Finite Group Databasebeta

← #6496447

Subgroups — #6496447

Order 512.

1965 conjugacy classes of subgroups.

The subgroup lattice has 875 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3226C211yesmaximal, characteristic, complemented
2C2×#2922C211yesmaximal, characteristic, complemented
3#35292C211yesmaximal, characteristic
4#35279C211yesmaximal, characteristic, complemented
5#33212C211yesmaximal, characteristic, complemented
6#33209C211yesmaximal, characteristic, complemented
7#33048C211yesmaximal, characteristic, complemented
8#33042C211yesmaximal, characteristic, complemented
9#29878C211yesmaximal, characteristic, complemented
10#29876C211yesmaximal, characteristic, complemented
11#29843C211yesmaximal, characteristic, complemented
12#29842C211yesmaximal, characteristic, complemented
13#24847C214yesmaximal, complemented
14#24712C214yesmaximal, complemented
15#24612C214yesmaximal, complemented
16#24562C214yesmaximal, complemented
17#21984C211yesmaximal, characteristic, complemented
18#21863C211yesmaximal, characteristic, complemented
19#21834C211yesmaximal, characteristic, complemented
20C2×#532C2211yescharacteristic
21C22×C4⋊Q8C2211yescharacteristic
22C2×C4×#41C2211yescharacteristic
23#3226—28no—
24C2×#500C2211yescharacteristic
25C2×#500C2211yescharacteristic
26C2×#486C2211yescharacteristic
27C2×#486C2211yescharacteristic
28C2×#480C2214yes—
29C2×#474C2214yes—
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#2628C2212yes—
50#2628C2212yes—
51#2624C2212yes—
52#2615C2212yes—
53#2592—21no—
54#2580—21no—
55#2568—21no—
56#2567—21no—
57#2563—21no—
58#2542—21no—
59#2540—21no—
60#2535—21no—
61#2487—21no—
62#2487—21no—
63#2414—21no—
64#2414—21no—
65#2409—21no—
66#2409—21no—
67#2407—21no—
68#2407—21no—
69#2324C2212yes—
70#2324C2212yes—
71#2317C2212yes—
72#2311C2212yes—
73#2285C2211yescharacteristic
74#2285C2211yescharacteristic
75#2087C2214yes—
76#2086C2214yes—
77#2076C2214yes—
78#2075C2214yes—
79#2067C2214yes—
80#2065C2214yes—
81#2034C2214yes—
82#2033C2214yes—
83#1990C2211yescharacteristic
84#1990C2211yescharacteristic
85#1990C2211yescharacteristic
86#1990C2211yescharacteristic
87#1990C2211yescharacteristic
88#1990C2211yescharacteristic
89#1987C2214yes—
90#1957C2211yescharacteristic
91#1957C2211yescharacteristic
92#1949C2214yes—
93#1944C2214yes—
94#1942C2214yes—
95#1936C2214yes—
96#1934C2214yes—
97#1895C2214yes—
98#1893C2214yes—
99#1875C2214yes—
100#1854C2214yes—
101#1845C2211yescharacteristic
102#1844C2211yescharacteristic
103#1834C2211yescharacteristic
104#1834C2211yescharacteristic
105#1824C2214yes—
106#1809C2214yes—
107#1808C2214yes—
108#1804C2214yes—
109C22×#41—21no—
110C22×#41C2311yescharacteristic
111C23×Q8—21no—
112C22×M16C2312yes—
113C23×C8C2312yes—
114#532—24no—
115#532—24no—
116C2×C4⋊Q8—21no—
117C2×C4⋊Q8—21no—
118C2×C4⋊Q8—24no—
119C2×C4⋊Q8—24no—
120C2×C4⋊Q8C2311yescharacteristic
121C2×C4⋊Q8C2311yescharacteristic
122C2×C4⋊Q8C2311yescharacteristic
123C2×C4⋊Q8C2312yes—
124C2×#127C2311yescharacteristic
125C2×#124—21no—
126C2×C22⋊Q8—21no—
127C2×C22⋊Q8—21no—
128C2×C22⋊Q8—21no—
129C2×C22⋊Q8—21no—
130C2×C22⋊Q8—21no—
131C2×C22⋊Q8—21no—
132C2×#121—21no—
133C2×#121—21no—
134C2×#121—21no—
135C2×#121—21no—
136C2×#121—21no—
137C2×#121C2312yes—
138C2×#121C2312yes—
139C2×#121C2312yes—
140C4×#41—24no—
141C4×#41—24no—
142C2×C4×Q8D411yescharacteristic
143C2×C4×Q8D411yescharacteristic
144C2×C4×D4—21no—
145C2×C4×D4D411yescharacteristic
146C2×C4×D4D411yescharacteristic
147C2×C4×D4D411yescharacteristic
148C2×C4×D4D411yescharacteristic
149C2×C4×D4D411yescharacteristic
150C2×C4×D4D411yescharacteristic
151C2×C4×D4C2312yes—
152C2×#117—21no—
153C2×#117C2312yes—
154C2×#117C2311yescharacteristic
155C2×#117C2311yescharacteristic
156C2×#117C2311yescharacteristic
157C22×C4⋊C4—21no—
158C22×C4⋊C4C2312yes—
159C22×C42C2311yescharacteristic
160C22×C42C2311yescharacteristic
161C22×C42C2311yescharacteristic
162#500—24no—
163#500—24no—
164#486—24no—
165#486—24no—
166#480—216no—
167#474—216no—
168#433—28no—
169#433—28no—
170#431—24no—
171#431—24no—
172#431—24no—
173#431D418yescomplemented
174C2×#107C2314yes—
175C2×#107C2314yes—
176C2×#107C2314yes—
177C2×#106C2314yes—
178#424—28no—
179C2×C4⋊C8C2312yes—
180C2×C4⋊C8C2312yes—
181C2×C4⋊C8C2312yes—
182C2×C4⋊C8C2312yes—
183C2×#102C2314yes—
184C2×#102C2314yes—
185C2×#102C2314yes—
186C2×#102C2314yes—
187#408—28no—
188C2×C22⋊C8C2312yes—
189C2×C22⋊C8C2312yes—
190C2×C22⋊C8C2312yes—
191C2×C22⋊C8C2312yes—
192C4×M16—24no—
193C2×#97C2312yes—
194C2×C4×C8—24no—
195C2×C4×C8C2311yescharacteristic
196C2×C4×C8C2312yes—
197C2×C4×C8C2311yescharacteristic
198C2×C4×C8C2311yescharacteristic
199C2×C4×C8C2311yescharacteristic
200#400—22no—
201#400—22no—
202#399—22no—
203#399—22no—
204#399—22no—
205#397—22no—
206#395—22no—
207#395—22no—
208#394—22no—
209#394—22no—
210#393—22no—
211#393—22no—
212#393—22no—
213#392—22no—
214#392—22no—
215#392—22no—
216#391—22no—
217#391—21no—
218#391—21no—
219#391—21no—
220#391—21no—
221#391—21no—
222#391—21no—
223#390—22no—
224#390—22no—
225#390—22no—
226#390—21no—
227#390—21no—
228#390—21no—
229#390—21no—
230#390C2312yes—
231#390C2312yes—
232#389—21no—
233#389—21no—
234#389—21no—
235#389—21no—
236#389—21no—
237#389—21no—
238#389C2312yes—
239#389C2312yes—
240#389C2312yes—
241#389C2312yes—
242#389C2312yes—
243#389C2312yes—
244#388—22no—
245#388—22no—
246#386—22no—
247#386—22no—
248#386—22no—
249#386—22no—
250#385—22no—
251#385—22no—
252#385—22no—
253#385—22no—
254#384—22no—
255#384C2311yescharacteristic
256#384C2311yescharacteristic
257#384C2311yescharacteristic
258#384C2311yescharacteristic
259#382—22no—
260#382—21no—
261#382C2312yes—
262#380—21no—
263#380—21no—
264#380—21no—
265#380—21no—
266#380—21no—
267#380—21no—
268#380—21no—
269#380—21no—
270#380—21no—
271#380C2312yes—
272#380C2312yes—
273#380C2312yes—
274#380C2312yes—
275#380C2312yes—
276#380C2312yes—
277#380C2312yes—
278C4×C4⋊C4—21no—
279C4×C4⋊C4—21no—
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×Q8—22no—
301C22×Q8—44no—
302C22×Q8—82no—
303C22×Q8—82no—
304C22×Q8C2×D411yescharacteristic
305C22×D4—22no—
306C22×D4—22no—
307C22×D4—22no—
308C22×D4—21no—
309C22×D4—21no—
310C22×D4C2×D411yescharacteristic
311C22×D4C2×D411yescharacteristic
312C22×D4C2×D411yescharacteristic
313C22×D4C2412yes—
314C23×C4—22no—
315C23×C4—22no—
316C23×C4C2×D411yescharacteristic
317C23×C4C2×D411yescharacteristic
318C23×C4C2×D411yescharacteristic
319C23×C4C2×D411yescharacteristic
320C23×C4C2×D411yescharacteristic
321C23×C4C2×D411yescharacteristic
322C23×C4C2411yescharacteristic
323C23×C4C2411yescharacteristic
324C23×C4C2411yescharacteristic
325C2×M16—24no—
326C2×M16—24no—
327C2×M16—42no—
328C22×C8—24no—
329C22×C8—24no—
330C22×C8—42no—
331C22×C8C2412yes—
332C22×C8C2412yes—
333C22×C8C2412yes—
334C22×C8C2412yes—
335C4⋊Q8—24no—
336C4⋊Q8—22no—
337C4⋊Q8—22no—
338C4⋊Q8—22no—
339C4⋊Q8—22no—
340C4⋊Q8—22no—
341C4⋊Q8—24no—
342C4⋊Q8—22no—
343C4⋊Q8—44no—
344C4⋊Q8—44no—
345#127—22no—
346#127—22no—
347#124—44no—
348C22⋊Q8—82no—
349C22⋊Q8—82no—
350C22⋊Q8—82no—
351C22⋊Q8—82no—
352C22⋊Q8—82no—
353C22⋊Q8—82no—
354#121—24no—
355#121—24no—
356#121—28no—
357#121—44no—
358#121—44no—
359#121—82no—
360#121—82no—
361#121—82no—
362#121—82no—
363C4×Q8—24no—
364C4×Q8—24no—
365C4×D4—24no—
366C4×D4—24no—
367C4×D4—24no—
368C4×D4—24no—
369C4×D4—24no—
370C4×D4—24no—
371C4×D4—24no—
372C4×D4—24no—
373C4×D4—44no—
374#117—22no—
375#117—22no—
376#117—22no—
377#117—22no—
378#117—22no—
379#117—22no—
380#117—44no—
381#117—82no—
382C2×C4⋊C4—24no—
383C2×C4⋊C4—24no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—22no—
387C2×C4⋊C4—22no—
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—21no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—21no—
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⋊C4C2×D411yescharacteristic
405C2×C4⋊C4C2×D411yescharacteristic
406C2×C4⋊C4C2×D411yescharacteristic
407C2×C4⋊C4C2×D411yescharacteristic
408C2×C4⋊C4C2×D411yescharacteristic
409C2×C4⋊C4C2×D411yescharacteristic
410C2×C4⋊C4C2412yes—
411C2×C4⋊C4C2412yes—
412C2×C4⋊C4C2412yes—
413C2×C4⋊C4C2412yes—
414C2×C4⋊C4C2412yes—
415C2×C4⋊C4C2412yes—
416C2×C4⋊C4C2412yes—
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×C22⋊C4—22no—
431C2×C22⋊C4—22no—
432C2×C22⋊C4—22no—
433C2×C22⋊C4C2×D411yescharacteristic
434C2×C22⋊C4C2×D411yescharacteristic
435C2×C22⋊C4C2×D411yescharacteristic
436C2×C22⋊C4C2×D411yescharacteristic
437C2×C22⋊C4C2×D411yescharacteristic
438C2×C22⋊C4C2×D411yescharacteristic
439C2×C42—22no—
440C2×C42—22no—
441C2×C42—22no—
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×D414yes—
452C2×C42#4114yes—
453C2×C42C2411yescharacteristic
454C2×C42C2411yescharacteristic
455C2×C42C2411yescharacteristic
456C2×C42C2411yescharacteristic
457#107—28no—
458#107—28no—
459#107—44no—
460#106—44no—
461C4⋊C8—24no—
462C4⋊C8—24no—
463C4⋊C8—24no—
464C4⋊C8C2×D418yes—
465#102—28no—
466#102—28no—
467#102—44no—
468#102—44no—
469C22⋊C8—24no—
470C22⋊C8—24no—
471C22⋊C8—24no—
472C22⋊C8C2×D418yes—
473#97—24no—
474C4×C8—24no—
475C4×C8—22no—
476C4×C8—22no—
477C4×C8C2×D414yes—
478C4×C8C2×D414yes—
479#95—22no—
480#95—22no—
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—44no—
507C2×Q8—42no—
508C2×Q8—42no—
509C2×Q8—42no—
510C2×Q8—42no—
511C2×Q8—42no—
512C2×Q8—42no—
513C2×Q8—42no—
514C2×Q8—42no—
515C2×Q8—82no—
516C2×Q8—82no—
517C2×Q8—816no—
518C2×D4—22no—
519C2×D4—22no—
520C2×D4—22no—
521C2×D4—22no—
522C2×D4—22no—
523C2×D4—22no—
524C2×D4—22no—
525C2×D4—22no—
526C2×D4—24no—
527C2×D4—24no—
528C2×D4—41no—
529C2×D4—41no—
530C2×D4—41no—
531C2×D4—44no—
532C2×D4—44no—
533C2×D4—44no—
534C2×D4—42no—
535C2×D4—42no—
536C2×D4—42no—
537C2×D4—42no—
538C2×D4—42no—
539C2×D4—42no—
540C2×D4—82no—
541C2×D4—82no—
542C2×D4—82no—
543C2×D4—82no—
544C2×D4—82no—
545C2×D4—82no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—21no—
551C22×C4—21no—
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—21no—
568C22×C4—21no—
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—44no—
579C22×C4—44no—
580C22×C4—82no—
581C22×C4—82no—
582C22×C4—82no—
583C22×C4—82no—
584C22×C4#12114yes—
585C22×C4#12114yes—
586C22×C4C22×D411yescharacteristic
587C22×C4C22×D411yescharacteristic
588C22×C4C22×D411yescharacteristic
589C22×C4C22×D411yescharacteristic
590C22×C4C22×D411yescharacteristic
591C22×C4C22×D411yescharacteristic
592C22×C4C22×D411yescharacteristic
593C22×C4C22×D411yescharacteristic
594C22×C4C22×D412yes—
595C22×C4C22×D411yescharacteristic
596C22×C4C22×D411yescharacteristic
597C22×C4C22×D411yescharacteristic
598C22×C4C2×#4112yes—
599C22×C42−1+414yes—
600C22×C4C2511yescharacteristic
601M16—48no—
602C2×C8—22no—
603C2×C8—22no—
604C2×C8—22no—
605C2×C8—22no—
606C2×C8—22no—
607C2×C8—22no—
608C2×C8—22no—
609C2×C8—22no—
610C2×C8—22no—
611C2×C8—22no—
612C2×C8—48no—
613C2×C8C22×D414yes—
614C2×C8C22×D414yes—
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—22no—
624C4⋊C4—22no—
625C4⋊C4—22no—
626C4⋊C4—22no—
627C4⋊C4—24no—
628C4⋊C4—24no—
629C4⋊C4—24no—
630C4⋊C4—24no—
631C4⋊C4—44no—
632C4⋊C4—44no—
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—42no—
642C4⋊C4—42no—
643C4⋊C4—42no—
644C4⋊C4—82no—
645C4⋊C4—82no—
646C4⋊C4—82no—
647C4⋊C4—82no—
648C4⋊C4—82no—
649C4⋊C4—82no—
650C22⋊C4—22no—
651C22⋊C4—22no—
652C22⋊C4—22no—
653C22⋊C4—22no—
654C22⋊C4—22no—
655C22⋊C4—22no—
656C22⋊C4—44no—
657C22⋊C4—44no—
658C22⋊C4—44no—
659C22⋊C4—44no—
660C22⋊C4—44no—
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—
671C22⋊C4—82no—
672C42—22no—
673C42—22no—
674C42—22no—
675C42—22no—
676C42—21no—
677C42—21no—
678C42—21no—
679C42—21no—
680C42—44no—
681C42—82no—
682C42#12114yes—
683C42#12114yes—
684C42C22×D412yes—
685C42C22×D412yes—
686C42C2×#4112yes—
687C42C2×#4112yes—
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—21no—
707C23—42no—
708C23—42no—
709C23—42no—
710C23—42no—
711C23—42no—
712C23—42no—
713C23—42no—
714C23C2×#12112yes—
715C23#53612yes—
716C23C23×D411yescharacteristic
717Q8—44no—
718Q8—88no—
719Q8—84no—
720Q8—84no—
721Q8—84no—
722D4—44no—
723D4—44no—
724D4—44no—
725D4—44no—
726D4—44no—
727D4—88no—
728D4—84no—
729D4—84no—
730D4—164no—
731D4—164no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—24no—
741C2×C4—24no—
742C2×C4—24no—
743C2×C4—24no—
744C2×C4—28no—
745C2×C4—28no—
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—21no—
760C2×C4—21no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—44no—
764C2×C4—44no—
765C2×C4—44no—
766C2×C4—44no—
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—42no—
787C2×C4—42no—
788C2×C4—88no—
789C2×C4—88no—
790C2×C4C2×#12112yes—
791C2×C4C2×#12112yes—
792C2×C4C2×#12112yes—
793C2×C4C2×#12112yes—
794C2×C4C2×#12112yes—
795C2×C4#53612yes—
796C2×C4#57612yes—
797C2×C4#57612yes—
798C2×C4#57712yes—
799C2×C4#57812yes—
800C2×C4C23×D411yescharacteristic
801C2×C4C22×#4111yescharacteristic
802C2×C4C2×2−1+412yes—
803C2×C4#58512yes—
804C8—24no—
805C8—24no—
806C8—42no—
807C8—42no—
808C22—22no—
809C22—22no—
810C22—22no—
811C22—22no—
812C22—22no—
813C22—22no—
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—41no—
828C22—41no—
829C22—82no—
830C22—82no—
831C22—82no—
832C22—82no—
833C22—82no—
834C22—82no—
835C22—82no—
836C22C22×#12111yescharacteristic
837C22C2×#53611yescharacteristic
838C22#344911yescharacteristic
839C22C2×#57611yescharacteristic
840C22C2×#57611yescharacteristic
841C22C2×#57711yescharacteristic
842C22C2×#57811yescharacteristic
843C4—22no—
844C4—22no—
845C4—22no—
846C4—22no—
847C4—41no—
848C4—41no—
849C4—41no—
850C4—41no—
851C4—41no—
852C4—82no—
853C4—82no—
854C4—82no—
855C4—82no—
856C4—82no—
857C4—82no—
858C4—82no—
859C4#305814yes—
860C4#306314yes—
861C4#348912yes—
862C4#349512yes—
863C2—42no—
864C2—42no—
865C2—81no—
866C2—162no—
867C2#3530611yescharacteristic
868C2C2×#305811yescharacteristic
869C2C2×#306311yescharacteristic
870C2#6087711yescharacteristic
871C2#6088011yescharacteristic
872C2#6100611yescharacteristic
873C2#6101411yescharacteristic
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×#3226C2semidirect
2. C2×#2922C2semidirect
4. #35279C2semidirect
5. #33212C2semidirect
6. #33209C2semidirect
7. #33048C2semidirect
8. #33042C2semidirect
9. #29878C2semidirect
10. #29876C2semidirect
11. #29843C2semidirect
12. #29842C2semidirect
13. #24847C2semidirect
14. #24712C2semidirect
15. #24612C2semidirect
16. #24562C2semidirect
17. #21984C2semidirect
18. #21863C2semidirect
19. #21834C2semidirect
173. #431D4semidirect

Maximal subgroups

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

subgroupindex
C2×#32262
C2×#29222
#352922
#352792
#332122
#332092
#330482
#330422
#298782
#298762
#298432
#298422
#248472
#247122
#246122
#245622
#219842
#218632
#218342