Finite Group Databasebeta

← #29718794

Subgroups — #29718794

Order 15616.

1098 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839820C211yesmaximal, characteristic, complemented
2#21451609C211yesmaximal, characteristic, complemented
3#21448401C211yesmaximal, characteristic, complemented
4#21447205C211yesmaximal, characteristic, complemented
5#21447191C211yesmaximal, characteristic, complemented
6#21447127C211yesmaximal, characteristic, complemented
7#21447127C211yesmaximal, characteristic, complemented
8#21446696C211yesmaximal, characteristic, complemented
9#21446686C211yesmaximal, characteristic, complemented
10#21446513C211yesmaximal, characteristic, complemented
11#21446499C211yesmaximal, characteristic, complemented
12#21446142C211yesmaximal, characteristic, complemented
13#21446020C211yesmaximal, characteristic, complemented
14#21445750C211yesmaximal, characteristic, complemented
15C2×C61×#447C211yesmaximal, characteristic
16C2×#14519736C2211yescharacteristic
17C2×#14519736C2211yescharacteristic
18#16839820—24no—
19C2×#14519711C2211yescharacteristic, complemented
20C2×#14519709C2211yescharacteristic, complemented
21C2×#14519706C2211yescharacteristic, complemented
22C2×#14519706C2211yescharacteristic, complemented
23C2×#14519698C2211yescharacteristic
24C2×#14519698C2211yescharacteristic
25C2×#14519698C2211yescharacteristic
26C2×#14519698C2211yescharacteristic
27C2×#14519698C2211yescharacteristic, complemented
28C2×#14519698C2211yescharacteristic, complemented
29C2×C22⋊#92418C2211yescharacteristic
30C2×#14519687C2211yescharacteristic, complemented
31C2×C8×Dic61C2211yescharacteristic, complemented
32#16839698—21no—
33#16839687—21no—
34#16839676—21no—
35#16839676—21no—
36#16839665—21no—
37#16839665—21no—
38#16839665C2211yescharacteristic
39#16839665C2211yescharacteristic
40#16839665C2211yescharacteristic
41#16839665C2211yescharacteristic
42#16839665C2211yescharacteristic, complemented
43#16839665C2211yescharacteristic, complemented
44#16839658C2211yescharacteristic, complemented
45#16839658C2211yescharacteristic, complemented
46#16839622C2211yescharacteristic
47#16839618—21no—
48#16839618—21no—
49#16839525C2211yescharacteristic, complemented
50#16839525C2211yescharacteristic, complemented
51#16839524C2211yescharacteristic, complemented
52#16839524C2211yescharacteristic, complemented
53C23×D4×C61C2211yescharacteristic
54C22×D8×C61C2211yescharacteristic
55C22×D8×C61C2211yescharacteristic
56C2×#121×C61C2211yescharacteristic
57C61×#447—24no—
58C2×#102×C61C2211yescharacteristic
59C2×#102×C61C2211yescharacteristic
60C2×C22⋊C8×C61C2211yescharacteristic
61C22×#92418C2311yescharacteristic
62C22×#92418C2311yescharacteristic
63#14519736—22no—
64#14519736—22no—
65#14519736—41no—
66#14519736—41no—
67C2×C4⋊Dic61D411yescharacteristic
68C2×C4⋊Dic61D411yescharacteristic
69C2×C4⋊Dic61C2311yescharacteristic
70C2×C4⋊Dic61C2311yescharacteristic
71C2×C4⋊Dic61C2311yescharacteristic
72C2×C4⋊Dic61C2311yescharacteristic
73C2×#11758196—21no—
74C2×#11758196—21no—
75C2×C22⋊Dic61—21no—
76C2×C22⋊Dic61—21no—
77C2×C22⋊Dic61—21no—
78C2×C22⋊Dic61—21no—
79C2×C22⋊Dic61—21no—
80C2×C22⋊Dic61—21no—
81C2×C22⋊Dic61—21no—
82C2×C22⋊Dic61—21no—
83C2×C22⋊Dic61—21no—
84C2×C22⋊Dic61—21no—
85C2×C22⋊Dic61—21no—
86C2×C22⋊Dic61—21no—
87C2×C22⋊Dic61—21no—
88C2×C22⋊Dic61—21no—
89C2×C22⋊Dic61D411yescharacteristic
90C2×C22⋊Dic61D411yescharacteristic
91C2×C4×Dic61—21no—
92C2×C4×Dic61C2311yescharacteristic
93C2×C4×Dic61C2311yescharacteristic
94#14519711—41no—
95#14519709—41no—
96#14519706—22no—
97#14519706—22no—
98#14519698—22no—
99#14519698—22no—
100#14519698—41no—
101#14519698—41no—
102#14519698—41no—
103#14519698—41no—
104C22⋊#92418—22no—
105#14519687—22no—
106C8×Dic61—22no—
107#14519684—21no—
108#14519684—21no—
109#14519684—21no—
110C25×C61—21no—
111C22×D4×C61—22no—
112C22×D4×C61—22no—
113C22×D4×C61—21no—
114C22×D4×C61—21no—
115C22×D4×C61—22no—
116C22×D4×C61—22no—
117C22×D4×C61—41no—
118C22×D4×C61—41no—
119C22×D4×C61C2311yescharacteristic
120C22×D4×C61C2311yescharacteristic
121C22×D4×C61C2311yescharacteristic
122C23×C4×C61C2311yescharacteristic
123C2×D8×C61—22no—
124C2×D8×C61—22no—
125C2×D8×C61—22no—
126C2×D8×C61—22no—
127C2×D8×C61—41no—
128C2×D8×C61—41no—
129C22×C8×C61C2311yescharacteristic
130C22×C8×C61C2311yescharacteristic
131#121×C61—22no—
132#121×C61—22no—
133C2×C4⋊C4×C61C2311yescharacteristic
134C2×C22⋊C4×C61—21no—
135#102×C61—22no—
136#102×C61—22no—
137C22⋊C8×C61D414yes—
138C24×C61—24no—
139C24×C61—21no—
140C24×C61—21no—
141C24×C61—21no—
142C24×C61—42no—
143C24×C61—42no—
144C24×C61—81no—
145C24×C61—81no—
146C24×C61—81no—
147C24×C61—81no—
148C24×C61C2×D411yescharacteristic
149C2×D4×C61—24no—
150C2×D4×C61—21no—
151C2×D4×C61—21no—
152C2×D4×C61—21no—
153C2×D4×C61—21no—
154C2×D4×C61—21no—
155C2×D4×C61—21no—
156C2×D4×C61—21no—
157C2×D4×C61—21no—
158C2×D4×C61—21no—
159C2×D4×C61—21no—
160C2×D4×C61—21no—
161C2×D4×C61—21no—
162C2×D4×C61—21no—
163C2×D4×C61—21no—
164C2×D4×C61—21no—
165C2×D4×C61—21no—
166C2×D4×C61—44no—
167C2×D4×C61—44no—
168C2×D4×C61—44no—
169C2×D4×C61—44no—
170C2×D4×C61—42no—
171C2×D4×C61—42no—
172C2×D4×C61—42no—
173C2×D4×C61—81no—
174C2×D4×C61—81no—
175C2×D4×C61#4112yes—
176C2×D4×C61#4112yes—
177C22×C4×C61—21no—
178C22×C4×C61—21no—
179C22×C4×C61—21no—
180C22×C4×C61—21no—
181C22×C4×C61—21no—
182C22×C4×C61C2×D411yescharacteristic
183C22×C4×C61C2×D412yes—
184C22×C4×C61#4112yes—
185C22×C4×C61C2411yescharacteristic
186C22×Dic61—21no—
187C22×Dic61—21no—
188C22×Dic61—21no—
189C22×Dic61—21no—
190C22×Dic61C2×D411yescharacteristic
191C22×Dic61C2×D411yescharacteristic
192C22×Dic61C2×D411yescharacteristic
193C22×Dic61C2×D411yescharacteristic
194D8×C61—44no—
195D8×C61—44no—
196C2×C8×C61—21no—
197C2×C8×C61—21no—
198C2×C8×C61—21no—
199C2×C8×C61—21no—
200C2×C8×C61C2×D412yes—
201C2×C8×C61C2×D412yes—
202C4⋊C4×C61—21no—
203C4⋊C4×C61—21no—
204C22⋊C4×C61—42no—
205C22⋊Dic61—22no—
206C22⋊Dic61—22no—
207C22⋊Dic61—42no—
208C22⋊Dic61—81no—
209C22⋊Dic61—81no—
210C22⋊Dic61—81no—
211C22⋊Dic61—81no—
212C22⋊Dic61—81no—
213C22⋊Dic61—81no—
214C22⋊Dic61—81no—
215C22⋊Dic61—81no—
216C22⋊Dic61—81no—
217C22⋊Dic61—81no—
218C22⋊Dic61—81no—
219C22⋊Dic61—81no—
220C22⋊Dic61—81no—
221C4⋊Dic61—22no—
222C4⋊Dic61—22no—
223C4⋊Dic61—21no—
224C4⋊Dic61—21no—
225C4⋊Dic61—21no—
226C4⋊Dic61—21no—
227C4⋊Dic61—21no—
228C4⋊Dic61—21no—
229C4⋊Dic61—21no—
230C4⋊Dic61—21no—
231#11758196—81no—
232#11758196—81no—
233C4×Dic61—21no—
234C4×Dic61—21no—
235C4×Dic61—21no—
236C4×Dic61—21no—
237C4×Dic61—42no—
238C2×#92418—21no—
239C2×#92418—21no—
240C2×#92418—21no—
241C2×#92418—21no—
242C2×#92418—21no—
243C2×#92418—21no—
244C23×C61—21no—
245C23×C61—21no—
246C23×C61—21no—
247C23×C61—21no—
248C23×C61—21no—
249C23×C61—21no—
250C23×C61—22no—
251C23×C61—22no—
252C23×C61—48no—
253C23×C61—41no—
254C23×C61—41no—
255C23×C61—41no—
256C23×C61—41no—
257C23×C61—41no—
258C23×C61—41no—
259C23×C61—41no—
260C23×C61—41no—
261C23×C61—41no—
262C23×C61—41no—
263C23×C61—41no—
264C23×C61—41no—
265C23×C61—41no—
266C23×C61—41no—
267C23×C61—41no—
268C23×C61—41no—
269C23×C61—41no—
270C23×C61—41no—
271C23×C61—41no—
272C23×C61—84no—
273C23×C61—84no—
274C23×C61—84no—
275C23×C61—84no—
276C23×C61—84no—
277C23×C61—84no—
278C23×C61#12112yes—
279C23×C61C22×D411yescharacteristic
280D4×C61—22no—
281D4×C61—22no—
282D4×C61—22no—
283D4×C61—22no—
284D4×C61—48no—
285D4×C61—41no—
286D4×C61—41no—
287D4×C61—41no—
288D4×C61—41no—
289D4×C61—41no—
290D4×C61—41no—
291D4×C61—41no—
292D4×C61—41no—
293D4×C61—84no—
294C2×C4×C61—21no—
295C2×C4×C61—21no—
296C2×C4×C61—22no—
297C2×C4×C61—22no—
298C2×C4×C61—22no—
299C2×C4×C61—22no—
300C2×C4×C61—41no—
301C2×C4×C61—41no—
302C2×C4×C61—41no—
303C2×C4×C61#12112yes—
304C2×C4×C61C22×D411yescharacteristic
305C2×C4×C61C2×#4111yescharacteristic
306C2×C4×C61C2×#4111yescharacteristic
307C2×C4×C61C2×#4111yescharacteristic
308C2×C4×C61H(5,𝔽2)11yescharacteristic
309C2×C4×C61H(5,𝔽2)11yescharacteristic
310C2×Dic61—21no—
311C2×Dic61—21no—
312C2×Dic61—21no—
313C2×Dic61—21no—
314C2×Dic61—21no—
315C2×Dic61—21no—
316C2×Dic61—21no—
317C2×Dic61—21no—
318C2×Dic61—21no—
319C2×Dic61—21no—
320C2×Dic61—21no—
321C2×Dic61—21no—
322C2×Dic61—41no—
323C2×Dic61—41no—
324C2×Dic61—41no—
325C2×Dic61—41no—
326C2×Dic61—41no—
327C2×Dic61—41no—
328C2×Dic61—41no—
329C2×Dic61—41no—
330C2×Dic61—41no—
331C2×Dic61—41no—
332C2×Dic61—41no—
333C2×Dic61—41no—
334C8×C61—22no—
335C8×C61—22no—
336#92418—41no—
337#92418—41no—
338#24512—611nomaximal, Sylow
339C22×C61—22no—
340C22×C61—22no—
341C22×C61—22no—
342C22×C61—41no—
343C22×C61—41no—
344C22×C61—41no—
345C22×C61—41no—
346C22×C61—42no—
347C22×C61—42no—
348C22×C61—42no—
349C22×C61—42no—
350C22×C61—42no—
351C22×C61—42no—
352C22×C61—816no—
353C22×C61—81no—
354C22×C61—81no—
355C22×C61—81no—
356C22×C61—81no—
357C22×C61—81no—
358C22×C61—81no—
359C22×C61—81no—
360C22×C61—81no—
361C22×C61—81no—
362C22×C61—81no—
363C22×C61—81no—
364C22×C61—81no—
365C22×C61—81no—
366C22×C61—81no—
367C22×C61—81no—
368C22×C61C2×#12111yescharacteristic
369C22×C61#52511yescharacteristic
370C22×C61#53511yescharacteristic
371C22×C61#57611yescharacteristic
372C22×C61#57611yescharacteristic
373C22×C61#57611yescharacteristic
374C22×C61#57711yescharacteristic
375C4×C61—22no—
376C4×C61—81no—
377C4×C61#54611yescharacteristic
378C4×C61#54611yescharacteristic
379C4×C61#55111yescharacteristic
380C4×C61#55111yescharacteristic
381Dic61—41no—
382Dic61—41no—
383Dic61—41no—
384Dic61—41no—
385Dic61—81no—
386Dic61—81no—
387Dic61—81no—
388Dic61—81no—
389C2×#447D6111yescharacteristic
390C2×#433—611no—
391#2624—611no—
392#2309—611no—
393#2067—611no—
394#2065—611no—
395#2054—611no—
396#2054—611no—
397#1972—611no—
398#1970—611no—
399#1936—611no—
400#1934—611no—
401#1875—611no—
402#1854—611no—
403#1786—611no—
404C2×C61—42no—
405C2×C61—82no—
406C2×C61—82no—
407C2×C61—161no—
408C2×C61#241111yescharacteristic
409C2×C61#305811yescharacteristic
410C2×C61#306211yescharacteristic
411C2×C61#311811yescharacteristic
412C2×C61#312211yescharacteristic
413C2×C61#322011yescharacteristic
414C2×C61#322411yescharacteristic
415C23×D4C2×D6111yescharacteristic
416C22×D8C2×D6111yescharacteristic
417C22×D8C2×D6111yescharacteristic
418C2×#121C2×D6111yescharacteristic
419C2×#117—611no—
420C2×#117—611no—
421#447—24no—
422#433—1224no—
423C2×#107—611no—
424C2×#106—611no—
425C2×C4⋊C8—611no—
426C2×C4⋊C8—611no—
427C2×#102—611no—
428C2×#102—611no—
429C2×#102—611no—
430C2×#102—611no—
431C2×#102—611no—
432C2×#102—611no—
433C2×#102C2×D6111yescharacteristic
434C2×#102C2×D6111yescharacteristic
435C2×C22⋊C8—611no—
436C2×C22⋊C8C2×D6111yescharacteristic
437C2×#97—611no—
438C2×C4×C8—611no—
439#399—1221no—
440#397—1221no—
441#394—1221no—
442#394—1221no—
443#390—611no—
444#390—611no—
445#390—611no—
446#390—611no—
447#390—611no—
448#390—611no—
449#390—1221no—
450#390—1221no—
451#389—611no—
452#389—611no—
453#380—611no—
454#379—1221no—
455#379—1221no—
456#340—611no—
457#340—611no—
458#340—611no—
459#340—611no—
460C61#2451211yescharacteristic, complemented, Sylow
461C25—21no—
462C22×D4—22no—
463C22×D4—22no—
464C22×D4—21no—
465C22×D4—21no—
466C22×D4—22no—
467C22×D4—22no—
468C22×D4—41no—
469C22×D4—41no—
470C22×D4C22×D6111yescharacteristic
471C22×D4C22×D6111yescharacteristic
472C22×D4C22×D6111yescharacteristic
473C23×C4C22×D6111yescharacteristic
474C2×D8—22no—
475C2×D8—22no—
476C2×D8—22no—
477C2×D8—22no—
478C2×D8—41no—
479C2×D8—41no—
480C22×C8—611no—
481C22×C8—611no—
482C22×C8C22×D6111yescharacteristic
483C22×C8C22×D6111yescharacteristic
484#121—22no—
485#121—22no—
486#117—1222no—
487#117—1222no—
488#117—2441no—
489#117—2441no—
490C2×C4⋊C4—611no—
491C2×C4⋊C4—611no—
492C2×C4⋊C4—611no—
493C2×C4⋊C4—611no—
494C2×C4⋊C4—611no—
495C2×C4⋊C4—611no—
496C2×C4⋊C4—1221no—
497C2×C4⋊C4—1221no—
498C2×C4⋊C4C22×D6111yescharacteristic
499C2×C22⋊C4—21no—
500C2×C22⋊C4—611no—
501C2×C22⋊C4—611no—
502C2×C22⋊C4—1221no—
503C2×C22⋊C4—1221no—
504C2×C22⋊C4—1221no—
505C2×C22⋊C4—1221no—
506C2×C22⋊C4—1221no—
507C2×C22⋊C4—1221no—
508C2×C22⋊C4—1221no—
509C2×C22⋊C4—1221no—
510C2×C22⋊C4—1221no—
511C2×C22⋊C4—1221no—
512C2×C22⋊C4—1221no—
513C2×C22⋊C4—1221no—
514C2×C22⋊C4—1221no—
515C2×C22⋊C4—1221no—
516C2×C42—611no—
517C2×C42—611no—
518C2×C42—1221no—
519#107—2441no—
520#106—2441no—
521C4⋊C8—1222no—
522C4⋊C8—1222no—
523#102—22no—
524#102—22no—
525#102—1222no—
526#102—1222no—
527#102—2441no—
528#102—2441no—
529#102—2441no—
530#102—2441no—
531C22⋊C8—1222no—
532C22⋊C8C22⋊D6114yes—
533#97—1222no—
534C4×C8—1222no—
535#95—1221no—
536#95—1221no—
537#95—1221no—
538C24—24no—
539C24—21no—
540C24—21no—
541C24—21no—
542C24—42no—
543C24—42no—
544C24—81no—
545C24—81no—
546C24—81no—
547C24—81no—
548C24D4×D6111yescharacteristic
549C2×D4—24no—
550C2×D4—21no—
551C2×D4—21no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4—21no—
557C2×D4—21no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—44no—
567C2×D4—44no—
568C2×D4—44no—
569C2×D4—44no—
570C2×D4—42no—
571C2×D4—42no—
572C2×D4—42no—
573C2×D4—81no—
574C2×D4—81no—
575C2×D4#1175822412yes—
576C2×D4#1175822412yes—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—611no—
583C22×C4—611no—
584C22×C4—611no—
585C22×C4—611no—
586C22×C4—1221no—
587C22×C4—1221no—
588C22×C4—1221no—
589C22×C4—1221no—
590C22×C4D4×D6111yescharacteristic
591C22×C4#1175822412yes—
592C22×C4C2×C22⋊D6112yes—
593C22×C4C23×D6111yescharacteristic
594D8—44no—
595D8—44no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8—1221no—
601C2×C8—1221no—
602C2×C8—1221no—
603C2×C8—1221no—
604C2×C8—1221no—
605C2×C8—1221no—
606C2×C8C2×C22⋊D6112yes—
607C2×C8C2×C22⋊D6112yes—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—1222no—
611C4⋊C4—1222no—
612C4⋊C4—1221no—
613C4⋊C4—1221no—
614C4⋊C4—1221no—
615C4⋊C4—1221no—
616C4⋊C4—1221no—
617C4⋊C4—1221no—
618C4⋊C4—1221no—
619C4⋊C4—1221no—
620C4⋊C4—4881no—
621C4⋊C4—4881no—
622C22⋊C4—42no—
623C22⋊C4—1222no—
624C22⋊C4—1222no—
625C22⋊C4—4881no—
626C22⋊C4—4881no—
627C22⋊C4—4881no—
628C22⋊C4—4881no—
629C22⋊C4—4881no—
630C22⋊C4—4881no—
631C22⋊C4—4881no—
632C22⋊C4—4881no—
633C22⋊C4—4881no—
634C22⋊C4—4881no—
635C22⋊C4—4881no—
636C22⋊C4—4881no—
637C22⋊C4—4881no—
638C22⋊C4—2442no—
639C42—1221no—
640C42—1221no—
641C42—1221no—
642C42—1221no—
643C42—2442no—
644C23—21no—
645C23—21no—
646C23—21no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—22no—
651C23—22no—
652C23—48no—
653C23—41no—
654C23—41no—
655C23—41no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23—41no—
672C23—84no—
673C23—84no—
674C23—84no—
675C23—84no—
676C23—84no—
677C23—84no—
678C23#1451974812yes—
679C23C2×D4×D6111yescharacteristic
680D4—22no—
681D4—22no—
682D4—22no—
683D4—22no—
684D4—48no—
685D4—41no—
686D4—41no—
687D4—41no—
688D4—41no—
689D4—41no—
690D4—41no—
691D4—41no—
692D4—41no—
693D4—84no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—1221no—
704C2×C4—1221no—
705C2×C4—1221no—
706C2×C4—1221no—
707C2×C4—1221no—
708C2×C4—1221no—
709C2×C4—1221no—
710C2×C4—1221no—
711C2×C4—1221no—
712C2×C4—1221no—
713C2×C4—1221no—
714C2×C4—1221no—
715C2×C4—2441no—
716C2×C4—2441no—
717C2×C4—2441no—
718C2×C4—2441no—
719C2×C4—2441no—
720C2×C4—2441no—
721C2×C4—2441no—
722C2×C4—2441no—
723C2×C4—2441no—
724C2×C4—2441no—
725C2×C4—2441no—
726C2×C4—2441no—
727C2×C4#1451974812yes—
728C2×C4C22×C22⋊D6111yescharacteristic
729C2×C4C2×#1175822411yescharacteristic
730C2×C4C2×#1175822411yescharacteristic
731C2×C4C2×#1175822411yescharacteristic
732C2×C4#1451982211yescharacteristic
733C2×C4#1451982211yescharacteristic
734C8—22no—
735C8—22no—
736C8—2441no—
737C8—2441no—
738C22—22no—
739C22—22no—
740C22—22no—
741C22—41no—
742C22—41no—
743C22—41no—
744C22—41no—
745C22—42no—
746C22—42no—
747C22—42no—
748C22—42no—
749C22—42no—
750C22—42no—
751C22—816no—
752C22—81no—
753C22—81no—
754C22—81no—
755C22—81no—
756C22—81no—
757C22—81no—
758C22—81no—
759C22—81no—
760C22—81no—
761C22—81no—
762C22—81no—
763C22—81no—
764C22—81no—
765C22—81no—
766C22—81no—
767C22C2×#1451974811yescharacteristic
768C22#1684026811yescharacteristic
769C22#1684032711yescharacteristic
770C22#1684056311yescharacteristic
771C22#1684056311yescharacteristic
772C22#1684056611yescharacteristic
773C22#1684057211yescharacteristic
774C4—22no—
775C4—81no—
776C4—4881no—
777C4—4881no—
778C4—4881no—
779C4—4881no—
780C4—2441no—
781C4—2441no—
782C4—2441no—
783C4—2441no—
784C4#1684040611yescharacteristic
785C4#1684040611yescharacteristic
786C4#1684044311yescharacteristic
787C4#1684044311yescharacteristic
788C2—42no—
789C2—82no—
790C2—82no—
791C2—161no—
792C2#2144920011yescharacteristic
793C2#2145546311yescharacteristic
794C2#2145549311yescharacteristic
795C2#2145599611yescharacteristic
796C2#2145605611yescharacteristic
797C2#2145686511yescharacteristic
798C2#2145690911yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
Fitting, prime radicalC2×C61×#447C2
socleC23×C61C22×D4
hypercenterC2×#447D61
hypocenterC61#24512
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#447

Complements

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

NH ≅ G/Ntype
1. C2×#16839820C2semidirect
2. #21451609C2semidirect
3. #21448401C2semidirect
4. #21447205C2semidirect
5. #21447191C2semidirect
6. #21447127C2semidirect
7. #21447127C2semidirect
8. #21446696C2semidirect
9. #21446686C2semidirect
10. #21446513C2semidirect
11. #21446499C2semidirect
12. #21446142C2semidirect
13. #21446020C2semidirect
14. #21445750C2semidirect
19. C2×#14519711C22semidirect
20. C2×#14519709C22semidirect
21. C2×#14519706C22semidirect
22. C2×#14519706C22semidirect
27. C2×#14519698C22semidirect
28. C2×#14519698C22semidirect
30. C2×#14519687C22semidirect
31. C2×C8×Dic61C22semidirect
42. #16839665C22semidirect
43. #16839665C22semidirect
44. #16839658C22semidirect
45. #16839658C22semidirect
49. #16839525C22semidirect
50. #16839525C22semidirect
51. #16839524C22semidirect
52. #16839524C22semidirect
460. C61#24512semidirect

Maximal subgroups

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

subgroupindex
C2×#168398202
#214516092
#214484012
#214472052
#214471912
#214471272
#214466962
#214466862
#214465132
#214464992
#214461422
#214460202
#214457502
C2×C61×#4472
#2451261