Finite Group Databasebeta

← #30564739

Subgroups — #30564739

Order 15616.

2090 conjugacy classes of subgroups.

The subgroup lattice has 890 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459615C211yesmaximal, characteristic
2C2×#16840425C211yesmaximal, characteristic
3#21457693C214yesmaximal, complemented
4#21457690C214yesmaximal, complemented
5#21457568C214yesmaximal, complemented
6#21457564C214yesmaximal, complemented
7#21456765C212yesmaximal, complemented
8#21456593C212yesmaximal, complemented
9#21456591C211yesmaximal, characteristic, complemented
10#21455855C212yesmaximal, complemented
11C2×#16839920C211yesmaximal, characteristic, complemented
12C2×#16839917C211yesmaximal, characteristic, complemented
13#451×D61C212yesmaximal, complemented
14#21454841C211yesmaximal, characteristic
15C61×#3189C211yesmaximal, characteristic, complemented
16C23×Dic122C2211yescharacteristic
17C22×Q8×D61C2211yescharacteristic
18C22×Dic244C2212yescomplemented
19C22×#11758202C2212yescomplemented
20C2×Q16×D61C2214yescomplemented
21#16840470C2212yes—
22#16840467—22no—
23#16840467C2212yes—
24#16840466—22no—
25Q8×C22⋊D61C2212yes—
26#16840425—22no—
27#16840425—22no—
28#16840425C2214yes—
29#16840425C2214yes—
30#16840425C2212yes—
31#16840391—21no—
32#16840388—21no—
33#16840387—21no—
34#16840314C2212yes—
35C2×#14519776—21no—
36C2×#14519775C2211yescharacteristic
37C2×#14519757C2211yescharacteristic
38C2×#14519756C2211yescharacteristic
39C2×#14519755—21no—
40C2×#14519754—21no—
41C22⋊Q8×D61C2212yes—
42#16840235—21no—
43C2×#14519742C2211yescharacteristic
44C2×C4×C22⋊D61C2211yescharacteristic
45C2×#14519737—21no—
46#16840140C2214yescomplemented
47#16840111C2214yescomplemented
48#16840099C2214yescomplemented
49#16840097C2212yes—
50#16840095C2212yescomplemented
51#16840056C2214yescomplemented
52#16840004C2214yescomplemented
53#16840002C2214yescomplemented
54#16840001C2214yescomplemented
55#16839971C2214yescomplemented
56#16839971C2214yescomplemented
57#16839970C2214yescomplemented
58#16839920C2212yes—
59#16839920C2212yes—
60#16839920C2214yescomplemented
61#16839919C2214yescomplemented
62#16839919C2214yescomplemented
63#16839918C2212yes—
64#16839917C2212yes—
65#16839917C2212yes—
66#16839917C2214yescomplemented
67#16839917C2212yescomplemented
68#16839916C2214yescomplemented
69#16839856C2214yescomplemented
70#16839854C2214yescomplemented
71C8×C22⋊D61C2214yes—
72#16839825C2214yes—
73#16839812C2212yes—
74C2×#14519702C2212yescomplemented
75C2×#14519700C2212yescomplemented
76#103×D61C2214yescomplemented
77C2×C22⋊#92418C2211yescharacteristic
78C22⋊C8×D61C2212yes—
79C2×C22⋊Q8×C61C2211yescharacteristic
80C2×C22⋊Q8×C61C2211yescharacteristic
81C61×#484C2212yes—
82C61×#484C2212yescomplemented
83C61×#467C2214yescomplemented
84C61×#451C2212yes—
85C61×#451C2212yescomplemented
86C2×C22⋊C8×C61C2211yescharacteristic
87C22×Dic122—21no—
88C22×Dic122—21no—
89C22×Dic122—21no—
90C22×Dic122—21no—
91C22×Dic122—44no—
92C22×Dic122C2311yescharacteristic
93C22×Dic122C2312yes—
94C22×Dic122C2312yes—
95C22×Dic122C2311yescharacteristic
96C22×Dic122C2311yescharacteristic
97C2×Q8×D61—22no—
98C2×Q8×D61—44no—
99C2×Q8×D61C2314yes—
100C2×Q8×D61C2312yes—
101C22×C22⋊D61D411yescharacteristic
102C23×Dic61—21no—
103C22×C4×D61—21no—
104C22×C4×D61C2311yescharacteristic
105C2×Dic244—44no—
106C2×Dic244C2314yes—
107C2×Dic244C2314yes—
108C2×#11758202—44no—
109C2×#11758202C2314yes—
110C2×#11758202C2314yes—
111C2×#11758202C2314yes—
112Q16×D61—48no—
113C22×#92418C2312yes—
114C2×C8×D61C2314yes—
115#14519776—22no—
116#14519776—24no—
117#14519776—24no—
118#14519776C2312yes—
119#14519775—22no—
120#14519775—22no—
121#14519775C2314yes—
122#14519775C2312yes—
123#14519767—22no—
124#14519767—22no—
125#14519767—22no—
126#14519757—22no—
127#14519757—22no—
128#14519757C2312yes—
129#14519757C2314yes—
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#14519755—24no—
140#14519755—24no—
141#14519754—22no—
142#14519754—22no—
143#14519754—22no—
144#14519754—22no—
145#14519754—24no—
146#14519754—24no—
147#14519753—22no—
148#14519753C2312yes—
149Q8×Dic61C2312yes—
150#14519742—22no—
151#14519742—22no—
152#14519742C2312yes—
153#14519742C2314yes—
154C4×C22⋊D61—22no—
155C4×C22⋊D61—22no—
156C4×C22⋊D61D412yes—
157C4×C22⋊D61D412yes—
158C4×C22⋊D61C2312yes—
159C4×C22⋊D61C2312yes—
160#14519737—22no—
161#14519737—22no—
162#14519737—24no—
163#14519737—24no—
164#14519733—22no—
165C2×C4⋊Dic61—21no—
166C2×C4⋊Dic61C2311yescharacteristic
167C2×#11758196—21no—
168C2×#11758196—21no—
169C2×#11758196—21no—
170C2×#11758196—21no—
171C2×#11758196D411yescharacteristic
172C4⋊C4×D61—22no—
173C4⋊C4×D61C2312yes—
174C2×C22⋊Dic61—21no—
175C2×C22⋊Dic61D411yescharacteristic
176C2×#11758198—21no—
177C2×#11758198D411yescharacteristic
178C22⋊C4×D61—22no—
179C2×C4×Dic61—21no—
180C2×C4×Dic61C2311yescharacteristic
181#14519710C2314yes—
182#14519706C2314yes—
183#14519702C2314yes—
184#14519702C2314yes—
185#14519701C2314yes—
186#14519700C2314yes—
187#14519700C2314yes—
188#14519700C2314yes—
189C22⋊#92418C2312yes—
190C22⋊#92418C2312yes—
191#14519689C2314yes—
192C8×Dic61C2314yes—
193C22×Q8×C61C2311yescharacteristic
194C22×Q8×C61C2311yescharacteristic
195C23×C4×C61C2311yescharacteristic
196C2×Q16×C61C2314yes—
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×C61C2314yes—
213#103×C61C2314yes—
214#103×C61C2314yes—
215C22⋊C8×C61C2312yes—
216C22⋊C8×C61C2312yes—
217C24×C61C2×D411yescharacteristic
218C23×D61C2×D411yescharacteristic
219C2×Q8×C61—21no—
220C2×Q8×C61—21no—
221C2×Q8×C61—42no—
222C2×Q8×C61—42no—
223C2×Q8×C61C2412yes—
224C2×Q8×C61C2412yes—
225C22×C4×C61—21no—
226C22×C4×C61—21no—
227C22×C4×C61—21no—
228C22×C4×C61—21no—
229C22×C4×C61—42no—
230C22×C4×C61C2×D411yescharacteristic
231C22×C4×C61C2×D411yescharacteristic
232C22×C4×C61C2×D411yescharacteristic
233C22×C4×C61C2411yescharacteristic
234C22×C4×C61C2411yescharacteristic
235C22×C4×C61C2411yescharacteristic
236C2×C22⋊D61Q1618yescomplemented
237C2×C22⋊D61C2×D412yes—
238C2×C22⋊D61C2×D412yes—
239C22×Dic61—21no—
240C22×Dic61—21no—
241C22×Dic61—22no—
242C22×Dic61—22no—
243C22×Dic61—21no—
244C22×Dic61—21no—
245C22×Dic61—44no—
246C22×Dic61C2×D411yescharacteristic
247C22×Dic61C2×D411yescharacteristic
248C22×Dic61C2×D411yescharacteristic
249Q8×D61—28no—
250Q8×D61—44no—
251Q8×D61—48no—
252Q8×D61—44no—
253C2×C4×D61—24no—
254C2×C4×D61—22no—
255C2×C4×D61—22no—
256C2×C4×D61—42no—
257C2×C4×D61—44no—
258C2×C4×D61C2×D412yes—
259C2×C4×D61C2412yes—
260C2×Dic122—21no—
261C2×Dic122—24no—
262C2×Dic122—24no—
263C2×Dic122—24no—
264C2×Dic122—22no—
265C2×Dic122—22no—
266C2×Dic122—21no—
267C2×Dic122—24no—
268C2×Dic122—21no—
269C2×Dic122—22no—
270C2×Dic122—22no—
271C2×Dic122—42no—
272C2×Dic122—42no—
273C2×Dic122—42no—
274C2×Dic122—42no—
275C2×Dic122—44no—
276C2×Dic122—44no—
277C2×Dic122—44no—
278C2×Dic122—44no—
279C2×Dic122C2412yes—
280C2×Dic122C2412yes—
281C2×Dic122C2412yes—
282Q16×C61—44no—
283C2×C8×C61—42no—
284C2×C8×C61C2414yes—
285C4⋊C4×C61—22no—
286C4⋊C4×C61—22no—
287C4⋊C4×C61—22no—
288C4⋊C4×C61—22no—
289C4⋊C4×C61—21no—
290C4⋊C4×C61—21no—
291C4⋊C4×C61C2412yes—
292C4⋊C4×C61C2412yes—
293C22⋊C4×C61—22no—
294C22⋊C4×C61—22no—
295C22⋊C4×C61—22no—
296C22⋊C4×C61—22no—
297C22⋊Dic61—22no—
298C22⋊Dic61—22no—
299C22⋊Dic61C2×D412yes—
300C22⋊Dic61C2×D412yes—
301#11758202—28no—
302#11758202—44no—
303#11758202—44no—
304#11758198—22no—
305#11758198—22no—
306#11758198—24no—
307#11758198C2×D412yes—
308#11758198C2×D412yes—
309C4⋊Dic61—21no—
310C4⋊Dic61—22no—
311C4⋊Dic61—24no—
312C4⋊Dic61—22no—
313C4⋊Dic61C2412yes—
314#11758196—22no—
315#11758196—22no—
316#11758196—22no—
317#11758196—22no—
318#11758196—24no—
319#11758196—24no—
320#11758196—24no—
321#11758196—22no—
322#11758196—22no—
323#11758196—22no—
324#11758196—22no—
325#11758196C2×D412yes—
326#11758196C2×D412yes—
327C4×Dic61—24no—
328C4×Dic61—22no—
329C4×Dic61—22no—
330C4×Dic61C2×D412yes—
331C4×Dic61C2412yes—
332C2×#92418—42no—
333C2×#92418C2414yes—
334Dic244—28no—
335Dic244—44no—
336C8×D61—44no—
337C23×C61—41no—
338C23×C61—41no—
339C23×C61C2×Q1614yescomplemented
340C23×C61C22×D411yescharacteristic
341C23×C61C22×D411yescharacteristic
342C23×C61C22×D411yescharacteristic
343C22×D61—41no—
344C22×D61—41no—
345C22×D61C2×Q1614yescomplemented
346C22×D61C22×D412yes—
347Q8×C61—24no—
348Q8×C61—24no—
349Q8×C61—42no—
350Q8×C61—81no—
351C2×C4×C61—22no—
352C2×C4×C61—22no—
353C2×C4×C61—22no—
354C2×C4×C61—22no—
355C2×C4×C61—22no—
356C2×C4×C61—22no—
357C2×C4×C61—22no—
358C2×C4×C61—41no—
359C2×C4×C61—41no—
360C2×C4×C61—41no—
361C2×C4×C61—42no—
362C2×C4×C61—42no—
363C2×C4×C61—81no—
364C2×C4×C61—81no—
365C2×C4×C61C22×D411yescharacteristic
366C2×C4×C61C22×D411yescharacteristic
367C2×C4×C61C22×D411yescharacteristic
368C2×C4×C61C2511yescharacteristic
369C22⋊D61C2×Q1618yescomplemented
370C22⋊D61C2×Q1618yescomplemented
371C2×Dic61—24no—
372C2×Dic61—22no—
373C2×Dic61—22no—
374C2×Dic61—22no—
375C2×Dic61—22no—
376C2×Dic61—41no—
377C2×Dic61—41no—
378C2×Dic61—44no—
379C2×Dic61—44no—
380C2×Dic61—42no—
381C2×Dic61—81no—
382C2×Dic61—81no—
383C2×Dic61C2×Q1614yescomplemented
384C2×Dic61C22×D412yes—
385C2×Dic61C22×D412yes—
386C2×Dic61C22×D412yes—
387C4×D61—24no—
388C4×D61—42no—
389C4×D61—48no—
390C4×D61—82no—
391C4×D61—82no—
392Dic122—24no—
393Dic122—22no—
394Dic122—24no—
395Dic122—22no—
396Dic122—22no—
397Dic122—48no—
398Dic122—44no—
399Dic122—44no—
400Dic122—42no—
401Dic122—82no—
402Dic122—82no—
403Dic122—81no—
404Dic122H(5,𝔽2)14yes—
405C8×C61—24no—
406#92418—24no—
407#61563—611nomaximal, Sylow
408C22×C61—21no—
409C22×C61—21no—
410C22×C61—21no—
411C22×C61—21no—
412C22×C61—21no—
413C22×C61—21no—
414C22×C61—44no—
415C22×C61C22×Q1612yes—
416C22×C61C22×Q1612yes—
417C22×C61C22×Q1612yes—
418C22×C61C23×D411yescharacteristic
419C2×D61—22no—
420C2×D61—22no—
421C2×D61—44no—
422C2×D61C22×Q1614yes—
423C4×C61—21no—
424C4×C61—21no—
425C4×C61—21no—
426C4×C61—42no—
427C4×C61—42no—
428C4×C61—42no—
429C4×C61—42no—
430C4×C61C2×H(5,𝔽2)12yes—
431Dic61—22no—
432Dic61—24no—
433Dic61—22no—
434Dic61—42no—
435Dic61—42no—
436Dic61—42no—
437Dic61C22×Q1614yes—
438#3501—611no—
439C2×D4×Q8—611no—
440#3299—614no—
441#3299—614no—
442D4×Q16—614no—
443D4×Q16—614no—
444#3209—612no—
445#3189—612no—
446#3189—611no—
447#3189D6111yescharacteristic, complemented
448#3104—612no—
449C2×#451—612no—
450C2×#451—611no—
451C2×#451—611no—
452#2972—611no—
453C2×C61—22no—
454C2×C61—22no—
455C2×C61—22no—
456C2×C61#348411yescharacteristic
457C2×C61C23×Q1611yescharacteristic
458C2×C61#358611yescharacteristic
459D61—24no—
460C23×Q8—611no—
461C23×Q8—611no—
462C22×Q16—612no—
463C22×Q16—614no—
464C22×Q16—612no—
465#554—612no—
466#554—612no—
467#554—1222no—
468#554—1222no—
469D4×Q8—612no—
470D4×Q8—614no—
471D4×Q8—614no—
472D4×Q8—612no—
473D4×Q8—1222no—
474D4×Q8—1222no—
475#544—1221no—
476#543—1221no—
477#543—1221no—
478#533—612no—
479C2×C4⋊Q8—611no—
480C2×C4⋊Q8—1221no—
481C2×C22⋊Q8—611no—
482C2×C22⋊Q8—612no—
483C2×C22⋊Q8—611no—
484C2×C22⋊Q8—1221no—
485C2×C22⋊Q8—1221no—
486C2×C22⋊Q8C2×D6111yescharacteristic
487C2×C22⋊Q8C2×D6111yescharacteristic
488#518—1221no—
489C2×C4×Q8—611no—
490C2×C4×D4—611no—
491C2×C4×D4—1221no—
492#494—614no—
493#487—614no—
494#484—612no—
495#484—612no—
496#484—614no—
497#484C2×D6112yes—
498#484C2×D6112yescomplemented
499#477—614no—
500#467—614no—
501#467—614no—
502#467—614no—
503#467C2×D6114yescomplemented
504#462—614no—
505#462—614no—
506#462—614no—
507#451—612no—
508#451—614no—
509#451—612no—
510#451—612no—
511#451—612no—
512#451—614no—
513#451—614no—
514#451—614no—
515#451—612no—
516#451—612no—
517#451—614no—
518#451C2×D6112yes—
519#451C2×D6112yescomplemented
520C4×Q16—614no—
521C4×Q16—614no—
522C8×D4—614no—
523C8×D4—614no—
524#431—612no—
525C2×#103—612no—
526C2×#103—612no—
527C2×#103—614no—
528C2×C22⋊C8—611no—
529C2×C22⋊C8—612no—
530C2×C22⋊C8C2×D6111yescharacteristic
531C61#6156311yescharacteristic, complemented, Sylow
532C22×Q8—614no—
533C22×Q8—612no—
534C22×Q8—611no—
535C22×Q8—612no—
536C22×Q8—612no—
537C22×Q8—611no—
538C22×Q8—611no—
539C22×Q8—1221no—
540C22×Q8—1222no—
541C22×Q8—1221no—
542C22×Q8—1221no—
543C22×Q8—1221no—
544C22×Q8—2444no—
545C22×Q8—2444no—
546C22×Q8C22×D6111yescharacteristic
547C22×Q8C22×D6111yescharacteristic
548C22×D4—611no—
549C23×C4—611no—
550C23×C4—1221no—
551C23×C4—1221no—
552C23×C4C22×D6111yescharacteristic
553C2×Q16—614no—
554C2×Q16—614no—
555C2×Q16—614no—
556C2×Q16—614no—
557C2×Q16—614no—
558C2×Q16—2444no—
559C2×Q16—2448no—
560C2×Q16—2444no—
561C2×Q16C22×D6114yes—
562C22×C8—612no—
563C22×C8—614no—
564C22×C8C22×D6112yes—
565C4⋊Q8—612no—
566C4⋊Q8—614no—
567C4⋊Q8—612no—
568C4⋊Q8—1222no—
569C4⋊Q8—1224no—
570C4⋊Q8—1224no—
571C4⋊Q8—1222no—
572C4⋊Q8—1222no—
573#125—1222no—
574#125—1222no—
575#125—1222no—
576C22⋊Q8—21no—
577C22⋊Q8—21no—
578C22⋊Q8—21no—
579C22⋊Q8—21no—
580C22⋊Q8—612no—
581C22⋊Q8—612no—
582C22⋊Q8—612no—
583C22⋊Q8—614no—
584C22⋊Q8—612no—
585C22⋊Q8—1224no—
586C22⋊Q8—1224no—
587C22⋊Q8—1222no—
588C22⋊Q8—1222no—
589C22⋊Q8—1222no—
590C22⋊Q8—1222no—
591C22⋊Q8—1224no—
592C22⋊Q8—1224no—
593C22⋊Q8—1222no—
594C22⋊Q8—1222no—
595C22⋊Q8—1222no—
596C22⋊Q8—1222no—
597C22⋊Q8—1222no—
598C22⋊Q8—1222no—
599C22⋊Q8—1222no—
600C22⋊Q8—1222no—
601C22⋊Q8—1221no—
602C22⋊Q8—1221no—
603C22⋊Q8C22×D6112yes—
604C22⋊Q8C22×D6112yes—
605C22⋊Q8C22×D6112yes—
606C22⋊Q8C22×D6112yes—
607C4×Q8—612no—
608C4×Q8—614no—
609C4×Q8—612no—
610C4×Q8—1222no—
611C4×Q8—1222no—
612C4×D4—612no—
613C4×D4—612no—
614C4×D4—612no—
615C4×D4—612no—
616C4×D4—1224no—
617C4×D4—1224no—
618C4×D4—1222no—
619C4×D4—1222no—
620C4×D4—1222no—
621C4×D4—1222no—
622#117—1222no—
623C2×C4⋊C4—21no—
624C2×C4⋊C4—21no—
625C2×C4⋊C4—611no—
626C2×C4⋊C4—611no—
627C2×C4⋊C4—612no—
628C2×C4⋊C4—1222no—
629C2×C4⋊C4—1221no—
630C2×C4⋊C4—1221no—
631C2×C4⋊C4—1221no—
632C2×C4⋊C4—1221no—
633C2×C4⋊C4—1221no—
634C2×C4⋊C4C22×D6111yescharacteristic
635C2×C4⋊C4C22×D6111yescharacteristic
636C2×C22⋊C4—21no—
637C2×C22⋊C4—21no—
638C2×C22⋊C4—611no—
639C2×C22⋊C4—611no—
640C2×C22⋊C4—1222no—
641C2×C22⋊C4—1221no—
642C2×C22⋊C4—1221no—
643C2×C42—611no—
644C2×C42—1221no—
645#107—614no—
646#107C22×D6114yes—
647C4⋊C8—614no—
648#103—614no—
649#103—614no—
650#103—614no—
651#103—614no—
652#103—614no—
653#103—614no—
654#103C22×D6114yes—
655#103C22×D6114yes—
656C22⋊C8—612no—
657C22⋊C8—612no—
658C22⋊C8—614no—
659C22⋊C8C22×D6112yes—
660C22⋊C8C22×D6112yes—
661C4×C8—614no—
662C24—611no—
663C24D4×D6111yescharacteristic
664C2×Q8—21no—
665C2×Q8—21no—
666C2×Q8—42no—
667C2×Q8—42no—
668C2×Q8—612no—
669C2×Q8—612no—
670C2×Q8—612no—
671C2×Q8—1222no—
672C2×Q8—1222no—
673C2×Q8—1224no—
674C2×Q8—1224no—
675C2×Q8—1224no—
676C2×Q8—1224no—
677C2×Q8—1221no—
678C2×Q8—1221no—
679C2×Q8—1222no—
680C2×Q8—1222no—
681C2×Q8—1221no—
682C2×Q8—1228no—
683C2×Q8—2442no—
684C2×Q8—2442no—
685C2×Q8—2442no—
686C2×Q8—2442no—
687C2×Q8—2444no—
688C2×Q8—2444no—
689C2×Q8—2444no—
690C2×Q8—2444no—
691C2×Q8—2444no—
692C2×Q8—2444no—
693C2×Q8—2448no—
694C2×Q8C23×D6112yes—
695C2×Q8C23×D6112yes—
696C2×D4—612no—
697C2×D4—612no—
698C2×D4—618no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—42no—
704C22×C4—611no—
705C22×C4—611no—
706C22×C4—611no—
707C22×C4—612no—
708C22×C4—612no—
709C22×C4—1222no—
710C22×C4—1222no—
711C22×C4—1224no—
712C22×C4—1221no—
713C22×C4—1221no—
714C22×C4—1221no—
715C22×C4—1221no—
716C22×C4—1222no—
717C22×C4—1222no—
718C22×C4—2442no—
719C22×C4—2444no—
720C22×C4—2444no—
721C22×C4D4×D6111yescharacteristic
722C22×C4D4×D6111yescharacteristic
723C22×C4D4×D6111yescharacteristic
724C22×C4C23×D6111yescharacteristic
725C22×C4C23×D6111yescharacteristic
726C22×C4C23×D6111yescharacteristic
727Q16—44no—
728Q16—1228no—
729Q16—1228no—
730Q16—2444no—
731Q16—2444no—
732Q16—2444no—
733C2×C8—42no—
734C2×C8—614no—
735C2×C8—2444no—
736C2×C8—2442no—
737C2×C8C23×D6114yes—
738C4⋊C4—22no—
739C4⋊C4—22no—
740C4⋊C4—22no—
741C4⋊C4—22no—
742C4⋊C4—21no—
743C4⋊C4—21no—
744C4⋊C4—612no—
745C4⋊C4—612no—
746C4⋊C4—612no—
747C4⋊C4—1222no—
748C4⋊C4—1224no—
749C4⋊C4—1224no—
750C4⋊C4—1222no—
751C4⋊C4—1224no—
752C4⋊C4—1222no—
753C4⋊C4—1224no—
754C4⋊C4—1222no—
755C4⋊C4—1222no—
756C4⋊C4—1222no—
757C4⋊C4—1222no—
758C4⋊C4—1222no—
759C4⋊C4—1221no—
760C4⋊C4—1222no—
761C4⋊C4—1222no—
762C4⋊C4C23×D6112yes—
763C4⋊C4C23×D6112yes—
764C22⋊C4—22no—
765C22⋊C4—22no—
766C22⋊C4—22no—
767C22⋊C4—22no—
768C22⋊C4—612no—
769C22⋊C4—612no—
770C22⋊C4—612no—
771C22⋊C4—612no—
772C22⋊C4—1224no—
773C22⋊C4—1222no—
774C22⋊C4—1222no—
775C22⋊C4—1222no—
776C22⋊C4—1222no—
777C42—612no—
778C42—612no—
779C42—1224no—
780C42—1222no—
781C42—1222no—
782C23—41no—
783C23—41no—
784C23—612no—
785C23—614no—
786C23—2441no—
787C23—2441no—
788C23Q16×D6114yescomplemented
789C23C2×D4×D6111yescharacteristic
790C23C2×D4×D6111yescharacteristic
791C23C2×D4×D6111yescharacteristic
792Q8—24no—
793Q8—24no—
794Q8—42no—
795Q8—81no—
796Q8—614no—
797Q8—1224no—
798Q8—1222no—
799Q8—1224no—
800Q8—1222no—
801Q8—1222no—
802Q8—4881no—
803Q8—4882no—
804Q8—4882no—
805Q8—2444no—
806Q8—2444no—
807Q8—2442no—
808Q8—2448no—
809D4—618no—
810D4—618no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—42no—
822C2×C4—42no—
823C2×C4—81no—
824C2×C4—81no—
825C2×C4—614no—
826C2×C4—612no—
827C2×C4—612no—
828C2×C4—612no—
829C2×C4—1224no—
830C2×C4—1222no—
831C2×C4—1224no—
832C2×C4—1222no—
833C2×C4—1222no—
834C2×C4—1222no—
835C2×C4—4882no—
836C2×C4—4882no—
837C2×C4—4881no—
838C2×C4—4881no—
839C2×C4—2442no—
840C2×C4—2448no—
841C2×C4—2441no—
842C2×C4—2441no—
843C2×C4—2444no—
844C2×C4—2444no—
845C2×C4—2442no—
846C2×C4C2×D4×D6111yescharacteristic
847C2×C4C2×D4×D6111yescharacteristic
848C2×C4C2×D4×D6111yescharacteristic
849C2×C4C24×D6111yescharacteristic
850C8—24no—
851C8—1224no—
852C22—21no—
853C22—21no—
854C22—21no—
855C22—21no—
856C22—21no—
857C22—21no—
858C22—44no—
859C22—614no—
860C22—1222no—
861C22—1222no—
862C22—2444no—
863C22C2×Q16×D6112yes—
864C22C2×Q16×D6112yes—
865C22C2×Q16×D6112yes—
866C22C22×D4×D6111yescharacteristic
867C4—21no—
868C4—21no—
869C4—21no—
870C4—42no—
871C4—42no—
872C4—42no—
873C4—42no—
874C4—614no—
875C4—1222no—
876C4—1222no—
877C4—1224no—
878C4—2442no—
879C4—2442no—
880C4—2442no—
881C4H(5,𝔽2)×D6112yes—
882C2—22no—
883C2—22no—
884C2—22no—
885C2—1224no—
886C2#2145945111yescharacteristic
887C2C22×Q16×D6111yescharacteristic
888C2#2146060311yescharacteristic
subgroupG/H
centerC22C22×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC61×#3189C2
socleC22×C61C23×D4
prime radicalC22×C22⋊D61D4
hypercenter#3189D61
hypocenterC61#61563
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
3. #21457693C2semidirect
4. #21457690C2semidirect
5. #21457568C2semidirect
6. #21457564C2semidirect
7. #21456765C2semidirect
8. #21456593C2semidirect
9. #21456591C2semidirect
10. #21455855C2semidirect
11. C2×#16839920C2semidirect
12. C2×#16839917C2semidirect
13. #451×D61C2semidirect
15. C61×#3189C2semidirect
18. C22×Dic244C22semidirect
19. C22×#11758202C22semidirect
20. C2×Q16×D61C22semidirect
46. #16840140C22semidirect
47. #16840111C22semidirect
48. #16840099C22semidirect
50. #16840095C22semidirect
51. #16840056C22semidirect
52. #16840004C22semidirect
53. #16840002C22semidirect
54. #16840001C22semidirect
55. #16839971C22semidirect
56. #16839971C22semidirect
57. #16839970C22semidirect
60. #16839920C22semidirect
61. #16839919C22semidirect
62. #16839919C22semidirect
66. #16839917C22semidirect
67. #16839917C22semidirect
68. #16839916C22semidirect
69. #16839856C22semidirect
70. #16839854C22semidirect
74. C2×#14519702C22semidirect
75. C2×#14519700C22semidirect
76. #103×D61C22semidirect
82. C61×#484C22semidirect
83. C61×#467C22semidirect
85. C61×#451C22semidirect
236. C2×C22⋊D61Q16semidirect
339. C23×C61C2×Q16semidirect
345. C22×D61C2×Q16semidirect
369. C22⋊D61C2×Q16semidirect
370. C22⋊D61C2×Q16semidirect
383. C2×Dic61C2×Q16semidirect
447. #3189D61semidirect
498. #484C2×D61semidirect
503. #467C2×D61semidirect
519. #451C2×D61semidirect
531. C61#61563semidirect
788. C23Q16×D61semidirect

Maximal subgroups

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

subgroupindex
#214596152
C2×#168404252
#214576932
#214576902
#214575682
#214575642
#214567652
#214565932
#214565912
#214558552
C2×#168399202
C2×#168399172
#451×D612
#214548412
C61×#31892
#6156361