Finite Group Databasebeta

← #6497468

Subgroups — #6497468

Order 512.

1875 conjugacy classes of subgroups.

The subgroup lattice has 834 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3165C211yesmaximal, characteristic, complemented
2C2×#2965C211yesmaximal, characteristic
3#35297C211yesmaximal, characteristic
4#35279C211yesmaximal, characteristic
5#33212C211yesmaximal, characteristic, complemented
6#33210C211yesmaximal, characteristic, complemented
7#33209C211yesmaximal, characteristic, complemented
8#33207C211yesmaximal, characteristic, complemented
9#29878C211yesmaximal, characteristic, complemented
10#29877C211yesmaximal, characteristic, complemented
11#29877C211yesmaximal, characteristic, complemented
12#29876C211yesmaximal, characteristic, complemented
13#28715C214yesmaximal, complemented
14#28686C214yesmaximal, complemented
15#27671C214yesmaximal, complemented
16#27668C214yesmaximal, complemented
17#21835C211yesmaximal, characteristic, complemented
18#21833C211yesmaximal, characteristic, complemented
19#20824C211yesmaximal, characteristic, complemented
20C2×#533C2211yescharacteristic
21C22×C4⋊Q8C2211yescharacteristic
22C2×C4×#41C2211yescharacteristic
23#3165—28no—
24C2×#501C2214yes—
25C2×#500C2211yescharacteristic
26C2×#500C2211yescharacteristic
27C2×#498C2211yescharacteristic
28C2×#498C2211yescharacteristic
29#2965—28no—
30C2×#446C2212yes—
31C2×#436C2212yes—
32C2×#435C2212yes—
33C2×#435C2212yes—
34C2×#431C2211yescharacteristic
35C2×#431C2211yescharacteristic
36C2×#431C2211yescharacteristic
37C2×#428C2214yes—
38C2×C4×M16C2211yescharacteristic
39C2×C4×M16C2211yescharacteristic
40C22×C4×C8C2211yescharacteristic
41#2857C2211yescharacteristic
42#2857C2211yescharacteristic
43#2857C2211yescharacteristic
44#2857C2211yescharacteristic
45#2857C2211yescharacteristic
46#2857C2211yescharacteristic
47#2857C2211yescharacteristic
48#2857C2211yescharacteristic
49#2628—21no—
50#2628—21no—
51#2625—21no—
52#2616—21no—
53#2584C2212yes—
54#2581—21no—
55#2568—21no—
56#2567C2212yes—
57#2563C2212yes—
58#2562C2212yes—
59#2542—21no—
60#2536—21no—
61#2487C2212yes—
62#2487C2212yes—
63#2485C2212yes—
64#2485C2212yes—
65#2415—21no—
66#2415—21no—
67#2409—21no—
68#2409—21no—
69#2323—21no—
70#2323—21no—
71#2317—21no—
72#2311—21no—
73#2285C2211yescharacteristic
74#2285C2211yescharacteristic
75#2088C2214yes—
76#2088C2214yes—
77#2087C2214yes—
78#2086C2214yes—
79#2077C2214yes—
80#2077C2214yes—
81#2076C2214yes—
82#2075C2214yes—
83#1990C2211yescharacteristic
84#1990C2211yescharacteristic
85#1990C2211yescharacteristic
86#1990C2211yescharacteristic
87#1990C2211yescharacteristic
88#1990C2211yescharacteristic
89#1990C2211yescharacteristic
90#1990C2211yescharacteristic
91#1989C2214yes—
92#1988C2214yes—
93#1944C2214yes—
94#1943C2214yes—
95#1942C2214yes—
96#1941C2214yes—
97#1845C2211yescharacteristic
98#1844C2211yescharacteristic
99#1834C2211yescharacteristic
100#1834C2211yescharacteristic
101#1825C2214yes—
102#1823C2214yes—
103#1809C2214yes—
104#1809C2214yes—
105#1809C2214yes—
106#1808C2214yes—
107#1807C2214yes—
108#1776C2214yes—
109C22×#41D411yescharacteristic
110C23×Q8—21no—
111C22×M16C2312yes—
112C22×M16C2312yes—
113C23×C8C2312yes—
114#533—24no—
115#533—24no—
116C2×C4⋊Q8—21no—
117C2×C4⋊Q8—21no—
118C2×C4⋊Q8—24no—
119C2×C4⋊Q8—24no—
120C2×C4⋊Q8C2312yes—
121C2×C4⋊Q8C2311yescharacteristic
122C2×C4⋊Q8C2311yescharacteristic
123C2×C4⋊Q8C2311yescharacteristic
124C2×C4⋊Q8C2311yescharacteristic
125C2×#125C2312yes—
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⋊Q8—21no—
133C2×C22⋊Q8—21no—
134C2×C22⋊Q8—21no—
135C2×C22⋊Q8—21no—
136C4×#41—24no—
137C4×#41—24no—
138C2×C4×Q8—21no—
139C2×C4×Q8—21no—
140C2×C4×Q8D411yescharacteristic
141C2×C4×Q8C2311yescharacteristic
142C2×C4×D4D411yescharacteristic
143C2×C4×D4D411yescharacteristic
144C2×C4×D4D411yescharacteristic
145C2×C4×D4C2311yescharacteristic
146C2×C4×D4C2311yescharacteristic
147C2×C4×D4C2311yescharacteristic
148C2×#117—21no—
149C2×#117—21no—
150C2×#117D411yescharacteristic
151C2×#117D411yescharacteristic
152C2×#117D411yescharacteristic
153C2×#117C2312yes—
154C22×C4⋊C4—21no—
155C22×C4⋊C4C2312yes—
156C22×C42C2311yescharacteristic
157C22×C42C2311yescharacteristic
158C22×C42C2311yescharacteristic
159#501—216no—
160#500—24no—
161#500—24no—
162#498—24no—
163#498—24no—
164#446—28no—
165#436—28no—
166#435—28no—
167#435—28no—
168#431—24no—
169#431—24no—
170#431—24no—
171#428—216no—
172C2×#107C2314yes—
173C2×#107C2314yes—
174C2×#107C2314yes—
175C2×#106C2314yes—
176C2×#106C2314yes—
177C2×#106C2314yes—
178C2×C4⋊C8C2312yes—
179C2×C4⋊C8C2312yes—
180C2×C4⋊C8C2312yes—
181C2×C22⋊C8C2312yes—
182C2×C22⋊C8C2312yes—
183C2×C22⋊C8C2312yes—
184C4×M16—24no—
185C4×M16D418yes—
186C2×#97C2312yes—
187C2×#97C2312yes—
188C2×C4×C8—24no—
189C2×C4×C8C2311yescharacteristic
190C2×C4×C8C2312yes—
191C2×C4×C8C2311yescharacteristic
192C2×C4×C8C2311yescharacteristic
193C2×C4×C8C2311yescharacteristic
194#400—22no—
195#400—22no—
196#400—22no—
197#399—22no—
198#399—22no—
199#398—22no—
200#397—22no—
201#397—22no—
202#395—22no—
203#395—22no—
204#395—22no—
205#394—22no—
206#394—22no—
207#394—22no—
208#393—22no—
209#393—22no—
210#391—22no—
211#391—21no—
212#391—21no—
213#391—21no—
214#391—21no—
215#391—21no—
216#391—21no—
217#391—21no—
218#391—21no—
219#390—22no—
220#389—22no—
221#389—22no—
222#389—21no—
223#389—21no—
224#389—21no—
225#389—21no—
226#389—21no—
227#389—21no—
228#389—21no—
229#389—21no—
230#389C2312yes—
231#389C2312yes—
232#389C2312yes—
233#389C2312yes—
234#389C2312yes—
235#389C2312yes—
236#389C2312yes—
237#389C2312yes—
238#388—22no—
239#388—22no—
240#388—22no—
241#388—22no—
242#387—22no—
243#387—22no—
244#386—22no—
245#386—22no—
246#385—22no—
247#385—22no—
248#384—22no—
249#384C2311yescharacteristic
250#384C2311yescharacteristic
251#384C2311yescharacteristic
252#384C2311yescharacteristic
253#382—22no—
254#382—21no—
255#382—21no—
256#380—21no—
257#380—21no—
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#380C2312yes—
267#380C2312yes—
268#380C2312yes—
269#380C2312yes—
270#380C2312yes—
271#380C2312yes—
272#380C2312yes—
273#380C2312yes—
274#380C2312yes—
275#380C2312yes—
276C4×C4⋊C4—21no—
277C4×C4⋊C4—21no—
278C4×C4⋊C4C2312yes—
279C4×C4⋊C4C2312yes—
280#340C2314yes—
281#340C2314yes—
282#340C2314yes—
283#340C2314yes—
284#340C2314yes—
285#340C2314yes—
286#340C2314yes—
287#340C2314yes—
288#340C2314yes—
289#340C2314yes—
290C2×#41—24no—
291C2×#41—24no—
292C2×#41—42no—
293C22×Q8—21no—
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×D4C2×D411yescharacteristic
303C22×D4C2×D411yescharacteristic
304C22×D4C2×D411yescharacteristic
305C23×C4—22no—
306C23×C4C2×D411yescharacteristic
307C23×C4C2×D411yescharacteristic
308C23×C4C2×D411yescharacteristic
309C23×C4C2×D411yescharacteristic
310C23×C4C2×D411yescharacteristic
311C23×C4C2×D411yescharacteristic
312C23×C4C2411yescharacteristic
313C23×C4C2411yescharacteristic
314C23×C4C2411yescharacteristic
315C2×M16—24no—
316C2×M16—24no—
317C2×M16—24no—
318C2×M16—24no—
319C2×M16—24no—
320C2×M16C2×D418yes—
321C22×C8—24no—
322C22×C8—24no—
323C22×C8—24no—
324C22×C8C2412yes—
325C22×C8C2412yes—
326C22×C8C2412yes—
327C22×C8C2412yes—
328C4⋊Q8—22no—
329C4⋊Q8—22no—
330C4⋊Q8—24no—
331C4⋊Q8—22no—
332C4⋊Q8—22no—
333C4⋊Q8—22no—
334C4⋊Q8—22no—
335C4⋊Q8—24no—
336C4⋊Q8—22no—
337C4⋊Q8—22no—
338C4⋊Q8—44no—
339C4⋊Q8—44no—
340#125—24no—
341#125—24no—
342C22⋊Q8—44no—
343C22⋊Q8—44no—
344C22⋊Q8—44no—
345C22⋊Q8—44no—
346C22⋊Q8—82no—
347C22⋊Q8—82no—
348C22⋊Q8—82no—
349C22⋊Q8—82no—
350C22⋊Q8—82no—
351C22⋊Q8—82no—
352C4×Q8—24no—
353C4×Q8—22no—
354C4×Q8—22no—
355C4×Q8—44no—
356C4×Q8—44no—
357C4×D4—24no—
358C4×D4—24no—
359C4×D4—22no—
360C4×D4—22no—
361C4×D4—22no—
362C4×D4—22no—
363C4×D4—24no—
364C4×D4—22no—
365C4×D4—22no—
366#117—24no—
367#117—24no—
368#117—24no—
369#117—24no—
370#117—24no—
371#117—44no—
372#117—82no—
373C2×C4⋊C4—24no—
374C2×C4⋊C4—24no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—22no—
378C2×C4⋊C4—22no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—22no—
384C2×C4⋊C4—22no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—21no—
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—22no—
398C2×C4⋊C4—22no—
399C2×C4⋊C4—44no—
400C2×C4⋊C4C2×D411yescharacteristic
401C2×C4⋊C4C2×D411yescharacteristic
402C2×C4⋊C4C2×D411yescharacteristic
403C2×C4⋊C4C2×D411yescharacteristic
404C2×C4⋊C4C2×D411yescharacteristic
405C2×C4⋊C4C2×D411yescharacteristic
406C2×C4⋊C4C2412yes—
407C2×C4⋊C4C2412yes—
408C2×C4⋊C4C2412yes—
409C2×C4⋊C4C2412yes—
410C2×C4⋊C4C2412yes—
411C2×C4⋊C4C2412yes—
412C2×C4⋊C4C2412yes—
413C2×C4⋊C4C2412yes—
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⋊C4C2×D411yescharacteristic
426C2×C22⋊C4C2×D411yescharacteristic
427C2×C22⋊C4C2×D411yescharacteristic
428C2×C22⋊C4C2×D411yescharacteristic
429C2×C22⋊C4C2×D411yescharacteristic
430C2×C22⋊C4C2×D411yescharacteristic
431C2×C42—22no—
432C2×C42—22no—
433C2×C42—22no—
434C2×C42—22no—
435C2×C42—22no—
436C2×C42—22no—
437C2×C42—22no—
438C2×C42C2×D411yescharacteristic
439C2×C42C2×D411yescharacteristic
440C2×C42C2×D411yescharacteristic
441C2×C42C2×D411yescharacteristic
442C2×C42C2×D411yescharacteristic
443C2×C42C2×D411yescharacteristic
444C2×C42C2×D414yes—
445C2×C42#4114yes—
446C2×C42C2411yescharacteristic
447C2×C42C2411yescharacteristic
448C2×C42C2411yescharacteristic
449C2×C42C2411yescharacteristic
450#107—28no—
451#107—28no—
452#107—28no—
453#106—28no—
454#106—28no—
455#106—28no—
456C4⋊C8—24no—
457C4⋊C8—24no—
458C4⋊C8—24no—
459C22⋊C8—24no—
460C22⋊C8—24no—
461C22⋊C8—24no—
462#97—24no—
463#97C2×D418yes—
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—416no—
493C2×Q8—22no—
494C2×Q8—22no—
495C2×Q8—41no—
496C2×Q8—42no—
497C2×Q8—42no—
498C2×Q8—44no—
499C2×Q8—42no—
500C2×Q8—42no—
501C2×Q8—42no—
502C2×Q8—42no—
503C2×Q8—42no—
504C2×Q8—42no—
505C2×Q8—42no—
506C2×Q8—42no—
507C2×Q8—42no—
508C2×Q8—42no—
509C2×Q8—82no—
510C2×Q8—82no—
511C2×Q8—816no—
512C2×D4—22no—
513C2×D4—22no—
514C2×D4—22no—
515C2×D4—22no—
516C2×D4—22no—
517C2×D4—22no—
518C2×D4—41no—
519C2×D4—41no—
520C2×D4—41no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
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—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
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—44no—
555C22×C4—82no—
556C22×C4—82no—
557C22×C4#12114yes—
558C22×C4#12114yes—
559C22×C4#13714yes—
560C22×C4C22×D411yescharacteristic
561C22×C4C22×D411yescharacteristic
562C22×C4C22×D411yescharacteristic
563C22×C4C22×D411yescharacteristic
564C22×C4C22×D411yescharacteristic
565C22×C4C22×D411yescharacteristic
566C22×C4C22×D411yescharacteristic
567C22×C4C22×D411yescharacteristic
568C22×C4C22×D412yes—
569C22×C4C22×D411yescharacteristic
570C22×C4C22×D411yescharacteristic
571C22×C4C22×D411yescharacteristic
572C22×C4C2×#4112yes—
573C22×C4C2511yescharacteristic
574M16—216no—
575M16—48no—
576C2×C8—22no—
577C2×C8—22no—
578C2×C8—22no—
579C2×C8—22no—
580C2×C8—22no—
581C2×C8—22no—
582C2×C8—22no—
583C2×C8—22no—
584C2×C8—48no—
585C2×C8C22×D414yes—
586C2×C8C22×D414yes—
587C2×C82−1+414yes—
588C2×C82−1+414yes—
589C4⋊C4—22no—
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—22no—
603C4⋊C4—24no—
604C4⋊C4—24no—
605C4⋊C4—24no—
606C4⋊C4—24no—
607C4⋊C4—44no—
608C4⋊C4—44no—
609C4⋊C4—44no—
610C4⋊C4—42no—
611C4⋊C4—42no—
612C4⋊C4—44no—
613C4⋊C4—44no—
614C4⋊C4—42no—
615C4⋊C4—42no—
616C4⋊C4—42no—
617C4⋊C4—44no—
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—
685C23C2×#13712yes—
686C23C23×D411yescharacteristic
687Q8—44no—
688Q8—88no—
689Q8—84no—
690Q8—84no—
691Q8—84no—
692Q8—84no—
693D4—44no—
694D4—44no—
695D4—44no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—24no—
705C2×C4—24no—
706C2×C4—28no—
707C2×C4—28no—
708C2×C4—28no—
709C2×C4—21no—
710C2×C4—21no—
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—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—44no—
729C2×C4—44no—
730C2×C4—44no—
731C2×C4—42no—
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—88no—
756C2×C4C2×#12112yes—
757C2×C4C2×#12112yes—
758C2×C4C2×#12112yes—
759C2×C4C2×#12112yes—
760C2×C4C2×#12112yes—
761C2×C4C2×#13712yes—
762C2×C4C2×#13712yes—
763C2×C4#57512yes—
764C2×C4#57612yes—
765C2×C4#57712yes—
766C2×C4C23×D411yescharacteristic
767C2×C4C22×#4111yescharacteristic
768C2×C4C2×2−1+412yes—
769C2×C4C2×2−1+412yes—
770C8—24no—
771C8—42no—
772C8—42no—
773C8#53618yes—
774C22—22no—
775C22—22no—
776C22—22no—
777C22—22no—
778C22—22no—
779C22—22no—
780C22—41no—
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—
795C22C22×#12111yescharacteristic
796C22#349911yescharacteristic
797C22#349911yescharacteristic
798C22C22×#13711yescharacteristic
799C22C2×#57511yescharacteristic
800C22C2×#57611yescharacteristic
801C22C2×#57711yescharacteristic
802C4—22no—
803C4—22no—
804C4—22no—
805C4—22no—
806C4—41no—
807C4—41no—
808C4—41no—
809C4—41no—
810C4—41no—
811C4—82no—
812C4—82no—
813C4—82no—
814C4—82no—
815C4—82no—
816C4—82no—
817C4—82no—
818C4—82no—
819C4#305614yes—
820C4#306214yes—
821C4C2×#53612yes—
822C4#350912yes—
823C2—42no—
824C2—42no—
825C2—81no—
826C2#3531611yescharacteristic
827C2C2×#305611yescharacteristic
828C2C2×#306211yescharacteristic
829C2#6247811yescharacteristic
830C2#6248011yescharacteristic
831C2#6248111yescharacteristic
832C2#6248311yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC22×#41D4
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×#3165C2semidirect
5. #33212C2semidirect
6. #33210C2semidirect
7. #33209C2semidirect
8. #33207C2semidirect
9. #29878C2semidirect
10. #29877C2semidirect
11. #29877C2semidirect
12. #29876C2semidirect
13. #28715C2semidirect
14. #28686C2semidirect
15. #27671C2semidirect
16. #27668C2semidirect
17. #21835C2semidirect
18. #21833C2semidirect
19. #20824C2semidirect

Maximal subgroups

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

subgroupindex
C2×#31652
C2×#29652
#352972
#352792
#332122
#332102
#332092
#332072
#298782
#298772
#298762
#287152
#286862
#276712
#276682
#218352
#218332
#208242