Finite Group Databasebeta

← #29607941

Subgroups — #29607941

Order 15616.

1750 conjugacy classes of subgroups.

The subgroup lattice has 1038 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839660C211yesmaximal, characteristic, complemented
2C2×#16839658C211yesmaximal, characteristic, complemented
3C2×#16839655C211yesmaximal, characteristic
4C2×#16839637C211yesmaximal, characteristic
5C2×#16839620C211yesmaximal, characteristic
6C2×#16839620C211yesmaximal, characteristic
7#21444083C211yesmaximal, characteristic, complemented
8#21444082C211yesmaximal, characteristic, complemented
9#21444071C211yesmaximal, characteristic, complemented
10#21444071C211yesmaximal, characteristic, complemented
11#21444062C211yesmaximal, characteristic
12#21444062C211yesmaximal, characteristic
13#21444052C211yesmaximal, characteristic, complemented
14#21444050C211yesmaximal, characteristic, complemented
15C2×C61×#388C211yesmaximal, characteristic
16C24×Dic61C2211yescharacteristic
17C22×C4⋊Dic61C2211yescharacteristic
18C22×C4⋊Dic61C2211yescharacteristic
19C22×C4⋊Dic61C2211yescharacteristic
20C22×#11758196C2211yescharacteristic
21C22×#11758196C2211yescharacteristic
22C22×#11758196C2211yescharacteristic
23C22×#11758196C2211yescharacteristic
24C22×#11758196C2211yescharacteristic
25C22×#11758196C2211yescharacteristic
26C22×C22⋊Dic61C2211yescharacteristic
27C22×C22⋊Dic61C2211yescharacteristic
28C22×C22⋊Dic61C2211yescharacteristic
29C22×C4×Dic61C2211yescharacteristic
30#16839660—24no—
31#16839658—24no—
32#16839655—24no—
33#16839637C418yescomplemented
34#16839620—24no—
35#16839620—24no—
36C2×#14519684C2211yescharacteristic
37C2×#14519684C2211yescharacteristic
38C2×#14519684C2211yescharacteristic
39C2×#14519684C2211yescharacteristic
40C2×#14519684C2211yescharacteristic
41C2×#14519684C2211yescharacteristic
42C2×#14519684C2211yescharacteristic
43C2×#14519684C2211yescharacteristic
44C2×#14519684C2211yescharacteristic
45C2×#14519684C2211yescharacteristic
46C2×#14519684C2211yescharacteristic
47C2×#14519684C2211yescharacteristic
48C2×#14519684C2211yescharacteristic
49C2×#14519684C2211yescharacteristic
50C22×C4⋊C4×C61C2211yescharacteristic
51C22×C22⋊C4×C61C2211yescharacteristic
52C22×C22⋊C4×C61C2211yescharacteristic
53C22×C22⋊C4×C61C2211yescharacteristic
54C22×C42×C61C2211yescharacteristic
55C61×#388—24no—
56C2×#95×C61C2211yescharacteristic
57C2×#95×C61C2211yescharacteristic
58C23×Dic61—22no—
59C23×Dic61—22no—
60C23×Dic61—22no—
61C23×Dic61—22no—
62C23×Dic61—41no—
63C23×Dic61—41no—
64C23×Dic61C2×C414yes—
65C23×Dic61C2311yescharacteristic
66C23×Dic61C2311yescharacteristic
67C23×Dic61C2311yescharacteristic
68C23×Dic61C2311yescharacteristic
69C23×Dic61C2311yescharacteristic
70C23×Dic61C2311yescharacteristic
71C23×Dic61C2311yescharacteristic
72C23×Dic61C2311yescharacteristic
73C2×C4⋊Dic61—22no—
74C2×C4⋊Dic61—22no—
75C2×C4⋊Dic61—22no—
76C2×C4⋊Dic61—22no—
77C2×C4⋊Dic61—22no—
78C2×C4⋊Dic61—22no—
79C2×C4⋊Dic61—41no—
80C2×C4⋊Dic61C2×C414yes—
81C2×C4⋊Dic61C2×C414yes—
82C2×#11758196—22no—
83C2×#11758196—22no—
84C2×#11758196—22no—
85C2×#11758196—22no—
86C2×#11758196—22no—
87C2×#11758196—22no—
88C2×#11758196—22no—
89C2×#11758196—22no—
90C2×#11758196—22no—
91C2×#11758196—22no—
92C2×#11758196—41no—
93C2×#11758196—41no—
94C2×#11758196—41no—
95C2×#11758196—41no—
96C2×#11758196—41no—
97C2×#11758196—41no—
98C2×#11758196—41no—
99C2×#11758196—41no—
100C2×C22⋊Dic61—22no—
101C2×C22⋊Dic61—22no—
102C2×C22⋊Dic61—22no—
103C2×C22⋊Dic61—22no—
104C2×C22⋊Dic61—41no—
105C2×C22⋊Dic61—41no—
106C2×C22⋊Dic61—41no—
107C2×C22⋊Dic61—41no—
108C2×C22⋊Dic61C2×C414yes—
109C2×C4×Dic61—22no—
110C2×C4×Dic61—22no—
111C2×C4×Dic61—41no—
112#14519684—22no—
113#14519684—22no—
114#14519684—22no—
115#14519684—22no—
116#14519684—22no—
117#14519684—22no—
118#14519684—41no—
119#14519684—41no—
120#14519684—41no—
121#14519684—41no—
122#14519684C2×C414yes—
123#14519684C2×C414yes—
124#14519684D414yes—
125#14519684D414yes—
126C25×C61C2311yescharacteristic
127C23×C4×C61C2311yescharacteristic
128C23×C4×C61C2311yescharacteristic
129C23×C4×C61C2311yescharacteristic
130C23×C4×C61C2311yescharacteristic
131C23×C4×C61C2311yescharacteristic
132C23×C4×C61C2311yescharacteristic
133C2×C4⋊C4×C61—22no—
134C2×C4⋊C4×C61—22no—
135C2×C4⋊C4×C61—41no—
136C2×C22⋊C4×C61—22no—
137C2×C22⋊C4×C61—22no—
138C2×C22⋊C4×C61—22no—
139C2×C22⋊C4×C61—22no—
140C2×C22⋊C4×C61—41no—
141C2×C22⋊C4×C61—41no—
142C2×C22⋊C4×C61C2×C414yes—
143C2×C22⋊C4×C61D414yes—
144C2×C22⋊C4×C61Q814yes—
145C2×C42×C61—22no—
146C2×C42×C61—22no—
147C2×C42×C61—41no—
148#95×C61—22no—
149#95×C61—22no—
150C24×C61—21no—
151C24×C61—21no—
152C24×C61—21no—
153C24×C61—21no—
154C24×C61—21no—
155C24×C61—21no—
156C24×C61—21no—
157C24×C61—21no—
158C24×C61—21no—
159C24×C61—21no—
160C24×C61—21no—
161C24×C61—21no—
162C24×C61C22×C412yes—
163C24×C61C2×D412yes—
164C24×C61C2×Q812yes—
165C24×C61C2411yescharacteristic
166C22×C4×C61—21no—
167C22×C4×C61—21no—
168C22×C4×C61—21no—
169C22×C4×C61—21no—
170C22×C4×C61—21no—
171C22×C4×C61—21no—
172C22×C4×C61—21no—
173C22×C4×C61—21no—
174C22×C4×C61—21no—
175C22×C4×C61—21no—
176C22×C4×C61—21no—
177C22×C4×C61—21no—
178C22×C4×C61—21no—
179C22×C4×C61—21no—
180C22×C4×C61—21no—
181C22×C4×C61—21no—
182C22×C4×C61—21no—
183C22×C4×C61—21no—
184C22×C4×C61—21no—
185C22×C4×C61—21no—
186C22×C4×C61—21no—
187C22×C4×C61—21no—
188C22×C4×C61—21no—
189C22×C4×C61—21no—
190C22×C4×C61—21no—
191C22×C4×C61—21no—
192C22×C4×C61—21no—
193C22×C4×C61—21no—
194C22×C4×C61—21no—
195C22×C4×C61—21no—
196C22×C4×C61—21no—
197C22×C4×C61—21no—
198C22×C4×C61—21no—
199C22×C4×C61—21no—
200C22×C4×C61C22×C412yes—
201C22×C4×C61C22×C412yes—
202C22×C4×C61C2×D412yes—
203C22×C4×C61C2×D412yes—
204C22×C4×C61C2×D412yes—
205C22×C4×C61C2×D412yes—
206C22×C4×C61C2×Q812yes—
207C22×C4×C61C2×Q812yes—
208C22×Dic61—21no—
209C22×Dic61—21no—
210C22×Dic61—21no—
211C22×Dic61—21no—
212C22×Dic61—21no—
213C22×Dic61—21no—
214C22×Dic61—21no—
215C22×Dic61—21no—
216C22×Dic61—21no—
217C22×Dic61—21no—
218C22×Dic61—21no—
219C22×Dic61—21no—
220C22×Dic61—21no—
221C22×Dic61—21no—
222C22×Dic61—21no—
223C22×Dic61—21no—
224C22×Dic61—21no—
225C22×Dic61—21no—
226C22×Dic61—21no—
227C22×Dic61—21no—
228C22×Dic61—21no—
229C22×Dic61—21no—
230C22×Dic61—21no—
231C22×Dic61—21no—
232C22×Dic61—21no—
233C22×Dic61—21no—
234C22×Dic61—21no—
235C22×Dic61—21no—
236C22×Dic61—21no—
237C22×Dic61—21no—
238C22×Dic61—21no—
239C22×Dic61—21no—
240C22×Dic61—28no—
241C22×Dic61—28no—
242C22×Dic61—21no—
243C22×Dic61—21no—
244C22×Dic61—21no—
245C22×Dic61—21no—
246C22×Dic61—21no—
247C22×Dic61—21no—
248C22×Dic61—21no—
249C22×Dic61—21no—
250C22×Dic61—21no—
251C22×Dic61—21no—
252C22×Dic61—21no—
253C22×Dic61—21no—
254C22×Dic61—21no—
255C22×Dic61—21no—
256C22×Dic61—44no—
257C22×Dic61—44no—
258C22×Dic61—44no—
259C22×Dic61—44no—
260C22×Dic61—44no—
261C22×Dic61C22×C412yes—
262C22×Dic61C22×C412yes—
263C22×Dic61C22×C412yes—
264C22×Dic61C22×C412yes—
265C22×Dic61C2×D412yes—
266C22×Dic61C2×D412yes—
267C22×Dic61C2×D412yes—
268C22×Dic61C2×D412yes—
269C22×Dic61#4112yes—
270C22×Dic61#4112yes—
271C4⋊C4×C61—44no—
272C22⋊C4×C61—44no—
273C22⋊C4×C61—44no—
274C22⋊C4×C61C4⋊C4116yescomplemented
275C42×C61—44no—
276C22⋊Dic61—44no—
277C22⋊Dic61—44no—
278C22⋊Dic61—44no—
279C4⋊Dic61—28no—
280C4⋊Dic61—28no—
281C4⋊Dic61—44no—
282#11758196—44no—
283#11758196—44no—
284#11758196—44no—
285#11758196—44no—
286#11758196—44no—
287#11758196—44no—
288C4×Dic61—44no—
289C23×C61—22no—
290C23×C61—22no—
291C23×C61—22no—
292C23×C61—22no—
293C23×C61—22no—
294C23×C61—22no—
295C23×C61—22no—
296C23×C61—22no—
297C23×C61—22no—
298C23×C61—22no—
299C23×C61—22no—
300C23×C61—22no—
301C23×C61—22no—
302C23×C61—22no—
303C23×C61—22no—
304C23×C61—22no—
305C23×C61—22no—
306C23×C61—22no—
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—41no—
323C23×C61C2×C4⋊C414yes—
324C23×C61C23×C411yescharacteristic
325C23×C61C22×D411yescharacteristic
326C23×C61C22×D411yescharacteristic
327C23×C61C22×D411yescharacteristic
328C23×C61C22×Q811yescharacteristic
329C23×C61C2×#4111yescharacteristic
330C23×C61C2×#4111yescharacteristic
331C23×C61H(5,𝔽2)11yescharacteristic
332C23×C61H(5,𝔽2)11yescharacteristic
333C23×C61H(5,𝔽2)11yescharacteristic
334C23×C61H(5,𝔽2)11yescharacteristic
335C23×C612−1+411yescharacteristic
336C23×C612−1+411yescharacteristic
337C23×C612−1+411yescharacteristic
338C23×C612−1+411yescharacteristic
339C2×C4×C61—22no—
340C2×C4×C61—22no—
341C2×C4×C61—22no—
342C2×C4×C61—22no—
343C2×C4×C61—22no—
344C2×C4×C61—22no—
345C2×C4×C61—22no—
346C2×C4×C61—22no—
347C2×C4×C61—22no—
348C2×C4×C61—22no—
349C2×C4×C61—22no—
350C2×C4×C61—22no—
351C2×C4×C61—22no—
352C2×C4×C61—22no—
353C2×C4×C61—22no—
354C2×C4×C61—22no—
355C2×C4×C61—22no—
356C2×C4×C61—22no—
357C2×C4×C61—41no—
358C2×C4×C61—41no—
359C2×C4×C61—41no—
360C2×C4×C61—41no—
361C2×C4×C61—41no—
362C2×C4×C61—41no—
363C2×C4×C61—41no—
364C2×C4×C61—41no—
365C2×C4×C61—41no—
366C2×C4×C61—41no—
367C2×C4×C61—41no—
368C2×C4×C61—41no—
369C2×C4×C61—41no—
370C2×C4×C61—41no—
371C2×C4×C61—41no—
372C2×C4×C61—41no—
373C2×C4×C61—41no—
374C2×C4×C61—41no—
375C2×C4×C61—41no—
376C2×C4×C61—41no—
377C2×C4×C61—41no—
378C2×C4×C61—41no—
379C2×C4×C61C2×C4⋊C414yes—
380C2×C4×C61C2×C4⋊C414yes—
381C2×Dic61—22no—
382C2×Dic61—22no—
383C2×Dic61—22no—
384C2×Dic61—22no—
385C2×Dic61—22no—
386C2×Dic61—22no—
387C2×Dic61—22no—
388C2×Dic61—22no—
389C2×Dic61—22no—
390C2×Dic61—22no—
391C2×Dic61—22no—
392C2×Dic61—22no—
393C2×Dic61—22no—
394C2×Dic61—22no—
395C2×Dic61—22no—
396C2×Dic61—22no—
397C2×Dic61—22no—
398C2×Dic61—22no—
399C2×Dic61—22no—
400C2×Dic61—22no—
401C2×Dic61—22no—
402C2×Dic61—22no—
403C2×Dic61—22no—
404C2×Dic61—22no—
405C2×Dic61—416no—
406C2×Dic61—41no—
407C2×Dic61—41no—
408C2×Dic61—41no—
409C2×Dic61—41no—
410C2×Dic61—41no—
411C2×Dic61—41no—
412C2×Dic61—41no—
413C2×Dic61—41no—
414C2×Dic61—41no—
415C2×Dic61—41no—
416C2×Dic61—41no—
417C2×Dic61—41no—
418C2×Dic61—41no—
419C2×Dic61—41no—
420C2×Dic61—41no—
421C2×Dic61—41no—
422C2×Dic61—41no—
423C2×Dic61—41no—
424C2×Dic61—41no—
425C2×Dic61—41no—
426C2×Dic61—41no—
427C2×Dic61—41no—
428C2×Dic61—41no—
429C2×Dic61—41no—
430C2×Dic61—41no—
431C2×Dic61—41no—
432C2×Dic61—41no—
433C2×Dic61—41no—
434C2×Dic61—41no—
435C2×Dic61—41no—
436C2×Dic61C4×D414yes—
437C2×Dic61C4×D414yes—
438#14402—611nomaximal, Sylow
439C22×C61—24no—
440C22×C61—24no—
441C22×C61—24no—
442C22×C61—42no—
443C22×C61—42no—
444C22×C61—42no—
445C22×C61—42no—
446C22×C61—42no—
447C22×C61—42no—
448C22×C61—42no—
449C22×C61—42no—
450C22×C61—42no—
451C22×C61—42no—
452C22×C61—42no—
453C22×C61—42no—
454C22×C61C22×C4⋊C411yescharacteristic
455C22×C61C2×C4×D411yescharacteristic
456C22×C61C2×C4×D411yescharacteristic
457C22×C61#51811yescharacteristic
458C22×C61#51911yescharacteristic
459C22×C61#52011yescharacteristic
460C22×C61#52011yescharacteristic
461C22×C61#53611yescharacteristic
462C22×C61#53611yescharacteristic
463C22×C61#53711yescharacteristic
464C22×C61#53711yescharacteristic
465C22×C61#53711yescharacteristic
466C22×C61#53711yescharacteristic
467C22×C61#54111yescharacteristic
468C22×C61#54111yescharacteristic
469C22×C61#54211yescharacteristic
470C22×C61#54211yescharacteristic
471C22×C61#54411yescharacteristic
472C22×C61#54411yescharacteristic
473C22×C61D4211yescharacteristic
474C22×C61D4211yescharacteristic
475C22×C61D4211yescharacteristic
476C22×C61#54611yescharacteristic
477C22×C61#54611yescharacteristic
478C22×C61#54711yescharacteristic
479C22×C61#54711yescharacteristic
480C22×C61D4×Q811yescharacteristic
481C22×C61D4×Q811yescharacteristic
482C22×C61#55111yescharacteristic
483C22×C61#55411yescharacteristic
484C22×C61#55411yescharacteristic
485C22×C61#56011yescharacteristic
486C22×C61#56211yescharacteristic
487C22×C61#56211yescharacteristic
488C22×C61#56311yescharacteristic
489C4×C61—24no—
490C4×C61—24no—
491C4×C61—42no—
492C4×C61—42no—
493C4×C61—81no—
494C4×C61—81no—
495Dic61—24no—
496Dic61—24no—
497Dic61—42no—
498Dic61—42no—
499Dic61—42no—
500Dic61—42no—
501Dic61—81no—
502Dic61—81no—
503C2×#389—611no—
504C2×#389—611no—
505C2×#388—611no—
506C2×#388D6111yescharacteristic
507C2×#385—611no—
508C2×#380—611no—
509C2×#380—611no—
510#1444—611no—
511#1444—611no—
512#1441—611no—
513#1441—611no—
514#1439—611no—
515#1439—611no—
516#1436—611no—
517#1436—611no—
518C2×C61—44no—
519C2×C61#231611yescharacteristic
520C2×C61#232311yescharacteristic
521C2×C61#232311yescharacteristic
522C2×C61D4×C4⋊C411yescharacteristic
523C2×C61D4×C4⋊C411yescharacteristic
524C2×C61#235811yescharacteristic
525C2×C61#237611yescharacteristic
526C2×C61#267211yescharacteristic
527C2×C61#267211yescharacteristic
528C2×C61#267511yescharacteristic
529C2×C61#267711yescharacteristic
530C2×C61#270411yescharacteristic
531C2×C61#270411yescharacteristic
532C2×C61#272211yescharacteristic
533C2×C61#274211yescharacteristic
534C24×C4—611no—
535C22×C4⋊C4—611no—
536C22×C4⋊C4—611no—
537C22×C4⋊C4—611no—
538C22×C4⋊C4—611no—
539C22×C4⋊C4—611no—
540C22×C4⋊C4—611no—
541C22×C4⋊C4—611no—
542C22×C4⋊C4—611no—
543C22×C4⋊C4—611no—
544C22×C4⋊C4C2×D6111yescharacteristic
545C22×C22⋊C4—611no—
546C22×C22⋊C4—611no—
547C22×C22⋊C4—611no—
548C22×C22⋊C4C2×D6111yescharacteristic
549C22×C22⋊C4C2×D6111yescharacteristic
550C22×C22⋊C4C2×D6111yescharacteristic
551C22×C42—611no—
552C22×C42C2×D6111yescharacteristic
553#389—1224no—
554#389—1224no—
555#388—24no—
556#388—1224no—
557#385—618no—
558#380—1224no—
559#380—1224no—
560C2×#95—611no—
561C2×#95—611no—
562C2×#95—611no—
563C2×#95—611no—
564C2×#95—611no—
565C2×#95—611no—
566C2×#95—611no—
567C2×#95—611no—
568C2×#95—611no—
569C2×#95—611no—
570C2×#95—611no—
571C2×#95—611no—
572C2×#95—611no—
573C2×#95—611no—
574C2×#95C2×D6111yescharacteristic
575C2×#95C2×D6111yescharacteristic
576C61#1440211yescharacteristic, complemented, Sylow
577C25C22×D6111yescharacteristic
578C23×C4—611no—
579C23×C4—611no—
580C23×C4—611no—
581C23×C4—611no—
582C23×C4—611no—
583C23×C4—611no—
584C23×C4—614no—
585C23×C4—611no—
586C23×C4—611no—
587C23×C4—1222no—
588C23×C4—1222no—
589C23×C4—1222no—
590C23×C4—1222no—
591C23×C4—2441no—
592C23×C4—2441no—
593C23×C4C22×D6111yescharacteristic
594C23×C4C22×D6111yescharacteristic
595C23×C4C22×D6111yescharacteristic
596C23×C4C22×D6111yescharacteristic
597C23×C4C22×D6111yescharacteristic
598C23×C4C22×D6111yescharacteristic
599C2×C4⋊C4—22no—
600C2×C4⋊C4—22no—
601C2×C4⋊C4—41no—
602C2×C4⋊C4—614no—
603C2×C4⋊C4—614no—
604C2×C4⋊C4—1222no—
605C2×C4⋊C4—1222no—
606C2×C4⋊C4—1222no—
607C2×C4⋊C4—1222no—
608C2×C4⋊C4—1222no—
609C2×C4⋊C4—1222no—
610C2×C4⋊C4—1222no—
611C2×C4⋊C4—1222no—
612C2×C4⋊C4—1222no—
613C2×C4⋊C4—1222no—
614C2×C4⋊C4—1222no—
615C2×C4⋊C4—1222no—
616C2×C4⋊C4—1222no—
617C2×C4⋊C4—1222no—
618C2×C4⋊C4—1222no—
619C2×C4⋊C4—1222no—
620C2×C4⋊C4—2441no—
621C2×C4⋊C4—2441no—
622C2×C4⋊C4—2441no—
623C2×C4⋊C4—2441no—
624C2×C4⋊C4—2441no—
625C2×C4⋊C4—2441no—
626C2×C4⋊C4—2441no—
627C2×C4⋊C4—2441no—
628C2×C4⋊C4—2441no—
629C2×C22⋊C4—22no—
630C2×C22⋊C4—22no—
631C2×C22⋊C4—22no—
632C2×C22⋊C4—22no—
633C2×C22⋊C4—41no—
634C2×C22⋊C4—41no—
635C2×C22⋊C4—614no—
636C2×C22⋊C4—1222no—
637C2×C22⋊C4—1222no—
638C2×C22⋊C4—1222no—
639C2×C22⋊C4—1222no—
640C2×C22⋊C4—2441no—
641C2×C22⋊C4—2441no—
642C2×C22⋊C4—2441no—
643C2×C22⋊C4—2441no—
644C2×C22⋊C4Dic12214yes—
645C2×C22⋊C4C4×D6114yes—
646C2×C22⋊C4C22⋊D6114yes—
647C2×C42—22no—
648C2×C42—22no—
649C2×C42—41no—
650C2×C42—1222no—
651C2×C42—1222no—
652C2×C42—2441no—
653#95—22no—
654#95—22no—
655#95—614no—
656#95—614no—
657#95—614no—
658#95—614no—
659#95—1222no—
660#95—1222no—
661#95—1222no—
662#95—1222no—
663#95—1222no—
664#95—1222no—
665#95—2441no—
666#95—2441no—
667#95—2441no—
668#95—2441no—
669C24—21no—
670C24—21no—
671C24—21no—
672C24—21no—
673C24—21no—
674C24—21no—
675C24—21no—
676C24—21no—
677C24—21no—
678C24—21no—
679C24—21no—
680C24—21no—
681C24C2×Dic12212yes—
682C24C2×C4×D6112yes—
683C24C2×C22⋊D6112yes—
684C24C23×D6111yescharacteristic
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—612no—
720C22×C4—612no—
721C22×C4—612no—
722C22×C4—612no—
723C22×C4—612no—
724C22×C4—612no—
725C22×C4—612no—
726C22×C4—612no—
727C22×C4—612no—
728C22×C4—612no—
729C22×C4—1228no—
730C22×C4—1228no—
731C22×C4—1221no—
732C22×C4—1221no—
733C22×C4—1221no—
734C22×C4—1221no—
735C22×C4—1221no—
736C22×C4—1221no—
737C22×C4—1221no—
738C22×C4—1221no—
739C22×C4—1221no—
740C22×C4—1221no—
741C22×C4—1221no—
742C22×C4—1221no—
743C22×C4—1221no—
744C22×C4—1221no—
745C22×C4—1221no—
746C22×C4—1221no—
747C22×C4—1221no—
748C22×C4—1221no—
749C22×C4—1221no—
750C22×C4—1221no—
751C22×C4—1221no—
752C22×C4—1221no—
753C22×C4—1221no—
754C22×C4—1221no—
755C22×C4—1221no—
756C22×C4—1221no—
757C22×C4—1221no—
758C22×C4—1221no—
759C22×C4—1221no—
760C22×C4—1221no—
761C22×C4—1221no—
762C22×C4—1221no—
763C22×C4—1221no—
764C22×C4—1221no—
765C22×C4—1221no—
766C22×C4—1221no—
767C22×C4—1221no—
768C22×C4—1221no—
769C22×C4—1221no—
770C22×C4—1221no—
771C22×C4—1221no—
772C22×C4—1221no—
773C22×C4—1221no—
774C22×C4—1221no—
775C22×C4—1221no—
776C22×C4—1221no—
777C22×C4—2444no—
778C22×C4—2444no—
779C22×C4—2444no—
780C22×C4—2444no—
781C22×C4—2444no—
782C22×C4C2×Dic12212yes—
783C22×C4C2×Dic12212yes—
784C22×C4C2×C4×D6112yes—
785C22×C4C2×C4×D6112yes—
786C22×C4D4×D6112yes—
787C22×C4D4×D6112yes—
788C22×C4C2×C22⋊D6112yes—
789C22×C4C2×C22⋊D6112yes—
790C4⋊C4—44no—
791C4⋊C4—1228no—
792C4⋊C4—1228no—
793C4⋊C4—2444no—
794C4⋊C4—2444no—
795C4⋊C4—2444no—
796C4⋊C4—2444no—
797C4⋊C4—2444no—
798C4⋊C4—2444no—
799C4⋊C4—2444no—
800C22⋊C4—44no—
801C22⋊C4—44no—
802C22⋊C4—2444no—
803C22⋊C4—2444no—
804C22⋊C4—2444no—
805C22⋊C4#11758196116yescomplemented
806C42—44no—
807C42—2444no—
808C23—22no—
809C23—22no—
810C23—22no—
811C23—22no—
812C23—22no—
813C23—22no—
814C23—22no—
815C23—22no—
816C23—22no—
817C23—22no—
818C23—22no—
819C23—22no—
820C23—22no—
821C23—22no—
822C23—22no—
823C23—22no—
824C23—22no—
825C23—22no—
826C23—41no—
827C23—41no—
828C23—41no—
829C23—41no—
830C23—41no—
831C23—41no—
832C23—41no—
833C23—41no—
834C23—41no—
835C23—41no—
836C23—41no—
837C23—41no—
838C23—41no—
839C23—41no—
840C23—41no—
841C23—41no—
842C23C2×#1175819614yes—
843C23C22×C4×D6111yescharacteristic
844C23C2×D4×D6111yescharacteristic
845C23C2×D4×D6111yescharacteristic
846C23C22×C22⋊D6111yescharacteristic
847C23C22×Dic12211yescharacteristic
848C23#41×D6111yescharacteristic
849C23#41×D6111yescharacteristic
850C23#1451982211yescharacteristic
851C23#1451982211yescharacteristic
852C23#1451982311yescharacteristic
853C23#1451982311yescharacteristic
854C23#1451982411yescharacteristic
855C23#1451982411yescharacteristic
856C23#1451982411yescharacteristic
857C23#1451982411yescharacteristic
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—22no—
870C2×C4—22no—
871C2×C4—22no—
872C2×C4—22no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—22no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—614no—
899C2×C4—614no—
900C2×C4—1222no—
901C2×C4—1222no—
902C2×C4—1222no—
903C2×C4—1222no—
904C2×C4—1222no—
905C2×C4—1222no—
906C2×C4—1222no—
907C2×C4—1222no—
908C2×C4—1222no—
909C2×C4—1222no—
910C2×C4—1222no—
911C2×C4—1222no—
912C2×C4—1222no—
913C2×C4—1222no—
914C2×C4—1222no—
915C2×C4—1222no—
916C2×C4—1222no—
917C2×C4—1222no—
918C2×C4—1222no—
919C2×C4—1222no—
920C2×C4—1222no—
921C2×C4—1222no—
922C2×C4—1222no—
923C2×C4—1222no—
924C2×C4—24416no—
925C2×C4—2441no—
926C2×C4—2441no—
927C2×C4—2441no—
928C2×C4—2441no—
929C2×C4—2441no—
930C2×C4—2441no—
931C2×C4—2441no—
932C2×C4—2441no—
933C2×C4—2441no—
934C2×C4—2441no—
935C2×C4—2441no—
936C2×C4—2441no—
937C2×C4—2441no—
938C2×C4—2441no—
939C2×C4—2441no—
940C2×C4—2441no—
941C2×C4—2441no—
942C2×C4—2441no—
943C2×C4—2441no—
944C2×C4—2441no—
945C2×C4—2441no—
946C2×C4—2441no—
947C2×C4—2441no—
948C2×C4—2441no—
949C2×C4—2441no—
950C2×C4—2441no—
951C2×C4—2441no—
952C2×C4—2441no—
953C2×C4—2441no—
954C2×C4—2441no—
955C2×C4C2×#1175819614yes—
956C2×C4C2×#1175819614yes—
957C22—24no—
958C22—24no—
959C22—24no—
960C22—42no—
961C22—42no—
962C22—42no—
963C22—42no—
964C22—42no—
965C22—42no—
966C22—42no—
967C22—42no—
968C22—42no—
969C22—42no—
970C22—42no—
971C22—42no—
972C22C22×#1175819611yescharacteristic
973C22C4×D4×D6111yescharacteristic
974C22C4×D4×D6111yescharacteristic
975C22#1684023611yescharacteristic
976C22#1684023911yescharacteristic
977C22#1684024111yescharacteristic
978C22#1684024111yescharacteristic
979C22#1684033211yescharacteristic
980C22#1684033411yescharacteristic
981C22#1684033911yescharacteristic
982C22#1684034011yescharacteristic
983C22#1684034011yescharacteristic
984C22#1684034111yescharacteristic
985C22#1684036911yescharacteristic
986C22#1684036911yescharacteristic
987C22#1684037611yescharacteristic
988C22#1684038011yescharacteristic
989C22#1684039011yescharacteristic
990C22#1684039011yescharacteristic
991C22D4×C22⋊D6111yescharacteristic
992C22D4×C22⋊D6111yescharacteristic
993C22#1684039611yescharacteristic
994C22#1684040411yescharacteristic
995C22#1684040511yescharacteristic
996C22#1684041111yescharacteristic
997C22#1684041111yescharacteristic
998C22D4×Dic12211yescharacteristic
999C22D4×Dic12211yescharacteristic
1000C22#1684043711yescharacteristic
1001C22#1684047111yescharacteristic
1002C22#1684047111yescharacteristic
1003C22#1684050011yescharacteristic
1004C22#1684050611yescharacteristic
1005C22#1684050911yescharacteristic
1006C22#1684051411yescharacteristic
1007C4—24no—
1008C4—24no—
1009C4—42no—
1010C4—42no—
1011C4—81no—
1012C4—81no—
1013C4—1224no—
1014C4—1224no—
1015C4—4881no—
1016C4—4881no—
1017C4—2442no—
1018C4—2442no—
1019C4—2442no—
1020C4—2442no—
1021C2—44no—
1022C2#2144843511yescharacteristic
1023C2#2144849411yescharacteristic
1024C2#2144849811yescharacteristic
1025C2D4×#1175819611yescharacteristic
1026C2D4×#1175819611yescharacteristic
1027C2#2144879711yescharacteristic
1028C2#2144896511yescharacteristic
1029C2#2145206511yescharacteristic
1030C2#2145207011yescharacteristic
1031C2#2145210911yescharacteristic
1032C2#2145213111yescharacteristic
1033C2#2145247411yescharacteristic
1034C2#2145247811yescharacteristic
1035C2#2145272311yescharacteristic
1036C2#2145294511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC2×C61×#388C2
socle, cosocleC24×C61C24
prime radicalC25×C61C23
hypercenterC2×#388D61
hypocenterC61#14402
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
1. C2×#16839660C2semidirect
2. C2×#16839658C2semidirect
7. #21444083C2semidirect
8. #21444082C2semidirect
9. #21444071C2semidirect
10. #21444071C2semidirect
13. #21444052C2semidirect
14. #21444050C2semidirect
33. #16839637C4semidirect
274. C22⋊C4×C61C4⋊C4semidirect
576. C61#14402semidirect
805. C22⋊C4#11758196semidirect

Maximal subgroups

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

subgroupindex
C2×#168396602
C2×#168396582
C2×#168396552
C2×#168396372
C2×#168396202
#214440832
#214440822
#214440712
#214440622
#214440522
#214440502
C2×C61×#3882
#1440261