Finite Group Databasebeta

← #30564849

Subgroups — #30564849

Order 15616.

2234 conjugacy classes of subgroups.

The subgroup lattice has 940 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459615C211yesmaximal, characteristic, complemented
2C2×#16840403C211yesmaximal, characteristic
3#21457906C214yesmaximal, complemented
4#21457898C214yesmaximal, complemented
5#21457326C214yesmaximal, complemented
6#21457322C214yesmaximal, complemented
7#21456821C212yesmaximal, complemented
8#21456624C212yesmaximal, complemented
9#21456591C211yesmaximal, characteristic, complemented
10#21455915C212yesmaximal, complemented
11#21455078C212yesmaximal, complemented
12C2×#16839915C211yesmaximal, characteristic, complemented
13C2×#16839912C211yesmaximal, characteristic, complemented
14#21454845C211yesmaximal, characteristic, complemented
15C61×#3189C211yesmaximal, characteristic, complemented
16C22×#11758226C2211yescharacteristic
17C23×D244C2211yescharacteristic
18C2×#14519809C2214yescomplemented
19C22×#11758190C2212yescomplemented
20C22×#11758201C2212yescomplemented
21#16840470C2212yescomplemented
22#16840467—22no—
23#16840467C2212yescomplemented
24#16840466—22no—
25Q8×C22⋊D61C2212yescomplemented
26#16840425C2212yescomplemented
27#16840403—22no—
28#16840403—22no—
29#16840403C2214yes—
30#16840403C2214yes—
31#16840391—21no—
32#16840388—21no—
33#16840387—21no—
34#16840314C2212yescomplemented
35C2×#14519766C2211yescharacteristic
36C2×#14519762—21no—
37C2×#14519756C2211yescharacteristic
38C22⋊Q8×D61C2212yescomplemented
39C2×#14519752—21no—
40C2×#14519752C2211yescharacteristic
41C2×#14519747—21no—
42#16840235—21no—
43C2×#14519739C2211yescharacteristic
44C2×C4×C22⋊D61C2211yescharacteristic
45C2×C22⋊C4×D61—21no—
46#16840155C2214yescomplemented
47#16840123C2214yescomplemented
48#16840097C2212yescomplemented
49#16840095C2212yescomplemented
50#16840077C2214yescomplemented
51#16840041C2214yescomplemented
52#16840011C2214yescomplemented
53#16840009C2214yescomplemented
54#16840001C2214yescomplemented
55#16839987C2214yescomplemented
56#16839986C2214yescomplemented
57#16839966C2214yescomplemented
58#16839927C2214yescomplemented
59#16839923C2214yescomplemented
60#16839918C2212yescomplemented
61#16839917C2212yescomplemented
62#16839915C2212yes—
63#16839915C2212yes—
64#16839915C2214yescomplemented
65#16839912C2212yes—
66#16839912C2212yes—
67#16839912C2214yescomplemented
68#16839902C2214yescomplemented
69#16839865C2214yescomplemented
70#16839861C2214yescomplemented
71#16839833C2214yescomplemented
72#16839830C2214yescomplemented
73#16839816C2212yescomplemented
74#16839762C2214yescomplemented
75C2×#14519699C2212yescomplemented
76C2×#14519697C2212yescomplemented
77#16839724C2212yescomplemented
78C2×C22⋊#92418C2211yescharacteristic
79C2×C22⋊Q8×C61C2211yescharacteristic
80C2×C22⋊Q8×C61C2211yescharacteristic
81C61×#484C2212yescomplemented
82C61×#484C2212yescomplemented
83C61×#467C2214yescomplemented
84C61×#451C2212yescomplemented
85C61×#451C2212yescomplemented
86C2×C22⋊C8×C61C2211yescharacteristic
87C24×D61—21no—
88C2×#11758226—22no—
89C2×#11758226—44no—
90C2×#11758226C2314yes—
91C22×Dic122C2311yescharacteristic
92C2×Q8×D61C2312yescomplemented
93C22×D244—21no—
94C22×D244—21no—
95C22×D244—21no—
96C22×D244—21no—
97C22×D244—21no—
98C22×D244—44no—
99C22×D244C2311yescharacteristic
100C22×D244C2312yes—
101C22×D244C2312yes—
102C22×D244C2311yescharacteristic
103C22×C22⋊D61D411yescharacteristic
104C22×C4×D61—21no—
105C22×C4×D61—21no—
106C22×C4×D61C2311yescharacteristic
107#14519809—48no—
108C2×#11758202C2314yescomplemented
109C2×#11758190—44no—
110C2×#11758190C2314yes—
111C2×#11758190C2314yes—
112C2×#11758201—44no—
113C2×#11758201C2314yes—
114C2×#11758201C2314yes—
115C2×#11758189C2314yescomplemented
116C22×#92418C2312yes—
117#14519776—22no—
118#14519776C2312yescomplemented
119#14519775—22no—
120#14519775C2312yescomplemented
121#14519767—22no—
122#14519767—22no—
123#14519767—22no—
124#14519766—22no—
125#14519766C2314yes—
126#14519762—24no—
127#14519762—24no—
128#14519757—22no—
129#14519757C2312yescomplemented
130#14519756—21no—
131#14519756—21no—
132#14519756—22no—
133#14519756—22no—
134#14519756C2312yes—
135#14519756C2312yes—
136#14519755—22no—
137#14519755—22no—
138#14519755—22no—
139#14519754—22no—
140#14519754—22no—
141#14519754—22no—
142#14519754—22no—
143#14519753—22no—
144#14519753C2312yescomplemented
145#14519752—22no—
146#14519752—24no—
147#14519752—24no—
148#14519752C2314yes—
149#14519747—24no—
150#14519747—24no—
151Q8×Dic61C2312yescomplemented
152#14519742—22no—
153#14519742C2312yescomplemented
154#14519739—22no—
155#14519739C2314yes—
156C4×C22⋊D61—22no—
157C4×C22⋊D61—22no—
158C4×C22⋊D61D412yes—
159C4×C22⋊D61D412yes—
160C4×C22⋊D61C2312yes—
161C4×C22⋊D61C2312yes—
162#14519737—22no—
163#14519737—22no—
164#14519733—22no—
165C2×C4⋊Dic61C2311yescharacteristic
166C2×#11758196—21no—
167C2×#11758196D411yescharacteristic
168C4⋊C4×D61—22no—
169C4⋊C4×D61C2312yescomplemented
170C2×C22⋊Dic61—21no—
171C2×C22⋊Dic61D411yescharacteristic
172C2×#11758198—21no—
173C2×#11758198—21no—
174C2×#11758198—21no—
175C2×#11758198—21no—
176C2×#11758198D411yescharacteristic
177C22⋊C4×D61—22no—
178C22⋊C4×D61—24no—
179C22⋊C4×D61—24no—
180C2×C4×Dic61C2311yescharacteristic
181#14519710C2314yescomplemented
182#14519706C2314yescomplemented
183#14519701C2314yescomplemented
184#14519700C2314yescomplemented
185#14519699C2314yes—
186#14519699C2314yes—
187#14519697C2314yes—
188#14519697C2314yes—
189C22⋊#92418C2312yes—
190C22⋊#92418C2312yes—
191#14519689C2314yescomplemented
192#14519687C2314yescomplemented
193C22×Q8×C61C2311yescharacteristic
194C22×Q8×C61C2311yescharacteristic
195C23×C4×C61C2311yescharacteristic
196C2×Q16×C61C2314yescomplemented
197C22×C8×C61C2312yes—
198C22⋊Q8×C61—21no—
199C22⋊Q8×C61—21no—
200C22⋊Q8×C61—21no—
201C22⋊Q8×C61—21no—
202C22⋊Q8×C61C2312yes—
203C22⋊Q8×C61C2312yes—
204C22⋊Q8×C61C2312yes—
205C22⋊Q8×C61C2312yes—
206C2×C4⋊C4×C61—21no—
207C2×C4⋊C4×C61—21no—
208C2×C4⋊C4×C61C2311yescharacteristic
209C2×C4⋊C4×C61C2311yescharacteristic
210C2×C22⋊C4×C61—21no—
211C2×C22⋊C4×C61—21no—
212#107×C61C2314yescomplemented
213#103×C61C2314yescomplemented
214#103×C61C2314yescomplemented
215C22⋊C8×C61C2312yes—
216C22⋊C8×C61C2312yes—
217C24×C61C2×D411yescharacteristic
218C23×D61—21no—
219C23×D61—21no—
220C23×D61—22no—
221C23×D61—22no—
222C23×D61—44no—
223C23×D61—44no—
224C23×D61—82no—
225C23×D61C2×D411yescharacteristic
226C2×Q8×C61—21no—
227C2×Q8×C61—21no—
228C2×Q8×C61—42no—
229C2×Q8×C61—42no—
230C2×Q8×C61C2412yes—
231C2×Q8×C61C2412yes—
232C22×C4×C61—21no—
233C22×C4×C61—21no—
234C22×C4×C61—21no—
235C22×C4×C61—21no—
236C22×C4×C61—42no—
237C22×C4×C61C2×D411yescharacteristic
238C22×C4×C61C2×D411yescharacteristic
239C22×C4×C61C2×D411yescharacteristic
240C22×C4×C61C2411yescharacteristic
241C22×C4×C61C2411yescharacteristic
242C22×C4×C61C2411yescharacteristic
243C2×C22⋊D61—24no—
244C2×C22⋊D61C2×D412yes—
245C2×C22⋊D61C2×D412yes—
246C22×Dic61—21no—
247C22×Dic61—21no—
248C22×Dic61C2×D411yescharacteristic
249C22×Dic61C2×D411yescharacteristic
250C22×Dic61C2×D411yescharacteristic
251#11758226—28no—
252#11758226—44no—
253#11758226—48no—
254Q8×D61—44no—
255C2×D244—21no—
256C2×D244—24no—
257C2×D244—24no—
258C2×D244—24no—
259C2×D244—24no—
260C2×D244—22no—
261C2×D244—22no—
262C2×D244—21no—
263C2×D244—24no—
264C2×D244—42no—
265C2×D244—42no—
266C2×D244—42no—
267C2×D244—44no—
268C2×D244—44no—
269C2×D244—44no—
270C2×D244—44no—
271C2×D244—82no—
272C2×D244C2412yes—
273C2×D244C2412yes—
274C2×C4×D61—24no—
275C2×C4×D61—22no—
276C2×C4×D61—22no—
277C2×C4×D61—24no—
278C2×C4×D61—42no—
279C2×C4×D61—44no—
280C2×C4×D61—82no—
281C2×C4×D61C2×D412yes—
282C2×C4×D61C2412yes—
283C2×Dic122—21no—
284C2×Dic122—22no—
285C2×Dic122—22no—
286C2×Dic122—42no—
287C2×Dic122C2412yes—
288Q16×C61—44no—
289C2×C8×C61—42no—
290C2×C8×C61C2414yes—
291C4⋊C4×C61—22no—
292C4⋊C4×C61—22no—
293C4⋊C4×C61—22no—
294C4⋊C4×C61—22no—
295C4⋊C4×C61—21no—
296C4⋊C4×C61—21no—
297C4⋊C4×C61C2412yes—
298C4⋊C4×C61C2412yes—
299C22⋊C4×C61—22no—
300C22⋊C4×C61—22no—
301C22⋊C4×C61—22no—
302C22⋊C4×C61—22no—
303C22⋊Dic61—22no—
304C22⋊Dic61—22no—
305C22⋊Dic61C2×D412yes—
306C22⋊Dic61C2×D412yes—
307#11758202—44no—
308#11758201—28no—
309#11758201—44no—
310#11758198—22no—
311#11758198—22no—
312#11758198—24no—
313#11758198—24no—
314#11758198—24no—
315#11758198—24no—
316#11758198C2×D412yes—
317#11758198C2×D412yes—
318C4⋊Dic61—21no—
319C4⋊Dic61—22no—
320C4⋊Dic61—22no—
321C4⋊Dic61C2412yes—
322#11758196—22no—
323#11758196—22no—
324#11758196—22no—
325#11758196—22no—
326#11758196—22no—
327#11758196—22no—
328#11758196—22no—
329#11758196—22no—
330#11758196C2×D412yes—
331#11758196C2×D412yes—
332C4×Dic61—22no—
333C4×Dic61—22no—
334C4×Dic61C2×D412yes—
335C4×Dic61C2412yes—
336C2×#92418—42no—
337C2×#92418C2414yes—
338#11758190—28no—
339#11758190—44no—
340#11758189—44no—
341C23×C61—41no—
342C23×C61—41no—
343C23×C61#13714yescomplemented
344C23×C61C22×D411yescharacteristic
345C23×C61C22×D411yescharacteristic
346C23×C61C22×D411yescharacteristic
347C22×D61—24no—
348C22×D61—22no—
349C22×D61—22no—
350C22×D61—22no—
351C22×D61—41no—
352C22×D61—41no—
353C22×D61—44no—
354C22×D61—44no—
355C22×D61—42no—
356C22×D61—42no—
357C22×D61—42no—
358C22×D61—42no—
359C22×D61—44no—
360C22×D61—44no—
361C22×D61—42no—
362C22×D61—82no—
363C22×D61—82no—
364C22×D61—816no—
365C22×D61C22×D412yes—
366Q8×C61—24no—
367Q8×C61—24no—
368Q8×C61—42no—
369Q8×C61—81no—
370C2×C4×C61—22no—
371C2×C4×C61—22no—
372C2×C4×C61—22no—
373C2×C4×C61—22no—
374C2×C4×C61—22no—
375C2×C4×C61—22no—
376C2×C4×C61—22no—
377C2×C4×C61—41no—
378C2×C4×C61—41no—
379C2×C4×C61—41no—
380C2×C4×C61—42no—
381C2×C4×C61—42no—
382C2×C4×C61—81no—
383C2×C4×C61—81no—
384C2×C4×C61C22×D411yescharacteristic
385C2×C4×C61C22×D411yescharacteristic
386C2×C4×C61C22×D411yescharacteristic
387C2×C4×C61C2511yescharacteristic
388C22⋊D61—24no—
389C22⋊D61—24no—
390C2×Dic61—22no—
391C2×Dic61—22no—
392C2×Dic61—22no—
393C2×Dic61—41no—
394C2×Dic61—41no—
395C2×Dic61—81no—
396C2×Dic61—81no—
397C2×Dic61C22×D412yes—
398C2×Dic61C22×D412yes—
399C2×Dic61C22×D412yes—
400D244—24no—
401D244—22no—
402D244—22no—
403D244—22no—
404D244—44no—
405D244—44no—
406D244—42no—
407D244—48no—
408D244—84no—
409D244H(5,𝔽2)14yes—
410C4×D61—24no—
411C4×D61—42no—
412C4×D61—48no—
413C4×D61—84no—
414C4×D61—82no—
415C4×D61—82no—
416Dic122—24no—
417Dic122—82no—
418Dic122—82no—
419Dic122—81no—
420C8×C61—24no—
421#92418—24no—
422#61570—611nomaximal, Sylow
423C22×C61—21no—
424C22×C61—21no—
425C22×C61—21no—
426C22×C61—21no—
427C22×C61—21no—
428C22×C61—21no—
429C22×C61—44no—
430C22×C61C2×#13712yes—
431C22×C61C2×#13712yes—
432C22×C61C2×#13712yes—
433C22×C61C23×D411yescharacteristic
434C2×D61—22no—
435C2×D61—22no—
436C2×D61—24no—
437C2×D61—22no—
438C2×D61—48no—
439C2×D61—42no—
440C2×D61—42no—
441C2×D61—42no—
442C2×D61—42no—
443C2×D61—42no—
444C2×D61—82no—
445C2×D61—88no—
446C2×D61—88no—
447C2×D61—84no—
448C4×C61—21no—
449C4×C61—21no—
450C4×C61—21no—
451C4×C61—42no—
452C4×C61—42no—
453C4×C61—42no—
454C4×C61—42no—
455C4×C61C2×H(5,𝔽2)12yes—
456Dic61—22no—
457Dic61—22no—
458Dic61—22no—
459Dic61—42no—
460Dic61—42no—
461#3501—611no—
462C2×#546—611no—
463#3314—614no—
464#3314—614no—
465#3266—614no—
466#3266—614no—
467#3215—612no—
468#3193—612no—
469#3189—611no—
470#3189D6111yescharacteristic, complemented
471#3110—612no—
472#3007—612no—
473C2×#450—611no—
474C2×#450—611no—
475#2973—611no—
476C2×C61—22no—
477C2×C61—22no—
478C2×C61—22no—
479C2×C61#348411yescharacteristic
480C2×C61C22×#13711yescharacteristic
481C2×C61#358511yescharacteristic
482D61—42no—
483D61—44no—
484D61—82no—
485C22×#41—611no—
486C23×D4—611no—
487C2×#137—614no—
488C22×SD16—612no—
489C22×SD16—612no—
490#554—612no—
491#554—612no—
492#554—1222no—
493#554—1222no—
494D4×Q8—612no—
495D4×Q8—612no—
496#546—614no—
497#546—614no—
498#546—1222no—
499#546—1222no—
500#544—1221no—
501#543—1221no—
502#543—1221no—
503#533—612no—
504C2×#124—611no—
505C2×#123—1221no—
506C2×C22⋊Q8—611no—
507C2×C22⋊Q8—612no—
508C2×C22⋊Q8C2×D6111yescharacteristic
509C2×C22⋊Q8C2×D6111yescharacteristic
510C2×#121—611no—
511C2×#121—1221no—
512C2×#120—1221no—
513#518—1221no—
514C2×C4×D4—611no—
515C2×C4×D4—611no—
516C22×C22⋊C4—1221no—
517#497—614no—
518#489—614no—
519#484—612no—
520#484—612no—
521#484C2×D6112yescomplemented
522#484C2×D6112yescomplemented
523#480—614no—
524#474—614no—
525#468—614no—
526#468—614no—
527#467—614no—
528#467C2×D6114yescomplemented
529#464—614no—
530#464—614no—
531#461—614no—
532#452—614no—
533#452—614no—
534#451—612no—
535#451—612no—
536#451C2×D6112yescomplemented
537#451C2×D6112yescomplemented
538#450—612no—
539#450—612no—
540#450—614no—
541#450—612no—
542#450—612no—
543#450—614no—
544#448—614no—
545#440—614no—
546#440—614no—
547#435—614no—
548#435—614no—
549#432—612no—
550#417—614no—
551C2×#102—612no—
552C2×#102—612no—
553#407—612no—
554C2×C22⋊C8—611no—
555C2×C22⋊C8C2×D6111yescharacteristic
556C61#6157011yescharacteristic, complemented, Sylow
557C25—1221no—
558C2×#41—614no—
559C2×#41—1222no—
560C2×#41—2444no—
561C22×Q8—612no—
562C22×Q8—611no—
563C22×Q8C22×D6111yescharacteristic
564C22×Q8C22×D6111yescharacteristic
565C22×D4—611no—
566C22×D4—611no—
567C22×D4—612no—
568C22×D4—612no—
569C22×D4—611no—
570C22×D4—1221no—
571C22×D4—1221no—
572C22×D4—1221no—
573C22×D4—1221no—
574C22×D4—1221no—
575C22×D4—2444no—
576C23×C4—611no—
577C23×C4—1221no—
578C23×C4—1221no—
579C23×C4C22×D6111yescharacteristic
580#137—2448no—
581C2×Q16—614no—
582C2×Q16C22×D6114yescomplemented
583C2×SD16—614no—
584C2×SD16—614no—
585C2×SD16—614no—
586C2×SD16—614no—
587C2×SD16—2444no—
588C2×SD16—2444no—
589C2×M16—614no—
590C22×C8—612no—
591C22×C8C22×D6112yes—
592C4⋊Q8—612no—
593C4⋊Q8—612no—
594C4⋊Q8—1222no—
595C4⋊Q8—1222no—
596#125—1222no—
597#125—1222no—
598#125—1222no—
599#124—614no—
600#124—1222no—
601#123—1224no—
602#123—1224no—
603C22⋊Q8—21no—
604C22⋊Q8—21no—
605C22⋊Q8—21no—
606C22⋊Q8—21no—
607C22⋊Q8—612no—
608C22⋊Q8—612no—
609C22⋊Q8—612no—
610C22⋊Q8—612no—
611C22⋊Q8—1222no—
612C22⋊Q8—1222no—
613C22⋊Q8—1222no—
614C22⋊Q8—1222no—
615C22⋊Q8—1222no—
616C22⋊Q8—1222no—
617C22⋊Q8—1222no—
618C22⋊Q8—1222no—
619C22⋊Q8—1222no—
620C22⋊Q8—1222no—
621C22⋊Q8—1222no—
622C22⋊Q8—1221no—
623C22⋊Q8—1221no—
624C22⋊Q8C22×D6112yes—
625C22⋊Q8C22×D6112yes—
626C22⋊Q8C22×D6112yes—
627C22⋊Q8C22×D6112yes—
628#121—614no—
629#121—1224no—
630#121—1224no—
631#121—1222no—
632#120—1224no—
633#120—1224no—
634C4×Q8—612no—
635C4×Q8—612no—
636C4×Q8—1222no—
637C4×D4—612no—
638C4×D4—612no—
639C4×D4—612no—
640C4×D4—612no—
641C4×D4—614no—
642C4×D4—1222no—
643C4×D4—1222no—
644C4×D4—1222no—
645C4×D4—1222no—
646C4×D4—1222no—
647#117—1222no—
648C2×C4⋊C4—21no—
649C2×C4⋊C4—21no—
650C2×C4⋊C4—611no—
651C2×C4⋊C4—611no—
652C2×C4⋊C4—612no—
653C2×C4⋊C4—1222no—
654C2×C4⋊C4—1221no—
655C2×C4⋊C4C22×D6111yescharacteristic
656C2×C4⋊C4C22×D6111yescharacteristic
657C2×C22⋊C4—21no—
658C2×C22⋊C4—21no—
659C2×C22⋊C4—611no—
660C2×C22⋊C4—611no—
661C2×C22⋊C4—1224no—
662C2×C22⋊C4—1224no—
663C2×C22⋊C4—1222no—
664C2×C22⋊C4—1221no—
665C2×C22⋊C4—1221no—
666C2×C22⋊C4—1221no—
667C2×C22⋊C4—1221no—
668C2×C22⋊C4—1221no—
669C2×C42—611no—
670#107—614no—
671#107C22×D6114yescomplemented
672C4⋊C8—614no—
673#103—614no—
674#103—614no—
675#103C22×D6114yescomplemented
676#103C22×D6114yescomplemented
677#102—614no—
678#102—614no—
679#102—614no—
680#102—614no—
681C22⋊C8—612no—
682C22⋊C8—612no—
683C22⋊C8—614no—
684C22⋊C8C22×D6112yes—
685C22⋊C8C22×D6112yes—
686#97—614no—
687C24—611no—
688C24—1221no—
689C24—1222no—
690C24—1222no—
691C24—1221no—
692C24—4882no—
693C24—2444no—
694C24—2444no—
695C24D4×D6111yescharacteristic
696#41—1228no—
697#41—2444no—
698#41—2448no—
699C2×Q8—21no—
700C2×Q8—21no—
701C2×Q8—42no—
702C2×Q8—42no—
703C2×Q8—612no—
704C2×Q8—1222no—
705C2×Q8—1222no—
706C2×Q8—1221no—
707C2×Q8—2442no—
708C2×Q8—2444no—
709C2×Q8C23×D6112yes—
710C2×Q8C23×D6112yes—
711C2×D4—612no—
712C2×D4—612no—
713C2×D4—612no—
714C2×D4—612no—
715C2×D4—1224no—
716C2×D4—1224no—
717C2×D4—1224no—
718C2×D4—1224no—
719C2×D4—1224no—
720C2×D4—1224no—
721C2×D4—1221no—
722C2×D4—1222no—
723C2×D4—1222no—
724C2×D4—1221no—
725C2×D4—4882no—
726C2×D4—2442no—
727C2×D4—2442no—
728C2×D4—2442no—
729C2×D4—2444no—
730C2×D4—2444no—
731C2×D4—2444no—
732C2×D4—2444no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—42no—
738C22×C4—611no—
739C22×C4—611no—
740C22×C4—611no—
741C22×C4—612no—
742C22×C4—612no—
743C22×C4—1224no—
744C22×C4—1224no—
745C22×C4—1222no—
746C22×C4—1222no—
747C22×C4—1221no—
748C22×C4—1221no—
749C22×C4—4882no—
750C22×C4—2442no—
751C22×C4—2444no—
752C22×C4D4×D6111yescharacteristic
753C22×C4D4×D6111yescharacteristic
754C22×C4D4×D6111yescharacteristic
755C22×C4C23×D6111yescharacteristic
756C22×C4C23×D6111yescharacteristic
757C22×C4C23×D6111yescharacteristic
758Q16—44no—
759Q16—2444no—
760SD16—1228no—
761SD16—1228no—
762SD16—2444no—
763SD16—2444no—
764M16—2444no—
765C2×C8—42no—
766C2×C8—614no—
767C2×C8—2442no—
768C2×C8C23×D6114yes—
769C4⋊C4—22no—
770C4⋊C4—22no—
771C4⋊C4—22no—
772C4⋊C4—22no—
773C4⋊C4—21no—
774C4⋊C4—21no—
775C4⋊C4—612no—
776C4⋊C4—612no—
777C4⋊C4—612no—
778C4⋊C4—1222no—
779C4⋊C4—1222no—
780C4⋊C4—1222no—
781C4⋊C4—1222no—
782C4⋊C4—1222no—
783C4⋊C4—1222no—
784C4⋊C4—1222no—
785C4⋊C4—1222no—
786C4⋊C4—1221no—
787C4⋊C4—1222no—
788C4⋊C4—1222no—
789C4⋊C4C23×D6112yes—
790C4⋊C4C23×D6112yes—
791C22⋊C4—22no—
792C22⋊C4—22no—
793C22⋊C4—22no—
794C22⋊C4—22no—
795C22⋊C4—612no—
796C22⋊C4—612no—
797C22⋊C4—612no—
798C22⋊C4—612no—
799C22⋊C4—1224no—
800C22⋊C4—1224no—
801C22⋊C4—1224no—
802C22⋊C4—1224no—
803C22⋊C4—1222no—
804C22⋊C4—1222no—
805C22⋊C4—1222no—
806C22⋊C4—1222no—
807C42—612no—
808C42—612no—
809C42—1222no—
810C42—1222no—
811C23—41no—
812C23—41no—
813C23—612no—
814C23—1224no—
815C23—1222no—
816C23—1222no—
817C23—1222no—
818C23—4882no—
819C23—4882no—
820C23—48816no—
821C23—2441no—
822C23—2441no—
823C23—2444no—
824C23—2444no—
825C23—2442no—
826C23—2442no—
827C23—2442no—
828C23—2442no—
829C23—2444no—
830C23—2444no—
831C23—2442no—
832C23#1451980914yescomplemented
833C23C2×D4×D6111yescharacteristic
834C23C2×D4×D6111yescharacteristic
835C23C2×D4×D6111yescharacteristic
836Q8—24no—
837Q8—24no—
838Q8—42no—
839Q8—81no—
840Q8—1224no—
841Q8—4881no—
842Q8—4882no—
843Q8—4882no—
844D4—614no—
845D4—1224no—
846D4—1224no—
847D4—1224no—
848D4—1222no—
849D4—1222no—
850D4—1222no—
851D4—4884no—
852D4—2444no—
853D4—2444no—
854D4—2442no—
855D4—2448no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—42no—
867C2×C4—42no—
868C2×C4—81no—
869C2×C4—81no—
870C2×C4—612no—
871C2×C4—612no—
872C2×C4—612no—
873C2×C4—1222no—
874C2×C4—1224no—
875C2×C4—1222no—
876C2×C4—1222no—
877C2×C4—4884no—
878C2×C4—4882no—
879C2×C4—4882no—
880C2×C4—4881no—
881C2×C4—4881no—
882C2×C4—2442no—
883C2×C4—2448no—
884C2×C4—2441no—
885C2×C4—2441no—
886C2×C4C2×D4×D6111yescharacteristic
887C2×C4C2×D4×D6111yescharacteristic
888C2×C4C2×D4×D6111yescharacteristic
889C2×C4C24×D6111yescharacteristic
890C8—24no—
891C8—1224no—
892C22—21no—
893C22—21no—
894C22—21no—
895C22—21no—
896C22—21no—
897C22—21no—
898C22—44no—
899C22—1222no—
900C22—1222no—
901C22—1222no—
902C22—1224no—
903C22—4884no—
904C22—4888no—
905C22—4888no—
906C22—4882no—
907C22—2448no—
908C22—2442no—
909C22—2442no—
910C22—2442no—
911C22—2442no—
912C22—2442no—
913C22C2×#1451980912yes—
914C22C2×#1451980912yes—
915C22C2×#1451980912yes—
916C22C22×D4×D6111yescharacteristic
917C4—21no—
918C4—21no—
919C4—21no—
920C4—42no—
921C4—42no—
922C4—42no—
923C4—42no—
924C4—1222no—
925C4—1222no—
926C4—1222no—
927C4—2442no—
928C4—2442no—
929C4H(5,𝔽2)×D6112yes—
930C2—22no—
931C2—22no—
932C2—22no—
933C2—4882no—
934C2—2442no—
935C2—2444no—
936C2#2145945111yescharacteristic
937C2C22×#1451980911yescharacteristic
938C2#2146059611yescharacteristic
subgroupG/H
centerC22C22×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC61×#3189C2
socleC22×C61C23×D4
prime radicalC2×#16840403C2
hypercenter#3189D61
hypocenterC61#61570
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3189

Complements

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

NH ≅ G/Ntype
1. #21459615C2semidirect
3. #21457906C2semidirect
4. #21457898C2semidirect
5. #21457326C2semidirect
6. #21457322C2semidirect
7. #21456821C2semidirect
8. #21456624C2semidirect
9. #21456591C2semidirect
10. #21455915C2semidirect
11. #21455078C2semidirect
12. C2×#16839915C2semidirect
13. C2×#16839912C2semidirect
14. #21454845C2semidirect
15. C61×#3189C2semidirect
18. C2×#14519809C22semidirect
19. C22×#11758190C22semidirect
20. C22×#11758201C22semidirect
21. #16840470C22semidirect
23. #16840467C22semidirect
25. Q8×C22⋊D61C22semidirect
26. #16840425C22semidirect
34. #16840314C22semidirect
38. C22⋊Q8×D61C22semidirect
46. #16840155C22semidirect
47. #16840123C22semidirect
48. #16840097C22semidirect
49. #16840095C22semidirect
50. #16840077C22semidirect
51. #16840041C22semidirect
52. #16840011C22semidirect
53. #16840009C22semidirect
54. #16840001C22semidirect
55. #16839987C22semidirect
56. #16839986C22semidirect
57. #16839966C22semidirect
58. #16839927C22semidirect
59. #16839923C22semidirect
60. #16839918C22semidirect
61. #16839917C22semidirect
64. #16839915C22semidirect
67. #16839912C22semidirect
68. #16839902C22semidirect
69. #16839865C22semidirect
70. #16839861C22semidirect
71. #16839833C22semidirect
72. #16839830C22semidirect
73. #16839816C22semidirect
74. #16839762C22semidirect
75. C2×#14519699C22semidirect
76. C2×#14519697C22semidirect
77. #16839724C22semidirect
81. C61×#484C22semidirect
82. C61×#484C22semidirect
83. C61×#467C22semidirect
84. C61×#451C22semidirect
85. C61×#451C22semidirect
92. C2×Q8×D61C23semidirect
108. C2×#11758202C23semidirect
115. C2×#11758189C23semidirect
118. #14519776C23semidirect
120. #14519775C23semidirect
129. #14519757C23semidirect
144. #14519753C23semidirect
151. Q8×Dic61C23semidirect
153. #14519742C23semidirect
169. C4⋊C4×D61C23semidirect
181. #14519710C23semidirect
182. #14519706C23semidirect
183. #14519701C23semidirect
184. #14519700C23semidirect
191. #14519689C23semidirect
192. #14519687C23semidirect
196. C2×Q16×C61C23semidirect
212. #107×C61C23semidirect
213. #103×C61C23semidirect
214. #103×C61C23semidirect
343. C23×C61#137semidirect
470. #3189D61semidirect
521. #484C2×D61semidirect
522. #484C2×D61semidirect
528. #467C2×D61semidirect
536. #451C2×D61semidirect
537. #451C2×D61semidirect
556. C61#61570semidirect
582. C2×Q16C22×D61semidirect
671. #107C22×D61semidirect
675. #103C22×D61semidirect
676. #103C22×D61semidirect
832. C23#14519809semidirect

Maximal subgroups

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

subgroupindex
#214596152
C2×#168404032
#214579062
#214578982
#214573262
#214573222
#214568212
#214566242
#214565912
#214559152
#214550782
C2×#168399152
C2×#168399122
#214548452
C61×#31892
#6157061