Finite Group Databasebeta

← #6606846

Subgroups — #6606846

Order 512.

2315 conjugacy classes of subgroups.

The subgroup lattice has 1328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3312C211yesmaximal, characteristic, complemented
2C2×#3314C211yesmaximal, characteristic
3C2×#3299C211yesmaximal, characteristic, complemented
4C2×#3296C211yesmaximal, characteristic
5#37865C211yesmaximal, characteristic, complemented
6#37676C211yesmaximal, characteristic
7#33229C211yesmaximal, characteristic, complemented
8#33188C211yesmaximal, characteristic, complemented
9#33172C211yesmaximal, characteristic, complemented
10#28523C211yesmaximal, characteristic, complemented
11#28456C211yesmaximal, characteristic, complemented
12#28427C211yesmaximal, characteristic, complemented
13#28424C211yesmaximal, characteristic, complemented
14#28407C211yesmaximal, characteristic, complemented
15#28403C211yesmaximal, characteristic, complemented
16#28359C211yesmaximal, characteristic, complemented
17#28356C211yesmaximal, characteristic, complemented
18#28345C211yesmaximal, characteristic, complemented
19#28342C211yesmaximal, characteristic, complemented
20#28338C211yesmaximal, characteristic, complemented
21#28335C211yesmaximal, characteristic, complemented
22#28333C211yesmaximal, characteristic, complemented
23#28330C211yesmaximal, characteristic, complemented
24#27921C211yesmaximal, characteristic, complemented
25#27919C211yesmaximal, characteristic, complemented
26#25735C211yesmaximal, characteristic, complemented
27#25730C211yesmaximal, characteristic, complemented
28#21703C211yesmaximal, characteristic, complemented
29#21205C211yesmaximal, characteristic, complemented
30C2×#1958C211yesmaximal, characteristic, complemented
31#20484C211yesmaximal, characteristic, complemented
32C2×#554C2211yescharacteristic
33C2×#552C2211yescharacteristic
34C2×D4×Q8C2211yescharacteristic
35C2×#546C2211yescharacteristic
36C2×#536C2211yescharacteristic
37C22×#124C2211yescharacteristic
38#3314—28no—
39#3312—28no—
40#3299—28no—
41#3296—28no—
42C2×#497C2211yescharacteristic
43C2×#497C2211yescharacteristic
44C2×#494C2211yescharacteristic, complemented
45C2×#491C2211yescharacteristic, complemented
46C2×#489C2211yescharacteristic
47C2×#488C2211yescharacteristic
48C2×#487C2211yescharacteristic, complemented
49C2×#484C2211yescharacteristic
50C2×#484C2211yescharacteristic
51C2×#484C2211yescharacteristic, complemented
52C2×#485C2211yescharacteristic, complemented
53C2×#482C2211yescharacteristic
54C2×#483C2211yescharacteristic
55C2×#483C2211yescharacteristic
56C2×#480C2211yescharacteristic
57C2×#479C2211yescharacteristic, complemented
58C2×#477C2211yescharacteristic, complemented
59C2×#478C2211yescharacteristic
60C2×#474C2211yescharacteristic
61C2×#470C2211yescharacteristic, complemented
62C2×#468C2211yescharacteristic
63C2×#467C2211yescharacteristic
64C2×#467C2211yescharacteristic
65C2×#467C2211yescharacteristic
66C2×#467C2211yescharacteristic
67C2×#467C2211yescharacteristic, complemented
68C2×#465C2211yescharacteristic
69C2×#464C2211yescharacteristic
70C2×#464C2211yescharacteristic
71C2×#462C2211yescharacteristic, complemented
72C2×#462C2211yescharacteristic, complemented
73C2×#452C2211yescharacteristic
74C2×#452C2211yescharacteristic
75C2×#451C2211yescharacteristic
76C2×#451C2211yescharacteristic
77C2×#451C2211yescharacteristic, complemented
78C2×#451C2211yescharacteristic, complemented
79C2×#450C2211yescharacteristic
80C2×#450C2211yescharacteristic
81C2×#441C2211yescharacteristic, complemented
82C2×#440C2211yescharacteristic
83C2×C4×Q16C2211yescharacteristic, complemented
84C2×C4×SD16C2211yescharacteristic
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×C4×C8C2211yescharacteristic
97#2857C2211yescharacteristic
98#2857C2211yescharacteristic
99#2719—22no—
100#2698—22no—
101#2674—22no—
102#2672—22no—
103#2660C2211yescharacteristic, complemented
104#2658C2211yescharacteristic
105#2621C2211yescharacteristic, complemented
106#2620C2211yescharacteristic
107#2568C2211yescharacteristic, complemented
108#2565C2211yescharacteristic, complemented
109#2547C2211yescharacteristic
110#2545C2211yescharacteristic
111#2503C2211yescharacteristic
112#2503C2211yescharacteristic, complemented
113#2502C2211yescharacteristic
114#2499C2211yescharacteristic, complemented
115#2438—22no—
116#2437—22no—
117#2436C2211yescharacteristic
118#2435C2211yescharacteristic
119#2434C2211yescharacteristic
120#2432C2211yescharacteristic
121#2419—22no—
122#2418—22no—
123#2327C2211yescharacteristic, complemented
124#2326C2211yescharacteristic
125#2317C2211yescharacteristic, complemented
126#2290C2211yescharacteristic
127C2×#382C2211yescharacteristic
128#2097C2211yescharacteristic, complemented
129#2097C2211yescharacteristic, complemented
130#2097C2211yescharacteristic, complemented
131#2097C2211yescharacteristic, complemented
132#2097C2211yescharacteristic, complemented
133#2097C2211yescharacteristic, complemented
134#2095C2211yescharacteristic, complemented
135#2095C2211yescharacteristic, complemented
136#2093C2211yescharacteristic
137#2093C2211yescharacteristic
138#2092C2211yescharacteristic
139#2092C2211yescharacteristic
140#2016C2211yescharacteristic, complemented
141#2016C2211yescharacteristic, complemented
142#2016C2211yescharacteristic, complemented
143#2016C2211yescharacteristic, complemented
144#2015C2211yescharacteristic
145#2015C2211yescharacteristic
146#2015C2211yescharacteristic
147#2015C2211yescharacteristic
148#2015C2211yescharacteristic
149#2015C2211yescharacteristic
150#2015C2211yescharacteristic
151#2015C2211yescharacteristic
152#1973C2211yescharacteristic
153#1973C2211yescharacteristic
154#1971C2211yescharacteristic, complemented
155#1971C2211yescharacteristic, complemented
156#1969C2211yescharacteristic, complemented
157#1969C2211yescharacteristic, complemented
158#1969C2211yescharacteristic, complemented
159#1969C2211yescharacteristic, complemented
160#1969C2211yescharacteristic, complemented
161#1969C2211yescharacteristic, complemented
162#1968C2211yescharacteristic
163#1968C2211yescharacteristic
164#1960C2211yescharacteristic, complemented
165#1960C2211yescharacteristic, complemented
166#1960C2211yescharacteristic, complemented
167#1960C2211yescharacteristic, complemented
168#1959C2211yescharacteristic
169#1959C2211yescharacteristic
170#1959C2211yescharacteristic
171#1959C2211yescharacteristic
172#1958C2211yescharacteristic
173#1958C2211yescharacteristic
174#1958C2211yescharacteristic
175#1958C2211yescharacteristic
176#1958C2211yescharacteristic
177#1958C2211yescharacteristic
178#1958C2211yescharacteristic
179#1958C2211yescharacteristic
180#1958C2211yescharacteristic
181#1958C2211yescharacteristic
182#1956C2211yescharacteristic, complemented
183#1956C2211yescharacteristic, complemented
184#1956C2211yescharacteristic, complemented
185#1956C2211yescharacteristic, complemented
186#1847C2211yescharacteristic, complemented
187#1847C2211yescharacteristic, complemented
188#1845C2211yescharacteristic, complemented
189#1771C2211yescharacteristic, complemented
190C8×C4⋊C4C2211yescharacteristic, complemented
191#1768C2211yescharacteristic, complemented
192#1753C2211yescharacteristic, complemented
193#1752C2211yescharacteristic
194C8×C22⋊C4C2211yescharacteristic
195C8×C22⋊C4C2211yescharacteristic, complemented
196#1750C2211yescharacteristic, complemented
197#1749C2211yescharacteristic
198#1726C2211yescharacteristic, complemented
199C22×#41C2311yescharacteristic
200C23×Q8C2311yescharacteristic
201C23×Q8C2311yescharacteristic
202C23×D4C2311yescharacteristic
203C22×Q16C2311yescharacteristic
204C22×Q16C2311yescharacteristic
205C22×Q16C2311yescharacteristic
206C22×Q16C2311yescharacteristic
207C22×Q16C2311yescharacteristic
208C22×Q16C2311yescharacteristic
209C22×Q16C2311yescharacteristic
210C22×Q16C2311yescharacteristic
211C22×SD16C2311yescharacteristic
212C22×SD16C2311yescharacteristic
213C22×SD16C2311yescharacteristic
214C22×SD16C2311yescharacteristic
215C22×M16C2311yescharacteristic
216C23×C8C2311yescharacteristic
217C23×C8C2311yescharacteristic
218C23×C8C2311yescharacteristic
219#554—24no—
220#554—24no—
221#552—24no—
222#552—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×C4⋊Q8C2311yescharacteristic
236C2×#126—21no—
237C2×#125—21no—
238C2×#125—21no—
239C2×#125C2311yescharacteristic
240C2×#124—24no—
241C2×#124—22no—
242C2×#124—42no—
243C2×#124C2311yescharacteristic
244C2×#124C2311yescharacteristic
245C2×#124C2311yescharacteristic
246C2×#124C2311yescharacteristic
247C2×#124C2311yescharacteristic
248C2×#124C2311yescharacteristic
249C2×#124C2311yescharacteristic
250C2×#123—21no—
251C2×#123—21no—
252C2×#123—22no—
253C2×C22⋊Q8—22no—
254C2×C22⋊Q8—21no—
255C2×C22⋊Q8—21no—
256C2×C22⋊Q8—21no—
257C2×C22⋊Q8—21no—
258C2×C22⋊Q8C2311yescharacteristic
259C2×C22⋊Q8C2311yescharacteristic
260C2×C22⋊Q8C2311yescharacteristic
261C2×C22⋊Q8C2311yescharacteristic
262C2×C22⋊Q8C2311yescharacteristic
263C2×C22⋊Q8C2311yescharacteristic
264C2×C22⋊Q8C2311yescharacteristic
265C2×#121—21no—
266C2×#121C2311yescharacteristic
267C2×#120—21no—
268C2×C4×Q8C2311yescharacteristic
269C2×C4×Q8C2311yescharacteristic
270C2×C4×Q8C2311yescharacteristic
271C2×C4×D4—21no—
272C2×C4×D4—21no—
273C2×C4×D4C2311yescharacteristic
274C2×C4×D4C2311yescharacteristic
275C2×#117—21no—
276C2×#117C2311yescharacteristic
277C2×#117C2311yescharacteristic
278C22×C4⋊C4C2311yescharacteristic
279C22×C4⋊C4C2311yescharacteristic
280C22×C4⋊C4C2311yescharacteristic
281C22×C22⋊C4—22no—
282C22×C22⋊C4—21no—
283C22×C42C2311yescharacteristic
284#497—24no—
285#497—42no—
286#494—42no—
287#491—24no—
288#489—24no—
289#488—24no—
290#487—24no—
291#485—24no—
292#484—24no—
293#484—24no—
294#484—24no—
295#483—24no—
296#483—24no—
297#482—24no—
298#480—24no—
299#479—24no—
300#478—24no—
301#477—24no—
302#474—24no—
303#470—24no—
304#468—24no—
305#467—24no—
306#467—24no—
307#467—24no—
308#467—24no—
309#467—24no—
310#465—24no—
311#464—24no—
312#464—24no—
313#462—24no—
314#462—24no—
315#452—24no—
316#452—24no—
317#451—24no—
318#451—24no—
319#451—24no—
320#451—24no—
321#450—24no—
322#450—24no—
323#441—24no—
324#440—24no—
325C4×Q16—24no—
326C4×SD16—24no—
327#435D418yes—
328C8×D4D418yes—
329C2×#107C2311yescharacteristic
330C2×#107C2311yescharacteristic
331C2×#107C2311yescharacteristic
332C2×#107C2311yescharacteristic
333C2×#107C2311yescharacteristic
334C2×#107C2311yescharacteristic
335C2×#107C2311yescharacteristic
336C2×#107C2311yescharacteristic
337C2×#106C2311yescharacteristic
338C2×#106C2311yescharacteristic
339C2×#106C2311yescharacteristic
340C2×#106C2311yescharacteristic
341C2×C4⋊C8C2311yescharacteristic
342C2×C4⋊C8C2311yescharacteristic
343#419—24no—
344#417—24no—
345#416—24no—
346C2×#103—24no—
347C2×#103—24no—
348C2×#103—24no—
349C2×#103C2311yescharacteristic
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×#103C2311yescharacteristic
373C2×#103C2311yescharacteristic
374C2×#103C2311yescharacteristic
375C2×#103C2311yescharacteristic
376C2×#103C2311yescharacteristic
377C2×#102—24no—
378C2×#102—24no—
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—
396C2×#97C2311yescharacteristic
397C2×#97C2311yescharacteristic
398C2×#97C2311yescharacteristic
399C2×#97C2311yescharacteristic
400C2×#97C2311yescharacteristic
401C2×C4×C8—42no—
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#397—22no—
419#397—22no—
420#397—22no—
421#396—22no—
422#396—22no—
423#395—22no—
424#395—22no—
425#394—22no—
426#394—22no—
427#394—22no—
428#393—22no—
429#391—22no—
430#391C2311yescharacteristic
431#391C2311yescharacteristic
432#391C2311yescharacteristic
433#391C2311yescharacteristic
434#391C2311yescharacteristic
435#391C2311yescharacteristic
436#391C2311yescharacteristic
437#391C2311yescharacteristic
438#391C2311yescharacteristic
439#391C2311yescharacteristic
440#390C2311yescharacteristic
441#390C2311yescharacteristic
442#389—22no—
443#389—22no—
444#389—22no—
445#388—22no—
446#388—22no—
447#388D412yes—
448#387—22no—
449#387—22no—
450#387—22no—
451#387—22no—
452#387D412yes—
453#386—22no—
454#386D412yes—
455#385—22no—
456#385—22no—
457#385—22no—
458#385—22no—
459#385—22no—
460#385D412yes—
461#384C2311yescharacteristic
462#384C2311yescharacteristic
463#384C2311yescharacteristic
464#384C2311yescharacteristic
465#382—22no—
466#382C2311yescharacteristic
467#382C2311yescharacteristic
468#382C2311yescharacteristic
469#382C2311yescharacteristic
470#382C2311yescharacteristic
471#382C2311yescharacteristic
472#381—22no—
473#381—22no—
474#380—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—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×Q8C2411yescharacteristic
517C22×D4—22no—
518C22×D4—21no—
519C22×D4—21no—
520C22×D4—22no—
521C22×D4—22no—
522C22×D4—21no—
523C22×D4—41no—
524C22×D4—41no—
525C22×D4—41no—
526C22×D4C2×D411yescharacteristic
527C22×D4C2411yescharacteristic
528C22×D4C2411yescharacteristic
529C23×C4—21no—
530C23×C4—21no—
531C23×C4—21no—
532C23×C4—21no—
533C23×C4—21no—
534C23×C4—21no—
535C23×C4—21no—
536C23×C4C2×D412yes—
537C23×C4C2411yescharacteristic
538C23×C4C2411yescharacteristic
539C2×Q16—22no—
540C2×Q16—22no—
541C2×Q16—22no—
542C2×Q16—22no—
543C2×Q16—22no—
544C2×Q16—22no—
545C2×Q16—22no—
546C2×Q16—22no—
547C2×Q16—22no—
548C2×Q16—22no—
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×Q16—41no—
561C2×Q16—41no—
562C2×Q16—41no—
563C2×SD16—22no—
564C2×SD16—22no—
565C2×SD16—22no—
566C2×SD16—22no—
567C2×SD16—22no—
568C2×SD16—22no—
569C2×SD16—41no—
570C2×SD16—41no—
571C2×SD16—41no—
572C2×SD16—41no—
573C2×SD16—41no—
574C2×SD16—41no—
575C2×M16—41no—
576C2×M16—41no—
577C2×M16C2×D414yes—
578C22×C8—41no—
579C22×C8—41no—
580C22×C8—41no—
581C22×C8—41no—
582C22×C8—41no—
583C22×C8—41no—
584C22×C8C2×D414yes—
585C22×C8C2×D414yes—
586C22×C8C2×D414yes—
587C22×C8C2411yescharacteristic
588C22×C8C2411yescharacteristic
589C22×C8C2411yescharacteristic
590C22×C8C2411yescharacteristic
591C22×C8C2411yescharacteristic
592C22×C8C2411yescharacteristic
593C22×C8C2411yescharacteristic
594C22×C8C2411yescharacteristic
595C4⋊Q8—22no—
596C4⋊Q8—22no—
597C4⋊Q8—22no—
598C4⋊Q8—22no—
599C4⋊Q8—22no—
600C4⋊Q8—22no—
601C4⋊Q8—22no—
602C4⋊Q8—22no—
603C4⋊Q8—22no—
604C4⋊Q8—41no—
605C4⋊Q8—41no—
606C4⋊Q8—41no—
607C4⋊Q8—44no—
608#126—44no—
609#125—22no—
610#125—22no—
611#125—44no—
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—48no—
622#124—41no—
623#124—41no—
624#124—41no—
625#124—41no—
626#124—41no—
627#124#4114yes—
628#123—48no—
629#123—44no—
630#123—44no—
631C22⋊Q8—22no—
632C22⋊Q8—22no—
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—48no—
646C22⋊Q8—44no—
647C22⋊Q8—44no—
648C22⋊Q8—44no—
649C22⋊Q8—44no—
650#121—22no—
651#121—22no—
652#121—44no—
653#120—44no—
654C4×Q8—22no—
655C4×Q8—22no—
656C4×Q8—22no—
657C4×Q8—22no—
658C4×Q8—22no—
659C4×Q8—22no—
660C4×D4—22no—
661C4×D4—22no—
662C4×D4—44no—
663C4×D4—44no—
664C4×D4C2×D414yes—
665C4×D4C2×D414yes—
666#117—22no—
667#117—22no—
668#117—22no—
669#117—22no—
670#117—44no—
671C2×C4⋊C4—22no—
672C2×C4⋊C4—22no—
673C2×C4⋊C4—22no—
674C2×C4⋊C4—22no—
675C2×C4⋊C4—22no—
676C2×C4⋊C4—22no—
677C2×C4⋊C4—21no—
678C2×C4⋊C4—21no—
679C2×C4⋊C4—21no—
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—21no—
689C2×C4⋊C4—21no—
690C2×C4⋊C4—21no—
691C2×C4⋊C4—21no—
692C2×C4⋊C4—21no—
693C2×C4⋊C4—22no—
694C2×C4⋊C4—22no—
695C2×C4⋊C4—21no—
696C2×C4⋊C4—21no—
697C2×C4⋊C4—22no—
698C2×C4⋊C4—22no—
699C2×C4⋊C4—22no—
700C2×C4⋊C4—22no—
701C2×C4⋊C4—22no—
702C2×C4⋊C4—22no—
703C2×C4⋊C4C2×D412yes—
704C2×C4⋊C4C2×D412yes—
705C2×C4⋊C4C2×D411yescharacteristic
706C2×C4⋊C4C2411yescharacteristic
707C2×C4⋊C4C2411yescharacteristic
708C2×C4⋊C4C2411yescharacteristic
709C2×C4⋊C4C2411yescharacteristic
710C2×C4⋊C4C2411yescharacteristic
711C2×C4⋊C4C2411yescharacteristic
712C2×C4⋊C4C2411yescharacteristic
713C2×C4⋊C4C2411yescharacteristic
714C2×C22⋊C4—22no—
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—22no—
728C2×C22⋊C4—21no—
729C2×C22⋊C4—21no—
730C2×C22⋊C4—22no—
731C2×C22⋊C4—22no—
732C2×C22⋊C4—22no—
733C2×C22⋊C4—22no—
734C2×C22⋊C4—48no—
735C2×C22⋊C4—44no—
736C2×C22⋊C4C2×D412yes—
737C2×C22⋊C4C2×D412yes—
738C2×C22⋊C4C2×D412yes—
739C2×C22⋊C4C2×D411yescharacteristic
740C2×C22⋊C4C2×D411yescharacteristic
741C2×C42—22no—
742C2×C42—22no—
743C2×C42—21no—
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#107—22no—
760#107—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#103—22no—
790#103—22no—
791#103—22no—
792#103—22no—
793#103—22no—
794#103—22no—
795#102—22no—
796#102—22no—
797#102—22no—
798#102—22no—
799#102—22no—
800#102—22no—
801#102—22no—
802#102—22no—
803#102—22no—
804#102—22no—
805#102—22no—
806#102—22no—
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—42no—
847C24—42no—
848C24—44no—
849C24—81no—
850C24—82no—
851C24C22×D411yescharacteristic
852C24C22×D411yescharacteristic
853#41—44no—
854#41—44no—
855#41—82no—
856#41—82no—
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—21no—
890C2×Q8—21no—
891C2×Q8—21no—
892C2×Q8—42no—
893C2×Q8—42no—
894C2×Q8—44no—
895C2×Q8—44no—
896C2×Q8—44no—
897C2×Q8—44no—
898C2×Q8—42no—
899C2×Q8—42no—
900C2×Q8—42no—
901C2×Q8—81no—
902C2×Q8—81no—
903C2×Q8—82no—
904C2×Q8—82no—
905C2×Q8—82no—
906C2×Q8—82no—
907C2×Q8—82no—
908C2×Q8C2×#4112yes—
909C2×D4—24no—
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—44no—
922C2×D4—44no—
923C2×D4—42no—
924C2×D4—42no—
925C2×D4—42no—
926C2×D4—42no—
927C2×D4—42no—
928C2×D4—82no—
929C2×D4—82no—
930C2×D4—81no—
931C2×D4—81no—
932C2×D4—82no—
933C2×D4#12714yes—
934C2×D4C2×#4112yes—
935C22×C4—21no—
936C22×C4—21no—
937C22×C4—21no—
938C22×C4—21no—
939C22×C4—21no—
940C22×C4—21no—
941C22×C4—21no—
942C22×C4—21no—
943C22×C4—24no—
944C22×C4—21no—
945C22×C4—24no—
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—42no—
960C22×C4—42no—
961C22×C4—42no—
962C22×C4—42no—
963C22×C4—42no—
964C22×C4—42no—
965C22×C4—42no—
966C22×C4—44no—
967C22×C4—42no—
968C22×C4—42no—
969C22×C4—42no—
970C22×C4—42no—
971C22×C4—81no—
972C22×C4—82no—
973C22×C4—81no—
974C22×C4—81no—
975C22×C4—82no—
976C22×C4—82no—
977C22×C4C22×D412yes—
978C22×C4C22×D412yes—
979C22×C4C22×D412yes—
980C22×C4C22×D411yescharacteristic
981C22×C4C22×D411yescharacteristic
982C22×C4C22×D411yescharacteristic
983C22×C4C22×D411yescharacteristic
984C22×C4C22×D412yes—
985C22×C4C22×D412yes—
986C22×C4C22×D412yes—
987C22×C4C22×D412yes—
988C22×C4C22×D412yes—
989C22×C4C2511yescharacteristic
990Q16—44no—
991Q16—44no—
992Q16—82no—
993Q16—82no—
994Q16—82no—
995Q16—82no—
996Q16—82no—
997Q16—82no—
998SD16—44no—
999SD16—44no—
1000SD16—82no—
1001SD16—82no—
1002M16—44no—
1003C2×C8—21no—
1004C2×C8—21no—
1005C2×C8—21no—
1006C2×C8—21no—
1007C2×C8—21no—
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—44no—
1020C2×C8—44no—
1021C2×C8—44no—
1022C2×C8C22×D412yes—
1023C2×C8C22×D412yes—
1024C2×C8C22×D412yes—
1025C2×C8C22×D412yes—
1026C2×C8C22×D412yes—
1027C2×C8C22×D412yes—
1028C2×C8C22×D412yes—
1029C2×C8C22×D412yes—
1030C4⋊C4—24no—
1031C4⋊C4—21no—
1032C4⋊C4—21no—
1033C4⋊C4—21no—
1034C4⋊C4—21no—
1035C4⋊C4—21no—
1036C4⋊C4—21no—
1037C4⋊C4—21no—
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—42no—
1048C4⋊C4—44no—
1049C4⋊C4—42no—
1050C4⋊C4—42no—
1051C4⋊C4—42no—
1052C4⋊C4—42no—
1053C4⋊C4—42no—
1054C4⋊C4—42no—
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—44no—
1068C4⋊C4—44no—
1069C4⋊C4—82no—
1070C4⋊C4—82no—
1071C4⋊C4—82no—
1072C4⋊C4—82no—
1073C4⋊C4—82no—
1074C4⋊C4#12714yes—
1075C22⋊C4—24no—
1076C22⋊C4—28no—
1077C22⋊C4—24no—
1078C22⋊C4—42no—
1079C22⋊C4—44no—
1080C22⋊C4—44no—
1081C22⋊C4—44no—
1082C22⋊C4—42no—
1083C22⋊C4—42no—
1084C22⋊C4—42no—
1085C22⋊C4—42no—
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—44no—
1095C22⋊C4—82no—
1096C22⋊C4—82no—
1097C22⋊C4—82no—
1098C22⋊C4#12714yes—
1099C22⋊C4#12714yes—
1100C42—24no—
1101C42—21no—
1102C42—21no—
1103C42—21no—
1104C42—21no—
1105C42—21no—
1106C42—21no—
1107C42—42no—
1108C42—42no—
1109C42—42no—
1110C42—42no—
1111C42C22×D412yes—
1112C42C22×D412yes—
1113C42C2×#4112yes—
1114C42H(5,𝔽2)12yes—
1115C23—22no—
1116C23—21no—
1117C23—21no—
1118C23—22no—
1119C23—21no—
1120C23—21no—
1121C23—22no—
1122C23—22no—
1123C23—42no—
1124C23—41no—
1125C23—41no—
1126C23—42no—
1127C23—42no—
1128C23—41no—
1129C23—41no—
1130C23—41no—
1131C23—42no—
1132C23—84no—
1133C23—88no—
1134C23—84no—
1135C23—164no—
1136C23—162no—
1137C23C2×#12712yes—
1138C23C2×#12712yes—
1139C23#57814yes—
1140C23C23×D411yescharacteristic
1141Q8—22no—
1142Q8—22no—
1143Q8—41no—
1144Q8—41no—
1145Q8—41no—
1146Q8—41no—
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—84no—
1166Q8—84no—
1167Q8—162no—
1168D4—28no—
1169D4—22no—
1170D4—22no—
1171D4—41no—
1172D4—41no—
1173D4—41no—
1174D4—41no—
1175D4—41no—
1176D4—41no—
1177D4—84no—
1178D4—84no—
1179D4—162no—
1180C2×C4—22no—
1181C2×C4—22no—
1182C2×C4—21no—
1183C2×C4—21no—
1184C2×C4—21no—
1185C2×C4—21no—
1186C2×C4—22no—
1187C2×C4—22no—
1188C2×C4—22no—
1189C2×C4—22no—
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—48no—
1207C2×C4—41no—
1208C2×C4—41no—
1209C2×C4—42no—
1210C2×C4—42no—
1211C2×C4—42no—
1212C2×C4—42no—
1213C2×C4—42no—
1214C2×C4—42no—
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—41no—
1236C2×C4—41no—
1237C2×C4—41no—
1238C2×C4—42no—
1239C2×C4—42no—
1240C2×C4—84no—
1241C2×C4—84no—
1242C2×C4—84no—
1243C2×C4—84no—
1244C2×C4—162no—
1245C2×C4—162no—
1246C2×C4—162no—
1247C2×C4C2×#12712yes—
1248C2×C4C2×#12712yes—
1249C2×C4C2×#12712yes—
1250C2×C4C2×#12712yes—
1251C2×C4#54614yes—
1252C2×C4C23×D411yescharacteristic
1253C2×C4C23×D411yescharacteristic
1254C2×C4C22×#4111yescharacteristic
1255C2×C4C2×H(5,𝔽2)11yescharacteristic
1256C2×C4#58511yescharacteristic
1257C2×C4#58511yescharacteristic
1258C8—22no—
1259C8—22no—
1260C8—22no—
1261C8—22no—
1262C8—22no—
1263C8—22no—
1264C8—22no—
1265C8—22no—
1266C22—24no—
1267C22—22no—
1268C22—22no—
1269C22—24no—
1270C22—22no—
1271C22—22no—
1272C22—22no—
1273C22—42no—
1274C22—42no—
1275C22—42no—
1276C22—44no—
1277C22—82no—
1278C22—81no—
1279C22—81no—
1280C22—82no—
1281C22—81no—
1282C22—81no—
1283C22—81no—
1284C22—82no—
1285C22—168no—
1286C22#315614yes—
1287C22C22×#12711yescharacteristic
1288C22C2×#54611yescharacteristic
1289C22#350011yescharacteristic
1290C22C2×#57812yes—
1291C22#358412yes—
1292C4—22no—
1293C4—22no—
1294C4—22no—
1295C4—22no—
1296C4—24no—
1297C4—42no—
1298C4—42no—
1299C4—42no—
1300C4—42no—
1301C4—81no—
1302C4—81no—
1303C4—81no—
1304C4—81no—
1305C4—81no—
1306C4—81no—
1307C4—81no—
1308C4—81no—
1309C4—81no—
1310C4—81no—
1311C4—81no—
1312C4—81no—
1313C4—81no—
1314C4D4×#4111yescharacteristic
1315C4D4×#4111yescharacteristic
1316C4#349611yescharacteristic
1317C4#349611yescharacteristic
1318C2—24no—
1319C2—42no—
1320C2—82no—
1321C2—161no—
1322C2#3626011yescharacteristic
1323C2C2×#315611yescharacteristic
1324C2#6064911yescharacteristic
1325C2#6117312yes—
1326C2#6255912yes—
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#546C22
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×#3312C2semidirect
3. C2×#3299C2semidirect
5. #37865C2semidirect
7. #33229C2semidirect
8. #33188C2semidirect
9. #33172C2semidirect
10. #28523C2semidirect
11. #28456C2semidirect
12. #28427C2semidirect
13. #28424C2semidirect
14. #28407C2semidirect
15. #28403C2semidirect
16. #28359C2semidirect
17. #28356C2semidirect
18. #28345C2semidirect
19. #28342C2semidirect
20. #28338C2semidirect
21. #28335C2semidirect
22. #28333C2semidirect
23. #28330C2semidirect
24. #27921C2semidirect
25. #27919C2semidirect
26. #25735C2semidirect
27. #25730C2semidirect
28. #21703C2semidirect
29. #21205C2semidirect
30. C2×#1958C2semidirect
31. #20484C2semidirect
44. C2×#494C22semidirect
45. C2×#491C22semidirect
48. C2×#487C22semidirect
51. C2×#484C22semidirect
52. C2×#485C22semidirect
57. C2×#479C22semidirect
58. C2×#477C22semidirect
61. C2×#470C22semidirect
67. C2×#467C22semidirect
71. C2×#462C22semidirect
72. C2×#462C22semidirect
77. C2×#451C22semidirect
78. C2×#451C22semidirect
81. C2×#441C22semidirect
83. C2×C4×Q16C22semidirect
88. C2×#419C22semidirect
92. C22×#103C22semidirect
95. C2×#405C22semidirect
103. #2660C22semidirect
105. #2621C22semidirect
107. #2568C22semidirect
108. #2565C22semidirect
112. #2503C22semidirect
114. #2499C22semidirect
123. #2327C22semidirect
125. #2317C22semidirect
128. #2097C22semidirect
129. #2097C22semidirect
130. #2097C22semidirect
131. #2097C22semidirect
132. #2097C22semidirect
133. #2097C22semidirect
134. #2095C22semidirect
135. #2095C22semidirect
140. #2016C22semidirect
141. #2016C22semidirect
142. #2016C22semidirect
143. #2016C22semidirect
154. #1971C22semidirect
155. #1971C22semidirect
156. #1969C22semidirect
157. #1969C22semidirect
158. #1969C22semidirect
159. #1969C22semidirect
160. #1969C22semidirect
161. #1969C22semidirect
164. #1960C22semidirect
165. #1960C22semidirect
166. #1960C22semidirect
167. #1960C22semidirect
182. #1956C22semidirect
183. #1956C22semidirect
184. #1956C22semidirect
185. #1956C22semidirect
186. #1847C22semidirect
187. #1847C22semidirect
188. #1845C22semidirect
189. #1771C22semidirect
190. C8×C4⋊C4C22semidirect
191. #1768C22semidirect
192. #1753C22semidirect
195. C8×C22⋊C4C22semidirect
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×#33122
C2×#33142
C2×#32992
C2×#32962
#378652
#376762
#332292
#331882
#331722
#285232
#284562
#284272
#284242
#284072
#284032
#283592
#283562
#283452
#283422
#283382
#283352
#283332
#283302
#279212
#279192
#257352
#257302
#217032
#212052
C2×#19582
#204842