Finite Group Databasebeta

← #6606892

Subgroups — #6606892

Order 512.

2372 conjugacy classes of subgroups.

The subgroup lattice has 1347 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3330C211yesmaximal, characteristic, complemented
2C2×#3327C211yesmaximal, characteristic, complemented
3C2×#3315C211yesmaximal, characteristic, complemented
4C2×#3308C211yesmaximal, characteristic, complemented
5#37863C211yesmaximal, characteristic, complemented
6#37680C211yesmaximal, characteristic, complemented
7#33229C211yesmaximal, characteristic, complemented
8#33186C211yesmaximal, characteristic, complemented
9#33182C211yesmaximal, characteristic, complemented
10#28523C211yesmaximal, characteristic, complemented
11#28453C211yesmaximal, characteristic, complemented
12#28433C211yesmaximal, characteristic, complemented
13#28428C211yesmaximal, characteristic, complemented
14#28405C211yesmaximal, characteristic, complemented
15#28401C211yesmaximal, characteristic, complemented
16#28367C211yesmaximal, characteristic, complemented
17#28360C211yesmaximal, characteristic, complemented
18#28358C211yesmaximal, characteristic, complemented
19#28358C211yesmaximal, characteristic, complemented
20#28356C211yesmaximal, characteristic, complemented
21#28356C211yesmaximal, characteristic, complemented
22#28337C211yesmaximal, characteristic, complemented
23#28333C211yesmaximal, characteristic, complemented
24#27921C211yesmaximal, characteristic, complemented
25#27910C211yesmaximal, characteristic, complemented
26#25737C211yesmaximal, characteristic, complemented
27#25723C211yesmaximal, characteristic, complemented
28#21696C211yesmaximal, characteristic, complemented
29#21205C211yesmaximal, characteristic, complemented
30#21200C211yesmaximal, characteristic, complemented
31#20490C211yesmaximal, characteristic, complemented
32C2×#552C2211yescharacteristic
33C2×#548C2211yescharacteristic
34C2×#547C2211yescharacteristic
35C2×#547C2211yescharacteristic
36C2×#536C2211yescharacteristic
37C2×#532C2211yescharacteristic
38#3330—28no—
39#3327—28no—
40#3315—28no—
41#3308—28no—
42C2×#497C2211yescharacteristic
43C2×#495C2211yescharacteristic
44C2×#495C2211yescharacteristic
45C2×#491C2211yescharacteristic
46C2×#489C2211yescharacteristic
47C2×#488C2211yescharacteristic
48C2×#487C2211yescharacteristic
49C2×#484C2211yescharacteristic
50C2×#484C2211yescharacteristic
51C2×#484C2211yescharacteristic
52C2×#484C2211yescharacteristic
53C2×#484C2211yescharacteristic
54C2×#485C2211yescharacteristic
55C2×#482C2211yescharacteristic
56C2×#480C2211yescharacteristic
57C2×#479C2211yescharacteristic
58C2×#477C2211yescharacteristic
59C2×#478C2211yescharacteristic
60C2×#474C2211yescharacteristic
61C2×#470C2211yescharacteristic
62C2×#470C2211yescharacteristic
63C2×#468C2211yescharacteristic
64C2×#468C2211yescharacteristic
65C2×#468C2211yescharacteristic
66C2×#468C2211yescharacteristic
67C2×#467C2211yescharacteristic
68C2×#466C2211yescharacteristic
69C2×#464C2211yescharacteristic
70C2×#462C2211yescharacteristic
71C2×#463C2211yescharacteristic
72C2×#461C2211yescharacteristic
73C2×#452C2211yescharacteristic
74C2×#452C2211yescharacteristic
75C2×#452C2211yescharacteristic
76C2×#449C2211yescharacteristic
77C2×#449C2211yescharacteristic
78C2×#449C2211yescharacteristic
79C2×#451C2211yescharacteristic
80C2×#448C2211yescharacteristic
81C2×#440C2211yescharacteristic
82C2×#440C2211yescharacteristic
83C2×C4×Q16C2211yescharacteristic
84C2×C4×D8C2211yescharacteristic
85C2×#436C2211yescharacteristic
86C2×#435C2211yescharacteristic
87C2×#417C2211yescharacteristic
88C2×#417C2211yescharacteristic
89C2×#417C2211yescharacteristic
90C2×#417C2211yescharacteristic
91C2×#417C2211yescharacteristic
92C2×#419C2211yescharacteristic
93C2×#416C2211yescharacteristic
94C22×#103C2211yescharacteristic
95C2×#405C2211yescharacteristic
96C2×C4×M16C2211yescharacteristic
97#2857C2211yescharacteristic
98#2850C2211yescharacteristic
99#2720—22no—
100#2718—22no—
101#2672—22no—
102#2671—22no—
103#2660C2211yescharacteristic
104#2658C2211yescharacteristic
105#2620C2211yescharacteristic
106#2620C2211yescharacteristic
107#2567C2211yescharacteristic
108#2566C2211yescharacteristic
109#2546C2211yescharacteristic
110#2544C2211yescharacteristic
111#2503C2211yescharacteristic
112#2502C2211yescharacteristic
113#2501C2211yescharacteristic
114#2500C2211yescharacteristic
115#2455—22no—
116#2449—22no—
117#2434C2211yescharacteristic
118#2432C2211yescharacteristic
119#2432C2211yescharacteristic
120#2431C2211yescharacteristic
121#2413—22no—
122#2406—22no—
123#2326C2211yescharacteristic
124#2326C2211yescharacteristic
125#2317C2211yescharacteristic
126#2290C2211yescharacteristic
127C2×#384C2211yescharacteristic
128#2097C2211yescharacteristic
129#2097C2211yescharacteristic
130#2095C2211yescharacteristic
131#2095C2211yescharacteristic
132#2095C2211yescharacteristic
133#2095C2211yescharacteristic
134#2095C2211yescharacteristic
135#2095C2211yescharacteristic
136#2093C2211yescharacteristic
137#2093C2211yescharacteristic
138#2092C2211yescharacteristic
139#2092C2211yescharacteristic
140#2016C2211yescharacteristic
141#2016C2211yescharacteristic
142#2016C2211yescharacteristic
143#2015C2211yescharacteristic
144#2015C2211yescharacteristic
145#2014C2211yescharacteristic
146#2013C2211yescharacteristic
147#2013C2211yescharacteristic
148#2013C2211yescharacteristic
149#2012C2211yescharacteristic
150#2012C2211yescharacteristic
151#2011C2211yescharacteristic
152#1973C2211yescharacteristic
153#1973C2211yescharacteristic
154#1973C2211yescharacteristic
155#1973C2211yescharacteristic
156#1970C2211yescharacteristic
157#1970C2211yescharacteristic
158#1969C2211yescharacteristic
159#1969C2211yescharacteristic
160#1969C2211yescharacteristic
161#1969C2211yescharacteristic
162#1968C2211yescharacteristic
163#1968C2211yescharacteristic
164#1960C2211yescharacteristic
165#1960C2211yescharacteristic
166#1960C2211yescharacteristic
167#1959C2211yescharacteristic
168#1959C2211yescharacteristic
169#1959C2211yescharacteristic
170#1959C2211yescharacteristic
171#1959C2211yescharacteristic
172#1959C2211yescharacteristic
173#1959C2211yescharacteristic
174#1958C2211yescharacteristic
175#1958C2211yescharacteristic
176#1958C2211yescharacteristic
177#1958C2211yescharacteristic
178#1957C2211yescharacteristic
179#1957C2211yescharacteristic
180#1956C2211yescharacteristic
181#1956C2211yescharacteristic
182#1956C2211yescharacteristic
183#1956C2211yescharacteristic
184#1956C2211yescharacteristic
185#1956C2211yescharacteristic
186#1847C2211yescharacteristic
187#1845C2211yescharacteristic
188#1845C2211yescharacteristic
189#1771C2211yescharacteristic
190C8×C4⋊C4C2211yescharacteristic
191#1768C2211yescharacteristic
192#1753C2211yescharacteristic
193#1753C2211yescharacteristic
194#1753C2211yescharacteristic
195C8×C22⋊C4C2211yescharacteristic
196#1750C2211yescharacteristic
197C4×C22⋊C8C2211yescharacteristic
198#1726C2211yescharacteristic
199C22×#41—21no—
200C22×#41C2311yescharacteristic
201C22×#41C2311yescharacteristic
202C22×#41C2311yescharacteristic
203C23×Q8C2311yescharacteristic
204C22×Q16C2311yescharacteristic
205C22×Q16C2311yescharacteristic
206C22×Q16C2311yescharacteristic
207C22×Q16C2311yescharacteristic
208C22×SD16C2311yescharacteristic
209C22×SD16C2311yescharacteristic
210C22×SD16C2311yescharacteristic
211C22×SD16C2311yescharacteristic
212C22×SD16C2311yescharacteristic
213C22×SD16C2311yescharacteristic
214C22×D8C2311yescharacteristic
215C22×D8C2311yescharacteristic
216C22×M16C2311yescharacteristic
217C22×M16C2311yescharacteristic
218C22×M16C2311yescharacteristic
219C23×C8C2311yescharacteristic
220#552—24no—
221#552—24no—
222#548—24no—
223#548—24no—
224#547—24no—
225#547—24no—
226#547—24no—
227#547—24no—
228#536—24no—
229#536—42no—
230#532—24no—
231#532—42no—
232C2×C4⋊Q8C2311yescharacteristic
233C2×C4⋊Q8C2311yescharacteristic
234C2×C4⋊Q8C2311yescharacteristic
235C2×C4⋊Q8C2311yescharacteristic
236C2×C4⋊Q8C2311yescharacteristic
237C2×C4⋊Q8C2311yescharacteristic
238C2×#127C2311yescharacteristic
239C2×#126—21no—
240C2×#125—21no—
241C2×#125C2311yescharacteristic
242C2×#124—21no—
243C2×#124C2311yescharacteristic
244C2×#124C2311yescharacteristic
245C2×#124C2311yescharacteristic
246C2×#124C2311yescharacteristic
247C2×#124C2311yescharacteristic
248C2×#124C2311yescharacteristic
249C2×#123—21no—
250C2×#123—21no—
251C2×#123—22no—
252C2×#123—21no—
253C2×#123—21no—
254C2×#123—21no—
255C2×#123—22no—
256C2×C22⋊Q8—22no—
257C2×C22⋊Q8—21no—
258C2×C22⋊Q8—21no—
259C2×C22⋊Q8C2311yescharacteristic
260C2×C22⋊Q8C2311yescharacteristic
261C2×C22⋊Q8C2311yescharacteristic
262C2×C22⋊Q8C2311yescharacteristic
263C2×C22⋊Q8C2311yescharacteristic
264C2×#121—21no—
265C2×#121—21no—
266C2×#121—22no—
267C2×#121C2311yescharacteristic
268C2×#121C2311yescharacteristic
269C2×#121C2311yescharacteristic
270C2×C4×Q8C2311yescharacteristic
271C2×C4×Q8C2311yescharacteristic
272C2×C4×D4—21no—
273C2×C4×D4—22no—
274C2×C4×D4C2311yescharacteristic
275C2×C4×D4C2311yescharacteristic
276C2×C4×D4C2311yescharacteristic
277C2×#117—21no—
278C2×#117C2311yescharacteristic
279C2×#117C2311yescharacteristic
280C22×C4⋊C4—22no—
281C22×C4⋊C4—21no—
282C22×C4⋊C4C2311yescharacteristic
283C22×C4⋊C4C2311yescharacteristic
284C22×C4⋊C4C2311yescharacteristic
285C22×C42C2311yescharacteristic
286#497—42no—
287#495—24no—
288#495—42no—
289#491—24no—
290#489—24no—
291#488—24no—
292#487—24no—
293#485—24no—
294#484—24no—
295#484—24no—
296#484—24no—
297#484—24no—
298#484—24no—
299#482—24no—
300#480—24no—
301#479—24no—
302#478—24no—
303#477—24no—
304#474—24no—
305#470—24no—
306#470—24no—
307#468—24no—
308#468—24no—
309#468—24no—
310#468—24no—
311#467—24no—
312#466—24no—
313#464—24no—
314#463—24no—
315#462—24no—
316#461—24no—
317#452—24no—
318#452—24no—
319#452—24no—
320#451—24no—
321#449—24no—
322#449—24no—
323#449—24no—
324#448—24no—
325#440—24no—
326#440—24no—
327C4×Q16—24no—
328C4×D8—24no—
329#436D418yescomplemented
330#435D418yescomplemented
331C2×#107C2311yescharacteristic
332C2×#107C2311yescharacteristic
333C2×#107C2311yescharacteristic
334C2×#107C2311yescharacteristic
335C2×#107C2311yescharacteristic
336C2×#107C2311yescharacteristic
337C2×#107C2311yescharacteristic
338C2×#107C2311yescharacteristic
339C2×#107C2311yescharacteristic
340C2×#107C2311yescharacteristic
341C2×#106C2311yescharacteristic
342C2×#106C2311yescharacteristic
343C2×C4⋊C8C2311yescharacteristic
344C2×C4⋊C8C2311yescharacteristic
345#419—24no—
346#417—24no—
347#417—24no—
348#417—24no—
349#417—24no—
350#417—24no—
351#416—24no—
352C2×#103—24no—
353C2×#103C2311yescharacteristic
354C2×#103C2311yescharacteristic
355C2×#103C2311yescharacteristic
356C2×#103C2311yescharacteristic
357C2×#103C2311yescharacteristic
358C2×#103C2311yescharacteristic
359C2×#103C2311yescharacteristic
360C2×#103C2311yescharacteristic
361C2×#103C2311yescharacteristic
362C2×#103C2311yescharacteristic
363C2×#103C2311yescharacteristic
364C2×#103C2311yescharacteristic
365C2×#103C2311yescharacteristic
366C2×#103C2311yescharacteristic
367C2×#103C2311yescharacteristic
368C2×#103C2311yescharacteristic
369C2×#103C2311yescharacteristic
370C2×#103C2311yescharacteristic
371C2×#103C2311yescharacteristic
372C2×#103C2311yescharacteristic
373C2×#103C2311yescharacteristic
374C2×#103C2311yescharacteristic
375C2×#103C2311yescharacteristic
376C2×#103C2311yescharacteristic
377C2×#103C2311yescharacteristic
378C2×#103C2311yescharacteristic
379C2×#102C2311yescharacteristic
380C2×#102C2311yescharacteristic
381C2×#102C2311yescharacteristic
382C2×#102C2311yescharacteristic
383C2×#102C2311yescharacteristic
384C2×#102C2311yescharacteristic
385C2×#102C2311yescharacteristic
386C2×#102C2311yescharacteristic
387C2×#102C2311yescharacteristic
388C2×#102C2311yescharacteristic
389C2×#102C2311yescharacteristic
390C2×#102C2311yescharacteristic
391C2×#102C2311yescharacteristic
392C2×#102C2311yescharacteristic
393C2×C22⋊C8C2311yescharacteristic
394C2×C22⋊C8C2311yescharacteristic
395C2×C22⋊C8C2311yescharacteristic
396C2×C22⋊C8C2311yescharacteristic
397#405—42no—
398C4×M16—42no—
399C2×#97C2311yescharacteristic
400C2×#97C2311yescharacteristic
401C2×#97C2311yescharacteristic
402C2×#97C2311yescharacteristic
403C2×#97C2311yescharacteristic
404C2×C4×C8C2311yescharacteristic
405C2×C4×C8C2311yescharacteristic
406C2×C4×C8C2311yescharacteristic
407C2×C4×C8C2311yescharacteristic
408C2×C4×C8C2311yescharacteristic
409C2×C4×C8C2311yescharacteristic
410C2×C4×C8C2311yescharacteristic
411#400—22no—
412#399—22no—
413#399—22no—
414#399—22no—
415#398—22no—
416#398—22no—
417#398—22no—
418#396—22no—
419#396—22no—
420#396—22no—
421#395—22no—
422#395—22no—
423#395—22no—
424#394—22no—
425#394—22no—
426#394—22no—
427#394—22no—
428#394—22no—
429#394—22no—
430#392—22no—
431#391C2311yescharacteristic
432#391C2311yescharacteristic
433#391C2311yescharacteristic
434#391C2311yescharacteristic
435#391C2311yescharacteristic
436#391C2311yescharacteristic
437#391C2311yescharacteristic
438#390C2311yescharacteristic
439#390C2311yescharacteristic
440#390C2311yescharacteristic
441#390C2311yescharacteristic
442#390C2311yescharacteristic
443#389—22no—
444#389—22no—
445#389—22no—
446#389—22no—
447#388—22no—
448#388—22no—
449#388—22no—
450#388—22no—
451#388D412yes—
452#387D412yes—
453#386—22no—
454#386—22no—
455#386—22no—
456#386D412yes—
457#385—22no—
458#385—22no—
459#385—22no—
460#385—22no—
461#385—22no—
462#385—22no—
463#385—22no—
464#385—22no—
465#385D412yes—
466#384—22no—
467#384C2311yescharacteristic
468#384C2311yescharacteristic
469#384C2311yescharacteristic
470#384C2311yescharacteristic
471#384C2311yescharacteristic
472#384C2311yescharacteristic
473#384C2311yescharacteristic
474#382C2311yescharacteristic
475#382C2311yescharacteristic
476#382C2311yescharacteristic
477#381—22no—
478#380—22no—
479C4×C4⋊C4C2311yescharacteristic
480C4×C22⋊C4C2311yescharacteristic
481C4×C22⋊C4C2311yescharacteristic
482#376C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489C2×#41—22no—
490C2×#41—22no—
491C2×#41—22no—
492C2×#41—22no—
493C2×#41—22no—
494C2×#41—22no—
495C2×#41—22no—
496C2×#41—22no—
497C2×#41—22no—
498C2×#41—41no—
499C2×#41—41no—
500C2×#41—41no—
501C2×#41—41no—
502C2×#41—41no—
503C2×#41—41no—
504C2×#41—41no—
505C2×#41—41no—
506C2×#41—41no—
507C2×#41—44no—
508C2×#41—84no—
509C22×Q8—21no—
510C22×Q8—21no—
511C22×Q8—22no—
512C22×Q8—22no—
513C22×Q8—22no—
514C22×Q8—41no—
515C22×Q8—41no—
516C22×Q8—41no—
517C22×Q8C2411yescharacteristic
518C22×Q8C2411yescharacteristic
519C22×Q8C2411yescharacteristic
520C22×Q8C2411yescharacteristic
521C22×Q8C2411yescharacteristic
522C22×D4—21no—
523C22×D4—21no—
524C22×D4—21no—
525C22×D4—21no—
526C22×D4—21no—
527C22×D4—21no—
528C22×D4—22no—
529C22×D4C2×D411yescharacteristic
530C22×D4C2411yescharacteristic
531C22×D4C2411yescharacteristic
532C22×D4C2411yescharacteristic
533C23×C4—21no—
534C23×C4—21no—
535C23×C4—21no—
536C23×C4—21no—
537C23×C4—21no—
538C23×C4—21no—
539C23×C4—21no—
540C23×C4—21no—
541C23×C4—21no—
542C23×C4C2×D412yes—
543C23×C4C2411yescharacteristic
544C23×C4C2411yescharacteristic
545C2×Q16—22no—
546C2×Q16—22no—
547C2×Q16—22no—
548C2×Q16—22no—
549C2×Q16—22no—
550C2×Q16—41no—
551C2×Q16—41no—
552C2×Q16—41no—
553C2×Q16—41no—
554C2×Q16—41no—
555C2×Q16—41no—
556C2×Q16—41no—
557C2×SD16—22no—
558C2×SD16—22no—
559C2×SD16—22no—
560C2×SD16—22no—
561C2×SD16—22no—
562C2×SD16—22no—
563C2×SD16—22no—
564C2×SD16—22no—
565C2×SD16—41no—
566C2×SD16—41no—
567C2×SD16—41no—
568C2×SD16—41no—
569C2×SD16—41no—
570C2×SD16—41no—
571C2×SD16—41no—
572C2×SD16—41no—
573C2×SD16—41no—
574C2×SD16—41no—
575C2×D8—22no—
576C2×D8—22no—
577C2×D8—22no—
578C2×D8—41no—
579C2×D8—41no—
580C2×D8—41no—
581C2×M16—41no—
582C2×M16—41no—
583C2×M16—41no—
584C2×M16—41no—
585C2×M16—41no—
586C2×M16—41no—
587C2×M16C2×D414yes—
588C2×M16C2×D414yes—
589C2×M16C2×D414yes—
590C22×C8—41no—
591C22×C8—41no—
592C22×C8C2×D414yes—
593C22×C8C2411yescharacteristic
594C22×C8C2411yescharacteristic
595C22×C8C2411yescharacteristic
596C22×C8C2411yescharacteristic
597C22×C8C2411yescharacteristic
598C22×C8C2411yescharacteristic
599C22×C8C2411yescharacteristic
600C22×C8C2411yescharacteristic
601C4⋊Q8—22no—
602C4⋊Q8—22no—
603C4⋊Q8—22no—
604C4⋊Q8—22no—
605C4⋊Q8—22no—
606C4⋊Q8—22no—
607C4⋊Q8—22no—
608C4⋊Q8—22no—
609C4⋊Q8—41no—
610C4⋊Q8—41no—
611C4⋊Q8—41no—
612C4⋊Q8—41no—
613#127—22no—
614#127—41no—
615#126—44no—
616#125—22no—
617#125—22no—
618#125—44no—
619#124—22no—
620#124—22no—
621#124—22no—
622#124—22no—
623#124—22no—
624#124—22no—
625#124—22no—
626#124—22no—
627#124—41no—
628#124—41no—
629#124—41no—
630#124—44no—
631#124#4114yescomplemented
632#123—48no—
633#123—44no—
634#123—44no—
635#123—44no—
636#123—44no—
637#123—44no—
638#123—84no—
639C22⋊Q8—22no—
640C22⋊Q8—22no—
641C22⋊Q8—22no—
642C22⋊Q8—22no—
643C22⋊Q8—22no—
644C22⋊Q8—22no—
645C22⋊Q8—22no—
646C22⋊Q8—22no—
647C22⋊Q8—22no—
648C22⋊Q8—22no—
649C22⋊Q8—48no—
650C22⋊Q8—44no—
651C22⋊Q8—44no—
652#121—22no—
653#121—22no—
654#121—22no—
655#121—22no—
656#121—22no—
657#121—22no—
658#121—48no—
659#121—44no—
660#121—44no—
661C4×Q8—22no—
662C4×Q8—22no—
663C4×Q8—22no—
664C4×Q8—22no—
665C4×D4—22no—
666C4×D4—22no—
667C4×D4—22no—
668C4×D4—22no—
669C4×D4—48no—
670C4×D4—44no—
671C4×D4C2×D414yes—
672C4×D4C2×D414yes—
673#117—22no—
674#117—22no—
675#117—22no—
676#117—22no—
677#117—44no—
678C2×C4⋊C4—22no—
679C2×C4⋊C4—22no—
680C2×C4⋊C4—22no—
681C2×C4⋊C4—22no—
682C2×C4⋊C4—22no—
683C2×C4⋊C4—22no—
684C2×C4⋊C4—21no—
685C2×C4⋊C4—21no—
686C2×C4⋊C4—21no—
687C2×C4⋊C4—21no—
688C2×C4⋊C4—21no—
689C2×C4⋊C4—21no—
690C2×C4⋊C4—21no—
691C2×C4⋊C4—21no—
692C2×C4⋊C4—22no—
693C2×C4⋊C4—21no—
694C2×C4⋊C4—21no—
695C2×C4⋊C4—21no—
696C2×C4⋊C4—22no—
697C2×C4⋊C4—22no—
698C2×C4⋊C4—21no—
699C2×C4⋊C4—21no—
700C2×C4⋊C4—21no—
701C2×C4⋊C4—21no—
702C2×C4⋊C4—22no—
703C2×C4⋊C4—22no—
704C2×C4⋊C4—22no—
705C2×C4⋊C4—22no—
706C2×C4⋊C4—22no—
707C2×C4⋊C4—22no—
708C2×C4⋊C4—22no—
709C2×C4⋊C4—22no—
710C2×C4⋊C4—44no—
711C2×C4⋊C4—84no—
712C2×C4⋊C4C2×D412yes—
713C2×C4⋊C4C2×D412yes—
714C2×C4⋊C4C2×D411yescharacteristic
715C2×C4⋊C4C2411yescharacteristic
716C2×C4⋊C4C2411yescharacteristic
717C2×C4⋊C4C2411yescharacteristic
718C2×C4⋊C4C2411yescharacteristic
719C2×C4⋊C4C2411yescharacteristic
720C2×C4⋊C4C2411yescharacteristic
721C2×C4⋊C4C2411yescharacteristic
722C2×C4⋊C4C2411yescharacteristic
723C2×C22⋊C4—22no—
724C2×C22⋊C4—21no—
725C2×C22⋊C4—21no—
726C2×C22⋊C4—21no—
727C2×C22⋊C4—21no—
728C2×C22⋊C4—21no—
729C2×C22⋊C4—21no—
730C2×C22⋊C4—22no—
731C2×C22⋊C4—21no—
732C2×C22⋊C4—21no—
733C2×C22⋊C4—21no—
734C2×C22⋊C4—21no—
735C2×C22⋊C4—21no—
736C2×C22⋊C4—21no—
737C2×C22⋊C4—21no—
738C2×C22⋊C4—22no—
739C2×C22⋊C4—22no—
740C2×C22⋊C4—22no—
741C2×C22⋊C4—22no—
742C2×C22⋊C4—22no—
743C2×C22⋊C4—22no—
744C2×C22⋊C4—22no—
745C2×C22⋊C4—22no—
746C2×C22⋊C4C2×D412yes—
747C2×C22⋊C4C2×D412yes—
748C2×C22⋊C4C2×D412yes—
749C2×C22⋊C4C2×D411yescharacteristic
750C2×C22⋊C4C2×D411yescharacteristic
751C2×C42—22no—
752C2×C42—22no—
753C2×C42—21no—
754C2×C42—21no—
755C2×C42—21no—
756C2×C42C2×D412yes—
757C2×C42C2411yescharacteristic
758C2×C42C2411yescharacteristic
759C2×C42C2411yescharacteristic
760C2×C42C2411yescharacteristic
761C2×C42C2411yescharacteristic
762#107—22no—
763#107—22no—
764#107—22no—
765#107—22no—
766#107—22no—
767#107—22no—
768#107—22no—
769#107—22no—
770#107—22no—
771#107—22no—
772#106—22no—
773#106—22no—
774C4⋊C8C2×D414yes—
775C4⋊C8C2×D414yes—
776#103—22no—
777#103—22no—
778#103—22no—
779#103—22no—
780#103—22no—
781#103—22no—
782#103—22no—
783#103—22no—
784#103—22no—
785#103—22no—
786#103—22no—
787#103—22no—
788#103—22no—
789#103—22no—
790#103—22no—
791#103—22no—
792#103—22no—
793#103—22no—
794#103—22no—
795#103—22no—
796#103—22no—
797#103—22no—
798#103—22no—
799#103—22no—
800#103—22no—
801#103—22no—
802#102—22no—
803#102—22no—
804#102—22no—
805#102—22no—
806#102—22no—
807#102—22no—
808#102—22no—
809#102—22no—
810#102—22no—
811#102—22no—
812#102—22no—
813#102—22no—
814#102—22no—
815#102—22no—
816C22⋊C8C2×D414yes—
817C22⋊C8C2×D414yes—
818C22⋊C8C2×D414yes—
819C22⋊C8C2×D414yes—
820#97—22no—
821#97—22no—
822#97—41no—
823#97—41no—
824#97C2×D414yes—
825C4×C8—22no—
826C4×C8—22no—
827C4×C8—41no—
828C4×C8—41no—
829C4×C8—41no—
830C4×C8—41no—
831C4×C8C2×D414yes—
832#95—22no—
833#95—22no—
834#95—22no—
835#95—22no—
836#95—22no—
837#95—22no—
838#95—22no—
839#95—22no—
840#95—22no—
841#95—22no—
842#95C2×D412yes—
843#95C2×D412yes—
844#95C2×D412yes—
845#95C2×D412yes—
846#95C2×D412yes—
847C24—21no—
848C24—21no—
849C24—21no—
850C24C22×D411yescharacteristic
851C24C22×D411yescharacteristic
852#41—44no—
853#41—44no—
854#41—44no—
855#41—44no—
856#41—44no—
857#41—44no—
858#41—82no—
859#41—82no—
860#41—82no—
861#41—82no—
862#41—82no—
863#41—82no—
864#41—816no—
865C2×Q8—21no—
866C2×Q8—21no—
867C2×Q8—21no—
868C2×Q8—21no—
869C2×Q8—21no—
870C2×Q8—21no—
871C2×Q8—21no—
872C2×Q8—21no—
873C2×Q8—21no—
874C2×Q8—21no—
875C2×Q8—21no—
876C2×Q8—21no—
877C2×Q8—21no—
878C2×Q8—21no—
879C2×Q8—21no—
880C2×Q8—21no—
881C2×Q8—21no—
882C2×Q8—21no—
883C2×Q8—21no—
884C2×Q8—21no—
885C2×Q8—21no—
886C2×Q8—21no—
887C2×Q8—21no—
888C2×Q8—21no—
889C2×Q8—21no—
890C2×Q8—21no—
891C2×Q8—21no—
892C2×Q8—21no—
893C2×Q8—21no—
894C2×Q8—42no—
895C2×Q8—44no—
896C2×Q8—44no—
897C2×Q8—42no—
898C2×Q8—42no—
899C2×Q8—81no—
900C2×Q8—82no—
901C2×Q8—82no—
902C2×Q8—82no—
903C2×Q8C2×#4112yes—
904C2×D4—21no—
905C2×D4—21no—
906C2×D4—21no—
907C2×D4—21no—
908C2×D4—21no—
909C2×D4—21no—
910C2×D4—21no—
911C2×D4—21no—
912C2×D4—21no—
913C2×D4—21no—
914C2×D4—21no—
915C2×D4—21no—
916C2×D4—21no—
917C2×D4—21no—
918C2×D4—21no—
919C2×D4—21no—
920C2×D4—21no—
921C2×D4—42no—
922C2×D4—44no—
923C2×D4—42no—
924C2×D4—42no—
925C2×D4—42no—
926C2×D4—44no—
927C2×D4—42no—
928C2×D4—42no—
929C2×D4—42no—
930C2×D4—42no—
931C2×D4—42no—
932C2×D4—42no—
933C2×D4—44no—
934C2×D4—82no—
935C2×D4—82no—
936C2×D4—81no—
937C2×D4—81no—
938C2×D4—81no—
939C2×D4—82no—
940C2×D4#12714yes—
941C2×D4C2×#4112yes—
942C22×C4—21no—
943C22×C4—21no—
944C22×C4—21no—
945C22×C4—21no—
946C22×C4—21no—
947C22×C4—21no—
948C22×C4—21no—
949C22×C4—21no—
950C22×C4—21no—
951C22×C4—24no—
952C22×C4—24no—
953C22×C4—21no—
954C22×C4—21no—
955C22×C4—21no—
956C22×C4—21no—
957C22×C4—21no—
958C22×C4—21no—
959C22×C4—21no—
960C22×C4—21no—
961C22×C4—21no—
962C22×C4—21no—
963C22×C4—21no—
964C22×C4—21no—
965C22×C4—42no—
966C22×C4—42no—
967C22×C4—42no—
968C22×C4—42no—
969C22×C4—42no—
970C22×C4—44no—
971C22×C4—44no—
972C22×C4—42no—
973C22×C4—42no—
974C22×C4—42no—
975C22×C4—42no—
976C22×C4—42no—
977C22×C4—42no—
978C22×C4—42no—
979C22×C4—42no—
980C22×C4—42no—
981C22×C4—82no—
982C22×C4—81no—
983C22×C4—81no—
984C22×C4—81no—
985C22×C4—82no—
986C22×C4—81no—
987C22×C4—82no—
988C22×C4C22×D412yes—
989C22×C4C22×D412yes—
990C22×C4C22×D411yescharacteristic
991C22×C4C22×D411yescharacteristic
992C22×C4C22×D411yescharacteristic
993C22×C4C22×D411yescharacteristic
994C22×C4C22×D412yes—
995C22×C4C22×D412yes—
996C22×C4C22×D412yes—
997C22×C4C22×D412yes—
998C22×C4C22×D412yes—
999C22×C4C22×D412yes—
1000C22×C4C2511yescharacteristic
1001Q16—44no—
1002Q16—82no—
1003Q16—82no—
1004Q16—82no—
1005SD16—44no—
1006SD16—44no—
1007SD16—82no—
1008SD16—82no—
1009SD16—82no—
1010SD16—82no—
1011D8—44no—
1012D8—82no—
1013M16—44no—
1014M16—44no—
1015M16—44no—
1016C2×C8—21no—
1017C2×C8—21no—
1018C2×C8—21no—
1019C2×C8—21no—
1020C2×C8—21no—
1021C2×C8—21no—
1022C2×C8—21no—
1023C2×C8—21no—
1024C2×C8—21no—
1025C2×C8—21no—
1026C2×C8—21no—
1027C2×C8—21no—
1028C2×C8—21no—
1029C2×C8—21no—
1030C2×C8—21no—
1031C2×C8—21no—
1032C2×C8—44no—
1033C2×C8C22×D412yes—
1034C2×C8C22×D412yes—
1035C2×C8C22×D412yes—
1036C2×C8C22×D412yes—
1037C2×C8C22×D412yes—
1038C2×C8C22×D412yes—
1039C2×C8C22×D412yes—
1040C2×C8C22×D412yes—
1041C4⋊C4—24no—
1042C4⋊C4—24no—
1043C4⋊C4—21no—
1044C4⋊C4—21no—
1045C4⋊C4—21no—
1046C4⋊C4—21no—
1047C4⋊C4—21no—
1048C4⋊C4—21no—
1049C4⋊C4—21no—
1050C4⋊C4—21no—
1051C4⋊C4—21no—
1052C4⋊C4—21no—
1053C4⋊C4—21no—
1054C4⋊C4—21no—
1055C4⋊C4—21no—
1056C4⋊C4—21no—
1057C4⋊C4—21no—
1058C4⋊C4—21no—
1059C4⋊C4—44no—
1060C4⋊C4—44no—
1061C4⋊C4—42no—
1062C4⋊C4—42no—
1063C4⋊C4—42no—
1064C4⋊C4—42no—
1065C4⋊C4—42no—
1066C4⋊C4—42no—
1067C4⋊C4—42no—
1068C4⋊C4—42no—
1069C4⋊C4—42no—
1070C4⋊C4—42no—
1071C4⋊C4—42no—
1072C4⋊C4—42no—
1073C4⋊C4—42no—
1074C4⋊C4—42no—
1075C4⋊C4—42no—
1076C4⋊C4—44no—
1077C4⋊C4—82no—
1078C4⋊C4—82no—
1079C4⋊C4—82no—
1080C4⋊C4—82no—
1081C4⋊C4—82no—
1082C4⋊C4—82no—
1083C4⋊C4—82no—
1084C4⋊C4—82no—
1085C4⋊C4#12714yes—
1086C22⋊C4—28no—
1087C22⋊C4—24no—
1088C22⋊C4—24no—
1089C22⋊C4—42no—
1090C22⋊C4—44no—
1091C22⋊C4—42no—
1092C22⋊C4—42no—
1093C22⋊C4—42no—
1094C22⋊C4—42no—
1095C22⋊C4—42no—
1096C22⋊C4—42no—
1097C22⋊C4—42no—
1098C22⋊C4—42no—
1099C22⋊C4—42no—
1100C22⋊C4—42no—
1101C22⋊C4—42no—
1102C22⋊C4—42no—
1103C22⋊C4—42no—
1104C22⋊C4—44no—
1105C22⋊C4—44no—
1106C22⋊C4—44no—
1107C22⋊C4—82no—
1108C22⋊C4—82no—
1109C22⋊C4—82no—
1110C22⋊C4—82no—
1111C22⋊C4—82no—
1112C22⋊C4#12714yes—
1113C22⋊C4#12714yes—
1114C42—24no—
1115C42—21no—
1116C42—21no—
1117C42—21no—
1118C42—21no—
1119C42—21no—
1120C42—21no—
1121C42—42no—
1122C42—42no—
1123C42—42no—
1124C42C22×D412yes—
1125C42C22×D412yes—
1126C42C2×#4112yes—
1127C42H(5,𝔽2)12yes—
1128C23—22no—
1129C23—22no—
1130C23—21no—
1131C23—21no—
1132C23—21no—
1133C23—21no—
1134C23—22no—
1135C23—22no—
1136C23—22no—
1137C23—42no—
1138C23—41no—
1139C23—41no—
1140C23—42no—
1141C23—42no—
1142C23—42no—
1143C23—41no—
1144C23—41no—
1145C23—41no—
1146C23—41no—
1147C23—41no—
1148C23—41no—
1149C23—42no—
1150C23—42no—
1151C23C2×#12712yes—
1152C23C2×#12712yes—
1153C23C23×D411yescharacteristic
1154Q8—22no—
1155Q8—22no—
1156Q8—41no—
1157Q8—41no—
1158Q8—41no—
1159Q8—41no—
1160Q8—41no—
1161Q8—41no—
1162Q8—41no—
1163Q8—41no—
1164Q8—41no—
1165Q8—41no—
1166Q8—41no—
1167Q8—41no—
1168Q8—41no—
1169Q8—41no—
1170Q8—41no—
1171Q8—41no—
1172Q8—41no—
1173Q8—41no—
1174Q8—84no—
1175Q8—84no—
1176D4—22no—
1177D4—22no—
1178D4—44no—
1179D4—41no—
1180D4—41no—
1181D4—41no—
1182D4—41no—
1183D4—41no—
1184D4—41no—
1185D4—41no—
1186D4—41no—
1187D4—41no—
1188D4—41no—
1189D4—88no—
1190D4—84no—
1191D4—84no—
1192D4—84no—
1193D4—84no—
1194D4—84no—
1195D4—84no—
1196C2×C4—22no—
1197C2×C4—22no—
1198C2×C4—22no—
1199C2×C4—22no—
1200C2×C4—21no—
1201C2×C4—21no—
1202C2×C4—21no—
1203C2×C4—21no—
1204C2×C4—22no—
1205C2×C4—22no—
1206C2×C4—22no—
1207C2×C4—22no—
1208C2×C4—22no—
1209C2×C4—22no—
1210C2×C4—22no—
1211C2×C4—22no—
1212C2×C4—22no—
1213C2×C4—22no—
1214C2×C4—22no—
1215C2×C4—22no—
1216C2×C4—22no—
1217C2×C4—22no—
1218C2×C4—22no—
1219C2×C4—22no—
1220C2×C4—22no—
1221C2×C4—48no—
1222C2×C4—41no—
1223C2×C4—41no—
1224C2×C4—42no—
1225C2×C4—42no—
1226C2×C4—42no—
1227C2×C4—42no—
1228C2×C4—42no—
1229C2×C4—42no—
1230C2×C4—42no—
1231C2×C4—41no—
1232C2×C4—41no—
1233C2×C4—41no—
1234C2×C4—41no—
1235C2×C4—41no—
1236C2×C4—41no—
1237C2×C4—41no—
1238C2×C4—41no—
1239C2×C4—41no—
1240C2×C4—41no—
1241C2×C4—41no—
1242C2×C4—41no—
1243C2×C4—41no—
1244C2×C4—41no—
1245C2×C4—41no—
1246C2×C4—41no—
1247C2×C4—41no—
1248C2×C4—41no—
1249C2×C4—41no—
1250C2×C4—41no—
1251C2×C4—42no—
1252C2×C4—84no—
1253C2×C4—84no—
1254C2×C4—84no—
1255C2×C4—84no—
1256C2×C4—84no—
1257C2×C4—84no—
1258C2×C4—84no—
1259C2×C4—84no—
1260C2×C4—84no—
1261C2×C4C2×#12712yes—
1262C2×C4C2×#12712yes—
1263C2×C4C2×#12712yes—
1264C2×C4C2×#12712yes—
1265C2×C4#54614yes—
1266C2×C4#57814yes—
1267C2×C4C23×D411yescharacteristic
1268C2×C4C23×D411yescharacteristic
1269C2×C4C22×#4111yescharacteristic
1270C2×C4C2×H(5,𝔽2)11yescharacteristic
1271C2×C4#58511yescharacteristic
1272C2×C4#58511yescharacteristic
1273C8—22no—
1274C8—22no—
1275C8—22no—
1276C8—22no—
1277C8—22no—
1278C8—22no—
1279C8—22no—
1280C8—22no—
1281C22—22no—
1282C22—22no—
1283C22—22no—
1284C22—22no—
1285C22—22no—
1286C22—22no—
1287C22—42no—
1288C22—42no—
1289C22—42no—
1290C22—42no—
1291C22—44no—
1292C22—42no—
1293C22—82no—
1294C22—81no—
1295C22—81no—
1296C22—82no—
1297C22—82no—
1298C22—82no—
1299C22—82no—
1300C22—81no—
1301C22—81no—
1302C22—81no—
1303C22—81no—
1304C22—81no—
1305C22—81no—
1306C22C22×#12711yescharacteristic
1307C22C2×#54611yescharacteristic
1308C22#350011yescharacteristic
1309C22C2×#57812yes—
1310C22#358512yes—
1311C4—24no—
1312C4—24no—
1313C4—22no—
1314C4—22no—
1315C4—22no—
1316C4—22no—
1317C4—42no—
1318C4—42no—
1319C4—42no—
1320C4—81no—
1321C4—81no—
1322C4—81no—
1323C4—81no—
1324C4—81no—
1325C4—81no—
1326C4—81no—
1327C4—81no—
1328C4—81no—
1329C4—81no—
1330C4—81no—
1331C4—81no—
1332C4D4×#4111yescharacteristic
1333C4D4×#4111yescharacteristic
1334C4#349611yescharacteristic
1335C4#349611yescharacteristic
1336C2—42no—
1337C2—42no—
1338C2—82no—
1339C2—161no—
1340C2—161no—
1341C2#3626011yescharacteristic
1342C2#6064411yescharacteristic
1343C2#6064811yescharacteristic
1344C2#6119412yes—
1345C2#6261912yes—
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2290 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3330C2semidirect
2. C2×#3327C2semidirect
3. C2×#3315C2semidirect
4. C2×#3308C2semidirect
5. #37863C2semidirect
6. #37680C2semidirect
7. #33229C2semidirect
8. #33186C2semidirect
9. #33182C2semidirect
10. #28523C2semidirect
11. #28453C2semidirect
12. #28433C2semidirect
13. #28428C2semidirect
14. #28405C2semidirect
15. #28401C2semidirect
16. #28367C2semidirect
17. #28360C2semidirect
18. #28358C2semidirect
19. #28358C2semidirect
20. #28356C2semidirect
21. #28356C2semidirect
22. #28337C2semidirect
23. #28333C2semidirect
24. #27921C2semidirect
25. #27910C2semidirect
26. #25737C2semidirect
27. #25723C2semidirect
28. #21696C2semidirect
29. #21205C2semidirect
30. #21200C2semidirect
31. #20490C2semidirect
329. #436D4semidirect
330. #435D4semidirect
631. #124#41semidirect

Maximal subgroups

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

subgroupindex
C2×#33302
C2×#33272
C2×#33152
C2×#33082
#378632
#376802
#332292
#331862
#331822
#285232
#284532
#284332
#284282
#284052
#284012
#283672
#283602
#283582
#283562
#283372
#283332
#279212
#279102
#257372
#257232
#216962
#212052
#212002
#204902