Finite Group Databasebeta

← C2×#35982 #7629431

Subgroups — C2×#35982 #7629431

Order 512.

9414 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#552C211yesmaximal, characteristic, complemented
2C22×#518C211yesmaximal, characteristic, complemented
3#35982C2132yesmaximal, direct product factor
4C2×#2562C212yesmaximal, complemented
5C2×#2598C212yesmaximal, complemented
6C2×#2454C212yesmaximal, complemented
7C2×#2427C212yesmaximal, complemented
8C2×#2435C211yesmaximal, characteristic, complemented
9C2×#2408C211yesmaximal, characteristic
10C2×#2480C214yesmaximal, complemented
11C2×#2418C214yesmaximal, complemented
12C2×#2625C211yesmaximal, characteristic, complemented
13C2×#2633C212yesmaximal, complemented
14C2×#2395C211yesmaximal, characteristic, complemented
15C2×#2392C212yesmaximal, complemented
16C2×#2367C212yesmaximal, complemented
17C2×#2361C212yesmaximal, complemented
18C2×#2347C211yesmaximal, characteristic, complemented
19C24×D4C2211yescharacteristic
20C2×#552—216no—
21C2×#552C22116yescomplemented
22C22×#126C2212yes—
23C22×#125C2212yescomplemented
24C22×#125C2211yescharacteristic, complemented
25C22×#124C2212yes—
26C22×#123C2212yes—
27C22×C22⋊Q8C2211yescharacteristic
28C22×C22⋊Q8C2211yescharacteristic, complemented
29C22×#121C2212yes—
30C22×#120C2212yes—
31C2×#518—216no—
32C2×#518C22116yescomplemented
33C22×C4×Q8C2211yescharacteristic, complemented
34C22×C4×D4C2212yes—
35C22×C4×D4C2212yes—
36C22×C4×D4C2212yes—
37C22×C4×D4C2211yescharacteristic
38C22×C4×D4C2212yes—
39C22×C4×D4C2214yescomplemented
40C22×#117C2211yescharacteristic
41C22×#117C2211yescharacteristic
42C22×#117C2212yescomplemented
43C23×C4⋊C4C2211yescharacteristic, complemented
44C23×C22⋊C4C2214yes—
45#2633C22132yescomplemented
46#2625C22116yescomplemented
47#2598C22132yescomplemented
48#2562C22132yescomplemented
49#2480C22164yescomplemented
50#2454C22132yescomplemented
51#2435C22116yescomplemented
52#2427C22132yescomplemented
53#2418C22164yescomplemented
54#2408C22116yes—
55#2395C22116yescomplemented
56C2×#400C2212yescomplemented
57C2×#400C2211yescharacteristic, complemented
58C2×#399C2214yescomplemented
59C2×#399C2211yescharacteristic, complemented
60#2392C22132yescomplemented
61C2×#398C2211yescharacteristic, complemented
62C2×#398C2212yescomplemented
63C2×#397C2214yes—
64C2×#397C2212yes—
65C2×#397C2214yescomplemented
66C2×#397C2211yescharacteristic, complemented
67C2×#396C2214yescomplemented
68C2×#394C2212yes—
69C2×#394C2212yes—
70C2×#394C2212yes—
71C2×#394C2212yes—
72C2×#394C2214yescomplemented
73C2×#392C2212yes—
74#2367C22132yescomplemented
75#2361C22132yescomplemented
76#2347C22116yescomplemented
77C2×#391C2212yescomplemented
78C2×#390C2212yes—
79C2×#390C2212yes—
80C2×#389C2212yescomplemented
81C2×#389C2212yescomplemented
82C2×#388C2214yes—
83C2×#388C2214yescomplemented
84C2×#388C2214yescomplemented
85C2×#388C2214yescomplemented
86C2×#386C2214yescomplemented
87C2×#386C2214yescomplemented
88C2×#385C2214yescomplemented
89C2×#385C2214yescomplemented
90C2×#385C2214yescomplemented
91C2×#383C2212yescomplemented
92C2×#380C2211yescharacteristic
93C2×#380C2214yescomplemented
94C2×#380C2214yescomplemented
95C2×#379C2214yes—
96C2×#379C2212yes—
97C2×C4×C4⋊C4C2212yescomplemented
98C2×C4×C4⋊C4C2212yescomplemented
99C2×C4×C4⋊C4C2212yescomplemented
100C2×C4×C22⋊C4C2211yescharacteristic
101C2×C4×C22⋊C4C2212yescomplemented
102C2×C4×C22⋊C4C2214yescomplemented
103C26C2312yes—
104C23×Q8C2311yescharacteristic
105C23×D4—216no—
106C23×D4—28no—
107C23×D4C2312yes—
108C23×D4C2318yes—
109C23×D4C2314yes—
110C23×D4C2311yescharacteristic
111C23×D4C2312yes—
112C24×C4C2311yescharacteristic
113C24×C4C2312yes—
114C24×C4C2311yescharacteristic
115C24×C4C2314yes—
116C24×C4C2314yes—
117#552—2128no—
118C2×#126—216no—
119C2×#126C23116yes—
120C2×#125—28no—
121C2×#125—216no—
122C2×#125C23116yescomplemented
123C2×#125C2318yescomplemented
124C2×#124—216no—
125C2×#124C23116yes—
126C2×#123—216no—
127C2×#123C23116yes—
128C2×C22⋊Q8—28no—
129C2×C22⋊Q8—28no—
130C2×C22⋊Q8C2318yes—
131C2×C22⋊Q8C2318yescomplemented
132C2×#121—216no—
133C2×#121C23116yes—
134C2×#120—48no—
135C2×#120C23116yes—
136#518—2128no—
137C2×C4×Q8—28no—
138C2×C4×Q8C2318yescomplemented
139C2×C4×D4—28no—
140C2×C4×D4—216no—
141C2×C4×D4—216no—
142C2×C4×D4—216no—
143C2×C4×D4—216no—
144C2×C4×D4—416no—
145C2×C4×D4C23116yes—
146C2×C4×D4C23116yes—
147C2×C4×D4C23116yes—
148C2×C4×D4C2318yes—
149C2×C4×D4C23116yes—
150C2×C4×D4C23132yescomplemented
151C2×#117—28no—
152C2×#117—216no—
153C2×#117D4116yescomplemented
154C2×#117C2318yes—
155C2×#117C2318yes—
156C2×#117C23116yescomplemented
157C22×C4⋊C4—28no—
158C22×C4⋊C4C2312yes—
159C22×C4⋊C4C2311yescharacteristic
160C22×C4⋊C4C2312yes—
161C22×C4⋊C4C2312yes—
162C22×C4⋊C4C2311yescharacteristic
163C22×C4⋊C4C2312yes—
164C22×C4⋊C4C2311yescharacteristic
165C22×C4⋊C4C2311yescharacteristic
166C22×C4⋊C4C2312yes—
167C22×C4⋊C4C2312yes—
168C22×C4⋊C4C2312yes—
169C22×C4⋊C4C2312yes—
170C22×C4⋊C4C2314yes—
171C22×C4⋊C4C2314yes—
172C22×C4⋊C4C2312yes—
173C22×C4⋊C4C2311yescharacteristic
174C22×C4⋊C4C2311yescharacteristic
175C22×C4⋊C4C2318yescomplemented
176C22×C22⋊C4—232no—
177C22×C22⋊C4C2311yescharacteristic
178C22×C22⋊C4C2312yes—
179C22×C22⋊C4C2314yes—
180C22×C22⋊C4C2312yes—
181C22×C22⋊C4C2314yes—
182C22×C22⋊C4C2314yes—
183C22×C22⋊C4C2312yes—
184C22×C22⋊C4C2314yes—
185C22×C22⋊C4C2311yescharacteristic
186C22×C22⋊C4C2312yes—
187C22×C22⋊C4C2314yes—
188C22×C22⋊C4C23132yes—
189C22×C22⋊C4C2314yes—
190C22×C22⋊C4C2314yes—
191C22×C22⋊C4C2312yes—
192C22×C22⋊C4C2314yes—
193C22×C22⋊C4C2312yes—
194C22×C22⋊C4C2314yes—
195C22×C22⋊C4C2312yes—
196C22×C22⋊C4C2312yes—
197C22×C42C2312yes—
198C22×C42C2312yes—
199C22×C42C2311yescharacteristic
200C22×C42C2312yes—
201C22×C42C2314yes—
202C22×C42C2312yes—
203#400C2318yescomplemented
204#400C23116yescomplemented
205#399C2318yescomplemented
206#399C23132yescomplemented
207#398C23116yescomplemented
208#398C2318yescomplemented
209#397C23132yes—
210#397C23116yes—
211#397C23132yescomplemented
212#397C2318yescomplemented
213#396C23132yescomplemented
214#394C23116yes—
215#394C23116yes—
216#394C23116yes—
217#394C23116yes—
218#394C23132yescomplemented
219#392C23116yes—
220#391C23116yescomplemented
221#390C23116yes—
222#390C23116yes—
223#389C23116yescomplemented
224#389C23116yescomplemented
225#388C23132yes—
226#388C23132yescomplemented
227#388C23132yescomplemented
228#388C23132yescomplemented
229#386C23132yescomplemented
230#386C23132yescomplemented
231#385C23132yescomplemented
232#385C23132yescomplemented
233#385C23132yescomplemented
234#383C23116yescomplemented
235#380C2318yes—
236#380C23132yescomplemented
237#380C23132yescomplemented
238#379C23116yes—
239#379C23132yes—
240C4×C4⋊C4C23116yescomplemented
241C4×C4⋊C4C23116yescomplemented
242C4×C4⋊C4C23116yescomplemented
243C4×C22⋊C4C2318yes—
244C4×C22⋊C4C23116yescomplemented
245C4×C22⋊C4C23132yescomplemented
246C2×#95C2312yes—
247C2×#95C2311yescharacteristic
248C2×#95C2311yescharacteristic
249C2×#95C2312yes—
250C2×#95C2314yes—
251C2×#95C2312yes—
252C2×#95C2312yes—
253C2×#95C2312yes—
254C2×#95C2314yes—
255C2×#95C2314yes—
256C2×#95C2314yes—
257C2×#95C2314yes—
258C25—28no—
259C25—216no—
260C25—44no—
261C25—44no—
262C25—48no—
263C25C2411yescharacteristic
264C25C2414yes—
265C25C2411yescharacteristic
266C25C2418yes—
267C22×Q8—24no—
268C22×Q8—28no—
269C22×Q8C2414yes—
270C22×D4—2128no—
271C22×D4—216no—
272C22×D4—264no—
273C22×D4—24no—
274C22×D4—216no—
275C22×D4—216no—
276C22×D4—24no—
277C22×D4—28no—
278C22×D4—28no—
279C22×D4—232no—
280C22×D4—28no—
281C22×D4—48no—
282C22×D4—42no—
283C22×D4#41116yes—
284C22×D4C2418yes—
285C22×D4C2414yes—
286C22×D4C24116yes—
287C22×D4C2418yes—
288C23×C4—28no—
289C23×C4—28no—
290C23×C4—28no—
291C23×C4—24no—
292C23×C4—28no—
293C23×C4—216no—
294C23×C4—216no—
295C23×C4—44no—
296C23×C4—48no—
297C23×C4—48no—
298C23×C4—48no—
299C23×C4—48no—
300C23×C4C2×D418yes—
301C23×C4C2414yes—
302C23×C4C2411yescharacteristic
303C23×C4C2412yes—
304C23×C4C2412yes—
305C23×C4C2412yes—
306C23×C4C2412yes—
307C23×C4C2411yescharacteristic
308C23×C4C2411yescharacteristic
309C23×C4C2412yes—
310C23×C4C2414yes—
311C23×C4C2412yes—
312C23×C4C2418yes—
313C23×C4C2414yes—
314C23×C4C2412yes—
315C23×C4C2412yes—
316C23×C4C2411yescharacteristic
317C23×C4C24116yes—
318C23×C4C24116yes—
319C23×C4C2411yescharacteristic
320#126—264no—
321#125—232no—
322#125—264no—
323#124—264no—
324#123—264no—
325C22⋊Q8—232no—
326C22⋊Q8—232no—
327#121—264no—
328#120—432no—
329C4×Q8—232no—
330C4×D4—232no—
331C4×D4—264no—
332C4×D4—264no—
333C4×D4—264no—
334C4×D4—264no—
335C4×D4—464no—
336#117—232no—
337#117—264no—
338#117C2×D4164yescomplemented
339C2×C4⋊C4—24no—
340C2×C4⋊C4—28no—
341C2×C4⋊C4—24no—
342C2×C4⋊C4—24no—
343C2×C4⋊C4—28no—
344C2×C4⋊C4—28no—
345C2×C4⋊C4—24no—
346C2×C4⋊C4—28no—
347C2×C4⋊C4—28no—
348C2×C4⋊C4—28no—
349C2×C4⋊C4—28no—
350C2×C4⋊C4—232no—
351C2×C4⋊C4—48no—
352C2×C4⋊C4—44no—
353C2×C4⋊C4—44no—
354C2×C4⋊C4—48no—
355C2×C4⋊C4C2×D418yes—
356C2×C4⋊C4C2×D418yes—
357C2×C4⋊C4C2414yes—
358C2×C4⋊C4C2418yes—
359C2×C4⋊C4C2414yes—
360C2×C4⋊C4C2414yes—
361C2×C4⋊C4C2418yes—
362C2×C4⋊C4C2418yes—
363C2×C4⋊C4C2414yes—
364C2×C4⋊C4C2418yes—
365C2×C4⋊C4C2418yes—
366C2×C4⋊C4C2418yes—
367C2×C4⋊C4C2418yes—
368C2×C4⋊C4C24116yes—
369C2×C4⋊C4C24116yes—
370C2×C4⋊C4C2418yes—
371C2×C4⋊C4C2418yes—
372C2×C4⋊C4C2414yes—
373C2×C4⋊C4C2414yes—
374C2×C22⋊C4—28no—
375C2×C22⋊C4—24no—
376C2×C22⋊C4—28no—
377C2×C22⋊C4—216no—
378C2×C22⋊C4—216no—
379C2×C22⋊C4—216no—
380C2×C22⋊C4—28no—
381C2×C22⋊C4—216no—
382C2×C22⋊C4—216no—
383C2×C22⋊C4—24no—
384C2×C22⋊C4—28no—
385C2×C22⋊C4—2128no—
386C2×C22⋊C4—48no—
387C2×C22⋊C4—44no—
388C2×C22⋊C4—48no—
389C2×C22⋊C4—44no—
390C2×C22⋊C4—48no—
391C2×C22⋊C4—44no—
392C2×C22⋊C4—48no—
393C2×C22⋊C4C2×D4116yes—
394C2×C22⋊C4C2418yes—
395C2×C22⋊C4C24116yes—
396C2×C22⋊C4C24116yes—
397C2×C22⋊C4C2414yes—
398C2×C22⋊C4C2418yes—
399C2×C22⋊C4C2414yes—
400C2×C22⋊C4C2418yes—
401C2×C22⋊C4C24116yes—
402C2×C22⋊C4C2418yes—
403C2×C22⋊C4C24116yes—
404C2×C22⋊C4C24116yes—
405C2×C22⋊C4C24116yes—
406C2×C22⋊C4C2418yes—
407C2×C22⋊C4C24116yes—
408C2×C22⋊C4C2418yes—
409C2×C22⋊C4C24116yes—
410C2×C22⋊C4C2418yes—
411C2×C22⋊C4C24116yes—
412C2×C22⋊C4C2418yes—
413C2×C42—28no—
414C2×C42—28no—
415C2×C42—24no—
416C2×C42—28no—
417C2×C42—48no—
418C2×C42C2×D4116yes—
419C2×C42C2418yes—
420C2×C42C2418yes—
421C2×C42C2414yes—
422C2×C42C2418yes—
423C2×C42C24116yes—
424C2×C42C2418yes—
425#95C2414yes—
426#95C2414yes—
427#95C2418yes—
428#95C2418yes—
429#95C2418yes—
430#95C24116yes—
431#95C2418yes—
432#95C2418yes—
433#95C24116yes—
434#95C24116yes—
435#95C24116yes—
436#95C24116yes—
437C24—264no—
438C24—22no—
439C24—28no—
440C24—24no—
441C24—24no—
442C24—28no—
443C24—28no—
444C24—22no—
445C24—28no—
446C24—28no—
447C24—24no—
448C24—24no—
449C24—22no—
450C24—28no—
451C24—22no—
452C24—216no—
453C24—232no—
454C24—48no—
455C24—48no—
456C24—416no—
457C24—816no—
458C24—816no—
459C24—832no—
460C24—832no—
461C24C22×D414yes—
462C24C2×#41116yes—
463C24H(5,𝔽2)14yes—
464C24C2512yes—
465C24C2518yes—
466C24C2512yes—
467C24C2511yescharacteristic
468C2×Q8—28no—
469C2×Q8—216no—
470C2×Q8—416no—
471C2×D4—264no—
472C2×D4—2256no—
473C2×D4—232no—
474C2×D4—28no—
475C2×D4—232no—
476C2×D4—232no—
477C2×D4—28no—
478C2×D4—264no—
479C2×D4—216no—
480C2×D4—216no—
481C2×D4—216no—
482C2×D4—416no—
483C2×D4—44no—
484C2×D4—416no—
485C2×D4—464no—
486C2×D4C2×#41132yes—
487C22×C4—24no—
488C22×C4—24no—
489C22×C4—28no—
490C22×C4—24no—
491C22×C4—232no—
492C22×C4—216no—
493C22×C4—22no—
494C22×C4—24no—
495C22×C4—24no—
496C22×C4—24no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—24no—
500C22×C4—24no—
501C22×C4—24no—
502C22×C4—24no—
503C22×C4—28no—
504C22×C4—28no—
505C22×C4—24no—
506C22×C4—28no—
507C22×C4—24no—
508C22×C4—22no—
509C22×C4—24no—
510C22×C4—216no—
511C22×C4—24no—
512C22×C4—24no—
513C22×C4—24no—
514C22×C4—24no—
515C22×C4—24no—
516C22×C4—28no—
517C22×C4—24no—
518C22×C4—22no—
519C22×C4—24no—
520C22×C4—24no—
521C22×C4—216no—
522C22×C4—28no—
523C22×C4—216no—
524C22×C4—232no—
525C22×C4—232no—
526C22×C4—48no—
527C22×C4—416no—
528C22×C4—416no—
529C22×C4—416no—
530C22×C4—416no—
531C22×C4—432no—
532C22×C4—416no—
533C22×C4—832no—
534C22×C4—832no—
535C22×C4C22×D418yes—
536C22×C4C22×D414yes—
537C22×C4C22×D418yes—
538C22×C4C22×D4116yes—
539C22×C4C22×D414yes—
540C22×C4C2×#4118yes—
541C22×C4C2514yes—
542C22×C4C2518yes—
543C22×C4C2514yes—
544C22×C4C2514yes—
545C22×C4C2514yes—
546C22×C4C2514yes—
547C22×C4C2512yes—
548C22×C4C2512yes—
549C22×C4C2512yes—
550C22×C4C2514yes—
551C22×C4C2512yes—
552C22×C4C2514yes—
553C22×C4C2514yes—
554C22×C4C2512yes—
555C4⋊C4—28no—
556C4⋊C4—216no—
557C4⋊C4—28no—
558C4⋊C4—28no—
559C4⋊C4—216no—
560C4⋊C4—216no—
561C4⋊C4—28no—
562C4⋊C4—216no—
563C4⋊C4—216no—
564C4⋊C4—216no—
565C4⋊C4—216no—
566C4⋊C4—416no—
567C4⋊C4—48no—
568C4⋊C4—48no—
569C4⋊C4—416no—
570C4⋊C4C22×D4116yes—
571C4⋊C4C22×D4116yes—
572C22⋊C4—216no—
573C22⋊C4—28no—
574C22⋊C4—216no—
575C22⋊C4—232no—
576C22⋊C4—232no—
577C22⋊C4—232no—
578C22⋊C4—216no—
579C22⋊C4—232no—
580C22⋊C4—232no—
581C22⋊C4—28no—
582C22⋊C4—216no—
583C22⋊C4—416no—
584C22⋊C4—48no—
585C22⋊C4—416no—
586C22⋊C4—48no—
587C22⋊C4—416no—
588C22⋊C4—48no—
589C22⋊C4—416no—
590C22⋊C4C22×D4132yes—
591C42—216no—
592C42—216no—
593C42—28no—
594C42—216no—
595C42—416no—
596C42C22×D4132yes—
597C23—264no—
598C23—22no—
599C23—28no—
600C23—24no—
601C23—24no—
602C23—28no—
603C23—28no—
604C23—22no—
605C23—28no—
606C23—28no—
607C23—24no—
608C23—24no—
609C23—22no—
610C23—28no—
611C23—22no—
612C23—28no—
613C23—232no—
614C23—28no—
615C23—28no—
616C23—28no—
617C23—216no—
618C23—232no—
619C23—232no—
620C23—44no—
621C23—416no—
622C23—416no—
623C23—44no—
624C23—416no—
625C23—48no—
626C23—48no—
627C23—416no—
628C23—48no—
629C23—832no—
630C23—832no—
631C23—816no—
632C23—816no—
633C23—8128no—
634C23C23×D414yes—
635C23C23×D412yes—
636C23C22×#41116yes—
637C23C22×#4114yes—
638C23C2×H(5,𝔽2)14yes—
639C23C2×H(5,𝔽2)12yes—
640C23#58512yes—
641C23#58514yes—
642C23C2611yescharacteristic
643Q8—416no—
644D4—264no—
645D4—264no—
646D4—464no—
647D4—416no—
648C2×C4—24no—
649C2×C4—24no—
650C2×C4—28no—
651C2×C4—24no—
652C2×C4—28no—
653C2×C4—216no—
654C2×C4—216no—
655C2×C4—232no—
656C2×C4—22no—
657C2×C4—24no—
658C2×C4—24no—
659C2×C4—24no—
660C2×C4—22no—
661C2×C4—24no—
662C2×C4—22no—
663C2×C4—24no—
664C2×C4—24no—
665C2×C4—24no—
666C2×C4—28no—
667C2×C4—28no—
668C2×C4—24no—
669C2×C4—28no—
670C2×C4—24no—
671C2×C4—22no—
672C2×C4—24no—
673C2×C4—24no—
674C2×C4—24no—
675C2×C4—24no—
676C2×C4—24no—
677C2×C4—24no—
678C2×C4—28no—
679C2×C4—24no—
680C2×C4—22no—
681C2×C4—24no—
682C2×C4—24no—
683C2×C4—432no—
684C2×C4—44no—
685C2×C4—48no—
686C2×C4—48no—
687C2×C4—48no—
688C2×C4—44no—
689C2×C4—44no—
690C2×C4—48no—
691C2×C4—48no—
692C2×C4—416no—
693C2×C4—48no—
694C2×C4—416no—
695C2×C4—832no—
696C2×C4—832no—
697C2×C4#525116yes—
698C2×C4C23×D418yes—
699C2×C4C23×D414yes—
700C2×C4C23×D418yes—
701C2×C4C23×D414yes—
702C2×C4C22×#4118yes—
703C22—28no—
704C22—216no—
705C22—216no—
706C22—24no—
707C22—24no—
708C22—24no—
709C22—24no—
710C22—216no—
711C22—48no—
712C22—44no—
713C22—44no—
714C22—48no—
715C22—44no—
716C22—48no—
717C22—48no—
718C22—42no—
719C22—416no—
720C22—464no—
721C22—416no—
722C22—42no—
723C22—864no—
724C22C2×#52514yes—
725C22#348814yes—
726C22#350014yes—
727C22#351318yes—
728C22#352118yes—
729C22C24×D411yescharacteristic
730C22C23×#4112yes—
731C22C22×H(5,𝔽2)11yescharacteristic
732C22C2×#58512yes—
733C22C2×#58511yescharacteristic
734C4—28no—
735C4—28no—
736C4—24no—
737C4—44no—
738C4—48no—
739C4—44no—
740C4—44no—
741C4—44no—
742C4—42no—
743C4—42no—
744C4—44no—
745C4—42no—
746C4—44no—
747C4C2×#52518yes—
748C2—44no—
749C2—416no—
750C2—44no—
751C2#3598218yesdirect product factor
752C2C22×#52511yescharacteristic
753C2C2×#351312yes—
754C2C2×#352112yes—
755C2C2×#348811yescharacteristic
756C2C2×#350011yescharacteristic
subgroupG/H
center, socleC24C25
commutator, Frattini, cosocleC23C26
prime radicalC2×#2408C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C22×#552C2semidirect
2. C22×#518C2semidirect
3. #35982C2direct (N × H)
4. C2×#2562C2semidirect
5. C2×#2598C2semidirect
6. C2×#2454C2semidirect
7. C2×#2427C2semidirect
8. C2×#2435C2semidirect
10. C2×#2480C2semidirect
11. C2×#2418C2semidirect
12. C2×#2625C2semidirect
13. C2×#2633C2semidirect
14. C2×#2395C2semidirect
15. C2×#2392C2semidirect
16. C2×#2367C2semidirect
17. C2×#2361C2semidirect
18. C2×#2347C2semidirect
21. C2×#552C22semidirect
23. C22×#125C22semidirect
24. C22×#125C22semidirect
28. C22×C22⋊Q8C22semidirect
32. C2×#518C22semidirect
33. C22×C4×Q8C22semidirect
39. C22×C4×D4C22semidirect
42. C22×#117C22semidirect
43. C23×C4⋊C4C22semidirect
45. #2633C22semidirect
46. #2625C22semidirect
47. #2598C22semidirect
48. #2562C22semidirect
49. #2480C22semidirect
50. #2454C22semidirect
51. #2435C22semidirect
52. #2427C22semidirect
53. #2418C22semidirect
55. #2395C22semidirect
56. C2×#400C22semidirect
57. C2×#400C22semidirect
58. C2×#399C22semidirect
59. C2×#399C22semidirect
60. #2392C22semidirect
61. C2×#398C22semidirect
62. C2×#398C22semidirect
65. C2×#397C22semidirect
66. C2×#397C22semidirect
67. C2×#396C22semidirect
72. C2×#394C22semidirect
74. #2367C22semidirect
75. #2361C22semidirect
76. #2347C22semidirect
77. C2×#391C22semidirect
80. C2×#389C22semidirect
81. C2×#389C22semidirect
83. C2×#388C22semidirect
84. C2×#388C22semidirect
85. C2×#388C22semidirect
86. C2×#386C22semidirect
87. C2×#386C22semidirect
88. C2×#385C22semidirect
89. C2×#385C22semidirect
90. C2×#385C22semidirect
91. C2×#383C22semidirect
93. C2×#380C22semidirect
94. C2×#380C22semidirect
97. C2×C4×C4⋊C4C22semidirect
98. C2×C4×C4⋊C4C22semidirect
99. C2×C4×C4⋊C4C22semidirect
101. C2×C4×C22⋊C4C22semidirect
102. C2×C4×C22⋊C4C22semidirect
122. C2×#125C23semidirect
123. C2×#125C23semidirect
131. C2×C22⋊Q8C23semidirect
138. C2×C4×Q8C23semidirect
150. C2×C4×D4C23semidirect
153. C2×#117D4semidirect
156. C2×#117C23semidirect
175. C22×C4⋊C4C23semidirect
203. #400C23semidirect
204. #400C23semidirect
205. #399C23semidirect
206. #399C23semidirect
207. #398C23semidirect
208. #398C23semidirect
211. #397C23semidirect
212. #397C23semidirect
213. #396C23semidirect
218. #394C23semidirect
220. #391C23semidirect
223. #389C23semidirect
224. #389C23semidirect
226. #388C23semidirect
227. #388C23semidirect
228. #388C23semidirect
229. #386C23semidirect
230. #386C23semidirect
231. #385C23semidirect
232. #385C23semidirect
233. #385C23semidirect
234. #383C23semidirect
236. #380C23semidirect
237. #380C23semidirect
240. C4×C4⋊C4C23semidirect
241. C4×C4⋊C4C23semidirect
242. C4×C4⋊C4C23semidirect
244. C4×C22⋊C4C23semidirect
245. C4×C22⋊C4C23semidirect
338. #117C2×D4semidirect
751. C2#35982direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#5522
C22×#5182
#359822
C2×#25622
C2×#25982
C2×#24542
C2×#24272
C2×#24352
C2×#24082
C2×#24802
C2×#24182
C2×#26252
C2×#26332
C2×#23952
C2×#23922
C2×#23672
C2×#23612
C2×#23472