Finite Group Databasebeta

← #6496448

Subgroups — #6496448

Order 512.

1851 conjugacy classes of subgroups.

The subgroup lattice has 835 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3230C211yesmaximal, characteristic, complemented
2C2×#2922C211yesmaximal, characteristic
3#35297C211yesmaximal, characteristic
4#35279C211yesmaximal, characteristic
5#33212C211yesmaximal, characteristic, complemented
6#33209C211yesmaximal, characteristic, complemented
7#33049C211yesmaximal, characteristic, complemented
8#33043C211yesmaximal, characteristic, complemented
9#29878C211yesmaximal, characteristic, complemented
10#29876C211yesmaximal, characteristic, complemented
11#29845C211yesmaximal, characteristic, complemented
12#29844C211yesmaximal, characteristic, complemented
13#24849C214yesmaximal, complemented
14#24714C214yesmaximal, complemented
15#24614C214yesmaximal, complemented
16#24564C214yesmaximal
17#21984C211yesmaximal, characteristic, complemented
18#21864C211yesmaximal, characteristic, complemented
19#21833C211yesmaximal, characteristic, complemented
20C2×#533C2211yescharacteristic
21C22×C4⋊Q8C2211yescharacteristic
22C2×C4×#41C2211yescharacteristic
23#3230—28no—
24C2×#500C2211yescharacteristic
25C2×#500C2211yescharacteristic
26C2×#487C2211yescharacteristic
27C2×#487C2211yescharacteristic
28C2×#484C2214yes—
29C2×#477C2214yes—
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#2857C2211yescharacteristic
48#2857C2211yescharacteristic
49#2628C2212yes—
50#2628C2212yes—
51#2625C2212yes—
52#2616C2212yes—
53#2584—21no—
54#2581—21no—
55#2568—21no—
56#2567—21no—
57#2563—21no—
58#2562—21no—
59#2542—21no—
60#2536—21no—
61#2487—21no—
62#2487—21no—
63#2485—21no—
64#2485—21no—
65#2415—21no—
66#2415—21no—
67#2409—21no—
68#2409—21no—
69#2323C2212yes—
70#2323C2212yes—
71#2317C2212yes—
72#2311C2212yes—
73#2285C2211yescharacteristic
74#2285C2211yescharacteristic
75#2087C2214yes—
76#2086C2214yes—
77#2076C2214yes—
78#2075C2214yes—
79#2068C2214yes—
80#2066C2214yes—
81#2036C2214yes—
82#2035C2214yes—
83#1990C2211yescharacteristic
84#1990C2211yescharacteristic
85#1990C2211yescharacteristic
86#1990C2211yescharacteristic
87#1990C2211yescharacteristic
88#1990C2211yescharacteristic
89#1988C2214yes—
90#1956C2211yescharacteristic
91#1956C2211yescharacteristic
92#1949C2214yes—
93#1944C2214yes—
94#1942C2214yes—
95#1935C2214yes—
96#1933C2214yes—
97#1894C2214yes—
98#1892C2214yes—
99#1873C2214yes—
100#1854C2214yes—
101#1845C2211yescharacteristic
102#1844C2211yescharacteristic
103#1834C2211yescharacteristic
104#1834C2211yescharacteristic
105#1823C2214yes—
106#1809C2214yes—
107#1808C2214yes—
108#1805C2214yes—
109C22×#41C2311yescharacteristic
110C23×Q8—21no—
111C22×M16C2312yes—
112C23×C8C2312yes—
113#533—24no—
114#533—24no—
115C2×C4⋊Q8—21no—
116C2×C4⋊Q8—21no—
117C2×C4⋊Q8—24no—
118C2×C4⋊Q8—24no—
119C2×C4⋊Q8C2311yescharacteristic
120C2×C4⋊Q8C2312yes—
121C2×C4⋊Q8C2311yescharacteristic
122C2×C4⋊Q8C2311yescharacteristic
123C2×C4⋊Q8C2311yescharacteristic
124C2×#125—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×C22⋊Q8—21no—
132C2×C22⋊Q8C2312yes—
133C2×C22⋊Q8C2312yes—
134C2×C22⋊Q8C2312yes—
135C4×#41—24no—
136C4×#41—24no—
137C2×C4×Q8—21no—
138C2×C4×Q8D411yescharacteristic
139C2×C4×Q8D411yescharacteristic
140C2×C4×Q8C2312yes—
141C2×C4×D4D411yescharacteristic
142C2×C4×D4D411yescharacteristic
143C2×C4×D4D411yescharacteristic
144C2×C4×D4D411yescharacteristic
145C2×C4×D4D411yescharacteristic
146C2×C4×D4D411yescharacteristic
147C2×#117—21no—
148C2×#117—21no—
149C2×#117C2312yes—
150C2×#117C2311yescharacteristic
151C2×#117C2311yescharacteristic
152C2×#117C2311yescharacteristic
153C22×C4⋊C4—21no—
154C22×C4⋊C4C2312yes—
155C22×C42C2311yescharacteristic
156C22×C42C2311yescharacteristic
157C22×C42C2311yescharacteristic
158#500—24no—
159#500—24no—
160#487—24no—
161#487—24no—
162#484—216no—
163#477—216no—
164#433—28no—
165#433—28no—
166#431—24no—
167#431—24no—
168#431—24no—
169#431D418yes—
170C2×#107C2314yes—
171C2×#107C2314yes—
172C2×#107C2314yes—
173C2×#106C2314yes—
174#424—28no—
175C2×C4⋊C8C2312yes—
176C2×C4⋊C8C2312yes—
177C2×C4⋊C8C2312yes—
178C2×C4⋊C8C2312yes—
179C2×#103C2314yes—
180C2×#103C2314yes—
181C2×#103C2314yes—
182C2×#103C2314yes—
183#408—28no—
184C2×C22⋊C8C2312yes—
185C2×C22⋊C8C2312yes—
186C2×C22⋊C8C2312yes—
187C2×C22⋊C8C2312yes—
188C4×M16—24no—
189C2×#97C2312yes—
190C2×C4×C8—24no—
191C2×C4×C8C2311yescharacteristic
192C2×C4×C8C2312yes—
193C2×C4×C8C2311yescharacteristic
194C2×C4×C8C2311yescharacteristic
195C2×C4×C8C2311yescharacteristic
196#400—22no—
197#400—22no—
198#400—22no—
199#399—22no—
200#399—22no—
201#398—22no—
202#397—22no—
203#397—22no—
204#395—22no—
205#395—22no—
206#395—22no—
207#394—22no—
208#394—22no—
209#394—22no—
210#393—22no—
211#393—22no—
212#391—22no—
213#391—21no—
214#391—21no—
215#391—21no—
216#391—21no—
217#391—21no—
218#391—21no—
219#391C2312yes—
220#391C2312yes—
221#390—22no—
222#389—22no—
223#389—22no—
224#389—21no—
225#389—21no—
226#389—21no—
227#389—21no—
228#389—21no—
229#389—21no—
230#389—21no—
231#389—21no—
232#389—21no—
233#389—21no—
234#389C2312yes—
235#389C2312yes—
236#389C2312yes—
237#389C2312yes—
238#389C2312yes—
239#389C2312yes—
240#388—22no—
241#388—22no—
242#388—22no—
243#388—22no—
244#387—22no—
245#387—22no—
246#386—22no—
247#386—22no—
248#385—22no—
249#385—22no—
250#384—22no—
251#384C2311yescharacteristic
252#384C2311yescharacteristic
253#384C2311yescharacteristic
254#384C2311yescharacteristic
255#382—22no—
256#382—21no—
257#382C2312yes—
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#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—
294C22×Q8—21no—
295C22×Q8—21no—
296C22×Q8—21no—
297C22×Q8—22no—
298C22×Q8—44no—
299C22×Q8—82no—
300C22×Q8—82no—
301C22×Q8C2×D411yescharacteristic
302C22×Q8C2412yes—
303C22×D4C2×D411yescharacteristic
304C22×D4C2×D411yescharacteristic
305C22×D4C2×D411yescharacteristic
306C23×C4—22no—
307C23×C4C2×D411yescharacteristic
308C23×C4C2×D411yescharacteristic
309C23×C4C2×D411yescharacteristic
310C23×C4C2×D411yescharacteristic
311C23×C4C2×D411yescharacteristic
312C23×C4C2×D411yescharacteristic
313C23×C4C2411yescharacteristic
314C23×C4C2411yescharacteristic
315C23×C4C2411yescharacteristic
316C2×M16—24no—
317C2×M16—24no—
318C2×M16—42no—
319C22×C8—24no—
320C22×C8—24no—
321C22×C8—42no—
322C22×C8C2412yes—
323C22×C8C2412yes—
324C22×C8C2412yes—
325C22×C8C2412yes—
326C4⋊Q8—24no—
327C4⋊Q8—22no—
328C4⋊Q8—22no—
329C4⋊Q8—22no—
330C4⋊Q8—22no—
331C4⋊Q8—22no—
332C4⋊Q8—22no—
333C4⋊Q8—24no—
334C4⋊Q8—22no—
335C4⋊Q8—22no—
336C4⋊Q8—44no—
337C4⋊Q8—44no—
338#125—44no—
339C22⋊Q8—24no—
340C22⋊Q8—24no—
341C22⋊Q8—28no—
342C22⋊Q8—44no—
343C22⋊Q8—44no—
344C22⋊Q8—82no—
345C22⋊Q8—82no—
346C22⋊Q8—82no—
347C22⋊Q8—82no—
348C22⋊Q8—82no—
349C22⋊Q8—82no—
350C4×Q8—24no—
351C4×Q8—24no—
352C4×Q8—24no—
353C4×Q8—24no—
354C4×Q8—44no—
355C4×D4—24no—
356C4×D4—24no—
357C4×D4—24no—
358C4×D4—24no—
359C4×D4—24no—
360C4×D4—24no—
361#117—22no—
362#117—22no—
363#117—22no—
364#117—22no—
365#117—22no—
366#117—22no—
367#117—44no—
368#117—44no—
369#117—82no—
370C2×C4⋊C4—24no—
371C2×C4⋊C4—24no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—22no—
375C2×C4⋊C4—22no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—22no—
382C2×C4⋊C4—22no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—22no—
386C2×C4⋊C4—22no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—22no—
392C2×C4⋊C4—22no—
393C2×C4⋊C4—22no—
394C2×C4⋊C4—22no—
395C2×C4⋊C4—22no—
396C2×C4⋊C4—22no—
397C2×C4⋊C4—44no—
398C2×C4⋊C4C2×D411yescharacteristic
399C2×C4⋊C4C2×D411yescharacteristic
400C2×C4⋊C4C2×D411yescharacteristic
401C2×C4⋊C4C2×D411yescharacteristic
402C2×C4⋊C4C2×D411yescharacteristic
403C2×C4⋊C4C2×D411yescharacteristic
404C2×C4⋊C4C2412yes—
405C2×C4⋊C4C2412yes—
406C2×C4⋊C4C2412yes—
407C2×C4⋊C4C2412yes—
408C2×C4⋊C4C2412yes—
409C2×C4⋊C4C2412yes—
410C2×C4⋊C4C2412yes—
411C2×C22⋊C4—22no—
412C2×C22⋊C4—22no—
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⋊C4C2×D411yescharacteristic
423C2×C22⋊C4C2×D411yescharacteristic
424C2×C22⋊C4C2×D411yescharacteristic
425C2×C22⋊C4C2×D411yescharacteristic
426C2×C22⋊C4C2×D411yescharacteristic
427C2×C22⋊C4C2×D411yescharacteristic
428C2×C42—22no—
429C2×C42—22no—
430C2×C42—22no—
431C2×C42—22no—
432C2×C42—22no—
433C2×C42—22no—
434C2×C42—22no—
435C2×C42C2×D411yescharacteristic
436C2×C42C2×D411yescharacteristic
437C2×C42C2×D411yescharacteristic
438C2×C42C2×D411yescharacteristic
439C2×C42C2×D411yescharacteristic
440C2×C42C2×D411yescharacteristic
441C2×C42C2×D414yes—
442C2×C42#4114yes—
443C2×C42C2411yescharacteristic
444C2×C42C2411yescharacteristic
445C2×C42C2411yescharacteristic
446C2×C42C2411yescharacteristic
447#107—28no—
448#107—28no—
449#107—44no—
450#106—44no—
451C4⋊C8—24no—
452C4⋊C8—24no—
453C4⋊C8—24no—
454C4⋊C8C2×D418yes—
455#103—28no—
456#103—28no—
457#103—44no—
458#103—44no—
459C22⋊C8—24no—
460C22⋊C8—24no—
461C22⋊C8—24no—
462C22⋊C8C2×D418yes—
463#97—24no—
464C4×C8—24no—
465C4×C8—22no—
466C4×C8—22no—
467C4×C8C2×D414yes—
468C4×C8C2×D414yes—
469#95—22no—
470#95—22no—
471#95—22no—
472#95—22no—
473#95—22no—
474#95—22no—
475#95—22no—
476#95—22no—
477#95—22no—
478#95—22no—
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—
489C24C22×D411yescharacteristic
490C24C22×D411yescharacteristic
491C24C22×D411yescharacteristic
492#41—48no—
493#41—48no—
494C2×Q8—22no—
495C2×Q8—22no—
496C2×Q8—22no—
497C2×Q8—22no—
498C2×Q8—24no—
499C2×Q8—24no—
500C2×Q8—41no—
501C2×Q8—42no—
502C2×Q8—44no—
503C2×Q8—42no—
504C2×Q8—42no—
505C2×Q8—42no—
506C2×Q8—42no—
507C2×Q8—42no—
508C2×Q8—42no—
509C2×Q8—42no—
510C2×Q8—42no—
511C2×Q8—82no—
512C2×Q8—82no—
513C2×Q8—816no—
514C2×D4—22no—
515C2×D4—22no—
516C2×D4—22no—
517C2×D4—22no—
518C2×D4—22no—
519C2×D4—22no—
520C2×D4—41no—
521C2×D4—41no—
522C2×D4—41no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—22no—
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—44no—
557C22×C4—82no—
558C22×C4—82no—
559C22×C4#12114yes—
560C22×C4#12114yes—
561C22×C4C22×D411yescharacteristic
562C22×C4C22×D411yescharacteristic
563C22×C4C22×D411yescharacteristic
564C22×C4C22×D411yescharacteristic
565C22×C4C22×D411yescharacteristic
566C22×C4C22×D411yescharacteristic
567C22×C4C22×D411yescharacteristic
568C22×C4C22×D411yescharacteristic
569C22×C4C22×D412yes—
570C22×C4C22×D411yescharacteristic
571C22×C4C22×D411yescharacteristic
572C22×C4C22×D411yescharacteristic
573C22×C4C2×#4112yes—
574C22×C42−1+414yes—
575C22×C4C2511yescharacteristic
576M16—48no—
577C2×C8—22no—
578C2×C8—22no—
579C2×C8—22no—
580C2×C8—22no—
581C2×C8—22no—
582C2×C8—22no—
583C2×C8—22no—
584C2×C8—22no—
585C2×C8—22no—
586C2×C8—22no—
587C2×C8—48no—
588C2×C8C22×D414yes—
589C2×C8C22×D414yes—
590C4⋊C4—22no—
591C4⋊C4—22no—
592C4⋊C4—22no—
593C4⋊C4—22no—
594C4⋊C4—22no—
595C4⋊C4—22no—
596C4⋊C4—22no—
597C4⋊C4—22no—
598C4⋊C4—22no—
599C4⋊C4—22no—
600C4⋊C4—22no—
601C4⋊C4—22no—
602C4⋊C4—24no—
603C4⋊C4—24no—
604C4⋊C4—24no—
605C4⋊C4—24no—
606C4⋊C4—44no—
607C4⋊C4—44no—
608C4⋊C4—44no—
609C4⋊C4—42no—
610C4⋊C4—42no—
611C4⋊C4—42no—
612C4⋊C4—42no—
613C4⋊C4—44no—
614C4⋊C4—44no—
615C4⋊C4—42no—
616C4⋊C4—44no—
617C4⋊C4—42no—
618C4⋊C4—42no—
619C4⋊C4—42no—
620C4⋊C4—42no—
621C4⋊C4—42no—
622C4⋊C4—42no—
623C4⋊C4—42no—
624C4⋊C4—42no—
625C4⋊C4—82no—
626C4⋊C4—82no—
627C4⋊C4—82no—
628C4⋊C4—82no—
629C4⋊C4—82no—
630C4⋊C4—82no—
631C22⋊C4—22no—
632C22⋊C4—22no—
633C22⋊C4—22no—
634C22⋊C4—22no—
635C22⋊C4—22no—
636C22⋊C4—22no—
637C22⋊C4—44no—
638C22⋊C4—44no—
639C22⋊C4—44no—
640C22⋊C4—44no—
641C22⋊C4—82no—
642C22⋊C4—82no—
643C22⋊C4—82no—
644C22⋊C4—82no—
645C22⋊C4—82no—
646C22⋊C4—82no—
647C22⋊C4—82no—
648C42—22no—
649C42—22no—
650C42—22no—
651C42—22no—
652C42—21no—
653C42—21no—
654C42—21no—
655C42—21no—
656C42—44no—
657C42—44no—
658C42—82no—
659C42#12114yes—
660C42#12114yes—
661C42C22×D412yes—
662C42C22×D412yes—
663C42C2×#4112yes—
664C42C2×#4112yes—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—21no—
677C23—21no—
678C23—21no—
679C23—21no—
680C23—21no—
681C23—21no—
682C23—21no—
683C23—21no—
684C23C2×#12112yes—
685C23#53612yes—
686C23C23×D411yescharacteristic
687Q8—44no—
688Q8—44no—
689Q8—44no—
690Q8—88no—
691Q8—84no—
692Q8—84no—
693Q8—84no—
694D4—44no—
695D4—44no—
696D4—44no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—24no—
706C2×C4—24no—
707C2×C4—24no—
708C2×C4—24no—
709C2×C4—28no—
710C2×C4—28no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—44no—
729C2×C4—44no—
730C2×C4—44no—
731C2×C4—44no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4—88no—
757C2×C4C2×#12112yes—
758C2×C4C2×#12112yes—
759C2×C4C2×#12112yes—
760C2×C4C2×#12112yes—
761C2×C4C2×#12112yes—
762C2×C4#53612yes—
763C2×C4#57612yes—
764C2×C4#57712yes—
765C2×C4#57812yes—
766C2×C4#57812yes—
767C2×C4C23×D411yescharacteristic
768C2×C4C22×#4111yescharacteristic
769C2×C4C2×2−1+412yes—
770C2×C4#58512yes—
771C8—24no—
772C8—24no—
773C8—42no—
774C8—42no—
775C22—22no—
776C22—22no—
777C22—22no—
778C22—22no—
779C22—22no—
780C22—22no—
781C22—41no—
782C22—41no—
783C22—41no—
784C22—41no—
785C22—41no—
786C22—41no—
787C22—41no—
788C22—41no—
789C22—41no—
790C22—41no—
791C22—41no—
792C22—41no—
793C22—41no—
794C22—41no—
795C22—41no—
796C22C22×#12111yescharacteristic
797C22C2×#53611yescharacteristic
798C22#344911yescharacteristic
799C22C2×#57611yescharacteristic
800C22C2×#57711yescharacteristic
801C22C2×#57811yescharacteristic
802C22C2×#57811yescharacteristic
803C4—22no—
804C4—22no—
805C4—22no—
806C4—22no—
807C4—41no—
808C4—41no—
809C4—41no—
810C4—41no—
811C4—41no—
812C4—82no—
813C4—82no—
814C4—82no—
815C4—82no—
816C4—82no—
817C4—82no—
818C4—82no—
819C4—82no—
820C4#305914yes—
821C4#306214yes—
822C4#348912yes—
823C4#349512yes—
824C2—42no—
825C2—42no—
826C2—81no—
827C2#3530611yescharacteristic
828C2C2×#305911yescharacteristic
829C2C2×#306211yescharacteristic
830C2#6087811yescharacteristic
831C2#6088011yescharacteristic
832C2#6100811yescharacteristic
833C2#6101411yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC22×#41C23
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×#3230C2semidirect
5. #33212C2semidirect
6. #33209C2semidirect
7. #33049C2semidirect
8. #33043C2semidirect
9. #29878C2semidirect
10. #29876C2semidirect
11. #29845C2semidirect
12. #29844C2semidirect
13. #24849C2semidirect
14. #24714C2semidirect
15. #24614C2semidirect
17. #21984C2semidirect
18. #21864C2semidirect
19. #21833C2semidirect

Maximal subgroups

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

subgroupindex
C2×#32302
C2×#29222
#352972
#352792
#332122
#332092
#330492
#330432
#298782
#298762
#298452
#298442
#248492
#247142
#246142
#245642
#219842
#218642
#218332