Finite Group Databasebeta

← #29691355

Subgroups — #29691355

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#21448515C211yesmaximal, characteristic, complemented
3#21448398C211yesmaximal, characteristic, complemented
4#21446684C211yesmaximal, characteristic, complemented
5#21446516C211yesmaximal, characteristic, complemented
6#21446505C211yesmaximal, characteristic, complemented
7#21446445C211yesmaximal, characteristic, complemented
8#21446442C211yesmaximal, characteristic, complemented
9#21446169C211yesmaximal, characteristic, complemented
10#21446165C211yesmaximal, characteristic, complemented
11#21446138C211yesmaximal, characteristic, complemented
12#21446017C211yesmaximal, characteristic, complemented
13#21445748C211yesmaximal, characteristic, complemented
14#21445588C211yesmaximal, characteristic, complemented
15C61×#1972C211yesmaximal, characteristic, complemented
16C22×D4×D61C2211yescharacteristic
17C22×#11758199C2211yescharacteristic
18C2×#14519748C2211yescharacteristic
19C2×D4×Dic61C2211yescharacteristic, complemented
20C2×#14519735C2211yescharacteristic
21C2×#14519734C2211yescharacteristic
22#16839894C418yescomplemented
23C2×#14519710C2211yescharacteristic, complemented
24C2×#14519699C2211yescharacteristic
25C2×#14519699C2211yescharacteristic
26C2×#14519698C2211yescharacteristic
27C2×#14519698C2211yescharacteristic
28C2×#14519698C2211yescharacteristic, complemented
29C2×#14519697C2211yescharacteristic
30C2×#14519689C2211yescharacteristic
31C2×#14519689C2211yescharacteristic
32C2×C4×#92418C2211yescharacteristic, complemented
33#16839665C2211yescharacteristic
34#16839664C2211yescharacteristic
35#16839663C2211yescharacteristic
36#16839662—21no—
37#16839662—21no—
38#16839662—21no—
39#16839660C2211yescharacteristic, complemented
40#16839650—21no—
41#16839639—21no—
42#16839634—21no—
43#16839619C2211yescharacteristic
44#16839617—21no—
45#16839617—21no—
46C4⋊C4×Dic61C2211yescharacteristic, complemented
47#16839525C2211yescharacteristic, complemented
48#16839525C2211yescharacteristic, complemented
49#16839524C2211yescharacteristic, complemented
50#16839524C2211yescharacteristic, complemented
51#16839516C2211yescharacteristic, complemented
52#16839516C2211yescharacteristic, complemented
53C22×D8×C61C2211yescharacteristic
54C2×#106×C61C2211yescharacteristic, complemented
55C2×#102×C61C2211yescharacteristic
56C2×#102×C61C2211yescharacteristic, complemented
57C2×#97×C61C2211yescharacteristic, complemented
58C61×#390C2211yescharacteristic
59C61×#390C2211yescharacteristic, 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
70C23×Dic61—21no—
71C22×C4×D61C2311yescharacteristic
72C2×#11758199—41no—
73C2×#11758199—41no—
74C2×#11758199C2×C414yes—
75C22×#92418C2311yescharacteristic
76C22×#92418C2311yescharacteristic
77#14519748—22no—
78#14519748C2×C414yes—
79D4×Dic61—41no—
80D4×Dic61—41no—
81#14519735—41no—
82#14519735—41no—
83#14519734—41no—
84#14519734—41no—
85C2×C4⋊Dic61C2311yescharacteristic
86C2×C4⋊Dic61C2311yescharacteristic
87C2×C4⋊Dic61C2311yescharacteristic
88C2×#11758196—21no—
89C2×#11758196D411yescharacteristic
90C2×#11758196D411yescharacteristic
91C2×C22⋊Dic61—21no—
92C2×C22⋊Dic61—21no—
93C2×C22⋊Dic61—21no—
94C2×C22⋊Dic61—21no—
95C2×#11758198—21no—
96C2×#11758198—21no—
97C2×#11758198—21no—
98C2×#11758198—21no—
99C2×#11758198—21no—
100C2×#11758198—21no—
101C2×#11758198D411yescharacteristic
102C2×#11758198D411yescharacteristic
103C2×C4×Dic61—21no—
104C2×C4×Dic61—21no—
105C2×C4×Dic61C2311yescharacteristic
106#14519710—41no—
107#14519699—41no—
108#14519699C2×C414yescomplemented
109#14519698—41no—
110#14519698—41no—
111#14519698C2×C414yescomplemented
112#14519697—41no—
113#14519689—22no—
114#14519689C2×C414yescomplemented
115C4×#92418—41no—
116#14519684—21no—
117#14519684—21no—
118#14519684—21no—
119C22×D4×C61C2311yescharacteristic
120C22×D4×C61C2311yescharacteristic
121C2×D8×C61—41no—
122C2×D8×C61—41no—
123C2×D8×C61C2×C414yes—
124C22×C8×C61C2311yescharacteristic
125C22×C8×C61C2311yescharacteristic
126C2×C4⋊C4×C61C2311yescharacteristic
127C2×C4⋊C4×C61C2311yescharacteristic
128C2×C22⋊C4×C61—21no—
129C2×C22⋊C4×C61—21no—
130C2×C22⋊C4×C61—21no—
131C2×C22⋊C4×C61—21no—
132C2×C42×C61C2311yescharacteristic
133#106×C61—41no—
134#102×C61—41no—
135#102×C61—41no—
136#97×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×C61C2×D411yescharacteristic
163C22×C4×C61C2×D411yescharacteristic
164C22×C4×C61C2411yescharacteristic
165C2×C22⋊D61—24no—
166C2×C22⋊D61—24no—
167C2×C22⋊D61—42no—
168C2×C22⋊D61—42no—
169C2×C22⋊D61—81no—
170C2×C22⋊D61—81no—
171C22×Dic61—21no—
172C22×Dic61—21no—
173C22×Dic61—21no—
174C22×Dic61—42no—
175C22×Dic61—81no—
176C22×Dic61—81no—
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—81no—
208C22⋊C4×C61—81no—
209C22⋊C4×C61—81no—
210C22⋊C4×C61—81no—
211C42×C61—21no—
212C42×C61—21no—
213C22⋊Dic61—24no—
214C22⋊Dic61—42no—
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×C61C23×C411yescharacteristic
302C2×C4×C61C2×#4111yescharacteristic
303C2×C4×C61H(5,𝔽2)11yescharacteristic
304C2×C4×C61H(5,𝔽2)11yescharacteristic
305C2×C4×C61H(5,𝔽2)11yescharacteristic
306C2×C4×C61H(5,𝔽2)11yescharacteristic
307C22⋊D61—48no—
308C22⋊D61—84no—
309C2×Dic61—21no—
310C2×Dic61—21no—
311C2×Dic61—22no—
312C2×Dic61—21no—
313C2×Dic61—21no—
314C2×Dic61—21no—
315C2×Dic61—21no—
316C2×Dic61—21no—
317C2×Dic61—21no—
318C2×Dic61—41no—
319C2×Dic61—41no—
320C2×Dic61—41no—
321C2×Dic61—41no—
322C2×Dic61—41no—
323C2×Dic61—41no—
324C2×Dic61—41no—
325C2×Dic61—41no—
326C2×Dic61—84no—
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#1972D6111yescharacteristic, complemented
395#1970—611no—
396#1936—611no—
397#1934—611no—
398#1926—611no—
399#1925—611no—
400#1879—611no—
401#1879—611no—
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×D4—611no—
422C2×#117—611no—
423C2×#117—611no—
424#447—618no—
425C2×#107—611no—
426C2×#106C2×D6111yescharacteristic, complemented
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×#97C2×D6111yescharacteristic, complemented
438C2×C4×C8—611no—
439#390—611no—
440#390—611no—
441#390—611no—
442#390—1221no—
443#390—1221no—
444#390—1221no—
445#390C2×D6111yescharacteristic
446#390C2×D6111yescharacteristic, complemented
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#340—611no—
459#336—611no—
460#336—611no—
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—611no—
475C23×C4—1221no—
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—2441no—
489C4×D4—2441no—
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—21no—
506C2×C22⋊C4—611no—
507C2×C22⋊C4—611no—
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—41no—
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—41no—
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—611no—
581C22×C4—612no—
582C22×C4—612no—
583C22×C4—611no—
584C22×C4—611no—
585C22×C4—1221no—
586C22×C4—1221no—
587C22×C4—1221no—
588C22×C4—1221no—
589C22×C4—1221no—
590C22×C4—1221no—
591C22×C4—1221no—
592C22×C4—4881no—
593C22×C4—4881no—
594C22×C4—2442no—
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—81no—
626C22⋊C4—81no—
627C22⋊C4—81no—
628C22⋊C4—81no—
629C22⋊C4—1224no—
630C22⋊C4—4881no—
631C22⋊C4—4881no—
632C22⋊C4—4881no—
633C22⋊C4—4881no—
634C22⋊C4—4881no—
635C22⋊C4—4881no—
636C22⋊C4—4881no—
637C22⋊C4—2441no—
638C22⋊C4—2441no—
639C22⋊C4—2442no—
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—612no—
710C2×C4—1221no—
711C2×C4—1221no—
712C2×C4—1222no—
713C2×C4—1222no—
714C2×C4—1222no—
715C2×C4—1222no—
716C2×C4—1222no—
717C2×C4—1221no—
718C2×C4—1221no—
719C2×C4—1221no—
720C2×C4—1221no—
721C2×C4—1221no—
722C2×C4—1221no—
723C2×C4—4884no—
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#1684032011yescharacteristic
773C22#1684032511yescharacteristic
774C22#1684056611yescharacteristic
775C22#1684056611yescharacteristic
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#1684034611yescharacteristic
792C2—82no—
793C2—82no—
794C2—4882no—
795C2—2442no—
796C2#2144847811yescharacteristic
797C2#2145464811yescharacteristic
798C2#2145466811yescharacteristic
799C2#2145666611yescharacteristic
800C2#2145668111yescharacteristic
801C2#2145686411yescharacteristic
802C2#2145690811yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1972C2
socleC23×C61C22×D4
prime radicalC2×#16839894C2
cosocleC22×C4×C61C24
hypercenter#1972D61
hypocenterC61#22056
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1972

Complements

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

NH ≅ G/Ntype
2. #21448515C2semidirect
3. #21448398C2semidirect
4. #21446684C2semidirect
5. #21446516C2semidirect
6. #21446505C2semidirect
7. #21446445C2semidirect
8. #21446442C2semidirect
9. #21446169C2semidirect
10. #21446165C2semidirect
11. #21446138C2semidirect
12. #21446017C2semidirect
13. #21445748C2semidirect
14. #21445588C2semidirect
15. C61×#1972C2semidirect
19. C2×D4×Dic61C22semidirect
22. #16839894C4semidirect
23. C2×#14519710C22semidirect
28. C2×#14519698C22semidirect
32. C2×C4×#92418C22semidirect
39. #16839660C22semidirect
46. C4⋊C4×Dic61C22semidirect
47. #16839525C22semidirect
48. #16839525C22semidirect
49. #16839524C22semidirect
50. #16839524C22semidirect
51. #16839516C22semidirect
52. #16839516C22semidirect
54. C2×#106×C61C22semidirect
56. C2×#102×C61C22semidirect
57. C2×#97×C61C22semidirect
59. C61×#390C22semidirect
69. C2×D4×D61C2×C4semidirect
108. #14519699C2×C4semidirect
111. #14519698C2×C4semidirect
114. #14519689C2×C4semidirect
394. #1972D61semidirect
426. C2×#106C2×D61semidirect
434. C2×#102C2×D61semidirect
437. C2×#97C2×D61semidirect
446. #390C2×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
#214485152
#214483982
#214466842
#214465162
#214465052
#214464452
#214464422
#214461692
#214461652
#214461382
#214460172
#214457482
#214455882
C61×#19722
#2205661