Finite Group Databasebeta

← #62063

Subgroups — #62063

Order 256.

928 conjugacy classes of subgroups.

The subgroup lattice has 887 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3561C211yesmaximal, characteristic, complemented
2#3513C211yesmaximal, characteristic, complemented
3#3401C211yesmaximal, characteristic, complemented
4#3394C211yesmaximal, characteristic, complemented
5#3376C211yesmaximal, characteristic, complemented
6#3360C211yesmaximal, characteristic, complemented
7#3326C211yesmaximal, characteristic, complemented
8#3312C211yesmaximal, characteristic, complemented
9#3306C211yesmaximal, characteristic, complemented
10#3301C211yesmaximal, characteristic, complemented
11#3298C211yesmaximal, characteristic, complemented
12#3296C211yesmaximal, characteristic, complemented
13#3282C211yesmaximal, characteristic, complemented
14D4×SD16C211yesmaximal, characteristic, complemented
15#3280C211yesmaximal, characteristic, complemented
16#3275C211yesmaximal, characteristic, complemented
17#3266C211yesmaximal, characteristic, complemented
18#3264C211yesmaximal, characteristic, complemented
19#3263C211yesmaximal, characteristic, complemented
20#3257C211yesmaximal, characteristic, complemented
21#3248C211yesmaximal, characteristic, complemented
22#3225C211yesmaximal, characteristic, complemented
23#3221C211yesmaximal, characteristic, complemented
24#3211C211yesmaximal, characteristic, complemented
25#3125C211yesmaximal, characteristic, complemented
26#3118C211yesmaximal, characteristic, complemented
27#3101C211yesmaximal, characteristic, complemented
28#3046C211yesmaximal, characteristic, complemented
29#3042C211yesmaximal, characteristic, complemented
30C2×#463C211yesmaximal, characteristic, complemented
31#2994C211yesmaximal, characteristic, complemented
32C2×#137C2211yescharacteristic, complemented
33C2×AGL(1,ℤ/8)C2211yescharacteristic
34C2×#135C2211yescharacteristic
35C22×SD16C2211yescharacteristic
36C22×SD16C2211yescharacteristic, complemented
37C22×D8C2211yescharacteristic
38#563—21no—
39#562—21no—
40#559C2211yescharacteristic, complemented
41#556C2211yescharacteristic, complemented
42#556C2211yescharacteristic, complemented
43#554C2211yescharacteristic, complemented
44#553—21no—
45#553C2211yescharacteristic, complemented
46#552C2211yescharacteristic
47#551—21no—
48#551—21no—
49#551—21no—
50#551—21no—
51D4×Q8C2211yescharacteristic
52D4×Q8C2211yescharacteristic, complemented
53#548C2211yescharacteristic, complemented
54#548C2211yescharacteristic, complemented
55#547C2211yescharacteristic
56#546—21no—
57#546C2211yescharacteristic
58#546C2211yescharacteristic
59#546C2211yescharacteristic, complemented
60#546C2211yescharacteristic, complemented
61D42C2211yescharacteristic
62#543—21no—
63#542—21no—
64#542—21no—
65#542C2211yescharacteristic, complemented
66#542C2211yescharacteristic, complemented
67#542C2211yescharacteristic, complemented
68#540C2211yescharacteristic, complemented
69#539—21no—
70#538—21no—
71#538—21no—
72#536C2211yescharacteristic, complemented
73#536C2211yescharacteristic, complemented
74#533C2211yescharacteristic, complemented
75#529C2211yescharacteristic
76#529C2211yescharacteristic
77C2×#124C2211yescharacteristic, complemented
78#525—21no—
79C2×#123—21no—
80#520C2211yescharacteristic, complemented
81#518C2211yescharacteristic, complemented
82C2×C4×D4C2211yescharacteristic
83#497C2211yescharacteristic, complemented
84#496C2211yescharacteristic
85#495C2211yescharacteristic, complemented
86#495C2211yescharacteristic, complemented
87#495C2211yescharacteristic, complemented
88#492C2211yescharacteristic, complemented
89#491C2211yescharacteristic, complemented
90#489C2211yescharacteristic, complemented
91#488C2211yescharacteristic, complemented
92#488C2211yescharacteristic, complemented
93#488C2211yescharacteristic, complemented
94#487C2211yescharacteristic, complemented
95#485C2211yescharacteristic, complemented
96#483C2211yescharacteristic, complemented
97#483C2211yescharacteristic, complemented
98#483C2211yescharacteristic, complemented
99#482C2211yescharacteristic, complemented
100#481C2211yescharacteristic, complemented
101#479C2211yescharacteristic, complemented
102#479C2211yescharacteristic, complemented
103#479C2211yescharacteristic, complemented
104#478C2211yescharacteristic, complemented
105#476C2211yescharacteristic, complemented
106#476C2211yescharacteristic, complemented
107#476C2211yescharacteristic, complemented
108#475C2211yescharacteristic, complemented
109#475C2211yescharacteristic, complemented
110#474C2211yescharacteristic, complemented
111#470C2211yescharacteristic, complemented
112#469C2211yescharacteristic
113#469C2211yescharacteristic, complemented
114#468C2211yescharacteristic, complemented
115#467C2211yescharacteristic, complemented
116#467C2211yescharacteristic, complemented
117#466C2211yescharacteristic, complemented
118#465C2211yescharacteristic
119#465C2211yescharacteristic
120#465C2211yescharacteristic, complemented
121#465C2211yescharacteristic, complemented
122#465C2211yescharacteristic, complemented
123#464C2211yescharacteristic, complemented
124#464C2211yescharacteristic, complemented
125#464C2211yescharacteristic, complemented
126#464C2211yescharacteristic, complemented
127#464C2211yescharacteristic, complemented
128#464C2211yescharacteristic, complemented
129#463C2211yescharacteristic
130#463C2211yescharacteristic
131#463C2211yescharacteristic
132#463C2211yescharacteristic
133#463C2211yescharacteristic
134#463C2211yescharacteristic
135#463C2211yescharacteristic, complemented
136#463C2211yescharacteristic, complemented
137#463C2211yescharacteristic, complemented
138#463C2211yescharacteristic, complemented
139#463C2211yescharacteristic, complemented
140#463C2211yescharacteristic, complemented
141#463C2211yescharacteristic, complemented
142#463C2211yescharacteristic, complemented
143#462C2211yescharacteristic, complemented
144#462C2211yescharacteristic, complemented
145#461C2211yescharacteristic, complemented
146#461C2211yescharacteristic, complemented
147#461C2211yescharacteristic, complemented
148#461C2211yescharacteristic, complemented
149#461C2211yescharacteristic, complemented
150#461C2211yescharacteristic, complemented
151#460C2211yescharacteristic, complemented
152#459C2211yescharacteristic
153#452C2211yescharacteristic, complemented
154#452C2211yescharacteristic, complemented
155#451C2211yescharacteristic, complemented
156#451C2211yescharacteristic, complemented
157#450C2211yescharacteristic
158#450C2211yescharacteristic
159#450C2211yescharacteristic, complemented
160#450C2211yescharacteristic, complemented
161#449C2211yescharacteristic
162#449C2211yescharacteristic
163#449C2211yescharacteristic, complemented
164#449C2211yescharacteristic, complemented
165#448C2211yescharacteristic
166#448C2211yescharacteristic, complemented
167#448C2211yescharacteristic, complemented
168#448C2211yescharacteristic, complemented
169#447C2211yescharacteristic
170#447C2211yescharacteristic
171#446C2211yescharacteristic, complemented
172C8×Q8C2211yescharacteristic, complemented
173#442C2211yescharacteristic
174#442C2211yescharacteristic, complemented
175#441C2211yescharacteristic, complemented
176#440C2211yescharacteristic, complemented
177C4×SD16C2211yescharacteristic, complemented
178C4×SD16C2211yescharacteristic, complemented
179C4×SD16C2211yescharacteristic, complemented
180C4×SD16C2211yescharacteristic, complemented
181C4×SD16C2211yescharacteristic, complemented
182C4×SD16C2211yescharacteristic, complemented
183C4×SD16C2211yescharacteristic, complemented
184C4×D8C2211yescharacteristic
185#436C2211yescharacteristic, complemented
186#435C2211yescharacteristic
187#435C2211yescharacteristic, complemented
188C8×D4C2211yescharacteristic
189C8×D4C2211yescharacteristic, complemented
190C8×D4C2211yescharacteristic, complemented
191#433C2211yescharacteristic, complemented
192#433C2211yescharacteristic, complemented
193#431C2211yescharacteristic, complemented
194#424C2211yescharacteristic, complemented
195#424C2211yescharacteristic, complemented
196C2×C4⋊C8C2211yescharacteristic, complemented
197#419C2211yescharacteristic, complemented
198#417C2211yescharacteristic, complemented
199#416C2211yescharacteristic, complemented
200C2×#103C2211yescharacteristic, complemented
201C2×#103C2211yescharacteristic, complemented
202C2×#102C2211yescharacteristic, complemented
203C2×#41—21no—
204C2×#41C2311yescharacteristic
205C2×#41C2311yescharacteristic
206C2×#41C2311yescharacteristic
207C22×Q8C2311yescharacteristic
208C22×Q8C2311yescharacteristic
209C22×Q8C2311yescharacteristic
210C22×D4—21no—
211C22×D4C2311yescharacteristic
212C22×D4C2311yescharacteristic
213C22×D4C2311yescharacteristic
214C23×C4—21no—
215#137—42no—
216AGL(1,ℤ/8)—42no—
217#135—42no—
218C2×Q16C2311yescharacteristic
219C2×Q16C2311yescharacteristic
220C2×Q16C2311yescharacteristic
221C2×Q16C2311yescharacteristic
222C2×SD16—42no—
223C2×SD16—42no—
224C2×SD16C2311yescharacteristic
225C2×SD16C2311yescharacteristic
226C2×SD16C2311yescharacteristic
227C2×SD16C2311yescharacteristic
228C2×SD16C2311yescharacteristic
229C2×SD16C2311yescharacteristic
230C2×SD16C2311yescharacteristic
231C2×SD16C2311yescharacteristic
232C2×SD16C2311yescharacteristic
233C2×SD16C2311yescharacteristic
234C2×SD16C2311yescharacteristic
235C2×SD16C2311yescharacteristic
236C2×SD16C2311yescharacteristic
237C2×SD16C2311yescharacteristic
238C2×D8—42no—
239C2×D8C2311yescharacteristic
240C2×D8C2311yescharacteristic
241C2×D8C2311yescharacteristic
242C2×D8C2311yescharacteristic
243C2×D8C2311yescharacteristic
244C2×D8C2311yescharacteristic
245C2×M16C2311yescharacteristic
246C2×M16C2311yescharacteristic
247C22×C8C2311yescharacteristic
248C22×C8C2311yescharacteristic
249C22×C8C2311yescharacteristic
250C22×C8C2311yescharacteristic
251C4⋊Q8—21no—
252C4⋊Q8—21no—
253C4⋊Q8C2311yescharacteristic
254C4⋊Q8C2311yescharacteristic
255C4⋊Q8C2311yescharacteristic
256C4⋊Q8C2311yescharacteristic
257C4⋊Q8C2311yescharacteristic
258#127C2311yescharacteristic
259#126—21no—
260#126—21no—
261#126—21no—
262#126—21no—
263#126—21no—
264#126—21no—
265#126—21no—
266#126—21no—
267#126—21no—
268#126—21no—
269#126D411yescharacteristic
270#126D411yescharacteristic
271#125—21no—
272#125—21no—
273#125D411yescharacteristic
274#125C2311yescharacteristic
275#125C2311yescharacteristic
276#124—21no—
277#124—21no—
278#124—21no—
279#124—21no—
280#124—21no—
281#124—21no—
282#124—21no—
283#124—21no—
284#124D411yescharacteristic
285#124C2311yescharacteristic
286#124C2311yescharacteristic
287#124C2311yescharacteristic
288#124C2311yescharacteristic
289#124C2311yescharacteristic
290#124C2311yescharacteristic
291#124C2311yescharacteristic
292#124C2311yescharacteristic
293#123—21no—
294#123—21no—
295#123—21no—
296#123—21no—
297#123—21no—
298#123—21no—
299#123—21no—
300#123—21no—
301#123—21no—
302#123—21no—
303#123—21no—
304#123—21no—
305#123—21no—
306#123—21no—
307#123—21no—
308#123—21no—
309#123—21no—
310#123—21no—
311#123—21no—
312#123—21no—
313#123D411yescharacteristic
314#123D411yescharacteristic
315C22⋊Q8—21no—
316C22⋊Q8—21no—
317C22⋊Q8—21no—
318C22⋊Q8—21no—
319C22⋊Q8—21no—
320C22⋊Q8—21no—
321C22⋊Q8—21no—
322C22⋊Q8—21no—
323C22⋊Q8—21no—
324C22⋊Q8—21no—
325C22⋊Q8—21no—
326C22⋊Q8—21no—
327C22⋊Q8—21no—
328C22⋊Q8—21no—
329C22⋊Q8—21no—
330C22⋊Q8—21no—
331C22⋊Q8—21no—
332C22⋊Q8—21no—
333C22⋊Q8—21no—
334C22⋊Q8—21no—
335C22⋊Q8D411yescharacteristic
336C22⋊Q8C2311yescharacteristic
337C22⋊Q8C2311yescharacteristic
338C22⋊Q8C2311yescharacteristic
339C22⋊Q8C2311yescharacteristic
340C22⋊Q8C2311yescharacteristic
341C22⋊Q8C2311yescharacteristic
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#121D411yescharacteristic
353#121C2311yescharacteristic
354#121C2311yescharacteristic
355#121C2311yescharacteristic
356#121C2311yescharacteristic
357#121C2311yescharacteristic
358#121C2311yescharacteristic
359#120—21no—
360#120—21no—
361#120—21no—
362#120—21no—
363#120—21no—
364#120—21no—
365C4×Q8—21no—
366C4×Q8C2311yescharacteristic
367C4×Q8C2311yescharacteristic
368C4×Q8C2311yescharacteristic
369C4×Q8C2311yescharacteristic
370C4×Q8C2311yescharacteristic
371C4×Q8C2311yescharacteristic
372C4×Q8C2311yescharacteristic
373C4×D4—21no—
374C4×D4—21no—
375C4×D4—21no—
376C4×D4—21no—
377C4×D4—21no—
378C4×D4—21no—
379C4×D4—21no—
380C4×D4—21no—
381C4×D4—21no—
382C4×D4—21no—
383C4×D4—21no—
384C4×D4—21no—
385C4×D4—21no—
386C4×D4C2311yescharacteristic
387C4×D4C2311yescharacteristic
388C4×D4C2311yescharacteristic
389C4×D4C2311yescharacteristic
390C4×D4C2311yescharacteristic
391C4×D4C2311yescharacteristic
392C4×D4C2311yescharacteristic
393C4×D4C2311yescharacteristic
394C4×D4C2311yescharacteristic
395C4×D4C2311yescharacteristic
396C4×D4C2311yescharacteristic
397C4×D4C2311yescharacteristic
398C4×D4C2311yescharacteristic
399#117—21no—
400#117—21no—
401#117—21no—
402#117—21no—
403#117—21no—
404#117—21no—
405#117C2311yescharacteristic
406#117C2311yescharacteristic
407#117C2311yescharacteristic
408C2×C4⋊C4—21no—
409C2×C4⋊C4—21no—
410C2×C4⋊C4C2311yescharacteristic
411C2×C4⋊C4C2311yescharacteristic
412C2×C22⋊C4—21no—
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—
420C2×C22⋊C4—21no—
421C2×C42C2311yescharacteristic
422#107C2311yescharacteristic
423#107C2311yescharacteristic
424#106C2311yescharacteristic
425#106C2311yescharacteristic
426#106C2311yescharacteristic
427#106C2311yescharacteristic
428#106C2311yescharacteristic
429#106C2311yescharacteristic
430C4⋊C8C2311yescharacteristic
431C4⋊C8C2311yescharacteristic
432C4⋊C8C2311yescharacteristic
433C4⋊C8C2311yescharacteristic
434C4⋊C8C2311yescharacteristic
435C4⋊C8C2311yescharacteristic
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#103C2311yescharacteristic
453#103C2311yescharacteristic
454#103C2311yescharacteristic
455#103C2311yescharacteristic
456#103C2311yescharacteristic
457#103C2311yescharacteristic
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
478#97C2311yescharacteristic
479#97C2311yescharacteristic
480C4×C8C2311yescharacteristic
481C4×C8C2311yescharacteristic
482C4×C8C2311yescharacteristic
483C4×C8C2311yescharacteristic
484C24—21no—
485C24—21no—
486C24—21no—
487#41—22no—
488#41—41no—
489#41—41no—
490#41—41no—
491#41—41no—
492#41—41no—
493#41—82no—
494C2×Q8—21no—
495C2×Q8—21no—
496C2×Q8—21no—
497C2×Q8—21no—
498C2×Q8—21no—
499C2×Q8—41no—
500C2×Q8—41no—
501C2×Q8—41no—
502C2×Q8—41no—
503C2×Q8—41no—
504C2×Q8—41no—
505C2×Q8C2×D411yescharacteristic
506C2×Q8C2411yescharacteristic
507C2×Q8C2411yescharacteristic
508C2×Q8C2411yescharacteristic
509C2×Q8C2411yescharacteristic
510C2×Q8C2411yescharacteristic
511C2×D4—22no—
512C2×D4—22no—
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—41no—
528C2×D4—41no—
529C2×D4—41no—
530C2×D4—41no—
531C2×D4—82no—
532C2×D4C2×D411yescharacteristic
533C2×D4C2×D411yescharacteristic
534C2×D4C2×D411yescharacteristic
535C2×D4C2411yescharacteristic
536C2×D4C2411yescharacteristic
537C2×D4C2411yescharacteristic
538C2×D4C2411yescharacteristic
539C2×D4C2411yescharacteristic
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—82no—
559C22×C4C2×D411yescharacteristic
560C22×C4C2×D411yescharacteristic
561C22×C4C2411yescharacteristic
562C22×C4C2411yescharacteristic
563C22×C4C2411yescharacteristic
564Q16—41no—
565Q16—41no—
566Q16—41no—
567Q16—41no—
568SD16—22no—
569SD16—22no—
570SD16—22no—
571SD16—22no—
572SD16—41no—
573SD16—41no—
574SD16—41no—
575SD16—41no—
576SD16—41no—
577SD16—41no—
578SD16—41no—
579SD16—41no—
580SD16—41no—
581SD16—41no—
582D8—22no—
583D8—22no—
584D8—41no—
585D8—41no—
586D8—41no—
587D8—41no—
588M16—41no—
589M16—41no—
590C2×C8—41no—
591C2×C8—41no—
592C2×C8—41no—
593C2×C8—41no—
594C2×C8C2411yescharacteristic
595C2×C8C2411yescharacteristic
596C2×C8C2411yescharacteristic
597C2×C8C2411yescharacteristic
598C2×C8C2411yescharacteristic
599C2×C8C2411yescharacteristic
600C2×C8C2411yescharacteristic
601C2×C8C2411yescharacteristic
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—21no—
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⋊C4C2×D411yescharacteristic
629C4⋊C4C2×D411yescharacteristic
630C4⋊C4C2×D411yescharacteristic
631C4⋊C4C2×D411yescharacteristic
632C4⋊C4C2×D411yescharacteristic
633C4⋊C4C2×D411yescharacteristic
634C4⋊C4C2×D411yescharacteristic
635C4⋊C4C2×D411yescharacteristic
636C4⋊C4C2×D411yescharacteristic
637C4⋊C4C2×D411yescharacteristic
638C4⋊C4C2411yescharacteristic
639C4⋊C4C2411yescharacteristic
640C4⋊C4C2411yescharacteristic
641C4⋊C4C2411yescharacteristic
642C4⋊C4C2411yescharacteristic
643C4⋊C4C2411yescharacteristic
644C22⋊C4—21no—
645C22⋊C4—21no—
646C22⋊C4—21no—
647C22⋊C4—21no—
648C22⋊C4—21no—
649C22⋊C4—21no—
650C22⋊C4—21no—
651C22⋊C4—21no—
652C22⋊C4—21no—
653C22⋊C4—21no—
654C22⋊C4—21no—
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⋊C4C2×D411yescharacteristic
684C22⋊C4C2×D411yescharacteristic
685C22⋊C4C2×D411yescharacteristic
686C22⋊C4C2×D411yescharacteristic
687C22⋊C4C2×D411yescharacteristic
688C22⋊C4C2×D411yescharacteristic
689C22⋊C4C2×D411yescharacteristic
690C22⋊C4C2×D411yescharacteristic
691C22⋊C4C2×D411yescharacteristic
692C22⋊C4C2×D411yescharacteristic
693C42—21no—
694C42—21no—
695C42—21no—
696C42—21no—
697C42—21no—
698C42—21no—
699C42—21no—
700C42C2×D411yescharacteristic
701C42C2×D411yescharacteristic
702C42C2411yescharacteristic
703C42C2411yescharacteristic
704C42C2411yescharacteristic
705C42C2411yescharacteristic
706C23—21no—
707C23—21no—
708C23—21no—
709C23—21no—
710C23—21no—
711C23—42no—
712C23—42no—
713C23—42no—
714C23—42no—
715C23—81no—
716C23—81no—
717C23—81no—
718C23—81no—
719C23—81no—
720C23C22×D411yescharacteristic
721C23C22×D411yescharacteristic
722C23C22×D411yescharacteristic
723Q8—21no—
724Q8—21no—
725Q8—21no—
726Q8—21no—
727Q8—21no—
728Q8—21no—
729Q8—21no—
730Q8—21no—
731Q8—21no—
732Q8—21no—
733Q8—41no—
734Q8—81no—
735Q8—81no—
736Q8—81no—
737Q8—81no—
738Q8—81no—
739D4—22no—
740D4—22no—
741D4—21no—
742D4—21no—
743D4—21no—
744D4—21no—
745D4—21no—
746D4—21no—
747D4—21no—
748D4—21no—
749D4—21no—
750D4—41no—
751D4—42no—
752D4—42no—
753D4—42no—
754D4—42no—
755D4—81no—
756D4—81no—
757D4—81no—
758D4—81no—
759D4—81no—
760D4—81no—
761D4—81no—
762D4—81no—
763D4—81no—
764D4—81no—
765D4H(5,𝔽2)12yes—
766C2×C4—22no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—41no—
785C2×C4—42no—
786C2×C4—42no—
787C2×C4—81no—
788C2×C4—81no—
789C2×C4—81no—
790C2×C4—81no—
791C2×C4—81no—
792C2×C4—81no—
793C2×C4—81no—
794C2×C4—81no—
795C2×C4—81no—
796C2×C4—81no—
797C2×C4—81no—
798C2×C4—81no—
799C2×C4—81no—
800C2×C4—81no—
801C2×C4—81no—
802C2×C4—81no—
803C2×C4C22×D411yescharacteristic
804C2×C4C22×D411yescharacteristic
805C2×C4C22×D411yescharacteristic
806C2×C4C22×D411yescharacteristic
807C2×C4C22×D411yescharacteristic
808C2×C4C22×D411yescharacteristic
809C2×C4C22×D411yescharacteristic
810C2×C4C22×D411yescharacteristic
811C2×C4C22×D411yescharacteristic
812C2×C4C22×D411yescharacteristic
813C2×C4C22×D411yescharacteristic
814C2×C4C2511yescharacteristic
815C8—21no—
816C8—21no—
817C8—21no—
818C8—21no—
819C8—21no—
820C8—21no—
821C8—21no—
822C8—21no—
823C22—21no—
824C22—21no—
825C22—21no—
826C22—21no—
827C22—21no—
828C22—21no—
829C22—22no—
830C22—21no—
831C22—21no—
832C22—41no—
833C22—41no—
834C22—41no—
835C22—41no—
836C22—41no—
837C22—41no—
838C22—41no—
839C22—41no—
840C22—41no—
841C22—41no—
842C22—41no—
843C22—41no—
844C22—41no—
845C22—41no—
846C22—84no—
847C22—162no—
848C22—162no—
849C22#57712yes—
850C22C23×D411yescharacteristic
851C4—21no—
852C4—21no—
853C4—21no—
854C4—21no—
855C4—21no—
856C4—21no—
857C4—21no—
858C4—21no—
859C4—21no—
860C4—21no—
861C4—21no—
862C4—41no—
863C4—41no—
864C4—41no—
865C4—41no—
866C4—41no—
867C4—41no—
868C4—41no—
869C4—41no—
870C4—41no—
871C4—41no—
872C4—41no—
873C4C2×H(5,𝔽2)11yescharacteristic
874C4#58511yescharacteristic
875C2—22no—
876C2—41no—
877C2—41no—
878C2—42no—
879C2—81no—
880C2—81no—
881C2—81no—
882C2—81no—
883C2#348811yescharacteristic
884C2C2×#57711yescharacteristic
885C2#358411yescharacteristic
subgroupG/H
center, socleC22C23×D4
commutator, Frattini, cosocleC2×C4C25
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ #529 ◁ G
LECSG ▷ C2×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #3561C2semidirect
2. #3513C2semidirect
3. #3401C2semidirect
4. #3394C2semidirect
5. #3376C2semidirect
6. #3360C2semidirect
7. #3326C2semidirect
8. #3312C2semidirect
9. #3306C2semidirect
10. #3301C2semidirect
11. #3298C2semidirect
12. #3296C2semidirect
13. #3282C2semidirect
14. D4×SD16C2semidirect
15. #3280C2semidirect
16. #3275C2semidirect
17. #3266C2semidirect
18. #3264C2semidirect
19. #3263C2semidirect
20. #3257C2semidirect
21. #3248C2semidirect
22. #3225C2semidirect
23. #3221C2semidirect
24. #3211C2semidirect
25. #3125C2semidirect
26. #3118C2semidirect
27. #3101C2semidirect
28. #3046C2semidirect
29. #3042C2semidirect
30. C2×#463C2semidirect
31. #2994C2semidirect
32. C2×#137C22semidirect
36. C22×SD16C22semidirect
40. #559C22semidirect
41. #556C22semidirect
42. #556C22semidirect
43. #554C22semidirect
45. #553C22semidirect
52. D4×Q8C22semidirect
53. #548C22semidirect
54. #548C22semidirect
59. #546C22semidirect
60. #546C22semidirect
65. #542C22semidirect
66. #542C22semidirect
67. #542C22semidirect
68. #540C22semidirect
72. #536C22semidirect
73. #536C22semidirect
74. #533C22semidirect
77. C2×#124C22semidirect
80. #520C22semidirect
81. #518C22semidirect
83. #497C22semidirect
85. #495C22semidirect
86. #495C22semidirect
87. #495C22semidirect
88. #492C22semidirect
89. #491C22semidirect
90. #489C22semidirect
91. #488C22semidirect
92. #488C22semidirect
93. #488C22semidirect
94. #487C22semidirect
95. #485C22semidirect
96. #483C22semidirect
97. #483C22semidirect
98. #483C22semidirect
99. #482C22semidirect
100. #481C22semidirect
101. #479C22semidirect
102. #479C22semidirect
103. #479C22semidirect
104. #478C22semidirect
105. #476C22semidirect
106. #476C22semidirect
107. #476C22semidirect
108. #475C22semidirect
109. #475C22semidirect
110. #474C22semidirect
111. #470C22semidirect
113. #469C22semidirect
114. #468C22semidirect
115. #467C22semidirect
116. #467C22semidirect
117. #466C22semidirect
120. #465C22semidirect
121. #465C22semidirect
122. #465C22semidirect
123. #464C22semidirect
124. #464C22semidirect
125. #464C22semidirect
126. #464C22semidirect
127. #464C22semidirect
128. #464C22semidirect
135. #463C22semidirect
136. #463C22semidirect
137. #463C22semidirect
138. #463C22semidirect
139. #463C22semidirect
140. #463C22semidirect
141. #463C22semidirect
142. #463C22semidirect
143. #462C22semidirect
144. #462C22semidirect
145. #461C22semidirect
146. #461C22semidirect
147. #461C22semidirect
148. #461C22semidirect
149. #461C22semidirect
150. #461C22semidirect
151. #460C22semidirect
153. #452C22semidirect
154. #452C22semidirect
155. #451C22semidirect
156. #451C22semidirect
159. #450C22semidirect
160. #450C22semidirect
163. #449C22semidirect
164. #449C22semidirect
166. #448C22semidirect
167. #448C22semidirect
168. #448C22semidirect
171. #446C22semidirect
172. C8×Q8C22semidirect
174. #442C22semidirect
175. #441C22semidirect
176. #440C22semidirect
177. C4×SD16C22semidirect
178. C4×SD16C22semidirect
179. C4×SD16C22semidirect
180. C4×SD16C22semidirect
181. C4×SD16C22semidirect
182. C4×SD16C22semidirect
183. C4×SD16C22semidirect
185. #436C22semidirect
187. #435C22semidirect
189. C8×D4C22semidirect
190. C8×D4C22semidirect
191. #433C22semidirect
192. #433C22semidirect
193. #431C22semidirect
194. #424C22semidirect
195. #424C22semidirect
196. C2×C4⋊C8C22semidirect
197. #419C22semidirect
198. #417C22semidirect
199. #416C22semidirect
200. C2×#103C22semidirect
201. C2×#103C22semidirect
202. C2×#102C22semidirect

Maximal subgroups

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

subgroupindex
#35612
#35132
#34012
#33942
#33762
#33602
#33262
#33122
#33062
#33012
#32982
#32962
#32822
D4×SD162
#32802
#32752
#32662
#32642
#32632
#32572
#32482
#32252
#32212
#32112
#31252
#31182
#31012
#30462
#30422
C2×#4632
#29942