Finite Group Databasebeta

← #29722392

Subgroups — #29722392

Order 15616.

1076 conjugacy classes of subgroups.

The subgroup lattice has 802 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840012C211yesmaximal, characteristic, complemented
2C2×#16839838C211yesmaximal, characteristic, complemented
3C2×#16839804C211yesmaximal, characteristic, complemented
4#21449260C211yesmaximal, characteristic, complemented
5#21449238C211yesmaximal, characteristic, complemented
6#21447205C211yesmaximal, characteristic, complemented
7#21447191C211yesmaximal, characteristic, complemented
8#21447007C211yesmaximal, characteristic, complemented
9#21447000C211yesmaximal, characteristic, complemented
10#21446686C211yesmaximal, characteristic, complemented
11#21446545C211yesmaximal, characteristic, complemented
12#21446142C211yesmaximal, characteristic, complemented
13#21446137C211yesmaximal, characteristic, complemented
14#21445849C211yesmaximal, characteristic, complemented
15C2×C61×#469C211yesmaximal, characteristic, complemented
16C22×#11758189C2211yescharacteristic
17C2×#14519749—21no—
18C2×#14519748C2211yescharacteristic
19C2×#14519748C2211yescharacteristic
20C2×C4×C22⋊D61C2211yescharacteristic
21C2×#14519736C2211yescharacteristic
22C22×C4⋊Dic61C2211yescharacteristic
23#16840012—24no—
24#16839838—24no—
25#16839804—24no—
26C2×#14519711C2211yescharacteristic
27C2×#14519711C2211yescharacteristic
28C2×#14519709C2211yescharacteristic
29C2×#14519709C2211yescharacteristic
30C2×#14519706C2211yescharacteristic
31C2×#14519698C2211yescharacteristic
32C2×#14519698C2211yescharacteristic
33C2×#14519698C2211yescharacteristic
34C2×#14519698C2211yescharacteristic
35C2×C22⋊#92418C2211yescharacteristic
36C2×#14519689C2211yescharacteristic
37C2×C8×Dic61C2211yescharacteristic
38#16839685—21no—
39#16839678—21no—
40#16839676—21no—
41#16839670—21no—
42#16839665C2211yescharacteristic
43#16839665C2211yescharacteristic
44#16839662—21no—
45#16839658C2211yescharacteristic
46#16839658C2211yescharacteristic
47#16839656—21no—
48#16839642—21no—
49#16839619C2211yescharacteristic
50#16839619C2211yescharacteristic
51#16839524C2211yescharacteristic
52#16839524C2211yescharacteristic
53#16839524C2211yescharacteristic
54#16839524C2211yescharacteristic
55C22×D8×C61C2211yescharacteristic
56C22×M16×C61C2211yescharacteristic
57C2×#121×C61C2211yescharacteristic
58C2×#121×C61C2211yescharacteristic
59C61×#469—24no—
60C2×#106×C61C2211yescharacteristic
61C2×#102×C61C2211yescharacteristic
62C2×#102×C61C2211yescharacteristic
63C22×C22⋊D61—21no—
64C22×C22⋊D61—21no—
65C22×C22⋊D61D411yescharacteristic
66C23×Dic61—21no—
67C22×C4×D61C2311yescharacteristic
68C2×#11758189—22no—
69C2×#11758189—22no—
70C2×#11758189—22no—
71C22×#92418C2311yescharacteristic
72C22×#92418C2311yescharacteristic
73#14519749—44no—
74#14519748—22no—
75#14519748—22no—
76#14519748—41no—
77#14519748—41no—
78C4×C22⋊D61—22no—
79C4×C22⋊D61—22no—
80#14519736—22no—
81#14519736—41no—
82C2×C4⋊Dic61—22no—
83C2×C4⋊Dic61—21no—
84C2×C4⋊Dic61—41no—
85C2×C4⋊Dic61C2311yescharacteristic
86C2×C4⋊Dic61C2311yescharacteristic
87C2×C4⋊Dic61C2311yescharacteristic
88C2×C4⋊Dic61C2311yescharacteristic
89C2×#11758196—21no—
90C2×#11758196—21no—
91C2×#11758196D411yescharacteristic
92C2×C22⋊Dic61—21no—
93C2×C22⋊Dic61—21no—
94C2×C22⋊Dic61—21no—
95C2×C22⋊Dic61—21no—
96C2×C22⋊Dic61—21no—
97C2×C22⋊Dic61—21no—
98C2×C22⋊Dic61—21no—
99C2×C22⋊Dic61D411yescharacteristic
100C2×#11758198—21no—
101C2×#11758198—21no—
102C2×#11758198D411yescharacteristic
103C2×C4×Dic61—21no—
104C2×C4×Dic61C2311yescharacteristic
105#14519711—22no—
106#14519711—22no—
107#14519709—22no—
108#14519709D414yescomplemented
109#14519706—22no—
110#14519698—22no—
111#14519698—22no—
112#14519698—41no—
113#14519698—41no—
114C22⋊#92418—22no—
115#14519689—22no—
116C8×Dic61—22no—
117#14519684—21no—
118#14519684—21no—
119#14519684—21no—
120#14519684—21no—
121C22×D4×C61—21no—
122C22×D4×C61—21no—
123C22×D4×C61C2311yescharacteristic
124C22×D4×C61C2311yescharacteristic
125C23×C4×C61C2311yescharacteristic
126C2×D8×C61—22no—
127C2×D8×C61—22no—
128C2×D8×C61—22no—
129C2×M16×C61—22no—
130C2×M16×C61—22no—
131C2×M16×C61D414yescomplemented
132C22×C8×C61C2311yescharacteristic
133C22×C8×C61C2311yescharacteristic
134#121×C61—22no—
135#121×C61—22no—
136#121×C61—22no—
137#121×C61—22no—
138C2×C4⋊C4×C61C2311yescharacteristic
139C2×C4⋊C4×C61C2311yescharacteristic
140C2×C22⋊C4×C61—21no—
141C2×C22⋊C4×C61—21no—
142#106×C61—22no—
143#102×C61—22no—
144#102×C61—22no—
145C24×C61—21no—
146C24×C61—21no—
147C24×C61C2×D411yescharacteristic
148C23×D61C2×D411yescharacteristic
149C2×D4×C61—21no—
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—42no—
162C2×D4×C61—42no—
163C2×D4×C61—42no—
164C2×D4×C61—42no—
165C2×D4×C61—81no—
166C2×D4×C61—81no—
167C22×C4×C61—21no—
168C22×C4×C61—21no—
169C22×C4×C61—21no—
170C22×C4×C61—21no—
171C22×C4×C61—21no—
172C22×C4×C61—21no—
173C22×C4×C61C2×D411yescharacteristic
174C22×C4×C61C2×D412yes—
175C22×C4×C61#4112yes—
176C22×C4×C61C2411yescharacteristic
177C2×C22⋊D61—22no—
178C2×C22⋊D61—22no—
179C2×C22⋊D61—41no—
180C2×C22⋊D61—42no—
181C2×C22⋊D61—42no—
182C2×C22⋊D61—42no—
183C2×C22⋊D61—42no—
184C2×C22⋊D61—81no—
185C2×C22⋊D61—81no—
186C22×Dic61—21no—
187C22×Dic61—21no—
188C22×Dic61—21no—
189C22×Dic61—21no—
190C22×Dic61—42no—
191C22×Dic61—42no—
192C22×Dic61—81no—
193C22×Dic61C2×D411yescharacteristic
194C22×Dic61C2×D411yescharacteristic
195C22×Dic61C2×D411yescharacteristic
196C2×C4×D61—21no—
197C2×C4×D61—21no—
198C2×C4×D61—21no—
199C2×C4×D61—21no—
200C2×C4×D61—21no—
201C2×C4×D61—21no—
202D8×C61—44no—
203M16×C61—28no—
204C2×C8×C61—21no—
205C2×C8×C61—21no—
206C2×C8×C61C2×D412yes—
207C2×C8×C61C2×D412yes—
208C2×C8×C61C2×D412yes—
209C2×C8×C61#4112yes—
210C4⋊C4×C61—21no—
211C4⋊C4×C61—21no—
212C4⋊C4×C61—21no—
213C4⋊C4×C61—21no—
214C22⋊C4×C61—42no—
215C22⋊C4×C61—42no—
216C22⋊Dic61—22no—
217C22⋊Dic61—42no—
218C22⋊Dic61—42no—
219C22⋊Dic61—42no—
220C22⋊Dic61—42no—
221C22⋊Dic61—42no—
222C22⋊Dic61—81no—
223C22⋊Dic61—81no—
224#11758198—22no—
225#11758198—42no—
226#11758198—81no—
227C4⋊Dic61—21no—
228C4⋊Dic61—21no—
229C4⋊Dic61—21no—
230C4⋊Dic61—21no—
231C4⋊Dic61—21no—
232C4⋊Dic61—21no—
233C4⋊Dic61—42no—
234C4⋊Dic61C2×D412yes—
235C4⋊Dic61C2×D412yes—
236#11758196—22no—
237#11758196—42no—
238#11758196—81no—
239C4×Dic61—21no—
240C4×Dic61—21no—
241C4×Dic61—42no—
242C2×#92418—21no—
243C2×#92418—21no—
244C2×#92418—21no—
245C2×#92418—21no—
246C2×#92418—21no—
247C2×#92418—21no—
248#11758189—44no—
249C23×C61—21no—
250C23×C61—21no—
251C23×C61—21no—
252C23×C61—21no—
253C23×C61—21no—
254C23×C61—21no—
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#12112yes—
270C23×C61C22×D411yescharacteristic
271C22×D61—21no—
272C22×D61—21no—
273C22×D61—21no—
274C22×D61—21no—
275C22×D61—21no—
276C22×D61—21no—
277C22×D61—21no—
278D4×C61—41no—
279D4×C61—41no—
280D4×C61—41no—
281D4×C61—41no—
282D4×C61—41no—
283D4×C61—41no—
284D4×C61—41no—
285D4×C61—41no—
286D4×C61—84no—
287D4×C61—84no—
288C2×C4×C61—21no—
289C2×C4×C61—21no—
290C2×C4×C61—22no—
291C2×C4×C61—22no—
292C2×C4×C61—22no—
293C2×C4×C61—22no—
294C2×C4×C61—41no—
295C2×C4×C61—41no—
296C2×C4×C61—41no—
297C2×C4×C61—41no—
298C2×C4×C61—41no—
299C2×C4×C61—41no—
300C2×C4×C61#12112yes—
301C2×C4×C61C22×D411yescharacteristic
302C2×C4×C61C22×D411yescharacteristic
303C2×C4×C61C2×#4111yescharacteristic
304C2×C4×C61C2×#4111yescharacteristic
305C2×C4×C61H(5,𝔽2)11yescharacteristic
306C2×C4×C612−1+411yescharacteristic
307C22⋊D61—44no—
308C22⋊D61—84no—
309C22⋊D61—84no—
310C2×Dic61—21no—
311C2×Dic61—21no—
312C2×Dic61—21no—
313C2×Dic61—21no—
314C2×Dic61—22no—
315C2×Dic61—22no—
316C2×Dic61—21no—
317C2×Dic61—21no—
318C2×Dic61—21no—
319C2×Dic61—21no—
320C2×Dic61—41no—
321C2×Dic61—41no—
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—84no—
331C2×Dic61AGL(1,ℤ/8)12yes—
332C4×D61—41no—
333C4×D61—41no—
334C4×D61—41no—
335C4×D61—41no—
336C8×C61—22no—
337C8×C61#12114yescomplemented
338#92418—41no—
339#92418—41no—
340#24792—611nomaximal, Sylow
341C22×C61—22no—
342C22×C61—22no—
343C22×C61—22no—
344C22×C61—41no—
345C22×C61—41no—
346C22×C61—41no—
347C22×C61—41no—
348C22×C61—81no—
349C22×C61—81no—
350C22×C61—81no—
351C22×C61—81no—
352C22×C61—81no—
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×C61C2×#12111yescharacteristic
363C22×C61D4211yescharacteristic
364C22×C61#54711yescharacteristic
365C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
366C22×C61#57511yescharacteristic
367C22×C61#57611yescharacteristic
368C22×C61#57711yescharacteristic
369C2×D61—41no—
370C2×D61—41no—
371C2×D61—41no—
372C2×D61—41no—
373C2×D61—41no—
374C2×D61—41no—
375C2×D61—41no—
376C4×C61—22no—
377C4×C61—81no—
378C4×C61—81no—
379C4×C61C2×#12111yescharacteristic
380C4×C61#53711yescharacteristic
381C4×C61#54811yescharacteristic
382C4×C61#55311yescharacteristic
383Dic61—22no—
384Dic61—41no—
385Dic61—42no—
386Dic61—42no—
387Dic61—41no—
388Dic61—81no—
389Dic61—81no—
390C2×#469—611no—
391C2×#469D6111yescharacteristic, complemented
392C2×#436—611no—
393C2×#428—611no—
394#2416—611no—
395#2414—611no—
396#2067—611no—
397#2065—611no—
398#2034—611no—
399#2033—611no—
400#1970—611no—
401#1941—611no—
402#1875—611no—
403#1874—611no—
404#1809—611no—
405C2×C61—42no—
406C2×C61—161no—
407C2×C61—161no—
408C2×C61#241611yescharacteristic
409C2×C61#305511yescharacteristic
410C2×C61#306211yescharacteristic
411C2×C61#327411yescharacteristic
412C2×C61#327511yescharacteristic
413C2×C61#335411yescharacteristic
414C2×C61#335511yescharacteristic
415D61—81no—
416C22×D8C2×D6111yescharacteristic
417C22×M16—611no—
418C22×M16C2×D6111yescharacteristic
419C2×#121—611no—
420C2×#121—611no—
421C2×#121—1221no—
422C2×#121C2×D6111yescharacteristic
423C2×#121C2×D6111yescharacteristic
424C2×C4×D4—611no—
425C2×#117—611no—
426C22×C4⋊C4—611no—
427#469—24no—
428#469—1224no—
429#436—1224no—
430#428—1224no—
431C2×#107—611no—
432C2×#107—611no—
433C2×#106—611no—
434C2×#106—611no—
435C2×#106C2×D6111yescharacteristic
436C2×C4⋊C8—611no—
437C2×#102—611no—
438C2×#102—611no—
439C2×#102—611no—
440C2×#102—611no—
441C2×#102C2×D6111yescharacteristic
442C2×#102C2×D6111yescharacteristic
443C2×C22⋊C8—611no—
444C2×C22⋊C8—611no—
445C2×C4×C8—611no—
446#396—1221no—
447#394—1221no—
448#394—1221no—
449#392—1221no—
450#390—611no—
451#390—611no—
452#390—1221no—
453#389—611no—
454#389—611no—
455#388—1221no—
456#386—1221no—
457#380—611no—
458#380—611no—
459#340—611no—
460#340—611no—
461#340—611no—
462#340—611no—
463C61#2479211yescharacteristic, complemented, Sylow
464C22×D4—21no—
465C22×D4—21no—
466C22×D4—611no—
467C22×D4—1221no—
468C22×D4—1221no—
469C22×D4C22×D6111yescharacteristic
470C22×D4C22×D6111yescharacteristic
471C23×C4—611no—
472C23×C4—1221no—
473C23×C4C22×D6111yescharacteristic
474C2×D8—22no—
475C2×D8—22no—
476C2×D8—22no—
477C2×M16—22no—
478C2×M16—22no—
479C2×M16—1222no—
480C2×M16—1222no—
481C2×M16—1222no—
482C2×M16C22⋊D6114yescomplemented
483C22×C8—611no—
484C22×C8—611no—
485C22×C8C22×D6111yescharacteristic
486C22×C8C22×D6111yescharacteristic
487#121—22no—
488#121—22no—
489#121—22no—
490#121—22no—
491#121—1222no—
492#121—1222no—
493#121—2441no—
494#121—2441no—
495#121—2444no—
496C4×D4—1222no—
497C4×D4—1222no—
498#117—1222no—
499#117—2441no—
500C2×C4⋊C4—611no—
501C2×C4⋊C4—611no—
502C2×C4⋊C4—611no—
503C2×C4⋊C4—611no—
504C2×C4⋊C4—611no—
505C2×C4⋊C4—1222no—
506C2×C4⋊C4—1221no—
507C2×C4⋊C4—1221no—
508C2×C4⋊C4—1221no—
509C2×C4⋊C4—2441no—
510C2×C4⋊C4C22×D6111yescharacteristic
511C2×C4⋊C4C22×D6111yescharacteristic
512C2×C22⋊C4—21no—
513C2×C22⋊C4—21no—
514C2×C22⋊C4—611no—
515C2×C22⋊C4—611no—
516C2×C22⋊C4—1221no—
517C2×C22⋊C4—1221no—
518C2×C22⋊C4—1221no—
519C2×C22⋊C4—1221no—
520C2×C22⋊C4—1221no—
521C2×C22⋊C4—1221no—
522C2×C22⋊C4—1221no—
523C2×C22⋊C4—1221no—
524C2×C22⋊C4—1221no—
525C2×C42—611no—
526C2×C42—1221no—
527#107—1222no—
528#107—1222no—
529#106—22no—
530#106—614no—
531#106—1222no—
532C4⋊C8—1222no—
533#102—22no—
534#102—22no—
535#102—1222no—
536#102—1222no—
537#102—2441no—
538#102—2441no—
539C22⋊C8—1222no—
540C22⋊C8—1222no—
541C4×C8—1222no—
542#95—1221no—
543#95—1221no—
544#95—1221no—
545#95—1221no—
546C24—21no—
547C24—21no—
548C24—611no—
549C24D4×D6111yescharacteristic
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—42no—
563C2×D4—42no—
564C2×D4—42no—
565C2×D4—42no—
566C2×D4—81no—
567C2×D4—81no—
568C2×D4—1222no—
569C2×D4—1222no—
570C2×D4—4881no—
571C2×D4—4881no—
572C2×D4—2442no—
573C2×D4—2442no—
574C2×D4—2441no—
575C2×D4—2442no—
576C2×D4—2442no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—611no—
584C22×C4—611no—
585C22×C4—611no—
586C22×C4—1221no—
587C22×C4—1221no—
588C22×C4—1221no—
589C22×C4—1221no—
590C22×C4—1221no—
591C22×C4—1221no—
592C22×C4—1221no—
593C22×C4—1221no—
594C22×C4—1221no—
595C22×C4—1221no—
596C22×C4—4881no—
597C22×C4—2442no—
598C22×C4—2442no—
599C22×C4D4×D6111yescharacteristic
600C22×C4#1175822412yes—
601C22×C4C2×C22⋊D6112yes—
602C22×C4C23×D6111yescharacteristic
603D8—44no—
604M16—28no—
605M16—2444no—
606C2×C8—21no—
607C2×C8—21no—
608C2×C8—1221no—
609C2×C8—1221no—
610C2×C8—1221no—
611C2×C8—1221no—
612C2×C8—1221no—
613C2×C8—1221no—
614C2×C8D4×D6112yes—
615C2×C8#1175822412yes—
616C2×C8C2×C22⋊D6112yes—
617C2×C8C2×C22⋊D6112yes—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—612no—
623C4⋊C4—612no—
624C4⋊C4—1221no—
625C4⋊C4—1221no—
626C4⋊C4—1222no—
627C4⋊C4—1221no—
628C4⋊C4—1221no—
629C4⋊C4—1221no—
630C4⋊C4—1221no—
631C4⋊C4—4881no—
632C4⋊C4—2442no—
633C4⋊C4—2442no—
634C22⋊C4—42no—
635C22⋊C4—42no—
636C22⋊C4—1222no—
637C22⋊C4—1222no—
638C22⋊C4—4881no—
639C22⋊C4—4881no—
640C22⋊C4—4881no—
641C22⋊C4—2442no—
642C22⋊C4—2442no—
643C22⋊C4—2442no—
644C22⋊C4—2442no—
645C22⋊C4—2442no—
646C22⋊C4—2442no—
647C42—1221no—
648C42—1221no—
649C42—2442no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—21no—
654C23—21no—
655C23—21no—
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—1221no—
671C23—1221no—
672C23—1221no—
673C23—1221no—
674C23—1221no—
675C23—1221no—
676C23—1221no—
677C23#1451974812yes—
678C23C2×D4×D6111yescharacteristic
679D4—41no—
680D4—41no—
681D4—41no—
682D4—41no—
683D4—41no—
684D4—41no—
685D4—41no—
686D4—41no—
687D4—84no—
688D4—84no—
689D4—4884no—
690D4—4884no—
691D4—2444no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—612no—
705C2×C4—1221no—
706C2×C4—1221no—
707C2×C4—1221no—
708C2×C4—1221no—
709C2×C4—1221no—
710C2×C4—1221no—
711C2×C4—1222no—
712C2×C4—1221no—
713C2×C4—1222no—
714C2×C4—1221no—
715C2×C4—4884no—
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—2441no—
728C2×C4—2441no—
729C2×C4—2441no—
730C2×C4#1451974812yes—
731C2×C4C2×D4×D6111yescharacteristic
732C2×C4C22×C22⋊D6111yescharacteristic
733C2×C4C2×#1175822411yescharacteristic
734C2×C4C2×#1175822411yescharacteristic
735C2×C4#1451982311yescharacteristic
736C2×C4#1451982411yescharacteristic
737C8—22no—
738C8—2441no—
739C8—2441no—
740C8#1451974914yescomplemented
741C22—22no—
742C22—22no—
743C22—22no—
744C22—41no—
745C22—41no—
746C22—41no—
747C22—41no—
748C22—81no—
749C22—81no—
750C22—81no—
751C22—81no—
752C22—81no—
753C22—81no—
754C22—81no—
755C22—81no—
756C22—81no—
757C22—81no—
758C22—81no—
759C22—81no—
760C22—81no—
761C22—81no—
762C22—2441no—
763C22—2441no—
764C22—2441no—
765C22—2441no—
766C22—2441no—
767C22—2441no—
768C22—2441no—
769C22C2×#1451974811yescharacteristic
770C22#1684039611yescharacteristic
771C22#1684041211yescharacteristic
772C22AGL(1,ℤ/8)×D6111yescharacteristic
773C22#1684055811yescharacteristic
774C22#1684056611yescharacteristic
775C22#1684057211yescharacteristic
776C4—22no—
777C4—81no—
778C4—81no—
779C4—1222no—
780C4—4881no—
781C4—4881no—
782C4—2442no—
783C4—2441no—
784C4—2442no—
785C4—2441no—
786C4C2×#1451974911yescharacteristic
787C4#1684034011yescharacteristic
788C4#1684041811yescharacteristic
789C4#1684046411yescharacteristic
790C2—42no—
791C2—161no—
792C2—161no—
793C2—4881no—
794C2#2144926011yescharacteristic
795C2#2145543211yescharacteristic
796C2#2145549311yescharacteristic
797C2#2145743611yescharacteristic
798C2#2145745711yescharacteristic
799C2#2145840911yescharacteristic
800C2#2145842011yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC2×C61×#469C2
socleC23×C61C22×D4
hypercenterC2×#469D61
hypocenterC61#24792
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#469

Complements

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

NH ≅ G/Ntype
1. C2×#16840012C2semidirect
2. C2×#16839838C2semidirect
3. C2×#16839804C2semidirect
4. #21449260C2semidirect
5. #21449238C2semidirect
6. #21447205C2semidirect
7. #21447191C2semidirect
8. #21447007C2semidirect
9. #21447000C2semidirect
10. #21446686C2semidirect
11. #21446545C2semidirect
12. #21446142C2semidirect
13. #21446137C2semidirect
14. #21445849C2semidirect
15. C2×C61×#469C2semidirect
108. #14519709D4semidirect
131. C2×M16×C61D4semidirect
337. C8×C61#121semidirect
391. C2×#469D61semidirect
463. C61#24792semidirect
482. C2×M16C22⋊D61semidirect
740. C8#14519749semidirect

Maximal subgroups

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

subgroupindex
C2×#168400122
C2×#168398382
C2×#168398042
#214492602
#214492382
#214472052
#214471912
#214470072
#214470002
#214466862
#214465452
#214461422
#214461372
#214458492
C2×C61×#4692
#2479261