Finite Group Databasebeta

← C2×#38024 #7635483

Subgroups — C2×#38024 #7635483

Order 512.

9932 conjugacy classes of subgroups.

The subgroup lattice has 1230 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#546C211yesmaximal, characteristic, complemented
2C22×#529C211yesmaximal, characteristic, complemented
3C2×#2707C212yesmaximal, complemented
4C2×#2705C212yesmaximal, complemented
5C2×#2691C212yesmaximal, complemented
6C2×#2676C212yesmaximal, complemented
7#38024C2132yesmaximal, direct product factor
8C2×#2855C211yesmaximal, characteristic, complemented
9C2×#2538C211yesmaximal, characteristic, complemented
10C2×#2592C211yesmaximal, characteristic, complemented
11C2×#2534C212yesmaximal, complemented
12C2×#2407C211yesmaximal, characteristic, complemented
13C2×#2417C211yesmaximal, characteristic, complemented
14C2×#2416C211yesmaximal, characteristic, complemented
15C2×#2408C211yesmaximal, characteristic, complemented
16C2×#2412C212yesmaximal, complemented
17C2×#2424C212yesmaximal, complemented
18C2×#2437C212yesmaximal, complemented
19C2×#2620C211yesmaximal, characteristic, complemented
20C2×#2624C211yesmaximal, characteristic, complemented
21C2×D4×C4⋊C4C211yesmaximal, characteristic, complemented
22C2×#2324C211yesmaximal, characteristic, complemented
23C2×#2311C211yesmaximal, characteristic, complemented
24C22×#390C211yesmaximal, characteristic, complemented
25C23×#41C2211yescharacteristic
26C24×D4C2211yescharacteristic
27C2×#546—216no—
28C2×#546C22116yescomplemented
29C2×#529—216no—
30C2×#529C22116yescomplemented
31C22×#126C2211yescharacteristic, complemented
32C22×#126C2211yescharacteristic, complemented
33C22×#125C2211yescharacteristic, complemented
34C22×#124C2211yescharacteristic
35C22×#124C2211yescharacteristic, complemented
36C22×#123C2211yescharacteristic
37C22×#123C2211yescharacteristic
38C22×#123C2212yes—
39C22×C22⋊Q8C2211yescharacteristic
40C22×C22⋊Q8C2211yescharacteristic
41C22×C22⋊Q8C2211yescharacteristic, complemented
42C22×C22⋊Q8C2212yescomplemented
43C22×#121C2211yescharacteristic
44C22×#121C2211yescharacteristic
45C22×#121C2211yescharacteristic
46C22×#121C2212yes—
47C22×#121C2211yescharacteristic
48C22×#121C2212yescomplemented
49C22×#120C2212yes—
50C22×#120C2212yes—
51C22×C4×Q8C2211yescharacteristic, complemented
52C22×C4×D4C2211yescharacteristic
53C22×C4×D4C2211yescharacteristic
54C22×C4×D4C2212yes—
55C22×C4×D4C2211yescharacteristic
56C22×C4×D4C2211yescharacteristic, complemented
57C22×#117C2211yescharacteristic, complemented
58C22×#117C2211yescharacteristic, complemented
59C23×C4⋊C4C2211yescharacteristic
60C23×C4⋊C4C2211yescharacteristic, complemented
61C23×C22⋊C4C2212yes—
62C23×C22⋊C4C2212yes—
63C23×C22⋊C4C2212yes—
64C23×C42C2211yescharacteristic
65#2855C22116yescomplemented
66#2707C22132yescomplemented
67#2705C22132yescomplemented
68#2691C22132yescomplemented
69#2676C22132yescomplemented
70#2624C22116yescomplemented
71#2620C22116yescomplemented
72#2592C22116yescomplemented
73#2538C22116yescomplemented
74#2534C22132yescomplemented
75#2437C22132yescomplemented
76#2424C22132yescomplemented
77#2417C22116yescomplemented
78#2416C22116yescomplemented
79#2412C22132yescomplemented
80#2408C22116yescomplemented
81#2407C22116yescomplemented
82C2×#399C2212yescomplemented
83C2×#398C2212yescomplemented
84C2×#397C2212yescomplemented
85C2×#397C2212yescomplemented
86C2×#396C2212yescomplemented
87C2×#396C2212yescomplemented
88C2×#396C2212yescomplemented
89C2×#396C2212yescomplemented
90C2×#396C2212yescomplemented
91C2×#396C2212yescomplemented
92C2×#394C2212yes—
93C2×#394C2212yescomplemented
94C2×#394C2212yescomplemented
95C2×#394C2212yescomplemented
96C2×#394C2212yescomplemented
97C2×#394C2212yescomplemented
98C2×#394C2212yescomplemented
99C2×#393C2212yescomplemented
100C2×#392C2212yes—
101C2×#392C2212yescomplemented
102D4×C4⋊C4C22116yescomplemented
103#2324C22116yescomplemented
104#2311C22116yescomplemented
105C2×#391C2211yescharacteristic, complemented
106C2×#391C2211yescharacteristic, complemented
107C2×#391C2211yescharacteristic, complemented
108C2×#390C2211yescharacteristic
109C2×#390C2211yescharacteristic
110C2×#390C2211yescharacteristic
111C2×#390C2211yescharacteristic
112C2×#390C2211yescharacteristic
113C2×#390C2211yescharacteristic
114C2×#390C2212yes—
115C2×#390C2212yes—
116C2×#390C22116yescomplemented
117C2×#390C2212yescomplemented
118C2×#389C2211yescharacteristic, complemented
119C2×#389C2211yescharacteristic, complemented
120C2×#389C2211yescharacteristic, complemented
121C2×#389C2212yescomplemented
122C2×#388C2212yescomplemented
123C2×#388C2212yescomplemented
124C2×#388C2212yescomplemented
125C2×#387C2212yescomplemented
126C2×#387C2212yescomplemented
127C2×#386C2212yes—
128C2×#386C2212yescomplemented
129C2×#386C2212yescomplemented
130C2×#386C2212yescomplemented
131C2×#386C2212yescomplemented
132C2×#386C2212yescomplemented
133C2×#385C2212yes—
134C2×#385C2212yes—
135C2×#385C2212yescomplemented
136C2×#385C2212yescomplemented
137C2×#385C2212yescomplemented
138C2×#384C2211yescharacteristic, complemented
139C2×#381C2212yes—
140C2×#380C2212yes—
141C2×#380C2211yescharacteristic
142C2×#380C2211yescharacteristic, complemented
143C2×#380C2211yescharacteristic, complemented
144C2×#380C2212yescomplemented
145C2×#380C2212yescomplemented
146C2×#380C2212yescomplemented
147C2×#379C2212yes—
148C2×C4×C4⋊C4C2211yescharacteristic, complemented
149C26C2312yes—
150C22×#41—28no—
151C22×#41—28no—
152C22×#41—44no—
153C22×#41C2318yes—
154C23×Q8C2311yescharacteristic
155C23×Q8C2311yescharacteristic
156C23×D4—28no—
157C23×D4—28no—
158C23×D4—44no—
159C23×D4C2311yescharacteristic
160C23×D4C2311yescharacteristic
161C23×D4C2312yes—
162C23×D4C2318yes—
163C23×D4C2312yes—
164C23×D4C2311yescharacteristic
165C23×D4C2311yescharacteristic
166C23×D4C2311yescharacteristic
167C23×D4C2312yes—
168C23×D4C2312yes—
169C23×D4C2312yes—
170C24×C4C2311yescharacteristic
171C24×C4C2311yescharacteristic
172C24×C4C2312yes—
173C24×C4C2311yescharacteristic
174C24×C4C2311yescharacteristic
175C24×C4C2311yescharacteristic
176C24×C4C2312yes—
177C24×C4C2312yes—
178C24×C4C2312yes—
179#546—2128no—
180#529—2128no—
181C2×#126—28no—
182C2×#126—28no—
183C2×#126C2318yescomplemented
184C2×#126C2318yescomplemented
185C2×#125—28no—
186C2×#125C2318yescomplemented
187C2×#124—28no—
188C2×#124—28no—
189C2×#124C2318yes—
190C2×#124C2318yescomplemented
191C2×#123—28no—
192C2×#123—216no—
193C2×#123—28no—
194C2×#123C2318yes—
195C2×#123C2318yes—
196C2×#123C23116yes—
197C2×C22⋊Q8—28no—
198C2×C22⋊Q8—28no—
199C2×C22⋊Q8—48no—
200C2×C22⋊Q8—44no—
201C2×C22⋊Q8C2318yes—
202C2×C22⋊Q8C2318yes—
203C2×C22⋊Q8C2318yescomplemented
204C2×C22⋊Q8C23116yescomplemented
205C2×#121—28no—
206C2×#121—28no—
207C2×#121—28no—
208C2×#121—216no—
209C2×#121—48no—
210C2×#121—44no—
211C2×#121C2318yes—
212C2×#121C2318yes—
213C2×#121C2318yes—
214C2×#121C23116yes—
215C2×#121C2318yes—
216C2×#121C23116yescomplemented
217C2×#120—216no—
218C2×#120—48no—
219C2×#120C23116yes—
220C2×#120C23116yes—
221C2×C4×Q8—28no—
222C2×C4×Q8C2318yescomplemented
223C2×C4×D4—28no—
224C2×C4×D4—28no—
225C2×C4×D4—28no—
226C2×C4×D4—48no—
227C2×C4×D4D4116yescomplemented
228C2×C4×D4C2318yes—
229C2×C4×D4C2318yes—
230C2×C4×D4C23116yes—
231C2×C4×D4C2318yes—
232C2×C4×D4C2318yescomplemented
233C2×#117—28no—
234C2×#117—28no—
235C2×#117C2318yescomplemented
236C2×#117C2318yescomplemented
237C22×C4⋊C4—44no—
238C22×C4⋊C4—44no—
239C22×C4⋊C4C2311yescharacteristic
240C22×C4⋊C4C2311yescharacteristic
241C22×C4⋊C4C2311yescharacteristic
242C22×C4⋊C4C2311yescharacteristic
243C22×C4⋊C4C2311yescharacteristic
244C22×C4⋊C4C2311yescharacteristic
245C22×C4⋊C4C2312yes—
246C22×C4⋊C4C2312yes—
247C22×C4⋊C4C2311yescharacteristic
248C22×C4⋊C4C2311yescharacteristic
249C22×C4⋊C4C2311yescharacteristic
250C22×C4⋊C4C2311yescharacteristic
251C22×C4⋊C4C2311yescharacteristic
252C22×C4⋊C4C2311yescharacteristic
253C22×C4⋊C4C2311yescharacteristic
254C22×C4⋊C4C2311yescharacteristic
255C22×C4⋊C4C2318yes—
256C22×C4⋊C4C2312yes—
257C22×C4⋊C4C2312yes—
258C22×C4⋊C4C2312yes—
259C22×C4⋊C4C2312yes—
260C22×C4⋊C4C2312yes—
261C22×C4⋊C4C2312yes—
262C22×C4⋊C4C2312yes—
263C22×C4⋊C4C2311yescharacteristic
264C22×C4⋊C4C2318yescomplemented
265C22×C22⋊C4—216no—
266C22×C22⋊C4—48no—
267C22×C22⋊C4—48no—
268C22×C22⋊C4C2311yescharacteristic
269C22×C22⋊C4C2312yes—
270C22×C22⋊C4C2312yes—
271C22×C22⋊C4C2312yes—
272C22×C22⋊C4C2312yes—
273C22×C22⋊C4C2311yescharacteristic
274C22×C22⋊C4C2311yescharacteristic
275C22×C22⋊C4C2311yescharacteristic
276C22×C22⋊C4C2311yescharacteristic
277C22×C22⋊C4C2311yescharacteristic
278C22×C22⋊C4C2311yescharacteristic
279C22×C22⋊C4C2312yes—
280C22×C22⋊C4C2312yes—
281C22×C22⋊C4C2312yes—
282C22×C22⋊C4C2312yes—
283C22×C22⋊C4C23116yes—
284C22×C22⋊C4C2312yes—
285C22×C22⋊C4C2311yescharacteristic
286C22×C22⋊C4C2312yes—
287C22×C22⋊C4C2312yes—
288C22×C22⋊C4C2312yes—
289C22×C22⋊C4C2312yes—
290C22×C22⋊C4C2312yes—
291C22×C22⋊C4C2312yes—
292C22×C22⋊C4C2312yes—
293C22×C22⋊C4C2312yes—
294C22×C22⋊C4C2312yes—
295C22×C22⋊C4C2312yes—
296C22×C22⋊C4C2312yes—
297C22×C22⋊C4C2312yes—
298C22×C22⋊C4C23116yes—
299C22×C22⋊C4C23116yes—
300C22×C22⋊C4C2312yes—
301C22×C22⋊C4C2312yes—
302C22×C22⋊C4C2311yescharacteristic
303C22×C22⋊C4C2311yescharacteristic
304C22×C42—28no—
305C22×C42C2318yes—
306C22×C42C2311yescharacteristic
307C22×C42C2311yescharacteristic
308C22×C42C2311yescharacteristic
309C22×C42C2311yescharacteristic
310C22×C42C2311yescharacteristic
311C22×C42C2312yes—
312C22×C42C2311yescharacteristic
313#399C23116yescomplemented
314#398C23116yescomplemented
315#397C23116yescomplemented
316#397C23116yescomplemented
317#396C23116yescomplemented
318#396C23116yescomplemented
319#396C23116yescomplemented
320#396C23116yescomplemented
321#396C23116yescomplemented
322#396C23116yescomplemented
323#394C23116yes—
324#394C23116yescomplemented
325#394C23116yescomplemented
326#394C23116yescomplemented
327#394C23116yescomplemented
328#394C23116yescomplemented
329#394C23116yescomplemented
330#393C23116yescomplemented
331#392C23116yes—
332#392C23116yescomplemented
333#391C2318yescomplemented
334#391C2318yescomplemented
335#391C2318yescomplemented
336#390C2318yes—
337#390C2318yes—
338#390C2318yes—
339#390C2318yes—
340#390C2318yes—
341#390C2318yes—
342#390C23116yes—
343#390C23116yes—
344#390C23116yescomplemented
345#389C2318yescomplemented
346#389C2318yescomplemented
347#389C23116yescomplemented
348#389C2318yescomplemented
349#388C23116yescomplemented
350#388C23116yescomplemented
351#388C23116yescomplemented
352#387C23116yescomplemented
353#387C23116yescomplemented
354#386C23116yes—
355#386C23116yescomplemented
356#386C23116yescomplemented
357#386C23116yescomplemented
358#386C23116yescomplemented
359#386C23116yescomplemented
360#385C23116yes—
361#385C23116yes—
362#385C23116yescomplemented
363#385C23116yescomplemented
364#385C23116yescomplemented
365#384C2318yescomplemented
366#381C23116yes—
367#380C2318yes—
368#380C23116yes—
369#380C23116yescomplemented
370#380C23116yescomplemented
371#380C2318yescomplemented
372#380C2318yescomplemented
373#380C23116yescomplemented
374#379C23116yes—
375C4×C4⋊C4C2318yescomplemented
376C2×#95C2312yes—
377C2×#95C2312yes—
378C2×#95C2312yes—
379C2×#95C2312yes—
380C2×#95C2312yes—
381C2×#95C2312yes—
382C2×#95C2312yes—
383C2×#95C2312yes—
384C2×#95C2312yes—
385C2×#95C2312yes—
386C2×#95C2312yes—
387C2×#95C2312yes—
388C2×#95C2312yes—
389C25—28no—
390C25—28no—
391C25—28no—
392C25—28no—
393C25—44no—
394C25—44no—
395C25—44no—
396C25C2412yes—
397C25C2411yescharacteristic
398C25C2411yescharacteristic
399C25C2412yes—
400C25C2418yes—
401C25C2411yescharacteristic
402C2×#41—232no—
403C2×#41—232no—
404C2×#41—416no—
405C2×#41—464no—
406C22×Q8—24no—
407C22×Q8—24no—
408C22×Q8—24no—
409C22×Q8—24no—
410C22×Q8—24no—
411C22×Q8—42no—
412C22×Q8C2414yes—
413C22×Q8C2414yes—
414C22×D4—24no—
415C22×D4—24no—
416C22×D4—24no—
417C22×D4—24no—
418C22×D4—28no—
419C22×D4—28no—
420C22×D4—28no—
421C22×D4—24no—
422C22×D4—24no—
423C22×D4—28no—
424C22×D4—28no—
425C22×D4—232no—
426C22×D4—24no—
427C22×D4—28no—
428C22×D4—24no—
429C22×D4—232no—
430C22×D4—24no—
431C22×D4—24no—
432C22×D4—24no—
433C22×D4—24no—
434C22×D4—416no—
435C22×D4—464no—
436C22×D4—44no—
437C22×D4—42no—
438C22×D4—44no—
439C22×D4—44no—
440C22×D4—44no—
441C22×D4—44no—
442C22×D4—44no—
443C22×D4—44no—
444C22×D4—44no—
445C22×D4—44no—
446C22×D4C2×D418yes—
447C22×D4#4118yes—
448C22×D4C2414yes—
449C22×D4C2414yes—
450C22×D4C2414yes—
451C22×D4C2418yes—
452C22×D4C2418yes—
453C22×D4C2414yes—
454C22×D4C2414yes—
455C22×D4C2418yes—
456C22×D4C2418yes—
457C22×D4C2418yes—
458C23×C4—24no—
459C23×C4—24no—
460C23×C4—24no—
461C23×C4—24no—
462C23×C4—24no—
463C23×C4—24no—
464C23×C4—28no—
465C23×C4—24no—
466C23×C4—24no—
467C23×C4—28no—
468C23×C4—28no—
469C23×C4—24no—
470C23×C4—24no—
471C23×C4—24no—
472C23×C4—24no—
473C23×C4—28no—
474C23×C4—42no—
475C23×C4—44no—
476C23×C4—44no—
477C23×C4—44no—
478C23×C4—44no—
479C23×C4—44no—
480C23×C4—44no—
481C23×C4—44no—
482C23×C4—44no—
483C23×C4C2×D418yes—
484C23×C4C2×D418yes—
485C23×C4C2414yes—
486C23×C4C2414yes—
487C23×C4C2411yescharacteristic
488C23×C4C2411yescharacteristic
489C23×C4C2412yes—
490C23×C4C2411yescharacteristic
491C23×C4C2411yescharacteristic
492C23×C4C2411yescharacteristic
493C23×C4C2411yescharacteristic
494C23×C4C2412yes—
495C23×C4C2412yes—
496C23×C4C2412yes—
497C23×C4C2412yes—
498C23×C4C2412yes—
499C23×C4C2414yes—
500C23×C4C2418yes—
501C23×C4C2414yes—
502C23×C4C2414yes—
503C23×C4C2411yescharacteristic
504C23×C4C2411yescharacteristic
505C23×C4C2411yescharacteristic
506C23×C4C2411yescharacteristic
507C23×C4C2411yescharacteristic
508C23×C4C2418yes—
509C23×C4C2418yes—
510C23×C4C2418yes—
511C23×C4C2411yescharacteristic
512#126—232no—
513#126—232no—
514#125—232no—
515#124—232no—
516#124—232no—
517#123—232no—
518#123—264no—
519#123—232no—
520C22⋊Q8—232no—
521C22⋊Q8—232no—
522C22⋊Q8—432no—
523C22⋊Q8—416no—
524#121—232no—
525#121—232no—
526#121—232no—
527#121—264no—
528#121—432no—
529#121—416no—
530#120—264no—
531#120—432no—
532C4×Q8—232no—
533C4×D4—232no—
534C4×D4—232no—
535C4×D4—232no—
536C4×D4—432no—
537C4×D4C2×D4164yescomplemented
538#117—232no—
539#117—232no—
540C2×C4⋊C4—24no—
541C2×C4⋊C4—24no—
542C2×C4⋊C4—24no—
543C2×C4⋊C4—24no—
544C2×C4⋊C4—24no—
545C2×C4⋊C4—24no—
546C2×C4⋊C4—24no—
547C2×C4⋊C4—24no—
548C2×C4⋊C4—24no—
549C2×C4⋊C4—24no—
550C2×C4⋊C4—28no—
551C2×C4⋊C4—24no—
552C2×C4⋊C4—24no—
553C2×C4⋊C4—24no—
554C2×C4⋊C4—24no—
555C2×C4⋊C4—28no—
556C2×C4⋊C4—416no—
557C2×C4⋊C4—416no—
558C2×C4⋊C4—44no—
559C2×C4⋊C4—44no—
560C2×C4⋊C4—44no—
561C2×C4⋊C4—44no—
562C2×C4⋊C4—44no—
563C2×C4⋊C4—44no—
564C2×C4⋊C4—44no—
565C2×C4⋊C4C2×D418yes—
566C2×C4⋊C4C2414yes—
567C2×C4⋊C4C2414yes—
568C2×C4⋊C4C2414yes—
569C2×C4⋊C4C2414yes—
570C2×C4⋊C4C2414yes—
571C2×C4⋊C4C2414yes—
572C2×C4⋊C4C2414yes—
573C2×C4⋊C4C2414yes—
574C2×C4⋊C4C2414yes—
575C2×C4⋊C4C2414yes—
576C2×C4⋊C4C2414yes—
577C2×C4⋊C4C2414yes—
578C2×C4⋊C4C2414yes—
579C2×C4⋊C4C2418yes—
580C2×C4⋊C4C2414yes—
581C2×C4⋊C4C2418yes—
582C2×C4⋊C4C2418yes—
583C2×C4⋊C4C2418yes—
584C2×C4⋊C4C2418yes—
585C2×C4⋊C4C2418yes—
586C2×C4⋊C4C2418yes—
587C2×C4⋊C4C2418yes—
588C2×C4⋊C4C2418yes—
589C2×C4⋊C4C2414yes—
590C2×C22⋊C4—28no—
591C2×C22⋊C4—24no—
592C2×C22⋊C4—24no—
593C2×C22⋊C4—24no—
594C2×C22⋊C4—24no—
595C2×C22⋊C4—28no—
596C2×C22⋊C4—28no—
597C2×C22⋊C4—28no—
598C2×C22⋊C4—28no—
599C2×C22⋊C4—24no—
600C2×C22⋊C4—24no—
601C2×C22⋊C4—28no—
602C2×C22⋊C4—24no—
603C2×C22⋊C4—24no—
604C2×C22⋊C4—28no—
605C2×C22⋊C4—28no—
606C2×C22⋊C4—28no—
607C2×C22⋊C4—264no—
608C2×C22⋊C4—432no—
609C2×C22⋊C4—44no—
610C2×C22⋊C4—44no—
611C2×C22⋊C4—44no—
612C2×C22⋊C4—44no—
613C2×C22⋊C4—44no—
614C2×C22⋊C4—44no—
615C2×C22⋊C4—432no—
616C2×C22⋊C4—44no—
617C2×C22⋊C4—44no—
618C2×C22⋊C4—44no—
619C2×C22⋊C4—44no—
620C2×C22⋊C4—44no—
621C2×C22⋊C4—44no—
622C2×C22⋊C4—44no—
623C2×C22⋊C4—44no—
624C2×C22⋊C4C2×D418yes—
625C2×C22⋊C4C2×D418yes—
626C2×C22⋊C4C2418yes—
627C2×C22⋊C4C2418yes—
628C2×C22⋊C4C2418yes—
629C2×C22⋊C4C2418yes—
630C2×C22⋊C4C2418yes—
631C2×C22⋊C4C2414yes—
632C2×C22⋊C4C2414yes—
633C2×C22⋊C4C2414yes—
634C2×C22⋊C4C2414yes—
635C2×C22⋊C4C2418yes—
636C2×C22⋊C4C2418yes—
637C2×C22⋊C4C2414yes—
638C2×C22⋊C4C2414yes—
639C2×C22⋊C4C2414yes—
640C2×C22⋊C4C2414yes—
641C2×C22⋊C4C2418yes—
642C2×C22⋊C4C2418yes—
643C2×C22⋊C4C2418yes—
644C2×C22⋊C4C2418yes—
645C2×C22⋊C4C2418yes—
646C2×C22⋊C4C2418yes—
647C2×C22⋊C4C2418yes—
648C2×C22⋊C4C2418yes—
649C2×C22⋊C4C2418yes—
650C2×C22⋊C4C2418yes—
651C2×C22⋊C4C2418yes—
652C2×C22⋊C4C2418yes—
653C2×C22⋊C4C2418yes—
654C2×C22⋊C4C2418yes—
655C2×C22⋊C4C2418yes—
656C2×C22⋊C4C2418yes—
657C2×C22⋊C4C2414yes—
658C2×C22⋊C4C2414yes—
659C2×C42—24no—
660C2×C42—24no—
661C2×C42—24no—
662C2×C42—24no—
663C2×C42—24no—
664C2×C42—232no—
665C2×C42—44no—
666C2×C42C2×D418yes—
667C2×C42C2414yes—
668C2×C42C2414yes—
669C2×C42C2414yes—
670C2×C42C2414yes—
671C2×C42C2414yes—
672C2×C42C2418yes—
673C2×C42C2414yes—
674#95C2418yes—
675#95C2418yes—
676#95C2418yes—
677#95C2418yes—
678#95C2418yes—
679#95C2418yes—
680#95C2418yes—
681#95C2418yes—
682#95C2418yes—
683#95C2418yes—
684#95C2418yes—
685#95C2418yes—
686#95C2418yes—
687C24—22no—
688C24—22no—
689C24—22no—
690C24—22no—
691C24—24no—
692C24—22no—
693C24—24no—
694C24—24no—
695C24—22no—
696C24—22no—
697C24—22no—
698C24—24no—
699C24—22no—
700C24—24no—
701C24—24no—
702C24—22no—
703C24—22no—
704C24—24no—
705C24—22no—
706C24—216no—
707C24—24no—
708C24—24no—
709C24—24no—
710C24—22no—
711C24—22no—
712C24—24no—
713C24—22no—
714C24—22no—
715C24—24no—
716C24—24no—
717C24—22no—
718C24—216no—
719C24—216no—
720C24—216no—
721C24—48no—
722C24—48no—
723C24—48no—
724C24—432no—
725C24—432no—
726C24—432no—
727C24—432no—
728C24—816no—
729C24—816no—
730C24—816no—
731C24C22×D414yes—
732C24C22×D414yes—
733C24C2×#4118yes—
734C24H(5,𝔽2)14yes—
735C242−1+414yes—
736C24C2514yes—
737C24C2512yes—
738C24C2512yes—
739C24C2514yes—
740C24C2512yes—
741C24C2511yescharacteristic
742#41—4128no—
743C2×Q8—28no—
744C2×Q8—28no—
745C2×Q8—28no—
746C2×Q8—28no—
747C2×Q8—28no—
748C2×Q8—44no—
749C2×Q8—416no—
750C2×Q8—416no—
751C2×D4—232no—
752C2×D4—28no—
753C2×D4—28no—
754C2×D4—28no—
755C2×D4—28no—
756C2×D4—216no—
757C2×D4—216no—
758C2×D4—216no—
759C2×D4—28no—
760C2×D4—28no—
761C2×D4—216no—
762C2×D4—216no—
763C2×D4—232no—
764C2×D4—28no—
765C2×D4—216no—
766C2×D4—28no—
767C2×D4—28no—
768C2×D4—28no—
769C2×D4—28no—
770C2×D4—28no—
771C2×D4—4128no—
772C2×D4—48no—
773C2×D4—44no—
774C2×D4—48no—
775C2×D4—416no—
776C2×D4—432no—
777C2×D4—48no—
778C2×D4—48no—
779C2×D4—48no—
780C2×D4—48no—
781C2×D4—48no—
782C2×D4—48no—
783C2×D4—48no—
784C2×D4—432no—
785C2×D4—416no—
786C2×D4—416no—
787C2×D4—816no—
788C2×D4—816no—
789C2×D4—816no—
790C2×D4C22×D4116yes—
791C2×D4C2×#41116yes—
792C22×C4—22no—
793C22×C4—22no—
794C22×C4—22no—
795C22×C4—22no—
796C22×C4—22no—
797C22×C4—22no—
798C22×C4—22no—
799C22×C4—22no—
800C22×C4—22no—
801C22×C4—22no—
802C22×C4—232no—
803C22×C4—232no—
804C22×C4—28no—
805C22×C4—28no—
806C22×C4—28no—
807C22×C4—28no—
808C22×C4—22no—
809C22×C4—22no—
810C22×C4—22no—
811C22×C4—28no—
812C22×C4—28no—
813C22×C4—22no—
814C22×C4—22no—
815C22×C4—24no—
816C22×C4—24no—
817C22×C4—22no—
818C22×C4—22no—
819C22×C4—24no—
820C22×C4—24no—
821C22×C4—216no—
822C22×C4—24no—
823C22×C4—24no—
824C22×C4—24no—
825C22×C4—24no—
826C22×C4—24no—
827C22×C4—28no—
828C22×C4—22no—
829C22×C4—22no—
830C22×C4—22no—
831C22×C4—22no—
832C22×C4—24no—
833C22×C4—22no—
834C22×C4—22no—
835C22×C4—24no—
836C22×C4—24no—
837C22×C4—24no—
838C22×C4—24no—
839C22×C4—24no—
840C22×C4—24no—
841C22×C4—28no—
842C22×C4—22no—
843C22×C4—22no—
844C22×C4—22no—
845C22×C4—22no—
846C22×C4—24no—
847C22×C4—22no—
848C22×C4—24no—
849C22×C4—216no—
850C22×C4—216no—
851C22×C4—28no—
852C22×C4—28no—
853C22×C4—28no—
854C22×C4—28no—
855C22×C4—216no—
856C22×C4—44no—
857C22×C4—48no—
858C22×C4—48no—
859C22×C4—48no—
860C22×C4—48no—
861C22×C4—48no—
862C22×C4—48no—
863C22×C4—48no—
864C22×C4—48no—
865C22×C4—416no—
866C22×C4—432no—
867C22×C4—416no—
868C22×C4—416no—
869C22×C4—816no—
870C22×C4—816no—
871C22×C4—816no—
872C22×C4C22×D414yes—
873C22×C4C22×D4116yes—
874C22×C4C22×D414yes—
875C22×C4C22×D414yes—
876C22×C4C22×D414yes—
877C22×C4C22×D4116yes—
878C22×C4C22×D414yes—
879C22×C4C2×#4114yes—
880C22×C4H(5,𝔽2)14yes—
881C22×C4H(5,𝔽2)14yes—
882C22×C4C2514yes—
883C22×C4C2514yes—
884C22×C4C2512yes—
885C22×C4C2512yes—
886C22×C4C2512yes—
887C22×C4C2514yes—
888C22×C4C2514yes—
889C22×C4C2514yes—
890C22×C4C2512yes—
891C22×C4C2512yes—
892C22×C4C2512yes—
893C22×C4C2514yes—
894C22×C4C2512yes—
895C22×C4C2512yes—
896C22×C4C2512yes—
897C22×C4C2512yes—
898C22×C4C2512yes—
899C22×C4C2512yes—
900C4⋊C4—28no—
901C4⋊C4—28no—
902C4⋊C4—28no—
903C4⋊C4—28no—
904C4⋊C4—28no—
905C4⋊C4—28no—
906C4⋊C4—28no—
907C4⋊C4—28no—
908C4⋊C4—28no—
909C4⋊C4—28no—
910C4⋊C4—216no—
911C4⋊C4—28no—
912C4⋊C4—28no—
913C4⋊C4—28no—
914C4⋊C4—28no—
915C4⋊C4—216no—
916C4⋊C4—48no—
917C4⋊C4—48no—
918C4⋊C4—48no—
919C4⋊C4—48no—
920C4⋊C4—48no—
921C4⋊C4—48no—
922C4⋊C4—48no—
923C4⋊C4C22×D4116yes—
924C22⋊C4—216no—
925C22⋊C4—28no—
926C22⋊C4—28no—
927C22⋊C4—28no—
928C22⋊C4—28no—
929C22⋊C4—216no—
930C22⋊C4—216no—
931C22⋊C4—216no—
932C22⋊C4—216no—
933C22⋊C4—28no—
934C22⋊C4—28no—
935C22⋊C4—216no—
936C22⋊C4—28no—
937C22⋊C4—28no—
938C22⋊C4—216no—
939C22⋊C4—216no—
940C22⋊C4—216no—
941C22⋊C4—48no—
942C22⋊C4—48no—
943C22⋊C4—48no—
944C22⋊C4—48no—
945C22⋊C4—48no—
946C22⋊C4—48no—
947C22⋊C4—48no—
948C22⋊C4—48no—
949C22⋊C4—48no—
950C22⋊C4—48no—
951C22⋊C4—48no—
952C22⋊C4—48no—
953C22⋊C4—48no—
954C22⋊C4—48no—
955C22⋊C4C22×D4116yes—
956C22⋊C4C22×D4116yes—
957C42—28no—
958C42—28no—
959C42—28no—
960C42—28no—
961C42—28no—
962C42—48no—
963C42C22×D4116yes—
964C23—22no—
965C23—22no—
966C23—22no—
967C23—22no—
968C23—28no—
969C23—28no—
970C23—28no—
971C23—28no—
972C23—28no—
973C23—28no—
974C23—24no—
975C23—22no—
976C23—24no—
977C23—24no—
978C23—22no—
979C23—22no—
980C23—22no—
981C23—24no—
982C23—22no—
983C23—24no—
984C23—24no—
985C23—22no—
986C23—28no—
987C23—28no—
988C23—216no—
989C23—28no—
990C23—216no—
991C23—216no—
992C23—22no—
993C23—24no—
994C23—22no—
995C23—24no—
996C23—24no—
997C23—24no—
998C23—22no—
999C23—22no—
1000C23—24no—
1001C23—22no—
1002C23—22no—
1003C23—24no—
1004C23—24no—
1005C23—22no—
1006C23—432no—
1007C23—432no—
1008C23—432no—
1009C23—48no—
1010C23—48no—
1011C23—44no—
1012C23—44no—
1013C23—44no—
1014C23—48no—
1015C23—44no—
1016C23—48no—
1017C23—44no—
1018C23—432no—
1019C23—48no—
1020C23—44no—
1021C23—48no—
1022C23—44no—
1023C23—48no—
1024C23—44no—
1025C23—48no—
1026C23—44no—
1027C23—48no—
1028C23—44no—
1029C23—48no—
1030C23—44no—
1031C23—48no—
1032C23—816no—
1033C23—816no—
1034C23—816no—
1035C23—8128no—
1036C23#537116yes—
1037C23C23×D414yes—
1038C23C23×D414yes—
1039C23C23×D412yes—
1040C23C22×#4118yes—
1041C23C22×#4112yes—
1042C23C2×H(5,𝔽2)14yes—
1043C23C2×H(5,𝔽2)12yes—
1044C23C2×H(5,𝔽2)12yes—
1045C23C2×H(5,𝔽2)12yes—
1046C23C2×2−1+414yes—
1047C23C2×2−1+412yes—
1048C23#58512yes—
1049C23C2611yescharacteristic
1050Q8—416no—
1051Q8—416no—
1052D4—232no—
1053D4—232no—
1054D4—416no—
1055D4—432no—
1056D4—432no—
1057D4—416no—
1058D4—416no—
1059D4—816no—
1060D4—816no—
1061D4—816no—
1062C2×C4—22no—
1063C2×C4—22no—
1064C2×C4—22no—
1065C2×C4—22no—
1066C2×C4—22no—
1067C2×C4—22no—
1068C2×C4—22no—
1069C2×C4—22no—
1070C2×C4—22no—
1071C2×C4—22no—
1072C2×C4—28no—
1073C2×C4—28no—
1074C2×C4—28no—
1075C2×C4—28no—
1076C2×C4—28no—
1077C2×C4—232no—
1078C2×C4—232no—
1079C2×C4—22no—
1080C2×C4—22no—
1081C2×C4—22no—
1082C2×C4—22no—
1083C2×C4—22no—
1084C2×C4—24no—
1085C2×C4—24no—
1086C2×C4—22no—
1087C2×C4—22no—
1088C2×C4—24no—
1089C2×C4—24no—
1090C2×C4—24no—
1091C2×C4—24no—
1092C2×C4—24no—
1093C2×C4—24no—
1094C2×C4—24no—
1095C2×C4—22no—
1096C2×C4—22no—
1097C2×C4—22no—
1098C2×C4—22no—
1099C2×C4—24no—
1100C2×C4—22no—
1101C2×C4—22no—
1102C2×C4—24no—
1103C2×C4—24no—
1104C2×C4—24no—
1105C2×C4—24no—
1106C2×C4—24no—
1107C2×C4—24no—
1108C2×C4—22no—
1109C2×C4—22no—
1110C2×C4—22no—
1111C2×C4—22no—
1112C2×C4—24no—
1113C2×C4—22no—
1114C2×C4—24no—
1115C2×C4—416no—
1116C2×C4—432no—
1117C2×C4—416no—
1118C2×C4—44no—
1119C2×C4—44no—
1120C2×C4—44no—
1121C2×C4—44no—
1122C2×C4—48no—
1123C2×C4—44no—
1124C2×C4—48no—
1125C2×C4—44no—
1126C2×C4—48no—
1127C2×C4—48no—
1128C2×C4—48no—
1129C2×C4—48no—
1130C2×C4—416no—
1131C2×C4—816no—
1132C2×C4—816no—
1133C2×C4—816no—
1134C2×C4#546116yes—
1135C2×C4C23×D414yes—
1136C2×C4C23×D414yes—
1137C2×C4C23×D414yes—
1138C2×C4C23×D414yes—
1139C2×C4C23×D414yes—
1140C2×C4C22×#4114yes—
1141C2×C4C2×H(5,𝔽2)14yes—
1142C2×C4C2×H(5,𝔽2)14yes—
1143C22—24no—
1144C22—24no—
1145C22—24no—
1146C22—24no—
1147C22—24no—
1148C22—232no—
1149C22—24no—
1150C22—28no—
1151C22—28no—
1152C22—24no—
1153C22—24no—
1154C22—24no—
1155C22—28no—
1156C22—42no—
1157C22—44no—
1158C22—42no—
1159C22—44no—
1160C22—42no—
1161C22—42no—
1162C22—44no—
1163C22—416no—
1164C22—432no—
1165C22—44no—
1166C22—42no—
1167C22—44no—
1168C22—42no—
1169C22—44no—
1170C22—42no—
1171C22—44no—
1172C22—42no—
1173C22—44no—
1174C22—42no—
1175C22—44no—
1176C22—42no—
1177C22—44no—
1178C22—42no—
1179C22—44no—
1180C22—864no—
1181C22—88no—
1182C22—816no—
1183C22C2×#53718yes—
1184C22C2×#53714yes—
1185C22C2×#54614yes—
1186C22#348814yes—
1187C22#351314yes—
1188C22#352014yes—
1189C22#354314yes—
1190C22#356114yes—
1191C22C24×D411yescharacteristic
1192C22C23×#4111yescharacteristic
1193C22C22×H(5,𝔽2)11yescharacteristic
1194C22C22×H(5,𝔽2)11yescharacteristic
1195C22C22×H(5,𝔽2)11yescharacteristic
1196C22C22×2−1+411yescharacteristic
1197C22C2×#58511yescharacteristic
1198C4—24no—
1199C4—24no—
1200C4—24no—
1201C4—24no—
1202C4—24no—
1203C4—44no—
1204C4—44no—
1205C4—44no—
1206C4—44no—
1207C4—42no—
1208C4—44no—
1209C4—42no—
1210C4—42no—
1211C4—42no—
1212C4—42no—
1213C4—42no—
1214C4—44no—
1215C4C2×#54618yes—
1216C2—28no—
1217C2—44no—
1218C2—48no—
1219C2—82no—
1220C2—84no—
1221C2#3802418yesdirect product factor
1222C2C22×#53711yescharacteristic
1223C2C22×#54611yescharacteristic
1224C2C2×#356111yescharacteristic
1225C2C2×#354311yescharacteristic
1226C2C2×#351311yescharacteristic
1227C2C2×#352011yescharacteristic
1228C2C2×#348811yescharacteristic
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. C22×#546C2semidirect
2. C22×#529C2semidirect
3. C2×#2707C2semidirect
4. C2×#2705C2semidirect
5. C2×#2691C2semidirect
6. C2×#2676C2semidirect
7. #38024C2direct (N × H)
8. C2×#2855C2semidirect
9. C2×#2538C2semidirect
10. C2×#2592C2semidirect
11. C2×#2534C2semidirect
12. C2×#2407C2semidirect
13. C2×#2417C2semidirect
14. C2×#2416C2semidirect
15. C2×#2408C2semidirect
16. C2×#2412C2semidirect
17. C2×#2424C2semidirect
18. C2×#2437C2semidirect
19. C2×#2620C2semidirect
20. C2×#2624C2semidirect
21. C2×D4×C4⋊C4C2semidirect
22. C2×#2324C2semidirect
23. C2×#2311C2semidirect
24. C22×#390C2semidirect
28. C2×#546C22semidirect
30. C2×#529C22semidirect
31. C22×#126C22semidirect
32. C22×#126C22semidirect
33. C22×#125C22semidirect
35. C22×#124C22semidirect
41. C22×C22⋊Q8C22semidirect
42. C22×C22⋊Q8C22semidirect
48. C22×#121C22semidirect
51. C22×C4×Q8C22semidirect
56. C22×C4×D4C22semidirect
57. C22×#117C22semidirect
58. C22×#117C22semidirect
60. C23×C4⋊C4C22semidirect
65. #2855C22semidirect
66. #2707C22semidirect
67. #2705C22semidirect
68. #2691C22semidirect
69. #2676C22semidirect
70. #2624C22semidirect
71. #2620C22semidirect
72. #2592C22semidirect
73. #2538C22semidirect
74. #2534C22semidirect
75. #2437C22semidirect
76. #2424C22semidirect
77. #2417C22semidirect
78. #2416C22semidirect
79. #2412C22semidirect
80. #2408C22semidirect
81. #2407C22semidirect
82. C2×#399C22semidirect
83. C2×#398C22semidirect
84. C2×#397C22semidirect
85. C2×#397C22semidirect
86. C2×#396C22semidirect
87. C2×#396C22semidirect
88. C2×#396C22semidirect
89. C2×#396C22semidirect
90. C2×#396C22semidirect
91. C2×#396C22semidirect
93. C2×#394C22semidirect
94. C2×#394C22semidirect
95. C2×#394C22semidirect
96. C2×#394C22semidirect
97. C2×#394C22semidirect
98. C2×#394C22semidirect
99. C2×#393C22semidirect
101. C2×#392C22semidirect
102. D4×C4⋊C4C22semidirect
103. #2324C22semidirect
104. #2311C22semidirect
105. C2×#391C22semidirect
106. C2×#391C22semidirect
107. C2×#391C22semidirect
116. C2×#390C22semidirect
117. C2×#390C22semidirect
118. C2×#389C22semidirect
119. C2×#389C22semidirect
120. C2×#389C22semidirect
121. C2×#389C22semidirect
122. C2×#388C22semidirect
123. C2×#388C22semidirect
124. C2×#388C22semidirect
125. C2×#387C22semidirect
126. C2×#387C22semidirect
128. C2×#386C22semidirect
129. C2×#386C22semidirect
130. C2×#386C22semidirect
131. C2×#386C22semidirect
132. C2×#386C22semidirect
135. C2×#385C22semidirect
136. C2×#385C22semidirect
137. C2×#385C22semidirect
138. C2×#384C22semidirect
142. C2×#380C22semidirect
143. C2×#380C22semidirect
144. C2×#380C22semidirect
145. C2×#380C22semidirect
146. C2×#380C22semidirect
148. C2×C4×C4⋊C4C22semidirect
183. C2×#126C23semidirect
184. C2×#126C23semidirect
186. C2×#125C23semidirect
190. C2×#124C23semidirect
203. C2×C22⋊Q8C23semidirect
204. C2×C22⋊Q8C23semidirect
216. C2×#121C23semidirect
222. C2×C4×Q8C23semidirect
227. C2×C4×D4D4semidirect
232. C2×C4×D4C23semidirect
235. C2×#117C23semidirect
236. C2×#117C23semidirect
264. C22×C4⋊C4C23semidirect
313. #399C23semidirect
314. #398C23semidirect
315. #397C23semidirect
316. #397C23semidirect
317. #396C23semidirect
318. #396C23semidirect
319. #396C23semidirect
320. #396C23semidirect
321. #396C23semidirect
322. #396C23semidirect
324. #394C23semidirect
325. #394C23semidirect
326. #394C23semidirect
327. #394C23semidirect
328. #394C23semidirect
329. #394C23semidirect
330. #393C23semidirect
332. #392C23semidirect
333. #391C23semidirect
334. #391C23semidirect
335. #391C23semidirect
344. #390C23semidirect
345. #389C23semidirect
346. #389C23semidirect
347. #389C23semidirect
348. #389C23semidirect
349. #388C23semidirect
350. #388C23semidirect
351. #388C23semidirect
352. #387C23semidirect
353. #387C23semidirect
355. #386C23semidirect
356. #386C23semidirect
357. #386C23semidirect
358. #386C23semidirect
359. #386C23semidirect
362. #385C23semidirect
363. #385C23semidirect
364. #385C23semidirect
365. #384C23semidirect
369. #380C23semidirect
370. #380C23semidirect
371. #380C23semidirect
372. #380C23semidirect
373. #380C23semidirect
375. C4×C4⋊C4C23semidirect
537. C4×D4C2×D4semidirect
1221. C2#38024direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#5462
C22×#5292
C2×#27072
C2×#27052
C2×#26912
C2×#26762
#380242
C2×#28552
C2×#25382
C2×#25922
C2×#25342
C2×#24072
C2×#24172
C2×#24162
C2×#24082
C2×#24122
C2×#24242
C2×#24372
C2×#26202
C2×#26242
C2×D4×C4⋊C42
C2×#23242
C2×#23112
C22×#3902