Finite Group Databasebeta

← #6436756

Subgroups — #6436756

Order 512.

2218 conjugacy classes of subgroups.

The subgroup lattice has 912 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3182C211yesmaximal, characteristic, complemented
2C2×#2920C211yesmaximal, characteristic, complemented
3#36625C211yesmaximal, characteristic, complemented
4#36624C211yesmaximal, characteristic
5#29878C211yesmaximal, characteristic, complemented
6#29876C211yesmaximal, characteristic, complemented
7#29845C211yesmaximal, characteristic, complemented
8#29844C211yesmaximal, characteristic, complemented
9#29843C211yesmaximal, characteristic, complemented
10#29842C211yesmaximal, characteristic, complemented
11#29807C211yesmaximal, characteristic, complemented
12#29807C211yesmaximal, characteristic, complemented
13#29784C214yesmaximal, complemented
14#29744C214yesmaximal, complemented
15#23711C214yesmaximal, complemented
16#23710C214yesmaximal, complemented
17#21410C211yesmaximal, characteristic, complemented
18#21409C211yesmaximal, characteristic, complemented
19#20824C211yesmaximal, characteristic, complemented
20C2×#533C2211yescharacteristic
21C2×#532C2211yescharacteristic
22C2×#525—21no—
23C23×C42C2211yescharacteristic
24#3182—28no—
25C2×#500C2211yescharacteristic, complemented
26C2×#492C2211yescharacteristic, complemented
27C2×#487C2211yescharacteristic, complemented
28C2×#486C2211yescharacteristic, complemented
29C2×#468C2214yes—
30C2×#440C2214yescomplemented
31#2920—28no—
32C2×#432C2212yes—
33C2×#432C2212yes—
34C2×#431C2211yescharacteristic
35C2×#431C2211yescharacteristic
36C2×#431C2211yescharacteristic
37C2×#431C2211yescharacteristic
38C2×#423C2212yes—
39C2×#407C2212yes—
40C2×C4×M16C2211yescharacteristic
41C2×C4×M16C2211yescharacteristic
42#2857C2211yescharacteristic
43#2857C2211yescharacteristic
44#2857C2211yescharacteristic
45#2857C2211yescharacteristic
46#2857C2211yescharacteristic
47#2857C2211yescharacteristic
48#2856C2211yescharacteristic
49#2856C2211yescharacteristic
50#2855—21no—
51#2855C2212yes—
52#2854—21no—
53#2854C2212yes—
54#2851—21no—
55#2851—21no—
56#2850—21no—
57#2850—21no—
58#2848—21no—
59#2848C2212yes—
60#2847—21no—
61#2847C2212yes—
62C4×C22⋊Q8—21no—
63C4×C22⋊Q8—21no—
64C4×C22⋊Q8C2212yes—
65C4×C22⋊Q8C2212yes—
66C4×#121—21no—
67C4×#121—21no—
68C4×#121C2212yes—
69C4×#121C2212yes—
70#2297—21no—
71#2296—21no—
72#2285C2211yescharacteristic
73#2285C2211yescharacteristic
74#2280—21no—
75#2087C2214yescomplemented
76#2086C2214yescomplemented
77#2076C2214yes—
78#2075C2214yes—
79#2068C2214yescomplemented
80#2067C2214yescomplemented
81#2066C2214yescomplemented
82#2065C2214yescomplemented
83#2055C2214yescomplemented
84#2055C2214yescomplemented
85#2036C2214yes—
86#2035C2214yes—
87#2034C2214yes—
88#2033C2214yes—
89#2000C2214yes—
90#2000C2214yes—
91#1990C2211yescharacteristic, complemented
92#1990C2211yescharacteristic, complemented
93#1990C2211yescharacteristic, complemented
94#1990C2211yescharacteristic, complemented
95#1957C2211yescharacteristic, complemented
96#1957C2211yescharacteristic, complemented
97#1956C2211yescharacteristic, complemented
98#1956C2211yescharacteristic, complemented
99#1895C2214yes—
100#1894C2214yes—
101#1845C2211yescharacteristic, complemented
102#1844C2211yescharacteristic, complemented
103#1834C2211yescharacteristic, complemented
104#1834C2211yescharacteristic, complemented
105#1809C2214yes—
106#1776C2214yescomplemented
107#1763C2214yescomplemented
108#1762C2214yescomplemented
109C22×#41—21no—
110C24×C4D411yescharacteristic
111C24×C4D411yescharacteristic
112C24×C4C2311yescharacteristic
113C22×SD16C2314yes—
114C22×M16C2312yes—
115C22×M16C2312yes—
116#533—24no—
117#533—24no—
118#532—24no—
119#532—24no—
120C2×C4⋊Q8C2311yescharacteristic
121C2×C4⋊Q8C2311yescharacteristic
122C2×C4⋊Q8C2311yescharacteristic
123C2×#127C2311yescharacteristic
124C2×#125—21no—
125C2×#124—21no—
126#525—48no—
127C2×#123—22no—
128C2×C22⋊Q8—21no—
129C2×C22⋊Q8—21no—
130C2×C22⋊Q8—21no—
131C2×C22⋊Q8—21no—
132C2×C22⋊Q8—21no—
133C2×C22⋊Q8C2312yes—
134C2×C22⋊Q8C2312yes—
135C2×C22⋊Q8C2312yes—
136C2×#121—21no—
137C2×#121—21no—
138C2×#121—21no—
139C2×#121—21no—
140C2×#121—21no—
141C2×#121C2312yes—
142C2×#121C2312yes—
143C2×#121C2312yes—
144C2×#120—22no—
145C2×C4×Q8—21no—
146C2×C4×Q8C2312yes—
147C2×C4×D4—22no—
148C2×C4×D4—22no—
149C2×C4×D4—21no—
150C2×C4×D4C2312yes—
151C2×#117—21no—
152C2×#117—21no—
153C2×#117—21no—
154C22×C42—24no—
155C22×C42—24no—
156C22×C42D411yescharacteristic
157C22×C42D411yescharacteristic
158C22×C42D411yescharacteristic
159C22×C42D411yescharacteristic
160C22×C42D411yescharacteristic
161C22×C42D411yescharacteristic
162C22×C42C2311yescharacteristic
163C22×C42C2311yescharacteristic
164C22×C42C2311yescharacteristic
165C22×C42C2311yescharacteristic
166C22×C42C2311yescharacteristic
167C22×C42C2311yescharacteristic
168#500—24no—
169#492—24no—
170#487—24no—
171#486—24no—
172#468—216no—
173#440—216no—
174#432—28no—
175#432—28no—
176#431—24no—
177#431—24no—
178#431—24no—
179#431—24no—
180C2×#107C2314yes—
181C2×#107C2314yes—
182C2×#106C2314yes—
183#423—28no—
184C2×C4⋊C8C2312yes—
185C2×C4⋊C8C2312yes—
186C2×C4⋊C8C2312yes—
187C2×C4⋊C8C2312yes—
188C2×#103C2314yes—
189C2×#103C2314yes—
190C2×#103C2314yes—
191C2×#102C2314yes—
192C2×#102C2314yes—
193C2×#102C2314yes—
194#407—28no—
195C2×C22⋊C8C2312yes—
196C2×C22⋊C8C2312yes—
197C2×C22⋊C8C2312yes—
198C2×C22⋊C8C2312yes—
199C4×M16—24no—
200C4×M16D418yescomplemented
201C2×#97C2312yes—
202C2×#97C2312yes—
203C2×C4×C8C2311yescharacteristic
204C2×C4×C8C2311yescharacteristic
205C2×C4×C8C2311yescharacteristic
206C2×C4×C8C2311yescharacteristic
207#391—21no—
208#391—21no—
209#391—21no—
210#391—21no—
211#391C2312yes—
212#391C2312yes—
213#390—21no—
214#390—21no—
215#390—21no—
216#390—21no—
217#390C2312yes—
218#390C2312yes—
219#389—21no—
220#389—21no—
221#389—21no—
222#389—21no—
223#389—21no—
224#389—21no—
225#389—21no—
226#389—21no—
227#389C2312yes—
228#389C2312yes—
229#389C2312yes—
230#389C2312yes—
231#388—22no—
232#388—22no—
233#388—22no—
234#388—22no—
235#387—22no—
236#387—22no—
237#387—22no—
238#387—22no—
239#386—22no—
240#386—22no—
241#386—22no—
242#386—22no—
243#386—22no—
244#386—22no—
245#385—22no—
246#385—22no—
247#385—22no—
248#385—22no—
249#385—22no—
250#385—22no—
251#384C2311yescharacteristic
252#384C2311yescharacteristic
253#384C2311yescharacteristic
254#384C2311yescharacteristic
255#382—21no—
256#382—21no—
257#381—22no—
258#380—21no—
259#380—21no—
260#380—21no—
261#380—21no—
262#380—21no—
263#380—21no—
264#380—21no—
265#380—21no—
266#380—21no—
267#380—21no—
268#380C2312yes—
269#380C2312yes—
270#380C2312yes—
271#380C2312yes—
272#380C2312yes—
273#380C2312yes—
274#379—22no—
275C4×C4⋊C4—21no—
276C4×C4⋊C4—21no—
277C4×C4⋊C4—22no—
278C4×C4⋊C4—22no—
279C4×C4⋊C4C2312yes—
280C4×C4⋊C4C2312yes—
281C4×C22⋊C4—22no—
282C4×C22⋊C4—22no—
283C4×C22⋊C4—22no—
284C4×C22⋊C4—22no—
285#340C2314yes—
286#340C2314yes—
287#340C2314yes—
288#340C2314yes—
289#340C2314yes—
290#340C2314yes—
291C25C2×D411yescharacteristic
292C2×#41—44no—
293C2×#41—44no—
294C2×#41—44no—
295C22×Q8—21no—
296C22×Q8—21no—
297C22×Q8C2412yes—
298C22×D4—22no—
299C22×D4—22no—
300C22×D4—22no—
301C22×D4—21no—
302C22×D4—21no—
303C22×D4C2412yes—
304C23×C4—24no—
305C23×C4—24no—
306C23×C4—24no—
307C23×C4—24no—
308C23×C4—22no—
309C23×C4—22no—
310C23×C4—22no—
311C23×C4—42no—
312C23×C4—42no—
313C23×C4—42no—
314C23×C4—42no—
315C23×C4C2×D411yescharacteristic
316C23×C4C2×D411yescharacteristic
317C23×C4C2×D411yescharacteristic
318C23×C4C2×D411yescharacteristic
319C23×C4C2×D411yescharacteristic
320C23×C4C2×D411yescharacteristic
321C23×C4C2×D411yescharacteristic
322C23×C4C2×D411yescharacteristic
323C23×C4C2×D411yescharacteristic
324C23×C4C2×D411yescharacteristic
325C23×C4C2×D411yescharacteristic
326C23×C4C2×D411yescharacteristic
327C23×C4C2×D411yescharacteristic
328C23×C4C2×D411yescharacteristic
329C23×C4C2×D411yescharacteristic
330C23×C4C2411yescharacteristic
331C23×C4C2411yescharacteristic
332C23×C4C2411yescharacteristic
333C2×SD16—28no—
334C2×SD16—44no—
335C2×SD16—44no—
336C2×M16—24no—
337C2×M16—42no—
338C2×M16—42no—
339C2×M16—42no—
340C2×M16—42no—
341C2×M16C2×D418yes—
342C22×C8C2412yes—
343C22×C8C2412yes—
344C22×C8C2412yes—
345C22×C8C2412yes—
346C4⋊Q8—22no—
347C4⋊Q8—22no—
348C4⋊Q8—22no—
349C4⋊Q8—22no—
350C4⋊Q8—22no—
351C4⋊Q8—22no—
352#127—22no—
353#127—22no—
354#125—44no—
355#124—44no—
356#123—48no—
357C22⋊Q8—24no—
358C22⋊Q8—24no—
359C22⋊Q8—44no—
360C22⋊Q8—44no—
361C22⋊Q8—44no—
362C22⋊Q8—44no—
363C22⋊Q8—44no—
364C22⋊Q8—44no—
365C22⋊Q8—44no—
366#121—24no—
367#121—24no—
368#121—44no—
369#121—44no—
370#121—44no—
371#121—44no—
372#121—44no—
373#121—44no—
374#121—44no—
375#120—48no—
376C4×Q8—24no—
377C4×Q8—24no—
378C4×Q8—44no—
379C4×D4—24no—
380C4×D4—24no—
381C4×D4—48no—
382C4×D4—48no—
383C4×D4—44no—
384#117—44no—
385#117—44no—
386#117—44no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4—21no—
393C2×C4⋊C4—21no—
394C2×C4⋊C4—22no—
395C2×C4⋊C4—22no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—22no—
398C2×C4⋊C4—22no—
399C2×C4⋊C4—21no—
400C2×C4⋊C4—21no—
401C2×C4⋊C4—21no—
402C2×C4⋊C4—21no—
403C2×C4⋊C4—22no—
404C2×C4⋊C4—22no—
405C2×C4⋊C4—22no—
406C2×C4⋊C4—22no—
407C2×C4⋊C4C2412yes—
408C2×C4⋊C4C2412yes—
409C2×C4⋊C4C2412yes—
410C2×C4⋊C4C2412yes—
411C2×C4⋊C4C2412yes—
412C2×C4⋊C4C2412yes—
413C2×C22⋊C4—22no—
414C2×C22⋊C4—22no—
415C2×C22⋊C4—22no—
416C2×C22⋊C4—22no—
417C2×C22⋊C4—22no—
418C2×C22⋊C4—22no—
419C2×C22⋊C4—22no—
420C2×C22⋊C4—22no—
421C2×C22⋊C4—22no—
422C2×C22⋊C4—22no—
423C2×C22⋊C4—22no—
424C2×C22⋊C4—22no—
425C2×C22⋊C4—22no—
426C2×C22⋊C4—22no—
427C2×C22⋊C4—22no—
428C2×C22⋊C4—22no—
429C2×C22⋊C4—22no—
430C2×C42—24no—
431C2×C42—24no—
432C2×C42—22no—
433C2×C42—22no—
434C2×C42—24no—
435C2×C42—24no—
436C2×C42—24no—
437C2×C42—24no—
438C2×C42—22no—
439C2×C42—22no—
440C2×C42—22no—
441C2×C42—22no—
442C2×C42—22no—
443C2×C42—22no—
444C2×C42—22no—
445C2×C42—22no—
446C2×C42—22no—
447C2×C42—22no—
448C2×C42—22no—
449C2×C42C2×D411yescharacteristic
450C2×C42C2×D411yescharacteristic
451C2×C42C2×D411yescharacteristic
452C2×C42C2×D411yescharacteristic
453C2×C42C2×D411yescharacteristic
454C2×C42C2×D411yescharacteristic
455C2×C42C2×D411yescharacteristic
456C2×C42C2×D411yescharacteristic
457C2×C42C2×D411yescharacteristic
458C2×C42C2×D411yescharacteristic
459C2×C42C2×D411yescharacteristic
460C2×C42C2×D411yescharacteristic
461C2×C42C2×D414yes—
462C2×C42#4114yes—
463C2×C42C2411yescharacteristic
464C2×C42C2411yescharacteristic
465C2×C42C2411yescharacteristic
466C2×C42C2411yescharacteristic
467#107—28no—
468#107—44no—
469#106—44no—
470C4⋊C8—24no—
471C4⋊C8—24no—
472C4⋊C8—24no—
473C4⋊C8—24no—
474#103—28no—
475#103—44no—
476#103—44no—
477#102—28no—
478#102—44no—
479#102—44no—
480C22⋊C8—24no—
481C22⋊C8—24no—
482C22⋊C8—24no—
483C22⋊C8—24no—
484#97—24no—
485#97C2×D418yes—
486C4×C8—22no—
487C4×C8—22no—
488C4×C8C2×D414yes—
489C4×C8C2×D414yes—
490#95—22no—
491#95—22no—
492#95—22no—
493#95—22no—
494#95—22no—
495#95—22no—
496#95—22no—
497#95—22no—
498#95—22no—
499#95—22no—
500#95—22no—
501#95—22no—
502#95—22no—
503#95—22no—
504#95—22no—
505#95—22no—
506C24—22no—
507C24—22no—
508C24—22no—
509C24—22no—
510C24—41no—
511C24—41no—
512C24—41no—
513C24—41no—
514C24C22×D411yescharacteristic
515C24C22×D411yescharacteristic
516C24C22×D411yescharacteristic
517#41—816no—
518C2×Q8—22no—
519C2×Q8—22no—
520C2×Q8—24no—
521C2×Q8—24no—
522C2×Q8—42no—
523C2×Q8—42no—
524C2×Q8—42no—
525C2×Q8—42no—
526C2×Q8—42no—
527C2×Q8—42no—
528C2×D4—22no—
529C2×D4—22no—
530C2×D4—24no—
531C2×D4—24no—
532C2×D4—44no—
533C2×D4—44no—
534C2×D4—44no—
535C2×D4—44no—
536C2×D4—44no—
537C2×D4—44no—
538C2×D4—44no—
539C2×D4—44no—
540C2×D4—44no—
541C2×D4—42no—
542C2×D4—42no—
543C2×D4—42no—
544C2×D4—42no—
545C2×D4—42no—
546C2×D4—42no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—41no—
594C22×C4—41no—
595C22×C4—41no—
596C22×C4—41no—
597C22×C4—41no—
598C22×C4—41no—
599C22×C4—41no—
600C22×C4—41no—
601C22×C4—41no—
602C22×C4—41no—
603C22×C4—41no—
604C22×C4—41no—
605C22×C4—416no—
606C22×C4—416no—
607C22×C4—48no—
608C22×C4—48no—
609C22×C4—44no—
610C22×C4—44no—
611C22×C4—44no—
612C22×C4#12114yes—
613C22×C4#12114yes—
614C22×C4AGL(1,ℤ/8)14yes—
615C22×C4#13714yes—
616C22×C4C22×D411yescharacteristic
617C22×C4C22×D411yescharacteristic
618C22×C4C22×D411yescharacteristic
619C22×C4C22×D411yescharacteristic
620C22×C4C22×D411yescharacteristic
621C22×C4C22×D411yescharacteristic
622C22×C4C22×D411yescharacteristic
623C22×C4C22×D412yes—
624C22×C4C22×D411yescharacteristic
625C22×C4C22×D411yescharacteristic
626C22×C4C22×D411yescharacteristic
627C22×C4C22×D411yescharacteristic
628C22×C4C2×#4112yes—
629C22×C4C2511yescharacteristic
630SD16—416no—
631M16—48no—
632M16—48no—
633C2×C8—22no—
634C2×C8—22no—
635C2×C8—22no—
636C2×C8—22no—
637C2×C8—22no—
638C2×C8—22no—
639C2×C8—22no—
640C2×C8—22no—
641C2×C8—22no—
642C2×C8—22no—
643C2×C8C22×D414yes—
644C2×C8C22×D414yes—
645C4⋊C4—22no—
646C4⋊C4—22no—
647C4⋊C4—22no—
648C4⋊C4—22no—
649C4⋊C4—24no—
650C4⋊C4—24no—
651C4⋊C4—24no—
652C4⋊C4—24no—
653C4⋊C4—44no—
654C4⋊C4—44no—
655C4⋊C4—44no—
656C4⋊C4—44no—
657C4⋊C4—42no—
658C4⋊C4—42no—
659C4⋊C4—42no—
660C4⋊C4—44no—
661C4⋊C4—44no—
662C4⋊C4—42no—
663C4⋊C4—42no—
664C4⋊C4—42no—
665C4⋊C4—44no—
666C4⋊C4—42no—
667C4⋊C4—44no—
668C4⋊C4—42no—
669C4⋊C4—42no—
670C4⋊C4—42no—
671C4⋊C4—42no—
672C4⋊C4—42no—
673C22⋊C4—44no—
674C22⋊C4—44no—
675C22⋊C4—44no—
676C22⋊C4—44no—
677C22⋊C4—44no—
678C22⋊C4—44no—
679C22⋊C4—44no—
680C22⋊C4—44no—
681C22⋊C4—44no—
682C22⋊C4—44no—
683C22⋊C4—44no—
684C22⋊C4—44no—
685C22⋊C4—44no—
686C22⋊C4—44no—
687C22⋊C4—44no—
688C22⋊C4—44no—
689C22⋊C4—44no—
690C42—22no—
691C42—22no—
692C42—22no—
693C42—22no—
694C42—22no—
695C42—22no—
696C42—22no—
697C42—22no—
698C42—22no—
699C42—22no—
700C42—21no—
701C42—21no—
702C42—21no—
703C42—21no—
704C42—44no—
705C42—44no—
706C42—44no—
707C42#12114yes—
708C42#12114yes—
709C42C22×D412yes—
710C42C22×D412yes—
711C42C2×#4112yes—
712C42C2×#4112yes—
713C23—21no—
714C23—21no—
715C23—21no—
716C23—21no—
717C23—21no—
718C23—21no—
719C23—21no—
720C23—21no—
721C23—21no—
722C23—21no—
723C23—21no—
724C23—21no—
725C23—21no—
726C23—21no—
727C23—21no—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—44no—
732C23—44no—
733C23—44no—
734C23—44no—
735C23—44no—
736C23—44no—
737C23—44no—
738C23—42no—
739C23—42no—
740C23—42no—
741C23—42no—
742C23—42no—
743C23—42no—
744C23—42no—
745C23C2×#12112yes—
746C23C2×AGL(1,ℤ/8)12yes—
747C23C2×#13712yes—
748C23C23×D411yescharacteristic
749Q8—44no—
750Q8—44no—
751Q8—84no—
752Q8—84no—
753D4—44no—
754D4—44no—
755D4—88no—
756D4—88no—
757D4—88no—
758D4—84no—
759D4—84no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—24no—
771C2×C4—24no—
772C2×C4—28no—
773C2×C4—28no—
774C2×C4—28no—
775C2×C4—28no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—21no—
788C2×C4—44no—
789C2×C4—44no—
790C2×C4—44no—
791C2×C4—44no—
792C2×C4—44no—
793C2×C4—44no—
794C2×C4—44no—
795C2×C4—44no—
796C2×C4—44no—
797C2×C4—42no—
798C2×C4—42no—
799C2×C4—42no—
800C2×C4—42no—
801C2×C4—44no—
802C2×C4—44no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—42no—
808C2×C4—42no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—42no—
813C2×C4—42no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—42no—
817C2×C4—42no—
818C2×C4—42no—
819C2×C4—42no—
820C2×C4—42no—
821C2×C4—42no—
822C2×C4—42no—
823C2×C4—42no—
824C2×C4—88no—
825C2×C4C2×#12112yes—
826C2×C4C2×#12112yes—
827C2×C4C2×#12112yes—
828C2×C4C2×#12112yes—
829C2×C4C2×#12112yes—
830C2×C4C2×AGL(1,ℤ/8)12yes—
831C2×C4C2×AGL(1,ℤ/8)12yes—
832C2×C4C2×#13712yes—
833C2×C4C2×#13712yes—
834C2×C4#57512yes—
835C2×C4#57512yes—
836C2×C4C23×D411yescharacteristic
837C2×C4C22×#4111yescharacteristic
838C2×C4#58512yes—
839C2×C4#58512yes—
840C8—24no—
841C8—24no—
842C8—42no—
843C8—42no—
844C22—22no—
845C22—22no—
846C22—22no—
847C22—22no—
848C22—22no—
849C22—22no—
850C22—22no—
851C22—22no—
852C22—22no—
853C22—416no—
854C22—41no—
855C22—41no—
856C22—41no—
857C22—41no—
858C22—41no—
859C22—41no—
860C22—41no—
861C22—41no—
862C22—41no—
863C22—41no—
864C22—41no—
865C22—41no—
866C22—82no—
867C22—82no—
868C22—82no—
869C22—82no—
870C22—82no—
871C22—82no—
872C22—82no—
873C22C22×#12111yescharacteristic
874C22#344911yescharacteristic
875C22#344911yescharacteristic
876C22C22×AGL(1,ℤ/8)11yescharacteristic
877C22C22×#13711yescharacteristic
878C22C2×#57511yescharacteristic
879C22C2×#57511yescharacteristic
880C4—22no—
881C4—22no—
882C4—22no—
883C4—22no—
884C4—22no—
885C4—41no—
886C4—41no—
887C4—41no—
888C4—41no—
889C4—82no—
890C4—82no—
891C4—82no—
892C4—82no—
893C4—82no—
894C4—82no—
895C4—82no—
896C4#305514yes—
897C4#305614yes—
898C4#344912yes—
899C4#345512yes—
900C2—42no—
901C2—42no—
902C2—42no—
903C2—162no—
904C2#3463311yescharacteristic
905C2C2×#305511yescharacteristic
906C2C2×#305611yescharacteristic
907C2#6096511yescharacteristic
908C2#6096611yescharacteristic
909C2#6096911yescharacteristic
910C2#6097211yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#36624C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C23×C42 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3182C2semidirect
2. C2×#2920C2semidirect
3. #36625C2semidirect
5. #29878C2semidirect
6. #29876C2semidirect
7. #29845C2semidirect
8. #29844C2semidirect
9. #29843C2semidirect
10. #29842C2semidirect
11. #29807C2semidirect
12. #29807C2semidirect
13. #29784C2semidirect
14. #29744C2semidirect
15. #23711C2semidirect
16. #23710C2semidirect
17. #21410C2semidirect
18. #21409C2semidirect
19. #20824C2semidirect
25. C2×#500C22semidirect
26. C2×#492C22semidirect
27. C2×#487C22semidirect
28. C2×#486C22semidirect
30. C2×#440C22semidirect
75. #2087C22semidirect
76. #2086C22semidirect
79. #2068C22semidirect
80. #2067C22semidirect
81. #2066C22semidirect
82. #2065C22semidirect
83. #2055C22semidirect
84. #2055C22semidirect
91. #1990C22semidirect
92. #1990C22semidirect
93. #1990C22semidirect
94. #1990C22semidirect
95. #1957C22semidirect
96. #1957C22semidirect
97. #1956C22semidirect
98. #1956C22semidirect
101. #1845C22semidirect
102. #1844C22semidirect
103. #1834C22semidirect
104. #1834C22semidirect
106. #1776C22semidirect
107. #1763C22semidirect
108. #1762C22semidirect
200. C4×M16D4semidirect

Maximal subgroups

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

subgroupindex
C2×#31822
C2×#29202
#366252
#366242
#298782
#298762
#298452
#298442
#298432
#298422
#298072
#297842
#297442
#237112
#237102
#214102
#214092
#208242