Finite Group Databasebeta

← #29696321

Subgroups — #29696321

Order 15616.

1194 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840477C211yesmaximal, characteristic
2C2×#16839835C211yesmaximal, characteristic, complemented
3#21448751C211yesmaximal, characteristic, complemented
4#21446792C211yesmaximal, characteristic, complemented
5#21446771C211yesmaximal, characteristic, complemented
6#21446254C211yesmaximal, characteristic, complemented
7#21446244C211yesmaximal, characteristic, complemented
8#21446138C211yesmaximal, characteristic, complemented
9#21446133C211yesmaximal, characteristic, complemented
10#21445913C211yesmaximal, characteristic, complemented
11#21445912C211yesmaximal, characteristic, complemented
12#21445829C211yesmaximal, characteristic, complemented
13#21445537C211yesmaximal, characteristic, complemented
14#21445534C211yesmaximal, characteristic, complemented
15C61×#1762C211yesmaximal, characteristic, complemented
16C22×#11758189C2211yescharacteristic
17C22×C8×D61C2211yescharacteristic
18#16840477—24no—
19#16840477C418yescomplemented
20C2×#14519777C2211yescharacteristic
21C2×#14519763—21no—
22C2×#14519763—21no—
23C2×#14519751—21no—
24C2×#14519748C2211yescharacteristic
25C2×#14519748C2211yescharacteristic
26C2×C4×D244C2211yescharacteristic
27C2×#14519736—21no—
28C2×#14519735C2211yescharacteristic
29C2×#14519735C2211yescharacteristic
30C2×#14519735C2211yescharacteristic
31C2×C4⋊C4×D61C2211yescharacteristic
32#16839835—24no—
33C2×C4⋊#92418C2211yescharacteristic
34C2×#14519698C2211yescharacteristic
35C2×#14519698C2211yescharacteristic
36C2×#14519689C2211yescharacteristic
37C2×#14519689C2211yescharacteristic
38#16839653—21no—
39#16839647—21no—
40#16839640—21no—
41#16839628C2211yescharacteristic
42#16839619C2211yescharacteristic
43#16839619C2211yescharacteristic
44C4×#11758198—21no—
45#16839525C2211yescharacteristic
46#16839525C2211yescharacteristic
47#16839525C2211yescharacteristic
48#16839525C2211yescharacteristic
49#16839524C2211yescharacteristic
50#16839524C2211yescharacteristic
51#16839524C2211yescharacteristic
52#16839524C2211yescharacteristic
53#16839524C2211yescharacteristic
54#16839524C2211yescharacteristic
55C2×C4×D4×C61C2211yescharacteristic
56C2×#102×C61C2211yescharacteristic
57C2×#102×C61C2211yescharacteristic
58C2×#97×C61C2211yescharacteristic
59C4×C4⋊C4×C61C2211yescharacteristic
60C61×#340C2211yescharacteristic
61C61×#340C2211yescharacteristic
62C22×Dic122—21no—
63C22×D244D411yescharacteristic
64C22×C22⋊D61—21no—
65C22×C22⋊D61—21no—
66C22×C4×D61—21no—
67C22×C4×D61C2311yescharacteristic
68C22×C4×D61C2311yescharacteristic
69C2×#11758189—22no—
70C2×#11758189—22no—
71C2×#11758189—41no—
72C22×#92418C2311yescharacteristic
73C22×#92418C2311yescharacteristic
74C2×C8×D61—22no—
75C2×C8×D61—22no—
76C2×C8×D61—41no—
77#14519777—22no—
78#14519777C2×C414yescomplemented
79#14519763—28no—
80#14519763—28no—
81#14519751—28no—
82#14519748—22no—
83#14519748—22no—
84#14519748C2×C414yes—
85#14519748C2×C414yescomplemented
86C4×D244C2×C414yes—
87C4×D244D414yes—
88#14519736—28no—
89#14519735—22no—
90#14519735—22no—
91#14519735—22no—
92#14519735—41no—
93#14519735C2×C414yes—
94#14519735C2×C414yescomplemented
95C2×C4⋊Dic61—21no—
96C2×C4⋊Dic61D411yescharacteristic
97C2×C4⋊Dic61C2311yescharacteristic
98C2×C4⋊Dic61C2311yescharacteristic
99C2×C4⋊Dic61C2311yescharacteristic
100C2×C4⋊Dic61C2311yescharacteristic
101C2×#11758196—21no—
102C4⋊C4×D61—22no—
103C4⋊C4×D61—41no—
104C2×C22⋊Dic61—21no—
105C2×C22⋊Dic61—21no—
106C2×#11758198—21no—
107C2×#11758198—21no—
108C2×#11758198—21no—
109C2×#11758198—21no—
110C2×#11758198—21no—
111C2×#11758198D411yescharacteristic
112C2×#11758198D411yescharacteristic
113C2×C4×Dic61—21no—
114C2×C4×Dic61—21no—
115C2×C4×Dic61—21no—
116C4⋊#92418—22no—
117#14519698—41no—
118#14519698—41no—
119#14519689—22no—
120#14519689—22no—
121#14519684—21no—
122#14519684—21no—
123#14519684—21no—
124#14519684—21no—
125C22×D4×C61C2311yescharacteristic
126C23×C4×C61—21no—
127C22×C8×C61C2311yescharacteristic
128C22×C8×C61C2311yescharacteristic
129C4×D4×C61—22no—
130C4×D4×C61C2×C414yescomplemented
131C2×C4⋊C4×C61C2311yescharacteristic
132C2×C4⋊C4×C61C2311yescharacteristic
133C2×C4⋊C4×C61C2311yescharacteristic
134C2×C22⋊C4×C61—21no—
135C2×C42×C61—21no—
136C2×C42×C61C2311yescharacteristic
137#102×C61—22no—
138#102×C61—22no—
139#97×C61—22no—
140#95×C61—21no—
141C24×C61—21no—
142C23×D61C2×D411yescharacteristic
143C23×D61C2×D411yescharacteristic
144C2×D4×C61—21no—
145C2×D4×C61—21no—
146C2×D4×C61—21no—
147C2×D4×C61—21no—
148C2×D4×C61—21no—
149C2×D4×C61C22×C412yes—
150C22×C4×C61—21no—
151C22×C4×C61—21no—
152C22×C4×C61—24no—
153C22×C4×C61—21no—
154C22×C4×C61—42no—
155C22×C4×C61—42no—
156C22×C4×C61C2×D411yescharacteristic
157C22×C4×C61C2×D411yescharacteristic
158C22×C4×C61C2411yescharacteristic
159C2×C22⋊D61—24no—
160C2×C22⋊D61—24no—
161C2×C22⋊D61—81no—
162C2×C22⋊D61—81no—
163C2×C22⋊D61—81no—
164C2×C22⋊D61—81no—
165C22×Dic61—21no—
166C22×Dic61—21no—
167C22×Dic61—21no—
168C22×Dic61—21no—
169C22×Dic61C2×D411yescharacteristic
170C22×Dic61C2×D411yescharacteristic
171C2×D244—41no—
172C2×D244—41no—
173C2×D244C22⋊C414yes—
174C2×C4×D61—21no—
175C2×C4×D61—21no—
176C2×C4×D61—21no—
177C2×C4×D61—21no—
178C2×C4×D61—21no—
179C2×C4×D61—21no—
180C2×C4×D61—21no—
181C2×C4×D61—21no—
182C2×C4×D61—42no—
183C2×C4×D61—42no—
184C2×C4×D61—81no—
185C2×C4×D61C22×C412yes—
186C2×C4×D61C22×C412yes—
187C2×C4×D61C2×D412yes—
188C2×C4×D61C2×D412yes—
189C2×Dic122—24no—
190C2×Dic122—81no—
191C2×Dic122—81no—
192C2×C8×C61—21no—
193C2×C8×C61—21no—
194C2×C8×C61—21no—
195C2×C8×C61—21no—
196C2×C8×C61—21no—
197C2×C8×C61#4112yes—
198C4⋊C4×C61—21no—
199C4⋊C4×C61—21no—
200C4⋊C4×C61—21no—
201C4⋊C4×C61—21no—
202C4⋊C4×C61C22×C412yes—
203C4⋊C4×C61#4112yes—
204C22⋊C4×C61—24no—
205C42×C61—81no—
206C42×C61C22×C412yes—
207C42×C61C2×D412yes—
208C22⋊Dic61—24no—
209C22⋊Dic61—24no—
210#11758198—24no—
211#11758198—24no—
212#11758198—42no—
213#11758198—42no—
214#11758198—81no—
215#11758198C22⋊C414yes—
216#11758198C22⋊C414yes—
217C4⋊Dic61—24no—
218C4⋊Dic61—21no—
219C4⋊Dic61—21no—
220C4⋊Dic61—21no—
221C4⋊Dic61—21no—
222C4⋊Dic61—21no—
223C4⋊Dic61—21no—
224C4⋊Dic61C22⋊C414yes—
225C4⋊Dic61C22×C412yes—
226C4⋊Dic61C22×C412yes—
227#11758196—42no—
228C4×Dic61—24no—
229C4×Dic61—24no—
230C4×Dic61—42no—
231C2×#92418—21no—
232C2×#92418—21no—
233C2×#92418—21no—
234C2×#92418—21no—
235C2×#92418—21no—
236C2×#92418—21no—
237#11758189—44no—
238C8×D61—44no—
239C23×C61—22no—
240C23×C61—41no—
241C23×C61—41no—
242C23×C61—41no—
243C23×C61—41no—
244C23×C61—41no—
245C23×C61—41no—
246C23×C61C22×D411yescharacteristic
247C22×D61—21no—
248C22×D61—21no—
249C22×D61—21no—
250C22×D61—21no—
251C22×D61—21no—
252C22×D61—21no—
253C22×D61—21no—
254C22×D61—21no—
255C22×D61—21no—
256C22×D61—21no—
257C22×D61—21no—
258C22×D61—21no—
259C22×D61C2×C22⋊C412yes—
260C22×D61C2×C22⋊C412yes—
261D4×C61—22no—
262D4×C61—22no—
263D4×C61—41no—
264D4×C61—41no—
265C2×C4×C61—21no—
266C2×C4×C61—21no—
267C2×C4×C61—21no—
268C2×C4×C61—21no—
269C2×C4×C61—22no—
270C2×C4×C61—22no—
271C2×C4×C61—48no—
272C2×C4×C61—41no—
273C2×C4×C61—41no—
274C2×C4×C61—41no—
275C2×C4×C61—41no—
276C2×C4×C61—41no—
277C2×C4×C61—41no—
278C2×C4×C61—41no—
279C2×C4×C61C2×C22⋊C412yes—
280C2×C4×C61C2×C22⋊C412yes—
281C2×C4×C61C23×C411yescharacteristic
282C2×C4×C61C22×D411yescharacteristic
283C2×C4×C61C2×#4111yescharacteristic
284C2×C4×C61C2×#4111yescharacteristic
285C2×C4×C61H(5,𝔽2)11yescharacteristic
286C2×C4×C612−1+411yescharacteristic
287C22⋊D61—84no—
288C22⋊D61—84no—
289C2×Dic61—21no—
290C2×Dic61—21no—
291C2×Dic61—21no—
292C2×Dic61—21no—
293C2×Dic61—22no—
294C2×Dic61—22no—
295C2×Dic61—41no—
296C2×Dic61—41no—
297C2×Dic61—41no—
298C2×Dic61—41no—
299C2×Dic61—41no—
300C2×Dic61—41no—
301C2×Dic61—41no—
302C2×Dic61—41no—
303C2×Dic61—41no—
304C2×Dic61—41no—
305C2×Dic61C2×C22⋊C412yes—
306C2×Dic61C2×C22⋊C412yes—
307D244—44no—
308C4×D61—22no—
309C4×D61—22no—
310C4×D61—22no—
311C4×D61—22no—
312C4×D61—22no—
313C4×D61—22no—
314C4×D61—22no—
315C4×D61—22no—
316C4×D61—84no—
317Dic122—84no—
318C8×C61—22no—
319C8×C61—41no—
320#92418—41no—
321#92418—41no—
322#22492—611nomaximal, Sylow
323C22×C61—42no—
324C22×C61—42no—
325C22×C61—42no—
326C22×C61—81no—
327C22×C61—81no—
328C22×C61—81no—
329C22×C61—81no—
330C22×C61C22×C22⋊C411yescharacteristic
331C22×C61#54611yescharacteristic
332C22×C61#54711yescharacteristic
333C22×C61#57511yescharacteristic
334C22×C61#57511yescharacteristic
335C22×C61#57611yescharacteristic
336C22×C61#57711yescharacteristic
337C2×D61—22no—
338C2×D61—22no—
339C2×D61—22no—
340C2×D61—22no—
341C2×D61—22no—
342C2×D61—22no—
343C2×D61—41no—
344C2×D61—41no—
345C2×D61—41no—
346C2×D61—41no—
347C2×D61—41no—
348C2×D61—41no—
349C2×D61—41no—
350C2×D61—41no—
351C4×C61—22no—
352C4×C61—22no—
353C4×C61—42no—
354C4×C61—42no—
355C4×C61—81no—
356C4×C61C4×#4111yescharacteristic
357C4×C61#52011yescharacteristic
358C4×C61#54611yescharacteristic
359C4×C61#54711yescharacteristic
360Dic61—22no—
361Dic61—22no—
362Dic61—42no—
363Dic61—42no—
364Dic61—81no—
365Dic61—81no—
366C2×#555—611no—
367C2×#435—611no—
368#2352—611no—
369#1993—611no—
370#1988—611no—
371#1895—611no—
372#1893—611no—
373#1875—611no—
374#1874—611no—
375#1825—611no—
376#1825—611no—
377#1804—611no—
378#1762D6111yescharacteristic, complemented
379#1736—611no—
380#1735—611no—
381C2×C61—82no—
382C2×C61#233911yescharacteristic
383C2×C61#289611yescharacteristic
384C2×C61#289711yescharacteristic
385C2×C61#331911yescharacteristic
386C2×C61#332111yescharacteristic
387C2×C61#334711yescharacteristic
388C2×C61#334811yescharacteristic
389D61—42no—
390D61—42no—
391C22×M16—611no—
392C23×C8—611no—
393#555—618no—
394#555—1224no—
395C2×C4⋊Q8—611no—
396C2×#124—1221no—
397C2×#124—1221no—
398C2×#121—611no—
399C2×#121—611no—
400C2×#121—1221no—
401C2×C4×D4—611no—
402C2×C4×D4C2×D6111yescharacteristic
403C2×#117—611no—
404C2×#117—611no—
405C2×#117—611no—
406C2×#117—1221no—
407C22×C4⋊C4—611no—
408#435—1224no—
409C2×C4⋊C8—611no—
410C2×#102—611no—
411C2×#102—611no—
412C2×#102C2×D6111yescharacteristic
413C2×#102C2×D6111yescharacteristic
414C2×C22⋊C8—611no—
415C2×C22⋊C8—611no—
416C2×#97C2×D6111yescharacteristic
417#388—1221no—
418#387—1221no—
419#386—1221no—
420#382—611no—
421#380—611no—
422#380—611no—
423C4×C4⋊C4C2×D6111yescharacteristic
424C4×C22⋊C4—1221no—
425#340—611no—
426#340—611no—
427#340—611no—
428#340—611no—
429#340—611no—
430#340—611no—
431#340—611no—
432#340—611no—
433#340—611no—
434#340—611no—
435#340C2×D6111yescharacteristic
436#340C2×D6111yescharacteristic
437C61#2249211yescharacteristic, complemented, Sylow
438C22×Q8—1221no—
439C22×D4—611no—
440C22×D4—1221no—
441C22×D4—1221no—
442C22×D4C22×D6111yescharacteristic
443C23×C4—21no—
444C23×C4—611no—
445C23×C4—611no—
446C23×C4—1221no—
447C2×M16—1222no—
448C2×M16—1222no—
449C2×M16—2441no—
450C22×C8—611no—
451C22×C8—611no—
452C22×C8—1222no—
453C22×C8—1222no—
454C22×C8—2441no—
455C22×C8C22×D6111yescharacteristic
456C22×C8C22×D6111yescharacteristic
457C4⋊Q8—614no—
458C4⋊Q8—1222no—
459#124—1228no—
460#124—1228no—
461#121—614no—
462#121—614no—
463#121—1228no—
464#121—1222no—
465#121—1222no—
466C4×D4—22no—
467C4×D4—614no—
468C4×D4—614no—
469C4×D4C4×D6114yescomplemented
470#117—614no—
471#117—614no—
472#117—1222no—
473#117—1222no—
474#117—1228no—
475#117—1222no—
476#117—2441no—
477C2×C4⋊C4—611no—
478C2×C4⋊C4—611no—
479C2×C4⋊C4—611no—
480C2×C4⋊C4—611no—
481C2×C4⋊C4—611no—
482C2×C4⋊C4—1221no—
483C2×C4⋊C4—1222no—
484C2×C4⋊C4—1221no—
485C2×C4⋊C4—2441no—
486C2×C4⋊C4C22×D6111yescharacteristic
487C2×C4⋊C4C22×D6111yescharacteristic
488C2×C4⋊C4C22×D6111yescharacteristic
489C2×C22⋊C4—21no—
490C2×C22⋊C4—611no—
491C2×C22⋊C4—611no—
492C2×C22⋊C4—1221no—
493C2×C22⋊C4—1221no—
494C2×C22⋊C4—1221no—
495C2×C22⋊C4—1221no—
496C2×C22⋊C4—1221no—
497C2×C22⋊C4—1221no—
498C2×C22⋊C4—1221no—
499C2×C42—21no—
500C2×C42—1221no—
501C2×C42—1221no—
502C2×C42—1221no—
503C2×C42C22×D6111yescharacteristic
504C4⋊C8—1222no—
505#102—22no—
506#102—22no—
507#102—2441no—
508#102—2441no—
509C22⋊C8—1222no—
510C22⋊C8—1222no—
511#97—22no—
512#95—21no—
513#95—1221no—
514#95—1221no—
515#95—1221no—
516#95—1221no—
517C24—21no—
518C24—611no—
519C24—611no—
520C2×Q8—1224no—
521C2×Q8—4881no—
522C2×Q8—4881no—
523C2×D4—21no—
524C2×D4—21no—
525C2×D4—21no—
526C2×D4—21no—
527C2×D4—21no—
528C2×D4—614no—
529C2×D4—1224no—
530C2×D4—1224no—
531C2×D4—4881no—
532C2×D4—4881no—
533C2×D4—4881no—
534C2×D4—4881no—
535C2×D4—2441no—
536C2×D4—2441no—
537C2×D4C2×C4×D6112yes—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—24no—
541C22×C4—21no—
542C22×C4—42no—
543C22×C4—42no—
544C22×C4—611no—
545C22×C4—611no—
546C22×C4—612no—
547C22×C4—612no—
548C22×C4—612no—
549C22×C4—612no—
550C22×C4—1221no—
551C22×C4—1221no—
552C22×C4—1221no—
553C22×C4—1221no—
554C22×C4—1221no—
555C22×C4—1221no—
556C22×C4—1221no—
557C22×C4—1221no—
558C22×C4—1221no—
559C22×C4—1221no—
560C22×C4—1221no—
561C22×C4—1221no—
562C22×C4—4881no—
563C22×C4—2442no—
564C22×C4—2442no—
565C22×C4D4×D6111yescharacteristic
566C22×C4D4×D6111yescharacteristic
567C22×C4C23×D6111yescharacteristic
568M16—2444no—
569C2×C8—21no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8—21no—
574C2×C8—1221no—
575C2×C8—1221no—
576C2×C8—1221no—
577C2×C8—1221no—
578C2×C8—1221no—
579C2×C8—1221no—
580C2×C8—2444no—
581C2×C8#1175822212yes—
582C4⋊C4—21no—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—21no—
586C4⋊C4—614no—
587C4⋊C4—612no—
588C4⋊C4—612no—
589C4⋊C4—1221no—
590C4⋊C4—1221no—
591C4⋊C4—1224no—
592C4⋊C4—1221no—
593C4⋊C4—1221no—
594C4⋊C4—1221no—
595C4⋊C4—1221no—
596C4⋊C4—2442no—
597C4⋊C4C2×C4×D6112yes—
598C4⋊C4#1175822212yes—
599C22⋊C4—24no—
600C22⋊C4—614no—
601C22⋊C4—614no—
602C22⋊C4—1224no—
603C22⋊C4—1224no—
604C22⋊C4—1224no—
605C22⋊C4—1224no—
606C22⋊C4—4881no—
607C22⋊C4—2442no—
608C22⋊C4—2442no—
609C42—81no—
610C42—1224no—
611C42—1224no—
612C42—2442no—
613C42C2×C4×D6112yes—
614C42D4×D6112yes—
615C23—22no—
616C23—41no—
617C23—41no—
618C23—41no—
619C23—41no—
620C23—41no—
621C23—41no—
622C23—612no—
623C23—612no—
624C23—1221no—
625C23—1221no—
626C23—1221no—
627C23—1221no—
628C23—1221no—
629C23—1221no—
630C23—1221no—
631C23—1221no—
632C23—1221no—
633C23—1221no—
634C23—1221no—
635C23—1221no—
636C23C2×D4×D6111yescharacteristic
637Q8—4884no—
638D4—22no—
639D4—22no—
640D4—41no—
641D4—41no—
642D4—4884no—
643D4—4884no—
644D4—2444no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—48no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—612no—
660C2×C4—612no—
661C2×C4—1221no—
662C2×C4—1221no—
663C2×C4—1221no—
664C2×C4—1221no—
665C2×C4—1222no—
666C2×C4—1222no—
667C2×C4—1222no—
668C2×C4—1222no—
669C2×C4—1222no—
670C2×C4—1222no—
671C2×C4—1222no—
672C2×C4—1222no—
673C2×C4—1222no—
674C2×C4—1222no—
675C2×C4—4884no—
676C2×C4—2441no—
677C2×C4—2441no—
678C2×C4—2441no—
679C2×C4—2441no—
680C2×C4—2441no—
681C2×C4—2441no—
682C2×C4—2441no—
683C2×C4—2441no—
684C2×C4—2441no—
685C2×C4—2441no—
686C2×C4C22⋊C4×D6112yes—
687C2×C4C22⋊C4×D6112yes—
688C2×C4C22×C4×D6111yescharacteristic
689C2×C4C2×D4×D6111yescharacteristic
690C2×C4C2×#1175822211yescharacteristic
691C2×C4C2×#1175822211yescharacteristic
692C2×C4#1451982311yescharacteristic
693C2×C4#1451982411yescharacteristic
694C8—22no—
695C8—41no—
696C8—2441no—
697C8—2441no—
698C22—42no—
699C22—42no—
700C22—42no—
701C22—81no—
702C22—81no—
703C22—81no—
704C22—81no—
705C22—1222no—
706C22—1222no—
707C22—1222no—
708C22—1222no—
709C22—1222no—
710C22—1222no—
711C22—2441no—
712C22—2441no—
713C22—2441no—
714C22—2441no—
715C22—2441no—
716C22—2441no—
717C22—2441no—
718C22—2441no—
719C22C2×C22⋊C4×D6111yescharacteristic
720C22#1684040811yescharacteristic
721C22#1684041711yescharacteristic
722C22#1684055811yescharacteristic
723C22#1684055811yescharacteristic
724C22#1684056611yescharacteristic
725C22#1684057111yescharacteristic
726C4—22no—
727C4—22no—
728C4—42no—
729C4—42no—
730C4—81no—
731C4—1222no—
732C4—1222no—
733C4—4881no—
734C4—4881no—
735C4—2442no—
736C4—2442no—
737C4C4×#1175822211yescharacteristic
738C4#1684024211yescharacteristic
739C4#1684040811yescharacteristic
740C4#1684041711yescharacteristic
741C2—82no—
742C2—2442no—
743C2—2442no—
744C2#2144865011yescharacteristic
745C2#2145433311yescharacteristic
746C2#2145434311yescharacteristic
747C2#2145798011yescharacteristic
748C2#2145801011yescharacteristic
749C2#2145832411yescharacteristic
750C2#2145833911yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1762C2
socleC23×C61C22×D4
prime radicalC2×#16840477C2
cosocleC22×C4×C61C24
hypercenter#1762D61
hypocenterC61#22492
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1762

Complements

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

NH ≅ G/Ntype
2. C2×#16839835C2semidirect
3. #21448751C2semidirect
4. #21446792C2semidirect
5. #21446771C2semidirect
6. #21446254C2semidirect
7. #21446244C2semidirect
8. #21446138C2semidirect
9. #21446133C2semidirect
10. #21445913C2semidirect
11. #21445912C2semidirect
12. #21445829C2semidirect
13. #21445537C2semidirect
14. #21445534C2semidirect
15. C61×#1762C2semidirect
19. #16840477C4semidirect
78. #14519777C2×C4semidirect
85. #14519748C2×C4semidirect
94. #14519735C2×C4semidirect
130. C4×D4×C61C2×C4semidirect
378. #1762D61semidirect
437. C61#22492semidirect
469. C4×D4C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168404772
C2×#168398352
#214487512
#214467922
#214467712
#214462542
#214462442
#214461382
#214461332
#214459132
#214459122
#214458292
#214455372
#214455342
C61×#17622
#2249261