Finite Group Databasebeta

← C22⋊C4×#11758198 #29601413

Subgroups — C22⋊C4×#11758198 #29601413

Order 15616.

4254 conjugacy classes of subgroups.

The subgroup lattice has 966 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#11758198C211yesmaximal, characteristic
2C22×C22⋊C4×D61C211yesmaximal, characteristic
3C2×#16839617C211yesmaximal, characteristic
4C2×C22⋊C4×Dic61C211yesmaximal, characteristic, complemented
5C2×C4×#11758198C212yesmaximal, complemented
6#21444057C212yesmaximal, complemented
7#21444055C212yesmaximal, complemented
8#21444042C211yesmaximal, characteristic, complemented
9#21444041C211yesmaximal, characteristic, complemented
10#21444040C212yesmaximal, complemented
11C2×C4×C22⋊C4×C61C211yesmaximal, characteristic, complemented
12C25×D61C2211yescharacteristic
13C24×Dic61C2211yescharacteristic
14C23×C4×D61C2212yes—
15C22×C22⋊Dic61C2211yescharacteristic
16C22×C22⋊Dic61C2211yescharacteristic
17C22×#11758198—28no—
18C22×#11758198C418yescomplemented
19C22×#11758198C2211yescharacteristic
20C22×#11758198C2212yes—
21C22×#11758198C2211yescharacteristic
22C22×#11758198C2211yescharacteristic
23C22×#11758198C2212yes—
24C22×#11758198C2212yes—
25C22×#11758198C2211yescharacteristic
26C2×C22⋊C4×D61—24no—
27C2×C22⋊C4×D61—24no—
28C2×C22⋊C4×D61C418yescomplemented
29C22×C4×Dic61C2212yescomplemented
30#16839617C418yescomplemented
31C22⋊C4×Dic61—24no—
32C4×#11758198—28no—
33C2×#14519684C2212yescomplemented
34C2×#14519684C2212yescomplemented
35C2×#14519684C2212yescomplemented
36C2×#14519684C2212yescomplemented
37C2×#14519684C2212yescomplemented
38C24×C4×C61C2211yescharacteristic
39C22×C22⋊C4×C61C2211yescharacteristic
40C22×C22⋊C4×C61C2211yescharacteristic
41C22×C42×C61C2212yescomplemented
42C4×C22⋊C4×C61—24no—
43C2×#95×C61C2212yescomplemented
44C24×D61—22no—
45C24×D61—22no—
46C24×D61—22no—
47C24×D61—22no—
48C24×D61—24no—
49C24×D61—24no—
50C24×D61—42no—
51C24×D61—42no—
52C24×D61C2×C414yes—
53C24×D61C2×C414yes—
54C24×D61C2×C414yes—
55C24×D61C2311yescharacteristic
56C24×D61C2311yescharacteristic
57C23×Dic61—22no—
58C23×Dic61—22no—
59C23×Dic61—24no—
60C23×Dic61—42no—
61C23×Dic61C2×C414yescomplemented
62C23×Dic61C2312yes—
63C23×Dic61C2311yescharacteristic
64C23×Dic61C2312yes—
65C23×Dic61C2311yescharacteristic
66C22×C4×D61—24no—
67C22×C4×D61—24no—
68C22×C4×D61—24no—
69C22×C4×D61—24no—
70C22×C4×D61—42no—
71C22×C4×D61—42no—
72C22×C4×D61C2×C418yescomplemented
73C2×C22⋊Dic61—22no—
74C2×C22⋊Dic61—22no—
75C2×C22⋊Dic61—22no—
76C2×C22⋊Dic61—22no—
77C2×C22⋊Dic61C2×C414yes—
78C2×C22⋊Dic61C2×C414yescomplemented
79C2×#11758198—24no—
80C2×#11758198—24no—
81C2×#11758198—24no—
82C2×#11758198—24no—
83C2×#11758198—24no—
84C2×#11758198—24no—
85C2×#11758198—24no—
86C2×#11758198—232no—
87C2×#11758198—42no—
88C2×#11758198—42no—
89C2×#11758198C2×C414yes—
90C2×#11758198C2×C414yes—
91C2×#11758198C2×C418yescomplemented
92C2×#11758198C2×C414yescomplemented
93C2×#11758198C2×C414yescomplemented
94C2×#11758198C2×C418yescomplemented
95C2×#11758198C2×C418yescomplemented
96C2×#11758198D418yes—
97C22⋊C4×D61—232no—
98C2×C4×Dic61—24no—
99C2×C4×Dic61—24no—
100C2×C4×Dic61—42no—
101#14519684—24no—
102#14519684—24no—
103#14519684—24no—
104#14519684—42no—
105#14519684—42no—
106C25×C61C2311yescharacteristic
107C23×C4×C61—22no—
108C23×C4×C61—22no—
109C23×C4×C61—24no—
110C23×C4×C61—42no—
111C23×C4×C61C2×C414yescomplemented
112C23×C4×C61C2311yescharacteristic
113C23×C4×C61C2312yes—
114C23×C4×C61C2312yes—
115C23×C4×C61C2311yescharacteristic
116C2×C22⋊C4×C61—22no—
117C2×C22⋊C4×C61—22no—
118C2×C22⋊C4×C61C2×C414yes—
119C2×C22⋊C4×C61C2×C414yescomplemented
120C2×C22⋊C4×C61D414yes—
121C2×C22⋊C4×C61D414yes—
122C2×C42×C61—24no—
123C2×C42×C61—24no—
124C2×C42×C61—42no—
125#95×C61—24no—
126C24×C61—22no—
127C24×C61—22no—
128C24×C61—22no—
129C24×C61—22no—
130C24×C61C22×C412yes—
131C24×C61C22×C412yes—
132C24×C61C22×C412yes—
133C24×C61C2×D412yes—
134C24×C61C2×D412yes—
135C24×C61#4112yes—
136C24×C61#4112yes—
137C24×C61C2411yescharacteristic
138C23×D61—21no—
139C23×D61—21no—
140C23×D61—21no—
141C23×D61—21no—
142C23×D61—22no—
143C23×D61—22no—
144C23×D61—28no—
145C23×D61—28no—
146C23×D61—28no—
147C23×D61—28no—
148C23×D61—28no—
149C23×D61—28no—
150C23×D61—22no—
151C23×D61—21no—
152C23×D61—21no—
153C23×D61—22no—
154C23×D61—21no—
155C23×D61—21no—
156C23×D61—22no—
157C23×D61—22no—
158C23×D61—28no—
159C23×D61—28no—
160C23×D61—216no—
161C23×D61—216no—
162C23×D61—48no—
163C23×D61—48no—
164C23×D61—44no—
165C23×D61—44no—
166C23×D61—48no—
167C23×D61—48no—
168C23×D61—48no—
169C23×D61—48no—
170C23×D61—48no—
171C23×D61—48no—
172C23×D61—48no—
173C23×D61—48no—
174C23×D61C42116yescomplemented
175C23×D61C22×C412yes—
176C23×D61C22×C412yes—
177C23×D61C22×C412yes—
178C23×D61C22×C412yes—
179C23×D61C22×C412yes—
180C23×D61C22×C412yes—
181C23×D61C2×D414yes—
182C23×D61#4114yes—
183C22×C4×C61—22no—
184C22×C4×C61—21no—
185C22×C4×C61—22no—
186C22×C4×C61—21no—
187C22×C4×C61—22no—
188C22×C4×C61—22no—
189C22×C4×C61—22no—
190C22×C4×C61—28no—
191C22×C4×C61—21no—
192C22×C4×C61—22no—
193C22×C4×C61—22no—
194C22×C4×C61—22no—
195C22×C4×C61—22no—
196C22×C4×C61—21no—
197C22×C4×C61—22no—
198C22×C4×C61—22no—
199C22×C4×C61—22no—
200C22×C4×C61—22no—
201C22×C4×C61—28no—
202C22×C4×C61—44no—
203C22×C4×C61—48no—
204C22×C4×C61—48no—
205C22×C4×C61C22×C414yes—
206C22×C4×C61C22×C412yes—
207C22×C4×C61C22×C414yes—
208C22×C4×C61C22×C412yes—
209C22×C4×C61C2×D414yes—
210C22×C4×C61C2×D414yes—
211C22×C4×C61C2×D414yes—
212C22×Dic61—21no—
213C22×Dic61—21no—
214C22×Dic61—22no—
215C22×Dic61—28no—
216C22×Dic61—22no—
217C22×Dic61—22no—
218C22×Dic61—22no—
219C22×Dic61—21no—
220C22×Dic61—22no—
221C22×Dic61—22no—
222C22×Dic61—22no—
223C22×Dic61—22no—
224C22×Dic61—21no—
225C22×Dic61—22no—
226C22×Dic61—22no—
227C22×Dic61—22no—
228C22×Dic61—22no—
229C22×Dic61—22no—
230C22×Dic61—22no—
231C22×Dic61—22no—
232C22×Dic61—28no—
233C22×Dic61—44no—
234C22×Dic61—48no—
235C22×Dic61—48no—
236C22×Dic61C22×C414yes—
237C22×Dic61C22×C412yes—
238C22×Dic61C22×C414yes—
239C22×Dic61C22×C412yes—
240C22×Dic61C2×D414yes—
241C2×C4×D61—216no—
242C2×C4×D61—216no—
243C2×C4×D61—48no—
244C2×C4×D61—48no—
245C2×C4×D61—48no—
246C2×C4×D61—48no—
247C2×C4×D61—48no—
248C22⋊C4×C61—28no—
249C22⋊C4×C61C22⋊C4116yescomplemented
250C42×C61—48no—
251C22⋊Dic61—28no—
252C22⋊Dic61—28no—
253#11758198—28no—
254#11758198—216no—
255#11758198—216no—
256#11758198—28no—
257#11758198—28no—
258#11758198—48no—
259#11758198C22⋊C4116yesdirect product factor
260C4×Dic61—48no—
261C23×C61—22no—
262C23×C61—22no—
263C23×C61—24no—
264C23×C61—24no—
265C23×C61—22no—
266C23×C61—22no—
267C23×C61—24no—
268C23×C61—24no—
269C23×C61—24no—
270C23×C61—24no—
271C23×C61—24no—
272C23×C61—24no—
273C23×C61—24no—
274C23×C61—24no—
275C23×C61—24no—
276C23×C61—24no—
277C23×C61C2×C4214yes—
278C23×C61C2×C22⋊C414yes—
279C23×C61#11714yes—
280C23×C61C4×D414yes—
281C23×C61C4×D414yes—
282C23×C61C4×D414yes—
283C23×C61C4×D414yes—
284C23×C61C23×C411yescharacteristic
285C23×C61C23×C411yescharacteristic
286C23×C61C23×C411yescharacteristic
287C23×C61C22×D412yes—
288C23×C61C22×D411yescharacteristic
289C23×C61C22×D411yescharacteristic
290C23×C61C2×#4112yes—
291C23×C61C2×#4111yescharacteristic
292C23×C61C2×#4111yescharacteristic
293C23×C61H(5,𝔽2)12yes—
294C23×C61H(5,𝔽2)12yes—
295C22×D61—22no—
296C22×D61—22no—
297C22×D61—22no—
298C22×D61—22no—
299C22×D61—22no—
300C22×D61—22no—
301C22×D61—24no—
302C22×D61—22no—
303C22×D61—22no—
304C22×D61—24no—
305C22×D61—24no—
306C22×D61—24no—
307C22×D61—24no—
308C22×D61—24no—
309C22×D61—24no—
310C22×D61—24no—
311C22×D61—24no—
312C22×D61—24no—
313C22×D61—22no—
314C22×D61—22no—
315C22×D61—22no—
316C22×D61—22no—
317C22×D61—24no—
318C22×D61—22no—
319C22×D61—22no—
320C22×D61—24no—
321C22×D61—22no—
322C22×D61—22no—
323C22×D61—24no—
324C22×D61—24no—
325C22×D61—22no—
326C22×D61—22no—
327C22×D61—232no—
328C22×D61—232no—
329C22×D61—416no—
330C22×D61—432no—
331C22×D61—416no—
332C22×D61—416no—
333C22×D61—416no—
334C22×D61—416no—
335C22×D61—432no—
336C22×D61—432no—
337C22×D61—432no—
338C22×D61—42no—
339C22×D61—42no—
340C22×D61—42no—
341C22×D61—42no—
342C22×D61—42no—
343C22×D61—42no—
344C22×D61—42no—
345C22×D61—42no—
346C22×D61C2×C4214yes—
347C22×D61C2×C4214yes—
348C22×D61C2×C22⋊C414yes—
349C22×D61#11714yes—
350C22×D61C4×D418yes—
351C22×D61C4×D418yes—
352C2×C4×C61—24no—
353C2×C4×C61—22no—
354C2×C4×C61—24no—
355C2×C4×C61—22no—
356C2×C4×C61—24no—
357C2×C4×C61—24no—
358C2×C4×C61—24no—
359C2×C4×C61—24no—
360C2×C4×C61—24no—
361C2×C4×C61—24no—
362C2×C4×C61—22no—
363C2×C4×C61—24no—
364C2×C4×C61—24no—
365C2×C4×C61—22no—
366C2×C4×C61—24no—
367C2×C4×C61—22no—
368C2×C4×C61—416no—
369C2×C4×C61—42no—
370C2×C4×C61—42no—
371C2×C4×C61—42no—
372C2×C4×C61—42no—
373C2×C4×C61—42no—
374C2×C4×C61—42no—
375C2×C4×C61C2×C22⋊C414yescomplemented
376C2×C4×C61C2×C22⋊C418yescomplemented
377C2×Dic61—22no—
378C2×Dic61—22no—
379C2×Dic61—24no—
380C2×Dic61—24no—
381C2×Dic61—22no—
382C2×Dic61—24no—
383C2×Dic61—24no—
384C2×Dic61—24no—
385C2×Dic61—24no—
386C2×Dic61—22no—
387C2×Dic61—24no—
388C2×Dic61—24no—
389C2×Dic61—22no—
390C2×Dic61—416no—
391C2×Dic61—42no—
392C2×Dic61—42no—
393C2×Dic61—42no—
394C2×Dic61—42no—
395C2×Dic61—42no—
396C2×Dic61—42no—
397C2×Dic61—42no—
398C2×Dic61—42no—
399C2×Dic61—42no—
400C2×Dic61—42no—
401C2×Dic61C2×C22⋊C414yescomplemented
402C4×D61—432no—
403C22⋊C42—611nomaximal, Sylow
404C22×C61—24no—
405C22×C61—24no—
406C22×C61—28no—
407C22×C61—28no—
408C22×C61—24no—
409C22×C61—24no—
410C22×C61—28no—
411C22×C61—28no—
412C22×C61—24no—
413C22×C61—24no—
414C22×C61C4×C22⋊C418yescomplemented
415C22×C61C22×C4211yescharacteristic
416C22×C61C22×C22⋊C411yescharacteristic
417C22×C61C22×C22⋊C411yescharacteristic
418C22×C61C2×#11711yescharacteristic
419C22×C61C2×#11711yescharacteristic
420C22×C61C2×C4×D412yes—
421C22×C61C2×C4×D412yes—
422C22×C61C2×C4×D411yescharacteristic
423C22×C61C2×C4×D411yescharacteristic
424C22×C61C2×C4×D411yescharacteristic
425C22×C61C2×C4×D411yescharacteristic
426C22×C61#51812yes—
427C22×C61#51812yes—
428C22×C61#51811yescharacteristic
429C22×C61#51811yescharacteristic
430C22×C61D4212yes—
431C22×C61D4212yes—
432C22×C61#54612yes—
433C22×C61#54612yes—
434C22×C61#54612yes—
435C22×C61#54612yes—
436C22×C61#55112yes—
437C22×C61#55112yes—
438C2×D61—28no—
439C2×D61—24no—
440C2×D61—24no—
441C2×D61—24no—
442C2×D61—24no—
443C2×D61—28no—
444C2×D61—28no—
445C2×D61—28no—
446C2×D61—24no—
447C2×D61—24no—
448C2×D61—24no—
449C2×D61—24no—
450C2×D61—24no—
451C2×D61—464no—
452C2×D61—44no—
453C2×D61—42no—
454C2×D61—42no—
455C2×D61—44no—
456C2×D61—42no—
457C2×D61—42no—
458C2×D61—44no—
459C2×D61—44no—
460C2×D61C4×C22⋊C418yescomplemented
461C4×C61—28no—
462C4×C61—24no—
463C4×C61—42no—
464C4×C61—44no—
465Dic61—24no—
466Dic61—44no—
467Dic61—42no—
468Dic61—44no—
469C23×C22⋊C4—611no—
470C23×C22⋊C4—611no—
471C2×#379—611no—
472C2×C4×C22⋊C4—612no—
473C2×C4×C22⋊C4—611no—
474C2×C4×C22⋊C4D6111yescharacteristic, complemented
475#1437—612no—
476#1437—612no—
477C22⋊#95—612no—
478C22⋊#95—611no—
479C22⋊#95—611no—
480C2×C61—28no—
481C2×C61C2×C4×C22⋊C411yescharacteristic
482C2×C61C2×C4×C22⋊C411yescharacteristic
483C2×C61#227311yescharacteristic
484C2×C61D4×C22⋊C412yes—
485C2×C61D4×C22⋊C411yescharacteristic
486C2×C61D4×C22⋊C411yescharacteristic
487C2×C61#234212yes—
488C2×C61#234211yescharacteristic
489C2×C61#234211yescharacteristic
490C2×C61#235812yes—
491C2×C61#235812yes—
492D61—28no—
493D61—44no—
494C26—611no—
495C24×C4—611no—
496C24×C4—612no—
497C24×C4C2×D6111yescharacteristic
498C22×C22⋊C4—611no—
499C22×C22⋊C4—611no—
500C22×C22⋊C4—611no—
501C22×C22⋊C4—618no—
502C22×C22⋊C4—611no—
503C22×C22⋊C4—611no—
504C22×C22⋊C4—612no—
505C22×C22⋊C4—611no—
506C22×C22⋊C4—612no—
507C22×C22⋊C4—612no—
508C22×C22⋊C4—618no—
509C22×C22⋊C4—1228no—
510C22×C22⋊C4—1224no—
511C22×C22⋊C4—1224no—
512C22×C22⋊C4C2×D6111yescharacteristic
513C22×C22⋊C4C2×D6111yescharacteristic
514C22×C42—612no—
515C22×C42C2×D6112yescomplemented
516#379—618no—
517C4×C22⋊C4—24no—
518C4×C22⋊C4—1228no—
519C4×C22⋊C4—1224no—
520C2×#95—612no—
521C2×#95—612no—
522C2×#95—612no—
523C2×#95—612no—
524C2×#95—612no—
525C2×#95C2×D6112yescomplemented
526C61C22⋊C4211yescharacteristic, complemented, Sylow
527C25—611no—
528C25—611no—
529C25—614no—
530C25—614no—
531C25—614no—
532C25—1224no—
533C25—1224no—
534C25—1222no—
535C25—1222no—
536C25—1222no—
537C25—1222no—
538C25—2442no—
539C25—2442no—
540C25C22×D6111yescharacteristic
541C23×C4—22no—
542C23×C4—22no—
543C23×C4—24no—
544C23×C4—42no—
545C23×C4—611no—
546C23×C4—612no—
547C23×C4—612no—
548C23×C4—611no—
549C23×C4—614no—
550C23×C4—618no—
551C23×C4—1224no—
552C23×C4—1224no—
553C23×C4—1224no—
554C23×C4—1222no—
555C23×C4—1222no—
556C23×C4—1224no—
557C23×C4—1224no—
558C23×C4—2442no—
559C23×C4—2442no—
560C23×C4—2442no—
561C23×C4C4×D6114yescomplemented
562C23×C4C22×D6112yes—
563C23×C4C22×D6111yescharacteristic
564C23×C4C22×D6112yes—
565C23×C4C22×D6111yescharacteristic
566C2×C22⋊C4—22no—
567C2×C22⋊C4—22no—
568C2×C22⋊C4—614no—
569C2×C22⋊C4—618no—
570C2×C22⋊C4—614no—
571C2×C22⋊C4—614no—
572C2×C22⋊C4—614no—
573C2×C22⋊C4—614no—
574C2×C22⋊C4—614no—
575C2×C22⋊C4—618no—
576C2×C22⋊C4—618no—
577C2×C22⋊C4—618no—
578C2×C22⋊C4—12232no—
579C2×C22⋊C4—1224no—
580C2×C22⋊C4—1224no—
581C2×C22⋊C4—1224no—
582C2×C22⋊C4—1224no—
583C2×C22⋊C4—1222no—
584C2×C22⋊C4—1222no—
585C2×C22⋊C4—1222no—
586C2×C22⋊C4—1222no—
587C2×C22⋊C4—1224no—
588C2×C22⋊C4—1224no—
589C2×C22⋊C4—1224no—
590C2×C22⋊C4—12232no—
591C2×C22⋊C4—2442no—
592C2×C22⋊C4—2442no—
593C2×C22⋊C4C4×D6114yes—
594C2×C22⋊C4C4×D6114yescomplemented
595C2×C22⋊C4D24414yes—
596C2×C22⋊C4C22⋊D6114yes—
597C2×C42—24no—
598C2×C42—24no—
599C2×C42—42no—
600C2×C42—1224no—
601C2×C42—1224no—
602C2×C42—2442no—
603#95—24no—
604#95—1224no—
605#95—1224no—
606#95—1224no—
607#95—2442no—
608#95—2442no—
609C24—22no—
610C24—22no—
611C24—22no—
612C24—22no—
613C24—612no—
614C24—612no—
615C24—612no—
616C24—614no—
617C24—614no—
618C24—612no—
619C24—612no—
620C24—612no—
621C24—6116no—
622C24—1228no—
623C24—1228no—
624C24—12216no—
625C24—12216no—
626C24—1221no—
627C24—1221no—
628C24—1221no—
629C24—1221no—
630C24—1222no—
631C24—1222no—
632C24—1222no—
633C24—1221no—
634C24—1221no—
635C24—1222no—
636C24—1221no—
637C24—1221no—
638C24—1222no—
639C24—1222no—
640C24—1228no—
641C24—1228no—
642C24—1228no—
643C24—1228no—
644C24—1228no—
645C24—1228no—
646C24—2448no—
647C24—2448no—
648C24—2444no—
649C24—2444no—
650C24—2448no—
651C24—2448no—
652C24—2448no—
653C24—2448no—
654C24—2448no—
655C24—2448no—
656C24—2448no—
657C24—2448no—
658C24C2×C4×D6112yes—
659C24C2×C4×D6112yes—
660C24C2×C4×D6112yes—
661C24C2×D24412yes—
662C24#1175822212yes—
663C24#1175822212yes—
664C24C2×C22⋊D6112yes—
665C24C23×D6111yescharacteristic
666C22×C4—22no—
667C22×C4—21no—
668C22×C4—22no—
669C22×C4—21no—
670C22×C4—22no—
671C22×C4—22no—
672C22×C4—22no—
673C22×C4—22no—
674C22×C4—22no—
675C22×C4—21no—
676C22×C4—22no—
677C22×C4—22no—
678C22×C4—22no—
679C22×C4—21no—
680C22×C4—22no—
681C22×C4—22no—
682C22×C4—22no—
683C22×C4—28no—
684C22×C4—28no—
685C22×C4—44no—
686C22×C4—48no—
687C22×C4—48no—
688C22×C4—612no—
689C22×C4—614no—
690C22×C4—614no—
691C22×C4—612no—
692C22×C4—614no—
693C22×C4—12216no—
694C22×C4—1228no—
695C22×C4—1221no—
696C22×C4—1221no—
697C22×C4—1222no—
698C22×C4—1222no—
699C22×C4—1222no—
700C22×C4—1222no—
701C22×C4—1222no—
702C22×C4—1221no—
703C22×C4—1222no—
704C22×C4—1222no—
705C22×C4—1222no—
706C22×C4—1222no—
707C22×C4—1222no—
708C22×C4—1221no—
709C22×C4—1222no—
710C22×C4—1222no—
711C22×C4—1222no—
712C22×C4—1222no—
713C22×C4—1222no—
714C22×C4—1228no—
715C22×C4—12216no—
716C22×C4—2448no—
717C22×C4—2448no—
718C22×C4—2448no—
719C22×C4—2448no—
720C22×C4—2448no—
721C22×C4—2444no—
722C22×C4—2448no—
723C22×C4—2448no—
724C22×C4C2×C4×D6114yes—
725C22×C4C2×C4×D6112yes—
726C22×C4C2×C4×D6112yes—
727C22×C4C2×C4×D6114yes—
728C22×C4C2×D24414yes—
729C22×C4D4×D6114yes—
730C22×C4C2×C22⋊D6114yes—
731C22⋊C4—28no—
732C22⋊C4—6116no—
733C22⋊C4—1228no—
734C22⋊C4—1228no—
735C22⋊C4—12216no—
736C22⋊C4—1228no—
737C22⋊C4—1228no—
738C22⋊C4—1228no—
739C22⋊C4—12216no—
740C22⋊C4—2448no—
741C22⋊C4#11758198116yesdirect product factor
742C42—48no—
743C42—2448no—
744C23—22no—
745C23—22no—
746C23—24no—
747C23—24no—
748C23—24no—
749C23—24no—
750C23—22no—
751C23—22no—
752C23—24no—
753C23—24no—
754C23—24no—
755C23—24no—
756C23—24no—
757C23—24no—
758C23—24no—
759C23—24no—
760C23—614no—
761C23—614no—
762C23—614no—
763C23—618no—
764C23—618no—
765C23—614no—
766C23—12232no—
767C23—1222no—
768C23—1222no—
769C23—1222no—
770C23—1222no—
771C23—1222no—
772C23—1222no—
773C23—1224no—
774C23—1224no—
775C23—1222no—
776C23—1222no—
777C23—1224no—
778C23—1224no—
779C23—1224no—
780C23—1224no—
781C23—1224no—
782C23—1224no—
783C23—1224no—
784C23—1224no—
785C23—1222no—
786C23—1222no—
787C23—1222no—
788C23—1222no—
789C23—1224no—
790C23—1224no—
791C23—1222no—
792C23—1222no—
793C23—1222no—
794C23—1222no—
795C23—1224no—
796C23—1224no—
797C23—1222no—
798C23—1222no—
799C23—12232no—
800C23—24416no—
801C23—24432no—
802C23—24432no—
803C23—24432no—
804C23—24416no—
805C23—24416no—
806C23—24432no—
807C23—24416no—
808C23—24416no—
809C23—2442no—
810C23—2442no—
811C23—2442no—
812C23—2442no—
813C23—2442no—
814C23—2442no—
815C23—2442no—
816C23—2442no—
817C23C42×D6114yes—
818C23C2×#1175819814yes—
819C23#1451973414yes—
820C23C4×C22⋊D6114yes—
821C23C4×C22⋊D6114yes—
822C23C4×D24414yes—
823C23C4×D24414yes—
824C23C22×C4×D6111yescharacteristic
825C23C22×C4×D6111yescharacteristic
826C23C22×C4×D6111yescharacteristic
827C23C2×D4×D6112yes—
828C23C22×C22⋊D6111yescharacteristic
829C23C22×D24411yescharacteristic
830C23#41×D6112yes—
831C23C2×#1175822211yescharacteristic
832C23C2×#1175822211yescharacteristic
833C23#1451982212yes—
834C23#1451982312yes—
835C2×C4—24no—
836C2×C4—22no—
837C2×C4—24no—
838C2×C4—22no—
839C2×C4—24no—
840C2×C4—24no—
841C2×C4—24no—
842C2×C4—24no—
843C2×C4—24no—
844C2×C4—24no—
845C2×C4—22no—
846C2×C4—24no—
847C2×C4—24no—
848C2×C4—22no—
849C2×C4—24no—
850C2×C4—22no—
851C2×C4—416no—
852C2×C4—42no—
853C2×C4—42no—
854C2×C4—42no—
855C2×C4—42no—
856C2×C4—42no—
857C2×C4—42no—
858C2×C4—614no—
859C2×C4—1222no—
860C2×C4—1222no—
861C2×C4—1224no—
862C2×C4—1224no—
863C2×C4—1222no—
864C2×C4—1224no—
865C2×C4—1224no—
866C2×C4—1224no—
867C2×C4—1224no—
868C2×C4—1222no—
869C2×C4—1224no—
870C2×C4—1224no—
871C2×C4—1222no—
872C2×C4—24432no—
873C2×C4—24416no—
874C2×C4—2442no—
875C2×C4—2442no—
876C2×C4—2442no—
877C2×C4—2442no—
878C2×C4—2442no—
879C2×C4—2442no—
880C2×C4—2442no—
881C2×C4—2442no—
882C2×C4—2442no—
883C2×C4—2442no—
884C2×C4C22⋊C4×D6114yescomplemented
885C2×C4C2×#1175819818yescomplemented
886C22—28no—
887C22—28no—
888C22—28no—
889C22—24no—
890C22—24no—
891C22—24no—
892C22—28no—
893C22—24no—
894C22—24no—
895C22—24no—
896C22—618no—
897C22—1228no—
898C22—1228no—
899C22—1228no—
900C22—1224no—
901C22—1224no—
902C22—1224no—
903C22—1228no—
904C22—1224no—
905C22—1224no—
906C22—1224no—
907C22—1224no—
908C22—1224no—
909C22—1224no—
910C22—24464no—
911C22—2444no—
912C22—2444no—
913C22—2444no—
914C22—2442no—
915C22—2442no—
916C22—2444no—
917C22—2442no—
918C22—2442no—
919C22C4×#1175819818yescomplemented
920C22C2×C42×D6111yescharacteristic
921C22C2×C22⋊C4×D6111yescharacteristic
922C22C22×#1175819811yescharacteristic
923C22#117×D6111yescharacteristic
924C22C2×#1451973411yescharacteristic
925C22C4×D4×D6112yes—
926C22C4×D4×D6112yes—
927C22C2×C4×C22⋊D6111yescharacteristic
928C22C2×C4×C22⋊D6111yescharacteristic
929C22C2×C4×D24411yescharacteristic
930C22C2×C4×D24411yescharacteristic
931C22#1684023412yes—
932C22#1684023412yes—
933C22#1684023511yescharacteristic
934C22#1684023611yescharacteristic
935C22D4×C22⋊D6112yes—
936C22D4×D24412yes—
937C22#1684040012yes—
938C22#1684040212yes—
939C22#1684040712yes—
940C22#1684040812yes—
941C22#1684043612yes—
942C22#1684044112yes—
943C4—28no—
944C4—24no—
945C4—44no—
946C4—42no—
947C4—1224no—
948C4—2444no—
949C4—2444no—
950C4—2442no—
951C2—28no—
952C2—1228no—
953C2—2444no—
954C2C4×C22⋊C4×D6111yescharacteristic
955C2C2×C4×#1175819811yescharacteristic
956C2#2144817111yescharacteristic
957C2D4×#1175819812yes—
958C2C22⋊C4×C22⋊D6111yescharacteristic
959C2C22⋊C4×D24411yescharacteristic
960C2#2144866212yes—
961C2#2144866911yescharacteristic
962C2#2144867111yescharacteristic
963C2#2144879612yes—
964C2#2144880112yes—
subgroupG/H
center, FrattiniC24C23×D61
commutatorC22×C61C22×C42
FittingC2×C4×C22⋊C4×C61C2
socle, cosocleC24×C61C24
prime radicalC25×D61C22
hypercenterC2×C4×C22⋊C4D61
hypocenterC61C22⋊C42
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
4. C2×C22⋊C4×Dic61C2semidirect
5. C2×C4×#11758198C2semidirect
6. #21444057C2semidirect
7. #21444055C2semidirect
8. #21444042C2semidirect
9. #21444041C2semidirect
10. #21444040C2semidirect
11. C2×C4×C22⋊C4×C61C2semidirect
18. C22×#11758198C4semidirect
28. C2×C22⋊C4×D61C4semidirect
29. C22×C4×Dic61C22semidirect
30. #16839617C4semidirect
33. C2×#14519684C22semidirect
34. C2×#14519684C22semidirect
35. C2×#14519684C22semidirect
36. C2×#14519684C22semidirect
37. C2×#14519684C22semidirect
41. C22×C42×C61C22semidirect
43. C2×#95×C61C22semidirect
61. C23×Dic61C2×C4semidirect
72. C22×C4×D61C2×C4semidirect
78. C2×C22⋊Dic61C2×C4semidirect
91. C2×#11758198C2×C4semidirect
92. C2×#11758198C2×C4semidirect
93. C2×#11758198C2×C4semidirect
94. C2×#11758198C2×C4semidirect
95. C2×#11758198C2×C4semidirect
111. C23×C4×C61C2×C4semidirect
119. C2×C22⋊C4×C61C2×C4semidirect
174. C23×D61C42semidirect
249. C22⋊C4×C61C22⋊C4semidirect
259. #11758198C22⋊C4direct (N × H)
375. C2×C4×C61C2×C22⋊C4semidirect
376. C2×C4×C61C2×C22⋊C4semidirect
401. C2×Dic61C2×C22⋊C4semidirect
414. C22×C61C4×C22⋊C4semidirect
460. C2×D61C4×C22⋊C4semidirect
474. C2×C4×C22⋊C4D61semidirect
515. C22×C42C2×D61semidirect
525. C2×#95C2×D61semidirect
526. C61C22⋊C42semidirect
561. C23×C4C4×D61semidirect
594. C2×C22⋊C4C4×D61semidirect
741. C22⋊C4#11758198direct (N × H)
884. C2×C4C22⋊C4×D61semidirect
885. C2×C4C2×#11758198semidirect
919. C22C4×#11758198semidirect

Maximal subgroups

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

subgroupindex
C23×#117581982
C22×C22⋊C4×D612
C2×#168396172
C2×C22⋊C4×Dic612
C2×C4×#117581982
#214440572
#214440552
#214440422
#214440412
#214440402
C2×C4×C22⋊C4×C612
C22⋊C4261