Finite Group Databasebeta

← #30550808

Subgroups — #30550808

Order 15616.

2130 conjugacy classes of subgroups.

The subgroup lattice has 946 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459148C211yesmaximal, characteristic
2C2×#16840335C211yesmaximal, characteristic, complemented
3#21456712C214yesmaximal, complemented
4#21456700C214yesmaximal, complemented
5#21456698C214yesmaximal, complemented
6#21456688C214yesmaximal, complemented
7#21455768C211yesmaximal, characteristic, complemented
8#21455763C211yesmaximal, characteristic, complemented
9#21455749C212yesmaximal, complemented
10#21455452C212yesmaximal, complemented
11#21455443C212yesmaximal, complemented
12#21455079C211yesmaximal, characteristic, complemented
13#21455051C212yesmaximal, complemented
14#21454262C211yesmaximal, characteristic, complemented
15C61×#3007C211yesmaximal, characteristic, complemented
16C22×#11758222C2211yescharacteristic
17C22×Q8×D61C2211yescharacteristic, complemented
18C2×#14519807C2212yes—
19C2×M16×D61C2212yescomplemented
20#16840340C2212yes—
21#16840340C2212yes—
22#16840336C2212yes—
23#16840335—22no—
24#16840335—22no—
25#16840335C2214yes—
26#16840335C2214yescomplemented
27#16840333—21no—
28#16840329C2212yes—
29#16840326—21no—
30#16840321—21no—
31#16840321—21no—
32#16840308—22no—
33C2×#14519776—21no—
34C2×#14519763—21no—
35#16840273—22no—
36#16840269C2212yes—
37#16840269C2212yes—
38C2×#14519762—21no—
39C2×#14519759—21no—
40C2×#14519757C2211yescharacteristic, complemented
41C2×#14519756C2211yescharacteristic
42C2×#14519753C2211yescharacteristic, complemented
43C2×#14519736C2211yescharacteristic
44C2×#14519735C2211yescharacteristic, complemented
45#16840104C2214yescomplemented
46#16840102C2214yescomplemented
47#16840101C2214yescomplemented
48#16840100C2214yescomplemented
49#16840098C2212yescomplemented
50#16840095C2212yescomplemented
51#16840093C2212yescomplemented
52#16840090C2212yescomplemented
53#16840085C2214yescomplemented
54#16840084C2214yescomplemented
55#16840019C2214yescomplemented
56#16840017C2214yescomplemented
57#16840007C2214yescomplemented
58#16840005C2214yescomplemented
59#16840002C2214yescomplemented
60#16840000C2214yescomplemented
61#16839990C2214yescomplemented
62#16839988C2214yescomplemented
63#16839924C2214yescomplemented
64#16839918C2212yescomplemented
65#16839916C2214yescomplemented
66#16839916C2214yescomplemented
67#16839913C2212yescomplemented
68#16839899C2214yescomplemented
69#16839899C2214yescomplemented
70#16839804C2212yescomplemented
71#16839802C2212yescomplemented
72#16839772C2212yescomplemented
73#16839771C2212yescomplemented
74#16839763C2212yes—
75#16839727C2214yes—
76#16839727C2214yescomplemented
77#16839726C2211yescharacteristic
78#16839725C2212yescomplemented
79C22×#41×C61C2211yescharacteristic
80C2×#137×C61C2212yes—
81C2×C22⋊Q8×C61C2211yescharacteristic
82C61×#452C2214yescomplemented
83C61×#451C2212yescomplemented
84C61×#450C2212yescomplemented
85C61×#417C2212yes—
86C61×#407C2211yescharacteristic
87C2×#11758222—44no—
88C2×#11758222D412yes—
89C2×#11758222D412yes—
90C2×#11758222C2312yes—
91C2×#11758222C2312yes—
92C22×Dic122—21no—
93C22×Dic122D411yescharacteristic
94C22×Dic122C2311yescharacteristic
95C2×Q8×D61—22no—
96C2×Q8×D61—44no—
97C2×Q8×D61C2314yes—
98C22×D244D411yescharacteristic
99C22×C22⋊D61D411yescharacteristic
100C22×C22⋊D61D411yescharacteristic
101C22×C4×D61—21no—
102C22×C4×D61C2311yescharacteristic
103C22×C4×D61C2311yescharacteristic
104#14519807—44no—
105C2×#11758202C2314yes—
106C2×#11758200C2314yes—
107C2×#11758194C2312yes—
108C2×#11758189C2314yes—
109M16×D61—44no—
110C2×C8×D61C2314yes—
111#14519776—24no—
112#14519776—24no—
113#14519775—22no—
114#14519773—22no—
115#14519766—22no—
116#14519764—22no—
117#14519763—24no—
118#14519763—24no—
119#14519762—24no—
120#14519762—24no—
121#14519760—22no—
122#14519760—22no—
123#14519759—24no—
124#14519759—24no—
125#14519758—22no—
126#14519758—22no—
127#14519757—22no—
128#14519757C2314yes—
129#14519756—21no—
130#14519756—21no—
131#14519756—22no—
132#14519756—22no—
133#14519756C2312yes—
134#14519756C2312yes—
135#14519753—22no—
136#14519753C2314yes—
137#14519753C2312yes—
138#14519753C2312yes—
139#14519753C2312yes—
140#14519753C2312yes—
141#14519751—22no—
142#14519751—22no—
143#14519749—22no—
144#14519749—22no—
145#14519749—22no—
146#14519749—22no—
147#14519748C2312yes—
148#14519748C2312yes—
149#14519748C2312yes—
150#14519748C2312yes—
151#14519746—22no—
152#14519746—22no—
153#14519745—22no—
154#14519745—22no—
155C4×C22⋊D61—22no—
156C4×C22⋊D61—22no—
157C4×C22⋊D61—22no—
158C4×C22⋊D61—22no—
159#14519736—21no—
160#14519736—21no—
161#14519736C2312yes—
162#14519736C2312yes—
163#14519735—22no—
164#14519735C2314yes—
165C2×C4⋊Dic61—21no—
166C2×C4⋊Dic61C2311yescharacteristic
167C2×C4⋊Dic61C2311yescharacteristic
168C2×C4⋊Dic61C2311yescharacteristic
169C2×#11758196—21no—
170C2×#11758196—21no—
171C2×C22⋊Dic61—21no—
172C2×C22⋊Dic61—21no—
173C2×#11758198—21no—
174C2×#11758198—21no—
175C2×#11758198—21no—
176C2×C4×Dic61—21no—
177C2×C4×Dic61—21no—
178#14519711C2314yes—
179#14519710C2314yes—
180#14519709C2314yes—
181#14519708C2314yes—
182#14519702C2314yes—
183#14519702C2314yes—
184#14519701C2314yes—
185#14519701C2314yes—
186#14519701C2314yes—
187#14519698C2314yes—
188C22⋊#92418C2312yes—
189C22⋊#92418C2312yes—
190#14519689C2314yes—
191#14519689C2314yes—
192C2×#41×C61—21no—
193C2×#41×C61—21no—
194C2×#41×C61—44no—
195C2×#41×C61C2312yes—
196C2×#41×C61C2312yes—
197C22×Q8×C61C2311yescharacteristic
198C22×Q8×C61C2311yescharacteristic
199C22×D4×C61—21no—
200C22×D4×C61C2311yescharacteristic
201C23×C4×C61—21no—
202C23×C4×C61C2311yescharacteristic
203#137×C61—44no—
204C2×Q16×C61C2314yes—
205C2×SD16×C61C2314yes—
206C2×M16×C61C2312yes—
207C22⋊Q8×C61—21no—
208C22⋊Q8×C61—21no—
209C22⋊Q8×C61C2312yes—
210C22⋊Q8×C61C2312yes—
211C2×C4⋊C4×C61—21no—
212C2×C4⋊C4×C61C2311yescharacteristic
213C2×C22⋊C4×C61—21no—
214#103×C61C2314yes—
215#102×C61C2314yes—
216C22⋊C8×C61C2312yes—
217C22⋊C8×C61C2312yes—
218C24×C61—21no—
219C24×C61C2×D411yescharacteristic
220C23×D61C2×D411yescharacteristic
221C23×D61C2×D411yescharacteristic
222#41×C61—24no—
223#41×C61—24no—
224#41×C61—42no—
225#41×C61—42no—
226#41×C61—44no—
227#41×C61—44no—
228C2×Q8×C61—21no—
229C2×Q8×C61—21no—
230C2×Q8×C61—24no—
231C2×Q8×C61—42no—
232C2×Q8×C61C2412yes—
233C2×Q8×C61C2412yes—
234C2×D4×C61—22no—
235C2×D4×C61—22no—
236C2×D4×C61—21no—
237C2×D4×C61—42no—
238C2×D4×C61—44no—
239C2×D4×C61C2412yes—
240C22×C4×C61—24no—
241C22×C4×C61—21no—
242C22×C4×C61—21no—
243C22×C4×C61—21no—
244C22×C4×C61—22no—
245C22×C4×C61—22no—
246C22×C4×C61—44no—
247C22×C4×C61C2×D411yescharacteristic
248C22×C4×C61C2×D411yescharacteristic
249C22×C4×C61C2×D411yescharacteristic
250C22×C4×C61C2411yescharacteristic
251C22×C4×C61C2411yescharacteristic
252C22×C4×C61C2411yescharacteristic
253C2×C22⋊D61—22no—
254C2×C22⋊D61—22no—
255C2×C22⋊D61—22no—
256C2×C22⋊D61—22no—
257C2×C22⋊D61—42no—
258C2×C22⋊D61—42no—
259C2×C22⋊D61C2×D412yes—
260C2×C22⋊D61C2×D412yes—
261C2×C22⋊D61C2×D412yes—
262C2×C22⋊D61C2×D412yes—
263C22×Dic61—21no—
264C22×Dic61—21no—
265C22×Dic61—21no—
266C22×Dic61—21no—
267C22×Dic61C2×D411yescharacteristic
268C22×Dic61C2×D411yescharacteristic
269Q8×D61—44no—
270Q8×D61—44no—
271Q8×D61—48no—
272#11758222—44no—
273#11758222—44no—
274#11758222—42no—
275#11758222—42no—
276#11758222—42no—
277#11758222—42no—
278C2×D244—42no—
279C2×D244C2×D412yes—
280C2×D244C2×D412yes—
281C2×C4×D61—24no—
282C2×C4×D61—24no—
283C2×C4×D61—24no—
284C2×C4×D61—44no—
285C2×C4×D61C2×D412yes—
286C2×C4×D61C2×D412yes—
287C2×C4×D61C2412yes—
288C2×C4×D61C2412yes—
289C2×Dic122—24no—
290C2×Dic122—21no—
291C2×Dic122—24no—
292C2×Dic122—42no—
293C2×Dic122—44no—
294C2×Dic122C2×D412yes—
295C2×Dic122C2×D412yes—
296C2×Dic122C2412yes—
297Q16×C61—44no—
298SD16×C61—44no—
299M16×C61—24no—
300C2×C8×C61C2414yes—
301C4⋊C4×C61—22no—
302C4⋊C4×C61—22no—
303C4⋊C4×C61—21no—
304C4⋊C4×C61C2412yes—
305C22⋊C4×C61—22no—
306C22⋊C4×C61—22no—
307C22⋊Dic61—22no—
308C22⋊Dic61—22no—
309C22⋊Dic61—22no—
310C22⋊Dic61—22no—
311C22⋊Dic61—22no—
312C22⋊Dic61—22no—
313C22⋊Dic61—22no—
314C22⋊Dic61—22no—
315#11758202—44no—
316#11758200—44no—
317#11758198—24no—
318#11758198—24no—
319#11758198—24no—
320#11758198—22no—
321#11758198—22no—
322#11758198—22no—
323#11758198—22no—
324C4⋊Dic61—21no—
325C4⋊Dic61—21no—
326C4⋊Dic61—21no—
327C4⋊Dic61—24no—
328C4⋊Dic61C2412yes—
329C4⋊Dic61C2412yes—
330C4⋊Dic61C2412yes—
331#11758196—22no—
332#11758196—22no—
333#11758196—24no—
334#11758196—22no—
335#11758196—22no—
336#11758196—22no—
337#11758196—22no—
338C4×Dic61—22no—
339C4×Dic61—22no—
340C4×Dic61—24no—
341#11758194—24no—
342C2×#92418C2414yes—
343#11758189—44no—
344C8×D61—44no—
345C23×C61—22no—
346C23×C61—22no—
347C23×C61—41no—
348C23×C61—41no—
349C23×C61—42no—
350C23×C61—81no—
351C23×C61—81no—
352C23×C61C22×D411yescharacteristic
353C23×C61C22×D411yescharacteristic
354C23×C61C22×D411yescharacteristic
355C22×D61—22no—
356C22×D61—22no—
357C22×D61—41no—
358C22×D61—41no—
359C22×D61—41no—
360C22×D61—41no—
361C22×D61C22×D412yes—
362C22×D61C22×D412yes—
363Q8×C61—22no—
364Q8×C61—24no—
365Q8×C61—22no—
366Q8×C61—42no—
367Q8×C61—42no—
368D4×C61—22no—
369D4×C61—22no—
370D4×C61—42no—
371D4×C61—44no—
372D4×C61—44no—
373C2×C4×C61—22no—
374C2×C4×C61—22no—
375C2×C4×C61—22no—
376C2×C4×C61—22no—
377C2×C4×C61—22no—
378C2×C4×C61—22no—
379C2×C4×C61—22no—
380C2×C4×C61—22no—
381C2×C4×C61—44no—
382C2×C4×C61—42no—
383C2×C4×C61—42no—
384C2×C4×C61—42no—
385C2×C4×C61—44no—
386C2×C4×C61C22×D411yescharacteristic
387C2×C4×C61C22×D411yescharacteristic
388C2×C4×C61C22×D411yescharacteristic
389C2×C4×C61H(5,𝔽2)14yes—
390C2×C4×C61C2511yescharacteristic
391C22⋊D61—42no—
392C22⋊D61—42no—
393C22⋊D61—42no—
394C22⋊D61—42no—
395C22⋊D61—82no—
396C22⋊D61—82no—
397C22⋊D61—82no—
398C22⋊D61—82no—
399C2×Dic61—22no—
400C2×Dic61—22no—
401C2×Dic61—22no—
402C2×Dic61—22no—
403C2×Dic61—22no—
404C2×Dic61—22no—
405C2×Dic61—42no—
406C2×Dic61—42no—
407C2×Dic61—81no—
408C2×Dic61—81no—
409C2×Dic61C22×D412yes—
410C2×Dic61C22×D412yes—
411D244—42no—
412D244—42no—
413C4×D61—24no—
414C4×D61—24no—
415C4×D61—22no—
416C4×D61—22no—
417C4×D61—22no—
418C4×D61—22no—
419C4×D61—48no—
420Dic122—24no—
421Dic122—42no—
422Dic122—42no—
423Dic122—48no—
424Dic122—42no—
425C8×C61—24no—
426#92418—24no—
427#60754—611nomaximal, Sylow
428C22×C61—21no—
429C22×C61—21no—
430C22×C61—21no—
431C22×C61—21no—
432C22×C61—21no—
433C22×C61—21no—
434C22×C61—21no—
435C22×C61—21no—
436C22×C61—42no—
437C22×C61—42no—
438C22×C61—42no—
439C22×C61—82no—
440C22×C61—84no—
441C22×C61#53412yes—
442C22×C61C23×D411yescharacteristic
443C2×D61—22no—
444C2×D61—22no—
445C2×D61—22no—
446C2×D61—22no—
447C2×D61—22no—
448C2×D61—22no—
449C2×D61—44no—
450C2×D61—82no—
451C4×C61—21no—
452C4×C61—21no—
453C4×C61—42no—
454C4×C61—42no—
455C4×C61—42no—
456C4×C61#53412yes—
457C4×C61C2×H(5,𝔽2)12yes—
458Dic61—22no—
459Dic61—22no—
460Dic61—42no—
461Dic61—42no—
462Dic61—42no—
463Dic61—42no—
464#3449—611no—
465C2×#536—611no—
466#3202—614no—
467#3201—614no—
468#3201—614no—
469#3200—614no—
470#3095—611no—
471#3095—611no—
472#3093—612no—
473#3056—612no—
474#3056—612no—
475#3007—611no—
476#3007D6111yescharacteristic, complemented
477#3004—612no—
478#2879—611no—
479C2×C61—22no—
480C2×C61—41no—
481C2×C61—41no—
482C2×C61—82no—
483C2×C61C2×#53411yescharacteristic
484C2×C61#358611yescharacteristic
485C2×C61#358611yescharacteristic
486D61—42no—
487D61—42no—
488C22×#41—611no—
489C22×#41C2×D6111yescharacteristic
490C23×Q8—611no—
491C2×#137—612no—
492C2×#137C2×D6112yes—
493C22×M16—612no—
494#537—612no—
495#537—612no—
496#536—612no—
497#536—614no—
498#536—614no—
499#536—1222no—
500#536—1222no—
501#536—1221no—
502#535—612no—
503#535—1221no—
504#534—1221no—
505#534—1221no—
506#532—1222no—
507C2×C4⋊Q8—1221no—
508C2×#124—1221no—
509#525—612no—
510#525—612no—
511#525—1222no—
512C2×#123—1221no—
513C2×#123—1221no—
514C2×C22⋊Q8—611no—
515C2×C22⋊Q8—611no—
516C2×C22⋊Q8—611no—
517C2×C22⋊Q8C2×D6111yescharacteristic
518C2×#117—611no—
519C2×#117—611no—
520#485—614no—
521#485—614no—
522#485—614no—
523#485—614no—
524#484—612no—
525#484—612no—
526#483—612no—
527#483—612no—
528#482—614no—
529#482—614no—
530#470—614no—
531#470—614no—
532#468—614no—
533#468—614no—
534#467—614no—
535#467—614no—
536#465—614no—
537#465—614no—
538#452—614no—
539#452C2×D6114yescomplemented
540#451—612no—
541#451—614no—
542#451—614no—
543#451C2×D6112yescomplemented
544#450—612no—
545#450C2×D6112yescomplemented
546#448—614no—
547#448—614no—
548#428—612no—
549#428—612no—
550#419—612no—
551#419—612no—
552#417—612no—
553#417C2×D6112yes—
554#408—614no—
555#408—614no—
556#407—611no—
557#407—612no—
558#407C2×D6111yescharacteristic
559C61#6075411yescharacteristic, complemented, Sylow
560C2×#41—21no—
561C2×#41—21no—
562C2×#41—44no—
563C2×#41—612no—
564C2×#41—612no—
565C2×#41—612no—
566C2×#41—612no—
567C2×#41—2444no—
568C2×#41C22×D6112yes—
569C2×#41C22×D6112yes—
570C22×Q8—611no—
571C22×Q8—614no—
572C22×Q8—611no—
573C22×Q8—1221no—
574C22×Q8—1222no—
575C22×Q8—2444no—
576C22×Q8C22×D6111yescharacteristic
577C22×Q8C22×D6111yescharacteristic
578C22×D4—21no—
579C22×D4—611no—
580C22×D4—611no—
581C22×D4—611no—
582C22×D4C22×D6111yescharacteristic
583C23×C4—21no—
584C23×C4—611no—
585C23×C4—611no—
586C23×C4—1221no—
587C23×C4C22×D6111yescharacteristic
588#137—44no—
589#137—2444no—
590C2×Q16—614no—
591C2×Q16C22×D6114yes—
592C2×SD16—614no—
593C2×SD16C22×D6114yes—
594C2×M16—612no—
595C2×M16—614no—
596C2×M16—2444no—
597C2×M16C22×D6112yes—
598C22×C8—614no—
599C4⋊Q8—1224no—
600C4⋊Q8—1224no—
601C4⋊Q8—1222no—
602#127—1222no—
603#124—1224no—
604#124—1224no—
605#124—1222no—
606#124—1222no—
607#123—1224no—
608#123—1224no—
609#123—1224no—
610#123—1224no—
611#123—1222no—
612#123—1222no—
613#123—1222no—
614#123—1222no—
615C22⋊Q8—21no—
616C22⋊Q8—21no—
617C22⋊Q8—614no—
618C22⋊Q8—612no—
619C22⋊Q8—612no—
620C22⋊Q8—612no—
621C22⋊Q8—612no—
622C22⋊Q8—612no—
623C22⋊Q8—612no—
624C22⋊Q8—614no—
625C22⋊Q8—1222no—
626C22⋊Q8—1222no—
627C22⋊Q8—1222no—
628C22⋊Q8—1222no—
629C22⋊Q8—1221no—
630C22⋊Q8—1221no—
631C22⋊Q8C22×D6112yes—
632C22⋊Q8C22×D6112yes—
633#121—612no—
634#121—612no—
635#121—612no—
636#121—612no—
637#121—1222no—
638#121—1222no—
639#121—1222no—
640#121—1222no—
641#121—1222no—
642#121—1222no—
643#120—1222no—
644#120—1222no—
645#120—1222no—
646#120—1222no—
647C4×D4—1222no—
648C4×D4—1222no—
649C4×D4—1222no—
650C4×D4—1222no—
651#117—612no—
652#117—612no—
653#117—614no—
654#117—1222no—
655#117—1221no—
656#117—1221no—
657C2×C4⋊C4—21no—
658C2×C4⋊C4—611no—
659C2×C4⋊C4—611no—
660C2×C4⋊C4—611no—
661C2×C4⋊C4—1221no—
662C2×C4⋊C4—1221no—
663C2×C4⋊C4—1221no—
664C2×C4⋊C4C22×D6111yescharacteristic
665C2×C22⋊C4—21no—
666C2×C22⋊C4—1221no—
667C2×C22⋊C4—1221no—
668C2×C22⋊C4—1221no—
669C2×C22⋊C4—1221no—
670C2×C22⋊C4—1221no—
671C2×C42—1221no—
672C2×C42—1221no—
673#107—614no—
674#107—614no—
675#106—614no—
676#106—614no—
677#103—614no—
678#103—614no—
679#103—614no—
680#103—614no—
681#103—614no—
682#103C22×D6114yes—
683#102—614no—
684#102C22×D6114yes—
685C22⋊C8—612no—
686C22⋊C8—612no—
687C22⋊C8—614no—
688C22⋊C8—614no—
689C22⋊C8C22×D6112yes—
690C22⋊C8C22×D6112yes—
691C24—21no—
692C24—611no—
693C24—611no—
694C24D4×D6111yescharacteristic
695#41—24no—
696#41—24no—
697#41—42no—
698#41—42no—
699#41—44no—
700#41—44no—
701#41—2444no—
702#41—2444no—
703#41—2442no—
704#41—2442no—
705#41—2442no—
706#41—2442no—
707C2×Q8—21no—
708C2×Q8—21no—
709C2×Q8—24no—
710C2×Q8—42no—
711C2×Q8—612no—
712C2×Q8—612no—
713C2×Q8—612no—
714C2×Q8—1224no—
715C2×Q8—1221no—
716C2×Q8—1224no—
717C2×Q8—2442no—
718C2×Q8—2444no—
719C2×Q8—2444no—
720C2×Q8—2444no—
721C2×Q8—2448no—
722C2×Q8C23×D6112yes—
723C2×Q8C23×D6112yes—
724C2×D4—22no—
725C2×D4—22no—
726C2×D4—21no—
727C2×D4—42no—
728C2×D4—44no—
729C2×D4—612no—
730C2×D4—612no—
731C2×D4—612no—
732C2×D4—612no—
733C2×D4—612no—
734C2×D4—612no—
735C2×D4—1222no—
736C2×D4—1222no—
737C2×D4—1222no—
738C2×D4—1222no—
739C2×D4—2442no—
740C2×D4—2442no—
741C2×D4—2442no—
742C2×D4C23×D6112yes—
743C22×C4—24no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—22no—
748C22×C4—22no—
749C22×C4—44no—
750C22×C4—611no—
751C22×C4—611no—
752C22×C4—612no—
753C22×C4—612no—
754C22×C4—612no—
755C22×C4—612no—
756C22×C4—1224no—
757C22×C4—1224no—
758C22×C4—1224no—
759C22×C4—1221no—
760C22×C4—1221no—
761C22×C4—1221no—
762C22×C4—1221no—
763C22×C4—2444no—
764C22×C4D4×D6111yescharacteristic
765C22×C4D4×D6111yescharacteristic
766C22×C4D4×D6111yescharacteristic
767C22×C4C23×D6111yescharacteristic
768C22×C4C23×D6111yescharacteristic
769C22×C4C23×D6111yescharacteristic
770Q16—44no—
771Q16—2444no—
772SD16—44no—
773SD16—2444no—
774M16—24no—
775M16—1224no—
776M16—2444no—
777C2×C8—614no—
778C2×C8—2444no—
779C2×C8C23×D6114yes—
780C4⋊C4—22no—
781C4⋊C4—22no—
782C4⋊C4—21no—
783C4⋊C4—612no—
784C4⋊C4—612no—
785C4⋊C4—612no—
786C4⋊C4—1224no—
787C4⋊C4—1224no—
788C4⋊C4—1222no—
789C4⋊C4—1222no—
790C4⋊C4—1222no—
791C4⋊C4—1222no—
792C4⋊C4—1221no—
793C4⋊C4—1221no—
794C4⋊C4—1221no—
795C4⋊C4—1222no—
796C4⋊C4—1222no—
797C4⋊C4C23×D6112yes—
798C22⋊C4—22no—
799C22⋊C4—22no—
800C22⋊C4—1224no—
801C22⋊C4—1224no—
802C22⋊C4—1224no—
803C22⋊C4—1222no—
804C22⋊C4—1222no—
805C22⋊C4—1222no—
806C22⋊C4—1222no—
807C22⋊C4—1222no—
808C22⋊C4—1222no—
809C22⋊C4—1222no—
810C22⋊C4—1222no—
811C22⋊C4—1222no—
812C22⋊C4—1222no—
813C22⋊C4—1222no—
814C22⋊C4—1222no—
815C42—1224no—
816C42—1222no—
817C42—1222no—
818C23—22no—
819C23—22no—
820C23—41no—
821C23—41no—
822C23—42no—
823C23—81no—
824C23—81no—
825C23—612no—
826C23—612no—
827C23—1222no—
828C23—1222no—
829C23—2441no—
830C23—2441no—
831C23—2441no—
832C23—2441no—
833C23C2×D4×D6111yescharacteristic
834C23C2×D4×D6111yescharacteristic
835C23C2×D4×D6111yescharacteristic
836Q8—24no—
837Q8—22no—
838Q8—22no—
839Q8—42no—
840Q8—42no—
841Q8—1224no—
842Q8—2442no—
843Q8—2442no—
844Q8—2448no—
845Q8—2442no—
846D4—22no—
847D4—22no—
848D4—42no—
849D4—44no—
850D4—44no—
851D4—4882no—
852D4—4882no—
853D4—4882no—
854D4—4882no—
855D4—2442no—
856D4—2442no—
857D4—2442no—
858D4—2442no—
859D4—2442no—
860D4—2442no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—44no—
870C2×C4—42no—
871C2×C4—42no—
872C2×C4—42no—
873C2×C4—44no—
874C2×C4—612no—
875C2×C4—612no—
876C2×C4—1222no—
877C2×C4—1222no—
878C2×C4—1224no—
879C2×C4—1224no—
880C2×C4—1222no—
881C2×C4—1222no—
882C2×C4—1222no—
883C2×C4—1222no—
884C2×C4—1222no—
885C2×C4—1222no—
886C2×C4—1222no—
887C2×C4—1222no—
888C2×C4—4881no—
889C2×C4—4881no—
890C2×C4—2448no—
891C2×C4—2442no—
892C2×C4—2442no—
893C2×C4C2×D4×D6111yescharacteristic
894C2×C4C2×D4×D6111yescharacteristic
895C2×C4C2×D4×D6111yescharacteristic
896C2×C4#1451982214yes—
897C2×C4C24×D6111yescharacteristic
898C8—24no—
899C8—1224no—
900C22—21no—
901C22—21no—
902C22—21no—
903C22—21no—
904C22—21no—
905C22—21no—
906C22—21no—
907C22—21no—
908C22—42no—
909C22—42no—
910C22—42no—
911C22—82no—
912C22—84no—
913C22—1222no—
914C22—1222no—
915C22—1222no—
916C22—1222no—
917C22—1222no—
918C22—1222no—
919C22—4882no—
920C22—2444no—
921C22#1684032212yes—
922C22C22×D4×D6111yescharacteristic
923C4—21no—
924C4—21no—
925C4—42no—
926C4—42no—
927C4—42no—
928C4—1222no—
929C4—1222no—
930C4—2442no—
931C4—2442no—
932C4—2442no—
933C4—2442no—
934C4#1684032212yes—
935C4C2×#1451982212yes—
936C2—22no—
937C2—41no—
938C2—41no—
939C2—82no—
940C2—2442no—
941C2—2442no—
942C2C2×#1684032211yescharacteristic
943C2#2146060211yescharacteristic
944C2#2146060311yescharacteristic
subgroupG/H
centerC22C22×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC61×#3007C2
socleC22×C61C23×D4
prime radical#21459148C2
hypercenter#3007D61
hypocenterC61#60754
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3007

Complements

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

NH ≅ G/Ntype
2. C2×#16840335C2semidirect
3. #21456712C2semidirect
4. #21456700C2semidirect
5. #21456698C2semidirect
6. #21456688C2semidirect
7. #21455768C2semidirect
8. #21455763C2semidirect
9. #21455749C2semidirect
10. #21455452C2semidirect
11. #21455443C2semidirect
12. #21455079C2semidirect
13. #21455051C2semidirect
14. #21454262C2semidirect
15. C61×#3007C2semidirect
17. C22×Q8×D61C22semidirect
19. C2×M16×D61C22semidirect
26. #16840335C22semidirect
40. C2×#14519757C22semidirect
42. C2×#14519753C22semidirect
44. C2×#14519735C22semidirect
45. #16840104C22semidirect
46. #16840102C22semidirect
47. #16840101C22semidirect
48. #16840100C22semidirect
49. #16840098C22semidirect
50. #16840095C22semidirect
51. #16840093C22semidirect
52. #16840090C22semidirect
53. #16840085C22semidirect
54. #16840084C22semidirect
55. #16840019C22semidirect
56. #16840017C22semidirect
57. #16840007C22semidirect
58. #16840005C22semidirect
59. #16840002C22semidirect
60. #16840000C22semidirect
61. #16839990C22semidirect
62. #16839988C22semidirect
63. #16839924C22semidirect
64. #16839918C22semidirect
65. #16839916C22semidirect
66. #16839916C22semidirect
67. #16839913C22semidirect
68. #16839899C22semidirect
69. #16839899C22semidirect
70. #16839804C22semidirect
71. #16839802C22semidirect
72. #16839772C22semidirect
73. #16839771C22semidirect
76. #16839727C22semidirect
78. #16839725C22semidirect
82. C61×#452C22semidirect
83. C61×#451C22semidirect
84. C61×#450C22semidirect
476. #3007D61semidirect
539. #452C2×D61semidirect
543. #451C2×D61semidirect
545. #450C2×D61semidirect
559. C61#60754semidirect

Maximal subgroups

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

subgroupindex
#214591482
C2×#168403352
#214567122
#214567002
#214566982
#214566882
#214557682
#214557632
#214557492
#214554522
#214554432
#214550792
#214550512
#214542622
C61×#30072
#6075461