Finite Group Databasebeta

← #6344111

Subgroups — #6344111

Order 512.

2959 conjugacy classes of subgroups.

The subgroup lattice has 1016 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3511C211yesmaximal, characteristic
2#60283C211yesmaximal, characteristic, complemented
3#60128C211yesmaximal, characteristic, complemented
4#17769C218yesmaximal, complemented
5#17765C214yesmaximal, complemented
6#17755C212yesmaximal, complemented
7#17744C211yesmaximal, characteristic, complemented
8#17744C212yesmaximal, complemented
9#17742C211yesmaximal, characteristic, complemented
10#17739C212yesmaximal, complemented
11#17731C211yesmaximal, characteristic, complemented
12#17731C212yesmaximal, complemented
13C2×#1556C211yesmaximal, characteristic, complemented
14#17727C214yesmaximal, complemented
15#3511—22no—
16#3511—21no—
17#3511—21no—
18#3511—21no—
19#3511—21no—
20#3511—22no—
21#3511C414yes—
22#3511C412yes—
23#3511C412yes—
24#3511C2212yes—
25#3511C2212yes—
26#3511C2214yes—
27C2×#556—21no—
28C2×#555C412yes—
29C2×#554C412yes—
30C2×#553C414yes—
31C2×#548—22no—
32C2×#547—21no—
33C2×#542—22no—
34C2×#537—21no—
35C2×#533C2212yes—
36C2×#532C2212yes—
37C2×#532C2211yescharacteristic
38C22×C4⋊Q8C2211yescharacteristic
39C2×#520—21no—
40C2×C4×#41C2211yescharacteristic
41#2989C2212yescomplemented
42#2989C2214yescomplemented
43#2988C2212yescomplemented
44#2984—21no—
45#2974—21no—
46#2974—22no—
47#2971—21no—
48#2970—22no—
49#2970—21no—
50#2925C2212yescomplemented
51#2925C2214yescomplemented
52#2924—21no—
53#2924—22no—
54#2923—21no—
55#2923—22no—
56#2920C2212yes—
57#2920C2211yescharacteristic
58#2920C2212yes—
59#2920C2211yescharacteristic
60C2×#432C2211yescharacteristic
61C2×#432C2211yescharacteristic
62C2×#432C2212yes—
63C2×#432C2212yes—
64#2906C2212yescomplemented
65#2880—21no—
66#2875—21no—
67#1561C2218yescomplemented
68#1557C2218yescomplemented
69#1557C2214yescomplemented
70#1556C2212yes—
71#1556C2212yes—
72#1556C2211yescharacteristic
73#1556C2212yes—
74#1556C2211yescharacteristic
75#1556C2212yes—
76#1556C2212yes—
77#1556C2214yescomplemented
78#1555C2211yescharacteristic
79#1555C2211yescharacteristic
80#1555C2212yes—
81#1553C2218yescomplemented
82#1553C2214yescomplemented
83#1552C2218yescomplemented
84#1552C2218yescomplemented
85#1549C2214yescomplemented
86#1547C2214yescomplemented
87#1547C2218yescomplemented
88#1546C2214yescomplemented
89#1544C2218yescomplemented
90#1540C2214yescomplemented
91#1540C2218yescomplemented
92C2×#332C2214yescomplemented
93C22×#41—21no—
94C22×#41—22no—
95C22×#41D411yescharacteristic
96C23×Q8—21no—
97C2×#131—22no—
98#556—22no—
99#556—22no—
100#556—24no—
101#556—22no—
102#556—22no—
103#556—24no—
104#555—22no—
105#555—22no—
106#555—24no—
107#555C2×C414yes—
108#555C2×C414yes—
109#555C2×C418yes—
110#554—22no—
111#554—22no—
112#554—24no—
113#554C2×C414yes—
114#554C2×C414yes—
115#554C2×C418yes—
116#553—24no—
117#553—24no—
118#553—24no—
119#553—24no—
120#553C2×C418yes—
121#553C2×C418yes—
122#553C2×C418yes—
123#553C2×C418yes—
124#548—24no—
125#548—24no—
126#548—24no—
127#548—24no—
128#548—24no—
129#548—24no—
130#548—24no—
131#548—24no—
132#547—22no—
133#547—22no—
134#547—24no—
135#547—22no—
136#547—24no—
137#547—22no—
138#542—24no—
139#542—24no—
140#542—24no—
141#542—24no—
142#542—24no—
143#542—24no—
144#542—24no—
145#542—24no—
146#537—22no—
147#537—22no—
148#537—24no—
149#537—22no—
150#537—22no—
151#537—24no—
152#533—22no—
153#533—22no—
154#533—22no—
155#533—22no—
156#533C2×C414yes—
157#533C2×C414yes—
158#533C2314yes—
159#533C2314yes—
160#532—21no—
161#532—21no—
162#532—21no—
163#532—21no—
164#532—22no—
165#532—22no—
166#532—22no—
167#532—22no—
168#532C2×C412yes—
169#532C2×C412yes—
170#532C2×C414yes—
171#532C2×C414yes—
172#532C2312yes—
173#532C2314yes—
174#532C2314yes—
175#532C2312yes—
176C2×C4⋊Q8—21no—
177C2×C4⋊Q8—21no—
178C2×C4⋊Q8—21no—
179C2×C4⋊Q8—21no—
180C2×C4⋊Q8—21no—
181C2×C4⋊Q8—21no—
182C2×C4⋊Q8C2×C412yes—
183C2×C4⋊Q8C2×C412yes—
184C2×C4⋊Q8C2×C412yes—
185C2×C4⋊Q8C2312yes—
186C2×C4⋊Q8C2312yes—
187C2×C4⋊Q8C2312yes—
188C2×C4⋊Q8C2311yescharacteristic
189C2×#127C2311yescharacteristic
190C2×#126—24no—
191C2×#125C2×C414yes—
192C2×#124—24no—
193C2×#124—21no—
194C2×#124—22no—
195C2×#123—24no—
196C2×C22⋊Q8—22no—
197C2×C22⋊Q8—22no—
198C2×C22⋊Q8—22no—
199C2×C22⋊Q8—24no—
200C2×#121—22no—
201C2×#121—24no—
202C2×#121—22no—
203C2×#121—21no—
204C2×#121C2×C412yes—
205C2×#121C2×C414yes—
206#520—24no—
207#520—22no—
208#520—22no—
209#520—22no—
210#520—22no—
211#520—24no—
212C4×#41C2×C411yescharacteristic
213C4×#41C2×C412yes—
214C4×#41C2×C411yescharacteristic
215C4×#41D412yes—
216C4×#41D411yescharacteristic
217C4×#41D411yescharacteristic
218C4×#41D411yescharacteristic
219C4×#41D411yescharacteristic
220C4×#41D412yes—
221C4×#41C2311yescharacteristic
222C4×#41C2311yescharacteristic
223C4×#41C2312yes—
224C2×C4×Q8—22no—
225C2×C4×Q8—22no—
226C2×C4×Q8C2×C411yescharacteristic
227C2×C4×Q8D411yescharacteristic
228C2×C4×D4—24no—
229C2×C4×D4—22no—
230C2×C4×D4—21no—
231C2×C4×D4C2×C414yes—
232C2×C4×D4C2×C412yes—
233C2×C4×D4C2×C412yes—
234C2×C4×D4C2×C411yescharacteristic
235C2×C4×D4D411yescharacteristic
236C2×C4×D4D412yes—
237C2×#117—22no—
238C2×#117C2×C414yes—
239C2×#117D411yescharacteristic
240C2×#117D412yes—
241C22×C4⋊C4—21no—
242C22×C4⋊C4—22no—
243C22×C4⋊C4C2×C412yes—
244C22×C42C2311yescharacteristic
245C22×C42C2312yes—
246#446—22no—
247#446—24no—
248C8×Q8—22no—
249#436—22no—
250#436—24no—
251#435—24no—
252#435—24no—
253#435—24no—
254C8×D4—22no—
255C8×D4—24no—
256#433—24no—
257#433—24no—
258#433—24no—
259#432—21no—
260#432—22no—
261#432—22no—
262#432—21no—
263#432—21no—
264#432—22no—
265#432—21no—
266#432—22no—
267#432—21no—
268#432—22no—
269#432—21no—
270#432—22no—
271#432C2314yes—
272#432C2314yes—
273#432C2312yes—
274#432C2311yescharacteristic
275#432C2311yescharacteristic
276#432C2312yes—
277#432C2311yescharacteristic
278#432C2312yes—
279#432C2311yescharacteristic
280#432C2312yes—
281#431—22no—
282#431—21no—
283#431—21no—
284#431—22no—
285#431C2314yes—
286#431C2312yes—
287#431C2314yes—
288#431C2312yes—
289#424—22no—
290#424—24no—
291#423C2312yes—
292#423C2312yes—
293#423C2314yes—
294#423C2314yes—
295C2×C4⋊C8C2312yes—
296C2×C4⋊C8C2312yes—
297C2×C4⋊C8C2314yes—
298C2×C4⋊C8C2314yes—
299#408—22no—
300#408—24no—
301#407—21no—
302#407—22no—
303#407—21no—
304#407—22no—
305C2×C22⋊C8—21no—
306C2×C22⋊C8—22no—
307C2×C22⋊C8—21no—
308C2×C22⋊C8—22no—
309#405—22no—
310#405—24no—
311C4×M16—21no—
312C4×M16—22no—
313C4×M16—21no—
314C4×M16—22no—
315C2×#97—21no—
316C2×#97—22no—
317C2×#97—21no—
318C2×#97—22no—
319#332C2318yes—
320#332C2318yes—
321#332C2314yes—
322#332C2318yes—
323#332C2314yes—
324#332C2318yes—
325#332C2318yes—
326#331C2314yes—
327#331C2314yes—
328#331C2318yes—
329C2×#41—22no—
330C2×#41—22no—
331C2×#41—24no—
332C2×#41—24no—
333C2×#41—22no—
334C2×#41—22no—
335C2×#41—24no—
336C2×#41—24no—
337C2×#41—44no—
338C2×#41—48no—
339C2×#41—88no—
340C2×#41C22⋊C412yes—
341C2×#41C22⋊C411yescharacteristic
342C2×#41C22⋊C411yescharacteristic
343C2×#41C2×D411yescharacteristic
344C2×#41C2×D411yescharacteristic
345C2×#41C2×D412yes—
346C22×Q8—22no—
347C22×Q8—22no—
348C22×Q8—22no—
349C22×Q8—21no—
350C22×Q8—22no—
351C22×Q8—22no—
352C22×Q8—22no—
353C22×Q8—84no—
354C22×Q8C22⋊C411yescharacteristic
355C22×D4—22no—
356C22×D4—24no—
357C22×D4—21no—
358C22×D4—21no—
359C22×D4C22⋊C411yescharacteristic
360C22×D4C22⋊C412yes—
361C22×D4C22×C412yes—
362C23×C4—22no—
363C23×C4—22no—
364C23×C4—24no—
365C23×C4C22×C411yescharacteristic
366C23×C4C22×C412yes—
367C23×C4C2×D411yescharacteristic
368C23×C4C2×D412yes—
369C23×C4C2×D411yescharacteristic
370C23×C4C2×D412yes—
371#131—48no—
372C2×M16—24no—
373C2×M16—22no—
374C2×M16—22no—
375C2×M16—24no—
376C22×C8—24no—
377C22×C8—22no—
378C22×C8—22no—
379C22×C8—24no—
380C4⋊Q8—22no—
381C4⋊Q8—22no—
382C4⋊Q8—22no—
383C4⋊Q8—22no—
384C4⋊Q8—22no—
385C4⋊Q8—22no—
386C4⋊Q8—22no—
387C4⋊Q8—22no—
388C4⋊Q8—22no—
389C4⋊Q8—22no—
390C4⋊Q8—22no—
391C4⋊Q8—22no—
392C4⋊Q8—21no—
393C4⋊Q8—21no—
394C4⋊Q8C22×C414yes—
395C4⋊Q8C22×C414yes—
396C4⋊Q8C22×C414yes—
397C4⋊Q8C22×C412yes—
398C4⋊Q8C2414yes—
399C4⋊Q8C2412yes—
400#127—21no—
401#127—21no—
402#127C22×C412yes—
403#127C2412yes—
404#126—28no—
405#126—28no—
406#126—28no—
407#126—28no—
408#125—24no—
409#125—24no—
410#125C22×C418yes—
411#125C22×C418yes—
412#124—28no—
413#124—28no—
414#124—28no—
415#124—28no—
416#124—22no—
417#124—22no—
418#124—24no—
419#124—24no—
420#124—22no—
421#124—22no—
422#124—24no—
423#124—24no—
424#123—28no—
425#123—28no—
426#123—28no—
427#123—28no—
428C22⋊Q8—24no—
429C22⋊Q8—24no—
430C22⋊Q8—28no—
431C22⋊Q8—24no—
432C22⋊Q8—24no—
433C22⋊Q8—24no—
434C22⋊Q8—24no—
435C22⋊Q8—24no—
436C22⋊Q8—24no—
437C22⋊Q8—24no—
438C22⋊Q8—24no—
439C22⋊Q8—28no—
440C22⋊Q8—28no—
441C22⋊Q8—28no—
442C22⋊Q8—28no—
443#121—24no—
444#121—24no—
445#121—28no—
446#121—28no—
447#121—28no—
448#121—28no—
449#121—28no—
450#121—24no—
451#121—24no—
452#121—22no—
453#121—22no—
454#121—22no—
455#121—22no—
456#121—24no—
457#121—24no—
458#121—24no—
459#121—24no—
460#121—22no—
461#121—22no—
462#121C22×C414yes—
463#121C22×C414yes—
464#121C22×C418yes—
465#121C22×C418yes—
466C4×Q8—24no—
467C4×Q8—24no—
468C4×Q8—24no—
469C4×Q8—24no—
470C4×Q8—24no—
471C4×Q8—24no—
472C4×Q8—24no—
473C4×Q8—24no—
474C4×Q8C22⋊C411yescharacteristic
475C4×Q8C22⋊C411yescharacteristic
476C4×Q8C22⋊C412yes—
477C4×Q8C22⋊C411yescharacteristic
478C4×Q8C22⋊C411yescharacteristic
479C4×Q8C22⋊C412yes—
480C4×Q8C22×C411yescharacteristic
481C4×Q8C22×C411yescharacteristic
482C4×Q8C22×C412yes—
483C4×Q8C2×D411yescharacteristic
484C4×Q8C2×D411yescharacteristic
485C4×Q8C2×D412yes—
486C4×D4—28no—
487C4×D4—28no—
488C4×D4—28no—
489C4×D4—28no—
490C4×D4—24no—
491C4×D4—24no—
492C4×D4—22no—
493C4×D4—22no—
494C4×D4—24no—
495C4×D4—24no—
496C4×D4—22no—
497C4×D4—22no—
498C4×D4—24no—
499C4×D4—24no—
500C4×D4—22no—
501C4×D4—22no—
502C4×D4C22⋊C412yes—
503C4×D4C22⋊C412yes—
504C4×D4C22⋊C412yes—
505C4×D4C22⋊C412yes—
506C4×D4C22⋊C411yescharacteristic
507C4×D4C22⋊C411yescharacteristic
508C4×D4C22⋊C412yes—
509C4×D4C22⋊C411yescharacteristic
510C4×D4C22⋊C411yescharacteristic
511C4×D4C22⋊C412yes—
512C4×D4C22⋊C412yes—
513C4×D4C22⋊C412yes—
514C4×D4C22⋊C412yes—
515C4×D4C22⋊C412yes—
516C4×D4C22×C418yes—
517C4×D4C22×C418yes—
518C4×D4C22×C414yes—
519C4×D4C22×C414yes—
520C4×D4C22×C412yes—
521C4×D4C22×C412yes—
522C4×D4C22×C412yes—
523C4×D4C22×C412yes—
524C4×D4C22×C411yescharacteristic
525C4×D4C22×C411yescharacteristic
526C4×D4C22×C412yes—
527C4×D4C2×D411yescharacteristic
528C4×D4C2×D412yes—
529C4×D4C2×D411yescharacteristic
530C4×D4C2×D412yes—
531C4×D4C2×D412yes—
532C4×D4C2×D412yes—
533C4×D4C2×D412yes—
534#117—24no—
535#117—24no—
536#117—28no—
537#117—24no—
538#117—24no—
539#117C22⋊C411yescharacteristic
540#117C22⋊C412yes—
541#117C22⋊C411yescharacteristic
542#117C22⋊C412yes—
543#117C22⋊C412yes—
544#117C22⋊C412yes—
545#117C22⋊C412yes—
546#117C22×C418yes—
547#117C22×C418yes—
548#117C2×D411yescharacteristic
549#117C2×D411yescharacteristic
550#117C2×D412yes—
551#117C2×D412yes—
552#117C2×D412yes—
553#117C2×D412yes—
554#117C2×D412yes—
555C2×C4⋊C4—22no—
556C2×C4⋊C4—24no—
557C2×C4⋊C4—22no—
558C2×C4⋊C4—22no—
559C2×C4⋊C4—22no—
560C2×C4⋊C4—22no—
561C2×C4⋊C4—22no—
562C2×C4⋊C4—24no—
563C2×C4⋊C4—22no—
564C2×C4⋊C4—22no—
565C2×C4⋊C4—22no—
566C2×C4⋊C4—21no—
567C2×C4⋊C4—28no—
568C2×C4⋊C4—24no—
569C2×C4⋊C4—24no—
570C2×C4⋊C4C22⋊C411yescharacteristic
571C2×C4⋊C4C22⋊C411yescharacteristic
572C2×C4⋊C4C22⋊C412yes—
573C2×C4⋊C4C22⋊C412yes—
574C2×C4⋊C4C22×C414yes—
575C2×C4⋊C4C22×C414yes—
576C2×C4⋊C4C22×C414yes—
577C2×C4⋊C4C22×C412yes—
578C2×C22⋊C4—24no—
579C2×C22⋊C4—24no—
580C2×C22⋊C4—22no—
581C2×C22⋊C4—24no—
582C2×C22⋊C4—22no—
583C2×C22⋊C4C22⋊C412yes—
584C2×C22⋊C4C22⋊C412yes—
585C2×C22⋊C4C22⋊C412yes—
586C2×C42—24no—
587C2×C42C22×C412yes—
588C2×C42C22×C411yescharacteristic
589C2×C42C22×C411yescharacteristic
590C2×C42C22×C411yescharacteristic
591C2×C42C22×C412yes—
592C2×C42C22×C412yes—
593C2×C42C2×D412yes—
594C2×C42C2×D411yescharacteristic
595C2×C42C2×D411yescharacteristic
596C2×C42C2×D412yes—
597C2×C42C2×D411yescharacteristic
598C2×C42C2×D411yescharacteristic
599C2×C42C2×D411yescharacteristic
600C2×C42C2×D411yescharacteristic
601C2×C42C2×D412yes—
602C2×C42C2×D412yes—
603C2×C42C2×D412yes—
604C2×C42C2×D412yes—
605C2×C42C2411yescharacteristic
606C2×C42C2411yescharacteristic
607C2×C42C2412yes—
608C2×C42C2412yes—
609C2×C42C2411yescharacteristic
610C4⋊C8—24no—
611C4⋊C8—22no—
612C4⋊C8—22no—
613C4⋊C8—24no—
614C4⋊C8—24no—
615C4⋊C8—22no—
616C4⋊C8—22no—
617C4⋊C8—24no—
618C4⋊C8C2412yes—
619C4⋊C8C2412yes—
620C4⋊C8C2414yes—
621C4⋊C8C2412yes—
622C4⋊C8C2414yes—
623C4⋊C8C2412yes—
624C22⋊C8—21no—
625C22⋊C8—22no—
626C22⋊C8—21no—
627C22⋊C8—21no—
628C22⋊C8—22no—
629C22⋊C8—22no—
630C22⋊C8—24no—
631C22⋊C8—22no—
632C22⋊C8—24no—
633C22⋊C8—21no—
634C22⋊C8—22no—
635C22⋊C8—24no—
636C22⋊C8—22no—
637C22⋊C8—24no—
638#97—21no—
639#97—22no—
640#97—21no—
641#97—21no—
642#97—22no—
643#97—24no—
644#97—22no—
645#97—22no—
646#97—24no—
647#97—21no—
648C4×C8—24no—
649C4×C8—22no—
650C4×C8—22no—
651C4×C8—24no—
652C24—22no—
653C24C2×C22⋊C411yescharacteristic
654C24C2×C22⋊C412yes—
655#41—24no—
656#41—24no—
657#41—44no—
658#41—44no—
659#41—42no—
660#41—42no—
661#41—48no—
662#41—48no—
663#41—48no—
664#41—48no—
665#41—88no—
666#41—88no—
667#41—88no—
668#41—88no—
669C2×Q8—22no—
670C2×Q8—24no—
671C2×Q8—24no—
672C2×Q8—24no—
673C2×Q8—22no—
674C2×Q8—24no—
675C2×Q8—42no—
676C2×Q8—48no—
677C2×Q8—44no—
678C2×Q8—84no—
679C2×Q8—84no—
680C2×Q8—84no—
681C2×Q8—84no—
682C2×Q8—84no—
683C2×Q8C2×C22⋊C411yescharacteristic
684C2×Q8C2×C22⋊C411yescharacteristic
685C2×Q8C2×C22⋊C412yes—
686C2×D4—24no—
687C2×D4—24no—
688C2×D4—28no—
689C2×D4—28no—
690C2×D4—22no—
691C2×D4—22no—
692C2×D4—22no—
693C2×D4—22no—
694C2×D4—22no—
695C2×D4—42no—
696C2×D4—44no—
697C2×D4—44no—
698C2×D4—44no—
699C2×D4—44no—
700C2×D4—48no—
701C2×D4—88no—
702C2×D4C2×C22⋊C412yes—
703C2×D4C2×C22⋊C412yes—
704C2×D4C2×C22⋊C411yescharacteristic
705C2×D4C2×C22⋊C411yescharacteristic
706C2×D4C2×C22⋊C412yes—
707C2×D4C2×C22⋊C412yes—
708C2×D4C2×C22⋊C412yes—
709C2×D4C23×C414yes—
710C22×C4—24no—
711C22×C4—22no—
712C22×C4—24no—
713C22×C4—24no—
714C22×C4—24no—
715C22×C4—24no—
716C22×C4—24no—
717C22×C4—28no—
718C22×C4—28no—
719C22×C4—42no—
720C22×C4—44no—
721C22×C4—44no—
722C22×C4—42no—
723C22×C4—44no—
724C22×C4—48no—
725C22×C4—84no—
726C22×C4—88no—
727C22×C4C2×C22⋊C412yes—
728C22×C4C2×C22⋊C411yescharacteristic
729C22×C4C2×C22⋊C411yescharacteristic
730C22×C4C2×C22⋊C411yescharacteristic
731C22×C4C2×C22⋊C411yescharacteristic
732C22×C4C2×C22⋊C411yescharacteristic
733C22×C4C2×C22⋊C412yes—
734C22×C4C2×C22⋊C412yes—
735C22×C4C2×C22⋊C412yes—
736C22×C4C2×C22⋊C412yes—
737C22×C4C2×C22⋊C411yescharacteristic
738C22×C4C2×C22⋊C411yescharacteristic
739C22×C4C2×C22⋊C412yes—
740C22×C4C2×C22⋊C412yes—
741C22×C4C2×C22⋊C411yescharacteristic
742C22×C4C2×C22⋊C411yescharacteristic
743C22×C4C2×C22⋊C412yes—
744C22×C4C2×C22⋊C412yes—
745C22×C4C23×C411yescharacteristic
746C22×C4C23×C411yescharacteristic
747C22×C4C23×C411yescharacteristic
748C22×C4C23×C412yes—
749C22×C4C23×C412yes—
750C22×C4C22×D411yescharacteristic
751C22×C4C22×D411yescharacteristic
752C22×C4C22×D411yescharacteristic
753C22×C4C22×D412yes—
754C22×C4C22×D411yescharacteristic
755C22×C4C22×D411yescharacteristic
756C22×C4C22×D412yes—
757C22×C4C22×D412yes—
758C22×C4C22×D412yes—
759C22×C4C22×D411yescharacteristic
760M16—48no—
761M16—44no—
762M16—82no—
763M16—84no—
764C2×C8—22no—
765C2×C8—24no—
766C2×C8—22no—
767C2×C8—22no—
768C2×C8—24no—
769C2×C8—22no—
770C2×C8—48no—
771C2×C8—44no—
772C2×C8—82no—
773C2×C8—84no—
774C4⋊C4—24no—
775C4⋊C4—24no—
776C4⋊C4—24no—
777C4⋊C4—28no—
778C4⋊C4—28no—
779C4⋊C4—24no—
780C4⋊C4—24no—
781C4⋊C4—24no—
782C4⋊C4—22no—
783C4⋊C4—28no—
784C4⋊C4—28no—
785C4⋊C4—22no—
786C4⋊C4—24no—
787C4⋊C4—22no—
788C4⋊C4C2×C22⋊C412yes—
789C4⋊C4C2×C22⋊C411yescharacteristic
790C4⋊C4C2×C22⋊C411yescharacteristic
791C4⋊C4C2×C22⋊C412yes—
792C4⋊C4C2×C22⋊C411yescharacteristic
793C4⋊C4C2×C22⋊C411yescharacteristic
794C4⋊C4C2×C22⋊C412yes—
795C4⋊C4C2×C22⋊C412yes—
796C4⋊C4C2×C22⋊C412yes—
797C4⋊C4C2×C22⋊C412yes—
798C4⋊C4C2×C22⋊C412yes—
799C4⋊C4C2×C22⋊C412yes—
800C4⋊C4C2×C22⋊C412yes—
801C4⋊C4C2×C22⋊C412yes—
802C4⋊C4C23×C418yes—
803C4⋊C4C23×C414yes—
804C22⋊C4—28no—
805C22⋊C4—28no—
806C22⋊C4—28no—
807C22⋊C4—28no—
808C22⋊C4—24no—
809C22⋊C4—24no—
810C22⋊C4—28no—
811C22⋊C4—28no—
812C22⋊C4—24no—
813C22⋊C4—24no—
814C22⋊C4C2×C22⋊C412yes—
815C22⋊C4C2×C22⋊C412yes—
816C22⋊C4C2×C22⋊C412yes—
817C22⋊C4C2×C22⋊C412yes—
818C22⋊C4C2×C22⋊C412yes—
819C22⋊C4C2×C22⋊C412yes—
820C22⋊C4C2×C22⋊C412yes—
821C22⋊C4C2×C22⋊C412yes—
822C22⋊C4C2×C22⋊C412yes—
823C22⋊C4C2×C22⋊C412yes—
824C22⋊C4C2×C22⋊C412yes—
825C22⋊C4C2×C22⋊C412yes—
826C42—28no—
827C42—28no—
828C42C2×C22⋊C412yes—
829C42C2×C22⋊C412yes—
830C42C2×C22⋊C411yescharacteristic
831C42C2×C22⋊C411yescharacteristic
832C42C2×C22⋊C412yes—
833C42C2×C22⋊C412yes—
834C42C2×C22⋊C411yescharacteristic
835C42C2×C22⋊C411yescharacteristic
836C42C2×C22⋊C411yescharacteristic
837C42C2×C22⋊C411yescharacteristic
838C42C2×C22⋊C412yes—
839C42C2×C22⋊C412yes—
840C42C23×C411yescharacteristic
841C42C23×C412yes—
842C42C23×C412yes—
843C42C23×C411yescharacteristic
844C42C23×C411yescharacteristic
845C42C22×D412yes—
846C42C22×D411yescharacteristic
847C42C22×D411yescharacteristic
848C42C22×D412yes—
849C42C22×D411yescharacteristic
850C42C22×D411yescharacteristic
851C42C22×D411yescharacteristic
852C42C22×D412yes—
853C42C22×D412yes—
854C42C22×D411yescharacteristic
855C42C2511yescharacteristic
856C23—22no—
857C23—22no—
858C23—24no—
859C23—24no—
860C23—41no—
861C23—42no—
862C23—42no—
863C23—44no—
864C23—44no—
865C23—44no—
866C23C22×C22⋊C412yes—
867C23C22×C22⋊C412yes—
868C23C22×C22⋊C411yescharacteristic
869C23C22×C22⋊C411yescharacteristic
870C23C22×C22⋊C411yescharacteristic
871Q8—22no—
872Q8—22no—
873Q8—42no—
874Q8—48no—
875Q8—44no—
876Q8—48no—
877Q8—44no—
878Q8—84no—
879Q8—84no—
880D4—24no—
881D4—24no—
882D4—22no—
883D4—22no—
884D4—42no—
885D4—42no—
886D4—42no—
887D4—44no—
888D4—44no—
889D4—44no—
890D4—44no—
891D4—48no—
892D4—48no—
893D4—44no—
894D4—44no—
895D4—88no—
896D4—88no—
897C2×C4—22no—
898C2×C4—24no—
899C2×C4—22no—
900C2×C4—22no—
901C2×C4—22no—
902C2×C4—24no—
903C2×C4—22no—
904C2×C4—24no—
905C2×C4—22no—
906C2×C4—22no—
907C2×C4—22no—
908C2×C4—24no—
909C2×C4—22no—
910C2×C4—22no—
911C2×C4—24no—
912C2×C4—24no—
913C2×C4—28no—
914C2×C4—42no—
915C2×C4—41no—
916C2×C4—41no—
917C2×C4—42no—
918C2×C4—42no—
919C2×C4—42no—
920C2×C4—41no—
921C2×C4—41no—
922C2×C4—41no—
923C2×C4—42no—
924C2×C4—42no—
925C2×C4—42no—
926C2×C4—42no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—42no—
930C2×C4—42no—
931C2×C4—48no—
932C2×C4—44no—
933C2×C4—48no—
934C2×C4—48no—
935C2×C4—88no—
936C2×C4—88no—
937C2×C4—84no—
938C2×C4—84no—
939C2×C4C22×C22⋊C412yes—
940C2×C4C22×C22⋊C412yes—
941C2×C4C22×C22⋊C411yescharacteristic
942C2×C4C22×C22⋊C411yescharacteristic
943C2×C4C22×C22⋊C411yescharacteristic
944C2×C4C22×C22⋊C411yescharacteristic
945C2×C4C22×C22⋊C411yescharacteristic
946C2×C4C22×C22⋊C412yes—
947C2×C4C22×C22⋊C412yes—
948C2×C4C22×C22⋊C412yes—
949C2×C4C22×C22⋊C412yes—
950C2×C4C22×C22⋊C411yescharacteristic
951C2×C4C22×C22⋊C411yescharacteristic
952C2×C4C22×C22⋊C411yescharacteristic
953C2×C4C22×C22⋊C411yescharacteristic
954C2×C4#57514yes—
955C2×C4C24×C411yescharacteristic
956C2×C4C23×D411yescharacteristic
957C2×C4C23×D411yescharacteristic
958C8—44no—
959C8—42no—
960C8—42no—
961C8—42no—
962C8—44no—
963C8—42no—
964C22—21no—
965C22—21no—
966C22—21no—
967C22—21no—
968C22—21no—
969C22—22no—
970C22—22no—
971C22—21no—
972C22—22no—
973C22—22no—
974C22—21no—
975C22—22no—
976C22—22no—
977C22—44no—
978C22—44no—
979C22—44no—
980C22—44no—
981C22—84no—
982C22—88no—
983C22#288912yes—
984C22#289612yes—
985C22C23×C22⋊C411yescharacteristic
986C4—21no—
987C4—21no—
988C4—22no—
989C4—22no—
990C4—21no—
991C4—21no—
992C4—21no—
993C4—21no—
994C4—22no—
995C4—22no—
996C4—21no—
997C4—22no—
998C4—22no—
999C4—21no—
1000C4—21no—
1001C4—44no—
1002C4—48no—
1003C4#289612yes—
1004C4C2×#57512yes—
1005C4#358512yes—
1006C2—22no—
1007C2—22no—
1008C2—41no—
1009C2—42no—
1010C2—42no—
1011C2—84no—
1012C2C2×#288911yescharacteristic
1013C2C2×#289611yescharacteristic
1014C2#6008711yescharacteristic
subgroupG/H
center, socleC22C23×C22⋊C4
commutatorC2×C4C24×C4
Frattini, cosocleC42C25
prime radicalC2×#3511C2
LCSG ▷ C2×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22 ◁ C2×C4×#41 ◁ G
LECSG ▷ C42 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #60283C2semidirect
3. #60128C2semidirect
4. #17769C2semidirect
5. #17765C2semidirect
6. #17755C2semidirect
7. #17744C2semidirect
8. #17744C2semidirect
9. #17742C2semidirect
10. #17739C2semidirect
11. #17731C2semidirect
12. #17731C2semidirect
13. C2×#1556C2semidirect
14. #17727C2semidirect
41. #2989C22semidirect
42. #2989C22semidirect
43. #2988C22semidirect
50. #2925C22semidirect
51. #2925C22semidirect
64. #2906C22semidirect
67. #1561C22semidirect
68. #1557C22semidirect
69. #1557C22semidirect
77. #1556C22semidirect
81. #1553C22semidirect
82. #1553C22semidirect
83. #1552C22semidirect
84. #1552C22semidirect
85. #1549C22semidirect
86. #1547C22semidirect
87. #1547C22semidirect
88. #1546C22semidirect
89. #1544C22semidirect
90. #1540C22semidirect
91. #1540C22semidirect
92. C2×#332C22semidirect

Maximal subgroups

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

subgroupindex
C2×#35112
#602832
#601282
#177692
#177652
#177552
#177442
#177422
#177392
#177312
C2×#15562
#177272