Finite Group Databasebeta

← #10575707

Subgroups — #10575707

Order 512.

6518 conjugacy classes of subgroups.

The subgroup lattice has 1108 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3444C211yesmaximal, characteristic
2C22×#533C211yesmaximal, characteristic, complemented
3#60866C218yesmaximal, complemented
4#60865C214yesmaximal, complemented
5#60864C214yesmaximal, complemented
6#60863C214yesmaximal, complemented
7#60862C214yesmaximal, complemented
8#60861C214yesmaximal, complemented
9#60860C214yesmaximal, complemented
10#60854C218yesmaximal, complemented
11#60846C218yesmaximal, complemented
12#60663C212yesmaximal, complemented
13#60618C212yesmaximal, complemented
14#60511C214yesmaximal, complemented
15#60484C214yesmaximal, complemented
16C2×#2920C211yesmaximal, characteristic, complemented
17#3444—22no—
18#3444—22no—
19#3444—22no—
20#3444—22no—
21#3444C2214yes—
22#3444C2214yes—
23#3444C2212yes—
24#3444C2212yes—
25#3444C2212yes—
26#3444C2212yes—
27C2×#533—22no—
28C2×#533—22no—
29C2×#533—22no—
30C2×#533—22no—
31C2×#533—22no—
32C2×#533—22no—
33C2×#533C2212yes—
34C2×#533C2212yes—
35C2×#533C2214yes—
36C2×#533C2214yes—
37C2×#533C2212yes—
38C2×#533C2211yescharacteristic
39C2×#533C2214yescomplemented
40C2×#533C2214yescomplemented
41C2×#533C2212yescomplemented
42C2×#533C2212yescomplemented
43C2×#532C2211yescharacteristic
44C2×#532C2212yes—
45C22×C4⋊Q8C2212yescomplemented
46C2×#529—22no—
47C2×#529—22no—
48C2×#529C2214yes—
49C22×#125C2212yescomplemented
50C2×#525—22no—
51C2×#525C2212yes—
52C22×C22⋊Q8—22no—
53C2×C4×#41—22no—
54C2×C4×#41C2212yes—
55C22×C4×Q8—22no—
56C22×#117C2212yes—
57C23×C42C2211yescharacteristic
58#3240C22132yescomplemented
59#3239C22116yescomplemented
60#3238C22116yescomplemented
61#3237C22116yescomplemented
62#3236C22116yescomplemented
63#3235C22116yescomplemented
64#3234C22116yescomplemented
65#3233C22132yescomplemented
66#3232C22132yescomplemented
67#3231C22116yescomplemented
68#3230C2218yescomplemented
69#3229C2218yescomplemented
70#3228C22116yescomplemented
71#3227C2218yescomplemented
72#3226C2218yescomplemented
73#3166C2218yescomplemented
74#3166C2218yescomplemented
75#3165C2218yescomplemented
76#3165C2218yescomplemented
77#3162C2218yescomplemented
78#3160C2218yescomplemented
79#3142C2218yescomplemented
80#3141C2218yescomplemented
81#3140C2218yescomplemented
82#3139C2214yescomplemented
83#3138C2214yescomplemented
84#3135C2218yescomplemented
85#3131C2218yescomplemented
86#3095C22116yes—
87#3094C22116yes—
88#3093C22116yescomplemented
89#3092C22116yescomplemented
90#3091C22132yescomplemented
91#3080C22116yescomplemented
92#3079C22116yescomplemented
93#3078C22116yescomplemented
94#3077C22116yescomplemented
95#3076C22132yescomplemented
96#2920C2214yes—
97#2920C2214yes—
98#2920C2212yescomplemented
99#2920C2212yescomplemented
100#2920C2212yescomplemented
101#2920C2212yescomplemented
102C2×#432C2214yescomplemented
103C2×#431C2214yescomplemented
104#2911C2218yes—
105C2×#423C2212yes—
106#2896C2218yes—
107C2×#407C2212yes—
108C2×C4×M16C2212yes—
109C22×#41—22no—
110C22×#41C2312yes—
111C23×Q8—22no—
112C24×C4D412yes—
113C24×C4C2311yescharacteristic
114C22×M16C2314yes—
115#533—22no—
116#533—24no—
117#533—24no—
118#533—24no—
119#533—22no—
120#533—22no—
121#533—24no—
122#533—24no—
123#533—24no—
124#533—24no—
125#533—24no—
126#533—24no—
127#533—24no—
128#533—22no—
129#533—24no—
130#533—24no—
131#533—24no—
132#533—24no—
133#533—24no—
134#533—24no—
135#533—24no—
136#533—24no—
137#533—24no—
138#533—24no—
139#533—24no—
140#533—24no—
141#533—22no—
142#533—22no—
143#533—22no—
144#533—22no—
145#533—22no—
146#533—22no—
147#533C2314yes—
148#533C2314yes—
149#533C2314yes—
150#533C2314yes—
151#533C2318yes—
152#533C2318yes—
153#533C2314yes—
154#533C2314yes—
155#533C2314yes—
156#533C2314yes—
157#533C2312yes—
158#533C2312yes—
159#533C2312yes—
160#533C2312yes—
161#533C2318yes—
162#533C2318yes—
163#533C2318yes—
164#533C2318yes—
165#532—22no—
166#532—22no—
167#532—22no—
168#532—22no—
169#532—22no—
170#532—22no—
171#532C2312yes—
172#532C2312yes—
173#532C2312yes—
174#532C2312yes—
175#532C2314yes—
176#532C2314yes—
177#532C2314yes—
178#532C2314yes—
179C2×C4⋊Q8—22no—
180C2×C4⋊Q8—22no—
181C2×C4⋊Q8—22no—
182C2×C4⋊Q8—22no—
183C2×C4⋊Q8—22no—
184C2×C4⋊Q8—22no—
185C2×C4⋊Q8C2311yescharacteristic
186C2×C4⋊Q8C2314yes—
187C2×C4⋊Q8C2314yes—
188C2×C4⋊Q8C2312yes—
189C2×C4⋊Q8C2314yes—
190C2×C4⋊Q8C2314yes—
191C2×C4⋊Q8C2314yes—
192C2×C4⋊Q8C2314yes—
193C2×#127C2311yescharacteristic
194#529—24no—
195#529—24no—
196#529—24no—
197#529—24no—
198#529—24no—
199#529—24no—
200#529—24no—
201#529—24no—
202#529—24no—
203#529—24no—
204#529—24no—
205#529—24no—
206#529—24no—
207#529—24no—
208#529—24no—
209#529—24no—
210#529—24no—
211#529—24no—
212#529—24no—
213#529—24no—
214#529C2318yes—
215#529C2318yes—
216#529C2318yes—
217#529C2318yes—
218C2×#126—24no—
219C2×#125—24no—
220C2×#125—24no—
221C2×#125—24no—
222C2×#125—22no—
223C2×#125C2314yes—
224C2×#125C2314yes—
225C2×#125C2312yes—
226C2×#125C2318yes—
227C2×#125C2318yes—
228C2×#124—22no—
229C2×#124C2312yes—
230#525—24no—
231#525—24no—
232#525—24no—
233#525—24no—
234#525—24no—
235#525—24no—
236#525—24no—
237#525—24no—
238#525—24no—
239#525—22no—
240#525—22no—
241#525C2318yes—
242#525C2314yes—
243#525C2314yes—
244C2×#123—24no—
245C2×#123—22no—
246C2×C22⋊Q8—24no—
247C2×C22⋊Q8—24no—
248C2×C22⋊Q8—24no—
249C2×C22⋊Q8—24no—
250C2×C22⋊Q8—24no—
251C2×C22⋊Q8—24no—
252C2×C22⋊Q8—24no—
253C2×C22⋊Q8—24no—
254C2×C22⋊Q8—24no—
255C2×C22⋊Q8—24no—
256C2×C22⋊Q8—24no—
257C2×C22⋊Q8—24no—
258C2×C22⋊Q8—22no—
259C2×C22⋊Q8—22no—
260C2×C22⋊Q8C2314yes—
261C2×#121—22no—
262C2×#121—22no—
263C2×#121C2314yes—
264C2×#120—22no—
265C4×#41—24no—
266C4×#41—24no—
267C4×#41—24no—
268C4×#41—24no—
269C4×#41—24no—
270C4×#41—24no—
271C4×#41—24no—
272C4×#41—24no—
273C4×#41—24no—
274C4×#41—22no—
275C4×#41—22no—
276C4×#41C2318yes—
277C4×#41C2314yes—
278C4×#41C2314yes—
279C2×C4×Q8—24no—
280C2×C4×Q8—24no—
281C2×C4×Q8—24no—
282C2×C4×Q8—24no—
283C2×C4×Q8—24no—
284C2×C4×Q8—24no—
285C2×C4×Q8—24no—
286C2×C4×Q8—24no—
287C2×C4×Q8—24no—
288C2×C4×Q8—24no—
289C2×C4×Q8—24no—
290C2×C4×Q8—24no—
291C2×C4×Q8—22no—
292C2×C4×Q8—22no—
293C2×C4×Q8C2314yes—
294C2×C4×D4—24no—
295C2×C4×D4—24no—
296C2×C4×D4—24no—
297C2×C4×D4—22no—
298C2×C4×D4—22no—
299C2×C4×D4C2314yes—
300C2×#117—24no—
301C2×#117—22no—
302C2×#117—24no—
303C2×#117—22no—
304C2×#117—22no—
305C2×#117—24no—
306C2×#117—22no—
307C2×#117C2318yes—
308C2×#117C2314yes—
309C2×#117C2318yes—
310C2×#117C2314yes—
311C2×#117C2312yes—
312C22×C4⋊C4—24no—
313C22×C4⋊C4—22no—
314C22×C4⋊C4C2314yes—
315C22×C22⋊C4—22no—
316C22×C42—22no—
317C22×C42—22no—
318C22×C42D412yes—
319C22×C42D412yes—
320C22×C42D412yes—
321C22×C42D412yes—
322C22×C42D412yes—
323C22×C42D412yes—
324C22×C42D412yes—
325C22×C42C2311yescharacteristic
326C22×C42C2311yescharacteristic
327C22×C42C2312yes—
328C22×C42C2312yes—
329C22×C42C2312yes—
330C22×C42C2312yes—
331C22×C42C2311yescharacteristic
332C22×C42C2311yescharacteristic
333C22×C42C2311yescharacteristic
334C22×C42C2311yescharacteristic
335#501C23132yescomplemented
336#501C23132yescomplemented
337#500C23116yescomplemented
338#499C23132yescomplemented
339#498C23116yescomplemented
340#491C23116yescomplemented
341#490C23116yescomplemented
342#489C23132yescomplemented
343#488C23132yescomplemented
344#487C23116yescomplemented
345#486C23116yescomplemented
346#485C23164yes—
347#484C23132yes—
348#483C23132yes—
349#482C23164yes—
350#481C23132yes—
351#480C23132yes—
352#479C23164yescomplemented
353#478C23164yescomplemented
354#477C23132yescomplemented
355#476C23132yescomplemented
356#475C23132yescomplemented
357#474C23132yescomplemented
358#432C2318yes—
359#432C2318yes—
360#432C2318yes—
361#432C2318yes—
362#431C2318yes—
363#431C2318yes—
364#431C2318yes—
365#431C2318yes—
366#428C23132yes—
367#428C23132yes—
368#427C23132yes—
369#423C2318yes—
370#423C2314yes—
371#423C2314yes—
372C2×C4⋊C8C2318yes—
373#419C23116yes—
374#418C23116yes—
375#417C23132yes—
376#416C23132yes—
377#407C2314yes—
378#407C2314yes—
379#407C2318yes—
380C2×C22⋊C8C2318yes—
381C4×M16C2314yes—
382C4×M16C2314yes—
383C4×M16C2314yes—
384C4×M16C2314yes—
385C2×#97C2314yes—
386C2×C4×C8C2314yes—
387C25C2×D411yescharacteristic
388C2×#41—22no—
389C2×#41—22no—
390C2×#41—24no—
391C2×#41—24no—
392C2×#41—24no—
393C2×#41—24no—
394C2×#41—216no—
395C2×#41—416no—
396C2×#41C2414yes—
397C2×#41C2414yes—
398C22×Q8—22no—
399C22×Q8—24no—
400C22×Q8—24no—
401C22×Q8—24no—
402C22×Q8—24no—
403C22×Q8—24no—
404C22×Q8—24no—
405C22×Q8—416no—
406C22×Q8C2412yes—
407C22×D4—22no—
408C22×D4—24no—
409C22×D4—22no—
410C22×D4C2412yes—
411C23×C4—28no—
412C23×C4—24no—
413C23×C4—22no—
414C23×C4—24no—
415C23×C4—48no—
416C23×C4C2×D412yes—
417C23×C4C2×D412yes—
418C23×C4C2×D411yescharacteristic
419C23×C4C2×D412yes—
420C23×C4C2×D411yescharacteristic
421C23×C4C2×D412yes—
422C23×C4C2×D412yes—
423C23×C4C2×D411yescharacteristic
424C23×C4C2×D412yes—
425C23×C4C2×D412yes—
426C23×C4C2×D412yes—
427C23×C4C2×D412yes—
428C23×C4C2×D412yes—
429C23×C4C2×D412yes—
430C23×C4C2×D412yes—
431C23×C4C2×D412yes—
432C23×C4C2×D412yes—
433C23×C4C2×D412yes—
434C23×C4C2×D412yes—
435C23×C4C2411yescharacteristic
436C23×C4C2412yes—
437C23×C4C2412yes—
438C23×C4C2411yescharacteristic
439C23×C4C2411yescharacteristic
440C2×M16—216no—
441C2×M16C2418yes—
442C2×M16C2418yes—
443C22×C8C2418yes—
444C4⋊Q8—24no—
445C4⋊Q8—24no—
446C4⋊Q8—24no—
447C4⋊Q8—24no—
448C4⋊Q8—24no—
449C4⋊Q8—24no—
450C4⋊Q8—24no—
451C4⋊Q8—24no—
452C4⋊Q8—24no—
453C4⋊Q8—24no—
454C4⋊Q8—24no—
455C4⋊Q8—24no—
456C4⋊Q8—22no—
457C4⋊Q8—22no—
458C4⋊Q8—22no—
459C4⋊Q8C2412yes—
460C4⋊Q8C2412yes—
461C4⋊Q8C2418yes—
462C4⋊Q8C2418yes—
463C4⋊Q8C2418yes—
464C4⋊Q8C2418yes—
465C4⋊Q8C2414yes—
466C4⋊Q8C2414yes—
467#127—22no—
468#127C2412yes—
469#127C2412yes—
470#126—28no—
471#126—28no—
472#126—28no—
473#126—28no—
474#125—24no—
475#125—24no—
476#125—28no—
477#125—28no—
478#125—28no—
479#125—28no—
480#125—28no—
481#125—24no—
482#125—24no—
483#125—24no—
484#125—24no—
485#125—24no—
486#125C24116yes—
487#125C2418yes—
488#125C2418yes—
489#125C2414yes—
490#125C2414yes—
491#124—24no—
492#124—24no—
493#124—24no—
494#124—24no—
495#124—24no—
496#124C2414yes—
497#124C2414yes—
498#123—28no—
499#123—28no—
500#123—28no—
501#123—28no—
502#123—24no—
503#123—24no—
504#123—28no—
505C22⋊Q8—28no—
506C22⋊Q8—28no—
507C22⋊Q8—28no—
508C22⋊Q8—28no—
509C22⋊Q8—28no—
510C22⋊Q8—28no—
511C22⋊Q8—28no—
512C22⋊Q8—28no—
513C22⋊Q8—28no—
514C22⋊Q8—28no—
515C22⋊Q8—28no—
516C22⋊Q8—28no—
517C22⋊Q8—28no—
518C22⋊Q8—28no—
519C22⋊Q8—28no—
520C22⋊Q8—28no—
521C22⋊Q8—24no—
522C22⋊Q8—24no—
523C22⋊Q8—24no—
524C22⋊Q8—24no—
525C22⋊Q8—24no—
526C22⋊Q8—24no—
527C22⋊Q8—24no—
528C22⋊Q8—24no—
529C22⋊Q8—24no—
530C22⋊Q8—24no—
531C22⋊Q8C2418yes—
532C22⋊Q8C2418yes—
533#121—24no—
534#121—24no—
535#121—24no—
536#121—24no—
537#121—24no—
538#121—24no—
539#121—24no—
540#121—24no—
541#121—24no—
542#121—24no—
543#121C2418yes—
544#121C2418yes—
545#120—24no—
546#120—28no—
547#120—24no—
548C4×Q8—28no—
549C4×Q8—28no—
550C4×Q8—28no—
551C4×Q8—28no—
552C4×Q8—28no—
553C4×Q8—28no—
554C4×Q8—28no—
555C4×Q8—28no—
556C4×Q8—28no—
557C4×Q8—28no—
558C4×Q8—28no—
559C4×Q8—28no—
560C4×Q8—28no—
561C4×Q8—28no—
562C4×Q8—28no—
563C4×Q8—28no—
564C4×Q8—24no—
565C4×Q8—24no—
566C4×Q8—24no—
567C4×Q8—24no—
568C4×Q8—24no—
569C4×Q8—24no—
570C4×Q8—24no—
571C4×Q8—24no—
572C4×Q8—24no—
573C4×Q8—24no—
574C4×Q8C2418yes—
575C4×Q8C2418yes—
576C4×D4—28no—
577C4×D4—28no—
578C4×D4—28no—
579C4×D4—28no—
580C4×D4—28no—
581C4×D4—28no—
582C4×D4—28no—
583C4×D4—28no—
584C4×D4—28no—
585C4×D4—28no—
586C4×D4—28no—
587C4×D4—28no—
588C4×D4—24no—
589C4×D4—24no—
590C4×D4—24no—
591C4×D4—24no—
592C4×D4—24no—
593C4×D4—24no—
594C4×D4—24no—
595C4×D4—24no—
596C4×D4—24no—
597C4×D4—24no—
598C4×D4C2418yes—
599C4×D4C2418yes—
600#117—28no—
601#117—28no—
602#117—28no—
603#117—28no—
604#117—24no—
605#117—28no—
606#117—24no—
607#117—24no—
608#117—24no—
609#117—24no—
610#117—24no—
611#117—22no—
612#117—22no—
613#117—28no—
614#117—28no—
615#117—28no—
616#117—28no—
617#117—24no—
618#117—24no—
619#117—28no—
620#117C2418yes—
621#117C2418yes—
622#117C24116yes—
623#117C2414yes—
624#117C2414yes—
625C2×C4⋊C4—28no—
626C2×C4⋊C4—28no—
627C2×C4⋊C4—28no—
628C2×C4⋊C4—28no—
629C2×C4⋊C4—28no—
630C2×C4⋊C4—28no—
631C2×C4⋊C4—24no—
632C2×C4⋊C4—24no—
633C2×C4⋊C4—24no—
634C2×C4⋊C4—24no—
635C2×C4⋊C4—24no—
636C2×C4⋊C4—24no—
637C2×C4⋊C4—24no—
638C2×C4⋊C4—24no—
639C2×C4⋊C4—24no—
640C2×C4⋊C4—22no—
641C2×C4⋊C4—22no—
642C2×C4⋊C4—24no—
643C2×C4⋊C4—24no—
644C2×C4⋊C4—24no—
645C2×C4⋊C4C2418yes—
646C2×C4⋊C4C2418yes—
647C2×C4⋊C4C2418yes—
648C2×C4⋊C4C2414yes—
649C2×C22⋊C4—28no—
650C2×C22⋊C4—28no—
651C2×C22⋊C4—24no—
652C2×C22⋊C4—24no—
653C2×C22⋊C4—24no—
654C2×C22⋊C4—22no—
655C2×C22⋊C4—24no—
656C2×C22⋊C4—24no—
657C2×C22⋊C4—24no—
658C2×C42—24no—
659C2×C42—22no—
660C2×C42—28no—
661C2×C42—24no—
662C2×C42—28no—
663C2×C42—24no—
664C2×C42—24no—
665C2×C42—24no—
666C2×C42—28no—
667C2×C42C2×D412yes—
668C2×C42C2×D411yescharacteristic
669C2×C42C2×D412yes—
670C2×C42C2×D412yes—
671C2×C42C2×D412yes—
672C2×C42C2×D412yes—
673C2×C42C2×D412yes—
674C2×C42C2×D412yes—
675C2×C42C2×D412yes—
676C2×C42C2×D412yes—
677C2×C42C2×D412yes—
678C2×C42C2×D412yes—
679C2×C42C2×D412yes—
680C2×C42C2×D412yes—
681C2×C42C2×D412yes—
682C2×C42C2×D412yes—
683C2×C42C2×D412yes—
684C2×C42C2×D412yes—
685C2×C42C2×D412yes—
686C2×C42C2×D411yescharacteristic
687C2×C42C2×D412yes—
688C2×C42C2×D411yescharacteristic
689C2×C42C2×D412yes—
690C2×C42C2×D412yes—
691C2×C42C2×D412yes—
692C2×C42C2×D412yes—
693C2×C42C2×D412yes—
694C2×C42C2×D412yes—
695C2×C42C2×D412yes—
696C2×C42C2×D412yes—
697C2×C42C2×D412yes—
698C2×C42C2×D412yes—
699C2×C42C2×D412yes—
700C2×C42C2×D412yes—
701C2×C42C2×D412yes—
702C2×C42C2×D412yes—
703C2×C42C2×D412yes—
704C2×C42C2×D412yes—
705C2×C42C2×D412yes—
706C2×C42C2×D412yes—
707C2×C42C2×D412yes—
708C2×C42C2×D412yes—
709C2×C42C2×D412yes—
710C2×C42C2×D411yescharacteristic
711C2×C42C2412yes—
712C2×C42C2411yescharacteristic
713C2×C42C2411yescharacteristic
714C2×C42C2412yes—
715C2×C42C2411yescharacteristic
716C2×C42C2412yes—
717C2×C42C2411yescharacteristic
718C2×C42C2412yes—
719C2×C42C2412yes—
720C2×C42C2412yes—
721C2×C42C2412yes—
722C2×C42C2411yescharacteristic
723C2×C42C2411yescharacteristic
724C2×C42C2412yes—
725C2×C42C2411yescharacteristic
726C2×C42C2411yescharacteristic
727C2×C42C2412yes—
728C2×C42C2412yes—
729#107C24164yes—
730#106C24164yes—
731C4⋊C8C24116yes—
732C4⋊C8C24116yes—
733#103C24164yes—
734#102C24164yes—
735C22⋊C8C24116yes—
736C22⋊C8C24116yes—
737#97C2418yes—
738#97C2418yes—
739C4×C8C2418yes—
740C4×C8C2418yes—
741C24—24no—
742C24—22no—
743C24—44no—
744C24C22×D411yescharacteristic
745C24C22×D412yes—
746C24C22×D412yes—
747C24C22×D411yescharacteristic
748C24C22×D411yescharacteristic
749#41—216no—
750#41—216no—
751#41—416no—
752#41—416no—
753#41—416no—
754#41—48no—
755#41—48no—
756#41—416no—
757C2×Q8—22no—
758C2×Q8—24no—
759C2×Q8—24no—
760C2×Q8—28no—
761C2×Q8—28no—
762C2×Q8—28no—
763C2×Q8—28no—
764C2×Q8—28no—
765C2×Q8—416no—
766C2×Q8—416no—
767C2×Q8—416no—
768C2×Q8—416no—
769C2×Q8—416no—
770C2×Q8—48no—
771C2×Q8—416no—
772C2×Q8C2514yes—
773C2×D4—24no—
774C2×D4—24no—
775C2×D4—28no—
776C2×D4—28no—
777C2×D4—22no—
778C2×D4—24no—
779C2×D4—24no—
780C2×D4—28no—
781C2×D4—48no—
782C2×D4—416no—
783C2×D4—48no—
784C2×D4C2514yes—
785C22×C4—24no—
786C22×C4—28no—
787C22×C4—24no—
788C22×C4—24no—
789C22×C4—28no—
790C22×C4—28no—
791C22×C4—28no—
792C22×C4—28no—
793C22×C4—28no—
794C22×C4—28no—
795C22×C4—24no—
796C22×C4—24no—
797C22×C4—22no—
798C22×C4—24no—
799C22×C4—28no—
800C22×C4—28no—
801C22×C4—28no—
802C22×C4—24no—
803C22×C4—28no—
804C22×C4—28no—
805C22×C4—24no—
806C22×C4—44no—
807C22×C4—44no—
808C22×C4—44no—
809C22×C4—44no—
810C22×C4—44no—
811C22×C4—44no—
812C22×C4—44no—
813C22×C4—44no—
814C22×C4—44no—
815C22×C4—44no—
816C22×C4—44no—
817C22×C4—416no—
818C22×C4—416no—
819C22×C4—48no—
820C22×C4C22×D412yes—
821C22×C4C22×D411yescharacteristic
822C22×C4C22×D412yes—
823C22×C4C22×D412yes—
824C22×C4C22×D412yes—
825C22×C4C22×D411yescharacteristic
826C22×C4C22×D412yes—
827C22×C4C22×D412yes—
828C22×C4C22×D412yes—
829C22×C4C22×D412yes—
830C22×C4C22×D412yes—
831C22×C4C22×D412yes—
832C22×C4C22×D412yes—
833C22×C4C22×D412yes—
834C22×C4C22×D412yes—
835C22×C4C22×D412yes—
836C22×C4C22×D412yes—
837C22×C4C22×D412yes—
838C22×C4C22×D412yes—
839C22×C4C22×D412yes—
840C22×C4C22×D412yes—
841C22×C4C22×D412yes—
842C22×C4C22×D412yes—
843C22×C4C22×D412yes—
844C22×C4C22×D412yes—
845C22×C4C22×D412yes—
846C22×C4C22×D412yes—
847C22×C4C22×D412yes—
848C22×C4C22×D412yes—
849C22×C4C22×D412yes—
850C22×C4C22×D412yes—
851C22×C4C22×D412yes—
852C22×C4C22×D412yes—
853C22×C4C22×D412yes—
854C22×C4C22×D412yes—
855C22×C4C22×D412yes—
856C22×C4C22×D412yes—
857C22×C4C22×D411yescharacteristic
858C22×C4C22×D411yescharacteristic
859C22×C4C22×D411yescharacteristic
860C22×C4C22×D412yes—
861C22×C42−1+418yes—
862C22×C4C2512yes—
863C22×C4C2512yes—
864C22×C4C2511yescharacteristic
865C22×C4C2511yescharacteristic
866C22×C4C2511yescharacteristic
867M16—216no—
868M16—216no—
869C2×C8—216no—
870C2×C8C25116yes—
871C4⋊C4—216no—
872C4⋊C4—216no—
873C4⋊C4—216no—
874C4⋊C4—216no—
875C4⋊C4—28no—
876C4⋊C4—28no—
877C4⋊C4—28no—
878C4⋊C4—28no—
879C4⋊C4—28no—
880C4⋊C4—28no—
881C4⋊C4—28no—
882C4⋊C4—24no—
883C4⋊C4—24no—
884C4⋊C4—24no—
885C4⋊C4—24no—
886C4⋊C4—28no—
887C4⋊C4—28no—
888C4⋊C4—28no—
889C4⋊C4—28no—
890C4⋊C4—28no—
891C4⋊C4—28no—
892C4⋊C4—24no—
893C4⋊C4C25116yes—
894C4⋊C4C2518yes—
895C22⋊C4—216no—
896C22⋊C4—28no—
897C22⋊C4—28no—
898C22⋊C4—28no—
899C22⋊C4—28no—
900C22⋊C4—24no—
901C22⋊C4—24no—
902C22⋊C4—28no—
903C22⋊C4—28no—
904C22⋊C4—28no—
905C22⋊C4—28no—
906C22⋊C4—28no—
907C22⋊C4—28no—
908C42—28no—
909C42—28no—
910C42—24no—
911C42—216no—
912C42—28no—
913C42—24no—
914C42—28no—
915C42C22×D411yescharacteristic
916C42C22×D411yescharacteristic
917C42C22×D412yes—
918C42C22×D412yes—
919C42C22×D412yes—
920C42C22×D411yescharacteristic
921C42C22×D412yes—
922C42C22×D411yescharacteristic
923C42C22×D412yes—
924C42C22×D412yes—
925C42C22×D412yes—
926C42C22×D412yes—
927C42C22×D412yes—
928C42C22×D412yes—
929C42C22×D412yes—
930C42C22×D412yes—
931C42C22×D412yes—
932C42C22×D412yes—
933C42C22×D412yes—
934C42C22×D412yes—
935C42C22×D412yes—
936C42C22×D412yes—
937C42C22×D412yes—
938C42C22×D412yes—
939C42C22×D412yes—
940C42C22×D412yes—
941C42C22×D412yes—
942C42C22×D412yes—
943C42C22×D412yes—
944C42C22×D412yes—
945C42C2511yescharacteristic
946C42C2511yescharacteristic
947C42C2511yescharacteristic
948C42C2511yescharacteristic
949C42C2512yes—
950C42C2512yes—
951C23—22no—
952C23—24no—
953C23—24no—
954C23—24no—
955C23—22no—
956C23—24no—
957C23—24no—
958C23—24no—
959C23—42no—
960C23—42no—
961C23—42no—
962C23—42no—
963C23—416no—
964C23—48no—
965C23—44no—
966C23#53614yes—
967C23C23×D412yes—
968C23C23×D411yescharacteristic
969C23C23×D411yescharacteristic
970C23C23×D411yescharacteristic
971C23C23×D412yes—
972Q8—28no—
973Q8—416no—
974Q8—416no—
975Q8—48no—
976Q8—44no—
977Q8—416no—
978Q8—416no—
979Q8—48no—
980D4—28no—
981D4—48no—
982D4—416no—
983D4—48no—
984D4—48no—
985D4—416no—
986D4—44no—
987D4—48no—
988C2×C4—24no—
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—24no—
992C2×C4—24no—
993C2×C4—24no—
994C2×C4—24no—
995C2×C4—24no—
996C2×C4—24no—
997C2×C4—24no—
998C2×C4—24no—
999C2×C4—24no—
1000C2×C4—24no—
1001C2×C4—24no—
1002C2×C4—24no—
1003C2×C4—24no—
1004C2×C4—24no—
1005C2×C4—24no—
1006C2×C4—24no—
1007C2×C4—24no—
1008C2×C4—24no—
1009C2×C4—24no—
1010C2×C4—24no—
1011C2×C4—24no—
1012C2×C4—24no—
1013C2×C4—24no—
1014C2×C4—24no—
1015C2×C4—24no—
1016C2×C4—28no—
1017C2×C4—216no—
1018C2×C4—42no—
1019C2×C4—42no—
1020C2×C4—42no—
1021C2×C4—42no—
1022C2×C4—42no—
1023C2×C4—42no—
1024C2×C4—42no—
1025C2×C4—42no—
1026C2×C4—42no—
1027C2×C4—42no—
1028C2×C4—42no—
1029C2×C4—42no—
1030C2×C4—416no—
1031C2×C4—48no—
1032C2×C4—416no—
1033C2×C4—416no—
1034C2×C4—44no—
1035C2×C4—416no—
1036C2×C4—48no—
1037C2×C4—48no—
1038C2×C4—416no—
1039C2×C4#53614yes—
1040C2×C4#53614yes—
1041C2×C4#53614yes—
1042C2×C4#57518yes—
1043C2×C4C23×D412yes—
1044C2×C4C23×D412yes—
1045C2×C4C23×D412yes—
1046C2×C4C23×D412yes—
1047C2×C4C23×D412yes—
1048C2×C4C23×D412yes—
1049C2×C4C23×D412yes—
1050C2×C4C23×D412yes—
1051C2×C4C23×D411yescharacteristic
1052C2×C4C23×D411yescharacteristic
1053C2×C4C23×D412yes—
1054C2×C4C23×D412yes—
1055C2×C4C23×D411yescharacteristic
1056C2×C4C2×2−1+414yes—
1057C2×C4C2×2−1+414yes—
1058C2×C4C2×2−1+414yes—
1059C2×C4C2611yescharacteristic
1060C8—216no—
1061C22—28no—
1062C22—22no—
1063C22—22no—
1064C22—22no—
1065C22—22no—
1066C22—22no—
1067C22—22no—
1068C22—22no—
1069C22—22no—
1070C22—44no—
1071C22—48no—
1072C22—48no—
1073C22—44no—
1074C22—48no—
1075C22—44no—
1076C22—88no—
1077C22C2×#53612yes—
1078C22C2×#53612yes—
1079C22C2×#53612yes—
1080C22C2×#57514yes—
1081C22C24×D411yescharacteristic
1082C4—22no—
1083C4—22no—
1084C4—22no—
1085C4—22no—
1086C4—22no—
1087C4—22no—
1088C4—22no—
1089C4—22no—
1090C4—48no—
1091C4—416no—
1092C4—44no—
1093C4C2×#53612yes—
1094C4C2×#53612yes—
1095C4C2×#53612yes—
1096C4C2×#57514yes—
1097C4C2×#57514yes—
1098C4C22×2−1+412yes—
1099C2—22no—
1100C2—24no—
1101C2—22no—
1102C2—22no—
1103C2—42no—
1104C2—84no—
1105C2C22×#53611yescharacteristic
1106C2C22×#57512yes—
subgroupG/H
centerC2×C4C23×D4
commutator, Frattini, cosocleC2×C4C26
socleC22C24×D4
prime radicalC2×#3444C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4 ◁ C23×C42 ◁ G
LECSG ▷ C2×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C22×#533C2semidirect
3. #60866C2semidirect
4. #60865C2semidirect
5. #60864C2semidirect
6. #60863C2semidirect
7. #60862C2semidirect
8. #60861C2semidirect
9. #60860C2semidirect
10. #60854C2semidirect
11. #60846C2semidirect
12. #60663C2semidirect
13. #60618C2semidirect
14. #60511C2semidirect
15. #60484C2semidirect
16. C2×#2920C2semidirect
39. C2×#533C22semidirect
40. C2×#533C22semidirect
41. C2×#533C22semidirect
42. C2×#533C22semidirect
45. C22×C4⋊Q8C22semidirect
49. C22×#125C22semidirect
58. #3240C22semidirect
59. #3239C22semidirect
60. #3238C22semidirect
61. #3237C22semidirect
62. #3236C22semidirect
63. #3235C22semidirect
64. #3234C22semidirect
65. #3233C22semidirect
66. #3232C22semidirect
67. #3231C22semidirect
68. #3230C22semidirect
69. #3229C22semidirect
70. #3228C22semidirect
71. #3227C22semidirect
72. #3226C22semidirect
73. #3166C22semidirect
74. #3166C22semidirect
75. #3165C22semidirect
76. #3165C22semidirect
77. #3162C22semidirect
78. #3160C22semidirect
79. #3142C22semidirect
80. #3141C22semidirect
81. #3140C22semidirect
82. #3139C22semidirect
83. #3138C22semidirect
84. #3135C22semidirect
85. #3131C22semidirect
88. #3093C22semidirect
89. #3092C22semidirect
90. #3091C22semidirect
91. #3080C22semidirect
92. #3079C22semidirect
93. #3078C22semidirect
94. #3077C22semidirect
95. #3076C22semidirect
98. #2920C22semidirect
99. #2920C22semidirect
100. #2920C22semidirect
101. #2920C22semidirect
102. C2×#432C22semidirect
103. C2×#431C22semidirect
335. #501C23semidirect
336. #501C23semidirect
337. #500C23semidirect
338. #499C23semidirect
339. #498C23semidirect
340. #491C23semidirect
341. #490C23semidirect
342. #489C23semidirect
343. #488C23semidirect
344. #487C23semidirect
345. #486C23semidirect
352. #479C23semidirect
353. #478C23semidirect
354. #477C23semidirect
355. #476C23semidirect
356. #475C23semidirect
357. #474C23semidirect

Maximal subgroups

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

subgroupindex
C2×#34442
C22×#5332
#608662
#608652
#608642
#608632
#608622
#608612
#608602
#608542
#608462
#606632
#606182
#605112
#604842
C2×#29202