Finite Group Databasebeta

← #29691353

Subgroups — #29691353

Order 15616.

1136 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839894C211yesmaximal, characteristic
2#21448506C211yesmaximal, characteristic, complemented
3#21448398C211yesmaximal, characteristic, complemented
4#21446692C211yesmaximal, characteristic, complemented
5#21446686C211yesmaximal, characteristic, complemented
6#21446513C211yesmaximal, characteristic, complemented
7#21446500C211yesmaximal, characteristic, complemented
8#21446443C211yesmaximal, characteristic, complemented
9#21446440C211yesmaximal, characteristic, complemented
10#21446167C211yesmaximal, characteristic, complemented
11#21446138C211yesmaximal, characteristic, complemented
12#21446021C211yesmaximal, characteristic, complemented
13#21445748C211yesmaximal, characteristic, complemented
14#21445584C211yesmaximal, characteristic, complemented
15C61×#1879C211yesmaximal, characteristic, complemented
16C22×D4×D61C2211yescharacteristic
17C22×#11758199C2211yescharacteristic
18C2×#14519748C2211yescharacteristic
19C2×#14519735C2211yescharacteristic
20C2×#14519734C2211yescharacteristic
21#16839894C418yescomplemented
22C2×#14519711C2211yescharacteristic, complemented
23C2×#14519708C2211yescharacteristic, complemented
24C2×#14519699C2211yescharacteristic
25C2×#14519699C2211yescharacteristic
26C2×#14519698C2211yescharacteristic
27C2×#14519698C2211yescharacteristic
28C2×#14519698C2211yescharacteristic, complemented
29C2×#14519697C2211yescharacteristic
30C2×#14519689C2211yescharacteristic
31C2×#14519689C2211yescharacteristic
32C2×#14519687C2211yescharacteristic, complemented
33C2×C8×Dic61C2211yescharacteristic, complemented
34#16839665C2211yescharacteristic
35#16839665C2211yescharacteristic, complemented
36#16839664C2211yescharacteristic
37#16839663C2211yescharacteristic
38#16839662—21no—
39#16839662—21no—
40#16839662—21no—
41#16839658C2211yescharacteristic, complemented
42#16839656—21no—
43#16839641—21no—
44#16839635—21no—
45#16839619C2211yescharacteristic
46#16839617—21no—
47#16839617—21no—
48C4×C4⋊Dic61C2211yescharacteristic, complemented
49#16839525C2211yescharacteristic, complemented
50#16839524C2211yescharacteristic, complemented
51#16839524C2211yescharacteristic, complemented
52#16839517C2211yescharacteristic, complemented
53C22×D8×C61C2211yescharacteristic
54C2×C4×D4×C61C2211yescharacteristic, complemented
55C2×#102×C61C2211yescharacteristic
56C2×#102×C61C2211yescharacteristic, complemented
57C61×#390C2211yescharacteristic
58C61×#340C2211yescharacteristic, complemented
59C61×#336C2211yescharacteristic, complemented
60C24×D61—21no—
61C22×D244C2311yescharacteristic
62C22×C22⋊D61—21no—
63C22×C22⋊D61—21no—
64C2×D4×D61—22no—
65C2×D4×D61—41no—
66C2×D4×D61—41no—
67C2×D4×D61—41no—
68C2×D4×D61—41no—
69C2×D4×D61C2×C414yescomplemented
70C22×C4×D61C2311yescharacteristic
71C2×#11758199—41no—
72C2×#11758199—41no—
73C2×#11758199C2×C414yes—
74C22×#92418C2311yescharacteristic
75C22×#92418C2311yescharacteristic
76#14519748—22no—
77#14519748C2×C414yes—
78#14519735—41no—
79#14519735—41no—
80#14519734—41no—
81#14519734—41no—
82C2×C4⋊Dic61C2311yescharacteristic
83C2×C4⋊Dic61C2311yescharacteristic
84C2×C4⋊Dic61C2311yescharacteristic
85C2×#11758196—21no—
86C2×#11758196D411yescharacteristic
87C2×#11758196D411yescharacteristic
88C2×C22⋊Dic61—21no—
89C2×C22⋊Dic61—21no—
90C2×C22⋊Dic61—21no—
91C2×C22⋊Dic61—21no—
92C2×C22⋊Dic61—21no—
93C2×#11758198—21no—
94C2×#11758198—21no—
95C2×#11758198—21no—
96C2×#11758198—21no—
97C2×#11758198—21no—
98C2×#11758198—21no—
99C2×#11758198D411yescharacteristic
100C2×#11758198D411yescharacteristic
101C2×C4×Dic61—21no—
102C2×C4×Dic61—21no—
103C2×C4×Dic61C2311yescharacteristic
104#14519711—41no—
105#14519708—41no—
106#14519699—41no—
107#14519699C2×C414yescomplemented
108#14519698—41no—
109#14519698—41no—
110#14519698C2×C414yescomplemented
111#14519697—41no—
112#14519689—22no—
113#14519689C2×C414yescomplemented
114#14519687—41no—
115C8×Dic61—41no—
116#14519684—21no—
117#14519684—21no—
118#14519684—21no—
119C22×D4×C61C2311yescharacteristic
120C22×D4×C61C2311yescharacteristic
121C23×C4×C61—21no—
122C2×D8×C61—41no—
123C2×D8×C61—41no—
124C2×D8×C61C2×C414yes—
125C22×C8×C61C2311yescharacteristic
126C22×C8×C61C2311yescharacteristic
127C4×D4×C61—41no—
128C4×D4×C61—41no—
129C2×C4⋊C4×C61C2311yescharacteristic
130C2×C4⋊C4×C61C2311yescharacteristic
131C2×C22⋊C4×C61—21no—
132C2×C22⋊C4×C61—21no—
133C2×C22⋊C4×C61—21no—
134C2×C42×C61C2311yescharacteristic
135#102×C61—41no—
136#102×C61—41no—
137C24×C61—21no—
138C24×C61—21no—
139C23×D61—21no—
140C23×D61—24no—
141C23×D61—42no—
142C23×D61—42no—
143C23×D61—81no—
144C23×D61—81no—
145C23×D61—81no—
146C23×D61—81no—
147C23×D61C2×D411yescharacteristic
148C2×D4×C61—21no—
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×C61C22×C412yes—
159C2×D4×C61C22×C412yes—
160C22×C4×C61—21no—
161C22×C4×C61—21no—
162C22×C4×C61—42no—
163C22×C4×C61—81no—
164C22×C4×C61—81no—
165C22×C4×C61C2×D411yescharacteristic
166C22×C4×C61C2×D411yescharacteristic
167C22×C4×C61C2411yescharacteristic
168C2×C22⋊D61—24no—
169C2×C22⋊D61—24no—
170C2×C22⋊D61—42no—
171C2×C22⋊D61—42no—
172C2×C22⋊D61—81no—
173C2×C22⋊D61—81no—
174C22×Dic61—21no—
175C22×Dic61—21no—
176C22×Dic61—21no—
177C22×Dic61C2×D411yescharacteristic
178C22×Dic61C2×D411yescharacteristic
179C22×Dic61C2×D411yescharacteristic
180D4×D61—44no—
181D4×D61—44no—
182D4×D61—44no—
183D4×D61—44no—
184C2×D244—21no—
185C2×D244—21no—
186C2×D244—21no—
187C2×D244—21no—
188C2×D244—21no—
189C2×D244C22×C412yes—
190C2×C4×D61—21no—
191C2×C4×D61—21no—
192C2×C4×D61—21no—
193C2×C4×D61—21no—
194C2×C4×D61C22×C412yes—
195C2×C4×D61#4112yes—
196D8×C61—44no—
197C2×C8×C61—21no—
198C2×C8×C61—21no—
199C2×C8×C61—21no—
200C2×C8×C61—21no—
201C2×C8×C61—21no—
202C2×C8×C61C22×C412yes—
203C4⋊C4×C61—21no—
204C4⋊C4×C61—21no—
205C4⋊C4×C61—21no—
206C4⋊C4×C61—21no—
207C22⋊C4×C61—42no—
208C22⋊C4×C61—81no—
209C22⋊C4×C61—81no—
210C42×C61—21no—
211C42×C61—21no—
212C22⋊Dic61—24no—
213C22⋊Dic61—81no—
214C22⋊Dic61—81no—
215C22⋊Dic61—81no—
216C22⋊Dic61—81no—
217#11758199—44no—
218#11758198—41no—
219#11758198—41no—
220#11758198—42no—
221#11758198—81no—
222#11758198—81no—
223#11758198—81no—
224#11758198—81no—
225#11758198—81no—
226C4⋊Dic61—21no—
227C4⋊Dic61—21no—
228C4⋊Dic61—21no—
229C4⋊Dic61—21no—
230C4⋊Dic61—21no—
231C4⋊Dic61C22×C412yes—
232#11758196—41no—
233#11758196—41no—
234#11758196—81no—
235C4×Dic61—21no—
236C4×Dic61—21no—
237C4×Dic61—42no—
238C4×Dic61—81no—
239C2×#92418—21no—
240C2×#92418—21no—
241C2×#92418—21no—
242C2×#92418—21no—
243C2×#92418—21no—
244C2×#92418C22×C412yes—
245C23×C61—22no—
246C23×C61—22no—
247C23×C61—41no—
248C23×C61—41no—
249C23×C61—41no—
250C23×C61—41no—
251C23×C61—41no—
252C23×C61—41no—
253C23×C61—41no—
254C23×C61—41no—
255C23×C61—41no—
256C23×C61—41no—
257C23×C61—41no—
258C23×C61—41no—
259C23×C61C22×D411yescharacteristic
260C22×D61—21no—
261C22×D61—21no—
262C22×D61—21no—
263C22×D61—21no—
264C22×D61—21no—
265C22×D61—21no—
266C22×D61—22no—
267C22×D61—48no—
268C22×D61—41no—
269C22×D61—41no—
270C22×D61—41no—
271C22×D61—41no—
272C22×D61—41no—
273C22×D61—41no—
274C22×D61—84no—
275C22×D61—84no—
276C22×D61—84no—
277C22×D61—84no—
278C22×D61—84no—
279C22×D61—84no—
280C22×D61C4×D412yes—
281D4×C61—22no—
282D4×C61—22no—
283D4×C61—22no—
284D4×C61—22no—
285D4×C61—41no—
286D4×C61—41no—
287D4×C61—41no—
288D4×C61—41no—
289C2×C4×C61—21no—
290C2×C4×C61—21no—
291C2×C4×C61—21no—
292C2×C4×C61—21no—
293C2×C4×C61—21no—
294C2×C4×C61—21no—
295C2×C4×C61—41no—
296C2×C4×C61—41no—
297C2×C4×C61—41no—
298C2×C4×C61—41no—
299C2×C4×C61—41no—
300C2×C4×C61—41no—
301C2×C4×C61—84no—
302C2×C4×C61C23×C411yescharacteristic
303C2×C4×C61C2×#4111yescharacteristic
304C2×C4×C61H(5,𝔽2)11yescharacteristic
305C2×C4×C61H(5,𝔽2)11yescharacteristic
306C2×C4×C61H(5,𝔽2)11yescharacteristic
307C2×C4×C61H(5,𝔽2)11yescharacteristic
308C22⋊D61—48no—
309C22⋊D61—84no—
310C2×Dic61—21no—
311C2×Dic61—21no—
312C2×Dic61—22no—
313C2×Dic61—21no—
314C2×Dic61—21no—
315C2×Dic61—21no—
316C2×Dic61—21no—
317C2×Dic61—21no—
318C2×Dic61—21no—
319C2×Dic61—41no—
320C2×Dic61—41no—
321C2×Dic61—41no—
322C2×Dic61—41no—
323C2×Dic61—41no—
324C2×Dic61—41no—
325C2×Dic61—41no—
326C2×Dic61—41no—
327C2×Dic61C4×D412yes—
328D244—22no—
329D244—22no—
330D244—41no—
331D244—41no—
332C4×D61—22no—
333C4×D61—22no—
334C4×D61—22no—
335C4×D61—22no—
336C8×C61—22no—
337C8×C61—41no—
338#92418—22no—
339#92418—41no—
340#22056—611nomaximal, Sylow
341C22×C61—42no—
342C22×C61—42no—
343C22×C61—42no—
344C22×C61—42no—
345C22×C61—42no—
346C22×C61—42no—
347C22×C61—81no—
348C22×C61—81no—
349C22×C61—81no—
350C22×C61—81no—
351C22×C61—81no—
352C22×C61—81no—
353C22×C61—81no—
354C22×C61—81no—
355C22×C61C2×C4×D411yescharacteristic
356C22×C61#53411yescharacteristic
357C22×C61#53511yescharacteristic
358C22×C61#57611yescharacteristic
359C22×C61#57611yescharacteristic
360C22×C61#57611yescharacteristic
361C22×C61#57711yescharacteristic
362C2×D61—22no—
363C2×D61—22no—
364C2×D61—22no—
365C2×D61—41no—
366C2×D61—41no—
367C2×D61—41no—
368C2×D61—41no—
369C2×D61—42no—
370C2×D61—42no—
371C2×D61—42no—
372C2×D61—816no—
373C2×D61—81no—
374C2×D61—81no—
375C2×D61—81no—
376C2×D61—81no—
377C4×C61—41no—
378C4×C61—41no—
379C4×C61—81no—
380C4×C61—81no—
381C4×C61#51811yescharacteristic
382C4×C61#51811yescharacteristic
383C4×C61#53811yescharacteristic
384C4×C61#53811yescharacteristic
385Dic61—22no—
386Dic61—41no—
387Dic61—41no—
388Dic61—42no—
389Dic61—81no—
390Dic61—81no—
391C2×#447—611no—
392#2324—611no—
393#2309—611no—
394#1972—611no—
395#1970—611no—
396#1936—611no—
397#1934—611no—
398#1926—611no—
399#1925—611no—
400#1879—611no—
401#1879D6111yescharacteristic, complemented
402#1875—611no—
403#1854—611no—
404#1786—611no—
405#1750—611no—
406C2×C61—82no—
407C2×C61—82no—
408C2×C61#232111yescharacteristic
409C2×C61#294611yescharacteristic
410C2×C61#294811yescharacteristic
411C2×C61#319811yescharacteristic
412C2×C61#319911yescharacteristic
413C2×C61#322011yescharacteristic
414C2×C61#322411yescharacteristic
415D61—42no—
416D61—82no—
417C23×D4—611no—
418C22×D8—611no—
419C22×D8C2×D6111yescharacteristic
420C2×#121—611no—
421C2×C4×D4C2×D6111yescharacteristic, complemented
422C2×#117—611no—
423C2×#117—611no—
424#447—618no—
425C2×#107—611no—
426C2×#106—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, complemented
435C2×C22⋊C8—611no—
436C2×C22⋊C8—611no—
437C2×#97—611no—
438C2×C4×C8—611no—
439#390—611no—
440#390—611no—
441#390—611no—
442#390—611no—
443#390—1221no—
444#390—1221no—
445#390—1221no—
446#390C2×D6111yescharacteristic
447#389—611no—
448#388—1221no—
449#386—1221no—
450#385—1221no—
451#380—611no—
452#379—1221no—
453#379—1221no—
454C4×C4⋊C4—611no—
455#340—611no—
456#340—611no—
457#340—611no—
458#340C2×D6111yescharacteristic, complemented
459#336—611no—
460#336C2×D6111yescharacteristic, complemented
461C61#2205611yescharacteristic, complemented, Sylow
462C25—1221no—
463C22×D4—614no—
464C22×D4—611no—
465C22×D4—1222no—
466C22×D4—1221no—
467C22×D4—1221no—
468C22×D4—2441no—
469C22×D4—2441no—
470C22×D4—2441no—
471C22×D4—2441no—
472C22×D4C22×D6111yescharacteristic
473C22×D4C22×D6111yescharacteristic
474C23×C4—21no—
475C23×C4—611no—
476C2×D8—41no—
477C2×D8—41no—
478C2×D8—614no—
479C2×D8—2441no—
480C2×D8—2441no—
481C2×D8C4×D6114yes—
482C22×C8—611no—
483C22×C8—611no—
484C22×C8C22×D6111yescharacteristic
485C22×C8C22×D6111yescharacteristic
486#121—614no—
487#121—1222no—
488C4×D4—41no—
489C4×D4—41no—
490#117—2441no—
491#117—2441no—
492#117—2441no—
493#117—2441no—
494C2×C4⋊C4—611no—
495C2×C4⋊C4—611no—
496C2×C4⋊C4—611no—
497C2×C4⋊C4—611no—
498C2×C4⋊C4—611no—
499C2×C4⋊C4—1221no—
500C2×C4⋊C4C22×D6111yescharacteristic
501C2×C4⋊C4C22×D6111yescharacteristic
502C2×C22⋊C4—21no—
503C2×C22⋊C4—21no—
504C2×C22⋊C4—21no—
505C2×C22⋊C4—611no—
506C2×C22⋊C4—611no—
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×C22⋊C4—1221no—
517C2×C22⋊C4—1221no—
518C2×C42—611no—
519C2×C42—1221no—
520C2×C42—1221no—
521C2×C42C22×D6111yescharacteristic
522#107—2441no—
523#106—2441no—
524#102—41no—
525#102—41no—
526#102—614no—
527#102—614no—
528#102—2441no—
529#102—2441no—
530#102—2441no—
531#102—2441no—
532C22⋊C8—614no—
533C22⋊C8—1222no—
534#97—2441no—
535C4×C8—2441no—
536#95—1221no—
537#95—1221no—
538#95—1221no—
539C24—21no—
540C24—21no—
541C24—611no—
542C24—1224no—
543C24—1221no—
544C24—4881no—
545C24—4881no—
546C24—4881no—
547C24—4881no—
548C24—2442no—
549C24—2442no—
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—612no—
561C2×D4—1224no—
562C2×D4—1224no—
563C2×D4—1221no—
564C2×D4—1221no—
565C2×D4—1221no—
566C2×D4—1221no—
567C2×D4—1221no—
568C2×D4—4881no—
569C2×D4—4881no—
570C2×D4—2444no—
571C2×D4—2444no—
572C2×D4—2444no—
573C2×D4—2444no—
574C2×D4—2442no—
575C2×D4—2442no—
576C2×D4C2×C4×D6112yes—
577C2×D4C2×C4×D6112yes—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—42no—
581C22×C4—81no—
582C22×C4—81no—
583C22×C4—611no—
584C22×C4—612no—
585C22×C4—612no—
586C22×C4—611no—
587C22×C4—611no—
588C22×C4—1221no—
589C22×C4—1221no—
590C22×C4—1221no—
591C22×C4—1221no—
592C22×C4—1221no—
593C22×C4—1221no—
594C22×C4—1221no—
595C22×C4D4×D6111yescharacteristic
596C22×C4D4×D6111yescharacteristic
597C22×C4C23×D6111yescharacteristic
598D8—44no—
599D8—2444no—
600C2×C8—21no—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8—21no—
605C2×C8—612no—
606C2×C8—1221no—
607C2×C8—1221no—
608C2×C8—1221no—
609C2×C8—1221no—
610C2×C8—1221no—
611C2×C8C2×C4×D6112yes—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—612no—
617C4⋊C4—1221no—
618C4⋊C4—1221no—
619C4⋊C4—1221no—
620C4⋊C4—1221no—
621C4⋊C4—1221no—
622C4⋊C4—4881no—
623C4⋊C4—2441no—
624C4⋊C4—2441no—
625C22⋊C4—42no—
626C22⋊C4—81no—
627C22⋊C4—81no—
628C22⋊C4—1224no—
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—2441no—
639C22⋊C4—2441no—
640C22⋊C4—2442no—
641C42—21no—
642C42—21no—
643C42—1221no—
644C42—1221no—
645C42—4881no—
646C42—2442no—
647C23—22no—
648C23—22no—
649C23—41no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23—41no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—612no—
662C23—1221no—
663C23—1221no—
664C23—1221no—
665C23—1221no—
666C23—1221no—
667C23—1221no—
668C23—1222no—
669C23—4884no—
670C23—4884no—
671C23—4884no—
672C23—4884no—
673C23—4884no—
674C23—4884no—
675C23—2448no—
676C23—2441no—
677C23—2441no—
678C23—2441no—
679C23—2441no—
680C23—2441no—
681C23—2441no—
682C23C2×D4×D6111yescharacteristic
683D4—22no—
684D4—22no—
685D4—22no—
686D4—22no—
687D4—41no—
688D4—41no—
689D4—41no—
690D4—41no—
691D4—1222no—
692D4—1222no—
693D4—4884no—
694D4—2448no—
695D4—2441no—
696D4—2441no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—84no—
710C2×C4—612no—
711C2×C4—1221no—
712C2×C4—1221no—
713C2×C4—1222no—
714C2×C4—1222no—
715C2×C4—1222no—
716C2×C4—1222no—
717C2×C4—1222no—
718C2×C4—1221no—
719C2×C4—1221no—
720C2×C4—1221no—
721C2×C4—1221no—
722C2×C4—1221no—
723C2×C4—1221no—
724C2×C4—2441no—
725C2×C4—2441no—
726C2×C4—2441no—
727C2×C4—2441no—
728C2×C4—2441no—
729C2×C4—2441no—
730C2×C4—2441no—
731C2×C4—2441no—
732C2×C4C22×C4×D6111yescharacteristic
733C2×C4#41×D6111yescharacteristic
734C2×C4#1451982211yescharacteristic
735C2×C4#1451982211yescharacteristic
736C2×C4#1451982211yescharacteristic
737C2×C4#1451982311yescharacteristic
738C8—22no—
739C8—41no—
740C8—1222no—
741C8—2441no—
742C22—42no—
743C22—42no—
744C22—42no—
745C22—42no—
746C22—42no—
747C22—42no—
748C22—81no—
749C22—81no—
750C22—81no—
751C22—81no—
752C22—81no—
753C22—81no—
754C22—81no—
755C22—81no—
756C22—1222no—
757C22—1222no—
758C22—1222no—
759C22—48816no—
760C22—4881no—
761C22—4881no—
762C22—4881no—
763C22—4881no—
764C22—2442no—
765C22—2442no—
766C22—2442no—
767C22—2441no—
768C22—2441no—
769C22—2441no—
770C22—2441no—
771C22C4×D4×D6111yescharacteristic
772C22#1684032211yescharacteristic
773C22#1684032811yescharacteristic
774C22#1684056311yescharacteristic
775C22#1684056411yescharacteristic
776C22#1684056611yescharacteristic
777C22#1684057211yescharacteristic
778C4—41no—
779C4—41no—
780C4—81no—
781C4—81no—
782C4—1222no—
783C4—4881no—
784C4—4881no—
785C4—2441no—
786C4—2441no—
787C4—2442no—
788C4#1684023411yescharacteristic
789C4#1684023511yescharacteristic
790C4#1684034411yescharacteristic
791C4#1684034811yescharacteristic
792C2—82no—
793C2—82no—
794C2—4882no—
795C2—2442no—
796C2#2144847511yescharacteristic
797C2#2145464811yescharacteristic
798C2#2145466611yescharacteristic
799C2#2145666811yescharacteristic
800C2#2145668211yescharacteristic
801C2#2145686611yescharacteristic
802C2#2145691011yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1879C2
socleC23×C61C22×D4
prime radicalC2×#16839894C2
cosocleC22×C4×C61C24
hypercenter#1879D61
hypocenterC61#22056
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1879

Complements

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

NH ≅ G/Ntype
2. #21448506C2semidirect
3. #21448398C2semidirect
4. #21446692C2semidirect
5. #21446686C2semidirect
6. #21446513C2semidirect
7. #21446500C2semidirect
8. #21446443C2semidirect
9. #21446440C2semidirect
10. #21446167C2semidirect
11. #21446138C2semidirect
12. #21446021C2semidirect
13. #21445748C2semidirect
14. #21445584C2semidirect
15. C61×#1879C2semidirect
21. #16839894C4semidirect
22. C2×#14519711C22semidirect
23. C2×#14519708C22semidirect
28. C2×#14519698C22semidirect
32. C2×#14519687C22semidirect
33. C2×C8×Dic61C22semidirect
35. #16839665C22semidirect
41. #16839658C22semidirect
48. C4×C4⋊Dic61C22semidirect
49. #16839525C22semidirect
50. #16839524C22semidirect
51. #16839524C22semidirect
52. #16839517C22semidirect
54. C2×C4×D4×C61C22semidirect
56. C2×#102×C61C22semidirect
58. C61×#340C22semidirect
59. C61×#336C22semidirect
69. C2×D4×D61C2×C4semidirect
107. #14519699C2×C4semidirect
110. #14519698C2×C4semidirect
113. #14519689C2×C4semidirect
401. #1879D61semidirect
421. C2×C4×D4C2×D61semidirect
434. C2×#102C2×D61semidirect
458. #340C2×D61semidirect
460. #336C2×D61semidirect
461. C61#22056semidirect

Maximal subgroups

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

subgroupindex
C2×#168398942
#214485062
#214483982
#214466922
#214466862
#214465132
#214465002
#214464432
#214464402
#214461672
#214461382
#214460212
#214457482
#214455842
C61×#18792
#2205661