Finite Group Databasebeta

← #61691

Subgroups — #61691

Order 256.

1023 conjugacy classes of subgroups.

The subgroup lattice has 934 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3547C211yesmaximal, characteristic, complemented
2#3500C211yesmaximal, characteristic, complemented
3#3327C211yesmaximal, characteristic, complemented
4#3323C211yesmaximal, characteristic, complemented
5#3321C211yesmaximal, characteristic, complemented
6#3319C211yesmaximal, characteristic, complemented
7#3316C211yesmaximal, characteristic, complemented
8#3314C211yesmaximal, characteristic, complemented
9#3300C211yesmaximal, characteristic, complemented
10#3296C211yesmaximal, characteristic, complemented
11#3285C211yesmaximal, characteristic, complemented
12#3282C211yesmaximal, characteristic, complemented
13#3277C211yesmaximal, characteristic, complemented
14#3275C211yesmaximal, characteristic, complemented
15#3270C211yesmaximal, characteristic, complemented
16#3269C211yesmaximal, characteristic, complemented
17#3267C211yesmaximal, characteristic, complemented
18#3266C211yesmaximal, characteristic, complemented
19#3215C211yesmaximal, characteristic, complemented
20#3211C211yesmaximal, characteristic, complemented
21#3202C211yesmaximal, characteristic, complemented
22#3201C211yesmaximal, characteristic, complemented
23#3200C211yesmaximal, characteristic, complemented
24#3198C211yesmaximal, characteristic, complemented
25#3111C211yesmaximal, characteristic, complemented
26#3107C211yesmaximal, characteristic, complemented
27#3013C211yesmaximal, characteristic, complemented
28#3012C211yesmaximal, characteristic, complemented
29#3011C211yesmaximal, characteristic, complemented
30#3009C211yesmaximal, characteristic, complemented
31#2981C211yesmaximal, characteristic, complemented
32C2×2−1+4C2211yescharacteristic
33C2×H(5,𝔽2)C2211yescharacteristic
34C2×#137C2211yescharacteristic
35C2×#137C2211yescharacteristic, complemented
36C2×#137C2211yescharacteristic, complemented
37C2×AGL(1,ℤ/8)C2211yescharacteristic
38C2×#135C2211yescharacteristic
39C2×#135C2211yescharacteristic, complemented
40C22×Q16C2211yescharacteristic, complemented
41C22×SD16C2211yescharacteristic
42#562—21no—
43#562—21no—
44#555—21no—
45#555C2211yescharacteristic, complemented
46#554C2211yescharacteristic, complemented
47#553—21no—
48#552C2211yescharacteristic, complemented
49#552C2211yescharacteristic, complemented
50D4×Q8C2211yescharacteristic, complemented
51#548C2211yescharacteristic
52#548C2211yescharacteristic
53#548C2211yescharacteristic
54#548C2211yescharacteristic
55#548C2211yescharacteristic, complemented
56#548C2211yescharacteristic, complemented
57#547C2211yescharacteristic, complemented
58#546—21no—
59#546—21no—
60#546—21no—
61#546—21no—
62#546C2211yescharacteristic
63#546C2211yescharacteristic
64#546C2211yescharacteristic
65#546C2211yescharacteristic
66#544—21no—
67#542—21no—
68#542—21no—
69#540—21no—
70#537C2211yescharacteristic
71#537C2211yescharacteristic, complemented
72#536—21no—
73#536C2211yescharacteristic
74#536C2211yescharacteristic
75#536C2211yescharacteristic, complemented
76#535—21no—
77#535C2211yescharacteristic
78#533C2211yescharacteristic, complemented
79#532—21no—
80#532C2211yescharacteristic
81#529C2211yescharacteristic, complemented
82C2×#124—21no—
83C2×#124C2211yescharacteristic
84C4×#41C2211yescharacteristic
85#497C2211yescharacteristic, complemented
86#497C2211yescharacteristic, complemented
87#495C2211yescharacteristic, complemented
88#495C2211yescharacteristic, complemented
89#489C2211yescharacteristic, complemented
90#489C2211yescharacteristic, complemented
91#488C2211yescharacteristic, complemented
92#488C2211yescharacteristic, complemented
93#485C2211yescharacteristic, complemented
94#485C2211yescharacteristic, complemented
95#485C2211yescharacteristic, complemented
96#485C2211yescharacteristic, complemented
97#485C2211yescharacteristic, complemented
98#484C2211yescharacteristic, complemented
99#483C2211yescharacteristic, complemented
100#482C2211yescharacteristic, complemented
101#482C2211yescharacteristic, complemented
102#482C2211yescharacteristic, complemented
103#481C2211yescharacteristic, complemented
104#480C2211yescharacteristic, complemented
105#479C2211yescharacteristic, complemented
106#478C2211yescharacteristic, complemented
107#475C2211yescharacteristic, complemented
108#474C2211yescharacteristic, complemented
109#470C2211yescharacteristic, complemented
110#470C2211yescharacteristic, complemented
111#470C2211yescharacteristic, complemented
112#469C2211yescharacteristic, complemented
113#468C2211yescharacteristic, complemented
114#468C2211yescharacteristic, complemented
115#468C2211yescharacteristic, complemented
116#468C2211yescharacteristic, complemented
117#467C2211yescharacteristic, complemented
118#467C2211yescharacteristic, complemented
119#467C2211yescharacteristic, complemented
120#466C2211yescharacteristic, complemented
121#465C2211yescharacteristic, complemented
122#465C2211yescharacteristic, complemented
123#465C2211yescharacteristic, complemented
124#465C2211yescharacteristic, complemented
125#464C2211yescharacteristic, complemented
126#464C2211yescharacteristic, complemented
127#464C2211yescharacteristic, complemented
128#464C2211yescharacteristic, complemented
129#464C2211yescharacteristic, complemented
130#464C2211yescharacteristic, complemented
131#464C2211yescharacteristic, complemented
132#463C2211yescharacteristic, complemented
133#463C2211yescharacteristic, complemented
134#463C2211yescharacteristic, complemented
135#462C2211yescharacteristic, complemented
136#461C2211yescharacteristic, complemented
137#452C2211yescharacteristic
138#452C2211yescharacteristic
139#452C2211yescharacteristic
140#452C2211yescharacteristic
141#452C2211yescharacteristic
142#452C2211yescharacteristic
143#452C2211yescharacteristic, complemented
144#452C2211yescharacteristic, complemented
145#452C2211yescharacteristic, complemented
146#452C2211yescharacteristic, complemented
147#452C2211yescharacteristic, complemented
148#451C2211yescharacteristic, complemented
149#451C2211yescharacteristic, complemented
150#451C2211yescharacteristic, complemented
151#451C2211yescharacteristic, complemented
152#451C2211yescharacteristic, complemented
153#451C2211yescharacteristic, complemented
154#451C2211yescharacteristic, complemented
155#451C2211yescharacteristic, complemented
156#450C2211yescharacteristic
157#450C2211yescharacteristic
158#450C2211yescharacteristic
159#450C2211yescharacteristic
160#450C2211yescharacteristic
161#450C2211yescharacteristic
162#449C2211yescharacteristic
163#449C2211yescharacteristic
164#449C2211yescharacteristic, complemented
165#449C2211yescharacteristic, complemented
166#449C2211yescharacteristic, complemented
167#448C2211yescharacteristic, complemented
168#448C2211yescharacteristic, complemented
169#448C2211yescharacteristic, complemented
170#448C2211yescharacteristic, complemented
171#447C2211yescharacteristic
172#447C2211yescharacteristic
173#442C2211yescharacteristic, complemented
174#441C2211yescharacteristic, complemented
175#440C2211yescharacteristic, complemented
176#440C2211yescharacteristic, complemented
177C4×Q16C2211yescharacteristic, complemented
178C4×Q16C2211yescharacteristic, complemented
179C4×SD16C2211yescharacteristic, complemented
180C4×SD16C2211yescharacteristic, complemented
181#436C2211yescharacteristic, complemented
182#436C2211yescharacteristic, complemented
183#435C2211yescharacteristic, complemented
184#435C2211yescharacteristic, complemented
185#435C2211yescharacteristic, complemented
186#435C2211yescharacteristic, complemented
187C8×D4C2211yescharacteristic, complemented
188C8×D4C2211yescharacteristic, complemented
189#432C2211yescharacteristic, complemented
190#431C2211yescharacteristic, complemented
191#419C2211yescharacteristic, complemented
192#418C2211yescharacteristic
193#417C2211yescharacteristic
194#417C2211yescharacteristic, complemented
195#416C2211yescharacteristic
196#416C2211yescharacteristic, complemented
197C2×#103C2211yescharacteristic, complemented
198C2×#102C2211yescharacteristic
199#408C2211yescharacteristic
200#408C2211yescharacteristic
201#408C2211yescharacteristic, complemented
202#408C2211yescharacteristic, complemented
2032−1+4—42no—
2042−1+4—42no—
205H(5,𝔽2)—42no—
206H(5,𝔽2)—42no—
207C2×#41—21no—
208C2×#41—21no—
209C2×#41—21no—
210C2×#41—21no—
211C2×#41C2311yescharacteristic
212C2×#41C2311yescharacteristic
213C2×#41C2311yescharacteristic
214C2×#41C2311yescharacteristic
215C2×#41C2311yescharacteristic
216C2×#41C2311yescharacteristic
217C2×#41C2311yescharacteristic
218C2×#41C2311yescharacteristic
219C2×#41C2311yescharacteristic
220C22×Q8—21no—
221C22×Q8C2311yescharacteristic
222C22×Q8C2311yescharacteristic
223C22×Q8C2311yescharacteristic
224C22×Q8C2311yescharacteristic
225C22×Q8C2311yescharacteristic
226C22×D4—21no—
227C22×D4—21no—
228C22×D4—21no—
229C22×D4C2311yescharacteristic
230C22×D4C2311yescharacteristic
231C22×D4C2311yescharacteristic
232#137—42no—
233#137—42no—
234#137—42no—
235AGL(1,ℤ/8)—42no—
236#135—42no—
237#135—42no—
238C2×Q16—42no—
239C2×Q16C2311yescharacteristic
240C2×Q16C2311yescharacteristic
241C2×Q16C2311yescharacteristic
242C2×Q16C2311yescharacteristic
243C2×Q16C2311yescharacteristic
244C2×Q16C2311yescharacteristic
245C2×Q16C2311yescharacteristic
246C2×Q16C2311yescharacteristic
247C2×Q16C2311yescharacteristic
248C2×SD16—42no—
249C2×SD16C2311yescharacteristic
250C2×SD16C2311yescharacteristic
251C2×SD16C2311yescharacteristic
252C2×SD16C2311yescharacteristic
253C2×SD16C2311yescharacteristic
254C2×SD16C2311yescharacteristic
255C2×SD16C2311yescharacteristic
256C2×SD16C2311yescharacteristic
257C2×SD16C2311yescharacteristic
258C2×SD16C2311yescharacteristic
259C2×SD16C2311yescharacteristic
260C2×SD16C2311yescharacteristic
261C2×D8C2311yescharacteristic
262C2×D8C2311yescharacteristic
263C2×D8C2311yescharacteristic
264C2×M16C2311yescharacteristic
265C2×M16C2311yescharacteristic
266C2×M16C2311yescharacteristic
267C2×M16C2311yescharacteristic
268C22×C8C2311yescharacteristic
269C22×C8C2311yescharacteristic
270C22×C8C2311yescharacteristic
271C22×C8C2311yescharacteristic
272C4⋊Q8—21no—
273C4⋊Q8—21no—
274C4⋊Q8—21no—
275C4⋊Q8—21no—
276C4⋊Q8D411yescharacteristic
277C4⋊Q8C2311yescharacteristic
278C4⋊Q8C2311yescharacteristic
279#127—21no—
280#127D411yescharacteristic
281#126—21no—
282#126—21no—
283#126—21no—
284#125—21no—
285#125—21no—
286#125—21no—
287#125—21no—
288#125C2311yescharacteristic
289#124—21no—
290#124—21no—
291#124—21no—
292#124—21no—
293#124—21no—
294#124—21no—
295#124—21no—
296#124—21no—
297#124—21no—
298#124—21no—
299#124—21no—
300#124—21no—
301#124—21no—
302#124—21no—
303#124D411yescharacteristic
304#124D411yescharacteristic
305#124C2311yescharacteristic
306#124C2311yescharacteristic
307#124C2311yescharacteristic
308#124C2311yescharacteristic
309#124C2311yescharacteristic
310#123—21no—
311#123—21no—
312#123—21no—
313#123—21no—
314#123—21no—
315#123—21no—
316#123—21no—
317#123—21no—
318#123—21no—
319#123—21no—
320#123—21no—
321#123—21no—
322#123—21no—
323#123—21no—
324#123—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⋊Q8—21no—
336C22⋊Q8—21no—
337C22⋊Q8—21no—
338C22⋊Q8C2311yescharacteristic
339C22⋊Q8C2311yescharacteristic
340C22⋊Q8C2311yescharacteristic
341C22⋊Q8C2311yescharacteristic
342C22⋊Q8C2311yescharacteristic
343C22⋊Q8C2311yescharacteristic
344C22⋊Q8C2311yescharacteristic
345C22⋊Q8C2311yescharacteristic
346C22⋊Q8C2311yescharacteristic
347C22⋊Q8C2311yescharacteristic
348C22⋊Q8C2311yescharacteristic
349C22⋊Q8C2311yescharacteristic
350C22⋊Q8C2311yescharacteristic
351#121—21no—
352#121—21no—
353#121—21no—
354#121—21no—
355#121—21no—
356#121—21no—
357#121—21no—
358#121—21no—
359#121—21no—
360#121—21no—
361#121—21no—
362#121—21no—
363#121—21no—
364#121—21no—
365#121—21no—
366#121—21no—
367#121—21no—
368#121—21no—
369#121D411yescharacteristic
370#121D411yescharacteristic
371#121D411yescharacteristic
372#121D411yescharacteristic
373#121C2311yescharacteristic
374#121C2311yescharacteristic
375#121C2311yescharacteristic
376#121C2311yescharacteristic
377#121C2311yescharacteristic
378#121C2311yescharacteristic
379#121C2311yescharacteristic
380#120—21no—
381#120—21no—
382#120—21no—
383#120—21no—
384#120—21no—
385#120—21no—
386C4×Q8—21no—
387C4×Q8C2311yescharacteristic
388C4×Q8C2311yescharacteristic
389C4×Q8C2311yescharacteristic
390C4×Q8C2311yescharacteristic
391C4×Q8C2311yescharacteristic
392C4×D4—21no—
393C4×D4—21no—
394C4×D4—21no—
395C4×D4—21no—
396C4×D4—21no—
397C4×D4—21no—
398C4×D4—21no—
399C4×D4—21no—
400C4×D4—21no—
401C4×D4—21no—
402C4×D4—21no—
403C4×D4C2311yescharacteristic
404C4×D4C2311yescharacteristic
405C4×D4C2311yescharacteristic
406C4×D4C2311yescharacteristic
407C4×D4C2311yescharacteristic
408C4×D4C2311yescharacteristic
409C4×D4C2311yescharacteristic
410#117—21no—
411#117—21no—
412#117—21no—
413#117—21no—
414#117—21no—
415#117—21no—
416#117C2311yescharacteristic
417#117C2311yescharacteristic
418#117C2311yescharacteristic
419C2×C4⋊C4—21no—
420C2×C4⋊C4C2311yescharacteristic
421C2×C4⋊C4C2311yescharacteristic
422C2×C22⋊C4—21no—
423C2×C22⋊C4—21no—
424C2×C22⋊C4—21no—
425C2×C22⋊C4—21no—
426C2×C22⋊C4—21no—
427C2×C22⋊C4—21no—
428C2×C42—21no—
429C2×C42C2311yescharacteristic
430#107C2311yescharacteristic
431#107C2311yescharacteristic
432#107C2311yescharacteristic
433#107C2311yescharacteristic
434#106C2311yescharacteristic
435#106C2311yescharacteristic
436#106C2311yescharacteristic
437#106C2311yescharacteristic
438C4⋊C8C2311yescharacteristic
439C4⋊C8C2311yescharacteristic
440C4⋊C8C2311yescharacteristic
441C4⋊C8C2311yescharacteristic
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#103C2311yescharacteristic
459#103C2311yescharacteristic
460#102C2311yescharacteristic
461#102C2311yescharacteristic
462#102C2311yescharacteristic
463#102C2311yescharacteristic
464#102C2311yescharacteristic
465#102C2311yescharacteristic
466#102C2311yescharacteristic
467#102C2311yescharacteristic
468#102C2311yescharacteristic
469#102C2311yescharacteristic
470#102C2311yescharacteristic
471#102C2311yescharacteristic
472#102C2311yescharacteristic
473#102C2311yescharacteristic
474C22⋊C8C2311yescharacteristic
475C22⋊C8C2311yescharacteristic
476C22⋊C8C2311yescharacteristic
477C22⋊C8C2311yescharacteristic
478C22⋊C8C2311yescharacteristic
479C22⋊C8C2311yescharacteristic
480C22⋊C8C2311yescharacteristic
481C22⋊C8C2311yescharacteristic
482C22⋊C8C2311yescharacteristic
483C22⋊C8C2311yescharacteristic
484C22⋊C8C2311yescharacteristic
485C22⋊C8C2311yescharacteristic
486#97C2311yescharacteristic
487#97C2311yescharacteristic
488C4×C8C2311yescharacteristic
489C4×C8C2311yescharacteristic
490C24—21no—
491C24—21no—
492C24—21no—
493#41—22no—
494#41—22no—
495#41—22no—
496#41—22no—
497#41—22no—
498#41—22no—
499#41—41no—
500#41—41no—
501#41—41no—
502#41—41no—
503#41—41no—
504#41—41no—
505#41—41no—
506#41—41no—
507#41—44no—
508#41—44no—
509#41—41no—
510#41—41no—
511#41—41no—
512#41—41no—
513#41—44no—
514#41—44no—
515C2×Q8—21no—
516C2×Q8—21no—
517C2×Q8—21no—
518C2×Q8—21no—
519C2×Q8—21no—
520C2×Q8—21no—
521C2×Q8—22no—
522C2×Q8—22no—
523C2×Q8—41no—
524C2×Q8—41no—
525C2×Q8—41no—
526C2×Q8—41no—
527C2×Q8—44no—
528C2×Q8—41no—
529C2×Q8—41no—
530C2×Q8—41no—
531C2×Q8—41no—
532C2×Q8C2×D411yescharacteristic
533C2×Q8C2×D411yescharacteristic
534C2×Q8C2411yescharacteristic
535C2×Q8C2411yescharacteristic
536C2×Q8C2411yescharacteristic
537C2×Q8C2411yescharacteristic
538C2×Q8C2411yescharacteristic
539C2×Q8C2411yescharacteristic
540C2×D4—21no—
541C2×D4—22no—
542C2×D4—22no—
543C2×D4—21no—
544C2×D4—21no—
545C2×D4—21no—
546C2×D4—21no—
547C2×D4—21no—
548C2×D4—21no—
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—21no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4—21no—
557C2×D4—21no—
558C2×D4—21no—
559C2×D4—41no—
560C2×D4—41no—
561C2×D4—41no—
562C2×D4—41no—
563C2×D4—44no—
564C2×D4—44no—
565C2×D4—44no—
566C2×D4C2×D411yescharacteristic
567C2×D4C2×D411yescharacteristic
568C2×D4C2×D411yescharacteristic
569C2×D4C2×D411yescharacteristic
570C2×D4C2×D411yescharacteristic
571C2×D4C2×D411yescharacteristic
572C2×D4C2×D411yescharacteristic
573C2×D4C2×D411yescharacteristic
574C2×D4C2×D411yescharacteristic
575C2×D4C2×D411yescharacteristic
576C2×D4C2411yescharacteristic
577C2×D4C2411yescharacteristic
578C2×D4C2411yescharacteristic
579C2×D4C2411yescharacteristic
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4C2×D411yescharacteristic
598C22×C4C2×D411yescharacteristic
599C22×C4C2411yescharacteristic
600C22×C4C2411yescharacteristic
601C22×C4C2411yescharacteristic
602C22×C4C2411yescharacteristic
603C22×C4C2411yescharacteristic
604Q16—22no—
605Q16—22no—
606Q16—22no—
607Q16—41no—
608Q16—41no—
609Q16—41no—
610Q16—41no—
611Q16—41no—
612Q16—41no—
613SD16—22no—
614SD16—22no—
615SD16—22no—
616SD16—22no—
617SD16—41no—
618SD16—41no—
619SD16—41no—
620SD16—41no—
621SD16—41no—
622SD16—41no—
623SD16—41no—
624SD16—41no—
625D8—22no—
626D8—41no—
627D8—41no—
628M16—41no—
629M16—41no—
630M16—41no—
631M16—41no—
632C2×C8—41no—
633C2×C8—41no—
634C2×C8—41no—
635C2×C8—41no—
636C2×C8C2411yescharacteristic
637C2×C8C2411yescharacteristic
638C2×C8C2411yescharacteristic
639C2×C8C2411yescharacteristic
640C2×C8C2411yescharacteristic
641C2×C8C2411yescharacteristic
642C2×C8C2411yescharacteristic
643C2×C8C2411yescharacteristic
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4—21no—
651C4⋊C4—21no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—21no—
655C4⋊C4—21no—
656C4⋊C4—21no—
657C4⋊C4—21no—
658C4⋊C4—21no—
659C4⋊C4—21no—
660C4⋊C4—21no—
661C4⋊C4—21no—
662C4⋊C4—21no—
663C4⋊C4—21no—
664C4⋊C4—21no—
665C4⋊C4—21no—
666C4⋊C4—21no—
667C4⋊C4—21no—
668C4⋊C4—21no—
669C4⋊C4C2×D411yescharacteristic
670C4⋊C4C2×D411yescharacteristic
671C4⋊C4C2×D411yescharacteristic
672C4⋊C4C2×D411yescharacteristic
673C4⋊C4C2411yescharacteristic
674C4⋊C4C2411yescharacteristic
675C4⋊C4C2411yescharacteristic
676C4⋊C4C2411yescharacteristic
677C4⋊C4C2411yescharacteristic
678C4⋊C4C2411yescharacteristic
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⋊C4—21no—
693C22⋊C4—21no—
694C22⋊C4—21no—
695C22⋊C4—21no—
696C22⋊C4—21no—
697C22⋊C4—21no—
698C22⋊C4—21no—
699C22⋊C4—21no—
700C22⋊C4—21no—
701C22⋊C4—21no—
702C22⋊C4—21no—
703C22⋊C4—21no—
704C22⋊C4—21no—
705C22⋊C4—21no—
706C22⋊C4—21no—
707C22⋊C4—21no—
708C22⋊C4—21no—
709C22⋊C4—21no—
710C22⋊C4—21no—
711C22⋊C4—21no—
712C22⋊C4—21no—
713C22⋊C4—21no—
714C22⋊C4—21no—
715C22⋊C4C2×D411yescharacteristic
716C22⋊C4C2×D411yescharacteristic
717C22⋊C4C2×D411yescharacteristic
718C22⋊C4C2×D411yescharacteristic
719C22⋊C4C2×D411yescharacteristic
720C22⋊C4C2×D411yescharacteristic
721C22⋊C4C2×D411yescharacteristic
722C22⋊C4C2×D411yescharacteristic
723C42—21no—
724C42—21no—
725C42—21no—
726C42—21no—
727C42—21no—
728C42—21no—
729C42—21no—
730C42—21no—
731C42C2×D411yescharacteristic
732C42C2×D411yescharacteristic
733C42C2411yescharacteristic
734C42C2411yescharacteristic
735C23—21no—
736C23—21no—
737C23—21no—
738C23—21no—
739C23—42no—
740C23—42no—
741C23—42no—
742C23—81no—
743C23—81no—
744C23—81no—
745C23—81no—
746C23—81no—
747C23—81no—
748C23C22×D411yescharacteristic
749C23C22×D411yescharacteristic
750C23C22×D411yescharacteristic
751C23C22×D411yescharacteristic
752C23C22×D411yescharacteristic
753Q8—21no—
754Q8—21no—
755Q8—21no—
756Q8—21no—
757Q8—21no—
758Q8—21no—
759Q8—21no—
760Q8—21no—
761Q8—21no—
762Q8—21no—
763Q8—21no—
764Q8—41no—
765Q8—41no—
766Q8—42no—
767Q8—42no—
768Q8—42no—
769Q8—81no—
770Q8—81no—
771Q8—81no—
772Q8H(5,𝔽2)12yes—
773D4—24no—
774D4—21no—
775D4—21no—
776D4—21no—
777D4—21no—
778D4—21no—
779D4—21no—
780D4—21no—
781D4—41no—
782D4—41no—
783D4—41no—
784D4—41no—
785D4—41no—
786D4—41no—
787D4—41no—
788D4—41no—
789D4—41no—
790D4—41no—
791D4—42no—
792D4—42no—
793D4—42no—
794D4—42no—
795D4—42no—
796D4—42no—
797D4—42no—
798D4—81no—
799D4—81no—
800D4—81no—
801D4—81no—
802D4—81no—
803D4—81no—
804D4—81no—
805D4—81no—
806D4—81no—
807D4H(5,𝔽2)12yes—
808C2×C4—24no—
809C2×C4—21no—
810C2×C4—21no—
811C2×C4—21no—
812C2×C4—21no—
813C2×C4—21no—
814C2×C4—21no—
815C2×C4—21no—
816C2×C4—21no—
817C2×C4—21no—
818C2×C4—21no—
819C2×C4—21no—
820C2×C4—21no—
821C2×C4—21no—
822C2×C4—21no—
823C2×C4—21no—
824C2×C4—21no—
825C2×C4—21no—
826C2×C4—21no—
827C2×C4—21no—
828C2×C4—21no—
829C2×C4—21no—
830C2×C4—21no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—42no—
834C2×C4—42no—
835C2×C4—42no—
836C2×C4—42no—
837C2×C4—42no—
838C2×C4—42no—
839C2×C4—42no—
840C2×C4—42no—
841C2×C4—81no—
842C2×C4—81no—
843C2×C4—81no—
844C2×C4—81no—
845C2×C4—81no—
846C2×C4—81no—
847C2×C4—81no—
848C2×C4—81no—
849C2×C4C22×D411yescharacteristic
850C2×C4C22×D411yescharacteristic
851C2×C4C22×D411yescharacteristic
852C2×C4C22×D411yescharacteristic
853C2×C4C22×D411yescharacteristic
854C2×C4C22×D411yescharacteristic
855C2×C4C22×D411yescharacteristic
856C2×C4C22×D411yescharacteristic
857C2×C4C22×D411yescharacteristic
858C2×C4C2511yescharacteristic
859C8—21no—
860C8—21no—
861C8—21no—
862C8—21no—
863C8—21no—
864C8—21no—
865C8—21no—
866C8—21no—
867C22—21no—
868C22—21no—
869C22—21no—
870C22—21no—
871C22—21no—
872C22—21no—
873C22—21no—
874C22—21no—
875C22—21no—
876C22—21no—
877C22—21no—
878C22—21no—
879C22—22no—
880C22—21no—
881C22—21no—
882C22—21no—
883C22—41no—
884C22—41no—
885C22—41no—
886C22—41no—
887C22—41no—
888C22—41no—
889C22—41no—
890C22—41no—
891C22—41no—
892C22—41no—
893C22—41no—
894C22—162no—
895C22—162no—
896C22—162no—
897C22C23×D411yescharacteristic
898C4—21no—
899C4—21no—
900C4—21no—
901C4—21no—
902C4—21no—
903C4—22no—
904C4—21no—
905C4—21no—
906C4—21no—
907C4—21no—
908C4—41no—
909C4—41no—
910C4—41no—
911C4—41no—
912C4—41no—
913C4—41no—
914C4—41no—
915C4—41no—
916C4—41no—
917C4—41no—
918C4—41no—
919C4C2×H(5,𝔽2)11yescharacteristic
920C4C2×H(5,𝔽2)11yescharacteristic
921C2—41no—
922C2—41no—
923C2—41no—
924C2—41no—
925C2—41no—
926C2—42no—
927C2—81no—
928C2—81no—
929C2—81no—
930C2#348411yescharacteristic
931C2#358411yescharacteristic
932C2#358611yescharacteristic
subgroupG/H
center, socleC22C23×D4
commutator, Frattini, cosocleC2×C4C25
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ #532 ◁ G
LECSG ▷ C2×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #3547C2semidirect
2. #3500C2semidirect
3. #3327C2semidirect
4. #3323C2semidirect
5. #3321C2semidirect
6. #3319C2semidirect
7. #3316C2semidirect
8. #3314C2semidirect
9. #3300C2semidirect
10. #3296C2semidirect
11. #3285C2semidirect
12. #3282C2semidirect
13. #3277C2semidirect
14. #3275C2semidirect
15. #3270C2semidirect
16. #3269C2semidirect
17. #3267C2semidirect
18. #3266C2semidirect
19. #3215C2semidirect
20. #3211C2semidirect
21. #3202C2semidirect
22. #3201C2semidirect
23. #3200C2semidirect
24. #3198C2semidirect
25. #3111C2semidirect
26. #3107C2semidirect
27. #3013C2semidirect
28. #3012C2semidirect
29. #3011C2semidirect
30. #3009C2semidirect
31. #2981C2semidirect
35. C2×#137C22semidirect
36. C2×#137C22semidirect
39. C2×#135C22semidirect
40. C22×Q16C22semidirect
45. #555C22semidirect
46. #554C22semidirect
48. #552C22semidirect
49. #552C22semidirect
50. D4×Q8C22semidirect
55. #548C22semidirect
56. #548C22semidirect
57. #547C22semidirect
71. #537C22semidirect
75. #536C22semidirect
78. #533C22semidirect
81. #529C22semidirect
85. #497C22semidirect
86. #497C22semidirect
87. #495C22semidirect
88. #495C22semidirect
89. #489C22semidirect
90. #489C22semidirect
91. #488C22semidirect
92. #488C22semidirect
93. #485C22semidirect
94. #485C22semidirect
95. #485C22semidirect
96. #485C22semidirect
97. #485C22semidirect
98. #484C22semidirect
99. #483C22semidirect
100. #482C22semidirect
101. #482C22semidirect
102. #482C22semidirect
103. #481C22semidirect
104. #480C22semidirect
105. #479C22semidirect
106. #478C22semidirect
107. #475C22semidirect
108. #474C22semidirect
109. #470C22semidirect
110. #470C22semidirect
111. #470C22semidirect
112. #469C22semidirect
113. #468C22semidirect
114. #468C22semidirect
115. #468C22semidirect
116. #468C22semidirect
117. #467C22semidirect
118. #467C22semidirect
119. #467C22semidirect
120. #466C22semidirect
121. #465C22semidirect
122. #465C22semidirect
123. #465C22semidirect
124. #465C22semidirect
125. #464C22semidirect
126. #464C22semidirect
127. #464C22semidirect
128. #464C22semidirect
129. #464C22semidirect
130. #464C22semidirect
131. #464C22semidirect
132. #463C22semidirect
133. #463C22semidirect
134. #463C22semidirect
135. #462C22semidirect
136. #461C22semidirect
143. #452C22semidirect
144. #452C22semidirect
145. #452C22semidirect
146. #452C22semidirect
147. #452C22semidirect
148. #451C22semidirect
149. #451C22semidirect
150. #451C22semidirect
151. #451C22semidirect
152. #451C22semidirect
153. #451C22semidirect
154. #451C22semidirect
155. #451C22semidirect
164. #449C22semidirect
165. #449C22semidirect
166. #449C22semidirect
167. #448C22semidirect
168. #448C22semidirect
169. #448C22semidirect
170. #448C22semidirect
173. #442C22semidirect
174. #441C22semidirect
175. #440C22semidirect
176. #440C22semidirect
177. C4×Q16C22semidirect
178. C4×Q16C22semidirect
179. C4×SD16C22semidirect
180. C4×SD16C22semidirect
181. #436C22semidirect
182. #436C22semidirect
183. #435C22semidirect
184. #435C22semidirect
185. #435C22semidirect
186. #435C22semidirect
187. C8×D4C22semidirect
188. C8×D4C22semidirect
189. #432C22semidirect
190. #431C22semidirect
191. #419C22semidirect
194. #417C22semidirect
196. #416C22semidirect
197. C2×#103C22semidirect
201. #408C22semidirect
202. #408C22semidirect

Maximal subgroups

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

subgroupindex
#35472
#35002
#33272
#33232
#33212
#33192
#33162
#33142
#33002
#32962
#32852
#32822
#32772
#32752
#32702
#32692
#32672
#32662
#32152
#32112
#32022
#32012
#32002
#31982
#31112
#31072
#30132
#30122
#30112
#30092
#29812