Finite Group Databasebeta

← #29850879

Subgroups — #29850879

Order 15616.

2040 conjugacy classes of subgroups.

The subgroup lattice has 856 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21451528C211yesmaximal, characteristic, complemented
2#21451507C212yesmaximal, complemented
3#21451490C211yesmaximal, characteristic, complemented
4#21451230C211yesmaximal, characteristic, complemented
5#21450879C212yesmaximal, complemented
6#21450677C212yesmaximal, complemented
7#21450587C212yesmaximal, complemented
8#21450054C212yesmaximal, complemented
9#21449934C212yesmaximal, complemented
10#21449086C212yesmaximal, complemented
11#21449085C211yesmaximal, characteristic, complemented
12#21449033C211yesmaximal, characteristic
13#21448367C212yesmaximal, complemented
14#21448362C211yesmaximal, characteristic, complemented
15#21448336C212yesmaximal, complemented
16#21448304C212yesmaximal, complemented
17#21448279C212yesmaximal, complemented
18C4×#14519733C212yesmaximal, complemented
19C61×#2572C211yesmaximal, characteristic, complemented
20C22×#11758224C2211yescharacteristic
21C2×#14519771C2212yes—
22C2×#14519766C2211yescharacteristic
23C2×#14519760C2212yes—
24C2×Q8×Dic61C2211yescharacteristic
25C2×#14519739C2211yescharacteristic
26C2×#14519737C2212yes—
27C2×#14519735C2211yescharacteristic
28C2×#14519733C2212yes—
29C2×#14519733C2212yes—
30C2×#14519733C2212yes—
31C22×C4×Dic61C2212yes—
32#16839702C2212yes—
33#16839698C2212yes—
34#16839697C2211yescharacteristic
35#16839696C2212yes—
36#16839696C2212yes—
37#16839692C2211yescharacteristic
38#16839691C2212yes—
39#16839689C2211yescharacteristic
40#16839685C2212yes—
41#16839685C2212yes—
42#16839682C2211yescharacteristic
43#16839681C2212yes—
44#16839680C2212yes—
45#16839677C2212yes—
46#16839675C2211yescharacteristic
47#16839671C2212yes—
48#16839670C2211yescharacteristic
49#16839666C2212yes—
50#16839666C2212yes—
51#16839664C2211yescharacteristic
52#16839662C2212yes—
53#16839662C2212yes—
54#16839662C2212yes—
55#16839662C2212yes—
56#16839659C2212yes—
57#16839657C2212yes—
58#16839655C2212yes—
59#16839654C2212yes—
60#16839654C2212yes—
61#16839653C2212yes—
62#16839651C2212yes—
63#16839651C2212yes—
64#16839651C2212yes—
65#16839651C2212yes—
66#16839651C2212yes—
67#16839651C2212yes—
68#16839644C2212yes—
69#16839644C2212yes—
70#16839644C2212yes—
71#16839644C2212yes—
72#16839644C2212yes—
73#16839642C2212yes—
74#16839641C2212yes—
75#16839639C2212yes—
76#16839639C2212yes—
77#16839634C2212yes—
78#16839627C2211yescharacteristic
79C4×#11758196C2212yes—
80C4×#11758196C2212yes—
81#16839613C2212yes—
82#16839613C2212yes—
83#16839613C2212yes—
84#16839613C2212yes—
85C22⋊C4×Dic61C2212yes—
86C22⋊C4×Dic61C2212yes—
87C22⋊C4×Dic61C2212yes—
88C4×C22⋊Dic61C2212yes—
89#16839609C2211yescharacteristic
90#16839609C2212yes—
91#16839609C2212yes—
92#16839609C2212yes—
93#16839609C2211yescharacteristic
94#16839607C2212yes—
95#16839607C2212yes—
96C42×Dic61C2212yes—
97C42×Dic61C2211yescharacteristic
98C61×#400C2211yescharacteristic
99C61×#394C2211yescharacteristic
100C61×#393C2212yes—
101C61×#391C2211yescharacteristic
102C61×#388C2212yes—
103C61×#386C2212yes—
104C61×#383C2212yes—
105C61×#381C2212yes—
106C4×C22⋊C4×C61C2212yes—
107C2×#11758224—28no—
108C2×#11758224—42no—
109C22×Dic122C2311yescharacteristic
110C22×D244C2311yescharacteristic
111C22×C22⋊D61C2312yes—
112C22×C22⋊D61C2312yes—
113C23×Dic61C2312yes—
114C23×Dic61C2312yes—
115C22×C4×D61C2311yescharacteristic
116C22×C4×D61C2311yescharacteristic
117#14519771—28no—
118#14519766—24no—
119#14519760—28no—
120Q8×Dic61—42no—
121#14519739—42no—
122#14519737—28no—
123#14519735—42no—
124#14519733—28no—
125#14519733—28no—
126#14519733—44no—
127C2×C4⋊Dic61C2311yescharacteristic
128C2×C4⋊Dic61C2312yes—
129C2×C4⋊Dic61C2311yescharacteristic
130C2×#11758196C2312yes—
131C2×#11758196C2312yes—
132C2×#11758196C2312yes—
133C2×#11758196C2312yes—
134C2×#11758196C2312yes—
135C2×#11758196C2312yes—
136C2×#11758196C2312yes—
137C2×#11758196C2312yes—
138C2×#11758196C2312yes—
139C2×#11758196C2312yes—
140C2×#11758196C2312yes—
141C2×C22⋊Dic61C2312yes—
142C2×C22⋊Dic61C2312yes—
143C2×C22⋊Dic61C2312yes—
144C2×C22⋊Dic61C2312yes—
145C2×#11758198C2312yes—
146C2×#11758198C2312yes—
147C2×#11758198C2312yes—
148C2×#11758198C2312yes—
149C2×#11758198C2312yes—
150C2×#11758198C2312yes—
151C2×#11758198C2312yes—
152C2×#11758198C2312yes—
153C2×#11758198C2312yes—
154C2×#11758198C2312yes—
155C2×#11758198C2311yescharacteristic
156C2×#11758198C2311yescharacteristic
157C2×C4×Dic61—28no—
158C2×C4×Dic61C2312yes—
159C2×C4×Dic61C2312yes—
160C2×C4×Dic61C2312yes—
161C2×C4×Dic61C2312yes—
162C2×C4×Dic61C2312yes—
163C2×C4×Dic61C2312yes—
164C2×C4×Dic61C2312yes—
165C2×C4×Dic61C2312yes—
166C2×C4×Dic61C2312yes—
167C2×C4×Dic61C2312yes—
168C2×C4×Dic61C2311yescharacteristic
169C2×C4×Dic61C2312yes—
170C2×C4×Dic61C2311yescharacteristic
171#14519684C2312yes—
172#14519684C2312yes—
173#14519684C2312yes—
174#14519684C2311yescharacteristic
175#14519684C2312yes—
176#14519684C2312yes—
177#14519684C2312yes—
178#14519684C2311yescharacteristic
179#14519684C2312yes—
180#14519684C2312yes—
181#14519684C2312yes—
182#14519684C2312yes—
183#14519684C2312yes—
184#14519684C2312yes—
185#14519684C2312yes—
186C22×Q8×C61C2311yescharacteristic
187C22×D4×C61C2311yescharacteristic
188C23×C4×C61C2312yes—
189C2×C4⋊C4×C61C2311yescharacteristic
190C2×C4⋊C4×C61C2311yescharacteristic
191C2×C22⋊C4×C61C2312yes—
192C2×C22⋊C4×C61C2312yes—
193C2×C22⋊C4×C61C2312yes—
194C2×C22⋊C4×C61C2312yes—
195C2×C22⋊C4×C61C2312yes—
196C2×C42×C61C2312yes—
197C2×C42×C61C2311yescharacteristic
198#95×C61C2312yes—
199#95×C61C2311yescharacteristic
200#95×C61C2312yes—
201#95×C61C2312yes—
202#95×C61C2312yes—
203#95×C61C2312yes—
204#95×C61C2312yes—
205#95×C61C2311yescharacteristic
206#95×C61C2312yes—
207C24×C61C2412yes—
208C23×D61C2411yescharacteristic
209C23×D61C2411yescharacteristic
210C2×Q8×C61—22no—
211C2×Q8×C61—41no—
212C2×Q8×C61—41no—
213C2×D4×C61—24no—
214C2×D4×C61—41no—
215C22×C4×C61—24no—
216C22×C4×C61—24no—
217C22×C4×C61—42no—
218C22×C4×C61C2411yescharacteristic
219C22×C4×C61C2411yescharacteristic
220C22×C4×C61C2412yes—
221C22×C4×C61C2412yes—
222C22×C4×C61C2412yes—
223C22×C4×C61C2412yes—
224C22×C4×C61C2411yescharacteristic
225C22×C4×C61C2412yes—
226C2×C22⋊D61—24no—
227C2×C22⋊D61—24no—
228C2×C22⋊D61—24no—
229C2×C22⋊D61—24no—
230C2×C22⋊D61—42no—
231C2×C22⋊D61—42no—
232C22×Dic61—24no—
233C22×Dic61—24no—
234C22×Dic61—24no—
235C22×Dic61—24no—
236C22×Dic61—24no—
237C22×Dic61#4118yes—
238C22×Dic61C2412yes—
239C22×Dic61C2411yescharacteristic
240C22×Dic61C2412yes—
241C22×Dic61C2412yes—
242C22×Dic61C2412yes—
243C22×Dic61C2412yes—
244C22×Dic61C2412yes—
245C22×Dic61C2411yescharacteristic
246#11758224—416no—
247C2×D244—22no—
248C2×D244—41no—
249C2×D244—41no—
250C2×C4×D61—24no—
251C2×C4×D61—24no—
252C2×C4×D61—22no—
253C2×C4×D61—22no—
254C2×Dic122—24no—
255C2×Dic122—41no—
256C4⋊C4×C61—41no—
257C4⋊C4×C61—41no—
258C22⋊C4×C61—24no—
259C22⋊C4×C61—24no—
260C22⋊C4×C61—24no—
261C22⋊C4×C61—42no—
262C22⋊C4×C61—42no—
263C42×C61—24no—
264C42×C61—41no—
265C22⋊Dic61—24no—
266C22⋊Dic61—24no—
267C22⋊Dic61—24no—
268C22⋊Dic61—42no—
269#11758198—24no—
270#11758198—24no—
271#11758198—24no—
272#11758198—24no—
273#11758198—24no—
274#11758198—24no—
275#11758198—24no—
276#11758198—24no—
277#11758198—42no—
278#11758198—42no—
279#11758198—41no—
280#11758198—41no—
281C4⋊Dic61—41no—
282C4⋊Dic61—41no—
283C4⋊Dic61—42no—
284#11758196—24no—
285#11758196—24no—
286#11758196—24no—
287#11758196—24no—
288#11758196—24no—
289#11758196—24no—
290#11758196—24no—
291#11758196—42no—
292#11758196—42no—
293#11758196—42no—
294#11758196#4118yescomplemented
295C4×Dic61—24no—
296C4×Dic61—24no—
297C4×Dic61—24no—
298C4×Dic61—24no—
299C4×Dic61—24no—
300C4×Dic61—24no—
301C4×Dic61—24no—
302C4×Dic61—24no—
303C4×Dic61—24no—
304C4×Dic61—24no—
305C4×Dic61—22no—
306C4×Dic61—42no—
307C4×Dic61#4114yescomplemented
308C23×C61—22no—
309C23×C61—22no—
310C23×C61—22no—
311C23×C61—22no—
312C23×C61—22no—
313C23×C61—22no—
314C23×C61C2×#4114yes—
315C23×C61C2511yescharacteristic
316C22×D61—22no—
317C22×D61—21no—
318C22×D61—21no—
319C22×D61—22no—
320C22×D61—22no—
321C22×D61—22no—
322C22×D61—21no—
323C22×D61—21no—
324C22×D61—21no—
325C22×D61—21no—
326Q8×C61—44no—
327D4×C61—44no—
328C2×C4×C61—22no—
329C2×C4×C61—21no—
330C2×C4×C61—22no—
331C2×C4×C61—21no—
332C2×C4×C61—22no—
333C2×C4×C61—22no—
334C2×C4×C61—22no—
335C2×C4×C61—22no—
336C2×C4×C61—22no—
337C2×C4×C61—22no—
338C2×C4×C61—22no—
339C2×C4×C61—22no—
340C2×C4×C61—22no—
341C2×C4×C61—22no—
342C2×C4×C61—22no—
343C2×C4×C61—22no—
344C2×C4×C61—21no—
345C2×C4×C61—21no—
346C2×C4×C61—22no—
347C2×C4×C61—22no—
348C2×C4×C61—48no—
349C2×C4×C61C2×#4114yes—
350C2×C4×C61C2×#4112yes—
351C22⋊D61—48no—
352C22⋊D61—48no—
353C2×Dic61—216no—
354C2×Dic61—22no—
355C2×Dic61—22no—
356C2×Dic61—22no—
357C2×Dic61—22no—
358C2×Dic61—22no—
359C2×Dic61—22no—
360C2×Dic61—22no—
361C2×Dic61—22no—
362C2×Dic61—216no—
363C2×Dic61—22no—
364C2×Dic61—22no—
365C2×Dic61—22no—
366C2×Dic61—22no—
367C2×Dic61—22no—
368C2×Dic61—22no—
369C2×Dic61—21no—
370C2×Dic61—22no—
371C2×Dic61C2×#4114yes—
372C2×Dic61C2×#4114yes—
373C2×Dic61C2×#4114yes—
374C2×Dic61C2×#4114yes—
375C2×Dic61C2×#4114yes—
376C2×Dic61H(5,𝔽2)12yes—
377D244—44no—
378C4×D61—44no—
379C4×D61—44no—
380Dic122—44no—
381#34871—611nomaximal, Sylow
382C22×C61—24no—
383C22×C61—24no—
384C22×C61—24no—
385C22×C61—42no—
386C22×C61—42no—
387C22×C61—42no—
388C22×C61—42no—
389C22×C61C22×#4111yescharacteristic
390C22×C61C22×#4112yes—
391C22×C61C22×#4112yes—
392C22×C61C2×H(5,𝔽2)11yescharacteristic
393C22×C61#58511yescharacteristic
394C2×D61—42no—
395C2×D61—42no—
396C2×D61—41no—
397C2×D61—41no—
398C2×D61—41no—
399C2×D61—41no—
400C2×D61—42no—
401C2×D61—42no—
402C2×D61—41no—
403C2×D61—41no—
404C4×C61—22no—
405C4×C61—24no—
406C4×C61—42no—
407C4×C61—42no—
408C4×C61—41no—
409C4×C61—41no—
410C4×C61—42no—
411C4×C61—42no—
412Dic61—24no—
413Dic61—24no—
414Dic61—24no—
415Dic61—24no—
416Dic61—42no—
417Dic61—41no—
418Dic61—42no—
419Dic61#55114yes—
420#2612—611no—
421#2610—612no—
422#2609—611no—
423#2586—611no—
424#2572D6111yescharacteristic, complemented
425#2554—612no—
426#2532—612no—
427#2526—612no—
428#2479—612no—
429#2471—612no—
430#2396—612no—
431#2395—611no—
432#2388—611no—
433C4×#126—612no—
434C4×#124—611no—
435C4×#123—612no—
436#2297—612no—
437#2293—612no—
438C4×#117—612no—
439C2×C61—44no—
440C2×C61#344412yes—
441C2×C61#346011yescharacteristic
442C2×C61C2×#55111yescharacteristic
443C2×C61#347512yes—
444C2×C61#348311yescharacteristic
445D61—81no—
446D61—81no—
447C22×#41—611no—
448C2×#126—612no—
449C2×#124—611no—
450C2×#123—612no—
451C2×C4×Q8—611no—
452C2×C4×D4—611no—
453C2×C4×D4—612no—
454C2×#117—611no—
455C2×#117—612no—
456C2×#117—612no—
457C2×#117—612no—
458C22×C42—612no—
459#400—612no—
460#400C2×D6111yescharacteristic
461#399—611no—
462#399—612no—
463#398—611no—
464#398—612no—
465#398—612no—
466#397—611no—
467#397—612no—
468#396—612no—
469#396—612no—
470#395—612no—
471#395—611no—
472#394—612no—
473#394—612no—
474#394C2×D6111yescharacteristic
475#393—611no—
476#393C2×D6112yes—
477#392—611no—
478#392—612no—
479#391—612no—
480#391—612no—
481#391C2×D6111yescharacteristic
482#390—612no—
483#390—612no—
484#390—612no—
485#390—612no—
486#390—611no—
487#389—612no—
488#389—612no—
489#388—612no—
490#388—612no—
491#388—612no—
492#388—612no—
493#388—612no—
494#388—612no—
495#388—612no—
496#388—612no—
497#388—612no—
498#388—612no—
499#388C2×D6112yes—
500#387—612no—
501#387—612no—
502#387—612no—
503#387—612no—
504#387—612no—
505#386—612no—
506#386—612no—
507#386—612no—
508#386—612no—
509#386C2×D6112yes—
510#385—612no—
511#383C2×D6112yes—
512#382—611no—
513#381C2×D6112yes—
514C4×C4⋊C4—612no—
515C4×C4⋊C4—612no—
516C4×C4⋊C4—612no—
517C4×C4⋊C4—612no—
518C4×C4⋊C4—612no—
519C4×C4⋊C4—612no—
520C4×C22⋊C4—612no—
521C4×C22⋊C4—612no—
522C4×C22⋊C4—612no—
523C4×C22⋊C4—612no—
524C4×C22⋊C4—611no—
525C4×C22⋊C4—612no—
526C4×C22⋊C4—612no—
527C4×C22⋊C4—611no—
528C4×C22⋊C4—612no—
529C4×C22⋊C4C2×D6112yes—
530#376—612no—
531#376—612no—
532C43—612no—
533C43—611no—
534C61#3487111yescharacteristic, complemented, Sylow
535C2×#41—1228no—
536C2×#41—2442no—
537C22×Q8—611no—
538C22×Q8C22×D6111yescharacteristic
539C22×D4—612no—
540C22×D4—612no—
541C22×D4—611no—
542C22×D4C22×D6111yescharacteristic
543C23×C4—612no—
544C23×C4—612no—
545C23×C4—611no—
546C23×C4—611no—
547C23×C4C22×D6112yes—
548#126—1228no—
549#124—1224no—
550#123—1228no—
551C4×Q8—2442no—
552C4×D4—1228no—
553C4×D4—2442no—
554#117—1228no—
555#117—1228no—
556#117—2444no—
557#117—2442no—
558C2×C4⋊C4—612no—
559C2×C4⋊C4—612no—
560C2×C4⋊C4—612no—
561C2×C4⋊C4—612no—
562C2×C4⋊C4—612no—
563C2×C4⋊C4—612no—
564C2×C4⋊C4—612no—
565C2×C4⋊C4—612no—
566C2×C4⋊C4—611no—
567C2×C4⋊C4—612no—
568C2×C4⋊C4—612no—
569C2×C4⋊C4—611no—
570C2×C4⋊C4—612no—
571C2×C4⋊C4—612no—
572C2×C4⋊C4C22×D6111yescharacteristic
573C2×C4⋊C4C22×D6111yescharacteristic
574C2×C22⋊C4—612no—
575C2×C22⋊C4—612no—
576C2×C22⋊C4—612no—
577C2×C22⋊C4—612no—
578C2×C22⋊C4—612no—
579C2×C22⋊C4—612no—
580C2×C22⋊C4—612no—
581C2×C22⋊C4—612no—
582C2×C22⋊C4—612no—
583C2×C22⋊C4—612no—
584C2×C22⋊C4—612no—
585C2×C22⋊C4—612no—
586C2×C22⋊C4—612no—
587C2×C22⋊C4—611no—
588C2×C22⋊C4—611no—
589C2×C22⋊C4—612no—
590C2×C22⋊C4C22×D6112yes—
591C2×C22⋊C4C22×D6112yes—
592C2×C22⋊C4C22×D6112yes—
593C2×C22⋊C4C22×D6112yes—
594C2×C22⋊C4C22×D6112yes—
595C2×C42—611no—
596C2×C42—612no—
597C2×C42—612no—
598C2×C42—612no—
599C2×C42—612no—
600C2×C42—612no—
601C2×C42—611no—
602C2×C42—612no—
603C2×C42—612no—
604C2×C42—612no—
605C2×C42—612no—
606C2×C42—612no—
607C2×C42—612no—
608C2×C42—1228no—
609C2×C42C22×D6112yes—
610C2×C42C22×D6111yescharacteristic
611#95—612no—
612#95—612no—
613#95—612no—
614#95—612no—
615#95—612no—
616#95—612no—
617#95—612no—
618#95—612no—
619#95—611no—
620#95—612no—
621#95—612no—
622#95—612no—
623#95—611no—
624#95—612no—
625#95—612no—
626#95C22×D6112yes—
627#95C22×D6112yes—
628#95C22×D6111yescharacteristic
629#95C22×D6112yes—
630#95C22×D6111yescharacteristic
631#95C22×D6112yes—
632#95C22×D6112yes—
633#95C22×D6112yes—
634#95C22×D6112yes—
635C24—611no—
636C24—611no—
637C24C23×D6112yes—
638#41—24416no—
639C2×Q8—22no—
640C2×Q8—41no—
641C2×Q8—41no—
642C2×Q8—1224no—
643C2×Q8—2441no—
644C2×D4—24no—
645C2×D4—41no—
646C2×D4—1224no—
647C2×D4—1224no—
648C2×D4—1224no—
649C2×D4—1224no—
650C2×D4—1222no—
651C2×D4—2441no—
652C2×D4—2441no—
653C2×D4—2442no—
654C2×D4—2442no—
655C22×C4—24no—
656C22×C4—24no—
657C22×C4—42no—
658C22×C4—611no—
659C22×C4—618no—
660C22×C4—612no—
661C22×C4—612no—
662C22×C4—612no—
663C22×C4—612no—
664C22×C4—611no—
665C22×C4—612no—
666C22×C4—612no—
667C22×C4—1222no—
668C22×C4—1224no—
669C22×C4—1222no—
670C22×C4—1224no—
671C22×C4—1224no—
672C22×C4—1224no—
673C22×C4—1224no—
674C22×C4—1224no—
675C22×C4—1224no—
676C22×C4C23×D6111yescharacteristic
677C22×C4C23×D6112yes—
678C22×C4C23×D6111yescharacteristic
679C22×C4C23×D6112yes—
680C22×C4C23×D6112yes—
681C22×C4C23×D6112yes—
682C22×C4C23×D6111yescharacteristic
683C22×C4C23×D6112yes—
684C4⋊C4—41no—
685C4⋊C4—41no—
686C4⋊C4—618no—
687C4⋊C4—1224no—
688C4⋊C4—1224no—
689C4⋊C4—1224no—
690C4⋊C4—1224no—
691C4⋊C4—1224no—
692C4⋊C4—1224no—
693C4⋊C4—1224no—
694C4⋊C4—2442no—
695C4⋊C4—2442no—
696C4⋊C4—2442no—
697C4⋊C4—2441no—
698C4⋊C4—2441no—
699C4⋊C4—2442no—
700C22⋊C4—24no—
701C22⋊C4—24no—
702C22⋊C4—24no—
703C22⋊C4—42no—
704C22⋊C4—42no—
705C22⋊C4—1224no—
706C22⋊C4—1224no—
707C22⋊C4—1224no—
708C22⋊C4—1224no—
709C22⋊C4—1224no—
710C22⋊C4—1224no—
711C22⋊C4—1224no—
712C22⋊C4—1224no—
713C22⋊C4—1224no—
714C22⋊C4—1224no—
715C22⋊C4—1224no—
716C22⋊C4—2442no—
717C22⋊C4—2441no—
718C22⋊C4—2441no—
719C22⋊C4—2442no—
720C22⋊C4—2442no—
721C42—24no—
722C42—41no—
723C42—614no—
724C42—1224no—
725C42—1224no—
726C42—1224no—
727C42—1224no—
728C42—1224no—
729C42—1224no—
730C42—1224no—
731C42—1224no—
732C42—1224no—
733C42—1222no—
734C42—1224no—
735C42—2442no—
736C23—22no—
737C23—22no—
738C23—22no—
739C23—22no—
740C23—22no—
741C23—22no—
742C23—1222no—
743C23—1221no—
744C23—1221no—
745C23—1222no—
746C23—1222no—
747C23—1222no—
748C23—1221no—
749C23—1221no—
750C23—1221no—
751C23—1221no—
752C23#41×D6114yes—
753C23C24×D6111yescharacteristic
754Q8—44no—
755Q8—2444no—
756D4—44no—
757D4—2444no—
758D4—2448no—
759D4—2448no—
760C2×C4—22no—
761C2×C4—21no—
762C2×C4—22no—
763C2×C4—21no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—48no—
781C2×C4—614no—
782C2×C4—612no—
783C2×C4—614no—
784C2×C4—614no—
785C2×C4—614no—
786C2×C4—614no—
787C2×C4—12216no—
788C2×C4—12216no—
789C2×C4—1222no—
790C2×C4—1222no—
791C2×C4—1222no—
792C2×C4—1222no—
793C2×C4—1222no—
794C2×C4—1222no—
795C2×C4—1222no—
796C2×C4—1222no—
797C2×C4—1222no—
798C2×C4—1222no—
799C2×C4—1222no—
800C2×C4—1222no—
801C2×C4—1222no—
802C2×C4—1221no—
803C2×C4—1222no—
804C2×C4—1222no—
805C2×C4—2444no—
806C2×C4—2444no—
807C2×C4#41×D6114yes—
808C2×C4#41×D6112yes—
809C22—24no—
810C22—24no—
811C22—24no—
812C22—42no—
813C22—42no—
814C22—42no—
815C22—42no—
816C22—2441no—
817C22—2441no—
818C22—2441no—
819C22—2441no—
820C22—2442no—
821C22—2442no—
822C22—2442no—
823C22—2442no—
824C22—2441no—
825C22—2441no—
826C22C2×#41×D6111yescharacteristic
827C22C2×#41×D6112yes—
828C22C2×#41×D6112yes—
829C22H(5,𝔽2)×D6111yescharacteristic
830C22#1684059711yescharacteristic
831C4—22no—
832C4—24no—
833C4—42no—
834C4—41no—
835C4—41no—
836C4—42no—
837C4—42no—
838C4—42no—
839C4—614no—
840C4—1224no—
841C4—1224no—
842C4—1224no—
843C4—1224no—
844C4—2442no—
845C4—2441no—
846C4—2442no—
847C2—44no—
848C2—4881no—
849C2—4881no—
850C2#2145911312yes—
851C2#2145923811yescharacteristic
852C2#551×D6111yescharacteristic
853C2#2145937412yes—
854C2#2145944411yescharacteristic
subgroupG/H
center, FrattiniC23C24×D61
commutator, socle, cosocleC23×C61C25
FittingC61×#2572C2
prime radical#21449033C2
hypercenter#2572D61
hypocenterC61#34871
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #2572

Complements

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

NH ≅ G/Ntype
1. #21451528C2semidirect
2. #21451507C2semidirect
3. #21451490C2semidirect
4. #21451230C2semidirect
5. #21450879C2semidirect
6. #21450677C2semidirect
7. #21450587C2semidirect
8. #21450054C2semidirect
9. #21449934C2semidirect
10. #21449086C2semidirect
11. #21449085C2semidirect
13. #21448367C2semidirect
14. #21448362C2semidirect
15. #21448336C2semidirect
16. #21448304C2semidirect
17. #21448279C2semidirect
18. C4×#14519733C2semidirect
19. C61×#2572C2semidirect
294. #11758196#41semidirect
307. C4×Dic61#41semidirect
424. #2572D61semidirect
534. C61#34871semidirect

Maximal subgroups

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

subgroupindex
#214515282
#214515072
#214514902
#214512302
#214508792
#214506772
#214505872
#214500542
#214499342
#214490862
#214490852
#214490332
#214483672
#214483622
#214483362
#214483042
#214482792
C4×#145197332
C61×#25722
#3487161