Finite Group Databasebeta

← #29695331

Subgroups — #29695331

Order 15616.

2102 conjugacy classes of subgroups.

The subgroup lattice has 1136 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×C22⋊D61C211yesmaximal, characteristic
2C22×#14519692C211yesmaximal, characteristic, complemented
3C2×#99×D61C211yesmaximal, characteristic, complemented
4#21448635C212yesmaximal, complemented
5#21446653C212yesmaximal, complemented
6#21446270C212yesmaximal, complemented
7#21446269C212yesmaximal, complemented
8#21445805C211yesmaximal, characteristic, complemented
9#21445732C211yesmaximal, characteristic, complemented
10#99×Dic61C211yesmaximal, characteristic, complemented
11C61×#1781C211yesmaximal, characteristic, complemented
12C23×C22⋊D61C411yescharacteristic, complemented
13C23×C22⋊D61C2211yescharacteristic
14C22×D4×D61C2211yescharacteristic
15D4×C22⋊D61—22no—
16D4×C22⋊D61—22no—
17D4×C22⋊D61—22no—
18D4×C22⋊D61—22no—
19C2×#14519773C411yescharacteristic, complemented
20C2×#14519751C411yescharacteristic, complemented
21C2×#14519749C411yescharacteristic, complemented
22C2×#14519749C2211yescharacteristic
23C2×#14519748C411yescharacteristic, complemented
24C2×#14519746C411yescharacteristic, complemented
25C2×#14519746C2211yescharacteristic
26C2×#14519745C411yescharacteristic, complemented
27C2×#14519745C2211yescharacteristic
28C2×D4×Dic61C2211yescharacteristic
29C2×C4×C22⋊D61C411yescharacteristic, complemented
30C2×#14519737—22no—
31C22×C22⋊Dic61C2212yescomplemented
32C2×C22⋊C4×D61C2212yescomplemented
33C2×#14519692—24no—
34C2×#14519692C2211yescharacteristic
35C2×#14519692C2211yescharacteristic
36C2×#14519692C2212yescomplemented
37C2×#14519691C2212yescomplemented
38C2×#14519691C2212yescomplemented
39#99×D61—24no—
40#16839662—22no—
41#16839639—22no—
42#16839638—22no—
43#16839620C2212yescomplemented
44#16839617C2212yescomplemented
45C22⋊C4×Dic61C2212yescomplemented
46#16839528C2212yescomplemented
47#16839528C2212yescomplemented
48C23×D4×C61C2211yescharacteristic
49C2×#99×C61C2211yescharacteristic
50C2×#99×C61C2211yescharacteristic
51C2×#99×C61C2212yescomplemented
52C61×#379C2212yescomplemented
53C24×D61C2×C411yescharacteristic, complemented
54C24×D61C2311yescharacteristic
55C22×D244C2×C411yescharacteristic, complemented
56C22×C22⋊D61—21no—
57C22×C22⋊D61—21no—
58C22×C22⋊D61—21no—
59C22×C22⋊D61—21no—
60C22×C22⋊D61—44no—
61C22×C22⋊D61—44no—
62C22×C22⋊D61C2×C411yescharacteristic
63C22×C22⋊D61C2×C411yescharacteristic
64C22×C22⋊D61C2×C411yescharacteristic
65C22×C22⋊D61C2×C411yescharacteristic
66C22×C22⋊D61C2×C411yescharacteristic, complemented
67C22×C22⋊D61C2×C411yescharacteristic, complemented
68C22×C22⋊D61C2×C411yescharacteristic, complemented
69C22×C22⋊D61C2×C411yescharacteristic, complemented
70C22×C22⋊D61C2×C411yescharacteristic, complemented
71C22×C22⋊D61C2×C411yescharacteristic, complemented
72C22×C22⋊D61D412yes—
73C22×C22⋊D61D412yes—
74C22×C22⋊D61D412yes—
75C22×C22⋊D61D412yes—
76C22×C22⋊D61C2311yescharacteristic
77C2×D4×D61—22no—
78C2×D4×D61—22no—
79C2×D4×D61—22no—
80C2×D4×D61—22no—
81C2×D4×D61—42no—
82C23×Dic61—22no—
83C23×Dic61C2×C411yescharacteristic, complemented
84C23×Dic61C2311yescharacteristic
85C22×C4×D61—22no—
86C22×C4×D61C2×C411yescharacteristic, complemented
87#14519773—22no—
88#14519773—22no—
89#14519751—22no—
90#14519751—22no—
91#14519749—22no—
92#14519749—22no—
93#14519749—22no—
94#14519749—22no—
95#14519748—22no—
96#14519748—22no—
97#14519746—22no—
98#14519746—22no—
99#14519746—22no—
100#14519746—22no—
101#14519745—22no—
102#14519745—22no—
103#14519745—22no—
104#14519745—22no—
105D4×Dic61—22no—
106D4×Dic61—22no—
107C4×C22⋊D61—21no—
108C4×C22⋊D61—21no—
109C4×C22⋊D61—21no—
110C4×C22⋊D61—21no—
111#14519737—48no—
112C2×C4⋊Dic61C2×C411yescharacteristic, complemented
113C2×#11758196—22no—
114C2×#11758196C2×C411yescharacteristic, complemented
115C2×C22⋊Dic61—24no—
116C2×C22⋊Dic61—22no—
117C2×C22⋊Dic61—42no—
118C2×C22⋊Dic61C2×C411yescharacteristic, complemented
119C2×C22⋊Dic61C2×C411yescharacteristic, complemented
120C2×C22⋊Dic61C2×C411yescharacteristic, complemented
121C2×C22⋊Dic61C2×C411yescharacteristic, complemented
122C2×C22⋊Dic61C2312yes—
123C2×C22⋊Dic61C2311yescharacteristic
124C2×C22⋊Dic61C2312yes—
125C2×#11758198—22no—
126C2×#11758198—22no—
127C2×#11758198—22no—
128C2×#11758198C2×C411yescharacteristic, complemented
129C2×#11758198C2×C411yescharacteristic, complemented
130C2×#11758198C2×C411yescharacteristic, complemented
131C22⋊C4×D61—24no—
132C22⋊C4×D61—42no—
133C2×C4×Dic61—22no—
134C2×C4×Dic61C2×C411yescharacteristic, complemented
135#14519692—22no—
136#14519692—24no—
137#14519692D414yescomplemented
138#14519691—24no—
139#14519691—42no—
140#14519684—22no—
141#14519684—22no—
142C25×C61C2×C411yescharacteristic, complemented
143C25×C61C2311yescharacteristic
144C22×D4×C61—22no—
145C22×D4×C61—22no—
146C22×D4×C61—22no—
147C22×D4×C61—22no—
148C22×D4×C61—42no—
149C22×D4×C61C2×C411yescharacteristic, complemented
150C22×D4×C61C2×C411yescharacteristic, complemented
151C22×D4×C61C2311yescharacteristic
152C22×D4×C61C2311yescharacteristic
153C23×C4×C61C2×C411yescharacteristic, complemented
154C2×C22⋊C4×C61—22no—
155C2×C22⋊C4×C61—22no—
156C2×C22⋊C4×C61C2312yes—
157C2×C22⋊C4×C61C2312yes—
158#99×C61—22no—
159#99×C61—22no—
160#99×C61—42no—
161C24×C61—21no—
162C24×C61—21no—
163C24×C61—22no—
164C24×C61—21no—
165C24×C61—21no—
166C24×C61—22no—
167C24×C61—42no—
168C24×C61—41no—
169C24×C61—42no—
170C24×C61—81no—
171C24×C61—81no—
172C24×C61C22×C411yescharacteristic
173C24×C61C22×C411yescharacteristic
174C24×C61C22×C411yescharacteristic
175C24×C61C22×C411yescharacteristic
176C24×C61C2×D412yes—
177C24×C61C2×D412yes—
178C24×C61C2411yescharacteristic
179C23×D61—21no—
180C23×D61—21no—
181C23×D61—22no—
182C23×D61—22no—
183C23×D61—21no—
184C23×D61—21no—
185C23×D61—42no—
186C23×D61—41no—
187C23×D61—42no—
188C23×D61—81no—
189C23×D61—81no—
190C23×D61C22×C411yescharacteristic
191C23×D61C22×C411yescharacteristic
192C23×D61C22×C411yescharacteristic
193C23×D61C2×D412yes—
194C23×D61C2×D412yes—
195C2×D4×C61—22no—
196C2×D4×C61—22no—
197C2×D4×C61—22no—
198C2×D4×C61—22no—
199C2×D4×C61—22no—
200C2×D4×C61—21no—
201C2×D4×C61—22no—
202C2×D4×C61—21no—
203C2×D4×C61—22no—
204C2×D4×C61—22no—
205C2×D4×C61—41no—
206C2×D4×C61—41no—
207C2×D4×C61—44no—
208C2×D4×C61—44no—
209C2×D4×C61—44no—
210C2×D4×C61—44no—
211C2×D4×C61C2×D412yes—
212C2×D4×C61#4112yes—
213C22×C4×C61—21no—
214C22×C4×C61—21no—
215C22×C4×C61—22no—
216C22×C4×C61—22no—
217C22×C4×C61—22no—
218C22×C4×C61—41no—
219C22×C4×C61C22×C411yescharacteristic
220C22×C4×C61C22×C411yescharacteristic
221C2×C22⋊D61—24no—
222C2×C22⋊D61—28no—
223C2×C22⋊D61—21no—
224C2×C22⋊D61—21no—
225C2×C22⋊D61—22no—
226C2×C22⋊D61—21no—
227C2×C22⋊D61—22no—
228C2×C22⋊D61—21no—
229C2×C22⋊D61—22no—
230C2×C22⋊D61—22no—
231C2×C22⋊D61—21no—
232C2×C22⋊D61—21no—
233C2×C22⋊D61—22no—
234C2×C22⋊D61—22no—
235C2×C22⋊D61—21no—
236C2×C22⋊D61—21no—
237C2×C22⋊D61—42no—
238C2×C22⋊D61—44no—
239C2×C22⋊D61—41no—
240C2×C22⋊D61—42no—
241C2×C22⋊D61—42no—
242C2×C22⋊D61—44no—
243C2×C22⋊D61—42no—
244C2×C22⋊D61—44no—
245C2×C22⋊D61—44no—
246C2×C22⋊D61—44no—
247C2×C22⋊D61—44no—
248C2×C22⋊D61—44no—
249C2×C22⋊D61—42no—
250C2×C22⋊D61—42no—
251C2×C22⋊D61—81no—
252C2×C22⋊D61—81no—
253C2×C22⋊D61C22⋊C411yescharacteristic
254C2×C22⋊D61C22⋊C411yescharacteristic
255C2×C22⋊D61C22⋊C411yescharacteristic
256C2×C22⋊D61C22⋊C412yes—
257C2×C22⋊D61C22⋊C412yes—
258C2×C22⋊D61C22⋊C412yes—
259C2×C22⋊D61C22⋊C412yes—
260C2×C22⋊D61C22⋊C412yes—
261C2×C22⋊D61C22⋊C412yes—
262C2×C22⋊D61C22⋊C411yescharacteristic
263C22×Dic61—22no—
264C22×Dic61—21no—
265C22×Dic61—21no—
266C22×Dic61—22no—
267C22×Dic61—42no—
268C22×Dic61—42no—
269C22×Dic61—44no—
270C22×Dic61—44no—
271C22×Dic61—82no—
272C22×Dic61C22×C411yescharacteristic
273C22×Dic61C22×C411yescharacteristic
274C22×Dic61C22×C411yescharacteristic
275C22×Dic61C22×C411yescharacteristic
276C22×Dic61C22×C411yescharacteristic
277C22×Dic61C2×D412yes—
278C22×Dic61C2×D412yes—
279D4×D61—44no—
280D4×D61—44no—
281D4×D61—44no—
282D4×D61—44no—
283C2×D244—22no—
284C2×D244—22no—
285C2×D244—41no—
286C2×C4×D61—21no—
287C2×C4×D61—21no—
288C2×C4×D61—22no—
289C2×C4×D61—41no—
290C2×C4×D61—44no—
291C2×C4×D61—44no—
292C2×C4×D61—82no—
293C22⋊C4×C61—22no—
294C22⋊C4×C61—22no—
295C22⋊C4×C61—22no—
296C22⋊C4×C61—22no—
297C22⋊C4×C61—44no—
298C22⋊C4×C61—82no—
299C22⋊Dic61—21no—
300C22⋊Dic61—21no—
301C22⋊Dic61—22no—
302C22⋊Dic61—22no—
303C22⋊Dic61—22no—
304C22⋊Dic61—22no—
305C22⋊Dic61—22no—
306C22⋊Dic61—22no—
307C22⋊Dic61—22no—
308C22⋊Dic61—44no—
309C22⋊Dic61C2×D414yescomplemented
310#11758198—21no—
311#11758198—21no—
312#11758198—22no—
313#11758198—22no—
314#11758198—44no—
315#11758198—44no—
316#11758198—82no—
317C4⋊Dic61—22no—
318#11758196—21no—
319#11758196—21no—
320#11758196—44no—
321C4×Dic61—21no—
322C4×Dic61—21no—
323C4×Dic61—44no—
324C23×C61—21no—
325C23×C61—21no—
326C23×C61—21no—
327C23×C61—21no—
328C23×C61—22no—
329C23×C61—22no—
330C23×C61—24no—
331C23×C61—22no—
332C23×C61—21no—
333C23×C61—21no—
334C23×C61—22no—
335C23×C61—22no—
336C23×C61—21no—
337C23×C61—21no—
338C23×C61—21no—
339C23×C61—41no—
340C23×C61—42no—
341C23×C61—41no—
342C23×C61—41no—
343C23×C61—42no—
344C23×C61—41no—
345C23×C61—42no—
346C23×C61—41no—
347C23×C61—42no—
348C23×C61—42no—
349C23×C61—41no—
350C23×C61—41no—
351C23×C61—42no—
352C23×C61—41no—
353C23×C61—41no—
354C23×C61—42no—
355C23×C61—81no—
356C23×C61—81no—
357C23×C61—82no—
358C23×C61—82no—
359C23×C61—84no—
360C23×C61—84no—
361C23×C61—84no—
362C23×C61C2×C22⋊C411yescharacteristic
363C23×C61C2×C22⋊C412yes—
364C23×C61C2×C22⋊C411yescharacteristic
365C23×C61C4×D412yescomplemented
366C23×C61C23×C411yescharacteristic
367C23×C61C22×D412yes—
368C23×C61C22×D411yescharacteristic
369C23×C61C2×#4111yescharacteristic
370C23×C61H(5,𝔽2)12yes—
371C22×D61—21no—
372C22×D61—21no—
373C22×D61—22no—
374C22×D61—22no—
375C22×D61—21no—
376C22×D61—21no—
377C22×D61—22no—
378C22×D61—22no—
379C22×D61—24no—
380C22×D61—22no—
381C22×D61—21no—
382C22×D61—21no—
383C22×D61—21no—
384C22×D61—42no—
385C22×D61—41no—
386C22×D61—42no—
387C22×D61—41no—
388C22×D61—42no—
389C22×D61—41no—
390C22×D61—42no—
391C22×D61—42no—
392C22×D61—42no—
393C22×D61—42no—
394C22×D61—41no—
395C22×D61—41no—
396C22×D61—81no—
397C22×D61—81no—
398C22×D61—82no—
399C22×D61—84no—
400C22×D61—82no—
401C22×D61—84no—
402C22×D61—84no—
403C22×D61C2×C22⋊C411yescharacteristic
404C22×D61C2×C22⋊C412yes—
405C22×D61C2×C22⋊C411yescharacteristic
406D4×C61—24no—
407D4×C61—24no—
408D4×C61—44no—
409D4×C61—44no—
410D4×C61—42no—
411D4×C61—42no—
412C2×C4×C61—21no—
413C2×C4×C61—21no—
414C2×C4×C61—21no—
415C2×C4×C61—21no—
416C2×C4×C61—21no—
417C2×C4×C61—42no—
418C2×C4×C61—42no—
419C2×C4×C61—42no—
420C2×C4×C61—42no—
421C2×C4×C61—42no—
422C2×C4×C61—42no—
423C2×C4×C61—42no—
424C2×C4×C61—42no—
425C2×C4×C61C4×D412yescomplemented
426C22⋊D61—22no—
427C22⋊D61—24no—
428C22⋊D61—22no—
429C22⋊D61—24no—
430C22⋊D61—22no—
431C22⋊D61—24no—
432C22⋊D61—42no—
433C22⋊D61—42no—
434C22⋊D61—42no—
435C22⋊D61—42no—
436C22⋊D61—44no—
437C22⋊D61—42no—
438C22⋊D61—42no—
439C22⋊D61—42no—
440C22⋊D61—42no—
441C22⋊D61—42no—
442C22⋊D61—42no—
443C22⋊D61—42no—
444C22⋊D61—82no—
445C22⋊D61—82no—
446C22⋊D61#9914yescomplemented
447C2×Dic61—24no—
448C2×Dic61—22no—
449C2×Dic61—21no—
450C2×Dic61—21no—
451C2×Dic61—21no—
452C2×Dic61—21no—
453C2×Dic61—21no—
454C2×Dic61—24no—
455C2×Dic61—41no—
456C2×Dic61—42no—
457C2×Dic61—42no—
458C2×Dic61—42no—
459C2×Dic61—42no—
460C2×Dic61—42no—
461C2×Dic61—41no—
462C2×Dic61—41no—
463C2×Dic61—42no—
464C2×Dic61—42no—
465C2×Dic61—42no—
466C2×Dic61—88no—
467C2×Dic61C2×C22⋊C411yescharacteristic
468C2×Dic61C2×C22⋊C412yes—
469C2×Dic61C2×C22⋊C411yescharacteristic
470D244—44no—
471C4×D61—42no—
472C4×D61—42no—
473C4×D61—88no—
474D4×#99—611nomaximal, Sylow
475C22×C61—21no—
476C22×C61—22no—
477C22×C61—21no—
478C22×C61—22no—
479C22×C61—21no—
480C22×C61—21no—
481C22×C61—22no—
482C22×C61—21no—
483C22×C61—22no—
484C22×C61—21no—
485C22×C61—22no—
486C22×C61—22no—
487C22×C61—21no—
488C22×C61—41no—
489C22×C61—41no—
490C22×C61—42no—
491C22×C61—44no—
492C22×C61—44no—
493C22×C61—42no—
494C22×C61—42no—
495C22×C61—42no—
496C22×C61—42no—
497C22×C61—41no—
498C22×C61—41no—
499C22×C61—41no—
500C22×C61—41no—
501C22×C61—41no—
502C22×C61—82no—
503C22×C61—82no—
504C22×C61—81no—
505C22×C61—81no—
506C22×C61—84no—
507C22×C61—81no—
508C22×C61—81no—
509C22×C61—84no—
510C22×C61C2×#9912yescomplemented
511C22×C61C22×C22⋊C411yescharacteristic
512C22×C61C2×C4×D411yescharacteristic
513C22×C61#51811yescharacteristic
514C22×C61D4212yes—
515C22×C61#54612yes—
516C2×D61—21no—
517C2×D61—21no—
518C2×D61—21no—
519C2×D61—22no—
520C2×D61—21no—
521C2×D61—22no—
522C2×D61—22no—
523C2×D61—21no—
524C2×D61—44no—
525C2×D61—44no—
526C2×D61—42no—
527C2×D61—42no—
528C2×D61—41no—
529C2×D61—41no—
530C2×D61—41no—
531C2×D61—84no—
532C2×D61—81no—
533C2×D61—81no—
534C2×D61—82no—
535C2×D61—82no—
536C2×D61—84no—
537C2×D61—81no—
538C2×D61—81no—
539C2×D61C2×#9912yescomplemented
540C4×C61—22no—
541C4×C61—41no—
542C4×C61—82no—
543C4×C61—82no—
544Dic61—21no—
545Dic61—22no—
546Dic61—44no—
547Dic61—41no—
548Dic61—41no—
549Dic61—41no—
550Dic61—82no—
551Dic61C2×#9912yescomplemented
552C2×D42—611no—
553C22×#99—611no—
554C22×#99—611no—
555D4×C22⋊C4—612no—
556#1964—612no—
557#1898—612no—
558#1898—612no—
559#1799—611no—
560#1781—611no—
561#1781D6111yescharacteristic, complemented
562C4×#99—611no—
563C2×C61—22no—
564C2×C61—22no—
565C2×C61—21no—
566C2×C61—21no—
567C2×C61—22no—
568C2×C61—42no—
569C2×C61—42no—
570C2×C61—41no—
571C2×C61—81no—
572C2×C61D4×C22⋊C411yescharacteristic
573C2×C61C22×#9911yescharacteristic
574C2×C61#288311yescharacteristic
575D61—22no—
576D61—42no—
577D61—41no—
578D61—81no—
579C23×D4—611no—
580C23×D4—611no—
581C23×D4—611no—
582C23×D4C2×D6111yescharacteristic
583D42—1222no—
584D42—1222no—
585D42—1222no—
586D42—1222no—
587C2×#127—611no—
588C2×#121—611no—
589C2×#121—611no—
590C2×#121—611no—
591C2×#121—611no—
592C2×#120—611no—
593C2×#120—611no—
594C2×#120—611no—
595C2×#120—611no—
596C2×C4×D4—611no—
597C2×C4×D4—611no—
598C2×C4×D4—1222no—
599C22×C22⋊C4—612no—
600C22×C22⋊C4—612no—
601C2×#99—611no—
602C2×#99—611no—
603C2×#99—612no—
604C2×#99—612no—
605C2×#99—612no—
606C2×#99—1224no—
607C2×#99—1224no—
608C2×#99C2×D6111yescharacteristic
609C2×#99C2×D6111yescharacteristic
610C2×#99C2×D6112yescomplemented
611#390—1222no—
612#386—1222no—
613#386—1222no—
614#380—612no—
615#379—612no—
616#379C2×D6112yescomplemented
617C4×C22⋊C4—612no—
618#342—612no—
619#342—612no—
620C61D4×#9911yescharacteristic, complemented, Sylow
621C25—611no—
622C25—611no—
623C25C4×D6111yescharacteristic, complemented
624C25C22×D6111yescharacteristic
625C22×D4—22no—
626C22×D4—22no—
627C22×D4—22no—
628C22×D4—22no—
629C22×D4—42no—
630C22×D4—611no—
631C22×D4—612no—
632C22×D4—611no—
633C22×D4—611no—
634C22×D4—611no—
635C22×D4—612no—
636C22×D4—612no—
637C22×D4—612no—
638C22×D4—611no—
639C22×D4—611no—
640C22×D4—611no—
641C22×D4—611no—
642C22×D4—611no—
643C22×D4—611no—
644C22×D4—611no—
645C22×D4—611no—
646C22×D4—1222no—
647C22×D4—1222no—
648C22×D4—1221no—
649C22×D4—1221no—
650C22×D4—1221no—
651C22×D4—1221no—
652C22×D4—1222no—
653C22×D4—1222no—
654C22×D4—2442no—
655C22×D4—2444no—
656C22×D4—2444no—
657C22×D4C4×D6111yescharacteristic, complemented
658C22×D4C4×D6111yescharacteristic, complemented
659C22×D4C22×D6111yescharacteristic
660C22×D4C22×D6111yescharacteristic
661C23×C4—611no—
662C23×C4—611no—
663C23×C4—611no—
664C23×C4—1222no—
665C23×C4—1222no—
666C23×C4C4×D6111yescharacteristic, complemented
667#127—1222no—
668#127—1222no—
669#121—1222no—
670#121—1222no—
671#121—1222no—
672#121—1222no—
673#121—1222no—
674#121—1222no—
675#121—1222no—
676#121—1222no—
677#120—1222no—
678#120—1222no—
679#120—1222no—
680#120—1222no—
681#120—1222no—
682#120—1222no—
683#120—1222no—
684#120—1222no—
685C4×D4—1221no—
686C4×D4—1221no—
687C4×D4—1221no—
688C4×D4—1221no—
689C4×D4—1222no—
690C4×D4—1222no—
691C4×D4—2448no—
692C2×C4⋊C4—611no—
693C2×C4⋊C4—611no—
694C2×C4⋊C4—1222no—
695C2×C22⋊C4—22no—
696C2×C22⋊C4—22no—
697C2×C22⋊C4—612no—
698C2×C22⋊C4—611no—
699C2×C22⋊C4—611no—
700C2×C22⋊C4—611no—
701C2×C22⋊C4—611no—
702C2×C22⋊C4—611no—
703C2×C22⋊C4—611no—
704C2×C22⋊C4—611no—
705C2×C22⋊C4—611no—
706C2×C22⋊C4—612no—
707C2×C22⋊C4—1224no—
708C2×C22⋊C4—1224no—
709C2×C22⋊C4—1222no—
710C2×C22⋊C4—1222no—
711C2×C22⋊C4—1222no—
712C2×C22⋊C4—1222no—
713C2×C22⋊C4—2442no—
714C2×C22⋊C4—2442no—
715C2×C22⋊C4C22×D6112yes—
716C2×C22⋊C4C22×D6112yes—
717C2×C42—611no—
718C2×C42—1222no—
719#99—22no—
720#99—22no—
721#99—42no—
722#99—614no—
723#99—1224no—
724#99—1224no—
725#99—1222no—
726#99—2442no—
727#95—1222no—
728#95—1222no—
729C24—21no—
730C24—21no—
731C24—22no—
732C24—21no—
733C24—21no—
734C24—22no—
735C24—41no—
736C24—42no—
737C24—42no—
738C24—81no—
739C24—81no—
740C24—611no—
741C24—612no—
742C24—611no—
743C24—612no—
744C24—611no—
745C24—1221no—
746C24—1221no—
747C24—1221no—
748C24—1221no—
749C24—1222no—
750C24—1222no—
751C24—4881no—
752C24—4881no—
753C24—2441no—
754C24—2442no—
755C24—2442no—
756C24C2×C4×D6111yescharacteristic
757C24C2×C4×D6111yescharacteristic
758C24C2×C4×D6111yescharacteristic
759C24C2×C4×D6111yescharacteristic
760C24D4×D6112yes—
761C24D4×D6112yes—
762C24C23×D6111yescharacteristic
763C2×D4—22no—
764C2×D4—22no—
765C2×D4—21no—
766C2×D4—22no—
767C2×D4—21no—
768C2×D4—22no—
769C2×D4—22no—
770C2×D4—22no—
771C2×D4—22no—
772C2×D4—22no—
773C2×D4—41no—
774C2×D4—41no—
775C2×D4—44no—
776C2×D4—44no—
777C2×D4—44no—
778C2×D4—44no—
779C2×D4—611no—
780C2×D4—611no—
781C2×D4—611no—
782C2×D4—611no—
783C2×D4—612no—
784C2×D4—612no—
785C2×D4—612no—
786C2×D4—612no—
787C2×D4—612no—
788C2×D4—612no—
789C2×D4—1222no—
790C2×D4—1221no—
791C2×D4—1221no—
792C2×D4—1228no—
793C2×D4—1224no—
794C2×D4—1222no—
795C2×D4—1222no—
796C2×D4—1222no—
797C2×D4—1221no—
798C2×D4—1221no—
799C2×D4—1221no—
800C2×D4—1222no—
801C2×D4—1221no—
802C2×D4—1222no—
803C2×D4—1221no—
804C2×D4—1221no—
805C2×D4—1222no—
806C2×D4—1222no—
807C2×D4—4881no—
808C2×D4—4881no—
809C2×D4—2441no—
810C2×D4—2444no—
811C2×D4—2442no—
812C2×D4—2441no—
813C2×D4—2442no—
814C2×D4—2444no—
815C2×D4—2444no—
816C2×D4—2444no—
817C2×D4—2444no—
818C2×D4—2444no—
819C2×D4—2442no—
820C2×D4—2444no—
821C2×D4—2442no—
822C2×D4—2444no—
823C2×D4—2444no—
824C2×D4—2444no—
825C2×D4—2444no—
826C2×D4—2442no—
827C2×D4—2442no—
828C2×D4D4×D6112yes—
829C2×D4#1175822412yes—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—22no—
833C22×C4—22no—
834C22×C4—22no—
835C22×C4—41no—
836C22×C4—611no—
837C22×C4—612no—
838C22×C4—611no—
839C22×C4—612no—
840C22×C4—611no—
841C22×C4—611no—
842C22×C4—611no—
843C22×C4—1221no—
844C22×C4—1221no—
845C22×C4—1221no—
846C22×C4—1221no—
847C22×C4—1222no—
848C22×C4—1222no—
849C22×C4—1222no—
850C22×C4—4882no—
851C22×C4—4882no—
852C22×C4—2441no—
853C22×C4—2444no—
854C22×C4—2444no—
855C22×C4—2442no—
856C22×C4—2444no—
857C22×C4—2442no—
858C22×C4—2444no—
859C22×C4C2×C4×D6111yescharacteristic
860C22×C4C2×C4×D6111yescharacteristic
861C4⋊C4—1221no—
862C4⋊C4—1221no—
863C4⋊C4—1222no—
864C4⋊C4—2444no—
865C22⋊C4—22no—
866C22⋊C4—22no—
867C22⋊C4—22no—
868C22⋊C4—22no—
869C22⋊C4—44no—
870C22⋊C4—82no—
871C22⋊C4—614no—
872C22⋊C4—1222no—
873C22⋊C4—1221no—
874C22⋊C4—1221no—
875C22⋊C4—1222no—
876C22⋊C4—1222no—
877C22⋊C4—1222no—
878C22⋊C4—1222no—
879C22⋊C4—1222no—
880C22⋊C4—1221no—
881C22⋊C4—1221no—
882C22⋊C4—1222no—
883C22⋊C4—1222no—
884C22⋊C4—1222no—
885C22⋊C4—4882no—
886C22⋊C4—2444no—
887C22⋊C4—2444no—
888C22⋊C4—2444no—
889C42—1221no—
890C42—1221no—
891C42—2444no—
892C23—21no—
893C23—21no—
894C23—21no—
895C23—21no—
896C23—24no—
897C23—22no—
898C23—22no—
899C23—22no—
900C23—21no—
901C23—21no—
902C23—22no—
903C23—22no—
904C23—21no—
905C23—21no—
906C23—21no—
907C23—42no—
908C23—41no—
909C23—41no—
910C23—41no—
911C23—42no—
912C23—41no—
913C23—41no—
914C23—42no—
915C23—42no—
916C23—42no—
917C23—41no—
918C23—41no—
919C23—42no—
920C23—41no—
921C23—41no—
922C23—42no—
923C23—81no—
924C23—81no—
925C23—82no—
926C23—82no—
927C23—84no—
928C23—84no—
929C23—84no—
930C23—611no—
931C23—611no—
932C23—612no—
933C23—1224no—
934C23—1222no—
935C23—1221no—
936C23—1221no—
937C23—1222no—
938C23—1222no—
939C23—1221no—
940C23—1221no—
941C23—1222no—
942C23—1222no—
943C23—1221no—
944C23—1221no—
945C23—1221no—
946C23—4881no—
947C23—4881no—
948C23—4884no—
949C23—4884no—
950C23—4882no—
951C23—4882no—
952C23—4884no—
953C23—2442no—
954C23—2441no—
955C23—2442no—
956C23—2441no—
957C23—2442no—
958C23—2441no—
959C23—2442no—
960C23—2442no—
961C23—2441no—
962C23—2441no—
963C23—2442no—
964C23—2442no—
965C23C22⋊C4×D6111yescharacteristic
966C23C22⋊C4×D6112yes—
967C23C22⋊C4×D6111yescharacteristic
968C23#1451973712yescomplemented
969C23C22×C4×D6111yescharacteristic
970C23C2×D4×D6112yes—
971C23C2×D4×D6111yescharacteristic
972C23C2×#1175822411yescharacteristic
973C23#1451982212yes—
974D4—24no—
975D4—24no—
976D4—44no—
977D4—44no—
978D4—42no—
979D4—42no—
980D4—614no—
981D4—1224no—
982D4—1222no—
983D4—1224no—
984D4—1222no—
985D4—1224no—
986D4—1222no—
987D4—4882no—
988D4—4882no—
989D4—2444no—
990D4—2442no—
991D4—2442no—
992D4—2442no—
993D4—2442no—
994D4—2442no—
995D4—2444no—
996D4—2442no—
997D4—2442no—
998D4—2442no—
999D4—2442no—
1000D4—2442no—
1001D4—2442no—
1002C2×C4—21no—
1003C2×C4—21no—
1004C2×C4—21no—
1005C2×C4—21no—
1006C2×C4—21no—
1007C2×C4—42no—
1008C2×C4—42no—
1009C2×C4—42no—
1010C2×C4—42no—
1011C2×C4—42no—
1012C2×C4—42no—
1013C2×C4—42no—
1014C2×C4—42no—
1015C2×C4—611no—
1016C2×C4—611no—
1017C2×C4—612no—
1018C2×C4—1224no—
1019C2×C4—1222no—
1020C2×C4—1221no—
1021C2×C4—1221no—
1022C2×C4—1221no—
1023C2×C4—1221no—
1024C2×C4—1221no—
1025C2×C4—1224no—
1026C2×C4—4888no—
1027C2×C4—4888no—
1028C2×C4—2442no—
1029C2×C4—2442no—
1030C2×C4—2442no—
1031C2×C4—2442no—
1032C2×C4—2441no—
1033C2×C4—2442no—
1034C2×C4—2442no—
1035C2×C4—2442no—
1036C2×C4—2442no—
1037C2×C4—2442no—
1038C2×C4—2442no—
1039C2×C4—2441no—
1040C2×C4—2441no—
1041C2×C4#1451973712yescomplemented
1042C22—21no—
1043C22—22no—
1044C22—21no—
1045C22—22no—
1046C22—21no—
1047C22—21no—
1048C22—21no—
1049C22—22no—
1050C22—22no—
1051C22—21no—
1052C22—22no—
1053C22—22no—
1054C22—21no—
1055C22—41no—
1056C22—41no—
1057C22—42no—
1058C22—44no—
1059C22—44no—
1060C22—42no—
1061C22—42no—
1062C22—42no—
1063C22—42no—
1064C22—41no—
1065C22—41no—
1066C22—41no—
1067C22—41no—
1068C22—41no—
1069C22—82no—
1070C22—82no—
1071C22—81no—
1072C22—81no—
1073C22—84no—
1074C22—81no—
1075C22—81no—
1076C22—84no—
1077C22—612no—
1078C22—1221no—
1079C22—1221no—
1080C22—1221no—
1081C22—1222no—
1082C22—1221no—
1083C22—1222no—
1084C22—1222no—
1085C22—1221no—
1086C22—4881no—
1087C22—4881no—
1088C22—4882no—
1089C22—4882no—
1090C22—4881no—
1091C22—4881no—
1092C22—4884no—
1093C22—4884no—
1094C22—2444no—
1095C22—2442no—
1096C22—2442no—
1097C22—2444no—
1098C22—2441no—
1099C22—2441no—
1100C22—2441no—
1101C22#99×D6112yescomplemented
1102C22C2×C22⋊C4×D6111yescharacteristic
1103C22C2×#1451973711yescharacteristic
1104C22#1684023511yescharacteristic
1105C22#1684039412yes—
1106C22#1684039912yes—
1107C4—22no—
1108C4—41no—
1109C4—82no—
1110C4—82no—
1111C4—612no—
1112C4—1221no—
1113C4—1222no—
1114C4—4882no—
1115C4—2444no—
1116C4—2441no—
1117C4—2441no—
1118C4—2441no—
1119C2—22no—
1120C2—22no—
1121C2—21no—
1122C2—21no—
1123C2—22no—
1124C2—41no—
1125C2—42no—
1126C2—42no—
1127C2—81no—
1128C2—1222no—
1129C2—4881no—
1130C2—2441no—
1131C2—2442no—
1132C2#2144863511yescharacteristic
1133C2C2×#99×D6111yescharacteristic
1134C2#2145427711yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC23×C61C23×C4
FrattiniC24C23×D61
FittingC61×#1781C2
socleC22×C61C22×C22⋊C4
prime radicalC2×D4×C22⋊D61C2
cosocleC24×C61C24
hypercenter#1781D61
hypocenterC61D4×#99
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. C22×#14519692C2semidirect
3. C2×#99×D61C2semidirect
4. #21448635C2semidirect
5. #21446653C2semidirect
6. #21446270C2semidirect
7. #21446269C2semidirect
8. #21445805C2semidirect
9. #21445732C2semidirect
10. #99×Dic61C2semidirect
11. C61×#1781C2semidirect
12. C23×C22⋊D61C4semidirect
19. C2×#14519773C4semidirect
20. C2×#14519751C4semidirect
21. C2×#14519749C4semidirect
23. C2×#14519748C4semidirect
24. C2×#14519746C4semidirect
26. C2×#14519745C4semidirect
29. C2×C4×C22⋊D61C4semidirect
31. C22×C22⋊Dic61C22semidirect
32. C2×C22⋊C4×D61C22semidirect
36. C2×#14519692C22semidirect
37. C2×#14519691C22semidirect
38. C2×#14519691C22semidirect
43. #16839620C22semidirect
44. #16839617C22semidirect
45. C22⋊C4×Dic61C22semidirect
46. #16839528C22semidirect
47. #16839528C22semidirect
51. C2×#99×C61C22semidirect
52. C61×#379C22semidirect
53. C24×D61C2×C4semidirect
55. C22×D244C2×C4semidirect
66. C22×C22⋊D61C2×C4semidirect
67. C22×C22⋊D61C2×C4semidirect
68. C22×C22⋊D61C2×C4semidirect
69. C22×C22⋊D61C2×C4semidirect
70. C22×C22⋊D61C2×C4semidirect
71. C22×C22⋊D61C2×C4semidirect
83. C23×Dic61C2×C4semidirect
86. C22×C4×D61C2×C4semidirect
112. C2×C4⋊Dic61C2×C4semidirect
114. C2×#11758196C2×C4semidirect
118. C2×C22⋊Dic61C2×C4semidirect
119. C2×C22⋊Dic61C2×C4semidirect
120. C2×C22⋊Dic61C2×C4semidirect
121. C2×C22⋊Dic61C2×C4semidirect
128. C2×#11758198C2×C4semidirect
129. C2×#11758198C2×C4semidirect
130. C2×#11758198C2×C4semidirect
134. C2×C4×Dic61C2×C4semidirect
137. #14519692D4semidirect
142. C25×C61C2×C4semidirect
149. C22×D4×C61C2×C4semidirect
150. C22×D4×C61C2×C4semidirect
153. C23×C4×C61C2×C4semidirect
309. C22⋊Dic61C2×D4semidirect
365. C23×C61C4×D4semidirect
425. C2×C4×C61C4×D4semidirect
446. C22⋊D61#99semidirect
510. C22×C61C2×#99semidirect
539. C2×D61C2×#99semidirect
551. Dic61C2×#99semidirect
561. #1781D61semidirect
610. C2×#99C2×D61semidirect
616. #379C2×D61semidirect
620. C61D4×#99semidirect
623. C25C4×D61semidirect
657. C22×D4C4×D61semidirect
658. C22×D4C4×D61semidirect
666. C23×C4C4×D61semidirect
968. C23#14519737semidirect
1041. C2×C4#14519737semidirect
1101. C22#99×D61semidirect

Maximal subgroups

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

subgroupindex
C2×D4×C22⋊D612
C22×#145196922
C2×#99×D612
#214486352
#214466532
#214462702
#214462692
#214458052
#214457322
#99×Dic612
C61×#17812
D4×#9961