2×C4⋊C4—131no—
407C2×C4⋊C4—131no—
408C2×C4⋊C4—131no—
409C2×C4⋊C4—131no—
410C2×C4⋊C4—261no—
411C2×C4⋊C4—261no—
412C2×C4⋊C4—261no—
413C2×C4⋊C4—261no—
414C2×C4⋊C4—261no—
415C2×C4⋊C4—268no—
416C2×C4⋊C4—261no—
417C2×C4⋊C4—261no—
418C2×C4⋊C4D5211yescharacteristic
419C2×C4⋊C4D5211yescharacteristic
420C2×C4⋊C4D5211yescharacteristic
421C2×C22⋊C4—261no—
422C2×C22⋊C4—261no—
423C2×C22⋊C4—261no—
424C2×C42—261no—
425C2×C42—261no—
426C2×C42—261no—
427C2×C42C22×D1311yescharacteristic
428C2×C42C22×D1311yescharacteristic
429C2×C42C22×D1311yescharacteristic
430C4⋊C8—22no—
431C4⋊C8—22no—
432C4⋊C8—22no—
433#102—134no—
434#102—262no—
435#102—262no—
436#102—262no—
437#97—22no—
438#97—22no—
439C4×C8—22no—
440#95—261no—
441#95—261no—
442#95—261no—
443#95—261no—
444#95—261no—
445#95—261no—
446#95—261no—
447C2×C13Q8×C22⋊C411yescharacteristic
448C2×C13#289611yescharacteristic
449C2×C13#289711yescharacteristic
450C2×C13#337011yescharacteristic
451C2×C13#337611yescharacteristic
452C2×C13#338811yescharacteristic
453C2×C13#338911yescharacteristic
454D13—44no—
455C24—261no—
456C2×Q8—41no—
457C2×Q8—41no—
458C2×Q8—264no—
459C2×Q8—1041no—
460C2×Q8—1041no—
461C2×Q8#610314yes—
462C2×D4—132no—
463C2×D4—132no—
464C2×D4—132no—
465C2×D4—261no—
466C2×D4—261no—
467C2×D4—261no—
468C22×C4—261no—
469C22×C4—261no—
470C22×C4—261no—
471C22×C4—261no—
472C22×C4—264no—
473C22×C4—264no—
474C22×C4—264no—
475C22×C4—261no—
476C22×C4—261no—
477C22×C4—261no—
478C22×C4—522no—
479C22×C4—522no—
480C22×C4—1041no—
481C22×C4—1041no—
482C22×C4—1041no—
483C22×C4—1041no—
484C22×C4C2×D5211yescharacteristic
485C22×C4C2×D5211yescharacteristic
486C22×C4C2×D5211yescharacteristic
487C22×C4C2×D5211yescharacteristic
488C22×C4C2×D5211yescharacteristic
489C22×C4C2×D5211yescharacteristic
490C22×C4C23×D1311yescharacteristic
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—21no—
494C2×C8—21no—
495C2×C8—21no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8Q8×D1312yes—
503C4⋊C4—132no—
504C4⋊C4—132no—
505C4⋊C4—132no—
506C4⋊C4—132no—
507C4⋊C4—264no—
508C4⋊C4—264no—
509C4⋊C4—264no—
510C4⋊C4—264no—
511C4⋊C4—264no—
512C4⋊C4—261no—
513C4⋊C4—261no—
514C4⋊C4—261no—
515C4⋊C4—261no—
516C4⋊C4—261no—
517C4⋊C4—261no—
518C4⋊C4—261no—
519C4⋊C4—261no—
520C4⋊C4—261no—
521C4⋊C4—261no—
522C4⋊C4—522no—
523C4⋊C4—1041no—
524C4⋊C4#610314yes—
525C4⋊C4#610314yes—
526C4⋊C4#610314yes—
527C22⋊C4—264no—
528C22⋊C4—264no—
529C22⋊C4—264no—
530C42—522no—
531C42—1041no—
532C42—1041no—
533C42C2×C4×D1312yes—
534C42C2×C4×D1312yes—
535C42C2×C4×D1312yes—
536C42C2×C22⋊D1312yes—
537C42C2×C22⋊D1312yes—
538C42C2×C22⋊D1312yes—
539C13#2252611yescharacteristic, complemented, Sylow
540C23—262no—
541C23—262no—
542C23—262no—
543C23—521no—
544C23—521no—
545C23—521no—
546C23—521no—
547C23C22×D5211yescharacteristic
548Q8—44no—
549Q8—1044no—
550D4—134no—
551D4—262no—
552D4—262no—
553D4—262no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—262no—
567C2×C4—262no—
568C2×C4—262no—
569C2×C4—262no—
570C2×C4—528no—
571C2×C4—521no—
572C2×C4—521no—
573C2×C4—521no—
574C2×C4—521no—
575C2×C4—521no—
576C2×C4—521no—
577C2×C4—521no—
578C2×C4—521no—
579C2×C4—521no—
580C2×C4—521no—
581C2×C4—521no—
582C2×C4—521no—
583C2×C4—521no—
584C2×C4—521no—
585C2×C4—521no—
586C2×C4—521no—
587C2×C4—521no—
588C2×C4—1044no—
589C2×C4—1044no—
590C2×C4C2×#610312yes—
591C2×C4C2×#610312yes—
592C2×C4C2×#610312yes—
593C2×C4C2×#610312yes—
594C2×C4C2×#610312yes—
595C2×C4C2×#610312yes—
596C2×C4C22×C4×D1311yescharacteristic
597C2×C4C2×Q8×D1311yescharacteristic
598C2×C4#8825411yescharacteristic
599C2×C4#41×D1311yescharacteristic
600C2×C4#8825711yescharacteristic
601C2×C4C22×C22⋊D1311yescharacteristic
602C8—22no—
603C8—41no—
604C8—41no—
605C8—41no—
606C22—264no—
607C22—522no—
608C22—522no—
609C22—522no—
610C22—522no—
611C22—522no—
612C22—522no—
613C22Q8×D5211yescharacteristic
614C22#1171928111yescharacteristic
615C22#1171945311yescharacteristic
616C22#1171945311yescharacteristic
617C22#1171945611yescharacteristic
618C22#1171945711yescharacteristic
619C22C22×#610311yescharacteristic
620C4—22no—
621C4—22no—
622C4—22no—
623C4—22no—
624C4—22no—
625C4—22no—
626C4—522no—
627C4—522no—
628C4—522no—
629C4—522no—
630C4—1041no—
631C4—1041no—
632C4—1041no—
633C4C4×Q8×D1311yescharacteristic
634C4#1171927711yescharacteristic
635C4Q8×C22⋊D1311yescharacteristic
636C4#1171953611yescharacteristic
637C2—524no—
638C2Q8×#610311yescharacteristic
639C2#1312335611yescharacteristic
640C2#1312336311yescharacteristic
641C2#1312759111yescharacteristic
642C2#1312766511yescharacteristic
643C2#1312778311yescharacteristic
644C2#1312779611yescharacteristic
subgroupG/H
centerC23C22×D52
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC2×C13×#446C2
socleC23×C13C22×D4
prime radicalC22×D52C23
cosocleC22×C4×C13C24
hypercenterC2×#446D13
hypocenterC13#22526
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#446

Complements

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

NH ≅ G/Ntype
2. #13117793C2semidirect
3. #13115809C2semidirect
4. #13115805C2semidirect
5. #13115801C2semidirect
6. #13115791C2semidirect
7. #13115791C2semidirect
8. #13115787C2semidirect
15. C2×C13×#446C2semidirect
19. #11719284C4semidirect
132. #88061Q8semidirect
219. C2×#446D13semidirect
539. C13#22526semidirect

Maximal subgroups

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

subgroupindex
C2×#117192842
#131177932
#131158092
#131158052
#131158012
#131157912
#131157872
#131148472
#131148372
#131146622
C4×#880612
C2×C13×#4462
#2252613