Finite Group Databasebeta

← #29715172

Subgroups — #29715172

Order 15616.

1556 conjugacy classes of subgroups.

The subgroup lattice has 926 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839981C211yesmaximal, characteristic, complemented
2C2×#16839959C211yesmaximal, characteristic, complemented
3C2×#16839924C211yesmaximal, characteristic, complemented
4C2×#16839913C211yesmaximal, characteristic, complemented
5#21448501C211yesmaximal, characteristic, complemented
6#21447055C211yesmaximal, characteristic, complemented
7#21447050C211yesmaximal, characteristic, complemented
8#21446913C211yesmaximal, characteristic, complemented
9#21446907C211yesmaximal, characteristic, complemented
10#21446752C211yesmaximal, characteristic, complemented
11#21446747C211yesmaximal, characteristic, complemented
12#21445803C211yesmaximal, characteristic, complemented
13#21445759C211yesmaximal, characteristic, complemented
14#21445750C211yesmaximal, characteristic, complemented
15C2×C61×#535C211yesmaximal, characteristic
16C22×#11758202C2211yescharacteristic, complemented
17C22×#11758200C2211yescharacteristic
18C22×#11758200C2211yescharacteristic
19C22×#11758200C2211yescharacteristic, complemented
20C2×#14519756C2211yescharacteristic
21C2×C4×Dic122C2211yescharacteristic, complemented
22#16839981—24no—
23#16839959—24no—
24#16839924—24no—
25#16839913—24no—
26C2×C4⋊#92418C2211yescharacteristic, complemented
27C2×C4⋊#92418C2211yescharacteristic, complemented
28C2×#14519701C2211yescharacteristic, complemented
29C2×#14519701C2211yescharacteristic, complemented
30C2×#14519701C2211yescharacteristic, complemented
31C2×#14519698C2211yescharacteristic
32C2×#14519698C2211yescharacteristic
33C2×#14519698C2211yescharacteristic
34C2×#14519698C2211yescharacteristic
35C2×#14519698C2211yescharacteristic
36C2×#14519698C2211yescharacteristic
37C2×#14519698C2211yescharacteristic, complemented
38C2×#14519698C2211yescharacteristic, complemented
39C2×#14519698C2211yescharacteristic, complemented
40C2×C22⋊#92418C2211yescharacteristic
41C2×C22⋊#92418C2211yescharacteristic
42#16839668C2211yescharacteristic, complemented
43#16839660C2211yescharacteristic, complemented
44#16839657—21no—
45#16839656—21no—
46#16839650—21no—
47#16839643—21no—
48#16839622C2211yescharacteristic
49C4×C4⋊Dic61C2211yescharacteristic, complemented
50#16839517C2211yescharacteristic, complemented
51#16839517C2211yescharacteristic, complemented
52C22×#41×C61C2211yescharacteristic
53C23×D4×C61C2211yescharacteristic
54C61×#535—24no—
55C61×#535—24no—
56C2×#127×C61C2211yescharacteristic
57C2×#127×C61C2211yescharacteristic
58C2×#124×C61C2211yescharacteristic
59C2×#124×C61C2211yescharacteristic
60C2×#121×C61—21no—
61C2×#121×C61—21no—
62C2×#120×C61—21no—
63C2×#120×C61—21no—
64C2×#117×C61C2211yescharacteristic
65C22×Dic122C2311yescharacteristic
66C2×#11758202—22no—
67C2×#11758202—22no—
68C2×#11758202—41no—
69C2×#11758200—22no—
70C2×#11758200—22no—
71C2×#11758200—22no—
72C2×#11758200—22no—
73C2×#11758200—22no—
74C2×#11758200—22no—
75C2×#11758200—41no—
76C2×#11758200—41no—
77C2×#11758200—41no—
78C22×#92418C2311yescharacteristic
79C22×#92418C2311yescharacteristic
80C22×#92418C2311yescharacteristic
81C22×#92418C2311yescharacteristic
82#14519756—22no—
83#14519756D414yescomplemented
84C4×Dic122—22no—
85C4×Dic122—22no—
86C2×C4⋊Dic61C2311yescharacteristic
87C2×C4⋊Dic61C2311yescharacteristic
88C2×C4⋊Dic61C2311yescharacteristic
89C2×#11758196—21no—
90C2×#11758196—21no—
91C2×#11758196—21no—
92C2×C22⋊Dic61—21no—
93C2×C22⋊Dic61—21no—
94C2×C4×Dic61—21no—
95C2×C4×Dic61—21no—
96C4⋊#92418—22no—
97C4⋊#92418—22no—
98#14519701—22no—
99#14519701—22no—
100#14519701—41no—
101#14519698—22no—
102#14519698—22no—
103#14519698—22no—
104#14519698—22no—
105#14519698—22no—
106#14519698—22no—
107#14519698—41no—
108#14519698—41no—
109#14519698—41no—
110C22⋊#92418—22no—
111C22⋊#92418—22no—
112#14519684—21no—
113#14519684—21no—
114#14519684—21no—
115#14519684—21no—
116#14519684—21no—
117C25×C61—21no—
118C2×#41×C61—22no—
119C2×#41×C61—22no—
120C2×#41×C61—22no—
121C2×#41×C61—22no—
122C2×#41×C61—41no—
123C2×#41×C61—41no—
124C22×Q8×C61C2311yescharacteristic
125C22×D4×C61—21no—
126C22×D4×C61—22no—
127C22×D4×C61—22no—
128C22×D4×C61—21no—
129C22×D4×C61—21no—
130C22×D4×C61—21no—
131C22×D4×C61—21no—
132C22×D4×C61—21no—
133C22×D4×C61—22no—
134C22×D4×C61—22no—
135C22×D4×C61—41no—
136C22×D4×C61—41no—
137C22×D4×C61C2311yescharacteristic
138C22×D4×C61C2311yescharacteristic
139C22×D4×C61C2311yescharacteristic
140C23×C4×C61—21no—
141C23×C4×C61C2311yescharacteristic
142#127×C61—22no—
143#127×C61—22no—
144#127×C61—22no—
145#127×C61D414yes—
146#124×C61—22no—
147#124×C61—22no—
148#124×C61—22no—
149#124×C61D414yes—
150#121×C61—28no—
151#121×C61—28no—
152#120×C61—28no—
153#120×C61—28no—
154#117×C61—22no—
155#117×C61—22no—
156C2×C4⋊C4×C61D411yescharacteristic
157C2×C4⋊C4×C61D411yescharacteristic
158C2×C22⋊C4×C61—21no—
159C2×C22⋊C4×C61—21no—
160C2×C22⋊C4×C61—21no—
161C2×C22⋊C4×C61—21no—
162C2×C22⋊C4×C61D411yescharacteristic
163C2×C22⋊C4×C61D411yescharacteristic
164C2×C42×C61C2311yescharacteristic
165C2×C42×C61C2311yescharacteristic
166C24×C61—24no—
167C24×C61—21no—
168C24×C61—21no—
169C24×C61—21no—
170C24×C61—42no—
171C24×C61—42no—
172C24×C61—81no—
173C24×C61—81no—
174C24×C61—81no—
175C24×C61—81no—
176C24×C61C2×D411yescharacteristic
177#41×C61—44no—
178#41×C61—44no—
179#41×C61—44no—
180#41×C61—44no—
181C2×Q8×C61—21no—
182C2×Q8×C61—21no—
183C2×Q8×C61—21no—
184C2×Q8×C61—21no—
185C2×Q8×C61—21no—
186C2×Q8×C61C2×D412yes—
187C2×D4×C61—24no—
188C2×D4×C61—24no—
189C2×D4×C61—24no—
190C2×D4×C61—24no—
191C2×D4×C61—24no—
192C2×D4×C61—24no—
193C2×D4×C61—21no—
194C2×D4×C61—21no—
195C2×D4×C61—21no—
196C2×D4×C61—21no—
197C2×D4×C61—21no—
198C2×D4×C61—21no—
199C2×D4×C61—21no—
200C2×D4×C61—21no—
201C2×D4×C61—21no—
202C2×D4×C61—21no—
203C2×D4×C61—21no—
204C2×D4×C61—21no—
205C2×D4×C61—21no—
206C2×D4×C61—21no—
207C2×D4×C61—21no—
208C2×D4×C61—44no—
209C2×D4×C61—44no—
210C2×D4×C61—44no—
211C2×D4×C61—44no—
212C2×D4×C61—42no—
213C2×D4×C61—42no—
214C2×D4×C61—42no—
215C2×D4×C61—42no—
216C2×D4×C61—81no—
217C2×D4×C61—81no—
218C2×D4×C61—81no—
219C2×D4×C61—81no—
220C2×D4×C61—81no—
221C2×D4×C61—81no—
222C2×D4×C61—81no—
223C2×D4×C61—81no—
224C2×D4×C61C2×D412yes—
225C2×D4×C61C2×D412yes—
226C2×D4×C61C2×D412yes—
227C22×C4×C61—21no—
228C22×C4×C61—21no—
229C22×C4×C61—21no—
230C22×C4×C61—21no—
231C22×C4×C61—24no—
232C22×C4×C61—21no—
233C22×C4×C61—42no—
234C22×C4×C61—42no—
235C22×C4×C61C2×D411yescharacteristic
236C22×C4×C61C2×D411yescharacteristic
237C22×C4×C61C2×D411yescharacteristic
238C22×C4×C61C2×D411yescharacteristic
239C22×C4×C61C2×D411yescharacteristic
240C22×C4×C61C2×D412yes—
241C22×C4×C61#4112yes—
242C22×C4×C61C2411yescharacteristic
243C22×Dic61—21no—
244C22×Dic61—21no—
245C22×Dic61—21no—
246C22×Dic61—21no—
247C2×Dic122—21no—
248C2×Dic122—21no—
249C2×Dic122—21no—
250C2×Dic122—21no—
251C2×Dic122—21no—
252C2×Dic122C2×D412yes—
253C4⋊C4×C61—22no—
254C4⋊C4×C61—22no—
255C22⋊C4×C61—24no—
256C22⋊C4×C61—24no—
257C22⋊C4×C61—24no—
258C22⋊C4×C61—24no—
259C22⋊C4×C61—22no—
260C22⋊C4×C61—22no—
261C42×C61—21no—
262C42×C61—21no—
263C42×C61C2×D412yes—
264C42×C61C2×D412yes—
265C22⋊Dic61—24no—
266C22⋊Dic61—81no—
267#11758202—44no—
268#11758200—44no—
269#11758200—44no—
270#11758200—44no—
271C4⋊Dic61—21no—
272C4⋊Dic61—21no—
273C4⋊Dic61—21no—
274C4⋊Dic61—21no—
275C4⋊Dic61—21no—
276C4⋊Dic61C2×D412yes—
277#11758196—24no—
278#11758196—42no—
279#11758196—81no—
280C4×Dic61—42no—
281C4×Dic61—81no—
282C2×#92418—21no—
283C2×#92418—21no—
284C2×#92418—21no—
285C2×#92418—21no—
286C2×#92418—21no—
287C2×#92418—21no—
288C2×#92418—21no—
289C2×#92418—21no—
290C2×#92418—21no—
291C2×#92418—21no—
292C2×#92418—21no—
293C2×#92418—21no—
294C23×C61—21no—
295C23×C61—21no—
296C23×C61—21no—
297C23×C61—21no—
298C23×C61—21no—
299C23×C61—21no—
300C23×C61—22no—
301C23×C61—22no—
302C23×C61—22no—
303C23×C61—48no—
304C23×C61—41no—
305C23×C61—41no—
306C23×C61—41no—
307C23×C61—41no—
308C23×C61—41no—
309C23×C61—41no—
310C23×C61—41no—
311C23×C61—41no—
312C23×C61—41no—
313C23×C61—41no—
314C23×C61—41no—
315C23×C61—41no—
316C23×C61—41no—
317C23×C61—41no—
318C23×C61—41no—
319C23×C61—41no—
320C23×C61—41no—
321C23×C61—41no—
322C23×C61—84no—
323C23×C61—84no—
324C23×C61—84no—
325C23×C61—84no—
326C23×C61—84no—
327C23×C61—84no—
328C23×C61#12112yes—
329C23×C61C22×D411yescharacteristic
330Q8×C61—22no—
331Q8×C61—22no—
332Q8×C61—41no—
333Q8×C61—41no—
334D4×C61—22no—
335D4×C61—22no—
336D4×C61—22no—
337D4×C61—22no—
338D4×C61—22no—
339D4×C61—22no—
340D4×C61—48no—
341D4×C61—48no—
342D4×C61—41no—
343D4×C61—41no—
344D4×C61—41no—
345D4×C61—41no—
346D4×C61—41no—
347D4×C61—41no—
348D4×C61—84no—
349D4×C61—84no—
350D4×C61—84no—
351D4×C61—84no—
352C2×C4×C61—21no—
353C2×C4×C61—21no—
354C2×C4×C61—21no—
355C2×C4×C61—21no—
356C2×C4×C61—21no—
357C2×C4×C61—21no—
358C2×C4×C61—22no—
359C2×C4×C61—22no—
360C2×C4×C61—22no—
361C2×C4×C61—22no—
362C2×C4×C61—21no—
363C2×C4×C61—21no—
364C2×C4×C61—22no—
365C2×C4×C61—21no—
366C2×C4×C61—21no—
367C2×C4×C61—21no—
368C2×C4×C61—21no—
369C2×C4×C61—48no—
370C2×C4×C61—41no—
371C2×C4×C61—41no—
372C2×C4×C61#12012yes—
373C2×C4×C61#12012yes—
374C2×C4×C61#12112yes—
375C2×C4×C61C22×D411yescharacteristic
376C2×C4×C61C22×D411yescharacteristic
377C2×C4×C61C22×D411yescharacteristic
378C2×C4×C61C2×#4111yescharacteristic
379C2×C4×C61H(5,𝔽2)11yescharacteristic
380C2×C4×C61H(5,𝔽2)11yescharacteristic
381C2×Dic61—22no—
382C2×Dic61—22no—
383C2×Dic61—41no—
384C2×Dic61—41no—
385C2×Dic61—41no—
386C2×Dic61—41no—
387C2×Dic61—41no—
388C2×Dic61—41no—
389C2×Dic61—41no—
390C2×Dic61—41no—
391C2×Dic61—41no—
392C2×Dic61—41no—
393Dic122—22no—
394Dic122—22no—
395Dic122—41no—
396Dic122—41no—
397#92418—41no—
398#92418—41no—
399#92418—41no—
400#92418—41no—
401#24220—611nomaximal, Sylow
402C22×C61—22no—
403C22×C61—22no—
404C22×C61—22no—
405C22×C61—41no—
406C22×C61—41no—
407C22×C61—41no—
408C22×C61—41no—
409C22×C61—42no—
410C22×C61—42no—
411C22×C61—42no—
412C22×C61—42no—
413C22×C61—42no—
414C22×C61—42no—
415C22×C61—42no—
416C22×C61—42no—
417C22×C61—42no—
418C22×C61—816no—
419C22×C61—81no—
420C22×C61—81no—
421C22×C61—81no—
422C22×C61—81no—
423C22×C61—81no—
424C22×C61—81no—
425C22×C61—81no—
426C22×C61—81no—
427C22×C61—81no—
428C22×C61—81no—
429C22×C61—81no—
430C22×C61—81no—
431C22×C61C2×#12011yescharacteristic
432C22×C61C2×#12111yescharacteristic
433C22×C61#53511yescharacteristic
434C22×C61#57611yescharacteristic
435C22×C61#57711yescharacteristic
436C22×C61#57711yescharacteristic
437C22×C61#57711yescharacteristic
438C4×C61—22no—
439C4×C61—22no—
440C4×C61—22no—
441C4×C61—42no—
442C4×C61—41no—
443C4×C61—41no—
444C4×C61D4211yescharacteristic
445C4×C61D4211yescharacteristic
446C4×C61#54611yescharacteristic
447C4×C61#54611yescharacteristic
448Dic61—42no—
449Dic61—42no—
450Dic61—81no—
451Dic61—81no—
452C2×#535D6111yescharacteristic
453C2×#464—611no—
454C2×#460—611no—
455C2×#452—611no—
456C2×#450—611no—
457#2323—611no—
458#2042—611no—
459#2041—611no—
460#2015—611no—
461#2014—611no—
462#1983—611no—
463#1982—611no—
464#1798—611no—
465#1788—611no—
466#1786—611no—
467C2×C61—42no—
468C2×C61—82no—
469C2×C61—82no—
470C2×C61—82no—
471C2×C61#240811yescharacteristic
472C2×C61#300911yescharacteristic
473C2×C61#301211yescharacteristic
474C2×C61#304311yescharacteristic
475C2×C61#304511yescharacteristic
476C2×C61#322211yescharacteristic
477C2×C61#322411yescharacteristic
478C22×#41C2×D6111yescharacteristic
479C23×D4C2×D6111yescharacteristic
480C22×Q16—611no—
481C22×SD16—611no—
482C22×SD16—611no—
483C22×SD16—611no—
484#535—24no—
485#535—24no—
486C2×#127C2×D6111yescharacteristic
487C2×#127C2×D6111yescharacteristic
488C2×#124C2×D6111yescharacteristic
489C2×#124C2×D6111yescharacteristic
490C2×C22⋊Q8—611no—
491C2×#121—21no—
492C2×#121—21no—
493C2×#120—21no—
494C2×#120—21no—
495C2×C4×Q8—611no—
496C2×#117C2×D6111yescharacteristic
497#464—1224no—
498#460—1224no—
499#452—1224no—
500#450—1224no—
501C2×C4⋊C8—611no—
502C2×C4⋊C8—611no—
503C2×#103—611no—
504C2×#103—611no—
505C2×#103—611no—
506C2×#102—611no—
507C2×#102—611no—
508C2×#102—611no—
509C2×#102—611no—
510C2×#102—611no—
511C2×#102—611no—
512C2×#102—611no—
513C2×#102—611no—
514C2×#102—611no—
515C2×C22⋊C8—611no—
516C2×C22⋊C8—611no—
517#391—611no—
518#389—611no—
519#389—1221no—
520#388—1221no—
521#388—1221no—
522#387—1221no—
523#380—611no—
524C4×C4⋊C4—611no—
525#336—611no—
526#336—611no—
527C61#2422011yescharacteristic, complemented, Sylow
528C25—21no—
529C2×#41—22no—
530C2×#41—22no—
531C2×#41—22no—
532C2×#41—22no—
533C2×#41—41no—
534C2×#41—41no—
535C22×Q8—611no—
536C22×Q8C22×D6111yescharacteristic
537C22×D4—21no—
538C22×D4—22no—
539C22×D4—22no—
540C22×D4—22no—
541C22×D4—22no—
542C22×D4—21no—
543C22×D4—21no—
544C22×D4—21no—
545C22×D4—21no—
546C22×D4—21no—
547C22×D4—41no—
548C22×D4—41no—
549C22×D4C22×D6111yescharacteristic
550C22×D4C22×D6111yescharacteristic
551C22×D4C22×D6111yescharacteristic
552C23×C4—21no—
553C23×C4C22×D6111yescharacteristic
554C2×Q16—1222no—
555C2×Q16—1222no—
556C2×Q16—2441no—
557C2×SD16—1222no—
558C2×SD16—1222no—
559C2×SD16—1222no—
560C2×SD16—1222no—
561C2×SD16—1222no—
562C2×SD16—1222no—
563C2×SD16—2441no—
564C2×SD16—2441no—
565C2×SD16—2441no—
566C22×C8—611no—
567C22×C8—611no—
568C22×C8—611no—
569C22×C8—611no—
570#127—22no—
571#127—22no—
572#127—22no—
573#127C22⋊D6114yes—
574#124—22no—
575#124—22no—
576#124—22no—
577#124C22⋊D6114yes—
578C22⋊Q8—614no—
579C22⋊Q8—1222no—
580#121—28no—
581#121—28no—
582#120—28no—
583#120—28no—
584C4×Q8—1222no—
585C4×Q8—1222no—
586#117—22no—
587#117—22no—
588C2×C4⋊C4—611no—
589C2×C4⋊C4—611no—
590C2×C4⋊C4—611no—
591C2×C4⋊C4—1221no—
592C2×C4⋊C4—1221no—
593C2×C4⋊C4—1221no—
594C2×C4⋊C4C22⋊D6111yescharacteristic
595C2×C4⋊C4C22⋊D6111yescharacteristic
596C2×C22⋊C4—21no—
597C2×C22⋊C4—21no—
598C2×C22⋊C4—21no—
599C2×C22⋊C4—21no—
600C2×C22⋊C4—1221no—
601C2×C22⋊C4—1221no—
602C2×C22⋊C4C22⋊D6111yescharacteristic
603C2×C22⋊C4C22⋊D6111yescharacteristic
604C2×C42—1221no—
605C2×C42—1221no—
606C2×C42C22×D6111yescharacteristic
607C2×C42C22×D6111yescharacteristic
608C4⋊C8—1222no—
609C4⋊C8—1222no—
610#103—1222no—
611#103—1222no—
612#103—2441no—
613#102—1222no—
614#102—1222no—
615#102—1222no—
616#102—1222no—
617#102—1222no—
618#102—1222no—
619#102—2441no—
620#102—2441no—
621#102—2441no—
622C22⋊C8—1222no—
623C22⋊C8—1222no—
624#95—1221no—
625#95—1221no—
626#95—1221no—
627#95—1221no—
628#95—1221no—
629C24—24no—
630C24—21no—
631C24—21no—
632C24—21no—
633C24—42no—
634C24—42no—
635C24—81no—
636C24—81no—
637C24—81no—
638C24—81no—
639C24C2×C22⋊D6111yescharacteristic
640#41—44no—
641#41—44no—
642#41—44no—
643#41—44no—
644C2×Q8—21no—
645C2×Q8—21no—
646C2×Q8—21no—
647C2×Q8—21no—
648C2×Q8—21no—
649C2×Q8—612no—
650C2×Q8—1221no—
651C2×Q8—1221no—
652C2×Q8—1221no—
653C2×Q8—1221no—
654C2×Q8—1221no—
655C2×Q8C2×C22⋊D6112yes—
656C2×D4—24no—
657C2×D4—24no—
658C2×D4—24no—
659C2×D4—24no—
660C2×D4—21no—
661C2×D4—21no—
662C2×D4—21no—
663C2×D4—21no—
664C2×D4—21no—
665C2×D4—21no—
666C2×D4—21no—
667C2×D4—21no—
668C2×D4—21no—
669C2×D4—21no—
670C2×D4—21no—
671C2×D4—21no—
672C2×D4—21no—
673C2×D4—21no—
674C2×D4—21no—
675C2×D4—24no—
676C2×D4—24no—
677C2×D4—44no—
678C2×D4—44no—
679C2×D4—44no—
680C2×D4—44no—
681C2×D4—42no—
682C2×D4—42no—
683C2×D4—42no—
684C2×D4—42no—
685C2×D4—81no—
686C2×D4—81no—
687C2×D4—81no—
688C2×D4—81no—
689C2×D4—81no—
690C2×D4—81no—
691C2×D4—81no—
692C2×D4—81no—
693C2×D4C2×C22⋊D6112yes—
694C2×D4C2×C22⋊D6112yes—
695C2×D4C2×C22⋊D6112yes—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—24no—
701C22×C4—21no—
702C22×C4—42no—
703C22×C4—42no—
704C22×C4—1221no—
705C22×C4—1221no—
706C22×C4—1221no—
707C22×C4—1221no—
708C22×C4D4×D6112yes—
709C22×C4#1175822412yes—
710C22×C4C2×C22⋊D6111yescharacteristic
711C22×C4C2×C22⋊D6111yescharacteristic
712C22×C4C2×C22⋊D6111yescharacteristic
713C22×C4C2×C22⋊D6111yescharacteristic
714C22×C4C2×C22⋊D6111yescharacteristic
715C22×C4C23×D6111yescharacteristic
716Q16—2444no—
717SD16—2444no—
718SD16—2444no—
719SD16—2444no—
720C2×C8—1221no—
721C2×C8—1221no—
722C2×C8—1221no—
723C2×C8—1221no—
724C2×C8—1221no—
725C2×C8—1221no—
726C2×C8—1221no—
727C2×C8—1221no—
728C2×C8—1221no—
729C2×C8—1221no—
730C2×C8—1221no—
731C2×C8—1221no—
732C4⋊C4—22no—
733C4⋊C4—22no—
734C4⋊C4—612no—
735C4⋊C4—1221no—
736C4⋊C4—1224no—
737C4⋊C4—1221no—
738C4⋊C4—1221no—
739C4⋊C4—1221no—
740C4⋊C4—1221no—
741C4⋊C4—4881no—
742C4⋊C4—2442no—
743C22⋊C4—24no—
744C22⋊C4—24no—
745C22⋊C4—24no—
746C22⋊C4—24no—
747C22⋊C4—22no—
748C22⋊C4—22no—
749C22⋊C4—1224no—
750C22⋊C4—4881no—
751C42—21no—
752C42—21no—
753C42—4881no—
754C42—2442no—
755C42C2×C22⋊D6112yes—
756C42C2×C22⋊D6112yes—
757C23—21no—
758C23—21no—
759C23—21no—
760C23—21no—
761C23—21no—
762C23—21no—
763C23—22no—
764C23—22no—
765C23—22no—
766C23—48no—
767C23—41no—
768C23—41no—
769C23—41no—
770C23—41no—
771C23—41no—
772C23—41no—
773C23—41no—
774C23—41no—
775C23—41no—
776C23—41no—
777C23—41no—
778C23—41no—
779C23—41no—
780C23—41no—
781C23—41no—
782C23—41no—
783C23—41no—
784C23—41no—
785C23—84no—
786C23—84no—
787C23—84no—
788C23—84no—
789C23—84no—
790C23—84no—
791C23#1451974812yes—
792C23C22×C22⋊D6111yescharacteristic
793Q8—22no—
794Q8—22no—
795Q8—41no—
796Q8—41no—
797Q8—1222no—
798Q8—1222no—
799Q8—2441no—
800Q8—2441no—
801D4—22no—
802D4—22no—
803D4—22no—
804D4—22no—
805D4—22no—
806D4—22no—
807D4—48no—
808D4—48no—
809D4—41no—
810D4—41no—
811D4—41no—
812D4—41no—
813D4—41no—
814D4—41no—
815D4—84no—
816D4—84no—
817D4—84no—
818D4—84no—
819C2×C4—21no—
820C2×C4—21no—
821C2×C4—21no—
822C2×C4—21no—
823C2×C4—21no—
824C2×C4—21no—
825C2×C4—22no—
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—22no—
829C2×C4—21no—
830C2×C4—21no—
831C2×C4—22no—
832C2×C4—21no—
833C2×C4—21no—
834C2×C4—21no—
835C2×C4—21no—
836C2×C4—48no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—1222no—
840C2×C4—1222no—
841C2×C4—2441no—
842C2×C4—2441no—
843C2×C4—2441no—
844C2×C4—2441no—
845C2×C4—2441no—
846C2×C4—2441no—
847C2×C4—2441no—
848C2×C4—2441no—
849C2×C4—2441no—
850C2×C4—2441no—
851C2×C4#1451974612yes—
852C2×C4#1451974612yes—
853C2×C4#1451974812yes—
854C2×C4C2×D4×D6111yescharacteristic
855C2×C4C22×C22⋊D6111yescharacteristic
856C2×C4C22×C22⋊D6111yescharacteristic
857C2×C4C2×#1175822411yescharacteristic
858C2×C4#1451982211yescharacteristic
859C2×C4#1451982211yescharacteristic
860C8—2441no—
861C8—2441no—
862C8—2441no—
863C8—2441no—
864C22—22no—
865C22—22no—
866C22—22no—
867C22—41no—
868C22—41no—
869C22—41no—
870C22—41no—
871C22—42no—
872C22—42no—
873C22—42no—
874C22—42no—
875C22—42no—
876C22—42no—
877C22—42no—
878C22—42no—
879C22—42no—
880C22—816no—
881C22—81no—
882C22—81no—
883C22—81no—
884C22—81no—
885C22—81no—
886C22—81no—
887C22—81no—
888C22—81no—
889C22—81no—
890C22—81no—
891C22—81no—
892C22—81no—
893C22C2×#1451974611yescharacteristic
894C22C2×#1451974811yescharacteristic
895C22#1684032911yescharacteristic
896C22#1684056511yescharacteristic
897C22#1684057311yescharacteristic
898C22#1684057311yescharacteristic
899C22#1684057311yescharacteristic
900C4—22no—
901C4—22no—
902C4—22no—
903C4—41no—
904C4—42no—
905C4—41no—
906C4—4881no—
907C4—4881no—
908C4—2442no—
909C4—2442no—
910C4D4×C22⋊D6111yescharacteristic
911C4D4×C22⋊D6111yescharacteristic
912C4#1684040611yescharacteristic
913C4#1684040611yescharacteristic
914C2—42no—
915C2—82no—
916C2—82no—
917C2—82no—
918C2#2144916911yescharacteristic
919C2#2145509611yescharacteristic
920C2#2145512311yescharacteristic
921C2#2145533611yescharacteristic
922C2#2145535411yescharacteristic
923C2#2145689111yescharacteristic
924C2#2145691311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
Fitting, prime radicalC2×C61×#535C2
socleC23×C61C22×D4
hypercenterC2×#535D61
hypocenterC61#24220
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#535

Complements

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

NH ≅ G/Ntype
1. C2×#16839981C2semidirect
2. C2×#16839959C2semidirect
3. C2×#16839924C2semidirect
4. C2×#16839913C2semidirect
5. #21448501C2semidirect
6. #21447055C2semidirect
7. #21447050C2semidirect
8. #21446913C2semidirect
9. #21446907C2semidirect
10. #21446752C2semidirect
11. #21446747C2semidirect
12. #21445803C2semidirect
13. #21445759C2semidirect
14. #21445750C2semidirect
16. C22×#11758202C22semidirect
19. C22×#11758200C22semidirect
21. C2×C4×Dic122C22semidirect
26. C2×C4⋊#92418C22semidirect
27. C2×C4⋊#92418C22semidirect
28. C2×#14519701C22semidirect
29. C2×#14519701C22semidirect
30. C2×#14519701C22semidirect
37. C2×#14519698C22semidirect
38. C2×#14519698C22semidirect
39. C2×#14519698C22semidirect
42. #16839668C22semidirect
43. #16839660C22semidirect
49. C4×C4⋊Dic61C22semidirect
50. #16839517C22semidirect
51. #16839517C22semidirect
83. #14519756D4semidirect
527. C61#24220semidirect

Maximal subgroups

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

subgroupindex
C2×#168399812
C2×#168399592
C2×#168399242
C2×#168399132
#214485012
#214470552
#214470502
#214469132
#214469072
#214467522
#214467472
#214458032
#214457592
#214457502
C2×C61×#5352
#2422061