Finite Group Databasebeta

← #188456

Subgroups — #188456

Order 512.

1844 conjugacy classes of subgroups.

The subgroup lattice has 843 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#525C211yesmaximal, characteristic
2#20626C211yesmaximal, characteristic, complemented
3C2×#1504C212yesmaximal
4C2×C4⋊#95C211yesmaximal, characteristic, complemented
5#8578C212yesmaximal, complemented
6#8577C212yesmaximal, complemented
7#8572C212yesmaximal, complemented
8#8571C212yesmaximal, complemented
9#8020C212yesmaximal, complemented
10C2×#525C2211yescharacteristic
11C2×C4×#41C411yescharacteristic, complemented
12C23×C4⋊C4—21no—
13C23×C42C2211yescharacteristic
14C2×#423—21no—
15C2×#407C2212yes—
16C4×C22⋊Q8C411yescharacteristic, complemented
17C4×C22⋊Q8C411yescharacteristic, complemented
18C4×C22⋊Q8C2211yescharacteristic
19C4×C22⋊Q8C2211yescharacteristic
20C4×#123—21no—
21C4×#123—21no—
22C4×#121C411yescharacteristic, complemented
23C4×#121C411yescharacteristic, complemented
24C4×#121C2211yescharacteristic
25C4×#121C2211yescharacteristic
26C4×#120—21no—
27C4×#120—21no—
28#2297C411yescharacteristic, complemented
29#2296C411yescharacteristic, complemented
30#2290—21no—
31#2290—21no—
32#2280C2211yescharacteristic
33C42×D4—21no—
34C42×D4—21no—
35C4×#117C411yescharacteristic, complemented
36C22×#95—21no—
37C22×#95C2212yes—
38#1797—21no—
39#1797—21no—
40#1797C2212yes—
41#1797C2212yes—
42#1728—21no—
43#1504—28no—
44C2×#328C2214yes—
45C2×#327C2214yes—
46C4⋊#95—21no—
47C4⋊#95—21no—
48C4⋊#95C2212yes—
49C4⋊#95C2212yes—
50#1294C2214yes—
51#1294C2214yes—
52C22×#41C2×C411yescharacteristic
53C24×C4—22no—
54C24×C4D411yescharacteristic
55C24×C4D411yescharacteristic
56C24×C4C2311yescharacteristic
57C22×M16—22no—
58#525—22no—
59#525—22no—
60#525D414yes—
61#525Q814yes—
62C2×#123—21no—
63C2×C22⋊Q8C2×C411yescharacteristic
64C2×C22⋊Q8C2311yescharacteristic
65C2×#121C2×C411yescharacteristic
66C2×#121C2311yescharacteristic
67C2×#120—21no—
68C4×#41—44no—
69C2×C4×Q8C2×C411yescharacteristic, complemented
70C2×C4×Q8C2×C411yescharacteristic, complemented
71C2×C4×D4—21no—
72C2×C4×D4—21no—
73C2×C4×D4—21no—
74C2×C4×D4—21no—
75C2×C4×D4—21no—
76C2×C4×D4—21no—
77C2×C4×D4—21no—
78C2×C4×D4—21no—
79C2×C4×D4C2×C411yescharacteristic, complemented
80C2×C4×D4C2×C411yescharacteristic, complemented
81C2×#117—21no—
82C2×#117C2×C411yescharacteristic
83C2×#117C2×C411yescharacteristic
84C2×#117C2×C411yescharacteristic
85C22×C4⋊C4—28no—
86C22×C4⋊C4—22no—
87C22×C4⋊C4—22no—
88C22×C4⋊C4—44no—
89C22×C4⋊C4—44no—
90C22×C42—21no—
91C22×C42—44no—
92C22×C42C2×C411yescharacteristic
93C22×C42C2×C411yescharacteristic
94C22×C42C2×C411yescharacteristic
95C22×C42C2×C411yescharacteristic
96C22×C42D411yescharacteristic
97C22×C42D411yescharacteristic
98C22×C42D411yescharacteristic
99C22×C42D411yescharacteristic
100C22×C42D411yescharacteristic
101C22×C42D411yescharacteristic
102C22×C42C2311yescharacteristic
103C22×C42C2311yescharacteristic
104#423—44no—
105C2×C4⋊C8—22no—
106C2×C4⋊C8—22no—
107#407—24no—
108#407—24no—
109C2×C22⋊C8—22no—
110C2×C22⋊C8C2314yes—
111#391C2×C411yescharacteristic, complemented
112#391C2×C411yescharacteristic, complemented
113#390C2×C411yescharacteristic, complemented
114#390C2×C411yescharacteristic, complemented
115#389C2×C411yescharacteristic, complemented
116#389C2×C411yescharacteristic, complemented
117#389C2×C411yescharacteristic, complemented
118#389C2×C411yescharacteristic, complemented
119#388—21no—
120#388—21no—
121#388—21no—
122#388—21no—
123#387—21no—
124#387—21no—
125#387—21no—
126#387—21no—
127#386—21no—
128#386—21no—
129#386—21no—
130#386—21no—
131#386—21no—
132#386—21no—
133#385—21no—
134#385—21no—
135#385—21no—
136#385—21no—
137#385—21no—
138#385—21no—
139#381—21no—
140#380C2×C411yescharacteristic
141#380C2×C411yescharacteristic
142#380C2311yescharacteristic
143#380C2311yescharacteristic
144#379—21no—
145C4×C4⋊C4—21no—
146C4×C4⋊C4—21no—
147C4×C4⋊C4—21no—
148C4×C4⋊C4—21no—
149C4×C4⋊C4—21no—
150C4×C4⋊C4—21no—
151C4×C4⋊C4C2×C411yescharacteristic, complemented
152C4×C4⋊C4C2×C411yescharacteristic, complemented
153C4×C4⋊C4C2×C411yescharacteristic, complemented
154C4×C4⋊C4C2×C411yescharacteristic, complemented
155C4×C22⋊C4—21no—
156C4×C22⋊C4—21no—
157C4×C22⋊C4—21no—
158C4×C22⋊C4—21no—
159C4×C22⋊C4—21no—
160C4×C22⋊C4—21no—
161C4×C22⋊C4—21no—
162C4×C22⋊C4—21no—
163C4×C22⋊C4—21no—
164C4×C22⋊C4—21no—
165C4×C22⋊C4—21no—
166C4×C22⋊C4—21no—
167C4×C22⋊C4—21no—
168C4×C22⋊C4—21no—
169#376—21no—
170C2×#95—24no—
171C2×#95—24no—
172C2×#95—22no—
173C2×#95—22no—
174C2×#95—22no—
175C2×#95—44no—
176C2×#95C2314yes—
177C43—21no—
178#336—22no—
179#336—22no—
180#328—28no—
181#327—28no—
182C25C2×D411yescharacteristic
183C2×#41—22no—
184C2×#41—42no—
185C2×#41—42no—
186C2×#41C4⋊C414yescomplemented
187C22×Q8C22×C411yescharacteristic
188C22×D4—21no—
189C22×D4—21no—
190C22×D4—21no—
191C22×D4C22×C411yescharacteristic
192C23×C4—24no—
193C23×C4—24no—
194C23×C4—22no—
195C23×C4—22no—
196C23×C4—21no—
197C23×C4—22no—
198C23×C4—22no—
199C23×C4—28no—
200C23×C4—24no—
201C23×C4—21no—
202C23×C4—21no—
203C23×C4—42no—
204C23×C4—42no—
205C23×C4—42no—
206C23×C4—42no—
207C23×C4—44no—
208C23×C4—44no—
209C23×C4—44no—
210C23×C4—44no—
211C23×C4—44no—
212C23×C4—44no—
213C23×C4C22⋊C411yescharacteristic
214C23×C4C22⋊C411yescharacteristic
215C23×C4C22⋊C411yescharacteristic
216C23×C4C22⋊C411yescharacteristic
217C23×C4C22⋊C411yescharacteristic
218C23×C4C22⋊C411yescharacteristic
219C23×C4C22⋊C411yescharacteristic
220C23×C4C22⋊C411yescharacteristic
221C23×C4C22×C411yescharacteristic
222C23×C4C22×C411yescharacteristic
223C23×C4C2×D411yescharacteristic
224C23×C4C2×D411yescharacteristic
225C23×C4C2×D411yescharacteristic
226C23×C4C2×D411yescharacteristic
227C23×C4C2×D411yescharacteristic
228C23×C4C2×D411yescharacteristic
229C23×C4C2×D411yescharacteristic
230C23×C4C2×D412yes—
231C23×C4C2×Q812yes—
232C23×C4#4112yes—
233C23×C4#4112yes—
234C23×C4C2411yescharacteristic
235C2×M16—44no—
236C2×M16—44no—
237C2×M16—44no—
238C22×C8—24no—
239#123—24no—
240#123—24no—
241C22⋊Q8—22no—
242C22⋊Q8—21no—
243C22⋊Q8—21no—
244C22⋊Q8C4⋊C414yescomplemented
245C22⋊Q8C2×D412yes—
246C22⋊Q8C2×Q812yes—
247#121—22no—
248#121—21no—
249#121—21no—
250#121C4⋊C414yescomplemented
251#121C2×D412yes—
252#121C2×Q812yes—
253#120—24no—
254#120—24no—
255C4×Q8—42no—
256C4×Q8—42no—
257C4×D4—24no—
258C4×D4—24no—
259C4×D4—24no—
260C4×D4—24no—
261C4×D4—42no—
262C4×D4—42no—
263C4×D4—44no—
264C4×D4—44no—
265C4×D4—44no—
266C4×D4—44no—
267C4×D4—42no—
268C4×D4—42no—
269C4×D4—42no—
270C4×D4—42no—
271#117—22no—
272#117—44no—
273#117—42no—
274#117—42no—
275#117C4⋊C414yescomplemented
276C2×C4⋊C4—21no—
277C2×C4⋊C4—21no—
278C2×C4⋊C4—28no—
279C2×C4⋊C4—28no—
280C2×C4⋊C4—21no—
281C2×C4⋊C4—21no—
282C2×C4⋊C4—21no—
283C2×C4⋊C4—21no—
284C2×C4⋊C4—21no—
285C2×C4⋊C4—21no—
286C2×C4⋊C4—432no—
287C2×C4⋊C4—44no—
288C2×C4⋊C4—44no—
289C2×C4⋊C4—44no—
290C2×C4⋊C4—44no—
291C2×C4⋊C4C22×C411yescharacteristic
292C2×C4⋊C4C22×C411yescharacteristic
293C2×C4⋊C4C22×C411yescharacteristic
294C2×C4⋊C4C22×C411yescharacteristic
295C2×C4⋊C4C22×C411yescharacteristic
296C2×C4⋊C4C22×C411yescharacteristic
297C2×C22⋊C4—21no—
298C2×C22⋊C4—21no—
299C2×C22⋊C4—21no—
300C2×C22⋊C4—21no—
301C2×C22⋊C4—21no—
302C2×C22⋊C4—21no—
303C2×C22⋊C4—21no—
304C2×C22⋊C4—21no—
305C2×C22⋊C4—21no—
306C2×C22⋊C4—21no—
307C2×C22⋊C4—21no—
308C2×C22⋊C4—21no—
309C2×C22⋊C4—21no—
310C2×C22⋊C4—21no—
311C2×C22⋊C4—21no—
312C2×C22⋊C4—21no—
313C2×C22⋊C4—21no—
314C2×C42—24no—
315C2×C42—24no—
316C2×C42—21no—
317C2×C42—21no—
318C2×C42—21no—
319C2×C42—21no—
320C2×C42—21no—
321C2×C42—21no—
322C2×C42—21no—
323C2×C42—21no—
324C2×C42—21no—
325C2×C42—42no—
326C2×C42—42no—
327C2×C42—42no—
328C2×C42—42no—
329C2×C42—42no—
330C2×C42—42no—
331C2×C42—42no—
332C2×C42—42no—
333C2×C42—44no—
334C2×C42—42no—
335C2×C42—42no—
336C2×C42C22⋊C411yescharacteristic
337C2×C42C22⋊C411yescharacteristic
338C2×C42C22⋊C411yescharacteristic
339C2×C42C22⋊C411yescharacteristic
340C2×C42C22⋊C411yescharacteristic
341C2×C42C22⋊C411yescharacteristic
342C2×C42C22⋊C411yescharacteristic
343C2×C42C22⋊C411yescharacteristic
344C2×C42C22×C411yescharacteristic
345C2×C42C22×C411yescharacteristic
346C2×C42C22×C411yescharacteristic
347C2×C42C22×C411yescharacteristic
348C2×C42C2×D411yescharacteristic
349C2×C42C2×D411yescharacteristic
350C2×C42C2×D411yescharacteristic
351C2×C42C2×D411yescharacteristic
352C4⋊C8—44no—
353C4⋊C8—44no—
354C22⋊C8—24no—
355C22⋊C8—24no—
356C22⋊C8—44no—
357#95—21no—
358#95—21no—
359#95—21no—
360#95—21no—
361#95—21no—
362#95—21no—
363#95—21no—
364#95—21no—
365#95—21no—
366#95—21no—
367#95—21no—
368#95—21no—
369#95—21no—
370#95—21no—
371#95—21no—
372#95—21no—
373#95—24no—
374#95—24no—
375#95—44no—
376#95—44no—
377#95—44no—
378C24—21no—
379C24—21no—
380C24—21no—
381C24—21no—
382C24—22no—
383C24—22no—
384C24—22no—
385C24—22no—
386C24—21no—
387C24C2×C22⋊C411yescharacteristic
388C24C2×C22⋊C411yescharacteristic
389C24#12112yes—
390C24C22⋊Q812yes—
391C24C22×D411yescharacteristic
392#41—48no—
393#41—48no—
394C2×Q8—21no—
395C2×Q8—41no—
396C2×Q8—41no—
397C2×Q8C2×C4⋊C412yescomplemented
398C2×D4—22no—
399C2×D4—22no—
400C2×D4—24no—
401C2×D4—24no—
402C2×D4—21no—
403C2×D4—41no—
404C2×D4—41no—
405C2×D4—41no—
406C2×D4—41no—
407C2×D4—41no—
408C2×D4—41no—
409C2×D4—42no—
410C2×D4—42no—
411C2×D4—42no—
412C2×D4—42no—
413C2×D4C2×C4⋊C412yescomplemented
414C22×C4—216no—
415C22×C4—216no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—24no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—28no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—41no—
456C22×C4—41no—
457C22×C4—41no—
458C22×C4—41no—
459C22×C4—41no—
460C22×C4—41no—
461C22×C4—41no—
462C22×C4—41no—
463C22×C4—41no—
464C22×C4—41no—
465C22×C4—41no—
466C22×C4—44no—
467C22×C4—41no—
468C22×C4—41no—
469C22×C4—41no—
470C22×C4—41no—
471C22×C4—44no—
472C22×C4—44no—
473C22×C4—44no—
474C22×C4—41no—
475C22×C4—42no—
476C22×C4—42no—
477C22×C4—42no—
478C22×C4—42no—
479C22×C4—48no—
480C22×C4—48no—
481C22×C4—416no—
482C22×C4—44no—
483C22×C4—416no—
484C22×C4—416no—
485C22×C4—44no—
486C22×C4—44no—
487C22×C4—44no—
488C22×C4—44no—
489C22×C4—44no—
490C22×C4—42no—
491C22×C4—42no—
492C22×C4—42no—
493C22×C4—42no—
494C22×C4—88no—
495C22×C4—88no—
496C22×C4—88no—
497C22×C4—88no—
498C22×C4#9914yes—
499C22×C4#10414yes—
500C22×C4C2×C22⋊C411yescharacteristic
501C22×C4C2×C22⋊C411yescharacteristic
502C22×C4C2×C22⋊C411yescharacteristic
503C22×C4C2×C22⋊C411yescharacteristic
504C22×C4C2×C22⋊C411yescharacteristic
505C22×C4C2×C22⋊C411yescharacteristic
506C22×C4C2×C22⋊C411yescharacteristic
507C22×C4C2×C22⋊C411yescharacteristic
508C22×C4C2×C22⋊C411yescharacteristic
509C22×C4C2×C22⋊C411yescharacteristic
510C22×C4C2×C4⋊C412yes—
511C22×C4C2×C4⋊C412yes—
512C22×C4#11712yes—
513C22×C4#11712yes—
514C22×C4#12112yes—
515C22×C4#12112yes—
516C22×C4#12112yes—
517C22×C4C22⋊Q812yes—
518C22×C4C22⋊Q812yes—
519C22×C4C22⋊Q812yes—
520C22×C4AGL(1,ℤ/8)12yes—
521C22×C4AGL(1,ℤ/8)12yes—
522C22×C4#13712yes—
523C22×C4#13712yes—
524C22×C4C23×C411yescharacteristic
525C22×C4C22×D411yescharacteristic
526C22×C4C22×D411yescharacteristic
527C22×C4C22×Q811yescharacteristic
528C22×C4C2×#4111yescharacteristic
529C22×C4C2×#4111yescharacteristic
530M16—88no—
531C2×C8—44no—
532C2×C8—44no—
533C2×C8—44no—
534C4⋊C4—21no—
535C4⋊C4—21no—
536C4⋊C4—22no—
537C4⋊C4—22no—
538C4⋊C4—24no—
539C4⋊C4—41no—
540C4⋊C4—41no—
541C4⋊C4—41no—
542C4⋊C4—41no—
543C4⋊C4—416no—
544C4⋊C4—416no—
545C4⋊C4—42no—
546C4⋊C4—42no—
547C4⋊C4—42no—
548C4⋊C4—42no—
549C4⋊C4—42no—
550C4⋊C4—42no—
551C4⋊C4C2×C4⋊C412yescomplemented
552C4⋊C4C2×C4⋊C412yescomplemented
553C22⋊C4—22no—
554C22⋊C4—22no—
555C22⋊C4—24no—
556C22⋊C4—24no—
557C22⋊C4—22no—
558C22⋊C4—22no—
559C22⋊C4—24no—
560C22⋊C4—42no—
561C22⋊C4—42no—
562C22⋊C4—41no—
563C22⋊C4—41no—
564C22⋊C4—41no—
565C22⋊C4—41no—
566C22⋊C4—42no—
567C22⋊C4—42no—
568C22⋊C4—42no—
569C22⋊C4—42no—
570C22⋊C4—42no—
571C22⋊C4—42no—
572C22⋊C4—42no—
573C22⋊C4—42no—
574C42—24no—
575C42—22no—
576C42—22no—
577C42—22no—
578C42—22no—
579C42—22no—
580C42—22no—
581C42—22no—
582C42—22no—
583C42—41no—
584C42—41no—
585C42—41no—
586C42—41no—
587C42—41no—
588C42—41no—
589C42—41no—
590C42—41no—
591C42—42no—
592C42—42no—
593C42—42no—
594C42—42no—
595C42—42no—
596C42—42no—
597C42—42no—
598C42—42no—
599C23—24no—
600C23—24no—
601C23—24no—
602C23—24no—
603C23—24no—
604C23—24no—
605C23—24no—
606C23—24no—
607C23—24no—
608C23—24no—
609C23—22no—
610C23—22no—
611C23—24no—
612C23—24no—
613C23—21no—
614C23—21no—
615C23—21no—
616C23—21no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—22no—
626C23—22no—
627C23—22no—
628C23—41no—
629C23—41no—
630C23—41no—
631C23—41no—
632C23—41no—
633C23—41no—
634C23#38012yes—
635C23#38012yes—
636C23C2×#9912yes—
637C23#41012yes—
638C23C2×#10412yes—
639C23#42112yes—
640C23C22×C22⋊C411yescharacteristic
641C23C2×#12111yescharacteristic
642C23C2×C22⋊Q811yescharacteristic
643C23C2×AGL(1,ℤ/8)11yescharacteristic
644C23C2×AGL(1,ℤ/8)11yescharacteristic
645C23C2×#13711yescharacteristic
646C23C2×#13711yescharacteristic
647Q8—42no—
648Q8—42no—
649D4—42no—
650D4—42no—
651D4—48no—
652D4—42no—
653D4—42no—
654D4—48no—
655D4—42no—
656D4—42no—
657C2×C4—24no—
658C2×C4—28no—
659C2×C4—24no—
660C2×C4—28no—
661C2×C4—24no—
662C2×C4—24no—
663C2×C4—24no—
664C2×C4—24no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—24no—
684C2×C4—28no—
685C2×C4—28no—
686C2×C4—24no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—44no—
709C2×C4—44no—
710C2×C4—44no—
711C2×C4—44no—
712C2×C4—48no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—48no—
722C2×C4—48no—
723C2×C4—48no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—84no—
737C2×C4—832no—
738C2×C4—84no—
739C2×C4—84no—
740C2×C4—84no—
741C2×C4—84no—
742C2×C4—84no—
743C2×C4#38012yes—
744C2×C4#38012yes—
745C2×C4C2×#9912yes—
746C2×C4C2×#9912yes—
747C2×C4#41712yes—
748C2×C4#41712yes—
749C2×C4#41712yes—
750C2×C4#41712yes—
751C2×C4C2×#10412yes—
752C2×C4C2×#10412yes—
753C2×C4C22×C4⋊C411yescharacteristic
754C2×C4C2×#11711yescharacteristic
755C2×C4C2×#12111yescharacteristic
756C2×C4C2×C22⋊Q811yescharacteristic
757C8—84no—
758C22—28no—
759C22—28no—
760C22—28no—
761C22—28no—
762C22—21no—
763C22—21no—
764C22—22no—
765C22—22no—
766C22—21no—
767C22—21no—
768C22—22no—
769C22—22no—
770C22—21no—
771C22—21no—
772C22—22no—
773C22—22no—
774C22—22no—
775C22—21no—
776C22—21no—
777C22—22no—
778C22—21no—
779C22—21no—
780C22—22no—
781C22—22no—
782C22—21no—
783C22—21no—
784C22—22no—
785C22—22no—
786C22—42no—
787C22—42no—
788C22—42no—
789C22—81no—
790C22—81no—
791C22—81no—
792C22—81no—
793C22#179914yes—
794C22#180614yes—
795C22C2×#38011yescharacteristic
796C22C22×#9911yescharacteristic
797C22C2×#41011yescharacteristic
798C22C2×#41711yescharacteristic
799C22C2×#41711yescharacteristic
800C22C22×#10411yescharacteristic
801C22C2×#42111yescharacteristic
802C22#303811yescharacteristic
803C22#303911yescharacteristic
804C22#307911yescharacteristic
805C22#307911yescharacteristic
806C4—22no—
807C4—22no—
808C4—22no—
809C4—21no—
810C4—22no—
811C4—21no—
812C4—21no—
813C4—21no—
814C4—22no—
815C4—22no—
816C4—22no—
817C4—42no—
818C4—42no—
819C4—42no—
820C4—41no—
821C4—41no—
822C4—88no—
823C4—81no—
824C4—81no—
825C4—81no—
826C4—81no—
827C4#150414yescomplemented
828C2—21no—
829C2—24no—
830C2—21no—
831C2—21no—
832C2—24no—
833C2—21no—
834C2—82no—
835C2C2×#150411yescharacteristic
836C2#1754611yescharacteristic
837C2#1758811yescharacteristic
838C2#1759211yescharacteristic
839C2C2×#179911yescharacteristic
840C2#2064811yescharacteristic
841C2C2×#180611yescharacteristic
subgroupG/H
center, socleC23C22×C22⋊C4
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
prime radicalC2×#525C22
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ C23×C42 ◁ G
LECSG ▷ C23×C4 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #20626C2semidirect
4. C2×C4⋊#95C2semidirect
5. #8578C2semidirect
6. #8577C2semidirect
7. #8572C2semidirect
8. #8571C2semidirect
9. #8020C2semidirect
11. C2×C4×#41C4semidirect
16. C4×C22⋊Q8C4semidirect
17. C4×C22⋊Q8C4semidirect
22. C4×#121C4semidirect
23. C4×#121C4semidirect
28. #2297C4semidirect
29. #2296C4semidirect
35. C4×#117C4semidirect
69. C2×C4×Q8C2×C4semidirect
70. C2×C4×Q8C2×C4semidirect
79. C2×C4×D4C2×C4semidirect
80. C2×C4×D4C2×C4semidirect
111. #391C2×C4semidirect
112. #391C2×C4semidirect
113. #390C2×C4semidirect
114. #390C2×C4semidirect
115. #389C2×C4semidirect
116. #389C2×C4semidirect
117. #389C2×C4semidirect
118. #389C2×C4semidirect
151. C4×C4⋊C4C2×C4semidirect
152. C4×C4⋊C4C2×C4semidirect
153. C4×C4⋊C4C2×C4semidirect
154. C4×C4⋊C4C2×C4semidirect
186. C2×#41C4⋊C4semidirect
244. C22⋊Q8C4⋊C4semidirect
250. #121C4⋊C4semidirect
275. #117C4⋊C4semidirect
397. C2×Q8C2×C4⋊C4semidirect
413. C2×D4C2×C4⋊C4semidirect
551. C4⋊C4C2×C4⋊C4semidirect
552. C4⋊C4C2×C4⋊C4semidirect
827. C4#1504semidirect

Maximal subgroups

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

subgroupindex
C4×#5252
#206262
C2×#15042
C2×C4⋊#952
#85782
#85772
#85722
#85712
#80202