Finite Group Databasebeta

← #29696449

Subgroups — #29696449

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×#16840458C211yesmaximal, characteristic
2#21448748C211yesmaximal, characteristic, complemented
3#21446784C211yesmaximal, characteristic, complemented
4#21446774C211yesmaximal, characteristic, complemented
5#21446257C211yesmaximal, characteristic, complemented
6#21446257C211yesmaximal, characteristic, complemented
7#21446139C211yesmaximal, characteristic, complemented
8#21446134C211yesmaximal, characteristic, complemented
9#21445915C211yesmaximal, characteristic, complemented
10#21445906C211yesmaximal, characteristic, complemented
11#21445830C211yesmaximal, characteristic, complemented
12C4×#14519699C211yesmaximal, characteristic, complemented
13#21445539C211yesmaximal, characteristic, complemented
14#21445539C211yesmaximal, characteristic, complemented
15C2×C61×#436C211yesmaximal, characteristic, complemented
16#16840458—24no—
17#16840458C418yescomplemented
18C2×#14519772—21no—
19C2×#14519769C2211yescharacteristic
20C2×#14519759—21no—
21C2×#14519751C2211yescharacteristic
22C2×#14519751C2211yescharacteristic
23C2×#14519749—21no—
24C2×C4×D244C2211yescharacteristic
25C2×#14519737—21no—
26C2×#14519736C2211yescharacteristic
27C2×#14519736C2211yescharacteristic
28C22×C4⋊Dic61C2211yescharacteristic
29C22×C4⋊Dic61C2211yescharacteristic
30C2×#14519699C2211yescharacteristic
31C2×#14519699C2211yescharacteristic
32C2×#14519699C2211yescharacteristic
33C2×#14519699C2211yescharacteristic
34#16839655—21no—
35#16839648—21no—
36#16839642—21no—
37#16839628C2211yescharacteristic
38#16839622C2211yescharacteristic
39#16839622C2211yescharacteristic
40C4×C4⋊Dic61C2211yescharacteristic
41C22⋊C4×Dic61—21no—
42#16839525C2211yescharacteristic
43#16839525C2211yescharacteristic
44#16839525C2211yescharacteristic
45#16839525C2211yescharacteristic
46#16839525C2211yescharacteristic
47#16839525C2211yescharacteristic
48#16839525C2211yescharacteristic
49#16839525C2211yescharacteristic
50#16839525C2211yescharacteristic
51#16839525C2211yescharacteristic
52#16839525C2211yescharacteristic
53#16839525C2211yescharacteristic
54C22×M16×C61C2211yescharacteristic
55C22×M16×C61C2211yescharacteristic
56C2×C4×D4×C61C2211yescharacteristic
57C61×#436—24no—
58C2×C4⋊C8×C61C2211yescharacteristic
59C2×C22⋊C8×C61C2211yescharacteristic
60C2×C22⋊C8×C61C2211yescharacteristic
61C2×C4×C8×C61C2211yescharacteristic
62C22×D244C2311yescharacteristic
63C22×C22⋊D61—21no—
64C22×C22⋊D61—21no—
65C23×Dic61—21no—
66C23×Dic61—21no—
67C22×C4×D61—21no—
68#14519772—28no—
69#14519769—22no—
70#14519769C2×C414yescomplemented
71#14519759—28no—
72#14519751—22no—
73#14519751—22no—
74#14519751C2×C414yes—
75#14519751C2×C414yescomplemented
76#14519749—28no—
77C4×D244—22no—
78C4×D244C2×C414yescomplemented
79#14519737—28no—
80#14519736—22no—
81#14519736—22no—
82#14519736—41no—
83#14519736C2×C414yes—
84C2×C4⋊Dic61—22no—
85C2×C4⋊Dic61—21no—
86C2×C4⋊Dic61—22no—
87C2×C4⋊Dic61—21no—
88C2×C4⋊Dic61—41no—
89C2×C4⋊Dic61C2×C414yescomplemented
90C2×C4⋊Dic61C2311yescharacteristic
91C2×C4⋊Dic61C2311yescharacteristic
92C2×C4⋊Dic61C2311yescharacteristic
93C2×C4⋊Dic61C2311yescharacteristic
94C2×C4⋊Dic61C2311yescharacteristic
95C2×C4⋊Dic61C2311yescharacteristic
96C2×C4⋊Dic61C2311yescharacteristic
97C2×#11758196—21no—
98C2×#11758196—21no—
99C2×C22⋊Dic61—21no—
100C2×C22⋊Dic61—21no—
101C2×C22⋊Dic61—21no—
102C2×C22⋊Dic61—21no—
103C2×#11758198—21no—
104C2×#11758198—21no—
105C2×#11758198—21no—
106C2×C4×Dic61—21no—
107C2×C4×Dic61—21no—
108C2×C4×Dic61—21no—
109#14519699—22no—
110#14519699—22no—
111#14519699—41no—
112#14519699—41no—
113#14519684—21no—
114#14519684—21no—
115#14519684—21no—
116#14519684—21no—
117#14519684—21no—
118C22×D4×C61D411yescharacteristic
119C23×C4×C61C2311yescharacteristic
120C23×C4×C61C2311yescharacteristic
121C2×M16×C61—22no—
122C2×M16×C61—22no—
123C2×M16×C61—22no—
124C2×M16×C61—22no—
125C2×M16×C61—41no—
126C2×M16×C61—41no—
127C22×C8×C61C2311yescharacteristic
128C22×C8×C61C2311yescharacteristic
129C22×C8×C61C2311yescharacteristic
130C22×C8×C61C2311yescharacteristic
131C4×D4×C61C2×C414yes—
132C4×D4×C61D414yes—
133C2×C4⋊C4×C61D411yescharacteristic
134C2×C22⋊C4×C61D411yescharacteristic
135C2×C22⋊C4×C61D411yescharacteristic
136C2×C42×C61C2311yescharacteristic
137C4⋊C8×C61—22no—
138C22⋊C8×C61—22no—
139C22⋊C8×C61—22no—
140C4×C8×C61—22no—
141C24×C61C2×D411yescharacteristic
142C24×C61C2×D411yescharacteristic
143C23×D61—21no—
144C2×D4×C61—41no—
145C2×D4×C61—41no—
146C2×D4×C61C22⋊C414yes—
147C22×C4×C61—21no—
148C22×C4×C61—21no—
149C22×C4×C61—21no—
150C22×C4×C61—21no—
151C22×C4×C61—21no—
152C22×C4×C61—21no—
153C22×C4×C61—21no—
154C22×C4×C61—21no—
155C22×C4×C61C22×C412yes—
156C22×C4×C61C22×C412yes—
157C22×C4×C61C2×D411yescharacteristic
158C22×C4×C61C2×D411yescharacteristic
159C22×C4×C61C2×D411yescharacteristic
160C22×C4×C61C2×D411yescharacteristic
161C22×C4×C61C2×D412yes—
162C22×C4×C61C2×D412yes—
163C22×C4×C61C2411yescharacteristic
164C2×C22⋊D61—24no—
165C2×C22⋊D61—24no—
166C2×C22⋊D61—42no—
167C2×C22⋊D61—42no—
168C2×C22⋊D61—81no—
169C2×C22⋊D61—81no—
170C22×Dic61—21no—
171C22×Dic61—21no—
172C22×Dic61—21no—
173C22×Dic61—21no—
174C22×Dic61—24no—
175C22×Dic61—21no—
176C22×Dic61—21no—
177C22×Dic61—21no—
178C22×Dic61—42no—
179C22×Dic61—42no—
180C22×Dic61—81no—
181C22×Dic61—81no—
182C22×Dic61—81no—
183C2×D244—21no—
184C2×D244—21no—
185C2×D244—21no—
186C2×D244—21no—
187C2×D244—21no—
188C2×D244C22×C412yes—
189C2×C4×D61—24no—
190C2×C4×D61—81no—
191C2×C4×D61—81no—
192M16×C61—44no—
193M16×C61—44no—
194C2×C8×C61—21no—
195C2×C8×C61—21no—
196C2×C8×C61—21no—
197C2×C8×C61—21no—
198C2×C8×C61—21no—
199C2×C8×C61—21no—
200C2×C8×C61—21no—
201C2×C8×C61—21no—
202C2×C8×C61—21no—
203C2×C8×C61—21no—
204C2×C8×C61—21no—
205C2×C8×C61#4112yes—
206C4⋊C4×C61C22⋊C414yes—
207C22⋊C4×C61C22⋊C414yes—
208C22⋊C4×C61C22⋊C414yes—
209C42×C61C22×C412yes—
210C42×C61C2×D412yes—
211C22⋊Dic61—24no—
212C22⋊Dic61—42no—
213C22⋊Dic61—42no—
214C22⋊Dic61—81no—
215#11758198—24no—
216#11758198—24no—
217#11758198—24no—
218C4⋊Dic61—24no—
219C4⋊Dic61—21no—
220C4⋊Dic61—21no—
221C4⋊Dic61—21no—
222C4⋊Dic61—21no—
223C4⋊Dic61—21no—
224C4⋊Dic61—21no—
225C4⋊Dic61—21no—
226C4⋊Dic61—21no—
227C4⋊Dic61—21no—
228C4⋊Dic61—21no—
229C4⋊Dic61—42no—
230C4⋊Dic61C22×C412yes—
231C4⋊Dic61C22×C412yes—
232C4⋊Dic61C22×C412yes—
233C4⋊Dic61#4112yes—
234#11758196—24no—
235#11758196—24no—
236C4×Dic61—24no—
237C4×Dic61—42no—
238C4×Dic61—81no—
239C23×C61—21no—
240C23×C61—21no—
241C23×C61—21no—
242C23×C61—21no—
243C23×C61—21no—
244C23×C61—21no—
245C23×C61—21no—
246C23×C61—21no—
247C23×C61—21no—
248C23×C61—21no—
249C23×C61—21no—
250C23×C61—21no—
251C23×C61C2×C22⋊C412yes—
252C23×C61C2×C22⋊C412yes—
253C23×C61C22×D411yescharacteristic
254C22×D61—22no—
255C22×D61—41no—
256C22×D61—41no—
257C22×D61—41no—
258C22×D61—41no—
259C22×D61—41no—
260C22×D61—41no—
261D4×C61—44no—
262C2×C4×C61—21no—
263C2×C4×C61—21no—
264C2×C4×C61—21no—
265C2×C4×C61—21no—
266C2×C4×C61—21no—
267C2×C4×C61—21no—
268C2×C4×C61—21no—
269C2×C4×C61—21no—
270C2×C4×C61—22no—
271C2×C4×C61—22no—
272C2×C4×C61—22no—
273C2×C4×C61—22no—
274C2×C4×C61—22no—
275C2×C4×C61—22no—
276C2×C4×C61—22no—
277C2×C4×C61—22no—
278C2×C4×C61C2×C22⋊C412yes—
279C2×C4×C61C2×C22⋊C412yes—
280C2×C4×C61C2×C22⋊C412yes—
281C2×C4×C61C2×C22⋊C412yes—
282C2×C4×C61C23×C411yescharacteristic
283C2×C4×C61C22×D411yescharacteristic
284C2×C4×C61C2×#4111yescharacteristic
285C2×C4×C61C2×#4111yescharacteristic
286C2×C4×C61H(5,𝔽2)11yescharacteristic
287C2×C4×C612−1+411yescharacteristic
288C22⋊D61—48no—
289C22⋊D61—84no—
290C2×Dic61—22no—
291C2×Dic61—22no—
292C2×Dic61—22no—
293C2×Dic61—22no—
294C2×Dic61—41no—
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×Dic61—41no—
306C2×Dic61—41no—
307C2×Dic61—41no—
308C2×Dic61—41no—
309C2×Dic61—41no—
310C2×Dic61—41no—
311C2×Dic61—84no—
312C2×Dic61—84no—
313D244—22no—
314D244—22no—
315D244—41no—
316D244—41no—
317C4×D61—84no—
318C8×C61—22no—
319C8×C61—41no—
320C8×C61—41no—
321C8×C61—41no—
322#22501—611nomaximal, Sylow
323C22×C61—22no—
324C22×C61—22no—
325C22×C61—22no—
326C22×C61—22no—
327C22×C61—22no—
328C22×C61—22no—
329C22×C61—41no—
330C22×C61—41no—
331C22×C61—41no—
332C22×C61—41no—
333C22×C61—41no—
334C22×C61—41no—
335C22×C61—41no—
336C22×C61—41no—
337C22×C61C22×C22⋊C411yescharacteristic
338C22×C61#54611yescharacteristic
339C22×C61#54711yescharacteristic
340C22×C61#57511yescharacteristic
341C22×C61#57511yescharacteristic
342C22×C61#57611yescharacteristic
343C22×C61#57711yescharacteristic
344C2×D61—42no—
345C2×D61—42no—
346C2×D61—42no—
347C2×D61—81no—
348C2×D61—81no—
349C2×D61—81no—
350C2×D61—81no—
351C4×C61—22no—
352C4×C61—22no—
353C4×C61—22no—
354C4×C61—22no—
355C4×C61C4×#4111yescharacteristic
356C4×C61#52011yescharacteristic
357C4×C61#54611yescharacteristic
358C4×C61#54711yescharacteristic
359Dic61—42no—
360Dic61—42no—
361Dic61—42no—
362Dic61—42no—
363Dic61—81no—
364Dic61—81no—
365Dic61—81no—
366C2×#553—611no—
367C2×#436D6111yescharacteristic, complemented
368#2352—611no—
369#1991—611no—
370#1989—611no—
371#1895—611no—
372#1895—611no—
373#1875—611no—
374#1874—611no—
375#1825—611no—
376#1823—611no—
377#1804—611no—
378C4×#102—611no—
379#1736—611no—
380#1736—611no—
381C2×C61—42no—
382C2×C61—42no—
383C2×C61#233911yescharacteristic
384C2×C61#289611yescharacteristic
385C2×C61#289711yescharacteristic
386C2×C61#332211yescharacteristic
387C2×C61#332611yescharacteristic
388C2×C61#335111yescharacteristic
389C2×C61#335511yescharacteristic
390D61—82no—
391C22×M16C2×D6111yescharacteristic
392C22×M16C2×D6111yescharacteristic
393#553—618no—
394#553—1224no—
395C2×#126—1221no—
396C2×#125—611no—
397C2×#123—1221no—
398C2×#121—611no—
399C2×#121—611no—
400C2×#121—1221no—
401C2×C4×D4—611no—
402C2×C4×D4—1221no—
403C2×C4×D4C2×D6111yescharacteristic
404C2×#117—611no—
405C2×#117—611no—
406C22×C4⋊C4—611no—
407C22×C4⋊C4—611no—
408#436—24no—
409C2×C4⋊C8C2×D6111yescharacteristic
410C2×#102—611no—
411C2×#102—611no—
412C2×#102—611no—
413C2×#102—611no—
414C2×C22⋊C8C2×D6111yescharacteristic
415C2×C22⋊C8C2×D6111yescharacteristic
416C2×C4×C8C2×D6111yescharacteristic
417#388—1221no—
418#387—1221no—
419#386—1221no—
420#382—611no—
421#380—611no—
422#380—611no—
423C4×C4⋊C4—611no—
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#340—611no—
436#340—611no—
437C61#2250111yescharacteristic, complemented, Sylow
438C22×D4—611no—
439C22×D4—1221no—
440C22×D4—1221no—
441C22×D4D24411yescharacteristic
442C23×C4—1221no—
443C23×C4—1221no—
444C23×C4—1221no—
445C23×C4C22×D6111yescharacteristic
446C23×C4C22×D6111yescharacteristic
447C2×M16—22no—
448C2×M16—22no—
449C2×M16—22no—
450C2×M16—22no—
451C2×M16—41no—
452C2×M16—41no—
453C22×C8C22×D6111yescharacteristic
454C22×C8C22×D6111yescharacteristic
455C22×C8C22×D6111yescharacteristic
456C22×C8C22×D6111yescharacteristic
457#126—1228no—
458#125—614no—
459#125—1222no—
460#123—1228no—
461#121—614no—
462#121—614no—
463#121—1228no—
464#121—1222no—
465#121—1222no—
466C4×D4—614no—
467C4×D4—1228no—
468C4×D4—1222no—
469C4×D4C4×D6114yes—
470C4×D4C22⋊D6114yes—
471#117—614no—
472#117—1222no—
473#117—1222no—
474#117—2441no—
475C2×C4⋊C4—614no—
476C2×C4⋊C4—611no—
477C2×C4⋊C4—611no—
478C2×C4⋊C4—611no—
479C2×C4⋊C4—611no—
480C2×C4⋊C4—611no—
481C2×C4⋊C4—611no—
482C2×C4⋊C4—611no—
483C2×C4⋊C4—1222no—
484C2×C4⋊C4—1221no—
485C2×C4⋊C4—1221no—
486C2×C4⋊C4—1221no—
487C2×C4⋊C4—1222no—
488C2×C4⋊C4—1221no—
489C2×C4⋊C4—2441no—
490C2×C4⋊C4D24411yescharacteristic
491C2×C22⋊C4—1221no—
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⋊C4D24411yescharacteristic
499C2×C22⋊C4D24411yescharacteristic
500C2×C42—1221no—
501C2×C42—1221no—
502C2×C42—1221no—
503C2×C42C22×D6111yescharacteristic
504C4⋊C8—22no—
505#102—1222no—
506#102—1222no—
507#102—2441no—
508#102—2441no—
509C22⋊C8—22no—
510C22⋊C8—22no—
511C4×C8—22no—
512#95—1221no—
513#95—1221no—
514#95—1221no—
515#95—1221no—
516#95—1221no—
517C24—1221no—
518C24C2×D24411yescharacteristic
519C24C2×D24411yescharacteristic
520C2×D4—41no—
521C2×D4—41no—
522C2×D4—612no—
523C2×D4—1224no—
524C2×D4—1224no—
525C2×D4—1221no—
526C2×D4—1221no—
527C2×D4—1221no—
528C2×D4—1221no—
529C2×D4—1221no—
530C2×D4—4881no—
531C2×D4—4881no—
532C2×D4—2442no—
533C2×D4—2442no—
534C2×D4#1175819814yes—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—1224no—
544C22×C4—1221no—
545C22×C4—1221no—
546C22×C4—1221no—
547C22×C4—1221no—
548C22×C4—1224no—
549C22×C4—1221no—
550C22×C4—1221no—
551C22×C4—1221no—
552C22×C4—4881no—
553C22×C4—4881no—
554C22×C4—4881no—
555C22×C4—4881no—
556C22×C4—4881no—
557C22×C4—2442no—
558C22×C4—2442no—
559C22×C4C2×C4×D6112yes—
560C22×C4C2×C4×D6112yes—
561C22×C4C2×D24411yescharacteristic
562C22×C4C2×D24411yescharacteristic
563C22×C4C2×D24411yescharacteristic
564C22×C4C2×D24411yescharacteristic
565C22×C4C2×C22⋊D6112yes—
566C22×C4C2×C22⋊D6112yes—
567C22×C4C23×D6111yescharacteristic
568M16—44no—
569M16—44no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8—21no—
574C2×C8—21no—
575C2×C8—21no—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8#1175822412yes—
582C4⋊C4—612no—
583C4⋊C4—612no—
584C4⋊C4—612no—
585C4⋊C4—612no—
586C4⋊C4—1221no—
587C4⋊C4—1221no—
588C4⋊C4—1221no—
589C4⋊C4—1221no—
590C4⋊C4—1224no—
591C4⋊C4—1224no—
592C4⋊C4—1224no—
593C4⋊C4—1221no—
594C4⋊C4—1221no—
595C4⋊C4—1221no—
596C4⋊C4—1221no—
597C4⋊C4—1221no—
598C4⋊C4—1221no—
599C4⋊C4—2442no—
600C4⋊C4#1175819814yes—
601C22⋊C4—1224no—
602C22⋊C4—1224no—
603C22⋊C4—1224no—
604C22⋊C4—1224no—
605C22⋊C4—4881no—
606C22⋊C4—2442no—
607C22⋊C4—2442no—
608C22⋊C4#1175819814yes—
609C22⋊C4#1175819814yes—
610C42—1224no—
611C42—4881no—
612C42—2442no—
613C42C2×C4×D6112yes—
614C42C2×C22⋊D6112yes—
615C23—21no—
616C23—21no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23—1222no—
628C23—2441no—
629C23—2441no—
630C23—2441no—
631C23—2441no—
632C23—2441no—
633C23—2441no—
634C23C2×#1175819812yes—
635C23C2×#1175819812yes—
636C23C22×D24411yescharacteristic
637D4—44no—
638D4—1222no—
639D4—1222no—
640D4—4884no—
641D4—2448no—
642D4—2441no—
643D4—2441no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—1222no—
661C2×C4—1222no—
662C2×C4—1222no—
663C2×C4—1222no—
664C2×C4—4884no—
665C2×C4—4884no—
666C2×C4—4884no—
667C2×C4—2441no—
668C2×C4—2441no—
669C2×C4—2441no—
670C2×C4—2441no—
671C2×C4—2441no—
672C2×C4—2441no—
673C2×C4—2441no—
674C2×C4—2441no—
675C2×C4—2441no—
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×C4C2×#1175819812yes—
685C2×C4C2×#1175819812yes—
686C2×C4C2×#1175819812yes—
687C2×C4C2×#1175819812yes—
688C2×C4C22×C4×D6111yescharacteristic
689C2×C4C22×C22⋊D6111yescharacteristic
690C2×C4#41×D6111yescharacteristic
691C2×C4C2×#1175822411yescharacteristic
692C2×C4#1451982211yescharacteristic
693C2×C4#1451982411yescharacteristic
694C8—22no—
695C8—41no—
696C8—41no—
697C8—41no—
698C22—22no—
699C22—22no—
700C22—22no—
701C22—22no—
702C22—22no—
703C22—22no—
704C22—41no—
705C22—41no—
706C22—41no—
707C22—41no—
708C22—41no—
709C22—41no—
710C22—41no—
711C22—41no—
712C22—4881no—
713C22—4881no—
714C22—4881no—
715C22—4881no—
716C22—2442no—
717C22—2442no—
718C22—2442no—
719C22C22×#1175819811yescharacteristic
720C22#1684040711yescharacteristic
721C22#1684041611yescharacteristic
722C22#1684056211yescharacteristic
723C22#1684056211yescharacteristic
724C22#1684056711yescharacteristic
725C22#1684057411yescharacteristic
726C4—22no—
727C4—22no—
728C4—22no—
729C4—22no—
730C4—4881no—
731C4—4881no—
732C4—4881no—
733C4—2442no—
734C4—2442no—
735C4—2442no—
736C4—2442no—
737C4C4×#1175822411yescharacteristic
738C4#1684024111yescharacteristic
739C4#1684040611yescharacteristic
740C4#1684041111yescharacteristic
741C2—42no—
742C2—42no—
743C2—4882no—
744C2#2144864411yescharacteristic
745C2#2145433911yescharacteristic
746C2#2145434611yescharacteristic
747C2#2145802211yescharacteristic
748C2#2145807411yescharacteristic
749C2#2145838111yescharacteristic
750C2#2145842411yescharacteristic
subgroupG/H
centerC23C22×D244
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC2×C61×#436C2
socleC23×C61C22×D4
prime radicalC2×#16840458C2
cosocleC22×C4×C61C24
hypercenterC2×#436D61
hypocenterC61#22501
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#436

Complements

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

NH ≅ G/Ntype
2. #21448748C2semidirect
3. #21446784C2semidirect
4. #21446774C2semidirect
5. #21446257C2semidirect
6. #21446257C2semidirect
7. #21446139C2semidirect
8. #21446134C2semidirect
9. #21445915C2semidirect
10. #21445906C2semidirect
11. #21445830C2semidirect
12. C4×#14519699C2semidirect
13. #21445539C2semidirect
14. #21445539C2semidirect
15. C2×C61×#436C2semidirect
17. #16840458C4semidirect
70. #14519769C2×C4semidirect
75. #14519751C2×C4semidirect
78. C4×D244C2×C4semidirect
89. C2×C4⋊Dic61C2×C4semidirect
367. C2×#436D61semidirect
437. C61#22501semidirect

Maximal subgroups

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

subgroupindex
C2×#168404582
#214487482
#214467842
#214467742
#214462572
#214461392
#214461342
#214459152
#214459062
#214458302
C4×#145196992
#214455392
C2×C61×#4362
#2250161