Finite Group Databasebeta

← #6606850

Subgroups — #6606850

Order 512.

2338 conjugacy classes of subgroups.

The subgroup lattice has 1332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3320C211yesmaximal, characteristic, complemented
2C2×#3316C211yesmaximal, characteristic, complemented
3C2×#3301C211yesmaximal, characteristic
4C2×#3299C211yesmaximal, characteristic, complemented
5#37862C211yesmaximal, characteristic, complemented
6#37675C211yesmaximal, characteristic, complemented
7#33229C211yesmaximal, characteristic, complemented
8#33188C211yesmaximal, characteristic, complemented
9#33173C211yesmaximal, characteristic, complemented
10#28526C211yesmaximal, characteristic, complemented
11#28453C211yesmaximal, characteristic, complemented
12#28426C211yesmaximal, characteristic, complemented
13#28423C211yesmaximal, characteristic, complemented
14#28407C211yesmaximal, characteristic, complemented
15#28400C211yesmaximal, characteristic, complemented
16#28358C211yesmaximal, characteristic, complemented
17#28355C211yesmaximal, characteristic, complemented
18#28348C211yesmaximal, characteristic, complemented
19#28347C211yesmaximal, characteristic, complemented
20#28338C211yesmaximal, characteristic, complemented
21#28336C211yesmaximal, characteristic, complemented
22#28334C211yesmaximal, characteristic, complemented
23#28333C211yesmaximal, characteristic, complemented
24#27922C211yesmaximal, characteristic, complemented
25#27913C211yesmaximal, characteristic, complemented
26#25737C211yesmaximal, characteristic, complemented
27#25726C211yesmaximal, characteristic, complemented
28#21703C211yesmaximal, characteristic, complemented
29#21205C211yesmaximal, characteristic, complemented
30C2×#1956C211yesmaximal, characteristic, complemented
31#20484C211yesmaximal, characteristic, complemented
32C2×#554C2211yescharacteristic
33C2×#553C2211yescharacteristic
34C2×D4×Q8C2211yescharacteristic
35C2×#548C2211yescharacteristic
36C2×#536C2211yescharacteristic
37C22×C4⋊Q8C2211yescharacteristic
38#3320—28no—
39#3316—28no—
40#3301—28no—
41#3299—28no—
42C2×#497C2211yescharacteristic
43C2×#497C2211yescharacteristic
44C2×#495C2211yescharacteristic
45C2×#491C2211yescharacteristic
46C2×#489C2211yescharacteristic
47C2×#488C2211yescharacteristic
48C2×#487C2211yescharacteristic
49C2×#484C2211yescharacteristic
50C2×#484C2211yescharacteristic
51C2×#484C2211yescharacteristic
52C2×#481C2211yescharacteristic
53C2×#481C2211yescharacteristic
54C2×#485C2211yescharacteristic
55C2×#485C2211yescharacteristic
56C2×#483C2211yescharacteristic
57C2×#479C2211yescharacteristic
58C2×#479C2211yescharacteristic
59C2×#477C2211yescharacteristic
60C2×#475C2211yescharacteristic
61C2×#470C2211yescharacteristic
62C2×#468C2211yescharacteristic
63C2×#467C2211yescharacteristic
64C2×#467C2211yescharacteristic
65C2×#466C2211yescharacteristic
66C2×#465C2211yescharacteristic
67C2×#465C2211yescharacteristic
68C2×#465C2211yescharacteristic
69C2×#464C2211yescharacteristic
70C2×#462C2211yescharacteristic
71C2×#463C2211yescharacteristic
72C2×#461C2211yescharacteristic
73C2×#452C2211yescharacteristic
74C2×#449C2211yescharacteristic
75C2×#451C2211yescharacteristic
76C2×#451C2211yescharacteristic
77C2×#451C2211yescharacteristic
78C2×#448C2211yescharacteristic
79C2×#448C2211yescharacteristic
80C2×#448C2211yescharacteristic
81C2×#441C2211yescharacteristic
82C2×#440C2211yescharacteristic
83C2×C4×Q16C2211yescharacteristic
84C2×C4×SD16C2211yescharacteristic
85C2×#435C2211yescharacteristic
86C2×C8×D4C2211yescharacteristic
87C2×#417C2211yescharacteristic
88C2×#419C2211yescharacteristic
89C2×#416C2211yescharacteristic
90C22×#103C2211yescharacteristic
91C22×#103C2211yescharacteristic
92C22×#103C2211yescharacteristic
93C22×#103C2211yescharacteristic
94C22×#103C2211yescharacteristic
95C2×#405C2211yescharacteristic
96C22×C4×C8C2211yescharacteristic
97#2850C2211yescharacteristic
98#2850C2211yescharacteristic
99#2721—22no—
100#2680—22no—
101#2677—22no—
102#2674—22no—
103#2660C2211yescharacteristic
104#2658C2211yescharacteristic
105#2621C2211yescharacteristic
106#2620C2211yescharacteristic
107#2565C2211yescharacteristic
108#2546C2211yescharacteristic
109#2545C2211yescharacteristic
110#2542C2211yescharacteristic
111#2504C2211yescharacteristic
112#2502C2211yescharacteristic
113#2501C2211yescharacteristic
114#2499C2211yescharacteristic
115#2449—22no—
116#2449—22no—
117#2443—22no—
118#2443—22no—
119#2436C2211yescharacteristic
120#2434C2211yescharacteristic
121#2434C2211yescharacteristic
122#2432C2211yescharacteristic
123#2327C2211yescharacteristic
124#2326C2211yescharacteristic
125#2317C2211yescharacteristic
126#2290C2211yescharacteristic
127C2×#384C2211yescharacteristic
128#2097C2211yescharacteristic
129#2097C2211yescharacteristic
130#2097C2211yescharacteristic
131#2097C2211yescharacteristic
132#2096C2211yescharacteristic
133#2096C2211yescharacteristic
134#2096C2211yescharacteristic
135#2096C2211yescharacteristic
136#2095C2211yescharacteristic
137#2095C2211yescharacteristic
138#2093C2211yescharacteristic
139#2093C2211yescharacteristic
140#2016C2211yescharacteristic
141#2016C2211yescharacteristic
142#2016C2211yescharacteristic
143#2016C2211yescharacteristic
144#2015C2211yescharacteristic
145#2015C2211yescharacteristic
146#2013C2211yescharacteristic
147#2013C2211yescharacteristic
148#2013C2211yescharacteristic
149#2013C2211yescharacteristic
150#2012C2211yescharacteristic
151#2012C2211yescharacteristic
152#1973C2211yescharacteristic
153#1973C2211yescharacteristic
154#1971C2211yescharacteristic
155#1971C2211yescharacteristic
156#1970C2211yescharacteristic
157#1969C2211yescharacteristic
158#1969C2211yescharacteristic
159#1969C2211yescharacteristic
160#1968C2211yescharacteristic
161#1968C2211yescharacteristic
162#1968C2211yescharacteristic
163#1968C2211yescharacteristic
164#1960C2211yescharacteristic
165#1960C2211yescharacteristic
166#1960C2211yescharacteristic
167#1960C2211yescharacteristic
168#1959C2211yescharacteristic
169#1959C2211yescharacteristic
170#1959C2211yescharacteristic
171#1959C2211yescharacteristic
172#1958C2211yescharacteristic
173#1958C2211yescharacteristic
174#1958C2211yescharacteristic
175#1958C2211yescharacteristic
176#1956C2211yescharacteristic
177#1956C2211yescharacteristic
178#1956C2211yescharacteristic
179#1956C2211yescharacteristic
180#1956C2211yescharacteristic
181#1956C2211yescharacteristic
182#1956C2211yescharacteristic
183#1956C2211yescharacteristic
184#1956C2211yescharacteristic
185#1956C2211yescharacteristic
186#1847C2211yescharacteristic
187#1847C2211yescharacteristic
188#1846C2211yescharacteristic
189#1771C2211yescharacteristic
190C8×C4⋊C4C2211yescharacteristic
191#1768C2211yescharacteristic
192#1753C2211yescharacteristic
193#1752C2211yescharacteristic
194C8×C22⋊C4C2211yescharacteristic
195C8×C22⋊C4C2211yescharacteristic
196#1750C2211yescharacteristic
197#1749C2211yescharacteristic
198#1726C2211yescharacteristic
199C22×#41C2311yescharacteristic
200C23×Q8C2311yescharacteristic
201C23×Q8C2311yescharacteristic
202C23×Q8C2311yescharacteristic
203C22×Q16C2311yescharacteristic
204C22×Q16C2311yescharacteristic
205C22×Q16C2311yescharacteristic
206C22×Q16C2311yescharacteristic
207C22×Q16C2311yescharacteristic
208C22×SD16C2311yescharacteristic
209C22×SD16C2311yescharacteristic
210C22×SD16C2311yescharacteristic
211C22×SD16C2311yescharacteristic
212C22×SD16C2311yescharacteristic
213C22×SD16C2311yescharacteristic
214C22×D8C2311yescharacteristic
215C22×M16C2311yescharacteristic
216C23×C8C2311yescharacteristic
217C23×C8C2311yescharacteristic
218C23×C8C2311yescharacteristic
219#554—24no—
220#554—24no—
221#553—24no—
222#553—24no—
223D4×Q8—24no—
224D4×Q8—24no—
225#548—24no—
226#548—24no—
227#536—24no—
228#536—42no—
229C2×C4⋊Q8—21no—
230C2×C4⋊Q8—24no—
231C2×C4⋊Q8—22no—
232C2×C4⋊Q8—42no—
233C2×C4⋊Q8C2311yescharacteristic
234C2×C4⋊Q8C2311yescharacteristic
235C2×C4⋊Q8C2311yescharacteristic
236C2×C4⋊Q8C2311yescharacteristic
237C2×C4⋊Q8C2311yescharacteristic
238C2×C4⋊Q8C2311yescharacteristic
239C2×C4⋊Q8C2311yescharacteristic
240C2×C4⋊Q8C2311yescharacteristic
241C2×#126—21no—
242C2×#125—21no—
243C2×#125C2311yescharacteristic
244C2×#124—21no—
245C2×#124C2311yescharacteristic
246C2×#124C2311yescharacteristic
247C2×#124C2311yescharacteristic
248C2×#124C2311yescharacteristic
249C2×#124C2311yescharacteristic
250C2×#123—22no—
251C2×#123—21no—
252C2×#123—22no—
253C2×C22⋊Q8—21no—
254C2×C22⋊Q8—22no—
255C2×C22⋊Q8—22no—
256C2×C22⋊Q8—21no—
257C2×C22⋊Q8—21no—
258C2×C22⋊Q8—21no—
259C2×C22⋊Q8—21no—
260C2×C22⋊Q8C2311yescharacteristic
261C2×C22⋊Q8C2311yescharacteristic
262C2×C22⋊Q8C2311yescharacteristic
263C2×C22⋊Q8C2311yescharacteristic
264C2×C22⋊Q8C2311yescharacteristic
265C2×#121—21no—
266C2×#121—21no—
267C2×#121C2311yescharacteristic
268C2×#121C2311yescharacteristic
269C2×#121C2311yescharacteristic
270C2×C4×Q8C2311yescharacteristic
271C2×C4×Q8C2311yescharacteristic
272C2×C4×Q8C2311yescharacteristic
273C2×C4×D4—21no—
274C2×C4×D4—21no—
275C2×C4×D4—21no—
276C2×C4×D4—21no—
277C2×C4×D4C2311yescharacteristic
278C2×C4×D4C2311yescharacteristic
279C2×#117C2311yescharacteristic
280C2×#117C2311yescharacteristic
281C22×C4⋊C4—22no—
282C22×C4⋊C4—22no—
283C22×C4⋊C4C2311yescharacteristic
284C22×C4⋊C4C2311yescharacteristic
285C22×C4⋊C4C2311yescharacteristic
286C22×C42C2311yescharacteristic
287#497—24no—
288#497—42no—
289#495—42no—
290#491—24no—
291#489—24no—
292#488—24no—
293#487—24no—
294#485—24no—
295#485—24no—
296#484—24no—
297#484—24no—
298#484—24no—
299#483—24no—
300#481—24no—
301#481—24no—
302#479—24no—
303#479—24no—
304#477—24no—
305#475—24no—
306#470—24no—
307#468—24no—
308#467—24no—
309#467—24no—
310#466—24no—
311#465—24no—
312#465—24no—
313#465—24no—
314#464—24no—
315#463—24no—
316#462—24no—
317#461—24no—
318#452—24no—
319#451—24no—
320#451—24no—
321#451—24no—
322#449—24no—
323#448—24no—
324#448—24no—
325#448—24no—
326#441—24no—
327#440—24no—
328C4×Q16—24no—
329C4×SD16—24no—
330#435D418yes—
331C8×D4D418yes—
332C2×#107C2311yescharacteristic
333C2×#107C2311yescharacteristic
334C2×#107C2311yescharacteristic
335C2×#107C2311yescharacteristic
336C2×#107C2311yescharacteristic
337C2×#107C2311yescharacteristic
338C2×#106C2311yescharacteristic
339C2×#106C2311yescharacteristic
340C2×#106C2311yescharacteristic
341C2×#106C2311yescharacteristic
342C2×#106C2311yescharacteristic
343C2×#106C2311yescharacteristic
344C2×C4⋊C8C2311yescharacteristic
345C2×C4⋊C8C2311yescharacteristic
346#419—24no—
347#417—24no—
348#416—24no—
349C2×#103—24no—
350C2×#103—24no—
351C2×#103—24no—
352C2×#103—24no—
353C2×#103—24no—
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×#103C2311yescharacteristic
380C2×#103C2311yescharacteristic
381C2×#103C2311yescharacteristic
382C2×#103C2311yescharacteristic
383C2×#103C2311yescharacteristic
384C2×#103C2311yescharacteristic
385C2×#103C2311yescharacteristic
386C2×#102C2311yescharacteristic
387C2×#102C2311yescharacteristic
388C2×#102C2311yescharacteristic
389C2×#102C2311yescharacteristic
390C2×#102C2311yescharacteristic
391C2×#102C2311yescharacteristic
392C2×#102C2311yescharacteristic
393C2×#102C2311yescharacteristic
394C2×C22⋊C8C2311yescharacteristic
395C2×C22⋊C8C2311yescharacteristic
396C2×C22⋊C8C2311yescharacteristic
397C2×C22⋊C8C2311yescharacteristic
398#405—42no—
399C2×#97C2311yescharacteristic
400C2×#97C2311yescharacteristic
401C2×#97C2311yescharacteristic
402C2×#97C2311yescharacteristic
403C2×#97C2311yescharacteristic
404C2×C4×C8—42no—
405C2×C4×C8C2311yescharacteristic
406C2×C4×C8C2311yescharacteristic
407C2×C4×C8C2311yescharacteristic
408C2×C4×C8C2311yescharacteristic
409C2×C4×C8C2311yescharacteristic
410C2×C4×C8C2311yescharacteristic
411C2×C4×C8C2311yescharacteristic
412#399—22no—
413#399—22no—
414#399—22no—
415#399—22no—
416#398—22no—
417#398—22no—
418#398—22no—
419#398—22no—
420#398—22no—
421#397—22no—
422#397—22no—
423#397—22no—
424#396—22no—
425#396—22no—
426#395—22no—
427#395—22no—
428#395—22no—
429#394—22no—
430#394—22no—
431#393—22no—
432#391C2311yescharacteristic
433#391C2311yescharacteristic
434#391C2311yescharacteristic
435#391C2311yescharacteristic
436#391C2311yescharacteristic
437#391C2311yescharacteristic
438#391C2311yescharacteristic
439#391C2311yescharacteristic
440#390C2311yescharacteristic
441#390C2311yescharacteristic
442#390C2311yescharacteristic
443#390C2311yescharacteristic
444#389—22no—
445#389—22no—
446#388—22no—
447#388—22no—
448#388—22no—
449#388—22no—
450#388D412yes—
451#387—22no—
452#387—22no—
453#387—22no—
454#387—22no—
455#387D412yes—
456#386—22no—
457#386—22no—
458#386—22no—
459#386—22no—
460#386D412yes—
461#385—22no—
462#385—22no—
463#385—22no—
464#385—22no—
465#385—22no—
466#385—22no—
467#385D412yes—
468#384—22no—
469#384C2311yescharacteristic
470#384C2311yescharacteristic
471#384C2311yescharacteristic
472#384C2311yescharacteristic
473#384C2311yescharacteristic
474#384C2311yescharacteristic
475#382C2311yescharacteristic
476#382C2311yescharacteristic
477#382C2311yescharacteristic
478#382C2311yescharacteristic
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—41no—
493C2×#41—41no—
494C2×#41—41no—
495C22×Q8—21no—
496C22×Q8—21no—
497C22×Q8—21no—
498C22×Q8—21no—
499C22×Q8—22no—
500C22×Q8—22no—
501C22×Q8—22no—
502C22×Q8—22no—
503C22×Q8—22no—
504C22×Q8—22no—
505C22×Q8—22no—
506C22×Q8—22no—
507C22×Q8—22no—
508C22×Q8—41no—
509C22×Q8—41no—
510C22×Q8—41no—
511C22×Q8—41no—
512C22×Q8—41no—
513C22×Q8—41no—
514C22×Q8—41no—
515C22×Q8—41no—
516C22×Q8—41no—
517C22×Q8C2411yescharacteristic
518C22×Q8C2411yescharacteristic
519C22×Q8C2411yescharacteristic
520C22×Q8C2411yescharacteristic
521C22×Q8C2411yescharacteristic
522C22×Q8C2411yescharacteristic
523C22×D4—21no—
524C22×D4—21no—
525C22×D4—21no—
526C22×D4—21no—
527C22×D4C2×D411yescharacteristic
528C22×D4C2411yescharacteristic
529C22×D4C2411yescharacteristic
530C23×C4—21no—
531C23×C4—21no—
532C23×C4—21no—
533C23×C4—21no—
534C23×C4—21no—
535C23×C4—21no—
536C23×C4—21no—
537C23×C4—21no—
538C23×C4C2×D412yes—
539C23×C4C2411yescharacteristic
540C23×C4C2411yescharacteristic
541C2×Q16—22no—
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×SD16—22no—
557C2×SD16—22no—
558C2×SD16—22no—
559C2×SD16—22no—
560C2×SD16—22no—
561C2×SD16—22no—
562C2×SD16—22no—
563C2×SD16—22no—
564C2×SD16—41no—
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×D8—22no—
575C2×D8—41no—
576C2×D8—41no—
577C2×M16—41no—
578C2×M16—41no—
579C2×M16C2×D414yes—
580C22×C8—41no—
581C22×C8—41no—
582C22×C8—41no—
583C22×C8—41no—
584C22×C8—41no—
585C22×C8—41no—
586C22×C8C2×D414yes—
587C22×C8C2×D414yes—
588C22×C8C2×D414yes—
589C22×C8C2411yescharacteristic
590C22×C8C2411yescharacteristic
591C22×C8C2411yescharacteristic
592C22×C8C2411yescharacteristic
593C22×C8C2411yescharacteristic
594C22×C8C2411yescharacteristic
595C22×C8C2411yescharacteristic
596C22×C8C2411yescharacteristic
597C4⋊Q8—22no—
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—22no—
607C4⋊Q8—48no—
608C4⋊Q8—41no—
609C4⋊Q8—41no—
610C4⋊Q8—41no—
611C4⋊Q8—41no—
612C4⋊Q8—41no—
613C4⋊Q8—44no—
614C4⋊Q8#4114yes—
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—41no—
627#124—41no—
628#124—41no—
629#124—44no—
630#123—48no—
631#123—44no—
632#123—84no—
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—48no—
644C22⋊Q8—44no—
645C22⋊Q8—44no—
646C22⋊Q8—44no—
647C22⋊Q8—44no—
648C22⋊Q8—44no—
649C22⋊Q8—84no—
650#121—22no—
651#121—22no—
652#121—22no—
653#121—22no—
654#121—22no—
655#121—22no—
656#121—44no—
657#121—44no—
658C4×Q8—22no—
659C4×Q8—22no—
660C4×Q8—22no—
661C4×Q8—22no—
662C4×Q8—22no—
663C4×Q8—22no—
664C4×D4—22no—
665C4×D4—22no—
666C4×D4—44no—
667C4×D4—44no—
668C4×D4—44no—
669C4×D4—44no—
670C4×D4C2×D414yes—
671C4×D4C2×D414yes—
672#117—22no—
673#117—22no—
674#117—22no—
675#117—22no—
676C2×C4⋊C4—22no—
677C2×C4⋊C4—22no—
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—22no—
685C2×C4⋊C4—22no—
686C2×C4⋊C4—22no—
687C2×C4⋊C4—22no—
688C2×C4⋊C4—21no—
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—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—48no—
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—21no—
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—21no—
731C2×C22⋊C4—21no—
732C2×C22⋊C4—21no—
733C2×C22⋊C4—21no—
734C2×C22⋊C4—21no—
735C2×C22⋊C4—22no—
736C2×C22⋊C4—22no—
737C2×C22⋊C4—22no—
738C2×C22⋊C4—22no—
739C2×C22⋊C4—22no—
740C2×C22⋊C4—22no—
741C2×C22⋊C4—22no—
742C2×C22⋊C4—22no—
743C2×C22⋊C4C2×D412yes—
744C2×C22⋊C4C2×D412yes—
745C2×C22⋊C4C2×D412yes—
746C2×C22⋊C4C2×D411yescharacteristic
747C2×C22⋊C4C2×D411yescharacteristic
748C2×C42—22no—
749C2×C42—22no—
750C2×C42—21no—
751C2×C42—21no—
752C2×C42—21no—
753C2×C42—21no—
754C2×C42C2×D412yes—
755C2×C42C2411yescharacteristic
756C2×C42C2411yescharacteristic
757C2×C42C2411yescharacteristic
758C2×C42C2411yescharacteristic
759C2×C42C2411yescharacteristic
760#107—22no—
761#107—22no—
762#107—22no—
763#107—22no—
764#107—22no—
765#107—22no—
766#106—22no—
767#106—22no—
768#106—22no—
769#106—22no—
770#106—22no—
771#106—22no—
772C4⋊C8C2×D414yes—
773C4⋊C8C2×D414yes—
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#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#103—22no—
803#103—22no—
804#103—22no—
805#103—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—
814C22⋊C8C2×D414yes—
815C22⋊C8C2×D414yes—
816C22⋊C8C2×D414yes—
817C22⋊C8C2×D414yes—
818#97—22no—
819#97—22no—
820#97—41no—
821#97—41no—
822#97C2×D414yes—
823C4×C8—22no—
824C4×C8—22no—
825C4×C8—41no—
826C4×C8—41no—
827C4×C8—41no—
828C4×C8—41no—
829C4×C8C2×D414yes—
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#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—
849C24C22×D411yescharacteristic
850C24C22×D411yescharacteristic
851#41—44no—
852#41—44no—
853#41—82no—
854#41—82no—
855C2×Q8—21no—
856C2×Q8—21no—
857C2×Q8—21no—
858C2×Q8—21no—
859C2×Q8—21no—
860C2×Q8—21no—
861C2×Q8—21no—
862C2×Q8—21no—
863C2×Q8—21no—
864C2×Q8—21no—
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—42no—
890C2×Q8—42no—
891C2×Q8—42no—
892C2×Q8—44no—
893C2×Q8—44no—
894C2×Q8—44no—
895C2×Q8—44no—
896C2×Q8—44no—
897C2×Q8—44no—
898C2×Q8—42no—
899C2×Q8—42no—
900C2×Q8—42no—
901C2×Q8—42no—
902C2×Q8—81no—
903C2×Q8—81no—
904C2×Q8—81no—
905C2×Q8—82no—
906C2×Q8—82no—
907C2×Q8—82no—
908C2×Q8—82no—
909C2×Q8—82no—
910C2×Q8—82no—
911C2×Q8—82no—
912C2×Q8C2×#4112yes—
913C2×Q8C2×#4112yes—
914C2×D4—24no—
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—42no—
928C2×D4—42no—
929C2×D4—42no—
930C2×D4—42no—
931C2×D4—44no—
932C2×D4—44no—
933C2×D4—42no—
934C2×D4—81no—
935C2×D4—82no—
936C2×D4#12714yes—
937C22×C4—24no—
938C22×C4—24no—
939C22×C4—24no—
940C22×C4—21no—
941C22×C4—21no—
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—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—42no—
963C22×C4—42no—
964C22×C4—42no—
965C22×C4—42no—
966C22×C4—42no—
967C22×C4—42no—
968C22×C4—42no—
969C22×C4—42no—
970C22×C4—42no—
971C22×C4—42no—
972C22×C4—42no—
973C22×C4—42no—
974C22×C4—81no—
975C22×C4—82no—
976C22×C4—81no—
977C22×C4—81no—
978C22×C4—81no—
979C22×C4—82no—
980C22×C4—82no—
981C22×C4—82no—
982C22×C4C22×D412yes—
983C22×C4C22×D412yes—
984C22×C4C22×D411yescharacteristic
985C22×C4C22×D411yescharacteristic
986C22×C4C22×D411yescharacteristic
987C22×C4C22×D411yescharacteristic
988C22×C4C22×D412yes—
989C22×C4C22×D412yes—
990C22×C4C22×D412yes—
991C22×C4C22×D412yes—
992C22×C4C22×D412yes—
993C22×C4C22×D412yes—
994C22×C4C2511yescharacteristic
995Q16—44no—
996Q16—44no—
997Q16—82no—
998Q16—82no—
999Q16—82no—
1000SD16—44no—
1001SD16—44no—
1002SD16—82no—
1003SD16—82no—
1004SD16—82no—
1005SD16—82no—
1006D8—82no—
1007M16—44no—
1008C2×C8—21no—
1009C2×C8—21no—
1010C2×C8—21no—
1011C2×C8—21no—
1012C2×C8—21no—
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—44no—
1025C2×C8—44no—
1026C2×C8—44no—
1027C2×C8C22×D412yes—
1028C2×C8C22×D412yes—
1029C2×C8C22×D412yes—
1030C2×C8C22×D412yes—
1031C2×C8C22×D412yes—
1032C2×C8C22×D412yes—
1033C2×C8C22×D412yes—
1034C2×C8C22×D412yes—
1035C4⋊C4—28no—
1036C4⋊C4—24no—
1037C4⋊C4—24no—
1038C4⋊C4—21no—
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—44no—
1055C4⋊C4—44no—
1056C4⋊C4—44no—
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—44no—
1076C4⋊C4—82no—
1077C4⋊C4—82no—
1078C4⋊C4—82no—
1079C4⋊C4—82no—
1080C4⋊C4—82no—
1081C4⋊C4#12714yes—
1082C22⋊C4—24no—
1083C22⋊C4—24no—
1084C22⋊C4—24no—
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—44no—
1099C22⋊C4—44no—
1100C22⋊C4—44no—
1101C22⋊C4—44no—
1102C22⋊C4—82no—
1103C22⋊C4—82no—
1104C22⋊C4—82no—
1105C22⋊C4#12714yes—
1106C22⋊C4#12714yes—
1107C42—24no—
1108C42—21no—
1109C42—21no—
1110C42—21no—
1111C42—21no—
1112C42—21no—
1113C42—21no—
1114C42—42no—
1115C42—42no—
1116C42—42no—
1117C42—42no—
1118C42C22×D412yes—
1119C42C22×D412yes—
1120C42C2×#4112yes—
1121C42H(5,𝔽2)12yes—
1122C23—21no—
1123C23—21no—
1124C23—22no—
1125C23—21no—
1126C23—21no—
1127C23—22no—
1128C23—22no—
1129C23—41no—
1130C23—41no—
1131C23—41no—
1132C23—41no—
1133C23—41no—
1134C23—41no—
1135C23—42no—
1136C23—42no—
1137C23—42no—
1138C23—42no—
1139C23C2×#12712yes—
1140C23C2×#12712yes—
1141C23#57814yes—
1142C23C23×D411yescharacteristic
1143Q8—22no—
1144Q8—22no—
1145Q8—22no—
1146Q8—22no—
1147Q8—41no—
1148Q8—41no—
1149Q8—41no—
1150Q8—41no—
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—84no—
1168Q8—84no—
1169Q8—84no—
1170Q8—162no—
1171D4—28no—
1172D4—41no—
1173D4—41no—
1174D4—41no—
1175D4—41no—
1176D4—41no—
1177D4—41no—
1178D4—41no—
1179D4—41no—
1180D4—84no—
1181D4—84no—
1182D4—84no—
1183D4—162no—
1184C2×C4—216no—
1185C2×C4—22no—
1186C2×C4—21no—
1187C2×C4—21no—
1188C2×C4—21no—
1189C2×C4—21no—
1190C2×C4—22no—
1191C2×C4—22no—
1192C2×C4—22no—
1193C2×C4—22no—
1194C2×C4—22no—
1195C2×C4—22no—
1196C2×C4—22no—
1197C2×C4—22no—
1198C2×C4—22no—
1199C2×C4—22no—
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—41no—
1212C2×C4—41no—
1213C2×C4—41no—
1214C2×C4—41no—
1215C2×C4—41no—
1216C2×C4—41no—
1217C2×C4—41no—
1218C2×C4—41no—
1219C2×C4—41no—
1220C2×C4—41no—
1221C2×C4—41no—
1222C2×C4—41no—
1223C2×C4—41no—
1224C2×C4—41no—
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—42no—
1236C2×C4—42no—
1237C2×C4—42no—
1238C2×C4—42no—
1239C2×C4—42no—
1240C2×C4—42no—
1241C2×C4—42no—
1242C2×C4—42no—
1243C2×C4—84no—
1244C2×C4—84no—
1245C2×C4—84no—
1246C2×C4—84no—
1247C2×C4—162no—
1248C2×C4—162no—
1249C2×C4—162no—
1250C2×C4—162no—
1251C2×C4C2×#12712yes—
1252C2×C4C2×#12712yes—
1253C2×C4C2×#12712yes—
1254C2×C4C2×#12712yes—
1255C2×C4#54614yes—
1256C2×C4#57714yes—
1257C2×C4C23×D411yescharacteristic
1258C2×C4C23×D411yescharacteristic
1259C2×C4C22×#4111yescharacteristic
1260C2×C4C2×H(5,𝔽2)11yescharacteristic
1261C2×C4#58511yescharacteristic
1262C2×C4#58511yescharacteristic
1263C8—22no—
1264C8—22no—
1265C8—22no—
1266C8—22no—
1267C8—22no—
1268C8—22no—
1269C8—22no—
1270C8—22no—
1271C22—24no—
1272C22—22no—
1273C22—22no—
1274C22—24no—
1275C22—22no—
1276C22—22no—
1277C22—22no—
1278C22—42no—
1279C22—42no—
1280C22—82no—
1281C22—82no—
1282C22—81no—
1283C22—81no—
1284C22—81no—
1285C22—81no—
1286C22—81no—
1287C22—81no—
1288C22—82no—
1289C22—82no—
1290C22#315614yes—
1291C22C22×#12711yescharacteristic
1292C22C2×#54611yescharacteristic
1293C22#350011yescharacteristic
1294C22C2×#57712yes—
1295C22C2×#57812yes—
1296C4—22no—
1297C4—22no—
1298C4—22no—
1299C4—22no—
1300C4—24no—
1301C4—24no—
1302C4—42no—
1303C4—42no—
1304C4—42no—
1305C4—42no—
1306C4—81no—
1307C4—81no—
1308C4—81no—
1309C4—81no—
1310C4—81no—
1311C4—81no—
1312C4—81no—
1313C4—81no—
1314C4—81no—
1315C4—81no—
1316C4—81no—
1317C4—81no—
1318C4D4×#4111yescharacteristic
1319C4D4×#4111yescharacteristic
1320C4#349611yescharacteristic
1321C4#349611yescharacteristic
1322C2—24no—
1323C2—42no—
1324C2—161no—
1325C2—161no—
1326C2#3626011yescharacteristic
1327C2C2×#315611yescharacteristic
1328C2#6064611yescharacteristic
1329C2#6116812yes—
1330C2#6255312yes—
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#3301C2
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×#3320C2semidirect
2. C2×#3316C2semidirect
4. C2×#3299C2semidirect
5. #37862C2semidirect
6. #37675C2semidirect
7. #33229C2semidirect
8. #33188C2semidirect
9. #33173C2semidirect
10. #28526C2semidirect
11. #28453C2semidirect
12. #28426C2semidirect
13. #28423C2semidirect
14. #28407C2semidirect
15. #28400C2semidirect
16. #28358C2semidirect
17. #28355C2semidirect
18. #28348C2semidirect
19. #28347C2semidirect
20. #28338C2semidirect
21. #28336C2semidirect
22. #28334C2semidirect
23. #28333C2semidirect
24. #27922C2semidirect
25. #27913C2semidirect
26. #25737C2semidirect
27. #25726C2semidirect
28. #21703C2semidirect
29. #21205C2semidirect
30. C2×#1956C2semidirect
31. #20484C2semidirect

Maximal subgroups

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

subgroupindex
C2×#33202
C2×#33162
C2×#33012
C2×#32992
#378622
#376752
#332292
#331882
#331732
#285262
#284532
#284262
#284232
#284072
#284002
#283582
#283552
#283482
#283472
#283382
#283362
#283342
#283332
#279222
#279132
#257372
#257262
#217032
#212052
C2×#19562
#204842