Finite Group Databasebeta

← #6606790

Subgroups — #6606790

Order 512.

2368 conjugacy classes of subgroups.

The subgroup lattice has 1350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3320C211yesmaximal, characteristic, complemented
2C2×#3314C211yesmaximal, characteristic, complemented
3C2×#3299C211yesmaximal, characteristic, complemented
4C2×#3297C211yesmaximal, characteristic
5#37862C211yesmaximal, characteristic, complemented
6#37676C211yesmaximal, characteristic, complemented
7#33229C211yesmaximal, characteristic, complemented
8#33184C211yesmaximal, characteristic, complemented
9#33182C211yesmaximal, characteristic, complemented
10#28523C211yesmaximal, characteristic, complemented
11#28453C211yesmaximal, characteristic, complemented
12#28427C211yesmaximal, characteristic, complemented
13#28426C211yesmaximal, characteristic, complemented
14#28414C211yesmaximal, characteristic, complemented
15#28411C211yesmaximal, characteristic, complemented
16#28359C211yesmaximal, characteristic, complemented
17#28358C211yesmaximal, characteristic, complemented
18#28350C211yesmaximal, characteristic, complemented
19#28348C211yesmaximal, characteristic, complemented
20#28346C211yesmaximal, characteristic, complemented
21#28342C211yesmaximal, characteristic, complemented
22#28333C211yesmaximal, characteristic, complemented
23#28331C211yesmaximal, characteristic, complemented
24#27921C211yesmaximal, characteristic, complemented
25#27910C211yesmaximal, characteristic, complemented
26#25737C211yesmaximal, characteristic, complemented
27#25724C211yesmaximal, characteristic, complemented
28#21696C211yesmaximal, characteristic, complemented
29#21205C211yesmaximal, characteristic, complemented
30C2×#1959C211yesmaximal, characteristic, complemented
31#20493C211yesmaximal, characteristic, complemented
32C2×#554C2211yescharacteristic
33C2×#553C2211yescharacteristic
34C2×D4×Q8C2211yescharacteristic
35C2×#546C2211yescharacteristic
36C2×#536C2211yescharacteristic
37C22×#124C2211yescharacteristic
38#3320—28no—
39#3314—28no—
40#3299—28no—
41#3297—28no—
42C2×#497C2211yescharacteristic, complemented
43C2×#495C2211yescharacteristic
44C2×#495C2211yescharacteristic
45C2×#491C2211yescharacteristic, complemented
46C2×#489C2211yescharacteristic
47C2×#488C2211yescharacteristic
48C2×#487C2211yescharacteristic, complemented
49C2×#484C2211yescharacteristic
50C2×#484C2211yescharacteristic
51C2×#484C2211yescharacteristic
52C2×#484C2211yescharacteristic
53C2×#484C2211yescharacteristic, complemented
54C2×#485C2211yescharacteristic, complemented
55C2×#482C2211yescharacteristic
56C2×#480C2211yescharacteristic
57C2×#479C2211yescharacteristic, complemented
58C2×#477C2211yescharacteristic, complemented
59C2×#478C2211yescharacteristic
60C2×#474C2211yescharacteristic
61C2×#468C2211yescharacteristic
62C2×#468C2211yescharacteristic, complemented
63C2×#467C2211yescharacteristic
64C2×#467C2211yescharacteristic
65C2×#467C2211yescharacteristic, complemented
66C2×#466C2211yescharacteristic
67C2×#465C2211yescharacteristic
68C2×#465C2211yescharacteristic
69C2×#464C2211yescharacteristic
70C2×#462C2211yescharacteristic, complemented
71C2×#463C2211yescharacteristic
72C2×#461C2211yescharacteristic, complemented
73C2×#452C2211yescharacteristic
74C2×#449C2211yescharacteristic
75C2×#451C2211yescharacteristic
76C2×#451C2211yescharacteristic, complemented
77C2×#448C2211yescharacteristic
78C2×#448C2211yescharacteristic, complemented
79C2×#450C2211yescharacteristic
80C2×#447C2211yescharacteristic
81C2×#440C2211yescharacteristic
82C2×#440C2211yescharacteristic, complemented
83C2×C4×Q16C2211yescharacteristic, complemented
84C2×C4×D8C2211yescharacteristic
85C2×#435C2211yescharacteristic
86C2×C8×D4C2211yescharacteristic
87C2×#417C2211yescharacteristic
88C2×#419C2211yescharacteristic, complemented
89C2×#416C2211yescharacteristic
90C22×#103C2211yescharacteristic
91C22×#103C2211yescharacteristic
92C22×#103C2211yescharacteristic, complemented
93C22×#102C2211yescharacteristic
94C22×#102C2211yescharacteristic
95C2×#405C2211yescharacteristic, complemented
96C22×#97C2211yescharacteristic
97#2857C2211yescharacteristic
98#2850C2211yescharacteristic
99#2721—22no—
100#2680—22no—
101#2674—22no—
102#2672—22no—
103#2660C2211yescharacteristic, complemented
104#2658C2211yescharacteristic
105#2620C2211yescharacteristic
106#2620C2211yescharacteristic, complemented
107#2565C2211yescharacteristic, complemented
108#2547C2211yescharacteristic
109#2545C2211yescharacteristic
110#2542C2211yescharacteristic, complemented
111#2504C2211yescharacteristic
112#2502C2211yescharacteristic
113#2501C2211yescharacteristic, complemented
114#2499C2211yescharacteristic, complemented
115#2449—22no—
116#2443—22no—
117#2437—22no—
118#2436C2211yescharacteristic
119#2435C2211yescharacteristic
120#2434C2211yescharacteristic
121#2432C2211yescharacteristic
122#2418—22no—
123#2326C2211yescharacteristic
124#2326C2211yescharacteristic, complemented
125#2317C2211yescharacteristic, complemented
126#2290C2211yescharacteristic
127C2×#384C2211yescharacteristic
128#2097C2211yescharacteristic, complemented
129#2097C2211yescharacteristic, complemented
130#2095C2211yescharacteristic, complemented
131#2095C2211yescharacteristic, complemented
132#2095C2211yescharacteristic, complemented
133#2095C2211yescharacteristic, complemented
134#2095C2211yescharacteristic, complemented
135#2095C2211yescharacteristic, complemented
136#2093C2211yescharacteristic
137#2093C2211yescharacteristic
138#2092C2211yescharacteristic
139#2092C2211yescharacteristic
140#2016C2211yescharacteristic, complemented
141#2016C2211yescharacteristic, complemented
142#2015C2211yescharacteristic
143#2015C2211yescharacteristic
144#2015C2211yescharacteristic
145#2015C2211yescharacteristic
146#2013C2211yescharacteristic, complemented
147#2013C2211yescharacteristic, complemented
148#2012C2211yescharacteristic
149#2012C2211yescharacteristic
150#2012C2211yescharacteristic
151#2012C2211yescharacteristic
152#1973C2211yescharacteristic
153#1973C2211yescharacteristic
154#1973C2211yescharacteristic, complemented
155#1973C2211yescharacteristic, complemented
156#1973C2211yescharacteristic, complemented
157#1973C2211yescharacteristic, complemented
158#1971C2211yescharacteristic, complemented
159#1971C2211yescharacteristic, complemented
160#1970C2211yescharacteristic
161#1970C2211yescharacteristic
162#1969C2211yescharacteristic, complemented
163#1969C2211yescharacteristic, complemented
164#1960C2211yescharacteristic, complemented
165#1960C2211yescharacteristic, complemented
166#1960C2211yescharacteristic, complemented
167#1959C2211yescharacteristic
168#1959C2211yescharacteristic
169#1959C2211yescharacteristic
170#1959C2211yescharacteristic
171#1959C2211yescharacteristic
172#1959C2211yescharacteristic
173#1959C2211yescharacteristic
174#1959C2211yescharacteristic
175#1959C2211yescharacteristic
176#1959C2211yescharacteristic
177#1959C2211yescharacteristic, complemented
178#1958C2211yescharacteristic
179#1958C2211yescharacteristic
180#1958C2211yescharacteristic
181#1958C2211yescharacteristic
182#1956C2211yescharacteristic, complemented
183#1956C2211yescharacteristic, complemented
184#1956C2211yescharacteristic, complemented
185#1956C2211yescharacteristic, complemented
186#1847C2211yescharacteristic, complemented
187#1845C2211yescharacteristic, complemented
188#1845C2211yescharacteristic, complemented
189#1771C2211yescharacteristic, complemented
190#1770C2211yescharacteristic, complemented
191#1768C2211yescharacteristic, complemented
192#1753C2211yescharacteristic, complemented
193#1752C2211yescharacteristic
194#1752C2211yescharacteristic, complemented
195C8×C22⋊C4C2211yescharacteristic
196#1750C2211yescharacteristic, complemented
197C4×C22⋊C8C2211yescharacteristic
198#1726C2211yescharacteristic, complemented
199C22×#41C2311yescharacteristic
200C23×Q8C2311yescharacteristic
201C23×Q8C2311yescharacteristic
202C23×D4C2311yescharacteristic
203C22×Q16C2311yescharacteristic
204C22×Q16C2311yescharacteristic
205C22×Q16C2311yescharacteristic
206C22×Q16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×SD16C2311yescharacteristic
209C22×SD16C2311yescharacteristic
210C22×SD16C2311yescharacteristic
211C22×SD16C2311yescharacteristic
212C22×SD16C2311yescharacteristic
213C22×D8C2311yescharacteristic
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#546—24no—
226#546—24no—
227#536—24no—
228#536—42no—
229C2×C4⋊Q8—21no—
230C2×C4⋊Q8C2311yescharacteristic
231C2×C4⋊Q8C2311yescharacteristic
232C2×C4⋊Q8C2311yescharacteristic
233C2×C4⋊Q8C2311yescharacteristic
234C2×C4⋊Q8C2311yescharacteristic
235C2×#126—21no—
236C2×#125—21no—
237C2×#125C2311yescharacteristic
238C2×#124—24no—
239C2×#124—22no—
240C2×#124—42no—
241C2×#124C2311yescharacteristic
242C2×#124C2311yescharacteristic
243C2×#124C2311yescharacteristic
244C2×#124C2311yescharacteristic
245C2×#124C2311yescharacteristic
246C2×#124C2311yescharacteristic
247C2×#124C2311yescharacteristic
248C2×#124C2311yescharacteristic
249C2×#123—21no—
250C2×#123—22no—
251C2×#123—21no—
252C2×#123—22no—
253C2×C22⋊Q8—22no—
254C2×C22⋊Q8—22no—
255C2×C22⋊Q8—21no—
256C2×C22⋊Q8—21no—
257C2×C22⋊Q8—21no—
258C2×C22⋊Q8—21no—
259C2×C22⋊Q8C2311yescharacteristic
260C2×C22⋊Q8C2311yescharacteristic
261C2×C22⋊Q8C2311yescharacteristic
262C2×C22⋊Q8C2311yescharacteristic
263C2×C22⋊Q8C2311yescharacteristic
264C2×#121—21no—
265C2×#121—21no—
266C2×#121C2311yescharacteristic
267C2×#121C2311yescharacteristic
268C2×#121C2311yescharacteristic
269C2×#120—21no—
270C2×C4×Q8C2311yescharacteristic
271C2×C4×Q8C2311yescharacteristic
272C2×C4×D4—21no—
273C2×C4×D4—21no—
274C2×C4×D4—21no—
275C2×C4×D4C2311yescharacteristic
276C2×C4×D4C2311yescharacteristic
277C2×C4×D4C2311yescharacteristic
278C2×#117C2311yescharacteristic
279C2×#117C2311yescharacteristic
280C22×C4⋊C4—22no—
281C22×C4⋊C4C2311yescharacteristic
282C22×C4⋊C4C2311yescharacteristic
283C22×C4⋊C4C2311yescharacteristic
284C22×C22⋊C4—22no—
285C22×C22⋊C4—21no—
286C22×C42C2311yescharacteristic
287#497—42no—
288#495—24no—
289#495—42no—
290#491—24no—
291#489—24no—
292#488—24no—
293#487—24no—
294#485—24no—
295#484—24no—
296#484—24no—
297#484—24no—
298#484—24no—
299#484—24no—
300#482—24no—
301#480—24no—
302#479—24no—
303#478—24no—
304#477—24no—
305#474—24no—
306#468—24no—
307#468—24no—
308#467—24no—
309#467—24no—
310#467—24no—
311#466—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#450—24no—
322#449—24no—
323#448—24no—
324#448—24no—
325#447—24no—
326#440—24no—
327#440—24no—
328C4×Q16—24no—
329C4×D8—24no—
330#435D418yes—
331C8×D4D418yes—
332C2×#107C2311yescharacteristic
333C2×#107C2311yescharacteristic
334C2×#107C2311yescharacteristic
335C2×#107C2311yescharacteristic
336C2×#107C2311yescharacteristic
337C2×#107C2311yescharacteristic
338C2×#107C2311yescharacteristic
339C2×#107C2311yescharacteristic
340C2×#107C2311yescharacteristic
341C2×#107C2311yescharacteristic
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×#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×#103C2311yescharacteristic
373C2×#103C2311yescharacteristic
374C2×#103C2311yescharacteristic
375C2×#103C2311yescharacteristic
376C2×#103C2311yescharacteristic
377C2×#103C2311yescharacteristic
378C2×#102—24no—
379C2×#102—24no—
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×C22⋊C8C2311yescharacteristic
395C2×C22⋊C8C2311yescharacteristic
396C2×C22⋊C8C2311yescharacteristic
397C2×C22⋊C8C2311yescharacteristic
398#405—42no—
399C2×#97—42no—
400C2×#97C2311yescharacteristic
401C2×#97C2311yescharacteristic
402C2×#97C2311yescharacteristic
403C2×#97C2311yescharacteristic
404C2×#97C2311yescharacteristic
405C2×#97C2311yescharacteristic
406C2×#97C2311yescharacteristic
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#397—22no—
420#397—22no—
421#397—22no—
422#396—22no—
423#396—22no—
424#396—22no—
425#395—22no—
426#395—22no—
427#394—22no—
428#394—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#390C2311yescharacteristic
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#387D412yes—
454#386—22no—
455#386—22no—
456#386—22no—
457#386D412yes—
458#385—22no—
459#385—22no—
460#385—22no—
461#385—22no—
462#385—22no—
463#385—22no—
464#385D412yes—
465#384—22no—
466#384C2311yescharacteristic
467#384C2311yescharacteristic
468#384C2311yescharacteristic
469#384C2311yescharacteristic
470#384C2311yescharacteristic
471#384C2311yescharacteristic
472#384C2311yescharacteristic
473#382C2311yescharacteristic
474#382C2311yescharacteristic
475#382C2311yescharacteristic
476#380—22no—
477#380—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—
490C2×#41—22no—
491C2×#41—22no—
492C2×#41—22no—
493C2×#41—41no—
494C2×#41—41no—
495C2×#41—41no—
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—41no—
506C22×Q8—41no—
507C22×Q8—41no—
508C22×Q8—41no—
509C22×Q8—41no—
510C22×Q8—41no—
511C22×Q8C2411yescharacteristic
512C22×Q8C2411yescharacteristic
513C22×Q8C2411yescharacteristic
514C22×Q8C2411yescharacteristic
515C22×Q8C2411yescharacteristic
516C22×D4—22no—
517C22×D4—21no—
518C22×D4—21no—
519C22×D4—21no—
520C22×D4—21no—
521C22×D4—22no—
522C22×D4—22no—
523C22×D4—21no—
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—41no—
548C2×Q16—41no—
549C2×Q16—41no—
550C2×Q16—41no—
551C2×Q16—41no—
552C2×Q16—41no—
553C2×Q16—41no—
554C2×SD16—22no—
555C2×SD16—22no—
556C2×SD16—22no—
557C2×SD16—22no—
558C2×SD16—22no—
559C2×SD16—22no—
560C2×SD16—22no—
561C2×SD16—22no—
562C2×SD16—41no—
563C2×SD16—41no—
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×D8—22no—
573C2×D8—22no—
574C2×D8—22no—
575C2×D8—41no—
576C2×D8—41no—
577C2×D8—41no—
578C2×M16—41no—
579C2×M16—41no—
580C2×M16C2×D414yes—
581C22×C8—41no—
582C22×C8—41no—
583C22×C8—41no—
584C22×C8—41no—
585C22×C8—41no—
586C22×C8—41no—
587C22×C8C2×D414yes—
588C22×C8C2×D414yes—
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—41no—
606C4⋊Q8—41no—
607C4⋊Q8—41no—
608C4⋊Q8—44no—
609#126—44no—
610#125—22no—
611#125—22no—
612#125—44no—
613#124—22no—
614#124—22no—
615#124—22no—
616#124—22no—
617#124—22no—
618#124—22no—
619#124—22no—
620#124—22no—
621#124—22no—
622#124—22no—
623#124—48no—
624#124—41no—
625#124—41no—
626#124—41no—
627#124—41no—
628#124—41no—
629#124#4114yes—
630#123—48no—
631#123—44no—
632#123—44no—
633#123—84no—
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—48no—
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—
658#120—44no—
659C4×Q8—22no—
660C4×Q8—22no—
661C4×Q8—22no—
662C4×Q8—22no—
663C4×D4—22no—
664C4×D4—22no—
665C4×D4—22no—
666C4×D4—22no—
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—21no—
685C2×C4⋊C4—21no—
686C2×C4⋊C4—21no—
687C2×C4⋊C4—21no—
688C2×C4⋊C4—21no—
689C2×C4⋊C4—21no—
690C2×C4⋊C4—21no—
691C2×C4⋊C4—21no—
692C2×C4⋊C4—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—22no—
700C2×C4⋊C4—22no—
701C2×C4⋊C4—22no—
702C2×C4⋊C4—22no—
703C2×C4⋊C4—22no—
704C2×C4⋊C4—22no—
705C2×C4⋊C4—22no—
706C2×C4⋊C4—22no—
707C2×C4⋊C4—84no—
708C2×C4⋊C4C2×D412yes—
709C2×C4⋊C4C2×D412yes—
710C2×C4⋊C4C2×D411yescharacteristic
711C2×C4⋊C4C2411yescharacteristic
712C2×C4⋊C4C2411yescharacteristic
713C2×C4⋊C4C2411yescharacteristic
714C2×C4⋊C4C2411yescharacteristic
715C2×C4⋊C4C2411yescharacteristic
716C2×C4⋊C4C2411yescharacteristic
717C2×C4⋊C4C2411yescharacteristic
718C2×C4⋊C4C2411yescharacteristic
719C2×C22⋊C4—22no—
720C2×C22⋊C4—21no—
721C2×C22⋊C4—21no—
722C2×C22⋊C4—21no—
723C2×C22⋊C4—21no—
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—22no—
738C2×C22⋊C4—22no—
739C2×C22⋊C4—22no—
740C2×C22⋊C4—22no—
741C2×C22⋊C4—22no—
742C2×C22⋊C4—22no—
743C2×C22⋊C4—22no—
744C2×C22⋊C4—48no—
745C2×C22⋊C4—44no—
746C2×C22⋊C4C2×D412yes—
747C2×C22⋊C4C2×D412yes—
748C2×C22⋊C4C2×D412yes—
749C2×C22⋊C4C2×D411yescharacteristic
750C2×C22⋊C4C2×D411yescharacteristic
751C2×C42—22no—
752C2×C42—22no—
753C2×C42—21no—
754C2×C42—21no—
755C2×C42—21no—
756C2×C42C2×D412yes—
757C2×C42C2411yescharacteristic
758C2×C42C2411yescharacteristic
759C2×C42C2411yescharacteristic
760C2×C42C2411yescharacteristic
761C2×C42C2411yescharacteristic
762#107—22no—
763#107—22no—
764#107—22no—
765#107—22no—
766#107—22no—
767#107—22no—
768#107—22no—
769#107—22no—
770#107—22no—
771#107—22no—
772#106—22no—
773#106—22no—
774C4⋊C8C2×D414yes—
775C4⋊C8C2×D414yes—
776#103—22no—
777#103—22no—
778#103—22no—
779#103—22no—
780#103—22no—
781#103—22no—
782#103—22no—
783#103—22no—
784#103—22no—
785#103—22no—
786#103—22no—
787#103—22no—
788#103—22no—
789#103—22no—
790#103—22no—
791#103—22no—
792#103—22no—
793#103—22no—
794#103—22no—
795#103—22no—
796#103—22no—
797#103—22no—
798#103—22no—
799#103—22no—
800#103—22no—
801#103—22no—
802#102—22no—
803#102—22no—
804#102—22no—
805#102—22no—
806#102—22no—
807#102—22no—
808#102—22no—
809#102—22no—
810#102—22no—
811#102—22no—
812#102—22no—
813#102—22no—
814#102—22no—
815#102—22no—
816C22⋊C8C2×D414yes—
817C22⋊C8C2×D414yes—
818C22⋊C8C2×D414yes—
819C22⋊C8C2×D414yes—
820#97—22no—
821#97—22no—
822#97—41no—
823#97—41no—
824#97—41no—
825#97—41no—
826#97C2×D414yes—
827C4×C8—22no—
828C4×C8—22no—
829C4×C8—41no—
830C4×C8—41no—
831C4×C8C2×D414yes—
832#95—22no—
833#95—22no—
834#95—22no—
835#95—22no—
836#95—22no—
837#95—22no—
838#95—22no—
839#95—22no—
840#95—22no—
841#95—22no—
842#95C2×D412yes—
843#95C2×D412yes—
844#95C2×D412yes—
845#95C2×D412yes—
846#95C2×D412yes—
847C24—21no—
848C24—21no—
849C24—21no—
850C24—42no—
851C24—42no—
852C24—44no—
853C24—81no—
854C24—82no—
855C24C22×D411yescharacteristic
856C24C22×D411yescharacteristic
857#41—44no—
858#41—44no—
859#41—82no—
860#41—82no—
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—21no—
890C2×Q8—42no—
891C2×Q8—42no—
892C2×Q8—44no—
893C2×Q8—44no—
894C2×Q8—44no—
895C2×Q8—44no—
896C2×Q8—42no—
897C2×Q8—42no—
898C2×Q8—42no—
899C2×Q8—81no—
900C2×Q8—81no—
901C2×Q8—82no—
902C2×Q8—82no—
903C2×Q8—82no—
904C2×Q8—82no—
905C2×Q8—82no—
906C2×Q8C2×#4112yes—
907C2×D4—24no—
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—44no—
926C2×D4—44no—
927C2×D4—42no—
928C2×D4—42no—
929C2×D4—42no—
930C2×D4—42no—
931C2×D4—44no—
932C2×D4—42no—
933C2×D4—42no—
934C2×D4—42no—
935C2×D4—82no—
936C2×D4—82no—
937C2×D4—81no—
938C2×D4—81no—
939C2×D4—82no—
940C2×D4—82no—
941C2×D4#12714yes—
942C2×D4C2×#4112yes—
943C22×C4—21no—
944C22×C4—21no—
945C22×C4—21no—
946C22×C4—21no—
947C22×C4—21no—
948C22×C4—21no—
949C22×C4—21no—
950C22×C4—21no—
951C22×C4—24no—
952C22×C4—21no—
953C22×C4—24no—
954C22×C4—21no—
955C22×C4—21no—
956C22×C4—21no—
957C22×C4—21no—
958C22×C4—21no—
959C22×C4—21no—
960C22×C4—21no—
961C22×C4—21no—
962C22×C4—21no—
963C22×C4—21no—
964C22×C4—21no—
965C22×C4—21no—
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—42no—
975C22×C4—42no—
976C22×C4—42no—
977C22×C4—42no—
978C22×C4—81no—
979C22×C4—82no—
980C22×C4—82no—
981C22×C4—81no—
982C22×C4—81no—
983C22×C4—82no—
984C22×C4—82no—
985C22×C4—82no—
986C22×C4C22×D412yes—
987C22×C4C22×D412yes—
988C22×C4C22×D412yes—
989C22×C4C22×D411yescharacteristic
990C22×C4C22×D411yescharacteristic
991C22×C4C22×D411yescharacteristic
992C22×C4C22×D411yescharacteristic
993C22×C4C22×D412yes—
994C22×C4C22×D412yes—
995C22×C4C22×D412yes—
996C22×C4C22×D412yes—
997C22×C4C22×D412yes—
998C22×C4C2511yescharacteristic
999Q16—44no—
1000Q16—82no—
1001Q16—82no—
1002Q16—82no—
1003SD16—44no—
1004SD16—44no—
1005SD16—82no—
1006SD16—82no—
1007SD16—82no—
1008SD16—82no—
1009D8—44no—
1010D8—82no—
1011M16—44no—
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—21no—
1025C2×C8—21no—
1026C2×C8—21no—
1027C2×C8—21no—
1028C2×C8—44no—
1029C2×C8—44no—
1030C2×C8—44no—
1031C2×C8C22×D412yes—
1032C2×C8C22×D412yes—
1033C2×C8C22×D412yes—
1034C2×C8C22×D412yes—
1035C2×C8C22×D412yes—
1036C2×C8C22×D412yes—
1037C2×C8C22×D412yes—
1038C2×C8C22×D412yes—
1039C4⋊C4—24no—
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—21no—
1056C4⋊C4—42no—
1057C4⋊C4—44no—
1058C4⋊C4—44no—
1059C4⋊C4—44no—
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—42no—
1074C4⋊C4—42no—
1075C4⋊C4—44no—
1076C4⋊C4—82no—
1077C4⋊C4—82no—
1078C4⋊C4—82no—
1079C4⋊C4—82no—
1080C4⋊C4—82no—
1081C4⋊C4—82no—
1082C4⋊C4#12714yes—
1083C22⋊C4—24no—
1084C22⋊C4—28no—
1085C22⋊C4—24no—
1086C22⋊C4—42no—
1087C22⋊C4—44no—
1088C22⋊C4—44no—
1089C22⋊C4—44no—
1090C22⋊C4—44no—
1091C22⋊C4—42no—
1092C22⋊C4—42no—
1093C22⋊C4—42no—
1094C22⋊C4—42no—
1095C22⋊C4—42no—
1096C22⋊C4—42no—
1097C22⋊C4—42no—
1098C22⋊C4—42no—
1099C22⋊C4—42no—
1100C22⋊C4—42no—
1101C22⋊C4—42no—
1102C22⋊C4—42no—
1103C22⋊C4—42no—
1104C22⋊C4—44no—
1105C22⋊C4—44no—
1106C22⋊C4—82no—
1107C22⋊C4—82no—
1108C22⋊C4—82no—
1109C22⋊C4—82no—
1110C22⋊C4—82no—
1111C22⋊C4#12714yes—
1112C22⋊C4#12714yes—
1113C42—24no—
1114C42—21no—
1115C42—21no—
1116C42—21no—
1117C42—21no—
1118C42—21no—
1119C42—21no—
1120C42—42no—
1121C42—42no—
1122C42—42no—
1123C42C22×D412yes—
1124C42C22×D412yes—
1125C42C2×#4112yes—
1126C42H(5,𝔽2)12yes—
1127C23—22no—
1128C23—21no—
1129C23—21no—
1130C23—22no—
1131C23—21no—
1132C23—21no—
1133C23—22no—
1134C23—22no—
1135C23—42no—
1136C23—41no—
1137C23—41no—
1138C23—42no—
1139C23—42no—
1140C23—42no—
1141C23—41no—
1142C23—41no—
1143C23—41no—
1144C23—41no—
1145C23—41no—
1146C23—41no—
1147C23—42no—
1148C23—42no—
1149C23—84no—
1150C23—88no—
1151C23—84no—
1152C23—164no—
1153C23—162no—
1154C23C2×#12712yes—
1155C23C2×#12712yes—
1156C23#57814yes—
1157C23C23×D411yescharacteristic
1158Q8—22no—
1159Q8—22no—
1160Q8—41no—
1161Q8—41no—
1162Q8—41no—
1163Q8—41no—
1164Q8—41no—
1165Q8—41no—
1166Q8—41no—
1167Q8—41no—
1168Q8—41no—
1169Q8—41no—
1170Q8—41no—
1171Q8—41no—
1172Q8—41no—
1173Q8—41no—
1174Q8—41no—
1175Q8—41no—
1176Q8—41no—
1177Q8—41no—
1178Q8—84no—
1179Q8—84no—
1180Q8—162no—
1181D4—28no—
1182D4—22no—
1183D4—22no—
1184D4—41no—
1185D4—41no—
1186D4—41no—
1187D4—41no—
1188D4—41no—
1189D4—41no—
1190D4—41no—
1191D4—41no—
1192D4—41no—
1193D4—41no—
1194D4—84no—
1195D4—84no—
1196D4—84no—
1197D4—162no—
1198D4—162no—
1199C2×C4—22no—
1200C2×C4—22no—
1201C2×C4—21no—
1202C2×C4—21no—
1203C2×C4—21no—
1204C2×C4—21no—
1205C2×C4—22no—
1206C2×C4—22no—
1207C2×C4—22no—
1208C2×C4—22no—
1209C2×C4—22no—
1210C2×C4—22no—
1211C2×C4—22no—
1212C2×C4—22no—
1213C2×C4—22no—
1214C2×C4—22no—
1215C2×C4—22no—
1216C2×C4—22no—
1217C2×C4—22no—
1218C2×C4—22no—
1219C2×C4—22no—
1220C2×C4—22no—
1221C2×C4—22no—
1222C2×C4—22no—
1223C2×C4—22no—
1224C2×C4—22no—
1225C2×C4—48no—
1226C2×C4—41no—
1227C2×C4—41no—
1228C2×C4—42no—
1229C2×C4—42no—
1230C2×C4—42no—
1231C2×C4—42no—
1232C2×C4—42no—
1233C2×C4—42no—
1234C2×C4—42no—
1235C2×C4—41no—
1236C2×C4—41no—
1237C2×C4—41no—
1238C2×C4—41no—
1239C2×C4—41no—
1240C2×C4—41no—
1241C2×C4—41no—
1242C2×C4—41no—
1243C2×C4—41no—
1244C2×C4—41no—
1245C2×C4—41no—
1246C2×C4—41no—
1247C2×C4—41no—
1248C2×C4—41no—
1249C2×C4—41no—
1250C2×C4—41no—
1251C2×C4—41no—
1252C2×C4—41no—
1253C2×C4—41no—
1254C2×C4—41no—
1255C2×C4—42no—
1256C2×C4—84no—
1257C2×C4—84no—
1258C2×C4—84no—
1259C2×C4—162no—
1260C2×C4—162no—
1261C2×C4—162no—
1262C2×C4—162no—
1263C2×C4—162no—
1264C2×C4C2×#12712yes—
1265C2×C4C2×#12712yes—
1266C2×C4C2×#12712yes—
1267C2×C4C2×#12712yes—
1268C2×C4#54614yes—
1269C2×C4C23×D411yescharacteristic
1270C2×C4C23×D411yescharacteristic
1271C2×C4C22×#4111yescharacteristic
1272C2×C4C2×H(5,𝔽2)11yescharacteristic
1273C2×C4#58511yescharacteristic
1274C2×C4#58511yescharacteristic
1275C8—22no—
1276C8—22no—
1277C8—22no—
1278C8—22no—
1279C8—22no—
1280C8—22no—
1281C8—22no—
1282C8—22no—
1283C22—24no—
1284C22—24no—
1285C22—22no—
1286C22—22no—
1287C22—22no—
1288C22—22no—
1289C22—22no—
1290C22—42no—
1291C22—42no—
1292C22—44no—
1293C22—42no—
1294C22—82no—
1295C22—81no—
1296C22—81no—
1297C22—82no—
1298C22—82no—
1299C22—82no—
1300C22—82no—
1301C22—81no—
1302C22—81no—
1303C22—81no—
1304C22—81no—
1305C22—81no—
1306C22—81no—
1307C22—168no—
1308C22#315614yes—
1309C22C22×#12711yescharacteristic
1310C22C2×#54611yescharacteristic
1311C22#350011yescharacteristic
1312C22C2×#57812yes—
1313C22#358512yes—
1314C4—24no—
1315C4—22no—
1316C4—22no—
1317C4—22no—
1318C4—22no—
1319C4—42no—
1320C4—42no—
1321C4—42no—
1322C4—42no—
1323C4—81no—
1324C4—81no—
1325C4—81no—
1326C4—81no—
1327C4—81no—
1328C4—81no—
1329C4—81no—
1330C4—81no—
1331C4—81no—
1332C4—81no—
1333C4—81no—
1334C4—81no—
1335C4D4×#4111yescharacteristic
1336C4D4×#4111yescharacteristic
1337C4#349611yescharacteristic
1338C4#349611yescharacteristic
1339C2—24no—
1340C2—42no—
1341C2—82no—
1342C2—161no—
1343C2—161no—
1344C2#3626011yescharacteristic
1345C2C2×#315611yescharacteristic
1346C2#6065011yescharacteristic
1347C2#6119412yes—
1348C2#6260412yes—
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#3297C2
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×#3314C2semidirect
3. C2×#3299C2semidirect
5. #37862C2semidirect
6. #37676C2semidirect
7. #33229C2semidirect
8. #33184C2semidirect
9. #33182C2semidirect
10. #28523C2semidirect
11. #28453C2semidirect
12. #28427C2semidirect
13. #28426C2semidirect
14. #28414C2semidirect
15. #28411C2semidirect
16. #28359C2semidirect
17. #28358C2semidirect
18. #28350C2semidirect
19. #28348C2semidirect
20. #28346C2semidirect
21. #28342C2semidirect
22. #28333C2semidirect
23. #28331C2semidirect
24. #27921C2semidirect
25. #27910C2semidirect
26. #25737C2semidirect
27. #25724C2semidirect
28. #21696C2semidirect
29. #21205C2semidirect
30. C2×#1959C2semidirect
31. #20493C2semidirect
42. C2×#497C22semidirect
45. C2×#491C22semidirect
48. C2×#487C22semidirect
53. C2×#484C22semidirect
54. C2×#485C22semidirect
57. C2×#479C22semidirect
58. C2×#477C22semidirect
62. C2×#468C22semidirect
65. C2×#467C22semidirect
70. C2×#462C22semidirect
72. C2×#461C22semidirect
76. C2×#451C22semidirect
78. C2×#448C22semidirect
82. C2×#440C22semidirect
83. C2×C4×Q16C22semidirect
88. C2×#419C22semidirect
92. C22×#103C22semidirect
95. C2×#405C22semidirect
103. #2660C22semidirect
106. #2620C22semidirect
107. #2565C22semidirect
110. #2542C22semidirect
113. #2501C22semidirect
114. #2499C22semidirect
124. #2326C22semidirect
125. #2317C22semidirect
128. #2097C22semidirect
129. #2097C22semidirect
130. #2095C22semidirect
131. #2095C22semidirect
132. #2095C22semidirect
133. #2095C22semidirect
134. #2095C22semidirect
135. #2095C22semidirect
140. #2016C22semidirect
141. #2016C22semidirect
146. #2013C22semidirect
147. #2013C22semidirect
154. #1973C22semidirect
155. #1973C22semidirect
156. #1973C22semidirect
157. #1973C22semidirect
158. #1971C22semidirect
159. #1971C22semidirect
162. #1969C22semidirect
163. #1969C22semidirect
164. #1960C22semidirect
165. #1960C22semidirect
166. #1960C22semidirect
177. #1959C22semidirect
182. #1956C22semidirect
183. #1956C22semidirect
184. #1956C22semidirect
185. #1956C22semidirect
186. #1847C22semidirect
187. #1845C22semidirect
188. #1845C22semidirect
189. #1771C22semidirect
190. #1770C22semidirect
191. #1768C22semidirect
192. #1753C22semidirect
194. #1752C22semidirect
196. #1750C22semidirect
198. #1726C22semidirect

Maximal subgroups

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

subgroupindex
C2×#33202
C2×#33142
C2×#32992
C2×#32972
#378622
#376762
#332292
#331842
#331822
#285232
#284532
#284272
#284262
#284142
#284112
#283592
#283582
#283502
#283482
#283462
#283422
#283332
#283312
#279212
#279102
#257372
#257242
#216962
#212052
C2×#19592
#204932