Finite Group Databasebeta

← #874301

Subgroups — #874301

Order 512.

2748 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2501C211yesmaximal, characteristic
2C2×#2423C211yesmaximal, characteristic, complemented
3#16794C214yesmaximal, complemented
4#15739C214yesmaximal, complemented
5#15669C214yesmaximal, complemented
6#15242C211yesmaximal, characteristic, complemented
7#15240C211yesmaximal, characteristic, complemented
8#15222C211yesmaximal, characteristic, complemented
9#15219C211yesmaximal, characteristic
10#15215C211yesmaximal, characteristic
11#15136C211yesmaximal, characteristic, complemented
12#14708C211yesmaximal, characteristic, complemented
13#14687C211yesmaximal, characteristic, complemented
14#14506C214yesmaximal, complemented
15#14139C211yesmaximal, characteristic, complemented
16#14026C211yesmaximal, characteristic, complemented
17#13926C211yesmaximal, characteristic, complemented
18#13881C211yesmaximal, characteristic, complemented
19C4×#388C211yesmaximal, characteristic, complemented
20C22×#124C2211yescharacteristic
21C22×#123C2212yes—
22C22×#123C2212yes—
23C22×C22⋊Q8C2211yescharacteristic
24C22×#121C2211yescharacteristic
25C22×C4×Q8C2211yescharacteristic
26C23×C4⋊C4C2211yescharacteristic
27#2501—28no—
28#2423—28no—
29C2×#399C2212yes—
30C2×#399C2212yes—
31C2×#399C2212yes—
32C2×#398C2212yes—
33C2×#397C2214yes—
34C2×#391C2211yescharacteristic
35C2×#391C2211yescharacteristic
36C2×#391C2211yescharacteristic
37C2×#391C2211yescharacteristic
38C2×#390C2211yescharacteristic
39C2×#390C2211yescharacteristic
40C2×#390C2211yescharacteristic
41C2×#390C2211yescharacteristic
42C2×#390C2211yescharacteristic
43C2×#389C2211yescharacteristic
44C2×#388C2212yes—
45C2×#388C2212yes—
46C2×#387C2212yes—
47C2×#384C2211yescharacteristic
48C2×#384C2211yescharacteristic
49C2×#384C2211yescharacteristic
50C2×#382C2214yes—
51C2×#382C2211yescharacteristic
52C2×#382C2211yescharacteristic
53C2×#382C2211yescharacteristic
54C2×#380C2211yescharacteristic
55C2×C4×C4⋊C4C2211yescharacteristic
56C2×C4×C22⋊C4C2211yescharacteristic
57C2×C4×C22⋊C4C2211yescharacteristic
58C2×C4×C22⋊C4C2211yescharacteristic
59C2×C43C2211yescharacteristic
60#1445C2214yes—
61#1445C2214yes—
62#1445C2214yes—
63#1442C2214yes—
64#1441C2214yes—
65#1441C2214yes—
66#1441C2214yes—
67#1440C2214yes—
68#1439C2214yes—
69#1439C2214yes—
70#1439C2214yes—
71#1439C2214yes—
72#1439C2214yes—
73#1438C2214yes—
74#1438C2214yes—
75#1437C2212yes—
76#1437C2214yes—
77#1437C2214yes—
78#1437C2214yes—
79#1436C2212yes—
80C4⋊#95C2211yescharacteristic
81C4⋊#95C2211yescharacteristic
82C4⋊#95C2211yescharacteristic
83C4⋊#95C2211yescharacteristic
84C4⋊#95C2211yescharacteristic
85C4⋊#95C2211yescharacteristic
86C4⋊#95C2214yes—
87C4⋊#95C2214yes—
88#1434C2212yes—
89C22⋊#95C2214yes—
90C22⋊#95C2214yes—
91C4×#95C2211yescharacteristic
92C4×#95C2211yescharacteristic
93C23×Q8C2311yescharacteristic
94C23×D4C2311yescharacteristic
95C23×D4C2312yes—
96C24×C4C2311yescharacteristic
97C24×C4C2312yes—
98C2×#124—24no—
99C2×#124—24no—
100C2×#124—42no—
101C2×#123—28no—
102C2×#123—28no—
103C2×#123—216no—
104C2×#123—48no—
105C2×C22⋊Q8—24no—
106C2×C22⋊Q8—24no—
107C2×C22⋊Q8—42no—
108C2×#121—24no—
109C2×#121—42no—
110C2×#121—42no—
111C2×C4×Q8—24no—
112C2×C4×Q8—24no—
113C2×C4×Q8—42no—
114C22×C4⋊C4—24no—
115C22×C4⋊C4—42no—
116C22×C4⋊C4—42no—
117C22×C4⋊C4C2312yes—
118C22×C4⋊C4C2312yes—
119C22×C4⋊C4C2312yes—
120C22×C4⋊C4C2312yes—
121C22×C4⋊C4C2311yescharacteristic
122C22×C4⋊C4C2311yescharacteristic
123C22×C4⋊C4C2311yescharacteristic
124C22×C4⋊C4C2311yescharacteristic
125C22×C4⋊C4C2311yescharacteristic
126C22×C4⋊C4C2311yescharacteristic
127C22×C4⋊C4C2312yes—
128C22×C4⋊C4C2312yes—
129C22×C4⋊C4C2312yes—
130C22×C4⋊C4C2312yes—
131C22×C4⋊C4C2312yes—
132C22×C4⋊C4C2312yes—
133C22×C4⋊C4C2312yes—
134C22×C22⋊C4C2312yes—
135C22×C22⋊C4C2312yes—
136C22×C22⋊C4C2312yes—
137C22×C22⋊C4C2312yes—
138C22×C22⋊C4C2314yes—
139C22×C22⋊C4C2312yes—
140C22×C22⋊C4C2312yes—
141C22×C22⋊C4C2311yescharacteristic
142C22×C22⋊C4C2312yes—
143C22×C22⋊C4C2312yes—
144C22×C22⋊C4C2312yes—
145C22×C22⋊C4C2314yes—
146C22×C22⋊C4C2314yes—
147C22×C22⋊C4C2314yes—
148C22×C22⋊C4C2311yescharacteristic
149C22×C42C2311yescharacteristic
150C22×C42C2311yescharacteristic
151C22×C42C2311yescharacteristic
152C22×C42C2312yes—
153C22×C42C2312yes—
154C22×C42C2312yes—
155C22×C42C2311yescharacteristic
156C22×C42C2311yescharacteristic
157C22×C42C2311yescharacteristic
158#399—28no—
159#399—28no—
160#399—28no—
161#398—28no—
162#397—48no—
163#391—24no—
164#391—42no—
165#391—42no—
166#391—42no—
167#390—24no—
168#390—24no—
169#390—42no—
170#390—42no—
171#390—42no—
172#389—24no—
173#388—28no—
174#388—28no—
175#387—28no—
176#384—24no—
177#384—24no—
178#384—24no—
179#382—42no—
180#382—48no—
181#382—42no—
182#382—42no—
183#380—24no—
184C4×C4⋊C4—42no—
185C4×C22⋊C4—24no—
186C4×C22⋊C4—42no—
187C4×C22⋊C4D418yes—
188C2×#95C2312yes—
189C2×#95C2312yes—
190C2×#95C2312yes—
191C2×#95C2312yes—
192C2×#95C2312yes—
193C2×#95C2312yes—
194C2×#95C2312yes—
195C2×#95C2312yes—
196C2×#95C2314yes—
197C2×#95C2314yes—
198C2×#95C2312yes—
199C2×#95C2314yes—
200C2×#95C2314yes—
201C2×#95C2314yes—
202C2×#95C2314yes—
203C2×#95C2314yes—
204C2×#95C2314yes—
205C2×#95C2312yes—
206C2×#95C2312yes—
207C2×#95C2314yes—
208C2×#95C2314yes—
209C2×#95C2314yes—
210C2×#95C2314yes—
211C2×#95C2311yescharacteristic
212C2×#95C2311yescharacteristic
213C43—24no—
214C25C2412yes—
215C25C2411yescharacteristic
216C22×Q8—22no—
217C22×Q8—22no—
218C22×Q8—22no—
219C22×Q8—22no—
220C22×Q8—22no—
221C22×Q8—22no—
222C22×Q8#4114yes—
223C22×D4—24no—
224C22×D4—28no—
225C22×D4—22no—
226C22×D4—22no—
227C22×D4—22no—
228C22×D4—22no—
229C22×D4—22no—
230C22×D4—22no—
231C22×D4—22no—
232C22×D4—42no—
233C22×D4—42no—
234C22×D4—44no—
235C23×C4—22no—
236C23×C4—22no—
237C23×C4—22no—
238C23×C4—22no—
239C23×C4—22no—
240C23×C4—22no—
241C23×C4—24no—
242C23×C4—28no—
243C23×C4—42no—
244C23×C4—42no—
245C23×C4—44no—
246C23×C4C2×D414yes—
247C23×C4C2412yes—
248C23×C4C2412yes—
249C23×C4C2412yes—
250C23×C4C2412yes—
251C23×C4C2412yes—
252C23×C4C2412yes—
253C23×C4C2412yes—
254C23×C4C2412yes—
255C23×C4C2411yescharacteristic
256C23×C4C2411yescharacteristic
257C23×C4C2412yes—
258C23×C4C2412yes—
259C23×C4C2412yes—
260C23×C4C2411yescharacteristic
261C23×C4C2411yescharacteristic
262C23×C4C2411yescharacteristic
263C23×C4C2411yescharacteristic
264#124—416no—
265#123—432no—
266#123—432no—
267C22⋊Q8—416no—
268#121—416no—
269C4×Q8—416no—
270C2×C4⋊C4—22no—
271C2×C4⋊C4—22no—
272C2×C4⋊C4—24no—
273C2×C4⋊C4—22no—
274C2×C4⋊C4—24no—
275C2×C4⋊C4—22no—
276C2×C4⋊C4—22no—
277C2×C4⋊C4—24no—
278C2×C4⋊C4—24no—
279C2×C4⋊C4—24no—
280C2×C4⋊C4—24no—
281C2×C4⋊C4—24no—
282C2×C4⋊C4—22no—
283C2×C4⋊C4—24no—
284C2×C4⋊C4—24no—
285C2×C4⋊C4—22no—
286C2×C4⋊C4—24no—
287C2×C4⋊C4—22no—
288C2×C4⋊C4—28no—
289C2×C4⋊C4—28no—
290C2×C4⋊C4—24no—
291C2×C4⋊C4—22no—
292C2×C4⋊C4—22no—
293C2×C4⋊C4—22no—
294C2×C4⋊C4—22no—
295C2×C4⋊C4—22no—
296C2×C4⋊C4—22no—
297C2×C4⋊C4—22no—
298C2×C4⋊C4—22no—
299C2×C4⋊C4—28no—
300C2×C4⋊C4—22no—
301C2×C4⋊C4—22no—
302C2×C4⋊C4—28no—
303C2×C4⋊C4—24no—
304C2×C4⋊C4—24no—
305C2×C4⋊C4—24no—
306C2×C4⋊C4—42no—
307C2×C4⋊C4—42no—
308C2×C4⋊C4—42no—
309C2×C4⋊C4—42no—
310C2×C4⋊C4—44no—
311C2×C4⋊C4—42no—
312C2×C4⋊C4—416no—
313C2×C4⋊C4—44no—
314C2×C4⋊C4—44no—
315C2×C22⋊C4—24no—
316C2×C22⋊C4—24no—
317C2×C22⋊C4—24no—
318C2×C22⋊C4—24no—
319C2×C22⋊C4—24no—
320C2×C22⋊C4—24no—
321C2×C22⋊C4—24no—
322C2×C22⋊C4—24no—
323C2×C22⋊C4—24no—
324C2×C22⋊C4—24no—
325C2×C22⋊C4—28no—
326C2×C22⋊C4—28no—
327C2×C22⋊C4—28no—
328C2×C22⋊C4—28no—
329C2×C22⋊C4—24no—
330C2×C22⋊C4—28no—
331C2×C22⋊C4—24no—
332C2×C22⋊C4—24no—
333C2×C22⋊C4—28no—
334C2×C22⋊C4—42no—
335C2×C22⋊C4—42no—
336C2×C22⋊C4—42no—
337C2×C22⋊C4—42no—
338C2×C22⋊C4—44no—
339C2×C22⋊C4—44no—
340C2×C22⋊C4—42no—
341C2×C22⋊C4—44no—
342C2×C22⋊C4—44no—
343C2×C22⋊C4—44no—
344C2×C22⋊C4—44no—
345C2×C22⋊C4—44no—
346C2×C22⋊C4—44no—
347C2×C22⋊C4—44no—
348C2×C22⋊C4—44no—
349C2×C22⋊C4—44no—
350C2×C22⋊C4C2×D414yes—
351C2×C22⋊C4C2×D414yes—
352C2×C22⋊C4#4118yes—
353C2×C42—22no—
354C2×C42—22no—
355C2×C42—24no—
356C2×C42—22no—
357C2×C42—22no—
358C2×C42—22no—
359C2×C42—24no—
360C2×C42—24no—
361C2×C42—22no—
362C2×C42—24no—
363C2×C42—24no—
364C2×C42—24no—
365C2×C42—22no—
366C2×C42—22no—
367C2×C42—24no—
368C2×C42—22no—
369C2×C42—22no—
370C2×C42—22no—
371C2×C42—22no—
372C2×C42—22no—
373C2×C42—22no—
374C2×C42—22no—
375C2×C42—42no—
376C2×C42—42no—
377C2×C42C2×D414yes—
378C2×C42C2×D414yes—
379C2×C42#4114yes—
380#95—24no—
381#95—24no—
382#95—24no—
383#95—24no—
384#95—24no—
385#95—24no—
386#95—24no—
387#95—24no—
388#95—42no—
389#95—42no—
390#95—42no—
391#95—44no—
392#95—44no—
393#95—44no—
394#95—44no—
395#95—44no—
396#95—44no—
397#95—44no—
398#95—44no—
399#95—44no—
400#95—44no—
401#95—44no—
402#95—44no—
403#95C2×D414yes—
404#95C2×D414yes—
405C24—21no—
406C24—21no—
407C24—22no—
408C24—21no—
409C24—21no—
410C24—21no—
411C24—22no—
412C24—21no—
413C24—22no—
414C24—22no—
415C24—24no—
416C24—22no—
417C24—22no—
418C24—24no—
419C24—22no—
420C24—22no—
421C24—22no—
422C24—24no—
423C24—22no—
424C24—24no—
425C24C22×D412yes—
426C24C2×#4114yes—
427C24C2511yescharacteristic
428C2×Q8—28no—
429C2×Q8—28no—
430C2×Q8—28no—
431C2×Q8—44no—
432C2×Q8—44no—
433C2×Q8—44no—
434C2×Q8—44no—
435C2×D4—48no—
436C2×D4—48no—
437C2×D4—48no—
438C2×D4—44no—
439C2×D4—44no—
440C2×D4—44no—
441C2×D4—44no—
442C2×D4—44no—
443C2×D4—44no—
444C2×D4—44no—
445C2×D4—88no—
446C2×D4—88no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—21no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—21no—
463C22×C4—22no—
464C22×C4—21no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—21no—
472C22×C4—22no—
473C22×C4—21no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—22no—
479C22×C4—21no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—28no—
485C22×C4—28no—
486C22×C4—28no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—24no—
499C22×C4—24no—
500C22×C4—24no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—24no—
507C22×C4—24no—
508C22×C4—24no—
509C22×C4—22no—
510C22×C4—24no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—24no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—24no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—24no—
529C22×C4—24no—
530C22×C4—24no—
531C22×C4—44no—
532C22×C4—44no—
533C22×C4—44no—
534C22×C4—44no—
535C22×C4—48no—
536C22×C4—48no—
537C22×C4—48no—
538C22×C4—88no—
539C22×C4—88no—
540C22×C4C22×D412yes—
541C22×C4C22×D412yes—
542C22×C4C22×D412yes—
543C22×C4C22×D412yes—
544C22×C4C22×D412yes—
545C22×C4C22×D412yes—
546C22×C4C2×#4114yes—
547C22×C4C2×#4114yes—
548C22×C4C2×#4114yes—
549C22×C4C2×#4114yes—
550C22×C4C2×#4112yes—
551C22×C4C2×#4112yes—
552C22×C4H(5,𝔽2)14yes—
553C22×C4H(5,𝔽2)12yes—
554C22×C4H(5,𝔽2)12yes—
555C22×C4H(5,𝔽2)12yes—
556C22×C42−1+414yes—
557C22×C42−1+412yes—
558C4⋊C4—48no—
559C4⋊C4—48no—
560C4⋊C4—48no—
561C4⋊C4—48no—
562C4⋊C4—48no—
563C4⋊C4—48no—
564C4⋊C4—48no—
565C4⋊C4—48no—
566C4⋊C4—44no—
567C4⋊C4—44no—
568C4⋊C4—44no—
569C4⋊C4—44no—
570C4⋊C4—48no—
571C4⋊C4—44no—
572C4⋊C4—44no—
573C4⋊C4—84no—
574C4⋊C4—84no—
575C22⋊C4—28no—
576C22⋊C4—416no—
577C22⋊C4—48no—
578C22⋊C4—48no—
579C22⋊C4—48no—
580C22⋊C4—48no—
581C22⋊C4—48no—
582C22⋊C4—48no—
583C22⋊C4—48no—
584C22⋊C4—48no—
585C22⋊C4—88no—
586C22⋊C4—84no—
587C22⋊C4—88no—
588C22⋊C4—88no—
589C22⋊C4#124116yescomplemented
590C42—216no—
591C42—28no—
592C42—28no—
593C42—28no—
594C42—48no—
595C42—48no—
596C42—44no—
597C42—44no—
598C42—44no—
599C23—22no—
600C23—22no—
601C23—22no—
602C23—22no—
603C23—24no—
604C23—24no—
605C23—22no—
606C23—22no—
607C23—24no—
608C23—24no—
609C23—24no—
610C23—24no—
611C23—41no—
612C23—41no—
613C23—41no—
614C23—42no—
615C23—42no—
616C23—41no—
617C23—42no—
618C23—42no—
619C23—42no—
620C23—42no—
621C23—42no—
622C23—42no—
623C23—42no—
624C23—42no—
625C23—42no—
626C23—42no—
627C23—42no—
628C23—42no—
629C23—44no—
630C23—44no—
631C23—44no—
632C23—42no—
633C23—42no—
634C23—44no—
635C23—44no—
636C23—44no—
637C23—44no—
638C23—44no—
639C23—42no—
640C23—44no—
641C23—44no—
642C23—44no—
643C23—44no—
644C23C2×#12414yes—
645C23C23×D411yescharacteristic
646C23C22×#4112yes—
647C23C22×#4111yescharacteristic
648C23C22×#4111yescharacteristic
649C23C2×H(5,𝔽2)11yescharacteristic
650C23C2×H(5,𝔽2)11yescharacteristic
651C23C2×H(5,𝔽2)12yes—
652C23C2×H(5,𝔽2)11yescharacteristic
653C23C2×2−1+411yescharacteristic
654C23C2×2−1+412yes—
655C23#58512yes—
656Q8—416no—
657D4—816no—
658D4—88no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—24no—
663C2×C4—24no—
664C2×C4—24no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—24no—
669C2×C4—24no—
670C2×C4—24no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—24no—
674C2×C4—22no—
675C2×C4—24no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—24no—
679C2×C4—24no—
680C2×C4—24no—
681C2×C4—24no—
682C2×C4—24no—
683C2×C4—22no—
684C2×C4—24no—
685C2×C4—24no—
686C2×C4—42no—
687C2×C4—41no—
688C2×C4—42no—
689C2×C4—41no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—41no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—41no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—416no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—44no—
729C2×C4—44no—
730C2×C4—44no—
731C2×C4—44no—
732C2×C4—44no—
733C2×C4—44no—
734C2×C4—42no—
735C2×C4—44no—
736C2×C4—44no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—44no—
744C2×C4—44no—
745C2×C4—44no—
746C2×C4—42no—
747C2×C4—44no—
748C2×C4—42no—
749C2×C4—816no—
750C2×C4C2×#12414yes—
751C2×C4C2×#12414yes—
752C2×C4#53514yes—
753C2×C4#53514yes—
754C2×C4#53914yes—
755C2×C4#54014yes—
756C2×C4#54614yes—
757C2×C4#54714yes—
758C2×C4#55114yes—
759C2×C4#56214yes—
760C22—24no—
761C22—24no—
762C22—24no—
763C22—42no—
764C22—44no—
765C22—42no—
766C22—44no—
767C22—42no—
768C22—44no—
769C22—42no—
770C22—44no—
771C22—82no—
772C22—84no—
773C22—82no—
774C22—82no—
775C22—84no—
776C22—82no—
777C22—84no—
778C22—82no—
779C22—82no—
780C22—82no—
781C22—84no—
782C22C22×#12411yescharacteristic
783C22C2×#53511yescharacteristic
784C22C2×#53511yescharacteristic
785C22C2×#53911yescharacteristic
786C22C2×#54011yescharacteristic
787C22C2×#54611yescharacteristic
788C22C2×#54711yescharacteristic
789C22C2×#55111yescharacteristic
790C22#347512yes—
791C22#348212yes—
792C22#349212yes—
793C22#349911yescharacteristic
794C22#350011yescharacteristic
795C22#350812yes—
796C22#350812yes—
797C22#351512yes—
798C22#351712yes—
799C22#352012yes—
800C22C2×#56211yescharacteristic
801C22#354412yes—
802C22#354612yes—
803C22#355412yes—
804C22#356112yes—
805C4—24no—
806C4—24no—
807C4—24no—
808C4—42no—
809C4—44no—
810C4—42no—
811C4—44no—
812C4—44no—
813C4—82no—
814C4—82no—
815C4—82no—
816C4—82no—
817C4—82no—
818C4—82no—
819C4—82no—
820C4—82no—
821C4#270618yes—
822C2—44no—
823C2—162no—
824C2#3528511yescharacteristic
825C2#3616411yescharacteristic
826C2#3630311yescharacteristic
827C2#3739111yescharacteristic
828C2#3786311yescharacteristic
829C2#3895611yescharacteristic
830C2#3992612yes—
831C2#4009912yes—
832C2#4610412yes—
833C2C2×#270611yescharacteristic
834C2#5927712yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC22×#121C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#2423C2semidirect
3. #16794C2semidirect
4. #15739C2semidirect
5. #15669C2semidirect
6. #15242C2semidirect
7. #15240C2semidirect
8. #15222C2semidirect
11. #15136C2semidirect
12. #14708C2semidirect
13. #14687C2semidirect
14. #14506C2semidirect
15. #14139C2semidirect
16. #14026C2semidirect
17. #13926C2semidirect
18. #13881C2semidirect
19. C4×#388C2semidirect
589. C22⋊C4#124semidirect

Maximal subgroups

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

subgroupindex
C2×#25012
C2×#24232
#167942
#157392
#156692
#152422
#152402
#152222
#152192
#152152
#151362
#147082
#146872
#145062
#141392
#140262
#139262
#138812
C4×#3882