Finite Group Databasebeta

← #6394012

Subgroups — #6394012

Order 512.

3012 conjugacy classes of subgroups.

The subgroup lattice has 808 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3515C211yesmaximal, characteristic
2C2×#2971C211yesmaximal, characteristic, complemented
3#34188C211yesmaximal, characteristic, complemented
4#22521C212yesmaximal, complemented
5#22519C212yesmaximal, complemented
6#22502C212yesmaximal, complemented
7#22501C214yesmaximal, complemented
8#22500C212yesmaximal, complemented
9#22499C214yesmaximal, complemented
10#21868C212yesmaximal, complemented
11#21867C211yesmaximal, characteristic, complemented
12#21839C211yesmaximal, characteristic, complemented
13#21838C212yesmaximal, complemented
14#21403C211yesmaximal, characteristic, complemented
15#21403C212yesmaximal, complemented
16#21325C212yesmaximal, complemented
17#21322C211yesmaximal, characteristic, complemented
18#3515—28no—
19#3515C4116yescomplemented
20C2×#557C2211yescharacteristic
21C2×#554C2211yescharacteristic
22C2×#554C2211yescharacteristic
23C2×#553C2212yes—
24C2×#552—22no—
25C2×#552—21no—
26C2×#552C2212yes—
27C2×#547—21no—
28C2×#547C2211yescharacteristic
29C2×#541—21no—
30C2×#539—22no—
31C2×#533C2211yescharacteristic
32C2×#529C2211yescharacteristic
33C2×#529C2212yes—
34C22×#125C2212yes—
35C2×#520—21no—
36C2×C4×#41C2211yescharacteristic
37#2971—28no—
38C2×C8×Q8C2212yes—
39C2×#436C2214yes—
40C2×#436C2212yes—
41C2×#432C2212yes—
42C2×#432C2211yescharacteristic
43C2×C4×M16C2211yescharacteristic
44C2×C4×M16C2212yes—
45#2355—21no—
46#2355C2212yes—
47#2354—21no—
48#2354C2212yes—
49#2352—22no—
50#2352C2214yes—
51#2314—22no—
52#2311—21no—
53#2285C2212yes—
54#2285C2211yescharacteristic
55#2285C2212yes—
56C2×#384C2211yescharacteristic
57#2274—21no—
58#1992C2212yes—
59#1992C2212yes—
60#1992C2211yescharacteristic
61#1992C2212yes—
62#1992C2212yes—
63#1992C2211yescharacteristic
64#1992C2212yes—
65#1991C2214yes—
66#1991C2214yes—
67#1990C2212yes—
68#1990C2212yes—
69#1989C2214yes—
70#1989C2214yes—
71#1988C2212yes—
72#1987C2212yes—
73#1959C2212yes—
74#1959C2211yescharacteristic
75#1959C2211yescharacteristic
76#1895C2214yes—
77#1895C2212yes—
78#1894C2212yes—
79#1894C2214yes—
80#1875C2214yes—
81#1874C2212yes—
82#1873C2214yes—
83#1872C2212yes—
84#1825C2214yes—
85#1824C2214yes—
86#1823C2214yes—
87#1805C2214yes—
88#1804C2214yes—
89#1803C2212yes—
90#1802C2212yes—
91C4×#103C2214yes—
92C4×#103C2212yes—
93C4×#102C2212yes—
94C4×#102C2214yes—
95#1736C2214yes—
96#1736C2214yes—
97#1736C2214yes—
98C22×#41—21no—
99C22×#41D411yescharacteristic
100C22×M16C2312yes—
101C22×M16C2314yes—
102#557—24no—
103#557C2×C418yescomplemented
104#554—24no—
105#554—24no—
106#554C2×C418yescomplemented
107#554C2×C418yescomplemented
108#553—28no—
109#553C2×C4116yes—
110#552—28no—
111#552—232no—
112#552—216no—
113#552C2×C4116yes—
114#547—216no—
115#547—24no—
116#547C2×C418yescomplemented
117#541—216no—
118#539—232no—
119#533—24no—
120#533C2×C418yes—
121C2×C4⋊Q8—21no—
122C2×C4⋊Q8C2311yescharacteristic
123C2×C4⋊Q8C2311yescharacteristic
124#529—28no—
125#529—24no—
126#529C2×C418yes—
127#529C2×C4116yescomplemented
128C2×#126—22no—
129C2×#126—22no—
130C2×#126—22no—
131C2×#126—21no—
132C2×#125—22no—
133C2×#125—22no—
134C2×#125—21no—
135C2×#125—22no—
136C2×#125—22no—
137C2×#125—28no—
138C2×#125C2×C4116yescomplemented
139C2×#125C2311yescharacteristic
140C2×#125C2312yes—
141C2×#125C2312yes—
142C2×#125C2312yes—
143C2×#124C2311yescharacteristic
144C2×#123—22no—
145C2×#123—21no—
146C2×#123—22no—
147C2×#123—22no—
148C2×#123—22no—
149C2×C22⋊Q8—21no—
150C2×C22⋊Q8—21no—
151C2×C22⋊Q8—21no—
152C2×C22⋊Q8—22no—
153C2×C22⋊Q8—21no—
154C2×C22⋊Q8—22no—
155C2×C22⋊Q8C2311yescharacteristic
156C2×C22⋊Q8C2312yes—
157C2×#121—22no—
158C2×#121C2311yescharacteristic
159C2×#121C2312yes—
160#520—216no—
161C4×#41C2×C418yes—
162C4×#41D418yes—
163C2×C4×Q8—21no—
164C2×C4×Q8—21no—
165C2×C4×Q8—21no—
166C2×C4×Q8D411yescharacteristic
167C2×C4×Q8C2311yescharacteristic
168C2×C4×Q8C2312yes—
169C2×C4×Q8C2311yescharacteristic
170C2×C4×D4—21no—
171C2×C4×D4—22no—
172C2×C4×D4—21no—
173C2×C4×D4—22no—
174C2×C4×D4D412yes—
175C2×C4×D4D411yescharacteristic
176C2×C4×D4C2311yescharacteristic
177C2×C4×D4C2312yes—
178C2×C4×D4C2312yes—
179C2×C4×D4C2311yescharacteristic
180C2×#117—21no—
181C2×#117—22no—
182C2×#117—22no—
183C2×#117—21no—
184C2×#117—22no—
185C2×#117D412yes—
186C2×#117D411yescharacteristic
187C2×#117C2312yes—
188C2×#117C2314yes—
189C22×C4⋊C4—22no—
190C22×C4⋊C4—22no—
191C22×C4⋊C4—21no—
192C22×C4⋊C4—21no—
193C22×C4⋊C4—21no—
194C22×C4⋊C4C2312yes—
195C22×C4⋊C4C2312yes—
196C22×C4⋊C4C2312yes—
197C22×C42C2312yes—
198C22×C42C2311yescharacteristic
199C8×Q8—28no—
200#436—28no—
201#436—216no—
202#432—28no—
203#432—24no—
204C2×C4⋊C8C2312yes—
205C2×C4⋊C8C2314yes—
206C2×#103C2312yes—
207C2×#103C2314yes—
208C2×#103C2312yes—
209C2×#102C2312yes—
210C2×#102C2314yes—
211C2×#102C2312yes—
212C2×C22⋊C8C2314yes—
213C2×C22⋊C8C2312yes—
214C4×M16—28no—
215C4×M16—24no—
216C2×#97C2311yescharacteristic
217C2×#97C2311yescharacteristic
218C2×#97C2312yes—
219C2×C4×C8C2312yes—
220C2×C4×C8C2314yes—
221#391—22no—
222#390—22no—
223#388—24no—
224#388—24no—
225#387—24no—
226#387—24no—
227#386—24no—
228#384—21no—
229#384—21no—
230#384C2312yes—
231#384C2312yes—
232#384C2311yescharacteristic
233#384C2311yescharacteristic
234#382—21no—
235#382—22no—
236#382C2314yes—
237#380—22no—
238#380—22no—
239#380—21no—
240#380—22no—
241#380C2314yes—
242#380C2312yes—
243C4×C4⋊C4—22no—
244C4×C4⋊C4—22no—
245C4×C4⋊C4—22no—
246C4×C4⋊C4—22no—
247C4×C4⋊C4—22no—
248C4×C4⋊C4—21no—
249C4×C4⋊C4C2314yes—
250C4×C4⋊C4C2312yes—
251C4×C22⋊C4—24no—
252#340C2314yes—
253#340C2314yes—
254#340C2314yes—
255#340C2314yes—
256#340C2314yes—
257#340C2314yes—
258#340C2312yes—
259#340C2314yes—
260#340C2312yes—
261#340C2314yes—
262#340C2314yes—
263#340C2312yes—
264#340C2314yes—
265#340C2312yes—
266C2×#41—28no—
267C2×#41—42no—
268C2×#41—42no—
269C2×#41—44no—
270C2×#41—44no—
271C2×#41C22⋊C418yes—
272C22×Q8—21no—
273C22×Q8—21no—
274C22×Q8C2×D411yescharacteristic
275C22×Q8C2411yescharacteristic
276C22×D4—22no—
277C22×D4—21no—
278C22×D4C2×D411yescharacteristic
279C22×D4C2×D412yes—
280C22×D4C2411yescharacteristic
281C23×C4—22no—
282C23×C4—22no—
283C23×C4—21no—
284C23×C4—22no—
285C23×C4—22no—
286C23×C4C2×D411yescharacteristic
287C23×C4C2×D412yes—
288C23×C4C2×D412yes—
289C23×C4C2×D411yescharacteristic
290C23×C4C2411yescharacteristic
291C23×C4C2412yes—
292C2×M16—28no—
293C2×M16—24no—
294C2×M16—24no—
295C2×M16—28no—
296C2×M16—42no—
297C2×M16—44no—
298C22×C8C2414yes—
299C22×C8C2412yes—
300C22×C8C2412yes—
301C4⋊Q8—28no—
302C4⋊Q8—22no—
303C4⋊Q8—22no—
304C4⋊Q8C22×C414yes—
305C4⋊Q8C22×C414yes—
306#126—216no—
307#126—216no—
308#126—28no—
309#126—216no—
310#125—216no—
311#125—216no—
312#125—28no—
313#125—216no—
314#125—216no—
315#125—22no—
316#125—24no—
317#125—24no—
318#125—24no—
319#125C22×C414yes—
320#125C22×C418yes—
321#125C22×C418yes—
322#125C22×C418yes—
323#124—22no—
324#124C22×C414yes—
325#123—216no—
326#123—28no—
327#123—216no—
328#123—216no—
329#123—216no—
330C22⋊Q8—28no—
331C22⋊Q8—28no—
332C22⋊Q8—28no—
333C22⋊Q8—22no—
334C22⋊Q8—24no—
335C22⋊Q8—216no—
336C22⋊Q8—28no—
337C22⋊Q8—216no—
338C22⋊Q8C22×C414yes—
339C22⋊Q8C22×C418yes—
340#121—216no—
341#121—24no—
342#121—22no—
343#121C22×C414yes—
344#121C22×C418yes—
345C4×Q8—28no—
346C4×Q8—28no—
347C4×Q8—28no—
348C4×Q8—24no—
349C4×Q8—22no—
350C4×Q8C22⋊C418yes—
351C4×Q8C22×C414yes—
352C4×Q8C22×C418yes—
353C4×Q8C22×C414yes—
354C4×Q8C2×D414yes—
355C4×D4—28no—
356C4×D4—216no—
357C4×D4—28no—
358C4×D4—216no—
359C4×D4—22no—
360C4×D4—24no—
361C4×D4C22⋊C418yes—
362C4×D4C22⋊C4116yes—
363C4×D4C22×C414yes—
364C4×D4C22×C418yes—
365C4×D4C22×C414yes—
366C4×D4C22×C418yes—
367C4×D4C2×D414yes—
368C4×D4C2×D418yes—
369#117—24no—
370#117—216no—
371#117—28no—
372#117—216no—
373#117—44no—
374#117—44no—
375#117—44no—
376#117—84no—
377#117C22⋊C418yes—
378#117C22⋊C4116yes—
379#117C22×C418yes—
380C2×C4⋊C4—216no—
381C2×C4⋊C4—216no—
382C2×C4⋊C4—22no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—22no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—22no—
388C2×C4⋊C4—22no—
389C2×C4⋊C4—22no—
390C2×C4⋊C4—22no—
391C2×C4⋊C4—22no—
392C2×C4⋊C4—22no—
393C2×C4⋊C4—24no—
394C2×C4⋊C4—24no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—22no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—21no—
399C2×C4⋊C4—22no—
400C2×C4⋊C4—28no—
401C2×C4⋊C4—22no—
402C2×C4⋊C4—22no—
403C2×C4⋊C4—22no—
404C2×C4⋊C4—21no—
405C2×C4⋊C4—21no—
406C2×C4⋊C4—21no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4—22no—
409C2×C4⋊C4—22no—
410C2×C4⋊C4—44no—
411C2×C4⋊C4—44no—
412C2×C4⋊C4—82no—
413C2×C4⋊C4C22×C418yes—
414C2×C4⋊C4C22×C418yes—
415C2×C4⋊C4C2×D411yescharacteristic
416C2×C4⋊C4C2×D412yes—
417C2×C4⋊C4C2×D411yescharacteristic
418C2×C4⋊C4C2×D412yes—
419C2×C4⋊C4C2414yes—
420C2×C4⋊C4C2412yes—
421C2×C4⋊C4C2412yes—
422C2×C4⋊C4C2411yescharacteristic
423C2×C4⋊C4C2411yescharacteristic
424C2×C4⋊C4C2412yes—
425C2×C4⋊C4C2412yes—
426C2×C22⋊C4—22no—
427C2×C22⋊C4—22no—
428C2×C22⋊C4—21no—
429C2×C22⋊C4—21no—
430C2×C22⋊C4—21no—
431C2×C22⋊C4—21no—
432C2×C22⋊C4—22no—
433C2×C22⋊C4—22no—
434C2×C22⋊C4—21no—
435C2×C22⋊C4—22no—
436C2×C22⋊C4—24no—
437C2×C22⋊C4—24no—
438C2×C22⋊C4C2×D412yes—
439C2×C22⋊C4C2×D412yes—
440C2×C22⋊C4C2×D412yes—
441C2×C42—22no—
442C2×C42—22no—
443C2×C42—21no—
444C2×C42—22no—
445C2×C42—24no—
446C2×C42—24no—
447C2×C42C22×C418yes—
448C2×C42C22×C414yes—
449C2×C42C2×D412yes—
450C2×C42C2×D411yescharacteristic
451C2×C42C2×D411yescharacteristic
452C2×C42C2×D412yes—
453C2×C42C2×D418yes—
454C2×C42C2×D414yes—
455C2×C42C2412yes—
456C2×C42C2411yescharacteristic
457C2×C42C2411yescharacteristic
458C4⋊C8—28no—
459C4⋊C8—24no—
460#103—24no—
461#103—44no—
462#103—42no—
463#102—24no—
464#102—44no—
465#102—42no—
466C22⋊C8—28no—
467C22⋊C8—24no—
468#97—22no—
469#97—22no—
470#97—24no—
471C4×C8—28no—
472C4×C8—24no—
473#95—24no—
474#95—24no—
475#95—24no—
476#95—22no—
477#95—24no—
478#95—22no—
479C24—21no—
480C24C22×D412yes—
481C24C22×D411yescharacteristic
482#41—416no—
483#41—432no—
484C2×Q8—24no—
485C2×Q8—24no—
486C2×Q8—22no—
487C2×Q8—22no—
488C2×Q8—21no—
489C2×Q8—22no—
490C2×Q8—22no—
491C2×Q8—42no—
492C2×Q8—42no—
493C2×Q8—81no—
494C2×Q8—81no—
495C2×Q8C2×C22⋊C414yes—
496C2×Q8C23×C412yes—
497C2×D4—28no—
498C2×D4—24no—
499C2×D4—22no—
500C2×D4—22no—
501C2×D4—21no—
502C2×D4—22no—
503C2×D4—22no—
504C2×D4—42no—
505C2×D4—42no—
506C2×D4—44no—
507C2×D4—44no—
508C2×D4—81no—
509C2×D4—81no—
510C2×D4C2×C22⋊C414yes—
511C2×D4C2×C22⋊C418yes—
512C2×D4C23×C412yes—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—24no—
517C22×C4—22no—
518C22×C4—24no—
519C22×C4—28no—
520C22×C4—21no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—28no—
526C22×C4—24no—
527C22×C4—28no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—24no—
531C22×C4—41no—
532C22×C4—42no—
533C22×C4—42no—
534C22×C4—41no—
535C22×C4—42no—
536C22×C4—42no—
537C22×C4—44no—
538C22×C4—44no—
539C22×C4—42no—
540C22×C4—42no—
541C22×C4—44no—
542C22×C4—82no—
543C22×C4—82no—
544C22×C4—82no—
545C22×C4—82no—
546C22×C4—82no—
547C22×C4—82no—
548C22×C4C2×C22⋊C414yes—
549C22×C4C2×C22⋊C418yes—
550C22×C4C2×C22⋊C418yes—
551C22×C4C2×C22⋊C414yes—
552C22×C4C23×C414yes—
553C22×C4C23×C412yes—
554C22×C4C22×D412yes—
555C22×C4C22×D412yes—
556C22×C4C22×D412yes—
557C22×C4C22×D411yescharacteristic
558C22×C4C22×D411yescharacteristic
559C22×C4C22×D411yescharacteristic
560C22×C4C22×D411yescharacteristic
561C22×C4C22×D414yes—
562C22×C4C22×D412yes—
563C22×C4C22×D411yescharacteristic
564C22×C4C2511yescharacteristic
565M16—48no—
566M16—416no—
567C2×C8—22no—
568C2×C8—22no—
569C2×C8—24no—
570C2×C8—22no—
571C2×C8—24no—
572C2×C8—22no—
573C2×C8—24no—
574C2×C8—22no—
575C2×C82−1+414yes—
576C4⋊C4—28no—
577C4⋊C4—24no—
578C4⋊C4—24no—
579C4⋊C4—28no—
580C4⋊C4—24no—
581C4⋊C4—28no—
582C4⋊C4—28no—
583C4⋊C4—28no—
584C4⋊C4—28no—
585C4⋊C4—28no—
586C4⋊C4—28no—
587C4⋊C4—24no—
588C4⋊C4—28no—
589C4⋊C4—24no—
590C4⋊C4—24no—
591C4⋊C4—28no—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—22no—
595C4⋊C4—22no—
596C4⋊C4—22no—
597C4⋊C4—22no—
598C4⋊C4—24no—
599C4⋊C4—22no—
600C4⋊C4—24no—
601C4⋊C4—22no—
602C4⋊C4—42no—
603C4⋊C4—44no—
604C4⋊C4—44no—
605C4⋊C4—42no—
606C4⋊C4—42no—
607C4⋊C4—42no—
608C4⋊C4—44no—
609C4⋊C4—82no—
610C4⋊C4—82no—
611C4⋊C4C2×C22⋊C414yes—
612C4⋊C4C2×C22⋊C418yes—
613C4⋊C4C2×C22⋊C414yes—
614C4⋊C4C2×C22⋊C418yes—
615C4⋊C4C23×C412yes—
616C4⋊C4C23×C412yes—
617C4⋊C4C23×C414yes—
618C4⋊C4C23×C414yes—
619C22⋊C4—28no—
620C22⋊C4—28no—
621C22⋊C4—24no—
622C22⋊C4—24no—
623C22⋊C4—24no—
624C22⋊C4—24no—
625C22⋊C4—28no—
626C22⋊C4—28no—
627C22⋊C4—24no—
628C22⋊C4—44no—
629C22⋊C4—84no—
630C22⋊C4—84no—
631C22⋊C4C2×C22⋊C418yes—
632C22⋊C4C2×C22⋊C418yes—
633C22⋊C4C2×C22⋊C418yes—
634C42—28no—
635C42—28no—
636C42—24no—
637C42—44no—
638C42—84no—
639C42—84no—
640C42C2×C22⋊C418yes—
641C42C2×C22⋊C414yes—
642C42C2×C22⋊C414yes—
643C42C2×C22⋊C418yes—
644C42C23×C412yes—
645C42C23×C414yes—
646C42C23×C412yes—
647C42C22×D414yes—
648C42C22×D412yes—
649C42C22×D412yes—
650C23—22no—
651C23—21no—
652C23—22no—
653C23—21no—
654C23—22no—
655C23—21no—
656C23—22no—
657C23—21no—
658C23—21no—
659C23—21no—
660C23—22no—
661C23—22no—
662C23—22no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23—41no—
669C23C22×C22⋊C412yes—
670C23C22×C22⋊C414yes—
671C23C23×D411yescharacteristic
672Q8—28no—
673Q8—24no—
674Q8—48no—
675Q8—42no—
676Q8—84no—
677D4—28no—
678D4—24no—
679D4—48no—
680D4—416no—
681D4—42no—
682D4—84no—
683C2×C4—22no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—22no—
688C2×C4—21no—
689C2×C4—22no—
690C2×C4—21no—
691C2×C4—22no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—28no—
698C2×C4—24no—
699C2×C4—28no—
700C2×C4—24no—
701C2×C4—28no—
702C2×C4—22no—
703C2×C4—24no—
704C2×C4—24no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—48no—
708C2×C4—44no—
709C2×C4—48no—
710C2×C4—416no—
711C2×C4—41no—
712C2×C4—42no—
713C2×C4—41no—
714C2×C4—42no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—48no—
722C2×C4—42no—
723C2×C4—44no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—44no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—44no—
731C2×C4—88no—
732C2×C4—88no—
733C2×C4—164no—
734C2×C4C22×C22⋊C412yes—
735C2×C4C22×C22⋊C414yes—
736C2×C4C22×C22⋊C412yes—
737C2×C4C22×C22⋊C412yes—
738C2×C4C22×C22⋊C414yes—
739C2×C4C22×C22⋊C412yes—
740C2×C4C22×C22⋊C414yes—
741C2×C4C22×C22⋊C412yes—
742C2×C4#57512yes—
743C2×C4#57512yes—
744C2×C4C24×C411yescharacteristic
745C2×C4C23×D411yescharacteristic
746C2×C4C2×2−1+412yes—
747C2×C4#58512yes—
748C8—24no—
749C8—44no—
750C8—42no—
751C22—22no—
752C22—24no—
753C22—24no—
754C22—22no—
755C22—24no—
756C22—22no—
757C22—42no—
758C22—41no—
759C22—42no—
760C22—41no—
761C22—41no—
762C22—42no—
763C22—42no—
764C22—41no—
765C22—42no—
766C22—42no—
767C22—42no—
768C22—81no—
769C22—81no—
770C22—81no—
771C22—81no—
772C22C23×C22⋊C411yescharacteristic
773C22#349911yescharacteristic
774C22#350011yescharacteristic
775C22C2×#57511yescharacteristic
776C22C2×#57511yescharacteristic
777C22#358511yescharacteristic
778C22#358611yescharacteristic
779C4—22no—
780C4—24no—
781C4—22no—
782C4—24no—
783C4—22no—
784C4—24no—
785C4—22no—
786C4—42no—
787C4—44no—
788C4—42no—
789C4—44no—
790C4—42no—
791C4—82no—
792C4—84no—
793C4—82no—
794C4#289614yes—
795C4C4×2−1+412yes—
796C4#348912yes—
797C2—42no—
798C2—44no—
799C2—82no—
800C2#3425911yescharacteristic
801C2C2×#289611yescharacteristic
802C2#6008911yescharacteristic
803C2#6251111yescharacteristic
804C2#6251211yescharacteristic
805C2#6259011yescharacteristic
806C2#6259111yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutatorC2×C4C24×C4
Frattini, cosocleC22×C4C25
prime radicalC2×#3515C2
LCSG ▷ C2×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
2. C2×#2971C2semidirect
3. #34188C2semidirect
4. #22521C2semidirect
5. #22519C2semidirect
6. #22502C2semidirect
7. #22501C2semidirect
8. #22500C2semidirect
9. #22499C2semidirect
10. #21868C2semidirect
11. #21867C2semidirect
12. #21839C2semidirect
13. #21838C2semidirect
14. #21403C2semidirect
15. #21403C2semidirect
16. #21325C2semidirect
17. #21322C2semidirect
19. #3515C4semidirect
103. #557C2×C4semidirect
106. #554C2×C4semidirect
107. #554C2×C4semidirect
116. #547C2×C4semidirect
127. #529C2×C4semidirect
138. C2×#125C2×C4semidirect

Maximal subgroups

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

subgroupindex
C2×#35152
C2×#29712
#341882
#225212
#225192
#225022
#225012
#225002
#224992
#218682
#218672
#218392
#218382
#214032
#213252
#213222