Finite Group Databasebeta

← #29708182

Subgroups — #29708182

Order 15616.

1272 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840294C211yesmaximal, characteristic, complemented
2C2×C4×#11758200C211yesmaximal, characteristic, complemented
3C4×#14519748C211yesmaximal, characteristic, complemented
4#21447155C211yesmaximal, characteristic, complemented
5#21447058C211yesmaximal, characteristic, complemented
6#21447024C211yesmaximal, characteristic, complemented
7#21447006C211yesmaximal, characteristic, complemented
8#21446963C211yesmaximal, characteristic, complemented
9#21446894C211yesmaximal, characteristic, complemented
10#21446823C211yesmaximal, characteristic, complemented
11#21446814C211yesmaximal, characteristic
12C4×#14519702C211yesmaximal, characteristic, complemented
13C4×#14519698C211yesmaximal, characteristic, complemented
14C4×#14519689C211yesmaximal, characteristic, complemented
15C2×C4×D8×C61C211yesmaximal, characteristic, complemented
16C22×#11758200C2211yescharacteristic
17#16840294—24no—
18#16840294—24no—
19C2×#14519770—21no—
20C2×#14519768C2211yescharacteristic
21C2×#14519764C2211yescharacteristic
22C2×#14519759—21no—
23C2×#14519757C2211yescharacteristic
24C2×#14519748C2211yescharacteristic
25C2×#14519748C2211yescharacteristic
26C2×C4×Dic122C2211yescharacteristic
27C2×C4×C22⋊D61—21no—
28C2×C4×C22⋊D61—21no—
29C2×#14519736—21no—
30C2×C42×D61C2211yescharacteristic
31C4×#11758200—24no—
32C2×#14519708C2211yescharacteristic
33C2×#14519702C2211yescharacteristic
34C2×#14519702C2211yescharacteristic
35C2×#14519700C2211yescharacteristic
36C2×#14519698C2211yescharacteristic
37C2×#14519698C2211yescharacteristic
38C2×#14519698C2211yescharacteristic
39C2×#14519689C2211yescharacteristic
40C2×#14519689C2211yescharacteristic
41C2×C4×#92418C2211yescharacteristic
42#16839665C2211yescharacteristic
43#16839658C2211yescharacteristic
44#16839650—21no—
45#16839638—21no—
46#16839619C2211yescharacteristic
47C4×C4⋊Dic61C2211yescharacteristic
48C4×C22⋊Dic61—21no—
49#16839525C2211yescharacteristic
50#16839525C2211yescharacteristic
51#16839524C2211yescharacteristic
52#16839524C2211yescharacteristic
53#16839516C2211yescharacteristic
54#16839516C2211yescharacteristic
55C22×D8×C61C2211yescharacteristic
56C2×C4×D4×C61C2211yescharacteristic
57C2×C4×D4×C61C2211yescharacteristic
58C4×D8×C61—24no—
59C2×#107×C61C2211yescharacteristic
60C2×#102×C61C2211yescharacteristic
61C2×#102×C61C2211yescharacteristic
62C2×C4×C8×C61C2211yescharacteristic
63C22×Dic122C2311yescharacteristic
64C22×C22⋊D61—21no—
65C22×C22⋊D61—21no—
66C22×C4×D61D411yescharacteristic
67C22×C4×D61D411yescharacteristic
68C22×C4×D61C2311yescharacteristic
69C2×#11758200—22no—
70C2×#11758200—22no—
71C2×#11758200—22no—
72C22×#92418C2311yescharacteristic
73C22×#92418C2311yescharacteristic
74#14519770—28no—
75#14519768—22no—
76#14519768—22no—
77#14519764—22no—
78#14519764—22no—
79#14519759—28no—
80#14519757—22no—
81#14519757—22no—
82#14519748—22no—
83#14519748—22no—
84#14519748—22no—
85#14519748—22no—
86C4×Dic122—22no—
87C4×Dic122D414yescomplemented
88C4×C22⋊D61—28no—
89C4×C22⋊D61—44no—
90#14519736—28no—
91C2×C4⋊Dic61—21no—
92C2×C4⋊Dic61—21no—
93C2×C4⋊Dic61C2311yescharacteristic
94C2×C4⋊Dic61C2311yescharacteristic
95C2×C4⋊Dic61C2311yescharacteristic
96C2×#11758196—21no—
97C2×#11758196—21no—
98C2×#11758196—21no—
99C2×C22⋊Dic61—21no—
100C2×C22⋊Dic61—21no—
101C2×C22⋊Dic61—21no—
102C2×C22⋊Dic61—21no—
103C2×C22⋊Dic61—21no—
104C2×C22⋊Dic61—21no—
105C2×#11758198—21no—
106C2×#11758198—21no—
107C2×C4×Dic61—21no—
108C2×C4×Dic61—21no—
109C2×C4×Dic61D411yescharacteristic
110C2×C4×Dic61D411yescharacteristic
111C2×C4×Dic61C2311yescharacteristic
112C42×D61—22no—
113C42×D61—22no—
114#14519708—22no—
115#14519702—22no—
116#14519702—22no—
117#14519700—22no—
118#14519698—22no—
119#14519698—22no—
120#14519698—22no—
121#14519689—22no—
122#14519689—22no—
123C4×#92418—22no—
124#14519684—21no—
125#14519684—21no—
126#14519684—21no—
127C22×D4×C61C2311yescharacteristic
128C22×D4×C61C2311yescharacteristic
129C23×C4×C61—21no—
130C23×C4×C61—21no—
131C2×D8×C61—22no—
132C2×D8×C61—22no—
133C2×D8×C61—22no—
134C22×C8×C61C2311yescharacteristic
135C22×C8×C61C2311yescharacteristic
136C4×D4×C61—22no—
137C4×D4×C61—22no—
138C4×D4×C61—22no—
139C4×D4×C61D414yescomplemented
140C2×C4⋊C4×C61C2311yescharacteristic
141C2×C4⋊C4×C61C2311yescharacteristic
142C2×C22⋊C4×C61—21no—
143C2×C22⋊C4×C61—21no—
144C2×C42×C61C2311yescharacteristic
145#107×C61—22no—
146#102×C61—22no—
147#102×C61—22no—
148C4×C8×C61—22no—
149C24×C61—21no—
150C24×C61—21no—
151C23×D61C2×D411yescharacteristic
152C2×D4×C61—21no—
153C2×D4×C61—21no—
154C2×D4×C61—21no—
155C2×D4×C61—21no—
156C2×D4×C61—21no—
157C2×D4×C61—21no—
158C2×D4×C61—21no—
159C2×D4×C61—21no—
160C2×D4×C61—21no—
161C2×D4×C61—21no—
162C2×D4×C61C2×D412yes—
163C2×D4×C61#4112yes—
164C22×C4×C61—21no—
165C22×C4×C61—24no—
166C22×C4×C61—21no—
167C22×C4×C61—42no—
168C22×C4×C61—42no—
169C22×C4×C61—42no—
170C22×C4×C61—42no—
171C22×C4×C61—42no—
172C22×C4×C61C2×D411yescharacteristic
173C22×C4×C61C2×D411yescharacteristic
174C22×C4×C61C2411yescharacteristic
175C2×C22⋊D61—24no—
176C2×C22⋊D61—24no—
177C2×C22⋊D61—42no—
178C2×C22⋊D61—42no—
179C2×C22⋊D61—42no—
180C2×C22⋊D61—42no—
181C22×Dic61—21no—
182C22×Dic61—21no—
183C22×Dic61—21no—
184C22×Dic61—21no—
185C22×Dic61C2×D411yescharacteristic
186C22×Dic61C2×D411yescharacteristic
187C22×Dic61C2×D411yescharacteristic
188C2×C4×D61—22no—
189C2×C4×D61—22no—
190C2×C4×D61—22no—
191C2×C4×D61—22no—
192C2×C4×D61—22no—
193C2×C4×D61—21no—
194C2×C4×D61—21no—
195C2×C4×D61—21no—
196C2×C4×D61—21no—
197C2×C4×D61—21no—
198C2×C4×D61—21no—
199C2×C4×D61—41no—
200C2×Dic122—21no—
201C2×Dic122—21no—
202C2×Dic122—21no—
203C2×Dic122—21no—
204C2×Dic122—21no—
205C2×Dic122C2×D412yes—
206D8×C61—28no—
207C2×C8×C61—21no—
208C2×C8×C61—21no—
209C2×C8×C61—21no—
210C2×C8×C61—21no—
211C2×C8×C61—21no—
212C2×C8×C61#4112yes—
213C4⋊C4×C61—21no—
214C4⋊C4×C61—21no—
215C4⋊C4×C61—21no—
216C4⋊C4×C61C2×D412yes—
217C22⋊C4×C61—24no—
218C22⋊C4×C61—42no—
219C42×C61C2×D412yes—
220C42×C61C2×D412yes—
221C22⋊Dic61—24no—
222C22⋊Dic61—24no—
223C22⋊Dic61—24no—
224C22⋊Dic61—24no—
225C22⋊Dic61—42no—
226C22⋊Dic61—42no—
227#11758200—28no—
228#11758198—24no—
229#11758198—42no—
230C4⋊Dic61—24no—
231C4⋊Dic61—24no—
232C4⋊Dic61—21no—
233C4⋊Dic61—21no—
234C4⋊Dic61—21no—
235C4⋊Dic61—21no—
236C4⋊Dic61C2×D412yes—
237C4⋊Dic61#4112yes—
238#11758196—24no—
239#11758196—24no—
240#11758196—42no—
241C4×Dic61—22no—
242C4×Dic61—22no—
243C4×Dic61—24no—
244C4×Dic61—21no—
245C4×Dic61—21no—
246C4×Dic61—42no—
247C2×#92418—21no—
248C2×#92418—21no—
249C2×#92418—21no—
250C2×#92418—21no—
251C2×#92418—21no—
252C2×#92418#4112yes—
253C23×C61—22no—
254C23×C61—22no—
255C23×C61—41no—
256C23×C61—41no—
257C23×C61—41no—
258C23×C61—41no—
259C23×C61—41no—
260C23×C61—41no—
261C23×C61—41no—
262C23×C61—41no—
263C23×C61—41no—
264C23×C61—41no—
265C23×C61—41no—
266C23×C61—41no—
267C23×C61C22×D411yescharacteristic
268C22×D61—21no—
269C22×D61—21no—
270C22×D61—21no—
271C22×D61—21no—
272C22×D61—21no—
273C22×D61—21no—
274C22×D61#13512yes—
275D4×C61—22no—
276D4×C61—22no—
277D4×C61—22no—
278D4×C61—22no—
279D4×C61—41no—
280D4×C61—41no—
281D4×C61—41no—
282D4×C61—41no—
283C2×C4×C61—21no—
284C2×C4×C61—21no—
285C2×C4×C61—22no—
286C2×C4×C61—41no—
287C2×C4×C61—41no—
288C2×C4×C61—48no—
289C2×C4×C61—41no—
290C2×C4×C61—41no—
291C2×C4×C61—41no—
292C2×C4×C61—84no—
293C2×C4×C61#12012yes—
294C2×C4×C61#12012yes—
295C2×C4×C61#13512yes—
296C2×C4×C61AGL(1,ℤ/8)12yes—
297C2×C4×C61C22×D411yescharacteristic
298C2×C4×C61C22×D411yescharacteristic
299C2×C4×C61C2×#4111yescharacteristic
300C2×C4×C61C2×#4111yescharacteristic
301C2×C4×C61C2×#4111yescharacteristic
302C2×C4×C61C2×#4111yescharacteristic
303C22⋊D61—48no—
304C22⋊D61—48no—
305C2×Dic61—21no—
306C2×Dic61—21no—
307C2×Dic61—21no—
308C2×Dic61—22no—
309C2×Dic61—22no—
310C2×Dic61—22no—
311C2×Dic61—21no—
312C2×Dic61—21no—
313C2×Dic61—21no—
314C2×Dic61—21no—
315C2×Dic61—21no—
316C2×Dic61—21no—
317C2×Dic61—41no—
318C2×Dic61—41no—
319C2×Dic61—41no—
320C2×Dic61—41no—
321C2×Dic61—41no—
322C2×Dic61—41no—
323C2×Dic61—41no—
324C2×Dic61—41no—
325C2×Dic61—41no—
326C4×D61—44no—
327C4×D61—41no—
328C4×D61—41no—
329C4×D61—41no—
330C4×D61—41no—
331C4×D61—44no—
332Dic122—22no—
333Dic122—22no—
334Dic122—41no—
335Dic122—41no—
336C8×C61—22no—
337C8×C61—41no—
338#92418—22no—
339#92418—41no—
340#23569—611nomaximal, Sylow
341C22×C61—42no—
342C22×C61—42no—
343C22×C61—42no—
344C22×C61—42no—
345C22×C61—42no—
346C22×C61—42no—
347C22×C61—81no—
348C22×C61—81no—
349C22×C61—81no—
350C22×C61—81no—
351C22×C61—81no—
352C22×C61—81no—
353C22×C61—81no—
354C22×C61—81no—
355C22×C61C2×#12011yescharacteristic
356C22×C61#52511yescharacteristic
357C22×C61#53211yescharacteristic
358C22×C61C2×#13511yescharacteristic
359C22×C61C2×#13511yescharacteristic
360C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
361C22×C61#57511yescharacteristic
362C2×D61—22no—
363C2×D61—22no—
364C2×D61—22no—
365C2×D61—41no—
366C2×D61—41no—
367C2×D61—41no—
368C2×D61—41no—
369C4×C61—22no—
370C4×C61—42no—
371C4×C61—81no—
372C4×C61#44914yes—
373C4×C61#52511yescharacteristic
374C4×C61#52511yescharacteristic
375C4×C61#53211yescharacteristic
376C4×C61#53211yescharacteristic
377Dic61—42no—
378Dic61—42no—
379Dic61—41no—
380Dic61—41no—
381Dic61—41no—
382Dic61—42no—
383Dic61—81no—
384C2×#529—611no—
385C2×C4×SD16—611no—
386C2×C4×D8D6111yescharacteristic, complemented
387C4×#121—611no—
388#2059—611no—
389#2042—611no—
390#2036—611no—
391#2034—611no—
392#2025—611no—
393#2012—611no—
394#2000—611no—
395#1999—611no—
396C4×#103—611no—
397C4×#102—611no—
398C4×C22⋊C8—611no—
399C2×C61—82no—
400C2×C61—82no—
401C2×C61#238811yescharacteristic
402C2×C61C2×#44911yescharacteristic
403C2×C61#300211yescharacteristic
404C2×C61#310211yescharacteristic
405C2×C61#310511yescharacteristic
406C2×C61#316811yescharacteristic
407C2×C61#317111yescharacteristic
408D61—42no—
409C22×SD16—611no—
410C22×D8C2×D6111yescharacteristic
411#529—1224no—
412#529—1224no—
413C2×#126—1221no—
414C2×#125—611no—
415C2×#124—611no—
416C2×#123—1221no—
417C2×C22⋊Q8—611no—
418C2×#121—611no—
419C2×#121—611no—
420C2×C4×Q8—611no—
421C2×C4×D4—1221no—
422C2×C4×D4—1221no—
423C2×C4×D4C2×D6111yescharacteristic
424C2×C4×D4C2×D6111yescharacteristic
425C2×#117—1221no—
426C22×C42—611no—
427C4×SD16—1224no—
428C4×D8—24no—
429C2×#107C2×D6111yescharacteristic
430C2×#106—611no—
431C2×#103—611no—
432C2×#103—611no—
433C2×#103—611no—
434C2×#102—611no—
435C2×#102—611no—
436C2×#102—611no—
437C2×#102C2×D6111yescharacteristic
438C2×#102C2×D6111yescharacteristic
439C2×C22⋊C8—611no—
440C2×C22⋊C8—611no—
441C2×C4×C8—611no—
442C2×C4×C8C2×D6111yescharacteristic
443#390—611no—
444#389—611no—
445#388—1221no—
446#386—1221no—
447#380—611no—
448C4×C4⋊C4—611no—
449C4×C22⋊C4—1221no—
450#340—611no—
451#340—611no—
452#340—611no—
453#340—611no—
454#336—611no—
455#336—611no—
456C61#2356911yescharacteristic, complemented, Sylow
457C22×Q8—611no—
458C22×D4—1221no—
459C22×D4—1221no—
460C22×D4C22×D6111yescharacteristic
461C22×D4C22×D6111yescharacteristic
462C23×C4—21no—
463C23×C4—21no—
464C23×C4—611no—
465C23×C4—611no—
466C23×C4—611no—
467C2×SD16—1222no—
468C2×SD16—1222no—
469C2×SD16—1222no—
470C2×D8—22no—
471C2×D8—22no—
472C2×D8—22no—
473C22×C8—611no—
474C22×C8—611no—
475C22×C8C22×D6111yescharacteristic
476C22×C8C22×D6111yescharacteristic
477#126—1228no—
478#125—1222no—
479#125—1222no—
480#124—1222no—
481#124—1222no—
482#123—1228no—
483C22⋊Q8—1222no—
484C22⋊Q8—1222no—
485#121—1222no—
486#121—1222no—
487#121—1222no—
488#121—1222no—
489C4×Q8—614no—
490C4×Q8—1222no—
491C4×D4—22no—
492C4×D4—22no—
493C4×D4—22no—
494C4×D4—1228no—
495C4×D4—2444no—
496C4×D4C22⋊D6114yescomplemented
497#117—1228no—
498C2×C4⋊C4—611no—
499C2×C4⋊C4—611no—
500C2×C4⋊C4—611no—
501C2×C4⋊C4—1221no—
502C2×C4⋊C4—1221no—
503C2×C4⋊C4—1221no—
504C2×C4⋊C4—1221no—
505C2×C4⋊C4—1221no—
506C2×C4⋊C4C22×D6111yescharacteristic
507C2×C4⋊C4C22×D6111yescharacteristic
508C2×C22⋊C4—21no—
509C2×C22⋊C4—21no—
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—611no—
519C2×C42—611no—
520C2×C42—611no—
521C2×C42—1221no—
522C2×C42—1222no—
523C2×C42—1222no—
524C2×C42—1221no—
525C2×C42C22×D6111yescharacteristic
526#107—22no—
527#106—1222no—
528#103—1222no—
529#103—1222no—
530#103—1222no—
531#102—22no—
532#102—22no—
533#102—1222no—
534#102—1222no—
535#102—1222no—
536C22⋊C8—1222no—
537C22⋊C8—1222no—
538C4×C8—22no—
539C4×C8—1222no—
540#95—1221no—
541#95—1221no—
542#95—1221no—
543C24—21no—
544C24—21no—
545C24—611no—
546C2×Q8—612no—
547C2×Q8—1221no—
548C2×Q8—1221no—
549C2×Q8—1221no—
550C2×Q8—1221no—
551C2×Q8—1221no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4—21no—
557C2×D4—21no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—1224no—
563C2×D4—1224no—
564C2×D4—2442no—
565C2×D4—2442no—
566C2×D4—2442no—
567C2×D4—2442no—
568C2×D4#1175822212yes—
569C2×D4C2×C22⋊D6112yes—
570C22×C4—21no—
571C22×C4—24no—
572C22×C4—21no—
573C22×C4—42no—
574C22×C4—42no—
575C22×C4—42no—
576C22×C4—42no—
577C22×C4—42no—
578C22×C4—611no—
579C22×C4—611no—
580C22×C4—611no—
581C22×C4—1222no—
582C22×C4—1221no—
583C22×C4—1221no—
584C22×C4—1221no—
585C22×C4—1221no—
586C22×C4—1221no—
587C22×C4—1221no—
588C22×C4—1221no—
589C22×C4—1221no—
590C22×C4—1221no—
591C22×C4—1222no—
592C22×C4—1222no—
593C22×C4—1222no—
594C22×C4—1222no—
595C22×C4—1221no—
596C22×C4—2441no—
597C22×C4D4×D6111yescharacteristic
598C22×C4D4×D6111yescharacteristic
599C22×C4C23×D6111yescharacteristic
600SD16—1228no—
601D8—28no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8—21no—
605C2×C8—21no—
606C2×C8—21no—
607C2×C8—612no—
608C2×C8—1221no—
609C2×C8—1221no—
610C2×C8—1221no—
611C2×C8—1221no—
612C2×C8—1221no—
613C2×C8#1175822212yes—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—612no—
618C4⋊C4—612no—
619C4⋊C4—1224no—
620C4⋊C4—1224no—
621C4⋊C4—1224no—
622C4⋊C4—1221no—
623C4⋊C4—1221no—
624C4⋊C4—1224no—
625C4⋊C4—1221no—
626C4⋊C4—1221no—
627C4⋊C4—2442no—
628C4⋊C4C2×C22⋊D6112yes—
629C22⋊C4—24no—
630C22⋊C4—42no—
631C22⋊C4—1224no—
632C22⋊C4—1224no—
633C22⋊C4—1224no—
634C22⋊C4—1224no—
635C22⋊C4—1224no—
636C22⋊C4—2442no—
637C22⋊C4—2442no—
638C22⋊C4—2442no—
639C42—1221no—
640C42—1221no—
641C42—1222no—
642C42—1222no—
643C42—1224no—
644C42—2442no—
645C42D4×D6112yes—
646C42C2×C22⋊D6112yes—
647C23—22no—
648C23—22no—
649C23—41no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23—41no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—612no—
662C23—1221no—
663C23—1221no—
664C23—1221no—
665C23—1221no—
666C23—1221no—
667C23—1221no—
668C23C2×D4×D6111yescharacteristic
669Q8—1222no—
670Q8—1222no—
671Q8—2441no—
672Q8—2441no—
673D4—22no—
674D4—22no—
675D4—22no—
676D4—22no—
677D4—41no—
678D4—41no—
679D4—41no—
680D4—41no—
681D4—2448no—
682D4—2448no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—22no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—48no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—84no—
693C2×C4—1221no—
694C2×C4—1221no—
695C2×C4—1221no—
696C2×C4—1222no—
697C2×C4—1222no—
698C2×C4—1221no—
699C2×C4—1222no—
700C2×C4—1221no—
701C2×C4—1221no—
702C2×C4—1221no—
703C2×C4—1221no—
704C2×C4—1221no—
705C2×C4—2444no—
706C2×C4—2441no—
707C2×C4—2441no—
708C2×C4—2441no—
709C2×C4—2441no—
710C2×C4—2441no—
711C2×C4—2441no—
712C2×C4—2441no—
713C2×C4—2441no—
714C2×C4—2441no—
715C2×C4—2441no—
716C2×C4—2441no—
717C2×C4—2441no—
718C2×C4—2441no—
719C2×C4—2444no—
720C2×C4#1451974512yes—
721C2×C4#1451974512yes—
722C2×C4#1451979612yes—
723C2×C4#1451980112yes—
724C2×C4C2×D4×D6111yescharacteristic
725C2×C4C22×C22⋊D6111yescharacteristic
726C2×C4#41×D6111yescharacteristic
727C2×C4#41×D6111yescharacteristic
728C2×C4C2×#1175822211yescharacteristic
729C2×C4C2×#1175822211yescharacteristic
730C8—22no—
731C8—41no—
732C8—1222no—
733C8—2441no—
734C22—42no—
735C22—42no—
736C22—42no—
737C22—42no—
738C22—42no—
739C22—42no—
740C22—81no—
741C22—81no—
742C22—81no—
743C22—81no—
744C22—81no—
745C22—81no—
746C22—81no—
747C22—81no—
748C22—1222no—
749C22—1222no—
750C22—1222no—
751C22—2441no—
752C22—2441no—
753C22—2441no—
754C22—2441no—
755C22C2×#1451974511yescharacteristic
756C22#1684027111yescharacteristic
757C22#1684030911yescharacteristic
758C22#135×D6111yescharacteristic
759C22C2×#1451979611yescharacteristic
760C22C2×#1451980111yescharacteristic
761C22#1684055911yescharacteristic
762C4—22no—
763C4—42no—
764C4—81no—
765C4—4881no—
766C4—2441no—
767C4—2442no—
768C4—2441no—
769C4—2441no—
770C4—2442no—
771C4—2442no—
772C4#1683990414yes—
773C4#1684027111yescharacteristic
774C4#1684027311yescharacteristic
775C4#1684030811yescharacteristic
776C4#1684030911yescharacteristic
777C2—82no—
778C2—82no—
779C2—2442no—
780C2#2144903411yescharacteristic
781C2C2×#1683990411yescharacteristic
782C2#2145503311yescharacteristic
783C2#2145583311yescharacteristic
784C2#2145586411yescharacteristic
785C2#2145638711yescharacteristic
786C2#2145641211yescharacteristic
subgroupG/H
centerC22×C4D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC2×C4×D8×C61C2
socleC23×C61C22×D4
prime radical#21446814C2
hypercenterC2×C4×D8D61
hypocenterC61#23569
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×D8

Complements

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

NH ≅ G/Ntype
1. C2×#16840294C2semidirect
2. C2×C4×#11758200C2semidirect
3. C4×#14519748C2semidirect
4. #21447155C2semidirect
5. #21447058C2semidirect
6. #21447024C2semidirect
7. #21447006C2semidirect
8. #21446963C2semidirect
9. #21446894C2semidirect
10. #21446823C2semidirect
12. C4×#14519702C2semidirect
13. C4×#14519698C2semidirect
14. C4×#14519689C2semidirect
15. C2×C4×D8×C61C2semidirect
87. C4×Dic122D4semidirect
139. C4×D4×C61D4semidirect
386. C2×C4×D8D61semidirect
456. C61#23569semidirect
496. C4×D4C22⋊D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168402942
C2×C4×#117582002
C4×#145197482
#214471552
#214470582
#214470242
#214470062
#214469632
#214468942
#214468232
#214468142
C4×#145197022
C4×#145196982
C4×#145196892
C2×C4×D8×C612
#2356961