Finite Group Databasebeta

← #62311

Subgroups — #62311

Order 256.

950 conjugacy classes of subgroups.

The subgroup lattice has 912 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3542C211yesmaximal, characteristic, complemented
2#3536C211yesmaximal, characteristic, complemented
3#3357C211yesmaximal, characteristic, complemented
4#3346C211yesmaximal, characteristic, complemented
5#3343C211yesmaximal, characteristic, complemented
6#3334C211yesmaximal, characteristic, complemented
7#3333C211yesmaximal, characteristic, complemented
8#3322C211yesmaximal, characteristic, complemented
9#3319C211yesmaximal, characteristic, complemented
10#3314C211yesmaximal, characteristic, complemented
11#3308C211yesmaximal, characteristic, complemented
12#3306C211yesmaximal, characteristic, complemented
13#3300C211yesmaximal, characteristic, complemented
14#3294C211yesmaximal, characteristic, complemented
15#3282C211yesmaximal, characteristic, complemented
16#3273C211yesmaximal, characteristic, complemented
17#3268C211yesmaximal, characteristic, complemented
18#3265C211yesmaximal, characteristic, complemented
19#3262C211yesmaximal, characteristic, complemented
20#3257C211yesmaximal, characteristic, complemented
21#3203C211yesmaximal, characteristic, complemented
22#3198C211yesmaximal, characteristic, complemented
23#3190C211yesmaximal, characteristic, complemented
24#3186C211yesmaximal, characteristic, complemented
25#3179C211yesmaximal, characteristic, complemented
26#3175C211yesmaximal, characteristic, complemented
27#3062C211yesmaximal, characteristic, complemented
28#3061C211yesmaximal, characteristic, complemented
29#3055C211yesmaximal, characteristic, complemented
30C2×#468C211yesmaximal, characteristic, complemented
31#2933C211yesmaximal, characteristic, complemented
32C2×AGL(1,ℤ/8)C2211yescharacteristic, complemented
33C2×AGL(1,ℤ/8)C2211yescharacteristic, complemented
34C2×#135C2211yescharacteristic, complemented
35C22×SD16C2211yescharacteristic, complemented
36C2×#131C2211yescharacteristic, complemented
37C22×M16C2211yescharacteristic, complemented
38#562—21no—
39#562—21no—
40#562—21no—
41#560—21no—
42#555C2211yescharacteristic
43#554C2211yescharacteristic, complemented
44#554C2211yescharacteristic, complemented
45#553C2211yescharacteristic
46#552C2211yescharacteristic, complemented
47#551—21no—
48#550C2211yescharacteristic
49#548C2211yescharacteristic
50#548C2211yescharacteristic, complemented
51#547C2211yescharacteristic
52#547C2211yescharacteristic, complemented
53#547C2211yescharacteristic, complemented
54#546—21no—
55#546—21no—
56#546—21no—
57#546C2211yescharacteristic
58#546C2211yescharacteristic, complemented
59#546C2211yescharacteristic, complemented
60#546C2211yescharacteristic, complemented
61D42C2211yescharacteristic, complemented
62#543—21no—
63#542C2211yescharacteristic, complemented
64#542C2211yescharacteristic, complemented
65#542C2211yescharacteristic, complemented
66#540—21no—
67#540C2211yescharacteristic, complemented
68#539—21no—
69#538—21no—
70#538—21no—
71#537—21no—
72#537C2211yescharacteristic, complemented
73#537C2211yescharacteristic, complemented
74#537C2211yescharacteristic, complemented
75#535—21no—
76#535C2211yescharacteristic, complemented
77#534—21no—
78#525C2211yescharacteristic
79#525C2211yescharacteristic
80C2×C22⋊Q8C2211yescharacteristic, complemented
81C2×#121C2211yescharacteristic
82C2×#121C2211yescharacteristic, complemented
83#501C2211yescharacteristic, complemented
84#500C2211yescharacteristic, complemented
85#496C2211yescharacteristic, complemented
86#495C2211yescharacteristic, complemented
87#489C2211yescharacteristic, complemented
88#489C2211yescharacteristic, complemented
89#488C2211yescharacteristic, complemented
90#486C2211yescharacteristic, complemented
91#485C2211yescharacteristic, complemented
92#485C2211yescharacteristic, complemented
93#485C2211yescharacteristic, complemented
94#484C2211yescharacteristic, complemented
95#484C2211yescharacteristic, complemented
96#483C2211yescharacteristic, complemented
97#482C2211yescharacteristic, complemented
98#481C2211yescharacteristic, complemented
99#480C2211yescharacteristic
100#480C2211yescharacteristic, complemented
101#480C2211yescharacteristic, complemented
102#480C2211yescharacteristic, complemented
103#480C2211yescharacteristic, complemented
104#480C2211yescharacteristic, complemented
105#480C2211yescharacteristic, complemented
106#480C2211yescharacteristic, complemented
107#479C2211yescharacteristic, complemented
108#478C2211yescharacteristic, complemented
109#477C2211yescharacteristic, complemented
110#477C2211yescharacteristic, complemented
111#476C2211yescharacteristic, complemented
112#474C2211yescharacteristic, complemented
113#474C2211yescharacteristic, complemented
114#474C2211yescharacteristic, complemented
115#469C2211yescharacteristic, complemented
116#469C2211yescharacteristic, complemented
117#469C2211yescharacteristic, complemented
118#468C2211yescharacteristic
119#468C2211yescharacteristic
120#468C2211yescharacteristic, complemented
121#468C2211yescharacteristic, complemented
122#468C2211yescharacteristic, complemented
123#468C2211yescharacteristic, complemented
124#468C2211yescharacteristic, complemented
125#468C2211yescharacteristic, complemented
126#468C2211yescharacteristic, complemented
127#468C2211yescharacteristic, complemented
128#468C2211yescharacteristic, complemented
129#468C2211yescharacteristic, complemented
130#468C2211yescharacteristic, complemented
131#467C2211yescharacteristic, complemented
132#467C2211yescharacteristic, complemented
133#467C2211yescharacteristic, complemented
134#466C2211yescharacteristic
135#466C2211yescharacteristic
136#466C2211yescharacteristic
137#466C2211yescharacteristic
138#466C2211yescharacteristic, complemented
139#466C2211yescharacteristic, complemented
140#466C2211yescharacteristic, complemented
141#466C2211yescharacteristic, complemented
142#465C2211yescharacteristic, complemented
143#465C2211yescharacteristic, complemented
144#465C2211yescharacteristic, complemented
145#465C2211yescharacteristic, complemented
146#465C2211yescharacteristic, complemented
147#464C2211yescharacteristic, complemented
148#464C2211yescharacteristic, complemented
149#463C2211yescharacteristic, complemented
150#463C2211yescharacteristic, complemented
151#463C2211yescharacteristic, complemented
152#463C2211yescharacteristic, complemented
153#460C2211yescharacteristic, complemented
154#459C2211yescharacteristic, complemented
155#452C2211yescharacteristic, complemented
156#452C2211yescharacteristic, complemented
157#452C2211yescharacteristic, complemented
158#452C2211yescharacteristic, complemented
159#451C2211yescharacteristic, complemented
160#450C2211yescharacteristic, complemented
161#449C2211yescharacteristic, complemented
162#449C2211yescharacteristic, complemented
163#449C2211yescharacteristic, complemented
164#449C2211yescharacteristic, complemented
165#448C2211yescharacteristic, complemented
166#447C2211yescharacteristic
167#447C2211yescharacteristic
168#447C2211yescharacteristic
169#447C2211yescharacteristic, complemented
170#447C2211yescharacteristic, complemented
171#442C2211yescharacteristic, complemented
172#440C2211yescharacteristic, complemented
173#440C2211yescharacteristic, complemented
174#440C2211yescharacteristic, complemented
175C4×Q16C2211yescharacteristic, complemented
176C4×SD16C2211yescharacteristic, complemented
177C4×D8C2211yescharacteristic, complemented
178C4×D8C2211yescharacteristic, complemented
179#436C2211yescharacteristic, complemented
180#436C2211yescharacteristic, complemented
181#435C2211yescharacteristic, complemented
182#435C2211yescharacteristic, complemented
183#435C2211yescharacteristic, complemented
184#435C2211yescharacteristic, complemented
185C8×D4C2211yescharacteristic, complemented
186C8×D4C2211yescharacteristic, complemented
187#428C2211yescharacteristic, complemented
188#428C2211yescharacteristic, complemented
189C2×#107C2211yescharacteristic, complemented
190C2×#107C2211yescharacteristic, complemented
191#424C2211yescharacteristic, complemented
192#418C2211yescharacteristic, complemented
193#417C2211yescharacteristic, complemented
194#417C2211yescharacteristic, complemented
195#417C2211yescharacteristic, complemented
196#416C2211yescharacteristic, complemented
197C2×#103C2211yescharacteristic, complemented
198C2×#102C2211yescharacteristic, complemented
199C2×#102C2211yescharacteristic, complemented
200#408C2211yescharacteristic, complemented
201C2×C22⋊C8C2211yescharacteristic, complemented
202#405C2211yescharacteristic, complemented
203C2×#41—21no—
204C2×#41—21no—
205C2×#41—21no—
206C2×#41C2311yescharacteristic
207C2×#41C2311yescharacteristic
208C2×#41C2311yescharacteristic
209C2×#41C2311yescharacteristic
210C2×#41C2311yescharacteristic
211C22×Q8C2311yescharacteristic
212C22×D4—21no—
213C22×D4—21no—
214C22×D4—21no—
215C22×D4C2311yescharacteristic
216C22×D4C2311yescharacteristic
217C22×D4C2311yescharacteristic
218C23×C4C2311yescharacteristic
219AGL(1,ℤ/8)—42no—
220AGL(1,ℤ/8)—42no—
221#135—42no—
222C2×Q16C2311yescharacteristic
223C2×Q16C2311yescharacteristic
224C2×SD16—42no—
225C2×SD16C2311yescharacteristic
226C2×SD16C2311yescharacteristic
227C2×SD16C2311yescharacteristic
228C2×SD16C2311yescharacteristic
229C2×SD16C2311yescharacteristic
230C2×SD16C2311yescharacteristic
231C2×SD16C2311yescharacteristic
232C2×SD16C2311yescharacteristic
233C2×D8C2311yescharacteristic
234C2×D8C2311yescharacteristic
235C2×D8C2311yescharacteristic
236C2×D8C2311yescharacteristic
237C2×D8C2311yescharacteristic
238C2×D8C2311yescharacteristic
239#131—42no—
240C2×M16—42no—
241C2×M16C2311yescharacteristic
242C2×M16C2311yescharacteristic
243C2×M16C2311yescharacteristic
244C2×M16C2311yescharacteristic
245C2×M16C2311yescharacteristic
246C2×M16C2311yescharacteristic
247C22×C8C2311yescharacteristic
248C22×C8C2311yescharacteristic
249C22×C8C2311yescharacteristic
250C22×C8C2311yescharacteristic
251C22×C8C2311yescharacteristic
252C22×C8C2311yescharacteristic
253C4⋊Q8C2311yescharacteristic
254C4⋊Q8C2311yescharacteristic
255C4⋊Q8C2311yescharacteristic
256#127—21no—
257#127—21no—
258#127C2311yescharacteristic
259#126—21no—
260#126—21no—
261#126—21no—
262#126—21no—
263#126—21no—
264#125—21no—
265#125—21no—
266#125—21no—
267#125C2311yescharacteristic
268#124—21no—
269#124—21no—
270#124—21no—
271#124—21no—
272#124—21no—
273#124—21no—
274#124—21no—
275#124—21no—
276#124C2311yescharacteristic
277#124C2311yescharacteristic
278#124C2311yescharacteristic
279#123—21no—
280#123—21no—
281#123—21no—
282#123—21no—
283#123—21no—
284#123—21no—
285#123—21no—
286#123—21no—
287#123—21no—
288#123—21no—
289#123—21no—
290#123—21no—
291#123—21no—
292#123—21no—
293#123—21no—
294#123—21no—
295#123—21no—
296#123—21no—
297#123D411yescharacteristic
298#123D411yescharacteristic
299C22⋊Q8—21no—
300C22⋊Q8—21no—
301C22⋊Q8—21no—
302C22⋊Q8—21no—
303C22⋊Q8—21no—
304C22⋊Q8—21no—
305C22⋊Q8—21no—
306C22⋊Q8—21no—
307C22⋊Q8—21no—
308C22⋊Q8—21no—
309C22⋊Q8—21no—
310C22⋊Q8—21no—
311C22⋊Q8—21no—
312C22⋊Q8—21no—
313C22⋊Q8—21no—
314C22⋊Q8—21no—
315C22⋊Q8—21no—
316C22⋊Q8D411yescharacteristic
317C22⋊Q8D411yescharacteristic
318C22⋊Q8C2311yescharacteristic
319C22⋊Q8C2311yescharacteristic
320C22⋊Q8C2311yescharacteristic
321C22⋊Q8C2311yescharacteristic
322C22⋊Q8C2311yescharacteristic
323C22⋊Q8C2311yescharacteristic
324C22⋊Q8C2311yescharacteristic
325C22⋊Q8C2311yescharacteristic
326C22⋊Q8C2311yescharacteristic
327#121—21no—
328#121—21no—
329#121—21no—
330#121—21no—
331#121—21no—
332#121—21no—
333#121—21no—
334#121—21no—
335#121—21no—
336#121—21no—
337#121—21no—
338#121—21no—
339#121—21no—
340#121—21no—
341#121—21no—
342#121—21no—
343#121—21no—
344#121—21no—
345#121—21no—
346#121—21no—
347#121—21no—
348#121—21no—
349#121—21no—
350#121—21no—
351#121—21no—
352#121—21no—
353#121D411yescharacteristic
354#121D411yescharacteristic
355#121C2311yescharacteristic
356#121C2311yescharacteristic
357#121C2311yescharacteristic
358#121C2311yescharacteristic
359#121C2311yescharacteristic
360#121C2311yescharacteristic
361#121C2311yescharacteristic
362#121C2311yescharacteristic
363#121C2311yescharacteristic
364#121C2311yescharacteristic
365#121C2311yescharacteristic
366#121C2311yescharacteristic
367#121C2311yescharacteristic
368#121C2311yescharacteristic
369#121C2311yescharacteristic
370#120—21no—
371#120—21no—
372#120—21no—
373#120—21no—
374#120—21no—
375#120—21no—
376#120—21no—
377#120—21no—
378#120—21no—
379#120D411yescharacteristic
380#120D411yescharacteristic
381C4×Q8C2311yescharacteristic
382C4×Q8C2311yescharacteristic
383C4×Q8C2311yescharacteristic
384C4×D4—21no—
385C4×D4—21no—
386C4×D4—21no—
387C4×D4—21no—
388C4×D4—21no—
389C4×D4—21no—
390C4×D4—21no—
391C4×D4—21no—
392C4×D4C2311yescharacteristic
393C4×D4C2311yescharacteristic
394C4×D4C2311yescharacteristic
395C4×D4C2311yescharacteristic
396C4×D4C2311yescharacteristic
397C4×D4C2311yescharacteristic
398C4×D4C2311yescharacteristic
399C4×D4C2311yescharacteristic
400C4×D4C2311yescharacteristic
401#117—21no—
402#117—21no—
403#117C2311yescharacteristic
404#117C2311yescharacteristic
405#117C2311yescharacteristic
406C2×C4⋊C4—21no—
407C2×C4⋊C4C2311yescharacteristic
408C2×C4⋊C4C2311yescharacteristic
409C2×C4⋊C4C2311yescharacteristic
410C2×C4⋊C4C2311yescharacteristic
411C2×C4⋊C4C2311yescharacteristic
412C2×C4⋊C4C2311yescharacteristic
413C2×C22⋊C4—21no—
414C2×C22⋊C4—21no—
415C2×C22⋊C4—21no—
416C2×C22⋊C4—21no—
417C2×C22⋊C4—21no—
418C2×C22⋊C4—21no—
419C2×C22⋊C4—21no—
420#107C2311yescharacteristic
421#107C2311yescharacteristic
422#107C2311yescharacteristic
423#107C2311yescharacteristic
424#107C2311yescharacteristic
425#107C2311yescharacteristic
426#107C2311yescharacteristic
427#107C2311yescharacteristic
428#107C2311yescharacteristic
429#107C2311yescharacteristic
430#107C2311yescharacteristic
431#107C2311yescharacteristic
432#106C2311yescharacteristic
433#106C2311yescharacteristic
434#106C2311yescharacteristic
435#106C2311yescharacteristic
436C4⋊C8C2311yescharacteristic
437C4⋊C8C2311yescharacteristic
438C4⋊C8C2311yescharacteristic
439C4⋊C8C2311yescharacteristic
440#103C2311yescharacteristic
441#103C2311yescharacteristic
442#103C2311yescharacteristic
443#103C2311yescharacteristic
444#103C2311yescharacteristic
445#103C2311yescharacteristic
446#103C2311yescharacteristic
447#103C2311yescharacteristic
448#103C2311yescharacteristic
449#103C2311yescharacteristic
450#103C2311yescharacteristic
451#103C2311yescharacteristic
452#102C2311yescharacteristic
453#102C2311yescharacteristic
454#102C2311yescharacteristic
455#102C2311yescharacteristic
456#102C2311yescharacteristic
457#102C2311yescharacteristic
458#102C2311yescharacteristic
459#102C2311yescharacteristic
460#102C2311yescharacteristic
461#102C2311yescharacteristic
462#102C2311yescharacteristic
463#102C2311yescharacteristic
464#102C2311yescharacteristic
465#102C2311yescharacteristic
466#102C2311yescharacteristic
467#102C2311yescharacteristic
468#102C2311yescharacteristic
469#102C2311yescharacteristic
470#102C2311yescharacteristic
471#102C2311yescharacteristic
472C22⋊C8C2311yescharacteristic
473C22⋊C8C2311yescharacteristic
474C22⋊C8C2311yescharacteristic
475C22⋊C8C2311yescharacteristic
476C22⋊C8C2311yescharacteristic
477C22⋊C8C2311yescharacteristic
478C22⋊C8C2311yescharacteristic
479C22⋊C8C2311yescharacteristic
480#97C2311yescharacteristic
481#97C2311yescharacteristic
482C4×C8C2311yescharacteristic
483C4×C8C2311yescharacteristic
484C24—21no—
485C24—21no—
486C24—21no—
487C24C2×D411yescharacteristic
488#41—41no—
489#41—41no—
490#41—41no—
491#41—41no—
492#41—41no—
493#41—41no—
494#41—41no—
495#41—41no—
496#41—41no—
497#41—41no—
498#41—82no—
499#41—82no—
500#41—82no—
501C2×Q8—21no—
502C2×Q8—21no—
503C2×Q8—21no—
504C2×Q8—21no—
505C2×Q8—41no—
506C2×Q8—41no—
507C2×Q8C2×D411yescharacteristic
508C2×Q8C2411yescharacteristic
509C2×Q8C2411yescharacteristic
510C2×Q8C2411yescharacteristic
511C2×D4—21no—
512C2×D4—21no—
513C2×D4—21no—
514C2×D4—21no—
515C2×D4—21no—
516C2×D4—21no—
517C2×D4—21no—
518C2×D4—21no—
519C2×D4—21no—
520C2×D4—21no—
521C2×D4—21no—
522C2×D4—21no—
523C2×D4—21no—
524C2×D4—21no—
525C2×D4—21no—
526C2×D4—21no—
527C2×D4—21no—
528C2×D4—21no—
529C2×D4—21no—
530C2×D4—21no—
531C2×D4—21no—
532C2×D4—21no—
533C2×D4—21no—
534C2×D4—21no—
535C2×D4—41no—
536C2×D4—41no—
537C2×D4—41no—
538C2×D4—41no—
539C2×D4—41no—
540C2×D4—41no—
541C2×D4—82no—
542C2×D4—82no—
543C2×D4—82no—
544C2×D4C2×D411yescharacteristic
545C2×D4C2×D411yescharacteristic
546C2×D4C2×D411yescharacteristic
547C2×D4C2×D411yescharacteristic
548C2×D4C2×D411yescharacteristic
549C2×D4C2×D411yescharacteristic
550C2×D4C2×D411yescharacteristic
551C2×D4C2411yescharacteristic
552C2×D4C2411yescharacteristic
553C2×D4C2411yescharacteristic
554C2×D4C2411yescharacteristic
555C2×D4C2411yescharacteristic
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—41no—
573C22×C4—41no—
574C22×C4C2×D411yescharacteristic
575C22×C4C2×D411yescharacteristic
576C22×C4C2×D411yescharacteristic
577C22×C4C2411yescharacteristic
578C22×C4C2411yescharacteristic
579C22×C4C2411yescharacteristic
580C22×C4C2411yescharacteristic
581C22×C4C2411yescharacteristic
582Q16—41no—
583Q16—41no—
584SD16—22no—
585SD16—22no—
586SD16—22no—
587SD16—41no—
588SD16—41no—
589SD16—41no—
590SD16—41no—
591SD16—41no—
592D8—22no—
593D8—41no—
594D8—41no—
595D8—41no—
596D8—41no—
597D8—41no—
598M16—22no—
599M16—22no—
600M16—22no—
601M16—41no—
602M16—41no—
603M16—41no—
604C2×C8—22no—
605C2×C8—22no—
606C2×C8—41no—
607C2×C8—41no—
608C2×C8—41no—
609C2×C8—41no—
610C2×C8C2411yescharacteristic
611C2×C8C2411yescharacteristic
612C2×C8C2411yescharacteristic
613C2×C8C2411yescharacteristic
614C2×C8C2411yescharacteristic
615C2×C8C2411yescharacteristic
616C2×C8C2411yescharacteristic
617C2×C8C2411yescharacteristic
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4—21no—
629C4⋊C4—21no—
630C4⋊C4—21no—
631C4⋊C4—21no—
632C4⋊C4—21no—
633C4⋊C4—21no—
634C4⋊C4—21no—
635C4⋊C4—21no—
636C4⋊C4—21no—
637C4⋊C4—21no—
638C4⋊C4—21no—
639C4⋊C4—21no—
640C4⋊C4—21no—
641C4⋊C4C2×D411yescharacteristic
642C4⋊C4C2×D411yescharacteristic
643C4⋊C4C2×D411yescharacteristic
644C4⋊C4C2×D411yescharacteristic
645C4⋊C4C2×D411yescharacteristic
646C4⋊C4C2×D411yescharacteristic
647C4⋊C4C2411yescharacteristic
648C4⋊C4C2411yescharacteristic
649C4⋊C4C2411yescharacteristic
650C4⋊C4C2411yescharacteristic
651C4⋊C4C2411yescharacteristic
652C4⋊C4C2411yescharacteristic
653C4⋊C4C2411yescharacteristic
654C4⋊C4C2411yescharacteristic
655C22⋊C4—21no—
656C22⋊C4—21no—
657C22⋊C4—21no—
658C22⋊C4—21no—
659C22⋊C4—21no—
660C22⋊C4—21no—
661C22⋊C4—21no—
662C22⋊C4—21no—
663C22⋊C4—21no—
664C22⋊C4—21no—
665C22⋊C4—21no—
666C22⋊C4—21no—
667C22⋊C4—21no—
668C22⋊C4—21no—
669C22⋊C4—21no—
670C22⋊C4—21no—
671C22⋊C4—21no—
672C22⋊C4—21no—
673C22⋊C4—21no—
674C22⋊C4—21no—
675C22⋊C4—21no—
676C22⋊C4—21no—
677C22⋊C4—21no—
678C22⋊C4—21no—
679C22⋊C4—21no—
680C22⋊C4—21no—
681C22⋊C4—21no—
682C22⋊C4—21no—
683C22⋊C4—21no—
684C22⋊C4—21no—
685C22⋊C4—21no—
686C22⋊C4—21no—
687C22⋊C4—21no—
688C22⋊C4—21no—
689C22⋊C4—21no—
690C22⋊C4—21no—
691C22⋊C4—21no—
692C22⋊C4C2×D411yescharacteristic
693C22⋊C4C2×D411yescharacteristic
694C22⋊C4C2×D411yescharacteristic
695C22⋊C4C2×D411yescharacteristic
696C22⋊C4C2×D411yescharacteristic
697C22⋊C4C2×D411yescharacteristic
698C22⋊C4C2×D411yescharacteristic
699C22⋊C4C2×D411yescharacteristic
700C22⋊C4C2×D411yescharacteristic
701C22⋊C4C2×D411yescharacteristic
702C42—21no—
703C42—21no—
704C42—21no—
705C42—21no—
706C42—21no—
707C42C2411yescharacteristic
708C42C2411yescharacteristic
709C23—22no—
710C23—21no—
711C23—21no—
712C23—21no—
713C23—21no—
714C23—21no—
715C23—41no—
716C23—41no—
717C23—42no—
718C23—42no—
719C23—81no—
720C23—81no—
721C23—81no—
722C23—81no—
723C23—81no—
724C23—81no—
725C23—81no—
726C23C22×D411yescharacteristic
727C23C22×D411yescharacteristic
728C23C22×D411yescharacteristic
729C23C22×D411yescharacteristic
730C23C22×D411yescharacteristic
731Q8—21no—
732Q8—21no—
733Q8—21no—
734Q8—21no—
735Q8—21no—
736Q8—21no—
737Q8—41no—
738Q8—81no—
739Q8—81no—
740Q8—81no—
741Q8—81no—
742D4—22no—
743D4—22no—
744D4—21no—
745D4—21no—
746D4—21no—
747D4—21no—
748D4—21no—
749D4—21no—
750D4—21no—
751D4—21no—
752D4—21no—
753D4—21no—
754D4—41no—
755D4—41no—
756D4—41no—
757D4—41no—
758D4—41no—
759D4—42no—
760D4—42no—
761D4—42no—
762D4—81no—
763D4—81no—
764D4—81no—
765D4—81no—
766D4—81no—
767D4—81no—
768D4—81no—
769D4—81no—
770D4—81no—
771D4—81no—
772D4—81no—
773D4—81no—
774D4—81no—
775D4—81no—
776D4—81no—
777D4—81no—
778D4—81no—
779D4—81no—
780D4—81no—
781D4—81no—
782D4—81no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—21no—
788C2×C4—21no—
789C2×C4—21no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—21no—
796C2×C4—21no—
797C2×C4—21no—
798C2×C4—21no—
799C2×C4—21no—
800C2×C4—21no—
801C2×C4—21no—
802C2×C4—21no—
803C2×C4—21no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—42no—
808C2×C4—42no—
809C2×C4—81no—
810C2×C4—81no—
811C2×C4—81no—
812C2×C4—81no—
813C2×C4—81no—
814C2×C4—81no—
815C2×C4—81no—
816C2×C4—81no—
817C2×C4—81no—
818C2×C4—81no—
819C2×C4—81no—
820C2×C4—81no—
821C2×C4—81no—
822C2×C4—81no—
823C2×C4C22×D411yescharacteristic
824C2×C4C22×D411yescharacteristic
825C2×C4C22×D411yescharacteristic
826C2×C4C22×D411yescharacteristic
827C2×C4C22×D411yescharacteristic
828C2×C4C22×D411yescharacteristic
829C2×C4C22×D411yescharacteristic
830C2×C4C22×D411yescharacteristic
831C2×C4C22×D411yescharacteristic
832C2×C4C2511yescharacteristic
833C8—21no—
834C8—21no—
835C8—21no—
836C8—21no—
837C8—21no—
838C8—21no—
839C8—21no—
840C8H(5,𝔽2)12yes—
841C22—21no—
842C22—21no—
843C22—21no—
844C22—21no—
845C22—21no—
846C22—21no—
847C22—21no—
848C22—21no—
849C22—21no—
850C22—21no—
851C22—21no—
852C22—21no—
853C22—21no—
854C22—21no—
855C22—41no—
856C22—41no—
857C22—41no—
858C22—41no—
859C22—41no—
860C22—41no—
861C22—41no—
862C22—41no—
863C22—41no—
864C22—41no—
865C22—41no—
866C22—41no—
867C22—41no—
868C22—41no—
869C22—41no—
870C22—82no—
871C22—162no—
872C22—162no—
873C22—162no—
874C22#57612yes—
875C22C23×D411yescharacteristic
876C4—21no—
877C4—21no—
878C4—21no—
879C4—21no—
880C4—21no—
881C4—21no—
882C4—21no—
883C4—21no—
884C4—21no—
885C4—41no—
886C4—41no—
887C4—41no—
888C4—41no—
889C4—41no—
890C4—41no—
891C4—41no—
892C4—41no—
893C4—41no—
894C4—41no—
895C4—41no—
896C4C2×H(5,𝔽2)11yescharacteristic
897C4#58511yescharacteristic
898C2—22no—
899C2—41no—
900C2—41no—
901C2—41no—
902C2—41no—
903C2—81no—
904C2—81no—
905C2—81no—
906C2—81no—
907C2—81no—
908C2#349611yescharacteristic
909C2C2×#57611yescharacteristic
910C2#358611yescharacteristic
subgroupG/H
center, socleC22C23×D4
commutator, Frattini, cosocleC2×C4C25
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ #525 ◁ G
LECSG ▷ C2×C4 ▷ C2 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #3542C2semidirect
2. #3536C2semidirect
3. #3357C2semidirect
4. #3346C2semidirect
5. #3343C2semidirect
6. #3334C2semidirect
7. #3333C2semidirect
8. #3322C2semidirect
9. #3319C2semidirect
10. #3314C2semidirect
11. #3308C2semidirect
12. #3306C2semidirect
13. #3300C2semidirect
14. #3294C2semidirect
15. #3282C2semidirect
16. #3273C2semidirect
17. #3268C2semidirect
18. #3265C2semidirect
19. #3262C2semidirect
20. #3257C2semidirect
21. #3203C2semidirect
22. #3198C2semidirect
23. #3190C2semidirect
24. #3186C2semidirect
25. #3179C2semidirect
26. #3175C2semidirect
27. #3062C2semidirect
28. #3061C2semidirect
29. #3055C2semidirect
30. C2×#468C2semidirect
31. #2933C2semidirect
32. C2×AGL(1,ℤ/8)C22semidirect
33. C2×AGL(1,ℤ/8)C22semidirect
34. C2×#135C22semidirect
35. C22×SD16C22semidirect
36. C2×#131C22semidirect
37. C22×M16C22semidirect
43. #554C22semidirect
44. #554C22semidirect
46. #552C22semidirect
50. #548C22semidirect
52. #547C22semidirect
53. #547C22semidirect
58. #546C22semidirect
59. #546C22semidirect
60. #546C22semidirect
61. D42C22semidirect
63. #542C22semidirect
64. #542C22semidirect
65. #542C22semidirect
67. #540C22semidirect
72. #537C22semidirect
73. #537C22semidirect
74. #537C22semidirect
76. #535C22semidirect
80. C2×C22⋊Q8C22semidirect
82. C2×#121C22semidirect
83. #501C22semidirect
84. #500C22semidirect
85. #496C22semidirect
86. #495C22semidirect
87. #489C22semidirect
88. #489C22semidirect
89. #488C22semidirect
90. #486C22semidirect
91. #485C22semidirect
92. #485C22semidirect
93. #485C22semidirect
94. #484C22semidirect
95. #484C22semidirect
96. #483C22semidirect
97. #482C22semidirect
98. #481C22semidirect
100. #480C22semidirect
101. #480C22semidirect
102. #480C22semidirect
103. #480C22semidirect
104. #480C22semidirect
105. #480C22semidirect
106. #480C22semidirect
107. #479C22semidirect
108. #478C22semidirect
109. #477C22semidirect
110. #477C22semidirect
111. #476C22semidirect
112. #474C22semidirect
113. #474C22semidirect
114. #474C22semidirect
115. #469C22semidirect
116. #469C22semidirect
117. #469C22semidirect
120. #468C22semidirect
121. #468C22semidirect
122. #468C22semidirect
123. #468C22semidirect
124. #468C22semidirect
125. #468C22semidirect
126. #468C22semidirect
127. #468C22semidirect
128. #468C22semidirect
129. #468C22semidirect
130. #468C22semidirect
131. #467C22semidirect
132. #467C22semidirect
133. #467C22semidirect
138. #466C22semidirect
139. #466C22semidirect
140. #466C22semidirect
141. #466C22semidirect
142. #465C22semidirect
143. #465C22semidirect
144. #465C22semidirect
145. #465C22semidirect
146. #465C22semidirect
147. #464C22semidirect
148. #464C22semidirect
149. #463C22semidirect
150. #463C22semidirect
151. #463C22semidirect
152. #463C22semidirect
153. #460C22semidirect
154. #459C22semidirect
155. #452C22semidirect
156. #452C22semidirect
157. #452C22semidirect
158. #452C22semidirect
159. #451C22semidirect
160. #450C22semidirect
161. #449C22semidirect
162. #449C22semidirect
163. #449C22semidirect
164. #449C22semidirect
165. #448C22semidirect
169. #447C22semidirect
170. #447C22semidirect
171. #442C22semidirect
172. #440C22semidirect
173. #440C22semidirect
174. #440C22semidirect
175. C4×Q16C22semidirect
176. C4×SD16C22semidirect
177. C4×D8C22semidirect
178. C4×D8C22semidirect
179. #436C22semidirect
180. #436C22semidirect
181. #435C22semidirect
182. #435C22semidirect
183. #435C22semidirect
184. #435C22semidirect
185. C8×D4C22semidirect
186. C8×D4C22semidirect
187. #428C22semidirect
188. #428C22semidirect
189. C2×#107C22semidirect
190. C2×#107C22semidirect
191. #424C22semidirect
192. #418C22semidirect
193. #417C22semidirect
194. #417C22semidirect
195. #417C22semidirect
196. #416C22semidirect
197. C2×#103C22semidirect
198. C2×#102C22semidirect
199. C2×#102C22semidirect
200. #408C22semidirect
201. C2×C22⋊C8C22semidirect
202. #405C22semidirect

Maximal subgroups

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

subgroupindex
#35422
#35362
#33572
#33462
#33432
#33342
#33332
#33222
#33192
#33142
#33082
#33062
#33002
#32942
#32822
#32732
#32682
#32652
#32622
#32572
#32032
#31982
#31902
#31862
#31792
#31752
#30622
#30612
#30552
C2×#4682
#29332