Finite Group Databasebeta

← C2×#21446360 #29682023

Subgroups — C2×#21446360 #29682023

Order 15616.

2078 conjugacy classes of subgroups.

The subgroup lattice has 1030 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840324C211yesmaximal, characteristic
2C2×#16840235C211yesmaximal, characteristic, complemented
3C22×#14519691C211yesmaximal, characteristic, complemented
4C22×#14519691C211yesmaximal, characteristic, complemented
5C22×#14519691C211yesmaximal, characteristic, complemented
6#21446360C218yesmaximal, direct product factor
7C2×#16839528C211yesmaximal, characteristic, complemented
8C2×C61×#342C211yesmaximal, characteristic, complemented
9C23×C22⋊D61C2211yescharacteristic
10C23×C22⋊D61C2211yescharacteristic
11#16840324—22no—
12#16840324—22no—
13#16840324C414yescomplemented
14#16840324C2214yes—
15C2×#14519761—21no—
16C2×#14519761C412yescomplemented
17C2×#14519751—22no—
18C2×#14519747—21no—
19C2×#14519747C412yescomplemented
20#16840235—22no—
21#16840235—22no—
22#16840235—22no—
23#16840235C2214yescomplemented
24C2×C4×C22⋊D61—22no—
25C2×#14519737—22no—
26C2×#14519733—21no—
27C22×C22⋊Dic61C2211yescharacteristic
28C22×C22⋊Dic61C2211yescharacteristic
29C2×C22⋊C4×D61—21no—
30C2×#14519691—22no—
31C2×#14519691—22no—
32C2×#14519691—22no—
33C2×#14519691—22no—
34C2×#14519691—22no—
35C2×#14519691—22no—
36C2×#14519691C2214yescomplemented
37C2×#14519691C2214yescomplemented
38C2×#14519691C2214yescomplemented
39#16839528C2214yescomplemented
40C22×C22⋊C4×C61C2211yescharacteristic
41C22×C22⋊C4×C61C2211yescharacteristic
42C22×C22⋊C4×C61C2211yescharacteristic
43C61×#342C2214yescomplemented
44C24×D61C2×C411yescharacteristic, complemented
45C24×D61D411yescharacteristic
46C22×D244—22no—
47C22×C22⋊D61—21no—
48C22×C22⋊D61—21no—
49C22×C22⋊D61—21no—
50C22×C22⋊D61—21no—
51C22×C22⋊D61—21no—
52C22×C22⋊D61—21no—
53C22×C22⋊D61—21no—
54C22×C22⋊D61—21no—
55C22×C22⋊D61—21no—
56C22×C22⋊D61—21no—
57C22×C22⋊D61—21no—
58C22×C22⋊D61—21no—
59C22×C22⋊D61—21no—
60C22×C22⋊D61—21no—
61C22×C22⋊D61—21no—
62C22×C22⋊D61—21no—
63C22×C22⋊D61—21no—
64C22×C22⋊D61—21no—
65C22×C22⋊D61—21no—
66C22×C22⋊D61—21no—
67C22×C22⋊D61C2×C412yes—
68C22×C22⋊D61C2×C412yes—
69C22×C22⋊D61C2×C412yescomplemented
70C22×C22⋊D61D412yes—
71C22×C22⋊D61D412yes—
72C22×C22⋊D61D412yes—
73C22×C22⋊D61C2312yes—
74C22×C22⋊D61C2312yes—
75C23×Dic61—21no—
76C23×Dic61—21no—
77C23×Dic61C2×C411yescharacteristic, complemented
78C23×Dic61D411yescharacteristic
79C22×C4×D61—22no—
80#14519761—24no—
81#14519761—24no—
82#14519761—24no—
83#14519761C2×C418yescomplemented
84#14519751—28no—
85#14519751—28no—
86#14519747—24no—
87#14519747—24no—
88#14519747—24no—
89#14519747C2×C418yescomplemented
90C4×C22⋊D61—28no—
91C4×C22⋊D61—28no—
92#14519737—28no—
93#14519737—28no—
94#14519733—24no—
95#14519733—24no—
96C2×C4⋊Dic61—22no—
97C2×#11758196—22no—
98C2×C22⋊Dic61—21no—
99C2×C22⋊Dic61—21no—
100C2×C22⋊Dic61—21no—
101C2×C22⋊Dic61—21no—
102C2×C22⋊Dic61—21no—
103C2×C22⋊Dic61—21no—
104C2×C22⋊Dic61—21no—
105C2×C22⋊Dic61—21no—
106C2×C22⋊Dic61D412yescomplemented
107C2×C22⋊Dic61D412yescomplemented
108C2×C22⋊Dic61C2312yes—
109C2×C22⋊Dic61C2312yes—
110C2×#11758198—22no—
111C2×#11758198—22no—
112C2×#11758198—22no—
113C22⋊C4×D61—24no—
114C22⋊C4×D61—24no—
115C2×C4×Dic61—22no—
116#14519691—28no—
117#14519691—28no—
118#14519691—28no—
119C25×C61C2311yescharacteristic
120C23×C4×C61—21no—
121C23×C4×C61—21no—
122C23×C4×C61—21no—
123C2×C22⋊C4×C61—21no—
124C2×C22⋊C4×C61—21no—
125C2×C22⋊C4×C61—21no—
126C2×C22⋊C4×C61—21no—
127C2×C22⋊C4×C61—21no—
128C2×C22⋊C4×C61—21no—
129C2×C22⋊C4×C61—21no—
130C2×C22⋊C4×C61—21no—
131C2×C22⋊C4×C61—21no—
132C2×C22⋊C4×C61—21no—
133C2×C22⋊C4×C61—21no—
134C2×C22⋊C4×C61C2×C412yescomplemented
135C2×C22⋊C4×C61C2×C412yescomplemented
136C2×C22⋊C4×C61D412yescomplemented
137C2×C22⋊C4×C61D412yescomplemented
138C2×C22⋊C4×C61C2312yes—
139C2×C22⋊C4×C61C2312yes—
140C2×C22⋊C4×C61C2312yes—
141C24×C61—82no—
142C24×C61C22×C411yescharacteristic
143C24×C61C22×C411yescharacteristic
144C24×C61C2×D411yescharacteristic
145C24×C61C2×D411yescharacteristic
146C24×C61C2×D411yescharacteristic
147C24×C61C2×D411yescharacteristic
148C24×C61C2×D411yescharacteristic
149C24×C61C2×D411yescharacteristic
150C24×C61C2×D411yescharacteristic
151C24×C61C2×D411yescharacteristic
152C24×C61#4111yescharacteristic
153C24×C61#4111yescharacteristic
154C24×C61#4111yescharacteristic
155C24×C61#4111yescharacteristic
156C24×C61C2411yescharacteristic
157C23×D61—21no—
158C23×D61—21no—
159C23×D61—21no—
160C23×D61—21no—
161C23×D61—21no—
162C23×D61—21no—
163C23×D61—21no—
164C23×D61—21no—
165C23×D61—21no—
166C23×D61—21no—
167C23×D61—82no—
168C23×D61—82no—
169C23×D61C22⋊C412yes—
170C23×D61C22⋊C412yes—
171C23×D61C22×C412yescomplemented
172C23×D61C2×D412yes—
173C22×C4×C61—22no—
174C22×C4×C61—22no—
175C22×C4×C61—22no—
176C22×C4×C61—22no—
177C22×C4×C61—22no—
178C22×C4×C61—22no—
179C22×C4×C61—22no—
180C22×C4×C61—41no—
181C22×C4×C61—41no—
182C22×C4×C61—82no—
183C22×C4×C61—82no—
184C22×C4×C61—82no—
185C2×C22⋊D61—22no—
186C2×C22⋊D61—22no—
187C2×C22⋊D61—22no—
188C2×C22⋊D61—22no—
189C2×C22⋊D61—22no—
190C2×C22⋊D61—22no—
191C2×C22⋊D61—22no—
192C2×C22⋊D61—22no—
193C2×C22⋊D61—22no—
194C2×C22⋊D61—22no—
195C2×C22⋊D61—22no—
196C2×C22⋊D61—22no—
197C2×C22⋊D61—22no—
198C2×C22⋊D61—22no—
199C2×C22⋊D61—22no—
200C2×C22⋊D61—22no—
201C2×C22⋊D61—22no—
202C2×C22⋊D61—22no—
203C2×C22⋊D61—22no—
204C2×C22⋊D61—22no—
205C2×C22⋊D61—22no—
206C2×C22⋊D61—22no—
207C2×C22⋊D61—22no—
208C2×C22⋊D61—22no—
209C2×C22⋊D61—22no—
210C2×C22⋊D61—22no—
211C2×C22⋊D61—22no—
212C2×C22⋊D61—22no—
213C2×C22⋊D61—22no—
214C2×C22⋊D61—22no—
215C2×C22⋊D61—22no—
216C2×C22⋊D61—22no—
217C2×C22⋊D61—22no—
218C2×C22⋊D61—22no—
219C2×C22⋊D61—22no—
220C2×C22⋊D61—22no—
221C2×C22⋊D61—41no—
222C2×C22⋊D61—41no—
223C2×C22⋊D61—41no—
224C2×C22⋊D61—41no—
225C2×C22⋊D61—41no—
226C2×C22⋊D61—41no—
227C2×C22⋊D61—41no—
228C2×C22⋊D61—41no—
229C2×C22⋊D61—41no—
230C2×C22⋊D61—41no—
231C2×C22⋊D61—41no—
232C2×C22⋊D61—41no—
233C2×C22⋊D61—41no—
234C2×C22⋊D61—41no—
235C2×C22⋊D61—41no—
236C2×C22⋊D61—41no—
237C2×C22⋊D61C22⋊C414yes—
238C2×C22⋊D61C22⋊C414yes—
239C2×C22⋊D61C22×C414yes—
240C2×C22⋊D61C2×D414yes—
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—22no—
252C22×Dic61—22no—
253C22×Dic61—22no—
254C22×Dic61—22no—
255C22×Dic61—41no—
256C22×Dic61—41no—
257C22×Dic61—82no—
258C22×Dic61—82no—
259C22×Dic61C22⋊C412yes—
260C22×Dic61C22⋊C412yes—
261C22×Dic61C22×C412yescomplemented
262C22×Dic61C2×D412yes—
263C2×D244—28no—
264C2×D244—84no—
265C2×C4×D61—28no—
266C2×C4×D61—84no—
267C22⋊C4×C61—22no—
268C22⋊C4×C61—22no—
269C22⋊C4×C61—22no—
270C22⋊C4×C61—22no—
271C22⋊C4×C61—22no—
272C22⋊C4×C61—22no—
273C22⋊C4×C61—22no—
274C22⋊C4×C61—22no—
275C22⋊C4×C61—41no—
276C22⋊C4×C61—41no—
277C22⋊C4×C61C22×C414yescomplemented
278C22⋊C4×C61C2×D414yescomplemented
279C22⋊Dic61—22no—
280C22⋊Dic61—22no—
281C22⋊Dic61—22no—
282C22⋊Dic61—22no—
283C22⋊Dic61—22no—
284C22⋊Dic61—41no—
285C22⋊Dic61—41no—
286C22⋊Dic61C2×D414yescomplemented
287#11758198—28no—
288#11758198—28no—
289#11758198—28no—
290C4⋊Dic61—28no—
291#11758196—28no—
292C4×Dic61—28no—
293C23×C61—42no—
294C23×C61—42no—
295C23×C61—42no—
296C23×C61—42no—
297C23×C61—42no—
298C23×C61—42no—
299C23×C61—42no—
300C23×C61—81no—
301C23×C61—81no—
302C23×C61—81no—
303C23×C61—81no—
304C23×C61—81no—
305C23×C61—81no—
306C23×C61—81no—
307C23×C61—81no—
308C23×C61C2×C22⋊C411yescharacteristic
309C23×C61C2×C22⋊C411yescharacteristic
310C23×C61C2×C22⋊C411yescharacteristic
311C23×C61C2×C22⋊C411yescharacteristic
312C23×C61C4×D411yescharacteristic
313C23×C61C4×D411yescharacteristic
314C23×C61C4×D411yescharacteristic
315C23×C61C4×D411yescharacteristic
316C23×C61C4×D411yescharacteristic
317C23×C61C4×D411yescharacteristic
318C23×C61C4×D411yescharacteristic
319C23×C61C4×D411yescharacteristic
320C23×C61#12011yescharacteristic
321C23×C61#12011yescharacteristic
322C23×C61#12011yescharacteristic
323C23×C61#12011yescharacteristic
324C23×C61#12111yescharacteristic
325C23×C61#12111yescharacteristic
326C23×C61#12111yescharacteristic
327C23×C61#12111yescharacteristic
328C23×C61#12111yescharacteristic
329C23×C61#12111yescharacteristic
330C23×C61#12111yescharacteristic
331C23×C61#12111yescharacteristic
332C23×C61#12311yescharacteristic
333C23×C61#12311yescharacteristic
334C23×C61#12311yescharacteristic
335C23×C61#12311yescharacteristic
336C23×C61C23×C411yescharacteristic
337C23×C61C22×D411yescharacteristic
338C23×C61C22×D411yescharacteristic
339C23×C61C22×D411yescharacteristic
340C23×C61C22×D411yescharacteristic
341C23×C61C2×#4111yescharacteristic
342C23×C61C2×#4111yescharacteristic
343C22×D61—22no—
344C22×D61—22no—
345C22×D61—22no—
346C22×D61—22no—
347C22×D61—22no—
348C22×D61—22no—
349C22×D61—22no—
350C22×D61—22no—
351C22×D61—22no—
352C22×D61—44no—
353C22×D61—44no—
354C22×D61—44no—
355C22×D61—41no—
356C22×D61—41no—
357C22×D61—41no—
358C22×D61—41no—
359C22×D61—82no—
360C22×D61—82no—
361C22×D61—82no—
362C22×D61—82no—
363C22×D61—82no—
364C22×D61—82no—
365C22×D61—82no—
366C22×D61—82no—
367C22×D61—82no—
368C22×D61—82no—
369C22×D61—82no—
370C22×D61C2×C22⋊C414yes—
371C2×C4×C61—24no—
372C2×C4×C61—24no—
373C2×C4×C61—44no—
374C2×C4×C61—44no—
375C2×C4×C61—42no—
376C2×C4×C61—82no—
377C2×C4×C61—82no—
378C2×C4×C61—82no—
379C2×C4×C61—82no—
380C2×C4×C61—82no—
381C2×C4×C61—82no—
382C2×C4×C61—82no—
383C22⋊D61—24no—
384C22⋊D61—24no—
385C22⋊D61—24no—
386C22⋊D61—24no—
387C22⋊D61—24no—
388C22⋊D61—24no—
389C22⋊D61—24no—
390C22⋊D61—24no—
391C22⋊D61—42no—
392C22⋊D61—42no—
393C22⋊D61—42no—
394C22⋊D61—42no—
395C22⋊D61—42no—
396C22⋊D61—42no—
397C22⋊D61—42no—
398C22⋊D61—42no—
399C2×Dic61—22no—
400C2×Dic61—22no—
401C2×Dic61—22no—
402C2×Dic61—22no—
403C2×Dic61—22no—
404C2×Dic61—22no—
405C2×Dic61—22no—
406C2×Dic61—22no—
407C2×Dic61—22no—
408C2×Dic61—24no—
409C2×Dic61—44no—
410C2×Dic61—41no—
411C2×Dic61—41no—
412C2×Dic61—41no—
413C2×Dic61—41no—
414C2×Dic61—42no—
415C2×Dic61—82no—
416C2×Dic61—82no—
417C2×Dic61—82no—
418C2×Dic61—82no—
419C2×Dic61—82no—
420C2×Dic61C2×C22⋊C414yes—
421D244—88no—
422C4×D61—88no—
423C2×#1913—611nomaximal, Sylow
424C22×C61—22no—
425C22×C61—22no—
426C22×C61—22no—
427C22×C61—22no—
428C22×C61—22no—
429C22×C61—22no—
430C22×C61—22no—
431C22×C61—41no—
432C22×C61—41no—
433C22×C61—41no—
434C22×C61—41no—
435C22×C61—41no—
436C22×C61—41no—
437C22×C61—41no—
438C22×C61—41no—
439C22×C61—41no—
440C22×C61—41no—
441C22×C61—41no—
442C22×C61—41no—
443C22×C61—41no—
444C22×C61—41no—
445C22×C61—41no—
446C22×C61—41no—
447C22×C61—41no—
448C22×C61—41no—
449C22×C61—41no—
450C22×C61—41no—
451C22×C61—41no—
452C22×C61—41no—
453C22×C61—41no—
454C22×C61—41no—
455C22×C61—41no—
456C22×C61—41no—
457C22×C61—41no—
458C22×C61—41no—
459C22×C61#38611yescharacteristic
460C22×C61#38611yescharacteristic
461C22×C61#38611yescharacteristic
462C22×C61#38611yescharacteristic
463C22×C61#38611yescharacteristic
464C22×C61#38611yescharacteristic
465C22×C61#38611yescharacteristic
466C22×C61#38611yescharacteristic
467C22×C61C22×C22⋊C411yescharacteristic
468C22×C61C2×C4×D411yescharacteristic
469C22×C61C2×C4×D411yescharacteristic
470C22×C61C2×#12011yescharacteristic
471C22×C61C2×#12111yescharacteristic
472C22×C61C2×#12111yescharacteristic
473C22×C61C2×#12311yescharacteristic
474C2×D61—24no—
475C2×D61—44no—
476C2×D61—44no—
477C2×D61—44no—
478C2×D61—44no—
479C2×D61—44no—
480C2×D61—42no—
481C2×D61—82no—
482C2×D61—82no—
483C2×D61—82no—
484C2×D61—82no—
485C2×D61—82no—
486C2×D61—82no—
487C2×D61—82no—
488C2×D61—82no—
489C2×D61—82no—
490C4×C61—44no—
491C4×C61—44no—
492C4×C61—82no—
493Dic61—24no—
494Dic61—44no—
495Dic61—42no—
496Dic61—82no—
497C2×#534—611no—
498C2×#518—611no—
499C22×#99—611no—
500C22×#99—611no—
501C22×#99—611no—
502#1913—618no—
503C2×#342—611no—
504C2×#342D6111yescharacteristic, complemented
505C2×C61—21no—
506C2×C61—21no—
507C2×C61—21no—
508C2×C61—21no—
509C2×C61—21no—
510C2×C61—21no—
511C2×C61—21no—
512C2×C61—21no—
513C2×C61—21no—
514C2×C61—21no—
515C2×C61—21no—
516C2×C61—21no—
517C2×C61—21no—
518C2×C61—21no—
519C2×C61#191312yescomplemented
520C2×C61C2×#38611yescharacteristic
521D61—44no—
522D61—82no—
523C23×D4—611no—
524C23×D4—611no—
525#534—614no—
526#534—614no—
527#534—1222no—
528#534—1222no—
529C2×#123—612no—
530C2×#123—1221no—
531C2×#121—1222no—
532C2×#120—612no—
533C2×#120—1221no—
534#518—614no—
535#518—1222no—
536#518—1222no—
537#518—1222no—
538C2×C4×D4—1222no—
539C2×C4×D4—1222no—
540C2×#117—1221no—
541C22×C22⋊C4—611no—
542C22×C22⋊C4—611no—
543C22×C22⋊C4—1221no—
544C22×C22⋊C4C2×D6111yescharacteristic
545C22×C22⋊C4C2×D6111yescharacteristic
546C22×C22⋊C4C2×D6111yescharacteristic
547C2×#99—614no—
548C2×#99—614no—
549C2×#99—614no—
550C2×#99—1222no—
551C2×#99—1222no—
552C2×#99—1222no—
553C2×#99—1222no—
554C2×#99—1222no—
555C2×#99—1222no—
556#342—614no—
557#342C2×D6114yescomplemented
558C61C2×#191311yescharacteristic, complemented, Sylow
559C25—611no—
560C25—611no—
561C25C22×D6111yescharacteristic
562C22×D4—612no—
563C22×D4—612no—
564C22×D4—612no—
565C22×D4—612no—
566C22×D4—612no—
567C22×D4—612no—
568C22×D4—612no—
569C22×D4—612no—
570C22×D4—1222no—
571C22×D4—1221no—
572C22×D4—1221no—
573C22×D4—1221no—
574C22×D4—1221no—
575C22×D4—1221no—
576C22×D4—1221no—
577C22×D4—1221no—
578C22×D4—1221no—
579C22×D4—1221no—
580C22×D4—1221no—
581C22×D4—1221no—
582C22×D4—1221no—
583C22×D4—1221no—
584C22×D4—1221no—
585C22×D4—1221no—
586C22×D4—1221no—
587C22×D4—1221no—
588C22×D4—1221no—
589C22×D4—1221no—
590C22×D4—1221no—
591C23×C4—21no—
592C23×C4—21no—
593C23×C4—21no—
594C23×C4—611no—
595C23×C4—611no—
596C23×C4—1222no—
597C23×C4—1221no—
598C23×C4—1221no—
599#123—618no—
600#123—1224no—
601#123—1224no—
602#123—1224no—
603#121—1228no—
604#121—1228no—
605#120—618no—
606#120—1224no—
607#120—1224no—
608#120—1224no—
609C4×D4—1228no—
610C4×D4—1228no—
611C4×D4—1228no—
612C4×D4—1228no—
613#117—1224no—
614#117—1224no—
615C2×C4⋊C4—1222no—
616C2×C4⋊C4—1222no—
617C2×C22⋊C4—21no—
618C2×C22⋊C4—21no—
619C2×C22⋊C4—21no—
620C2×C22⋊C4—21no—
621C2×C22⋊C4—21no—
622C2×C22⋊C4—21no—
623C2×C22⋊C4—21no—
624C2×C22⋊C4—21no—
625C2×C22⋊C4—21no—
626C2×C22⋊C4—21no—
627C2×C22⋊C4—21no—
628C2×C22⋊C4—612no—
629C2×C22⋊C4—612no—
630C2×C22⋊C4—612no—
631C2×C22⋊C4—612no—
632C2×C22⋊C4—1224no—
633C2×C22⋊C4—1224no—
634C2×C22⋊C4—1222no—
635C2×C22⋊C4—1222no—
636C2×C22⋊C4—1222no—
637C2×C22⋊C4—1221no—
638C2×C22⋊C4—1221no—
639C2×C22⋊C4—1221no—
640C2×C22⋊C4—1221no—
641C2×C22⋊C4—1221no—
642C2×C22⋊C4—1221no—
643C2×C22⋊C4—1221no—
644C2×C22⋊C4—1221no—
645C2×C22⋊C4C4×D6112yescomplemented
646C2×C22⋊C4C4×D6112yescomplemented
647C2×C22⋊C4D24412yescomplemented
648C2×C22⋊C4D24412yescomplemented
649C2×C22⋊C4C22×D6112yes—
650C2×C22⋊C4C22×D6112yes—
651C2×C22⋊C4C22×D6112yes—
652C2×C42—1222no—
653#99—1228no—
654#99—1228no—
655#99—1228no—
656C24—82no—
657C24—612no—
658C24—612no—
659C24—612no—
660C24—612no—
661C24—1221no—
662C24—1221no—
663C24—1221no—
664C24—1221no—
665C24—1221no—
666C24—1221no—
667C24—1221no—
668C24—1221no—
669C24—1221no—
670C24—1221no—
671C24—4882no—
672C24—4882no—
673C24C2×C4×D6111yescharacteristic
674C24C2×C4×D6111yescharacteristic
675C24C2×D24411yescharacteristic
676C24C2×D24411yescharacteristic
677C24#1175822211yescharacteristic
678C24#1175822211yescharacteristic
679C24D4×D6111yescharacteristic
680C24D4×D6111yescharacteristic
681C24D4×D6111yescharacteristic
682C24D4×D6111yescharacteristic
683C24D4×D6111yescharacteristic
684C24D4×D6111yescharacteristic
685C24#1175822611yescharacteristic
686C24#1175822611yescharacteristic
687C24C23×D6111yescharacteristic
688C2×D4—614no—
689C2×D4—614no—
690C2×D4—614no—
691C2×D4—614no—
692C2×D4—1228no—
693C2×D4—1222no—
694C2×D4—1222no—
695C2×D4—1222no—
696C2×D4—1222no—
697C2×D4—1222no—
698C2×D4—1222no—
699C2×D4—1222no—
700C2×D4—1222no—
701C2×D4—1222no—
702C2×D4—1222no—
703C2×D4—1222no—
704C2×D4—1222no—
705C2×D4—1222no—
706C2×D4—1222no—
707C2×D4—1222no—
708C2×D4—1222no—
709C2×D4—1222no—
710C2×D4—1222no—
711C2×D4—1222no—
712C2×D4—1222no—
713C2×D4—1222no—
714C2×D4—1222no—
715C2×D4—1222no—
716C2×D4—1222no—
717C2×D4—1222no—
718C2×D4—1222no—
719C2×D4—1222no—
720C2×D4—1222no—
721C2×D4—1222no—
722C2×D4—1222no—
723C2×D4—1222no—
724C2×D4—1222no—
725C2×D4—1222no—
726C2×D4—1222no—
727C2×D4—1222no—
728C2×D4—1222no—
729C2×D4—4884no—
730C2×D4—2441no—
731C2×D4—2441no—
732C2×D4—2441no—
733C2×D4—2441no—
734C2×D4—2441no—
735C2×D4—2441no—
736C2×D4—2441no—
737C2×D4—2441no—
738C2×D4—2441no—
739C2×D4—2441no—
740C2×D4—2441no—
741C2×D4—2441no—
742C2×D4—2441no—
743C2×D4—2441no—
744C2×D4—2441no—
745C2×D4—2441no—
746C22×C4—22no—
747C22×C4—22no—
748C22×C4—22no—
749C22×C4—22no—
750C22×C4—22no—
751C22×C4—22no—
752C22×C4—22no—
753C22×C4—41no—
754C22×C4—41no—
755C22×C4—82no—
756C22×C4—82no—
757C22×C4—82no—
758C22×C4—612no—
759C22×C4—612no—
760C22×C4—612no—
761C22×C4—612no—
762C22×C4—1228no—
763C22×C4—1221no—
764C22×C4—1221no—
765C22×C4—1221no—
766C22×C4—1221no—
767C22×C4—1222no—
768C22×C4—1222no—
769C22×C4—1221no—
770C22×C4—1221no—
771C22×C4—1221no—
772C22×C4—1221no—
773C22×C4—1221no—
774C22×C4—1221no—
775C22×C4—1222no—
776C22×C4—1222no—
777C22×C4—4884no—
778C22×C4—4882no—
779C22×C4—4882no—
780C22×C4—2441no—
781C22×C4—2441no—
782C4⋊C4—1228no—
783C4⋊C4—1228no—
784C22⋊C4—22no—
785C22⋊C4—22no—
786C22⋊C4—22no—
787C22⋊C4—22no—
788C22⋊C4—22no—
789C22⋊C4—22no—
790C22⋊C4—22no—
791C22⋊C4—22no—
792C22⋊C4—41no—
793C22⋊C4—41no—
794C22⋊C4—614no—
795C22⋊C4—1228no—
796C22⋊C4—1228no—
797C22⋊C4—1228no—
798C22⋊C4—1222no—
799C22⋊C4—1222no—
800C22⋊C4—1222no—
801C22⋊C4—1222no—
802C22⋊C4—1222no—
803C22⋊C4—2441no—
804C22⋊C4—2441no—
805C22⋊C4C2×C4×D6114yescomplemented
806C22⋊C4C2×D24414yescomplemented
807C42—1228no—
808C23—42no—
809C23—42no—
810C23—42no—
811C23—42no—
812C23—42no—
813C23—42no—
814C23—42no—
815C23—81no—
816C23—81no—
817C23—81no—
818C23—81no—
819C23—81no—
820C23—81no—
821C23—81no—
822C23—81no—
823C23—614no—
824C23—1222no—
825C23—1222no—
826C23—1222no—
827C23—1222no—
828C23—1222no—
829C23—1222no—
830C23—1222no—
831C23—1222no—
832C23—1222no—
833C23—4882no—
834C23—4882no—
835C23—4882no—
836C23—4882no—
837C23—4882no—
838C23—4882no—
839C23—4882no—
840C23—4882no—
841C23—4882no—
842C23—4882no—
843C23—4882no—
844C23—2444no—
845C23—2444no—
846C23—2444no—
847C23—2441no—
848C23—2441no—
849C23—2441no—
850C23—2441no—
851C23C22⋊C4×D6111yescharacteristic
852C23C22⋊C4×D6111yescharacteristic
853C23C22⋊C4×D6111yescharacteristic
854C23C22⋊C4×D6111yescharacteristic
855C23#1451973911yescharacteristic
856C23#1451973911yescharacteristic
857C23#1451973911yescharacteristic
858C23#1451973911yescharacteristic
859C23C4×D24411yescharacteristic
860C23C4×D24411yescharacteristic
861C23C4×D24411yescharacteristic
862C23C4×D24411yescharacteristic
863C23#1451974711yescharacteristic
864C23#1451974711yescharacteristic
865C23#1451974711yescharacteristic
866C23#1451974711yescharacteristic
867C23#1451975011yescharacteristic
868C23#1451975011yescharacteristic
869C23#1451975011yescharacteristic
870C23#1451975011yescharacteristic
871C23#1451975211yescharacteristic
872C23#1451975211yescharacteristic
873C23#1451975211yescharacteristic
874C23#1451975211yescharacteristic
875C23#1451976211yescharacteristic
876C23#1451976211yescharacteristic
877C23#1451976211yescharacteristic
878C23#1451976211yescharacteristic
879C23C22×C4×D6111yescharacteristic
880C23C2×D4×D6111yescharacteristic
881C23C2×D4×D6111yescharacteristic
882C23C2×D4×D6111yescharacteristic
883C23C22×D24411yescharacteristic
884C23C2×#1175822211yescharacteristic
885C23C2×#1175822611yescharacteristic
886D4—1224no—
887D4—1224no—
888D4—1224no—
889D4—1224no—
890D4—1224no—
891D4—1224no—
892D4—1224no—
893D4—1224no—
894D4—4888no—
895D4—2442no—
896D4—2442no—
897D4—2442no—
898D4—2442no—
899D4—2442no—
900D4—2442no—
901D4—2442no—
902D4—2442no—
903C2×C4—24no—
904C2×C4—24no—
905C2×C4—44no—
906C2×C4—44no—
907C2×C4—42no—
908C2×C4—82no—
909C2×C4—82no—
910C2×C4—82no—
911C2×C4—82no—
912C2×C4—82no—
913C2×C4—82no—
914C2×C4—82no—
915C2×C4—614no—
916C2×C4—1222no—
917C2×C4—1222no—
918C2×C4—1222no—
919C2×C4—1222no—
920C2×C4—1222no—
921C2×C4—1222no—
922C2×C4—1222no—
923C2×C4—1222no—
924C2×C4—1222no—
925C2×C4—1224no—
926C2×C4—4888no—
927C2×C4—4882no—
928C2×C4—4882no—
929C2×C4—4882no—
930C2×C4—4882no—
931C2×C4—4882no—
932C2×C4—2442no—
933C2×C4—2444no—
934C2×C4—2441no—
935C2×C4—2441no—
936C2×C4—2441no—
937C2×C4—2441no—
938C22—22no—
939C22—22no—
940C22—22no—
941C22—22no—
942C22—22no—
943C22—22no—
944C22—22no—
945C22—41no—
946C22—41no—
947C22—41no—
948C22—41no—
949C22—41no—
950C22—41no—
951C22—41no—
952C22—41no—
953C22—41no—
954C22—41no—
955C22—41no—
956C22—41no—
957C22—41no—
958C22—41no—
959C22—41no—
960C22—41no—
961C22—41no—
962C22—41no—
963C22—41no—
964C22—41no—
965C22—41no—
966C22—41no—
967C22—41no—
968C22—41no—
969C22—41no—
970C22—41no—
971C22—41no—
972C22—41no—
973C22—1224no—
974C22—4882no—
975C22—4882no—
976C22—4882no—
977C22—4882no—
978C22—4882no—
979C22—4882no—
980C22—4882no—
981C22—4882no—
982C22—4882no—
983C22—2444no—
984C22—2444no—
985C22—2444no—
986C22—2444no—
987C22—2442no—
988C22—2444no—
989C22#1683964011yescharacteristic
990C22#1683964011yescharacteristic
991C22#1683964011yescharacteristic
992C22#1683964011yescharacteristic
993C22#1683964011yescharacteristic
994C22#1683964011yescharacteristic
995C22#1683964011yescharacteristic
996C22#1683964011yescharacteristic
997C22C2×C22⋊C4×D6111yescharacteristic
998C22C2×#1451973911yescharacteristic
999C22C2×C4×D24411yescharacteristic
1000C22C2×#1451974711yescharacteristic
1001C22C2×#1451975011yescharacteristic
1002C22C2×#1451975211yescharacteristic
1003C22C2×#1451976211yescharacteristic
1004C4—44no—
1005C4—44no—
1006C4—82no—
1007C4—1224no—
1008C4—4882no—
1009C4—2444no—
1010C4—2442no—
1011C2—21no—
1012C2—21no—
1013C2—21no—
1014C2—21no—
1015C2—21no—
1016C2—21no—
1017C2—21no—
1018C2—21no—
1019C2—21no—
1020C2—21no—
1021C2—21no—
1022C2—21no—
1023C2—21no—
1024C2—21no—
1025C2—4882no—
1026C2—2444no—
1027C2#2144636012yesdirect product factor
1028C2C2×#1683964011yescharacteristic
subgroupG/H
centerC22#16839640
commutatorC23×C61C23×C4
FrattiniC24C23×D61
FittingC2×C61×#342C2
socleC22×C61#386
prime radicalC2×#16840324C2
cosocleC24×C61C24
hypercenterC2×#342D61
hypocenterC61C2×#1913
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C25 ◁ C2×#342

Complements

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

NH ≅ G/Ntype
2. C2×#16840235C2semidirect
3. C22×#14519691C2semidirect
4. C22×#14519691C2semidirect
5. C22×#14519691C2semidirect
6. #21446360C2direct (N × H)
7. C2×#16839528C2semidirect
8. C2×C61×#342C2semidirect
13. #16840324C4semidirect
16. C2×#14519761C4semidirect
19. C2×#14519747C4semidirect
23. #16840235C22semidirect
36. C2×#14519691C22semidirect
37. C2×#14519691C22semidirect
38. C2×#14519691C22semidirect
39. #16839528C22semidirect
43. C61×#342C22semidirect
44. C24×D61C2×C4semidirect
69. C22×C22⋊D61C2×C4semidirect
77. C23×Dic61C2×C4semidirect
83. #14519761C2×C4semidirect
89. #14519747C2×C4semidirect
106. C2×C22⋊Dic61D4semidirect
107. C2×C22⋊Dic61D4semidirect
134. C2×C22⋊C4×C61C2×C4semidirect
135. C2×C22⋊C4×C61C2×C4semidirect
136. C2×C22⋊C4×C61D4semidirect
137. C2×C22⋊C4×C61D4semidirect
171. C23×D61C22×C4semidirect
261. C22×Dic61C22×C4semidirect
277. C22⋊C4×C61C22×C4semidirect
278. C22⋊C4×C61C2×D4semidirect
286. C22⋊Dic61C2×D4semidirect
504. C2×#342D61semidirect
519. C2×C61#1913semidirect
557. #342C2×D61semidirect
558. C61C2×#1913semidirect
645. C2×C22⋊C4C4×D61semidirect
646. C2×C22⋊C4C4×D61semidirect
647. C2×C22⋊C4D244semidirect
648. C2×C22⋊C4D244semidirect
805. C22⋊C4C2×C4×D61semidirect
806. C22⋊C4C2×D244semidirect
1027. C2#21446360direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168403242
C2×#168402352
C22×#145196912
#214463602
C2×#168395282
C2×C61×#3422
C2×#191361