Finite Group Databasebeta

← C2×#21446358 #29682021

Subgroups — C2×#21446358 #29682021

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×#16840321C211yesmaximal, characteristic
2C2×#16840235C211yesmaximal, characteristic, complemented
3C22×#14519692C211yesmaximal, characteristic, complemented
4C22×#14519691C211yesmaximal, characteristic, complemented
5#21446358C218yesmaximal, direct product factor
6C2×#16839529C211yesmaximal, characteristic, complemented
7C2×#16839528C211yesmaximal, characteristic, complemented
8C22×#99×C61C211yesmaximal, characteristic, complemented
9C23×C22⋊D61C2211yescharacteristic
10#16840321—22no—
11#16840321—22no—
12#16840321C414yescomplemented
13#16840321C2214yes—
14C2×#14519760C412yescomplemented
15C2×#14519758—21no—
16C2×#14519749—22no—
17C2×#14519746C412yescomplemented
18C2×#14519745—21no—
19#16840235—22no—
20#16840235—22no—
21#16840235—22no—
22#16840235C2214yescomplemented
23C2×C4×C22⋊D61—22no—
24C2×#14519737—22no—
25C2×#14519733—21no—
26C22×C22⋊Dic61C2211yescharacteristic
27C22×C22⋊Dic61C2211yescharacteristic
28C22×C22⋊Dic61C2211yescharacteristic
29C2×C22⋊C4×D61—21no—
30C2×#14519692—22no—
31C2×#14519692—22no—
32C2×#14519692C2214yescomplemented
33C2×#14519691—22no—
34C2×#14519691—22no—
35C2×#14519691C2214yescomplemented
36#16839529C2214yescomplemented
37#16839528C2214yescomplemented
38C23×D4×C61C2211yescharacteristic
39C22×C22⋊C4×C61C2211yescharacteristic
40C22×C22⋊C4×C61C2211yescharacteristic
41C2×#99×C61—22no—
42C2×#99×C61—22no—
43C2×#99×C61C2214yescomplemented
44C24×D61D411yescharacteristic
45C22×C22⋊D61—21no—
46C22×C22⋊D61—21no—
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—22no—
54C22×C22⋊D61C2×C412yes—
55C22×C22⋊D61C2×C412yes—
56C22×C22⋊D61D412yes—
57C22×C22⋊D61D412yes—
58C22×C22⋊D61D412yes—
59C22×C22⋊D61C2312yes—
60C23×Dic61—21no—
61C23×Dic61—21no—
62C23×Dic61—21no—
63C23×Dic61D411yescharacteristic
64C22×C4×D61—22no—
65#14519760—24no—
66#14519760C2×C418yescomplemented
67#14519758—24no—
68#14519758—24no—
69#14519749—28no—
70#14519749—28no—
71#14519746—24no—
72#14519746C2×C418yescomplemented
73#14519745—24no—
74#14519745—24no—
75C4×C22⋊D61—28no—
76C4×C22⋊D61—28no—
77#14519737—28no—
78#14519737—28no—
79#14519733—24no—
80#14519733—24no—
81C2×#11758196—22no—
82C2×#11758196—22no—
83C2×C22⋊Dic61—21no—
84C2×C22⋊Dic61—21no—
85C2×C22⋊Dic61—21no—
86C2×C22⋊Dic61—21no—
87C2×C22⋊Dic61—21no—
88C2×C22⋊Dic61—21no—
89C2×C22⋊Dic61—22no—
90C2×C22⋊Dic61—21no—
91C2×C22⋊Dic61—21no—
92C2×C22⋊Dic61—21no—
93C2×C22⋊Dic61—21no—
94C2×C22⋊Dic61—21no—
95C2×C22⋊Dic61C2×C412yescomplemented
96C2×C22⋊Dic61C2×C412yescomplemented
97C2×C22⋊Dic61D412yescomplemented
98C2×C22⋊Dic61D412yescomplemented
99C2×C22⋊Dic61C2312yes—
100C2×C22⋊Dic61C2312yes—
101C2×C22⋊Dic61C2312yes—
102C2×#11758198—22no—
103C2×#11758198—22no—
104C22⋊C4×D61—24no—
105C22⋊C4×D61—24no—
106C2×C4×Dic61—22no—
107#14519692—28no—
108#14519691—28no—
109C25×C61C2×C411yescharacteristic, complemented
110C25×C61C2311yescharacteristic
111C22×D4×C61—21no—
112C22×D4×C61—21no—
113C22×D4×C61—21no—
114C22×D4×C61—21no—
115C22×D4×C61—21no—
116C22×D4×C61—21no—
117C22×D4×C61—21no—
118C22×D4×C61—21no—
119C22×D4×C61—21no—
120C22×D4×C61—21no—
121C22×D4×C61—21no—
122C22×D4×C61—21no—
123C22×D4×C61C2×C412yescomplemented
124C22×D4×C61C2312yes—
125C23×C4×C61—21no—
126C23×C4×C61—21no—
127C23×C4×C61C2×C411yescharacteristic, complemented
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×C61—21no—
135C2×C22⋊C4×C61—21no—
136C2×C22⋊C4×C61D412yescomplemented
137C2×C22⋊C4×C61D412yescomplemented
138C2×C22⋊C4×C61C2312yes—
139C2×C22⋊C4×C61C2312yes—
140#99×C61—28no—
141C24×C61—21no—
142C24×C61—21no—
143C24×C61—21no—
144C24×C61—21no—
145C24×C61—21no—
146C24×C61—21no—
147C24×C61—82no—
148C24×C61—82no—
149C24×C61C22×C411yescharacteristic
150C24×C61C22×C411yescharacteristic
151C24×C61C22×C412yescomplemented
152C24×C61C2×D411yescharacteristic
153C24×C61C2×D411yescharacteristic
154C24×C61C2×D411yescharacteristic
155C24×C61C2×D411yescharacteristic
156C24×C61C2×D411yescharacteristic
157C24×C61C2×D411yescharacteristic
158C24×C61C2×D411yescharacteristic
159C24×C61C2×D411yescharacteristic
160C24×C61#4111yescharacteristic
161C24×C61#4111yescharacteristic
162C24×C61#4111yescharacteristic
163C24×C61#4111yescharacteristic
164C24×C61C2411yescharacteristic
165C23×D61—21no—
166C23×D61—21no—
167C23×D61—21no—
168C23×D61—21no—
169C23×D61—82no—
170C23×D61C22⋊C412yes—
171C23×D61C22⋊C412yes—
172C23×D61C2×D412yes—
173C2×D4×C61—22no—
174C2×D4×C61—22no—
175C2×D4×C61—22no—
176C2×D4×C61—22no—
177C2×D4×C61—22no—
178C2×D4×C61—22no—
179C2×D4×C61—22no—
180C2×D4×C61—22no—
181C2×D4×C61—22no—
182C2×D4×C61—22no—
183C2×D4×C61—22no—
184C2×D4×C61—22no—
185C2×D4×C61—41no—
186C2×D4×C61—41no—
187C2×D4×C61—41no—
188C2×D4×C61—41no—
189C2×D4×C61—41no—
190C2×D4×C61—41no—
191C2×D4×C61—41no—
192C2×D4×C61—41no—
193C2×D4×C61—41no—
194C2×D4×C61—41no—
195C2×D4×C61—41no—
196C2×D4×C61—41no—
197C2×D4×C61—41no—
198C2×D4×C61—41no—
199C2×D4×C61—41no—
200C2×D4×C61—41no—
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—22no—
208C22×C4×C61—22no—
209C22×C4×C61—22no—
210C22×C4×C61—22no—
211C22×C4×C61—41no—
212C22×C4×C61—41no—
213C22×C4×C61—82no—
214C22×C4×C61—82no—
215C22×C4×C61C22×C412yescomplemented
216C2×C22⋊D61—22no—
217C2×C22⋊D61—22no—
218C2×C22⋊D61—22no—
219C2×C22⋊D61—22no—
220C2×C22⋊D61—22no—
221C2×C22⋊D61—22no—
222C2×C22⋊D61—22no—
223C2×C22⋊D61—22no—
224C2×C22⋊D61—22no—
225C2×C22⋊D61—22no—
226C2×C22⋊D61—22no—
227C2×C22⋊D61—22no—
228C2×C22⋊D61—22no—
229C2×C22⋊D61—22no—
230C2×C22⋊D61—22no—
231C2×C22⋊D61—22no—
232C2×C22⋊D61—22no—
233C2×C22⋊D61—22no—
234C2×C22⋊D61—22no—
235C2×C22⋊D61—22no—
236C2×C22⋊D61—22no—
237C2×C22⋊D61—22no—
238C2×C22⋊D61—22no—
239C2×C22⋊D61—22no—
240C2×C22⋊D61—28no—
241C2×C22⋊D61—84no—
242C2×C22⋊D61C22⋊C414yes—
243C2×C22⋊D61C22⋊C414yes—
244C2×C22⋊D61C22×C414yes—
245C2×C22⋊D61C2×D414yes—
246C22×Dic61—21no—
247C22×Dic61—21no—
248C22×Dic61—21no—
249C22×Dic61—21no—
250C22×Dic61—22no—
251C22×Dic61—22no—
252C22×Dic61—22no—
253C22×Dic61—22no—
254C22×Dic61—22no—
255C22×Dic61—22no—
256C22×Dic61—22no—
257C22×Dic61—41no—
258C22×Dic61—41no—
259C22×Dic61—82no—
260C22×Dic61—82no—
261C22×Dic61—82no—
262C22×Dic61C22⋊C412yes—
263C22×Dic61C22⋊C412yes—
264C22×Dic61C2×D412yes—
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—41no—
273C22⋊C4×C61—41no—
274C22⋊C4×C61C2×D414yescomplemented
275C22⋊Dic61—22no—
276C22⋊Dic61—22no—
277C22⋊Dic61—22no—
278C22⋊Dic61—22no—
279C22⋊Dic61—22no—
280C22⋊Dic61—22no—
281C22⋊Dic61—28no—
282C22⋊Dic61—22no—
283C22⋊Dic61—22no—
284C22⋊Dic61—41no—
285C22⋊Dic61—41no—
286C22⋊Dic61C22×C414yescomplemented
287C22⋊Dic61C2×D414yescomplemented
288#11758198—28no—
289#11758198—28no—
290#11758196—28no—
291#11758196—28no—
292C4×Dic61—28no—
293C23×C61—22no—
294C23×C61—22no—
295C23×C61—22no—
296C23×C61—42no—
297C23×C61—42no—
298C23×C61—42no—
299C23×C61—42no—
300C23×C61—42no—
301C23×C61—42no—
302C23×C61—42no—
303C23×C61—44no—
304C23×C61—41no—
305C23×C61—41no—
306C23×C61—41no—
307C23×C61—41no—
308C23×C61—82no—
309C23×C61—82no—
310C23×C61—81no—
311C23×C61—81no—
312C23×C61—81no—
313C23×C61—81no—
314C23×C61—81no—
315C23×C61—81no—
316C23×C61—81no—
317C23×C61—81no—
318C23×C61—82no—
319C23×C61—82no—
320C23×C61—82no—
321C23×C61—82no—
322C23×C61C2×C22⋊C411yescharacteristic
323C23×C61C2×C22⋊C411yescharacteristic
324C23×C61C2×C22⋊C411yescharacteristic
325C23×C61C2×C22⋊C411yescharacteristic
326C23×C61C4×D411yescharacteristic
327C23×C61C4×D411yescharacteristic
328C23×C61C4×D411yescharacteristic
329C23×C61C4×D411yescharacteristic
330C23×C61C4×D411yescharacteristic
331C23×C61C4×D411yescharacteristic
332C23×C61C4×D411yescharacteristic
333C23×C61C4×D411yescharacteristic
334C23×C61#12011yescharacteristic
335C23×C61#12011yescharacteristic
336C23×C61#12011yescharacteristic
337C23×C61#12011yescharacteristic
338C23×C61#12111yescharacteristic
339C23×C61#12111yescharacteristic
340C23×C61#12111yescharacteristic
341C23×C61#12111yescharacteristic
342C23×C61#12111yescharacteristic
343C23×C61#12111yescharacteristic
344C23×C61#12111yescharacteristic
345C23×C61#12111yescharacteristic
346C23×C61#12311yescharacteristic
347C23×C61#12311yescharacteristic
348C23×C61#12311yescharacteristic
349C23×C61#12311yescharacteristic
350C23×C61C23×C411yescharacteristic
351C23×C61C22×D411yescharacteristic
352C23×C61C22×D411yescharacteristic
353C23×C61C22×D411yescharacteristic
354C23×C61C22×D411yescharacteristic
355C23×C61C2×#4111yescharacteristic
356C23×C61C2×#4111yescharacteristic
357C22×D61—22no—
358C22×D61—22no—
359C22×D61—22no—
360C22×D61—22no—
361C22×D61—22no—
362C22×D61—22no—
363C22×D61—44no—
364C22×D61—44no—
365C22×D61—82no—
366C22×D61—82no—
367C22×D61—82no—
368C22×D61—82no—
369C22×D61—82no—
370C22×D61C2×C22⋊C414yes—
371D4×C61—42no—
372D4×C61—42no—
373D4×C61—42no—
374D4×C61—42no—
375D4×C61—42no—
376D4×C61—42no—
377D4×C61—42no—
378D4×C61—42no—
379C2×C4×C61—22no—
380C2×C4×C61—22no—
381C2×C4×C61—22no—
382C2×C4×C61—24no—
383C2×C4×C61—44no—
384C2×C4×C61—41no—
385C2×C4×C61—41no—
386C2×C4×C61—41no—
387C2×C4×C61—41no—
388C2×C4×C61—42no—
389C2×C4×C61—82no—
390C2×C4×C61—82no—
391C2×C4×C61—82no—
392C2×C4×C61—82no—
393C2×C4×C61—82no—
394C22⋊D61—24no—
395C22⋊D61—24no—
396C22⋊D61—24no—
397C22⋊D61—24no—
398C22⋊D61—24no—
399C22⋊D61—24no—
400C22⋊D61—24no—
401C22⋊D61—24no—
402C22⋊D61—88no—
403C2×Dic61—22no—
404C2×Dic61—22no—
405C2×Dic61—22no—
406C2×Dic61—22no—
407C2×Dic61—22no—
408C2×Dic61—22no—
409C2×Dic61—24no—
410C2×Dic61—24no—
411C2×Dic61—44no—
412C2×Dic61—44no—
413C2×Dic61—42no—
414C2×Dic61—82no—
415C2×Dic61—82no—
416C2×Dic61—82no—
417C2×Dic61—82no—
418C2×Dic61—82no—
419C2×Dic61—82no—
420C2×Dic61—82no—
421C2×Dic61C2×C22⋊C414yes—
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—44no—
460C22×C61—42no—
461C22×C61—82no—
462C22×C61—82no—
463C22×C61—82no—
464C22×C61—82no—
465C22×C61—82no—
466C22×C61—82no—
467C22×C61#38611yescharacteristic
468C22×C61#38611yescharacteristic
469C22×C61#38611yescharacteristic
470C22×C61#38611yescharacteristic
471C22×C61#38611yescharacteristic
472C22×C61#38611yescharacteristic
473C22×C61#38611yescharacteristic
474C22×C61#38611yescharacteristic
475C22×C61C22×C22⋊C411yescharacteristic
476C22×C61C2×C4×D411yescharacteristic
477C22×C61C2×C4×D411yescharacteristic
478C22×C61C2×#12011yescharacteristic
479C22×C61C2×#12111yescharacteristic
480C22×C61C2×#12111yescharacteristic
481C22×C61C2×#12311yescharacteristic
482C2×D61—24no—
483C2×D61—44no—
484C2×D61—44no—
485C2×D61—44no—
486C2×D61—44no—
487C2×D61—82no—
488C2×D61—82no—
489C2×D61—82no—
490C4×C61—44no—
491C4×C61—42no—
492C4×C61—82no—
493Dic61—24no—
494Dic61—44no—
495Dic61—44no—
496Dic61—82no—
497C2×#534—611no—
498C2×#518—611no—
499C22×#99—611no—
500C22×#99—611no—
501C22×#99D6111yescharacteristic, complemented
502#1913—618no—
503C2×#342—611no—
504C2×#342—611no—
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—82no—
520C2×C61#191312yescomplemented
521C2×C61C2×#38611yescharacteristic
522D61—44no—
523C23×D4—611no—
524C23×D4C2×D6111yescharacteristic
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—611no—
544C22×C22⋊C4—1221no—
545C22×C22⋊C4C2×D6111yescharacteristic
546C22×C22⋊C4C2×D6111yescharacteristic
547C2×#99—22no—
548C2×#99—22no—
549C2×#99—614no—
550C2×#99—614no—
551C2×#99—1222no—
552C2×#99—1222no—
553C2×#99—1222no—
554C2×#99—1222no—
555C2×#99C2×D6114yescomplemented
556#342—614no—
557#342—614no—
558C61C2×#191311yescharacteristic, complemented, Sylow
559C25—611no—
560C25C4×D6111yescharacteristic, complemented
561C25C22×D6111yescharacteristic
562C22×D4—21no—
563C22×D4—21no—
564C22×D4—21no—
565C22×D4—21no—
566C22×D4—21no—
567C22×D4—21no—
568C22×D4—21no—
569C22×D4—21no—
570C22×D4—21no—
571C22×D4—21no—
572C22×D4—21no—
573C22×D4—21no—
574C22×D4—612no—
575C22×D4—612no—
576C22×D4—612no—
577C22×D4—612no—
578C22×D4—612no—
579C22×D4—612no—
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—1222no—
589C22×D4C4×D6112yescomplemented
590C22×D4C22×D6112yes—
591C23×C4—21no—
592C23×C4—21no—
593C23×C4—611no—
594C23×C4—1222no—
595C23×C4—1221no—
596C23×C4—1221no—
597C23×C4—1221no—
598C23×C4C4×D6111yescharacteristic, complemented
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—612no—
626C2×C22⋊C4—612no—
627C2×C22⋊C4—612no—
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⋊C4—1221no—
646C2×C22⋊C4—1221no—
647C2×C22⋊C4—1221no—
648C2×C22⋊C4C22⋊D6112yescomplemented
649C2×C22⋊C4C22⋊D6112yescomplemented
650C2×C22⋊C4C22×D6112yes—
651C2×C22⋊C4C22×D6112yes—
652C2×C42—1222no—
653#99—28no—
654#99—1228no—
655#99—1228no—
656C24—21no—
657C24—21no—
658C24—21no—
659C24—21no—
660C24—21no—
661C24—21no—
662C24—82no—
663C24—82no—
664C24—612no—
665C24—612no—
666C24—612no—
667C24—1221no—
668C24—1221no—
669C24—1221no—
670C24—1221no—
671C24—4882no—
672C24C2×C4×D6111yescharacteristic
673C24C2×C4×D6111yescharacteristic
674C24C2×C4×D6112yescomplemented
675C24#1175822211yescharacteristic
676C24#1175822211yescharacteristic
677C24D4×D6111yescharacteristic
678C24D4×D6111yescharacteristic
679C24D4×D6111yescharacteristic
680C24D4×D6111yescharacteristic
681C24D4×D6111yescharacteristic
682C24D4×D6111yescharacteristic
683C24#1175822411yescharacteristic
684C24#1175822411yescharacteristic
685C24C2×C22⋊D6111yescharacteristic
686C24C2×C22⋊D6111yescharacteristic
687C24C23×D6111yescharacteristic
688C2×D4—22no—
689C2×D4—22no—
690C2×D4—22no—
691C2×D4—22no—
692C2×D4—22no—
693C2×D4—22no—
694C2×D4—22no—
695C2×D4—22no—
696C2×D4—22no—
697C2×D4—22no—
698C2×D4—22no—
699C2×D4—22no—
700C2×D4—41no—
701C2×D4—41no—
702C2×D4—41no—
703C2×D4—41no—
704C2×D4—41no—
705C2×D4—41no—
706C2×D4—41no—
707C2×D4—41no—
708C2×D4—41no—
709C2×D4—41no—
710C2×D4—41no—
711C2×D4—41no—
712C2×D4—41no—
713C2×D4—41no—
714C2×D4—41no—
715C2×D4—41no—
716C2×D4—614no—
717C2×D4—614no—
718C2×D4—614no—
719C2×D4—614no—
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—1222no—
730C2×D4—1222no—
731C2×D4—1222no—
732C2×D4—1222no—
733C2×D4—1222no—
734C2×D4—1222no—
735C2×D4—1222no—
736C2×D4—1222no—
737C2×D4—1222no—
738C2×D4—1222no—
739C2×D4—1222no—
740C2×D4—1222no—
741C2×D4—1222no—
742C2×D4—1222no—
743C2×D4—1222no—
744C2×D4—1228no—
745C2×D4—4884no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—22no—
753C22×C4—22no—
754C22×C4—22no—
755C22×C4—22no—
756C22×C4—41no—
757C22×C4—41no—
758C22×C4—82no—
759C22×C4—82no—
760C22×C4—612no—
761C22×C4—612no—
762C22×C4—612no—
763C22×C4—1228no—
764C22×C4—1221no—
765C22×C4—1221no—
766C22×C4—1221no—
767C22×C4—1221no—
768C22×C4—1222no—
769C22×C4—1222no—
770C22×C4—1222no—
771C22×C4—1222no—
772C22×C4—1222no—
773C22×C4—1222no—
774C22×C4—1222no—
775C22×C4—4884no—
776C22×C4—4882no—
777C22×C4—4882no—
778C22×C4—4882no—
779C22×C4—2441no—
780C22×C4—2441no—
781C22×C4C2×C4×D6112yescomplemented
782C4⋊C4—1228no—
783C4⋊C4—1228no—
784C22⋊C4—22no—
785C22⋊C4—22no—
786C22⋊C4—22no—
787C22⋊C4—22no—
788C22⋊C4—22no—
789C22⋊C4—41no—
790C22⋊C4—41no—
791C22⋊C4—614no—
792C22⋊C4—614no—
793C22⋊C4—1228no—
794C22⋊C4—1228no—
795C22⋊C4—1228no—
796C22⋊C4—1222no—
797C22⋊C4—1222no—
798C22⋊C4—1222no—
799C22⋊C4—1222no—
800C22⋊C4—1222no—
801C22⋊C4—1222no—
802C22⋊C4—1222no—
803C22⋊C4—1222no—
804C22⋊C4—2441no—
805C22⋊C4—2441no—
806C22⋊C4C2×C22⋊D6114yescomplemented
807C42—1228no—
808C23—22no—
809C23—22no—
810C23—22no—
811C23—42no—
812C23—42no—
813C23—42no—
814C23—42no—
815C23—42no—
816C23—42no—
817C23—42no—
818C23—44no—
819C23—41no—
820C23—41no—
821C23—41no—
822C23—41no—
823C23—82no—
824C23—82no—
825C23—81no—
826C23—81no—
827C23—81no—
828C23—81no—
829C23—81no—
830C23—81no—
831C23—81no—
832C23—81no—
833C23—82no—
834C23—82no—
835C23—82no—
836C23—82no—
837C23—614no—
838C23—1222no—
839C23—1222no—
840C23—1222no—
841C23—1222no—
842C23—1222no—
843C23—1222no—
844C23—4882no—
845C23—4882no—
846C23—4882no—
847C23—4882no—
848C23—4882no—
849C23—2444no—
850C23—2444no—
851C23C22⋊C4×D6111yescharacteristic
852C23C22⋊C4×D6111yescharacteristic
853C23C22⋊C4×D6111yescharacteristic
854C23C22⋊C4×D6111yescharacteristic
855C23#1451973711yescharacteristic
856C23#1451973711yescharacteristic
857C23#1451973711yescharacteristic
858C23#1451973711yescharacteristic
859C23C4×C22⋊D6111yescharacteristic
860C23C4×C22⋊D6111yescharacteristic
861C23C4×C22⋊D6111yescharacteristic
862C23C4×C22⋊D6111yescharacteristic
863C23#1451974511yescharacteristic
864C23#1451974511yescharacteristic
865C23#1451974511yescharacteristic
866C23#1451974511yescharacteristic
867C23#1451974811yescharacteristic
868C23#1451974811yescharacteristic
869C23#1451974811yescharacteristic
870C23#1451974811yescharacteristic
871C23#1451975011yescharacteristic
872C23#1451975011yescharacteristic
873C23#1451975011yescharacteristic
874C23#1451975011yescharacteristic
875C23#1451975911yescharacteristic
876C23#1451975911yescharacteristic
877C23#1451975911yescharacteristic
878C23#1451975911yescharacteristic
879C23C22×C4×D6111yescharacteristic
880C23C2×D4×D6111yescharacteristic
881C23C2×D4×D6111yescharacteristic
882C23C2×D4×D6111yescharacteristic
883C23C22×C22⋊D6111yescharacteristic
884C23C2×#1175822411yescharacteristic
885C23C2×#1175822211yescharacteristic
886D4—42no—
887D4—42no—
888D4—42no—
889D4—42no—
890D4—42no—
891D4—42no—
892D4—42no—
893D4—42no—
894D4—1224no—
895D4—1224no—
896D4—1224no—
897D4—1224no—
898D4—1224no—
899D4—1224no—
900D4—1224no—
901D4—1224no—
902D4—4888no—
903C2×C4—22no—
904C2×C4—22no—
905C2×C4—22no—
906C2×C4—24no—
907C2×C4—44no—
908C2×C4—41no—
909C2×C4—41no—
910C2×C4—41no—
911C2×C4—41no—
912C2×C4—42no—
913C2×C4—82no—
914C2×C4—82no—
915C2×C4—82no—
916C2×C4—82no—
917C2×C4—82no—
918C2×C4—614no—
919C2×C4—1222no—
920C2×C4—1222no—
921C2×C4—1222no—
922C2×C4—1222no—
923C2×C4—1222no—
924C2×C4—1222no—
925C2×C4—1224no—
926C2×C4—1224no—
927C2×C4—4888no—
928C2×C4—4882no—
929C2×C4—4882no—
930C2×C4—4882no—
931C2×C4—4882no—
932C2×C4—4882no—
933C2×C4—4882no—
934C2×C4—4882no—
935C2×C4—2442no—
936C2×C4—2444no—
937C2×C4—2444no—
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—44no—
974C22—42no—
975C22—82no—
976C22—82no—
977C22—82no—
978C22—82no—
979C22—82no—
980C22—82no—
981C22—1224no—
982C22—4882no—
983C22—4882no—
984C22—4882no—
985C22—2444no—
986C22—2444no—
987C22—2444no—
988C22—2444no—
989C22#1683963811yescharacteristic
990C22#1683963811yescharacteristic
991C22#1683963811yescharacteristic
992C22#1683963811yescharacteristic
993C22#1683963811yescharacteristic
994C22#1683963811yescharacteristic
995C22#1683963811yescharacteristic
996C22#1683963811yescharacteristic
997C22C2×C22⋊C4×D6111yescharacteristic
998C22C2×#1451973711yescharacteristic
999C22C2×C4×C22⋊D6111yescharacteristic
1000C22C2×#1451974511yescharacteristic
1001C22C2×#1451974811yescharacteristic
1002C22C2×#1451975011yescharacteristic
1003C22C2×#1451975911yescharacteristic
1004C4—44no—
1005C4—42no—
1006C4—82no—
1007C4—1224no—
1008C4—4882no—
1009C4—2444no—
1010C4—2444no—
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—82no—
1026C2—2444no—
1027C2#2144635812yesdirect product factor
1028C2C2×#1683963811yescharacteristic
subgroupG/H
centerC22#16839638
commutatorC23×C61C23×C4
FrattiniC24C23×D61
FittingC22×#99×C61C2
socleC22×C61#386
prime radicalC2×#16840321C2
cosocleC24×C61C24
hypercenterC22×#99D61
hypocenterC61C2×#1913
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C25 ◁ C22×#99

Complements

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

NH ≅ G/Ntype
2. C2×#16840235C2semidirect
3. C22×#14519692C2semidirect
4. C22×#14519691C2semidirect
5. #21446358C2direct (N × H)
6. C2×#16839529C2semidirect
7. C2×#16839528C2semidirect
8. C22×#99×C61C2semidirect
12. #16840321C4semidirect
14. C2×#14519760C4semidirect
17. C2×#14519746C4semidirect
22. #16840235C22semidirect
32. C2×#14519692C22semidirect
35. C2×#14519691C22semidirect
36. #16839529C22semidirect
37. #16839528C22semidirect
43. C2×#99×C61C22semidirect
66. #14519760C2×C4semidirect
72. #14519746C2×C4semidirect
95. C2×C22⋊Dic61C2×C4semidirect
96. C2×C22⋊Dic61C2×C4semidirect
97. C2×C22⋊Dic61D4semidirect
98. C2×C22⋊Dic61D4semidirect
109. C25×C61C2×C4semidirect
123. C22×D4×C61C2×C4semidirect
127. C23×C4×C61C2×C4semidirect
136. C2×C22⋊C4×C61D4semidirect
137. C2×C22⋊C4×C61D4semidirect
151. C24×C61C22×C4semidirect
215. C22×C4×C61C22×C4semidirect
274. C22⋊C4×C61C2×D4semidirect
286. C22⋊Dic61C22×C4semidirect
287. C22⋊Dic61C2×D4semidirect
501. C22×#99D61semidirect
520. C2×C61#1913semidirect
555. C2×#99C2×D61semidirect
558. C61C2×#1913semidirect
560. C25C4×D61semidirect
589. C22×D4C4×D61semidirect
598. C23×C4C4×D61semidirect
648. C2×C22⋊C4C22⋊D61semidirect
649. C2×C22⋊C4C22⋊D61semidirect
674. C24C2×C4×D61semidirect
781. C22×C4C2×C4×D61semidirect
806. C22⋊C4C2×C22⋊D61semidirect
1027. C2#21446358direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168403212
C2×#168402352
C22×#145196922
C22×#145196912
#214463582
C2×#168395292
C2×#168395282
C22×#99×C612
C2×#191361