Finite Group Databasebeta

← #10577302

Subgroups — #10577302

Order 512.

7766 conjugacy classes of subgroups.

The subgroup lattice has 1077 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#62773C211yesmaximal, characteristic
2C22×D4×Q8C211yesmaximal, characteristic, complemented
3#61602C218yesmaximal, complemented
4#61593C218yesmaximal, complemented
5#61584C214yesmaximal, complemented
6#61574C218yesmaximal, complemented
7#61563C212yesmaximal, complemented
8#61562C212yesmaximal, complemented
9#61157C218yesmaximal, complemented
10D4×#137C218yesmaximal, complemented
11#60800C212yesmaximal, complemented
12#60751C214yesmaximal, complemented
13#60560C212yesmaximal, complemented
14C2×#3004C214yesmaximal, complemented
15#60230C211yesmaximal, characteristic, complemented
16C24×Q8C2212yescomplemented
17C22×#137C2218yescomplemented
18#3520C2214yes—
19#3519C2214yes—
20#3513—24no—
21#3506C2212yes—
22#3505C2214yes—
23#3501C2211yescharacteristic
24#3496C2211yescharacteristic
25#3492—21no—
26#3490—22no—
27#3484—21no—
28#3481—24no—
29#3475C2214yes—
30D4×#41C2214yes—
31C2×D4×Q8—21no—
32C2×D4×Q8—22no—
33C2×D4×Q8—21no—
34C2×D4×Q8—24no—
35C2×D4×Q8—24no—
36C2×D4×Q8C2212yes—
37C2×D4×Q8C2214yescomplemented
38C2×D4×Q8C2218yescomplemented
39C2×D4×Q8C2212yescomplemented
40C2×D4×Q8C2218yescomplemented
41#3460—21no—
42#3459—22no—
43#3444C2212yes—
44C22×C4⋊Q8—21no—
45C22×C4⋊Q8C2211yescharacteristic, complemented
46C2×#525C2214yes—
47C22×C22⋊Q8—22no—
48C22×C22⋊Q8C2212yescomplemented
49C4×H(5,𝔽2)—21no—
50C22×C4×Q8C2211yescharacteristic, complemented
51C22×C4×D4—21no—
52C22×C4×D4C2211yescharacteristic
53#3329C22116yescomplemented
54#3328C22116yescomplemented
55#3320C22132yescomplemented
56#3312C22132yescomplemented
57#3299C22116yescomplemented
58#3298C22116yescomplemented
59D4×Q16C22116yescomplemented
60D4×SD16C22116yescomplemented
61#3278C22116yescomplemented
62#3276C22116yescomplemented
63#3270C22132yescomplemented
64#3266C22132yescomplemented
65#3218C2218yescomplemented
66#3218C2218yescomplemented
67#3209C2214yescomplemented
68#3209C2214yescomplemented
69#3206C2214yescomplemented
70#3206C2214yescomplemented
71#3196C22116yescomplemented
72#3195C2218yescomplemented
73#3193C2218yescomplemented
74#3190C22116yescomplemented
75#3189C2218yescomplemented
76#3187C2218yescomplemented
77#3152C2214yescomplemented
78#3139C2214yescomplemented
79#3117C2218yescomplemented
80#3113C2214yescomplemented
81#3112C2214yescomplemented
82#3108C2218yescomplemented
83#3104C2214yescomplemented
84#3103C2214yescomplemented
85#3095C2218yescomplemented
86#3092C2214yescomplemented
87#3078C2214yescomplemented
88#3056C22116yescomplemented
89#3039C2218yescomplemented
90#3037C2214yescomplemented
91#3007C2218yescomplemented
92#3004C2218yescomplemented
93#3004C2214yescomplemented
94#3004C22116yescomplemented
95#3004C22116yescomplemented
96#3004C22116yescomplemented
97C2×#451C2218yescomplemented
98C2×#451C2218yescomplemented
99C2×#448C2218yescomplemented
100C2×#448C2218yescomplemented
101#2975C2212yescomplemented
102#2974C2218yescomplemented
103#2973C2214yescomplemented
104#2972C2212yes—
105C4×#137C2218yescomplemented
106D4×M16C2218yescomplemented
107#2920C2212yescomplemented
108C2×#419C2218yescomplemented
109C2×#407C2214yescomplemented
110C2×H(5,𝔽2)—21no—
111C22×#41C2314yes—
112C23×Q8—22no—
113C23×Q8—22no—
114C23×Q8—24no—
115C23×Q8—24no—
116C23×Q8—22no—
117C23×Q8—416no—
118C23×Q8C2311yescharacteristic
119C23×Q8C2318yes—
120C23×Q8C2312yes—
121C23×Q8C2314yes—
122C23×Q8C2318yes—
123C23×Q8C2314yes—
124C23×D4D411yescharacteristic
125C24×C4—22no—
126C24×C4C2312yes—
127C2×#137—432no—
128C2×#137C2318yes—
129C2×#137C23116yes—
130C2×#137C23132yescomplemented
131C22×Q16C23116yescomplemented
132C22×SD16C23116yescomplemented
133C22×M16C2318yes—
134#559—24no—
135#556C2314yes—
136#555C2314yes—
137#554—24no—
138#554—24no—
139#554C2314yes—
140#553—28no—
141#553—24no—
142#553—24no—
143#553C2318yes—
144#552—24no—
145#552C2318yes—
146#551—28no—
147#551—28no—
148#551—28no—
149#550C2314yes—
150D4×Q8—28no—
151D4×Q8—28no—
152D4×Q8—28no—
153D4×Q8—216no—
154D4×Q8—28no—
155D4×Q8—216no—
156D4×Q8—28no—
157D4×Q8—216no—
158D4×Q8—28no—
159D4×Q8C23116yes—
160D4×Q8C23116yes—
161D4×Q8C23132yes—
162D4×Q8C2314yes—
163#548C2318yes—
164#547—24no—
165#547C2314yes—
166#547C2314yes—
167#546—24no—
168#546—24no—
169#546—24no—
170#546—28no—
171#546—28no—
172#546C2318yes—
173D42—24no—
174D42—24no—
175D42C2314yes—
176#544—21no—
177#543—22no—
178#542—24no—
179#540—24no—
180#539—28no—
181#539—24no—
182#538—28no—
183#538—24no—
184#538—24no—
185#537—21no—
186#535—22no—
187#534—24no—
188#534—22no—
189#533C2312yes—
190#533C2312yes—
191#533C2312yes—
192#532—24no—
193#532C2312yes—
194#532C2312yes—
195#532C2312yes—
196C2×C4⋊Q8—22no—
197C2×C4⋊Q8—22no—
198C2×C4⋊Q8—24no—
199C2×C4⋊Q8—28no—
200C2×C4⋊Q8—28no—
201C2×C4⋊Q8—21no—
202C2×C4⋊Q8—22no—
203C2×C4⋊Q8—21no—
204C2×C4⋊Q8—22no—
205C2×C4⋊Q8C2314yes—
206C2×C4⋊Q8C2312yes—
207C2×C4⋊Q8C2314yes—
208C2×C4⋊Q8C2312yes—
209#529—28no—
210#529—24no—
211#529—22no—
212#529—22no—
213#529—22no—
214#529—22no—
215#529C2314yes—
216#529C2314yes—
217#525—24no—
218#525—24no—
219#525—24no—
220#525—24no—
221#525—22no—
222#525—22no—
223#525—28no—
224#525C2314yes—
225#525C2318yes—
226#525C2318yes—
227#525C2318yes—
228C2×#123—24no—
229C2×C22⋊Q8—22no—
230C2×C22⋊Q8—24no—
231C2×C22⋊Q8—24no—
232C2×C22⋊Q8—22no—
233C2×C22⋊Q8—24no—
234C2×C22⋊Q8—24no—
235C2×C22⋊Q8—24no—
236C2×C22⋊Q8—24no—
237C2×C22⋊Q8—216no—
238C2×C22⋊Q8—216no—
239C2×C22⋊Q8C2318yes—
240C2×C22⋊Q8C2314yes—
241C2×C22⋊Q8C2318yes—
242C2×C22⋊Q8C2314yes—
243C2×C22⋊Q8C2314yes—
244C2×C22⋊Q8C2314yes—
245C2×#121C2314yes—
246C2×#121C2314yes—
247C2×#120—24no—
248#520—24no—
249#520—22no—
250#518—21no—
251#518—24no—
252#518—24no—
253C4×#41—24no—
254C4×#41—22no—
255C4×#41—22no—
256C4×#41C2314yes—
257C2×C4×Q8—21no—
258C2×C4×Q8—22no—
259C2×C4×Q8—22no—
260C2×C4×Q8—21no—
261C2×C4×Q8C2314yes—
262C2×C4×Q8C2312yes—
263C2×C4×Q8C2314yes—
264C2×C4×Q8C2312yes—
265C2×C4×D4—22no—
266C2×C4×D4—24no—
267C2×C4×D4—22no—
268C2×C4×D4—28no—
269C2×C4×D4—28no—
270C2×C4×D4—24no—
271C2×C4×D4—24no—
272C2×C4×D4—24no—
273C2×C4×D4D411yescharacteristic
274C2×C4×D4D412yes—
275C2×C4×D4D411yescharacteristic
276C2×C4×D4D414yes—
277C2×C4×D4D414yes—
278C2×C4×D4C2314yes—
279C2×C4×D4C2311yescharacteristic
280C2×C4×D4C2312yes—
281C2×C4×D4C2314yes—
282C2×C4×D4C2311yescharacteristic
283C2×#117C2314yes—
284C22×C4⋊C4—21no—
285C22×C4⋊C4—21no—
286C22×C4⋊C4—21no—
287C22×C4⋊C4—22no—
288C22×C4⋊C4D411yescharacteristic
289C22×C4⋊C4C2311yescharacteristic
290C22×C22⋊C4—22no—
291C22×C22⋊C4D412yes—
292C22×C42—21no—
293C22×C42C2311yescharacteristic
294#497C23116yescomplemented
295#494C2318yescomplemented
296#492C2318yescomplemented
297#491C23116yescomplemented
298#487C2318yescomplemented
299#487C2318yescomplemented
300#485C23132yescomplemented
301#484C2318yes—
302#484C23116yescomplemented
303#483C2318yes—
304#483C23116yescomplemented
305#481C2318yes—
306#480C2318yes—
307#479C23116yescomplemented
308#477C2318yescomplemented
309#475C2318yescomplemented
310#470C23132yescomplemented
311#468C23132yescomplemented
312#467C23132yescomplemented
313#465C23132yescomplemented
314#464C23116yescomplemented
315#462C23116yescomplemented
316#462C2318yescomplemented
317#462C23116yescomplemented
318#461C23116yescomplemented
319#461C23116yescomplemented
320#460C2318yescomplemented
321#452C23132yescomplemented
322#451C2318yes—
323#451C2318yes—
324#451C23116yes—
325#451C23116yes—
326#451C23132yescomplemented
327#451C23116yescomplemented
328#451C23132yescomplemented
329#450C23116yescomplemented
330#448C2318yes—
331#448C2318yes—
332#448C23116yes—
333#448C23116yes—
334#448C23132yescomplemented
335#448C23132yescomplemented
336#441C23116yescomplemented
337#440C23116yescomplemented
338C4×Q16C23116yescomplemented
339C4×SD16C23116yescomplemented
340#436C23116yes—
341#435C23132yes—
342C8×D4C23116yes—
343#432C2314yes—
344#432C2314yes—
345#431C2314yes—
346#431C2314yes—
347#428C2318yes—
348#423C2314yes—
349#419C2318yes—
350#419C23116yes—
351#419C23132yescomplemented
352#417C2318yes—
353C2×#103C23116yescomplemented
354C2×#103C23116yescomplemented
355#407C2314yes—
356#407C2318yes—
357#407C2318yes—
358#407C2318yes—
359C2×C22⋊C8C2318yes—
360C2×C22⋊C8C2318yes—
361C4×M16C2314yes—
362C25C2×D412yes—
363H(5,𝔽2)—48no—
364C2×#41—24no—
365C2×#41—22no—
366C2×#41—22no—
367C2×#41—24no—
368C2×#41—24no—
369C2×#41—416no—
370C2×#41C2414yes—
371C2×#41C2418yes—
372C22×Q8—28no—
373C22×Q8—21no—
374C22×Q8—21no—
375C22×Q8—21no—
376C22×Q8—28no—
377C22×Q8—24no—
378C22×Q8—28no—
379C22×Q8—24no—
380C22×Q8—22no—
381C22×Q8—22no—
382C22×Q8—22no—
383C22×Q8—28no—
384C22×Q8—28no—
385C22×Q8—28no—
386C22×Q8—28no—
387C22×Q8—28no—
388C22×Q8—28no—
389C22×Q8—232no—
390C22×Q8—416no—
391C22×Q8—48no—
392C22×Q8—416no—
393C22×Q8—416no—
394C22×Q8—432no—
395C22×Q8—416no—
396C22×Q8—416no—
397C22×Q8—432no—
398C22×Q8—416no—
399C22×Q8—432no—
400C22×Q8C2412yes—
401C22×Q8C2412yes—
402C22×Q8C2414yes—
403C22×Q8C24116yes—
404C22×Q8C24116yes—
405C22×Q8C2412yes—
406C22×Q8C2414yes—
407C22×Q8C2414yes—
408C22×Q8C2414yes—
409C22×D4—28no—
410C22×D4—24no—
411C22×D4—24no—
412C22×D4—24no—
413C22×D4—24no—
414C22×D4C2×D412yes—
415C22×D4C2×D411yescharacteristic
416C22×D4C2×D414yes—
417C22×D4C2×D414yes—
418C22×D4C2×D411yescharacteristic
419C22×D4C2414yes—
420C23×C4—21no—
421C23×C4—21no—
422C23×C4—22no—
423C23×C4—28no—
424C23×C4—28no—
425C23×C4—24no—
426C23×C4—24no—
427C23×C4—24no—
428C23×C4—48no—
429C23×C4—416no—
430C23×C4C2×D411yescharacteristic
431C23×C4C2×D411yescharacteristic
432C23×C4C2×D412yes—
433C23×C4C2×D412yes—
434C23×C4C2×D414yes—
435C23×C4C2×D414yes—
436C23×C4C2×D412yes—
437C23×C4C2411yescharacteristic
438C23×C4C2414yes—
439C23×C4C2412yes—
440C23×C4C2414yes—
441C23×C4C2412yes—
442#137—232no—
443#137—432no—
444#137—464no—
445C2×Q16—432no—
446C2×Q16C24116yes—
447C2×Q16C24132yes—
448C2×SD16—432no—
449C2×SD16C24116yes—
450C2×SD16C24132yes—
451C2×M16—416no—
452C2×M16C2418yes—
453C2×M16C24116yes—
454C22×C8C24116yes—
455C4⋊Q8—216no—
456C4⋊Q8—216no—
457C4⋊Q8—232no—
458C4⋊Q8—24no—
459C4⋊Q8—24no—
460C4⋊Q8—24no—
461C4⋊Q8—24no—
462C4⋊Q8—24no—
463C4⋊Q8—24no—
464C4⋊Q8—24no—
465C4⋊Q8C2418yes—
466C4⋊Q8C2418yes—
467C4⋊Q8C2412yes—
468C4⋊Q8C2412yes—
469C4⋊Q8C2412yes—
470#127—24no—
471#127C2412yes—
472#126—28no—
473#126—28no—
474#126—28no—
475#126—24no—
476#126—24no—
477#125—28no—
478#125—24no—
479#125—22no—
480#125—22no—
481#125C2414yes—
482#124—24no—
483#124—28no—
484#124—28no—
485#124—22no—
486#124—22no—
487#124C2414yes—
488#123—28no—
489#123—24no—
490#123—28no—
491#123—28no—
492#123—28no—
493#123—24no—
494#123—24no—
495#123—28no—
496#123—28no—
497#123—28no—
498#123—28no—
499C22⋊Q8—28no—
500C22⋊Q8—28no—
501C22⋊Q8—28no—
502C22⋊Q8—28no—
503C22⋊Q8—28no—
504C22⋊Q8—28no—
505C22⋊Q8—24no—
506C22⋊Q8—24no—
507C22⋊Q8—24no—
508C22⋊Q8—24no—
509C22⋊Q8—22no—
510C22⋊Q8—22no—
511C22⋊Q8—22no—
512C22⋊Q8—22no—
513C22⋊Q8—28no—
514C22⋊Q8—24no—
515C22⋊Q8—232no—
516C22⋊Q8—232no—
517C22⋊Q8—232no—
518C22⋊Q8—232no—
519C22⋊Q8—28no—
520C22⋊Q8—28no—
521C22⋊Q8C24116yes—
522C22⋊Q8C24116yes—
523C22⋊Q8C2414yes—
524C22⋊Q8C2414yes—
525C22⋊Q8C2418yes—
526C22⋊Q8C2418yes—
527#121—28no—
528#121—28no—
529#121—24no—
530#121—24no—
531#121—24no—
532#121—24no—
533#121—24no—
534#121—24no—
535#121—22no—
536#121—22no—
537#121—22no—
538#121—22no—
539#121—24no—
540#121—28no—
541#121—28no—
542#121C2414yes—
543#121C2414yes—
544#121C2418yes—
545#121C2418yes—
546#120—24no—
547#120—28no—
548#120—28no—
549#120—28no—
550#120—28no—
551#120—28no—
552C4×Q8—24no—
553C4×Q8—24no—
554C4×Q8—24no—
555C4×Q8—24no—
556C4×Q8—24no—
557C4×Q8—24no—
558C4×Q8—24no—
559C4×Q8—22no—
560C4×Q8—22no—
561C4×Q8—22no—
562C4×Q8—22no—
563C4×Q8C2418yes—
564C4×Q8C2418yes—
565C4×Q8C2414yes—
566C4×Q8C2414yes—
567C4×D4—232no—
568C4×D4—216no—
569C4×D4—216no—
570C4×D4—24no—
571C4×D4—24no—
572C4×D4—28no—
573C4×D4—24no—
574C4×D4—24no—
575C4×D4—28no—
576C4×D4—28no—
577C4×D4—28no—
578C4×D4—28no—
579C4×D4—28no—
580C4×D4—24no—
581C4×D4—24no—
582C4×D4—24no—
583C4×D4—24no—
584C4×D4—24no—
585C4×D4—28no—
586C4×D4—28no—
587C4×D4—22no—
588C4×D4—22no—
589C4×D4—22no—
590C4×D4—22no—
591C4×D4C2×D414yes—
592C4×D4C2×D414yes—
593C4×D4C2×D418yes—
594C4×D4C2×D414yes—
595C4×D4C2×D418yes—
596C4×D4C2×D414yes—
597C4×D4C2×D414yes—
598C4×D4C2×D418yes—
599C4×D4C2×D414yes—
600C4×D4C2414yes—
601C4×D4C2414yes—
602C4×D4C2414yes—
603C4×D4C2418yes—
604C4×D4C2414yes—
605#117—24no—
606#117—24no—
607#117—22no—
608#117—22no—
609#117—24no—
610#117—28no—
611#117—24no—
612#117—24no—
613#117—24no—
614#117C2414yes—
615#117C2418yes—
616C2×C4⋊C4—24no—
617C2×C4⋊C4—24no—
618C2×C4⋊C4—22no—
619C2×C4⋊C4—22no—
620C2×C4⋊C4—24no—
621C2×C4⋊C4—22no—
622C2×C4⋊C4—24no—
623C2×C4⋊C4—22no—
624C2×C4⋊C4—24no—
625C2×C4⋊C4—22no—
626C2×C4⋊C4—24no—
627C2×C4⋊C4—22no—
628C2×C4⋊C4—28no—
629C2×C4⋊C4—24no—
630C2×C4⋊C4—28no—
631C2×C4⋊C4—24no—
632C2×C4⋊C4—21no—
633C2×C4⋊C4—21no—
634C2×C4⋊C4—21no—
635C2×C4⋊C4—24no—
636C2×C4⋊C4—24no—
637C2×C4⋊C4—24no—
638C2×C4⋊C4C2×D411yescharacteristic
639C2×C4⋊C4C2×D411yescharacteristic
640C2×C4⋊C4C2×D412yes—
641C2×C4⋊C4C2×D414yes—
642C2×C4⋊C4C2×D414yes—
643C2×C4⋊C4C2412yes—
644C2×C4⋊C4C2412yes—
645C2×C4⋊C4C2412yes—
646C2×C4⋊C4C2414yes—
647C2×C4⋊C4C2414yes—
648C2×C22⋊C4—28no—
649C2×C22⋊C4—28no—
650C2×C22⋊C4—24no—
651C2×C22⋊C4—24no—
652C2×C22⋊C4—24no—
653C2×C22⋊C4—24no—
654C2×C22⋊C4—24no—
655C2×C22⋊C4—24no—
656C2×C22⋊C4—24no—
657C2×C22⋊C4—28no—
658C2×C22⋊C4C2×D412yes—
659C2×C22⋊C4C2×D412yes—
660C2×C22⋊C4C2×D412yes—
661C2×C22⋊C4C2×D412yes—
662C2×C22⋊C4C2×D418yes—
663C2×C22⋊C4C2×D418yes—
664C2×C42—24no—
665C2×C42—24no—
666C2×C42—24no—
667C2×C42—22no—
668C2×C42—22no—
669C2×C42—24no—
670C2×C42C2×D411yescharacteristic
671C2×C42C2×D412yes—
672C2×C42C2×D411yescharacteristic
673C2×C42C2×D412yes—
674C2×C42C2412yes—
675C2×C42C2411yescharacteristic
676C2×C42C2412yes—
677C2×C42C2411yescharacteristic
678#107C24116yes—
679#106C24116yes—
680C4⋊C8C2418yes—
681C4⋊C8C2418yes—
682#103C24116yes—
683#103C24116yes—
684#103C24132yes—
685#103C24132yes—
686#103C24116yes—
687#102C24116yes—
688C22⋊C8C2418yes—
689C22⋊C8C2418yes—
690C22⋊C8C24116yes—
691C22⋊C8C24116yes—
692#97C2418yes—
693C4×C8C2418yes—
694C24—28no—
695C24—24no—
696C24—44no—
697C24—44no—
698C24C22×D411yescharacteristic
699C24C22×D414yes—
700C24C22×D414yes—
701C24C22×D412yes—
702C24C22×D412yes—
703#41—216no—
704#41—416no—
705#41—416no—
706#41—48no—
707#41—88no—
708#41—84no—
709#41—88no—
710C2×Q8—28no—
711C2×Q8—28no—
712C2×Q8—28no—
713C2×Q8—28no—
714C2×Q8—28no—
715C2×Q8—22no—
716C2×Q8—22no—
717C2×Q8—22no—
718C2×Q8—22no—
719C2×Q8—216no—
720C2×Q8—216no—
721C2×Q8—24no—
722C2×Q8—24no—
723C2×Q8—24no—
724C2×Q8—22no—
725C2×Q8—24no—
726C2×Q8—24no—
727C2×Q8—232no—
728C2×Q8—232no—
729C2×Q8—216no—
730C2×Q8—432no—
731C2×Q8—416no—
732C2×Q8—416no—
733C2×Q8—48no—
734C2×Q8—48no—
735C2×Q8—432no—
736C2×Q8—432no—
737C2×Q8—416no—
738C2×Q8—432no—
739C2×Q8—416no—
740C2×Q8—48no—
741C2×Q8—48no—
742C2×Q8—48no—
743C2×Q8—48no—
744C2×Q8—432no—
745C2×Q8—432no—
746C2×Q8—432no—
747C2×Q8—432no—
748C2×Q8H(5,𝔽2)18yescomplemented
749C2×Q8C2518yes—
750C2×Q8C2514yes—
751C2×Q8C2514yes—
752C2×D4—28no—
753C2×D4—216no—
754C2×D4—216no—
755C2×D4—24no—
756C2×D4—28no—
757C2×D4—24no—
758C2×D4—24no—
759C2×D4—28no—
760C2×D4—28no—
761C2×D4—24no—
762C2×D4—22no—
763C2×D4—22no—
764C2×D4—24no—
765C2×D4—48no—
766C2×D4—416no—
767C2×D4—416no—
768C2×D4—88no—
769C2×D4—88no—
770C2×D4#13718yescomplemented
771C2×D4C22×D418yes—
772C2×D4C22×D414yes—
773C2×D4C22×D414yes—
774C2×D4C2514yes—
775C22×C4—28no—
776C22×C4—22no—
777C22×C4—22no—
778C22×C4—22no—
779C22×C4—24no—
780C22×C4—216no—
781C22×C4—24no—
782C22×C4—22no—
783C22×C4—22no—
784C22×C4—22no—
785C22×C4—24no—
786C22×C4—24no—
787C22×C4—24no—
788C22×C4—24no—
789C22×C4—216no—
790C22×C4—216no—
791C22×C4—24no—
792C22×C4—24no—
793C22×C4—24no—
794C22×C4—24no—
795C22×C4—24no—
796C22×C4—28no—
797C22×C4—44no—
798C22×C4—48no—
799C22×C4—44no—
800C22×C4—44no—
801C22×C4—48no—
802C22×C4—44no—
803C22×C4—48no—
804C22×C4—44no—
805C22×C4—42no—
806C22×C4—432no—
807C22×C4—416no—
808C22×C4—432no—
809C22×C4—416no—
810C22×C4—44no—
811C22×C4—48no—
812C22×C4—88no—
813C22×C4C22×D412yes—
814C22×C4C22×D412yes—
815C22×C4C22×D411yescharacteristic
816C22×C4C22×D414yes—
817C22×C4C22×D411yescharacteristic
818C22×C4C22×D411yescharacteristic
819C22×C4C22×D411yescharacteristic
820C22×C4C22×D412yes—
821C22×C4C22×D414yes—
822C22×C4C22×D414yes—
823C22×C4C22×D411yescharacteristic
824C22×C4C22×D412yes—
825C22×C4C22×D411yescharacteristic
826C22×C4C22×D414yes—
827C22×C4C22×D414yes—
828C22×C4C22×D412yes—
829C22×C4C22×D414yes—
830C22×C4C22×D412yes—
831C22×C4C22×D414yes—
832C22×C4C22×D414yes—
833C22×C4C22×D411yescharacteristic
834C22×C4C2511yescharacteristic
835C22×C4C2511yescharacteristic
836C22×C4C2514yes—
837C22×C4C2514yes—
838C22×C4C2511yescharacteristic
839Q16—232no—
840Q16—432no—
841SD16—232no—
842SD16—432no—
843M16—216no—
844M16—416no—
845C2×C8—416no—
846C2×C8C25116yes—
847C4⋊C4—28no—
848C4⋊C4—28no—
849C4⋊C4—28no—
850C4⋊C4—28no—
851C4⋊C4—28no—
852C4⋊C4—28no—
853C4⋊C4—216no—
854C4⋊C4—216no—
855C4⋊C4—22no—
856C4⋊C4—22no—
857C4⋊C4—22no—
858C4⋊C4—22no—
859C4⋊C4—28no—
860C4⋊C4—24no—
861C4⋊C4—24no—
862C4⋊C4—28no—
863C4⋊C4—24no—
864C4⋊C4—24no—
865C4⋊C4—22no—
866C4⋊C4—24no—
867C4⋊C4—24no—
868C4⋊C4—22no—
869C4⋊C4—22no—
870C4⋊C4—24no—
871C4⋊C4—24no—
872C4⋊C4C22×D414yes—
873C4⋊C4C22×D414yes—
874C4⋊C4C22×D418yes—
875C4⋊C4C2514yes—
876C4⋊C4C2514yes—
877C4⋊C4C2514yes—
878C22⋊C4—216no—
879C22⋊C4—216no—
880C22⋊C4—24no—
881C22⋊C4—24no—
882C22⋊C4—28no—
883C22⋊C4—24no—
884C22⋊C4—28no—
885C22⋊C4—28no—
886C22⋊C4—24no—
887C22⋊C4—28no—
888C22⋊C4—24no—
889C22⋊C4—24no—
890C22⋊C4—28no—
891C22⋊C4—24no—
892C22⋊C4—24no—
893C22⋊C4—24no—
894C22⋊C4C22×D418yes—
895C22⋊C4C22×D418yes—
896C22⋊C4C22×D418yes—
897C22⋊C4C22×D418yes—
898C42—24no—
899C42—28no—
900C42—28no—
901C42—24no—
902C42—28no—
903C42—24no—
904C42C22×D412yes—
905C42C22×D412yes—
906C42C22×D412yes—
907C42C22×D412yes—
908C42C22×D412yes—
909C42C22×D412yes—
910C42C2512yes—
911C42C2512yes—
912C23—22no—
913C23—22no—
914C23—22no—
915C23—28no—
916C23—28no—
917C23—28no—
918C23—28no—
919C23—24no—
920C23—24no—
921C23—42no—
922C23—44no—
923C23—42no—
924C23—42no—
925C23—44no—
926C23—42no—
927C23—432no—
928C23—48no—
929C23—84no—
930C23—84no—
931C23C2×#13718yescomplemented
932C23C23×D414yes—
933C23C23×D411yescharacteristic
934C23C23×D411yescharacteristic
935C23C23×D414yes—
936C23C23×D411yescharacteristic
937Q8—28no—
938Q8—28no—
939Q8—24no—
940Q8—28no—
941Q8—216no—
942Q8—28no—
943Q8—432no—
944Q8—432no—
945Q8—48no—
946Q8—48no—
947Q8—48no—
948Q8—44no—
949Q8—84no—
950Q8—82no—
951Q8C2×H(5,𝔽2)18yes—
952D4—216no—
953D4—28no—
954D4—28no—
955D4—48no—
956D4—48no—
957D4—48no—
958D4—416no—
959D4—44no—
960D4—84no—
961D4—82no—
962D4—88no—
963D4—88no—
964D4C2×#137116yescomplemented
965C2×C4—28no—
966C2×C4—28no—
967C2×C4—24no—
968C2×C4—24no—
969C2×C4—28no—
970C2×C4—22no—
971C2×C4—28no—
972C2×C4—22no—
973C2×C4—28no—
974C2×C4—28no—
975C2×C4—22no—
976C2×C4—22no—
977C2×C4—22no—
978C2×C4—22no—
979C2×C4—28no—
980C2×C4—28no—
981C2×C4—24no—
982C2×C4—24no—
983C2×C4—24no—
984C2×C4—24no—
985C2×C4—24no—
986C2×C4—24no—
987C2×C4—28no—
988C2×C4—44no—
989C2×C4—44no—
990C2×C4—44no—
991C2×C4—44no—
992C2×C4—42no—
993C2×C4—44no—
994C2×C4—42no—
995C2×C4—41no—
996C2×C4—42no—
997C2×C4—41no—
998C2×C4—432no—
999C2×C4—432no—
1000C2×C4—44no—
1001C2×C4—44no—
1002C2×C4—48no—
1003C2×C4—48no—
1004C2×C4—44no—
1005C2×C4—48no—
1006C2×C4—48no—
1007C2×C4—48no—
1008C2×C4—48no—
1009C2×C4—88no—
1010C2×C4—84no—
1011C2×C4—84no—
1012C2×C4—84no—
1013C2×C4C2×#13714yescomplemented
1014C2×C4C23×D412yes—
1015C2×C4C23×D412yes—
1016C2×C4C23×D414yes—
1017C2×C4C23×D411yescharacteristic
1018C2×C4C23×D411yescharacteristic
1019C2×C4C23×D412yes—
1020C2×C4C23×D414yes—
1021C2×C4C23×D411yescharacteristic
1022C2×C4C23×D412yes—
1023C2×C4C2×H(5,𝔽2)14yes—
1024C2×C4C2611yescharacteristic
1025C8—216no—
1026C22—28no—
1027C22—21no—
1028C22—21no—
1029C22—24no—
1030C22—21no—
1031C22—21no—
1032C22—21no—
1033C22—21no—
1034C22—24no—
1035C22—24no—
1036C22—24no—
1037C22—24no—
1038C22—48no—
1039C22—416no—
1040C22—416no—
1041C22—48no—
1042C22—44no—
1043C22—44no—
1044C22—44no—
1045C22—168no—
1046C22#348412yes—
1047C22C22×#13712yes—
1048C22C22×#13718yes—
1049C22#358612yes—
1050C22C24×D411yescharacteristic
1051C4—28no—
1052C4—21no—
1053C4—21no—
1054C4—24no—
1055C4—24no—
1056C4—22no—
1057C4—22no—
1058C4—22no—
1059C4—48no—
1060C4—44no—
1061C4—44no—
1062C4—44no—
1063C4—44no—
1064C4#348412yes—
1065C4C22×#13714yes—
1066C4C22×H(5,𝔽2)12yes—
1067C2—22no—
1068C2—22no—
1069C2—22no—
1070C2—28no—
1071C2—44no—
1072C2—84no—
1073C2C2×#348411yescharacteristic
1074C2C23×#13711yescharacteristic
1075C2C2×#358611yescharacteristic
subgroupG/H
center, socleC22C24×D4
commutator, Frattini, cosocleC2×C4C26
prime radical#62773C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C22×C4×D4 ◁ G
LECSG ▷ C2×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C22×D4×Q8C2semidirect
3. #61602C2semidirect
4. #61593C2semidirect
5. #61584C2semidirect
6. #61574C2semidirect
7. #61563C2semidirect
8. #61562C2semidirect
9. #61157C2semidirect
10. D4×#137C2semidirect
11. #60800C2semidirect
12. #60751C2semidirect
13. #60560C2semidirect
14. C2×#3004C2semidirect
15. #60230C2semidirect
16. C24×Q8C22semidirect
17. C22×#137C22semidirect
37. C2×D4×Q8C22semidirect
38. C2×D4×Q8C22semidirect
39. C2×D4×Q8C22semidirect
40. C2×D4×Q8C22semidirect
45. C22×C4⋊Q8C22semidirect
48. C22×C22⋊Q8C22semidirect
50. C22×C4×Q8C22semidirect
53. #3329C22semidirect
54. #3328C22semidirect
55. #3320C22semidirect
56. #3312C22semidirect
57. #3299C22semidirect
58. #3298C22semidirect
59. D4×Q16C22semidirect
60. D4×SD16C22semidirect
61. #3278C22semidirect
62. #3276C22semidirect
63. #3270C22semidirect
64. #3266C22semidirect
65. #3218C22semidirect
66. #3218C22semidirect
67. #3209C22semidirect
68. #3209C22semidirect
69. #3206C22semidirect
70. #3206C22semidirect
71. #3196C22semidirect
72. #3195C22semidirect
73. #3193C22semidirect
74. #3190C22semidirect
75. #3189C22semidirect
76. #3187C22semidirect
77. #3152C22semidirect
78. #3139C22semidirect
79. #3117C22semidirect
80. #3113C22semidirect
81. #3112C22semidirect
82. #3108C22semidirect
83. #3104C22semidirect
84. #3103C22semidirect
85. #3095C22semidirect
86. #3092C22semidirect
87. #3078C22semidirect
88. #3056C22semidirect
89. #3039C22semidirect
90. #3037C22semidirect
91. #3007C22semidirect
92. #3004C22semidirect
93. #3004C22semidirect
94. #3004C22semidirect
95. #3004C22semidirect
96. #3004C22semidirect
97. C2×#451C22semidirect
98. C2×#451C22semidirect
99. C2×#448C22semidirect
100. C2×#448C22semidirect
101. #2975C22semidirect
102. #2974C22semidirect
103. #2973C22semidirect
105. C4×#137C22semidirect
106. D4×M16C22semidirect
107. #2920C22semidirect
108. C2×#419C22semidirect
109. C2×#407C22semidirect
130. C2×#137C23semidirect
131. C22×Q16C23semidirect
132. C22×SD16C23semidirect
294. #497C23semidirect
295. #494C23semidirect
296. #492C23semidirect
297. #491C23semidirect
298. #487C23semidirect
299. #487C23semidirect
300. #485C23semidirect
302. #484C23semidirect
304. #483C23semidirect
307. #479C23semidirect
308. #477C23semidirect
309. #475C23semidirect
310. #470C23semidirect
311. #468C23semidirect
312. #467C23semidirect
313. #465C23semidirect
314. #464C23semidirect
315. #462C23semidirect
316. #462C23semidirect
317. #462C23semidirect
318. #461C23semidirect
319. #461C23semidirect
320. #460C23semidirect
321. #452C23semidirect
326. #451C23semidirect
327. #451C23semidirect
328. #451C23semidirect
329. #450C23semidirect
334. #448C23semidirect
335. #448C23semidirect
336. #441C23semidirect
337. #440C23semidirect
338. C4×Q16C23semidirect
339. C4×SD16C23semidirect
351. #419C23semidirect
353. C2×#103C23semidirect
354. C2×#103C23semidirect
748. C2×Q8H(5,𝔽2)semidirect
770. C2×D4#137semidirect
931. C23C2×#137semidirect
964. D4C2×#137semidirect
1013. C2×C4C2×#137semidirect

Maximal subgroups

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

subgroupindex
#627732
C22×D4×Q82
#616022
#615932
#615842
#615742
#615632
#615622
#611572
D4×#1372
#608002
#607512
#605602
C2×#30042
#602302