Finite Group Databasebeta

← #29607985

Subgroups — #29607985

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×#16839661C211yesmaximal, characteristic, complemented
2C2×#16839655C211yesmaximal, characteristic
3C2×#16839637C211yesmaximal, characteristic
4C2×#16839637C211yesmaximal, characteristic
5C2×#16839637C211yesmaximal, characteristic
6C2×#16839632C211yesmaximal, characteristic, complemented
7#21444084C211yesmaximal, characteristic, complemented
8#21444084C211yesmaximal, characteristic, complemented
9#21444076C211yesmaximal, characteristic, complemented
10#21444072C211yesmaximal, characteristic, complemented
11#21444064C211yesmaximal, characteristic
12#21444064C211yesmaximal, characteristic
13#21444053C211yesmaximal, characteristic, complemented
14#21444046C211yesmaximal, characteristic, complemented
15C2×C61×#388C211yesmaximal, characteristic
16C24×Dic61C2211yescharacteristic
17C22×C4⋊Dic61C2211yescharacteristic
18C22×C4⋊Dic61C2211yescharacteristic
19C22×C4⋊Dic61C2211yescharacteristic
20C22×C4⋊Dic61C2211yescharacteristic
21C22×C4⋊Dic61C2211yescharacteristic
22C22×C4⋊Dic61C2211yescharacteristic
23C22×C4⋊Dic61C2211yescharacteristic
24C22×C4⋊Dic61C2211yescharacteristic
25C22×C4⋊Dic61C2211yescharacteristic
26C22×C22⋊Dic61C2211yescharacteristic
27C22×C22⋊Dic61C2211yescharacteristic
28C22×C22⋊Dic61C2211yescharacteristic
29C22×C4×Dic61C2211yescharacteristic
30#16839661—24no—
31#16839655—24no—
32#16839637—24no—
33#16839637—24no—
34#16839637—24no—
35#16839632—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×#388C418yescomplemented
56C2×#95×C61C2211yescharacteristic
57C2×#95×C61C2211yescharacteristic
58C23×Dic61—22no—
59C23×Dic61—22no—
60C23×Dic61—22no—
61C23×Dic61—41no—
62C23×Dic61—41no—
63C23×Dic61—41no—
64C23×Dic61—41no—
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—22no—
80C2×C4⋊Dic61—22no—
81C2×C4⋊Dic61—22no—
82C2×C4⋊Dic61—22no—
83C2×C4⋊Dic61—22no—
84C2×C4⋊Dic61—22no—
85C2×C4⋊Dic61—22no—
86C2×C4⋊Dic61—22no—
87C2×C4⋊Dic61—41no—
88C2×C4⋊Dic61—41no—
89C2×C4⋊Dic61—41no—
90C2×C4⋊Dic61—41no—
91C2×C4⋊Dic61—41no—
92C2×C4⋊Dic61—41no—
93C2×C4⋊Dic61—41no—
94C2×C4⋊Dic61—41no—
95C2×C4⋊Dic61—41no—
96C2×C4⋊Dic61—41no—
97C2×C4⋊Dic61—41no—
98C2×C4⋊Dic61—41no—
99C2×C4⋊Dic61D414yes—
100C2×C22⋊Dic61—22no—
101C2×C22⋊Dic61—22no—
102C2×C22⋊Dic61—22no—
103C2×C22⋊Dic61—22no—
104C2×C22⋊Dic61—22no—
105C2×C22⋊Dic61—41no—
106C2×C22⋊Dic61—41no—
107C2×C22⋊Dic61—41no—
108C2×C22⋊Dic61—41no—
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—22no—
119#14519684—22no—
120#14519684—22no—
121#14519684—22no—
122#14519684—41no—
123#14519684—41no—
124#14519684—41no—
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×C61C2×C414yescomplemented
136C2×C22⋊C4×C61—22no—
137C2×C22⋊C4×C61—22no—
138C2×C22⋊C4×C61—22no—
139C2×C22⋊C4×C61—22no—
140C2×C22⋊C4×C61C2×C414yes—
141C2×C22⋊C4×C61C2×C414yes—
142C2×C22⋊C4×C61C2×C414yes—
143C2×C22⋊C4×C61D414yes—
144C2×C22⋊C4×C61Q814yes—
145C2×C42×C61—22no—
146C2×C42×C61—22no—
147C2×C42×C61C2×C414yescomplemented
148#95×C61C2×C414yescomplemented
149#95×C61C2×C414yescomplemented
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×C61C22×C412yes—
195C22×C4×C61C22×C412yes—
196C22×C4×C61C22×C412yes—
197C22×C4×C61C22×C412yes—
198C22×C4×C61C22×C412yes—
199C22×C4×C61C22×C412yes—
200C22×C4×C61C2×D412yes—
201C22×C4×C61C2×D412yes—
202C22×C4×C61C2×D412yes—
203C22×C4×C61C2×D412yes—
204C22×C4×C61C2×Q812yes—
205C22×C4×C61C2×Q812yes—
206C22×C4×C61#4112yes—
207C22×C4×C61#4112yes—
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—21no—
241C22×Dic61—21no—
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—21no—
257C22×Dic61—21no—
258C22×Dic61—21no—
259C22×Dic61—21no—
260C22×Dic61—44no—
261C22×Dic61—44no—
262C22×Dic61—44no—
263C22×Dic61—44no—
264C22×Dic61—44no—
265C22×Dic61—44no—
266C22×Dic61—44no—
267C22×Dic61C2×D412yes—
268C22×Dic61C2×D412yes—
269C22×Dic61C2×D412yes—
270C22×Dic61C2×D412yes—
271C4⋊C4×C61—28no—
272C22⋊C4×C61—28no—
273C22⋊C4×C61—28no—
274C22⋊C4×C61C4⋊C4116yescomplemented
275C42×C61—28no—
276C22⋊Dic61—44no—
277C22⋊Dic61—44no—
278C22⋊Dic61—44no—
279C4⋊Dic61—44no—
280C4⋊Dic61—44no—
281C4⋊Dic61—44no—
282C4⋊Dic61—44no—
283C4⋊Dic61—44no—
284C4⋊Dic61—44no—
285C4⋊Dic61—44no—
286C4⋊Dic61—44no—
287C4⋊Dic61—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—22no—
358C2×C4×C61—22no—
359C2×C4×C61—22no—
360C2×C4×C61—22no—
361C2×C4×C61—22no—
362C2×C4×C61—22no—
363C2×C4×C61—22no—
364C2×C4×C61—22no—
365C2×C4×C61—22no—
366C2×C4×C61—22no—
367C2×C4×C61—22no—
368C2×C4×C61—22no—
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×C61C2×C4⋊C414yes—
378C2×C4×C61C2×C4⋊C414yes—
379C2×C4×C61C4×D414yes—
380C2×C4×C61C4×D414yes—
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—416no—
394C2×Dic61—41no—
395C2×Dic61—41no—
396C2×Dic61—41no—
397C2×Dic61—41no—
398C2×Dic61—41no—
399C2×Dic61—41no—
400C2×Dic61—41no—
401C2×Dic61—41no—
402C2×Dic61—41no—
403C2×Dic61—41no—
404C2×Dic61—41no—
405C2×Dic61—41no—
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×Dic61—41no—
437C2×Dic61—41no—
438#14405—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#52011yescharacteristic
458C22×C61#52011yescharacteristic
459C22×C61#52011yescharacteristic
460C22×C61#52011yescharacteristic
461C22×C61#53411yescharacteristic
462C22×C61#53511yescharacteristic
463C22×C61#53511yescharacteristic
464C22×C61#53611yescharacteristic
465C22×C61#53611yescharacteristic
466C22×C61#53611yescharacteristic
467C22×C61#53911yescharacteristic
468C22×C61#53911yescharacteristic
469C22×C61#54211yescharacteristic
470C22×C61#54211yescharacteristic
471C22×C61#54411yescharacteristic
472C22×C61#54411yescharacteristic
473C22×C61D4211yescharacteristic
474C22×C61D4211yescharacteristic
475C22×C61D4211yescharacteristic
476C22×C61#54711yescharacteristic
477C22×C61#54711yescharacteristic
478C22×C61#54711yescharacteristic
479C22×C61#54811yescharacteristic
480C22×C61D4×Q811yescharacteristic
481C22×C61D4×Q811yescharacteristic
482C22×C61#55311yescharacteristic
483C22×C61#55411yescharacteristic
484C22×C61#55411yescharacteristic
485C22×C61#56011yescharacteristic
486C22×C61#56311yescharacteristic
487C22×C61#56311yescharacteristic
488C22×C61#56311yescharacteristic
489C4×C61—24no—
490C4×C61—24no—
491C4×C61—24no—
492C4×C61—24no—
493C4×C61—42no—
494C4×C61—42no—
495Dic61—42no—
496Dic61—42no—
497Dic61—42no—
498Dic61—42no—
499Dic61—81no—
500Dic61—81no—
501Dic61—81no—
502Dic61—81no—
503C2×#389—611no—
504C2×#388—611no—
505C2×#388D6111yescharacteristic
506C2×#385—611no—
507C2×#385—611no—
508C2×#385—611no—
509C2×#384—611no—
510#1444—611no—
511#1444—611no—
512#1442—611no—
513#1441—611no—
514#1439—611no—
515#1439—611no—
516#1436—611no—
517#1434—611no—
518C2×C61—44no—
519C2×C61#231711yescharacteristic
520C2×C61#232211yescharacteristic
521C2×C61#232611yescharacteristic
522C2×C61D4×C4⋊C411yescharacteristic
523C2×C61D4×C4⋊C411yescharacteristic
524C2×C61#236111yescharacteristic
525C2×C61#238311yescharacteristic
526C2×C61#266911yescharacteristic
527C2×C61#267411yescharacteristic
528C2×C61#267711yescharacteristic
529C2×C61#268011yescharacteristic
530C2×C61#271811yescharacteristic
531C2×C61#272011yescharacteristic
532C2×C61#272911yescharacteristic
533C2×C61#279011yescharacteristic
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#388—1224no—
555#388Dic6118yescomplemented
556#385—1224no—
557#385—1224no—
558#385—1224no—
559#384—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#1440511yescharacteristic, complemented, Sylow
577C25C22×D6111yescharacteristic
578C23×C4—611no—
579C23×C4—611no—
580C23×C4—611no—
581C23×C4—611no—
582C23×C4—611no—
583C23×C4—611no—
584C23×C4—611no—
585C23×C4—611no—
586C23×C4—1222no—
587C23×C4—1222no—
588C23×C4—1222no—
589C23×C4—2441no—
590C23×C4—2441no—
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—614no—
602C2×C4⋊C4—1222no—
603C2×C4⋊C4—1222no—
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—2441no—
617C2×C4⋊C4—2441no—
618C2×C4⋊C4—2441no—
619C2×C4⋊C4—2441no—
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⋊C4C2×Dic6114yescomplemented
629C2×C22⋊C4—22no—
630C2×C22⋊C4—22no—
631C2×C22⋊C4—22no—
632C2×C22⋊C4—22no—
633C2×C22⋊C4—1222no—
634C2×C22⋊C4—1222no—
635C2×C22⋊C4—1222no—
636C2×C22⋊C4—1222no—
637C2×C22⋊C4—1222no—
638C2×C22⋊C4—2441no—
639C2×C22⋊C4—2441no—
640C2×C22⋊C4—2441no—
641C2×C22⋊C4—2441no—
642C2×C22⋊C4Dic12214yes—
643C2×C22⋊C4D24414yes—
644C2×C22⋊C4C2×Dic6114yes—
645C2×C22⋊C4C2×Dic6114yes—
646C2×C22⋊C4C2×Dic6114yes—
647C2×C42—22no—
648C2×C42—22no—
649C2×C42—1222no—
650C2×C42—1222no—
651C2×C42—2441no—
652C2×C42C2×Dic6114yescomplemented
653#95—614no—
654#95—1222no—
655#95—1222no—
656#95—1222no—
657#95—1222no—
658#95—1222no—
659#95—1222no—
660#95—1222no—
661#95—1222no—
662#95—1222no—
663#95—1222no—
664#95—2441no—
665#95—2441no—
666#95—2441no—
667#95C2×Dic6114yescomplemented
668#95C2×Dic6114yescomplemented
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×D24412yes—
683C24C22×Dic6112yes—
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—612no—
714C22×C4—612no—
715C22×C4—612no—
716C22×C4—612no—
717C22×C4—1221no—
718C22×C4—1221no—
719C22×C4—1221no—
720C22×C4—1221no—
721C22×C4—1221no—
722C22×C4—1221no—
723C22×C4—1221no—
724C22×C4—1221no—
725C22×C4—1221no—
726C22×C4—1221no—
727C22×C4—1221no—
728C22×C4—1221no—
729C22×C4—1221no—
730C22×C4—1221no—
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—2444no—
770C22×C4—2444no—
771C22×C4—2444no—
772C22×C4—2444no—
773C22×C4—2444no—
774C22×C4—2444no—
775C22×C4—2444no—
776C22×C4C2×Dic12212yes—
777C22×C4C2×Dic12212yes—
778C22×C4C2×D24412yes—
779C22×C4C2×D24412yes—
780C22×C4D4×D6112yes—
781C22×C4D4×D6112yes—
782C22×C4#1175822412yes—
783C22×C4#1175822412yes—
784C22×C4C22×Dic6112yes—
785C22×C4C22×Dic6112yes—
786C22×C4C22×Dic6112yes—
787C22×C4C22×Dic6112yes—
788C22×C4C22×Dic6112yes—
789C22×C4C22×Dic6112yes—
790C4⋊C4—28no—
791C4⋊C4—2444no—
792C4⋊C4—2444no—
793C4⋊C4—2444no—
794C4⋊C4—2444no—
795C4⋊C4—2444no—
796C4⋊C4—2444no—
797C4⋊C4—2444no—
798C4⋊C4—2444no—
799C4⋊C4—2444no—
800C22⋊C4—28no—
801C22⋊C4—28no—
802C22⋊C4—2444no—
803C22⋊C4—2444no—
804C22⋊C4—2444no—
805C22⋊C4C4⋊Dic61116yescomplemented
806C42—28no—
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×C4⋊Dic6114yes—
843C23C23×Dic6111yescharacteristic
844C23C2×D4×D6111yescharacteristic
845C23C2×D4×D6111yescharacteristic
846C23C22×D24411yescharacteristic
847C23C22×Dic12211yescharacteristic
848C23C2×#1175822411yescharacteristic
849C23C2×#1175822411yescharacteristic
850C23#1451982311yescharacteristic
851C23#1451982311yescharacteristic
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—22no—
877C2×C4—22no—
878C2×C4—22no—
879C2×C4—22no—
880C2×C4—22no—
881C2×C4—22no—
882C2×C4—22no—
883C2×C4—22no—
884C2×C4—22no—
885C2×C4—22no—
886C2×C4—22no—
887C2×C4—22no—
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—1222no—
897C2×C4—1222no—
898C2×C4—1222no—
899C2×C4—1222no—
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—2441no—
909C2×C4—2441no—
910C2×C4—2441no—
911C2×C4—2441no—
912C2×C4—2441no—
913C2×C4—2441no—
914C2×C4—2441no—
915C2×C4—2441no—
916C2×C4—2441no—
917C2×C4—2441no—
918C2×C4—2441no—
919C2×C4—2441no—
920C2×C4—2441no—
921C2×C4—2441no—
922C2×C4—2441no—
923C2×C4—2441no—
924C2×C4—2441no—
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—24416no—
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×C4C2×C4⋊Dic6114yes—
954C2×C4C2×C4⋊Dic6114yes—
955C2×C4D4×Dic6114yes—
956C2×C4D4×Dic6114yes—
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×C4⋊Dic6111yescharacteristic
973C22C2×D4×Dic6111yescharacteristic
974C22C2×D4×Dic6111yescharacteristic
975C22#1684024511yescharacteristic
976C22#1684024511yescharacteristic
977C22#1684024511yescharacteristic
978C22#1684024511yescharacteristic
979C22#1684032311yescharacteristic
980C22#1684033011yescharacteristic
981C22#1684033111yescharacteristic
982C22#1684033211yescharacteristic
983C22#1684033411yescharacteristic
984C22#1684033811yescharacteristic
985C22#1684035611yescharacteristic
986C22#1684035611yescharacteristic
987C22#1684038111yescharacteristic
988C22#1684038111yescharacteristic
989C22#1684039011yescharacteristic
990C22#1684039011yescharacteristic
991C22#1684039611yescharacteristic
992C22D4×D24411yescharacteristic
993C22D4×D24411yescharacteristic
994C22#1684041211yescharacteristic
995C22#1684041611yescharacteristic
996C22#1684041611yescharacteristic
997C22#1684041811yescharacteristic
998C22D4×Dic12211yescharacteristic
999C22D4×Dic12211yescharacteristic
1000C22#1684046411yescharacteristic
1001C22#1684046911yescharacteristic
1002C22#1684046911yescharacteristic
1003C22#1684050311yescharacteristic
1004C22#1684051411yescharacteristic
1005C22#1684051411yescharacteristic
1006C22#1684051411yescharacteristic
1007C4—24no—
1008C4—24no—
1009C4—24no—
1010C4—24no—
1011C4—42no—
1012C4—42no—
1013C4—4881no—
1014C4—4881no—
1015C4—4881no—
1016C4—4881no—
1017C4—2442no—
1018C4—2442no—
1019C4—2442no—
1020C4—2442no—
1021C2—44no—
1022C2#2144844211yescharacteristic
1023C2#2144849111yescharacteristic
1024C2#2144853211yescharacteristic
1025C2D4×C4⋊Dic6111yescharacteristic
1026C2D4×C4⋊Dic6111yescharacteristic
1027C2#2144883911yescharacteristic
1028C2#2144901111yescharacteristic
1029C2#2145203411yescharacteristic
1030C2#2145209811yescharacteristic
1031C2#2145213111yescharacteristic
1032C2#2145215711yescharacteristic
1033C2#2145266711yescharacteristic
1034C2#2145269611yescharacteristic
1035C2#2145280211yescharacteristic
1036C2#2145358911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC2×C61×#388C2
socle, cosocleC24×C61C24
prime radicalC25×C61C23
hypercenterC2×#388D61
hypocenterC61#14405
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
1. C2×#16839661C2semidirect
6. C2×#16839632C2semidirect
7. #21444084C2semidirect
8. #21444084C2semidirect
9. #21444076C2semidirect
10. #21444072C2semidirect
13. #21444053C2semidirect
14. #21444046C2semidirect
55. C61×#388C4semidirect
135. C2×C4⋊C4×C61C2×C4semidirect
147. C2×C42×C61C2×C4semidirect
148. #95×C61C2×C4semidirect
149. #95×C61C2×C4semidirect
274. C22⋊C4×C61C4⋊C4semidirect
555. #388Dic61semidirect
576. C61#14405semidirect
628. C2×C4⋊C4C2×Dic61semidirect
652. C2×C42C2×Dic61semidirect
667. #95C2×Dic61semidirect
668. #95C2×Dic61semidirect
805. C22⋊C4C4⋊Dic61semidirect

Maximal subgroups

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

subgroupindex
C2×#168396612
C2×#168396552
C2×#168396372
C2×#168396322
#214440842
#214440762
#214440722
#214440642
#214440532
#214440462
C2×C61×#3882
#1440561