Finite Group Databasebeta

← #29603494

Subgroups — #29603494

Order 15616.

2358 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
1C22×#14519763C211yesmaximal, characteristic
2C22×C4×Dic122C211yesmaximal, characteristic, complemented
3C2×#16839666C211yesmaximal, characteristic, complemented
4C2×#16839662C211yesmaximal, characteristic
5C2×#16839662C211yesmaximal, characteristic
6#21444065C211yesmaximal, characteristic, complemented
7#21444064C211yesmaximal, characteristic, complemented
8#21444063C211yesmaximal, characteristic, complemented
9#21444062C211yesmaximal, characteristic, complemented
10#21444057C211yesmaximal, characteristic, complemented
11#21444056C211yesmaximal, characteristic, complemented
12#21444055C211yesmaximal, characteristic, complemented
13#21444047C211yesmaximal, characteristic, complemented
14#95×Dic61C211yesmaximal, characteristic, complemented
15C61×#1437C211yesmaximal, characteristic, complemented
16C23×Dic122C2211yescharacteristic
17C23×C22⋊D61C2211yescharacteristic
18C2×#14519763—24no—
19C2×#14519763—24no—
20C2×#14519763C418yescomplemented
21C2×C4×Dic122—24no—
22C2×C4×Dic122—24no—
23C2×C4×Dic122—24no—
24C22×C4⋊Dic61C2211yescharacteristic
25C22×#11758196C2211yescharacteristic
26C22×#11758196C2211yescharacteristic
27C22×#11758196C2211yescharacteristic
28C22×C22⋊Dic61C2211yescharacteristic
29C22×C22⋊Dic61C2211yescharacteristic
30C22×C22⋊Dic61C2211yescharacteristic
31C22×#11758198C2211yescharacteristic
32C22×#11758198C2211yescharacteristic
33C22×#11758198C2211yescharacteristic
34C22×#11758198C2211yescharacteristic
35C22×#11758198C2211yescharacteristic
36C22×#11758198C2211yescharacteristic
37C22×C4×Dic61C2211yescharacteristic
38C22×C4×Dic61C2211yescharacteristic
39C22×C4×Dic61C2211yescharacteristic
40C22×C4×Dic61C2211yescharacteristic
41#16839666—24no—
42#16839662—24no—
43#16839662—24no—
44C2×#14519684C2211yescharacteristic
45C2×#14519684C2211yescharacteristic
46C2×#14519684C2211yescharacteristic
47C2×#14519684C2211yescharacteristic
48C2×#14519684C2211yescharacteristic
49C2×#14519684C2211yescharacteristic
50C2×#14519684C2211yescharacteristic
51C2×#14519684C2211yescharacteristic
52C2×#14519684C2211yescharacteristic
53C22×C22⋊C4×C61C2211yescharacteristic
54C22×C22⋊C4×C61C2211yescharacteristic
55C22×C22⋊C4×C61C2211yescharacteristic
56C22×C42×C61C2211yescharacteristic
57C2×#95×C61C2211yescharacteristic
58C2×#95×C61C2211yescharacteristic
59C2×#95×C61C2211yescharacteristic
60C24×D61C2311yescharacteristic
61C22×Dic122—22no—
62C22×Dic122—22no—
63C22×Dic122—22no—
64C22×Dic122—22no—
65C22×Dic122C2×C414yes—
66C22×Dic122D414yes—
67C22×Dic122D414yes—
68C22×C22⋊D61—22no—
69C22×C22⋊D61—22no—
70C22×C22⋊D61—22no—
71C22×C22⋊D61—22no—
72C22×C22⋊D61—22no—
73C22×C22⋊D61—22no—
74C22×C22⋊D61C2×C414yes—
75C23×Dic61C2311yescharacteristic
76C23×Dic61C2311yescharacteristic
77C23×Dic61C2311yescharacteristic
78C23×Dic61C2311yescharacteristic
79C23×Dic61C2311yescharacteristic
80C23×Dic61C2311yescharacteristic
81C23×Dic61C2311yescharacteristic
82#14519763—232no—
83C4×Dic122—232no—
84C2×C4⋊Dic61—22no—
85C2×C4⋊Dic61—22no—
86C2×C4⋊Dic61—22no—
87C2×#11758196—22no—
88C2×#11758196—22no—
89C2×#11758196—22no—
90C2×#11758196—22no—
91C2×#11758196—22no—
92C2×#11758196—22no—
93C2×#11758196—22no—
94C2×#11758196—22no—
95C2×#11758196D414yes—
96C2×C22⋊Dic61—22no—
97C2×C22⋊Dic61—22no—
98C2×C22⋊Dic61—22no—
99C2×C22⋊Dic61—22no—
100C2×C22⋊Dic61—22no—
101C2×C22⋊Dic61—41no—
102C2×C22⋊Dic61—41no—
103C2×C22⋊Dic61—41no—
104C2×C22⋊Dic61C2×C414yes—
105C2×#11758198—22no—
106C2×#11758198—22no—
107C2×#11758198—22no—
108C2×#11758198—22no—
109C2×#11758198—22no—
110C2×#11758198—22no—
111C2×#11758198—22no—
112C2×#11758198—22no—
113C2×#11758198—22no—
114C2×#11758198—22no—
115C2×#11758198—22no—
116C2×#11758198—22no—
117C2×#11758198—41no—
118C2×#11758198—41no—
119C2×#11758198—41no—
120C2×#11758198—41no—
121C2×#11758198C2×C414yes—
122C2×#11758198C2×C414yes—
123C2×C4×Dic61—22no—
124C2×C4×Dic61—22no—
125C2×C4×Dic61—22no—
126C2×C4×Dic61—22no—
127C2×C4×Dic61—22no—
128C2×C4×Dic61—22no—
129C2×C4×Dic61—22no—
130C2×C4×Dic61—22no—
131C2×C4×Dic61—22no—
132C2×C4×Dic61—22no—
133C2×C4×Dic61C2×C414yes—
134C2×C4×Dic61D414yes—
135#14519684—22no—
136#14519684—22no—
137#14519684—22no—
138#14519684—22no—
139#14519684—22no—
140#14519684—22no—
141#14519684—41no—
142#14519684—41no—
143#14519684—41no—
144C25×C61C2311yescharacteristic
145C23×C4×C61C2311yescharacteristic
146C23×C4×C61C2311yescharacteristic
147C23×C4×C61C2311yescharacteristic
148C23×C4×C61C2311yescharacteristic
149C23×C4×C61C2311yescharacteristic
150C23×C4×C61C2311yescharacteristic
151C2×C22⋊C4×C61—22no—
152C2×C22⋊C4×C61—22no—
153C2×C22⋊C4×C61—22no—
154C2×C22⋊C4×C61—22no—
155C2×C22⋊C4×C61—22no—
156C2×C22⋊C4×C61—22no—
157C2×C22⋊C4×C61—22no—
158C2×C22⋊C4×C61—41no—
159C2×C22⋊C4×C61C2×C414yes—
160C2×C42×C61—22no—
161C2×C42×C61—22no—
162C2×C42×C61—22no—
163#95×C61—22no—
164#95×C61—22no—
165#95×C61—41no—
166C24×C61—21no—
167C24×C61—21no—
168C24×C61—21no—
169C24×C61—21no—
170C24×C61—21no—
171C24×C61—21no—
172C24×C61—21no—
173C24×C61—21no—
174C24×C61—21no—
175C24×C61—21no—
176C24×C61—21no—
177C24×C61—21no—
178C24×C61—21no—
179C24×C61—21no—
180C24×C61C22×C412yes—
181C24×C61C2411yescharacteristic
182C23×D61—21no—
183C23×D61—21no—
184C23×D61—21no—
185C23×D61—21no—
186C23×D61—21no—
187C23×D61—21no—
188C23×D61—21no—
189C23×D61—21no—
190C23×D61—21no—
191C23×D61—21no—
192C23×D61—21no—
193C23×D61—21no—
194C23×D61—21no—
195C23×D61—21no—
196C23×D61C22×C412yes—
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×C61—21no—
223C22×C4×C61—21no—
224C22×C4×C61—21no—
225C22×C4×C61—21no—
226C22×C4×C61—21no—
227C22×C4×C61—21no—
228C22×C4×C61—21no—
229C22×C4×C61—21no—
230C22×C4×C61C22×C412yes—
231C22×C4×C61C22×C412yes—
232C22×C4×C61C2×D412yes—
233C22×C4×C61C2×D412yes—
234C22×C4×C61C2×D412yes—
235C22×C4×C61C2×D412yes—
236C22×C4×C61#4112yes—
237C22×C4×C61#4112yes—
238C22×C4×C61#4112yes—
239C2×C22⋊D61—28no—
240C2×C22⋊D61—28no—
241C2×C22⋊D61—28no—
242C2×C22⋊D61—44no—
243C2×C22⋊D61—44no—
244C2×C22⋊D61—44no—
245C2×C22⋊D61—44no—
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×Dic61C2×D412yes—
287C22×Dic61C2×D412yes—
288C22×Dic61C2×D412yes—
289C22×Dic61C2×D412yes—
290C22×Dic61C2×D412yes—
291C22×Dic61C2×D412yes—
292C22×Dic61#4112yes—
293C22×Dic61#4112yes—
294C22×Dic61#4112yes—
295C2×Dic122—28no—
296C2×Dic122—28no—
297C2×Dic122—28no—
298C2×Dic122—28no—
299C2×Dic122—28no—
300C2×Dic122—28no—
301C2×Dic122C22⋊C4116yescomplemented
302C22⋊C4×C61—28no—
303C22⋊C4×C61—44no—
304C22⋊C4×C61—44no—
305C42×C61—28no—
306C22⋊Dic61—28no—
307C22⋊Dic61—44no—
308C22⋊Dic61—44no—
309#11758198—28no—
310#11758198—28no—
311#11758198—44no—
312#11758198—44no—
313#11758198—44no—
314#11758198—44no—
315C4⋊Dic61—28no—
316#11758196—28no—
317#11758196—28no—
318#11758196—44no—
319C4×Dic61—28no—
320C4×Dic61—28no—
321C4×Dic61—28no—
322C4×Dic61—44no—
323C23×C61—22no—
324C23×C61—22no—
325C23×C61—22no—
326C23×C61—22no—
327C23×C61—22no—
328C23×C61—22no—
329C23×C61—22no—
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×C61—41no—
357C23×C61—41no—
358C23×C61C23×C411yescharacteristic
359C23×C61C22×D411yescharacteristic
360C23×C61C22×D411yescharacteristic
361C23×C61C22×D411yescharacteristic
362C23×C61C22×D411yescharacteristic
363C23×C61C2×#4111yescharacteristic
364C23×C61C2×#4111yescharacteristic
365C23×C61C2×#4111yescharacteristic
366C23×C61C2×#4111yescharacteristic
367C23×C61C2×#4111yescharacteristic
368C23×C61C2×#4111yescharacteristic
369C23×C61H(5,𝔽2)11yescharacteristic
370C23×C61H(5,𝔽2)11yescharacteristic
371C23×C612−1+411yescharacteristic
372C23×C612−1+411yescharacteristic
373C22×D61—22no—
374C22×D61—22no—
375C22×D61—22no—
376C22×D61—22no—
377C22×D61—22no—
378C22×D61—22no—
379C22×D61—22no—
380C22×D61—41no—
381C22×D61—41no—
382C22×D61—41no—
383C22×D61—41no—
384C22×D61—41no—
385C22×D61—41no—
386C22×D61—41no—
387C22×D61—41no—
388C22×D61—41no—
389C22×D61—41no—
390C22×D61—41no—
391C22×D61—41no—
392C22×D61—41no—
393C22×D61—41no—
394C22×D61—41no—
395C22×D61—41no—
396C22×D61—41no—
397C22×D61—41no—
398C22×D61—41no—
399C22×D61—41no—
400C22×D61—41no—
401C22×D61—41no—
402C22×D61—41no—
403C22×D61—41no—
404C22×D61—41no—
405C22×D61—41no—
406C22×D61—41no—
407C22×D61—41no—
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—22no—
428C2×C4×C61—22no—
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×C61—41no—
447C2×C4×C61—41no—
448C2×C4×C61C2×C22⋊C414yes—
449C2×C4×C61#12414yescomplemented
450C22⋊D61—416no—
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—22no—
468C2×Dic61—22no—
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×Dic61C2×C22⋊C414yes—
493C2×Dic61C2×C22⋊C414yes—
494C2×Dic61C4×D414yes—
495C2×Dic61C4×D414yes—
496C2×Dic61#12014yes—
497C2×Dic61#12114yes—
498C2×Dic61#12114yes—
499C2×Dic61#12314yes—
500Dic122—232no—
501#14026—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×C61C22×C22⋊C411yescharacteristic
518C22×C61C2×C4×D411yescharacteristic
519C22×C61C2×C4×D411yescharacteristic
520C22×C61C4×#4111yescharacteristic
521C22×C61C4×#4111yescharacteristic
522C22×C61#52011yescharacteristic
523C22×C61#52011yescharacteristic
524C22×C61C2×#12011yescharacteristic
525C22×C61C2×#12111yescharacteristic
526C22×C61C2×#12111yescharacteristic
527C22×C61C2×#12311yescharacteristic
528C22×C61C2×#12411yescharacteristic
529C22×C61#52911yescharacteristic
530C22×C61#52911yescharacteristic
531C22×C61#53211yescharacteristic
532C22×C61#53511yescharacteristic
533C22×C61#53611yescharacteristic
534C22×C61#54211yescharacteristic
535C22×C61#54211yescharacteristic
536C22×C61#54611yescharacteristic
537C22×C61#54611yescharacteristic
538C22×C61#54811yescharacteristic
539C22×C61#54811yescharacteristic
540C22×C61#54811yescharacteristic
541C22×C61#54811yescharacteristic
542C22×C61#54811yescharacteristic
543C22×C61#54811yescharacteristic
544C22×C61#55011yescharacteristic
545C22×C61#55011yescharacteristic
546C22×C61#55011yescharacteristic
547C22×C61#55011yescharacteristic
548C22×C61#55611yescharacteristic
549C22×C61#55611yescharacteristic
550C22×C61#55911yescharacteristic
551C22×C61#55911yescharacteristic
552C2×D61—42no—
553C2×D61—42no—
554C2×D61—42no—
555C2×D61—42no—
556C2×D61—42no—
557C2×D61—42no—
558C2×D61—42no—
559C2×D61—81no—
560C2×D61—81no—
561C2×D61—81no—
562C2×D61—81no—
563C2×D61—81no—
564C2×D61—81no—
565C2×D61—81no—
566C2×D61—81no—
567C4×C61—24no—
568C4×C61—24no—
569C4×C61—42no—
570C4×C61—42no—
571C4×C61—42no—
572C4×C61—81no—
573Dic61—24no—
574Dic61—42no—
575Dic61—42no—
576Dic61—42no—
577Dic61—42no—
578Dic61—81no—
579Dic61#38618yes—
580C22×#124—611no—
581C22×C4×Q8—611no—
582C2×#391—611no—
583C2×#390—611no—
584C2×#390—611no—
585#1439—611no—
586#1439—611no—
587#1439—611no—
588#1439—611no—
589#1437—611no—
590#1437—611no—
591#1437—611no—
592#1437D6111yescharacteristic, complemented
593C4⋊#95—611no—
594C4×#95—611no—
595C2×C61—82no—
596C2×C61C2×#38611yescharacteristic
597C2×C61C4×#12411yescharacteristic
598C2×C61#232611yescharacteristic
599C2×C61#234111yescharacteristic
600C2×C61#234111yescharacteristic
601C2×C61#236711yescharacteristic
602C2×C61#236711yescharacteristic
603C2×C61#242611yescharacteristic
604C2×C61#242611yescharacteristic
605C2×C61#243111yescharacteristic
606C2×C61#243611yescharacteristic
607C2×C61#244811yescharacteristic
608C2×C61#244811yescharacteristic
609C2×C61#254511yescharacteristic
610C2×C61#254811yescharacteristic
611D61—82no—
612C23×Q8—611no—
613C23×D4—611no—
614C2×#124—618no—
615C2×#124—1224no—
616C2×#124—1224no—
617C2×C4×Q8—1224no—
618C2×C4×Q8—1224no—
619C2×C4×Q8—1224no—
620C22×C4⋊C4—611no—
621C22×C4⋊C4—611no—
622C22×C4⋊C4—611no—
623C22×C4⋊C4—611no—
624C22×C22⋊C4—611no—
625C22×C22⋊C4—611no—
626C22×C22⋊C4—611no—
627C22×C22⋊C4—611no—
628C22×C22⋊C4—611no—
629C22×C22⋊C4—611no—
630C22×C22⋊C4—611no—
631C22×C22⋊C4—611no—
632C22×C22⋊C4—611no—
633C22×C22⋊C4C2×D6111yescharacteristic
634C22×C22⋊C4C2×D6111yescharacteristic
635C22×C22⋊C4C2×D6111yescharacteristic
636C22×C42—611no—
637C22×C42—611no—
638C22×C42—611no—
639C22×C42—611no—
640C22×C42C2×D6111yescharacteristic
641#391—1224no—
642#390—1224no—
643#390—1224no—
644C2×#95—611no—
645C2×#95—611no—
646C2×#95—611no—
647C2×#95—611no—
648C2×#95—611no—
649C2×#95—611no—
650C2×#95—611no—
651C2×#95—611no—
652C2×#95—611no—
653C2×#95C2×D6111yescharacteristic
654C2×#95C2×D6111yescharacteristic
655C2×#95C2×D6111yescharacteristic
656C61#1402611yescharacteristic, complemented, Sylow
657C25—611no—
658C25C22×D6111yescharacteristic
659C22×Q8—614no—
660C22×Q8—614no—
661C22×Q8—614no—
662C22×Q8—1222no—
663C22×Q8—1222no—
664C22×Q8—1222no—
665C22×Q8—1222no—
666C22×D4—614no—
667C22×D4—1222no—
668C22×D4—1222no—
669C22×D4—1222no—
670C22×D4—1222no—
671C22×D4—1222no—
672C22×D4—1222no—
673C23×C4—611no—
674C23×C4—611no—
675C23×C4—611no—
676C23×C4—611no—
677C23×C4—611no—
678C23×C4—611no—
679C23×C4—611no—
680C23×C4C22×D6111yescharacteristic
681C23×C4C22×D6111yescharacteristic
682C23×C4C22×D6111yescharacteristic
683C23×C4C22×D6111yescharacteristic
684C23×C4C22×D6111yescharacteristic
685C23×C4C22×D6111yescharacteristic
686#124—12232no—
687C4×Q8—12232no—
688C2×C4⋊C4—614no—
689C2×C4⋊C4—1222no—
690C2×C4⋊C4—1222no—
691C2×C4⋊C4—1222no—
692C2×C4⋊C4—1222no—
693C2×C4⋊C4—1222no—
694C2×C4⋊C4—1222no—
695C2×C4⋊C4—1222no—
696C2×C4⋊C4—1222no—
697C2×C4⋊C4—1222no—
698C2×C4⋊C4—1222no—
699C2×C4⋊C4—1222no—
700C2×C22⋊C4—22no—
701C2×C22⋊C4—22no—
702C2×C22⋊C4—22no—
703C2×C22⋊C4—22no—
704C2×C22⋊C4—22no—
705C2×C22⋊C4—22no—
706C2×C22⋊C4—22no—
707C2×C22⋊C4—41no—
708C2×C22⋊C4—614no—
709C2×C22⋊C4—614no—
710C2×C22⋊C4—614no—
711C2×C22⋊C4—1222no—
712C2×C22⋊C4—1222no—
713C2×C22⋊C4—1222no—
714C2×C22⋊C4—1222no—
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—1222no—
726C2×C22⋊C4—1222no—
727C2×C22⋊C4—1222no—
728C2×C22⋊C4—2441no—
729C2×C22⋊C4—2441no—
730C2×C22⋊C4—2441no—
731C2×C22⋊C4—2441no—
732C2×C22⋊C4—2441no—
733C2×C22⋊C4—2441no—
734C2×C22⋊C4—2441no—
735C2×C22⋊C4C4×D6114yes—
736C2×C42—22no—
737C2×C42—22no—
738C2×C42—22no—
739C2×C42—614no—
740C2×C42—614no—
741C2×C42—1222no—
742C2×C42—1222no—
743C2×C42—1222no—
744C2×C42—1222no—
745C2×C42—1222no—
746C2×C42—1222no—
747C2×C42—1222no—
748C2×C42—1222no—
749C2×C42—1222no—
750C2×C42—1222no—
751#95—22no—
752#95—22no—
753#95—41no—
754#95—1222no—
755#95—1222no—
756#95—1222no—
757#95—1222no—
758#95—1222no—
759#95—1222no—
760#95—2441no—
761#95—2441no—
762#95—2441no—
763C24—21no—
764C24—21no—
765C24—21no—
766C24—21no—
767C24—21no—
768C24—21no—
769C24—21no—
770C24—21no—
771C24—21no—
772C24—21no—
773C24—21no—
774C24—21no—
775C24—21no—
776C24—21no—
777C24—612no—
778C24—1221no—
779C24—1221no—
780C24—1221no—
781C24—1221no—
782C24—1221no—
783C24—1221no—
784C24—1221no—
785C24—1221no—
786C24—1221no—
787C24—1221no—
788C24—1221no—
789C24—1221no—
790C24—1221no—
791C24—1221no—
792C24C2×C4×D6112yes—
793C24C23×D6111yescharacteristic
794C2×Q8—6116no—
795C2×Q8—1228no—
796C2×Q8—1228no—
797C2×Q8—1228no—
798C2×Q8—1228no—
799C2×Q8—1228no—
800C2×Q8—1228no—
801C2×D4—1228no—
802C2×D4—1228no—
803C2×D4—1228no—
804C2×D4—2444no—
805C2×D4—2444no—
806C2×D4—2444no—
807C2×D4—2444no—
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—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—612no—
842C22×C4—612no—
843C22×C4—612no—
844C22×C4—612no—
845C22×C4—612no—
846C22×C4—612no—
847C22×C4—612no—
848C22×C4—612no—
849C22×C4—612no—
850C22×C4—612no—
851C22×C4—612no—
852C22×C4—612no—
853C22×C4—612no—
854C22×C4—612no—
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—1221no—
872C22×C4—1221no—
873C22×C4—1221no—
874C22×C4—1221no—
875C22×C4—1221no—
876C22×C4—1221no—
877C22×C4—1221no—
878C22×C4—1221no—
879C22×C4—1221no—
880C22×C4—1221no—
881C22×C4—1221no—
882C22×C4—1221no—
883C22×C4—1221no—
884C22×C4—1221no—
885C22×C4—1221no—
886C22×C4—1221no—
887C22×C4—1221no—
888C22×C4—1221no—
889C22×C4—1221no—
890C22×C4C2×C4×D6112yes—
891C22×C4C2×C4×D6112yes—
892C22×C4#1175822212yes—
893C22×C4#1175822212yes—
894C22×C4D4×D6112yes—
895C22×C4D4×D6112yes—
896C22×C4D4×D6112yes—
897C22×C4D4×D6112yes—
898C22×C4#1175822412yes—
899C4⋊C4—1228no—
900C4⋊C4—1228no—
901C4⋊C4—1228no—
902C4⋊C4—2444no—
903C22⋊C4—28no—
904C22⋊C4—44no—
905C22⋊C4—44no—
906C22⋊C4—1228no—
907C22⋊C4—1228no—
908C22⋊C4—1228no—
909C22⋊C4—2444no—
910C22⋊C4—2444no—
911C22⋊C4—2444no—
912C22⋊C4—2444no—
913C22⋊C4—2444no—
914C22⋊C4—2444no—
915C42—28no—
916C42—1228no—
917C42—1228no—
918C42—1228no—
919C42—2444no—
920C23—22no—
921C23—22no—
922C23—22no—
923C23—22no—
924C23—22no—
925C23—22no—
926C23—22no—
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—41no—
954C23—41no—
955C23—1222no—
956C23—1222no—
957C23—1222no—
958C23—1222no—
959C23—1222no—
960C23—1222no—
961C23—1222no—
962C23—2441no—
963C23—2441no—
964C23—2441no—
965C23—2441no—
966C23—2441no—
967C23—2441no—
968C23—2441no—
969C23—2441no—
970C23—2441no—
971C23—2441no—
972C23—2441no—
973C23—2441no—
974C23—2441no—
975C23—2441no—
976C23—2441no—
977C23—2441no—
978C23—2441no—
979C23—2441no—
980C23—2441no—
981C23—2441no—
982C23—2441no—
983C23—2441no—
984C23—2441no—
985C23—2441no—
986C23—2441no—
987C23—2441no—
988C23—2441no—
989C23—2441no—
990C23C22×C4×D6111yescharacteristic
991C23C2×D4×D6111yescharacteristic
992C23C2×D4×D6111yescharacteristic
993C23C2×D4×D6111yescharacteristic
994C23C2×D4×D6111yescharacteristic
995C23#41×D6111yescharacteristic
996C23#41×D6111yescharacteristic
997C23#41×D6111yescharacteristic
998C23C2×#1175822411yescharacteristic
999C23C2×#1175822211yescharacteristic
1000C23C2×#1175822211yescharacteristic
1001C23#1451982211yescharacteristic
1002C23#1451982311yescharacteristic
1003C23#1451982411yescharacteristic
1004C23#1451982411yescharacteristic
1005Q8—12232no—
1006D4—24416no—
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—22no—
1026C2×C4—22no—
1027C2×C4—22no—
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—41no—
1045C2×C4—41no—
1046C2×C4—41no—
1047C2×C4—614no—
1048C2×C4—614no—
1049C2×C4—614no—
1050C2×C4—614no—
1051C2×C4—614no—
1052C2×C4—614no—
1053C2×C4—614no—
1054C2×C4—614no—
1055C2×C4—1222no—
1056C2×C4—1222no—
1057C2×C4—1222no—
1058C2×C4—1222no—
1059C2×C4—1222no—
1060C2×C4—1222no—
1061C2×C4—1222no—
1062C2×C4—1222no—
1063C2×C4—1222no—
1064C2×C4—1222no—
1065C2×C4—1222no—
1066C2×C4—1222no—
1067C2×C4—1222no—
1068C2×C4—1222no—
1069C2×C4—1222no—
1070C2×C4—1222no—
1071C2×C4—1222no—
1072C2×C4—1222no—
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×C4C22⋊C4×D6114yes—
1097C2×C4#1451976314yescomplemented
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—4881no—
1114C22—4881no—
1115C22—4881no—
1116C22—4881no—
1117C22—4881no—
1118C22—4881no—
1119C22—4881no—
1120C22—4881no—
1121C22—2442no—
1122C22—2442no—
1123C22—2442no—
1124C22—2442no—
1125C22—2442no—
1126C22—2442no—
1127C22—2442no—
1128C22C2×C22⋊C4×D6111yescharacteristic
1129C22C4×D4×D6111yescharacteristic
1130C22C4×D4×D6111yescharacteristic
1131C22C4×#1175822411yescharacteristic
1132C22C4×#1175822211yescharacteristic
1133C22#1684024111yescharacteristic
1134C22#1684024211yescharacteristic
1135C22#120×D6111yescharacteristic
1136C22#121×D6111yescharacteristic
1137C22#121×D6111yescharacteristic
1138C22#123×D6111yescharacteristic
1139C22C2×#1451976311yescharacteristic
1140C22#1684029011yescharacteristic
1141C22#1684029211yescharacteristic
1142C22#1684030911yescharacteristic
1143C22#1684032811yescharacteristic
1144C22#1684033411yescharacteristic
1145C22#1684037611yescharacteristic
1146C22#1684037811yescharacteristic
1147C22#1684040211yescharacteristic
1148C22#1684040411yescharacteristic
1149C22#1684041811yescharacteristic
1150C22#1684041811yescharacteristic
1151C22#1684042011yescharacteristic
1152C22#1684042111yescharacteristic
1153C22#1684042111yescharacteristic
1154C22#1684042111yescharacteristic
1155C22#1684043011yescharacteristic
1156C22#1684043211yescharacteristic
1157C22#1684043311yescharacteristic
1158C22#1684043311yescharacteristic
1159C22#1684047911yescharacteristic
1160C22#1684048011yescharacteristic
1161C22#1684049411yescharacteristic
1162C22#1684049511yescharacteristic
1163C4—24no—
1164C4—24no—
1165C4—42no—
1166C4—42no—
1167C4—42no—
1168C4—81no—
1169C4—618no—
1170C4—1224no—
1171C4—4881no—
1172C4—2442no—
1173C4—2442no—
1174C4—2442no—
1175C4—2442no—
1176C2—82no—
1177C2—4882no—
1178C2#386×D6111yescharacteristic
1179C2C4×#1451976311yescharacteristic
1180C2#2144852811yescharacteristic
1181C2#2144865811yescharacteristic
1182C2#2144865911yescharacteristic
1183C2#2144889111yescharacteristic
1184C2#2144889311yescharacteristic
1185C2#2144938211yescharacteristic
1186C2#2144938411yescharacteristic
1187C2#2144943611yescharacteristic
1188C2#2144947511yescharacteristic
1189C2#2144961411yescharacteristic
1190C2#2144961611yescharacteristic
1191C2#2145079711yescharacteristic
1192C2#2145082011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC61×#1437C2
socle, cosocleC24×C61C24
prime radicalC23×C22⋊D61C22
hypercenter#1437D61
hypocenterC61#14026
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ #1437

Complements

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

NH ≅ G/Ntype
2. C22×C4×Dic122C2semidirect
3. C2×#16839666C2semidirect
6. #21444065C2semidirect
7. #21444064C2semidirect
8. #21444063C2semidirect
9. #21444062C2semidirect
10. #21444057C2semidirect
11. #21444056C2semidirect
12. #21444055C2semidirect
13. #21444047C2semidirect
14. #95×Dic61C2semidirect
15. C61×#1437C2semidirect
20. C2×#14519763C4semidirect
301. C2×Dic122C22⋊C4semidirect
449. C2×C4×C61#124semidirect
592. #1437D61semidirect
656. C61#14026semidirect
1097. C2×C4#14519763semidirect

Maximal subgroups

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

subgroupindex
C22×#145197632
C22×C4×Dic1222
C2×#168396662
C2×#168396622
#214440652
#214440642
#214440632
#214440622
#214440572
#214440562
#214440552
#214440472
#95×Dic612
C61×#14372
#1402661