Finite Group Databasebeta

← #29586518

Subgroups — #29586518

Order 15616.

1922 conjugacy classes of subgroups.

The subgroup lattice has 1090 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519748C211yesmaximal, characteristic
2C22×#14519698C211yesmaximal, characteristic, complemented
3C22×#14519689C211yesmaximal, characteristic, complemented
4C2×#16839619C211yesmaximal, characteristic, complemented
5C2×#16839525C211yesmaximal, characteristic, complemented
6C2×#16839524C211yesmaximal, characteristic, complemented
7C22×#102×C61C211yesmaximal, characteristic, complemented
8C23×C22⋊D61—21no—
9C23×C4×D61C2211yescharacteristic
10C23×#92418C2211yescharacteristic
11C2×#14519748—22no—
12C2×#14519748—22no—
13C2×#14519748—22no—
14C2×#14519748—22no—
15C2×#14519748—22no—
16C2×#14519748C414yescomplemented
17C22×C4⋊Dic61C2211yescharacteristic
18C22×C4⋊Dic61C2211yescharacteristic
19C22×C22⋊Dic61—21no—
20C22×#11758198—21no—
21C2×#14519698—22no—
22C2×#14519698—22no—
23C2×#14519698—22no—
24C2×#14519689—22no—
25C2×#14519689—22no—
26C2×#14519689—22no—
27#16839619—22no—
28#16839619—22no—
29C2×#14519684—21no—
30#16839525—22no—
31#16839524—22no—
32C23×D4×C61C2211yescharacteristic
33C23×C8×C61C2211yescharacteristic
34C22×C4⋊C4×C61C2211yescharacteristic
35C2×#102×C61—22no—
36C2×#102×C61—22no—
37C2×#102×C61—22no—
38C24×D61D411yescharacteristic
39C22×C22⋊D61—24no—
40C22×C22⋊D61—24no—
41C22×C22⋊D61—24no—
42C22×C22⋊D61—42no—
43C22×C22⋊D61—42no—
44C22×C22⋊D61—42no—
45C22×C22⋊D61—42no—
46C23×Dic61—21no—
47C23×Dic61—21no—
48C23×Dic61D411yescharacteristic
49C22×C4×D61—21no—
50C22×C4×D61—21no—
51C22×C4×D61—21no—
52C22×C4×D61—21no—
53C22×C4×D61—21no—
54C22×C4×D61—21no—
55C22×C4×D61—21no—
56C22×C4×D61—21no—
57C22×C4×D61—21no—
58C22×C4×D61—21no—
59C22×C4×D61—21no—
60C22×C4×D61—21no—
61C22×C4×D61C2×C412yes—
62C22×C4×D61D412yes—
63C22×#92418—21no—
64C22×#92418—21no—
65C22×#92418—21no—
66C22×#92418—21no—
67C22×#92418—21no—
68C22×#92418—21no—
69C22×#92418D412yescomplemented
70#14519748—28no—
71#14519748—28no—
72#14519748—28no—
73#14519748—28no—
74C2×C4⋊Dic61—21no—
75C2×C4⋊Dic61—21no—
76C2×C4⋊Dic61—21no—
77C2×C4⋊Dic61—21no—
78C2×C4⋊Dic61—21no—
79C2×C4⋊Dic61—21no—
80C2×C4⋊Dic61—21no—
81C2×C4⋊Dic61—21no—
82C2×C4⋊Dic61C2×C412yes—
83C2×C4⋊Dic61D412yes—
84C2×C4⋊Dic61D412yes—
85C2×C4⋊Dic61D412yescomplemented
86C2×C22⋊Dic61—24no—
87C2×C22⋊Dic61—24no—
88C2×C22⋊Dic61—24no—
89C2×#11758198—24no—
90C2×#11758198—42no—
91C2×#11758198—42no—
92#14519698—28no—
93#14519689—28no—
94#14519684—24no—
95C25×C61—21no—
96C22×D4×C61—21no—
97C22×D4×C61—21no—
98C22×D4×C61—21no—
99C22×D4×C61—21no—
100C22×D4×C61—21no—
101C22×D4×C61—21no—
102C22×D4×C61—21no—
103C22×D4×C61—21no—
104C22×D4×C61—21no—
105C22×D4×C61—21no—
106C22×D4×C61—21no—
107C22×D4×C61C2×C412yes—
108C22×D4×C61D412yes—
109C22×D4×C61D412yes—
110C23×C4×C61—21no—
111C23×C4×C61C2311yescharacteristic
112C22×C8×C61—21no—
113C22×C8×C61—21no—
114C22×C8×C61—21no—
115C22×C8×C61—21no—
116C22×C8×C61—21no—
117C22×C8×C61—21no—
118C22×C8×C61D412yescomplemented
119C2×C4⋊C4×C61—21no—
120C2×C4⋊C4×C61—21no—
121C2×C4⋊C4×C61—21no—
122C2×C4⋊C4×C61—21no—
123C2×C4⋊C4×C61—21no—
124C2×C4⋊C4×C61D412yescomplemented
125#102×C61—28no—
126C24×C61—22no—
127C24×C61—22no—
128C24×C61—22no—
129C24×C61—41no—
130C24×C61—41no—
131C24×C61—41no—
132C24×C61—41no—
133C24×C61—41no—
134C24×C61—41no—
135C24×C61—41no—
136C24×C61—41no—
137C24×C61—41no—
138C24×C61—41no—
139C24×C61—41no—
140C24×C61—41no—
141C24×C61C2×D411yescharacteristic
142C23×D61—21no—
143C23×D61—21no—
144C23×D61—21no—
145C23×D61—21no—
146C23×D61—21no—
147C23×D61—21no—
148C23×D61—21no—
149C23×D61—21no—
150C23×D61—21no—
151C23×D61—21no—
152C23×D61—21no—
153C23×D61—21no—
154C23×D61C22⋊C412yes—
155C23×D61D812yes—
156C23×D61SD1612yes—
157C2×D4×C61—22no—
158C2×D4×C61—22no—
159C2×D4×C61—22no—
160C2×D4×C61—22no—
161C2×D4×C61—22no—
162C2×D4×C61—22no—
163C2×D4×C61—22no—
164C2×D4×C61—22no—
165C2×D4×C61—22no—
166C2×D4×C61—22no—
167C2×D4×C61—22no—
168C2×D4×C61—22no—
169C2×D4×C61—22no—
170C2×D4×C61—22no—
171C2×D4×C61—22no—
172C2×D4×C61—41no—
173C2×D4×C61—41no—
174C2×D4×C61—41no—
175C2×D4×C61—41no—
176C2×D4×C61—41no—
177C2×D4×C61—41no—
178C2×D4×C61—41no—
179C2×D4×C61—41no—
180C2×D4×C61—41no—
181C2×D4×C61—41no—
182C2×D4×C61—41no—
183C2×D4×C61—41no—
184C2×D4×C61C22⋊C414yescomplemented
185C22×C4×C61—22no—
186C22×C4×C61—41no—
187C22×C4×C61—41no—
188C22×C4×C61—41no—
189C22×C4×C61—41no—
190C22×C4×C61—41no—
191C22×C4×C61—41no—
192C22×C4×C61C22×C411yescharacteristic
193C22×C4×C61C2×D411yescharacteristic
194C22×C4×C61C2×D411yescharacteristic
195C22×C4×C61C2×D411yescharacteristic
196C22×C4×C61C2×D411yescharacteristic
197C22×C4×C61C2×D411yescharacteristic
198C22×C4×C61C2×D411yescharacteristic
199C22×C4×C61C2×D411yescharacteristic
200C22×C4×C61C2×D411yescharacteristic
201C22×C4×C61C2×D411yescharacteristic
202C22×C4×C61#4111yescharacteristic
203C22×C4×C61#4111yescharacteristic
204C22×C4×C61#4111yescharacteristic
205C22×C4×C61#4111yescharacteristic
206C2×C22⋊D61—216no—
207C2×C22⋊D61—48no—
208C2×C22⋊D61—48no—
209C2×C22⋊D61—48no—
210C2×C22⋊D61—48no—
211C2×C22⋊D61—48no—
212C2×C22⋊D61—48no—
213C22×Dic61—22no—
214C22×Dic61—21no—
215C22×Dic61—21no—
216C22×Dic61—21no—
217C22×Dic61—22no—
218C22×Dic61—22no—
219C22×Dic61—21no—
220C22×Dic61—21no—
221C22×Dic61—21no—
222C22×Dic61—22no—
223C22×Dic61—41no—
224C22×Dic61—41no—
225C22×Dic61—41no—
226C22×Dic61—41no—
227C22×Dic61—41no—
228C22×Dic61—41no—
229C22×Dic61—41no—
230C22×Dic61—41no—
231C22×Dic61—41no—
232C22×Dic61—41no—
233C22×Dic61C22⋊C412yes—
234C2×C4×D61—22no—
235C2×C4×D61—22no—
236C2×C4×D61—22no—
237C2×C4×D61—22no—
238C2×C4×D61—22no—
239C2×C4×D61—22no—
240C2×C4×D61—22no—
241C2×C4×D61—22no—
242C2×C4×D61—22no—
243C2×C4×D61—22no—
244C2×C4×D61—22no—
245C2×C4×D61—22no—
246C2×C4×D61—41no—
247C2×C4×D61—41no—
248C2×C4×D61—41no—
249C2×C4×D61—41no—
250C2×C4×D61—41no—
251C2×C4×D61—41no—
252C2×C4×D61—41no—
253C2×C4×D61—41no—
254C2×C4×D61—41no—
255C2×C4×D61—41no—
256C2×C4×D61—41no—
257C2×C4×D61—41no—
258C2×C4×D61—41no—
259C2×C4×D61—41no—
260C2×C4×D61—41no—
261C2×C4×D61—41no—
262C2×C8×C61—22no—
263C2×C8×C61—22no—
264C2×C8×C61—22no—
265C2×C8×C61—41no—
266C2×C8×C61—41no—
267C2×C8×C61—41no—
268C2×C8×C61—41no—
269C4⋊C4×C61—22no—
270C4⋊C4×C61—22no—
271C4⋊C4×C61—41no—
272C4⋊C4×C61—41no—
273C22⋊Dic61—216no—
274#11758198—48no—
275C4⋊Dic61—22no—
276C4⋊Dic61—22no—
277C4⋊Dic61—22no—
278C4⋊Dic61—22no—
279C4⋊Dic61—22no—
280C4⋊Dic61—41no—
281C4⋊Dic61—41no—
282C4⋊Dic61C22⋊C414yescomplemented
283C2×#92418—22no—
284C2×#92418—22no—
285C2×#92418—22no—
286C2×#92418—41no—
287C2×#92418—41no—
288C2×#92418—41no—
289C2×#92418—41no—
290C23×C61—24no—
291C23×C61—42no—
292C23×C61—42no—
293C23×C61—42no—
294C23×C61—42no—
295C23×C61—42no—
296C23×C61—42no—
297C23×C61—42no—
298C23×C61—42no—
299C23×C61—42no—
300C23×C61—42no—
301C23×C61—42no—
302C23×C61—42no—
303C23×C61—42no—
304C23×C61—42no—
305C23×C61—42no—
306C23×C61—42no—
307C23×C61—42no—
308C23×C61—42no—
309C23×C61—81no—
310C23×C61—81no—
311C23×C61—81no—
312C23×C61—81no—
313C23×C61—81no—
314C23×C61—81no—
315C23×C61—81no—
316C23×C61—81no—
317C23×C61—81no—
318C23×C61—81no—
319C23×C61—81no—
320C23×C61—81no—
321C23×C61—81no—
322C23×C61—81no—
323C23×C61—81no—
324C23×C61—81no—
325C23×C61C2×C22⋊C411yescharacteristic
326C23×C61#12011yescharacteristic
327C23×C61#12011yescharacteristic
328C23×C61#12011yescharacteristic
329C23×C61#12111yescharacteristic
330C23×C61#12111yescharacteristic
331C23×C61#12311yescharacteristic
332C23×C61C2×D811yescharacteristic
333C23×C61C2×SD1611yescharacteristic
334C23×C61#13511yescharacteristic
335C23×C61#13511yescharacteristic
336C23×C61AGL(1,ℤ/8)11yescharacteristic
337C23×C61AGL(1,ℤ/8)11yescharacteristic
338C23×C61AGL(1,ℤ/8)11yescharacteristic
339C23×C61#13711yescharacteristic
340C22×D61—22no—
341C22×D61—22no—
342C22×D61—22no—
343C22×D61—22no—
344C22×D61—22no—
345C22×D61—22no—
346C22×D61—22no—
347C22×D61—22no—
348C22×D61—22no—
349C22×D61—22no—
350C22×D61—22no—
351C22×D61—22no—
352C22×D61—22no—
353C22×D61—22no—
354C22×D61—22no—
355C22×D61—22no—
356C22×D61—22no—
357C22×D61—22no—
358C22×D61—41no—
359C22×D61—41no—
360C22×D61—41no—
361C22×D61—41no—
362C22×D61—41no—
363C22×D61—41no—
364C22×D61—41no—
365C22×D61—41no—
366C22×D61—41no—
367C22×D61—41no—
368C22×D61—41no—
369C22×D61—41no—
370C22×D61—41no—
371C22×D61—41no—
372C22×D61—41no—
373C22×D61—41no—
374C22×D61#10214yescomplemented
375D4×C61—24no—
376D4×C61—24no—
377D4×C61—42no—
378D4×C61—42no—
379D4×C61—42no—
380D4×C61—42no—
381D4×C61—42no—
382D4×C61—42no—
383C2×C4×C61—42no—
384C2×C4×C61—42no—
385C2×C4×C61—42no—
386C2×C4×C61—81no—
387C2×C4×C61—81no—
388C2×C4×C61—81no—
389C2×C4×C61—81no—
390C2×C4×C61C2×C22⋊C411yescharacteristic
391C2×C4×C61C2×C22⋊C411yescharacteristic
392C2×C4×C61C4×D411yescharacteristic
393C2×C4×C61C4×D411yescharacteristic
394C2×C4×C61C4×D411yescharacteristic
395C2×C4×C61C4×D411yescharacteristic
396C2×C4×C61#12011yescharacteristic
397C2×C4×C61#12011yescharacteristic
398C2×C4×C61#12011yescharacteristic
399C2×C4×C61#12011yescharacteristic
400C2×C4×C61#12011yescharacteristic
401C2×C4×C61#12111yescharacteristic
402C2×C4×C61#12111yescharacteristic
403C2×C4×C61#12111yescharacteristic
404C2×C4×C61#12111yescharacteristic
405C2×C4×C61#12111yescharacteristic
406C2×C4×C61#12111yescharacteristic
407C2×C4×C61#12111yescharacteristic
408C2×C4×C61#12111yescharacteristic
409C2×C4×C61#12111yescharacteristic
410C2×C4×C61#12111yescharacteristic
411C2×C4×C61#12311yescharacteristic
412C2×C4×C61#12311yescharacteristic
413C2×C4×C61#12311yescharacteristic
414C2×C4×C61#12411yescharacteristic
415C2×C4×C61#12411yescharacteristic
416C2×C4×C61#12711yescharacteristic
417C2×C4×C61#12711yescharacteristic
418C22⋊D61—432no—
419C2×Dic61—24no—
420C2×Dic61—22no—
421C2×Dic61—22no—
422C2×Dic61—22no—
423C2×Dic61—41no—
424C2×Dic61—41no—
425C2×Dic61—41no—
426C2×Dic61—41no—
427C2×Dic61—42no—
428C2×Dic61—42no—
429C2×Dic61—42no—
430C2×Dic61—42no—
431C2×Dic61—42no—
432C2×Dic61—42no—
433C2×Dic61—42no—
434C2×Dic61—42no—
435C2×Dic61—42no—
436C2×Dic61—81no—
437C2×Dic61—81no—
438C2×Dic61—81no—
439C2×Dic61—81no—
440C4×D61—42no—
441C4×D61—42no—
442C4×D61—42no—
443C4×D61—42no—
444C4×D61—42no—
445C4×D61—42no—
446C4×D61—42no—
447C4×D61—42no—
448C8×C61—42no—
449#92418—42no—
450#10969—611nomaximal, Sylow
451C22×C61—44no—
452C22×C61—44no—
453C22×C61—44no—
454C22×C61—82no—
455C22×C61—82no—
456C22×C61—82no—
457C22×C61—82no—
458C22×C61—82no—
459C22×C61—82no—
460C22×C61—82no—
461C22×C61—82no—
462C22×C61—82no—
463C22×C61—82no—
464C22×C61—82no—
465C22×C61—82no—
466C22×C61#37911yescharacteristic
467C22×C61#38611yescharacteristic
468C22×C61#38611yescharacteristic
469C22×C61#39211yescharacteristic
470C22×C61#39211yescharacteristic
471C22×C61#39411yescharacteristic
472C22×C61#39411yescharacteristic
473C22×C61C2×#10211yescharacteristic
474C22×C61#41611yescharacteristic
475C22×C61#41711yescharacteristic
476C22×C61#41811yescharacteristic
477C22×C61#44711yescharacteristic
478C22×C61#44711yescharacteristic
479C22×C61#44711yescharacteristic
480C22×C61#44811yescharacteristic
481C22×C61#44911yescharacteristic
482C22×C61#44911yescharacteristic
483C22×C61#44911yescharacteristic
484C22×C61#44911yescharacteristic
485C22×C61#45011yescharacteristic
486C22×C61#45011yescharacteristic
487C22×C61#45211yescharacteristic
488C22×C61#45211yescharacteristic
489C22×C61#46511yescharacteristic
490C22×C61#46511yescharacteristic
491C22×C61#46611yescharacteristic
492C22×C61#46611yescharacteristic
493C22×C61#46811yescharacteristic
494C22×C61#46811yescharacteristic
495C22×C61#46911yescharacteristic
496C22×C61#46911yescharacteristic
497C22×C61#48011yescharacteristic
498C22×C61#48111yescharacteristic
499C22×C61#48211yescharacteristic
500C22×C61#48211yescharacteristic
501C2×D61—24no—
502C2×D61—24no—
503C2×D61—24no—
504C2×D61—42no—
505C2×D61—42no—
506C2×D61—42no—
507C2×D61—42no—
508C2×D61—42no—
509C2×D61—42no—
510C2×D61—42no—
511C2×D61—42no—
512C2×D61—42no—
513C2×D61—42no—
514C2×D61—42no—
515C2×D61—42no—
516C4×C61—82no—
517C4×C61#38611yescharacteristic
518C4×C61#38611yescharacteristic
519C4×C61#39011yescharacteristic
520C4×C61#39011yescharacteristic
521C4×C61#39211yescharacteristic
522C4×C61#39211yescharacteristic
523C4×C61#39411yescharacteristic
524C4×C61#39411yescharacteristic
525Dic61—42no—
526Dic61—44no—
527Dic61—82no—
528C22×#121—611no—
529C22×#102—611no—
530C22×#102D6111yescharacteristic, complemented
531C22×C22⋊C8—611no—
532C2×#380—611no—
533C2×#340—611no—
534C2×#340—611no—
535C2×C61—84no—
536C2×C61#143811yescharacteristic
537C2×C61#178611yescharacteristic
538C2×C61#178811yescharacteristic
539C2×C61#187411yescharacteristic
540C2×C61#187511yescharacteristic
541C2×C61#189311yescharacteristic
542C2×C61#189511yescharacteristic
543C2×C61#199911yescharacteristic
544C2×C61#199911yescharacteristic
545C2×C61#200011yescharacteristic
546C2×C61#200011yescharacteristic
547C2×C61#203311yescharacteristic
548C2×C61#203311yescharacteristic
549C2×C61#203411yescharacteristic
550C2×C61#203411yescharacteristic
551D61—44no—
552C23×D4—1221no—
553C23×D4C2×D6111yescharacteristic
554C24×C4—611no—
555C23×C8—611no—
556C23×C8C2×D6111yescharacteristic
557C2×#121—614no—
558C2×#121—1222no—
559C2×#121—1222no—
560C2×#121—1222no—
561C2×#121—1222no—
562C2×#121—1222no—
563C22×C4⋊C4—611no—
564C22×C4⋊C4—611no—
565C22×C4⋊C4C2×D6111yescharacteristic
566C22×C22⋊C4—1221no—
567C22×C22⋊C4—1221no—
568C2×#102—22no—
569C2×#102—22no—
570C2×#102—22no—
571C2×#102—1222no—
572C2×#102—1222no—
573C2×#102—1222no—
574C2×C22⋊C8—1222no—
575C2×C22⋊C8—1222no—
576C2×C22⋊C8—1222no—
577#380—1222no—
578#380—1222no—
579C2×#95—1221no—
580#340—1222no—
581#340—1222no—
582C61#1096911yescharacteristic, complemented, Sylow
583C25—21no—
584C25—611no—
585C22×D4—21no—
586C22×D4—21no—
587C22×D4—21no—
588C22×D4—21no—
589C22×D4—21no—
590C22×D4—21no—
591C22×D4—21no—
592C22×D4—21no—
593C22×D4—21no—
594C22×D4—21no—
595C22×D4—21no—
596C22×D4—1224no—
597C22×D4—1224no—
598C22×D4—1224no—
599C22×D4—2442no—
600C22×D4—2442no—
601C22×D4—2442no—
602C22×D4—2442no—
603C22×D4C4×D6112yes—
604C22×D4D24412yes—
605C22×D4C22⋊D6112yes—
606C23×C4—21no—
607C23×C4—611no—
608C23×C4—612no—
609C23×C4—612no—
610C23×C4—1221no—
611C23×C4—1221no—
612C23×C4—1221no—
613C23×C4—1221no—
614C23×C4—1221no—
615C23×C4—1221no—
616C23×C4—1221no—
617C23×C4—1221no—
618C23×C4—1221no—
619C23×C4—1221no—
620C23×C4—1221no—
621C23×C4—1221no—
622C23×C4—1221no—
623C23×C4—1221no—
624C23×C4C22×D6111yescharacteristic
625C22×C8—21no—
626C22×C8—21no—
627C22×C8—21no—
628C22×C8—21no—
629C22×C8—21no—
630C22×C8—21no—
631C22×C8—612no—
632C22×C8—1221no—
633C22×C8—1221no—
634C22×C8—1221no—
635C22×C8—1221no—
636C22×C8—1221no—
637C22×C8—1221no—
638C22×C8C22⋊D6112yescomplemented
639#121—1228no—
640#121—1228no—
641#121—1228no—
642#121—1228no—
643C2×C4⋊C4—21no—
644C2×C4⋊C4—21no—
645C2×C4⋊C4—21no—
646C2×C4⋊C4—21no—
647C2×C4⋊C4—21no—
648C2×C4⋊C4—612no—
649C2×C4⋊C4—612no—
650C2×C4⋊C4—612no—
651C2×C4⋊C4—612no—
652C2×C4⋊C4—1221no—
653C2×C4⋊C4—1221no—
654C2×C4⋊C4—1221no—
655C2×C4⋊C4—1221no—
656C2×C4⋊C4—1221no—
657C2×C4⋊C4—1221no—
658C2×C4⋊C4—1221no—
659C2×C4⋊C4—1221no—
660C2×C4⋊C4C22⋊D6112yescomplemented
661C2×C22⋊C4—1224no—
662C2×C22⋊C4—1224no—
663C2×C22⋊C4—1224no—
664C2×C22⋊C4—1224no—
665C2×C22⋊C4—2442no—
666C2×C22⋊C4—2442no—
667#102—28no—
668#102—1228no—
669C22⋊C8—1228no—
670#95—1224no—
671C24—22no—
672C24—22no—
673C24—22no—
674C24—41no—
675C24—41no—
676C24—41no—
677C24—41no—
678C24—41no—
679C24—41no—
680C24—41no—
681C24—41no—
682C24—41no—
683C24—41no—
684C24—41no—
685C24—41no—
686C24—612no—
687C24—612no—
688C24—612no—
689C24—1221no—
690C24—1221no—
691C24—1221no—
692C24—1221no—
693C24—1221no—
694C24—1221no—
695C24—1221no—
696C24—1221no—
697C24—1221no—
698C24—1221no—
699C24—1221no—
700C24—1221no—
701C24D4×D6111yescharacteristic
702C2×D4—22no—
703C2×D4—22no—
704C2×D4—22no—
705C2×D4—22no—
706C2×D4—22no—
707C2×D4—22no—
708C2×D4—22no—
709C2×D4—22no—
710C2×D4—22no—
711C2×D4—22no—
712C2×D4—22no—
713C2×D4—22no—
714C2×D4—22no—
715C2×D4—22no—
716C2×D4—22no—
717C2×D4—41no—
718C2×D4—41no—
719C2×D4—41no—
720C2×D4—41no—
721C2×D4—41no—
722C2×D4—41no—
723C2×D4—41no—
724C2×D4—41no—
725C2×D4—41no—
726C2×D4—41no—
727C2×D4—41no—
728C2×D4—41no—
729C2×D4—12216no—
730C2×D4—2448no—
731C2×D4—2448no—
732C2×D4—2448no—
733C2×D4—2448no—
734C2×D4—2448no—
735C2×D4—2448no—
736C2×D4#1175819814yescomplemented
737C22×C4—22no—
738C22×C4—41no—
739C22×C4—41no—
740C22×C4—41no—
741C22×C4—41no—
742C22×C4—41no—
743C22×C4—41no—
744C22×C4—612no—
745C22×C4—1222no—
746C22×C4—1221no—
747C22×C4—1221no—
748C22×C4—1222no—
749C22×C4—1221no—
750C22×C4—1222no—
751C22×C4—1221no—
752C22×C4—1221no—
753C22×C4—1221no—
754C22×C4—1222no—
755C22×C4—1222no—
756C22×C4—1222no—
757C22×C4—1222no—
758C22×C4—1222no—
759C22×C4—1222no—
760C22×C4—1222no—
761C22×C4—1222no—
762C22×C4—1222no—
763C22×C4—1222no—
764C22×C4—1222no—
765C22×C4—1222no—
766C22×C4—1222no—
767C22×C4—2441no—
768C22×C4—2441no—
769C22×C4—2441no—
770C22×C4—2441no—
771C22×C4—2441no—
772C22×C4—2441no—
773C22×C4—2441no—
774C22×C4—2441no—
775C22×C4—2441no—
776C22×C4—2441no—
777C22×C4—2441no—
778C22×C4—2441no—
779C22×C4—2441no—
780C22×C4—2441no—
781C22×C4—2441no—
782C22×C4—2441no—
783C22×C4—2441no—
784C22×C4—2441no—
785C22×C4—2441no—
786C22×C4—2441no—
787C22×C4—2441no—
788C22×C4—2441no—
789C22×C4—2441no—
790C22×C4—2441no—
791C22×C4—2441no—
792C22×C4—2441no—
793C22×C4C2×C4×D6111yescharacteristic
794C22×C4C2×D24411yescharacteristic
795C22×C4#1175822211yescharacteristic
796C22×C4#1175822211yescharacteristic
797C22×C4D4×D6111yescharacteristic
798C22×C4D4×D6111yescharacteristic
799C22×C4D4×D6111yescharacteristic
800C22×C4D4×D6111yescharacteristic
801C22×C4D4×D6111yescharacteristic
802C22×C4#1175822411yescharacteristic
803C22×C4#1175822411yescharacteristic
804C22×C4C2×C22⋊D6111yescharacteristic
805C22×C4C2×C22⋊D6111yescharacteristic
806C22×C4C2×C22⋊D6111yescharacteristic
807C2×C8—22no—
808C2×C8—22no—
809C2×C8—22no—
810C2×C8—41no—
811C2×C8—41no—
812C2×C8—41no—
813C2×C8—41no—
814C2×C8—1222no—
815C2×C8—1222no—
816C2×C8—1222no—
817C2×C8—2441no—
818C2×C8—2441no—
819C2×C8—2441no—
820C2×C8—2441no—
821C4⋊C4—22no—
822C4⋊C4—22no—
823C4⋊C4—41no—
824C4⋊C4—41no—
825C4⋊C4—614no—
826C4⋊C4—1222no—
827C4⋊C4—1222no—
828C4⋊C4—1222no—
829C4⋊C4—1222no—
830C4⋊C4—1222no—
831C4⋊C4—2441no—
832C4⋊C4—2441no—
833C22⋊C4—12216no—
834C22⋊C4—2448no—
835C23—24no—
836C23—42no—
837C23—42no—
838C23—42no—
839C23—42no—
840C23—42no—
841C23—42no—
842C23—42no—
843C23—42no—
844C23—42no—
845C23—42no—
846C23—42no—
847C23—42no—
848C23—42no—
849C23—42no—
850C23—42no—
851C23—42no—
852C23—42no—
853C23—42no—
854C23—81no—
855C23—81no—
856C23—81no—
857C23—81no—
858C23—81no—
859C23—81no—
860C23—81no—
861C23—81no—
862C23—81no—
863C23—81no—
864C23—81no—
865C23—81no—
866C23—81no—
867C23—81no—
868C23—81no—
869C23—81no—
870C23—614no—
871C23—1222no—
872C23—1222no—
873C23—1222no—
874C23—1222no—
875C23—1222no—
876C23—1222no—
877C23—1222no—
878C23—1222no—
879C23—1222no—
880C23—1222no—
881C23—1222no—
882C23—1222no—
883C23—1222no—
884C23—1222no—
885C23—1222no—
886C23—1222no—
887C23—1222no—
888C23—1222no—
889C23—2441no—
890C23—2441no—
891C23—2441no—
892C23—2441no—
893C23—2441no—
894C23—2441no—
895C23—2441no—
896C23—2441no—
897C23—2441no—
898C23—2441no—
899C23—2441no—
900C23—2441no—
901C23—2441no—
902C23—2441no—
903C23—2441no—
904C23—2441no—
905C23C22⋊C4×D6111yescharacteristic
906C23#1451974511yescharacteristic
907C23#1451974511yescharacteristic
908C23#1451974711yescharacteristic
909C23#1451974811yescharacteristic
910C23#1451975011yescharacteristic
911C23#1451975911yescharacteristic
912C23D8×D6111yescharacteristic
913C23SD16×D6111yescharacteristic
914C23#1451979611yescharacteristic
915C23#1451979811yescharacteristic
916C23#1451980111yescharacteristic
917C23#1451980111yescharacteristic
918C23#1451980411yescharacteristic
919C23#1451980611yescharacteristic
920D4—24no—
921D4—24no—
922D4—42no—
923D4—42no—
924D4—42no—
925D4—42no—
926D4—42no—
927D4—42no—
928D4—24432no—
929C2×C4—42no—
930C2×C4—42no—
931C2×C4—42no—
932C2×C4—81no—
933C2×C4—81no—
934C2×C4—81no—
935C2×C4—81no—
936C2×C4—1222no—
937C2×C4—1224no—
938C2×C4—1222no—
939C2×C4—1222no—
940C2×C4—4881no—
941C2×C4—4881no—
942C2×C4—4881no—
943C2×C4—4881no—
944C2×C4—2442no—
945C2×C4—2442no—
946C2×C4—2442no—
947C2×C4—2442no—
948C2×C4—2442no—
949C2×C4—2442no—
950C2×C4—2442no—
951C2×C4—2442no—
952C2×C4—2442no—
953C2×C4—2441no—
954C2×C4—2441no—
955C2×C4—2441no—
956C2×C4—2441no—
957C2×C4—2442no—
958C2×C4—2442no—
959C2×C4—2442no—
960C2×C4—2442no—
961C2×C4—2442no—
962C2×C4—2442no—
963C2×C4—2442no—
964C2×C4—2442no—
965C2×C4C22⋊C4×D6111yescharacteristic
966C2×C4C2×#1175819811yescharacteristic
967C2×C4#1451973711yescharacteristic
968C2×C4#1451973711yescharacteristic
969C2×C4C4×C22⋊D6111yescharacteristic
970C2×C4C4×C22⋊D6111yescharacteristic
971C2×C4#1451974511yescharacteristic
972C2×C4#1451974511yescharacteristic
973C2×C4#1451974611yescharacteristic
974C2×C4#1451974711yescharacteristic
975C2×C4#1451974711yescharacteristic
976C2×C4#1451974811yescharacteristic
977C2×C4#1451974911yescharacteristic
978C2×C4#1451974911yescharacteristic
979C2×C4#1451974911yescharacteristic
980C2×C4#1451974911yescharacteristic
981C2×C4#1451975011yescharacteristic
982C2×C4#1451975011yescharacteristic
983C2×C4#1451975011yescharacteristic
984C2×C4#1451975111yescharacteristic
985C2×C4#1451975111yescharacteristic
986C2×C4#1451975911yescharacteristic
987C2×C4#1451976011yescharacteristic
988C2×C4#1451976111yescharacteristic
989C2×C4#1451976311yescharacteristic
990C2×C4#1451976311yescharacteristic
991C2×C4#1451977311yescharacteristic
992C2×C4#1451977311yescharacteristic
993C8—42no—
994C8—2442no—
995C22—44no—
996C22—44no—
997C22—44no—
998C22—82no—
999C22—82no—
1000C22—82no—
1001C22—82no—
1002C22—82no—
1003C22—82no—
1004C22—82no—
1005C22—82no—
1006C22—82no—
1007C22—82no—
1008C22—82no—
1009C22—82no—
1010C22—1224no—
1011C22—1224no—
1012C22—1224no—
1013C22—2442no—
1014C22—2442no—
1015C22—2442no—
1016C22—2442no—
1017C22—2442no—
1018C22—2442no—
1019C22—2442no—
1020C22—2442no—
1021C22—2442no—
1022C22—2442no—
1023C22—2442no—
1024C22—2442no—
1025C22#1683961711yescharacteristic
1026C22#1683963811yescharacteristic
1027C22#1683963811yescharacteristic
1028C22#1683967011yescharacteristic
1029C22#1683967111yescharacteristic
1030C22#1683967711yescharacteristic
1031C22#1683967811yescharacteristic
1032C22#102×D6111yescharacteristic
1033C22#1683975511yescharacteristic
1034C22#1683976011yescharacteristic
1035C22#1683976511yescharacteristic
1036C22#1683989411yescharacteristic
1037C22#1683989411yescharacteristic
1038C22#1683989711yescharacteristic
1039C22#1683989911yescharacteristic
1040C22#1683990411yescharacteristic
1041C22#1683990411yescharacteristic
1042C22#1683990611yescharacteristic
1043C22#1683990811yescharacteristic
1044C22#1683991111yescharacteristic
1045C22#1683991411yescharacteristic
1046C22#1683992111yescharacteristic
1047C22#1683992511yescharacteristic
1048C22#1683998811yescharacteristic
1049C22#1683999011yescharacteristic
1050C22#1683999511yescharacteristic
1051C22#1683999711yescharacteristic
1052C22#1684000511yescharacteristic
1053C22#1684000711yescharacteristic
1054C22#1684001211yescharacteristic
1055C22#1684001411yescharacteristic
1056C22#1684007411yescharacteristic
1057C22#1684007911yescharacteristic
1058C22#1684008411yescharacteristic
1059C22#1684008511yescharacteristic
1060C4—82no—
1061C4—4882no—
1062C4—2444no—
1063C4—2442no—
1064C4#1683963911yescharacteristic
1065C4#1683964111yescharacteristic
1066C4#1683966211yescharacteristic
1067C4#1683966211yescharacteristic
1068C4#1683967011yescharacteristic
1069C4#1683967111yescharacteristic
1070C4#1683967711yescharacteristic
1071C4#1683967811yescharacteristic
1072C2—84no—
1073C2—2444no—
1074C2#2144405811yescharacteristic
1075C2#2144574811yescharacteristic
1076C2#2144575611yescharacteristic
1077C2#2144613311yescharacteristic
1078C2#2144613811yescharacteristic
1079C2#2144624411yescharacteristic
1080C2#2144625411yescharacteristic
1081C2#2144681411yescharacteristic
1082C2#2144681611yescharacteristic
1083C2#2144681911yescharacteristic
1084C2#2144682311yescharacteristic
1085C2#2144699911yescharacteristic
1086C2#2144700011yescharacteristic
1087C2#2144700611yescharacteristic
1088C2#2144700711yescharacteristic
subgroupG/H
centerC24D4×D61
commutatorC22×C4×C61C22×C4
FrattiniC23×C4C22×D61
FittingC22×#102×C61C2
socleC24×C61C2×D4
prime radicalC22×#14519748C2
cosocleC23×C4×C61C23
hypercenterC22×#102D61
hypocenterC61#10969
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C24 ◁ C23×C4 ◁ C22×#102

Complements

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

NH ≅ G/Ntype
2. C22×#14519698C2semidirect
3. C22×#14519689C2semidirect
4. C2×#16839619C2semidirect
5. C2×#16839525C2semidirect
6. C2×#16839524C2semidirect
7. C22×#102×C61C2semidirect
16. C2×#14519748C4semidirect
69. C22×#92418D4semidirect
85. C2×C4⋊Dic61D4semidirect
118. C22×C8×C61D4semidirect
124. C2×C4⋊C4×C61D4semidirect
184. C2×D4×C61C22⋊C4semidirect
282. C4⋊Dic61C22⋊C4semidirect
374. C22×D61#102semidirect
530. C22×#102D61semidirect
582. C61#10969semidirect
638. C22×C8C22⋊D61semidirect
660. C2×C4⋊C4C22⋊D61semidirect
736. C2×D4#11758198semidirect

Maximal subgroups

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

subgroupindex
C22×#145197482
C22×#145196982
C22×#145196892
C2×#168396192
C2×#168395252
C2×#168395242
C22×#102×C612
#1096961