Finite Group Databasebeta

← #6606789

Subgroups — #6606789

Order 512.

2530 conjugacy classes of subgroups.

The subgroup lattice has 1395 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3308C211yesmaximal, characteristic, complemented
2C2×#3310C211yesmaximal, characteristic, complemented
3C2×#3300C211yesmaximal, characteristic, complemented
4C2×#3294C211yesmaximal, characteristic, complemented
5#37863C211yesmaximal, characteristic, complemented
6#37677C211yesmaximal, characteristic, complemented
7#33228C211yesmaximal, characteristic, complemented
8#33183C211yesmaximal, characteristic, complemented
9#33182C211yesmaximal, characteristic, complemented
10#28523C211yesmaximal, characteristic, complemented
11#28452C211yesmaximal, characteristic, complemented
12#28428C211yesmaximal, characteristic, complemented
13#28425C211yesmaximal, characteristic, complemented
14#28418C211yesmaximal, characteristic, complemented
15#28409C211yesmaximal, characteristic, complemented
16#28360C211yesmaximal, characteristic, complemented
17#28357C211yesmaximal, characteristic, complemented
18#28349C211yesmaximal, characteristic, complemented
19#28346C211yesmaximal, characteristic, complemented
20#28344C211yesmaximal, characteristic, complemented
21#28342C211yesmaximal, characteristic, complemented
22#28335C211yesmaximal, characteristic, complemented
23#28329C211yesmaximal, characteristic, complemented
24#27921C211yesmaximal, characteristic, complemented
25#27909C211yesmaximal, characteristic, complemented
26#25736C211yesmaximal, characteristic, complemented
27#25724C211yesmaximal, characteristic, complemented
28#21696C211yesmaximal, characteristic, complemented
29#21206C211yesmaximal, characteristic, complemented
30C2×#1959C211yesmaximal, characteristic, complemented
31#20493C211yesmaximal, characteristic, complemented
32C2×#552C2211yescharacteristic
33C2×#548C2211yescharacteristic
34C2×#547C2211yescharacteristic
35C2×D42C2211yescharacteristic
36C2×#535C2211yescharacteristic
37C22×#124C2211yescharacteristic
38#3310—28no—
39#3308—28no—
40#3300—28no—
41#3294—28no—
42C2×#496C2211yescharacteristic, complemented
43C2×#495C2211yescharacteristic
44C2×#495C2211yescharacteristic, complemented
45C2×#490C2211yescharacteristic
46C2×#489C2211yescharacteristic, complemented
47C2×#488C2211yescharacteristic, complemented
48C2×#486C2211yescharacteristic
49C2×#484C2211yescharacteristic, complemented
50C2×#485C2211yescharacteristic, complemented
51C2×#482C2211yescharacteristic
52C2×#480C2211yescharacteristic
53C2×#480C2211yescharacteristic
54C2×#480C2211yescharacteristic
55C2×#480C2211yescharacteristic, complemented
56C2×#480C2211yescharacteristic, complemented
57C2×#479C2211yescharacteristic, complemented
58C2×#477C2211yescharacteristic, complemented
59C2×#478C2211yescharacteristic
60C2×#474C2211yescharacteristic
61C2×#468C2211yescharacteristic
62C2×#468C2211yescharacteristic, complemented
63C2×#467C2211yescharacteristic, complemented
64C2×#466C2211yescharacteristic
65C2×#466C2211yescharacteristic
66C2×#466C2211yescharacteristic, complemented
67C2×#465C2211yescharacteristic
68C2×#465C2211yescharacteristic, complemented
69C2×#464C2211yescharacteristic, complemented
70C2×#460C2211yescharacteristic
71C2×#463C2211yescharacteristic, complemented
72C2×#459C2211yescharacteristic
73C2×#452C2211yescharacteristic, complemented
74C2×#449C2211yescharacteristic, complemented
75C2×#451C2211yescharacteristic, complemented
76C2×#448C2211yescharacteristic, complemented
77C2×#450C2211yescharacteristic
78C2×#450C2211yescharacteristic
79C2×#447C2211yescharacteristic
80C2×#447C2211yescharacteristic
81C2×#440C2211yescharacteristic
82C2×#440C2211yescharacteristic, complemented
83C2×C4×Q16C2211yescharacteristic, complemented
84C2×C4×D8C2211yescharacteristic
85C2×#435C2211yescharacteristic
86C2×C8×D4C2211yescharacteristic
87C2×#417C2211yescharacteristic, complemented
88C2×#418C2211yescharacteristic
89C2×#416C2211yescharacteristic, complemented
90C22×#103C2211yescharacteristic, complemented
91C22×#103C2211yescharacteristic, complemented
92C22×#102C2211yescharacteristic
93C22×#102C2211yescharacteristic
94C22×#102C2211yescharacteristic
95C2×#405C2211yescharacteristic, complemented
96C22×#97C2211yescharacteristic, complemented
97#2856C2211yescharacteristic
98#2850C2211yescharacteristic, complemented
99#2720—22no—
100#2718—22no—
101#2676—22no—
102#2670—22no—
103#2660C2211yescharacteristic, complemented
104#2657C2211yescharacteristic
105#2620C2211yescharacteristic
106#2620C2211yescharacteristic, complemented
107#2567C2211yescharacteristic, complemented
108#2566C2211yescharacteristic, complemented
109#2548C2211yescharacteristic
110#2544C2211yescharacteristic
111#2503C2211yescharacteristic, complemented
112#2502C2211yescharacteristic, complemented
113#2501C2211yescharacteristic, complemented
114#2500C2211yescharacteristic, complemented
115#2436C2211yescharacteristic
116#2435C2211yescharacteristic
117#2433C2211yescharacteristic
118#2431C2211yescharacteristic
119#2424—22no—
120#2413—22no—
121#2410—22no—
122#2406—22no—
123#2326C2211yescharacteristic
124#2326C2211yescharacteristic, complemented
125#2317C2211yescharacteristic, complemented
126#2290C2211yescharacteristic
127C2×#384C2211yescharacteristic, complemented
128#2097C2211yescharacteristic, complemented
129#2097C2211yescharacteristic, complemented
130#2095C2211yescharacteristic, complemented
131#2095C2211yescharacteristic, complemented
132#2093C2211yescharacteristic
133#2093C2211yescharacteristic, complemented
134#2093C2211yescharacteristic, complemented
135#2093C2211yescharacteristic, complemented
136#2093C2211yescharacteristic, complemented
137#2093C2211yescharacteristic, complemented
138#2092C2211yescharacteristic
139#2092C2211yescharacteristic, complemented
140#2015C2211yescharacteristic
141#2015C2211yescharacteristic, complemented
142#2015C2211yescharacteristic, complemented
143#2015C2211yescharacteristic, complemented
144#2014C2211yescharacteristic
145#2014C2211yescharacteristic, complemented
146#2012C2211yescharacteristic
147#2012C2211yescharacteristic, complemented
148#2012C2211yescharacteristic, complemented
149#2012C2211yescharacteristic, complemented
150#2011C2211yescharacteristic
151#2011C2211yescharacteristic, complemented
152#1973C2211yescharacteristic
153#1973C2211yescharacteristic, complemented
154#1973C2211yescharacteristic, complemented
155#1973C2211yescharacteristic, complemented
156#1973C2211yescharacteristic, complemented
157#1973C2211yescharacteristic, complemented
158#1972C2211yescharacteristic, complemented
159#1972C2211yescharacteristic, complemented
160#1970C2211yescharacteristic
161#1970C2211yescharacteristic, complemented
162#1969C2211yescharacteristic, complemented
163#1969C2211yescharacteristic, complemented
164#1961C2211yescharacteristic
165#1961C2211yescharacteristic, complemented
166#1961C2211yescharacteristic, complemented
167#1959C2211yescharacteristic
168#1959C2211yescharacteristic
169#1959C2211yescharacteristic
170#1959C2211yescharacteristic
171#1959C2211yescharacteristic, complemented
172#1959C2211yescharacteristic, complemented
173#1959C2211yescharacteristic, complemented
174#1959C2211yescharacteristic, complemented
175#1959C2211yescharacteristic, complemented
176#1959C2211yescharacteristic, complemented
177#1959C2211yescharacteristic, complemented
178#1958C2211yescharacteristic
179#1958C2211yescharacteristic, complemented
180#1958C2211yescharacteristic, complemented
181#1958C2211yescharacteristic, complemented
182#1957C2211yescharacteristic
183#1957C2211yescharacteristic, complemented
184#1957C2211yescharacteristic, complemented
185#1957C2211yescharacteristic, complemented
186#1847C2211yescharacteristic, complemented
187#1845C2211yescharacteristic, complemented
188#1845C2211yescharacteristic, complemented
189#1771C2211yescharacteristic, complemented
190#1770C2211yescharacteristic, complemented
191#1768C2211yescharacteristic, complemented
192#1753C2211yescharacteristic, complemented
193#1752C2211yescharacteristic, complemented
194#1752C2211yescharacteristic, complemented
195C8×C22⋊C4C2211yescharacteristic, complemented
196#1750C2211yescharacteristic, complemented
197C4×C22⋊C8C2211yescharacteristic, complemented
198#1726C2211yescharacteristic, complemented
199C22×#41—21no—
200C22×#41C2311yescharacteristic
201C23×Q8C2311yescharacteristic
202C23×D4—21no—
203C23×D4C2311yescharacteristic
204C23×D4C2311yescharacteristic
205C22×Q16C2311yescharacteristic
206C22×Q16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×SD16C2311yescharacteristic
209C22×SD16C2311yescharacteristic
210C22×SD16C2311yescharacteristic
211C22×SD16C2311yescharacteristic
212C22×SD16C2311yescharacteristic
213C22×D8C2311yescharacteristic
214C22×D8C2311yescharacteristic
215C22×D8C2311yescharacteristic
216C22×D8C2311yescharacteristic
217C22×M16C2311yescharacteristic
218C23×C8C2311yescharacteristic
219C23×C8C2311yescharacteristic
220C23×C8C2311yescharacteristic
221#552—24no—
222#552—24no—
223#548—24no—
224#548—24no—
225#547—24no—
226#547—24no—
227D42—24no—
228D42—24no—
229#535—24no—
230#535—42no—
231C2×C4⋊Q8C2311yescharacteristic
232C2×#127C2311yescharacteristic
233C2×#127C2311yescharacteristic
234C2×#127C2311yescharacteristic
235C2×#127C2311yescharacteristic
236C2×#126—21no—
237C2×#125—21no—
238C2×#125C2311yescharacteristic
239C2×#124—21no—
240C2×#124—24no—
241C2×#124—22no—
242C2×#124—42no—
243C2×#124C2311yescharacteristic
244C2×#124C2311yescharacteristic
245C2×#124C2311yescharacteristic
246C2×#124C2311yescharacteristic
247C2×#124C2311yescharacteristic
248C2×#124C2311yescharacteristic
249C2×#124C2311yescharacteristic
250C2×#124C2311yescharacteristic
251C2×#123—21no—
252C2×#123—21no—
253C2×#123—21no—
254C2×#123—22no—
255C2×C22⋊Q8—21no—
256C2×C22⋊Q8—21no—
257C2×C22⋊Q8C2311yescharacteristic
258C2×C22⋊Q8C2311yescharacteristic
259C2×C22⋊Q8C2311yescharacteristic
260C2×#121—21no—
261C2×#121—22no—
262C2×#121—21no—
263C2×#121—22no—
264C2×#121C2311yescharacteristic
265C2×#121C2311yescharacteristic
266C2×#121C2311yescharacteristic
267C2×#121C2311yescharacteristic
268C2×#121C2311yescharacteristic
269C2×#120—22no—
270C2×#120—21no—
271C2×#120—21no—
272C2×#120—22no—
273C2×C4×Q8C2311yescharacteristic
274C2×C4×Q8C2311yescharacteristic
275C2×C4×D4—21no—
276C2×C4×D4C2311yescharacteristic
277C2×C4×D4C2311yescharacteristic
278C2×C4×D4C2311yescharacteristic
279C2×#117—21no—
280C2×#117C2311yescharacteristic
281C2×#117C2311yescharacteristic
282C22×C4⋊C4—22no—
283C22×C4⋊C4C2311yescharacteristic
284C22×C4⋊C4C2311yescharacteristic
285C22×C4⋊C4C2311yescharacteristic
286C22×C22⋊C4—22no—
287C22×C42C2311yescharacteristic
288#496—42no—
289#495—24no—
290#495—42no—
291#490—24no—
292#489—24no—
293#488—24no—
294#486—24no—
295#485—24no—
296#484—24no—
297#482—24no—
298#480—24no—
299#480—24no—
300#480—24no—
301#480—24no—
302#480—24no—
303#479—24no—
304#478—24no—
305#477—24no—
306#474—24no—
307#468—24no—
308#468—24no—
309#467—24no—
310#466—24no—
311#466—24no—
312#466—24no—
313#465—24no—
314#465—24no—
315#464—24no—
316#463—24no—
317#460—24no—
318#459—24no—
319#452—24no—
320#451—24no—
321#450—24no—
322#450—24no—
323#449—24no—
324#448—24no—
325#447—24no—
326#447—24no—
327#440—24no—
328#440—24no—
329C4×Q16—24no—
330C4×D8—24no—
331#435D418yescomplemented
332C8×D4D418yescomplemented
333C2×#107C2311yescharacteristic
334C2×#107C2311yescharacteristic
335C2×#107C2311yescharacteristic
336C2×#107C2311yescharacteristic
337C2×#107C2311yescharacteristic
338C2×#107C2311yescharacteristic
339C2×#107C2311yescharacteristic
340C2×#107C2311yescharacteristic
341C2×#107C2311yescharacteristic
342C2×#107C2311yescharacteristic
343C2×#106C2311yescharacteristic
344C2×#106C2311yescharacteristic
345C2×C4⋊C8C2311yescharacteristic
346C2×C4⋊C8C2311yescharacteristic
347#418—24no—
348#417—24no—
349#416—24no—
350C2×#103—24no—
351C2×#103—24no—
352C2×#103C2311yescharacteristic
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×#102—24no—
367C2×#102—24no—
368C2×#102—24no—
369C2×#102C2311yescharacteristic
370C2×#102C2311yescharacteristic
371C2×#102C2311yescharacteristic
372C2×#102C2311yescharacteristic
373C2×#102C2311yescharacteristic
374C2×#102C2311yescharacteristic
375C2×#102C2311yescharacteristic
376C2×#102C2311yescharacteristic
377C2×#102C2311yescharacteristic
378C2×#102C2311yescharacteristic
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×#102C2311yescharacteristic
394C2×#102C2311yescharacteristic
395C2×C22⋊C8C2311yescharacteristic
396C2×C22⋊C8C2311yescharacteristic
397C2×C22⋊C8C2311yescharacteristic
398C2×C22⋊C8C2311yescharacteristic
399#405—42no—
400C2×#97—42no—
401C2×#97C2311yescharacteristic
402C2×#97C2311yescharacteristic
403C2×#97C2311yescharacteristic
404C2×#97C2311yescharacteristic
405C2×#97C2311yescharacteristic
406C2×#97C2311yescharacteristic
407C2×#97C2311yescharacteristic
408C2×C4×C8C2311yescharacteristic
409C2×C4×C8C2311yescharacteristic
410C2×C4×C8C2311yescharacteristic
411C2×C4×C8C2311yescharacteristic
412C2×C4×C8C2311yescharacteristic
413#400—22no—
414#399—22no—
415#398—22no—
416#398—22no—
417#396—22no—
418#396—22no—
419#396—22no—
420#395—22no—
421#395—22no—
422#394—22no—
423#394—22no—
424#394—22no—
425#394—22no—
426#394—22no—
427#394—22no—
428#393—22no—
429#392—22no—
430#392—22no—
431#392—22no—
432#392—22no—
433#391C2311yescharacteristic
434#391C2311yescharacteristic
435#391C2311yescharacteristic
436#391C2311yescharacteristic
437#391C2311yescharacteristic
438#390—22no—
439#390—22no—
440#390C2311yescharacteristic
441#390C2311yescharacteristic
442#390C2311yescharacteristic
443#390C2311yescharacteristic
444#390C2311yescharacteristic
445#390C2311yescharacteristic
446#390C2311yescharacteristic
447#389—22no—
448#389—22no—
449#388—22no—
450#388—22no—
451#388—22no—
452#388—22no—
453#388D412yes—
454#387D412yes—
455#386—22no—
456#386—22no—
457#386—22no—
458#386—22no—
459#386D412yes—
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#379—22no—
479C4×C4⋊C4C2311yescharacteristic
480C4×C22⋊C4C2311yescharacteristic
481C4×C22⋊C4C2311yescharacteristic
482#376C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489C25—21no—
490C25—21no—
491C2×#41—22no—
492C2×#41—22no—
493C2×#41—22no—
494C2×#41—41no—
495C2×#41—41no—
496C2×#41—41no—
497C2×#41—44no—
498C2×#41—84no—
499C22×Q8—21no—
500C22×Q8—21no—
501C22×Q8—22no—
502C22×Q8—22no—
503C22×Q8—22no—
504C22×Q8—41no—
505C22×Q8—41no—
506C22×Q8—41no—
507C22×Q8C2411yescharacteristic
508C22×Q8C2411yescharacteristic
509C22×Q8C2411yescharacteristic
510C22×D4—22no—
511C22×D4—22no—
512C22×D4—21no—
513C22×D4—21no—
514C22×D4—21no—
515C22×D4—21no—
516C22×D4—21no—
517C22×D4—21no—
518C22×D4—22no—
519C22×D4—22no—
520C22×D4—22no—
521C22×D4—22no—
522C22×D4—21no—
523C22×D4—21no—
524C22×D4—22no—
525C22×D4—21no—
526C22×D4—22no—
527C22×D4—21no—
528C22×D4—22no—
529C22×D4—41no—
530C22×D4—41no—
531C22×D4—41no—
532C22×D4—41no—
533C22×D4—41no—
534C22×D4—41no—
535C22×D4—44no—
536C22×D4—84no—
537C22×D4C2×D411yescharacteristic
538C22×D4C2411yescharacteristic
539C22×D4C2411yescharacteristic
540C22×D4C2411yescharacteristic
541C22×D4C2411yescharacteristic
542C22×D4C2411yescharacteristic
543C23×C4—21no—
544C23×C4—21no—
545C23×C4—21no—
546C23×C4—21no—
547C23×C4—21no—
548C23×C4—21no—
549C23×C4—21no—
550C23×C4C2×D412yes—
551C23×C4C2411yescharacteristic
552C23×C4C2411yescharacteristic
553C2×Q16—22no—
554C2×Q16—22no—
555C2×Q16—22no—
556C2×Q16—41no—
557C2×Q16—41no—
558C2×Q16—41no—
559C2×SD16—22no—
560C2×SD16—22no—
561C2×SD16—22no—
562C2×SD16—22no—
563C2×SD16—22no—
564C2×SD16—22no—
565C2×SD16—22no—
566C2×SD16—22no—
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×SD16—41no—
576C2×SD16—41no—
577C2×D8—22no—
578C2×D8—22no—
579C2×D8—22no—
580C2×D8—22no—
581C2×D8—22no—
582C2×D8—41no—
583C2×D8—41no—
584C2×D8—41no—
585C2×D8—41no—
586C2×D8—41no—
587C2×D8—41no—
588C2×D8—41no—
589C2×M16—41no—
590C2×M16—41no—
591C2×M16C2×D414yes—
592C22×C8—41no—
593C22×C8—41no—
594C22×C8—41no—
595C22×C8—41no—
596C22×C8—41no—
597C22×C8—41no—
598C22×C8C2×D414yes—
599C22×C8C2×D414yes—
600C22×C8C2×D414yes—
601C22×C8C2411yescharacteristic
602C22×C8C2411yescharacteristic
603C22×C8C2411yescharacteristic
604C22×C8C2411yescharacteristic
605C22×C8C2411yescharacteristic
606C22×C8C2411yescharacteristic
607C22×C8C2411yescharacteristic
608C22×C8C2411yescharacteristic
609C4⋊Q8—22no—
610C4⋊Q8—22no—
611#127—22no—
612#127—22no—
613#127—22no—
614#127—22no—
615#127—22no—
616#127—41no—
617#127—41no—
618#127—41no—
619#126—44no—
620#125—22no—
621#125—22no—
622#125—44no—
623#124—22no—
624#124—22no—
625#124—22no—
626#124—22no—
627#124—22no—
628#124—22no—
629#124—22no—
630#124—22no—
631#124—22no—
632#124—22no—
633#124—48no—
634#124—41no—
635#124—41no—
636#124—41no—
637#124—41no—
638#124—41no—
639#124—44no—
640#124#4114yescomplemented
641#123—44no—
642#123—44no—
643#123—44no—
644#123—84no—
645C22⋊Q8—22no—
646C22⋊Q8—22no—
647C22⋊Q8—22no—
648C22⋊Q8—22no—
649C22⋊Q8—22no—
650C22⋊Q8—22no—
651C22⋊Q8—44no—
652C22⋊Q8—44no—
653#121—22no—
654#121—22no—
655#121—22no—
656#121—22no—
657#121—22no—
658#121—22no—
659#121—22no—
660#121—22no—
661#121—22no—
662#121—22no—
663#121—48no—
664#121—44no—
665#121—44no—
666#121—84no—
667#120—48no—
668#120—44no—
669#120—44no—
670#120—84no—
671C4×Q8—22no—
672C4×Q8—22no—
673C4×Q8—22no—
674C4×Q8—22no—
675C4×D4—22no—
676C4×D4—22no—
677C4×D4—22no—
678C4×D4—22no—
679C4×D4—44no—
680C4×D4C2×D414yes—
681C4×D4C2×D414yes—
682#117—22no—
683#117—22no—
684#117—22no—
685#117—22no—
686#117—44no—
687C2×C4⋊C4—22no—
688C2×C4⋊C4—22no—
689C2×C4⋊C4—22no—
690C2×C4⋊C4—22no—
691C2×C4⋊C4—22no—
692C2×C4⋊C4—22no—
693C2×C4⋊C4—21no—
694C2×C4⋊C4—21no—
695C2×C4⋊C4—21no—
696C2×C4⋊C4—21no—
697C2×C4⋊C4—21no—
698C2×C4⋊C4—21no—
699C2×C4⋊C4—21no—
700C2×C4⋊C4—21no—
701C2×C4⋊C4—21no—
702C2×C4⋊C4—21no—
703C2×C4⋊C4—21no—
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—22no—
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—22no—
729C2×C22⋊C4—22no—
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—22no—
737C2×C22⋊C4—21no—
738C2×C22⋊C4—21no—
739C2×C22⋊C4—21no—
740C2×C22⋊C4—21no—
741C2×C22⋊C4—22no—
742C2×C22⋊C4—22no—
743C2×C22⋊C4—22no—
744C2×C22⋊C4—22no—
745C2×C22⋊C4—22no—
746C2×C22⋊C4—22no—
747C2×C22⋊C4—22no—
748C2×C22⋊C4—22no—
749C2×C22⋊C4—22no—
750C2×C22⋊C4—48no—
751C2×C22⋊C4C2×D412yes—
752C2×C22⋊C4C2×D412yes—
753C2×C22⋊C4C2×D412yes—
754C2×C22⋊C4C2×D411yescharacteristic
755C2×C22⋊C4C2×D411yescharacteristic
756C2×C42—22no—
757C2×C42—22no—
758C2×C42—21no—
759C2×C42—21no—
760C2×C42—21no—
761C2×C42C2×D412yes—
762C2×C42C2411yescharacteristic
763C2×C42C2411yescharacteristic
764C2×C42C2411yescharacteristic
765C2×C42C2411yescharacteristic
766C2×C42C2411yescharacteristic
767#107—22no—
768#107—22no—
769#107—22no—
770#107—22no—
771#107—22no—
772#107—22no—
773#107—22no—
774#107—22no—
775#107—22no—
776#107—22no—
777#106—22no—
778#106—22no—
779C4⋊C8C2×D414yes—
780C4⋊C8C2×D414yes—
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#102—22no—
796#102—22no—
797#102—22no—
798#102—22no—
799#102—22no—
800#102—22no—
801#102—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—
816#102—22no—
817#102—22no—
818#102—22no—
819#102—22no—
820#102—22no—
821C22⋊C8C2×D414yes—
822C22⋊C8C2×D414yes—
823C22⋊C8C2×D414yes—
824C22⋊C8C2×D414yes—
825#97—22no—
826#97—22no—
827#97—41no—
828#97—41no—
829#97—41no—
830#97—41no—
831#97C2×D414yes—
832C4×C8—22no—
833C4×C8—22no—
834C4×C8—41no—
835C4×C8—41no—
836C4×C8C2×D414yes—
837#95—22no—
838#95—22no—
839#95—22no—
840#95—22no—
841#95—22no—
842#95—22no—
843#95—22no—
844#95—22no—
845#95C2×D412yes—
846#95C2×D412yes—
847#95C2×D412yes—
848#95C2×D412yes—
849#95C2×D412yes—
850C24—21no—
851C24—21no—
852C24—21no—
853C24—21no—
854C24—21no—
855C24—42no—
856C24—42no—
857C24—42no—
858C24—42no—
859C24—44no—
860C24—81no—
861C24—81no—
862C24—82no—
863C24—82no—
864C24—82no—
865C24C22×D411yescharacteristic
866C24C22×D411yescharacteristic
867#41—44no—
868#41—44no—
869#41—82no—
870#41—82no—
871#41—816no—
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—42no—
890C2×Q8—44no—
891C2×Q8—44no—
892C2×Q8—42no—
893C2×Q8—42no—
894C2×Q8—81no—
895C2×Q8—82no—
896C2×Q8—82no—
897C2×Q8—82no—
898C2×Q8C2×#4112yes—
899C2×D4—24no—
900C2×D4—21no—
901C2×D4—21no—
902C2×D4—21no—
903C2×D4—21no—
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—21no—
922C2×D4—21no—
923C2×D4—21no—
924C2×D4—21no—
925C2×D4—21no—
926C2×D4—21no—
927C2×D4—21no—
928C2×D4—21no—
929C2×D4—44no—
930C2×D4—44no—
931C2×D4—44no—
932C2×D4—44no—
933C2×D4—42no—
934C2×D4—42no—
935C2×D4—42no—
936C2×D4—44no—
937C2×D4—42no—
938C2×D4—42no—
939C2×D4—42no—
940C2×D4—42no—
941C2×D4—42no—
942C2×D4—42no—
943C2×D4—44no—
944C2×D4—44no—
945C2×D4—44no—
946C2×D4—42no—
947C2×D4—42no—
948C2×D4—42no—
949C2×D4—42no—
950C2×D4—44no—
951C2×D4—82no—
952C2×D4—82no—
953C2×D4—82no—
954C2×D4—82no—
955C2×D4—81no—
956C2×D4—81no—
957C2×D4—82no—
958C2×D4—82no—
959C2×D4—82no—
960C2×D4—82no—
961C2×D4—82no—
962C2×D4—82no—
963C2×D4—82no—
964C2×D4—82no—
965C2×D4—82no—
966C2×D4—82no—
967C2×D4—81no—
968C2×D4—82no—
969C2×D4—816no—
970C2×D4#12714yes—
971C2×D4C2×#4112yes—
972C22×C4—21no—
973C22×C4—21no—
974C22×C4—21no—
975C22×C4—21no—
976C22×C4—21no—
977C22×C4—21no—
978C22×C4—21no—
979C22×C4—21no—
980C22×C4—24no—
981C22×C4—21no—
982C22×C4—24no—
983C22×C4—21no—
984C22×C4—21no—
985C22×C4—21no—
986C22×C4—21no—
987C22×C4—21no—
988C22×C4—21no—
989C22×C4—21no—
990C22×C4—21no—
991C22×C4—21no—
992C22×C4—21no—
993C22×C4—42no—
994C22×C4—42no—
995C22×C4—42no—
996C22×C4—42no—
997C22×C4—42no—
998C22×C4—42no—
999C22×C4—42no—
1000C22×C4—44no—
1001C22×C4—44no—
1002C22×C4—42no—
1003C22×C4—42no—
1004C22×C4—42no—
1005C22×C4—82no—
1006C22×C4—81no—
1007C22×C4—82no—
1008C22×C4—81no—
1009C22×C4—82no—
1010C22×C4C22×D412yes—
1011C22×C4C22×D412yes—
1012C22×C4C22×D412yes—
1013C22×C4C22×D411yescharacteristic
1014C22×C4C22×D411yescharacteristic
1015C22×C4C22×D411yescharacteristic
1016C22×C4C22×D411yescharacteristic
1017C22×C4C22×D412yes—
1018C22×C4C22×D412yes—
1019C22×C4C22×D412yes—
1020C22×C4C22×D412yes—
1021C22×C4C22×D412yes—
1022C22×C4C2511yescharacteristic
1023Q16—44no—
1024Q16—82no—
1025SD16—44no—
1026SD16—44no—
1027SD16—82no—
1028SD16—82no—
1029SD16—82no—
1030SD16—82no—
1031D8—44no—
1032D8—82no—
1033D8—82no—
1034D8—82no—
1035M16—44no—
1036C2×C8—21no—
1037C2×C8—21no—
1038C2×C8—21no—
1039C2×C8—21no—
1040C2×C8—21no—
1041C2×C8—21no—
1042C2×C8—21no—
1043C2×C8—21no—
1044C2×C8—21no—
1045C2×C8—21no—
1046C2×C8—21no—
1047C2×C8—21no—
1048C2×C8—21no—
1049C2×C8—21no—
1050C2×C8—21no—
1051C2×C8—21no—
1052C2×C8—44no—
1053C2×C8—44no—
1054C2×C8—44no—
1055C2×C8C22×D412yes—
1056C2×C8C22×D412yes—
1057C2×C8C22×D412yes—
1058C2×C8C22×D412yes—
1059C2×C8C22×D412yes—
1060C2×C8C22×D412yes—
1061C2×C8C22×D412yes—
1062C2×C8C22×D412yes—
1063C4⋊C4—24no—
1064C4⋊C4—21no—
1065C4⋊C4—21no—
1066C4⋊C4—21no—
1067C4⋊C4—21no—
1068C4⋊C4—21no—
1069C4⋊C4—21no—
1070C4⋊C4—21no—
1071C4⋊C4—21no—
1072C4⋊C4—21no—
1073C4⋊C4—21no—
1074C4⋊C4—21no—
1075C4⋊C4—21no—
1076C4⋊C4—21no—
1077C4⋊C4—21no—
1078C4⋊C4—21no—
1079C4⋊C4—21no—
1080C4⋊C4—42no—
1081C4⋊C4—42no—
1082C4⋊C4—42no—
1083C4⋊C4—42no—
1084C4⋊C4—42no—
1085C4⋊C4—42no—
1086C4⋊C4—42no—
1087C4⋊C4—42no—
1088C4⋊C4—42no—
1089C4⋊C4—42no—
1090C4⋊C4—42no—
1091C4⋊C4—42no—
1092C4⋊C4—82no—
1093C4⋊C4—82no—
1094C4⋊C4—82no—
1095C4⋊C4—82no—
1096C4⋊C4—82no—
1097C4⋊C4—82no—
1098C4⋊C4—82no—
1099C4⋊C4#12714yes—
1100C22⋊C4—24no—
1101C22⋊C4—28no—
1102C22⋊C4—24no—
1103C22⋊C4—42no—
1104C22⋊C4—44no—
1105C22⋊C4—44no—
1106C22⋊C4—44no—
1107C22⋊C4—44no—
1108C22⋊C4—42no—
1109C22⋊C4—42no—
1110C22⋊C4—42no—
1111C22⋊C4—42no—
1112C22⋊C4—42no—
1113C22⋊C4—42no—
1114C22⋊C4—42no—
1115C22⋊C4—42no—
1116C22⋊C4—42no—
1117C22⋊C4—42no—
1118C22⋊C4—42no—
1119C22⋊C4—42no—
1120C22⋊C4—42no—
1121C22⋊C4—44no—
1122C22⋊C4—44no—
1123C22⋊C4—82no—
1124C22⋊C4—82no—
1125C22⋊C4—82no—
1126C22⋊C4—82no—
1127C22⋊C4—82no—
1128C22⋊C4—82no—
1129C22⋊C4—82no—
1130C22⋊C4#12714yes—
1131C22⋊C4#12714yes—
1132C42—24no—
1133C42—21no—
1134C42—21no—
1135C42—21no—
1136C42—21no—
1137C42—21no—
1138C42—21no—
1139C42—42no—
1140C42—42no—
1141C42—42no—
1142C42C22×D412yes—
1143C42C22×D412yes—
1144C42C2×#4112yes—
1145C42H(5,𝔽2)12yes—
1146C23—22no—
1147C23—21no—
1148C23—21no—
1149C23—22no—
1150C23—21no—
1151C23—21no—
1152C23—22no—
1153C23—22no—
1154C23—42no—
1155C23—41no—
1156C23—41no—
1157C23—42no—
1158C23—42no—
1159C23—42no—
1160C23—42no—
1161C23—42no—
1162C23—41no—
1163C23—41no—
1164C23—41no—
1165C23—41no—
1166C23—41no—
1167C23—41no—
1168C23—41no—
1169C23—41no—
1170C23—41no—
1171C23—41no—
1172C23—41no—
1173C23—41no—
1174C23—42no—
1175C23—42no—
1176C23—42no—
1177C23—42no—
1178C23—84no—
1179C23—84no—
1180C23—88no—
1181C23—84no—
1182C23—84no—
1183C23—164no—
1184C23—162no—
1185C23—162no—
1186C23—164no—
1187C23—164no—
1188C23C2×#12712yes—
1189C23C2×#12712yes—
1190C23#57614yes—
1191C23C23×D411yescharacteristic
1192Q8—22no—
1193Q8—22no—
1194Q8—41no—
1195Q8—41no—
1196Q8—41no—
1197Q8—41no—
1198Q8—41no—
1199Q8—41no—
1200Q8—41no—
1201Q8—41no—
1202Q8—41no—
1203Q8—41no—
1204Q8—84no—
1205Q8—84no—
1206D4—28no—
1207D4—22no—
1208D4—22no—
1209D4—41no—
1210D4—41no—
1211D4—41no—
1212D4—41no—
1213D4—41no—
1214D4—41no—
1215D4—41no—
1216D4—41no—
1217D4—41no—
1218D4—41no—
1219D4—41no—
1220D4—41no—
1221D4—41no—
1222D4—41no—
1223D4—41no—
1224D4—41no—
1225D4—41no—
1226D4—41no—
1227D4—84no—
1228D4—84no—
1229D4—84no—
1230D4—84no—
1231D4—84no—
1232D4—84no—
1233D4—84no—
1234D4—84no—
1235D4—84no—
1236D4—164no—
1237D4—162no—
1238D4—164no—
1239D4—164no—
1240C2×C4—22no—
1241C2×C4—22no—
1242C2×C4—21no—
1243C2×C4—21no—
1244C2×C4—21no—
1245C2×C4—21no—
1246C2×C4—22no—
1247C2×C4—22no—
1248C2×C4—22no—
1249C2×C4—22no—
1250C2×C4—22no—
1251C2×C4—22no—
1252C2×C4—22no—
1253C2×C4—22no—
1254C2×C4—22no—
1255C2×C4—22no—
1256C2×C4—22no—
1257C2×C4—22no—
1258C2×C4—22no—
1259C2×C4—22no—
1260C2×C4—22no—
1261C2×C4—22no—
1262C2×C4—22no—
1263C2×C4—22no—
1264C2×C4—22no—
1265C2×C4—22no—
1266C2×C4—48no—
1267C2×C4—41no—
1268C2×C4—41no—
1269C2×C4—42no—
1270C2×C4—41no—
1271C2×C4—41no—
1272C2×C4—41no—
1273C2×C4—41no—
1274C2×C4—41no—
1275C2×C4—41no—
1276C2×C4—41no—
1277C2×C4—41no—
1278C2×C4—41no—
1279C2×C4—41no—
1280C2×C4—41no—
1281C2×C4—41no—
1282C2×C4—41no—
1283C2×C4—41no—
1284C2×C4—42no—
1285C2×C4—42no—
1286C2×C4—42no—
1287C2×C4—42no—
1288C2×C4—42no—
1289C2×C4—42no—
1290C2×C4—42no—
1291C2×C4—84no—
1292C2×C4—84no—
1293C2×C4—84no—
1294C2×C4—84no—
1295C2×C4—84no—
1296C2×C4—84no—
1297C2×C4—84no—
1298C2×C4C2×#12712yes—
1299C2×C4C2×#12712yes—
1300C2×C4C2×#12712yes—
1301C2×C4C2×#12712yes—
1302C2×C4#54614yes—
1303C2×C4C23×D411yescharacteristic
1304C2×C4C23×D411yescharacteristic
1305C2×C4C22×#4111yescharacteristic
1306C2×C4C2×H(5,𝔽2)11yescharacteristic
1307C2×C4#58511yescharacteristic
1308C2×C4#58511yescharacteristic
1309C8—22no—
1310C8—22no—
1311C8—22no—
1312C8—22no—
1313C8—22no—
1314C8—22no—
1315C8—22no—
1316C8—22no—
1317C22—24no—
1318C22—24no—
1319C22—22no—
1320C22—22no—
1321C22—22no—
1322C22—22no—
1323C22—22no—
1324C22—42no—
1325C22—42no—
1326C22—44no—
1327C22—42no—
1328C22—82no—
1329C22—81no—
1330C22—81no—
1331C22—82no—
1332C22—82no—
1333C22—82no—
1334C22—82no—
1335C22—82no—
1336C22—82no—
1337C22—82no—
1338C22—82no—
1339C22—81no—
1340C22—81no—
1341C22—81no—
1342C22—81no—
1343C22—81no—
1344C22—81no—
1345C22—81no—
1346C22—81no—
1347C22—81no—
1348C22—81no—
1349C22—81no—
1350C22—81no—
1351C22—168no—
1352C22—168no—
1353C22#315514yes—
1354C22C22×#12711yescharacteristic
1355C22C2×#54611yescharacteristic
1356C22#350011yescharacteristic
1357C22C2×#57612yes—
1358C22#358612yes—
1359C4—24no—
1360C4—22no—
1361C4—22no—
1362C4—22no—
1363C4—22no—
1364C4—42no—
1365C4—42no—
1366C4—42no—
1367C4—42no—
1368C4—81no—
1369C4—81no—
1370C4—81no—
1371C4—81no—
1372C4—81no—
1373C4—81no—
1374C4—81no—
1375C4—81no—
1376C4—81no—
1377C4—81no—
1378C4D4×#4111yescharacteristic
1379C4D4×#4111yescharacteristic
1380C4#349611yescharacteristic
1381C4#349611yescharacteristic
1382C2—24no—
1383C2—42no—
1384C2—82no—
1385C2—161no—
1386C2—161no—
1387C2—161no—
1388C2—161no—
1389C2#3626011yescharacteristic
1390C2C2×#315511yescharacteristic
1391C2#6065111yescharacteristic
1392C2#6119112yes—
1393C2#6260512yes—
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×#3308C2semidirect
2. C2×#3310C2semidirect
3. C2×#3300C2semidirect
4. C2×#3294C2semidirect
5. #37863C2semidirect
6. #37677C2semidirect
7. #33228C2semidirect
8. #33183C2semidirect
9. #33182C2semidirect
10. #28523C2semidirect
11. #28452C2semidirect
12. #28428C2semidirect
13. #28425C2semidirect
14. #28418C2semidirect
15. #28409C2semidirect
16. #28360C2semidirect
17. #28357C2semidirect
18. #28349C2semidirect
19. #28346C2semidirect
20. #28344C2semidirect
21. #28342C2semidirect
22. #28335C2semidirect
23. #28329C2semidirect
24. #27921C2semidirect
25. #27909C2semidirect
26. #25736C2semidirect
27. #25724C2semidirect
28. #21696C2semidirect
29. #21206C2semidirect
30. C2×#1959C2semidirect
31. #20493C2semidirect
42. C2×#496C22semidirect
44. C2×#495C22semidirect
46. C2×#489C22semidirect
47. C2×#488C22semidirect
49. C2×#484C22semidirect
50. C2×#485C22semidirect
55. C2×#480C22semidirect
56. C2×#480C22semidirect
57. C2×#479C22semidirect
58. C2×#477C22semidirect
62. C2×#468C22semidirect
63. C2×#467C22semidirect
66. C2×#466C22semidirect
68. C2×#465C22semidirect
69. C2×#464C22semidirect
71. C2×#463C22semidirect
73. C2×#452C22semidirect
74. C2×#449C22semidirect
75. C2×#451C22semidirect
76. C2×#448C22semidirect
82. C2×#440C22semidirect
83. C2×C4×Q16C22semidirect
87. C2×#417C22semidirect
89. C2×#416C22semidirect
90. C22×#103C22semidirect
91. C22×#103C22semidirect
95. C2×#405C22semidirect
96. C22×#97C22semidirect
98. #2850C22semidirect
103. #2660C22semidirect
106. #2620C22semidirect
107. #2567C22semidirect
108. #2566C22semidirect
111. #2503C22semidirect
112. #2502C22semidirect
113. #2501C22semidirect
114. #2500C22semidirect
124. #2326C22semidirect
125. #2317C22semidirect
127. C2×#384C22semidirect
128. #2097C22semidirect
129. #2097C22semidirect
130. #2095C22semidirect
131. #2095C22semidirect
133. #2093C22semidirect
134. #2093C22semidirect
135. #2093C22semidirect
136. #2093C22semidirect
137. #2093C22semidirect
139. #2092C22semidirect
141. #2015C22semidirect
142. #2015C22semidirect
143. #2015C22semidirect
145. #2014C22semidirect
147. #2012C22semidirect
148. #2012C22semidirect
149. #2012C22semidirect
151. #2011C22semidirect
153. #1973C22semidirect
154. #1973C22semidirect
155. #1973C22semidirect
156. #1973C22semidirect
157. #1973C22semidirect
158. #1972C22semidirect
159. #1972C22semidirect
161. #1970C22semidirect
162. #1969C22semidirect
163. #1969C22semidirect
165. #1961C22semidirect
166. #1961C22semidirect
171. #1959C22semidirect
172. #1959C22semidirect
173. #1959C22semidirect
174. #1959C22semidirect
175. #1959C22semidirect
176. #1959C22semidirect
177. #1959C22semidirect
179. #1958C22semidirect
180. #1958C22semidirect
181. #1958C22semidirect
183. #1957C22semidirect
184. #1957C22semidirect
185. #1957C22semidirect
186. #1847C22semidirect
187. #1845C22semidirect
188. #1845C22semidirect
189. #1771C22semidirect
190. #1770C22semidirect
191. #1768C22semidirect
192. #1753C22semidirect
193. #1752C22semidirect
194. #1752C22semidirect
195. C8×C22⋊C4C22semidirect
196. #1750C22semidirect
197. C4×C22⋊C8C22semidirect
198. #1726C22semidirect
331. #435D4semidirect
332. C8×D4D4semidirect
640. #124#41semidirect

Maximal subgroups

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

subgroupindex
C2×#33082
C2×#33102
C2×#33002
C2×#32942
#378632
#376772
#332282
#331832
#331822
#285232
#284522
#284282
#284252
#284182
#284092
#283602
#283572
#283492
#283462
#283442
#283422
#283352
#283292
#279212
#279092
#257362
#257242
#216962
#212062
C2×#19592
#204932