Finite Group Databasebeta

← C2×#52981 #8092820

Subgroups — C2×#52981 #8092820

Order 512.

7148 conjugacy classes of subgroups.

The subgroup lattice has 1152 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#52981C2132yesmaximal, direct product factor
2C2×#2705C212yesmaximal, complemented
3C2×#2697C212yesmaximal, complemented
4C2×#2685C212yesmaximal, complemented
5C2×#2678C212yesmaximal, complemented
6C2×#2842C212yesmaximal, complemented
7C2×#2829C212yesmaximal, complemented
8C2×#2837C212yesmaximal, complemented
9C2×#2813C212yesmaximal, complemented
10C2×#2538C211yesmaximal, characteristic, complemented
11C2×#2540C211yesmaximal, characteristic, complemented
12C2×#2497C211yesmaximal, characteristic, complemented
13C2×#2512C211yesmaximal, characteristic, complemented
14C2×#2501C211yesmaximal, characteristic, complemented
15C2×#2448C211yesmaximal, characteristic, complemented
16C2×#2426C211yesmaximal, characteristic, complemented
17C2×#2435C211yesmaximal, characteristic, complemented
18C2×#2417C211yesmaximal, characteristic, complemented
19C2×#2416C211yesmaximal, characteristic, complemented
20C2×#2408C211yesmaximal, characteristic, complemented
21C2×#2408C211yesmaximal, characteristic, complemented
22C2×#2620C211yesmaximal, characteristic, complemented
23C2×#2624C211yesmaximal, characteristic, complemented
24C2×#2392C211yesmaximal, characteristic, complemented
25C24×D4C2211yescharacteristic
26C22×#126C2212yescomplemented
27C22×#124C2211yescharacteristic
28C22×#124C2211yescharacteristic
29C22×#123C2212yescomplemented
30C22×#123C2212yescomplemented
31C22×C22⋊Q8C2211yescharacteristic
32C22×C22⋊Q8C2211yescharacteristic, complemented
33C22×C22⋊Q8C2211yescharacteristic, complemented
34C22×#121C2211yescharacteristic
35C22×#121C2211yescharacteristic
36C22×#121C2211yescharacteristic
37C22×#121C2211yescharacteristic
38C22×#121C2212yescomplemented
39C22×#120C2212yes—
40C22×#120C2212yes—
41C22×C4×Q8C2211yescharacteristic, complemented
42C22×C4×D4C2211yescharacteristic
43C22×C4×D4C2211yescharacteristic
44C22×C4×D4C2211yescharacteristic, complemented
45C22×#117C2211yescharacteristic, complemented
46C23×C4⋊C4C2211yescharacteristic, complemented
47#2842C22132yescomplemented
48#2837C22132yescomplemented
49#2829C22132yescomplemented
50#2813C22132yescomplemented
51#2705C22132yescomplemented
52#2697C22132yescomplemented
53#2685C22132yescomplemented
54#2678C22132yescomplemented
55#2624C22116yescomplemented
56#2620C22116yescomplemented
57#2540C22116yescomplemented
58#2538C22116yescomplemented
59#2512C22116yescomplemented
60#2501C22116yescomplemented
61#2497C22116yescomplemented
62#2448C22116yescomplemented
63#2435C22116yescomplemented
64#2426C22116yescomplemented
65#2417C22116yescomplemented
66#2416C22116yescomplemented
67#2408C22116yescomplemented
68#2408C22116yescomplemented
69C2×#400C2212yescomplemented
70C2×#399C2212yescomplemented
71C2×#399C2212yescomplemented
72C2×#399C2212yescomplemented
73C2×#399C2212yescomplemented
74C2×#399C2212yescomplemented
75#2392C22116yescomplemented
76C2×#398C2211yescharacteristic, complemented
77C2×#398C2212yescomplemented
78C2×#397C2212yescomplemented
79C2×#397C2212yescomplemented
80C2×#397C2211yescharacteristic, complemented
81C2×#397C2212yescomplemented
82C2×#396C2211yescharacteristic
83C2×#396C2212yes—
84C2×#396C2212yes—
85C2×#396C2212yes—
86C2×#396C2212yescomplemented
87C2×#396C2212yescomplemented
88C2×#396C2212yescomplemented
89C2×#396C2212yescomplemented
90C2×#396C2212yescomplemented
91C2×#396C2212yescomplemented
92C2×#396C2211yescharacteristic, complemented
93C2×#394C2212yes—
94C2×#394C2212yes—
95C2×#394C2212yes—
96C2×#394C2212yes—
97C2×#394C2211yescharacteristic
98C2×#394C2211yescharacteristic
99C2×#394C2211yescharacteristic, complemented
100C2×#394C2212yescomplemented
101C2×#394C2212yescomplemented
102C2×#394C2212yescomplemented
103C2×#394C2212yescomplemented
104C2×#394C2212yescomplemented
105C2×#394C2212yescomplemented
106C2×#392C2212yes—
107C2×#392C2212yes—
108C2×#392C2211yescharacteristic
109C2×#392C2212yescomplemented
110C2×#391C2211yescharacteristic, complemented
111C2×#390C2211yescharacteristic
112C2×#390C2211yescharacteristic
113C2×#390C2211yescharacteristic
114C2×#390C2212yes—
115C2×#390C2211yescharacteristic
116C2×#390C2211yescharacteristic
117C2×#390C2211yescharacteristic
118C2×#390C2212yescomplemented
119C2×#390C2212yescomplemented
120C2×#390C2212yescomplemented
121C2×#389C2211yescharacteristic, complemented
122C2×#389C2211yescharacteristic, complemented
123C2×#389C2212yescomplemented
124C2×#389C2211yescharacteristic, complemented
125C2×#388C2212yes—
126C2×#388C2212yescomplemented
127C2×#388C2212yescomplemented
128C2×#388C2212yescomplemented
129C2×#388C2212yescomplemented
130C2×#387C2212yescomplemented
131C2×#386C2212yes—
132C2×#386C2212yescomplemented
133C2×#384C2211yescharacteristic, complemented
134C2×#384C2211yescharacteristic, complemented
135C2×#380C2211yescharacteristic
136C2×#380C2211yescharacteristic
137C2×#380C2212yescomplemented
138C2×#380C2211yescharacteristic, complemented
139C2×#379C2212yes—
140C2×#379C2212yes—
141C2×#379C2212yes—
142C2×#379C2212yes—
143C2×C4×C4⋊C4C2211yescharacteristic, complemented
144C2×C4×C4⋊C4C2211yescharacteristic, complemented
145C2×C4×C22⋊C4C2211yescharacteristic
146C2×C4×C22⋊C4C2211yescharacteristic, complemented
147C26C2312yes—
148C23×Q8C2311yescharacteristic
149C23×D4—44no—
150C23×D4—44no—
151C23×D4—44no—
152C23×D4C2311yescharacteristic
153C23×D4C2311yescharacteristic
154C23×D4C2311yescharacteristic
155C23×D4C2311yescharacteristic
156C23×D4C2311yescharacteristic
157C23×D4C2312yes—
158C23×D4C2312yes—
159C23×D4C2312yes—
160C23×D4C2318yes—
161C23×D4C2312yes—
162C23×D4C2312yes—
163C24×C4C2311yescharacteristic
164C24×C4C2311yescharacteristic
165C24×C4C2311yescharacteristic
166C24×C4C2312yes—
167C2×#126—48no—
168C2×#126C23116yescomplemented
169C2×#124—44no—
170C2×#124—44no—
171C2×#124C2318yes—
172C2×#124C2318yes—
173C2×#123—48no—
174C2×#123—48no—
175C2×#123C23116yescomplemented
176C2×#123C23116yescomplemented
177C2×C22⋊Q8—44no—
178C2×C22⋊Q8—44no—
179C2×C22⋊Q8—44no—
180C2×C22⋊Q8C2318yes—
181C2×C22⋊Q8C2318yescomplemented
182C2×C22⋊Q8C2318yescomplemented
183C2×#121—44no—
184C2×#121—44no—
185C2×#121—44no—
186C2×#121—44no—
187C2×#121—48no—
188C2×#121C2318yes—
189C2×#121C2318yes—
190C2×#121C2318yes—
191C2×#121C2318yes—
192C2×#121C23116yescomplemented
193C2×#120—48no—
194C2×#120—48no—
195C2×#120C23116yes—
196C2×#120C23116yes—
197C2×C4×Q8—44no—
198C2×C4×Q8C2318yescomplemented
199C2×C4×D4—44no—
200C2×C4×D4—44no—
201C2×C4×D4—44no—
202C2×C4×D4C2318yes—
203C2×C4×D4C2318yes—
204C2×C4×D4C2318yescomplemented
205C2×#117—44no—
206C2×#117C2318yescomplemented
207C22×C4⋊C4—44no—
208C22×C4⋊C4C2311yescharacteristic
209C22×C4⋊C4C2312yes—
210C22×C4⋊C4C2311yescharacteristic
211C22×C4⋊C4C2311yescharacteristic
212C22×C4⋊C4C2311yescharacteristic
213C22×C4⋊C4C2311yescharacteristic
214C22×C4⋊C4C2311yescharacteristic
215C22×C4⋊C4C2311yescharacteristic
216C22×C4⋊C4C2312yes—
217C22×C4⋊C4C2311yescharacteristic
218C22×C4⋊C4C2311yescharacteristic
219C22×C4⋊C4C2312yes—
220C22×C4⋊C4C2311yescharacteristic
221C22×C4⋊C4C2312yes—
222C22×C4⋊C4C2312yes—
223C22×C4⋊C4C2312yes—
224C22×C4⋊C4C2312yes—
225C22×C4⋊C4C2312yes—
226C22×C4⋊C4C2311yescharacteristic
227C22×C4⋊C4C2311yescharacteristic
228C22×C4⋊C4C2312yes—
229C22×C4⋊C4C2312yes—
230C22×C4⋊C4C2312yes—
231C22×C4⋊C4C2312yes—
232C22×C4⋊C4C2318yescomplemented
233C22×C22⋊C4C2311yescharacteristic
234C22×C22⋊C4C2311yescharacteristic
235C22×C22⋊C4C2311yescharacteristic
236C22×C22⋊C4C2312yes—
237C22×C22⋊C4C2312yes—
238C22×C22⋊C4C2311yescharacteristic
239C22×C22⋊C4C2311yescharacteristic
240C22×C22⋊C4C2311yescharacteristic
241C22×C22⋊C4C2312yes—
242C22×C22⋊C4C2312yes—
243C22×C22⋊C4C2312yes—
244C22×C22⋊C4C2311yescharacteristic
245C22×C22⋊C4C2312yes—
246C22×C22⋊C4C2312yes—
247C22×C22⋊C4C2312yes—
248C22×C22⋊C4C2312yes—
249C22×C22⋊C4C2311yescharacteristic
250C22×C22⋊C4C2312yes—
251C22×C22⋊C4C2311yescharacteristic
252C22×C22⋊C4C2312yes—
253C22×C22⋊C4C2312yes—
254C22×C22⋊C4C2312yes—
255C22×C22⋊C4C2312yes—
256C22×C22⋊C4C2312yes—
257C22×C22⋊C4C2312yes—
258C22×C22⋊C4C2312yes—
259C22×C22⋊C4C2311yescharacteristic
260C22×C22⋊C4C2311yescharacteristic
261C22×C22⋊C4C2312yes—
262C22×C22⋊C4C2312yes—
263C22×C22⋊C4C2311yescharacteristic
264C22×C22⋊C4C2312yes—
265C22×C22⋊C4C2312yes—
266C22×C22⋊C4C2312yes—
267C22×C22⋊C4C2312yes—
268C22×C22⋊C4C2312yes—
269C22×C22⋊C4C2312yes—
270C22×C22⋊C4C2312yes—
271C22×C42C2311yescharacteristic
272C22×C42C2311yescharacteristic
273C22×C42C2311yescharacteristic
274C22×C42C2311yescharacteristic
275C22×C42C2312yes—
276C22×C42C2312yes—
277#400C23116yescomplemented
278#399C23116yescomplemented
279#399C23116yescomplemented
280#399C23116yescomplemented
281#399C23116yescomplemented
282#399C23116yescomplemented
283#398C23116yescomplemented
284#398C2318yescomplemented
285#397C2318yescomplemented
286#397C23116yescomplemented
287#397C23116yescomplemented
288#397C23116yescomplemented
289#396C2318yes—
290#396C23116yes—
291#396C23116yes—
292#396C23116yes—
293#396C23116yescomplemented
294#396C23116yescomplemented
295#396C23116yescomplemented
296#396C23116yescomplemented
297#396C23116yescomplemented
298#396C23116yescomplemented
299#396C2318yescomplemented
300#394C23116yes—
301#394C23116yes—
302#394C23116yes—
303#394C23116yes—
304#394C2318yes—
305#394C2318yes—
306#394C23116yescomplemented
307#394C23116yescomplemented
308#394C23116yescomplemented
309#394C23116yescomplemented
310#394C23116yescomplemented
311#394C2318yescomplemented
312#394C23116yescomplemented
313#392C23116yes—
314#392C2318yes—
315#392C23116yes—
316#392C23116yescomplemented
317#391C2318yescomplemented
318#390C2318yes—
319#390C2318yes—
320#390C2318yes—
321#390C2318yes—
322#390C2318yes—
323#390C2318yes—
324#390C23116yes—
325#390C23116yescomplemented
326#390C23116yescomplemented
327#390C23116yescomplemented
328#389C23116yescomplemented
329#389C2318yescomplemented
330#389C2318yescomplemented
331#389C2318yescomplemented
332#388C23116yes—
333#388C23116yescomplemented
334#388C23116yescomplemented
335#388C23116yescomplemented
336#388C23116yescomplemented
337#387C23116yescomplemented
338#386C23116yes—
339#386C23116yescomplemented
340#384C2318yescomplemented
341#384C2318yescomplemented
342#380C2318yes—
343#380C2318yes—
344#380C2318yescomplemented
345#380C23116yescomplemented
346#379C23116yes—
347#379C23116yes—
348#379C23116yes—
349#379C23116yes—
350C4×C4⋊C4C2318yescomplemented
351C4×C4⋊C4C2318yescomplemented
352C4×C22⋊C4C2318yes—
353C4×C22⋊C4C2318yescomplemented
354C2×#95C2312yes—
355C2×#95C2312yes—
356C2×#95C2311yescharacteristic
357C2×#95C2312yes—
358C2×#95C2311yescharacteristic
359C2×#95C2311yescharacteristic
360C2×#95C2311yescharacteristic
361C2×#95C2311yescharacteristic
362C2×#95C2312yes—
363C2×#95C2312yes—
364C2×#95C2312yes—
365C2×#95C2312yes—
366C2×#95C2312yes—
367C2×#95C2311yescharacteristic
368C2×#95C2312yes—
369C25—28no—
370C25—44no—
371C25—44no—
372C25—44no—
373C25—44no—
374C25—44no—
375C25—44no—
376C25C2412yes—
377C25C2412yes—
378C25C2411yescharacteristic
379C25C2411yescharacteristic
380C25C2411yescharacteristic
381C25C2418yes—
382C22×Q8—24no—
383C22×Q8—24no—
384C22×Q8—24no—
385C22×Q8C2414yes—
386C22×D4—24no—
387C22×D4—24no—
388C22×D4—24no—
389C22×D4—24no—
390C22×D4—28no—
391C22×D4—28no—
392C22×D4—24no—
393C22×D4—24no—
394C22×D4—24no—
395C22×D4—24no—
396C22×D4—24no—
397C22×D4—24no—
398C22×D4—24no—
399C22×D4—416no—
400C22×D4—416no—
401C22×D4—416no—
402C22×D4—42no—
403C22×D4—42no—
404C22×D4—42no—
405C22×D4—44no—
406C22×D4—44no—
407C22×D4—44no—
408C22×D4—42no—
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—464no—
420C22×D4C2414yes—
421C22×D4C2414yes—
422C22×D4C2414yes—
423C22×D4C2414yes—
424C22×D4C2414yes—
425C22×D4C2418yes—
426C22×D4C2418yes—
427C22×D4C2418yes—
428C22×D4C2418yes—
429C22×D4C2418yes—
430C23×C4—28no—
431C23×C4—24no—
432C23×C4—24no—
433C23×C4—24no—
434C23×C4—24no—
435C23×C4—24no—
436C23×C4—24no—
437C23×C4—24no—
438C23×C4—24no—
439C23×C4—24no—
440C23×C4—44no—
441C23×C4—44no—
442C23×C4C2414yes—
443C23×C4C2414yes—
444C23×C4C2414yes—
445C23×C4C2411yescharacteristic
446C23×C4C2411yescharacteristic
447C23×C4C2411yescharacteristic
448C23×C4C2412yes—
449C23×C4C2411yescharacteristic
450C23×C4C2411yescharacteristic
451C23×C4C2412yes—
452C23×C4C2411yescharacteristic
453C23×C4C2411yescharacteristic
454C23×C4C2412yes—
455C23×C4C2411yescharacteristic
456C23×C4C2412yes—
457C23×C4C2412yes—
458C23×C4C2411yescharacteristic
459C23×C4C2412yes—
460C23×C4C2411yescharacteristic
461C23×C4C2411yescharacteristic
462C23×C4C2418yes—
463C23×C4C2411yescharacteristic
464#126—432no—
465#124—416no—
466#124—416no—
467#123—432no—
468#123—432no—
469C22⋊Q8—416no—
470C22⋊Q8—416no—
471C22⋊Q8—416no—
472#121—416no—
473#121—416no—
474#121—416no—
475#121—416no—
476#121—432no—
477#120—432no—
478#120—432no—
479C4×Q8—416no—
480C4×D4—416no—
481C4×D4—416no—
482C4×D4—416no—
483#117—416no—
484C2×C4⋊C4—24no—
485C2×C4⋊C4—24no—
486C2×C4⋊C4—24no—
487C2×C4⋊C4—24no—
488C2×C4⋊C4—24no—
489C2×C4⋊C4—28no—
490C2×C4⋊C4—24no—
491C2×C4⋊C4—416no—
492C2×C4⋊C4—44no—
493C2×C4⋊C4—42no—
494C2×C4⋊C4—44no—
495C2×C4⋊C4—42no—
496C2×C4⋊C4—42no—
497C2×C4⋊C4—42no—
498C2×C4⋊C4—42no—
499C2×C4⋊C4—42no—
500C2×C4⋊C4—44no—
501C2×C4⋊C4—44no—
502C2×C4⋊C4—44no—
503C2×C4⋊C4—44no—
504C2×C4⋊C4—44no—
505C2×C4⋊C4—44no—
506C2×C4⋊C4—44no—
507C2×C4⋊C4—44no—
508C2×C4⋊C4—44no—
509C2×C4⋊C4C2414yes—
510C2×C4⋊C4C2414yes—
511C2×C4⋊C4C2414yes—
512C2×C4⋊C4C2414yes—
513C2×C4⋊C4C2414yes—
514C2×C4⋊C4C2418yes—
515C2×C4⋊C4C2414yes—
516C2×C4⋊C4C2418yes—
517C2×C4⋊C4C2414yes—
518C2×C4⋊C4C2414yes—
519C2×C4⋊C4C2414yes—
520C2×C4⋊C4C2414yes—
521C2×C4⋊C4C2414yes—
522C2×C4⋊C4C2418yes—
523C2×C4⋊C4C2418yes—
524C2×C4⋊C4C2418yes—
525C2×C4⋊C4C2418yes—
526C2×C4⋊C4C2418yes—
527C2×C4⋊C4C2418yes—
528C2×C4⋊C4C2418yes—
529C2×C4⋊C4C2418yes—
530C2×C4⋊C4C2418yes—
531C2×C4⋊C4C2414yes—
532C2×C4⋊C4C2418yes—
533C2×C22⋊C4—24no—
534C2×C22⋊C4—24no—
535C2×C22⋊C4—28no—
536C2×C22⋊C4—28no—
537C2×C22⋊C4—24no—
538C2×C22⋊C4—44no—
539C2×C22⋊C4—44no—
540C2×C22⋊C4—42no—
541C2×C22⋊C4—42no—
542C2×C22⋊C4—42no—
543C2×C22⋊C4—42no—
544C2×C22⋊C4—42no—
545C2×C22⋊C4—42no—
546C2×C22⋊C4—42no—
547C2×C22⋊C4—42no—
548C2×C22⋊C4—42no—
549C2×C22⋊C4—44no—
550C2×C22⋊C4—44no—
551C2×C22⋊C4—44no—
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⋊C4—44no—
568C2×C22⋊C4—44no—
569C2×C22⋊C4—44no—
570C2×C22⋊C4—44no—
571C2×C22⋊C4C2418yes—
572C2×C22⋊C4C2418yes—
573C2×C22⋊C4C2414yes—
574C2×C22⋊C4C2414yes—
575C2×C22⋊C4C2414yes—
576C2×C22⋊C4C2414yes—
577C2×C22⋊C4C2414yes—
578C2×C22⋊C4C2414yes—
579C2×C22⋊C4C2414yes—
580C2×C22⋊C4C2414yes—
581C2×C22⋊C4C2414yes—
582C2×C22⋊C4C2414yes—
583C2×C22⋊C4C2414yes—
584C2×C22⋊C4C2418yes—
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⋊C4C2418yes—
600C2×C22⋊C4C2418yes—
601C2×C22⋊C4C2418yes—
602C2×C22⋊C4C2418yes—
603C2×C22⋊C4C2418yes—
604C2×C22⋊C4C2418yes—
605C2×C22⋊C4C2418yes—
606C2×C22⋊C4C2414yes—
607C2×C22⋊C4C2418yes—
608C2×C22⋊C4C2418yes—
609C2×C42—24no—
610C2×C42—24no—
611C2×C42—24no—
612C2×C42—24no—
613C2×C42—44no—
614C2×C42—44no—
615C2×C42C2414yes—
616C2×C42C2414yes—
617C2×C42C2414yes—
618C2×C42C2414yes—
619C2×C42C2418yes—
620C2×C42C2418yes—
621#95C2414yes—
622#95C2414yes—
623#95C2414yes—
624#95C2414yes—
625#95C2414yes—
626#95C2414yes—
627#95C2418yes—
628#95C2418yes—
629#95C2418yes—
630#95C2418yes—
631#95C2418yes—
632#95C2418yes—
633#95C2418yes—
634#95C2418yes—
635#95C2418yes—
636C24—22no—
637C24—22no—
638C24—22no—
639C24—22no—
640C24—22no—
641C24—22no—
642C24—22no—
643C24—22no—
644C24—22no—
645C24—22no—
646C24—22no—
647C24—22no—
648C24—24no—
649C24—24no—
650C24—24no—
651C24—22no—
652C24—22no—
653C24—22no—
654C24—22no—
655C24—24no—
656C24—24no—
657C24—24no—
658C24—24no—
659C24—24no—
660C24—24no—
661C24—24no—
662C24—22no—
663C24—22no—
664C24—24no—
665C24—24no—
666C24—24no—
667C24—24no—
668C24—22no—
669C24—216no—
670C24—48no—
671C24—48no—
672C24—48no—
673C24—48no—
674C24—48no—
675C24—48no—
676C24—432no—
677C24—816no—
678C24—816no—
679C24—816no—
680C24—816no—
681C24—816no—
682C24—816no—
683C24H(5,𝔽2)14yes—
684C242−1+414yes—
685C24C2514yes—
686C24C2514yes—
687C24C2512yes—
688C24C2512yes—
689C24C2512yes—
690C24C2511yescharacteristic
691C2×Q8—28no—
692C2×Q8—28no—
693C2×Q8—28no—
694C2×Q8—416no—
695C2×D4—28no—
696C2×D4—28no—
697C2×D4—28no—
698C2×D4—28no—
699C2×D4—216no—
700C2×D4—216no—
701C2×D4—28no—
702C2×D4—28no—
703C2×D4—28no—
704C2×D4—28no—
705C2×D4—28no—
706C2×D4—28no—
707C2×D4—28no—
708C2×D4—44no—
709C2×D4—44no—
710C2×D4—44no—
711C2×D4—48no—
712C2×D4—48no—
713C2×D4—48no—
714C2×D4—44no—
715C2×D4—416no—
716C2×D4—48no—
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—416no—
727C2×D4—416no—
728C2×D4—432no—
729C2×D4—4128no—
730C2×D4—416no—
731C2×D4—416no—
732C2×D4—816no—
733C2×D4—816no—
734C2×D4—816no—
735C2×D4—816no—
736C22×C4—22no—
737C22×C4—22no—
738C22×C4—22no—
739C22×C4—22no—
740C22×C4—22no—
741C22×C4—22no—
742C22×C4—22no—
743C22×C4—22no—
744C22×C4—22no—
745C22×C4—22no—
746C22×C4—24no—
747C22×C4—24no—
748C22×C4—24no—
749C22×C4—24no—
750C22×C4—22no—
751C22×C4—22no—
752C22×C4—22no—
753C22×C4—24no—
754C22×C4—22no—
755C22×C4—22no—
756C22×C4—24no—
757C22×C4—24no—
758C22×C4—24no—
759C22×C4—22no—
760C22×C4—24no—
761C22×C4—24no—
762C22×C4—24no—
763C22×C4—22no—
764C22×C4—22no—
765C22×C4—22no—
766C22×C4—22no—
767C22×C4—22no—
768C22×C4—24no—
769C22×C4—24no—
770C22×C4—24no—
771C22×C4—24no—
772C22×C4—22no—
773C22×C4—24no—
774C22×C4—22no—
775C22×C4—22no—
776C22×C4—22no—
777C22×C4—22no—
778C22×C4—22no—
779C22×C4—22no—
780C22×C4—22no—
781C22×C4—22no—
782C22×C4—22no—
783C22×C4—22no—
784C22×C4—24no—
785C22×C4—24no—
786C22×C4—216no—
787C22×C4—28no—
788C22×C4—28no—
789C22×C4—28no—
790C22×C4—28no—
791C22×C4—28no—
792C22×C4—28no—
793C22×C4—28no—
794C22×C4—28no—
795C22×C4—28no—
796C22×C4—48no—
797C22×C4—48no—
798C22×C4—416no—
799C22×C4—416no—
800C22×C4—416no—
801C22×C4—816no—
802C22×C4H(5,𝔽2)14yes—
803C22×C4H(5,𝔽2)14yes—
804C22×C4H(5,𝔽2)14yes—
805C22×C4H(5,𝔽2)14yes—
806C22×C4C2512yes—
807C22×C4C2512yes—
808C22×C4C2512yes—
809C22×C4C2512yes—
810C22×C4C2512yes—
811C22×C4C2514yes—
812C22×C4C2514yes—
813C22×C4C2514yes—
814C22×C4C2512yes—
815C22×C4C2512yes—
816C22×C4C2512yes—
817C22×C4C2514yes—
818C22×C4C2514yes—
819C22×C4C2514yes—
820C22×C4C2512yes—
821C22×C4C2512yes—
822C22×C4C2512yes—
823C22×C4C2512yes—
824C4⋊C4—28no—
825C4⋊C4—28no—
826C4⋊C4—28no—
827C4⋊C4—28no—
828C4⋊C4—28no—
829C4⋊C4—216no—
830C4⋊C4—28no—
831C4⋊C4—48no—
832C4⋊C4—44no—
833C4⋊C4—48no—
834C4⋊C4—44no—
835C4⋊C4—44no—
836C4⋊C4—44no—
837C4⋊C4—44no—
838C4⋊C4—44no—
839C4⋊C4—48no—
840C4⋊C4—48no—
841C4⋊C4—48no—
842C4⋊C4—48no—
843C4⋊C4—48no—
844C4⋊C4—48no—
845C4⋊C4—48no—
846C4⋊C4—48no—
847C4⋊C4—48no—
848C22⋊C4—28no—
849C22⋊C4—28no—
850C22⋊C4—216no—
851C22⋊C4—216no—
852C22⋊C4—28no—
853C22⋊C4—48no—
854C22⋊C4—48no—
855C22⋊C4—44no—
856C22⋊C4—44no—
857C22⋊C4—44no—
858C22⋊C4—44no—
859C22⋊C4—44no—
860C22⋊C4—44no—
861C22⋊C4—44no—
862C22⋊C4—44no—
863C22⋊C4—44no—
864C22⋊C4—48no—
865C22⋊C4—48no—
866C22⋊C4—48no—
867C22⋊C4—48no—
868C22⋊C4—48no—
869C22⋊C4—48no—
870C22⋊C4—48no—
871C22⋊C4—48no—
872C22⋊C4—48no—
873C22⋊C4—48no—
874C22⋊C4—48no—
875C22⋊C4—48no—
876C22⋊C4—48no—
877C22⋊C4—48no—
878C22⋊C4—48no—
879C22⋊C4—48no—
880C22⋊C4—48no—
881C22⋊C4—48no—
882C22⋊C4—48no—
883C22⋊C4—48no—
884C22⋊C4—48no—
885C22⋊C4—48no—
886C42—28no—
887C42—28no—
888C42—28no—
889C42—28no—
890C42—48no—
891C42—48no—
892C23—22no—
893C23—22no—
894C23—22no—
895C23—22no—
896C23—22no—
897C23—22no—
898C23—22no—
899C23—22no—
900C23—22no—
901C23—22no—
902C23—22no—
903C23—22no—
904C23—28no—
905C23—28no—
906C23—28no—
907C23—28no—
908C23—28no—
909C23—28no—
910C23—24no—
911C23—24no—
912C23—24no—
913C23—22no—
914C23—22no—
915C23—22no—
916C23—22no—
917C23—24no—
918C23—24no—
919C23—24no—
920C23—24no—
921C23—24no—
922C23—24no—
923C23—24no—
924C23—22no—
925C23—22no—
926C23—24no—
927C23—24no—
928C23—24no—
929C23—24no—
930C23—22no—
931C23—44no—
932C23—44no—
933C23—44no—
934C23—44no—
935C23—44no—
936C23—44no—
937C23—44no—
938C23—44no—
939C23—432no—
940C23—44no—
941C23—48no—
942C23—48no—
943C23—44no—
944C23—44no—
945C23—48no—
946C23—48no—
947C23—48no—
948C23—48no—
949C23—44no—
950C23—48no—
951C23—48no—
952C23—44no—
953C23—48no—
954C23—48no—
955C23—44no—
956C23—48no—
957C23—48no—
958C23—44no—
959C23—48no—
960C23—48no—
961C23—816no—
962C23—816no—
963C23—816no—
964C23—816no—
965C23—816no—
966C23—816no—
967C23—8128no—
968C23C2×H(5,𝔽2)14yes—
969C23C2×H(5,𝔽2)12yes—
970C23C2×H(5,𝔽2)12yes—
971C23C2×H(5,𝔽2)12yes—
972C23C2×H(5,𝔽2)12yes—
973C23C2×H(5,𝔽2)12yes—
974C23C2×2−1+414yes—
975C23C2×2−1+412yes—
976C23#58512yes—
977C23C2611yescharacteristic
978Q8—416no—
979D4—416no—
980D4—416no—
981D4—416no—
982D4—432no—
983D4—416no—
984D4—416no—
985D4—816no—
986D4—816no—
987D4—816no—
988D4—816no—
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—28no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—24no—
1001C2×C4—24no—
1002C2×C4—24no—
1003C2×C4—24no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—24no—
1008C2×C4—22no—
1009C2×C4—24no—
1010C2×C4—22no—
1011C2×C4—24no—
1012C2×C4—24no—
1013C2×C4—22no—
1014C2×C4—24no—
1015C2×C4—24no—
1016C2×C4—24no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—22no—
1021C2×C4—24no—
1022C2×C4—22no—
1023C2×C4—24no—
1024C2×C4—24no—
1025C2×C4—24no—
1026C2×C4—22no—
1027C2×C4—24no—
1028C2×C4—22no—
1029C2×C4—22no—
1030C2×C4—22no—
1031C2×C4—22no—
1032C2×C4—22no—
1033C2×C4—22no—
1034C2×C4—22no—
1035C2×C4—22no—
1036C2×C4—22no—
1037C2×C4—24no—
1038C2×C4—22no—
1039C2×C4—24no—
1040C2×C4—44no—
1041C2×C4—44no—
1042C2×C4—44no—
1043C2×C4—48no—
1044C2×C4—44no—
1045C2×C4—44no—
1046C2×C4—44no—
1047C2×C4—44no—
1048C2×C4—44no—
1049C2×C4—48no—
1050C2×C4—48no—
1051C2×C4—48no—
1052C2×C4—48no—
1053C2×C4—44no—
1054C2×C4—44no—
1055C2×C4—48no—
1056C2×C4—416no—
1057C2×C4—416no—
1058C2×C4—416no—
1059C2×C4—816no—
1060C2×C4#560116yes—
1061C2×C4C2×H(5,𝔽2)14yes—
1062C2×C4C2×H(5,𝔽2)14yes—
1063C2×C4C2×H(5,𝔽2)14yes—
1064C2×C4C2×H(5,𝔽2)14yes—
1065C22—24no—
1066C22—24no—
1067C22—24no—
1068C22—24no—
1069C22—24no—
1070C22—24no—
1071C22—42no—
1072C22—42no—
1073C22—42no—
1074C22—42no—
1075C22—42no—
1076C22—42no—
1077C22—42no—
1078C22—416no—
1079C22—416no—
1080C22—42no—
1081C22—42no—
1082C22—42no—
1083C22—44no—
1084C22—44no—
1085C22—44no—
1086C22—44no—
1087C22—42no—
1088C22—44no—
1089C22—44no—
1090C22—42no—
1091C22—44no—
1092C22—44no—
1093C22—42no—
1094C22—44no—
1095C22—44no—
1096C22—42no—
1097C22—44no—
1098C22—44no—
1099C22—42no—
1100C22—44no—
1101C22—44no—
1102C22—864no—
1103C22—88no—
1104C22—816no—
1105C22—816no—
1106C22C2×#56014yes—
1107C22#353614yes—
1108C22#353614yes—
1109C22#354214yes—
1110C22#354314yes—
1111C22#354614yes—
1112C22#356114yes—
1113C22C22×H(5,𝔽2)11yescharacteristic
1114C22C22×H(5,𝔽2)11yescharacteristic
1115C22C22×H(5,𝔽2)11yescharacteristic
1116C22C22×H(5,𝔽2)11yescharacteristic
1117C22C22×H(5,𝔽2)11yescharacteristic
1118C22C22×2−1+411yescharacteristic
1119C22C2×#58511yescharacteristic
1120C4—24no—
1121C4—42no—
1122C4—42no—
1123C4—42no—
1124C4—44no—
1125C4—44no—
1126C4—44no—
1127C4—42no—
1128C4—42no—
1129C4—44no—
1130C4—42no—
1131C4—42no—
1132C4—42no—
1133C4—44no—
1134C4—42no—
1135C4—42no—
1136C4—44no—
1137C4C2×#56018yes—
1138C2—44no—
1139C2—44no—
1140C2—82no—
1141C2—84no—
1142C2—84no—
1143C2#5298118yesdirect product factor
1144C2C22×#56011yescharacteristic
1145C2C2×#354211yescharacteristic
1146C2C2×#353611yescharacteristic
1147C2C2×#353611yescharacteristic
1148C2C2×#356111yescharacteristic
1149C2C2×#354311yescharacteristic
1150C2C2×#354611yescharacteristic
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. #52981C2direct (N × H)
2. C2×#2705C2semidirect
3. C2×#2697C2semidirect
4. C2×#2685C2semidirect
5. C2×#2678C2semidirect
6. C2×#2842C2semidirect
7. C2×#2829C2semidirect
8. C2×#2837C2semidirect
9. C2×#2813C2semidirect
10. C2×#2538C2semidirect
11. C2×#2540C2semidirect
12. C2×#2497C2semidirect
13. C2×#2512C2semidirect
14. C2×#2501C2semidirect
15. C2×#2448C2semidirect
16. C2×#2426C2semidirect
17. C2×#2435C2semidirect
18. C2×#2417C2semidirect
19. C2×#2416C2semidirect
20. C2×#2408C2semidirect
21. C2×#2408C2semidirect
22. C2×#2620C2semidirect
23. C2×#2624C2semidirect
24. C2×#2392C2semidirect
26. C22×#126C22semidirect
29. C22×#123C22semidirect
30. C22×#123C22semidirect
32. C22×C22⋊Q8C22semidirect
33. C22×C22⋊Q8C22semidirect
38. C22×#121C22semidirect
41. C22×C4×Q8C22semidirect
44. C22×C4×D4C22semidirect
45. C22×#117C22semidirect
46. C23×C4⋊C4C22semidirect
47. #2842C22semidirect
48. #2837C22semidirect
49. #2829C22semidirect
50. #2813C22semidirect
51. #2705C22semidirect
52. #2697C22semidirect
53. #2685C22semidirect
54. #2678C22semidirect
55. #2624C22semidirect
56. #2620C22semidirect
57. #2540C22semidirect
58. #2538C22semidirect
59. #2512C22semidirect
60. #2501C22semidirect
61. #2497C22semidirect
62. #2448C22semidirect
63. #2435C22semidirect
64. #2426C22semidirect
65. #2417C22semidirect
66. #2416C22semidirect
67. #2408C22semidirect
68. #2408C22semidirect
69. C2×#400C22semidirect
70. C2×#399C22semidirect
71. C2×#399C22semidirect
72. C2×#399C22semidirect
73. C2×#399C22semidirect
74. C2×#399C22semidirect
75. #2392C22semidirect
76. C2×#398C22semidirect
77. C2×#398C22semidirect
78. C2×#397C22semidirect
79. C2×#397C22semidirect
80. C2×#397C22semidirect
81. C2×#397C22semidirect
86. C2×#396C22semidirect
87. C2×#396C22semidirect
88. C2×#396C22semidirect
89. C2×#396C22semidirect
90. C2×#396C22semidirect
91. C2×#396C22semidirect
92. C2×#396C22semidirect
99. C2×#394C22semidirect
100. C2×#394C22semidirect
101. C2×#394C22semidirect
102. C2×#394C22semidirect
103. C2×#394C22semidirect
104. C2×#394C22semidirect
105. C2×#394C22semidirect
109. C2×#392C22semidirect
110. C2×#391C22semidirect
118. C2×#390C22semidirect
119. C2×#390C22semidirect
120. C2×#390C22semidirect
121. C2×#389C22semidirect
122. C2×#389C22semidirect
123. C2×#389C22semidirect
124. C2×#389C22semidirect
126. C2×#388C22semidirect
127. C2×#388C22semidirect
128. C2×#388C22semidirect
129. C2×#388C22semidirect
130. C2×#387C22semidirect
132. C2×#386C22semidirect
133. C2×#384C22semidirect
134. C2×#384C22semidirect
137. C2×#380C22semidirect
138. C2×#380C22semidirect
143. C2×C4×C4⋊C4C22semidirect
144. C2×C4×C4⋊C4C22semidirect
146. C2×C4×C22⋊C4C22semidirect
168. C2×#126C23semidirect
175. C2×#123C23semidirect
176. C2×#123C23semidirect
181. C2×C22⋊Q8C23semidirect
182. C2×C22⋊Q8C23semidirect
192. C2×#121C23semidirect
198. C2×C4×Q8C23semidirect
204. C2×C4×D4C23semidirect
206. C2×#117C23semidirect
232. C22×C4⋊C4C23semidirect
277. #400C23semidirect
278. #399C23semidirect
279. #399C23semidirect
280. #399C23semidirect
281. #399C23semidirect
282. #399C23semidirect
283. #398C23semidirect
284. #398C23semidirect
285. #397C23semidirect
286. #397C23semidirect
287. #397C23semidirect
288. #397C23semidirect
293. #396C23semidirect
294. #396C23semidirect
295. #396C23semidirect
296. #396C23semidirect
297. #396C23semidirect
298. #396C23semidirect
299. #396C23semidirect
306. #394C23semidirect
307. #394C23semidirect
308. #394C23semidirect
309. #394C23semidirect
310. #394C23semidirect
311. #394C23semidirect
312. #394C23semidirect
316. #392C23semidirect
317. #391C23semidirect
325. #390C23semidirect
326. #390C23semidirect
327. #390C23semidirect
328. #389C23semidirect
329. #389C23semidirect
330. #389C23semidirect
331. #389C23semidirect
333. #388C23semidirect
334. #388C23semidirect
335. #388C23semidirect
336. #388C23semidirect
337. #387C23semidirect
339. #386C23semidirect
340. #384C23semidirect
341. #384C23semidirect
344. #380C23semidirect
345. #380C23semidirect
350. C4×C4⋊C4C23semidirect
351. C4×C4⋊C4C23semidirect
353. C4×C22⋊C4C23semidirect
1143. C2#52981direct (N × H)

Maximal subgroups

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

subgroupindex
#529812
C2×#27052
C2×#26972
C2×#26852
C2×#26782
C2×#28422
C2×#28292
C2×#28372
C2×#28132
C2×#25382
C2×#25402
C2×#24972
C2×#25122
C2×#25012
C2×#24482
C2×#24262
C2×#24352
C2×#24172
C2×#24162
C2×#24082
C2×#26202
C2×#26242
C2×#23922