Finite Group Databasebeta

← #29886623

Subgroups — #29886623

Order 15616.

1716 conjugacy classes of subgroups.

The subgroup lattice has 850 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21454029C212yesmaximal, complemented
2#21454027C212yesmaximal, complemented
3#21454014C212yesmaximal, complemented
4#21454012C212yesmaximal, complemented
5#21453947C212yesmaximal, complemented
6#21453945C212yesmaximal, complemented
7#21453938C212yesmaximal, complemented
8#21453936C212yesmaximal, complemented
9#21449127C211yesmaximal, characteristic, complemented
10#21449098C211yesmaximal, characteristic, complemented
11#21449080C212yesmaximal, complemented
12#21449076C212yesmaximal, complemented
13#21449063C212yesmaximal, complemented
14#21449059C211yesmaximal, characteristic, complemented
15#21449057C211yesmaximal, characteristic, complemented
16#21449055C212yesmaximal, complemented
17#21448316C211yesmaximal, characteristic, complemented
18#21448283C211yesmaximal, characteristic, complemented
19C61×#2293C211yesmaximal, characteristic, complemented
20C2×C4×D244C2211yescharacteristic
21C2×C4×D244C2212yes—
22C2×C4×C22⋊D61C2212yes—
23C2×C4×C22⋊D61C2212yes—
24C2×C4×C22⋊D61C2212yes—
25C2×#14519734C2211yescharacteristic
26C2×#14519734C2212yes—
27#16839704C2212yes—
28#16839703C2212yes—
29#16839701C2212yes—
30#16839700C2212yes—
31#16839698C2212yes—
32#16839698C2212yes—
33#16839697C2212yes—
34#16839697C2212yes—
35#16839696C2212yes—
36#16839696C2212yes—
37#16839695C2212yes—
38#16839694C2211yescharacteristic
39#16839694C2212yes—
40#16839693C2211yescharacteristic
41#16839693C2212yes—
42#16839692C2212yes—
43#16839691C2212yes—
44#16839691C2212yes—
45#16839690C2212yes—
46#16839690C2212yes—
47#16839690C2212yes—
48#16839689C2211yescharacteristic
49#16839689C2212yes—
50#16839688C2211yescharacteristic
51#16839688C2212yes—
52#16839687C2212yes—
53#16839686C2212yes—
54#16839685C2212yes—
55#16839685C2212yes—
56#16839684C2212yes—
57#16839684C2212yes—
58#16839684C2212yes—
59#16839680C2211yescharacteristic
60#16839680C2212yes—
61#16839679C2212yes—
62#16839679C2212yes—
63#16839678C2212yes—
64#16839678C2212yes—
65#16839678C2212yes—
66#16839678C2212yes—
67#16839677C2212yes—
68#16839677C2212yes—
69#16839677C2212yes—
70#16839677C2212yes—
71#16839677C2212yes—
72#16839676C2211yescharacteristic
73#16839672C2211yescharacteristic
74#16839671C2212yes—
75#16839671C2212yes—
76#16839671C2212yes—
77#16839670C2211yescharacteristic
78#16839670C2212yes—
79#16839664C2212yes—
80#16839660C2212yes—
81#16839653C2212yes—
82#16839653C2212yes—
83#16839653C2212yes—
84#16839653C2212yes—
85#16839646C2212yes—
86#16839646C2212yes—
87C4×#11758196C2212yes—
88C4×#11758196C2211yescharacteristic
89C4×#11758196C2211yescharacteristic
90C4×C4⋊Dic61C2211yescharacteristic
91C4×C4⋊Dic61C2212yes—
92C4×#11758198C2212yes—
93C4×#11758198C2211yescharacteristic
94C4×#11758198C2212yes—
95C4×#11758198C2211yescharacteristic
96C4×C22⋊Dic61C2212yes—
97#16839608C2211yescharacteristic
98C2×C4×D4×C61C2211yescharacteristic
99C2×#117×C61C2212yes—
100C61×#390C2212yes—
101C61×#389C2212yes—
102C61×#388C2212yes—
103C61×#388C2212yes—
104C4×C4⋊C4×C61C2211yescharacteristic
105C4×C22⋊C4×C61C2212yes—
106C43×C61C2211yescharacteristic
107C22×D244C2311yescharacteristic
108C22×D244C2312yes—
109C22×C22⋊D61C2312yes—
110C22×C22⋊D61C2312yes—
111C22×C22⋊D61C2312yes—
112C22×C4×D61C2311yescharacteristic
113C22×C4×D61C2312yes—
114C4×D244—24no—
115C4×D244—44no—
116C4×C22⋊D61—44no—
117C4×C22⋊D61—44no—
118C4×C22⋊D61—44no—
119#14519734—24no—
120#14519734—44no—
121C2×C4⋊Dic61C2311yescharacteristic
122C2×C4⋊Dic61C2312yes—
123C2×C4⋊Dic61C2312yes—
124C2×C4⋊Dic61C2312yes—
125C2×C4⋊Dic61C2312yes—
126C2×#11758196C2311yescharacteristic
127C2×#11758196C2311yescharacteristic
128C2×#11758196C2312yes—
129C2×#11758196C2312yes—
130C2×#11758196C2312yes—
131C2×#11758196C2312yes—
132C2×#11758196C2312yes—
133C2×#11758196C2312yes—
134C2×#11758196C2312yes—
135C2×#11758196C2312yes—
136C2×#11758196C2312yes—
137C2×C22⋊Dic61C2312yes—
138C2×C22⋊Dic61C2312yes—
139C2×C22⋊Dic61C2312yes—
140C2×C22⋊Dic61C2312yes—
141C2×C22⋊Dic61C2312yes—
142C2×#11758198C2312yes—
143C2×#11758198C2311yescharacteristic
144C2×#11758198C2311yescharacteristic
145C2×#11758198C2312yes—
146C2×#11758198C2312yes—
147C2×#11758198C2312yes—
148C2×#11758198C2312yes—
149C2×#11758198C2312yes—
150C2×#11758198C2312yes—
151C2×#11758198C2312yes—
152C2×#11758198C2312yes—
153C2×#11758198C2312yes—
154C2×#11758198C2312yes—
155C2×#11758198C2312yes—
156C2×#11758198C2312yes—
157C2×#11758198C2312yes—
158C2×C4×Dic61C2312yes—
159C2×C4×Dic61C2311yescharacteristic
160C2×C4×Dic61C2311yescharacteristic
161C2×C4×Dic61C2311yescharacteristic
162#14519684C2312yes—
163#14519684C2312yes—
164#14519684C2312yes—
165#14519684C2312yes—
166#14519684C2312yes—
167#14519684C2312yes—
168#14519684C2312yes—
169#14519684C2312yes—
170#14519684C2312yes—
171#14519684C2311yescharacteristic
172#14519684C2312yes—
173#14519684C2312yes—
174#14519684C2312yes—
175#14519684C2312yes—
176#14519684C2312yes—
177#14519684C2311yescharacteristic
178#14519684C2312yes—
179#14519684C2312yes—
180C22×D4×C61C2311yescharacteristic
181C23×C4×C61C2312yes—
182C4×D4×C61—24no—
183#117×C61—44no—
184C2×C4⋊C4×C61C2311yescharacteristic
185C2×C4⋊C4×C61C2312yes—
186C2×C4⋊C4×C61C2312yes—
187C2×C4⋊C4×C61C2312yes—
188C2×C22⋊C4×C61C2312yes—
189C2×C22⋊C4×C61C2312yes—
190C2×C22⋊C4×C61C2312yes—
191C2×C22⋊C4×C61C2312yes—
192C2×C22⋊C4×C61C2312yes—
193C2×C42×C61C2311yescharacteristic
194C2×C42×C61C2312yes—
195C2×C42×C61C2311yescharacteristic
196C2×C42×C61C2312yes—
197C2×C42×C61C2312yes—
198C2×C42×C61C2311yescharacteristic
199#95×C61C2311yescharacteristic
200#95×C61C2312yes—
201#95×C61C2312yes—
202#95×C61C2311yescharacteristic
203C24×C61C2412yes—
204C23×D61C2411yescharacteristic
205C23×D61C2412yes—
206C2×D4×C61—22no—
207C2×D4×C61—42no—
208C22×C4×C61—24no—
209C22×C4×C61—24no—
210C22×C4×C61—24no—
211C22×C4×C61C2412yes—
212C22×C4×C61C2412yes—
213C22×C4×C61C2412yes—
214C22×C4×C61C2412yes—
215C22×C4×C61C2412yes—
216C22×C4×C61C2411yescharacteristic
217C22×C4×C61C2411yescharacteristic
218C22×C4×C61C2411yescharacteristic
219C2×C22⋊D61—42no—
220C2×C22⋊D61—42no—
221C2×C22⋊D61—42no—
222C2×C22⋊D61—42no—
223C2×C22⋊D61—42no—
224C2×C22⋊D61—42no—
225C2×C22⋊D61—42no—
226C2×C22⋊D61—42no—
227C2×C22⋊D61—42no—
228C22×Dic61C2411yescharacteristic
229C22×Dic61C2412yes—
230C22×Dic61C2412yes—
231C22×Dic61C2412yes—
232C22×Dic61C2412yes—
233C22×Dic61C2411yescharacteristic
234C22×Dic61C2411yescharacteristic
235C22×Dic61C2412yes—
236C2×D244—22no—
237C2×D244—42no—
238C2×D244—42no—
239C2×D244—42no—
240C2×D244—42no—
241C2×C4×D61—22no—
242C2×C4×D61—24no—
243C2×C4×D61—24no—
244C2×C4×D61—22no—
245C2×C4×D61—24no—
246C2×C4×D61—22no—
247C4⋊C4×C61—22no—
248C4⋊C4×C61—42no—
249C4⋊C4×C61—42no—
250C4⋊C4×C61—42no—
251C22⋊C4×C61—24no—
252C22⋊C4×C61—42no—
253C22⋊C4×C61—42no—
254C22⋊C4×C61—42no—
255C22⋊C4×C61—42no—
256C42×C61—22no—
257C42×C61—24no—
258C42×C61—22no—
259C42×C61—42no—
260C42×C61—42no—
261C42×C61#4114yes—
262C22⋊Dic61—42no—
263C22⋊Dic61—42no—
264C22⋊Dic61—42no—
265C22⋊Dic61—42no—
266C22⋊Dic61—42no—
267#11758198—22no—
268#11758198—22no—
269#11758198—24no—
270#11758198—42no—
271#11758198—42no—
272#11758198—42no—
273#11758198—42no—
274#11758198—42no—
275#11758198—42no—
276#11758198—42no—
277#11758198—42no—
278#11758198—42no—
279#11758198—42no—
280#11758198—42no—
281#11758198—42no—
282#11758198—42no—
283C4⋊Dic61—22no—
284C4⋊Dic61—42no—
285C4⋊Dic61—42no—
286C4⋊Dic61—42no—
287C4⋊Dic61—42no—
288#11758196—22no—
289#11758196—22no—
290#11758196—42no—
291#11758196—42no—
292#11758196—42no—
293#11758196—42no—
294#11758196—42no—
295#11758196—42no—
296#11758196—42no—
297#11758196—42no—
298#11758196—42no—
299C4×Dic61—22no—
300C4×Dic61—24no—
301C4×Dic61—22no—
302C4×Dic61—22no—
303C23×C61—22no—
304C23×C61—22no—
305C23×C61—22no—
306C23×C61—22no—
307C23×C61—22no—
308C23×C61—22no—
309C23×C61—22no—
310C23×C61C2511yescharacteristic
311C22×D61—21no—
312C22×D61—22no—
313C22×D61—22no—
314C22×D61—21no—
315C22×D61—22no—
316C22×D61—21no—
317C22×D61—22no—
318C22×D61—22no—
319C22×D61—22no—
320C22×D61—22no—
321C22×D61—22no—
322C22×D61—22no—
323D4×C61—44no—
324C2×C4×C61—22no—
325C2×C4×C61—22no—
326C2×C4×C61—22no—
327C2×C4×C61—22no—
328C2×C4×C61—22no—
329C2×C4×C61—22no—
330C2×C4×C61—22no—
331C2×C4×C61—22no—
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—48no—
342C2×C4×C61C2×#4112yes—
343C2×C4×C61C2×#4112yes—
344C2×C4×C61C2×#4112yes—
345C2×C4×C61H(5,𝔽2)12yes—
346C2×C4×C61H(5,𝔽2)12yes—
347C22⋊D61—48no—
348C22⋊D61—48no—
349C22⋊D61—48no—
350C2×Dic61—21no—
351C2×Dic61—21no—
352C2×Dic61—21no—
353C2×Dic61—22no—
354C2×Dic61—22no—
355C2×Dic61—22no—
356C2×Dic61—22no—
357C2×Dic61—22no—
358C2×Dic61—22no—
359C2×Dic61—21no—
360C2×Dic61—22no—
361C2×Dic61—21no—
362C2×Dic61—22no—
363C2×Dic61—22no—
364C2×Dic61—22no—
365C2×Dic61—22no—
366C2×Dic61—22no—
367C2×Dic61—22no—
368C2×Dic61—22no—
369C2×Dic61—22no—
370C2×Dic61—22no—
371C2×Dic61—22no—
372D244—44no—
373D244—48no—
374C4×D61—44no—
375C4×D61—48no—
376#36692—611nomaximal, Sylow
377C22×C61—42no—
378C22×C61—42no—
379C22×C61—42no—
380C22×C61—42no—
381C22×C61—42no—
382C22×C61—42no—
383C22×C61—42no—
384C22×C61C22×#4111yescharacteristic
385C22×C61C2×H(5,𝔽2)11yescharacteristic
386C22×C61C2×H(5,𝔽2)11yescharacteristic
387C22×C61#58512yes—
388C22×C61#58512yes—
389C2×D61—41no—
390C2×D61—42no—
391C2×D61—42no—
392C2×D61—41no—
393C2×D61—41no—
394C2×D61—42no—
395C2×D61—42no—
396C2×D61—42no—
397C2×D61—42no—
398C2×D61—42no—
399C2×D61—42no—
400C2×D61—42no—
401C4×C61—22no—
402C4×C61—22no—
403C4×C61—42no—
404C4×C61—42no—
405C4×C61—42no—
406C4×C61—42no—
407C4×C61—42no—
408C4×C61#54014yes—
409Dic61—41no—
410Dic61—42no—
411Dic61—41no—
412Dic61—41no—
413Dic61—42no—
414Dic61—42no—
415Dic61—42no—
416Dic61—42no—
417#2837—612no—
418#2837—612no—
419#2836—612no—
420#2836—612no—
421#2829—612no—
422#2829—612no—
423#2828—612no—
424#2828—612no—
425#2402—611no—
426#2397—611no—
427#2395—612no—
428#2395—612no—
429#2392—611no—
430#2392—612no—
431#2392—611no—
432#2392—612no—
433#2298—611no—
434#2293—611no—
435#2293D6111yescharacteristic, complemented
436C2×C61—82no—
437C2×C61C2×#54011yescharacteristic
438C2×C61#345511yescharacteristic
439C2×C61#345511yescharacteristic
440C2×C61#352912yes—
441C2×C61#352912yes—
442D61—82no—
443D61—81no—
444C2×C4×D4—612no—
445C2×C4×D4—612no—
446C2×C4×D4—612no—
447C2×C4×D4—611no—
448C2×C4×D4—612no—
449C2×C4×D4C2×D6111yescharacteristic
450C2×#117—611no—
451C2×#117—612no—
452C2×#117C2×D6112yes—
453#400—612no—
454#400—612no—
455#400—612no—
456#400—612no—
457#399—612no—
458#399—612no—
459#399—612no—
460#399—612no—
461#398—612no—
462#398—612no—
463#398—611no—
464#398—612no—
465#398—612no—
466#398—611no—
467#398—612no—
468#398—612no—
469#397—612no—
470#397—611no—
471#397—612no—
472#397—612no—
473#397—612no—
474#397—612no—
475#397—612no—
476#397—611no—
477#397—612no—
478#397—612no—
479#396—612no—
480#396—612no—
481#396—612no—
482#396—612no—
483#396—612no—
484#396—612no—
485#394—611no—
486#394—612no—
487#394—612no—
488#394—612no—
489#394—612no—
490#394—612no—
491#394—612no—
492#394—612no—
493#394—612no—
494#394—612no—
495#394—612no—
496#394—612no—
497#394—612no—
498#394—611no—
499#392—611no—
500#392—612no—
501#392—612no—
502#392—612no—
503#392—612no—
504#392—611no—
505#390—612no—
506#390C2×D6112yes—
507#389—612no—
508#389C2×D6112yes—
509#388—612no—
510#388—612no—
511#388—612no—
512#388—612no—
513#388C2×D6112yes—
514#388C2×D6112yes—
515#387—612no—
516#387—612no—
517C4×C4⋊C4—612no—
518C4×C4⋊C4—612no—
519C4×C4⋊C4—611no—
520C4×C4⋊C4—611no—
521C4×C4⋊C4—611no—
522C4×C4⋊C4C2×D6111yescharacteristic
523C4×C22⋊C4—612no—
524C4×C22⋊C4—611no—
525C4×C22⋊C4—611no—
526C4×C22⋊C4—612no—
527C4×C22⋊C4—612no—
528C4×C22⋊C4C2×D6112yes—
529#376—611no—
530C43C2×D6111yescharacteristic
531C61#3669211yescharacteristic, complemented, Sylow
532C22×D4—612no—
533C22×D4—612no—
534C22×D4—612no—
535C22×D4—611no—
536C22×D4—612no—
537C22×D4C22×D6111yescharacteristic
538C23×C4—611no—
539C23×C4—612no—
540C23×C4C22×D6112yes—
541C4×D4—24no—
542C4×D4—1224no—
543C4×D4—2444no—
544C4×D4—2444no—
545C4×D4—2444no—
546C4×D4—2444no—
547#117—44no—
548#117—1224no—
549#117—2444no—
550C2×C4⋊C4—611no—
551C2×C4⋊C4—611no—
552C2×C4⋊C4—611no—
553C2×C4⋊C4—612no—
554C2×C4⋊C4—612no—
555C2×C4⋊C4—612no—
556C2×C4⋊C4—612no—
557C2×C4⋊C4—612no—
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⋊C4C22×D6111yescharacteristic
567C2×C4⋊C4C22×D6112yes—
568C2×C4⋊C4C22×D6112yes—
569C2×C4⋊C4C22×D6112yes—
570C2×C22⋊C4—611no—
571C2×C22⋊C4—611no—
572C2×C22⋊C4—612no—
573C2×C22⋊C4—612no—
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—612no—
588C2×C22⋊C4—612no—
589C2×C22⋊C4—612no—
590C2×C22⋊C4—612no—
591C2×C22⋊C4C22×D6112yes—
592C2×C22⋊C4C22×D6112yes—
593C2×C22⋊C4C22×D6112yes—
594C2×C22⋊C4C22×D6112yes—
595C2×C22⋊C4C22×D6112yes—
596C2×C42—612no—
597C2×C42—611no—
598C2×C42—611no—
599C2×C42—611no—
600C2×C42C22×D6111yescharacteristic
601C2×C42C22×D6111yescharacteristic
602C2×C42C22×D6112yes—
603C2×C42C22×D6112yes—
604C2×C42C22×D6112yes—
605C2×C42C22×D6111yescharacteristic
606#95—612no—
607#95—612no—
608#95—612no—
609#95—612no—
610#95—612no—
611#95—612no—
612#95—612no—
613#95—612no—
614#95—612no—
615#95—612no—
616#95—612no—
617#95—612no—
618#95—611no—
619#95—611no—
620#95—612no—
621#95—612no—
622#95—612no—
623#95—612no—
624#95C22×D6112yes—
625#95C22×D6112yes—
626#95C22×D6111yescharacteristic
627#95C22×D6111yescharacteristic
628C24—611no—
629C24—612no—
630C24C23×D6112yes—
631C2×D4—22no—
632C2×D4—42no—
633C2×D4—1222no—
634C2×D4—2442no—
635C2×D4—2442no—
636C2×D4—2442no—
637C2×D4—2442no—
638C2×D4—2442no—
639C2×D4—2442no—
640C2×D4—2442no—
641C2×D4—2442no—
642C2×D4—2442no—
643C2×D4—2442no—
644C2×D4—2442no—
645C2×D4—2442no—
646C2×D4—2442no—
647C22×C4—24no—
648C22×C4—24no—
649C22×C4—24no—
650C22×C4—611no—
651C22×C4—611no—
652C22×C4—612no—
653C22×C4—612no—
654C22×C4—612no—
655C22×C4—612no—
656C22×C4—612no—
657C22×C4—611no—
658C22×C4—1222no—
659C22×C4—1224no—
660C22×C4—1222no—
661C22×C4—1224no—
662C22×C4—1224no—
663C22×C4—1222no—
664C22×C4C23×D6112yes—
665C22×C4C23×D6112yes—
666C22×C4C23×D6112yes—
667C22×C4C23×D6112yes—
668C22×C4C23×D6112yes—
669C22×C4C23×D6111yescharacteristic
670C22×C4C23×D6111yescharacteristic
671C22×C4C23×D6111yescharacteristic
672C4⋊C4—22no—
673C4⋊C4—42no—
674C4⋊C4—42no—
675C4⋊C4—42no—
676C4⋊C4—1222no—
677C4⋊C4—1222no—
678C4⋊C4—1222no—
679C4⋊C4—2442no—
680C4⋊C4—2442no—
681C4⋊C4—2442no—
682C4⋊C4—2442no—
683C4⋊C4—2442no—
684C4⋊C4—2442no—
685C4⋊C4—2442no—
686C4⋊C4—2442no—
687C4⋊C4—2442no—
688C4⋊C4—2442no—
689C4⋊C4—2442no—
690C4⋊C4—2442no—
691C4⋊C4—2442no—
692C22⋊C4—24no—
693C22⋊C4—42no—
694C22⋊C4—42no—
695C22⋊C4—42no—
696C22⋊C4—42no—
697C22⋊C4—1222no—
698C22⋊C4—1222no—
699C22⋊C4—1224no—
700C22⋊C4—2442no—
701C22⋊C4—2442no—
702C22⋊C4—2442no—
703C22⋊C4—2442no—
704C22⋊C4—2442no—
705C22⋊C4—2442no—
706C22⋊C4—2442no—
707C22⋊C4—2442no—
708C22⋊C4—2442no—
709C22⋊C4—2442no—
710C22⋊C4—2442no—
711C22⋊C4—2442no—
712C22⋊C4—2442no—
713C22⋊C4—2442no—
714C22⋊C4—2442no—
715C22⋊C4—2442no—
716C22⋊C4—2442no—
717C22⋊C4—2442no—
718C42—22no—
719C42—24no—
720C42—22no—
721C42—42no—
722C42—42no—
723C42—1222no—
724C42—1222no—
725C42—1224no—
726C42—1222no—
727C42#1175822214yes—
728C23—22no—
729C23—22no—
730C23—22no—
731C23—22no—
732C23—22no—
733C23—22no—
734C23—22no—
735C23—1221no—
736C23—1222no—
737C23—1221no—
738C23—1222no—
739C23—1222no—
740C23—1221no—
741C23—1222no—
742C23—1222no—
743C23—1222no—
744C23—1222no—
745C23—1222no—
746C23—1222no—
747C23C24×D6111yescharacteristic
748D4—44no—
749D4—2444no—
750D4—2448no—
751D4—2448no—
752D4—2448no—
753D4—2448no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—48no—
772C2×C4—1221no—
773C2×C4—1221no—
774C2×C4—1222no—
775C2×C4—1221no—
776C2×C4—1222no—
777C2×C4—1222no—
778C2×C4—1221no—
779C2×C4—1222no—
780C2×C4—1222no—
781C2×C4—1222no—
782C2×C4—1221no—
783C2×C4—1222no—
784C2×C4—1222no—
785C2×C4—1222no—
786C2×C4—1222no—
787C2×C4—1222no—
788C2×C4—1222no—
789C2×C4—1222no—
790C2×C4—1222no—
791C2×C4—1222no—
792C2×C4—1222no—
793C2×C4—1222no—
794C2×C4—2444no—
795C2×C4—2448no—
796C2×C4C2×#1175822212yes—
797C2×C4C2×#1175822212yes—
798C2×C4C2×#1175822212yes—
799C2×C4#1451982212yes—
800C2×C4#1451982312yes—
801C22—42no—
802C22—42no—
803C22—42no—
804C22—42no—
805C22—42no—
806C22—42no—
807C22—42no—
808C22—2442no—
809C22—2441no—
810C22—2441no—
811C22—2442no—
812C22—2441no—
813C22—2442no—
814C22—2442no—
815C22—2442no—
816C22—2442no—
817C22—2442no—
818C22—2442no—
819C22—2442no—
820C22C22×#1175822211yescharacteristic
821C22C2×#1451982211yescharacteristic
822C22C2×#1451982311yescharacteristic
823C22#1684059812yes—
824C22#1684059812yes—
825C4—22no—
826C4—22no—
827C4—42no—
828C4—42no—
829C4—42no—
830C4—42no—
831C4—42no—
832C4—2441no—
833C4—2441no—
834C4—2442no—
835C4—2441no—
836C4—2442no—
837C4—2442no—
838C4—2442no—
839C4—2442no—
840C4#1684036314yes—
841C2—82no—
842C2—4882no—
843C2—4881no—
844C2C2×#1684036311yescharacteristic
845C2#2145920411yescharacteristic
846C2#2145920911yescharacteristic
847C2#2145995512yes—
848C2#2145995812yes—
subgroupG/H
centerC22×C4C23×D61
commutator, socle, cosocleC23×C61C25
FrattiniC23C24×D61
FittingC61×#2293C2
hypercenter#2293D61
hypocenterC61#36692
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ #2293

Complements

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

NH ≅ G/Ntype
1. #21454029C2semidirect
2. #21454027C2semidirect
3. #21454014C2semidirect
4. #21454012C2semidirect
5. #21453947C2semidirect
6. #21453945C2semidirect
7. #21453938C2semidirect
8. #21453936C2semidirect
9. #21449127C2semidirect
10. #21449098C2semidirect
11. #21449080C2semidirect
12. #21449076C2semidirect
13. #21449063C2semidirect
14. #21449059C2semidirect
15. #21449057C2semidirect
16. #21449055C2semidirect
17. #21448316C2semidirect
18. #21448283C2semidirect
19. C61×#2293C2semidirect
435. #2293D61semidirect
531. C61#36692semidirect

Maximal subgroups

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

subgroupindex
#214540292
#214540272
#214540142
#214540122
#214539472
#214539452
#214539382
#214539362
#214491272
#214490982
#214490802
#214490762
#214490632
#214490592
#214490572
#214490552
#214483162
#214482832
C61×#22932
#3669261