Finite Group Databasebeta

← #363934

Subgroups — #363934

Order 512.

3094 conjugacy classes of subgroups.

The subgroup lattice has 847 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#554C211yesmaximal, characteristic
2C2×#1892C211yesmaximal, characteristic, complemented
3C2×#1872C211yesmaximal, characteristic, complemented
4C2×#1869C211yesmaximal, characteristic
5C2×#1824C211yesmaximal, characteristic, complemented
6C22×#340C211yesmaximal, characteristic, complemented
7#13872C211yesmaximal, characteristic
8#11384C212yesmaximal, complemented
9#10970C212yesmaximal, complemented
10#10789C212yesmaximal, complemented
11#10730C212yesmaximal, complemented
12C24×C8C2211yescharacteristic
13C2×#554—24no—
14C2×#554—24no—
15C2×#554—24no—
16C2×#554—24no—
17C2×#554—24no—
18C2×#554C418yescomplemented
19C22×C4⋊Q8C2211yescharacteristic
20C22×#125—21no—
21C22×C22⋊Q8—21no—
22C22×C22⋊Q8—21no—
23C22×C22⋊Q8C2211yescharacteristic
24C22×C22⋊Q8C2211yescharacteristic
25C22×C4×Q8C2211yescharacteristic
26C22×C4×D4—21no—
27C22×C4×D4C2211yescharacteristic
28C23×C4⋊C4C2211yescharacteristic
29C23×C4⋊C4C2211yescharacteristic
30C23×C4⋊C4C2211yescharacteristic
31C22×#103C2212yes—
32C22×#103C2212yes—
33C22×C22⋊C8C2211yescharacteristic
34C22×C22⋊C8C2212yes—
35C2×#386—21no—
36C2×#380C2211yescharacteristic
37C2×#380C2212yes—
38#1892—24no—
39#1872—24no—
40#1869—24no—
41#1824—24no—
42C2×#340—24no—
43C2×#340C2212yes—
44C2×#340C2212yes—
45C2×#340C2212yes—
46C2×#340C2212yes—
47C2×#340C2212yes—
48C2×#340C2212yes—
49C2×#336C2212yes—
50#1441—21no—
51#1439—21no—
52C4⋊#95C2212yes—
53C22⋊#95—21no—
54C23×Q8—21no—
55C23×Q8C2311yescharacteristic
56C23×D4D411yescharacteristic
57C24×C4—21no—
58C24×C4—21no—
59C24×C4—21no—
60C24×C4C2311yescharacteristic
61C24×C4C2311yescharacteristic
62C23×C8—22no—
63C23×C8—24no—
64C23×C8—22no—
65C23×C8—22no—
66C23×C8—42no—
67C23×C8C2312yes—
68C23×C8C2312yes—
69#554—232no—
70#554—232no—
71#554—232no—
72#554—232no—
73C2×C4⋊Q8—22no—
74C2×C4⋊Q8—22no—
75C2×C4⋊Q8—22no—
76C2×C4⋊Q8—22no—
77C2×C4⋊Q8—22no—
78C2×C4⋊Q8C2×C414yescomplemented
79C2×#125—28no—
80C2×#125—28no—
81C2×#125—28no—
82C2×C22⋊Q8—28no—
83C2×C22⋊Q8—28no—
84C2×C22⋊Q8—28no—
85C2×C22⋊Q8—28no—
86C2×C22⋊Q8—22no—
87C2×C22⋊Q8—22no—
88C2×C22⋊Q8—22no—
89C2×C22⋊Q8—22no—
90C2×C22⋊Q8—22no—
91C2×C22⋊Q8—22no—
92C2×C22⋊Q8—22no—
93C2×C22⋊Q8—22no—
94C2×C22⋊Q8—28no—
95C2×C22⋊Q8—28no—
96C2×C22⋊Q8C2×C414yes—
97C2×C22⋊Q8C2×C414yescomplemented
98C2×C22⋊Q8D414yes—
99C2×C22⋊Q8D414yes—
100C2×C4×Q8—22no—
101C2×C4×Q8—22no—
102C2×C4×Q8—22no—
103C2×C4×Q8—22no—
104C2×C4×Q8—22no—
105C2×C4×Q8C2×C414yescomplemented
106C2×C4×D4—28no—
107C2×C4×D4—28no—
108C2×C4×D4—28no—
109C2×C4×D4—22no—
110C2×C4×D4—22no—
111C2×C4×D4—22no—
112C2×C4×D4—22no—
113C2×C4×D4C2×C414yes—
114C2×C4×D4D414yes—
115C22×C4⋊C4—21no—
116C22×C4⋊C4—21no—
117C22×C4⋊C4—22no—
118C22×C4⋊C4—22no—
119C22×C4⋊C4—22no—
120C22×C4⋊C4—22no—
121C22×C4⋊C4—21no—
122C22×C4⋊C4—21no—
123C22×C4⋊C4—21no—
124C22×C4⋊C4—21no—
125C22×C4⋊C4—22no—
126C22×C4⋊C4—22no—
127C22×C4⋊C4—22no—
128C22×C4⋊C4—22no—
129C22×C4⋊C4—22no—
130C22×C4⋊C4—24no—
131C22×C4⋊C4—22no—
132C22×C4⋊C4—21no—
133C22×C4⋊C4—42no—
134C22×C4⋊C4C2×C414yes—
135C22×C4⋊C4C2×C414yescomplemented
136C22×C4⋊C4D411yescharacteristic
137C22×C4⋊C4D414yes—
138C22×C4⋊C4D414yes—
139C22×C4⋊C4C2312yes—
140C22×C4⋊C4C2312yes—
141C22×C4⋊C4C2311yescharacteristic
142C22×C4⋊C4C2311yescharacteristic
143C22×C4⋊C4C2311yescharacteristic
144C22×C22⋊C4—21no—
145C22×C22⋊C4—21no—
146C22×C22⋊C4—21no—
147C22×C22⋊C4—22no—
148C22×C22⋊C4D411yescharacteristic
149C22×C22⋊C4D411yescharacteristic
150C22×C42—21no—
151C22×C42C2311yescharacteristic
152C2×#103—24no—
153C2×#103—24no—
154C2×#103—24no—
155C2×#103—24no—
156C2×#103—42no—
157C2×#103—42no—
158C2×C22⋊C8—22no—
159C2×C22⋊C8—24no—
160C2×C22⋊C8—22no—
161C2×C22⋊C8—22no—
162C2×C22⋊C8—24no—
163C2×C22⋊C8—42no—
164#386—44no—
165#380—22no—
166#380—22no—
167#380—24no—
168#380—42no—
169C2×#95—22no—
170C2×#95—22no—
171C2×#95—21no—
172C2×#95—22no—
173#340—24no—
174#340—24no—
175#340—24no—
176#340—24no—
177#340—24no—
178#340—24no—
179#336—24no—
180C25C2×D411yescharacteristic
181C25C2×D411yescharacteristic
182C22×Q8—24no—
183C22×Q8—24no—
184C22×Q8—24no—
185C22×Q8—21no—
186C22×Q8—21no—
187C22×Q8—21no—
188C22×Q8—22no—
189C22×Q8—22no—
190C22×Q8—22no—
191C22×Q8—22no—
192C22×Q8—82no—
193C22×Q8—82no—
194C22×Q8C22×C412yes—
195C22×Q8C2×D412yes—
196C22×Q8C2×D412yes—
197C22×D4—22no—
198C22×D4—22no—
199C22×D4—22no—
200C22×D4—22no—
201C22×D4C22⋊C414yes—
202C22×D4SD1614yes—
203C22×D4Q1614yes—
204C23×C4—22no—
205C23×C4—22no—
206C23×C4—22no—
207C23×C4—22no—
208C23×C4—21no—
209C23×C4—21no—
210C23×C4—21no—
211C23×C4—21no—
212C23×C4—24no—
213C23×C4—24no—
214C23×C4—24no—
215C23×C4—24no—
216C23×C4—24no—
217C23×C4—24no—
218C23×C4—21no—
219C23×C4—21no—
220C23×C4—21no—
221C23×C4—21no—
222C23×C4—22no—
223C23×C4—22no—
224C23×C4—22no—
225C23×C4—22no—
226C23×C4—22no—
227C23×C4—22no—
228C23×C4—44no—
229C23×C4—42no—
230C23×C4—42no—
231C23×C4—42no—
232C23×C4—82no—
233C23×C4—82no—
234C23×C4—82no—
235C23×C4—82no—
236C23×C4—82no—
237C23×C4C22×C412yes—
238C23×C4C22×C412yes—
239C23×C4C2×D411yescharacteristic
240C23×C4C2×D411yescharacteristic
241C23×C4C2×D412yes—
242C23×C4C2×D411yescharacteristic
243C23×C4C2×D412yes—
244C23×C4C2×D412yes—
245C23×C4C2×D412yes—
246C23×C4C2×D412yes—
247C23×C4C2×D411yescharacteristic
248C23×C4C2×D412yes—
249C23×C4C2411yescharacteristic
250C22×C8—28no—
251C22×C8—22no—
252C22×C8—22no—
253C22×C8—22no—
254C22×C8—22no—
255C22×C8—22no—
256C22×C8—22no—
257C22×C8—22no—
258C22×C8—22no—
259C22×C8—22no—
260C22×C8—22no—
261C22×C8—22no—
262C22×C8—22no—
263C22×C8—22no—
264C22×C8—48no—
265C22×C8—48no—
266C22×C8—44no—
267C22×C8—44no—
268C22×C8#4114yes—
269C4⋊Q8—28no—
270C4⋊Q8—28no—
271C4⋊Q8—28no—
272C4⋊Q8—28no—
273#125—264no—
274C22⋊Q8—28no—
275C22⋊Q8—28no—
276C22⋊Q8—264no—
277C22⋊Q8—264no—
278C22⋊Q8—28no—
279C22⋊Q8—28no—
280C22⋊Q8—28no—
281C22⋊Q8—28no—
282C22⋊Q8—28no—
283C22⋊Q8C22⋊C4116yescomplemented
284C4×Q8—28no—
285C4×Q8—28no—
286C4×Q8—28no—
287C4×Q8—28no—
288C4×D4—264no—
289C4×D4—28no—
290C4×D4—28no—
291C4×D4—28no—
292C4×D4—28no—
293C2×C4⋊C4—24no—
294C2×C4⋊C4—24no—
295C2×C4⋊C4—28no—
296C2×C4⋊C4—28no—
297C2×C4⋊C4—24no—
298C2×C4⋊C4—24no—
299C2×C4⋊C4—24no—
300C2×C4⋊C4—24no—
301C2×C4⋊C4—24no—
302C2×C4⋊C4—24no—
303C2×C4⋊C4—24no—
304C2×C4⋊C4—28no—
305C2×C4⋊C4—24no—
306C2×C4⋊C4—24no—
307C2×C4⋊C4—24no—
308C2×C4⋊C4—24no—
309C2×C4⋊C4—24no—
310C2×C4⋊C4—24no—
311C2×C4⋊C4—24no—
312C2×C4⋊C4—28no—
313C2×C4⋊C4—28no—
314C2×C4⋊C4—24no—
315C2×C4⋊C4—24no—
316C2×C4⋊C4—22no—
317C2×C4⋊C4—22no—
318C2×C4⋊C4—21no—
319C2×C4⋊C4—21no—
320C2×C4⋊C4—21no—
321C2×C4⋊C4—21no—
322C2×C4⋊C4—21no—
323C2×C4⋊C4—21no—
324C2×C4⋊C4—21no—
325C2×C4⋊C4—21no—
326C2×C4⋊C4—21no—
327C2×C4⋊C4—28no—
328C2×C4⋊C4—28no—
329C2×C4⋊C4—28no—
330C2×C4⋊C4—22no—
331C2×C4⋊C4—22no—
332C2×C4⋊C4—22no—
333C2×C4⋊C4—22no—
334C2×C4⋊C4—22no—
335C2×C4⋊C4—22no—
336C2×C4⋊C4—22no—
337C2×C4⋊C4—22no—
338C2×C4⋊C4—22no—
339C2×C4⋊C4—22no—
340C2×C4⋊C4—22no—
341C2×C4⋊C4—48no—
342C2×C4⋊C4—44no—
343C2×C4⋊C4—44no—
344C2×C4⋊C4—42no—
345C2×C4⋊C4C22⋊C414yes—
346C2×C4⋊C4C22⋊C4116yescomplemented
347C2×C4⋊C4C22×C412yes—
348C2×C4⋊C4C22×C412yes—
349C2×C4⋊C4C22×C412yes—
350C2×C4⋊C4C2×D412yes—
351C2×C4⋊C4C2×D412yes—
352C2×C4⋊C4C2×D412yes—
353C2×C4⋊C4C2×D412yes—
354C2×C4⋊C4C2×D412yes—
355C2×C4⋊C4C2×D412yes—
356C2×C4⋊C4#4114yes—
357C2×C22⋊C4—24no—
358C2×C22⋊C4—24no—
359C2×C22⋊C4—24no—
360C2×C22⋊C4—24no—
361C2×C22⋊C4—24no—
362C2×C22⋊C4—24no—
363C2×C22⋊C4—22no—
364C2×C22⋊C4—22no—
365C2×C22⋊C4—22no—
366C2×C22⋊C4—22no—
367C2×C22⋊C4—44no—
368C2×C22⋊C4—42no—
369C2×C22⋊C4—44no—
370C2×C22⋊C4—42no—
371C2×C22⋊C4—42no—
372C2×C22⋊C4—82no—
373C2×C22⋊C4C22⋊C414yes—
374C2×C22⋊C4C22⋊C414yes—
375C2×C42—24no—
376C2×C42—24no—
377C2×C42—24no—
378C2×C42—21no—
379C2×C42—21no—
380C2×C42—21no—
381C2×C42—21no—
382C2×C42C22×C412yes—
383C2×C42C2×D412yes—
384#103—48no—
385#103—48no—
386C22⋊C8—48no—
387C22⋊C8—44no—
388#95—44no—
389#95—42no—
390#95—44no—
391#95—82no—
392C24—22no—
393C24—22no—
394C24—22no—
395C24—22no—
396C24—21no—
397C24—21no—
398C24—22no—
399C24—22no—
400C24—21no—
401C24—21no—
402C24—22no—
403C24—22no—
404C24C2×C22⋊C412yes—
405C24C2×C22⋊C412yes—
406C24#12012yes—
407C24#12012yes—
408C24C2×SD1612yes—
409C24C2×SD1612yes—
410C24C2×Q1612yes—
411C24C2×Q1612yes—
412C24#13712yes—
413C24#13712yes—
414C24C22×D411yescharacteristic
415C2×Q8—216no—
416C2×Q8—22no—
417C2×Q8—22no—
418C2×Q8—22no—
419C2×Q8—24no—
420C2×Q8—24no—
421C2×Q8—24no—
422C2×Q8—24no—
423C2×Q8—24no—
424C2×Q8—24no—
425C2×Q8—41no—
426C2×Q8—41no—
427C2×Q8—42no—
428C2×Q8—41no—
429C2×Q8—41no—
430C2×Q8—42no—
431C2×Q8—42no—
432C2×Q8—42no—
433C2×Q8—88no—
434C2×Q8—84no—
435C2×Q8—84no—
436C2×Q8—88no—
437C2×Q8C2×C22⋊C414yes—
438C2×D4—28no—
439C2×D4—28no—
440C2×D4—28no—
441C2×D4—28no—
442C2×D4—28no—
443C2×D4—28no—
444C2×D4#103116yescomplemented
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—24no—
452C22×C4—24no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—24no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—24no—
459C22×C4—24no—
460C22×C4—24no—
461C22×C4—24no—
462C22×C4—24no—
463C22×C4—24no—
464C22×C4—24no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—216no—
486C22×C4—216no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—24no—
490C22×C4—24no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—24no—
494C22×C4—24no—
495C22×C4—24no—
496C22×C4—42no—
497C22×C4—42no—
498C22×C4—42no—
499C22×C4—42no—
500C22×C4—42no—
501C22×C4—42no—
502C22×C4—42no—
503C22×C4—42no—
504C22×C4—41no—
505C22×C4—41no—
506C22×C4—42no—
507C22×C4—41no—
508C22×C4—41no—
509C22×C4—42no—
510C22×C4—42no—
511C22×C4—42no—
512C22×C4—42no—
513C22×C4—42no—
514C22×C4—48no—
515C22×C4—42no—
516C22×C4—42no—
517C22×C4—42no—
518C22×C4—42no—
519C22×C4—42no—
520C22×C4—42no—
521C22×C4—42no—
522C22×C4—42no—
523C22×C4—42no—
524C22×C4—42no—
525C22×C4—42no—
526C22×C4—42no—
527C22×C4—42no—
528C22×C4—88no—
529C22×C4—88no—
530C22×C4—84no—
531C22×C4—84no—
532C22×C4—88no—
533C22×C4—84no—
534C22×C4—84no—
535C22×C4—88no—
536C22×C4—88no—
537C22×C4—88no—
538C22×C4—84no—
539C22×C4—84no—
540C22×C4C2×C22⋊C412yes—
541C22×C4C2×C22⋊C412yes—
542C22×C4C2×C22⋊C414yes—
543C22×C4C2×C22⋊C414yes—
544C22×C4C2×C22⋊C412yes—
545C22×C4C2×C22⋊C412yes—
546C22×C4#12014yes—
547C22×C4#12014yes—
548C22×C4#12012yes—
549C22×C4#12012yes—
550C22×C4C2×SD1612yes—
551C22×C4C2×Q1612yes—
552C22×C4C23×C411yescharacteristic
553C22×C4C22×D411yescharacteristic
554C22×C4C22×D411yescharacteristic
555C22×C4C22×D411yescharacteristic
556C22×C4C22×D411yescharacteristic
557C22×C4C22×D411yescharacteristic
558C22×C4C2×#4112yes—
559C22×C4C2×#4112yes—
560C22×C4H(5,𝔽2)12yes—
561C22×C42−1+412yes—
562C2×C8—24no—
563C2×C8—24no—
564C2×C8—24no—
565C2×C8—416no—
566C2×C8—42no—
567C2×C8—42no—
568C2×C8—42no—
569C2×C8—42no—
570C2×C8—42no—
571C2×C8—42no—
572C2×C8—42no—
573C2×C8—42no—
574C2×C8—42no—
575C2×C8—42no—
576C2×C8—42no—
577C4⋊C4—216no—
578C4⋊C4—216no—
579C4⋊C4—216no—
580C4⋊C4—216no—
581C4⋊C4—22no—
582C4⋊C4—22no—
583C4⋊C4—22no—
584C4⋊C4—22no—
585C4⋊C4—22no—
586C4⋊C4—22no—
587C4⋊C4—22no—
588C4⋊C4—22no—
589C4⋊C4—22no—
590C4⋊C4—216no—
591C4⋊C4—216no—
592C4⋊C4—28no—
593C4⋊C4—24no—
594C4⋊C4—24no—
595C4⋊C4—48no—
596C4⋊C4—42no—
597C4⋊C4—42no—
598C4⋊C4—42no—
599C4⋊C4—42no—
600C4⋊C4—42no—
601C4⋊C4—42no—
602C4⋊C4C2×C22⋊C414yes—
603C4⋊C4C2×C22⋊C414yes—
604C4⋊C4C2×C22⋊C414yes—
605C22⋊C4—216no—
606C22⋊C4—216no—
607C22⋊C4—28no—
608C22⋊C4—28no—
609C22⋊C4—88no—
610C22⋊C4—84no—
611C42—216no—
612C42—22no—
613C42—22no—
614C42—22no—
615C42—22no—
616C23—24no—
617C23—24no—
618C23—24no—
619C23—24no—
620C23—24no—
621C23—24no—
622C23—22no—
623C23—22no—
624C23—24no—
625C23—22no—
626C23—22no—
627C23—24no—
628C23—24no—
629C23—24no—
630C23—24no—
631C23—24no—
632C23—24no—
633C23—24no—
634C23—24no—
635C23—22no—
636C23—24no—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—24no—
642C23—24no—
643C23—22no—
644C23—42no—
645C23—42no—
646C23—41no—
647C23—41no—
648C23—42no—
649C23—41no—
650C23—41no—
651C23—42no—
652C23—42no—
653C23—42no—
654C23#37914yes—
655C23C2×#10314yes—
656C23C2×#10314yes—
657C23#41914yes—
658C23#44814yes—
659C23#44814yes—
660C23#45114yes—
661C23#45114yes—
662C23C22×C22⋊C411yescharacteristic
663C23C2×#12011yescharacteristic
664C23C2×#12011yescharacteristic
665C23#54612yes—
666C23#54712yes—
667C23C22×SD1611yescharacteristic
668C23C22×Q1611yescharacteristic
669C23C2×#13711yescharacteristic
670C23C2×#13711yescharacteristic
671C23#57612yes—
672C23#57712yes—
673Q8—28no—
674Q8—42no—
675Q8—42no—
676Q8—42no—
677Q8—44no—
678Q8—42no—
679Q8—816no—
680D4—232no—
681C2×C4—24no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—24no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—24no—
692C2×C4—28no—
693C2×C4—24no—
694C2×C4—24no—
695C2×C4—28no—
696C2×C4—24no—
697C2×C4—24no—
698C2×C4—24no—
699C2×C4—24no—
700C2×C4—22no—
701C2×C4—24no—
702C2×C4—22no—
703C2×C4—24no—
704C2×C4—24no—
705C2×C4—44no—
706C2×C4—44no—
707C2×C4—44no—
708C2×C4—44no—
709C2×C4—41no—
710C2×C4—42no—
711C2×C4—41no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—44no—
715C2×C4—41no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—41no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—44no—
725C2×C4—44no—
726C2×C4—44no—
727C2×C4—42no—
728C2×C4—44no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—44no—
732C2×C4—42no—
733C2×C4—44no—
734C2×C4—44no—
735C2×C4—44no—
736C2×C4—816no—
737C2×C4—816no—
738C2×C4—816no—
739C2×C4—82no—
740C2×C4—82no—
741C2×C4—82no—
742C2×C4—82no—
743C2×C4—82no—
744C2×C4—82no—
745C2×C4—82no—
746C2×C4—82no—
747C2×C4—82no—
748C2×C4—82no—
749C2×C4—82no—
750C2×C4#37914yes—
751C2×C4C2×#10314yes—
752C2×C4C22×C22⋊C411yescharacteristic
753C2×C4C22×C22⋊C411yescharacteristic
754C2×C4C4×#4112yes—
755C2×C4#52012yes—
756C2×C4C2×#12011yescharacteristic
757C2×C4C2×#12011yescharacteristic
758C2×C4#52511yescharacteristic
759C2×C4#52511yescharacteristic
760C2×C4#53212yes—
761C2×C4#53511yescharacteristic
762C2×C4#53611yescharacteristic
763C2×C4#53712yes—
764C2×C4#54612yes—
765C2×C4#54612yes—
766C2×C4#54612yes—
767C2×C4#54712yes—
768C2×C4#54712yes—
769C2×C4#54712yes—
770C8—44no—
771C8—82no—
772C22—24no—
773C22—24no—
774C22—24no—
775C22—24no—
776C22—24no—
777C22—24no—
778C22—28no—
779C22—28no—
780C22—28no—
781C22—28no—
782C22—24no—
783C22—28no—
784C22—42no—
785C22—42no—
786C22—42no—
787C22—42no—
788C22—42no—
789C22—42no—
790C22—44no—
791C22—44no—
792C22—44no—
793C22#178718yes—
794C22C2×#37911yescharacteristic
795C22#233912yes—
796C22#240411yescharacteristic
797C22#240611yescharacteristic
798C22#243012yes—
799C22C22×#10311yescharacteristic
800C22C2×#41911yescharacteristic
801C22#289712yes—
802C22C2×#44811yescharacteristic
803C22C2×#44811yescharacteristic
804C22C2×#45111yescharacteristic
805C22C2×#45111yescharacteristic
806C22#300811yescharacteristic
807C22#300911yescharacteristic
808C22#301212yes—
809C22#329512yes—
810C22#329912yes—
811C22#331412yes—
812C22#331612yes—
813C22#333512yes—
814C22#333812yes—
815C22#334412yes—
816C22#334612yes—
817C4—24no—
818C4—24no—
819C4—42no—
820C4—44no—
821C4—44no—
822C4—44no—
823C4—42no—
824C4—44no—
825C4—84no—
826C4—162no—
827C4#229711yescharacteristic
828C4#231111yescharacteristic
829C4#233912yes—
830C4#240411yescharacteristic
831C4#240611yescharacteristic
832C4#243012yes—
833C2—28no—
834C2—44no—
835C2#1395611yescharacteristic
836C2C2×#178711yescharacteristic
837C2#2060211yescharacteristic
838C2#2248712yes—
839C2#2249712yes—
840C2#2396911yescharacteristic
841C2#2397011yescharacteristic
842C2#2409711yescharacteristic
843C2#2409811yescharacteristic
844C2#2554312yes—
845C2#2554512yes—
subgroupG/H
center, socleC24C22×D4
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
prime radicalC23×D4D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C22×C4×D4 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#1892C2semidirect
3. C2×#1872C2semidirect
5. C2×#1824C2semidirect
6. C22×#340C2semidirect
8. #11384C2semidirect
9. #10970C2semidirect
10. #10789C2semidirect
11. #10730C2semidirect
18. C2×#554C4semidirect
78. C2×C4⋊Q8C2×C4semidirect
97. C2×C22⋊Q8C2×C4semidirect
105. C2×C4×Q8C2×C4semidirect
135. C22×C4⋊C4C2×C4semidirect
283. C22⋊Q8C22⋊C4semidirect
346. C2×C4⋊C4C22⋊C4semidirect
444. C2×D4#103semidirect

Maximal subgroups

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

subgroupindex
C22×#5542
C2×#18922
C2×#18722
C2×#18692
C2×#18242
C22×#3402
#138722
#113842
#109702
#107892
#107302