Finite Group Databasebeta

← #6571539

Subgroups — #6571539

Order 512.

4287 conjugacy classes of subgroups.

The subgroup lattice has 888 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3499C211yesmaximal, characteristic, complemented
2C2×#3294C212yesmaximal, complemented
3#36258C211yesmaximal, characteristic, complemented
4#29660C211yesmaximal, characteristic, complemented
5#29638C212yesmaximal, complemented
6#25933C212yesmaximal, complemented
7#25903C211yesmaximal, characteristic, complemented
8#25533C214yesmaximal, complemented
9#25496C212yesmaximal, complemented
10#24326C212yesmaximal, complemented
11#24298C211yesmaximal, characteristic, complemented
12#23960C214yesmaximal, complemented
13#23930C212yesmaximal, complemented
14#23567C211yesmaximal, characteristic, complemented
15C2×#2023C212yesmaximal, complemented
16#22485C212yesmaximal, complemented
17#22469C211yesmaximal, characteristic, complemented
18C22×2−1+4—21no—
19#3499—216no—
20C2×D4×Q8—21no—
21C2×D4×Q8C2212yescomplemented
22C2×#547—21no—
23C2×#547—22no—
24C2×#547C2212yes—
25C2×#547C2214yescomplemented
26C2×#546—21no—
27C2×D42C2211yescharacteristic
28C2×#536—22no—
29C2×#536—21no—
30C2×#532C2211yescharacteristic, complemented
31C2×#532C2212yescomplemented
32C22×C4⋊Q8C2211yescharacteristic, complemented
33C22×C4⋊Q8C2212yescomplemented
34C2×C4×#41C2211yescharacteristic
35#3294—216no—
36C2×#486C2212yes—
37C2×#480C2214yes—
38C2×#474C2212yes—
39C2×#466C2214yes—
40C2×#459C2212yes—
41C2×#447C2214yes—
42C2×C4×D8C2212yes—
43C2×C8×D4C2212yes—
44C22×#102C2214yes—
45#2856C2211yescharacteristic
46#2854C2212yes—
47#2548C2211yescharacteristic
48#2538C2211yescharacteristic
49#2426—21no—
50#2424—22no—
51#2416C2212yes—
52#2414—21no—
53#2411—22no—
54#2408C2212yes—
55D4×C4⋊C4C2211yescharacteristic
56D4×C22⋊C4—21no—
57C4×#121C2211yescharacteristic
58C2×#390C2212yes—
59#2057C2214yescomplemented
60#2057C2211yescharacteristic, complemented
61#2057C2212yescomplemented
62#2041C2211yescharacteristic, complemented
63#2033C2212yescomplemented
64#2023C2214yes—
65#2023C2211yescharacteristic
66#2023C2212yes—
67#2023C2212yescomplemented
68#2023C2212yescomplemented
69#2023C2214yescomplemented
70#2023C2214yescomplemented
71#2023C2212yescomplemented
72#2011C2211yescharacteristic
73#2011C2212yescomplemented
74#1999C2212yes—
75#1999C2214yescomplemented
76#1990C2212yescomplemented
77#1988C2212yescomplemented
78#1984C2212yescomplemented
79#1893C2214yescomplemented
80#1879C2214yes—
81#1879C2214yescomplemented
82#1879C2214yescomplemented
83#1874C2212yes—
84#1874C2214yescomplemented
85#1874C2214yescomplemented
86#1869C2214yescomplemented
87#1862C2214yescomplemented
88#1852C2212yescomplemented
89#1823C2214yescomplemented
90#1817C2212yescomplemented
91#1802C2212yescomplemented
92#1797C2211yescharacteristic, complemented
93C4×#102C2212yescomplemented
94C4×C22⋊C8C2211yescharacteristic, complemented
95C2×#340C2214yescomplemented
96C2×#336C2212yescomplemented
97C2×2−1+4—216no—
98C2×2−1+4—48no—
99C2×2−1+4—48no—
100C22×#41—22no—
101C22×#41—24no—
102C22×#41—22no—
103C22×#41—21no—
104C22×#41D411yescharacteristic
105C23×Q8—22no—
106C23×Q8—22no—
107C23×Q8—21no—
108C23×D4—21no—
109C23×D4C2312yes—
110C22×D8C2312yes—
111C22×D8C2314yes—
112C23×C8C2314yes—
113D4×Q8—216no—
114D4×Q8—28no—
115D4×Q8—28no—
116#547—216no—
117#547—232no—
118#547—216no—
119#547—28no—
120#547—216no—
121#547D4116yescomplemented
122#546—48no—
123D42—28no—
124#536—216no—
125#536—232no—
126#532—216no—
127#532—28no—
128C2×C4⋊Q8—28no—
129C2×C4⋊Q8—216no—
130C2×C4⋊Q8—21no—
131C2×C4⋊Q8—22no—
132C2×C4⋊Q8—21no—
133C2×C4⋊Q8—22no—
134C2×C4⋊Q8C2311yescharacteristic
135C2×C4⋊Q8C2312yes—
136C2×C4⋊Q8C2314yes—
137C2×C4⋊Q8C2312yes—
138C2×#127C2311yescharacteristic
139C2×#127C2311yescharacteristic
140C2×#124—21no—
141C2×#124—21no—
142C2×#124—22no—
143C2×#123—22no—
144C2×#123—24no—
145C2×#123—24no—
146C2×#123—24no—
147C2×C22⋊Q8—21no—
148C2×C22⋊Q8—22no—
149C2×C22⋊Q8—24no—
150C2×C22⋊Q8—22no—
151C2×C22⋊Q8—24no—
152C2×#121—22no—
153C2×#121—21no—
154C2×#121—22no—
155C2×#121—21no—
156C2×#121—21no—
157C2×#121—21no—
158C2×#121C2312yes—
159C2×#121C2312yes—
160C2×#121C2311yescharacteristic
161C2×#121C2314yes—
162C2×#121C2312yes—
163C2×#120—22no—
164C2×#120—22no—
165C4×#41—28no—
166C2×C4×Q8D411yescharacteristic
167C2×C4×Q8C2311yescharacteristic
168C2×C4×D4—21no—
169C2×C4×D4—21no—
170C2×C4×D4—21no—
171C2×C4×D4—22no—
172C2×C4×D4D411yescharacteristic
173C2×C4×D4D412yes—
174C2×C4×D4C2314yes—
175C2×C4×D4C2311yescharacteristic
176C2×C4×D4C2312yes—
177C2×C4×D4C2312yes—
178C2×C4×D4C2311yescharacteristic
179C2×#117D412yes—
180C2×#117D411yescharacteristic
181C22×C4⋊C4—22no—
182C22×C4⋊C4—21no—
183C22×C4⋊C4C2312yes—
184C22×C4⋊C4C2314yes—
185C22×C4⋊C4C2312yes—
186C22×C22⋊C4—22no—
187C22×C22⋊C4—22no—
188C22×C42C2311yescharacteristic
189C22×C42C2312yes—
190#486—28no—
191#480—216no—
192#474—28no—
193#466—216no—
194#459—28no—
195#447—216no—
196C4×D8—28no—
197C8×D4—28no—
198C2×#107C2312yes—
199C2×#107C2314yes—
200C2×C4⋊C8C2312yes—
201C2×#102—216no—
202C2×#102C2314yes—
203C2×#102C2314yes—
204C2×#102C2314yes—
205C2×#102C2312yes—
206C2×#102C2312yes—
207C2×#102C2314yes—
208C2×#102C2314yes—
209C2×#102C2312yes—
210C2×#102C2312yes—
211C2×C22⋊C8C2314yes—
212C2×C22⋊C8C2312yes—
213C2×C22⋊C8C2312yes—
214C2×C4×C8C2312yes—
215#396—22no—
216#396—22no—
217#394—22no—
218#394—22no—
219#394—22no—
220#392—22no—
221#390—21no—
222#390—21no—
223#390—21no—
224#390—22no—
225#390—22no—
226#390C2312yes—
227#390C2312yes—
228#390C2312yes—
229#390C2312yes—
230#390C2311yescharacteristic
231#389—21no—
232#389C2311yescharacteristic
233#389C2312yes—
234#388—22no—
235#388—22no—
236#388—21no—
237#386—22no—
238#386—21no—
239#386—22no—
240#385—22no—
241#384C2311yescharacteristic
242#380—21no—
243#380C2312yes—
244#380C2311yescharacteristic
245#379—22no—
246C4×C4⋊C4C2311yescharacteristic
247C4×C22⋊C4—21no—
248#340C2314yes—
249#340C2312yes—
250#340C2314yes—
251#340C2314yes—
252#340C2314yes—
253#340C2314yes—
254#340C2312yes—
255#336C2312yes—
256#336C2311yescharacteristic
257#336C2314yes—
258#336C2314yes—
259#336C2311yescharacteristic
260C25—22no—
2612−1+4—4128no—
262C2×#41—216no—
263C2×#41—28no—
264C2×#41—232no—
265C2×#41—24no—
266C2×#41—216no—
267C2×#41—24no—
268C2×#41—48no—
269C2×#41—44no—
270C2×#41—416no—
271C2×#41—416no—
272C2×#41—48no—
273C2×#41—48no—
274C2×#41—48no—
275C2×#41—44no—
276C2×#41D818yescomplemented
277C22×Q8—216no—
278C22×Q8—28no—
279C22×Q8—216no—
280C22×Q8—24no—
281C22×Q8—22no—
282C22×Q8—21no—
283C22×Q8—22no—
284C22×Q8—48no—
285C22×Q8—44no—
286C22×Q8—48no—
287C22×Q8—48no—
288C22×Q8—48no—
289C22×Q8—44no—
290C22×Q8C2×D411yescharacteristic
291C22×D4—22no—
292C22×D4—24no—
293C22×D4—24no—
294C22×D4—22no—
295C22×D4—21no—
296C22×D4—22no—
297C22×D4—21no—
298C22×D4—21no—
299C22×D4—28no—
300C22×D4—21no—
301C22×D4—22no—
302C22×D4—21no—
303C22×D4—44no—
304C22×D4—42no—
305C22×D4—44no—
306C22×D4—44no—
307C22×D4—44no—
308C22×D4C2×D412yes—
309C22×D4C2×D411yescharacteristic
310C22×D4C2412yes—
311C22×D4C2412yes—
312C22×D4C2411yescharacteristic
313C23×C4—22no—
314C23×C4—24no—
315C23×C4—24no—
316C23×C4—22no—
317C23×C4—22no—
318C23×C4—21no—
319C23×C4C2×D412yes—
320C23×C4C2×D411yescharacteristic
321C23×C4C2×D412yes—
322C23×C4C2×D411yescharacteristic
323C23×C4C2411yescharacteristic
324C23×C4C2412yes—
325C2×D8—24no—
326C2×D8—24no—
327C2×D8—28no—
328C2×D8—42no—
329C2×D8—44no—
330C2×D8—44no—
331C22×C8—28no—
332C22×C8—44no—
333C22×C8—44no—
334C22×C8C2412yes—
335C22×C8C2414yes—
336C22×C8C2412yes—
337C4⋊Q8—28no—
338C4⋊Q8—216no—
339C4⋊Q8—28no—
340C4⋊Q8—216no—
341C4⋊Q8—28no—
342C4⋊Q8—24no—
343C4⋊Q8—28no—
344C4⋊Q8—28no—
345C4⋊Q8—24no—
346C4⋊Q8C2×D418yes—
347#127—24no—
348#127—24no—
349#124—216no—
350#124—28no—
351#124—44no—
352#123—232no—
353#123—232no—
354#123—232no—
355#123—48no—
356C22⋊Q8—216no—
357C22⋊Q8—232no—
358C22⋊Q8—232no—
359C22⋊Q8—216no—
360C22⋊Q8—44no—
361#121—216no—
362#121—28no—
363#121—24no—
364#121—28no—
365#121—24no—
366#121—22no—
367#121—28no—
368#121—41no—
369#121—48no—
370#121—44no—
371#121—44no—
372#121—44no—
373#121—82no—
374#121C2×D4116yes—
375#120—48no—
376#120—48no—
377C4×Q8—24no—
378C4×Q8—24no—
379C4×D4—28no—
380C4×D4—216no—
381C4×D4—24no—
382C4×D4—28no—
383C4×D4—28no—
384C4×D4—28no—
385C4×D4—28no—
386C4×D4—24no—
387C4×D4—24no—
388C4×D4—44no—
389C4×D4—44no—
390C4×D4C2×D418yes—
391C4×D4C2×D418yes—
392#117—24no—
393#117—28no—
394C2×C4⋊C4—216no—
395C2×C4⋊C4—28no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—22no—
398C2×C4⋊C4—24no—
399C2×C4⋊C4—22no—
400C2×C4⋊C4—22no—
401C2×C4⋊C4—24no—
402C2×C4⋊C4—28no—
403C2×C4⋊C4—28no—
404C2×C4⋊C4—21no—
405C2×C4⋊C4—21no—
406C2×C4⋊C4—22no—
407C2×C4⋊C4—22no—
408C2×C4⋊C4—21no—
409C2×C4⋊C4—44no—
410C2×C4⋊C4C2×D411yescharacteristic
411C2×C4⋊C4C2×D412yes—
412C2×C4⋊C4C2×D412yes—
413C2×C4⋊C4C2×D4116yes—
414C2×C4⋊C4C2×D411yescharacteristic
415C2×C4⋊C4C2411yescharacteristic
416C2×C4⋊C4C2412yes—
417C2×C4⋊C4C2411yescharacteristic
418C2×C4⋊C4C2411yescharacteristic
419C2×C4⋊C4C2414yes—
420C2×C4⋊C4C2412yes—
421C2×C22⋊C4—22no—
422C2×C22⋊C4—24no—
423C2×C22⋊C4—24no—
424C2×C22⋊C4—22no—
425C2×C22⋊C4—22no—
426C2×C22⋊C4—21no—
427C2×C22⋊C4—21no—
428C2×C22⋊C4—21no—
429C2×C22⋊C4—22no—
430C2×C22⋊C4—22no—
431C2×C22⋊C4—22no—
432C2×C22⋊C4—22no—
433C2×C22⋊C4—21no—
434C2×C22⋊C4—22no—
435C2×C22⋊C4—22no—
436C2×C22⋊C4—21no—
437C2×C22⋊C4—22no—
438C2×C22⋊C4—22no—
439C2×C22⋊C4—22no—
440C2×C22⋊C4—22no—
441C2×C22⋊C4—48no—
442C2×C22⋊C4—84no—
443C2×C22⋊C4C2×D412yes—
444C2×C22⋊C4C2×D412yes—
445C2×C22⋊C4C2×D412yes—
446C2×C42—28no—
447C2×C42—24no—
448C2×C42—21no—
449C2×C42C2×D411yescharacteristic
450C2×C42C2×D412yes—
451C2×C42C2×D411yescharacteristic
452C2×C42C2×D412yes—
453C2×C42C2412yes—
454C2×C42C2411yescharacteristic
455C2×C42C2411yescharacteristic
456#107—24no—
457#107—28no—
458C4⋊C8—24no—
459#102—24no—
460#102—24no—
461#102—28no—
462#102—28no—
463#102—28no—
464#102—28no—
465#102—42no—
466#102—42no—
467#102—44no—
468C22⋊C8—28no—
469C22⋊C8—42no—
470C22⋊C8—42no—
471C4×C8—24no—
472#95—21no—
473#95—21no—
474#95—21no—
475#95—22no—
476#95—22no—
477C24—21no—
478C24—22no—
479C24—22no—
480C24—44no—
481C24—44no—
482C24—44no—
483C24—44no—
484C24—82no—
485C24—82no—
486C24—82no—
487C24C22×D411yescharacteristic
488C24C22×D412yes—
489#41—232no—
490#41—464no—
491#41—432no—
492#41—4128no—
493#41—464no—
494C2×Q8—216no—
495C2×Q8—28no—
496C2×Q8—24no—
497C2×Q8—22no—
498C2×Q8—28no—
499C2×Q8—22no—
500C2×Q8—44no—
501C2×Q8—42no—
502C2×Q8—48no—
503C2×Q8—464no—
504C2×Q8—432no—
505C2×Q8—464no—
506C2×Q8—48no—
507C2×Q8—42no—
508C2×Q8—44no—
509C2×Q8—44no—
510C2×Q8—44no—
511C2×Q8C2×D814yes—
512C2×D4—24no—
513C2×D4—24no—
514C2×D4—24no—
515C2×D4—28no—
516C2×D4—24no—
517C2×D4—216no—
518C2×D4—22no—
519C2×D4—22no—
520C2×D4—24no—
521C2×D4—22no—
522C2×D4—22no—
523C2×D4—22no—
524C2×D4—22no—
525C2×D4—22no—
526C2×D4—22no—
527C2×D4—21no—
528C2×D4—24no—
529C2×D4—22no—
530C2×D4—416no—
531C2×D4—42no—
532C2×D4—42no—
533C2×D4—44no—
534C2×D4—44no—
535C2×D4—44no—
536C2×D4—48no—
537C2×D4—48no—
538C2×D4—42no—
539C2×D4—44no—
540C2×D4—42no—
541C2×D4—44no—
542C2×D4—44no—
543C2×D4—44no—
544C2×D4—44no—
545C2×D4—42no—
546C2×D4—42no—
547C2×D4—42no—
548C2×D4—42no—
549C2×D4—42no—
550C2×D4—42no—
551C2×D4—88no—
552C2×D4—82no—
553C2×D4—81no—
554C2×D4—81no—
555C2×D4—81no—
556C2×D4—82no—
557C2×D4—82no—
558C2×D4—816no—
559C2×D4#12014yes—
560C2×D4C2×D818yes—
561C2×D4C2×D814yes—
562C2×D4AGL(1,ℤ/8)14yes—
563C2×D4C22×D414yes—
564C2×D42−1+412yescomplemented
565C22×C4—24no—
566C22×C4—24no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—24no—
571C22×C4—22no—
572C22×C4—28no—
573C22×C4—216no—
574C22×C4—24no—
575C22×C4—216no—
576C22×C4—24no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—28no—
580C22×C4—24no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—22no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—22no—
590C22×C4—41no—
591C22×C4—42no—
592C22×C4—48no—
593C22×C4—44no—
594C22×C4—44no—
595C22×C4—48no—
596C22×C4—48no—
597C22×C4—48no—
598C22×C4—44no—
599C22×C4—44no—
600C22×C4—44no—
601C22×C4—42no—
602C22×C4—42no—
603C22×C4—42no—
604C22×C4—82no—
605C22×C4—82no—
606C22×C4C2×D818yes—
607C22×C4C2×D814yes—
608C22×C4C22×D411yescharacteristic
609C22×C4C22×D412yes—
610C22×C4C22×D412yes—
611C22×C4C22×D411yescharacteristic
612C22×C4C22×D418yes—
613C22×C4C22×D411yescharacteristic
614C22×C4C22×D412yes—
615C22×C4C22×D411yescharacteristic
616C22×C4C22×D411yescharacteristic
617C22×C4C2511yescharacteristic
618D8—48no—
619D8—88no—
620C2×C8—22no—
621C2×C8—22no—
622C2×C8—24no—
623C2×C8—22no—
624C2×C8—22no—
625C2×C8—22no—
626C2×C8—24no—
627C2×C8—22no—
628C2×C8—24no—
629C2×C8—88no—
630C4⋊C4—28no—
631C4⋊C4—24no—
632C4⋊C4—216no—
633C4⋊C4—28no—
634C4⋊C4—28no—
635C4⋊C4—216no—
636C4⋊C4—24no—
637C4⋊C4—24no—
638C4⋊C4—22no—
639C4⋊C4—22no—
640C4⋊C4—24no—
641C4⋊C4—22no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—22no—
645C4⋊C4—24no—
646C4⋊C4—42no—
647C4⋊C4—42no—
648C4⋊C4—44no—
649C4⋊C4—82no—
650C4⋊C4—81no—
651C4⋊C4#12014yes—
652C4⋊C4C22×D418yes—
653C4⋊C4C22×D414yes—
654C22⋊C4—28no—
655C22⋊C4—216no—
656C22⋊C4—24no—
657C22⋊C4—216no—
658C22⋊C4—28no—
659C22⋊C4—24no—
660C22⋊C4—42no—
661C22⋊C4—44no—
662C22⋊C4—42no—
663C22⋊C4—42no—
664C22⋊C4—44no—
665C22⋊C4—42no—
666C22⋊C4—44no—
667C22⋊C4—44no—
668C22⋊C4—44no—
669C22⋊C4—44no—
670C22⋊C4—42no—
671C22⋊C4—44no—
672C22⋊C4—82no—
673C22⋊C4—82no—
674C22⋊C4—82no—
675C22⋊C4—82no—
676C22⋊C4#12018yes—
677C42—24no—
678C42—22no—
679C42—24no—
680C42—22no—
681C42—22no—
682C42—24no—
683C42—42no—
684C42C22×D414yes—
685C23—22no—
686C23—22no—
687C23—22no—
688C23—22no—
689C23—21no—
690C23—21no—
691C23—21no—
692C23—21no—
693C23—21no—
694C23—21no—
695C23—24no—
696C23—22no—
697C23—42no—
698C23—41no—
699C23—41no—
700C23—42no—
701C23—41no—
702C23—42no—
703C23—41no—
704C23—42no—
705C23—42no—
706C23—41no—
707C23—41no—
708C23—42no—
709C23—42no—
710C23—42no—
711C23—42no—
712C23—42no—
713C23—42no—
714C23—42no—
715C23—42no—
716C23—88no—
717C23—88no—
718C23—88no—
719C23—88no—
720C23—164no—
721C23—164no—
722C23—164no—
723C23C2×#12014yes—
724C23C22×D812yes—
725C23C22×D814yes—
726C23C2×AGL(1,ℤ/8)14yes—
727C23C23×D411yescharacteristic
728Q8—28no—
729Q8—416no—
730Q8—48no—
731Q8—432no—
732Q8—416no—
733D4—216no—
734D4—24no—
735D4—24no—
736D4—24no—
737D4—48no—
738D4—48no—
739D4—416no—
740D4—432no—
741D4—42no—
742D4—44no—
743D4—42no—
744D4—42no—
745D4—44no—
746D4—88no—
747D4—84no—
748D4—88no—
749D4—84no—
750D4—162no—
751D4—164no—
752D4#447116yes—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—216no—
761C2×C4—21no—
762C2×C4—22no—
763C2×C4—21no—
764C2×C4—28no—
765C2×C4—28no—
766C2×C4—28no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—21no—
770C2×C4—28no—
771C2×C4—24no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—22no—
775C2×C4—44no—
776C2×C4—48no—
777C2×C4—432no—
778C2×C4—416no—
779C2×C4—432no—
780C2×C4—44no—
781C2×C4—42no—
782C2×C4—44no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—42no—
786C2×C4—416no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—42no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—42no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—42no—
799C2×C4—84no—
800C2×C4—164no—
801C2×C4C2×#12014yes—
802C2×C4C2×#12012yes—
803C2×C4C2×#12012yes—
804C2×C4C22×D814yes—
805C2×C4C22×D812yes—
806C2×C4C22×D812yes—
807C2×C4C2×AGL(1,ℤ/8)12yes—
808C2×C4#57712yes—
809C2×C4C23×D412yes—
810C2×C4C2×2−1+411yescharacteristic
811C2×C4#58512yes—
812C2×C4#58511yescharacteristic
813C8—42no—
814C8—42no—
815C8—44no—
816C22—24no—
817C22—24no—
818C22—24no—
819C22—24no—
820C22—24no—
821C22—24no—
822C22—22no—
823C22—22no—
824C22—22no—
825C22—41no—
826C22—41no—
827C22—41no—
828C22—41no—
829C22—42no—
830C22—42no—
831C22—44no—
832C22—44no—
833C22—42no—
834C22—44no—
835C22—82no—
836C22—81no—
837C22—82no—
838C22—81no—
839C22—82no—
840C22—82no—
841C22—81no—
842C22—81no—
843C22—82no—
844C22—82no—
845C22—82no—
846C22—82no—
847C22—82no—
848C22—82no—
849C22—82no—
850C22—1616no—
851C22C2×#44718yes—
852C22C22×#12011yescharacteristic
853C22#348911yescharacteristic
854C22#350011yescharacteristic
855C22C23×D811yescharacteristic
856C22C22×AGL(1,ℤ/8)11yescharacteristic
857C22C2×#57711yescharacteristic
858C22#358611yescharacteristic
859C4—22no—
860C4—24no—
861C4—22no—
862C4—22no—
863C4—24no—
864C4—48no—
865C4—44no—
866C4—42no—
867C4—41no—
868C4—81no—
869C4—82no—
870C4—81no—
871C4—81no—
872C4C2×#44714yes—
873C4#348912yes—
874C4#350012yes—
875C2—28no—
876C2—42no—
877C2—84no—
878C2—82no—
879C2—162no—
880C2#3607811yescharacteristic
881C2C22×#44711yescharacteristic
882C2#6037411yescharacteristic
883C2#6209511yescharacteristic
884C2#6212811yescharacteristic
885C2#6252911yescharacteristic
886C2#6258311yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C2×C4×#41 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3499C2semidirect
2. C2×#3294C2semidirect
3. #36258C2semidirect
4. #29660C2semidirect
5. #29638C2semidirect
6. #25933C2semidirect
7. #25903C2semidirect
8. #25533C2semidirect
9. #25496C2semidirect
10. #24326C2semidirect
11. #24298C2semidirect
12. #23960C2semidirect
13. #23930C2semidirect
14. #23567C2semidirect
15. C2×#2023C2semidirect
16. #22485C2semidirect
17. #22469C2semidirect
21. C2×D4×Q8C22semidirect
25. C2×#547C22semidirect
30. C2×#532C22semidirect
31. C2×#532C22semidirect
32. C22×C4⋊Q8C22semidirect
33. C22×C4⋊Q8C22semidirect
59. #2057C22semidirect
60. #2057C22semidirect
61. #2057C22semidirect
62. #2041C22semidirect
63. #2033C22semidirect
67. #2023C22semidirect
68. #2023C22semidirect
69. #2023C22semidirect
70. #2023C22semidirect
71. #2023C22semidirect
73. #2011C22semidirect
75. #1999C22semidirect
76. #1990C22semidirect
77. #1988C22semidirect
78. #1984C22semidirect
79. #1893C22semidirect
81. #1879C22semidirect
82. #1879C22semidirect
84. #1874C22semidirect
85. #1874C22semidirect
86. #1869C22semidirect
87. #1862C22semidirect
88. #1852C22semidirect
89. #1823C22semidirect
90. #1817C22semidirect
91. #1802C22semidirect
92. #1797C22semidirect
93. C4×#102C22semidirect
94. C4×C22⋊C8C22semidirect
95. C2×#340C22semidirect
96. C2×#336C22semidirect
121. #547D4semidirect
276. C2×#41D8semidirect
564. C2×D42−1+4semidirect

Maximal subgroups

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

subgroupindex
C2×#34992
C2×#32942
#362582
#296602
#296382
#259332
#259032
#255332
#254962
#243262
#242982
#239602
#239302
#235672
C2×#20232
#224852
#224692