Finite Group Databasebeta

← #29585531

Subgroups — #29585531

Order 15616.

1350 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840242C211yesmaximal, characteristic
2C22×#14519703C211yesmaximal, characteristic
3C2×#16839761C211yesmaximal, characteristic
4C2×#16839530C211yesmaximal, characteristic, complemented
5C2×#16839521C211yesmaximal, characteristic, complemented
6#21444048C211yesmaximal, characteristic, complemented
7C61×#1736C211yesmaximal, characteristic, complemented
8C22×#11758222C2211yescharacteristic
9C22×#11758194C2211yescharacteristic
10#16840242—22no—
11#16840242—22no—
12#16840242—22no—
13#16840242C414yescomplemented
14C2×C4×Dic122—21no—
15C2×C4×D244—21no—
16C2×#14519737—22no—
17C2×#14519735—21no—
18C22×C4⋊Dic61C2211yescharacteristic
19C2×C4⋊C4×D61—21no—
20C22×C4×Dic61C2211yescharacteristic
21C2×#14519703—22no—
22C2×#14519703—22no—
23C2×#14519703C414yescomplemented
24#16839761—22no—
25#16839761C414yescomplemented
26C2×#14519700—21no—
27C2×#14519697—21no—
28C2×#14519684—22no—
29#16839530—22no—
30#16839521—22no—
31C22×M16×C61C2211yescharacteristic
32C2×#117×C61C2211yescharacteristic
33C22×C4⋊C4×C61C2211yescharacteristic
34C61×#340—21no—
35C61×#340—21no—
36C2×#11758222—21no—
37C2×#11758222—21no—
38C2×#11758222—21no—
39C2×#11758222—21no—
40C2×#11758222—21no—
41C2×#11758222—21no—
42C2×#11758222C2×C412yes—
43C2×#11758222C2×C412yes—
44C2×#11758222C2×C412yes—
45C2×#11758222D412yes—
46C2×#11758222D412yes—
47C2×#11758222Q812yes—
48C22×Dic122D411yescharacteristic
49C22×D244D411yescharacteristic
50C22×C22⋊D61—21no—
51C23×Dic61—21no—
52C23×Dic61D412yes—
53C22×C4×D61—21no—
54C22×C4×D61—22no—
55C2×#11758194—21no—
56C2×#11758194—21no—
57C2×#11758194—21no—
58C2×#11758194—21no—
59C2×#11758194—21no—
60C2×#11758194C2×C412yescomplemented
61C22×#92418—21no—
62C4×Dic122—24no—
63C4×Dic122—24no—
64C4×D244—24no—
65C4×D244—24no—
66#14519737—28no—
67#14519737—28no—
68#14519735—24no—
69#14519735—24no—
70C2×C4⋊Dic61—21no—
71C2×C4⋊Dic61—21no—
72C2×C4⋊Dic61—21no—
73C2×C4⋊Dic61—21no—
74C2×C4⋊Dic61C2×C412yes—
75C2×C4⋊Dic61D412yes—
76C2×#11758196—22no—
77C4⋊C4×D61—24no—
78C4⋊C4×D61—24no—
79C2×#11758198—22no—
80C2×C4×Dic61—22no—
81C2×C4×Dic61—21no—
82C2×C4×Dic61—21no—
83C2×C4×Dic61—21no—
84C2×C4×Dic61—21no—
85C2×C4×Dic61—21no—
86C2×C4×Dic61C2×C412yescomplemented
87#14519703—28no—
88#14519700—24no—
89#14519697—24no—
90#14519684—44no—
91C23×C4×C61—21no—
92C23×C4×C61C2311yescharacteristic
93C2×M16×C61—21no—
94C2×M16×C61—21no—
95C2×M16×C61—21no—
96C2×M16×C61—21no—
97C2×M16×C61—21no—
98C2×M16×C61C2×C412yescomplemented
99C22×C8×C61—21no—
100#117×C61—21no—
101#117×C61—21no—
102#117×C61C2×C412yes—
103#117×C61D412yes—
104C2×C4⋊C4×C61—21no—
105C2×C4⋊C4×C61—21no—
106C2×C4⋊C4×C61—21no—
107C2×C4⋊C4×C61—21no—
108C2×C4⋊C4×C61—21no—
109C2×C4⋊C4×C61C2×C412yescomplemented
110C2×C4⋊C4×C61D411yescharacteristic
111C2×C4⋊C4×C61D411yescharacteristic
112C2×C22⋊C4×C61—21no—
113C2×C42×C61—21no—
114C24×C61C2×D411yescharacteristic
115C23×D61—21no—
116C22×C4×C61—21no—
117C22×C4×C61—21no—
118C22×C4×C61—22no—
119C22×C4×C61—42no—
120C22×C4×C61—42no—
121C22×C4×C61—41no—
122C22×C4×C61—41no—
123C22×C4×C61C22×C411yescharacteristic
124C22×C4×C61C22×C411yescharacteristic
125C22×C4×C61C22×C411yescharacteristic
126C22×C4×C61C2×D411yescharacteristic
127C22×C4×C61C2×D411yescharacteristic
128C22×C4×C61C2×D411yescharacteristic
129C22×C4×C61C2×D411yescharacteristic
130C22×C4×C61C2×D411yescharacteristic
131C22×C4×C61C2×D411yescharacteristic
132C22×C4×C61C2×Q811yescharacteristic
133C22×C4×C61#4111yescharacteristic
134C22×C4×C61#4111yescharacteristic
135C22×C4×C61#4111yescharacteristic
136C22×C4×C61#4111yescharacteristic
137C2×C22⋊D61—22no—
138C2×C22⋊D61—22no—
139C2×C22⋊D61—22no—
140C2×C22⋊D61—22no—
141C2×C22⋊D61—22no—
142C2×C22⋊D61—22no—
143C22×Dic61—21no—
144C22×Dic61—22no—
145C22×Dic61—22no—
146C22×Dic61—22no—
147C22×Dic61—22no—
148C22×Dic61—22no—
149C22×Dic61—41no—
150C22×Dic61—41no—
151C22×Dic61—41no—
152C22×Dic61—41no—
153C22×Dic61—42no—
154C22×Dic61—42no—
155C22×Dic61C22⋊C414yes—
156#11758222—22no—
157#11758222—22no—
158#11758222—22no—
159#11758222—22no—
160#11758222—22no—
161#11758222—22no—
162#11758222—22no—
163#11758222—22no—
164#11758222—22no—
165#11758222—22no—
166#11758222—22no—
167#11758222—22no—
168#11758222C4214yes—
169#11758222C22⋊C414yes—
170#11758222C4⋊C414yes—
171#11758222C4⋊C414yes—
172C2×D244—21no—
173C2×D244—21no—
174C2×D244—21no—
175C2×D244C22⋊C412yes—
176C2×D244C22⋊C412yes—
177C2×D244C4⋊C412yes—
178C2×C4×D61—22no—
179C2×C4×D61—22no—
180C2×C4×D61—22no—
181C2×C4×D61—22no—
182C2×C4×D61—22no—
183C2×C4×D61—22no—
184C2×C4×D61—28no—
185C2×C4×D61—82no—
186C2×C4×D61—82no—
187C2×Dic122—21no—
188C2×Dic122—21no—
189C2×Dic122—21no—
190C2×Dic122C22⋊C412yes—
191C2×Dic122C22⋊C412yes—
192C2×Dic122C4⋊C412yes—
193M16×C61—22no—
194M16×C61—22no—
195M16×C61—41no—
196M16×C61—41no—
197C2×C8×C61—22no—
198C2×C8×C61—41no—
199C2×C8×C61—41no—
200C4⋊C4×C61—21no—
201C4⋊C4×C61—21no—
202C4⋊C4×C61—22no—
203C4⋊C4×C61—22no—
204C4⋊C4×C61—41no—
205C4⋊C4×C61—41no—
206C4⋊C4×C61C22⋊C412yes—
207C4⋊C4×C61C22⋊C412yes—
208C22⋊C4×C61—22no—
209C22⋊C4×C61—22no—
210C42×C61—22no—
211C42×C61—22no—
212#11758198—28no—
213C4⋊Dic61—22no—
214C4⋊Dic61—22no—
215C4⋊Dic61—22no—
216C4⋊Dic61—22no—
217#11758196—28no—
218C4×Dic61—28no—
219C4×Dic61—22no—
220C4×Dic61—22no—
221C4×Dic61—41no—
222C4×Dic61—41no—
223#11758194—22no—
224#11758194—22no—
225#11758194—41no—
226#11758194—41no—
227C2×#92418—22no—
228C2×#92418—41no—
229C2×#92418—41no—
230C23×C61—21no—
231C23×C61—21no—
232C23×C61—21no—
233C23×C61—21no—
234C23×C61C2×C22⋊C411yescharacteristic
235C23×C61C4×D411yescharacteristic
236C23×C61C4×D411yescharacteristic
237C23×C61#12011yescharacteristic
238C23×C61#12011yescharacteristic
239C23×C61#12111yescharacteristic
240C23×C61C22⋊Q811yescharacteristic
241C22×D61—22no—
242C22×D61—22no—
243C22×D61—22no—
244C22×D61—41no—
245C22×D61—41no—
246C22×D61—41no—
247C22×D61—41no—
248C2×C4×C61—22no—
249C2×C4×C61—22no—
250C2×C4×C61—41no—
251C2×C4×C61—41no—
252C2×C4×C61—41no—
253C2×C4×C61—41no—
254C2×C4×C61—44no—
255C2×C4×C61—42no—
256C2×C4×C61—82no—
257C2×C4×C61—81no—
258C2×C4×C61—81no—
259C2×C4×C61C2×C4211yescharacteristic
260C2×C4×C61C2×C22⋊C411yescharacteristic
261C2×C4×C61C2×C22⋊C411yescharacteristic
262C2×C4×C61C2×C22⋊C411yescharacteristic
263C2×C4×C61C2×C22⋊C411yescharacteristic
264C2×C4×C61C2×C4⋊C411yescharacteristic
265C2×C4×C61C2×C4⋊C411yescharacteristic
266C2×C4×C61C2×C4⋊C411yescharacteristic
267C2×C4×C61#11711yescharacteristic
268C2×C4×C61#11711yescharacteristic
269C2×C4×C61C4×D411yescharacteristic
270C2×C4×C61C4×D411yescharacteristic
271C2×C4×C61C4×D411yescharacteristic
272C2×C4×C61C4×D411yescharacteristic
273C2×C4×C61C4×D411yescharacteristic
274C2×C4×C61C4×D411yescharacteristic
275C2×C4×C61#12011yescharacteristic
276C2×C4×C61#12011yescharacteristic
277C2×C4×C61#12111yescharacteristic
278C2×C4×C61#12111yescharacteristic
279C2×C4×C61#12111yescharacteristic
280C2×C4×C61C22⋊Q811yescharacteristic
281C2×C4×C61C22⋊Q811yescharacteristic
282C2×C4×C61C22⋊Q811yescharacteristic
283C2×C4×C61#12311yescharacteristic
284C2×C4×C61#12311yescharacteristic
285C2×C4×C61#12311yescharacteristic
286C2×C4×C61#12311yescharacteristic
287C22⋊D61—24no—
288C22⋊D61—24no—
289C22⋊D61—24no—
290C22⋊D61—24no—
291C2×Dic61—22no—
292C2×Dic61—22no—
293C2×Dic61—22no—
294C2×Dic61—24no—
295C2×Dic61—24no—
296C2×Dic61—42no—
297C2×Dic61—42no—
298C2×Dic61—42no—
299C2×Dic61—42no—
300C2×Dic61—42no—
301C2×Dic61—42no—
302C2×Dic61—42no—
303C2×Dic61—42no—
304C2×Dic61—44no—
305C2×Dic61—82no—
306D244—22no—
307D244—22no—
308D244—22no—
309D244#9514yescomplemented
310C4×D61—24no—
311C4×D61—24no—
312C4×D61—24no—
313C4×D61—24no—
314C4×D61—88no—
315Dic122—22no—
316Dic122—22no—
317Dic122—22no—
318Dic122#9514yescomplemented
319C8×C61—42no—
320#92418—42no—
321#10781—611nomaximal, Sylow
322C22×C61—21no—
323C22×C61—21no—
324C22×C61—21no—
325C22×C61—21no—
326C22×C61—21no—
327C22×C61—21no—
328C22×C61—21no—
329C22×C61—21no—
330C22×C61—21no—
331C22×C61—21no—
332C22×C61—21no—
333C22×C61—21no—
334C22×C61C4×C22⋊C411yescharacteristic
335C22×C61#37911yescharacteristic
336C22×C61#38011yescharacteristic
337C22×C61#38511yescharacteristic
338C22×C61#38511yescharacteristic
339C22×C61#38611yescharacteristic
340C22×C61#38611yescharacteristic
341C22×C61#45311yescharacteristic
342C22×C61#45411yescharacteristic
343C22×C61#45511yescharacteristic
344C22×C61#45611yescharacteristic
345C2×D61—24no—
346C2×D61—42no—
347C2×D61—42no—
348C2×D61—42no—
349C2×D61—42no—
350C2×D61—42no—
351C2×D61—42no—
352C4×C61—42no—
353C4×C61—42no—
354C4×C61—82no—
355C4×C61C2×#9511yescharacteristic
356C4×C61C4×C22⋊C411yescharacteristic
357C4×C61#38011yescharacteristic
358C4×C61#38111yescharacteristic
359C4×C61#38511yescharacteristic
360C4×C61#38511yescharacteristic
361C4×C61#38611yescharacteristic
362C4×C61#38611yescharacteristic
363Dic61—24no—
364Dic61—44no—
365Dic61—44no—
366C2×#520—611no—
367C22×#104—611no—
368C2×#417—611no—
369C2×#343—611no—
370#1736D6111yescharacteristic, complemented
371C2×#339—611no—
372C4⋊#95—611no—
373C2×C61—21no—
374C2×C61—21no—
375C2×C61—21no—
376C2×C61—21no—
377C2×C61C22⋊#9511yescharacteristic
378C2×C61#179211yescharacteristic
379C2×C61#179311yescharacteristic
380C2×C61#185911yescharacteristic
381C2×C61#186011yescharacteristic
382C2×C61#188211yescharacteristic
383C2×C61#188311yescharacteristic
384D61—44no—
385C22×#41—611no—
386C22×M16—611no—
387C22×M16C2×D6111yescharacteristic
388#520—614no—
389#520—1222no—
390#520—1222no—
391#520—1222no—
392C2×C4×Q8—1221no—
393C2×C4×D4—1221no—
394C2×C4×D4—1222no—
395C2×#117—1221no—
396C2×#117C2×D6111yescharacteristic
397C22×C4⋊C4—611no—
398C22×C4⋊C4—1221no—
399C22×C4⋊C4C2×D6111yescharacteristic
400C22×C42—611no—
401C2×#104—614no—
402C2×#104—1222no—
403C2×#104—1222no—
404#417—614no—
405#417—1222no—
406C2×#103—1221no—
407C2×#102—1221no—
408C2×#95—1222no—
409#343—1222no—
410#340—21no—
411#340—21no—
412#339—1222no—
413C61#1078111yescharacteristic, complemented, Sylow
414C2×#41—612no—
415C2×#41—612no—
416C2×#41—612no—
417C2×#41—612no—
418C2×#41—612no—
419C2×#41—612no—
420C2×#41—1221no—
421C2×#41—1221no—
422C2×#41—1221no—
423C2×#41—1221no—
424C2×#41—1221no—
425C2×#41—1221no—
426C22×Q8—611no—
427C22×D4—611no—
428C22×D4—1221no—
429C23×C4—21no—
430C23×C4—612no—
431C23×C4—1222no—
432C23×C4—1221no—
433C23×C4—1221no—
434C23×C4C22×D6111yescharacteristic
435C2×M16—21no—
436C2×M16—21no—
437C2×M16—21no—
438C2×M16—21no—
439C2×M16—21no—
440C2×M16—612no—
441C2×M16—1221no—
442C2×M16—1221no—
443C2×M16—1221no—
444C2×M16—1221no—
445C2×M16—1221no—
446C2×M16C4×D6112yescomplemented
447C22×C8—21no—
448C22×C8—1221no—
449C4×Q8—1224no—
450C4×Q8—1224no—
451C4×D4—1224no—
452C4×D4—1224no—
453C4×D4—1228no—
454C4×D4—1228no—
455#117—21no—
456#117—21no—
457#117—1224no—
458#117—1224no—
459#117C4×D6112yes—
460#117D24412yes—
461C2×C4⋊C4—21no—
462C2×C4⋊C4—21no—
463C2×C4⋊C4—21no—
464C2×C4⋊C4—21no—
465C2×C4⋊C4—21no—
466C2×C4⋊C4—612no—
467C2×C4⋊C4—612no—
468C2×C4⋊C4—1224no—
469C2×C4⋊C4—1222no—
470C2×C4⋊C4—1221no—
471C2×C4⋊C4—1221no—
472C2×C4⋊C4—1221no—
473C2×C4⋊C4—1221no—
474C2×C4⋊C4—1224no—
475C2×C4⋊C4C4×D6112yescomplemented
476C2×C4⋊C4C22⋊D6111yescharacteristic
477C2×C4⋊C4C22⋊D6111yescharacteristic
478C2×C22⋊C4—21no—
479C2×C22⋊C4—1222no—
480C2×C42—21no—
481C2×C42—612no—
482C2×C42—1222no—
483C2×C42—1221no—
484C2×C42—1221no—
485C2×C42—1221no—
486C2×C42—1221no—
487C2×C42—1221no—
488#104—1228no—
489#103—1224no—
490#102—1224no—
491#95—2444no—
492C24—1221no—
493C24D4×D6111yescharacteristic
494#41—614no—
495#41—614no—
496#41—614no—
497#41—614no—
498#41—1222no—
499#41—1222no—
500#41—1222no—
501#41—1222no—
502#41—1222no—
503#41—1222no—
504#41—1222no—
505#41—1222no—
506#41—1222no—
507#41—1222no—
508#41—1222no—
509#41—1222no—
510C2×Q8—612no—
511C2×Q8—612no—
512C2×Q8—612no—
513C2×Q8—1221no—
514C2×Q8—1221no—
515C2×Q8—1221no—
516C2×D4—612no—
517C2×D4—612no—
518C2×D4—612no—
519C2×D4—1222no—
520C2×D4—1222no—
521C2×D4—1222no—
522C2×D4—1222no—
523C2×D4—1222no—
524C2×D4—1222no—
525C2×D4—1221no—
526C2×D4—1221no—
527C2×D4—1221no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—22no—
531C22×C4—42no—
532C22×C4—42no—
533C22×C4—41no—
534C22×C4—41no—
535C22×C4—614no—
536C22×C4—1228no—
537C22×C4—1221no—
538C22×C4—1222no—
539C22×C4—1222no—
540C22×C4—1222no—
541C22×C4—1222no—
542C22×C4—1222no—
543C22×C4—1222no—
544C22×C4—1222no—
545C22×C4—1222no—
546C22×C4—1222no—
547C22×C4—1222no—
548C22×C4—1222no—
549C22×C4—4882no—
550C22×C4—4882no—
551C22×C4—2442no—
552C22×C4—2442no—
553C22×C4—2441no—
554C22×C4—2441no—
555C22×C4—2441no—
556C22×C4—2441no—
557C22×C4C2×C4×D6111yescharacteristic
558C22×C4C2×C4×D6111yescharacteristic
559C22×C4C2×C4×D6111yescharacteristic
560C22×C4C2×D24411yescharacteristic
561C22×C4#1175822211yescharacteristic
562C22×C4#1175822211yescharacteristic
563C22×C4D4×D6111yescharacteristic
564C22×C4D4×D6111yescharacteristic
565C22×C4D4×D6111yescharacteristic
566C22×C4D4×D6111yescharacteristic
567C22×C4#1175822411yescharacteristic
568C22×C4Q8×D6111yescharacteristic
569C22×C4#1175822611yescharacteristic
570C22×C4C2×C22⋊D6111yescharacteristic
571M16—22no—
572M16—22no—
573M16—41no—
574M16—41no—
575M16—1222no—
576M16—1222no—
577M16—2441no—
578M16—2441no—
579C2×C8—22no—
580C2×C8—41no—
581C2×C8—41no—
582C2×C8—1222no—
583C2×C8—2441no—
584C2×C8—2441no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—22no—
588C4⋊C4—22no—
589C4⋊C4—41no—
590C4⋊C4—41no—
591C4⋊C4—1228no—
592C4⋊C4—1222no—
593C4⋊C4—1222no—
594C4⋊C4—1222no—
595C4⋊C4—1222no—
596C4⋊C4#1175819812yes—
597C4⋊C4#1175819812yes—
598C22⋊C4—22no—
599C22⋊C4—22no—
600C22⋊C4—1228no—
601C42—22no—
602C42—22no—
603C42—1228no—
604C42—1222no—
605C42—1222no—
606C42—2441no—
607C42—2441no—
608C23—21no—
609C23—21no—
610C23—21no—
611C23—21no—
612C23—1222no—
613C23—1222no—
614C23—1222no—
615C23—2441no—
616C23—2441no—
617C23—2441no—
618C23—2441no—
619C23C22⋊C4×D6111yescharacteristic
620C23#1451973711yescharacteristic
621C23#1451973911yescharacteristic
622C23#1451974511yescharacteristic
623C23#1451974711yescharacteristic
624C23#1451975011yescharacteristic
625C23#1451975511yescharacteristic
626Q8—614no—
627Q8—1222no—
628Q8—1222no—
629Q8—1222no—
630D4—614no—
631D4—1224no—
632D4—1224no—
633D4—1224no—
634D4—1224no—
635D4—1222no—
636D4—1222no—
637D4—1222no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—44no—
645C2×C4—42no—
646C2×C4—82no—
647C2×C4—81no—
648C2×C4—81no—
649C2×C4—1222no—
650C2×C4—1222no—
651C2×C4—1222no—
652C2×C4—1224no—
653C2×C4—1224no—
654C2×C4—1224no—
655C2×C4—1224no—
656C2×C4—1224no—
657C2×C4—1224no—
658C2×C4—4888no—
659C2×C4—4882no—
660C2×C4—2442no—
661C2×C4—2442no—
662C2×C4—2442no—
663C2×C4—2442no—
664C2×C4—2442no—
665C2×C4—2442no—
666C2×C4—2442no—
667C2×C4—2442no—
668C2×C4—2444no—
669C2×C4C42×D6111yescharacteristic
670C2×C4C22⋊C4×D6111yescharacteristic
671C2×C4C22⋊C4×D6111yescharacteristic
672C2×C4C22⋊C4×D6111yescharacteristic
673C2×C4C2×#1175819811yescharacteristic
674C2×C4C4⋊C4×D6111yescharacteristic
675C2×C4C4⋊C4×D6111yescharacteristic
676C2×C4C4⋊C4×D6111yescharacteristic
677C2×C4#1451973411yescharacteristic
678C2×C4#1451973511yescharacteristic
679C2×C4#1451973711yescharacteristic
680C2×C4C4×C22⋊D6111yescharacteristic
681C2×C4C4×C22⋊D6111yescharacteristic
682C2×C4#1451973911yescharacteristic
683C2×C4C4×D24411yescharacteristic
684C2×C4C4×D24411yescharacteristic
685C2×C4#1451974511yescharacteristic
686C2×C4#1451974711yescharacteristic
687C2×C4#1451974811yescharacteristic
688C2×C4#1451975011yescharacteristic
689C2×C4#1451975211yescharacteristic
690C2×C4#1451975311yescharacteristic
691C2×C4#1451975511yescharacteristic
692C2×C4#1451975711yescharacteristic
693C2×C4#1451975911yescharacteristic
694C2×C4#1451975911yescharacteristic
695C2×C4#1451976211yescharacteristic
696C2×C4#1451976211yescharacteristic
697C8—42no—
698C8—2442no—
699C22—21no—
700C22—21no—
701C22—21no—
702C22—21no—
703C22—21no—
704C22—21no—
705C22—21no—
706C22—21no—
707C22—21no—
708C22—21no—
709C22—21no—
710C22—21no—
711C22—1224no—
712C22—2442no—
713C22—2442no—
714C22—2442no—
715C22—2442no—
716C22—2442no—
717C22—2442no—
718C22#1683960911yescharacteristic
719C22#1683961711yescharacteristic
720C22#1683962111yescharacteristic
721C22#1683963311yescharacteristic
722C22#1683963611yescharacteristic
723C22#1683963811yescharacteristic
724C22#1683964011yescharacteristic
725C22#1683992811yescharacteristic
726C22#1683993311yescharacteristic
727C22#1683993811yescharacteristic
728C22#1683994311yescharacteristic
729C4—42no—
730C4—42no—
731C4—82no—
732C4—1224no—
733C4—2444no—
734C4—2444no—
735C4#95×D6111yescharacteristic
736C4C4×#1175819811yescharacteristic
737C4#1683961911yescharacteristic
738C4#1683962411yescharacteristic
739C4#1683963311yescharacteristic
740C4#1683963611yescharacteristic
741C4#1683963811yescharacteristic
742C4#1683964011yescharacteristic
743C2—21no—
744C2—21no—
745C2—21no—
746C2—21no—
747C2—2444no—
748C2#2144404011yescharacteristic
749C2#2144577111yescharacteristic
750C2#2144577611yescharacteristic
751C2#2144604211yescharacteristic
752C2#2144604911yescharacteristic
753C2#2144618511yescharacteristic
754C2#2144619211yescharacteristic
subgroupG/H
centerC23#14519745
commutatorC2×C4×C61C2×C42
FrattiniC23×C4C22×D61
FittingC61×#1736C2
socleC23×C61#120
prime radicalC22×#11758222C22
cosocleC23×C4×C61C23
hypercenter#1736D61
hypocenterC61#10781
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1736

Complements

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

NH ≅ G/Ntype
4. C2×#16839530C2semidirect
5. C2×#16839521C2semidirect
6. #21444048C2semidirect
7. C61×#1736C2semidirect
13. #16840242C4semidirect
23. C2×#14519703C4semidirect
25. #16839761C4semidirect
60. C2×#11758194C2×C4semidirect
86. C2×C4×Dic61C2×C4semidirect
98. C2×M16×C61C2×C4semidirect
109. C2×C4⋊C4×C61C2×C4semidirect
309. D244#95semidirect
318. Dic122#95semidirect
370. #1736D61semidirect
413. C61#10781semidirect
446. C2×M16C4×D61semidirect
475. C2×C4⋊C4C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168402422
C22×#145197032
C2×#168397612
C2×#168395302
C2×#168395212
#214440482
C61×#17362
#1078161