Finite Group Databasebeta

← #29691360

Subgroups — #29691360

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×#16839895C211yesmaximal, characteristic
2#21448514C211yesmaximal, characteristic, complemented
3#21448399C211yesmaximal, characteristic, complemented
4#21446692C211yesmaximal, characteristic, complemented
5#21446682C211yesmaximal, characteristic, complemented
6#21446517C211yesmaximal, characteristic, complemented
7#21446503C211yesmaximal, characteristic, complemented
8#21446444C211yesmaximal, characteristic, complemented
9#21446437C211yesmaximal, characteristic, complemented
10#21446165C211yesmaximal, characteristic, complemented
11#21446165C211yesmaximal, characteristic, complemented
12#21446018C211yesmaximal, characteristic, complemented
13#21445751C211yesmaximal, characteristic, complemented
14#21445587C211yesmaximal, characteristic, complemented
15C61×#1875C211yesmaximal, characteristic, complemented
16C23×D244C2211yescharacteristic
17C22×#11758199C2211yescharacteristic
18C22×#11758199C2211yescharacteristic
19C2×D4×Dic61C2211yescharacteristic, complemented
20C2×#14519736C2211yescharacteristic
21#16839895C418yescomplemented
22C2×#14519710C2211yescharacteristic, complemented
23C2×#14519708C2211yescharacteristic, complemented
24C2×#14519699C2211yescharacteristic
25C2×#14519699C2211yescharacteristic
26C2×#14519699C2211yescharacteristic
27C2×#14519699C2211yescharacteristic
28C2×#14519697C2211yescharacteristic
29C2×#14519697C2211yescharacteristic
30C2×C22⋊#92418C2211yescharacteristic
31C2×#14519687C2211yescharacteristic, complemented
32C2×C8×Dic61C2211yescharacteristic, complemented
33#16839665—21no—
34#16839665C2211yescharacteristic, complemented
35#16839664—21no—
36#16839664—21no—
37#16839663C2211yescharacteristic
38#16839663C2211yescharacteristic
39#16839663C2211yescharacteristic
40#16839663C2211yescharacteristic
41#16839661C2211yescharacteristic, complemented
42#16839655—21no—
43#16839642—21no—
44#16839637—21no—
45#16839622C2211yescharacteristic
46#16839617—21no—
47#16839617—21no—
48C4⋊C4×Dic61C2211yescharacteristic, complemented
49#16839524C2211yescharacteristic, complemented
50#16839524C2211yescharacteristic, complemented
51#16839516C2211yescharacteristic, complemented
52#16839516C2211yescharacteristic, complemented
53C2×#121×C61C2211yescharacteristic
54C2×#117×C61C2211yescharacteristic
55C2×#102×C61C2211yescharacteristic, complemented
56C2×#102×C61C2211yescharacteristic, complemented
57C2×C22⋊C8×C61C2211yescharacteristic
58C61×#340C2211yescharacteristic, complemented
59C61×#340C2211yescharacteristic, complemented
60C24×D61—21no—
61C22×D244—21no—
62C22×D244—22no—
63C22×D244—41no—
64C22×D244—41no—
65C22×D244—41no—
66C22×D244—41no—
67C22×D244C2×C414yescomplemented
68C22×D244C2311yescharacteristic
69C22×D244C2311yescharacteristic
70C23×Dic61—21no—
71C2×#11758199—41no—
72C2×#11758199—41no—
73C2×#11758199—41no—
74C2×#11758199—41no—
75C2×#11758199C2×C414yes—
76C2×#11758199C2×C414yes—
77C22×#92418C2311yescharacteristic
78C22×#92418C2311yescharacteristic
79D4×Dic61—41no—
80D4×Dic61—41no—
81#14519736—41no—
82#14519736—41no—
83C2×C4⋊Dic61—21no—
84C2×C4⋊Dic61D411yescharacteristic
85C2×C4⋊Dic61D411yescharacteristic
86C2×C4⋊Dic61C2311yescharacteristic
87C2×C4⋊Dic61C2311yescharacteristic
88C2×C22⋊Dic61—21no—
89C2×C22⋊Dic61—21no—
90C2×C22⋊Dic61—21no—
91C2×C22⋊Dic61—21no—
92C2×C22⋊Dic61D411yescharacteristic
93C2×C22⋊Dic61D411yescharacteristic
94C2×#11758198—21no—
95C2×#11758198—21no—
96C2×#11758198—21no—
97C2×#11758198—21no—
98C2×#11758198—21no—
99C2×#11758198—21no—
100C2×#11758198—21no—
101C2×#11758198—21no—
102C2×C4×Dic61—21no—
103C2×C4×Dic61C2311yescharacteristic
104C2×C4×Dic61C2311yescharacteristic
105#14519710—41no—
106#14519708—41no—
107#14519699—41no—
108#14519699—41no—
109#14519699—41no—
110#14519699—41no—
111#14519697C2×C414yescomplemented
112#14519697C2×C414yescomplemented
113C22⋊#92418C2×C414yescomplemented
114#14519687—41no—
115C8×Dic61—41no—
116#14519684—21no—
117#14519684—21no—
118#14519684—21no—
119C22×D4×C61—21no—
120C22×D4×C61C2311yescharacteristic
121C23×C4×C61C2311yescharacteristic
122C22×C8×C61C2311yescharacteristic
123C22×C8×C61C2311yescharacteristic
124#121×C61—22no—
125#121×C61C2×C414yes—
126#117×C61—41no—
127#117×C61—41no—
128C2×C4⋊C4×C61C2311yescharacteristic
129C2×C4⋊C4×C61C2311yescharacteristic
130C2×C4⋊C4×C61C2311yescharacteristic
131C2×C22⋊C4×C61—21no—
132C2×C22⋊C4×C61—21no—
133C2×C42×C61—21no—
134#102×C61—41no—
135#102×C61—41no—
136C22⋊C8×C61—22no—
137C24×C61—21no—
138C24×C61C2×D411yescharacteristic
139C23×D61—21no—
140C23×D61—21no—
141C23×D61—24no—
142C23×D61—42no—
143C23×D61—42no—
144C23×D61—81no—
145C23×D61—81no—
146C23×D61—81no—
147C23×D61—81no—
148C2×D4×C61—24no—
149C2×D4×C61—21no—
150C2×D4×C61—21no—
151C2×D4×C61—21no—
152C2×D4×C61—21no—
153C2×D4×C61—21no—
154C2×D4×C61—81no—
155C2×D4×C61—81no—
156C2×D4×C61C22×C412yes—
157C22×C4×C61—21no—
158C22×C4×C61—21no—
159C22×C4×C61—21no—
160C22×C4×C61—21no—
161C22×C4×C61—21no—
162C22×C4×C61—21no—
163C22×C4×C61—21no—
164C22×C4×C61C22×C412yes—
165C22×C4×C61C2×D411yescharacteristic
166C22×C4×C61#4112yes—
167C22×C4×C61C2411yescharacteristic
168C22×Dic61—21no—
169C22×Dic61—21no—
170C22×Dic61—42no—
171C22×Dic61—81no—
172C22×Dic61—81no—
173C22×Dic61C2×D411yescharacteristic
174C22×Dic61C2×D411yescharacteristic
175C22×Dic61C2×D411yescharacteristic
176C22×Dic61C2×D411yescharacteristic
177C2×D244—21no—
178C2×D244—21no—
179C2×D244—21no—
180C2×D244—21no—
181C2×D244—21no—
182C2×D244—21no—
183C2×D244—21no—
184C2×D244—21no—
185C2×D244—24no—
186C2×D244—21no—
187C2×D244—21no—
188C2×D244—44no—
189C2×D244—44no—
190C2×D244—42no—
191C2×D244—42no—
192C2×D244—44no—
193C2×D244—44no—
194C2×D244C22×C412yes—
195C2×D244C22×C412yes—
196C2×C8×C61—21no—
197C2×C8×C61—21no—
198C2×C8×C61—21no—
199C2×C8×C61—21no—
200C2×C8×C61—21no—
201C2×C8×C61—21no—
202C4⋊C4×C61—21no—
203C4⋊C4×C61—21no—
204C4⋊C4×C61—21no—
205C4⋊C4×C61—21no—
206C4⋊C4×C61—21no—
207C4⋊C4×C61C22×C412yes—
208C22⋊C4×C61—24no—
209C22⋊C4×C61—42no—
210C42×C61—42no—
211C22⋊Dic61—41no—
212C22⋊Dic61—41no—
213C22⋊Dic61—42no—
214C22⋊Dic61—81no—
215C22⋊Dic61—81no—
216C22⋊Dic61—81no—
217#11758199—44no—
218#11758199—44no—
219#11758198—81no—
220#11758198—81no—
221#11758198—81no—
222#11758198—81no—
223#11758198—81no—
224#11758198—81no—
225#11758198—81no—
226#11758198—81no—
227C4⋊Dic61—21no—
228C4⋊Dic61—21no—
229C4⋊Dic61—21no—
230C4⋊Dic61—21no—
231C4⋊Dic61—41no—
232C4⋊Dic61—41no—
233C4⋊Dic61—81no—
234C4×Dic61—21no—
235C4×Dic61—21no—
236C4×Dic61—21no—
237C4×Dic61—21no—
238C4×Dic61—81no—
239C2×#92418—21no—
240C2×#92418—21no—
241C2×#92418—21no—
242C2×#92418—21no—
243C2×#92418C22×C412yes—
244C2×#92418C22×C412yes—
245C23×C61—21no—
246C23×C61—21no—
247C23×C61—21no—
248C23×C61—21no—
249C23×C61—21no—
250C23×C61—21no—
251C23×C61—22no—
252C23×C61—41no—
253C23×C61—41no—
254C23×C61—41no—
255C23×C61—41no—
256C23×C61—41no—
257C23×C61—41no—
258C23×C61C4×D412yes—
259C23×C61C22×D411yescharacteristic
260C22×D61—22no—
261C22×D61—22no—
262C22×D61—48no—
263C22×D61—41no—
264C22×D61—41no—
265C22×D61—41no—
266C22×D61—41no—
267C22×D61—41no—
268C22×D61—41no—
269C22×D61—41no—
270C22×D61—41no—
271C22×D61—41no—
272C22×D61—41no—
273C22×D61—41no—
274C22×D61—41no—
275C22×D61—84no—
276C22×D61—84no—
277C22×D61—84no—
278C22×D61—84no—
279C22×D61—84no—
280C22×D61—84no—
281D4×C61—22no—
282D4×C61—22no—
283D4×C61—41no—
284D4×C61—41no—
285D4×C61—84no—
286C2×C4×C61—21no—
287C2×C4×C61—21no—
288C2×C4×C61—22no—
289C2×C4×C61—22no—
290C2×C4×C61—22no—
291C2×C4×C61—22no—
292C2×C4×C61—22no—
293C2×C4×C61—41no—
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—41no—
301C2×C4×C61C4×D412yes—
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
308C2×Dic61—21no—
309C2×Dic61—21no—
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—41no—
321C2×Dic61—41no—
322C2×Dic61—41no—
323C2×Dic61—41no—
324C2×Dic61—41no—
325C2×Dic61—41no—
326C2×Dic61—84no—
327D244—22no—
328D244—22no—
329D244—22no—
330D244—22no—
331D244—48no—
332D244—41no—
333D244—41no—
334D244—41no—
335D244—41no—
336C8×C61—41no—
337C8×C61—41no—
338#92418—22no—
339#92418—22no—
340#22056—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—42no—
349C22×C61—42no—
350C22×C61—42no—
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—42no—
363C2×D61—42no—
364C2×D61—42no—
365C2×D61—42no—
366C2×D61—42no—
367C2×D61—42no—
368C2×D61—816no—
369C2×D61—81no—
370C2×D61—81no—
371C2×D61—81no—
372C2×D61—81no—
373C2×D61—81no—
374C2×D61—81no—
375C2×D61—81no—
376C2×D61—81no—
377C4×C61—22no—
378C4×C61—42no—
379C4×C61—81no—
380C4×C61—81no—
381C4×C61#51811yescharacteristic
382C4×C61#51811yescharacteristic
383C4×C61#53811yescharacteristic
384C4×C61#53811yescharacteristic
385Dic61—41no—
386Dic61—41no—
387Dic61—41no—
388Dic61—41no—
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#1879—611no—
402#1875D6111yescharacteristic, complemented
403#1854—611no—
404#1786—611no—
405#1750—611no—
406C2×C61—42no—
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—82no—
416D61—82no—
417C23×D4—611no—
418C22×D8—611no—
419C22×D8—611no—
420C2×#121C2×D6111yescharacteristic
421C2×C4×D4—611no—
422C2×#117—611no—
423C2×#117C2×D6111yescharacteristic
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, complemented
434C2×#102C2×D6111yescharacteristic, complemented
435C2×C22⋊C8—611no—
436C2×C22⋊C8C2×D6111yescharacteristic
437C2×#97—611no—
438C2×C4×C8—611no—
439#390—611no—
440#390—611no—
441#390—611no—
442#390—611no—
443#390—611no—
444#390—1221no—
445#390—1221no—
446#390—1221no—
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#340C2×D6111yescharacteristic, complemented
458#340C2×D6111yescharacteristic, complemented
459#336—611no—
460#336—611no—
461C61#2205611yescharacteristic, complemented, Sylow
462C25—1221no—
463C22×D4—21no—
464C22×D4—614no—
465C22×D4—611no—
466C22×D4—611no—
467C22×D4—1221no—
468C22×D4—1222no—
469C22×D4—2441no—
470C22×D4—2441no—
471C22×D4—2441no—
472C22×D4—2441no—
473C22×D4C22×D6111yescharacteristic
474C23×C4—1221no—
475C23×C4C22×D6111yescharacteristic
476C2×D8—614no—
477C2×D8—614no—
478C2×D8—2441no—
479C2×D8—2441no—
480C2×D8—2441no—
481C2×D8—2441no—
482C22×C8—611no—
483C22×C8—611no—
484C22×C8C22×D6111yescharacteristic
485C22×C8C22×D6111yescharacteristic
486#121—22no—
487#121C4×D6114yes—
488C4×D4—2441no—
489C4×D4—2441no—
490#117—41no—
491#117—41no—
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—1221no—
499C2×C4⋊C4C22×D6111yescharacteristic
500C2×C4⋊C4C22×D6111yescharacteristic
501C2×C4⋊C4C22×D6111yescharacteristic
502C2×C22⋊C4—21no—
503C2×C22⋊C4—21no—
504C2×C22⋊C4—611no—
505C2×C22⋊C4—611no—
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×C22⋊C4—1221no—
517C2×C22⋊C4—1221no—
518C2×C42—21no—
519C2×C42—611no—
520C2×C42—611no—
521C2×C42—1221no—
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—22no—
533C22⋊C8—614no—
534#97—2441no—
535C4×C8—2441no—
536#95—1221no—
537#95—1221no—
538#95—1221no—
539C24—21no—
540C24—1224no—
541C24—1221no—
542C24—1221no—
543C24—4881no—
544C24—4881no—
545C24—4881no—
546C24—4881no—
547C24—2442no—
548C24—2442no—
549C24D4×D6111yescharacteristic
550C2×D4—24no—
551C2×D4—21no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4—81no—
557C2×D4—81no—
558C2×D4—612no—
559C2×D4—612no—
560C2×D4—1221no—
561C2×D4—1221no—
562C2×D4—1221no—
563C2×D4—1221no—
564C2×D4—1221no—
565C2×D4—1221no—
566C2×D4—1221no—
567C2×D4—1221no—
568C2×D4—1221no—
569C2×D4—1221no—
570C2×D4—1224no—
571C2×D4—2444no—
572C2×D4—2444no—
573C2×D4—2442no—
574C2×D4—2442no—
575C2×D4—2444no—
576C2×D4—2444no—
577C2×D4C2×C4×D6112yes—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—611no—
586C22×C4—611no—
587C22×C4—611no—
588C22×C4—611no—
589C22×C4—1221no—
590C22×C4—1221no—
591C22×C4—4881no—
592C22×C4—4881no—
593C22×C4—2442no—
594C22×C4C2×C4×D6112yes—
595C22×C4D4×D6111yescharacteristic
596C22×C4#1175822412yes—
597C22×C4C23×D6111yescharacteristic
598D8—2444no—
599D8—2444no—
600C2×C8—21no—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8—21no—
605C2×C8—21no—
606C2×C8—612no—
607C2×C8—612no—
608C2×C8—1221no—
609C2×C8—1221no—
610C2×C8—1221no—
611C2×C8—1221no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—1221no—
618C4⋊C4—1221no—
619C4⋊C4—1221no—
620C4⋊C4—1221no—
621C4⋊C4—4881no—
622C4⋊C4—2441no—
623C4⋊C4—2441no—
624C4⋊C4C2×C4×D6112yes—
625C22⋊C4—24no—
626C22⋊C4—42no—
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—2441no—
639C22⋊C4—2441no—
640C22⋊C4—2442no—
641C42—42no—
642C42—1221no—
643C42—1221no—
644C42—1221no—
645C42—1221no—
646C42—4881no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—22no—
654C23—41no—
655C23—41no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—1222no—
661C23—1222no—
662C23—4884no—
663C23—4884no—
664C23—4884no—
665C23—4884no—
666C23—4884no—
667C23—4884no—
668C23—2448no—
669C23—2441no—
670C23—2441no—
671C23—2441no—
672C23—2441no—
673C23—2441no—
674C23—2441no—
675C23—2441no—
676C23—2441no—
677C23—2441no—
678C23—2441no—
679C23—2441no—
680C23—2441no—
681C23#1451973712yes—
682C23C2×D4×D6111yescharacteristic
683D4—22no—
684D4—22no—
685D4—41no—
686D4—41no—
687D4—84no—
688D4—1222no—
689D4—1222no—
690D4—1222no—
691D4—1222no—
692D4—2448no—
693D4—2441no—
694D4—2441no—
695D4—2441no—
696D4—2441no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—1221no—
713C2×C4—1221no—
714C2×C4—1221no—
715C2×C4—1221no—
716C2×C4—1221no—
717C2×C4—1221no—
718C2×C4—1221no—
719C2×C4—1221no—
720C2×C4—1221no—
721C2×C4—1221no—
722C2×C4—1221no—
723C2×C4—1221no—
724C2×C4—4884no—
725C2×C4—2441no—
726C2×C4—2441no—
727C2×C4—2441no—
728C2×C4—2441no—
729C2×C4—2441no—
730C2×C4—2441no—
731C2×C4#1451973712yes—
732C2×C4C22×C4×D6111yescharacteristic
733C2×C4C2×#1175822411yescharacteristic
734C2×C4#1451982211yescharacteristic
735C2×C4#1451982211yescharacteristic
736C2×C4#1451982311yescharacteristic
737C2×C4#1451982311yescharacteristic
738C8—41no—
739C8—41no—
740C8—1222no—
741C8—1222no—
742C22—22no—
743C22—22no—
744C22—22no—
745C22—41no—
746C22—41no—
747C22—41no—
748C22—41no—
749C22—42no—
750C22—42no—
751C22—42no—
752C22—81no—
753C22—81no—
754C22—81no—
755C22—81no—
756C22—48816no—
757C22—4881no—
758C22—4881no—
759C22—4881no—
760C22—4881no—
761C22—4881no—
762C22—4881no—
763C22—4881no—
764C22—4881no—
765C22—2442no—
766C22—2442no—
767C22—2442no—
768C22—2442no—
769C22—2442no—
770C22—2442no—
771C22C2×#1451973711yescharacteristic
772C22#1684032311yescharacteristic
773C22#1684032711yescharacteristic
774C22#1684056411yescharacteristic
775C22#1684056611yescharacteristic
776C22#1684056611yescharacteristic
777C22#1684056911yescharacteristic
778C4—22no—
779C4—42no—
780C4—81no—
781C4—81no—
782C4—4881no—
783C4—4881no—
784C4—2441no—
785C4—2441no—
786C4—2441no—
787C4—2441no—
788C4#1684023411yescharacteristic
789C4#1684023411yescharacteristic
790C4#1684034911yescharacteristic
791C4#1684034911yescharacteristic
792C2—42no—
793C2—82no—
794C2—4882no—
795C2—4882no—
796C2#2144848211yescharacteristic
797C2#2145465411yescharacteristic
798C2#2145466711yescharacteristic
799C2#2145666911yescharacteristic
800C2#2145668311yescharacteristic
801C2#2145686711yescharacteristic
802C2#2145691111yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1875C2
socleC23×C61C22×D4
prime radicalC2×#16839895C2
cosocleC22×C4×C61C24
hypercenter#1875D61
hypocenterC61#22056
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1875

Complements

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

NH ≅ G/Ntype
2. #21448514C2semidirect
3. #21448399C2semidirect
4. #21446692C2semidirect
5. #21446682C2semidirect
6. #21446517C2semidirect
7. #21446503C2semidirect
8. #21446444C2semidirect
9. #21446437C2semidirect
10. #21446165C2semidirect
11. #21446165C2semidirect
12. #21446018C2semidirect
13. #21445751C2semidirect
14. #21445587C2semidirect
15. C61×#1875C2semidirect
19. C2×D4×Dic61C22semidirect
21. #16839895C4semidirect
22. C2×#14519710C22semidirect
23. C2×#14519708C22semidirect
31. C2×#14519687C22semidirect
32. C2×C8×Dic61C22semidirect
34. #16839665C22semidirect
41. #16839661C22semidirect
48. C4⋊C4×Dic61C22semidirect
49. #16839524C22semidirect
50. #16839524C22semidirect
51. #16839516C22semidirect
52. #16839516C22semidirect
55. C2×#102×C61C22semidirect
56. C2×#102×C61C22semidirect
58. C61×#340C22semidirect
59. C61×#340C22semidirect
67. C22×D244C2×C4semidirect
111. #14519697C2×C4semidirect
112. #14519697C2×C4semidirect
113. C22⋊#92418C2×C4semidirect
402. #1875D61semidirect
433. C2×#102C2×D61semidirect
434. C2×#102C2×D61semidirect
457. #340C2×D61semidirect
458. #340C2×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×#168398952
#214485142
#214483992
#214466922
#214466822
#214465172
#214465032
#214464442
#214464372
#214461652
#214460182
#214457512
#214455872
C61×#18752
#2205661