Finite Group Databasebeta

← #6684008

Subgroups — #6684008

Order 512.

1850 conjugacy classes of subgroups.

The subgroup lattice has 806 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3229C211yesmaximal, characteristic, complemented
2C2×#3165C211yesmaximal, characteristic, complemented
3#36129C211yesmaximal, characteristic
4#36129C211yesmaximal, characteristic
5#33049C211yesmaximal, characteristic, complemented
6#30969C214yesmaximal, complemented
7#30793C214yesmaximal, complemented
8#30281C211yesmaximal, characteristic, complemented
9#29878C211yesmaximal, characteristic, complemented
10#28688C211yesmaximal, characteristic, complemented
11#28653C211yesmaximal, characteristic, complemented
12#26356C214yesmaximal, complemented
13#26149C214yesmaximal
14#25904C211yesmaximal, characteristic, complemented
15#25811C211yesmaximal, characteristic, complemented
16#25811C211yesmaximal, characteristic, complemented
17#25674C211yesmaximal, characteristic, complemented
18#22246C211yesmaximal, characteristic, complemented
19#21102C211yesmaximal, characteristic
20C2×#533C2211yescharacteristic
21C2×#533C2211yescharacteristic
22C22×C4⋊Q8C2211yescharacteristic
23C22×C4⋊Q8C2211yescharacteristic
24#3229—28no—
25#3165—28no—
26C2×#501C2214yes—
27C2×#500C2211yescharacteristic
28C2×#500C2211yescharacteristic
29C2×#498C2211yescharacteristic
30C2×#498C2211yescharacteristic
31C2×#498C2211yescharacteristic
32C2×#498C2211yescharacteristic
33C2×#487C2211yescharacteristic
34C2×#487C2211yescharacteristic
35C2×#487C2211yescharacteristic
36C2×#483C2214yes—
37C2×#475C2214yes—
38C2×#431C2211yescharacteristic
39C2×#428C2214yes—
40C2×C4×M16C2211yescharacteristic
41#2862C2211yescharacteristic
42#2862C2211yescharacteristic
43#2857C2211yescharacteristic
44#2857C2211yescharacteristic
45#2857C2211yescharacteristic
46#2857C2211yescharacteristic
47#2550—21no—
48#2550C2212yes—
49#2492—21no—
50#2492C2212yes—
51#2451—21no—
52#2451C2212yes—
53#2446—21no—
54#2446—21no—
55#2442—21no—
56#2442C2212yes—
57#2439—21no—
58#2439C2212yes—
59#2429—21no—
60#2429—21no—
61#2417—21no—
62#2417C2212yes—
63#2409—21no—
64#2409—21no—
65#2360—21no—
66#2360C2212yes—
67#2352—21no—
68#2352C2212yes—
69Q8×C22⋊C4—21no—
70Q8×C22⋊C4—21no—
71C4×C4⋊Q8C2211yescharacteristic
72C4×C4⋊Q8C2211yescharacteristic
73C42×D4C2211yescharacteristic
74#2097C2214yes—
75#2097C2214yes—
76#2087C2214yes—
77#2085C2214yes—
78#2076C2214yes—
79#2066C2214yes—
80#2058C2214yes—
81#2058C2214yes—
82#2036C2214yes—
83#2026C2214yes—
84#1990C2211yescharacteristic
85#1990C2211yescharacteristic
86#1990C2211yescharacteristic
87#1990C2211yescharacteristic
88#1990C2211yescharacteristic
89#1956C2211yescharacteristic
90#1949C2214yes—
91#1935C2214yes—
92#1927C2214yes—
93#1924C2212yes—
94#1920C2214yes—
95#1919C2214yes—
96#1917C2212yes—
97#1894C2214yes—
98#1873C2214yes—
99#1870C2212yes—
100#1863C2214yes—
101#1853C2214yes—
102#1853C2214yes—
103#1851C2212yes—
104#1834C2211yescharacteristic
105C4×C4⋊C8C2211yescharacteristic
106C4×C22⋊C8C2211yescharacteristic
107C4×C22⋊C8C2211yescharacteristic
108#1744C2211yescharacteristic
109C23×Q8—21no—
110C23×Q8—21no—
111C22×M16C2312yes—
112#533—24no—
113#533—24no—
114#533—42no—
115#533—42no—
116C2×C4⋊Q8—24no—
117C2×C4⋊Q8—24no—
118C2×C4⋊Q8—21no—
119C2×C4⋊Q8—21no—
120C2×C4⋊Q8—21no—
121C2×C4⋊Q8—21no—
122C2×C4⋊Q8—42no—
123C2×C4⋊Q8—42no—
124C2×C4⋊Q8C2311yescharacteristic
125C2×C4⋊Q8C2311yescharacteristic
126C2×C4⋊Q8C2311yescharacteristic
127C2×C4⋊Q8C2311yescharacteristic
128C2×C4⋊Q8C2312yes—
129C2×C4⋊Q8C2312yes—
130C2×C4⋊Q8C2311yescharacteristic
131C2×C4⋊Q8C2311yescharacteristic
132C2×#125—21no—
133C2×#125C2312yes—
134C2×C22⋊Q8—21no—
135C2×C22⋊Q8—21no—
136C2×C22⋊Q8—21no—
137C2×C22⋊Q8—21no—
138C2×C22⋊Q8—21no—
139C2×C22⋊Q8—21no—
140C2×C22⋊Q8C2312yes—
141C2×C22⋊Q8C2312yes—
142C2×C4×Q8—21no—
143C2×C4×Q8—21no—
144C2×C4×Q8—21no—
145C2×C4×Q8—21no—
146C2×C4×Q8—21no—
147C2×C4×Q8C2312yes—
148C2×C4×D4D411yescharacteristic
149C2×C4×D4D411yescharacteristic
150C2×C4×D4C2311yescharacteristic
151C2×#117—21no—
152C2×#117C2312yes—
153C22×C4⋊C4—21no—
154C22×C4⋊C4—21no—
155C22×C4⋊C4C2312yes—
156C22×C4⋊C4C2312yes—
157C22×C42C2311yescharacteristic
158C22×C42C2311yescharacteristic
159#501—216no—
160#500—24no—
161#500—24no—
162#498—24no—
163#498—24no—
164#498—42no—
165#498D418yescomplemented
166#487—24no—
167#487—24no—
168#487—42no—
169#483—216no—
170#475—216no—
171#431—24no—
172#428—216no—
173C2×#107C2314yes—
174C2×#107C2314yes—
175C2×#106C2314yes—
176C2×#106C2314yes—
177C2×#106C2314yes—
178C2×#106C2314yes—
179C2×C4⋊C8C2312yes—
180C2×C4⋊C8C2312yes—
181C2×#103C2314yes—
182C2×#103C2314yes—
183C2×#103C2314yes—
184C2×#103C2314yes—
185C2×C22⋊C8C2312yes—
186C2×C22⋊C8C2312yes—
187C2×C22⋊C8C2312yes—
188C4×M16—24no—
189C2×#97C2312yes—
190C2×C4×C8C2311yescharacteristic
191C2×C4×C8C2311yescharacteristic
192C2×C4×C8C2311yescharacteristic
193C2×C4×C8C2311yescharacteristic
194#400—22no—
195#400—22no—
196#398—22no—
197#398—22no—
198#398—22no—
199#398—22no—
200#396—22no—
201#396—22no—
202#395—22no—
203#395—22no—
204#393—22no—
205#393—22no—
206#391—21no—
207#391—21no—
208#391—21no—
209#391—21no—
210#391—21no—
211#391—21no—
212#391—21no—
213#391—21no—
214#391—21no—
215#391—21no—
216#391—21no—
217#391—22no—
218#391—22no—
219#391—22no—
220#391—22no—
221#391C2312yes—
222#391C2312yes—
223#391C2312yes—
224#389—21no—
225#389—21no—
226#389—21no—
227#389—21no—
228#389—21no—
229#389—21no—
230#389—21no—
231#389—22no—
232#389—22no—
233#389C2312yes—
234#389C2312yes—
235#389C2312yes—
236#389C2312yes—
237#389C2312yes—
238#388—22no—
239#388—22no—
240#387—22no—
241#387—22no—
242#387—22no—
243#387—22no—
244#386—22no—
245#386—22no—
246#385—22no—
247#385—22no—
248#384C2311yescharacteristic
249#384C2311yescharacteristic
250#382—21no—
251#382—21no—
252#382C2312yes—
253#382C2312yes—
254#380—21no—
255#380—21no—
256#380—21no—
257#380—21no—
258#380—21no—
259#380—22no—
260#380—22no—
261#380C2312yes—
262#380C2312yes—
263#380C2312yes—
264C4×C4⋊C4—21no—
265C4×C4⋊C4—21no—
266C4×C4⋊C4D411yescharacteristic
267C4×C4⋊C4D411yescharacteristic
268C4×C4⋊C4C2312yes—
269C4×C4⋊C4C2312yes—
270C4×C4⋊C4C2311yescharacteristic
271C4×C22⋊C4—22no—
272C4×C22⋊C4—22no—
273C4×C22⋊C4D411yescharacteristic
274C4×C22⋊C4D411yescharacteristic
275C4×C22⋊C4D411yescharacteristic
276C4×C22⋊C4D411yescharacteristic
277C4×C22⋊C4C2311yescharacteristic
278C4×C22⋊C4C2311yescharacteristic
279C43C2311yescharacteristic
280#340C2314yes—
281#340C2314yes—
282#340C2314yes—
283#340C2314yes—
284#340C2314yes—
285#340C2314yes—
286#336C2312yes—
287#336C2312yes—
288#336C2312yes—
289#336C2312yes—
290#336C2312yes—
291C22×Q8—21no—
292C22×Q8—21no—
293C22×Q8—21no—
294C22×Q8—21no—
295C22×Q8—21no—
296C22×Q8—22no—
297C22×Q8—22no—
298C22×Q8—44no—
299C22×Q8—44no—
300C22×Q8—44no—
301C22×Q8—44no—
302C22×Q8—82no—
303C22×Q8—82no—
304C22×Q8C2412yes—
305C22×D4C2×D411yescharacteristic
306C23×C4—22no—
307C23×C4—22no—
308C23×C4C2×D411yescharacteristic
309C23×C4C2×D411yescharacteristic
310C23×C4C2×D411yescharacteristic
311C23×C4C2×D411yescharacteristic
312C23×C4C2411yescharacteristic
313C23×C4C2411yescharacteristic
314C2×M16—24no—
315C2×M16—24no—
316C2×M16—24no—
317C22×C8C2412yes—
318C22×C8C2412yes—
319C22×C8C2412yes—
320C22×C8C2412yes—
321C4⋊Q8—24no—
322C4⋊Q8—24no—
323C4⋊Q8—22no—
324C4⋊Q8—22no—
325C4⋊Q8—22no—
326C4⋊Q8—22no—
327C4⋊Q8—22no—
328C4⋊Q8—22no—
329C4⋊Q8—22no—
330C4⋊Q8—22no—
331C4⋊Q8—22no—
332C4⋊Q8—22no—
333C4⋊Q8—42no—
334C4⋊Q8—42no—
335C4⋊Q8—44no—
336C4⋊Q8—44no—
337C4⋊Q8—44no—
338C4⋊Q8—44no—
339C4⋊Q8C2×D414yes—
340C4⋊Q8C2×D414yes—
341#125—24no—
342#125—42no—
343#125—44no—
344C22⋊Q8—28no—
345C22⋊Q8—24no—
346C22⋊Q8—42no—
347C22⋊Q8—44no—
348C22⋊Q8—44no—
349C22⋊Q8—44no—
350C22⋊Q8—44no—
351C22⋊Q8—82no—
352C22⋊Q8—82no—
353C4×Q8—24no—
354C4×Q8—42no—
355C4×Q8—44no—
356C4×Q8—44no—
357C4×Q8—44no—
358C4×Q8—82no—
359C4×Q8—82no—
360C4×D4—24no—
361C4×D4—24no—
362C4×D4—42no—
363#117—24no—
364#117—42no—
365#117—44no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—24no—
369C2×C4⋊C4—24no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—22no—
373C2×C4⋊C4—22no—
374C2×C4⋊C4—22no—
375C2×C4⋊C4—22no—
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—22no—
387C2×C4⋊C4—22no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—22no—
390C2×C4⋊C4—22no—
391C2×C4⋊C4—22no—
392C2×C4⋊C4—22no—
393C2×C4⋊C4—42no—
394C2×C4⋊C4—42no—
395C2×C4⋊C4—44no—
396C2×C4⋊C4—44no—
397C2×C4⋊C4C2×D411yescharacteristic
398C2×C4⋊C4C2×D411yescharacteristic
399C2×C4⋊C4C2×D411yescharacteristic
400C2×C4⋊C4C2412yes—
401C2×C4⋊C4C2412yes—
402C2×C4⋊C4C2412yes—
403C2×C4⋊C4C2412yes—
404C2×C4⋊C4C2412yes—
405C2×C4⋊C4C2412yes—
406C2×C4⋊C4C2412yes—
407C2×C22⋊C4—22no—
408C2×C22⋊C4—22no—
409C2×C22⋊C4—22no—
410C2×C22⋊C4—22no—
411C2×C22⋊C4—22no—
412C2×C22⋊C4—22no—
413C2×C22⋊C4C2×D411yescharacteristic
414C2×C22⋊C4C2×D411yescharacteristic
415C2×C22⋊C4C2×D411yescharacteristic
416C2×C22⋊C4C2×D411yescharacteristic
417C2×C22⋊C4C2×D411yescharacteristic
418C2×C22⋊C4C2×D411yescharacteristic
419C2×C42—22no—
420C2×C42—22no—
421C2×C42—22no—
422C2×C42—22no—
423C2×C42—22no—
424C2×C42—22no—
425C2×C42—22no—
426C2×C42—22no—
427C2×C42C2×D411yescharacteristic
428C2×C42C2×D411yescharacteristic
429C2×C42C2×D411yescharacteristic
430C2×C42C2×D411yescharacteristic
431C2×C42C2×D411yescharacteristic
432C2×C42C2×D411yescharacteristic
433C2×C42C2×D411yescharacteristic
434C2×C42C2×D411yescharacteristic
435C2×C42C2411yescharacteristic
436C2×C42C2411yescharacteristic
437C2×C42C2411yescharacteristic
438C2×C42C2411yescharacteristic
439C2×C42C2411yescharacteristic
440#107—28no—
441#107—28no—
442#106—28no—
443#106—28no—
444#106—44no—
445#106C2×D4116yes—
446C4⋊C8—24no—
447C4⋊C8—24no—
448#103—28no—
449#103—28no—
450#103—28no—
451#103—44no—
452C22⋊C8—24no—
453C22⋊C8—24no—
454C22⋊C8—24no—
455#97—24no—
456C4×C8—22no—
457C4×C8—22no—
458C4×C8—22no—
459C4×C8C2×D414yes—
460#95—22no—
461#95—22no—
462#95—22no—
463#95—22no—
464#95—22no—
465#95—22no—
466#95—22no—
467#95—22no—
468#95—22no—
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#95C2×D411yescharacteristic
481#95C2×D411yescharacteristic
482#95C2×D411yescharacteristic
483#95C2×D411yescharacteristic
484#95C2×D411yescharacteristic
485#95C2×D411yescharacteristic
486C24C22×D411yescharacteristic
487C24C22×D411yescharacteristic
488C2×Q8—24no—
489C2×Q8—24no—
490C2×Q8—22no—
491C2×Q8—22no—
492C2×Q8—24no—
493C2×Q8—24no—
494C2×Q8—44no—
495C2×Q8—44no—
496C2×Q8—44no—
497C2×Q8—42no—
498C2×Q8—42no—
499C2×Q8—42no—
500C2×Q8—42no—
501C2×Q8—44no—
502C2×Q8—42no—
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×Q8—816no—
515C2×D4—22no—
516C2×D4—22no—
517C2×D4—41no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—21no—
521C22×C4—21no—
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—21no—
535C22×C4—21no—
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—44no—
545C22×C4—44no—
546C22×C4—44no—
547C22×C4—44no—
548C22×C4—82no—
549C22×C4—82no—
550C22×C4#13714yes—
551C22×C4C22×D411yescharacteristic
552C22×C4C22×D411yescharacteristic
553C22×C4C22×D411yescharacteristic
554C22×C4C22×D411yescharacteristic
555C22×C4C22×D411yescharacteristic
556C22×C4C22×D411yescharacteristic
557C22×C4C22×D411yescharacteristic
558C22×C4C22×D411yescharacteristic
559C22×C4C22×D411yescharacteristic
560C22×C4C22×D411yescharacteristic
561C22×C4C22×D411yescharacteristic
562C22×C4C22×D411yescharacteristic
563C22×C42−1+414yes—
564C22×C4C2511yescharacteristic
565M16—216no—
566C2×C8—22no—
567C2×C8—22no—
568C2×C8—22no—
569C2×C8—22no—
570C2×C8—22no—
571C2×C8—22no—
572C2×C8—22no—
573C2×C8—22no—
574C2×C8—22no—
575C2×C8—22no—
576C2×C8C22×D414yes—
577C2×C82−1+414yes—
578C4⋊C4—22no—
579C4⋊C4—24no—
580C4⋊C4—24no—
581C4⋊C4—22no—
582C4⋊C4—22no—
583C4⋊C4—22no—
584C4⋊C4—22no—
585C4⋊C4—22no—
586C4⋊C4—22no—
587C4⋊C4—22no—
588C4⋊C4—22no—
589C4⋊C4—22no—
590C4⋊C4—24no—
591C4⋊C4—24no—
592C4⋊C4—41no—
593C4⋊C4—44no—
594C4⋊C4—44no—
595C4⋊C4—44no—
596C4⋊C4—44no—
597C4⋊C4—44no—
598C4⋊C4—44no—
599C4⋊C4—44no—
600C4⋊C4—44no—
601C4⋊C4—44no—
602C4⋊C4—44no—
603C4⋊C4—42no—
604C4⋊C4—42no—
605C4⋊C4—42no—
606C4⋊C4—42no—
607C4⋊C4—42no—
608C4⋊C4—42no—
609C4⋊C4—42no—
610C4⋊C4—42no—
611C4⋊C4—42no—
612C4⋊C4—82no—
613C4⋊C4—82no—
614C4⋊C4—82no—
615C4⋊C4—82no—
616C4⋊C4C22×D414yes—
617C4⋊C4C22×D414yes—
618C22⋊C4—22no—
619C22⋊C4—22no—
620C22⋊C4—22no—
621C22⋊C4—22no—
622C22⋊C4—41no—
623C22⋊C4—41no—
624C22⋊C4—44no—
625C22⋊C4—44no—
626C22⋊C4—44no—
627C22⋊C4—44no—
628C22⋊C4—82no—
629C22⋊C4—82no—
630C42—22no—
631C42—22no—
632C42—22no—
633C42—22no—
634C42—22no—
635C42—22no—
636C42—22no—
637C42—22no—
638C42—21no—
639C42—21no—
640C42—21no—
641C42—21no—
642C42—22no—
643C42—22no—
644C42—44no—
645C42—44no—
646C42—82no—
647C42—82no—
648C42C22×D412yes—
649C42H(5,𝔽2)12yes—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—21no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—21no—
659C23—21no—
660C23—21no—
661C23—21no—
662C23#53612yes—
663C23C2×#13712yes—
664C23C23×D411yescharacteristic
665Q8—48no—
666Q8—48no—
667Q8—44no—
668Q8—44no—
669Q8—88no—
670Q8—88no—
671Q8—84no—
672Q8—84no—
673Q8—84no—
674D4—44no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—24no—
680C2×C4—28no—
681C2×C4—24no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—24no—
690C2×C4—24no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
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—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—44no—
714C2×C4—44no—
715C2×C4—44no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—88no—
736C2×C4—88no—
737C2×C4#53612yes—
738C2×C4D4212yes—
739C2×C4D4212yes—
740C2×C4C2×#13712yes—
741C2×C4C2×#13712yes—
742C2×C4#57512yes—
743C2×C4#57712yes—
744C2×C4#57712yes—
745C2×C4C23×D411yescharacteristic
746C2×C4C2×H(5,𝔽2)11yescharacteristic
747C2×C4C2×2−1+412yes—
748C2×C4C2×2−1+412yes—
749C8—24no—
750C8—24no—
751C8—42no—
752C8—42no—
753C22—22no—
754C22—22no—
755C22—22no—
756C22—22no—
757C22—22no—
758C22—22no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—41no—
763C22—41no—
764C22—41no—
765C22—41no—
766C22—41no—
767C22C2×#53611yescharacteristic
768C22C2×D4211yescharacteristic
769C22#349911yescharacteristic
770C22C22×#13711yescharacteristic
771C22C2×#57511yescharacteristic
772C22C2×#57711yescharacteristic
773C22C2×#57711yescharacteristic
774C4—22no—
775C4—22no—
776C4—41no—
777C4—41no—
778C4—41no—
779C4—41no—
780C4—44no—
781C4—41no—
782C4—41no—
783C4—44no—
784C4—41no—
785C4—41no—
786C4—82no—
787C4—82no—
788C4—82no—
789C4—82no—
790C4—82no—
791C4—82no—
792C4#326614yes—
793C4#327514yes—
794C4#348612yes—
795C4#355212yes—
796C2—42no—
797C2—42no—
798C2#3767511yescharacteristic
799C2#6086511yescharacteristic
800C2#6088111yescharacteristic
801C2C2×#326611yescharacteristic
802C2C2×#327511yescharacteristic
803C2#6247811yescharacteristic
804C2#6248311yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC22×D4C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C42×D4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3229C2semidirect
2. C2×#3165C2semidirect
5. #33049C2semidirect
6. #30969C2semidirect
7. #30793C2semidirect
8. #30281C2semidirect
9. #29878C2semidirect
10. #28688C2semidirect
11. #28653C2semidirect
12. #26356C2semidirect
14. #25904C2semidirect
15. #25811C2semidirect
16. #25811C2semidirect
17. #25674C2semidirect
18. #22246C2semidirect
165. #498D4semidirect

Maximal subgroups

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

subgroupindex
C2×#32292
C2×#31652
#361292
#330492
#309692
#307932
#302812
#298782
#286882
#286532
#263562
#261492
#259042
#258112
#256742
#222462
#211022