Finite Group Databasebeta

← #29717709

Subgroups — #29717709

Order 15616.

1442 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840001C211yesmaximal, characteristic, complemented
2C2×#16839924C211yesmaximal, characteristic, complemented
3C2×#16839918C211yesmaximal, characteristic, complemented
4C2×#16839758C211yesmaximal, characteristic, complemented
5#21449248C211yesmaximal, characteristic, complemented
6#21447055C211yesmaximal, characteristic, complemented
7#21446998C211yesmaximal, characteristic, complemented
8#21446913C211yesmaximal, characteristic, complemented
9#21446822C211yesmaximal, characteristic, complemented
10#21446160C211yesmaximal, characteristic, complemented
11#21446132C211yesmaximal, characteristic, complemented
12#21446112C211yesmaximal, characteristic, complemented
13#21446073C211yesmaximal, characteristic, complemented
14#21445754C211yesmaximal, characteristic, complemented
15C2×C61×#548C211yesmaximal, characteristic
16C22×#11758202C2211yescharacteristic
17C22×#11758202C2211yescharacteristic
18C22×#11758200C2211yescharacteristic
19C23×#92418C2211yescharacteristic
20C2×#14519756C2211yescharacteristic
21C2×#14519756C2211yescharacteristic
22C2×#14519736C2211yescharacteristic
23#16840001—24no—
24#16839924—24no—
25#16839918—24no—
26C2×#14519710C2211yescharacteristic
27#16839758—24no—
28C2×#14519701C2211yescharacteristic
29C2×#14519701C2211yescharacteristic
30C2×#14519701C2211yescharacteristic
31C2×#14519701C2211yescharacteristic
32C2×#14519701C2211yescharacteristic
33C2×#14519701C2211yescharacteristic
34C2×#14519700C2211yescharacteristic
35C2×#14519698C2211yescharacteristic
36C2×#14519698C2211yescharacteristic
37C2×#14519698C2211yescharacteristic
38C2×C22⋊#92418C2211yescharacteristic
39C2×C22⋊#92418C2211yescharacteristic
40C2×C22⋊#92418C2211yescharacteristic
41#16839690—21no—
42#16839676—21no—
43#16839668C2211yescharacteristic
44#16839660C2211yescharacteristic
45#16839657—21no—
46#16839656—21no—
47#16839622C2211yescharacteristic
48#16839524C2211yescharacteristic
49#16839524C2211yescharacteristic
50#16839517C2211yescharacteristic
51#16839517C2211yescharacteristic
52C22×#41×C61C2211yescharacteristic
53C23×Q8×C61C2211yescharacteristic
54C61×#548—24no—
55C61×#548—24no—
56C2×#124×C61—21no—
57C2×#124×C61C2211yescharacteristic
58C2×C22⋊Q8×C61—21no—
59C2×C22⋊Q8×C61C2211yescharacteristic
60C2×#121×C61—21no—
61C2×#121×C61C2211yescharacteristic
62C2×C4×Q8×C61C2211yescharacteristic
63C2×C4×D4×C61—21no—
64C2×C4×D4×C61C2211yescharacteristic
65C22×Dic122C2311yescharacteristic
66C2×#11758202—22no—
67C2×#11758202—22no—
68C2×#11758202—22no—
69C2×#11758202—22no—
70C2×#11758202—22no—
71C2×#11758202—41no—
72C2×#11758200—22no—
73C2×#11758200—41no—
74C2×#11758200—41no—
75C22×#92418—22no—
76C22×#92418—22no—
77C22×#92418—41no—
78C22×#92418C2311yescharacteristic
79C22×#92418C2311yescharacteristic
80C22×#92418C2311yescharacteristic
81C22×#92418C2311yescharacteristic
82#14519756—22no—
83#14519756—22no—
84#14519756—22no—
85#14519756—41no—
86#14519736—22no—
87#14519736—41no—
88C2×C4⋊Dic61C2311yescharacteristic
89C2×C4⋊Dic61C2311yescharacteristic
90C2×C4⋊Dic61C2311yescharacteristic
91C2×#11758196—21no—
92C2×#11758196—21no—
93C2×#11758196—21no—
94C2×C22⋊Dic61—21no—
95C2×C22⋊Dic61—21no—
96C2×C22⋊Dic61—21no—
97C2×C22⋊Dic61—21no—
98C2×C4×Dic61—21no—
99#14519710—22no—
100#14519701—22no—
101#14519701—22no—
102#14519701—22no—
103#14519701—22no—
104#14519701—41no—
105#14519701D414yescomplemented
106#14519700—22no—
107#14519698—22no—
108#14519698—22no—
109#14519698—22no—
110C22⋊#92418—22no—
111C22⋊#92418—22no—
112C22⋊#92418—41no—
113#14519684—21no—
114#14519684—21no—
115#14519684—21no—
116#14519684—21no—
117C2×#41×C61—22no—
118C2×#41×C61—22no—
119C2×#41×C61—22no—
120C2×#41×C61—41no—
121C2×#41×C61—41no—
122C2×#41×C61D414yes—
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×D4×C61—21no—
133C22×D4×C61—21no—
134C22×D4×C61D411yescharacteristic
135C22×D4×C61C2311yescharacteristic
136C23×C4×C61—21no—
137C23×C4×C61—21no—
138C23×C4×C61C2311yescharacteristic
139C23×C4×C61C2311yescharacteristic
140#124×C61—28no—
141#124×C61—22no—
142#124×C61—22no—
143C22⋊Q8×C61—28no—
144C22⋊Q8×C61—22no—
145C22⋊Q8×C61D414yes—
146#121×C61—28no—
147#121×C61—22no—
148#121×C61—22no—
149C4×Q8×C61—22no—
150C4×Q8×C61—22no—
151C4×D4×C61—28no—
152C4×D4×C61—22no—
153C4×D4×C61—22no—
154C2×C4⋊C4×C61—21no—
155C2×C4⋊C4×C61—21no—
156C2×C4⋊C4×C61D411yescharacteristic
157C2×C4⋊C4×C61C2311yescharacteristic
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×C61—21no—
165C2×C42×C61C2311yescharacteristic
166C24×C61—21no—
167C24×C61C2×D411yescharacteristic
168C24×C61C2×D411yescharacteristic
169#41×C61—28no—
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—42no—
183C2×Q8×C61—42no—
184C2×Q8×C61—44no—
185C2×Q8×C61—44no—
186C2×Q8×C61—44no—
187C2×Q8×C61—44no—
188C2×Q8×C61C2×D412yes—
189C2×Q8×C61C2×D412yes—
190C2×Q8×C61C2×D412yes—
191C2×Q8×C61#4112yes—
192C2×D4×C61—24no—
193C2×D4×C61—22no—
194C2×D4×C61—24no—
195C2×D4×C61—22no—
196C2×D4×C61—21no—
197C2×D4×C61—21no—
198C2×D4×C61—21no—
199C2×D4×C61—21no—
200C2×D4×C61—21no—
201C2×D4×C61—41no—
202C2×D4×C61—42no—
203C2×D4×C61—42no—
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—21no—
212C22×C4×C61—24no—
213C22×C4×C61—21no—
214C22×C4×C61—21no—
215C22×C4×C61—24no—
216C22×C4×C61—21no—
217C22×C4×C61—21no—
218C22×C4×C61—21no—
219C22×C4×C61—21no—
220C22×C4×C61—21no—
221C22×C4×C61—21no—
222C22×C4×C61—42no—
223C22×C4×C61—42no—
224C22×C4×C61—42no—
225C22×C4×C61—42no—
226C22×C4×C61C2×D411yescharacteristic
227C22×C4×C61C2×D411yescharacteristic
228C22×C4×C61C2×D411yescharacteristic
229C22×C4×C61C2×D411yescharacteristic
230C22×C4×C61C2×D412yes—
231C22×C4×C61C2×D412yes—
232C22×C4×C61C2411yescharacteristic
233C22×Dic61—21no—
234C22×Dic61—21no—
235C22×Dic61—21no—
236C22×Dic61—21no—
237C2×Dic122—21no—
238C2×Dic122—21no—
239C2×Dic122—21no—
240C2×Dic122—21no—
241C2×Dic122—21no—
242C2×Dic122—21no—
243C4⋊C4×C61—24no—
244C4⋊C4×C61—24no—
245C4⋊C4×C61—22no—
246C4⋊C4×C61—21no—
247C4⋊C4×C61C2×D412yes—
248C22⋊C4×C61—24no—
249C22⋊C4×C61—24no—
250C22⋊C4×C61—24no—
251C22⋊C4×C61—24no—
252C22⋊C4×C61—22no—
253C22⋊C4×C61—22no—
254C42×C61—24no—
255C42×C61—21no—
256C42×C61—21no—
257C22⋊Dic61—42no—
258C22⋊Dic61—42no—
259C22⋊Dic61—42no—
260C22⋊Dic61—42no—
261#11758202—44no—
262#11758202—44no—
263#11758200—44no—
264C4⋊Dic61—21no—
265C4⋊Dic61—21no—
266C4⋊Dic61—21no—
267C4⋊Dic61—21no—
268C4⋊Dic61—21no—
269C4⋊Dic61C2×D412yes—
270#11758196—42no—
271#11758196—42no—
272#11758196—42no—
273C4×Dic61—42no—
274C2×#92418—21no—
275C2×#92418—21no—
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—44no—
286C2×#92418C2×D412yes—
287C23×C61—21no—
288C23×C61—21no—
289C23×C61—21no—
290C23×C61—21no—
291C23×C61—21no—
292C23×C61—21no—
293C23×C61—21no—
294C23×C61—21no—
295C23×C61—21no—
296C23×C61—21no—
297C23×C61—21no—
298C23×C61—21no—
299C23×C61—22no—
300C23×C61—41no—
301C23×C61—41no—
302C23×C61—41no—
303C23×C61—41no—
304C23×C61—41no—
305C23×C61—41no—
306C23×C61#12012yes—
307C23×C61#13512yes—
308C23×C61C22×D411yescharacteristic
309Q8×C61—22no—
310Q8×C61—22no—
311Q8×C61—22no—
312Q8×C61—22no—
313Q8×C61—22no—
314Q8×C61—48no—
315Q8×C61—41no—
316Q8×C61—41no—
317Q8×C61#12114yes—
318D4×C61—22no—
319D4×C61—22no—
320D4×C61—48no—
321D4×C61—44no—
322D4×C61—48no—
323D4×C61—41no—
324D4×C61—41no—
325C2×C4×C61—22no—
326C2×C4×C61—21no—
327C2×C4×C61—22no—
328C2×C4×C61—21no—
329C2×C4×C61—22no—
330C2×C4×C61—22no—
331C2×C4×C61—22no—
332C2×C4×C61—22no—
333C2×C4×C61—22no—
334C2×C4×C61—21no—
335C2×C4×C61—21no—
336C2×C4×C61—22no—
337C2×C4×C61—22no—
338C2×C4×C61—21no—
339C2×C4×C61—21no—
340C2×C4×C61—21no—
341C2×C4×C61—21no—
342C2×C4×C61—21no—
343C2×C4×C61—21no—
344C2×C4×C61—21no—
345C2×C4×C61—48no—
346C2×C4×C61—48no—
347C2×C4×C61—41no—
348C2×C4×C61—41no—
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×C61C22×D411yescharacteristic
357C2×C4×C61C22×D411yescharacteristic
358C2×C4×C61C22×D411yescharacteristic
359C2×C4×C61C2×#4111yescharacteristic
360C2×C4×C61H(5,𝔽2)11yescharacteristic
361C2×C4×C61H(5,𝔽2)11yescharacteristic
362C2×Dic61—22no—
363C2×Dic61—41no—
364C2×Dic61—41no—
365C2×Dic61—41no—
366C2×Dic61—41no—
367C2×Dic61—41no—
368C2×Dic61—41no—
369C2×Dic61—41no—
370C2×Dic61—41no—
371C2×Dic61—41no—
372C2×Dic61—41no—
373C2×Dic61—41no—
374Dic122—41no—
375Dic122—41no—
376Dic122—41no—
377Dic122—41no—
378#92418—22no—
379#92418—41no—
380#92418—41no—
381#92418—41no—
382#24433—611nomaximal, Sylow
383C22×C61—22no—
384C22×C61—22no—
385C22×C61—22no—
386C22×C61—22no—
387C22×C61—22no—
388C22×C61—22no—
389C22×C61—41no—
390C22×C61—41no—
391C22×C61—41no—
392C22×C61—41no—
393C22×C61—41no—
394C22×C61—41no—
395C22×C61—41no—
396C22×C61—41no—
397C22×C61—42no—
398C22×C61—42no—
399C22×C61—42no—
400C22×C61—81no—
401C22×C61—81no—
402C22×C61—81no—
403C22×C61—81no—
404C22×C61C2×#12011yescharacteristic
405C22×C61D4211yescharacteristic
406C22×C61#54611yescharacteristic
407C22×C61C2×#13511yescharacteristic
408C22×C61#57511yescharacteristic
409C22×C61#57811yescharacteristic
410C22×C61#57811yescharacteristic
411C4×C61—22no—
412C4×C61—24no—
413C4×C61—41no—
414C4×C61—42no—
415C4×C61—41no—
416C4×C61—42no—
417C4×C61—41no—
418C4×C61C2×#12111yescharacteristic
419C4×C61#53411yescharacteristic
420C4×C61D4211yescharacteristic
421C4×C61#54611yescharacteristic
422Dic61—42no—
423Dic61—81no—
424Dic61—81no—
425Dic61—81no—
426C2×#548D6111yescharacteristic
427C2×#467—611no—
428C2×#452—611no—
429C2×#451—611no—
430C2×#416—611no—
431#2415—611no—
432#2042—611no—
433#2033—611no—
434#2015—611no—
435#2000—611no—
436#1878—611no—
437#1873—611no—
438#1869—611no—
439#1863—611no—
440#1787—611no—
441C2×C61—42no—
442C2×C61—42no—
443C2×C61—82no—
444C2×C61#241011yescharacteristic
445C2×C61#300211yescharacteristic
446C2×C61#301111yescharacteristic
447C2×C61#326911yescharacteristic
448C2×C61#328511yescharacteristic
449C2×C61#330011yescharacteristic
450C2×C61#331311yescharacteristic
451C22×#41C2×D6111yescharacteristic
452C23×Q8C2×D6111yescharacteristic
453C22×Q16—611no—
454C22×Q16—611no—
455C22×SD16—611no—
456C23×C8—611no—
457#548—24no—
458#548—24no—
459C2×#124—21no—
460C2×#124C2×D6111yescharacteristic
461C2×C22⋊Q8—21no—
462C2×C22⋊Q8—611no—
463C2×C22⋊Q8—611no—
464C2×C22⋊Q8C2×D6111yescharacteristic
465C2×#121—21no—
466C2×#121C2×D6111yescharacteristic
467C2×C4×Q8C2×D6111yescharacteristic
468C2×C4×D4—21no—
469C2×C4×D4C2×D6111yescharacteristic
470C2×#117—611no—
471#467—1224no—
472#452—1224no—
473#451—1224no—
474C2×#107—611no—
475#416—1224no—
476C2×#103—611no—
477C2×#103—611no—
478C2×#103—611no—
479C2×#103—611no—
480C2×#103—611no—
481C2×#103—611no—
482C2×#103—611no—
483C2×#102—611no—
484C2×#102—611no—
485C2×#102—611no—
486C2×C22⋊C8—611no—
487C2×C22⋊C8—611no—
488C2×C22⋊C8—611no—
489#397—1221no—
490#394—1221no—
491#391—611no—
492#389—611no—
493#389—1221no—
494#388—1221no—
495#380—611no—
496#340—611no—
497#340—611no—
498#336—611no—
499#336—611no—
500C61#2443311yescharacteristic, complemented, Sylow
501C2×#41—22no—
502C2×#41—22no—
503C2×#41—22no—
504C2×#41—41no—
505C2×#41—41no—
506C2×#41C22⋊D6114yes—
507C22×Q8—22no—
508C22×Q8—22no—
509C22×Q8—21no—
510C22×Q8—22no—
511C22×Q8—22no—
512C22×Q8—41no—
513C22×Q8—41no—
514C22×Q8—611no—
515C22×Q8C22×D6111yescharacteristic
516C22×Q8C22×D6111yescharacteristic
517C22×D4—21no—
518C22×D4—21no—
519C22×D4C22⋊D6111yescharacteristic
520C22×D4C22×D6111yescharacteristic
521C23×C4—21no—
522C23×C4—21no—
523C23×C4C22×D6111yescharacteristic
524C23×C4C22×D6111yescharacteristic
525C2×Q16—1222no—
526C2×Q16—1222no—
527C2×Q16—1222no—
528C2×Q16—1222no—
529C2×Q16—1222no—
530C2×Q16—2441no—
531C2×SD16—1222no—
532C2×SD16—2441no—
533C2×SD16—2441no—
534C22×C8—611no—
535C22×C8—611no—
536C22×C8—611no—
537C22×C8—611no—
538C22×C8—1222no—
539C22×C8—1222no—
540C22×C8—2441no—
541#124—28no—
542#124—22no—
543#124—22no—
544C22⋊Q8—28no—
545C22⋊Q8—22no—
546C22⋊Q8—1222no—
547C22⋊Q8—1222no—
548C22⋊Q8—1222no—
549C22⋊Q8—2441no—
550C22⋊Q8C22⋊D6114yes—
551#121—28no—
552#121—22no—
553#121—22no—
554C4×Q8—22no—
555C4×Q8—22no—
556C4×D4—28no—
557C4×D4—22no—
558C4×D4—22no—
559#117—1222no—
560#117—2441no—
561C2×C4⋊C4—21no—
562C2×C4⋊C4—21no—
563C2×C4⋊C4—611no—
564C2×C4⋊C4—611no—
565C2×C4⋊C4—611no—
566C2×C4⋊C4—1221no—
567C2×C4⋊C4—1221no—
568C2×C4⋊C4—1221no—
569C2×C4⋊C4C22⋊D6111yescharacteristic
570C2×C4⋊C4C22×D6111yescharacteristic
571C2×C22⋊C4—21no—
572C2×C22⋊C4—21no—
573C2×C22⋊C4—21no—
574C2×C22⋊C4—21no—
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—21no—
582C2×C42—1221no—
583C2×C42C22×D6111yescharacteristic
584#107—1222no—
585#103—614no—
586#103—1222no—
587#103—1222no—
588#103—1222no—
589#103—1222no—
590#103—1222no—
591#103—2441no—
592#102—1222no—
593#102—1222no—
594#102—1222no—
595C22⋊C8—1222no—
596C22⋊C8—1222no—
597C22⋊C8—2441no—
598#95—1221no—
599#95—1221no—
600#95—1221no—
601#95—1221no—
602C24—21no—
603C24C2×C22⋊D6111yescharacteristic
604C24C2×C22⋊D6111yescharacteristic
605#41—28no—
606#41—44no—
607#41—44no—
608#41—44no—
609C2×Q8—24no—
610C2×Q8—21no—
611C2×Q8—21no—
612C2×Q8—21no—
613C2×Q8—21no—
614C2×Q8—21no—
615C2×Q8—21no—
616C2×Q8—21no—
617C2×Q8—21no—
618C2×Q8—42no—
619C2×Q8—42no—
620C2×Q8—44no—
621C2×Q8—44no—
622C2×Q8—44no—
623C2×Q8—44no—
624C2×Q8—1221no—
625C2×Q8—1221no—
626C2×Q8—1221no—
627C2×Q8—1221no—
628C2×Q8—1221no—
629C2×Q8—1221no—
630C2×Q8D4×D6112yes—
631C2×Q8#1175822412yes—
632C2×Q8C2×C22⋊D6112yes—
633C2×Q8C2×C22⋊D6112yes—
634C2×D4—24no—
635C2×D4—22no—
636C2×D4—24no—
637C2×D4—22no—
638C2×D4—21no—
639C2×D4—21no—
640C2×D4—21no—
641C2×D4—21no—
642C2×D4—21no—
643C2×D4—41no—
644C2×D4—42no—
645C2×D4—42no—
646C2×D4—42no—
647C2×D4—42no—
648C2×D4C2×C22⋊D6112yes—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—24no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—24no—
664C22×C4—42no—
665C22×C4—42no—
666C22×C4—42no—
667C22×C4—42no—
668C22×C4—1221no—
669C22×C4—1221no—
670C22×C4—1221no—
671C22×C4—1221no—
672C22×C4C2×C22⋊D6111yescharacteristic
673C22×C4C2×C22⋊D6111yescharacteristic
674C22×C4C2×C22⋊D6111yescharacteristic
675C22×C4C2×C22⋊D6112yes—
676C22×C4C2×C22⋊D6112yes—
677C22×C4C2×C22⋊D6111yescharacteristic
678C22×C4C23×D6111yescharacteristic
679Q16—2444no—
680Q16—2444no—
681SD16—2444no—
682C2×C8—612no—
683C2×C8—1221no—
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—2444no—
695C4⋊C4—24no—
696C4⋊C4—21no—
697C4⋊C4—24no—
698C4⋊C4—22no—
699C4⋊C4—612no—
700C4⋊C4—1221no—
701C4⋊C4—1221no—
702C4⋊C4—1221no—
703C4⋊C4—1221no—
704C4⋊C4—1221no—
705C4⋊C4—2442no—
706C4⋊C4—2442no—
707C4⋊C4—2442no—
708C4⋊C4C2×C22⋊D6112yes—
709C22⋊C4—24no—
710C22⋊C4—24no—
711C22⋊C4—24no—
712C22⋊C4—24no—
713C22⋊C4—22no—
714C22⋊C4—22no—
715C22⋊C4—2442no—
716C22⋊C4—2442no—
717C22⋊C4—2442no—
718C22⋊C4—2442no—
719C42—24no—
720C42—21no—
721C42—21no—
722C42—2442no—
723C23—21no—
724C23—21no—
725C23—21no—
726C23—21no—
727C23—21no—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—21no—
732C23—21no—
733C23—21no—
734C23—21no—
735C23—22no—
736C23—41no—
737C23—41no—
738C23—41no—
739C23—41no—
740C23—41no—
741C23—41no—
742C23#1451974612yes—
743C23#1451979712yes—
744C23C22×C22⋊D6111yescharacteristic
745Q8—22no—
746Q8—22no—
747Q8—22no—
748Q8—22no—
749Q8—22no—
750Q8—48no—
751Q8—41no—
752Q8—41no—
753Q8—2441no—
754Q8—2441no—
755Q8—2441no—
756Q8—2441no—
757Q8#1451974914yes—
758D4—22no—
759D4—22no—
760D4—48no—
761D4—44no—
762D4—48no—
763D4—41no—
764D4—41no—
765C2×C4—22no—
766C2×C4—21no—
767C2×C4—22no—
768C2×C4—21no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—48no—
786C2×C4—48no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—1222no—
796C2×C4—2441no—
797C2×C4—2441no—
798C2×C4—2441no—
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×C4C2×D4×D6111yescharacteristic
809C2×C4C22×C22⋊D6111yescharacteristic
810C2×C4C22×C22⋊D6111yescharacteristic
811C2×C4C2×#1175822411yescharacteristic
812C2×C4#1451982211yescharacteristic
813C2×C4#1451982211yescharacteristic
814C8—1222no—
815C8—2441no—
816C8—2441no—
817C8—2441no—
818C22—22no—
819C22—22no—
820C22—22no—
821C22—22no—
822C22—22no—
823C22—22no—
824C22—41no—
825C22—41no—
826C22—41no—
827C22—41no—
828C22—41no—
829C22—41no—
830C22—41no—
831C22—41no—
832C22—42no—
833C22—42no—
834C22—42no—
835C22—81no—
836C22—81no—
837C22—81no—
838C22—81no—
839C22C2×#1451974611yescharacteristic
840C22D4×C22⋊D6111yescharacteristic
841C22#1684040611yescharacteristic
842C22C2×#1451979711yescharacteristic
843C22#1684056011yescharacteristic
844C22#1684057711yescharacteristic
845C22#1684057711yescharacteristic
846C4—22no—
847C4—24no—
848C4—41no—
849C4—41no—
850C4—42no—
851C4—41no—
852C4—42no—
853C4—4881no—
854C4—4881no—
855C4—4881no—
856C4—2442no—
857C4C2×#1451974911yescharacteristic
858C4#1684032111yescharacteristic
859C4D4×C22⋊D6111yescharacteristic
860C4#1684040611yescharacteristic
861C2—42no—
862C2—42no—
863C2—82no—
864C2#2144919311yescharacteristic
865C2#2145503711yescharacteristic
866C2#2145511411yescharacteristic
867C2#2145737511yescharacteristic
868C2#2145755611yescharacteristic
869C2#2145770611yescharacteristic
870C2#2145788511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
Fitting, prime radicalC2×C61×#548C2
socleC23×C61C22×D4
hypercenterC2×#548D61
hypocenterC61#24433
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#548

Complements

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

NH ≅ G/Ntype
1. C2×#16840001C2semidirect
2. C2×#16839924C2semidirect
3. C2×#16839918C2semidirect
4. C2×#16839758C2semidirect
5. #21449248C2semidirect
6. #21447055C2semidirect
7. #21446998C2semidirect
8. #21446913C2semidirect
9. #21446822C2semidirect
10. #21446160C2semidirect
11. #21446132C2semidirect
12. #21446112C2semidirect
13. #21446073C2semidirect
14. #21445754C2semidirect
105. #14519701D4semidirect
500. C61#24433semidirect

Maximal subgroups

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

subgroupindex
C2×#168400012
C2×#168399242
C2×#168399182
C2×#168397582
#214492482
#214470552
#214469982
#214469132
#214468222
#214461602
#214461322
#214461122
#214460732
#214457542
C2×C61×#5482
#2443361