Finite Group Databasebeta

← #29715157

Subgroups — #29715157

Order 15616.

1420 conjugacy classes of subgroups.

The subgroup lattice has 874 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839974C211yesmaximal, characteristic, complemented
2C2×#16839964C211yesmaximal, characteristic, complemented
3C2×#16839907C211yesmaximal, characteristic
4C2×#16839901C211yesmaximal, characteristic, complemented
5#21448512C211yesmaximal, characteristic, complemented
6#21447062C211yesmaximal, characteristic, complemented
7#21447055C211yesmaximal, characteristic, complemented
8#21446902C211yesmaximal, characteristic, complemented
9#21446896C211yesmaximal, characteristic, complemented
10#21446752C211yesmaximal, characteristic, complemented
11#21446743C211yesmaximal, characteristic, complemented
12#21445803C211yesmaximal, characteristic, complemented
13#21445759C211yesmaximal, characteristic, complemented
14#21445754C211yesmaximal, characteristic, complemented
15C2×C61×#536C211yesmaximal, characteristic, complemented
16C22×#11758201C2211yescharacteristic
17C22×#11758201C2211yescharacteristic
18C22×#11758201C2211yescharacteristic
19C22×#11758199C2211yescharacteristic
20C2×#14519751C2211yescharacteristic
21C2×C4×D244C2211yescharacteristic
22#16839974—24no—
23#16839964—24no—
24#16839907—24no—
25#16839901—24no—
26C2×C4⋊#92418C2211yescharacteristic
27C2×C4⋊#92418C2211yescharacteristic
28C2×#14519701C2211yescharacteristic
29C2×#14519701C2211yescharacteristic
30C2×#14519701C2211yescharacteristic
31C2×#14519701C2211yescharacteristic
32C2×#14519701C2211yescharacteristic
33C2×#14519701C2211yescharacteristic
34C2×#14519701C2211yescharacteristic
35C2×#14519701C2211yescharacteristic
36C2×#14519701C2211yescharacteristic
37C2×#14519698C2211yescharacteristic
38C2×#14519698C2211yescharacteristic
39C2×#14519698C2211yescharacteristic
40C2×C22⋊#92418C2211yescharacteristic
41C2×C22⋊#92418C2211yescharacteristic
42#16839664C2211yescharacteristic
43#16839662—21no—
44#16839660C2211yescharacteristic
45#16839652—21no—
46#16839638—21no—
47#16839633—21no—
48#16839622C2211yescharacteristic
49C4×C4⋊Dic61C2211yescharacteristic
50#16839517C2211yescharacteristic
51#16839517C2211yescharacteristic
52C22×#41×C61C2211yescharacteristic
53C23×Q8×C61C2211yescharacteristic
54C61×#536—24no—
55C61×#536—24no—
56C2×C4⋊Q8×C61C2211yescharacteristic
57C2×C4⋊Q8×C61C2211yescharacteristic
58C2×#124×C61C2211yescharacteristic
59C2×#124×C61C2211yescharacteristic
60C2×#123×C61—21no—
61C2×#123×C61—21no—
62C2×C22⋊Q8×C61—21no—
63C2×C22⋊Q8×C61—21no—
64C2×#117×C61C2211yescharacteristic
65C22×D244C2311yescharacteristic
66C22×C22⋊D61—21no—
67C22×C4×D61—21no—
68C2×#11758201—22no—
69C2×#11758201—22no—
70C2×#11758201—22no—
71C2×#11758201—22no—
72C2×#11758201—22no—
73C2×#11758201—22no—
74C2×#11758201—41no—
75C2×#11758201—41no—
76C2×#11758201—41no—
77C2×#11758199—22no—
78C2×#11758199—22no—
79C2×#11758199—41no—
80C22×#92418C2311yescharacteristic
81C22×#92418C2311yescharacteristic
82C22×#92418C2311yescharacteristic
83C22×#92418C2311yescharacteristic
84#14519751—22no—
85#14519751D414yes—
86C4×D244—22no—
87C4×D244—22no—
88C2×C4⋊Dic61C2311yescharacteristic
89C2×C4⋊Dic61C2311yescharacteristic
90C2×C4⋊Dic61C2311yescharacteristic
91C2×#11758196—21no—
92C2×C22⋊Dic61—21no—
93C2×#11758198—21no—
94C2×#11758198—21no—
95C2×#11758198—21no—
96C2×#11758198—21no—
97C2×C4×Dic61—21no—
98C4⋊#92418—22no—
99C4⋊#92418—22no—
100#14519701—22no—
101#14519701—22no—
102#14519701—22no—
103#14519701—22no—
104#14519701—22no—
105#14519701—22no—
106#14519701—41no—
107#14519701—41no—
108#14519701—41no—
109#14519698—22no—
110#14519698—22no—
111#14519698—41no—
112C22⋊#92418—22no—
113C22⋊#92418—22no—
114#14519684—21no—
115#14519684—21no—
116#14519684—21no—
117C2×#41×C61—22no—
118C2×#41×C61—22no—
119C2×#41×C61—22no—
120C2×#41×C61—22no—
121C2×#41×C61—41no—
122C2×#41×C61—41no—
123C22×Q8×C61—22no—
124C22×Q8×C61—22no—
125C22×Q8×C61—21no—
126C22×Q8×C61—22no—
127C22×Q8×C61—22no—
128C22×Q8×C61—41no—
129C22×Q8×C61—41no—
130C22×Q8×C61C2311yescharacteristic
131C22×Q8×C61C2311yescharacteristic
132C22×Q8×C61C2311yescharacteristic
133C22×D4×C61—21no—
134C22×D4×C61C2311yescharacteristic
135C23×C4×C61—21no—
136C23×C4×C61—21no—
137C23×C4×C61C2311yescharacteristic
138C4⋊Q8×C61—22no—
139C4⋊Q8×C61—22no—
140C4⋊Q8×C61—22no—
141C4⋊Q8×C61D414yescomplemented
142#124×C61—22no—
143#124×C61—22no—
144#124×C61—22no—
145#124×C61D414yescomplemented
146#123×C61—28no—
147#123×C61—28no—
148C22⋊Q8×C61—28no—
149C22⋊Q8×C61—28no—
150#117×C61—22no—
151#117×C61—22no—
152C2×C4⋊C4×C61—21no—
153C2×C4⋊C4×C61—21no—
154C2×C4⋊C4×C61—21no—
155C2×C4⋊C4×C61—21no—
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—21no—
167C24×C61C2×D411yescharacteristic
168C23×D61—21no—
169#41×C61—44no—
170#41×C61—44no—
171#41×C61—44no—
172#41×C61—44no—
173C2×Q8×C61—24no—
174C2×Q8×C61—21no—
175C2×Q8×C61—21no—
176C2×Q8×C61—21no—
177C2×Q8×C61—21no—
178C2×Q8×C61—21no—
179C2×Q8×C61—21no—
180C2×Q8×C61—21no—
181C2×Q8×C61—21no—
182C2×Q8×C61—21no—
183C2×Q8×C61—21no—
184C2×Q8×C61—21no—
185C2×Q8×C61—21no—
186C2×Q8×C61—21no—
187C2×Q8×C61—21no—
188C2×Q8×C61—21no—
189C2×Q8×C61—44no—
190C2×Q8×C61—44no—
191C2×Q8×C61—44no—
192C2×Q8×C61—44no—
193C2×Q8×C61—42no—
194C2×Q8×C61—42no—
195C2×Q8×C61C2×D412yes—
196C2×Q8×C61C2×D412yes—
197C2×Q8×C61C2×D412yes—
198C2×D4×C61—24no—
199C2×D4×C61—21no—
200C2×D4×C61—21no—
201C2×D4×C61—21no—
202C2×D4×C61—21no—
203C2×D4×C61—21no—
204C2×D4×C61—42no—
205C2×D4×C61—42no—
206C2×D4×C61C2×D412yes—
207C22×C4×C61—21no—
208C22×C4×C61—21no—
209C22×C4×C61—21no—
210C22×C4×C61—21no—
211C22×C4×C61—24no—
212C22×C4×C61—24no—
213C22×C4×C61—21no—
214C22×C4×C61—21no—
215C22×C4×C61—21no—
216C22×C4×C61—42no—
217C22×C4×C61—42no—
218C22×C4×C61—42no—
219C22×C4×C61—42no—
220C22×C4×C61C2×D411yescharacteristic
221C22×C4×C61C2×D411yescharacteristic
222C22×C4×C61C2×D411yescharacteristic
223C22×C4×C61C2×D411yescharacteristic
224C22×C4×C61C2×D411yescharacteristic
225C22×C4×C61C2×D412yes—
226C22×C4×C61#4112yes—
227C22×C4×C61C2411yescharacteristic
228C2×C22⋊D61—24no—
229C2×C22⋊D61—81no—
230C2×C22⋊D61—81no—
231C22×Dic61—21no—
232C22×Dic61—21no—
233C22×Dic61—21no—
234C2×D244—21no—
235C2×D244—21no—
236C2×D244—21no—
237C2×D244—21no—
238C2×D244—21no—
239C2×D244C2×D412yes—
240C2×C4×D61—42no—
241C2×C4×D61—81no—
242C2×C4×D61—81no—
243C4⋊C4×C61—24no—
244C4⋊C4×C61—24no—
245C4⋊C4×C61—24no—
246C4⋊C4×C61—24no—
247C4⋊C4×C61—22no—
248C4⋊C4×C61—22no—
249C22⋊C4×C61—24no—
250C22⋊C4×C61—24no—
251C22⋊C4×C61—24no—
252C22⋊C4×C61—24no—
253C22⋊C4×C61—22no—
254C22⋊C4×C61—22no—
255C42×C61—21no—
256C42×C61—21no—
257C42×C61C2×D412yes—
258C42×C61C2×D412yes—
259C22⋊Dic61—81no—
260#11758201—44no—
261#11758201—44no—
262#11758201—44no—
263#11758199—44no—
264#11758198—24no—
265#11758198—42no—
266#11758198—81no—
267#11758198—81no—
268C4⋊Dic61—21no—
269C4⋊Dic61—21no—
270C4⋊Dic61—21no—
271C4⋊Dic61—21no—
272C4⋊Dic61—21no—
273C4⋊Dic61C2×D412yes—
274#11758196—81no—
275C4×Dic61—81no—
276C2×#92418—21no—
277C2×#92418—21no—
278C2×#92418—21no—
279C2×#92418—21no—
280C2×#92418—21no—
281C2×#92418—21no—
282C2×#92418—21no—
283C2×#92418—21no—
284C2×#92418—21no—
285C2×#92418—21no—
286C2×#92418—21no—
287C2×#92418—21no—
288C23×C61—21no—
289C23×C61—21no—
290C23×C61—21no—
291C23×C61—21no—
292C23×C61—21no—
293C23×C61—21no—
294C23×C61—22no—
295C23×C61—41no—
296C23×C61—41no—
297C23×C61—41no—
298C23×C61—41no—
299C23×C61—41no—
300C23×C61—41no—
301C23×C61#12112yes—
302C23×C61C22×D411yescharacteristic
303C22×D61—22no—
304C22×D61—41no—
305C22×D61—41no—
306C22×D61—41no—
307C22×D61—41no—
308C22×D61—41no—
309C22×D61—41no—
310Q8×C61—22no—
311Q8×C61—22no—
312Q8×C61—22no—
313Q8×C61—22no—
314Q8×C61—22no—
315Q8×C61—22no—
316Q8×C61—48no—
317Q8×C61—41no—
318Q8×C61—41no—
319Q8×C61—41no—
320Q8×C61—41no—
321Q8×C61—41no—
322Q8×C61—41no—
323D4×C61—22no—
324D4×C61—22no—
325D4×C61—48no—
326D4×C61—41no—
327D4×C61—41no—
328C2×C4×C61—21no—
329C2×C4×C61—21no—
330C2×C4×C61—21no—
331C2×C4×C61—21no—
332C2×C4×C61—21no—
333C2×C4×C61—21no—
334C2×C4×C61—22no—
335C2×C4×C61—22no—
336C2×C4×C61—22no—
337C2×C4×C61—22no—
338C2×C4×C61—21no—
339C2×C4×C61—21no—
340C2×C4×C61—22no—
341C2×C4×C61—22no—
342C2×C4×C61—22no—
343C2×C4×C61—21no—
344C2×C4×C61—21no—
345C2×C4×C61—21no—
346C2×C4×C61—21no—
347C2×C4×C61—48no—
348C2×C4×C61—48no—
349C2×C4×C61—41no—
350C2×C4×C61—41no—
351C2×C4×C61—41no—
352C2×C4×C61—41no—
353C2×C4×C61—41no—
354C2×C4×C61—41no—
355C2×C4×C61#12012yes—
356C2×C4×C61#12012yes—
357C2×C4×C61#12112yes—
358C2×C4×C61C22×D411yescharacteristic
359C2×C4×C61C22×D411yescharacteristic
360C2×C4×C61C22×D411yescharacteristic
361C2×C4×C61C2×#4111yescharacteristic
362C2×C4×C61H(5,𝔽2)11yescharacteristic
363C2×C4×C61H(5,𝔽2)11yescharacteristic
364C22⋊D61—84no—
365C2×Dic61—22no—
366C2×Dic61—41no—
367C2×Dic61—41no—
368C2×Dic61—41no—
369C2×Dic61—41no—
370C2×Dic61—41no—
371C2×Dic61—41no—
372C2×Dic61—41no—
373C2×Dic61—41no—
374D244—22no—
375D244—22no—
376D244—41no—
377D244—41no—
378C4×D61—84no—
379#92418—41no—
380#92418—41no—
381#92418—41no—
382#92418—41no—
383#24219—611nomaximal, Sylow
384C22×C61—22no—
385C22×C61—22no—
386C22×C61—22no—
387C22×C61—41no—
388C22×C61—41no—
389C22×C61—41no—
390C22×C61—41no—
391C22×C61—42no—
392C22×C61—42no—
393C22×C61—42no—
394C22×C61—81no—
395C22×C61—81no—
396C22×C61—81no—
397C22×C61—81no—
398C22×C61C2×#12011yescharacteristic
399C22×C61C2×#12111yescharacteristic
400C22×C61#53511yescharacteristic
401C22×C61#57711yescharacteristic
402C22×C61#57711yescharacteristic
403C22×C61#57711yescharacteristic
404C22×C61#57811yescharacteristic
405C2×D61—42no—
406C2×D61—42no—
407C2×D61—42no—
408C2×D61—81no—
409C2×D61—81no—
410C2×D61—81no—
411C2×D61—81no—
412C4×C61—22no—
413C4×C61—22no—
414C4×C61—22no—
415C4×C61—42no—
416C4×C61—42no—
417C4×C61—42no—
418C4×C61—41no—
419C4×C61—41no—
420C4×C61D4211yescharacteristic
421C4×C61D4211yescharacteristic
422C4×C61#54611yescharacteristic
423C4×C61#54611yescharacteristic
424Dic61—42no—
425Dic61—81no—
426Dic61—81no—
427C2×#536D6111yescharacteristic, complemented
428C2×#463—611no—
429C2×#461—611no—
430C2×#449—611no—
431C2×#448—611no—
432#2324—611no—
433#2043—611no—
434#2042—611no—
435#2013—611no—
436#2012—611no—
437#1983—611no—
438#1981—611no—
439#1798—611no—
440#1788—611no—
441#1787—611no—
442C2×C61—42no—
443C2×C61—82no—
444C2×C61#240811yescharacteristic
445C2×C61#301011yescharacteristic
446C2×C61#301311yescharacteristic
447C2×C61#304211yescharacteristic
448C2×C61#304611yescharacteristic
449C2×C61#322111yescharacteristic
450C2×C61#322511yescharacteristic
451D61—82no—
452C22×#41C2×D6111yescharacteristic
453C23×Q8C2×D6111yescharacteristic
454C22×SD16—611no—
455C22×SD16—611no—
456C22×SD16—611no—
457C22×D8—611no—
458#536—24no—
459#536—24no—
460C2×C4⋊Q8C2×D6111yescharacteristic
461C2×C4⋊Q8C2×D6111yescharacteristic
462C2×#124C2×D6111yescharacteristic
463C2×#124C2×D6111yescharacteristic
464C2×#123—21no—
465C2×#123—21no—
466C2×C22⋊Q8—21no—
467C2×C22⋊Q8—21no—
468C2×#121—611no—
469C2×C4×D4—611no—
470C2×#117C2×D6111yescharacteristic
471#463—1224no—
472#461—1224no—
473#449—1224no—
474#448—1224no—
475C2×C4⋊C8—611no—
476C2×C4⋊C8—611no—
477C2×#103—611no—
478C2×#103—611no—
479C2×#103—611no—
480C2×#103—611no—
481C2×#103—611no—
482C2×#103—611no—
483C2×#103—611no—
484C2×#103—611no—
485C2×#103—611no—
486C2×#102—611no—
487C2×#102—611no—
488C2×#102—611no—
489C2×C22⋊C8—611no—
490C2×C22⋊C8—611no—
491#390—611no—
492#390—1221no—
493#389—611no—
494#388—1221no—
495#386—1221no—
496#385—1221no—
497#380—611no—
498C4×C4⋊C4—611no—
499#336—611no—
500#336—611no—
501C61#2421911yescharacteristic, complemented, Sylow
502C2×#41—22no—
503C2×#41—22no—
504C2×#41—22no—
505C2×#41—22no—
506C2×#41—41no—
507C2×#41—41no—
508C22×Q8—22no—
509C22×Q8—22no—
510C22×Q8—21no—
511C22×Q8—22no—
512C22×Q8—22no—
513C22×Q8—41no—
514C22×Q8—41no—
515C22×Q8C22×D6111yescharacteristic
516C22×Q8C22×D6111yescharacteristic
517C22×Q8C22×D6111yescharacteristic
518C22×D4—21no—
519C22×D4—611no—
520C22×D4—1221no—
521C22×D4C22×D6111yescharacteristic
522C23×C4—21no—
523C23×C4—21no—
524C23×C4—1221no—
525C23×C4C22×D6111yescharacteristic
526C2×SD16—1222no—
527C2×SD16—1222no—
528C2×SD16—1222no—
529C2×SD16—1222no—
530C2×SD16—1222no—
531C2×SD16—1222no—
532C2×SD16—2441no—
533C2×SD16—2441no—
534C2×SD16—2441no—
535C2×D8—1222no—
536C2×D8—1222no—
537C2×D8—2441no—
538C22×C8—611no—
539C22×C8—611no—
540C22×C8—611no—
541C22×C8—611no—
542C4⋊Q8—22no—
543C4⋊Q8—22no—
544C4⋊Q8—22no—
545C4⋊Q8C22⋊D6114yescomplemented
546#124—22no—
547#124—22no—
548#124—22no—
549#124C22⋊D6114yescomplemented
550#123—28no—
551#123—28no—
552C22⋊Q8—28no—
553C22⋊Q8—28no—
554#121—614no—
555#121—1222no—
556C4×D4—1222no—
557C4×D4—1222no—
558#117—22no—
559#117—22no—
560C2×C4⋊C4—21no—
561C2×C4⋊C4—21no—
562C2×C4⋊C4—21no—
563C2×C4⋊C4—21no—
564C2×C4⋊C4—611no—
565C2×C4⋊C4—611no—
566C2×C4⋊C4—611no—
567C2×C4⋊C4—1221no—
568C2×C4⋊C4C22⋊D6111yescharacteristic
569C2×C4⋊C4C22⋊D6111yescharacteristic
570C2×C22⋊C4—21no—
571C2×C22⋊C4—21no—
572C2×C22⋊C4—21no—
573C2×C22⋊C4—21no—
574C2×C22⋊C4—1221no—
575C2×C22⋊C4—1221no—
576C2×C22⋊C4—1221no—
577C2×C22⋊C4—1221no—
578C2×C22⋊C4—1221no—
579C2×C22⋊C4C22⋊D6111yescharacteristic
580C2×C22⋊C4C22⋊D6111yescharacteristic
581C2×C42—1221no—
582C2×C42C22×D6111yescharacteristic
583C2×C42C22×D6111yescharacteristic
584C4⋊C8—1222no—
585C4⋊C8—1222no—
586#103—1222no—
587#103—1222no—
588#103—1222no—
589#103—1222no—
590#103—1222no—
591#103—1222no—
592#103—2441no—
593#103—2441no—
594#103—2441no—
595#102—1222no—
596#102—1222no—
597#102—2441no—
598C22⋊C8—1222no—
599C22⋊C8—1222no—
600#95—1221no—
601#95—1221no—
602#95—1221no—
603C24—21no—
604C24—1221no—
605C24C2×C22⋊D6111yescharacteristic
606#41—44no—
607#41—44no—
608#41—44no—
609#41—44no—
610C2×Q8—24no—
611C2×Q8—21no—
612C2×Q8—21no—
613C2×Q8—21no—
614C2×Q8—21no—
615C2×Q8—21no—
616C2×Q8—21no—
617C2×Q8—21no—
618C2×Q8—21no—
619C2×Q8—21no—
620C2×Q8—21no—
621C2×Q8—21no—
622C2×Q8—21no—
623C2×Q8—21no—
624C2×Q8—21no—
625C2×Q8—21no—
626C2×Q8—44no—
627C2×Q8—44no—
628C2×Q8—44no—
629C2×Q8—44no—
630C2×Q8—42no—
631C2×Q8—42no—
632C2×Q8C2×C22⋊D6112yes—
633C2×Q8C2×C22⋊D6112yes—
634C2×Q8C2×C22⋊D6112yes—
635C2×D4—24no—
636C2×D4—21no—
637C2×D4—21no—
638C2×D4—21no—
639C2×D4—21no—
640C2×D4—21no—
641C2×D4—42no—
642C2×D4—42no—
643C2×D4—612no—
644C2×D4—1224no—
645C2×D4—1221no—
646C2×D4—1221no—
647C2×D4—1221no—
648C2×D4—1221no—
649C2×D4—1221no—
650C2×D4—4881no—
651C2×D4—4881no—
652C2×D4C2×C22⋊D6112yes—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—24no—
658C22×C4—24no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—42no—
663C22×C4—42no—
664C22×C4—42no—
665C22×C4—42no—
666C22×C4—1221no—
667C22×C4—1221no—
668C22×C4—1221no—
669C22×C4—4881no—
670C22×C4—4881no—
671C22×C4—2442no—
672C22×C4D4×D6112yes—
673C22×C4#1175822412yes—
674C22×C4C2×C22⋊D6111yescharacteristic
675C22×C4C2×C22⋊D6111yescharacteristic
676C22×C4C2×C22⋊D6111yescharacteristic
677C22×C4C2×C22⋊D6111yescharacteristic
678C22×C4C2×C22⋊D6111yescharacteristic
679C22×C4C23×D6111yescharacteristic
680SD16—2444no—
681SD16—2444no—
682SD16—2444no—
683D8—2444no—
684C2×C8—1221no—
685C2×C8—1221no—
686C2×C8—1221no—
687C2×C8—1221no—
688C2×C8—1221no—
689C2×C8—1221no—
690C2×C8—1221no—
691C2×C8—1221no—
692C2×C8—1221no—
693C2×C8—1221no—
694C2×C8—1221no—
695C2×C8—1221no—
696C4⋊C4—24no—
697C4⋊C4—24no—
698C4⋊C4—24no—
699C4⋊C4—24no—
700C4⋊C4—22no—
701C4⋊C4—22no—
702C4⋊C4—612no—
703C4⋊C4—1221no—
704C4⋊C4—1221no—
705C4⋊C4—1221no—
706C4⋊C4—1221no—
707C4⋊C4—1221no—
708C4⋊C4—4881no—
709C22⋊C4—24no—
710C22⋊C4—24no—
711C22⋊C4—24no—
712C22⋊C4—24no—
713C22⋊C4—22no—
714C22⋊C4—22no—
715C22⋊C4—1224no—
716C22⋊C4—4881no—
717C22⋊C4—4881no—
718C22⋊C4—4881no—
719C22⋊C4—2442no—
720C42—21no—
721C42—21no—
722C42—4881no—
723C42C2×C22⋊D6112yes—
724C42C2×C22⋊D6112yes—
725C23—21no—
726C23—21no—
727C23—21no—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—22no—
732C23—41no—
733C23—41no—
734C23—41no—
735C23—41no—
736C23—41no—
737C23—41no—
738C23—1222no—
739C23—2441no—
740C23—2441no—
741C23—2441no—
742C23—2441no—
743C23—2441no—
744C23—2441no—
745C23#1451974812yes—
746C23C22×C22⋊D6111yescharacteristic
747Q8—22no—
748Q8—22no—
749Q8—22no—
750Q8—22no—
751Q8—22no—
752Q8—22no—
753Q8—48no—
754Q8—41no—
755Q8—41no—
756Q8—41no—
757Q8—41no—
758Q8—41no—
759Q8—41no—
760D4—22no—
761D4—22no—
762D4—48no—
763D4—41no—
764D4—41no—
765D4—1222no—
766D4—1222no—
767D4—4884no—
768D4—2441no—
769D4—2441no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—21no—
788C2×C4—21no—
789C2×C4—48no—
790C2×C4—48no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—1222no—
798C2×C4—4884no—
799C2×C4—2441no—
800C2×C4—2441no—
801C2×C4—2441no—
802C2×C4—2441no—
803C2×C4—2441no—
804C2×C4—2441no—
805C2×C4—2441no—
806C2×C4—2441no—
807C2×C4#1451974612yes—
808C2×C4#1451974612yes—
809C2×C4#1451974812yes—
810C2×C4C2×D4×D6111yescharacteristic
811C2×C4C22×C22⋊D6111yescharacteristic
812C2×C4C22×C22⋊D6111yescharacteristic
813C2×C4C2×#1175822411yescharacteristic
814C2×C4#1451982211yescharacteristic
815C2×C4#1451982211yescharacteristic
816C8—2441no—
817C8—2441no—
818C8—2441no—
819C8—2441no—
820C22—22no—
821C22—22no—
822C22—22no—
823C22—41no—
824C22—41no—
825C22—41no—
826C22—41no—
827C22—42no—
828C22—42no—
829C22—42no—
830C22—81no—
831C22—81no—
832C22—81no—
833C22—81no—
834C22—4881no—
835C22—4881no—
836C22—4881no—
837C22—4881no—
838C22—2442no—
839C22—2442no—
840C22—2442no—
841C22C2×#1451974611yescharacteristic
842C22C2×#1451974811yescharacteristic
843C22#1684032911yescharacteristic
844C22#1684057011yescharacteristic
845C22#1684057011yescharacteristic
846C22#1684057011yescharacteristic
847C22#1684057711yescharacteristic
848C4—22no—
849C4—22no—
850C4—22no—
851C4—41no—
852C4—41no—
853C4—42no—
854C4—42no—
855C4—42no—
856C4—4881no—
857C4—4881no—
858C4—2442no—
859C4D4×C22⋊D6111yescharacteristic
860C4D4×C22⋊D6111yescharacteristic
861C4#1684040611yescharacteristic
862C4#1684040611yescharacteristic
863C2—42no—
864C2—82no—
865C2—4882no—
866C2#2144916911yescharacteristic
867C2#2145510511yescharacteristic
868C2#2145513411yescharacteristic
869C2#2145532711yescharacteristic
870C2#2145536511yescharacteristic
871C2#2145688011yescharacteristic
872C2#2145692811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC2×C61×#536C2
socleC23×C61C22×D4
prime radicalC2×#16839907C2
hypercenterC2×#536D61
hypocenterC61#24219
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#536

Complements

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

NH ≅ G/Ntype
1. C2×#16839974C2semidirect
2. C2×#16839964C2semidirect
4. C2×#16839901C2semidirect
5. #21448512C2semidirect
6. #21447062C2semidirect
7. #21447055C2semidirect
8. #21446902C2semidirect
9. #21446896C2semidirect
10. #21446752C2semidirect
11. #21446743C2semidirect
12. #21445803C2semidirect
13. #21445759C2semidirect
14. #21445754C2semidirect
15. C2×C61×#536C2semidirect
141. C4⋊Q8×C61D4semidirect
145. #124×C61D4semidirect
427. C2×#536D61semidirect
501. C61#24219semidirect
545. C4⋊Q8C22⋊D61semidirect
549. #124C22⋊D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168399742
C2×#168399642
C2×#168399072
C2×#168399012
#214485122
#214470622
#214470552
#214469022
#214468962
#214467522
#214467432
#214458032
#214457592
#214457542
C2×C61×#5362
#2421961