Finite Group Databasebeta

← #29603166

Subgroups — #29603166

Order 15616.

2278 conjugacy classes of subgroups.

The subgroup lattice has 1194 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839638C211yesmaximal, characteristic
2C2×#16839638C211yesmaximal, characteristic
3C2×#16839638C211yesmaximal, characteristic
4C2×#16839619C211yesmaximal, characteristic, complemented
5C2×C4×#11758198C211yesmaximal, characteristic, complemented
6C2×#95×D61C211yesmaximal, characteristic, complemented
7#21444080C211yesmaximal, characteristic, complemented
8#21444078C211yesmaximal, characteristic, complemented
9#21444066C211yesmaximal, characteristic, complemented
10#21444064C211yesmaximal, characteristic, complemented
11#21444056C211yesmaximal, characteristic, complemented
12#21444053C211yesmaximal, characteristic, complemented
13#21444046C211yesmaximal, characteristic, complemented
14#21444040C211yesmaximal, characteristic, complemented
15C2×C61×#388C211yesmaximal, characteristic, complemented
16C23×C22⋊D61C2211yescharacteristic
17C23×C4×D61C2211yescharacteristic
18C23×C4×D61C2211yescharacteristic
19C23×C4×D61C2211yescharacteristic
20C22×C4⋊Dic61C2211yescharacteristic
21C22×C22⋊Dic61C2211yescharacteristic
22C22×C22⋊Dic61C2211yescharacteristic
23C22×C22⋊Dic61C2211yescharacteristic
24C22×#11758198C2211yescharacteristic
25C22×#11758198C2211yescharacteristic
26C22×#11758198C2211yescharacteristic
27C22×C4×Dic61C2211yescharacteristic
28#16839638—24no—
29#16839638—24no—
30#16839638C418yescomplemented
31#16839619—24no—
32C4×#11758198—24no—
33C2×#14519684C2211yescharacteristic
34C2×#14519684C2211yescharacteristic
35C2×#14519684C2211yescharacteristic
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
49#95×D61—24no—
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
58C24×D61C2311yescharacteristic
59C22×C22⋊D61—22no—
60C22×C22⋊D61—22no—
61C22×C22⋊D61—22no—
62C22×C22⋊D61—22no—
63C22×C22⋊D61—22no—
64C22×C22⋊D61—22no—
65C22×C22⋊D61C2×C414yes—
66C23×Dic61C2311yescharacteristic
67C23×Dic61C2311yescharacteristic
68C23×Dic61C2311yescharacteristic
69C23×Dic61C2311yescharacteristic
70C23×Dic61C2311yescharacteristic
71C23×Dic61C2311yescharacteristic
72C23×Dic61C2311yescharacteristic
73C22×C4×D61—22no—
74C22×C4×D61—22no—
75C22×C4×D61—22no—
76C22×C4×D61—22no—
77C22×C4×D61—22no—
78C22×C4×D61—22no—
79C22×C4×D61—22no—
80C22×C4×D61—22no—
81C22×C4×D61—22no—
82C22×C4×D61—22no—
83C22×C4×D61—22no—
84C22×C4×D61—22no—
85C22×C4×D61—22no—
86C22×C4×D61—41no—
87C22×C4×D61—41no—
88C22×C4×D61—41no—
89C22×C4×D61—41no—
90C22×C4×D61—41no—
91C22×C4×D61—41no—
92C22×C4×D61C2×C414yes—
93C22×C4×D61D414yes—
94C2×C4⋊Dic61—22no—
95C2×C4⋊Dic61—22no—
96C2×C4⋊Dic61—41no—
97C2×C22⋊Dic61—22no—
98C2×C22⋊Dic61—22no—
99C2×C22⋊Dic61—22no—
100C2×C22⋊Dic61—41no—
101C2×C22⋊Dic61—41no—
102C2×C22⋊Dic61—41no—
103C2×C22⋊Dic61—41no—
104C2×C22⋊Dic61—41no—
105C2×C22⋊Dic61C2×C414yescomplemented
106C2×#11758198—22no—
107C2×#11758198—22no—
108C2×#11758198—22no—
109C2×#11758198—22no—
110C2×#11758198—22no—
111C2×#11758198—22no—
112C2×#11758198—22no—
113C2×#11758198C2×C414yes—
114C2×#11758198D414yes—
115C2×C4×Dic61—22no—
116C2×C4×Dic61—41no—
117C2×C4×Dic61—41no—
118#14519684—22no—
119#14519684—22no—
120#14519684—22no—
121#14519684—22no—
122#14519684—22no—
123#14519684—22no—
124#14519684—22no—
125#14519684—22no—
126#14519684—22no—
127#14519684—22no—
128#14519684—22no—
129#14519684—22no—
130#14519684—41no—
131#14519684—41no—
132#14519684C2×C414yescomplemented
133#14519684C2×C414yescomplemented
134C25×C61C2311yescharacteristic
135C23×C4×C61C2311yescharacteristic
136C23×C4×C61C2311yescharacteristic
137C23×C4×C61C2311yescharacteristic
138C23×C4×C61C2311yescharacteristic
139C23×C4×C61C2311yescharacteristic
140C23×C4×C61C2311yescharacteristic
141C2×C4⋊C4×C61—22no—
142C2×C4⋊C4×C61—22no—
143C2×C4⋊C4×C61—41no—
144C2×C22⋊C4×C61—22no—
145C2×C22⋊C4×C61—22no—
146C2×C22⋊C4×C61—22no—
147C2×C22⋊C4×C61—22no—
148C2×C22⋊C4×C61—22no—
149C2×C22⋊C4×C61—22no—
150C2×C22⋊C4×C61—22no—
151C2×C22⋊C4×C61—41no—
152C2×C22⋊C4×C61C2×C414yescomplemented
153C2×C42×C61—22no—
154C2×C42×C61—22no—
155C2×C42×C61—22no—
156#95×C61—22no—
157#95×C61D414yescomplemented
158C24×C61—21no—
159C24×C61—21no—
160C24×C61—21no—
161C24×C61—21no—
162C24×C61—21no—
163C24×C61—21no—
164C24×C61—21no—
165C24×C61—21no—
166C24×C61—21no—
167C24×C61—21no—
168C24×C61—21no—
169C24×C61—21no—
170C24×C61—21no—
171C24×C61—21no—
172C24×C61C22×C412yes—
173C24×C61C2411yescharacteristic
174C23×D61—21no—
175C23×D61—21no—
176C23×D61—21no—
177C23×D61—21no—
178C23×D61—21no—
179C23×D61—21no—
180C23×D61—21no—
181C23×D61—21no—
182C23×D61C22×C412yes—
183C23×D61C2×D412yes—
184C23×D61C2×D412yes—
185C23×D61#4112yes—
186C23×D61#4112yes—
187C23×D61#4112yes—
188C23×D61#4112yes—
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×C61—21no—
201C22×C4×C61—21no—
202C22×C4×C61—21no—
203C22×C4×C61—21no—
204C22×C4×C61—21no—
205C22×C4×C61—21no—
206C22×C4×C61—21no—
207C22×C4×C61—21no—
208C22×C4×C61—21no—
209C22×C4×C61—21no—
210C22×C4×C61—21no—
211C22×C4×C61—21no—
212C22×C4×C61—21no—
213C22×C4×C61—21no—
214C22×C4×C61—21no—
215C22×C4×C61—21no—
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×C61C22×C412yes—
223C22×C4×C61C22×C412yes—
224C22×C4×C61C2×D412yes—
225C22×C4×C61C2×D412yes—
226C22×C4×C61C2×D412yes—
227C22×C4×C61C2×D412yes—
228C22×C4×C61C2×D412yes—
229C22×C4×C61#4112yes—
230C22×C4×C61#4112yes—
231C2×C22⋊D61—28no—
232C2×C22⋊D61—28no—
233C2×C22⋊D61—28no—
234C2×C22⋊D61—44no—
235C2×C22⋊D61—44no—
236C2×C22⋊D61—44no—
237C2×C22⋊D61—44no—
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—21no—
261C22×Dic61—21no—
262C22×Dic61—21no—
263C22×Dic61—21no—
264C22×Dic61—21no—
265C22×Dic61—21no—
266C22×Dic61—21no—
267C22×Dic61—21no—
268C22×Dic61—21no—
269C22×Dic61—21no—
270C22×Dic61—21no—
271C22×Dic61—21no—
272C22×Dic61—21no—
273C22×Dic61—21no—
274C22×Dic61—21no—
275C22×Dic61—21no—
276C22×Dic61—21no—
277C22×Dic61—21no—
278C22×Dic61—21no—
279C22×Dic61—21no—
280C22×Dic61—21no—
281C22×Dic61C22×C412yes—
282C22×Dic61C22×C412yes—
283C22×Dic61C22×C412yes—
284C22×Dic61C2×D412yes—
285C22×Dic61C2×D412yes—
286C22×Dic61#4112yes—
287C2×C4×D61—28no—
288C2×C4×D61—28no—
289C2×C4×D61—28no—
290C2×C4×D61—28no—
291C2×C4×D61—28no—
292C2×C4×D61—44no—
293C2×C4×D61—44no—
294C2×C4×D61—44no—
295C2×C4×D61—44no—
296C2×C4×D61—44no—
297C2×C4×D61—44no—
298C2×C4×D61—44no—
299C2×C4×D61—44no—
300C2×C4×D61—44no—
301C2×C4×D61—44no—
302C2×C4×D61—44no—
303C2×C4×D61—44no—
304C2×C4×D61—44no—
305C2×C4×D61—44no—
306C2×C4×D61—44no—
307C2×C4×D61—44no—
308C4⋊C4×C61—44no—
309C22⋊C4×C61—28no—
310C22⋊C4×C61—44no—
311C22⋊C4×C61—44no—
312C42×C61—44no—
313C22⋊Dic61—44no—
314C22⋊Dic61—44no—
315C22⋊Dic61—44no—
316#11758198—28no—
317#11758198—28no—
318#11758198—44no—
319C4⋊Dic61—44no—
320C4×Dic61—44no—
321C23×C61—22no—
322C23×C61—22no—
323C23×C61—22no—
324C23×C61—22no—
325C23×C61—22no—
326C23×C61—22no—
327C23×C61—22no—
328C23×C61—41no—
329C23×C61—41no—
330C23×C61—41no—
331C23×C61—41no—
332C23×C61—41no—
333C23×C61—41no—
334C23×C61—41no—
335C23×C61—41no—
336C23×C61—41no—
337C23×C61—41no—
338C23×C61—41no—
339C23×C61—41no—
340C23×C61—41no—
341C23×C61—41no—
342C23×C61—41no—
343C23×C61—41no—
344C23×C61—41no—
345C23×C61—41no—
346C23×C61—41no—
347C23×C61—41no—
348C23×C61—41no—
349C23×C61—41no—
350C23×C61—41no—
351C23×C61—41no—
352C23×C61—41no—
353C23×C61—41no—
354C23×C61—41no—
355C23×C61—41no—
356C23×C61C23×C411yescharacteristic
357C23×C61C22×D411yescharacteristic
358C23×C61C22×D411yescharacteristic
359C23×C61C22×D411yescharacteristic
360C23×C61C2×#4111yescharacteristic
361C23×C61C2×#4111yescharacteristic
362C23×C61C2×#4111yescharacteristic
363C23×C61C2×#4111yescharacteristic
364C23×C61C2×#4111yescharacteristic
365C23×C61C2×#4111yescharacteristic
366C23×C61C2×#4111yescharacteristic
367C23×C61H(5,𝔽2)11yescharacteristic
368C23×C61H(5,𝔽2)11yescharacteristic
369C23×C61H(5,𝔽2)11yescharacteristic
370C23×C612−1+411yescharacteristic
371C22×D61—22no—
372C22×D61—22no—
373C22×D61—22no—
374C22×D61—22no—
375C22×D61—22no—
376C22×D61—22no—
377C22×D61—22no—
378C22×D61—22no—
379C22×D61—22no—
380C22×D61—22no—
381C22×D61—22no—
382C22×D61—22no—
383C22×D61—22no—
384C22×D61—22no—
385C22×D61—22no—
386C22×D61—22no—
387C22×D61—22no—
388C22×D61—22no—
389C22×D61—22no—
390C22×D61—22no—
391C22×D61—22no—
392C22×D61—22no—
393C22×D61—22no—
394C22×D61—22no—
395C22×D61—22no—
396C22×D61—22no—
397C22×D61—22no—
398C22×D61—22no—
399C22×D61#11714yes—
400C22×D61C4×D414yes—
401C22×D61C4×D414yes—
402C22×D61#12114yes—
403C22×D61#12314yes—
404C22×D61#12414yes—
405C22×D61#12614yes—
406C2×C4×C61—22no—
407C2×C4×C61—22no—
408C2×C4×C61—22no—
409C2×C4×C61—22no—
410C2×C4×C61—22no—
411C2×C4×C61—22no—
412C2×C4×C61—22no—
413C2×C4×C61—22no—
414C2×C4×C61—22no—
415C2×C4×C61—22no—
416C2×C4×C61—22no—
417C2×C4×C61—22no—
418C2×C4×C61—22no—
419C2×C4×C61—22no—
420C2×C4×C61—22no—
421C2×C4×C61—22no—
422C2×C4×C61—22no—
423C2×C4×C61—22no—
424C2×C4×C61—22no—
425C2×C4×C61—22no—
426C2×C4×C61—22no—
427C2×C4×C61—41no—
428C2×C4×C61—41no—
429C2×C4×C61—41no—
430C2×C4×C61—41no—
431C2×C4×C61—41no—
432C2×C4×C61—41no—
433C2×C4×C61—41no—
434C2×C4×C61—41no—
435C2×C4×C61—41no—
436C2×C4×C61—41no—
437C2×C4×C61—41no—
438C2×C4×C61—41no—
439C2×C4×C61—41no—
440C2×C4×C61—41no—
441C2×C4×C61—41no—
442C2×C4×C61—41no—
443C2×C4×C61—41no—
444C2×C4×C61—41no—
445C2×C4×C61—41no—
446C2×C4×C61C4×D414yes—
447C2×C4×C61#12114yes—
448C22⋊D61—416no—
449C2×Dic61—22no—
450C2×Dic61—22no—
451C2×Dic61—22no—
452C2×Dic61—22no—
453C2×Dic61—22no—
454C2×Dic61—22no—
455C2×Dic61—22no—
456C2×Dic61—22no—
457C2×Dic61—22no—
458C2×Dic61—22no—
459C2×Dic61—22no—
460C2×Dic61—22no—
461C2×Dic61—22no—
462C2×Dic61—22no—
463C2×Dic61—22no—
464C2×Dic61—22no—
465C2×Dic61—22no—
466C2×Dic61—22no—
467C2×Dic61—41no—
468C2×Dic61—41no—
469C2×Dic61—41no—
470C2×Dic61—41no—
471C2×Dic61—41no—
472C2×Dic61—41no—
473C2×Dic61—41no—
474C2×Dic61—41no—
475C2×Dic61—41no—
476C2×Dic61—41no—
477C2×Dic61—41no—
478C2×Dic61—41no—
479C2×Dic61—41no—
480C2×Dic61—41no—
481C2×Dic61—41no—
482C2×Dic61—41no—
483C2×Dic61—41no—
484C2×Dic61—41no—
485C2×Dic61—41no—
486C2×Dic61—41no—
487C2×Dic61—41no—
488C2×Dic61—41no—
489C2×Dic61—41no—
490C2×Dic61—41no—
491C2×Dic61—41no—
492C2×Dic61—41no—
493C2×Dic61—41no—
494C2×Dic61—41no—
495C2×Dic61—41no—
496C2×Dic61—41no—
497C2×Dic61—41no—
498C4×D61—416no—
499C4×D61—416no—
500C4×D61—416no—
501#13999—611nomaximal, Sylow
502C22×C61—42no—
503C22×C61—42no—
504C22×C61—42no—
505C22×C61—42no—
506C22×C61—42no—
507C22×C61—42no—
508C22×C61—42no—
509C22×C61—81no—
510C22×C61—81no—
511C22×C61—81no—
512C22×C61—81no—
513C22×C61—81no—
514C22×C61—81no—
515C22×C61—81no—
516C22×C61—81no—
517C22×C61C2×#11711yescharacteristic
518C22×C61C2×C4×D411yescharacteristic
519C22×C61C2×C4×D411yescharacteristic
520C22×C61C2×C4×D411yescharacteristic
521C22×C61C4×#4111yescharacteristic
522C22×C61#51811yescharacteristic
523C22×C61#52011yescharacteristic
524C22×C61C2×#12111yescharacteristic
525C22×C61C2×#12111yescharacteristic
526C22×C61C2×#12311yescharacteristic
527C22×C61#52511yescharacteristic
528C22×C61C2×#12411yescharacteristic
529C22×C61C2×#12611yescharacteristic
530C22×C61#52911yescharacteristic
531C22×C61#53211yescharacteristic
532C22×C61#53411yescharacteristic
533C22×C61#53711yescharacteristic
534C22×C61#53811yescharacteristic
535C22×C61#53911yescharacteristic
536C22×C61D4211yescharacteristic
537C22×C61#54611yescharacteristic
538C22×C61#54611yescharacteristic
539C22×C61#54611yescharacteristic
540C22×C61#54611yescharacteristic
541C22×C61#54711yescharacteristic
542C22×C61#54811yescharacteristic
543C22×C61#55111yescharacteristic
544C22×C61#55111yescharacteristic
545C22×C61#55111yescharacteristic
546C22×C61#55111yescharacteristic
547C22×C61#55211yescharacteristic
548C22×C61#55211yescharacteristic
549C22×C61#55311yescharacteristic
550C22×C61#55311yescharacteristic
551C22×C61#55311yescharacteristic
552C2×D61—24no—
553C2×D61—24no—
554C2×D61—24no—
555C2×D61—24no—
556C2×D61—24no—
557C2×D61—24no—
558C2×D61—24no—
559C2×D61—24no—
560C2×D61—24no—
561C2×D61—24no—
562C2×D61—24no—
563C2×D61—24no—
564C2×D61—24no—
565C2×D61—24no—
566C2×D61#38818yescomplemented
567C4×C61—24no—
568C4×C61—24no—
569C4×C61—42no—
570C4×C61—42no—
571C4×C61—42no—
572C4×C61—81no—
573Dic61—42no—
574Dic61—42no—
575Dic61—42no—
576Dic61—42no—
577Dic61—42no—
578Dic61—42no—
579Dic61—81no—
580C2×#388D6111yescharacteristic, complemented
581C2×#386—611no—
582C2×#386—611no—
583C2×#386—611no—
584C2×#380—611no—
585C2×C4×C22⋊C4—611no—
586C22×#95—611no—
587#1443—611no—
588#1442—611no—
589#1440—611no—
590#1439—611no—
591#1437—611no—
592#1436—611no—
593#1434—611no—
594C22⋊#95—611no—
595C2×C61—82no—
596C2×C61C2×#38811yescharacteristic
597C2×C61C4×#12111yescharacteristic
598C2×C61#232511yescharacteristic
599C2×C61#235211yescharacteristic
600C2×C61#235311yescharacteristic
601C2×C61#235811yescharacteristic
602C2×C61#235911yescharacteristic
603C2×C61#241211yescharacteristic
604C2×C61#241611yescharacteristic
605C2×C61#247211yescharacteristic
606C2×C61#248111yescharacteristic
607C2×C61#248811yescharacteristic
608C2×C61#249811yescharacteristic
609C2×C61#251011yescharacteristic
610C2×C61#254311yescharacteristic
611D61—28no—
612C23×D4—611no—
613C24×C4—611no—
614C24×C4—611no—
615C24×C4—611no—
616C22×C4⋊C4—611no—
617C22×C4⋊C4C2×D6111yescharacteristic
618C22×C22⋊C4—611no—
619C22×C22⋊C4—611no—
620C22×C22⋊C4—611no—
621C22×C22⋊C4—611no—
622C22×C22⋊C4—611no—
623C22×C22⋊C4—611no—
624C22×C22⋊C4C2×D6111yescharacteristic
625C22×C22⋊C4C2×D6111yescharacteristic
626C22×C22⋊C4C2×D6111yescharacteristic
627C22×C42—611no—
628C22×C42C2×D6111yescharacteristic
629#388—24no—
630#386—618no—
631#386—1224no—
632#386—1224no—
633#380—1224no—
634C4×C22⋊C4—1224no—
635C2×#95—611no—
636C2×#95—611no—
637C2×#95—611no—
638C2×#95—611no—
639C2×#95—611no—
640C2×#95—611no—
641C2×#95—611no—
642C2×#95—611no—
643C2×#95—611no—
644C2×#95—611no—
645C2×#95—611no—
646C2×#95—611no—
647C2×#95—611no—
648C2×#95—611no—
649C2×#95—611no—
650C2×#95—611no—
651C2×#95—1224no—
652C2×#95C2×D6111yescharacteristic
653C2×#95C2×D6111yescharacteristic
654C61#1399911yescharacteristic, complemented, Sylow
655C25—611no—
656C25C22×D6111yescharacteristic
657C22×D4—614no—
658C22×D4—1222no—
659C22×D4—1222no—
660C22×D4—1222no—
661C22×D4—1222no—
662C22×D4—1222no—
663C22×D4—1222no—
664C23×C4—611no—
665C23×C4—611no—
666C23×C4—611no—
667C23×C4—611no—
668C23×C4—611no—
669C23×C4—611no—
670C23×C4—614no—
671C23×C4—614no—
672C23×C4—611no—
673C23×C4—1222no—
674C23×C4—1222no—
675C23×C4—1222no—
676C23×C4—1222no—
677C23×C4—1222no—
678C23×C4—1222no—
679C23×C4—1222no—
680C23×C4—1222no—
681C23×C4—1222no—
682C23×C4—1222no—
683C23×C4—1222no—
684C23×C4—1222no—
685C23×C4—1222no—
686C23×C4—2441no—
687C23×C4—2441no—
688C23×C4—2441no—
689C23×C4—2441no—
690C23×C4—2441no—
691C23×C4—2441no—
692C23×C4C22×D6111yescharacteristic
693C23×C4C22×D6111yescharacteristic
694C23×C4C22×D6111yescharacteristic
695C23×C4C22×D6111yescharacteristic
696C23×C4C22×D6111yescharacteristic
697C23×C4C22×D6111yescharacteristic
698C2×C4⋊C4—22no—
699C2×C4⋊C4—22no—
700C2×C4⋊C4—41no—
701C2×C4⋊C4—1222no—
702C2×C4⋊C4—1222no—
703C2×C4⋊C4—2441no—
704C2×C22⋊C4—22no—
705C2×C22⋊C4—22no—
706C2×C22⋊C4—22no—
707C2×C22⋊C4—22no—
708C2×C22⋊C4—22no—
709C2×C22⋊C4—22no—
710C2×C22⋊C4—22no—
711C2×C22⋊C4—41no—
712C2×C22⋊C4—614no—
713C2×C22⋊C4—614no—
714C2×C22⋊C4—614no—
715C2×C22⋊C4—1222no—
716C2×C22⋊C4—1222no—
717C2×C22⋊C4—1222no—
718C2×C22⋊C4—1222no—
719C2×C22⋊C4—1222no—
720C2×C22⋊C4—1222no—
721C2×C22⋊C4—1222no—
722C2×C22⋊C4—1222no—
723C2×C22⋊C4—1222no—
724C2×C22⋊C4—1222no—
725C2×C22⋊C4—2441no—
726C2×C22⋊C4—2441no—
727C2×C22⋊C4—2441no—
728C2×C22⋊C4—2441no—
729C2×C22⋊C4—2441no—
730C2×C22⋊C4C4×D6114yescomplemented
731C2×C42—22no—
732C2×C42—22no—
733C2×C42—22no—
734C2×C42—1222no—
735C2×C42—2441no—
736C2×C42—2441no—
737#95—22no—
738#95—614no—
739#95—614no—
740#95—1222no—
741#95—1222no—
742#95—1222no—
743#95—1222no—
744#95—1222no—
745#95—1222no—
746#95—1222no—
747#95—1222no—
748#95—1222no—
749#95—1222no—
750#95—1222no—
751#95—1222no—
752#95—2441no—
753#95—2441no—
754#95C22⋊D6114yescomplemented
755C24—21no—
756C24—21no—
757C24—21no—
758C24—21no—
759C24—21no—
760C24—21no—
761C24—21no—
762C24—21no—
763C24—21no—
764C24—21no—
765C24—21no—
766C24—21no—
767C24—21no—
768C24—21no—
769C24—612no—
770C24—612no—
771C24—612no—
772C24—612no—
773C24—612no—
774C24—612no—
775C24—612no—
776C24—1221no—
777C24—1221no—
778C24—1221no—
779C24—1221no—
780C24—1221no—
781C24—1221no—
782C24—1221no—
783C24—1221no—
784C24C2×C4×D6112yes—
785C24C23×D6111yescharacteristic
786C2×D4—1228no—
787C2×D4—1228no—
788C2×D4—1228no—
789C2×D4—2444no—
790C2×D4—2444no—
791C2×D4—2444no—
792C2×D4—2444no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—612no—
827C22×C4—612no—
828C22×C4—612no—
829C22×C4—612no—
830C22×C4—612no—
831C22×C4—612no—
832C22×C4—1228no—
833C22×C4—1228no—
834C22×C4—1228no—
835C22×C4—1221no—
836C22×C4—1221no—
837C22×C4—1221no—
838C22×C4—1221no—
839C22×C4—1221no—
840C22×C4—1221no—
841C22×C4—1221no—
842C22×C4—1221no—
843C22×C4—1221no—
844C22×C4—1221no—
845C22×C4—1221no—
846C22×C4—1221no—
847C22×C4—1221no—
848C22×C4—1221no—
849C22×C4—1221no—
850C22×C4—1221no—
851C22×C4—1221no—
852C22×C4—1221no—
853C22×C4—1221no—
854C22×C4—1221no—
855C22×C4—1221no—
856C22×C4—1221no—
857C22×C4—1221no—
858C22×C4—1221no—
859C22×C4—1221no—
860C22×C4—1221no—
861C22×C4—1221no—
862C22×C4—1221no—
863C22×C4—1221no—
864C22×C4—1221no—
865C22×C4—1221no—
866C22×C4—1221no—
867C22×C4—1221no—
868C22×C4—1221no—
869C22×C4—1221no—
870C22×C4—1221no—
871C22×C4—1228no—
872C22×C4—1228no—
873C22×C4—1221no—
874C22×C4—1221no—
875C22×C4—1221no—
876C22×C4—1221no—
877C22×C4—1221no—
878C22×C4—1221no—
879C22×C4—1221no—
880C22×C4—2444no—
881C22×C4—2444no—
882C22×C4—2444no—
883C22×C4—2444no—
884C22×C4—2444no—
885C22×C4—2444no—
886C22×C4—2444no—
887C22×C4—2444no—
888C22×C4—2444no—
889C22×C4—2444no—
890C22×C4—2444no—
891C22×C4—2444no—
892C22×C4—2444no—
893C22×C4—2444no—
894C22×C4—2444no—
895C22×C4—2444no—
896C22×C4C2×C4×D6112yes—
897C22×C4C2×C4×D6112yes—
898C22×C4#1175822212yes—
899C22×C4D4×D6112yes—
900C22×C4D4×D6112yes—
901C22×C4#1175822412yes—
902C22×C4C2×C22⋊D6112yes—
903C22×C4C2×C22⋊D6112yes—
904C22×C4C2×C22⋊D6112yes—
905C4⋊C4—44no—
906C4⋊C4—2444no—
907C22⋊C4—28no—
908C22⋊C4—44no—
909C22⋊C4—44no—
910C22⋊C4—1228no—
911C22⋊C4—1228no—
912C22⋊C4—2444no—
913C22⋊C4—2444no—
914C22⋊C4—2444no—
915C22⋊C4—2444no—
916C42—44no—
917C42—2444no—
918C23—22no—
919C23—22no—
920C23—22no—
921C23—22no—
922C23—22no—
923C23—22no—
924C23—22no—
925C23—41no—
926C23—41no—
927C23—41no—
928C23—41no—
929C23—41no—
930C23—41no—
931C23—41no—
932C23—41no—
933C23—41no—
934C23—41no—
935C23—41no—
936C23—41no—
937C23—41no—
938C23—41no—
939C23—41no—
940C23—41no—
941C23—41no—
942C23—41no—
943C23—41no—
944C23—41no—
945C23—41no—
946C23—41no—
947C23—41no—
948C23—41no—
949C23—41no—
950C23—41no—
951C23—41no—
952C23—41no—
953C23—614no—
954C23—614no—
955C23—614no—
956C23—614no—
957C23—614no—
958C23—614no—
959C23—614no—
960C23—1222no—
961C23—1222no—
962C23—1222no—
963C23—1222no—
964C23—1222no—
965C23—1222no—
966C23—1222no—
967C23—1222no—
968C23—1222no—
969C23—1222no—
970C23—1222no—
971C23—1222no—
972C23—1222no—
973C23—1222no—
974C23—1222no—
975C23—1222no—
976C23—1222no—
977C23—1222no—
978C23—1222no—
979C23—1222no—
980C23—1222no—
981C23—1222no—
982C23—1222no—
983C23—1222no—
984C23—1222no—
985C23—1222no—
986C23—1222no—
987C23—1222no—
988C23C22×C4×D6111yescharacteristic
989C23C2×D4×D6111yescharacteristic
990C23C2×D4×D6111yescharacteristic
991C23C22×C22⋊D6111yescharacteristic
992C23#41×D6111yescharacteristic
993C23#41×D6111yescharacteristic
994C23#41×D6111yescharacteristic
995C23#41×D6111yescharacteristic
996C23#41×D6111yescharacteristic
997C23C2×#1175822411yescharacteristic
998C23C2×#1175822211yescharacteristic
999C23#1451982211yescharacteristic
1000C23#1451982311yescharacteristic
1001C23#1451982311yescharacteristic
1002C23#1451982411yescharacteristic
1003D4—24416no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—22no—
1013C2×C4—22no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—22no—
1021C2×C4—22no—
1022C2×C4—22no—
1023C2×C4—22no—
1024C2×C4—22no—
1025C2×C4—41no—
1026C2×C4—41no—
1027C2×C4—41no—
1028C2×C4—41no—
1029C2×C4—41no—
1030C2×C4—41no—
1031C2×C4—41no—
1032C2×C4—41no—
1033C2×C4—41no—
1034C2×C4—41no—
1035C2×C4—41no—
1036C2×C4—41no—
1037C2×C4—41no—
1038C2×C4—41no—
1039C2×C4—41no—
1040C2×C4—41no—
1041C2×C4—41no—
1042C2×C4—41no—
1043C2×C4—41no—
1044C2×C4—1222no—
1045C2×C4—1222no—
1046C2×C4—1222no—
1047C2×C4—1222no—
1048C2×C4—1222no—
1049C2×C4—1222no—
1050C2×C4—1222no—
1051C2×C4—1222no—
1052C2×C4—1222no—
1053C2×C4—1222no—
1054C2×C4—1222no—
1055C2×C4—1222no—
1056C2×C4—1222no—
1057C2×C4—1222no—
1058C2×C4—1222no—
1059C2×C4—1222no—
1060C2×C4—1222no—
1061C2×C4—1222no—
1062C2×C4—24416no—
1063C2×C4—24416no—
1064C2×C4—24416no—
1065C2×C4—2441no—
1066C2×C4—2441no—
1067C2×C4—2441no—
1068C2×C4—2441no—
1069C2×C4—2441no—
1070C2×C4—2441no—
1071C2×C4—2441no—
1072C2×C4—2441no—
1073C2×C4—2441no—
1074C2×C4—2441no—
1075C2×C4—2441no—
1076C2×C4—2441no—
1077C2×C4—2441no—
1078C2×C4—2441no—
1079C2×C4—2441no—
1080C2×C4—2441no—
1081C2×C4—2441no—
1082C2×C4—2441no—
1083C2×C4—2441no—
1084C2×C4—2441no—
1085C2×C4—2441no—
1086C2×C4—2441no—
1087C2×C4—2441no—
1088C2×C4—2441no—
1089C2×C4—2441no—
1090C2×C4—2441no—
1091C2×C4—2441no—
1092C2×C4—2441no—
1093C2×C4—2441no—
1094C2×C4—2441no—
1095C2×C4—2441no—
1096C2×C4C4×C22⋊D6114yes—
1097C2×C4#1451974814yes—
1098C22—42no—
1099C22—42no—
1100C22—42no—
1101C22—42no—
1102C22—42no—
1103C22—42no—
1104C22—42no—
1105C22—81no—
1106C22—81no—
1107C22—81no—
1108C22—81no—
1109C22—81no—
1110C22—81no—
1111C22—81no—
1112C22—81no—
1113C22—618no—
1114C22—1224no—
1115C22—1224no—
1116C22—1224no—
1117C22—1224no—
1118C22—1224no—
1119C22—1224no—
1120C22—1224no—
1121C22—1224no—
1122C22—1224no—
1123C22—1224no—
1124C22—1224no—
1125C22—1224no—
1126C22—1224no—
1127C22—1224no—
1128C22#117×D6111yescharacteristic
1129C22C4×D4×D6111yescharacteristic
1130C22C4×D4×D6111yescharacteristic
1131C22C2×C4×C22⋊D6111yescharacteristic
1132C22C4×#1175822411yescharacteristic
1133C22#1684023411yescharacteristic
1134C22#1684024211yescharacteristic
1135C22#121×D6111yescharacteristic
1136C22C2×#1451974811yescharacteristic
1137C22#123×D6111yescharacteristic
1138C22#1684026911yescharacteristic
1139C22#124×D6111yescharacteristic
1140C22#126×D6111yescharacteristic
1141C22#1684029411yescharacteristic
1142C22#1684030911yescharacteristic
1143C22#1684032311yescharacteristic
1144C22#1684034111yescharacteristic
1145C22#1684034611yescharacteristic
1146C22#1684035311yescharacteristic
1147C22D4×C22⋊D6111yescharacteristic
1148C22#1684040011yescharacteristic
1149C22#1684040011yescharacteristic
1150C22#1684040511yescharacteristic
1151C22#1684040811yescharacteristic
1152C22#1684041211yescharacteristic
1153C22#1684041911yescharacteristic
1154C22#1684043511yescharacteristic
1155C22#1684043511yescharacteristic
1156C22#1684044111yescharacteristic
1157C22#1684044211yescharacteristic
1158C22#1684044811yescharacteristic
1159C22#1684045111yescharacteristic
1160C22#1684045611yescharacteristic
1161C22#1684045911yescharacteristic
1162C22#1684046311yescharacteristic
1163C4—24no—
1164C4—24no—
1165C4—42no—
1166C4—42no—
1167C4—42no—
1168C4—81no—
1169C4—4881no—
1170C4—2442no—
1171C4—2442no—
1172C4—2442no—
1173C4—2442no—
1174C4—2442no—
1175C4—2442no—
1176C2—82no—
1177C2—1228no—
1178C2#388×D6111yescharacteristic
1179C2C4×#1451974811yescharacteristic
1180C2#2144852311yescharacteristic
1181C2#2144874911yescharacteristic
1182C2#2144875411yescharacteristic
1183C2#2144879611yescharacteristic
1184C2#2144881011yescharacteristic
1185C2#2144921111yescharacteristic
1186C2#2144925511yescharacteristic
1187C2#2144994111yescharacteristic
1188C2#2145007611yescharacteristic
1189C2#2145014411yescharacteristic
1190C2#2145026211yescharacteristic
1191C2#2145038411yescharacteristic
1192C2#2145078411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC2×C61×#388C2
socle, cosocleC24×C61C24
prime radicalC23×C22⋊D61C22
hypercenterC2×#388D61
hypocenterC61#13999
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
4. C2×#16839619C2semidirect
5. C2×C4×#11758198C2semidirect
6. C2×#95×D61C2semidirect
7. #21444080C2semidirect
8. #21444078C2semidirect
9. #21444066C2semidirect
10. #21444064C2semidirect
11. #21444056C2semidirect
12. #21444053C2semidirect
13. #21444046C2semidirect
14. #21444040C2semidirect
15. C2×C61×#388C2semidirect
30. #16839638C4semidirect
105. C2×C22⋊Dic61C2×C4semidirect
132. #14519684C2×C4semidirect
133. #14519684C2×C4semidirect
152. C2×C22⋊C4×C61C2×C4semidirect
157. #95×C61D4semidirect
566. C2×D61#388semidirect
580. C2×#388D61semidirect
654. C61#13999semidirect
730. C2×C22⋊C4C4×D61semidirect
754. #95C22⋊D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168396382
C2×#168396192
C2×C4×#117581982
C2×#95×D612
#214440802
#214440782
#214440662
#214440642
#214440562
#214440532
#214440462
#214440402
C2×C61×#3882
#1399961