Finite Group Databasebeta

← #6496452

Subgroups — #6496452

Order 512.

1937 conjugacy classes of subgroups.

The subgroup lattice has 873 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3228C211yesmaximal, characteristic, complemented
2C2×#2922C211yesmaximal, characteristic, complemented
3#35292C211yesmaximal, characteristic
4#35280C211yesmaximal, characteristic, complemented
5#33210C211yesmaximal, characteristic, complemented
6#33209C211yesmaximal, characteristic, complemented
7#33048C211yesmaximal, characteristic, complemented
8#33042C211yesmaximal, characteristic, complemented
9#29878C211yesmaximal, characteristic, complemented
10#29877C211yesmaximal, characteristic, complemented
11#29842C211yesmaximal, characteristic, complemented
12#29842C211yesmaximal, characteristic, complemented
13#24848C214yesmaximal, complemented
14#24713C214yesmaximal, complemented
15#24615C214yesmaximal, complemented
16#24565C214yesmaximal, complemented
17#21982C211yesmaximal, characteristic, complemented
18#21859C211yesmaximal, characteristic, complemented
19#21835C211yesmaximal, characteristic, complemented
20C2×#533C2211yescharacteristic
21C2×#532C2211yescharacteristic
22C2×C4×#41C2211yescharacteristic
23#3228—28no—
24C2×#500C2211yescharacteristic
25C2×#498C2211yescharacteristic
26C2×#486C2211yescharacteristic
27C2×#486C2211yescharacteristic
28C2×#482C2214yes—
29C2×#478C2214yes—
30#2922—28no—
31C2×#433C2212yes—
32C2×#433C2212yes—
33C2×#431C2211yescharacteristic
34C2×#431C2211yescharacteristic
35C2×#431C2211yescharacteristic
36C2×#431C2211yescharacteristic
37C2×#424C2212yes—
38C2×#408C2212yes—
39C2×C4×M16C2211yescharacteristic
40C22×C4×C8C2211yescharacteristic
41#2857C2211yescharacteristic
42#2857C2211yescharacteristic
43#2857C2211yescharacteristic
44#2857C2211yescharacteristic
45#2857C2211yescharacteristic
46#2857C2211yescharacteristic
47#2856C2211yescharacteristic
48#2856C2211yescharacteristic
49#2629C2212yes—
50#2629C2212yes—
51#2624C2212yes—
52#2615C2212yes—
53#2592—21no—
54#2582—21no—
55#2582—21no—
56#2580—21no—
57#2540—21no—
58#2538—21no—
59#2538—21no—
60#2535—21no—
61#2417—21no—
62#2417—21no—
63#2417—21no—
64#2417—21no—
65#2414—21no—
66#2414—21no—
67#2407—21no—
68#2407—21no—
69#2324C2212yes—
70#2324C2212yes—
71#2316C2212yes—
72#2311C2212yes—
73#2285C2211yescharacteristic
74C2×#384C2211yescharacteristic
75#2088C2214yes—
76#2087C2214yes—
77#2077C2214yes—
78#2076C2214yes—
79#2067C2214yes—
80#2067C2214yes—
81#2033C2214yes—
82#2033C2214yes—
83#1990C2211yescharacteristic
84#1990C2211yescharacteristic
85#1990C2211yescharacteristic
86#1990C2211yescharacteristic
87#1990C2211yescharacteristic
88#1990C2211yescharacteristic
89#1989C2214yes—
90#1957C2211yescharacteristic
91#1957C2211yescharacteristic
92#1947C2214yes—
93#1943C2214yes—
94#1942C2214yes—
95#1936C2214yes—
96#1934C2214yes—
97#1895C2214yes—
98#1893C2214yes—
99#1874C2214yes—
100#1852C2214yes—
101#1845C2211yescharacteristic
102#1845C2211yescharacteristic
103#1834C2211yescharacteristic
104#1834C2211yescharacteristic
105#1825C2214yes—
106#1809C2214yes—
107#1808C2214yes—
108#1802C2214yes—
109C22×#41—21no—
110C22×#41C2311yescharacteristic
111C22×M16C2312yes—
112C23×C8C2312yes—
113#533—24no—
114#533—24no—
115#532—24no—
116#532—24no—
117C2×C4⋊Q8C2311yescharacteristic
118C2×C4⋊Q8C2311yescharacteristic
119C2×C4⋊Q8C2311yescharacteristic
120C2×#127C2311yescharacteristic
121C2×#125C2312yes—
122C2×#124—21no—
123C2×C22⋊Q8—21no—
124C2×C22⋊Q8—21no—
125C2×C22⋊Q8—21no—
126C2×C22⋊Q8—21no—
127C2×C22⋊Q8—21no—
128C2×C22⋊Q8—21no—
129C2×C22⋊Q8—21no—
130C2×C22⋊Q8—21no—
131C2×#121—21no—
132C2×#121—21no—
133C2×#121—21no—
134C2×#121—21no—
135C2×#121—21no—
136C2×#121C2312yes—
137C2×#121C2312yes—
138C2×#121C2312yes—
139C4×#41—24no—
140C4×#41—24no—
141C2×C4×Q8—21no—
142C2×C4×Q8—21no—
143C2×C4×Q8D411yescharacteristic
144C2×C4×Q8D411yescharacteristic
145C2×C4×D4—21no—
146C2×C4×D4D411yescharacteristic
147C2×C4×D4D411yescharacteristic
148C2×C4×D4D411yescharacteristic
149C2×C4×D4D411yescharacteristic
150C2×C4×D4D411yescharacteristic
151C2×C4×D4D411yescharacteristic
152C2×C4×D4C2312yes—
153C2×#117—21no—
154C2×#117C2312yes—
155C2×#117C2311yescharacteristic
156C2×#117C2311yescharacteristic
157C2×#117C2311yescharacteristic
158C22×C4⋊C4—21no—
159C22×C4⋊C4—21no—
160C22×C4⋊C4C2312yes—
161C22×C42C2311yescharacteristic
162C22×C42C2311yescharacteristic
163C22×C42C2311yescharacteristic
164#500—24no—
165#498—24no—
166#486—24no—
167#486—24no—
168#482—216no—
169#478—216no—
170#433—28no—
171#433—28no—
172#431—24no—
173#431—24no—
174#431—24no—
175#431D418yescomplemented
176C2×#107C2314yes—
177C2×#107C2314yes—
178C2×#107C2314yes—
179C2×#106C2314yes—
180#424—28no—
181C2×C4⋊C8C2312yes—
182C2×C4⋊C8C2312yes—
183C2×C4⋊C8C2312yes—
184C2×C4⋊C8C2312yes—
185C2×#102C2314yes—
186C2×#102C2314yes—
187C2×#102C2314yes—
188C2×#102C2314yes—
189#408—28no—
190C2×C22⋊C8C2312yes—
191C2×C22⋊C8C2312yes—
192C2×C22⋊C8C2312yes—
193C2×C22⋊C8C2312yes—
194C4×M16—24no—
195C2×#97C2312yes—
196C2×C4×C8—24no—
197C2×C4×C8C2311yescharacteristic
198C2×C4×C8C2312yes—
199C2×C4×C8C2311yescharacteristic
200C2×C4×C8C2311yescharacteristic
201C2×C4×C8C2311yescharacteristic
202#399—22no—
203#398—22no—
204#398—22no—
205#398—22no—
206#398—22no—
207#397—22no—
208#396—22no—
209#396—22no—
210#396—22no—
211#396—22no—
212#394—22no—
213#394—22no—
214#393—22no—
215#392—22no—
216#392—22no—
217#392—22no—
218#391—22no—
219#391—21no—
220#391—21no—
221#391—21no—
222#391—21no—
223#391—21no—
224#391—21no—
225#390—22no—
226#390—22no—
227#390—22no—
228#390—21no—
229#390—21no—
230#390—21no—
231#390—21no—
232#390C2312yes—
233#390C2312yes—
234#389—22no—
235#389—22no—
236#389—21no—
237#389—21no—
238#389—21no—
239#389—21no—
240#389—21no—
241#389—21no—
242#389C2312yes—
243#389C2312yes—
244#389C2312yes—
245#389C2312yes—
246#389C2312yes—
247#389C2312yes—
248#388—22no—
249#388—22no—
250#386—22no—
251#386—22no—
252#386—22no—
253#386—22no—
254#385—22no—
255#385—22no—
256#384—21no—
257#384—21no—
258#384C2312yes—
259#384C2311yescharacteristic
260#384C2311yescharacteristic
261#384C2311yescharacteristic
262#384C2311yescharacteristic
263#382—21no—
264#380—21no—
265#380—21no—
266#380—21no—
267#380—21no—
268#380—21no—
269#380—21no—
270#380—21no—
271#380—22no—
272#380—22no—
273#380C2312yes—
274#380C2312yes—
275#380C2312yes—
276#380C2312yes—
277#380C2312yes—
278#380C2312yes—
279#380C2312yes—
280C4×C4⋊C4—21no—
281C4×C4⋊C4C2312yes—
282#340C2314yes—
283#340C2314yes—
284#340C2314yes—
285#340C2314yes—
286#340C2314yes—
287#340C2314yes—
288#340C2314yes—
289#340C2314yes—
290C2×#41—22no—
291C2×#41—22no—
292C2×#41—24no—
293C2×#41—42no—
294C2×#41—44no—
295C2×#41—82no—
296C2×#41—82no—
297C22×Q8—21no—
298C22×Q8—21no—
299C22×Q8—21no—
300C22×Q8C2×D411yescharacteristic
301C22×D4—22no—
302C22×D4—22no—
303C22×D4—22no—
304C22×D4—21no—
305C22×D4—21no—
306C22×D4C2×D411yescharacteristic
307C22×D4C2×D411yescharacteristic
308C22×D4C2×D411yescharacteristic
309C22×D4C2412yes—
310C23×C4—22no—
311C23×C4—22no—
312C23×C4C2×D411yescharacteristic
313C23×C4C2×D411yescharacteristic
314C23×C4C2×D411yescharacteristic
315C23×C4C2×D411yescharacteristic
316C23×C4C2×D411yescharacteristic
317C23×C4C2×D411yescharacteristic
318C23×C4C2411yescharacteristic
319C23×C4C2411yescharacteristic
320C23×C4C2411yescharacteristic
321C2×M16—24no—
322C2×M16—24no—
323C2×M16—42no—
324C22×C8—24no—
325C22×C8—24no—
326C22×C8—42no—
327C22×C8C2412yes—
328C22×C8C2412yes—
329C22×C8C2412yes—
330C22×C8C2412yes—
331C4⋊Q8—22no—
332C4⋊Q8—22no—
333C4⋊Q8—22no—
334C4⋊Q8—22no—
335C4⋊Q8—22no—
336C4⋊Q8—22no—
337#127—22no—
338#127—22no—
339#125—24no—
340#125—24no—
341#124—44no—
342C22⋊Q8—44no—
343C22⋊Q8—44no—
344C22⋊Q8—82no—
345C22⋊Q8—82no—
346C22⋊Q8—82no—
347C22⋊Q8—82no—
348C22⋊Q8—82no—
349C22⋊Q8—82no—
350#121—24no—
351#121—24no—
352#121—28no—
353#121—44no—
354#121—44no—
355#121—82no—
356#121—82no—
357#121—82no—
358#121—82no—
359C4×Q8—24no—
360C4×Q8—24no—
361C4×Q8—44no—
362C4×Q8—44no—
363C4×D4—24no—
364C4×D4—24no—
365C4×D4—24no—
366C4×D4—24no—
367C4×D4—24no—
368C4×D4—24no—
369C4×D4—24no—
370C4×D4—24no—
371C4×D4—44no—
372#117—22no—
373#117—22no—
374#117—22no—
375#117—22no—
376#117—22no—
377#117—22no—
378#117—24no—
379#117—24no—
380#117—82no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—22no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—21no—
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—22no—
396C2×C4⋊C4—22no—
397C2×C4⋊C4—22no—
398C2×C4⋊C4—22no—
399C2×C4⋊C4—22no—
400C2×C4⋊C4—22no—
401C2×C4⋊C4—22no—
402C2×C4⋊C4—22no—
403C2×C4⋊C4—44no—
404C2×C4⋊C4—82no—
405C2×C4⋊C4—82no—
406C2×C4⋊C4C2×D411yescharacteristic
407C2×C4⋊C4C2×D411yescharacteristic
408C2×C4⋊C4C2×D411yescharacteristic
409C2×C4⋊C4C2×D411yescharacteristic
410C2×C4⋊C4C2×D411yescharacteristic
411C2×C4⋊C4C2×D411yescharacteristic
412C2×C4⋊C4C2412yes—
413C2×C4⋊C4C2412yes—
414C2×C4⋊C4C2412yes—
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⋊C4C2×D411yescharacteristic
436C2×C22⋊C4C2×D411yescharacteristic
437C2×C22⋊C4C2×D411yescharacteristic
438C2×C22⋊C4C2×D411yescharacteristic
439C2×C22⋊C4C2×D411yescharacteristic
440C2×C22⋊C4C2×D411yescharacteristic
441C2×C42—22no—
442C2×C42—22no—
443C2×C42—22no—
444C2×C42—22no—
445C2×C42—22no—
446C2×C42—22no—
447C2×C42C2×D411yescharacteristic
448C2×C42C2×D411yescharacteristic
449C2×C42C2×D411yescharacteristic
450C2×C42C2×D411yescharacteristic
451C2×C42C2×D411yescharacteristic
452C2×C42C2×D411yescharacteristic
453C2×C42C2×D414yes—
454C2×C42#4114yes—
455C2×C42C2411yescharacteristic
456C2×C42C2411yescharacteristic
457C2×C42C2411yescharacteristic
458C2×C42C2411yescharacteristic
459#107—28no—
460#107—44no—
461#107—44no—
462#106—28no—
463C4⋊C8—24no—
464C4⋊C8—24no—
465C4⋊C8—24no—
466C4⋊C8C2×D418yes—
467#102—28no—
468#102—28no—
469#102—44no—
470#102—44no—
471C22⋊C8—24no—
472C22⋊C8—24no—
473C22⋊C8—24no—
474C22⋊C8C2×D418yes—
475#97—24no—
476C4×C8—24no—
477C4×C8—22no—
478C4×C8—22no—
479C4×C8C2×D414yes—
480C4×C8C2×D414yes—
481#95—22no—
482#95—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#95—22no—
492#95—22no—
493#95—22no—
494#95—22no—
495C24—22no—
496C24C22×D411yescharacteristic
497C24C22×D411yescharacteristic
498C24C22×D411yescharacteristic
499#41—48no—
500#41—48no—
501#41—816no—
502C2×Q8—22no—
503C2×Q8—22no—
504C2×Q8—41no—
505C2×Q8—42no—
506C2×Q8—42no—
507C2×Q8—42no—
508C2×Q8—42no—
509C2×Q8—42no—
510C2×Q8—42no—
511C2×Q8—42no—
512C2×Q8—42no—
513C2×Q8—42no—
514C2×D4—22no—
515C2×D4—22no—
516C2×D4—22no—
517C2×D4—22no—
518C2×D4—22no—
519C2×D4—22no—
520C2×D4—22no—
521C2×D4—22no—
522C2×D4—24no—
523C2×D4—24no—
524C2×D4—41no—
525C2×D4—41no—
526C2×D4—41no—
527C2×D4—44no—
528C2×D4—44no—
529C2×D4—44no—
530C2×D4—42no—
531C2×D4—42no—
532C2×D4—42no—
533C2×D4—42no—
534C2×D4—42no—
535C2×D4—42no—
536C2×D4—82no—
537C2×D4—82no—
538C2×D4—82no—
539C2×D4—82no—
540C2×D4—82no—
541C2×D4—82no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—21no—
547C22×C4—21no—
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—21no—
564C22×C4—21no—
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—44no—
575C22×C4—44no—
576C22×C4—82no—
577C22×C4—82no—
578C22×C4—82no—
579C22×C4—82no—
580C22×C4#12114yes—
581C22×C4#12114yes—
582C22×C4C22×D411yescharacteristic
583C22×C4C22×D411yescharacteristic
584C22×C4C22×D411yescharacteristic
585C22×C4C22×D411yescharacteristic
586C22×C4C22×D411yescharacteristic
587C22×C4C22×D411yescharacteristic
588C22×C4C22×D411yescharacteristic
589C22×C4C22×D411yescharacteristic
590C22×C4C22×D412yes—
591C22×C4C22×D411yescharacteristic
592C22×C4C22×D411yescharacteristic
593C22×C4C22×D411yescharacteristic
594C22×C4C2×#4112yes—
595C22×C42−1+414yes—
596C22×C4C2511yescharacteristic
597M16—48no—
598C2×C8—22no—
599C2×C8—22no—
600C2×C8—22no—
601C2×C8—22no—
602C2×C8—22no—
603C2×C8—22no—
604C2×C8—22no—
605C2×C8—22no—
606C2×C8—22no—
607C2×C8—22no—
608C2×C8—48no—
609C2×C8C22×D414yes—
610C2×C8C22×D414yes—
611C4⋊C4—22no—
612C4⋊C4—22no—
613C4⋊C4—22no—
614C4⋊C4—22no—
615C4⋊C4—22no—
616C4⋊C4—22no—
617C4⋊C4—22no—
618C4⋊C4—22no—
619C4⋊C4—22no—
620C4⋊C4—22no—
621C4⋊C4—22no—
622C4⋊C4—22no—
623C4⋊C4—24no—
624C4⋊C4—24no—
625C4⋊C4—24no—
626C4⋊C4—24no—
627C4⋊C4—44no—
628C4⋊C4—42no—
629C4⋊C4—44no—
630C4⋊C4—44no—
631C4⋊C4—42no—
632C4⋊C4—42no—
633C4⋊C4—42no—
634C4⋊C4—42no—
635C4⋊C4—42no—
636C4⋊C4—42no—
637C4⋊C4—42no—
638C4⋊C4—42no—
639C4⋊C4—42no—
640C4⋊C4—42no—
641C4⋊C4—82no—
642C4⋊C4—82no—
643C4⋊C4—82no—
644C4⋊C4—82no—
645C4⋊C4—82no—
646C4⋊C4—82no—
647C4⋊C4—82no—
648C4⋊C4—82no—
649C22⋊C4—22no—
650C22⋊C4—22no—
651C22⋊C4—22no—
652C22⋊C4—22no—
653C22⋊C4—22no—
654C22⋊C4—22no—
655C22⋊C4—44no—
656C22⋊C4—44no—
657C22⋊C4—44no—
658C22⋊C4—44no—
659C22⋊C4—44no—
660C22⋊C4—82no—
661C22⋊C4—82no—
662C22⋊C4—82no—
663C22⋊C4—82no—
664C22⋊C4—82no—
665C22⋊C4—82no—
666C22⋊C4—82no—
667C22⋊C4—82no—
668C22⋊C4—82no—
669C22⋊C4—82no—
670C22⋊C4—82no—
671C42—22no—
672C42—22no—
673C42—22no—
674C42—22no—
675C42—21no—
676C42—21no—
677C42—21no—
678C42—21no—
679C42—44no—
680C42—82no—
681C42#12114yes—
682C42#12114yes—
683C42C22×D412yes—
684C42C22×D412yes—
685C42C2×#4112yes—
686C42C2×#4112yes—
687C23—21no—
688C23—21no—
689C23—21no—
690C23—21no—
691C23—21no—
692C23—21no—
693C23—21no—
694C23—21no—
695C23—21no—
696C23—21no—
697C23—21no—
698C23—21no—
699C23—21no—
700C23—21no—
701C23—21no—
702C23—21no—
703C23—21no—
704C23—21no—
705C23—21no—
706C23—42no—
707C23—42no—
708C23—42no—
709C23—42no—
710C23—42no—
711C23—42no—
712C23—42no—
713C23C2×#12112yes—
714C23#53612yes—
715C23C23×D411yescharacteristic
716Q8—44no—
717Q8—84no—
718Q8—84no—
719Q8—84no—
720D4—44no—
721D4—44no—
722D4—44no—
723D4—44no—
724D4—44no—
725D4—88no—
726D4—84no—
727D4—84no—
728D4—164no—
729D4—164no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—24no—
739C2×C4—24no—
740C2×C4—24no—
741C2×C4—24no—
742C2×C4—28no—
743C2×C4—28no—
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—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—44no—
762C2×C4—44no—
763C2×C4—44no—
764C2×C4—44no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—42no—
772C2×C4—42no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—42no—
778C2×C4—42no—
779C2×C4—42no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—42no—
786C2×C4—88no—
787C2×C4—164no—
788C2×C4C2×#12112yes—
789C2×C4C2×#12112yes—
790C2×C4C2×#12112yes—
791C2×C4C2×#12112yes—
792C2×C4C2×#12112yes—
793C2×C4#53612yes—
794C2×C4#57612yes—
795C2×C4#57612yes—
796C2×C4#57712yes—
797C2×C4#57812yes—
798C2×C4C23×D411yescharacteristic
799C2×C4C22×#4111yescharacteristic
800C2×C4C2×2−1+412yes—
801C2×C4#58512yes—
802C8—24no—
803C8—24no—
804C8—42no—
805C8—42no—
806C22—22no—
807C22—22no—
808C22—22no—
809C22—22no—
810C22—22no—
811C22—22no—
812C22—41no—
813C22—41no—
814C22—41no—
815C22—41no—
816C22—41no—
817C22—41no—
818C22—41no—
819C22—41no—
820C22—41no—
821C22—41no—
822C22—41no—
823C22—41no—
824C22—41no—
825C22—41no—
826C22—41no—
827C22—82no—
828C22—82no—
829C22—82no—
830C22—82no—
831C22—82no—
832C22—82no—
833C22—82no—
834C22C22×#12111yescharacteristic
835C22C2×#53611yescharacteristic
836C22#344911yescharacteristic
837C22C2×#57611yescharacteristic
838C22C2×#57611yescharacteristic
839C22C2×#57711yescharacteristic
840C22C2×#57811yescharacteristic
841C4—22no—
842C4—22no—
843C4—22no—
844C4—22no—
845C4—41no—
846C4—41no—
847C4—41no—
848C4—41no—
849C4—41no—
850C4—82no—
851C4—82no—
852C4—82no—
853C4—82no—
854C4—82no—
855C4—82no—
856C4—82no—
857C4#306114yes—
858C4#306214yes—
859C4#348912yes—
860C4#349512yes—
861C2—42no—
862C2—42no—
863C2—81no—
864C2—162no—
865C2#3530611yescharacteristic
866C2C2×#306111yescharacteristic
867C2C2×#306211yescharacteristic
868C2#6087711yescharacteristic
869C2#6088011yescharacteristic
870C2#6100811yescharacteristic
871C2#6101111yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#35292C2
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×#3228C2semidirect
2. C2×#2922C2semidirect
4. #35280C2semidirect
5. #33210C2semidirect
6. #33209C2semidirect
7. #33048C2semidirect
8. #33042C2semidirect
9. #29878C2semidirect
10. #29877C2semidirect
11. #29842C2semidirect
12. #29842C2semidirect
13. #24848C2semidirect
14. #24713C2semidirect
15. #24615C2semidirect
16. #24565C2semidirect
17. #21982C2semidirect
18. #21859C2semidirect
19. #21835C2semidirect
175. #431D4semidirect

Maximal subgroups

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

subgroupindex
C2×#32282
C2×#29222
#352922
#352802
#332102
#332092
#330482
#330422
#298782
#298772
#298422
#248482
#247132
#246152
#245652
#219822
#218592
#218352