Finite Group Databasebeta

← #29712657

Subgroups — #29712657

Order 15616.

1520 conjugacy classes of subgroups.

The subgroup lattice has 894 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840272C211yesmaximal, characteristic
2C2×#16840094C211yesmaximal, characteristic, complemented
3C2×#16840074C211yesmaximal, characteristic, complemented
4#380×D61C211yesmaximal, characteristic, complemented
5#21447023C211yesmaximal, characteristic, complemented
6#21447022C211yesmaximal, characteristic, complemented
7#21447005C211yesmaximal, characteristic, complemented
8#21446133C211yesmaximal, characteristic, complemented
9#21446125C211yesmaximal, characteristic, complemented
10#21446021C211yesmaximal, characteristic, complemented
11#21446017C211yesmaximal, characteristic, complemented
12#21445756C211yesmaximal, characteristic, complemented
13#21445756C211yesmaximal, characteristic, complemented
14#21445728C211yesmaximal, characteristic, complemented
15C61×#2034C211yesmaximal, characteristic, complemented
16C22×#11758224C2211yescharacteristic
17C23×C4×D61C2211yescharacteristic
18#16840272—24no—
19#16840272—24no—
20C2×#14519759—21no—
21C2×#14519757C2211yescharacteristic
22C2×#14519756C2211yescharacteristic
23C2×#14519748C2211yescharacteristic
24C2×#14519745—21no—
25C2×D4×Dic61—21no—
26C2×#14519737—21no—
27C2×#14519735C2211yescharacteristic
28C2×C4⋊C4×D61C2211yescharacteristic
29C2×C4⋊C4×D61C2211yescharacteristic
30C2×C22⋊C4×D61—21no—
31#16840094—24no—
32#16840074—24no—
33C2×#14519711C2211yescharacteristic, complemented
34C2×#14519710C2211yescharacteristic, complemented
35C2×#14519708C2211yescharacteristic, complemented
36C2×#14519702C2211yescharacteristic, complemented
37C2×#14519702C2211yescharacteristic, complemented
38C2×#14519700C2211yescharacteristic, complemented
39C2×#14519700C2211yescharacteristic, complemented
40C2×#14519698C2211yescharacteristic, complemented
41C2×#14519698C2211yescharacteristic, complemented
42C2×C22⋊#92418C2211yescharacteristic
43C2×#14519689C2211yescharacteristic
44C2×#14519689C2211yescharacteristic
45C2×#14519689C2211yescharacteristic
46C2×#14519689C2211yescharacteristic
47#16839622C2211yescharacteristic
48#16839621—21no—
49#16839620—21no—
50#16839619C2211yescharacteristic
51#16839619C2211yescharacteristic
52#95×D61—21no—
53#16839525C2211yescharacteristic, complemented
54#16839524C2211yescharacteristic, complemented
55#16839524C2211yescharacteristic, complemented
56C2×#121×C61C2211yescharacteristic
57C2×#106×C61C2211yescharacteristic, complemented
58C2×#102×C61C2211yescharacteristic, complemented
59C2×#102×C61C2211yescharacteristic, complemented
60C2×C22⋊C8×C61C2211yescharacteristic
61C61×#380C2211yescharacteristic
62C61×#340C2211yescharacteristic, complemented
63C24×D61D411yescharacteristic
64C2×#11758224—22no—
65C2×#11758224—22no—
66C2×#11758224—22no—
67C2×#11758224—22no—
68C2×#11758224—41no—
69C2×#11758224—41no—
70C22×Dic122C2311yescharacteristic
71C22×C22⋊D61—21no—
72C22×C22⋊D61—21no—
73C23×Dic61—21no—
74C23×Dic61D411yescharacteristic
75C22×C4×D61—22no—
76C22×C4×D61—22no—
77C22×C4×D61—22no—
78C22×C4×D61—22no—
79C22×C4×D61—21no—
80C22×C4×D61—21no—
81C22×C4×D61—41no—
82C22×C4×D61—41no—
83C22×C4×D61D411yescharacteristic
84C22×C4×D61D411yescharacteristic
85C22×C4×D61C2311yescharacteristic
86C22×C4×D61C2311yescharacteristic
87C22×#92418C2311yescharacteristic
88C22×#92418C2311yescharacteristic
89#14519759—28no—
90#14519757—22no—
91#14519757D414yes—
92#14519756—22no—
93#14519756—22no—
94#14519748—22no—
95#14519748D414yes—
96#14519745—28no—
97D4×Dic61—28no—
98#14519737—28no—
99#14519735—22no—
100#14519735—22no—
101C2×C4⋊Dic61—21no—
102C2×C4⋊Dic61C2311yescharacteristic
103C2×C4⋊Dic61C2311yescharacteristic
104C2×C4⋊Dic61C2311yescharacteristic
105C2×#11758196—21no—
106C2×#11758196—21no—
107C2×#11758196—21no—
108C4⋊C4×D61—22no—
109C4⋊C4×D61—22no—
110C4⋊C4×D61—41no—
111C4⋊C4×D61—41no—
112C2×C22⋊Dic61—21no—
113C2×C22⋊Dic61—21no—
114C2×C22⋊Dic61—21no—
115C2×#11758198—21no—
116C2×#11758198—21no—
117C2×#11758198—21no—
118C2×#11758198—21no—
119C22⋊C4×D61—44no—
120C2×C4×Dic61—21no—
121#14519711—22no—
122#14519710—22no—
123#14519708—22no—
124#14519702—22no—
125#14519702—41no—
126#14519700—22no—
127#14519700—41no—
128#14519698—22no—
129#14519698—41no—
130C22⋊#92418—41no—
131#14519689—22no—
132#14519689—22no—
133#14519689—22no—
134#14519689—22no—
135#14519684—21no—
136#14519684—21no—
137#14519684—21no—
138C22×D4×C61—21no—
139C22×D4×C61C2311yescharacteristic
140C23×C4×C61C2311yescharacteristic
141C22×C8×C61C2311yescharacteristic
142C22×C8×C61C2311yescharacteristic
143#121×C61—22no—
144#121×C61—22no—
145C2×C4⋊C4×C61C2311yescharacteristic
146C2×C4⋊C4×C61C2311yescharacteristic
147C2×C4⋊C4×C61C2311yescharacteristic
148C2×C22⋊C4×C61—21no—
149C2×C22⋊C4×C61—21no—
150#106×C61—22no—
151#102×C61—22no—
152#102×C61—41no—
153C22⋊C8×C61—41no—
154#95×C61—21no—
155C24×C61—21no—
156C24×C61C2×D411yescharacteristic
157C23×D61—22no—
158C23×D61—22no—
159C23×D61—22no—
160C23×D61—22no—
161C23×D61—22no—
162C23×D61—41no—
163C23×D61—41no—
164C23×D61C2×D411yescharacteristic
165C23×D61C2×D411yescharacteristic
166C2×D4×C61—24no—
167C2×D4×C61—21no—
168C2×D4×C61—21no—
169C2×D4×C61—21no—
170C2×D4×C61—21no—
171C2×D4×C61—21no—
172C2×D4×C61—42no—
173C2×D4×C61—42no—
174C2×D4×C61C2×D412yes—
175C22×C4×C61—21no—
176C22×C4×C61—21no—
177C22×C4×C61—21no—
178C22×C4×C61—21no—
179C22×C4×C61—21no—
180C22×C4×C61—21no—
181C22×C4×C61—21no—
182C22×C4×C61—21no—
183C22×C4×C61—21no—
184C22×C4×C61C2×D411yescharacteristic
185C22×C4×C61C2411yescharacteristic
186C2×C22⋊D61—24no—
187C2×C22⋊D61—24no—
188C2×C22⋊D61—42no—
189C2×C22⋊D61—42no—
190C2×C22⋊D61—42no—
191C2×C22⋊D61—42no—
192C22×Dic61—24no—
193C22×Dic61—21no—
194C22×Dic61—21no—
195C22×Dic61—22no—
196C22×Dic61—22no—
197C22×Dic61—21no—
198C22×Dic61—21no—
199C22×Dic61—41no—
200C22×Dic61—42no—
201C22×Dic61—42no—
202C22×Dic61C2×D411yescharacteristic
203C22×Dic61C2×D411yescharacteristic
204#11758224—44no—
205#11758224—44no—
206#11758224—44no—
207#11758224—44no—
208C2×C4×D61—21no—
209C2×C4×D61—21no—
210C2×C4×D61—21no—
211C2×C4×D61—21no—
212C2×C4×D61—21no—
213C2×C4×D61—21no—
214C2×C4×D61—21no—
215C2×C4×D61—21no—
216C2×C4×D61—22no—
217C2×C4×D61—22no—
218C2×C4×D61—22no—
219C2×C4×D61—22no—
220C2×C4×D61—44no—
221C2×C4×D61—44no—
222C2×C4×D61—44no—
223C2×C4×D61—44no—
224C2×C4×D61—41no—
225C2×C4×D61—41no—
226C2×C4×D61—42no—
227C2×C4×D61—42no—
228C2×C4×D61—42no—
229C2×C4×D61—42no—
230C2×C4×D61—42no—
231C2×C4×D61—42no—
232C2×C4×D61C2×D412yes—
233C2×C4×D61C2×D412yes—
234C2×C4×D61#4112yes—
235C2×C4×D61#4112yes—
236C2×Dic122—21no—
237C2×Dic122—21no—
238C2×Dic122—21no—
239C2×Dic122—21no—
240C2×Dic122—21no—
241C2×Dic122C2×D412yes—
242C2×C8×C61—21no—
243C2×C8×C61—21no—
244C2×C8×C61—21no—
245C2×C8×C61—21no—
246C2×C8×C61—21no—
247C2×C8×C61—21no—
248C4⋊C4×C61—21no—
249C4⋊C4×C61—21no—
250C4⋊C4×C61—21no—
251C4⋊C4×C61—21no—
252C4⋊C4×C61—21no—
253C4⋊C4×C61C2×D412yes—
254C22⋊C4×C61—24no—
255C22⋊C4×C61—42no—
256C22⋊Dic61—24no—
257C22⋊Dic61—24no—
258C22⋊Dic61—42no—
259#11758198—24no—
260#11758198—24no—
261#11758198—42no—
262#11758198—42no—
263C4⋊Dic61—21no—
264C4⋊Dic61—24no—
265C4⋊Dic61—21no—
266C4⋊Dic61—21no—
267C4⋊Dic61—21no—
268C4⋊Dic61—21no—
269C4⋊Dic61C2×D412yes—
270#11758196—24no—
271#11758196—42no—
272#11758196—42no—
273C4×Dic61—24no—
274C2×#92418—21no—
275C2×#92418—21no—
276C2×#92418—21no—
277C2×#92418—21no—
278C2×#92418—21no—
279C2×#92418—21no—
280C23×C61—21no—
281C23×C61—21no—
282C23×C61—21no—
283C23×C61—21no—
284C23×C61—21no—
285C23×C61—21no—
286C23×C61—22no—
287C23×C61—41no—
288C23×C61—41no—
289C23×C61—41no—
290C23×C61—41no—
291C23×C61—41no—
292C23×C61—41no—
293C23×C61#13712yes—
294C23×C61C22×D411yescharacteristic
295C22×D61—21no—
296C22×D61—21no—
297C22×D61—21no—
298C22×D61—21no—
299C22×D61—28no—
300C22×D61—21no—
301C22×D61—21no—
302C22×D61—21no—
303C22×D61—21no—
304C22×D61—21no—
305C22×D61—21no—
306C22×D61—44no—
307C22×D61—44no—
308C22×D61—44no—
309C22×D61—44no—
310C22×D61—44no—
311C22×D61—44no—
312C22×D61#12012yes—
313C22×D61#12312yes—
314C22×D61#13512yes—
315C22×D61AGL(1,ℤ/8)12yes—
316D4×C61—22no—
317D4×C61—22no—
318D4×C61—48no—
319D4×C61—41no—
320D4×C61—41no—
321C2×C4×C61—22no—
322C2×C4×C61—21no—
323C2×C4×C61—21no—
324C2×C4×C61—21no—
325C2×C4×C61—41no—
326C2×C4×C61—41no—
327C2×C4×C61—41no—
328C2×C4×C61—41no—
329C2×C4×C61—41no—
330C2×C4×C61—41no—
331C2×C4×C61—41no—
332C2×C4×C61—41no—
333C2×C4×C61—41no—
334C2×C4×C61—41no—
335C2×C4×C61—41no—
336C2×C4×C61—41no—
337C2×C4×C61C22×D411yescharacteristic
338C2×C4×C61C22×D411yescharacteristic
339C2×C4×C61C2×#4111yescharacteristic
340C2×C4×C61C2×#4111yescharacteristic
341C2×C4×C61H(5,𝔽2)11yescharacteristic
342C2×C4×C61H(5,𝔽2)11yescharacteristic
343C22⋊D61—48no—
344C22⋊D61—48no—
345C2×Dic61—21no—
346C2×Dic61—21no—
347C2×Dic61—21no—
348C2×Dic61—21no—
349C2×Dic61—22no—
350C2×Dic61—22no—
351C2×Dic61—44no—
352C2×Dic61—48no—
353C2×Dic61—41no—
354C2×Dic61—41no—
355C2×Dic61—41no—
356C2×Dic61—41no—
357C2×Dic61—41no—
358C2×Dic61—41no—
359C2×Dic61—41no—
360C2×Dic61—41no—
361C2×Dic61—41no—
362C2×Dic61—41no—
363C2×Dic61#12012yes—
364C2×Dic61#12312yes—
365C4×D61—22no—
366C4×D61—22no—
367C4×D61—22no—
368C4×D61—22no—
369C4×D61—22no—
370C4×D61—22no—
371C4×D61—22no—
372C4×D61—22no—
373C4×D61—44no—
374C4×D61—44no—
375C4×D61—84no—
376C4×D61—84no—
377Dic122—22no—
378Dic122—22no—
379Dic122—41no—
380Dic122—41no—
381C8×C61—41no—
382C8×C61—41no—
383#92418—41no—
384#92418—41no—
385#24004—611nomaximal, Sylow
386C22×C61—22no—
387C22×C61—22no—
388C22×C61—22no—
389C22×C61—41no—
390C22×C61—41no—
391C22×C61—41no—
392C22×C61—41no—
393C22×C61—42no—
394C22×C61—42no—
395C22×C61—42no—
396C22×C61—81no—
397C22×C61—81no—
398C22×C61—81no—
399C22×C61—81no—
400C22×C61C2×#12011yescharacteristic
401C22×C61C2×#12311yescharacteristic
402C22×C61#53411yescharacteristic
403C22×C61C2×#13511yescharacteristic
404C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
405C22×C61C2×#13711yescharacteristic
406C22×C61#57511yescharacteristic
407C2×D61—22no—
408C2×D61—22no—
409C2×D61—22no—
410C2×D61—22no—
411C2×D61—22no—
412C2×D61—22no—
413C2×D61—22no—
414C2×D61—22no—
415C2×D61—22no—
416C2×D61—416no—
417C2×D61—41no—
418C2×D61—41no—
419C2×D61—41no—
420C2×D61—41no—
421C2×D61#44914yes—
422C4×C61—41no—
423C4×C61—42no—
424C4×C61—81no—
425C4×C61—81no—
426C4×C61#54611yescharacteristic
427C4×C61#54611yescharacteristic
428C4×C61#54611yescharacteristic
429C4×C61#54611yescharacteristic
430Dic61—22no—
431Dic61—22no—
432Dic61—42no—
433Dic61—42no—
434Dic61—81no—
435Dic61—81no—
436C2×#525—611no—
437C2×#483—611no—
438C2×#480—611no—
439C2×#380—611no—
440#2036—611no—
441#2036—611no—
442#2034—611no—
443#2034D6111yescharacteristic, complemented
444#1874—611no—
445#1872—611no—
446#1854—611no—
447#1854—611no—
448#1788—611no—
449#1788—611no—
450#1779—611no—
451C2×C61—42no—
452C2×C61—82no—
453C2×C61#240511yescharacteristic
454C2×C61C2×#44911yescharacteristic
455C2×C61#300711yescharacteristic
456C2×C61#309111yescharacteristic
457C2×C61#309211yescharacteristic
458C2×C61#319011yescharacteristic
459C2×C61#319411yescharacteristic
460D61—24no—
461D61—42no—
462C22×#41—611no—
463C24×C4—611no—
464#525—1224no—
465#525—1224no—
466C2×#123—1221no—
467C2×C22⋊Q8—611no—
468C2×C22⋊Q8—611no—
469C2×#121—611no—
470C2×#121C2×D6111yescharacteristic
471C2×#120—1221no—
472C2×C4×D4—1221no—
473C2×C4×D4—1221no—
474C2×#117—611no—
475C22×C4⋊C4—611no—
476C22×C4⋊C4—611no—
477C22×C22⋊C4—1221no—
478#483—1224no—
479#480—1224no—
480C2×#107—611no—
481C2×#107—611no—
482C2×#106—611no—
483C2×#106C2×D6111yescharacteristic, complemented
484C2×#103—611no—
485C2×#103—611no—
486C2×#103—611no—
487C2×#103—611no—
488C2×#102—611no—
489C2×#102—611no—
490C2×#102C2×D6111yescharacteristic, complemented
491C2×#102C2×D6111yescharacteristic, complemented
492C2×C22⋊C8—611no—
493C2×C22⋊C8—611no—
494C2×C22⋊C8—611no—
495C2×C22⋊C8—611no—
496C2×C22⋊C8—611no—
497C2×C22⋊C8C2×D6111yescharacteristic
498#380—611no—
499#380—611no—
500#380—611no—
501#380—1221no—
502#380—1221no—
503#380C2×D6111yescharacteristic
504C2×#95—1221no—
505#340—611no—
506#340—611no—
507#340—611no—
508#340C2×D6111yescharacteristic, complemented
509C61#2400411yescharacteristic, complemented, Sylow
510C25—611no—
511C2×#41—1222no—
512C2×#41—1222no—
513C2×#41—1222no—
514C2×#41—1222no—
515C2×#41—2441no—
516C2×#41—2441no—
517C22×Q8—611no—
518C22×D4—21no—
519C22×D4—1221no—
520C22×D4—1221no—
521C22×D4C22×D6111yescharacteristic
522C23×C4—611no—
523C23×C4—611no—
524C23×C4—611no—
525C23×C4—611no—
526C23×C4—611no—
527C23×C4—1222no—
528C23×C4—1222no—
529C23×C4—1222no—
530C23×C4—1222no—
531C23×C4—1221no—
532C23×C4—1221no—
533C23×C4—1221no—
534C23×C4—2441no—
535C23×C4—2441no—
536C23×C4C22×D6111yescharacteristic
537C22×C8—611no—
538C22×C8—611no—
539C22×C8C22×D6111yescharacteristic
540C22×C8C22×D6111yescharacteristic
541#123—1228no—
542C22⋊Q8—614no—
543C22⋊Q8—1222no—
544C22⋊Q8—1222no—
545C22⋊Q8—1222no—
546#121—22no—
547#121—22no—
548#121—614no—
549#121—1222no—
550#120—1228no—
551C4×D4—1228no—
552C4×D4—1228no—
553#117—1222no—
554#117—1222no—
555C2×C4⋊C4—611no—
556C2×C4⋊C4—611no—
557C2×C4⋊C4—611no—
558C2×C4⋊C4—1222no—
559C2×C4⋊C4—1222no—
560C2×C4⋊C4—1221no—
561C2×C4⋊C4—1221no—
562C2×C4⋊C4—1221no—
563C2×C4⋊C4—1221no—
564C2×C4⋊C4—2441no—
565C2×C4⋊C4—2441no—
566C2×C4⋊C4C22×D6111yescharacteristic
567C2×C4⋊C4C22×D6111yescharacteristic
568C2×C4⋊C4C22×D6111yescharacteristic
569C2×C22⋊C4—21no—
570C2×C22⋊C4—21no—
571C2×C22⋊C4—1221no—
572C2×C22⋊C4—1221no—
573C2×C22⋊C4—1221no—
574C2×C22⋊C4—1221no—
575C2×C22⋊C4—1221no—
576C2×C22⋊C4—1221no—
577C2×C22⋊C4—1221no—
578C2×C22⋊C4—2444no—
579C2×C42—1221no—
580#107—1222no—
581#107—1222no—
582#106—22no—
583#106—1222no—
584#103—1222no—
585#103—1222no—
586#103—2441no—
587#103—2441no—
588#102—22no—
589#102—41no—
590#102—1222no—
591#102—2441no—
592C22⋊C8—41no—
593C22⋊C8—1222no—
594C22⋊C8—1222no—
595C22⋊C8—1222no—
596C22⋊C8—1222no—
597C22⋊C8—2441no—
598#95—21no—
599#95—1221no—
600#95—1221no—
601#95—1221no—
602C24—21no—
603C24—611no—
604C24—611no—
605C24—1222no—
606C24—1222no—
607C24—1222no—
608C24—1222no—
609C24—1222no—
610C24—2441no—
611C24—2441no—
612C24D4×D6111yescharacteristic
613#41—2444no—
614#41—2444no—
615#41—2444no—
616#41—2444no—
617C2×Q8—612no—
618C2×Q8—1221no—
619C2×Q8—1221no—
620C2×Q8—1221no—
621C2×Q8—1221no—
622C2×Q8—1221no—
623C2×D4—24no—
624C2×D4—21no—
625C2×D4—21no—
626C2×D4—21no—
627C2×D4—21no—
628C2×D4—21no—
629C2×D4—42no—
630C2×D4—42no—
631C2×D4—1224no—
632C2×D4—1224no—
633C2×D4—2442no—
634C2×D4—2442no—
635C2×D4—2442no—
636C2×D4—2442no—
637C2×D4D4×D6112yes—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—611no—
648C22×C4—611no—
649C22×C4—612no—
650C22×C4—612no—
651C22×C4—612no—
652C22×C4—612no—
653C22×C4—1222no—
654C22×C4—1222no—
655C22×C4—1222no—
656C22×C4—1222no—
657C22×C4—1222no—
658C22×C4—1222no—
659C22×C4—1221no—
660C22×C4—1221no—
661C22×C4—1221no—
662C22×C4—1221no—
663C22×C4—1221no—
664C22×C4—1221no—
665C22×C4—1221no—
666C22×C4—1221no—
667C22×C4—1224no—
668C22×C4—1221no—
669C22×C4—1221no—
670C22×C4—1221no—
671C22×C4—1221no—
672C22×C4—2441no—
673C22×C4—2441no—
674C22×C4—2444no—
675C22×C4—2444no—
676C22×C4—2444no—
677C22×C4—2444no—
678C22×C4—2442no—
679C22×C4—2442no—
680C22×C4—2442no—
681C22×C4—2442no—
682C22×C4—2442no—
683C22×C4—2442no—
684C22×C4—2442no—
685C22×C4—2441no—
686C22×C4—2442no—
687C22×C4D4×D6111yescharacteristic
688C22×C4C23×D6111yescharacteristic
689C2×C8—21no—
690C2×C8—21no—
691C2×C8—21no—
692C2×C8—21no—
693C2×C8—21no—
694C2×C8—21no—
695C2×C8—1221no—
696C2×C8—1221no—
697C2×C8—1221no—
698C2×C8—1221no—
699C2×C8—1221no—
700C2×C8—1221no—
701C4⋊C4—21no—
702C4⋊C4—21no—
703C4⋊C4—21no—
704C4⋊C4—21no—
705C4⋊C4—21no—
706C4⋊C4—612no—
707C4⋊C4—1224no—
708C4⋊C4—1224no—
709C4⋊C4—1221no—
710C4⋊C4—1221no—
711C4⋊C4—1221no—
712C4⋊C4—1221no—
713C4⋊C4—1221no—
714C4⋊C4—2442no—
715C4⋊C4—2442no—
716C4⋊C4D4×D6112yes—
717C22⋊C4—24no—
718C22⋊C4—42no—
719C22⋊C4—1224no—
720C22⋊C4—1224no—
721C22⋊C4—1224no—
722C22⋊C4—1224no—
723C22⋊C4—2442no—
724C22⋊C4—2442no—
725C22⋊C4—2442no—
726C42—1224no—
727C23—21no—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—21no—
732C23—21no—
733C23—22no—
734C23—41no—
735C23—41no—
736C23—41no—
737C23—41no—
738C23—41no—
739C23—41no—
740C23—612no—
741C23—612no—
742C23—612no—
743C23—612no—
744C23—1228no—
745C23—1221no—
746C23—1221no—
747C23—1221no—
748C23—1221no—
749C23—1221no—
750C23—1221no—
751C23—1221no—
752C23—1221no—
753C23—1221no—
754C23—1221no—
755C23—2444no—
756C23—2444no—
757C23—2444no—
758C23—2444no—
759C23—2444no—
760C23—2444no—
761C23#1451980612yes—
762C23C2×D4×D6111yescharacteristic
763Q8—1222no—
764Q8—1222no—
765Q8—2441no—
766Q8—2441no—
767D4—22no—
768D4—22no—
769D4—48no—
770D4—41no—
771D4—41no—
772D4—2448no—
773D4—2448no—
774C2×C4—22no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—612no—
791C2×C4—612no—
792C2×C4—1221no—
793C2×C4—1221no—
794C2×C4—1221no—
795C2×C4—1221no—
796C2×C4—1222no—
797C2×C4—1222no—
798C2×C4—1222no—
799C2×C4—1222no—
800C2×C4—1222no—
801C2×C4—1222no—
802C2×C4—1222no—
803C2×C4—1222no—
804C2×C4—1222no—
805C2×C4—1222no—
806C2×C4—4884no—
807C2×C4—4884no—
808C2×C4—2444no—
809C2×C4—2444no—
810C2×C4—2444no—
811C2×C4—2448no—
812C2×C4—2441no—
813C2×C4—2441no—
814C2×C4—2441no—
815C2×C4—2441no—
816C2×C4—2441no—
817C2×C4—2441no—
818C2×C4—2441no—
819C2×C4—2441no—
820C2×C4—2441no—
821C2×C4—2441no—
822C2×C4C2×D4×D6111yescharacteristic
823C2×C4C2×D4×D6111yescharacteristic
824C2×C4#41×D6111yescharacteristic
825C2×C4#41×D6111yescharacteristic
826C2×C4#1451982211yescharacteristic
827C2×C4#1451982311yescharacteristic
828C8—41no—
829C8—41no—
830C8—2441no—
831C8—2441no—
832C22—22no—
833C22—22no—
834C22—22no—
835C22—41no—
836C22—41no—
837C22—41no—
838C22—41no—
839C22—42no—
840C22—42no—
841C22—42no—
842C22—81no—
843C22—81no—
844C22—81no—
845C22—81no—
846C22—614no—
847C22—1222no—
848C22—1222no—
849C22—1222no—
850C22—1222no—
851C22—1222no—
852C22—1222no—
853C22—1222no—
854C22—1222no—
855C22—1222no—
856C22—24416no—
857C22—2441no—
858C22—2441no—
859C22—2441no—
860C22—2441no—
861C22#120×D6111yescharacteristic
862C22#123×D6111yescharacteristic
863C22#1684032011yescharacteristic
864C22#135×D6111yescharacteristic
865C22AGL(1,ℤ/8)×D6111yescharacteristic
866C22C2×#1451980611yescharacteristic
867C22#1684055811yescharacteristic
868C4—41no—
869C4—42no—
870C4—81no—
871C4—81no—
872C4—1222no—
873C4—1222no—
874C4—4881no—
875C4—4881no—
876C4—2442no—
877C4—2442no—
878C4#1684040111yescharacteristic
879C4#1684040411yescharacteristic
880C4#1684040511yescharacteristic
881C4#1684040911yescharacteristic
882C2—42no—
883C2—82no—
884C2—1224no—
885C2—2442no—
886C2#2144914111yescharacteristic
887C2#449×D6111yescharacteristic
888C2#2145507411yescharacteristic
889C2#2145573111yescharacteristic
890C2#2145574111yescharacteristic
891C2#2145659511yescharacteristic
892C2#2145662811yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2034C2
socleC23×C61C22×D4
prime radicalC2×#16840272C2
hypercenter#2034D61
hypocenterC61#24004
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2034

Complements

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

NH ≅ G/Ntype
2. C2×#16840094C2semidirect
3. C2×#16840074C2semidirect
4. #380×D61C2semidirect
5. #21447023C2semidirect
6. #21447022C2semidirect
7. #21447005C2semidirect
8. #21446133C2semidirect
9. #21446125C2semidirect
10. #21446021C2semidirect
11. #21446017C2semidirect
12. #21445756C2semidirect
13. #21445756C2semidirect
14. #21445728C2semidirect
15. C61×#2034C2semidirect
33. C2×#14519711C22semidirect
34. C2×#14519710C22semidirect
35. C2×#14519708C22semidirect
36. C2×#14519702C22semidirect
37. C2×#14519702C22semidirect
38. C2×#14519700C22semidirect
39. C2×#14519700C22semidirect
40. C2×#14519698C22semidirect
41. C2×#14519698C22semidirect
53. #16839525C22semidirect
54. #16839524C22semidirect
55. #16839524C22semidirect
57. C2×#106×C61C22semidirect
58. C2×#102×C61C22semidirect
59. C2×#102×C61C22semidirect
62. C61×#340C22semidirect
443. #2034D61semidirect
483. C2×#106C2×D61semidirect
490. C2×#102C2×D61semidirect
491. C2×#102C2×D61semidirect
508. #340C2×D61semidirect
509. C61#24004semidirect

Maximal subgroups

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

subgroupindex
C2×#168402722
C2×#168400942
C2×#168400742
#380×D612
#214470232
#214470222
#214470052
#214461332
#214461252
#214460212
#214460172
#214457562
#214457282
C61×#20342
#2400461