Finite Group Databasebeta

← #6683988

Subgroups — #6683988

Order 512.

2024 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3230C211yesmaximal, characteristic, complemented
2C22×#500C211yesmaximal, characteristic, complemented
3#36129C211yesmaximal, characteristic
4D4×C4⋊Q8C211yesmaximal, characteristic
5#33043C211yesmaximal, characteristic, complemented
6#30957C214yesmaximal, complemented
7#30779C214yesmaximal, complemented
8#30279C211yesmaximal, characteristic, complemented
9#29878C211yesmaximal, characteristic, complemented
10#28689C211yesmaximal, characteristic, complemented
11#28656C211yesmaximal, characteristic, complemented
12#26342C214yesmaximal, complemented
13#26132C214yesmaximal
14#25902C211yesmaximal, characteristic, complemented
15#25813C211yesmaximal, characteristic, complemented
16#25813C211yesmaximal, characteristic, complemented
17#25674C211yesmaximal, characteristic, complemented
18#22248C211yesmaximal, characteristic, complemented
19#21101C211yesmaximal, characteristic
20C2×D4×Q8—21no—
21C2×#533C2211yescharacteristic
22C22×C4⋊Q8C2211yescharacteristic
23C22×C4⋊Q8C2211yescharacteristic
24C22×C4⋊Q8C2211yescharacteristic
25#3230—28no—
26C2×#500—28no—
27C2×#500C2211yescharacteristic
28C2×#500C2211yescharacteristic
29C2×#500C2214yes—
30C2×#500C2211yescharacteristic
31C2×#500C2211yescharacteristic
32C2×#500C2211yescharacteristic
33C2×#500C2211yescharacteristic
34C2×#487C2211yescharacteristic
35C2×#487C2211yescharacteristic
36C2×#487C2211yescharacteristic
37C2×#484C2214yes—
38C2×#477C2214yes—
39C2×#431C2211yescharacteristic
40C22×#107C2214yes—
41C22×C4×C8C2211yescharacteristic
42#2868C2211yescharacteristic
43#2862C2211yescharacteristic
44#2857C2211yescharacteristic
45#2857C2211yescharacteristic
46#2857C2211yescharacteristic
47#2857C2211yescharacteristic
48#2551—21no—
49#2551C2212yes—
50#2550—21no—
51#2546—21no—
52#2492C2212yes—
53#2451C2212yes—
54#2446—21no—
55#2442—21no—
56#2440—21no—
57#2440—21no—
58#2440C2212yes—
59#2440C2212yes—
60#2439—21no—
61#2434—21no—
62#2434—21no—
63#2429—21no—
64#2417C2212yes—
65#2409—21no—
66#2360C2212yes—
67#2352—21no—
68D4×C4⋊C4—21no—
69D4×C4⋊C4C2212yes—
70Q8×C22⋊C4—21no—
71C4×C4⋊Q8C2211yescharacteristic
72C4×C4⋊Q8C2211yescharacteristic
73C42×D4C2211yescharacteristic
74#2095C2214yes—
75#2095C2214yes—
76#2087C2214yes—
77#2083C2214yes—
78#2076C2214yes—
79#2068C2214yes—
80#2057C2214yes—
81#2057C2214yes—
82#2036C2214yes—
83#2024C2214yes—
84#1990C2211yescharacteristic
85#1990C2211yescharacteristic
86#1990C2211yescharacteristic
87#1990C2211yescharacteristic
88#1990C2211yescharacteristic
89#1956C2211yescharacteristic
90#1947C2214yes—
91#1933C2214yes—
92#1928C2214yes—
93#1923C2212yes—
94#1921C2214yes—
95#1921C2214yes—
96#1916C2212yes—
97#1892C2214yes—
98#1872C2214yes—
99#1869C2212yes—
100#1863C2214yes—
101#1852C2214yes—
102#1852C2214yes—
103#1850C2212yes—
104#1834C2211yescharacteristic
105C4×C4⋊C8C2211yescharacteristic
106C4×C22⋊C8C2211yescharacteristic
107C4×C22⋊C8C2211yescharacteristic
108#1744C2211yescharacteristic
109C23×Q8—21no—
110C23×Q8—21no—
111C23×Q8—21no—
112C23×C8C2312yes—
113D4×Q8—48no—
114#533—24no—
115#533—42no—
116C2×C4⋊Q8—22no—
117C2×C4⋊Q8—24no—
118C2×C4⋊Q8—24no—
119C2×C4⋊Q8—24no—
120C2×C4⋊Q8—21no—
121C2×C4⋊Q8—21no—
122C2×C4⋊Q8—21no—
123C2×C4⋊Q8—21no—
124C2×C4⋊Q8—21no—
125C2×C4⋊Q8—21no—
126C2×C4⋊Q8—21no—
127C2×C4⋊Q8—21no—
128C2×C4⋊Q8—42no—
129C2×C4⋊Q8—42no—
130C2×C4⋊Q8—42no—
131C2×C4⋊Q8C2311yescharacteristic
132C2×C4⋊Q8C2311yescharacteristic
133C2×C4⋊Q8C2311yescharacteristic
134C2×C4⋊Q8C2311yescharacteristic
135C2×C4⋊Q8C2312yes—
136C2×C4⋊Q8C2312yes—
137C2×C4⋊Q8C2312yes—
138C2×C4⋊Q8C2311yescharacteristic
139C2×C4⋊Q8C2311yescharacteristic
140C2×#125—21no—
141C2×C22⋊Q8—21no—
142C2×C22⋊Q8—21no—
143C2×C22⋊Q8—21no—
144C2×C22⋊Q8—21no—
145C2×C22⋊Q8—22no—
146C2×C22⋊Q8—22no—
147C2×C22⋊Q8C2312yes—
148C2×C22⋊Q8C2312yes—
149C2×C4×Q8—21no—
150C2×C4×Q8—21no—
151C2×C4×Q8—21no—
152C2×C4×Q8C2312yes—
153C2×C4×D4—22no—
154C2×C4×D4D411yescharacteristic
155C2×C4×D4D411yescharacteristic
156C2×C4×D4C2311yescharacteristic
157C2×#117—21no—
158C22×C4⋊C4—21no—
159C22×C4⋊C4—21no—
160C22×C4⋊C4—21no—
161C22×C4⋊C4C2312yes—
162C22×C4⋊C4C2312yes—
163C22×C4⋊C4C2312yes—
164C22×C42C2311yescharacteristic
165C22×C42C2311yescharacteristic
166#500—24no—
167#500—24no—
168#500—24no—
169#500—216no—
170#500—24no—
171#500—42no—
172#500D418yescomplemented
173#487—24no—
174#487—24no—
175#487—42no—
176#484—216no—
177#477—216no—
178#431—24no—
179C2×#107—216no—
180C2×#107C2314yes—
181C2×#107C2314yes—
182C2×#107C2314yes—
183C2×#107C2314yes—
184C2×#107C2314yes—
185C2×#107C2314yes—
186C2×C4⋊C8C2312yes—
187C2×C4⋊C8C2312yes—
188C2×#103C2314yes—
189C2×#103C2314yes—
190C2×#103C2314yes—
191C2×#103C2314yes—
192C2×C22⋊C8C2312yes—
193C2×C22⋊C8C2312yes—
194C2×C22⋊C8C2312yes—
195C2×C4×C8—24no—
196C2×C4×C8C2312yes—
197C2×C4×C8C2311yescharacteristic
198C2×C4×C8C2311yescharacteristic
199C2×C4×C8C2311yescharacteristic
200C2×C4×C8C2311yescharacteristic
201#400—22no—
202#398—22no—
203#398—22no—
204#398—22no—
205#398—22no—
206#396—22no—
207#395—22no—
208#395—22no—
209#395—22no—
210#395—22no—
211#395—22no—
212#393—22no—
213#391—21no—
214#391—21no—
215#391—21no—
216#391—21no—
217#391—21no—
218#391—21no—
219#391—21no—
220#391—22no—
221#391—22no—
222#391C2312yes—
223#391C2312yes—
224#391C2312yes—
225#389—22no—
226#389—22no—
227#389—21no—
228#389—21no—
229#389—21no—
230#389—21no—
231#389—21no—
232#389—21no—
233#389—21no—
234#389—22no—
235#389C2312yes—
236#389C2312yes—
237#389C2312yes—
238#389C2312yes—
239#389C2312yes—
240#388—22no—
241#387—22no—
242#387—22no—
243#386—22no—
244#385—22no—
245#385—22no—
246#385—22no—
247#385—22no—
248#385—22no—
249#384—21no—
250#384—21no—
251#384C2311yescharacteristic
252#384C2311yescharacteristic
253#384C2312yes—
254#384C2312yes—
255#382—21no—
256#382—21no—
257#380—21no—
258#380—21no—
259#380—21no—
260#380—21no—
261#380—21no—
262#380—22no—
263#380C2312yes—
264#380C2312yes—
265#380C2312yes—
266C4×C4⋊C4—21no—
267C4×C4⋊C4—21no—
268C4×C4⋊C4D411yescharacteristic
269C4×C4⋊C4D411yescharacteristic
270C4×C4⋊C4C2312yes—
271C4×C4⋊C4C2312yes—
272C4×C4⋊C4C2311yescharacteristic
273C4×C22⋊C4—22no—
274C4×C22⋊C4D411yescharacteristic
275C4×C22⋊C4D411yescharacteristic
276C4×C22⋊C4D411yescharacteristic
277C4×C22⋊C4D411yescharacteristic
278C4×C22⋊C4C2311yescharacteristic
279C4×C22⋊C4C2311yescharacteristic
280C43C2311yescharacteristic
281#340C2314yes—
282#340C2314yes—
283#340C2314yes—
284#340C2314yes—
285#340C2314yes—
286#340C2314yes—
287#336C2312yes—
288#336C2312yes—
289#336C2312yes—
290#336C2312yes—
291#336C2312yes—
292C22×Q8—21no—
293C22×Q8—21no—
294C22×Q8—21no—
295C22×Q8—21no—
296C22×Q8—21no—
297C22×Q8—22no—
298C22×Q8—22no—
299C22×Q8—22no—
300C22×Q8—44no—
301C22×Q8—44no—
302C22×Q8—44no—
303C22×Q8—44no—
304C22×Q8—44no—
305C22×Q8—44no—
306C22×Q8—82no—
307C22×Q8—82no—
308C22×Q8—82no—
309C22×Q8C2412yes—
310C22×D4C2×D411yescharacteristic
311C23×C4—22no—
312C23×C4—22no—
313C23×C4—22no—
314C23×C4C2×D411yescharacteristic
315C23×C4C2×D411yescharacteristic
316C23×C4C2×D411yescharacteristic
317C23×C4C2×D411yescharacteristic
318C23×C4C2411yescharacteristic
319C23×C4C2411yescharacteristic
320C22×C8—24no—
321C22×C8—24no—
322C22×C8—24no—
323C22×C8C2412yes—
324C22×C8C2412yes—
325C22×C8C2412yes—
326C22×C8C2412yes—
327C4⋊Q8—24no—
328C4⋊Q8—24no—
329C4⋊Q8—24no—
330C4⋊Q8—22no—
331C4⋊Q8—22no—
332C4⋊Q8—22no—
333C4⋊Q8—22no—
334C4⋊Q8—22no—
335C4⋊Q8—22no—
336C4⋊Q8—22no—
337C4⋊Q8—22no—
338C4⋊Q8—22no—
339C4⋊Q8—22no—
340C4⋊Q8—42no—
341C4⋊Q8—42no—
342C4⋊Q8—42no—
343C4⋊Q8—44no—
344C4⋊Q8—44no—
345C4⋊Q8—44no—
346C4⋊Q8—44no—
347C4⋊Q8—44no—
348C4⋊Q8—44no—
349C4⋊Q8—44no—
350C4⋊Q8—48no—
351C4⋊Q8—82no—
352C4⋊Q8C2×D414yes—
353C4⋊Q8C2×D414yes—
354#125—44no—
355C22⋊Q8—28no—
356C22⋊Q8—24no—
357C22⋊Q8—48no—
358C22⋊Q8—48no—
359C22⋊Q8—42no—
360C22⋊Q8—44no—
361C22⋊Q8—44no—
362C22⋊Q8—44no—
363C22⋊Q8—82no—
364C4×Q8—24no—
365C4×Q8—42no—
366C4×Q8—44no—
367C4×Q8—44no—
368C4×Q8—82no—
369C4×D4—24no—
370C4×D4—24no—
371C4×D4—48no—
372C4×D4Q1618yes—
373#117—44no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—24no—
377C2×C4⋊C4—24no—
378C2×C4⋊C4—24no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—22no—
383C2×C4⋊C4—22no—
384C2×C4⋊C4—22no—
385C2×C4⋊C4—22no—
386C2×C4⋊C4—22no—
387C2×C4⋊C4—22no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—22no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—22no—
392C2×C4⋊C4—21no—
393C2×C4⋊C4—21no—
394C2×C4⋊C4—22no—
395C2×C4⋊C4—22no—
396C2×C4⋊C4—22no—
397C2×C4⋊C4—22no—
398C2×C4⋊C4—22no—
399C2×C4⋊C4—22no—
400C2×C4⋊C4—21no—
401C2×C4⋊C4—21no—
402C2×C4⋊C4—22no—
403C2×C4⋊C4—22no—
404C2×C4⋊C4—22no—
405C2×C4⋊C4—22no—
406C2×C4⋊C4—42no—
407C2×C4⋊C4—42no—
408C2×C4⋊C4—42no—
409C2×C4⋊C4—44no—
410C2×C4⋊C4—44no—
411C2×C4⋊C4—44no—
412C2×C4⋊C4C2×D411yescharacteristic
413C2×C4⋊C4C2×D411yescharacteristic
414C2×C4⋊C4C2×D411yescharacteristic
415C2×C4⋊C4C2412yes—
416C2×C4⋊C4C2412yes—
417C2×C4⋊C4C2412yes—
418C2×C4⋊C4C2412yes—
419C2×C4⋊C4C2412yes—
420C2×C4⋊C4C2412yes—
421C2×C4⋊C4C2412yes—
422C2×C22⋊C4—22no—
423C2×C22⋊C4—22no—
424C2×C22⋊C4—22no—
425C2×C22⋊C4—22no—
426C2×C22⋊C4—22no—
427C2×C22⋊C4C2×D411yescharacteristic
428C2×C22⋊C4C2×D411yescharacteristic
429C2×C22⋊C4C2×D411yescharacteristic
430C2×C22⋊C4C2×D411yescharacteristic
431C2×C22⋊C4C2×D411yescharacteristic
432C2×C22⋊C4C2×D411yescharacteristic
433C2×C42—22no—
434C2×C42—22no—
435C2×C42—22no—
436C2×C42—22no—
437C2×C42—22no—
438C2×C42—22no—
439C2×C42—22no—
440C2×C42C2×D411yescharacteristic
441C2×C42C2×D411yescharacteristic
442C2×C42C2×D411yescharacteristic
443C2×C42C2×D411yescharacteristic
444C2×C42C2×D411yescharacteristic
445C2×C42C2×D411yescharacteristic
446C2×C42C2×D411yescharacteristic
447C2×C42C2×D411yescharacteristic
448C2×C42C2411yescharacteristic
449C2×C42C2411yescharacteristic
450C2×C42C2411yescharacteristic
451C2×C42C2411yescharacteristic
452C2×C42C2411yescharacteristic
453#107—28no—
454#107—28no—
455#107—28no—
456#107—28no—
457#107—44no—
458#107C2×D4116yes—
459C4⋊C8—24no—
460C4⋊C8—24no—
461#103—28no—
462#103—28no—
463#103—28no—
464#103—44no—
465C22⋊C8—24no—
466C22⋊C8—24no—
467C22⋊C8—24no—
468C4×C8—24no—
469C4×C8—22no—
470C4×C8—22no—
471C4×C8—22no—
472C4×C8C2×D414yes—
473#95—22no—
474#95—22no—
475#95—22no—
476#95—22no—
477#95—22no—
478#95—22no—
479#95—22no—
480#95—22no—
481#95—22no—
482#95—22no—
483#95—22no—
484#95—22no—
485#95—22no—
486#95—22no—
487#95—22no—
488#95—22no—
489#95C2×D411yescharacteristic
490#95C2×D411yescharacteristic
491#95C2×D411yescharacteristic
492#95C2×D411yescharacteristic
493#95C2×D411yescharacteristic
494#95C2×D411yescharacteristic
495C24C22×D411yescharacteristic
496C24C22×D411yescharacteristic
497C2×Q8—24no—
498C2×Q8—24no—
499C2×Q8—22no—
500C2×Q8—22no—
501C2×Q8—24no—
502C2×Q8—24no—
503C2×Q8—44no—
504C2×Q8—44no—
505C2×Q8—44no—
506C2×Q8—44no—
507C2×Q8—42no—
508C2×Q8—42no—
509C2×Q8—42no—
510C2×Q8—42no—
511C2×Q8—42no—
512C2×Q8—44no—
513C2×Q8—42no—
514C2×Q8—42no—
515C2×Q8—44no—
516C2×Q8—42no—
517C2×Q8—42no—
518C2×Q8—42no—
519C2×Q8—42no—
520C2×Q8—42no—
521C2×Q8—42no—
522C2×Q8—82no—
523C2×Q8—82no—
524C2×Q8—82no—
525C2×Q8—816no—
526C2×Q8—816no—
527C2×Q8—816no—
528C2×D4—22no—
529C2×D4—22no—
530C2×D4C2×Q1614yes—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—44no—
556C22×C4—44no—
557C22×C4—44no—
558C22×C4—44no—
559C22×C4—44no—
560C22×C4—44no—
561C22×C4—82no—
562C22×C4—82no—
563C22×C4—82no—
564C22×C4C2×Q1614yes—
565C22×C4C2×Q1614yes—
566C22×C4AGL(1,ℤ/8)14yes—
567C22×C4C22×D411yescharacteristic
568C22×C4C22×D411yescharacteristic
569C22×C4C22×D411yescharacteristic
570C22×C4C22×D411yescharacteristic
571C22×C4C22×D411yescharacteristic
572C22×C4C22×D411yescharacteristic
573C22×C4C22×D411yescharacteristic
574C22×C4C22×D411yescharacteristic
575C22×C4C22×D411yescharacteristic
576C22×C4C22×D411yescharacteristic
577C22×C4C22×D411yescharacteristic
578C22×C4C22×D411yescharacteristic
579C22×C42−1+414yes—
580C22×C4C2511yescharacteristic
581C2×C8—216no—
582C2×C8—22no—
583C2×C8—22no—
584C2×C8—22no—
585C2×C8—22no—
586C2×C8—22no—
587C2×C8—22no—
588C2×C8—22no—
589C2×C8—22no—
590C2×C8—22no—
591C2×C8—22no—
592C2×C8C22×D414yes—
593C2×C82−1+414yes—
594C4⋊C4—22no—
595C4⋊C4—24no—
596C4⋊C4—24no—
597C4⋊C4—22no—
598C4⋊C4—22no—
599C4⋊C4—22no—
600C4⋊C4—22no—
601C4⋊C4—22no—
602C4⋊C4—22no—
603C4⋊C4—22no—
604C4⋊C4—22no—
605C4⋊C4—22no—
606C4⋊C4—24no—
607C4⋊C4—24no—
608C4⋊C4—44no—
609C4⋊C4—44no—
610C4⋊C4—44no—
611C4⋊C4—44no—
612C4⋊C4—44no—
613C4⋊C4—44no—
614C4⋊C4—44no—
615C4⋊C4—44no—
616C4⋊C4—44no—
617C4⋊C4—44no—
618C4⋊C4—44no—
619C4⋊C4—44no—
620C4⋊C4—44no—
621C4⋊C4—42no—
622C4⋊C4—42no—
623C4⋊C4—42no—
624C4⋊C4—42no—
625C4⋊C4—42no—
626C4⋊C4—42no—
627C4⋊C4—44no—
628C4⋊C4—42no—
629C4⋊C4—42no—
630C4⋊C4—42no—
631C4⋊C4—82no—
632C4⋊C4—82no—
633C4⋊C4—82no—
634C4⋊C4—82no—
635C4⋊C4C2×Q1614yes—
636C4⋊C4C22×D414yes—
637C4⋊C4C22×D414yes—
638C22⋊C4—22no—
639C22⋊C4—22no—
640C22⋊C4—22no—
641C22⋊C4—22no—
642C22⋊C4—44no—
643C22⋊C4—44no—
644C22⋊C4—44no—
645C22⋊C4—44no—
646C22⋊C4—82no—
647C22⋊C4C2×Q1614yes—
648C22⋊C4C2×Q1614yes—
649C42—22no—
650C42—22no—
651C42—22no—
652C42—22no—
653C42—22no—
654C42—22no—
655C42—22no—
656C42—21no—
657C42—21no—
658C42—21no—
659C42—21no—
660C42—22no—
661C42—22no—
662C42—44no—
663C42—44no—
664C42—82no—
665C42C2×Q1614yes—
666C42C22×D412yes—
667C42H(5,𝔽2)12yes—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—21no—
677C23—21no—
678C23#53612yes—
679C23C22×Q1612yes—
680C23C22×Q1612yes—
681C23C2×AGL(1,ℤ/8)12yes—
682C23C23×D411yescharacteristic
683Q8—48no—
684Q8—48no—
685Q8—44no—
686Q8—44no—
687Q8—88no—
688Q8—88no—
689Q8—88no—
690Q8—84no—
691Q8—84no—
692Q8—84no—
693D4—28no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—24no—
707C2×C4—28no—
708C2×C4—28no—
709C2×C4—28no—
710C2×C4—24no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—24no—
716C2×C4—24no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—44no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—88no—
751C2×C4—88no—
752C2×C4—88no—
753C2×C4#53612yes—
754C2×C4D4212yes—
755C2×C4D4212yes—
756C2×C4C22×Q1612yes—
757C2×C4C22×Q1612yes—
758C2×C4C22×Q1612yes—
759C2×C4C22×Q1612yes—
760C2×C4C22×Q1612yes—
761C2×C4C2×AGL(1,ℤ/8)12yes—
762C2×C4C2×AGL(1,ℤ/8)12yes—
763C2×C4#57612yes—
764C2×C4#57812yes—
765C2×C4C23×D411yescharacteristic
766C2×C4C2×H(5,𝔽2)11yescharacteristic
767C2×C4C2×2−1+412yes—
768C2×C4C2×2−1+412yes—
769C8—24no—
770C8—24no—
771C8—42no—
772C8—42no—
773C22—22no—
774C22—22no—
775C22—22no—
776C22—22no—
777C22—22no—
778C22—22no—
779C22—22no—
780C22—22no—
781C22—22no—
782C22—41no—
783C22—41no—
784C22—41no—
785C22—41no—
786C22#323014yescomplemented
787C22C2×#53611yescharacteristic
788C22C2×D4211yescharacteristic
789C22#349911yescharacteristic
790C22C23×Q1611yescharacteristic
791C22C22×AGL(1,ℤ/8)11yescharacteristic
792C22C2×#57611yescharacteristic
793C22C2×#57811yescharacteristic
794C4—22no—
795C4—22no—
796C4—22no—
797C4—22no—
798C4—22no—
799C4—22no—
800C4—41no—
801C4—41no—
802C4—41no—
803C4—44no—
804C4—44no—
805C4—41no—
806C4—82no—
807C4—82no—
808C4—82no—
809C4—82no—
810C4—82no—
811C4—82no—
812C4#326414yes—
813C4D4×Q1614yes—
814C4#348612yes—
815C4#355212yes—
816C2—24no—
817C2—42no—
818C2#3767511yescharacteristic
819C2C2×#323011yescharacteristic
820C2#6088011yescharacteristic
821C2C2×#326411yescharacteristic
822C2C2×D4×Q1611yescharacteristic
823C2#6247211yescharacteristic
824C2#6247911yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC22×D4C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C42×D4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3230C2semidirect
2. C22×#500C2semidirect
5. #33043C2semidirect
6. #30957C2semidirect
7. #30779C2semidirect
8. #30279C2semidirect
9. #29878C2semidirect
10. #28689C2semidirect
11. #28656C2semidirect
12. #26342C2semidirect
14. #25902C2semidirect
15. #25813C2semidirect
16. #25813C2semidirect
17. #25674C2semidirect
18. #22248C2semidirect
172. #500D4semidirect
786. C22#3230semidirect

Maximal subgroups

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

subgroupindex
C2×#32302
C22×#5002
#361292
D4×C4⋊Q82
#330432
#309572
#307792
#302792
#298782
#286892
#286562
#263422
#261322
#259022
#258132
#256742
#222482
#211012