Finite Group Databasebeta

← #29695348

Subgroups — #29695348

Order 15616.

1668 conjugacy classes of subgroups.

The subgroup lattice has 984 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840406C211yesmaximal, characteristic
2C2×#16839734C211yesmaximal, characteristic, complemented
3C22×#14519692C211yesmaximal, characteristic, complemented
4#21448670C212yesmaximal, complemented
5#21446653C212yesmaximal, complemented
6#21446274C212yesmaximal, complemented
7#21446270C212yesmaximal, complemented
8#21445805C211yesmaximal, characteristic, complemented
9#21445735C211yesmaximal, characteristic, complemented
10#99×Dic61C211yesmaximal, characteristic, complemented
11C61×#1781C211yesmaximal, characteristic, complemented
12C22×#11758224C2211yescharacteristic
13#16840406—22no—
14#16840406—22no—
15#16840406—22no—
16#16840406—22no—
17C2×#14519764C411yescharacteristic, complemented
18C2×#14519758C411yescharacteristic, complemented
19C2×#14519758C2211yescharacteristic
20C2×#14519756C411yescharacteristic, complemented
21C2×#14519749C411yescharacteristic, complemented
22C2×#14519749C2211yescharacteristic
23C2×#14519748C411yescharacteristic, complemented
24C2×#14519746C411yescharacteristic, complemented
25C2×#14519746C2211yescharacteristic
26C2×D4×Dic61C2211yescharacteristic
27C2×C4×C22⋊D61C411yescharacteristic, complemented
28C2×#14519733C2212yescomplemented
29C22×C22⋊Dic61C411yescharacteristic, complemented
30C22×C22⋊Dic61C2212yes—
31C22×C22⋊Dic61C2211yescharacteristic
32#16839734—24no—
33C2×#14519692—24no—
34C2×#14519692C2211yescharacteristic
35C2×#14519692C2212yes—
36C2×#14519692C2211yescharacteristic
37C2×#14519691C2212yescomplemented
38C2×#14519691C2212yescomplemented
39#16839656—22no—
40#16839650—22no—
41#16839634—22no—
42#16839623C2212yescomplemented
43#16839620C2212yescomplemented
44C22⋊C4×Dic61—22no—
45C22⋊C4×Dic61C2212yescomplemented
46#16839528C2212yescomplemented
47#16839528C2212yescomplemented
48C23×D4×C61C2211yescharacteristic
49C2×#99×C61C2211yescharacteristic
50C2×#99×C61C2211yescharacteristic
51C2×#99×C61C2212yes—
52C61×#379C2212yes—
53C2×#11758224—22no—
54C2×#11758224—22no—
55C2×#11758224—22no—
56C2×#11758224—22no—
57C2×#11758224—42no—
58C22×Dic122C2×C411yescharacteristic, complemented
59C22×C22⋊D61C2×C411yescharacteristic
60C22×C22⋊D61C2×C411yescharacteristic
61C22×C22⋊D61C2×C411yescharacteristic, complemented
62C22×C22⋊D61C2×C411yescharacteristic, complemented
63C22×C22⋊D61C2311yescharacteristic
64C23×Dic61—22no—
65C23×Dic61C2×C411yescharacteristic, complemented
66C23×Dic61C2×C411yescharacteristic, complemented
67C23×Dic61C2311yescharacteristic
68C23×Dic61C2311yescharacteristic
69C22×C4×D61C2×C411yescharacteristic, complemented
70#14519764—22no—
71#14519764—22no—
72#14519758—22no—
73#14519758—22no—
74#14519758—22no—
75#14519758—22no—
76#14519756—22no—
77#14519756—22no—
78#14519749—22no—
79#14519749—22no—
80#14519749—22no—
81#14519749—22no—
82#14519748—22no—
83#14519748—22no—
84#14519746—22no—
85#14519746—22no—
86#14519746—22no—
87#14519746—22no—
88D4×Dic61—22no—
89D4×Dic61—22no—
90C4×C22⋊D61—21no—
91C4×C22⋊D61—21no—
92C4×C22⋊D61—21no—
93C4×C22⋊D61—21no—
94#14519733—24no—
95#14519733—42no—
96C2×C4⋊Dic61C2×C411yescharacteristic, complemented
97C2×#11758196—22no—
98C2×#11758196—22no—
99C2×#11758196C2×C411yescharacteristic, complemented
100C2×#11758196C2×C411yescharacteristic, complemented
101C2×#11758196C2×C411yescharacteristic, complemented
102C2×C22⋊Dic61—21no—
103C2×C22⋊Dic61—21no—
104C2×C22⋊Dic61—21no—
105C2×C22⋊Dic61—21no—
106C2×C22⋊Dic61—24no—
107C2×C22⋊Dic61—22no—
108C2×C22⋊Dic61—42no—
109C2×C22⋊Dic61C2×C411yescharacteristic
110C2×C22⋊Dic61C2×C411yescharacteristic
111C2×C22⋊Dic61C2×C411yescharacteristic
112C2×C22⋊Dic61C2×C411yescharacteristic
113C2×C22⋊Dic61C2×C411yescharacteristic
114C2×C22⋊Dic61C2×C411yescharacteristic
115C2×C22⋊Dic61C2×C411yescharacteristic, complemented
116C2×C22⋊Dic61C2×C411yescharacteristic, complemented
117C2×C22⋊Dic61C2×C411yescharacteristic, complemented
118C2×C22⋊Dic61C2×C411yescharacteristic, complemented
119C2×C22⋊Dic61D412yes—
120C2×C22⋊Dic61D412yes—
121C2×C22⋊Dic61D412yes—
122C2×C22⋊Dic61D412yes—
123C2×C22⋊Dic61C2312yes—
124C2×C22⋊Dic61C2311yescharacteristic
125C2×C22⋊Dic61C2312yes—
126C2×#11758198C2×C411yescharacteristic, complemented
127C2×C4×Dic61—22no—
128C2×C4×Dic61—22no—
129C2×C4×Dic61C2×C411yescharacteristic, complemented
130#14519692—22no—
131#14519692—24no—
132#14519692D414yescomplemented
133#14519691—24no—
134#14519691—42no—
135#14519684—22no—
136#14519684—22no—
137#14519684—22no—
138#14519684—22no—
139C25×C61C2×C411yescharacteristic
140C25×C61C2311yescharacteristic
141C22×D4×C61—22no—
142C22×D4×C61—22no—
143C22×D4×C61—22no—
144C22×D4×C61—22no—
145C22×D4×C61—42no—
146C22×D4×C61C2×C411yescharacteristic
147C22×D4×C61C2×C411yescharacteristic
148C22×D4×C61C2311yescharacteristic
149C22×D4×C61C2311yescharacteristic
150C23×C4×C61C2×C411yescharacteristic
151C2×C22⋊C4×C61—22no—
152C2×C22⋊C4×C61—22no—
153C2×C22⋊C4×C61C2312yes—
154C2×C22⋊C4×C61C2312yes—
155#99×C61—22no—
156#99×C61—22no—
157#99×C61—42no—
158C24×C61—21no—
159C24×C61—21no—
160C24×C61—22no—
161C24×C61—21no—
162C24×C61—21no—
163C24×C61—22no—
164C24×C61—41no—
165C24×C61—42no—
166C24×C61—42no—
167C24×C61—81no—
168C24×C61—81no—
169C24×C61C22×C411yescharacteristic
170C24×C61C22×C411yescharacteristic
171C24×C61C22×C411yescharacteristic
172C24×C61C22×C411yescharacteristic
173C24×C61C2×D412yes—
174C24×C61C2×D412yes—
175C24×C61C2411yescharacteristic
176C23×D61C22×C411yescharacteristic
177C2×D4×C61—22no—
178C2×D4×C61—22no—
179C2×D4×C61—22no—
180C2×D4×C61—22no—
181C2×D4×C61—22no—
182C2×D4×C61—21no—
183C2×D4×C61—22no—
184C2×D4×C61—21no—
185C2×D4×C61—22no—
186C2×D4×C61—22no—
187C2×D4×C61—41no—
188C2×D4×C61—41no—
189C2×D4×C61—44no—
190C2×D4×C61—44no—
191C2×D4×C61—44no—
192C2×D4×C61—44no—
193C2×D4×C61C2×D412yes—
194C2×D4×C61#4112yes—
195C22×C4×C61—21no—
196C22×C4×C61—21no—
197C22×C4×C61—22no—
198C22×C4×C61—22no—
199C22×C4×C61—22no—
200C22×C4×C61—41no—
201C22×C4×C61C22×C411yescharacteristic
202C22×C4×C61C22×C411yescharacteristic
203C2×C22⋊D61—21no—
204C2×C22⋊D61—21no—
205C2×C22⋊D61—22no—
206C2×C22⋊D61—21no—
207C2×C22⋊D61—22no—
208C2×C22⋊D61—21no—
209C2×C22⋊D61—22no—
210C2×C22⋊D61—22no—
211C2×C22⋊D61—22no—
212C2×C22⋊D61—22no—
213C2×C22⋊D61—41no—
214C2×C22⋊D61—42no—
215C2×C22⋊D61—81no—
216C2×C22⋊D61—81no—
217C22×Dic61—21no—
218C22×Dic61—21no—
219C22×Dic61—22no—
220C22×Dic61—22no—
221C22×Dic61—22no—
222C22×Dic61—21no—
223C22×Dic61—21no—
224C22×Dic61—21no—
225C22×Dic61—21no—
226C22×Dic61—22no—
227C22×Dic61—41no—
228C22×Dic61—44no—
229C22×Dic61—44no—
230C22×Dic61—81no—
231C22×Dic61—82no—
232C22×Dic61—81no—
233C22×Dic61C22×C411yescharacteristic
234C22×Dic61C22×C411yescharacteristic
235C22×Dic61C22×C411yescharacteristic
236C22×Dic61C22×C411yescharacteristic
237C22×Dic61C22×C411yescharacteristic
238C22×Dic61C22×C411yescharacteristic
239C22×Dic61C22×C411yescharacteristic
240C22×Dic61C2×D412yes—
241C22×Dic61C2×D412yes—
242C22×Dic61C2×D412yes—
243C22×Dic61C2×D412yes—
244#11758224—44no—
245#11758224—44no—
246#11758224—44no—
247#11758224—44no—
248C2×C4×D61—22no—
249C2×C4×D61—21no—
250C2×C4×D61—21no—
251C2×C4×D61—41no—
252C2×Dic122—22no—
253C2×Dic122—22no—
254C2×Dic122—41no—
255C22⋊C4×C61—22no—
256C22⋊C4×C61—22no—
257C22⋊C4×C61—22no—
258C22⋊C4×C61—22no—
259C22⋊C4×C61—44no—
260C22⋊C4×C61—82no—
261C22⋊Dic61—21no—
262C22⋊Dic61—21no—
263C22⋊Dic61—22no—
264C22⋊Dic61—22no—
265C22⋊Dic61—22no—
266C22⋊Dic61—21no—
267C22⋊Dic61—21no—
268C22⋊Dic61—21no—
269C22⋊Dic61—21no—
270C22⋊Dic61—22no—
271C22⋊Dic61—22no—
272C22⋊Dic61—22no—
273C22⋊Dic61—22no—
274C22⋊Dic61—44no—
275C22⋊Dic61C22⋊C411yescharacteristic
276C22⋊Dic61C22⋊C411yescharacteristic
277C22⋊Dic61C22⋊C411yescharacteristic
278C22⋊Dic61C22⋊C411yescharacteristic
279C22⋊Dic61C22⋊C412yes—
280C22⋊Dic61C22⋊C412yes—
281C22⋊Dic61C22⋊C412yes—
282C22⋊Dic61C22⋊C412yes—
283C22⋊Dic61C22⋊C412yes—
284C22⋊Dic61C22⋊C412yes—
285C22⋊Dic61C2×D414yes—
286#11758198—21no—
287#11758198—21no—
288C4⋊Dic61—22no—
289#11758196—21no—
290#11758196—21no—
291#11758196—22no—
292#11758196—22no—
293#11758196—44no—
294#11758196—82no—
295C4×Dic61—21no—
296C4×Dic61—21no—
297C4×Dic61—44no—
298C4×Dic61—82no—
299C23×C61—21no—
300C23×C61—21no—
301C23×C61—21no—
302C23×C61—21no—
303C23×C61—22no—
304C23×C61—22no—
305C23×C61—24no—
306C23×C61—22no—
307C23×C61—21no—
308C23×C61—21no—
309C23×C61—22no—
310C23×C61—22no—
311C23×C61—21no—
312C23×C61—21no—
313C23×C61—21no—
314C23×C61—42no—
315C23×C61—41no—
316C23×C61—41no—
317C23×C61—41no—
318C23×C61—42no—
319C23×C61—41no—
320C23×C61—41no—
321C23×C61—42no—
322C23×C61—42no—
323C23×C61—42no—
324C23×C61—41no—
325C23×C61—41no—
326C23×C61—42no—
327C23×C61—41no—
328C23×C61—41no—
329C23×C61—42no—
330C23×C61—81no—
331C23×C61—81no—
332C23×C61—82no—
333C23×C61—82no—
334C23×C61—84no—
335C23×C61—84no—
336C23×C61—84no—
337C23×C61C2×C22⋊C411yescharacteristic
338C23×C61C2×C22⋊C412yes—
339C23×C61C2×C22⋊C411yescharacteristic
340C23×C61C4×D412yes—
341C23×C61C23×C411yescharacteristic
342C23×C61C22×D412yes—
343C23×C61C22×D411yescharacteristic
344C23×C61C2×#4111yescharacteristic
345C23×C61H(5,𝔽2)12yes—
346C22×D61—21no—
347C22×D61—21no—
348C22×D61—21no—
349C22×D61—41no—
350C22×D61—41no—
351D4×C61—24no—
352D4×C61—24no—
353D4×C61—44no—
354D4×C61—44no—
355D4×C61—42no—
356D4×C61—42no—
357C2×C4×C61—21no—
358C2×C4×C61—21no—
359C2×C4×C61—21no—
360C2×C4×C61—21no—
361C2×C4×C61—21no—
362C2×C4×C61—42no—
363C2×C4×C61—42no—
364C2×C4×C61—42no—
365C2×C4×C61—42no—
366C2×C4×C61—42no—
367C2×C4×C61—42no—
368C2×C4×C61—42no—
369C2×C4×C61—42no—
370C2×C4×C61C4×D412yes—
371C22⋊D61—44no—
372C22⋊D61—42no—
373C22⋊D61—42no—
374C22⋊D61—42no—
375C22⋊D61—42no—
376C22⋊D61—82no—
377C22⋊D61—82no—
378C2×Dic61—21no—
379C2×Dic61—21no—
380C2×Dic61—21no—
381C2×Dic61—21no—
382C2×Dic61—22no—
383C2×Dic61—22no—
384C2×Dic61—22no—
385C2×Dic61—22no—
386C2×Dic61—21no—
387C2×Dic61—21no—
388C2×Dic61—21no—
389C2×Dic61—21no—
390C2×Dic61—21no—
391C2×Dic61—24no—
392C2×Dic61—42no—
393C2×Dic61—42no—
394C2×Dic61—41no—
395C2×Dic61—41no—
396C2×Dic61—42no—
397C2×Dic61—42no—
398C2×Dic61—42no—
399C2×Dic61—42no—
400C2×Dic61—41no—
401C2×Dic61—41no—
402C2×Dic61—42no—
403C2×Dic61—42no—
404C2×Dic61—42no—
405C2×Dic61—81no—
406C2×Dic61—81no—
407C2×Dic61—88no—
408C2×Dic61C2×C22⋊C411yescharacteristic
409C2×Dic61C2×C22⋊C411yescharacteristic
410C2×Dic61C2×C22⋊C412yes—
411C2×Dic61C2×C22⋊C412yes—
412C2×Dic61C2×C22⋊C411yescharacteristic
413C2×Dic61C2×C22⋊C411yescharacteristic
414C4×D61—42no—
415C4×D61—42no—
416Dic122—44no—
417#22405—611nomaximal, Sylow
418C22×C61—21no—
419C22×C61—22no—
420C22×C61—21no—
421C22×C61—22no—
422C22×C61—21no—
423C22×C61—21no—
424C22×C61—22no—
425C22×C61—21no—
426C22×C61—22no—
427C22×C61—21no—
428C22×C61—22no—
429C22×C61—22no—
430C22×C61—21no—
431C22×C61—41no—
432C22×C61—41no—
433C22×C61—42no—
434C22×C61—44no—
435C22×C61—44no—
436C22×C61—42no—
437C22×C61—42no—
438C22×C61—42no—
439C22×C61—42no—
440C22×C61—41no—
441C22×C61—41no—
442C22×C61—41no—
443C22×C61—41no—
444C22×C61—41no—
445C22×C61—82no—
446C22×C61—82no—
447C22×C61—81no—
448C22×C61—81no—
449C22×C61—84no—
450C22×C61—81no—
451C22×C61—81no—
452C22×C61—84no—
453C22×C61#41012yescomplemented
454C22×C61C22×C22⋊C411yescharacteristic
455C22×C61C2×C4×D411yescharacteristic
456C22×C61#51811yescharacteristic
457C22×C61D4212yes—
458C22×C61#54612yes—
459C2×D61—41no—
460C2×D61—41no—
461C2×D61—41no—
462C2×D61—81no—
463C2×D61—81no—
464C4×C61—22no—
465C4×C61—41no—
466C4×C61—82no—
467C4×C61—82no—
468Dic61—22no—
469Dic61—21no—
470Dic61—21no—
471Dic61—21no—
472Dic61—21no—
473Dic61—22no—
474Dic61—44no—
475Dic61—41no—
476Dic61—41no—
477Dic61—41no—
478Dic61—82no—
479C2×#546—611no—
480C2×#410—611no—
481C22×#99—611no—
482#2342—612no—
483#1964—612no—
484#1899—612no—
485#1898—612no—
486#1799—611no—
487#1782—611no—
488#1781D6111yescharacteristic, complemented
489C4×#99—611no—
490C2×C61—22no—
491C2×C61—22no—
492C2×C61—21no—
493C2×C61—21no—
494C2×C61—22no—
495C2×C61—42no—
496C2×C61—41no—
497C2×C61—42no—
498C2×C61—81no—
499C2×C61D4×C22⋊C411yescharacteristic
500C2×C61C2×#41011yescharacteristic
501C2×C61#288311yescharacteristic
502D61—81no—
503C22×#41—611no—
504C23×D4C2×D6111yescharacteristic
505#546—1222no—
506#546—1222no—
507#546—1222no—
508#546—1222no—
509C2×#124—611no—
510C2×#123—611no—
511C2×#123—611no—
512C2×C22⋊Q8—611no—
513C2×#121—611no—
514C2×#121—611no—
515C2×#121—611no—
516C2×#120—611no—
517C2×#120—611no—
518C2×C4×D4—611no—
519C2×C4×D4—611no—
520C2×#117—612no—
521C22×C22⋊C4—611no—
522C22×C22⋊C4—611no—
523C22×C22⋊C4—612no—
524#410—1224no—
525C2×#99—611no—
526C2×#99—611no—
527C2×#99—612no—
528C2×#99—612no—
529C2×#99—612no—
530C2×#99—1224no—
531C2×#99C2×D6111yescharacteristic
532C2×#99C2×D6111yescharacteristic
533C2×#99C2×D6112yes—
534#388—1222no—
535#388—1222no—
536#385—1222no—
537#381—612no—
538#380—612no—
539#379C2×D6112yes—
540C4×C22⋊C4—612no—
541C4×C22⋊C4—1222no—
542#342—612no—
543#342—612no—
544C61#2240511yescharacteristic, complemented, Sylow
545C25C4×D6111yescharacteristic
546C25C22×D6111yescharacteristic
547C2×#41—1222no—
548C2×#41—1222no—
549C2×#41—1222no—
550C2×#41—1222no—
551C2×#41—2442no—
552C22×Q8—611no—
553C22×D4—22no—
554C22×D4—22no—
555C22×D4—22no—
556C22×D4—22no—
557C22×D4—42no—
558C22×D4—611no—
559C22×D4—611no—
560C22×D4—611no—
561C22×D4—611no—
562C22×D4—611no—
563C22×D4C4×D6111yescharacteristic
564C22×D4C4×D6111yescharacteristic
565C22×D4C22×D6111yescharacteristic
566C22×D4C22×D6111yescharacteristic
567C23×C4—611no—
568C23×C4—611no—
569C23×C4—611no—
570C23×C4—611no—
571C23×C4—611no—
572C23×C4—1222no—
573C23×C4C4×D6111yescharacteristic
574#124—1222no—
575#124—1222no—
576#123—1222no—
577#123—1222no—
578#123—1222no—
579#123—1222no—
580C22⋊Q8—1222no—
581C22⋊Q8—1222no—
582#121—1222no—
583#121—1222no—
584#121—1222no—
585#121—1222no—
586#121—1222no—
587#121—1222no—
588#120—1222no—
589#120—1222no—
590#120—1222no—
591#120—1222no—
592C4×D4—1221no—
593C4×D4—1221no—
594C4×D4—1221no—
595C4×D4—1221no—
596C4×D4—1222no—
597C4×D4—1222no—
598#117—1224no—
599#117—2442no—
600C2×C4⋊C4—611no—
601C2×C4⋊C4—611no—
602C2×C4⋊C4—611no—
603C2×C4⋊C4—611no—
604C2×C4⋊C4—1222no—
605C2×C4⋊C4—1222no—
606C2×C22⋊C4—22no—
607C2×C22⋊C4—22no—
608C2×C22⋊C4—611no—
609C2×C22⋊C4—611no—
610C2×C22⋊C4—611no—
611C2×C22⋊C4—611no—
612C2×C22⋊C4—612no—
613C2×C22⋊C4—612no—
614C2×C22⋊C4—612no—
615C2×C22⋊C4—612no—
616C2×C22⋊C4—612no—
617C2×C22⋊C4—611no—
618C2×C22⋊C4—611no—
619C2×C22⋊C4—611no—
620C2×C22⋊C4—611no—
621C2×C22⋊C4—611no—
622C2×C22⋊C4—611no—
623C2×C22⋊C4—611no—
624C2×C22⋊C4—611no—
625C2×C22⋊C4—612no—
626C2×C22⋊C4—1221no—
627C2×C22⋊C4—1221no—
628C2×C22⋊C4—1221no—
629C2×C22⋊C4—1221no—
630C2×C22⋊C4—1224no—
631C2×C22⋊C4—1222no—
632C2×C22⋊C4—2442no—
633C2×C22⋊C4C22×D6112yes—
634C2×C22⋊C4C22×D6112yes—
635C2×C42—611no—
636C2×C42—1222no—
637C2×C42—1222no—
638#99—22no—
639#99—22no—
640#99—42no—
641#99—614no—
642#99—1224no—
643#99—1224no—
644#99—1222no—
645#99—2442no—
646#95—1222no—
647#95—1222no—
648#95—1222no—
649#95—1222no—
650C24—21no—
651C24—21no—
652C24—22no—
653C24—21no—
654C24—21no—
655C24—22no—
656C24—41no—
657C24—42no—
658C24—42no—
659C24—81no—
660C24—81no—
661C24—611no—
662C24C2×C4×D6111yescharacteristic
663C24C2×C4×D6111yescharacteristic
664C24C2×C4×D6111yescharacteristic
665C24C2×C4×D6111yescharacteristic
666C24D4×D6112yes—
667C24D4×D6112yes—
668C24C23×D6111yescharacteristic
669#41—2444no—
670#41—2444no—
671#41—2444no—
672#41—2444no—
673C2×Q8—1222no—
674C2×Q8—1222no—
675C2×Q8—2441no—
676C2×D4—22no—
677C2×D4—22no—
678C2×D4—21no—
679C2×D4—22no—
680C2×D4—21no—
681C2×D4—22no—
682C2×D4—22no—
683C2×D4—22no—
684C2×D4—22no—
685C2×D4—22no—
686C2×D4—41no—
687C2×D4—41no—
688C2×D4—44no—
689C2×D4—44no—
690C2×D4—44no—
691C2×D4—44no—
692C2×D4—1222no—
693C2×D4—1222no—
694C2×D4—1222no—
695C2×D4—1221no—
696C2×D4—1222no—
697C2×D4—1221no—
698C2×D4—1222no—
699C2×D4—1221no—
700C2×D4—1221no—
701C2×D4—1222no—
702C2×D4—4881no—
703C2×D4—4881no—
704C2×D4—2441no—
705C2×D4—2442no—
706C2×D4D4×D6112yes—
707C2×D4#1175822412yes—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—22no—
711C22×C4—22no—
712C22×C4—22no—
713C22×C4—41no—
714C22×C4—611no—
715C22×C4—611no—
716C22×C4—612no—
717C22×C4—612no—
718C22×C4—611no—
719C22×C4—611no—
720C22×C4—612no—
721C22×C4—612no—
722C22×C4—611no—
723C22×C4—611no—
724C22×C4—611no—
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—1222no—
734C22×C4—1222no—
735C22×C4—1222no—
736C22×C4—1222no—
737C22×C4—1222no—
738C22×C4—4882no—
739C22×C4—4881no—
740C22×C4—4881no—
741C22×C4—2441no—
742C22×C4—2441no—
743C22×C4—2444no—
744C22×C4—2444no—
745C22×C4C2×C4×D6111yescharacteristic
746C22×C4C2×C4×D6111yescharacteristic
747C4⋊C4—1221no—
748C4⋊C4—1221no—
749C4⋊C4—1222no—
750C4⋊C4—1222no—
751C4⋊C4—1222no—
752C4⋊C4—4882no—
753C4⋊C4—2444no—
754C22⋊C4—22no—
755C22⋊C4—22no—
756C22⋊C4—22no—
757C22⋊C4—22no—
758C22⋊C4—44no—
759C22⋊C4—82no—
760C22⋊C4—611no—
761C22⋊C4—611no—
762C22⋊C4—611no—
763C22⋊C4—611no—
764C22⋊C4—612no—
765C22⋊C4—612no—
766C22⋊C4—612no—
767C22⋊C4—612no—
768C22⋊C4—612no—
769C22⋊C4—612no—
770C22⋊C4—614no—
771C22⋊C4—1221no—
772C22⋊C4—1221no—
773C22⋊C4—1221no—
774C22⋊C4—1221no—
775C22⋊C4—1221no—
776C22⋊C4—1221no—
777C22⋊C4—1222no—
778C22⋊C4—1222no—
779C22⋊C4—1222no—
780C22⋊C4—1222no—
781C22⋊C4—1221no—
782C22⋊C4—1221no—
783C22⋊C4—1222no—
784C22⋊C4—1222no—
785C22⋊C4—1222no—
786C22⋊C4—2444no—
787C42—1221no—
788C42—1221no—
789C42—4882no—
790C42—2444no—
791C23—21no—
792C23—21no—
793C23—21no—
794C23—21no—
795C23—24no—
796C23—22no—
797C23—22no—
798C23—22no—
799C23—21no—
800C23—21no—
801C23—22no—
802C23—22no—
803C23—21no—
804C23—21no—
805C23—21no—
806C23—42no—
807C23—41no—
808C23—41no—
809C23—41no—
810C23—42no—
811C23—41no—
812C23—41no—
813C23—42no—
814C23—42no—
815C23—42no—
816C23—41no—
817C23—41no—
818C23—42no—
819C23—41no—
820C23—41no—
821C23—42no—
822C23—81no—
823C23—81no—
824C23—82no—
825C23—82no—
826C23—84no—
827C23—84no—
828C23—84no—
829C23—1221no—
830C23—1221no—
831C23—1221no—
832C23—2441no—
833C23—2441no—
834C23C22⋊C4×D6111yescharacteristic
835C23C22⋊C4×D6112yes—
836C23C22⋊C4×D6111yescharacteristic
837C23#1451973712yes—
838C23C22×C4×D6111yescharacteristic
839C23C2×D4×D6112yes—
840C23C2×D4×D6111yescharacteristic
841C23C2×#1175822411yescharacteristic
842C23#1451982212yes—
843Q8—2444no—
844D4—24no—
845D4—24no—
846D4—44no—
847D4—44no—
848D4—42no—
849D4—42no—
850D4—4882no—
851D4—4882no—
852D4—2444no—
853D4—2442no—
854D4—2442no—
855D4—2442no—
856D4—2442no—
857C2×C4—21no—
858C2×C4—21no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—21no—
862C2×C4—42no—
863C2×C4—42no—
864C2×C4—42no—
865C2×C4—42no—
866C2×C4—42no—
867C2×C4—42no—
868C2×C4—42no—
869C2×C4—42no—
870C2×C4—611no—
871C2×C4—611no—
872C2×C4—612no—
873C2×C4—611no—
874C2×C4—611no—
875C2×C4—612no—
876C2×C4—1221no—
877C2×C4—1221no—
878C2×C4—1221no—
879C2×C4—1221no—
880C2×C4—1222no—
881C2×C4—1222no—
882C2×C4—1222no—
883C2×C4—1222no—
884C2×C4—1221no—
885C2×C4—1221no—
886C2×C4—1221no—
887C2×C4—1221no—
888C2×C4—1221no—
889C2×C4—1224no—
890C2×C4—4881no—
891C2×C4—4881no—
892C2×C4—4888no—
893C2×C4—2442no—
894C2×C4—2442no—
895C2×C4—2442no—
896C2×C4—2442no—
897C2×C4—2441no—
898C2×C4—2441no—
899C2×C4—2442no—
900C2×C4—2442no—
901C2×C4—2442no—
902C2×C4—2442no—
903C2×C4—2442no—
904C2×C4—2442no—
905C2×C4—2442no—
906C2×C4—2441no—
907C2×C4—2441no—
908C2×C4#1451973712yes—
909C22—21no—
910C22—22no—
911C22—21no—
912C22—22no—
913C22—21no—
914C22—21no—
915C22—21no—
916C22—22no—
917C22—22no—
918C22—21no—
919C22—22no—
920C22—22no—
921C22—21no—
922C22—41no—
923C22—41no—
924C22—42no—
925C22—44no—
926C22—44no—
927C22—42no—
928C22—42no—
929C22—42no—
930C22—42no—
931C22—41no—
932C22—41no—
933C22—41no—
934C22—41no—
935C22—41no—
936C22—82no—
937C22—82no—
938C22—81no—
939C22—81no—
940C22—84no—
941C22—81no—
942C22—81no—
943C22—84no—
944C22—4881no—
945C22—4881no—
946C22—2441no—
947C22—2441no—
948C22—2441no—
949C22#1683973412yescomplemented
950C22C2×C22⋊C4×D6111yescharacteristic
951C22C2×#1451973711yescharacteristic
952C22#1684023511yescharacteristic
953C22#1684039412yes—
954C22#1684039912yes—
955C4—22no—
956C4—41no—
957C4—82no—
958C4—82no—
959C4—1221no—
960C4—1221no—
961C4—1222no—
962C4—1221no—
963C4—1221no—
964C4—1222no—
965C4—4882no—
966C4—2444no—
967C4—2441no—
968C4—2441no—
969C4—2441no—
970C2—22no—
971C2—22no—
972C2—21no—
973C2—21no—
974C2—22no—
975C2—41no—
976C2—42no—
977C2—42no—
978C2—81no—
979C2—4881no—
980C2#2144863511yescharacteristic
981C2C2×#1683973411yescharacteristic
982C2#2145427711yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC23×C61C23×C4
FrattiniC24C23×D61
FittingC61×#1781C2
socleC22×C61C22×C22⋊C4
prime radicalC2×#16840406C2
cosocleC24×C61C24
hypercenter#1781D61
hypocenterC61#22405
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C25 ◁ #1781

Complements

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

NH ≅ G/Ntype
2. C2×#16839734C2semidirect
3. C22×#14519692C2semidirect
4. #21448670C2semidirect
5. #21446653C2semidirect
6. #21446274C2semidirect
7. #21446270C2semidirect
8. #21445805C2semidirect
9. #21445735C2semidirect
10. #99×Dic61C2semidirect
11. C61×#1781C2semidirect
17. C2×#14519764C4semidirect
18. C2×#14519758C4semidirect
20. C2×#14519756C4semidirect
21. C2×#14519749C4semidirect
23. C2×#14519748C4semidirect
24. C2×#14519746C4semidirect
27. C2×C4×C22⋊D61C4semidirect
28. C2×#14519733C22semidirect
29. C22×C22⋊Dic61C4semidirect
37. C2×#14519691C22semidirect
38. C2×#14519691C22semidirect
42. #16839623C22semidirect
43. #16839620C22semidirect
45. C22⋊C4×Dic61C22semidirect
46. #16839528C22semidirect
47. #16839528C22semidirect
58. C22×Dic122C2×C4semidirect
61. C22×C22⋊D61C2×C4semidirect
62. C22×C22⋊D61C2×C4semidirect
65. C23×Dic61C2×C4semidirect
66. C23×Dic61C2×C4semidirect
69. C22×C4×D61C2×C4semidirect
96. C2×C4⋊Dic61C2×C4semidirect
99. C2×#11758196C2×C4semidirect
100. C2×#11758196C2×C4semidirect
101. C2×#11758196C2×C4semidirect
115. C2×C22⋊Dic61C2×C4semidirect
116. C2×C22⋊Dic61C2×C4semidirect
117. C2×C22⋊Dic61C2×C4semidirect
118. C2×C22⋊Dic61C2×C4semidirect
126. C2×#11758198C2×C4semidirect
129. C2×C4×Dic61C2×C4semidirect
132. #14519692D4semidirect
453. C22×C61#410semidirect
488. #1781D61semidirect
544. C61#22405semidirect
949. C22#16839734semidirect

Maximal subgroups

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

subgroupindex
C2×#168404062
C2×#168397342
C22×#145196922
#214486702
#214466532
#214462742
#214462702
#214458052
#214457352
#99×Dic612
C61×#17812
#2240561