Finite Group Databasebeta

← #6483237

Subgroups — #6483237

Order 512.

2170 conjugacy classes of subgroups.

The subgroup lattice has 853 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3210C211yesmaximal, characteristic, complemented
2C2×#3207C211yesmaximal, characteristic
3#35298C211yesmaximal, characteristic, complemented
4#34207C211yesmaximal, characteristic, complemented
5#32919C214yesmaximal, complemented
6#29729C214yesmaximal, complemented
7#28717C211yesmaximal, characteristic, complemented
8#28716C211yesmaximal, characteristic, complemented
9#28616C211yesmaximal, characteristic, complemented
10#28615C211yesmaximal, characteristic, complemented
11#28614C211yesmaximal, characteristic, complemented
12#28613C211yesmaximal, characteristic, complemented
13#28444C211yesmaximal, characteristic, complemented
14#28443C211yesmaximal, characteristic, complemented
15#28262C214yesmaximal, complemented
16#28172C214yesmaximal, complemented
17#21860C211yesmaximal, characteristic, complemented
18#21859C211yesmaximal, characteristic, complemented
19#20809C211yesmaximal, characteristic, complemented
20C2×#533C2211yescharacteristic
21C2×#532C2211yescharacteristic
22C2×#532C2211yescharacteristic
23C2×#520C2212yes—
24#3210—28no—
25#3207—28no—
26C2×#494C2211yescharacteristic
27C2×#493C2211yescharacteristic
28C2×#492C2211yescharacteristic
29C2×#492C2211yescharacteristic
30C2×#487C2211yescharacteristic
31C2×#487C2211yescharacteristic
32C2×#486C2211yescharacteristic
33C2×#486C2211yescharacteristic
34C2×#464C2214yes—
35C2×#464C2214yes—
36C2×#463C2214yes—
37C2×#463C2214yes—
38C2×#452C2214yes—
39C2×#449C2214yes—
40C2×#431C2211yescharacteristic
41C2×#431C2211yescharacteristic
42#2868C2211yescharacteristic
43#2862C2211yescharacteristic
44#2858C2211yescharacteristic
45#2858C2211yescharacteristic
46#2620C2212yes—
47#2620C2212yes—
48#2566—21no—
49#2566—21no—
50#2545—21no—
51#2545—21no—
52#2500—21no—
53#2500—21no—
54#2432—21no—
55#2432—21no—
56#2361—21no—
57#2361—21no—
58#2361—21no—
59#2361—21no—
60#2354—21no—
61#2354—21no—
62D4×C4⋊C4—21no—
63D4×C4⋊C4—21no—
64#2326C2212yes—
65#2326C2212yes—
66#2326C2212yes—
67#2326C2212yes—
68#2311C2212yes—
69C4×C4⋊Q8C2211yescharacteristic
70C4×C4⋊Q8C2211yescharacteristic
71C4×#127C2211yescharacteristic
72C4×#127C2211yescharacteristic
73C2×#384C2211yescharacteristic
74C4×#117C2211yescharacteristic
75#2072C2214yes—
76#2071C2214yes—
77#2056C2214yes—
78#2055C2214yes—
79#2055C2214yes—
80#2054C2214yes—
81#2015C2214yes—
82#2012C2214yes—
83#1990C2211yescharacteristic
84#1990C2211yescharacteristic
85#1990C2211yescharacteristic
86#1990C2211yescharacteristic
87#1957C2211yescharacteristic
88#1957C2211yescharacteristic
89#1956C2211yescharacteristic
90#1956C2211yescharacteristic
91#1880C2214yes—
92#1879C2214yes—
93#1878C2214yes—
94#1877C2214yes—
95#1874C2214yes—
96#1872C2214yes—
97#1843C2212yes—
98#1832C2212yes—
99#1803C2214yes—
100#1803C2214yes—
101#1802C2214yes—
102#1802C2214yes—
103#1798C2212yes—
104#1798C2212yes—
105C4×C4⋊C8C2211yescharacteristic
106C4×C4⋊C8C2211yescharacteristic
107C4×C4⋊C8C2211yescharacteristic
108C4×C4⋊C8C2211yescharacteristic
109C22×#41—21no—
110C22×#41C2312yes—
111C22×Q16C2314yes—
112C22×SD16C2314yes—
113C22×SD16C2314yes—
114C22×D8C2314yes—
115#533—24no—
116#533—24no—
117#532—24no—
118#532—24no—
119#532—24no—
120#532D418yes—
121C2×C4⋊Q8—21no—
122C2×C4⋊Q8—21no—
123C2×C4⋊Q8C2311yescharacteristic
124C2×C4⋊Q8C2311yescharacteristic
125C2×C4⋊Q8C2311yescharacteristic
126C2×C4⋊Q8C2311yescharacteristic
127C2×#127C2311yescharacteristic
128C2×#127C2311yescharacteristic
129C2×#125—21no—
130C2×#124—21no—
131C2×#124—21no—
132C2×#124—21no—
133C2×#124C2312yes—
134C2×#124C2312yes—
135C2×#124C2312yes—
136C2×C22⋊Q8—21no—
137C2×C22⋊Q8C2312yes—
138C2×#121—21no—
139C2×#121—21no—
140C2×#121—21no—
141C2×#121C2312yes—
142#520—48no—
143C2×C4×Q8—21no—
144C2×C4×Q8C2312yes—
145C2×C4×Q8C2312yes—
146C2×C4×Q8C2312yes—
147C2×C4×D4—22no—
148C2×C4×D4—22no—
149C2×C4×D4—21no—
150C2×C4×D4—21no—
151C2×C4×D4—21no—
152C2×C4×D4—21no—
153C2×C4×D4—21no—
154C2×C4×D4—21no—
155C2×C4×D4—21no—
156C2×C4×D4C2312yes—
157C2×C4×D4C2312yes—
158C2×C4×D4C2312yes—
159C2×#117—21no—
160C2×#117—22no—
161C2×#117C2311yescharacteristic
162C2×#117C2311yescharacteristic
163C22×C4⋊C4—21no—
164C22×C4⋊C4—21no—
165C22×C4⋊C4—22no—
166C22×C4⋊C4C2312yes—
167C22×C42C2311yescharacteristic
168#494—24no—
169#493—24no—
170#492—24no—
171#492—24no—
172#487—24no—
173#487—24no—
174#486—24no—
175#486—24no—
176#464—216no—
177#464—48no—
178#463—216no—
179#463—48no—
180#452—216no—
181#449—216no—
182#431—24no—
183#431—24no—
184C2×C4⋊C8C2312yes—
185C2×C4⋊C8C2312yes—
186C2×C4⋊C8C2312yes—
187C2×C4⋊C8C2312yes—
188C2×C4⋊C8C2312yes—
189C2×C4⋊C8C2312yes—
190C2×#103C2314yes—
191C2×#103C2314yes—
192C2×#103C2314yes—
193C2×#103C2314yes—
194C2×#102C2314yes—
195C2×#102C2314yes—
196C2×#102C2314yes—
197C2×#102C2314yes—
198C2×C22⋊C8C2312yes—
199C2×C22⋊C8C2312yes—
200C2×C4×C8C2311yescharacteristic
201C2×C4×C8C2311yescharacteristic
202C2×C4×C8C2311yescharacteristic
203C2×C4×C8C2311yescharacteristic
204#396—22no—
205#396—22no—
206#396—22no—
207#396—22no—
208#394—22no—
209#394—22no—
210#394—22no—
211#394—22no—
212#391—21no—
213#391—21no—
214#391C2312yes—
215#391C2312yes—
216#391C2312yes—
217#391C2312yes—
218#390—21no—
219#390—21no—
220#390—21no—
221#390—21no—
222#390—21no—
223#390—21no—
224#390—21no—
225#390—21no—
226#390—21no—
227#390—21no—
228#390C2312yes—
229#390C2312yes—
230#390C2312yes—
231#390C2312yes—
232#389—21no—
233#389—21no—
234#389—21no—
235#389—21no—
236#388—22no—
237#388—22no—
238#388—22no—
239#388—22no—
240#388—22no—
241#388—22no—
242#388—22no—
243#388—22no—
244#386—22no—
245#386—22no—
246#385—22no—
247#385—22no—
248#385—22no—
249#385—22no—
250#385—22no—
251#385—22no—
252#385—22no—
253#385—22no—
254#384—21no—
255#384—21no—
256#384—21no—
257#384—21no—
258#384C2311yescharacteristic
259#384C2311yescharacteristic
260#384C2312yes—
261#384C2312yes—
262#384C2312yes—
263#382—21no—
264#382—21no—
265#380—22no—
266#380—22no—
267C4×C4⋊C4—21no—
268C4×C4⋊C4—21no—
269C4×C4⋊C4—21no—
270C4×C4⋊C4—21no—
271C4×C4⋊C4D411yescharacteristic
272C4×C4⋊C4D411yescharacteristic
273C4×C4⋊C4D411yescharacteristic
274C4×C4⋊C4D411yescharacteristic
275C4×C22⋊C4D411yescharacteristic
276C4×C22⋊C4D411yescharacteristic
277C4×C22⋊C4D411yescharacteristic
278C4×C22⋊C4D411yescharacteristic
279#376C2311yescharacteristic
280#376C2311yescharacteristic
281C43C2311yescharacteristic
282C43C2311yescharacteristic
283#340C2314yes—
284#340C2314yes—
285#340C2314yes—
286#340C2314yes—
287#336C2312yes—
288#336C2312yes—
289#336C2312yes—
290#336C2312yes—
291C2×#41—24no—
292C2×#41—44no—
293C2×#41—44no—
294C2×#41—44no—
295C2×#41—82no—
296C2×#41—82no—
297C2×#41C2×D418yes—
298C22×Q8—21no—
299C22×Q8—21no—
300C22×Q8C2412yes—
301C22×Q8C2412yes—
302C22×D4—22no—
303C22×D4—22no—
304C22×D4—21no—
305C22×D4—21no—
306C22×D4—21no—
307C22×D4—21no—
308C22×D4C2412yes—
309C22×D4C2412yes—
310C23×C4—22no—
311C23×C4—22no—
312C23×C4—22no—
313C23×C4—22no—
314C23×C4—22no—
315C23×C4C2×D411yescharacteristic
316C23×C4C2×D411yescharacteristic
317C23×C4C2411yescharacteristic
318C2×Q16—28no—
319C2×Q16—44no—
320C2×Q16—44no—
321C2×SD16—28no—
322C2×SD16—28no—
323C2×SD16—44no—
324C2×SD16—44no—
325C2×SD16—44no—
326C2×SD16—44no—
327C2×D8—28no—
328C2×D8—44no—
329C2×D8—44no—
330C22×C8C2412yes—
331C22×C8C2412yes—
332C22×C8C2412yes—
333C22×C8C2412yes—
334C4⋊Q8—22no—
335C4⋊Q8—22no—
336C4⋊Q8—22no—
337C4⋊Q8—22no—
338C4⋊Q8—22no—
339C4⋊Q8—22no—
340C4⋊Q8—22no—
341C4⋊Q8—82no—
342C4⋊Q8—82no—
343C4⋊Q8C2×D414yes—
344#127—22no—
345#127—22no—
346#127—22no—
347#127C2×D414yes—
348#125—44no—
349#124—24no—
350#124—28no—
351#124—44no—
352#124—44no—
353#124—82no—
354#124—82no—
355#124C2×D418yes—
356C22⋊Q8—24no—
357C22⋊Q8—24no—
358C22⋊Q8—44no—
359#121—28no—
360#121—28no—
361#121—24no—
362#121—24no—
363#121—44no—
364C4×Q8—24no—
365C4×Q8—24no—
366C4×Q8—28no—
367C4×Q8—44no—
368C4×Q8—44no—
369C4×D4—28no—
370C4×D4—28no—
371C4×D4—24no—
372C4×D4—24no—
373C4×D4—28no—
374C4×D4—44no—
375C4×D4—48no—
376C4×D4—48no—
377C4×D4—44no—
378C4×D4—82no—
379C4×D4—82no—
380C4×D4—82no—
381C4×D4—82no—
382#117—24no—
383#117—42no—
384#117—48no—
385#117—44no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—22no—
389C2×C4⋊C4—22no—
390C2×C4⋊C4—22no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4—21no—
393C2×C4⋊C4—21no—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—21no—
399C2×C4⋊C4—22no—
400C2×C4⋊C4—22no—
401C2×C4⋊C4—22no—
402C2×C4⋊C4—22no—
403C2×C4⋊C4—22no—
404C2×C4⋊C4—22no—
405C2×C4⋊C4—22no—
406C2×C4⋊C4—22no—
407C2×C4⋊C4—44no—
408C2×C4⋊C4—48no—
409C2×C4⋊C4—82no—
410C2×C4⋊C4—82no—
411C2×C4⋊C4C2×D411yescharacteristic
412C2×C4⋊C4C2×D411yescharacteristic
413C2×C4⋊C4C2×D411yescharacteristic
414C2×C4⋊C4C2×D411yescharacteristic
415C2×C4⋊C4C2412yes—
416C2×C4⋊C4C2412yes—
417C2×C4⋊C4C2412yes—
418C2×C4⋊C4C2412yes—
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×C22⋊C4—22no—
431C2×C22⋊C4—22no—
432C2×C22⋊C4—22no—
433C2×C22⋊C4—22no—
434C2×C22⋊C4—22no—
435C2×C22⋊C4—22no—
436C2×C22⋊C4—22no—
437C2×C22⋊C4—22no—
438C2×C22⋊C4C2×D411yescharacteristic
439C2×C22⋊C4C2×D411yescharacteristic
440C2×C22⋊C4C2×D411yescharacteristic
441C2×C22⋊C4C2×D411yescharacteristic
442C2×C42—22no—
443C2×C42—22no—
444C2×C42—22no—
445C2×C42C2×D411yescharacteristic
446C2×C42C2×D411yescharacteristic
447C2×C42C2×D411yescharacteristic
448C2×C42C2×D411yescharacteristic
449C2×C42C2×D411yescharacteristic
450C2×C42C2×D411yescharacteristic
451C2×C42C2×D411yescharacteristic
452C2×C42C2×D411yescharacteristic
453C2×C42C2×D411yescharacteristic
454C2×C42C2×D411yescharacteristic
455C2×C42C2×D414yes—
456C2×C42#4114yes—
457C2×C42C2411yescharacteristic
458C2×C42C2411yescharacteristic
459C2×C42C2411yescharacteristic
460C2×C42C2411yescharacteristic
461C2×C42C2411yescharacteristic
462C2×C42C2411yescharacteristic
463C4⋊C8—24no—
464C4⋊C8—24no—
465C4⋊C8—24no—
466C4⋊C8—24no—
467C4⋊C8—42no—
468C4⋊C8—42no—
469#103—28no—
470#103—28no—
471#103—44no—
472#103—44no—
473#102—28no—
474#102—28no—
475#102—44no—
476#102—44no—
477C22⋊C8—24no—
478C22⋊C8—24no—
479C4×C8—22no—
480C4×C8—22no—
481C4×C8—22no—
482C4×C8—22no—
483#95—22no—
484#95—22no—
485#95—22no—
486#95—22no—
487#95—22no—
488#95—22no—
489#95—22no—
490#95—22no—
491#95C2×D411yescharacteristic
492#95C2×D411yescharacteristic
493#95C2×D411yescharacteristic
494#95C2×D411yescharacteristic
495#95C2×D411yescharacteristic
496#95C2×D411yescharacteristic
497#95C2×D411yescharacteristic
498#95C2×D411yescharacteristic
499C24—22no—
500C24—22no—
501C24C22×D411yescharacteristic
502#41—416no—
503#41—416no—
504#41—816no—
505C2×Q8—22no—
506C2×Q8—22no—
507C2×Q8—22no—
508C2×Q8—24no—
509C2×Q8—24no—
510C2×Q8—24no—
511C2×Q8—24no—
512C2×Q8—42no—
513C2×Q8—42no—
514C2×Q8—42no—
515C2×Q8—42no—
516C2×Q8—42no—
517C2×Q8—42no—
518C2×Q8C22×D414yes—
519C2×D4—28no—
520C2×D4—24no—
521C2×D4—24no—
522C2×D4—22no—
523C2×D4—22no—
524C2×D4—22no—
525C2×D4—24no—
526C2×D4—24no—
527C2×D4—24no—
528C2×D4—24no—
529C2×D4—44no—
530C2×D4—44no—
531C2×D4—44no—
532C2×D4—42no—
533C2×D4—42no—
534C2×D4—42no—
535C2×D4—42no—
536C2×D4—42no—
537C2×D4—42no—
538C2×D4—42no—
539C2×D4—42no—
540C2×D4—42no—
541C2×D4—42no—
542C2×D4—82no—
543C2×D4—82no—
544C2×D4C22×D414yes—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—28no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—44no—
559C22×C4—44no—
560C22×C4—44no—
561C22×C4—44no—
562C22×C4—44no—
563C22×C4—44no—
564C22×C4—82no—
565C22×C4—82no—
566C22×C4—82no—
567C22×C4—82no—
568C22×C4—82no—
569C22×C4—82no—
570C22×C4—82no—
571C22×C4—82no—
572C22×C4#12114yes—
573C22×C4#12114yes—
574C22×C4C22×D411yescharacteristic
575C22×C4C22×D411yescharacteristic
576C22×C4C22×D411yescharacteristic
577C22×C4C22×D411yescharacteristic
578C22×C4C22×D411yescharacteristic
579C22×C4C22×D411yescharacteristic
580C22×C4C22×D411yescharacteristic
581C22×C4C22×D411yescharacteristic
582C22×C4C22×D411yescharacteristic
583C22×C4C22×D412yes—
584C22×C4C22×D411yescharacteristic
585C22×C4C22×D411yescharacteristic
586C22×C4C22×D411yescharacteristic
587C22×C4C22×D411yescharacteristic
588C22×C4C2×#4112yes—
589C22×C4C2511yescharacteristic
590Q16—88no—
591SD16—88no—
592SD16—88no—
593D8—88no—
594C2×C8—22no—
595C2×C8—22no—
596C2×C8—22no—
597C2×C8—22no—
598C2×C8—22no—
599C2×C8—22no—
600C2×C8—22no—
601C2×C8—22no—
602C2×C8—22no—
603C2×C8—22no—
604C2×C8—22no—
605C2×C8—22no—
606C4⋊C4—24no—
607C4⋊C4—24no—
608C4⋊C4—22no—
609C4⋊C4—22no—
610C4⋊C4—22no—
611C4⋊C4—22no—
612C4⋊C4—22no—
613C4⋊C4—22no—
614C4⋊C4—24no—
615C4⋊C4—24no—
616C4⋊C4—41no—
617C4⋊C4—41no—
618C4⋊C4—44no—
619C4⋊C4—44no—
620C4⋊C4—42no—
621C4⋊C4—42no—
622C4⋊C4—42no—
623C4⋊C4—44no—
624C4⋊C4—44no—
625C4⋊C4—42no—
626C4⋊C4—44no—
627C4⋊C4—42no—
628C4⋊C4—42no—
629C4⋊C4—42no—
630C4⋊C4—42no—
631C4⋊C4—82no—
632C4⋊C4—82no—
633C4⋊C4—82no—
634C4⋊C4—82no—
635C4⋊C4—82no—
636C4⋊C4—82no—
637C22⋊C4—28no—
638C22⋊C4—28no—
639C22⋊C4—22no—
640C22⋊C4—22no—
641C22⋊C4—41no—
642C22⋊C4—41no—
643C22⋊C4—44no—
644C22⋊C4—44no—
645C22⋊C4—44no—
646C22⋊C4—44no—
647C22⋊C4—44no—
648C22⋊C4—44no—
649C22⋊C4—44no—
650C22⋊C4—44no—
651C22⋊C4—44no—
652C22⋊C4—82no—
653C22⋊C4—82no—
654C22⋊C4—82no—
655C22⋊C4—82no—
656C22⋊C4—82no—
657C22⋊C4—82no—
658C22⋊C4—82no—
659C22⋊C4—82no—
660C42—22no—
661C42—22no—
662C42—22no—
663C42—22no—
664C42—22no—
665C42—22no—
666C42—22no—
667C42—22no—
668C42—22no—
669C42—22no—
670C42—22no—
671C42—44no—
672C42—44no—
673C42—44no—
674C42#12114yes—
675C42#12114yes—
676C42C22×D412yes—
677C42C22×D412yes—
678C42C2×#4112yes—
679C42C2×#4112yes—
680C42H(5,𝔽2)14yes—
681C23—21no—
682C23—21no—
683C23—21no—
684C23—21no—
685C23—21no—
686C23—21no—
687C23—24no—
688C23—42no—
689C23—42no—
690C23—42no—
691C23—42no—
692C23—42no—
693C23—42no—
694C23—42no—
695C23—42no—
696C23—42no—
697C23—42no—
698C23—42no—
699C23—42no—
700C23—42no—
701C23C2×#12112yes—
702C23C23×D411yescharacteristic
703Q8—28no—
704Q8—44no—
705Q8—44no—
706Q8—44no—
707Q8—84no—
708Q8—84no—
709D4—28no—
710D4—416no—
711D4—44no—
712D4—44no—
713D4—44no—
714D4—48no—
715D4—48no—
716D4—88no—
717D4—84no—
718D4—84no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—24no—
730C2×C4—24no—
731C2×C4—28no—
732C2×C4—28no—
733C2×C4—24no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—416no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—88no—
771C2×C4—164no—
772C2×C4—164no—
773C2×C4—164no—
774C2×C4C2×#12112yes—
775C2×C4C2×#12112yes—
776C2×C4C2×#12112yes—
777C2×C4C2×#12112yes—
778C2×C4C2×#12112yes—
779C2×C4#53512yes—
780C2×C4#53512yes—
781C2×C4#57612yes—
782C2×C4#57712yes—
783C2×C4#57712yes—
784C2×C4#57812yes—
785C2×C4C23×D411yescharacteristic
786C2×C4C22×#4111yescharacteristic
787C2×C4C2×H(5,𝔽2)12yes—
788C2×C4#58512yes—
789C8—42no—
790C8—42no—
791C8—42no—
792C8—42no—
793C22—22no—
794C22—22no—
795C22—22no—
796C22—41no—
797C22—41no—
798C22—41no—
799C22—41no—
800C22—44no—
801C22—44no—
802C22—44no—
803C22—82no—
804C22—82no—
805C22—82no—
806C22—82no—
807C22—82no—
808C22—82no—
809C22—82no—
810C22—82no—
811C22—82no—
812C22—82no—
813C22—82no—
814C22C22×#12111yescharacteristic
815C22C2×#53511yescharacteristic
816C22#344911yescharacteristic
817C22C2×#57611yescharacteristic
818C22C2×#57711yescharacteristic
819C22C2×#57711yescharacteristic
820C22C2×#57811yescharacteristic
821C4—22no—
822C4—22no—
823C4—22no—
824C4—22no—
825C4—22no—
826C4—41no—
827C4—41no—
828C4—41no—
829C4—41no—
830C4—44no—
831C4—41no—
832C4—41no—
833C4—82no—
834C4—82no—
835C4—82no—
836C4—82no—
837C4—82no—
838C4#304514yes—
839C4#304614yes—
840C4#349612yes—
841C4#350612yes—
842C2—42no—
843C2—84no—
844C2—162no—
845C2#3516511yescharacteristic
846C2C2×#304511yescharacteristic
847C2C2×#304611yescharacteristic
848C2#6082211yescharacteristic
849C2#6082411yescharacteristic
850C2#6101411yescharacteristic
851C2#6101511yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#3207C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#117 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3210C2semidirect
3. #35298C2semidirect
4. #34207C2semidirect
5. #32919C2semidirect
6. #29729C2semidirect
7. #28717C2semidirect
8. #28716C2semidirect
9. #28616C2semidirect
10. #28615C2semidirect
11. #28614C2semidirect
12. #28613C2semidirect
13. #28444C2semidirect
14. #28443C2semidirect
15. #28262C2semidirect
16. #28172C2semidirect
17. #21860C2semidirect
18. #21859C2semidirect
19. #20809C2semidirect

Maximal subgroups

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

subgroupindex
C2×#32102
C2×#32072
#352982
#342072
#329192
#297292
#287172
#287162
#286162
#286152
#286142
#286132
#284442
#284432
#282622
#281722
#218602
#218592
#208092