Finite Group Databasebeta

← #6606897

Subgroups — #6606897

Order 512.

2325 conjugacy classes of subgroups.

The subgroup lattice has 1343 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3331C211yesmaximal, characteristic, complemented
2C2×#3323C211yesmaximal, characteristic, complemented
3C2×#3315C211yesmaximal, characteristic, complemented
4C2×#3314C211yesmaximal, characteristic, complemented
5#37865C211yesmaximal, characteristic, complemented
6#37682C211yesmaximal, characteristic
7#33229C211yesmaximal, characteristic, complemented
8#33186C211yesmaximal, characteristic, complemented
9#33180C211yesmaximal, characteristic, complemented
10#28525C211yesmaximal, characteristic, complemented
11#28456C211yesmaximal, characteristic, complemented
12#28436C211yesmaximal, characteristic, complemented
13#28427C211yesmaximal, characteristic, complemented
14#28408C211yesmaximal, characteristic, complemented
15#28403C211yesmaximal, characteristic, complemented
16#28366C211yesmaximal, characteristic, complemented
17#28362C211yesmaximal, characteristic, complemented
18#28361C211yesmaximal, characteristic, complemented
19#28360C211yesmaximal, characteristic, complemented
20#28356C211yesmaximal, characteristic, complemented
21#28356C211yesmaximal, characteristic, complemented
22#28338C211yesmaximal, characteristic, complemented
23#28330C211yesmaximal, characteristic, complemented
24#27922C211yesmaximal, characteristic, complemented
25#27912C211yesmaximal, characteristic, complemented
26#25732C211yesmaximal, characteristic, complemented
27#25719C211yesmaximal, characteristic, complemented
28#21695C211yesmaximal, characteristic, complemented
29#21206C211yesmaximal, characteristic, complemented
30#21201C211yesmaximal, characteristic, complemented
31#20490C211yesmaximal, characteristic, complemented
32C2×#554C2211yescharacteristic
33C2×#552C2211yescharacteristic
34C2×#547C2211yescharacteristic
35C2×#546C2211yescharacteristic
36C2×#535C2211yescharacteristic
37C2×#532C2211yescharacteristic
38#3331—28no—
39#3323—28no—
40#3315—28no—
41#3314—28no—
42C2×#497C2211yescharacteristic
43C2×#494C2211yescharacteristic, complemented
44C2×#492C2211yescharacteristic
45C2×#491C2211yescharacteristic, complemented
46C2×#489C2211yescharacteristic
47C2×#488C2211yescharacteristic
48C2×#487C2211yescharacteristic, complemented
49C2×#484C2211yescharacteristic
50C2×#484C2211yescharacteristic, complemented
51C2×#481C2211yescharacteristic
52C2×#485C2211yescharacteristic
53C2×#485C2211yescharacteristic
54C2×#483C2211yescharacteristic
55C2×#483C2211yescharacteristic, complemented
56C2×#480C2211yescharacteristic
57C2×#478C2211yescharacteristic
58C2×#478C2211yescharacteristic, complemented
59C2×#476C2211yescharacteristic, complemented
60C2×#474C2211yescharacteristic
61C2×#470C2211yescharacteristic
62C2×#470C2211yescharacteristic
63C2×#470C2211yescharacteristic, complemented
64C2×#470C2211yescharacteristic, complemented
65C2×#468C2211yescharacteristic
66C2×#468C2211yescharacteristic
67C2×#467C2211yescharacteristic
68C2×#467C2211yescharacteristic
69C2×#464C2211yescharacteristic
70C2×#464C2211yescharacteristic
71C2×#462C2211yescharacteristic, complemented
72C2×#462C2211yescharacteristic, complemented
73C2×#452C2211yescharacteristic
74C2×#452C2211yescharacteristic
75C2×#452C2211yescharacteristic
76C2×#452C2211yescharacteristic
77C2×#452C2211yescharacteristic, complemented
78C2×#452C2211yescharacteristic, complemented
79C2×#450C2211yescharacteristic
80C2×#450C2211yescharacteristic
81C2×#440C2211yescharacteristic
82C2×#440C2211yescharacteristic, complemented
83C2×C4×SD16C2211yescharacteristic
84C2×C4×SD16C2211yescharacteristic, complemented
85C2×#436C2211yescharacteristic
86C2×#435C2211yescharacteristic
87C2×#417C2211yescharacteristic
88C2×#417C2211yescharacteristic
89C2×#417C2211yescharacteristic
90C2×#417C2211yescharacteristic, complemented
91C2×#417C2211yescharacteristic, complemented
92C2×#418C2211yescharacteristic
93C2×#416C2211yescharacteristic
94C22×#102C2211yescharacteristic
95C2×#405C2211yescharacteristic
96C2×C4×M16C2211yescharacteristic, complemented
97#2857C2211yescharacteristic, complemented
98#2850C2211yescharacteristic
99#2719—22no—
100#2698—22no—
101#2671—22no—
102#2668—22no—
103#2660C2211yescharacteristic, complemented
104#2658C2211yescharacteristic
105#2621C2211yescharacteristic
106#2621C2211yescharacteristic
107#2568C2211yescharacteristic, complemented
108#2565C2211yescharacteristic, complemented
109#2547C2211yescharacteristic
110#2544C2211yescharacteristic
111#2503C2211yescharacteristic
112#2503C2211yescharacteristic, complemented
113#2502C2211yescharacteristic, complemented
114#2499C2211yescharacteristic
115#2443—22no—
116#2438—22no—
117#2435C2211yescharacteristic
118#2432C2211yescharacteristic
119#2432C2211yescharacteristic
120#2431C2211yescharacteristic
121#2419—22no—
122#2418—22no—
123#2328C2211yescharacteristic
124#2327C2211yescharacteristic, complemented
125#2317C2211yescharacteristic
126#2290C2211yescharacteristic
127C2×#382C2211yescharacteristic, complemented
128#2097C2211yescharacteristic, complemented
129#2097C2211yescharacteristic, complemented
130#2097C2211yescharacteristic, complemented
131#2097C2211yescharacteristic, complemented
132#2096C2211yescharacteristic, complemented
133#2095C2211yescharacteristic, complemented
134#2094C2211yescharacteristic
135#2093C2211yescharacteristic, complemented
136#2092C2211yescharacteristic
137#2092C2211yescharacteristic
138#2092C2211yescharacteristic
139#2092C2211yescharacteristic, complemented
140#2016C2211yescharacteristic, complemented
141#2016C2211yescharacteristic, complemented
142#2015C2211yescharacteristic
143#2015C2211yescharacteristic
144#2015C2211yescharacteristic
145#2015C2211yescharacteristic
146#2015C2211yescharacteristic
147#2015C2211yescharacteristic
148#2015C2211yescharacteristic, complemented
149#2015C2211yescharacteristic, complemented
150#2014C2211yescharacteristic
151#2014C2211yescharacteristic
152#1973C2211yescharacteristic
153#1973C2211yescharacteristic, complemented
154#1971C2211yescharacteristic, complemented
155#1971C2211yescharacteristic, complemented
156#1969C2211yescharacteristic, complemented
157#1969C2211yescharacteristic, complemented
158#1969C2211yescharacteristic, complemented
159#1969C2211yescharacteristic, complemented
160#1968C2211yescharacteristic
161#1968C2211yescharacteristic
162#1968C2211yescharacteristic
163#1968C2211yescharacteristic, complemented
164#1961C2211yescharacteristic
165#1961C2211yescharacteristic
166#1961C2211yescharacteristic
167#1960C2211yescharacteristic, complemented
168#1960C2211yescharacteristic, complemented
169#1960C2211yescharacteristic, complemented
170#1960C2211yescharacteristic, complemented
171#1959C2211yescharacteristic
172#1959C2211yescharacteristic
173#1959C2211yescharacteristic
174#1958C2211yescharacteristic
175#1958C2211yescharacteristic
176#1958C2211yescharacteristic
177#1958C2211yescharacteristic
178#1958C2211yescharacteristic
179#1958C2211yescharacteristic
180#1958C2211yescharacteristic, complemented
181#1958C2211yescharacteristic, complemented
182#1957C2211yescharacteristic
183#1957C2211yescharacteristic
184#1956C2211yescharacteristic, complemented
185#1956C2211yescharacteristic, complemented
186#1847C2211yescharacteristic, complemented
187#1846C2211yescharacteristic, complemented
188#1846C2211yescharacteristic, complemented
189#1771C2211yescharacteristic, complemented
190C8×C4⋊C4C2211yescharacteristic, complemented
191#1768C2211yescharacteristic, complemented
192#1753C2211yescharacteristic
193#1753C2211yescharacteristic, complemented
194#1753C2211yescharacteristic, complemented
195C8×C22⋊C4C2211yescharacteristic
196#1750C2211yescharacteristic
197C4×C22⋊C8C2211yescharacteristic, complemented
198#1726C2211yescharacteristic, complemented
199C22×#41C2311yescharacteristic
200C22×#41C2311yescharacteristic
201C22×#41C2311yescharacteristic
202C23×D4C2311yescharacteristic
203C22×Q16C2311yescharacteristic
204C22×Q16C2311yescharacteristic
205C22×Q16C2311yescharacteristic
206C22×Q16C2311yescharacteristic
207C22×Q16C2311yescharacteristic
208C22×Q16C2311yescharacteristic
209C22×SD16C2311yescharacteristic
210C22×SD16C2311yescharacteristic
211C22×SD16C2311yescharacteristic
212C22×SD16C2311yescharacteristic
213C22×SD16C2311yescharacteristic
214C22×SD16C2311yescharacteristic
215C22×M16C2311yescharacteristic
216C22×M16C2311yescharacteristic
217C22×M16C2311yescharacteristic
218C23×C8C2311yescharacteristic
219#554—24no—
220#554—24no—
221#552—24no—
222#552—24no—
223#547—24no—
224#547—24no—
225#546—24no—
226#546—24no—
227#535—24no—
228#535—42no—
229#532—24no—
230#532—42no—
231C2×C4⋊Q8C2311yescharacteristic
232C2×C4⋊Q8C2311yescharacteristic
233C2×C4⋊Q8C2311yescharacteristic
234C2×C4⋊Q8C2311yescharacteristic
235C2×C4⋊Q8C2311yescharacteristic
236C2×#127C2311yescharacteristic
237C2×#127C2311yescharacteristic
238C2×#126—21no—
239C2×#125—21no—
240C2×#125—21no—
241C2×#125C2311yescharacteristic
242C2×#124C2311yescharacteristic
243C2×#124C2311yescharacteristic
244C2×#124C2311yescharacteristic
245C2×#124C2311yescharacteristic
246C2×#124C2311yescharacteristic
247C2×#124C2311yescharacteristic
248C2×#123—21no—
249C2×#123—21no—
250C2×#123—21no—
251C2×#123—21no—
252C2×C22⋊Q8—21no—
253C2×C22⋊Q8—21no—
254C2×C22⋊Q8C2311yescharacteristic
255C2×C22⋊Q8C2311yescharacteristic
256C2×C22⋊Q8C2311yescharacteristic
257C2×C22⋊Q8C2311yescharacteristic
258C2×C22⋊Q8C2311yescharacteristic
259C2×C22⋊Q8C2311yescharacteristic
260C2×C22⋊Q8C2311yescharacteristic
261C2×#121—21no—
262C2×#121—22no—
263C2×#121—22no—
264C2×#121—21no—
265C2×#121C2311yescharacteristic
266C2×#120—21no—
267C2×#120—22no—
268C2×C4×Q8C2311yescharacteristic
269C2×C4×Q8C2311yescharacteristic
270C2×C4×D4—21no—
271C2×C4×D4—22no—
272C2×C4×D4C2311yescharacteristic
273C2×C4×D4C2311yescharacteristic
274C2×C4×D4C2311yescharacteristic
275C2×#117—21no—
276C2×#117C2311yescharacteristic
277C2×#117C2311yescharacteristic
278C22×C4⋊C4—21no—
279C22×C4⋊C4C2311yescharacteristic
280C22×C4⋊C4C2311yescharacteristic
281C22×C4⋊C4C2311yescharacteristic
282C22×C22⋊C4—21no—
283C22×C42C2311yescharacteristic
284#497—42no—
285#494—42no—
286#492—24no—
287#491—24no—
288#489—24no—
289#488—24no—
290#487—24no—
291#485—24no—
292#485—24no—
293#484—24no—
294#484—24no—
295#483—24no—
296#483—24no—
297#481—24no—
298#480—24no—
299#478—24no—
300#478—24no—
301#476—24no—
302#474—24no—
303#470—24no—
304#470—24no—
305#470—24no—
306#470—24no—
307#468—24no—
308#468—24no—
309#467—24no—
310#467—24no—
311#464—24no—
312#464—24no—
313#462—24no—
314#462—24no—
315#452—24no—
316#452—24no—
317#452—24no—
318#452—24no—
319#452—24no—
320#452—24no—
321#450—24no—
322#450—24no—
323#440—24no—
324#440—24no—
325C4×SD16—24no—
326C4×SD16—24no—
327#436D418yescomplemented
328#435D418yescomplemented
329C2×#107C2311yescharacteristic
330C2×#107C2311yescharacteristic
331C2×#107C2311yescharacteristic
332C2×#107C2311yescharacteristic
333C2×#107C2311yescharacteristic
334C2×#107C2311yescharacteristic
335C2×#106C2311yescharacteristic
336C2×#106C2311yescharacteristic
337C2×#106C2311yescharacteristic
338C2×#106C2311yescharacteristic
339C2×#106C2311yescharacteristic
340C2×#106C2311yescharacteristic
341C2×C4⋊C8C2311yescharacteristic
342C2×C4⋊C8C2311yescharacteristic
343#418—24no—
344#417—24no—
345#417—24no—
346#417—24no—
347#417—24no—
348#417—24no—
349#416—24no—
350C2×#103C2311yescharacteristic
351C2×#103C2311yescharacteristic
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×#103C2311yescharacteristic
367C2×#103C2311yescharacteristic
368C2×#103C2311yescharacteristic
369C2×#103C2311yescharacteristic
370C2×#103C2311yescharacteristic
371C2×#103C2311yescharacteristic
372C2×#102—24no—
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×C22⋊C8C2311yescharacteristic
392C2×C22⋊C8C2311yescharacteristic
393C2×C22⋊C8C2311yescharacteristic
394C2×C22⋊C8C2311yescharacteristic
395#405—42no—
396C4×M16—42no—
397C2×#97C2311yescharacteristic
398C2×#97C2311yescharacteristic
399C2×#97C2311yescharacteristic
400C2×#97C2311yescharacteristic
401C2×#97C2311yescharacteristic
402C2×C4×C8C2311yescharacteristic
403C2×C4×C8C2311yescharacteristic
404C2×C4×C8C2311yescharacteristic
405C2×C4×C8C2311yescharacteristic
406C2×C4×C8C2311yescharacteristic
407C2×C4×C8C2311yescharacteristic
408C2×C4×C8C2311yescharacteristic
409#400—22no—
410#400—22no—
411#400—22no—
412#399—22no—
413#399—22no—
414#398—22no—
415#398—22no—
416#398—22no—
417#398—22no—
418#398—22no—
419#397—22no—
420#397—22no—
421#397—22no—
422#397—22no—
423#395—22no—
424#394—22no—
425#394—22no—
426#394—22no—
427#394—22no—
428#392—22no—
429#391—22no—
430#391C2311yescharacteristic
431#391C2311yescharacteristic
432#391C2311yescharacteristic
433#391C2311yescharacteristic
434#391C2311yescharacteristic
435#391C2311yescharacteristic
436#391C2311yescharacteristic
437#391C2311yescharacteristic
438#391C2311yescharacteristic
439#390C2311yescharacteristic
440#390C2311yescharacteristic
441#390C2311yescharacteristic
442#389—22no—
443#389—22no—
444#388—22no—
445#388D412yes—
446#387—22no—
447#387—22no—
448#387—22no—
449#387—22no—
450#387D412yes—
451#386—22no—
452#386—22no—
453#386—22no—
454#386—22no—
455#386—22no—
456#386D412yes—
457#385—22no—
458#385—22no—
459#385—22no—
460#385—22no—
461#385D412yes—
462#384C2311yescharacteristic
463#384C2311yescharacteristic
464#384C2311yescharacteristic
465#382—22no—
466#382C2311yescharacteristic
467#382C2311yescharacteristic
468#382C2311yescharacteristic
469#382C2311yescharacteristic
470#382C2311yescharacteristic
471#382C2311yescharacteristic
472#382C2311yescharacteristic
473#381—22no—
474#381—22no—
475#380—22no—
476#380—22no—
477#379—22no—
478C4×C4⋊C4C2311yescharacteristic
479C4×C22⋊C4C2311yescharacteristic
480C4×C22⋊C4C2311yescharacteristic
481#376C2311yescharacteristic
482C2×#95—22no—
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489C25—21no—
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—22no—
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—41no—
508C22×Q8—21no—
509C22×Q8C2411yescharacteristic
510C22×Q8C2411yescharacteristic
511C22×Q8C2411yescharacteristic
512C22×Q8C2411yescharacteristic
513C22×Q8C2411yescharacteristic
514C22×D4—22no—
515C22×D4—21no—
516C22×D4—21no—
517C22×D4—21no—
518C22×D4—21no—
519C22×D4—22no—
520C22×D4—22no—
521C22×D4—22no—
522C22×D4—21no—
523C22×D4—22no—
524C22×D4—41no—
525C22×D4—41no—
526C22×D4—41no—
527C22×D4C2×D411yescharacteristic
528C22×D4C2411yescharacteristic
529C22×D4C2411yescharacteristic
530C22×D4C2411yescharacteristic
531C23×C4—21no—
532C23×C4—21no—
533C23×C4—21no—
534C23×C4—21no—
535C23×C4—21no—
536C23×C4—21no—
537C23×C4—21no—
538C23×C4—21no—
539C23×C4C2×D412yes—
540C23×C4C2411yescharacteristic
541C23×C4C2411yescharacteristic
542C2×Q16—22no—
543C2×Q16—22no—
544C2×Q16—22no—
545C2×Q16—22no—
546C2×Q16—22no—
547C2×Q16—22no—
548C2×Q16—41no—
549C2×Q16—41no—
550C2×Q16—41no—
551C2×Q16—41no—
552C2×Q16—41no—
553C2×Q16—41no—
554C2×Q16—41no—
555C2×Q16—41no—
556C2×Q16—41no—
557C2×Q16—41no—
558C2×Q16—41no—
559C2×Q16—41no—
560C2×SD16—22no—
561C2×SD16—22no—
562C2×SD16—22no—
563C2×SD16—22no—
564C2×SD16—22no—
565C2×SD16—22no—
566C2×SD16—22no—
567C2×SD16—22no—
568C2×SD16—22no—
569C2×SD16—22no—
570C2×SD16—41no—
571C2×SD16—41no—
572C2×SD16—41no—
573C2×SD16—41no—
574C2×SD16—41no—
575C2×SD16—41no—
576C2×SD16—41no—
577C2×SD16—41no—
578C2×M16—41no—
579C2×M16—41no—
580C2×M16—41no—
581C2×M16—41no—
582C2×M16—41no—
583C2×M16—41no—
584C2×M16C2×D414yes—
585C2×M16C2×D414yes—
586C2×M16C2×D414yes—
587C22×C8—41no—
588C22×C8—41no—
589C22×C8C2×D414yes—
590C22×C8C2411yescharacteristic
591C22×C8C2411yescharacteristic
592C22×C8C2411yescharacteristic
593C22×C8C2411yescharacteristic
594C22×C8C2411yescharacteristic
595C22×C8C2411yescharacteristic
596C22×C8C2411yescharacteristic
597C22×C8C2411yescharacteristic
598C4⋊Q8—22no—
599C4⋊Q8—22no—
600C4⋊Q8—22no—
601C4⋊Q8—22no—
602C4⋊Q8—22no—
603C4⋊Q8—22no—
604C4⋊Q8—22no—
605C4⋊Q8—22no—
606C4⋊Q8—41no—
607C4⋊Q8—41no—
608#127—22no—
609#127—22no—
610#127—41no—
611#127#4114yes—
612#126—44no—
613#125—22no—
614#125—22no—
615#125—44no—
616#125—44no—
617#124—22no—
618#124—22no—
619#124—22no—
620#124—22no—
621#124—22no—
622#124—22no—
623#124—22no—
624#124—41no—
625#124—41no—
626#124—41no—
627#124—41no—
628#124—41no—
629#123—44no—
630#123—44no—
631#123—44no—
632#123—44no—
633C22⋊Q8—22no—
634C22⋊Q8—22no—
635C22⋊Q8—22no—
636C22⋊Q8—22no—
637C22⋊Q8—22no—
638C22⋊Q8—22no—
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—44no—
648C22⋊Q8—44no—
649#121—22no—
650#121—22no—
651#121—48no—
652#121—48no—
653#121—44no—
654#121—44no—
655#120—48no—
656#120—44no—
657C4×Q8—22no—
658C4×Q8—22no—
659C4×Q8—22no—
660C4×Q8—22no—
661C4×D4—22no—
662C4×D4—22no—
663C4×D4—22no—
664C4×D4—22no—
665C4×D4—48no—
666C4×D4—44no—
667C4×D4C2×D414yes—
668C4×D4C2×D414yes—
669#117—22no—
670#117—22no—
671#117—22no—
672#117—22no—
673#117—44no—
674C2×C4⋊C4—22no—
675C2×C4⋊C4—22no—
676C2×C4⋊C4—22no—
677C2×C4⋊C4—22no—
678C2×C4⋊C4—22no—
679C2×C4⋊C4—22no—
680C2×C4⋊C4—21no—
681C2×C4⋊C4—21no—
682C2×C4⋊C4—21no—
683C2×C4⋊C4—21no—
684C2×C4⋊C4—21no—
685C2×C4⋊C4—21no—
686C2×C4⋊C4—21no—
687C2×C4⋊C4—21no—
688C2×C4⋊C4—22no—
689C2×C4⋊C4—21no—
690C2×C4⋊C4—21no—
691C2×C4⋊C4—21no—
692C2×C4⋊C4—21no—
693C2×C4⋊C4—21no—
694C2×C4⋊C4—21no—
695C2×C4⋊C4—21no—
696C2×C4⋊C4—21no—
697C2×C4⋊C4—21no—
698C2×C4⋊C4—22no—
699C2×C4⋊C4—22no—
700C2×C4⋊C4—22no—
701C2×C4⋊C4—22no—
702C2×C4⋊C4—22no—
703C2×C4⋊C4—44no—
704C2×C4⋊C4C2×D412yes—
705C2×C4⋊C4C2×D412yes—
706C2×C4⋊C4C2×D411yescharacteristic
707C2×C4⋊C4C2411yescharacteristic
708C2×C4⋊C4C2411yescharacteristic
709C2×C4⋊C4C2411yescharacteristic
710C2×C4⋊C4C2411yescharacteristic
711C2×C4⋊C4C2411yescharacteristic
712C2×C4⋊C4C2411yescharacteristic
713C2×C4⋊C4C2411yescharacteristic
714C2×C4⋊C4C2411yescharacteristic
715C2×C22⋊C4—21no—
716C2×C22⋊C4—21no—
717C2×C22⋊C4—21no—
718C2×C22⋊C4—21no—
719C2×C22⋊C4—21no—
720C2×C22⋊C4—21no—
721C2×C22⋊C4—21no—
722C2×C22⋊C4—21no—
723C2×C22⋊C4—21no—
724C2×C22⋊C4—21no—
725C2×C22⋊C4—22no—
726C2×C22⋊C4—22no—
727C2×C22⋊C4—21no—
728C2×C22⋊C4—21no—
729C2×C22⋊C4—22no—
730C2×C22⋊C4—22no—
731C2×C22⋊C4—21no—
732C2×C22⋊C4—22no—
733C2×C22⋊C4—22no—
734C2×C22⋊C4—22no—
735C2×C22⋊C4—22no—
736C2×C22⋊C4—44no—
737C2×C22⋊C4C2×D412yes—
738C2×C22⋊C4C2×D412yes—
739C2×C22⋊C4C2×D412yes—
740C2×C22⋊C4C2×D411yescharacteristic
741C2×C22⋊C4C2×D411yescharacteristic
742C2×C42—22no—
743C2×C42—22no—
744C2×C42—21no—
745C2×C42—21no—
746C2×C42—21no—
747C2×C42C2×D412yes—
748C2×C42C2411yescharacteristic
749C2×C42C2411yescharacteristic
750C2×C42C2411yescharacteristic
751C2×C42C2411yescharacteristic
752C2×C42C2411yescharacteristic
753#107—22no—
754#107—22no—
755#107—22no—
756#107—22no—
757#107—22no—
758#107—22no—
759#106—22no—
760#106—22no—
761#106—22no—
762#106—22no—
763#106—22no—
764#106—22no—
765C4⋊C8C2×D414yes—
766C4⋊C8C2×D414yes—
767#103—22no—
768#103—22no—
769#103—22no—
770#103—22no—
771#103—22no—
772#103—22no—
773#103—22no—
774#103—22no—
775#103—22no—
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#102—22no—
790#102—22no—
791#102—22no—
792#102—22no—
793#102—22no—
794#102—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—
807C22⋊C8C2×D414yes—
808C22⋊C8C2×D414yes—
809C22⋊C8C2×D414yes—
810C22⋊C8C2×D414yes—
811#97—22no—
812#97—22no—
813#97—41no—
814#97—41no—
815#97C2×D414yes—
816C4×C8—22no—
817C4×C8—22no—
818C4×C8—41no—
819C4×C8—41no—
820C4×C8—41no—
821C4×C8—41no—
822C4×C8C2×D414yes—
823#95—22no—
824#95—22no—
825#95—22no—
826#95—22no—
827#95—22no—
828#95—22no—
829#95—22no—
830#95—22no—
831#95—22no—
832#95—22no—
833#95—22no—
834#95—22no—
835#95—22no—
836#95—22no—
837#95—22no—
838#95—22no—
839#95C2×D412yes—
840#95C2×D412yes—
841#95C2×D412yes—
842#95C2×D412yes—
843#95C2×D412yes—
844C24—21no—
845C24—21no—
846C24—21no—
847C24—42no—
848C24—42no—
849C24—81no—
850C24—82no—
851C24—82no—
852C24C22×D411yescharacteristic
853C24C22×D411yescharacteristic
854#41—44no—
855#41—44no—
856#41—44no—
857#41—44no—
858#41—44no—
859#41—44no—
860#41—82no—
861#41—82no—
862#41—82no—
863#41—82no—
864#41—82no—
865#41—82no—
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—21no—
895C2×Q8—21no—
896C2×Q8—42no—
897C2×Q8—82no—
898C2×D4—28no—
899C2×D4—21no—
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—44no—
916C2×D4—44no—
917C2×D4—42no—
918C2×D4—42no—
919C2×D4—44no—
920C2×D4—42no—
921C2×D4—42no—
922C2×D4—42no—
923C2×D4—42no—
924C2×D4—42no—
925C2×D4—42no—
926C2×D4—42no—
927C2×D4—42no—
928C2×D4—82no—
929C2×D4—82no—
930C2×D4—82no—
931C2×D4—82no—
932C2×D4—81no—
933C2×D4—82no—
934C2×D4—82no—
935C2×D4—81no—
936C2×D4—81no—
937C2×D4—81no—
938C2×D4—82no—
939C2×D4#12714yes—
940C2×D4C2×#4112yes—
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—24no—
951C22×C4—21no—
952C22×C4—21no—
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—42no—
965C22×C4—42no—
966C22×C4—42no—
967C22×C4—42no—
968C22×C4—42no—
969C22×C4—44no—
970C22×C4—42no—
971C22×C4—42no—
972C22×C4—42no—
973C22×C4—42no—
974C22×C4—42no—
975C22×C4—42no—
976C22×C4—42no—
977C22×C4—42no—
978C22×C4—82no—
979C22×C4—81no—
980C22×C4—81no—
981C22×C4—81no—
982C22×C4—82no—
983C22×C4—82no—
984C22×C4—82no—
985C22×C4C22×D412yes—
986C22×C4C22×D412yes—
987C22×C4C22×D412yes—
988C22×C4C22×D411yescharacteristic
989C22×C4C22×D411yescharacteristic
990C22×C4C22×D411yescharacteristic
991C22×C4C22×D411yescharacteristic
992C22×C4C22×D412yes—
993C22×C4C22×D412yes—
994C22×C4C22×D412yes—
995C22×C4C22×D412yes—
996C22×C4C22×D412yes—
997C22×C4C2511yescharacteristic
998Q16—82no—
999Q16—82no—
1000Q16—82no—
1001Q16—82no—
1002Q16—82no—
1003Q16—82no—
1004SD16—44no—
1005SD16—44no—
1006SD16—44no—
1007SD16—44no—
1008SD16—82no—
1009SD16—82no—
1010M16—44no—
1011M16—44no—
1012M16—44no—
1013C2×C8—21no—
1014C2×C8—21no—
1015C2×C8—21no—
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—44no—
1030C2×C8C22×D412yes—
1031C2×C8C22×D412yes—
1032C2×C8C22×D412yes—
1033C2×C8C22×D412yes—
1034C2×C8C22×D412yes—
1035C2×C8C22×D412yes—
1036C2×C8C22×D412yes—
1037C2×C8C22×D412yes—
1038C4⋊C4—24no—
1039C4⋊C4—21no—
1040C4⋊C4—21no—
1041C4⋊C4—21no—
1042C4⋊C4—21no—
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—42no—
1056C4⋊C4—42no—
1057C4⋊C4—42no—
1058C4⋊C4—42no—
1059C4⋊C4—42no—
1060C4⋊C4—42no—
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—44no—
1074C4⋊C4—44no—
1075C4⋊C4—82no—
1076C4⋊C4—82no—
1077C4⋊C4—82no—
1078C4⋊C4—82no—
1079C4⋊C4#12714yes—
1080C22⋊C4—24no—
1081C22⋊C4—42no—
1082C22⋊C4—42no—
1083C22⋊C4—44no—
1084C22⋊C4—44no—
1085C22⋊C4—44no—
1086C22⋊C4—42no—
1087C22⋊C4—42no—
1088C22⋊C4—42no—
1089C22⋊C4—42no—
1090C22⋊C4—42no—
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—44no—
1100C22⋊C4—82no—
1101C22⋊C4—82no—
1102C22⋊C4—82no—
1103C22⋊C4—82no—
1104C22⋊C4#12714yes—
1105C22⋊C4#12714yes—
1106C42—24no—
1107C42—21no—
1108C42—21no—
1109C42—21no—
1110C42—21no—
1111C42—21no—
1112C42—21no—
1113C42—42no—
1114C42—42no—
1115C42—42no—
1116C42C22×D412yes—
1117C42C22×D412yes—
1118C42C2×#4112yes—
1119C42H(5,𝔽2)12yes—
1120C23—22no—
1121C23—22no—
1122C23—22no—
1123C23—22no—
1124C23—21no—
1125C23—21no—
1126C23—21no—
1127C23—21no—
1128C23—22no—
1129C23—22no—
1130C23—42no—
1131C23—42no—
1132C23—42no—
1133C23—42no—
1134C23—41no—
1135C23—41no—
1136C23—41no—
1137C23—41no—
1138C23—42no—
1139C23—42no—
1140C23—41no—
1141C23—41no—
1142C23—41no—
1143C23—84no—
1144C23—84no—
1145C23—162no—
1146C23—164no—
1147C23—164no—
1148C23C2×#12712yes—
1149C23C2×#12712yes—
1150C23C23×D411yescharacteristic
1151Q8—41no—
1152Q8—41no—
1153Q8—41no—
1154Q8—41no—
1155Q8—41no—
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—162no—
1172D4—22no—
1173D4—22no—
1174D4—22no—
1175D4—22no—
1176D4—44no—
1177D4—41no—
1178D4—41no—
1179D4—41no—
1180D4—41no—
1181D4—41no—
1182D4—41no—
1183D4—41no—
1184D4—41no—
1185D4—88no—
1186D4—84no—
1187D4—84no—
1188D4—84no—
1189D4—84no—
1190D4—164no—
1191D4—162no—
1192C2×C4—22no—
1193C2×C4—22no—
1194C2×C4—22no—
1195C2×C4—22no—
1196C2×C4—21no—
1197C2×C4—21no—
1198C2×C4—21no—
1199C2×C4—21no—
1200C2×C4—22no—
1201C2×C4—22no—
1202C2×C4—22no—
1203C2×C4—22no—
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—42no—
1218C2×C4—42no—
1219C2×C4—42no—
1220C2×C4—42no—
1221C2×C4—42no—
1222C2×C4—42no—
1223C2×C4—42no—
1224C2×C4—42no—
1225C2×C4—41no—
1226C2×C4—41no—
1227C2×C4—41no—
1228C2×C4—41no—
1229C2×C4—41no—
1230C2×C4—41no—
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—84no—
1249C2×C4—84no—
1250C2×C4—84no—
1251C2×C4—84no—
1252C2×C4—84no—
1253C2×C4—84no—
1254C2×C4—162no—
1255C2×C4—162no—
1256C2×C4—162no—
1257C2×C4C2×#12712yes—
1258C2×C4C2×#12712yes—
1259C2×C4C2×#12712yes—
1260C2×C4C2×#12712yes—
1261C2×C4#54614yes—
1262C2×C4C23×D411yescharacteristic
1263C2×C4C23×D411yescharacteristic
1264C2×C4C22×#4111yescharacteristic
1265C2×C4C2×H(5,𝔽2)11yescharacteristic
1266C2×C4#58511yescharacteristic
1267C2×C4#58511yescharacteristic
1268C8—22no—
1269C8—22no—
1270C8—22no—
1271C8—22no—
1272C8—22no—
1273C8—22no—
1274C8—22no—
1275C8—22no—
1276C22—22no—
1277C22—22no—
1278C22—22no—
1279C22—22no—
1280C22—22no—
1281C22—22no—
1282C22—42no—
1283C22—42no—
1284C22—42no—
1285C22—42no—
1286C22—44no—
1287C22—44no—
1288C22—42no—
1289C22—42no—
1290C22—82no—
1291C22—82no—
1292C22—81no—
1293C22—81no—
1294C22—81no—
1295C22—81no—
1296C22—82no—
1297C22—82no—
1298C22—81no—
1299C22—81no—
1300C22—81no—
1301C22—168no—
1302C22C22×#12711yescharacteristic
1303C22C2×#54611yescharacteristic
1304C22#350011yescharacteristic
1305C22#358412yes—
1306C22#358612yes—
1307C4—24no—
1308C4—22no—
1309C4—22no—
1310C4—22no—
1311C4—22no—
1312C4—42no—
1313C4—42no—
1314C4—42no—
1315C4—81no—
1316C4—81no—
1317C4—81no—
1318C4—81no—
1319C4—81no—
1320C4—81no—
1321C4—81no—
1322C4—81no—
1323C4—81no—
1324C4—81no—
1325C4—81no—
1326C4—81no—
1327C4—81no—
1328C4D4×#4111yescharacteristic
1329C4D4×#4111yescharacteristic
1330C4#349611yescharacteristic
1331C4#349611yescharacteristic
1332C2—42no—
1333C2—42no—
1334C2—82no—
1335C2—82no—
1336C2—161no—
1337C2#3626011yescharacteristic
1338C2#6064511yescharacteristic
1339C2#6064911yescharacteristic
1340C2#6118812yes—
1341C2#6261212yes—
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#37682C2
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×#3331C2semidirect
2. C2×#3323C2semidirect
3. C2×#3315C2semidirect
4. C2×#3314C2semidirect
5. #37865C2semidirect
7. #33229C2semidirect
8. #33186C2semidirect
9. #33180C2semidirect
10. #28525C2semidirect
11. #28456C2semidirect
12. #28436C2semidirect
13. #28427C2semidirect
14. #28408C2semidirect
15. #28403C2semidirect
16. #28366C2semidirect
17. #28362C2semidirect
18. #28361C2semidirect
19. #28360C2semidirect
20. #28356C2semidirect
21. #28356C2semidirect
22. #28338C2semidirect
23. #28330C2semidirect
24. #27922C2semidirect
25. #27912C2semidirect
26. #25732C2semidirect
27. #25719C2semidirect
28. #21695C2semidirect
29. #21206C2semidirect
30. #21201C2semidirect
31. #20490C2semidirect
43. C2×#494C22semidirect
45. C2×#491C22semidirect
48. C2×#487C22semidirect
50. C2×#484C22semidirect
55. C2×#483C22semidirect
58. C2×#478C22semidirect
59. C2×#476C22semidirect
63. C2×#470C22semidirect
64. C2×#470C22semidirect
71. C2×#462C22semidirect
72. C2×#462C22semidirect
77. C2×#452C22semidirect
78. C2×#452C22semidirect
82. C2×#440C22semidirect
84. C2×C4×SD16C22semidirect
90. C2×#417C22semidirect
91. C2×#417C22semidirect
96. C2×C4×M16C22semidirect
97. #2857C22semidirect
103. #2660C22semidirect
107. #2568C22semidirect
108. #2565C22semidirect
112. #2503C22semidirect
113. #2502C22semidirect
124. #2327C22semidirect
127. C2×#382C22semidirect
128. #2097C22semidirect
129. #2097C22semidirect
130. #2097C22semidirect
131. #2097C22semidirect
132. #2096C22semidirect
133. #2095C22semidirect
135. #2093C22semidirect
139. #2092C22semidirect
140. #2016C22semidirect
141. #2016C22semidirect
148. #2015C22semidirect
149. #2015C22semidirect
153. #1973C22semidirect
154. #1971C22semidirect
155. #1971C22semidirect
156. #1969C22semidirect
157. #1969C22semidirect
158. #1969C22semidirect
159. #1969C22semidirect
163. #1968C22semidirect
167. #1960C22semidirect
168. #1960C22semidirect
169. #1960C22semidirect
170. #1960C22semidirect
180. #1958C22semidirect
181. #1958C22semidirect
184. #1956C22semidirect
185. #1956C22semidirect
186. #1847C22semidirect
187. #1846C22semidirect
188. #1846C22semidirect
189. #1771C22semidirect
190. C8×C4⋊C4C22semidirect
191. #1768C22semidirect
193. #1753C22semidirect
194. #1753C22semidirect
197. C4×C22⋊C8C22semidirect
198. #1726C22semidirect
327. #436D4semidirect
328. #435D4semidirect

Maximal subgroups

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

subgroupindex
C2×#33312
C2×#33232
C2×#33152
C2×#33142
#378652
#376822
#332292
#331862
#331802
#285252
#284562
#284362
#284272
#284082
#284032
#283662
#283622
#283612
#283602
#283562
#283382
#283302
#279222
#279122
#257322
#257192
#216952
#212062
#212012
#204902