Finite Group Databasebeta

← C2×#42581 #7640969

Subgroups — C2×#42581 #7640969

Order 512.

7744 conjugacy classes of subgroups.

The subgroup lattice has 1164 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2778C212yesmaximal, complemented
2C2×#2697C212yesmaximal, complemented
3C2×#2678C212yesmaximal, complemented
4C2×#2676C212yesmaximal, complemented
5#42581C2132yesmaximal, direct product factor
6C2×#2825C212yesmaximal, complemented
7C2×#2548C211yesmaximal, characteristic, complemented
8C2×#2538C211yesmaximal, characteristic, complemented
9C2×#2500C211yesmaximal, characteristic, complemented
10C2×#2494C211yesmaximal, characteristic, complemented
11C2×#2414C211yesmaximal, characteristic, complemented
12C2×#2428C211yesmaximal, characteristic, complemented
13C2×#2428C211yesmaximal, characteristic, complemented
14C2×#2422C211yesmaximal, characteristic, complemented
15C2×#2433C211yesmaximal, characteristic, complemented
16C2×#2408C211yesmaximal, characteristic, complemented
17C2×#2472C212yesmaximal, complemented
18C2×#2644C211yesmaximal, characteristic, complemented
19C2×#2648C212yesmaximal, complemented
20C2×#2617C212yesmaximal, complemented
21C2×#2398C211yesmaximal, characteristic, complemented
22C2×#2363C211yesmaximal, characteristic, complemented
23C2×D4×C22⋊C4C211yesmaximal, characteristic, complemented
24C2×#2328C211yesmaximal, characteristic, complemented
25C24×D4C2211yescharacteristic
26C22×#127C2211yescharacteristic
27C22×#127C2211yescharacteristic
28C22×#124C2212yescomplemented
29C22×#123C2212yes—
30C22×C22⋊Q8C2212yescomplemented
31C22×#121C2211yescharacteristic
32C22×#121C2211yescharacteristic
33C22×#121C2211yescharacteristic
34C22×#121C2211yescharacteristic, complemented
35C22×#121C2212yescomplemented
36C22×#121C2212yescomplemented
37C22×#120C2212yes—
38C22×#120C2212yes—
39C22×#120C2212yes—
40C22×C4×Q8C2211yescharacteristic, complemented
41C22×C4×D4C2211yescharacteristic
42C22×C4×D4C2211yescharacteristic
43C22×C4×D4C2211yescharacteristic
44C22×C4×D4C2211yescharacteristic, complemented
45C22×#117C2211yescharacteristic, complemented
46C23×C22⋊C4C2212yes—
47#2825C22132yescomplemented
48#2778C22132yescomplemented
49#2697C22132yescomplemented
50#2678C22132yescomplemented
51#2676C22132yescomplemented
52#2648C22132yescomplemented
53#2644C22116yescomplemented
54#2617C22132yescomplemented
55#2548C22116yescomplemented
56#2538C22116yescomplemented
57#2500C22116yescomplemented
58#2494C22116yescomplemented
59#2472C22132yescomplemented
60#2433C22116yescomplemented
61#2428C22116yescomplemented
62#2428C22116yescomplemented
63#2422C22116yescomplemented
64#2414C22116yescomplemented
65#2408C22116yescomplemented
66C2×#401C2212yescomplemented
67#2398C22116yescomplemented
68C2×#400C2211yescharacteristic, complemented
69C2×#400C2211yescharacteristic, complemented
70C2×#397C2211yescharacteristic
71C2×#397C2212yes—
72C2×#397C2212yescomplemented
73C2×#397C2212yescomplemented
74C2×#397C2211yescharacteristic, complemented
75C2×#397C2212yescomplemented
76C2×#397C2212yescomplemented
77C2×#396C2212yescomplemented
78C2×#396C2212yescomplemented
79C2×#396C2212yescomplemented
80C2×#394C2212yes—
81C2×#394C2212yes—
82C2×#394C2211yescharacteristic
83C2×#394C2211yescharacteristic
84C2×#394C2212yescomplemented
85C2×#394C2212yescomplemented
86C2×#394C2212yescomplemented
87C2×#394C2212yescomplemented
88C2×#394C2212yescomplemented
89C2×#394C2212yescomplemented
90C2×#394C2212yescomplemented
91C2×#393C2211yescharacteristic
92C2×#393C2211yescharacteristic, complemented
93C2×#392C2212yes—
94C2×#392C2212yes—
95C2×#392C2212yes—
96C2×#392C2212yes—
97C2×#392C2212yescomplemented
98C2×#392C2212yescomplemented
99#2363C22116yescomplemented
100D4×C22⋊C4C22116yescomplemented
101#2328C22116yescomplemented
102C2×#390C2211yescharacteristic
103C2×#390C2211yescharacteristic
104C2×#390C2211yescharacteristic
105C2×#390C2211yescharacteristic
106C2×#390C2211yescharacteristic
107C2×#390C2211yescharacteristic
108C2×#390C2212yes—
109C2×#390C2212yescomplemented
110C2×#390C2211yescharacteristic, complemented
111C2×#390C2212yescomplemented
112C2×#390C2211yescharacteristic, complemented
113C2×#389C2211yescharacteristic, complemented
114C2×#389C2211yescharacteristic, complemented
115C2×#389C2211yescharacteristic, complemented
116C2×#389C2211yescharacteristic, complemented
117C2×#388C2212yes—
118C2×#388C2212yescomplemented
119C2×#388C2212yescomplemented
120C2×#388C2212yescomplemented
121C2×#388C2212yescomplemented
122C2×#387C2212yescomplemented
123C2×#386C2212yes—
124C2×#386C2212yes—
125C2×#386C2212yescomplemented
126C2×#386C2212yescomplemented
127C2×#386C2212yescomplemented
128C2×#386C2212yescomplemented
129C2×#386C2212yescomplemented
130C2×#386C2212yescomplemented
131C2×#386C2212yescomplemented
132C2×#385C2212yescomplemented
133C2×#384C2211yescharacteristic, complemented
134C2×#382C2211yescharacteristic, complemented
135C2×#380C2211yescharacteristic
136C2×#380C2211yescharacteristic
137C2×#380C2212yescomplemented
138C2×#379C2212yes—
139C2×#379C2212yes—
140C2×C4×C4⋊C4C2211yescharacteristic, complemented
141C2×C4×C22⋊C4C2211yescharacteristic
142C2×C4×C22⋊C4C2211yescharacteristic
143C2×C4×C22⋊C4C2212yescomplemented
144C2×C4×C22⋊C4C2211yescharacteristic, complemented
145C2×C4×C22⋊C4C2211yescharacteristic, complemented
146C2×#376C2211yescharacteristic, complemented
147C26C2312yes—
148C23×Q8C2311yescharacteristic
149C23×D4—28no—
150C23×D4—44no—
151C23×D4—44no—
152C23×D4C2311yescharacteristic
153C23×D4C2311yescharacteristic
154C23×D4C2311yescharacteristic
155C23×D4C2318yes—
156C23×D4C2312yes—
157C23×D4C2311yescharacteristic
158C23×D4C2312yes—
159C23×D4C2312yes—
160C23×D4C2312yes—
161C23×D4C2312yes—
162C23×D4C2312yes—
163C23×D4C2312yes—
164C23×D4C2312yes—
165C23×D4C2312yes—
166C24×C4C2311yescharacteristic
167C24×C4C2311yescharacteristic
168C24×C4C2312yes—
169C24×C4C2312yes—
170C24×C4C2312yes—
171C2×#127—28no—
172C2×#127—44no—
173C2×#127C2318yes—
174C2×#127C2318yes—
175C2×#124—48no—
176C2×#124C23116yescomplemented
177C2×#123—48no—
178C2×#123C23116yes—
179C2×C22⋊Q8—48no—
180C2×C22⋊Q8C23116yescomplemented
181C2×#121—28no—
182C2×#121—48no—
183C2×#121—48no—
184C2×#121—44no—
185C2×#121—44no—
186C2×#121—44no—
187C2×#121C2318yes—
188C2×#121C2318yes—
189C2×#121C2318yes—
190C2×#121C23116yescomplemented
191C2×#121C2318yescomplemented
192C2×#121C23116yescomplemented
193C2×#120—48no—
194C2×#120—48no—
195C2×#120—48no—
196C2×#120C23116yes—
197C2×#120C23116yes—
198C2×#120C23116yes—
199C2×C4×Q8—44no—
200C2×C4×Q8C2318yescomplemented
201C2×C4×D4—44no—
202C2×C4×D4—44no—
203C2×C4×D4—44no—
204C2×C4×D4—44no—
205C2×C4×D4C2318yes—
206C2×C4×D4C2318yes—
207C2×C4×D4C2318yes—
208C2×C4×D4C2318yescomplemented
209C2×#117—44no—
210C2×#117C2318yescomplemented
211C22×C4⋊C4C2312yes—
212C22×C4⋊C4C2311yescharacteristic
213C22×C4⋊C4C2311yescharacteristic
214C22×C4⋊C4C2311yescharacteristic
215C22×C4⋊C4C2311yescharacteristic
216C22×C4⋊C4C2311yescharacteristic
217C22×C4⋊C4C2311yescharacteristic
218C22×C4⋊C4C2311yescharacteristic
219C22×C4⋊C4C2312yes—
220C22×C4⋊C4C2311yescharacteristic
221C22×C4⋊C4C2311yescharacteristic
222C22×C4⋊C4C2312yes—
223C22×C4⋊C4C2312yes—
224C22×C4⋊C4C2312yes—
225C22×C4⋊C4C2312yes—
226C22×C22⋊C4—48no—
227C22×C22⋊C4C2312yes—
228C22×C22⋊C4C2311yescharacteristic
229C22×C22⋊C4C2311yescharacteristic
230C22×C22⋊C4C2311yescharacteristic
231C22×C22⋊C4C2311yescharacteristic
232C22×C22⋊C4C2312yes—
233C22×C22⋊C4C2312yes—
234C22×C22⋊C4C2311yescharacteristic
235C22×C22⋊C4C2312yes—
236C22×C22⋊C4C2311yescharacteristic
237C22×C22⋊C4C2312yes—
238C22×C22⋊C4C23116yes—
239C22×C22⋊C4C2311yescharacteristic
240C22×C22⋊C4C2312yes—
241C22×C22⋊C4C2312yes—
242C22×C22⋊C4C2312yes—
243C22×C22⋊C4C2312yes—
244C22×C22⋊C4C2312yes—
245C22×C22⋊C4C2312yes—
246C22×C22⋊C4C2312yes—
247C22×C22⋊C4C2312yes—
248C22×C22⋊C4C2312yes—
249C22×C22⋊C4C2311yescharacteristic
250C22×C22⋊C4C2311yescharacteristic
251C22×C22⋊C4C2312yes—
252C22×C22⋊C4C2312yes—
253C22×C22⋊C4C2312yes—
254C22×C22⋊C4C2312yes—
255C22×C22⋊C4C2311yescharacteristic
256C22×C22⋊C4C2312yes—
257C22×C22⋊C4C2312yes—
258C22×C22⋊C4C2312yes—
259C22×C22⋊C4C2312yes—
260C22×C22⋊C4C2312yes—
261C22×C22⋊C4C2312yes—
262C22×C22⋊C4C2312yes—
263C22×C22⋊C4C2312yes—
264C22×C42C2311yescharacteristic
265C22×C42C2311yescharacteristic
266C22×C42C2311yescharacteristic
267C22×C42C2311yescharacteristic
268C22×C42C2311yescharacteristic
269C22×C42C2312yes—
270C22×C42C2312yes—
271#401C23116yescomplemented
272#400C2318yescomplemented
273#400C2318yescomplemented
274#397C23116yes—
275#397C2318yes—
276#397C2318yescomplemented
277#397C23116yescomplemented
278#397C23116yescomplemented
279#397C23116yescomplemented
280#397C23116yescomplemented
281#396C23116yescomplemented
282#396C23116yescomplemented
283#396C23116yescomplemented
284#394C2318yes—
285#394C23116yes—
286#394C23116yes—
287#394C2318yes—
288#394C23116yescomplemented
289#394C23116yescomplemented
290#394C23116yescomplemented
291#394C23116yescomplemented
292#394C23116yescomplemented
293#394C23116yescomplemented
294#394C23116yescomplemented
295#393C2318yes—
296#393C2318yescomplemented
297#392C23116yes—
298#392C23116yes—
299#392C23116yes—
300#392C23116yes—
301#392C23116yescomplemented
302#392C23116yescomplemented
303#390C2318yes—
304#390C2318yes—
305#390C2318yes—
306#390C2318yes—
307#390C2318yes—
308#390C2318yes—
309#390C23116yes—
310#390C2318yescomplemented
311#390C23116yescomplemented
312#390C23116yescomplemented
313#390C2318yescomplemented
314#389C2318yescomplemented
315#389C2318yescomplemented
316#389C2318yescomplemented
317#389C2318yescomplemented
318#388C23116yes—
319#388C23116yescomplemented
320#388C23116yescomplemented
321#388C23116yescomplemented
322#388C23116yescomplemented
323#387C23116yescomplemented
324#386C23116yes—
325#386C23116yes—
326#386C23116yescomplemented
327#386C23116yescomplemented
328#386C23116yescomplemented
329#386C23116yescomplemented
330#386C23116yescomplemented
331#386C23116yescomplemented
332#386C23116yescomplemented
333#385C23116yescomplemented
334#384C2318yescomplemented
335#382C2318yescomplemented
336#380C2318yes—
337#380C2318yes—
338#380C23116yescomplemented
339#379C23116yes—
340#379C23116yes—
341C4×C4⋊C4C2318yescomplemented
342C4×C22⋊C4C2318yes—
343C4×C22⋊C4C2318yes—
344C4×C22⋊C4C23116yescomplemented
345C4×C22⋊C4C2318yescomplemented
346C4×C22⋊C4C2318yescomplemented
347#376C2318yescomplemented
348C2×#95C2311yescharacteristic
349C2×#95C2311yescharacteristic
350C2×#95C2312yes—
351C2×#95C2312yes—
352C2×#95C2312yes—
353C2×#95C2312yes—
354C2×#95C2311yescharacteristic
355C2×#95C2311yescharacteristic
356C2×#95C2311yescharacteristic
357C2×#95C2311yescharacteristic
358C2×#95C2311yescharacteristic
359C2×#95C2312yes—
360C2×#95C2311yescharacteristic
361C2×#95C2311yescharacteristic
362C2×#95C2311yescharacteristic
363C2×#95C2312yes—
364C2×#95C2312yes—
365C2×#95C2312yes—
366C2×#95C2312yes—
367C2×#95C2311yescharacteristic
368C2×#95C2311yescharacteristic
369C25—28no—
370C25—28no—
371C25—44no—
372C25—44no—
373C25—44no—
374C25—44no—
375C25—44no—
376C25C2412yes—
377C25C2411yescharacteristic
378C25C2412yes—
379C25C2412yes—
380C25C2411yescharacteristic
381C25C2418yes—
382C22×Q8—24no—
383C22×Q8—24no—
384C22×Q8—42no—
385C22×Q8C2414yes—
386C22×D4—28no—
387C22×D4—24no—
388C22×D4—28no—
389C22×D4—28no—
390C22×D4—28no—
391C22×D4—28no—
392C22×D4—232no—
393C22×D4—24no—
394C22×D4—24no—
395C22×D4—24no—
396C22×D4—24no—
397C22×D4—24no—
398C22×D4—24no—
399C22×D4—24no—
400C22×D4—24no—
401C22×D4—28no—
402C22×D4—416no—
403C22×D4—416no—
404C22×D4—42no—
405C22×D4—44no—
406C22×D4—44no—
407C22×D4—42no—
408C22×D4—44no—
409C22×D4—44no—
410C22×D4—44no—
411C22×D4—44no—
412C22×D4—44no—
413C22×D4—44no—
414C22×D4—44no—
415C22×D4—44no—
416C22×D4—44no—
417C22×D4—44no—
418C22×D4—44no—
419C22×D4—44no—
420C22×D4—44no—
421C22×D4—44no—
422C22×D4—44no—
423C22×D4—44no—
424C22×D4—44no—
425C22×D4—44no—
426C22×D4—44no—
427C22×D4—464no—
428C22×D4#4118yes—
429C22×D4C2414yes—
430C22×D4C2414yes—
431C22×D4C2414yes—
432C22×D4C2414yes—
433C22×D4C2418yes—
434C22×D4C2418yes—
435C22×D4C2418yes—
436C22×D4C2418yes—
437C22×D4C2418yes—
438C22×D4C2418yes—
439C22×D4C2418yes—
440C22×D4C2418yes—
441C22×D4C2418yes—
442C23×C4—24no—
443C23×C4—24no—
444C23×C4—24no—
445C23×C4—24no—
446C23×C4—24no—
447C23×C4—24no—
448C23×C4—28no—
449C23×C4—44no—
450C23×C4—44no—
451C23×C4—44no—
452C23×C4—44no—
453C23×C4—44no—
454C23×C4—44no—
455C23×C4—44no—
456C23×C4—44no—
457C23×C4C2414yes—
458C23×C4C2414yes—
459C23×C4C2411yescharacteristic
460C23×C4C2411yescharacteristic
461C23×C4C2411yescharacteristic
462C23×C4C2412yes—
463C23×C4C2412yes—
464C23×C4C2412yes—
465C23×C4C2411yescharacteristic
466C23×C4C2411yescharacteristic
467C23×C4C2411yescharacteristic
468C23×C4C2412yes—
469C23×C4C2412yes—
470C23×C4C2411yescharacteristic
471C23×C4C2411yescharacteristic
472C23×C4C2411yescharacteristic
473C23×C4C2411yescharacteristic
474C23×C4C2411yescharacteristic
475C23×C4C2411yescharacteristic
476C23×C4C2418yes—
477C23×C4C2418yes—
478C23×C4C2418yes—
479C23×C4C2411yescharacteristic
480#127—232no—
481#127—416no—
482#124—432no—
483#123—432no—
484C22⋊Q8—432no—
485#121—232no—
486#121—432no—
487#121—432no—
488#121—416no—
489#121—416no—
490#121—416no—
491#120—432no—
492#120—432no—
493#120—432no—
494C4×Q8—416no—
495C4×D4—416no—
496C4×D4—416no—
497C4×D4—416no—
498C4×D4—416no—
499#117—416no—
500C2×C4⋊C4—24no—
501C2×C4⋊C4—24no—
502C2×C4⋊C4—24no—
503C2×C4⋊C4—24no—
504C2×C4⋊C4—24no—
505C2×C4⋊C4—28no—
506C2×C4⋊C4—42no—
507C2×C4⋊C4—42no—
508C2×C4⋊C4—42no—
509C2×C4⋊C4—42no—
510C2×C4⋊C4—44no—
511C2×C4⋊C4—44no—
512C2×C4⋊C4—44no—
513C2×C4⋊C4—44no—
514C2×C4⋊C4—44no—
515C2×C4⋊C4C2414yes—
516C2×C4⋊C4C2414yes—
517C2×C4⋊C4C2414yes—
518C2×C4⋊C4C2414yes—
519C2×C4⋊C4C2414yes—
520C2×C4⋊C4C2418yes—
521C2×C4⋊C4C2414yes—
522C2×C4⋊C4C2414yes—
523C2×C4⋊C4C2414yes—
524C2×C4⋊C4C2414yes—
525C2×C4⋊C4C2418yes—
526C2×C4⋊C4C2418yes—
527C2×C4⋊C4C2418yes—
528C2×C4⋊C4C2418yes—
529C2×C4⋊C4C2418yes—
530C2×C22⋊C4—28no—
531C2×C22⋊C4—24no—
532C2×C22⋊C4—28no—
533C2×C22⋊C4—24no—
534C2×C22⋊C4—24no—
535C2×C22⋊C4—28no—
536C2×C22⋊C4—24no—
537C2×C22⋊C4—28no—
538C2×C22⋊C4—24no—
539C2×C22⋊C4—24no—
540C2×C22⋊C4—28no—
541C2×C22⋊C4—432no—
542C2×C22⋊C4—44no—
543C2×C22⋊C4—44no—
544C2×C22⋊C4—44no—
545C2×C22⋊C4—42no—
546C2×C22⋊C4—44no—
547C2×C22⋊C4—42no—
548C2×C22⋊C4—44no—
549C2×C22⋊C4—44no—
550C2×C22⋊C4—42no—
551C2×C22⋊C4—42no—
552C2×C22⋊C4—44no—
553C2×C22⋊C4—44no—
554C2×C22⋊C4—44no—
555C2×C22⋊C4—44no—
556C2×C22⋊C4—44no—
557C2×C22⋊C4—44no—
558C2×C22⋊C4—44no—
559C2×C22⋊C4—44no—
560C2×C22⋊C4—44no—
561C2×C22⋊C4—44no—
562C2×C22⋊C4—44no—
563C2×C22⋊C4—44no—
564C2×C22⋊C4—44no—
565C2×C22⋊C4—44no—
566C2×C22⋊C4—44no—
567C2×C22⋊C4C2414yes—
568C2×C22⋊C4C2418yes—
569C2×C22⋊C4C2414yes—
570C2×C22⋊C4C2414yes—
571C2×C22⋊C4C2418yes—
572C2×C22⋊C4C2418yes—
573C2×C22⋊C4C2418yes—
574C2×C22⋊C4C2414yes—
575C2×C22⋊C4C2414yes—
576C2×C22⋊C4C2418yes—
577C2×C22⋊C4C2414yes—
578C2×C22⋊C4C2418yes—
579C2×C22⋊C4C2418yes—
580C2×C22⋊C4C2418yes—
581C2×C22⋊C4C2414yes—
582C2×C22⋊C4C2418yes—
583C2×C22⋊C4C2418yes—
584C2×C22⋊C4C2414yes—
585C2×C22⋊C4C2418yes—
586C2×C22⋊C4C2418yes—
587C2×C22⋊C4C2418yes—
588C2×C22⋊C4C2418yes—
589C2×C22⋊C4C2418yes—
590C2×C22⋊C4C2418yes—
591C2×C22⋊C4C2418yes—
592C2×C22⋊C4C2418yes—
593C2×C22⋊C4C2418yes—
594C2×C22⋊C4C2418yes—
595C2×C22⋊C4C2418yes—
596C2×C22⋊C4C2418yes—
597C2×C22⋊C4C2418yes—
598C2×C22⋊C4C2418yes—
599C2×C22⋊C4C2414yes—
600C2×C22⋊C4C2414yes—
601C2×C22⋊C4C2418yes—
602C2×C22⋊C4C2418yes—
603C2×C42—24no—
604C2×C42—24no—
605C2×C42—24no—
606C2×C42—24no—
607C2×C42—24no—
608C2×C42—44no—
609C2×C42—44no—
610C2×C42C2414yes—
611C2×C42C2414yes—
612C2×C42C2414yes—
613C2×C42C2414yes—
614C2×C42C2414yes—
615C2×C42C2418yes—
616C2×C42C2418yes—
617#95C2414yes—
618#95C2414yes—
619#95C2414yes—
620#95C2414yes—
621#95C2414yes—
622#95C2414yes—
623#95C2414yes—
624#95C2414yes—
625#95C2414yes—
626#95C2414yes—
627#95C2414yes—
628#95C2418yes—
629#95C2414yes—
630#95C2418yes—
631#95C2418yes—
632#95C2418yes—
633#95C2418yes—
634#95C2418yes—
635#95C2418yes—
636#95C2418yes—
637#95C2418yes—
638C24—22no—
639C24—22no—
640C24—24no—
641C24—22no—
642C24—24no—
643C24—22no—
644C24—24no—
645C24—24no—
646C24—24no—
647C24—22no—
648C24—24no—
649C24—22no—
650C24—22no—
651C24—24no—
652C24—24no—
653C24—24no—
654C24—24no—
655C24—22no—
656C24—22no—
657C24—22no—
658C24—24no—
659C24—24no—
660C24—24no—
661C24—22no—
662C24—24no—
663C24—24no—
664C24—24no—
665C24—24no—
666C24—22no—
667C24—24no—
668C24—22no—
669C24—24no—
670C24—24no—
671C24—216no—
672C24—216no—
673C24—48no—
674C24—48no—
675C24—48no—
676C24—48no—
677C24—48no—
678C24—432no—
679C24—432no—
680C24—816no—
681C24—816no—
682C24—816no—
683C24—816no—
684C24—816no—
685C24C2×#4118yes—
686C24H(5,𝔽2)14yes—
687C24C2514yes—
688C24C2512yes—
689C24C2514yes—
690C24C2514yes—
691C24C2512yes—
692C24C2511yescharacteristic
693C2×Q8—28no—
694C2×Q8—28no—
695C2×Q8—44no—
696C2×Q8—416no—
697C2×D4—216no—
698C2×D4—28no—
699C2×D4—216no—
700C2×D4—216no—
701C2×D4—216no—
702C2×D4—216no—
703C2×D4—232no—
704C2×D4—28no—
705C2×D4—28no—
706C2×D4—28no—
707C2×D4—28no—
708C2×D4—28no—
709C2×D4—28no—
710C2×D4—28no—
711C2×D4—28no—
712C2×D4—216no—
713C2×D4—44no—
714C2×D4—48no—
715C2×D4—48no—
716C2×D4—44no—
717C2×D4—48no—
718C2×D4—48no—
719C2×D4—48no—
720C2×D4—48no—
721C2×D4—48no—
722C2×D4—48no—
723C2×D4—48no—
724C2×D4—48no—
725C2×D4—48no—
726C2×D4—48no—
727C2×D4—48no—
728C2×D4—48no—
729C2×D4—48no—
730C2×D4—48no—
731C2×D4—48no—
732C2×D4—48no—
733C2×D4—48no—
734C2×D4—48no—
735C2×D4—48no—
736C2×D4—4128no—
737C2×D4—416no—
738C2×D4—432no—
739C2×D4—416no—
740C2×D4—416no—
741C2×D4—816no—
742C2×D4—816no—
743C2×D4—816no—
744C2×D4—816no—
745C2×D4—816no—
746C2×D4—816no—
747C2×D4—816no—
748C2×D4—816no—
749C2×D4C2×#41116yes—
750C22×C4—22no—
751C22×C4—22no—
752C22×C4—22no—
753C22×C4—22no—
754C22×C4—22no—
755C22×C4—22no—
756C22×C4—22no—
757C22×C4—24no—
758C22×C4—22no—
759C22×C4—22no—
760C22×C4—22no—
761C22×C4—22no—
762C22×C4—22no—
763C22×C4—22no—
764C22×C4—22no—
765C22×C4—22no—
766C22×C4—24no—
767C22×C4—24no—
768C22×C4—24no—
769C22×C4—24no—
770C22×C4—22no—
771C22×C4—24no—
772C22×C4—22no—
773C22×C4—22no—
774C22×C4—22no—
775C22×C4—22no—
776C22×C4—22no—
777C22×C4—24no—
778C22×C4—24no—
779C22×C4—22no—
780C22×C4—22no—
781C22×C4—22no—
782C22×C4—22no—
783C22×C4—22no—
784C22×C4—24no—
785C22×C4—24no—
786C22×C4—24no—
787C22×C4—22no—
788C22×C4—24no—
789C22×C4—22no—
790C22×C4—24no—
791C22×C4—24no—
792C22×C4—22no—
793C22×C4—22no—
794C22×C4—24no—
795C22×C4—22no—
796C22×C4—22no—
797C22×C4—22no—
798C22×C4—22no—
799C22×C4—28no—
800C22×C4—28no—
801C22×C4—28no—
802C22×C4—28no—
803C22×C4—28no—
804C22×C4—28no—
805C22×C4—216no—
806C22×C4—48no—
807C22×C4—48no—
808C22×C4—48no—
809C22×C4—48no—
810C22×C4—48no—
811C22×C4—48no—
812C22×C4—48no—
813C22×C4—48no—
814C22×C4—416no—
815C22×C4—416no—
816C22×C4—816no—
817C22×C4—816no—
818C22×C4—816no—
819C22×C4C2×#4114yes—
820C22×C4H(5,𝔽2)14yes—
821C22×C4H(5,𝔽2)14yes—
822C22×C4H(5,𝔽2)14yes—
823C22×C4H(5,𝔽2)14yes—
824C22×C4C2512yes—
825C22×C4C2512yes—
826C22×C4C2512yes—
827C22×C4C2512yes—
828C22×C4C2512yes—
829C22×C4C2512yes—
830C22×C4C2514yes—
831C22×C4C2514yes—
832C22×C4C2512yes—
833C22×C4C2512yes—
834C22×C4C2514yes—
835C22×C4C2514yes—
836C22×C4C2512yes—
837C22×C4C2512yes—
838C22×C4C2514yes—
839C22×C4C2512yes—
840C22×C4C2512yes—
841C22×C4C2512yes—
842C4⋊C4—28no—
843C4⋊C4—28no—
844C4⋊C4—28no—
845C4⋊C4—28no—
846C4⋊C4—28no—
847C4⋊C4—216no—
848C4⋊C4—44no—
849C4⋊C4—44no—
850C4⋊C4—44no—
851C4⋊C4—44no—
852C4⋊C4—48no—
853C4⋊C4—48no—
854C4⋊C4—48no—
855C4⋊C4—48no—
856C4⋊C4—48no—
857C22⋊C4—216no—
858C22⋊C4—28no—
859C22⋊C4—216no—
860C22⋊C4—28no—
861C22⋊C4—28no—
862C22⋊C4—216no—
863C22⋊C4—28no—
864C22⋊C4—216no—
865C22⋊C4—28no—
866C22⋊C4—28no—
867C22⋊C4—216no—
868C22⋊C4—48no—
869C22⋊C4—48no—
870C22⋊C4—48no—
871C22⋊C4—44no—
872C22⋊C4—48no—
873C22⋊C4—44no—
874C22⋊C4—48no—
875C22⋊C4—48no—
876C22⋊C4—44no—
877C22⋊C4—44no—
878C22⋊C4—48no—
879C22⋊C4—48no—
880C22⋊C4—48no—
881C22⋊C4—48no—
882C22⋊C4—48no—
883C22⋊C4—48no—
884C22⋊C4—48no—
885C22⋊C4—48no—
886C22⋊C4—48no—
887C22⋊C4—48no—
888C22⋊C4—48no—
889C22⋊C4—48no—
890C22⋊C4—48no—
891C22⋊C4—48no—
892C22⋊C4—48no—
893C42—28no—
894C42—28no—
895C42—28no—
896C42—28no—
897C42—28no—
898C42—48no—
899C42—48no—
900C23—22no—
901C23—22no—
902C23—24no—
903C23—22no—
904C23—24no—
905C23—22no—
906C23—24no—
907C23—24no—
908C23—24no—
909C23—22no—
910C23—24no—
911C23—22no—
912C23—216no—
913C23—216no—
914C23—216no—
915C23—28no—
916C23—28no—
917C23—28no—
918C23—22no—
919C23—24no—
920C23—24no—
921C23—24no—
922C23—24no—
923C23—22no—
924C23—22no—
925C23—22no—
926C23—24no—
927C23—24no—
928C23—24no—
929C23—22no—
930C23—24no—
931C23—24no—
932C23—24no—
933C23—24no—
934C23—22no—
935C23—24no—
936C23—22no—
937C23—24no—
938C23—24no—
939C23—432no—
940C23—432no—
941C23—44no—
942C23—44no—
943C23—48no—
944C23—44no—
945C23—48no—
946C23—48no—
947C23—48no—
948C23—44no—
949C23—44no—
950C23—48no—
951C23—48no—
952C23—48no—
953C23—44no—
954C23—48no—
955C23—44no—
956C23—48no—
957C23—48no—
958C23—48no—
959C23—44no—
960C23—48no—
961C23—44no—
962C23—48no—
963C23—48no—
964C23—48no—
965C23—44no—
966C23—48no—
967C23—48no—
968C23—44no—
969C23—48no—
970C23—816no—
971C23—816no—
972C23—816no—
973C23—816no—
974C23—816no—
975C23—8128no—
976C23C22×#4118yes—
977C23C22×#4112yes—
978C23C2×H(5,𝔽2)14yes—
979C23C2×H(5,𝔽2)12yes—
980C23C2×H(5,𝔽2)12yes—
981C23C2×H(5,𝔽2)12yes—
982C23C2×H(5,𝔽2)12yes—
983C23C2×H(5,𝔽2)12yes—
984C23#58512yes—
985C23C2611yescharacteristic
986Q8—416no—
987D4—232no—
988D4—416no—
989D4—432no—
990D4—416no—
991D4—416no—
992D4—816no—
993D4—816no—
994D4—816no—
995D4—816no—
996D4—816no—
997D4—816no—
998D4—816no—
999D4—816no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—28no—
1005C2×C4—28no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—24no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—22no—
1013C2×C4—22no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—24no—
1019C2×C4—24no—
1020C2×C4—24no—
1021C2×C4—24no—
1022C2×C4—22no—
1023C2×C4—24no—
1024C2×C4—22no—
1025C2×C4—22no—
1026C2×C4—22no—
1027C2×C4—22no—
1028C2×C4—22no—
1029C2×C4—24no—
1030C2×C4—24no—
1031C2×C4—22no—
1032C2×C4—22no—
1033C2×C4—22no—
1034C2×C4—22no—
1035C2×C4—22no—
1036C2×C4—24no—
1037C2×C4—24no—
1038C2×C4—24no—
1039C2×C4—22no—
1040C2×C4—24no—
1041C2×C4—22no—
1042C2×C4—24no—
1043C2×C4—24no—
1044C2×C4—22no—
1045C2×C4—22no—
1046C2×C4—24no—
1047C2×C4—22no—
1048C2×C4—22no—
1049C2×C4—22no—
1050C2×C4—22no—
1051C2×C4—44no—
1052C2×C4—44no—
1053C2×C4—44no—
1054C2×C4—48no—
1055C2×C4—44no—
1056C2×C4—48no—
1057C2×C4—44no—
1058C2×C4—44no—
1059C2×C4—44no—
1060C2×C4—44no—
1061C2×C4—44no—
1062C2×C4—48no—
1063C2×C4—48no—
1064C2×C4—48no—
1065C2×C4—44no—
1066C2×C4—416no—
1067C2×C4—416no—
1068C2×C4—816no—
1069C2×C4—816no—
1070C2×C4—816no—
1071C2×C4#538116yes—
1072C2×C4C22×#4114yes—
1073C2×C4C2×H(5,𝔽2)14yes—
1074C2×C4C2×H(5,𝔽2)14yes—
1075C2×C4C2×H(5,𝔽2)14yes—
1076C2×C4C2×H(5,𝔽2)14yes—
1077C22—24no—
1078C22—28no—
1079C22—24no—
1080C22—28no—
1081C22—28no—
1082C22—24no—
1083C22—44no—
1084C22—42no—
1085C22—44no—
1086C22—44no—
1087C22—42no—
1088C22—42no—
1089C22—432no—
1090C22—416no—
1091C22—42no—
1092C22—44no—
1093C22—44no—
1094C22—42no—
1095C22—44no—
1096C22—44no—
1097C22—42no—
1098C22—44no—
1099C22—44no—
1100C22—42no—
1101C22—44no—
1102C22—42no—
1103C22—44no—
1104C22—44no—
1105C22—44no—
1106C22—42no—
1107C22—44no—
1108C22—42no—
1109C22—44no—
1110C22—44no—
1111C22—42no—
1112C22—44no—
1113C22—44no—
1114C22—864no—
1115C22—88no—
1116C22—816no—
1117C22—816no—
1118C22C2×#53814yes—
1119C22#351414yes—
1120C22#351914yes—
1121C22#353714yes—
1122C22#354214yes—
1123C22#354314yes—
1124C22#354614yes—
1125C22C23×#4111yescharacteristic
1126C22C22×H(5,𝔽2)11yescharacteristic
1127C22C22×H(5,𝔽2)11yescharacteristic
1128C22C22×H(5,𝔽2)11yescharacteristic
1129C22C22×H(5,𝔽2)11yescharacteristic
1130C22C22×H(5,𝔽2)11yescharacteristic
1131C22C2×#58511yescharacteristic
1132C4—24no—
1133C4—24no—
1134C4—44no—
1135C4—42no—
1136C4—42no—
1137C4—44no—
1138C4—44no—
1139C4—44no—
1140C4—42no—
1141C4—44no—
1142C4—42no—
1143C4—42no—
1144C4—42no—
1145C4—42no—
1146C4—42no—
1147C4—42no—
1148C4—42no—
1149C4C2×#53818yes—
1150C2—48no—
1151C2—44no—
1152C2—84no—
1153C2—82no—
1154C2—84no—
1155C2#4258118yesdirect product factor
1156C2C22×#53811yescharacteristic
1157C2C2×#354211yescharacteristic
1158C2C2×#353711yescharacteristic
1159C2C2×#354311yescharacteristic
1160C2C2×#354611yescharacteristic
1161C2C2×#351911yescharacteristic
1162C2C2×#351411yescharacteristic
subgroupG/H
center, socleC24C25
commutator, Frattini, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#2778C2semidirect
2. C2×#2697C2semidirect
3. C2×#2678C2semidirect
4. C2×#2676C2semidirect
5. #42581C2direct (N × H)
6. C2×#2825C2semidirect
7. C2×#2548C2semidirect
8. C2×#2538C2semidirect
9. C2×#2500C2semidirect
10. C2×#2494C2semidirect
11. C2×#2414C2semidirect
12. C2×#2428C2semidirect
13. C2×#2428C2semidirect
14. C2×#2422C2semidirect
15. C2×#2433C2semidirect
16. C2×#2408C2semidirect
17. C2×#2472C2semidirect
18. C2×#2644C2semidirect
19. C2×#2648C2semidirect
20. C2×#2617C2semidirect
21. C2×#2398C2semidirect
22. C2×#2363C2semidirect
23. C2×D4×C22⋊C4C2semidirect
24. C2×#2328C2semidirect
28. C22×#124C22semidirect
30. C22×C22⋊Q8C22semidirect
34. C22×#121C22semidirect
35. C22×#121C22semidirect
36. C22×#121C22semidirect
40. C22×C4×Q8C22semidirect
44. C22×C4×D4C22semidirect
45. C22×#117C22semidirect
47. #2825C22semidirect
48. #2778C22semidirect
49. #2697C22semidirect
50. #2678C22semidirect
51. #2676C22semidirect
52. #2648C22semidirect
53. #2644C22semidirect
54. #2617C22semidirect
55. #2548C22semidirect
56. #2538C22semidirect
57. #2500C22semidirect
58. #2494C22semidirect
59. #2472C22semidirect
60. #2433C22semidirect
61. #2428C22semidirect
62. #2428C22semidirect
63. #2422C22semidirect
64. #2414C22semidirect
65. #2408C22semidirect
66. C2×#401C22semidirect
67. #2398C22semidirect
68. C2×#400C22semidirect
69. C2×#400C22semidirect
72. C2×#397C22semidirect
73. C2×#397C22semidirect
74. C2×#397C22semidirect
75. C2×#397C22semidirect
76. C2×#397C22semidirect
77. C2×#396C22semidirect
78. C2×#396C22semidirect
79. C2×#396C22semidirect
84. C2×#394C22semidirect
85. C2×#394C22semidirect
86. C2×#394C22semidirect
87. C2×#394C22semidirect
88. C2×#394C22semidirect
89. C2×#394C22semidirect
90. C2×#394C22semidirect
92. C2×#393C22semidirect
97. C2×#392C22semidirect
98. C2×#392C22semidirect
99. #2363C22semidirect
100. D4×C22⋊C4C22semidirect
101. #2328C22semidirect
109. C2×#390C22semidirect
110. C2×#390C22semidirect
111. C2×#390C22semidirect
112. C2×#390C22semidirect
113. C2×#389C22semidirect
114. C2×#389C22semidirect
115. C2×#389C22semidirect
116. C2×#389C22semidirect
118. C2×#388C22semidirect
119. C2×#388C22semidirect
120. C2×#388C22semidirect
121. C2×#388C22semidirect
122. C2×#387C22semidirect
125. C2×#386C22semidirect
126. C2×#386C22semidirect
127. C2×#386C22semidirect
128. C2×#386C22semidirect
129. C2×#386C22semidirect
130. C2×#386C22semidirect
131. C2×#386C22semidirect
132. C2×#385C22semidirect
133. C2×#384C22semidirect
134. C2×#382C22semidirect
137. C2×#380C22semidirect
140. C2×C4×C4⋊C4C22semidirect
143. C2×C4×C22⋊C4C22semidirect
144. C2×C4×C22⋊C4C22semidirect
145. C2×C4×C22⋊C4C22semidirect
146. C2×#376C22semidirect
176. C2×#124C23semidirect
180. C2×C22⋊Q8C23semidirect
190. C2×#121C23semidirect
191. C2×#121C23semidirect
192. C2×#121C23semidirect
200. C2×C4×Q8C23semidirect
208. C2×C4×D4C23semidirect
210. C2×#117C23semidirect
271. #401C23semidirect
272. #400C23semidirect
273. #400C23semidirect
276. #397C23semidirect
277. #397C23semidirect
278. #397C23semidirect
279. #397C23semidirect
280. #397C23semidirect
281. #396C23semidirect
282. #396C23semidirect
283. #396C23semidirect
288. #394C23semidirect
289. #394C23semidirect
290. #394C23semidirect
291. #394C23semidirect
292. #394C23semidirect
293. #394C23semidirect
294. #394C23semidirect
296. #393C23semidirect
301. #392C23semidirect
302. #392C23semidirect
310. #390C23semidirect
311. #390C23semidirect
312. #390C23semidirect
313. #390C23semidirect
314. #389C23semidirect
315. #389C23semidirect
316. #389C23semidirect
317. #389C23semidirect
319. #388C23semidirect
320. #388C23semidirect
321. #388C23semidirect
322. #388C23semidirect
323. #387C23semidirect
326. #386C23semidirect
327. #386C23semidirect
328. #386C23semidirect
329. #386C23semidirect
330. #386C23semidirect
331. #386C23semidirect
332. #386C23semidirect
333. #385C23semidirect
334. #384C23semidirect
335. #382C23semidirect
338. #380C23semidirect
341. C4×C4⋊C4C23semidirect
344. C4×C22⋊C4C23semidirect
345. C4×C22⋊C4C23semidirect
346. C4×C22⋊C4C23semidirect
347. #376C23semidirect
1155. C2#42581direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#27782
C2×#26972
C2×#26782
C2×#26762
#425812
C2×#28252
C2×#25482
C2×#25382
C2×#25002
C2×#24942
C2×#24142
C2×#24282
C2×#24222
C2×#24332
C2×#24082
C2×#24722
C2×#26442
C2×#26482
C2×#26172
C2×#23982
C2×#23632
C2×D4×C22⋊C42
C2×#23282