Finite Group Databasebeta

← #29691300

Subgroups — #29691300

Order 15616.

1080 conjugacy classes of subgroups.

The subgroup lattice has 766 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839912C211yesmaximal, characteristic
2#21448503C211yesmaximal, characteristic, complemented
3#21448399C211yesmaximal, characteristic
4#21446697C211yesmaximal, characteristic, complemented
5#21446670C211yesmaximal, characteristic, complemented
6#21446517C211yesmaximal, characteristic, complemented
7#21446503C211yesmaximal, characteristic, complemented
8#21446444C211yesmaximal, characteristic, complemented
9#21446437C211yesmaximal, characteristic, complemented
10#21446172C211yesmaximal, characteristic, complemented
11#21446172C211yesmaximal, characteristic, complemented
12#21446018C211yesmaximal, characteristic, complemented
13#21445751C211yesmaximal, characteristic
14#21445587C211yesmaximal, characteristic, complemented
15C61×#1873C211yesmaximal, characteristic, complemented
16C23×D244C2211yescharacteristic
17C22×#11758201C2211yescharacteristic
18C22×#11758201C2211yescharacteristic
19C2×Q8×Dic61C2211yescharacteristic, complemented
20C2×#14519736C2211yescharacteristic
21#16839912C418yescomplemented
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#16839669C2211yescharacteristic, complemented
34#16839664—21no—
35#16839664—21no—
36#16839663C2211yescharacteristic
37#16839663C2211yescharacteristic
38#16839663C2211yescharacteristic
39#16839663C2211yescharacteristic
40#16839661—21no—
41#16839661C2211yescharacteristic, complemented
42#16839655—21no—
43#16839655—21no—
44#16839648—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×C22⋊Q8×C61C2211yescharacteristic
54C2×#117×C61C2211yescharacteristic
55C2×#103×C61C2211yescharacteristic, complemented
56C2×#103×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×C414yes—
68C22×D244C2311yescharacteristic
69C22×D244C2311yescharacteristic
70C2×#11758201—41no—
71C2×#11758201—41no—
72C2×#11758201—41no—
73C2×#11758201—41no—
74C2×#11758201C2×C414yes—
75C2×#11758201C2×C414yes—
76C22×#92418C2311yescharacteristic
77C22×#92418C2311yescharacteristic
78Q8×Dic61—41no—
79Q8×Dic61—41no—
80#14519736—41no—
81#14519736—41no—
82C2×C4⋊Dic61—21no—
83C2×C4⋊Dic61—21no—
84C2×C4⋊Dic61D411yescharacteristic
85C2×C4⋊Dic61D411yescharacteristic
86C2×C4⋊Dic61C2311yescharacteristic
87C2×C4⋊Dic61C2311yescharacteristic
88C2×C22⋊Dic61—21no—
89C2×C22⋊Dic61D411yescharacteristic
90C2×C22⋊Dic61D411yescharacteristic
91C2×#11758198—21no—
92C2×#11758198—21no—
93C2×#11758198—21no—
94C2×#11758198—21no—
95C2×#11758198—21no—
96C2×#11758198—21no—
97C2×#11758198—21no—
98C2×#11758198—21no—
99C2×C4×Dic61—21no—
100C2×C4×Dic61—21no—
101C2×C4×Dic61C2311yescharacteristic
102C2×C4×Dic61C2311yescharacteristic
103#14519710—41no—
104#14519708—41no—
105#14519699—41no—
106#14519699—41no—
107#14519699—41no—
108#14519699—41no—
109#14519697C2×C414yes—
110#14519697C2×C414yes—
111C22⋊#92418C2×C414yes—
112#14519687—41no—
113C8×Dic61—41no—
114#14519684—21no—
115#14519684—21no—
116#14519684—21no—
117#14519684—21no—
118#14519684—21no—
119C22×Q8×C61C2311yescharacteristic
120C23×C4×C61C2311yescharacteristic
121C22×C8×C61C2311yescharacteristic
122C22×C8×C61C2311yescharacteristic
123C22⋊Q8×C61—22no—
124C22⋊Q8×C61C2×C414yes—
125#117×C61—41no—
126#117×C61—41no—
127C2×C4⋊C4×C61—21no—
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#103×C61—41no—
135#103×C61—41no—
136C22⋊C8×C61—22no—
137C24×C61C2×D411yescharacteristic
138C23×D61—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—
147C2×Q8×C61—21no—
148C2×Q8×C61—21no—
149C2×Q8×C61—21no—
150C2×Q8×C61—21no—
151C2×Q8×C61—21no—
152C2×Q8×C61C22×C412yes—
153C22×C4×C61—21no—
154C22×C4×C61—21no—
155C22×C4×C61—21no—
156C22×C4×C61—21no—
157C22×C4×C61—21no—
158C22×C4×C61—21no—
159C22×C4×C61—21no—
160C22×C4×C61—21no—
161C22×C4×C61C22×C412yes—
162C22×C4×C61C2×D411yescharacteristic
163C22×C4×C61#4112yes—
164C22×C4×C61C2411yescharacteristic
165C22×Dic61—21no—
166C22×Dic61—21no—
167C22×Dic61C2×D411yescharacteristic
168C22×Dic61C2×D411yescharacteristic
169C22×Dic61C2×D411yescharacteristic
170C22×Dic61C2×D411yescharacteristic
171C2×D244—21no—
172C2×D244—21no—
173C2×D244—21no—
174C2×D244—21no—
175C2×D244—21no—
176C2×D244—21no—
177C2×D244—21no—
178C2×D244—21no—
179C2×D244—24no—
180C2×D244—21no—
181C2×D244—21no—
182C2×D244—44no—
183C2×D244—44no—
184C2×D244—42no—
185C2×D244—42no—
186C2×D244—44no—
187C2×D244—44no—
188C2×D244C22×C412yes—
189C2×D244C22×C412yes—
190C2×C8×C61—21no—
191C2×C8×C61—21no—
192C2×C8×C61—21no—
193C2×C8×C61—21no—
194C2×C8×C61—21no—
195C2×C8×C61—21no—
196C4⋊C4×C61—24no—
197C4⋊C4×C61—21no—
198C4⋊C4×C61—21no—
199C4⋊C4×C61—21no—
200C4⋊C4×C61—21no—
201C4⋊C4×C61—21no—
202C4⋊C4×C61C22×C412yes—
203C22⋊C4×C61—24no—
204C22⋊C4×C61—42no—
205C42×C61—42no—
206C22⋊Dic61—41no—
207C22⋊Dic61—41no—
208C22⋊Dic61—81no—
209#11758201—44no—
210#11758201—44no—
211#11758198—81no—
212#11758198—81no—
213#11758198—81no—
214#11758198—81no—
215#11758198—81no—
216#11758198—81no—
217#11758198—81no—
218#11758198—81no—
219C4⋊Dic61—21no—
220C4⋊Dic61—21no—
221C4⋊Dic61—21no—
222C4⋊Dic61—21no—
223C4⋊Dic61—41no—
224C4⋊Dic61—41no—
225C4⋊Dic61—42no—
226C4⋊Dic61—81no—
227C4×Dic61—21no—
228C4×Dic61—21no—
229C4×Dic61—21no—
230C4×Dic61—21no—
231C4×Dic61—42no—
232C4×Dic61—81no—
233C2×#92418—21no—
234C2×#92418—21no—
235C2×#92418—21no—
236C2×#92418—21no—
237C2×#92418C22×C412yes—
238C2×#92418C22×C412yes—
239C23×C61—21no—
240C23×C61—21no—
241C23×C61—21no—
242C23×C61—21no—
243C23×C61—21no—
244C23×C61—21no—
245C23×C61C4×D412yes—
246C23×C61C22×D411yescharacteristic
247C22×D61—22no—
248C22×D61—22no—
249C22×D61—48no—
250C22×D61—41no—
251C22×D61—41no—
252C22×D61—41no—
253C22×D61—41no—
254C22×D61—41no—
255C22×D61—41no—
256C22×D61—41no—
257C22×D61—41no—
258C22×D61—41no—
259C22×D61—41no—
260C22×D61—41no—
261C22×D61—41no—
262C22×D61—84no—
263C22×D61—84no—
264C22×D61—84no—
265C22×D61—84no—
266C22×D61—84no—
267C22×D61—84no—
268Q8×C61—22no—
269Q8×C61—22no—
270Q8×C61—41no—
271Q8×C61—41no—
272C2×C4×C61—21no—
273C2×C4×C61—21no—
274C2×C4×C61—22no—
275C2×C4×C61—22no—
276C2×C4×C61—22no—
277C2×C4×C61—22no—
278C2×C4×C61—22no—
279C2×C4×C61—22no—
280C2×C4×C61—41no—
281C2×C4×C61—41no—
282C2×C4×C61—41no—
283C2×C4×C61—41no—
284C2×C4×C61—41no—
285C2×C4×C61—41no—
286C2×C4×C61—41no—
287C2×C4×C61—41no—
288C2×C4×C61—41no—
289C2×C4×C61—41no—
290C2×C4×C61C4×D412yes—
291C2×C4×C61C23×C411yescharacteristic
292C2×C4×C61C2×#4111yescharacteristic
293C2×C4×C61H(5,𝔽2)11yescharacteristic
294C2×C4×C61H(5,𝔽2)11yescharacteristic
295C2×C4×C61H(5,𝔽2)11yescharacteristic
296C2×C4×C61H(5,𝔽2)11yescharacteristic
297C2×Dic61—21no—
298C2×Dic61—21no—
299C2×Dic61—21no—
300C2×Dic61—21no—
301C2×Dic61—21no—
302C2×Dic61—21no—
303C2×Dic61—21no—
304C2×Dic61—21no—
305C2×Dic61—21no—
306C2×Dic61—21no—
307C2×Dic61—21no—
308C2×Dic61—21no—
309C2×Dic61—41no—
310C2×Dic61—41no—
311C2×Dic61—41no—
312C2×Dic61—41no—
313C2×Dic61—41no—
314C2×Dic61—41no—
315D244—22no—
316D244—22no—
317D244—22no—
318D244—22no—
319D244—48no—
320D244—41no—
321D244—41no—
322D244—41no—
323D244—41no—
324C8×C61—41no—
325C8×C61—41no—
326#92418—22no—
327#92418—22no—
328#22052—611nomaximal, Sylow
329C22×C61—22no—
330C22×C61—22no—
331C22×C61—22no—
332C22×C61—41no—
333C22×C61—41no—
334C22×C61—41no—
335C22×C61—41no—
336C22×C61C2×C4×D411yescharacteristic
337C22×C61#53411yescharacteristic
338C22×C61#53511yescharacteristic
339C22×C61#57611yescharacteristic
340C22×C61#57711yescharacteristic
341C22×C61#57711yescharacteristic
342C22×C61#57711yescharacteristic
343C2×D61—42no—
344C2×D61—42no—
345C2×D61—42no—
346C2×D61—42no—
347C2×D61—42no—
348C2×D61—42no—
349C2×D61—816no—
350C2×D61—81no—
351C2×D61—81no—
352C2×D61—81no—
353C2×D61—81no—
354C2×D61—81no—
355C2×D61—81no—
356C2×D61—81no—
357C2×D61—81no—
358C4×C61—22no—
359C4×C61—42no—
360C4×C61—42no—
361C4×C61—81no—
362C4×C61—81no—
363C4×C61#51811yescharacteristic
364C4×C61#51811yescharacteristic
365C4×C61#53811yescharacteristic
366C4×C61#53811yescharacteristic
367Dic61—41no—
368Dic61—41no—
369Dic61—41no—
370Dic61—41no—
371Dic61—81no—
372Dic61—81no—
373C2×#450—611no—
374#2323—611no—
375#2309—611no—
376#1973—611no—
377#1968—611no—
378#1936—611no—
379#1934—611no—
380#1926—611no—
381#1925—611no—
382#1880—611no—
383#1880—611no—
384#1873D6111yescharacteristic, complemented
385#1854—611no—
386#1786—611no—
387#1750—611no—
388C2×C61—42no—
389C2×C61#232111yescharacteristic
390C2×C61#294611yescharacteristic
391C2×C61#294911yescharacteristic
392C2×C61#319811yescharacteristic
393C2×C61#320011yescharacteristic
394C2×C61#322211yescharacteristic
395C2×C61#322411yescharacteristic
396D61—82no—
397D61—82no—
398C23×D4—611no—
399C22×SD16—611no—
400C22×SD16—611no—
401C2×C22⋊Q8C2×D6111yescharacteristic
402C2×C4×Q8—611no—
403C2×#117—611no—
404C2×#117C2×D6111yescharacteristic
405#450—618no—
406C2×#107—611no—
407C2×#106—611no—
408C2×#103C2×D6111yescharacteristic, complemented
409C2×#103C2×D6111yescharacteristic, complemented
410C2×#102—611no—
411C2×#102—611no—
412C2×#102—611no—
413C2×#102—611no—
414C2×#102—611no—
415C2×#102—611no—
416C2×C22⋊C8—611no—
417C2×C22⋊C8C2×D6111yescharacteristic
418C2×#97—611no—
419C2×C4×C8—611no—
420#391—611no—
421#390—611no—
422#390—611no—
423#390—611no—
424#390—611no—
425#390—1221no—
426#390—1221no—
427#389—611no—
428#389—1221no—
429#388—1221no—
430#388—1221no—
431#387—1221no—
432#380—611no—
433#379—1221no—
434#379—1221no—
435C4×C4⋊C4—611no—
436#340—611no—
437#340—611no—
438#340C2×D6111yescharacteristic, complemented
439#340C2×D6111yescharacteristic, complemented
440#336—611no—
441#336—611no—
442C61#2205211yescharacteristic, complemented, Sylow
443C25—1221no—
444C22×Q8C22×D6111yescharacteristic
445C22×D4—614no—
446C22×D4—611no—
447C22×D4—611no—
448C22×D4—1221no—
449C22×D4—1222no—
450C22×D4—2441no—
451C22×D4—2441no—
452C22×D4—2441no—
453C22×D4—2441no—
454C23×C4C22×D6111yescharacteristic
455C2×SD16—614no—
456C2×SD16—614no—
457C2×SD16—2441no—
458C2×SD16—2441no—
459C2×SD16—2441no—
460C2×SD16—2441no—
461C22×C8—611no—
462C22×C8—611no—
463C22×C8C22×D6111yescharacteristic
464C22×C8C22×D6111yescharacteristic
465C22⋊Q8—22no—
466C22⋊Q8C4×D6114yes—
467C4×Q8—2441no—
468C4×Q8—2441no—
469#117—41no—
470#117—41no—
471#117—2441no—
472#117—2441no—
473C2×C4⋊C4—21no—
474C2×C4⋊C4—611no—
475C2×C4⋊C4—611no—
476C2×C4⋊C4—611no—
477C2×C4⋊C4—611no—
478C2×C4⋊C4—1221no—
479C2×C4⋊C4—1221no—
480C2×C4⋊C4C22×D6111yescharacteristic
481C2×C4⋊C4C22×D6111yescharacteristic
482C2×C4⋊C4C22×D6111yescharacteristic
483C2×C22⋊C4—21no—
484C2×C22⋊C4—21no—
485C2×C22⋊C4—611no—
486C2×C22⋊C4—611no—
487C2×C22⋊C4—1221no—
488C2×C22⋊C4—1221no—
489C2×C22⋊C4—1221no—
490C2×C22⋊C4—1221no—
491C2×C22⋊C4—1221no—
492C2×C22⋊C4—1221no—
493C2×C22⋊C4—1221no—
494C2×C22⋊C4—1221no—
495C2×C22⋊C4—1221no—
496C2×C42—21no—
497C2×C42—611no—
498C2×C42—611no—
499C2×C42—1221no—
500C2×C42—1221no—
501#107—2441no—
502#106—2441no—
503#103—41no—
504#103—41no—
505#102—614no—
506#102—614no—
507#102—2441no—
508#102—2441no—
509#102—2441no—
510#102—2441no—
511C22⋊C8—22no—
512C22⋊C8—614no—
513#97—2441no—
514C4×C8—2441no—
515#95—1221no—
516#95—1221no—
517#95—1221no—
518#95—1221no—
519#95—1221no—
520C24—1224no—
521C24—1221no—
522C24—1221no—
523C24—4881no—
524C24—4881no—
525C24—4881no—
526C24—4881no—
527C24—2442no—
528C24—2442no—
529C24D4×D6111yescharacteristic
530C2×Q8—21no—
531C2×Q8—21no—
532C2×Q8—21no—
533C2×Q8—21no—
534C2×Q8—21no—
535C2×Q8C2×C4×D6112yes—
536C2×D4—612no—
537C2×D4—612no—
538C2×D4—1221no—
539C2×D4—1221no—
540C2×D4—1221no—
541C2×D4—1221no—
542C2×D4—1221no—
543C2×D4—1221no—
544C2×D4—1221no—
545C2×D4—1221no—
546C2×D4—1221no—
547C2×D4—1221no—
548C2×D4—1224no—
549C2×D4—2444no—
550C2×D4—2444no—
551C2×D4—2442no—
552C2×D4—2442no—
553C2×D4—2444no—
554C2×D4—2444no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—611no—
564C22×C4—611no—
565C22×C4—611no—
566C22×C4—611no—
567C22×C4—1221no—
568C22×C4—1221no—
569C22×C4C2×C4×D6112yes—
570C22×C4D4×D6111yescharacteristic
571C22×C4#1175822412yes—
572C22×C4C23×D6111yescharacteristic
573SD16—2444no—
574SD16—2444no—
575C2×C8—21no—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8—612no—
582C2×C8—612no—
583C2×C8—1221no—
584C2×C8—1221no—
585C2×C8—1221no—
586C2×C8—1221no—
587C4⋊C4—21no—
588C4⋊C4—24no—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—1221no—
594C4⋊C4—1221no—
595C4⋊C4—1221no—
596C4⋊C4—1221no—
597C4⋊C4—4881no—
598C4⋊C4—2441no—
599C4⋊C4—2441no—
600C4⋊C4—2442no—
601C4⋊C4C2×C4×D6112yes—
602C22⋊C4—24no—
603C22⋊C4—42no—
604C22⋊C4—4881no—
605C22⋊C4—4881no—
606C22⋊C4—4881no—
607C22⋊C4—4881no—
608C22⋊C4—4881no—
609C22⋊C4—4881no—
610C22⋊C4—4881no—
611C22⋊C4—4881no—
612C22⋊C4—4881no—
613C22⋊C4—2441no—
614C22⋊C4—2441no—
615C42—42no—
616C42—1221no—
617C42—1221no—
618C42—1221no—
619C42—1221no—
620C42—4881no—
621C42—2442no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23—21no—
628C23—1222no—
629C23—1222no—
630C23—4884no—
631C23—4884no—
632C23—4884no—
633C23—4884no—
634C23—4884no—
635C23—4884no—
636C23—2448no—
637C23—2441no—
638C23—2441no—
639C23—2441no—
640C23—2441no—
641C23—2441no—
642C23—2441no—
643C23—2441no—
644C23—2441no—
645C23—2441no—
646C23—2441no—
647C23—2441no—
648C23—2441no—
649C23#1451973712yes—
650C23C2×D4×D6111yescharacteristic
651Q8—22no—
652Q8—22no—
653Q8—41no—
654Q8—41no—
655D4—1222no—
656D4—1222no—
657D4—1222no—
658D4—1222no—
659D4—2448no—
660D4—2441no—
661D4—2441no—
662D4—2441no—
663D4—2441no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—1221no—
683C2×C4—1221no—
684C2×C4—1221no—
685C2×C4—1221no—
686C2×C4—1221no—
687C2×C4—1221no—
688C2×C4—1221no—
689C2×C4—1221no—
690C2×C4—1221no—
691C2×C4—1221no—
692C2×C4—1221no—
693C2×C4—1221no—
694C2×C4—2441no—
695C2×C4—2441no—
696C2×C4—2441no—
697C2×C4—2441no—
698C2×C4—2441no—
699C2×C4—2441no—
700C2×C4#1451973712yes—
701C2×C4C22×C4×D6111yescharacteristic
702C2×C4C2×#1175822411yescharacteristic
703C2×C4#1451982211yescharacteristic
704C2×C4#1451982211yescharacteristic
705C2×C4#1451982311yescharacteristic
706C2×C4#1451982311yescharacteristic
707C8—41no—
708C8—41no—
709C8—1222no—
710C8—1222no—
711C22—22no—
712C22—22no—
713C22—22no—
714C22—41no—
715C22—41no—
716C22—41no—
717C22—41no—
718C22—48816no—
719C22—4881no—
720C22—4881no—
721C22—4881no—
722C22—4881no—
723C22—4881no—
724C22—4881no—
725C22—4881no—
726C22—4881no—
727C22—2442no—
728C22—2442no—
729C22—2442no—
730C22—2442no—
731C22—2442no—
732C22—2442no—
733C22C2×#1451973711yescharacteristic
734C22#1684032311yescharacteristic
735C22#1684032711yescharacteristic
736C22#1684056411yescharacteristic
737C22#1684056911yescharacteristic
738C22#1684057111yescharacteristic
739C22#1684057111yescharacteristic
740C4—22no—
741C4—42no—
742C4—42no—
743C4—81no—
744C4—81no—
745C4—4881no—
746C4—4881no—
747C4—2441no—
748C4—2441no—
749C4—2441no—
750C4—2441no—
751C4#1684023411yescharacteristic
752C4#1684023411yescharacteristic
753C4#1684034911yescharacteristic
754C4#1684034911yescharacteristic
755C2—42no—
756C2—4882no—
757C2—4882no—
758C2#2144848211yescharacteristic
759C2#2145465411yescharacteristic
760C2#2145467411yescharacteristic
761C2#2145667711yescharacteristic
762C2#2145669011yescharacteristic
763C2#2145688911yescharacteristic
764C2#2145691911yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1873C2
socleC23×C61C22×D4
prime radicalC23×D244C22
cosocleC22×C4×C61C24
hypercenter#1873D61
hypocenterC61#22052
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1873

Complements

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

NH ≅ G/Ntype
2. #21448503C2semidirect
4. #21446697C2semidirect
5. #21446670C2semidirect
6. #21446517C2semidirect
7. #21446503C2semidirect
8. #21446444C2semidirect
9. #21446437C2semidirect
10. #21446172C2semidirect
11. #21446172C2semidirect
12. #21446018C2semidirect
14. #21445587C2semidirect
15. C61×#1873C2semidirect
19. C2×Q8×Dic61C22semidirect
21. #16839912C4semidirect
22. C2×#14519710C22semidirect
23. C2×#14519708C22semidirect
31. C2×#14519687C22semidirect
32. C2×C8×Dic61C22semidirect
33. #16839669C22semidirect
41. #16839661C22semidirect
48. C4⋊C4×Dic61C22semidirect
49. #16839524C22semidirect
50. #16839524C22semidirect
51. #16839516C22semidirect
52. #16839516C22semidirect
55. C2×#103×C61C22semidirect
56. C2×#103×C61C22semidirect
58. C61×#340C22semidirect
59. C61×#340C22semidirect
384. #1873D61semidirect
408. C2×#103C2×D61semidirect
409. C2×#103C2×D61semidirect
438. #340C2×D61semidirect
439. #340C2×D61semidirect
442. C61#22052semidirect

Maximal subgroups

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

subgroupindex
C2×#168399122
#214485032
#214483992
#214466972
#214466702
#214465172
#214465032
#214464442
#214464372
#214461722
#214460182
#214457512
#214455872
C61×#18732
#2205261