Finite Group Databasebeta

← #367429

Subgroups — #367429

Order 512.

1686 conjugacy classes of subgroups.

The subgroup lattice has 923 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#1939C211yesmaximal, characteristic, complemented
2C2×#1850C211yesmaximal, characteristic
3C2×#1850C211yesmaximal, characteristic
4C2×#1797C211yesmaximal, characteristic
5C2×C8×C22⋊C4C211yesmaximal, characteristic
6C22×#336C211yesmaximal, characteristic
7C4×#385C211yesmaximal, characteristic
8#11322C211yesmaximal, characteristic, complemented
9#11255C211yesmaximal, characteristic, complemented
10#11202C211yesmaximal, characteristic, complemented
11#11202C211yesmaximal, characteristic, complemented
12#10876C211yesmaximal, characteristic, complemented
13#10876C211yesmaximal, characteristic, complemented
14#10834C211yesmaximal, characteristic, complemented
15#10714C211yesmaximal, characteristic
16C24×C8C2211yescharacteristic
17C24×C8C2211yescharacteristic
18C23×C42C2211yescharacteristic
19C22×C4⋊C8C2211yescharacteristic
20C22×C4⋊C8C2211yescharacteristic
21C22×C4⋊C8C2211yescharacteristic
22C22×C4⋊C8C2211yescharacteristic
23C22×C4⋊C8C2211yescharacteristic
24C22×C4⋊C8C2211yescharacteristic
25C22×C22⋊C8C2211yescharacteristic
26C22×C22⋊C8C2211yescharacteristic
27C22×C4×C8C2211yescharacteristic
28C22×C4×C8C2211yescharacteristic
29C2×#385C411yescharacteristic
30C2×#385C411yescharacteristic
31C2×C4×C4⋊C4C2211yescharacteristic
32C2×C4×C4⋊C4C2211yescharacteristic
33C2×C4×C22⋊C4C2211yescharacteristic
34C2×C4×C22⋊C4C2211yescharacteristic
35#1939—24no—
36#1850—24no—
37#1850—24no—
38#1797—24no—
39C8×C22⋊C4—24no—
40C2×#336—24no—
41C2×#336C2211yescharacteristic
42C2×#336C2211yescharacteristic
43C2×#336C2211yescharacteristic
44C2×#336C2211yescharacteristic
45C2×#336C2211yescharacteristic
46C2×#336C2211yescharacteristic
47C2×#336C2211yescharacteristic
48C2×#336C2211yescharacteristic
49C2×#336C2211yescharacteristic
50C2×#336C2211yescharacteristic
51C2×#336C2211yescharacteristic
52C2×#336C2211yescharacteristic
53C2×#336C2211yescharacteristic
54C2×#336C2211yescharacteristic
55C2×#336C2211yescharacteristic
56C2×#336C2211yescharacteristic
57#1436C411yescharacteristic
58#1436C411yescharacteristic
59#1436C411yescharacteristic
60#1436C411yescharacteristic
61C22⋊#95C411yescharacteristic
62C22⋊#95C411yescharacteristic
63C4×#95C2211yescharacteristic
64C4×#95C2211yescharacteristic
65C24×C4C2×C411yescharacteristic
66C24×C4C2×C411yescharacteristic
67C24×C4C2311yescharacteristic
68C23×C8—22no—
69C23×C8—22no—
70C23×C8—22no—
71C23×C8—22no—
72C23×C8—22no—
73C23×C8—22no—
74C23×C8—22no—
75C23×C8—22no—
76C23×C8—22no—
77C23×C8—41no—
78C23×C8—41no—
79C23×C8—41no—
80C23×C8—41no—
81C23×C8Q814yes—
82C23×C8C2311yescharacteristic
83C23×C8C2311yescharacteristic
84C23×C8C2311yescharacteristic
85C23×C8C2311yescharacteristic
86C23×C8C2311yescharacteristic
87C23×C8C2311yescharacteristic
88C23×C8C2311yescharacteristic
89C23×C8C2311yescharacteristic
90C22×C4⋊C4C2×C411yescharacteristic
91C22×C4⋊C4C2×C411yescharacteristic
92C22×C4⋊C4C2×C411yescharacteristic
93C22×C4⋊C4C2×C411yescharacteristic
94C22×C22⋊C4C2×C411yescharacteristic
95C22×C22⋊C4C2×C411yescharacteristic
96C22×C22⋊C4C2×C411yescharacteristic
97C22×C22⋊C4C2×C411yescharacteristic
98C22×C42—22no—
99C22×C42—22no—
100C22×C42—22no—
101C22×C42—22no—
102C22×C42—41no—
103C22×C42—41no—
104C22×C42C2×C411yescharacteristic
105C22×C42C2×C411yescharacteristic
106C22×C42C2311yescharacteristic
107C22×C42C2311yescharacteristic
108C22×C42C2311yescharacteristic
109C22×C42C2311yescharacteristic
110C22×C42C2311yescharacteristic
111C22×C42C2311yescharacteristic
112C2×C4⋊C8—22no—
113C2×C4⋊C8—22no—
114C2×C4⋊C8—22no—
115C2×C4⋊C8—22no—
116C2×C4⋊C8—22no—
117C2×C4⋊C8—22no—
118C2×C4⋊C8—22no—
119C2×C4⋊C8—22no—
120C2×C4⋊C8—22no—
121C2×C4⋊C8—22no—
122C2×C4⋊C8—22no—
123C2×C4⋊C8—22no—
124C2×C4⋊C8—41no—
125C2×C4⋊C8—41no—
126C2×C4⋊C8—41no—
127C2×C4⋊C8—41no—
128C2×C4⋊C8—41no—
129C2×C4⋊C8—41no—
130C2×C22⋊C8—22no—
131C2×C22⋊C8—22no—
132C2×C22⋊C8—22no—
133C2×C22⋊C8—22no—
134C2×C22⋊C8—22no—
135C2×C22⋊C8D414yes—
136C2×C4×C8—22no—
137C2×C4×C8—22no—
138C2×C4×C8—22no—
139C2×C4×C8—22no—
140C2×C4×C8—41no—
141C2×C4×C8—41no—
142#385—24no—
143#385C818yescomplemented
144C4×C4⋊C4—22no—
145C4×C4⋊C4—22no—
146C4×C4⋊C4—41no—
147C4×C4⋊C4—41no—
148C4×C22⋊C4—22no—
149C4×C22⋊C4—22no—
150C4×C22⋊C4D414yes—
151C4×C22⋊C4Q814yes—
152C2×#95C2×C411yescharacteristic
153C2×#95C2×C411yescharacteristic
154C2×#95C2×C411yescharacteristic
155C2×#95C2×C411yescharacteristic
156C2×#95C2×C411yescharacteristic
157C2×#95C2×C411yescharacteristic
158C2×#95C2×C411yescharacteristic
159C2×#95C2×C411yescharacteristic
160C2×#95C2×C411yescharacteristic
161C2×#95C2×C411yescharacteristic
162C2×#95C2×C411yescharacteristic
163C2×#95C2×C411yescharacteristic
164C2×#95C2×C411yescharacteristic
165C2×#95C2×C411yescharacteristic
166C2×#95C2×C411yescharacteristic
167C2×#95C2×C411yescharacteristic
168#336—22no—
169#336—22no—
170#336—22no—
171#336—22no—
172#336—22no—
173#336—22no—
174#336—22no—
175#336—22no—
176#336—22no—
177#336—22no—
178#336—22no—
179#336—22no—
180#336—22no—
181#336—41no—
182#336—41no—
183#336D414yes—
184C25C22×C411yescharacteristic
185C23×C4—21no—
186C23×C4—21no—
187C23×C4—21no—
188C23×C4—21no—
189C23×C4—21no—
190C23×C4—21no—
191C23×C4—21no—
192C23×C4—21no—
193C23×C4—22no—
194C23×C4—22no—
195C23×C4—22no—
196C23×C4—22no—
197C23×C4—22no—
198C23×C4—22no—
199C23×C4—22no—
200C23×C4—22no—
201C23×C4—22no—
202C23×C4—41no—
203C23×C4—41no—
204C23×C4—41no—
205C23×C4—41no—
206C23×C4C2×C814yes—
207C23×C4C22×C411yescharacteristic
208C23×C4C22×C411yescharacteristic
209C23×C4C22×C411yescharacteristic
210C23×C4C22×C411yescharacteristic
211C23×C4C22×C411yescharacteristic
212C23×C4C22×C411yescharacteristic
213C23×C4C22×C411yescharacteristic
214C23×C4C22×C411yescharacteristic
215C23×C4C22×C411yescharacteristic
216C23×C4C22×C411yescharacteristic
217C23×C4C22×C411yescharacteristic
218C23×C4C22×C411yescharacteristic
219C23×C4C22×C411yescharacteristic
220C23×C4C2×D412yes—
221C23×C4C2×D412yes—
222C23×C4C2×Q812yes—
223C23×C4C2×Q812yes—
224C23×C4#4112yes—
225C23×C4#4112yes—
226C23×C4C2411yescharacteristic
227C22×C8—21no—
228C22×C8—21no—
229C22×C8—21no—
230C22×C8—21no—
231C22×C8—28no—
232C22×C8—28no—
233C22×C8—21no—
234C22×C8—21no—
235C22×C8—21no—
236C22×C8—21no—
237C22×C8—21no—
238C22×C8—21no—
239C22×C8—21no—
240C22×C8—21no—
241C22×C8—21no—
242C22×C8—21no—
243C22×C8—21no—
244C22×C8—21no—
245C22×C8—21no—
246C22×C8—21no—
247C22×C8—21no—
248C22×C8—21no—
249C22×C8—21no—
250C22×C8—21no—
251C22×C8—21no—
252C22×C8—21no—
253C22×C8—21no—
254C22×C8—21no—
255C22×C8—21no—
256C22×C8—21no—
257C22×C8—21no—
258C22×C8—21no—
259C22×C8—21no—
260C22×C8—21no—
261C22×C8—21no—
262C22×C8—21no—
263C22×C8—28no—
264C22×C8—21no—
265C22×C8—21no—
266C22×C8—21no—
267C22×C8—21no—
268C22×C8—21no—
269C22×C8—21no—
270C22×C8—21no—
271C22×C8—21no—
272C22×C8—21no—
273C22×C8—21no—
274C22×C8—21no—
275C22×C8—21no—
276C22×C8—21no—
277C22×C8—21no—
278C22×C8—44no—
279C22×C8—44no—
280C22×C8—44no—
281C22×C8—44no—
282C22×C8—44no—
283C22×C8—44no—
284C22×C8—44no—
285C22×C8—44no—
286C22×C8—44no—
287C22×C8—44no—
288C22×C8—44no—
289C22×C8C2×D412yes—
290C22×C8C2×D412yes—
291C22×C8C2×D412yes—
292C22×C8C2×D412yes—
293C22×C8C2×Q812yes—
294C22×C8C2×Q812yes—
295C22×C8#4112yes—
296C22×C8#4112yes—
297C2×C4⋊C4—22no—
298C2×C4⋊C4—22no—
299C2×C4⋊C4—22no—
300C2×C4⋊C4—22no—
301C2×C4⋊C4—22no—
302C2×C4⋊C4—22no—
303C2×C4⋊C4—41no—
304C2×C4⋊C4—41no—
305C2×C4⋊C4—41no—
306C2×C4⋊C4—41no—
307C2×C4⋊C4C2×C814yescomplemented
308C2×C4⋊C4C2×C814yescomplemented
309C2×C22⋊C4—22no—
310C2×C22⋊C4—22no—
311C2×C22⋊C4—22no—
312C2×C22⋊C4—22no—
313C2×C22⋊C4—22no—
314C2×C22⋊C4—22no—
315C2×C22⋊C4—22no—
316C2×C22⋊C4C4⋊C414yes—
317C2×C22⋊C4C4⋊C414yes—
318C2×C22⋊C4C2×C814yes—
319C2×C22⋊C4C2×C814yes—
320C2×C22⋊C4M1614yes—
321C2×C42—21no—
322C2×C42—21no—
323C2×C42—21no—
324C2×C42—21no—
325C2×C42—21no—
326C2×C42—21no—
327C2×C42—21no—
328C2×C42—21no—
329C2×C42—21no—
330C2×C42—21no—
331C2×C42—21no—
332C2×C42—21no—
333C2×C42—22no—
334C2×C42—22no—
335C2×C42—22no—
336C2×C42—22no—
337C2×C42—21no—
338C2×C42—21no—
339C2×C42—21no—
340C2×C42—21no—
341C2×C42—21no—
342C2×C42—21no—
343C2×C42—21no—
344C2×C42—21no—
345C2×C42—21no—
346C2×C42—21no—
347C2×C42—21no—
348C2×C42—21no—
349C2×C42—21no—
350C2×C42—21no—
351C2×C42—21no—
352C2×C42—21no—
353C2×C42—21no—
354C2×C42—21no—
355C2×C42—44no—
356C2×C42—44no—
357C2×C42—44no—
358C2×C42—44no—
359C2×C42—41no—
360C2×C42—41no—
361C2×C42C2×D412yes—
362C2×C42C2×D412yes—
363C2×C42C2×D412yes—
364C2×C42C2×Q812yes—
365C2×C42C2×Q812yes—
366C2×C42#4112yes—
367C4⋊C8—44no—
368C4⋊C8—44no—
369C4⋊C8—44no—
370C4⋊C8—44no—
371C4⋊C8—44no—
372C4⋊C8—44no—
373C22⋊C8—28no—
374C22⋊C8—44no—
375C4×C8—44no—
376C4×C8—44no—
377#95—22no—
378#95—22no—
379#95—22no—
380#95—22no—
381#95—22no—
382#95—22no—
383#95—22no—
384#95—22no—
385#95—41no—
386#95—41no—
387#95—41no—
388#95—41no—
389#95C4⋊C414yes—
390#95C4⋊C414yes—
391#95C2×C814yescomplemented
392#95C2×C814yescomplemented
393C24—21no—
394C24—21no—
395C24—21no—
396C24—21no—
397C24—21no—
398C24—21no—
399C24—21no—
400C24—21no—
401C24C2×C4⋊C412yes—
402C24C4×D412yes—
403C24C4×Q812yes—
404C24C22×C812yes—
405C24C2×M1612yes—
406C24#13112yes—
407C24#13112yes—
408C24C23×C411yescharacteristic
409C22×C4—21no—
410C22×C4—21no—
411C22×C4—21no—
412C22×C4—21no—
413C22×C4—21no—
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—21no—
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—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—28no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—28no—
493C22×C4—28no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—44no—
509C22×C4—44no—
510C22×C4—44no—
511C22×C4—44no—
512C22×C4—44no—
513C22×C4—44no—
514C22×C4—44no—
515C22×C4—44no—
516C22×C4—44no—
517C22×C4—44no—
518C22×C4—44no—
519C22×C4C2×C4⋊C412yes—
520C22×C4C2×C4⋊C412yes—
521C22×C4C2×C4⋊C412yes—
522C22×C4C2×C4⋊C412yes—
523C22×C4C2×C4⋊C412yes—
524C22×C4C4×D412yes—
525C22×C4C4×D412yes—
526C22×C4C4×D412yes—
527C22×C4C4×Q812yes—
528C22×C4#12114yes—
529C22×C4C22⋊Q814yes—
530C22×C4#12514yes—
531C22×C4C4⋊Q814yes—
532C22×C4C22×C812yes—
533C22×C4C22×C812yes—
534C22×C4C22×C812yes—
535C22×C4C22×C812yes—
536C22×C4C22×C812yes—
537C22×C4C22×C812yes—
538C22×C4C2×M1612yes—
539C22×C4C2×M1612yes—
540C22×C4#13112yes—
541C22×C4#13112yes—
542C22×C4C22×D411yescharacteristic
543C22×C4C22×D411yescharacteristic
544C22×C4C22×D411yescharacteristic
545C22×C4C22×Q811yescharacteristic
546C22×C4C22×Q811yescharacteristic
547C22×C4C2×#4111yescharacteristic
548C22×C4C2×#4111yescharacteristic
549C22×C4C2×#4111yescharacteristic
550C22×C4C2×#4111yescharacteristic
551C22×C4C2×#4111yescharacteristic
552C22×C4H(5,𝔽2)11yescharacteristic
553C22×C4H(5,𝔽2)11yescharacteristic
554C22×C4H(5,𝔽2)11yescharacteristic
555C22×C42−1+411yescharacteristic
556C2×C8—22no—
557C2×C8—22no—
558C2×C8—22no—
559C2×C8—22no—
560C2×C8—22no—
561C2×C8—22no—
562C2×C8—22no—
563C2×C8—22no—
564C2×C8—22no—
565C2×C8—22no—
566C2×C8—22no—
567C2×C8—22no—
568C2×C8—22no—
569C2×C8—22no—
570C2×C8—22no—
571C2×C8—22no—
572C2×C8—22no—
573C2×C8—22no—
574C2×C8—22no—
575C2×C8—22no—
576C2×C8—22no—
577C2×C8—416no—
578C2×C8—416no—
579C2×C8—41no—
580C2×C8—41no—
581C2×C8—41no—
582C2×C8—41no—
583C2×C8—41no—
584C2×C8—41no—
585C2×C8—41no—
586C2×C8—41no—
587C2×C8—41no—
588C2×C8—41no—
589C2×C8—41no—
590C2×C8—41no—
591C2×C8—41no—
592C2×C8—41no—
593C2×C8—41no—
594C2×C8—41no—
595C2×C8—41no—
596C2×C8—41no—
597C2×C8—41no—
598C2×C8—41no—
599C2×C8—41no—
600C2×C8—41no—
601C2×C8—41no—
602C2×C8—41no—
603C2×C8—41no—
604C2×C8—41no—
605C2×C8—41no—
606C2×C8—41no—
607C2×C8—41no—
608C2×C8—41no—
609C2×C8—41no—
610C2×C8—41no—
611C2×C8—41no—
612C2×C8—41no—
613C2×C8C22⋊Q814yes—
614C4⋊C4—28no—
615C4⋊C4—44no—
616C4⋊C4—44no—
617C4⋊C4—44no—
618C22⋊C4—28no—
619C22⋊C4—28no—
620C22⋊C4—44no—
621C22⋊C4C4⋊C8116yescomplemented
622C42—22no—
623C42—22no—
624C42—22no—
625C42—22no—
626C42—22no—
627C42—22no—
628C42—22no—
629C42—22no—
630C42—22no—
631C42—22no—
632C42—22no—
633C42—22no—
634C42—44no—
635C42—44no—
636C42—41no—
637C42—41no—
638C42—41no—
639C42—41no—
640C42—41no—
641C42—41no—
642C42—41no—
643C42—41no—
644C42—41no—
645C42—41no—
646C42—41no—
647C42—41no—
648C23—22no—
649C23—22no—
650C23—22no—
651C23—22no—
652C23—22no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—22no—
657C23—22no—
658C23—22no—
659C23—22no—
660C23—22no—
661C23—22no—
662C23—22no—
663C23—22no—
664C23—22no—
665C23—22no—
666C23—22no—
667C23—22no—
668C23—22no—
669C23—22no—
670C23—22no—
671C23—22no—
672C23—22no—
673C23—22no—
674C23—22no—
675C23—22no—
676C23#38914yes—
677C23C2×C4⋊C814yes—
678C23#42414yes—
679C23C8×D414yes—
680C23#43614yes—
681C23C8×Q814yes—
682C23#44614yes—
683C23C22×C4⋊C411yescharacteristic
684C23C2×C4×D411yescharacteristic
685C23C2×C4×D411yescharacteristic
686C23C2×C4×Q811yescharacteristic
687C23C4×#4111yescharacteristic
688C23#51811yescharacteristic
689C23#52011yescharacteristic
690C23C23×C811yescharacteristic
691C23C22×M1611yescharacteristic
692C23C2×#13111yescharacteristic
693C23C2×#13111yescharacteristic
694C23C2×#13111yescharacteristic
695C23C2×#13111yescharacteristic
696C23#56811yescharacteristic
697C23#56811yescharacteristic
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—24no—
723C2×C4—24no—
724C2×C4—24no—
725C2×C4—24no—
726C2×C4—24no—
727C2×C4—24no—
728C2×C4—24no—
729C2×C4—24no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—416no—
752C2×C4—416no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4#38914yes—
796C2×C4C2×C4⋊C814yes—
797C2×C4C2×C4⋊C814yes—
798C2×C4C8×D414yes—
799C2×C4C2×#12111yescharacteristic
800C2×C4C2×C22⋊Q811yescharacteristic
801C2×C4C2×C22⋊Q811yescharacteristic
802C2×C4#52511yescharacteristic
803C2×C4C2×#12511yescharacteristic
804C2×C4#52911yescharacteristic
805C2×C4C2×C4⋊Q811yescharacteristic
806C2×C4#53311yescharacteristic
807C2×C4#53811yescharacteristic
808C2×C4#53911yescharacteristic
809C2×C4#54311yescharacteristic
810C2×C4#54411yescharacteristic
811C2×C4D4211yescharacteristic
812C2×C4D4211yescharacteristic
813C2×C4#54611yescharacteristic
814C2×C4#54611yescharacteristic
815C2×C4#54611yescharacteristic
816C2×C4#54611yescharacteristic
817C2×C4#54611yescharacteristic
818C2×C4#54711yescharacteristic
819C2×C4#54711yescharacteristic
820C2×C4D4×Q811yescharacteristic
821C2×C4#55111yescharacteristic
822C2×C4#55111yescharacteristic
823C2×C4#55211yescharacteristic
824C2×C4#55411yescharacteristic
825C2×C4#55411yescharacteristic
826C2×C4#55411yescharacteristic
827C8—24no—
828C8—42no—
829C8—42no—
830C8—42no—
831C8—42no—
832C8—42no—
833C8—81no—
834C8—81no—
835C22—24no—
836C22—24no—
837C22—24no—
838C22—24no—
839C22—24no—
840C22—24no—
841C22—24no—
842C22—24no—
843C22—24no—
844C22—24no—
845C22—24no—
846C22—24no—
847C22—24no—
848C22—24no—
849C22#193918yescomplemented
850C22C2×#38911yescharacteristic
851C22C4×C22⋊Q811yescharacteristic
852C22#232911yescharacteristic
853C22D4×C4⋊C411yescharacteristic
854C22#234911yescharacteristic
855C22#235811yescharacteristic
856C22#235911yescharacteristic
857C22C22×C4⋊C811yescharacteristic
858C22C2×#42411yescharacteristic
859C22#290611yescharacteristic
860C22#290611yescharacteristic
861C22C2×C8×D411yescharacteristic
862C22C2×C8×D411yescharacteristic
863C22C2×#43611yescharacteristic
864C22#292911yescharacteristic
865C22#293311yescharacteristic
866C22#293311yescharacteristic
867C22#293311yescharacteristic
868C22D4×M1611yescharacteristic
869C22C2×C8×Q811yescharacteristic
870C22C2×#44611yescharacteristic
871C22#296011yescharacteristic
872C22#296111yescharacteristic
873C22C8×#4111yescharacteristic
874C22#296611yescharacteristic
875C22#296811yescharacteristic
876C22#297011yescharacteristic
877C22#297211yescharacteristic
878C22#297411yescharacteristic
879C22#297611yescharacteristic
880C22#297711yescharacteristic
881C22#298811yescharacteristic
882C22#299011yescharacteristic
883C22#299211yescharacteristic
884C22#299411yescharacteristic
885C4—24no—
886C4—24no—
887C4—24no—
888C4—24no—
889C4—42no—
890C4—42no—
891C4—42no—
892C4—42no—
893C4—42no—
894C4—42no—
895C4—42no—
896C4—81no—
897C4—81no—
898C4#242411yescharacteristic
899C4#242511yescharacteristic
900C4#243711yescharacteristic
901C4#243811yescharacteristic
902C4#244011yescharacteristic
903C4#247311yescharacteristic
904C4#250511yescharacteristic
905C4#254911yescharacteristic
906C2—28no—
907C2#1400411yescharacteristic
908C2C2×#193911yescharacteristic
909C2#2114811yescharacteristic
910C2C8×C22⋊Q811yescharacteristic
911C2#2159911yescharacteristic
912C2#2228711yescharacteristic
913C2#2229111yescharacteristic
914C2D4×C4⋊C811yescharacteristic
915C2#2264711yescharacteristic
916C2#2269611yescharacteristic
917C2#2269711yescharacteristic
918C2#2284211yescharacteristic
919C2#2284811yescharacteristic
920C2#2290011yescharacteristic
921C2#2291011yescharacteristic
subgroupG/H
center, Frattini, cosocleC23×C4C24
commutatorC23C23×C8
socleC24C23×C4
prime radicalC25C22×C4
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C4 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#1939C2semidirect
8. #11322C2semidirect
9. #11255C2semidirect
10. #11202C2semidirect
11. #11202C2semidirect
12. #10876C2semidirect
13. #10876C2semidirect
14. #10834C2semidirect
143. #385C8semidirect
307. C2×C4⋊C4C2×C8semidirect
308. C2×C4⋊C4C2×C8semidirect
391. #95C2×C8semidirect
392. #95C2×C8semidirect
621. C22⋊C4C4⋊C8semidirect
849. C22#1939semidirect

Maximal subgroups

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

subgroupindex
C2×#19392
C2×#18502
C2×#17972
C2×C8×C22⋊C42
C22×#3362
C4×#3852
#113222
#112552
#112022
#108762
#108342
#107142