Finite Group Databasebeta

← #123451

Subgroups — #123451

Order 512.

1974 conjugacy classes of subgroups.

The subgroup lattice has 1031 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#405C211yesmaximal, characteristic
2C22×#341C211yesmaximal, characteristic
3C2×#1735C211yesmaximal, characteristic
4C22×#339C211yesmaximal, characteristic
5C22×#339C211yesmaximal, characteristic
6C2×#1729C211yesmaximal, characteristic
7C22×#336C211yesmaximal, characteristic
8C23×M16C2211yescharacteristic
9C23×M16C2211yescharacteristic
10C24×C8C2211yescharacteristic
11C24×C8C2211yescharacteristic
12C22×#117C2211yescharacteristic
13C22×#117C2211yescharacteristic
14C23×C42C2211yescharacteristic
15C2×#405—22no—
16C2×#405—22no—
17C2×#405—22no—
18C2×#405—22no—
19C2×#405—22no—
20C2×#405C414yescomplemented
21C22×#97—21no—
22C22×C4×C8—21no—
23C2×#341—22no—
24C2×#341—22no—
25C2×#341C414yescomplemented
26#1735—22no—
27#1735—22no—
28C2×#340C414yescomplemented
29C2×#339—22no—
30C2×#339—22no—
31C2×#339—22no—
32C2×#339—22no—
33C2×#339C414yescomplemented
34C2×#339C414yescomplemented
35#1729—22no—
36#1729C414yescomplemented
37C2×#336—22no—
38C2×#336—22no—
39C2×#336—21no—
40C2×#336—21no—
41C2×#336C414yescomplemented
42C24×C4—21no—
43C24×C4C2311yescharacteristic
44C22×M16—21no—
45C22×M16—21no—
46C22×M16—21no—
47C22×M16—21no—
48C22×M16—21no—
49C22×M16—21no—
50C22×M16—21no—
51C22×M16—21no—
52C22×M16—21no—
53C22×M16—21no—
54C22×M16—21no—
55C22×M16—21no—
56C22×M16—21no—
57C22×M16—21no—
58C22×M16—21no—
59C22×M16—21no—
60C22×M16—21no—
61C22×M16—21no—
62C22×M16C2×C412yes—
63C22×M16C2×C412yes—
64C22×M16C2×C412yes—
65C22×M16C2×C412yes—
66C22×M16C2×C412yes—
67C22×M16C2×C412yes—
68C22×M16D412yes—
69C22×M16D412yes—
70C22×M16D412yes—
71C22×M16Q812yes—
72C23×C8—21no—
73C23×C8—21no—
74C23×C8—21no—
75C23×C8—21no—
76C23×C8—21no—
77C23×C8—21no—
78C23×C8—21no—
79C23×C8—21no—
80C23×C8—21no—
81C23×C8—21no—
82C23×C8—21no—
83C23×C8—21no—
84C23×C8—21no—
85C23×C8—21no—
86C23×C8—21no—
87C23×C8—21no—
88C23×C8—21no—
89C23×C8—21no—
90C23×C8—21no—
91C23×C8—21no—
92C23×C8—21no—
93C23×C8—21no—
94C23×C8C2×C412yes—
95C23×C8C2×C412yes—
96C23×C8C2×C412yes—
97C23×C8C2×C412yes—
98C23×C8C2×C412yes—
99C23×C8C2×C412yes—
100C23×C8D412yes—
101C23×C8D412yes—
102C23×C8D411yescharacteristic
103C23×C8D411yescharacteristic
104C23×C8Q812yes—
105C2×#117—21no—
106C2×#117—21no—
107C2×#117—21no—
108C2×#117—21no—
109C2×#117—21no—
110C2×#117—21no—
111C2×#117—21no—
112C2×#117—21no—
113C2×#117—21no—
114C2×#117—21no—
115C2×#117—21no—
116C2×#117—21no—
117C2×#117—21no—
118C2×#117—21no—
119C2×#117—21no—
120C2×#117—21no—
121C2×#117C2×C412yes—
122C2×#117C2×C412yes—
123C2×#117C2×C412yes—
124C2×#117C2×C412yes—
125C2×#117D412yes—
126C2×#117D412yes—
127C2×#117D412yes—
128C2×#117Q812yes—
129C22×C4⋊C4C2×C412yes—
130C22×C4⋊C4C2×C412yes—
131C22×C22⋊C4—21no—
132C22×C22⋊C4—21no—
133C22×C42—21no—
134C22×C42—21no—
135C22×C42—21no—
136C22×C42—21no—
137C22×C42—21no—
138C22×C42—21no—
139C22×C42—21no—
140C22×C42—21no—
141C22×C42—21no—
142C22×C42—21no—
143C22×C42—21no—
144C22×C42—21no—
145C22×C42—21no—
146C22×C42C2×C412yes—
147C22×C42C2×C412yes—
148C22×C42C2×C412yes—
149#405—28no—
150#405—28no—
151#405—28no—
152#405—28no—
153C2×#97—24no—
154C2×#97—24no—
155C2×#97—24no—
156C2×C4×C8—24no—
157C2×C4×C8—24no—
158C2×C4×C8—24no—
159#341—28no—
160#340—28no—
161#339—28no—
162#339—28no—
163#336—28no—
164#336—24no—
165#336—24no—
166C25#4111yescharacteristic
167C23×C4—28no—
168C23×C4—22no—
169C23×C4—22no—
170C23×C4—22no—
171C23×C4—22no—
172C23×C4—22no—
173C23×C4—44no—
174C23×C4—41no—
175C23×C4—41no—
176C23×C4—41no—
177C23×C4—41no—
178C23×C4C22×C411yescharacteristic
179C23×C4C22×C411yescharacteristic
180C23×C4C22×C411yescharacteristic
181C23×C4C22×C411yescharacteristic
182C23×C4C22×C411yescharacteristic
183C23×C4C22×C411yescharacteristic
184C23×C4C22×C411yescharacteristic
185C23×C4C2×D411yescharacteristic
186C23×C4C2×D411yescharacteristic
187C23×C4C2×D411yescharacteristic
188C23×C4C2×D411yescharacteristic
189C23×C4C2×D411yescharacteristic
190C23×C4C2×D411yescharacteristic
191C23×C4C2×D411yescharacteristic
192C23×C4C2×D411yescharacteristic
193C23×C4C2×D411yescharacteristic
194C23×C4C2×Q811yescharacteristic
195C23×C4C2×Q811yescharacteristic
196C23×C4C2×Q811yescharacteristic
197C23×C4#4111yescharacteristic
198C23×C4#4111yescharacteristic
199C23×C4#4111yescharacteristic
200C23×C4#4111yescharacteristic
201C23×C4#4111yescharacteristic
202C23×C4#4111yescharacteristic
203C23×C4#4111yescharacteristic
204C23×C4#4111yescharacteristic
205C23×C4#4111yescharacteristic
206C23×C4#4111yescharacteristic
207C23×C4#4111yescharacteristic
208C2×M16—22no—
209C2×M16—22no—
210C2×M16—22no—
211C2×M16—22no—
212C2×M16—22no—
213C2×M16—22no—
214C2×M16—22no—
215C2×M16—22no—
216C2×M16—22no—
217C2×M16—22no—
218C2×M16—22no—
219C2×M16—22no—
220C2×M16—22no—
221C2×M16—22no—
222C2×M16—22no—
223C2×M16—22no—
224C2×M16—22no—
225C2×M16—22no—
226C2×M16—22no—
227C2×M16—22no—
228C2×M16—22no—
229C2×M16—22no—
230C2×M16—22no—
231C2×M16—22no—
232C2×M16—22no—
233C2×M16—22no—
234C2×M16—22no—
235C2×M16—22no—
236C2×M16—22no—
237C2×M16—22no—
238C2×M16—22no—
239C2×M16—22no—
240C2×M16—22no—
241C2×M16—22no—
242C2×M16—22no—
243C2×M16—22no—
244C2×M16—41no—
245C2×M16—41no—
246C2×M16—41no—
247C2×M16—41no—
248C2×M16—41no—
249C2×M16—41no—
250C2×M16—41no—
251C2×M16—41no—
252C2×M16—41no—
253C2×M16—41no—
254C2×M16—41no—
255C2×M16—41no—
256C2×M16C4214yes—
257C2×M16C4214yes—
258C2×M16C22⋊C414yes—
259C2×M16C22⋊C414yes—
260C2×M16C22⋊C414yes—
261C2×M16C4⋊C414yes—
262C2×M16C4⋊C414yes—
263C2×M16C4⋊C414yes—
264C22×C8—22no—
265C22×C8—22no—
266C22×C8—22no—
267C22×C8—22no—
268C22×C8—22no—
269C22×C8—22no—
270C22×C8—22no—
271C22×C8—22no—
272C22×C8—22no—
273C22×C8—22no—
274C22×C8—22no—
275C22×C8—22no—
276C22×C8—22no—
277C22×C8—22no—
278C22×C8—22no—
279C22×C8—21no—
280C22×C8—21no—
281C22×C8—21no—
282C22×C8—21no—
283C22×C8—22no—
284C22×C8—22no—
285C22×C8—22no—
286C22×C8—22no—
287C22×C8—22no—
288C22×C8—22no—
289C22×C8—22no—
290C22×C8—22no—
291C22×C8—22no—
292C22×C8—22no—
293C22×C8—22no—
294C22×C8—22no—
295C22×C8—22no—
296C22×C8—22no—
297C22×C8—22no—
298C22×C8—21no—
299C22×C8—21no—
300C22×C8—22no—
301C22×C8—21no—
302C22×C8—21no—
303C22×C8—22no—
304C22×C8—22no—
305C22×C8—22no—
306C22×C8—22no—
307C22×C8—22no—
308C22×C8—22no—
309C22×C8—22no—
310C22×C8—22no—
311C22×C8—22no—
312C22×C8—22no—
313C22×C8—22no—
314C22×C8—22no—
315C22×C8—22no—
316C22×C8—22no—
317C22×C8—22no—
318C22×C8—22no—
319C22×C8—22no—
320C22×C8—22no—
321C22×C8—22no—
322C22×C8—22no—
323C22×C8—22no—
324C22×C8—41no—
325C22×C8—41no—
326C22×C8—41no—
327C22×C8—41no—
328C22×C8—41no—
329C22×C8—41no—
330C22×C8—41no—
331C22×C8—41no—
332C22×C8—41no—
333C22×C8—41no—
334C22×C8—41no—
335C22×C8—41no—
336C22×C8—41no—
337C22×C8—41no—
338C22×C8—41no—
339C22×C8—41no—
340C22×C8—41no—
341C22×C8—41no—
342C22×C8—41no—
343C22×C8—41no—
344C22×C8C4214yes—
345C22×C8C4214yes—
346C22×C8C22⋊C414yes—
347C22×C8C22⋊C412yes—
348C22×C8C22⋊C412yes—
349C22×C8C22⋊C412yes—
350C22×C8C22⋊C412yes—
351C22×C8C4⋊C414yes—
352C22×C8C4⋊C414yes—
353C22×C8C4⋊C412yes—
354C22×C8C4⋊C412yes—
355#117—22no—
356#117—22no—
357#117—22no—
358#117—22no—
359#117—22no—
360#117—22no—
361#117—22no—
362#117—22no—
363#117—22no—
364#117—22no—
365#117—22no—
366#117—22no—
367#117—22no—
368#117—22no—
369#117—22no—
370#117—22no—
371#117—22no—
372#117—22no—
373#117—22no—
374#117—22no—
375#117—41no—
376#117—41no—
377#117—41no—
378#117—41no—
379#117—41no—
380#117—41no—
381#117—41no—
382#117—41no—
383#117C22⋊C414yes—
384#117C22⋊C414yes—
385#117C4⋊C414yes—
386#117C4⋊C414yes—
387C2×C4⋊C4—22no—
388C2×C4⋊C4—22no—
389C2×C4⋊C4—22no—
390C2×C4⋊C4—22no—
391C2×C4⋊C4—22no—
392C2×C4⋊C4—22no—
393C2×C4⋊C4—22no—
394C2×C4⋊C4—22no—
395C2×C4⋊C4C4214yes—
396C2×C4⋊C4C4214yes—
397C2×C4⋊C4C22⋊C414yes—
398C2×C4⋊C4C4⋊C414yes—
399C2×C22⋊C4—22no—
400C2×C22⋊C4—22no—
401C2×C22⋊C4—22no—
402C2×C22⋊C4—22no—
403C2×C22⋊C4—22no—
404C2×C22⋊C4—22no—
405C2×C22⋊C4—22no—
406C2×C22⋊C4—22no—
407C2×C22⋊C4—41no—
408C2×C22⋊C4—41no—
409C2×C22⋊C4—41no—
410C2×C22⋊C4—41no—
411C2×C42—22no—
412C2×C42—22no—
413C2×C42—22no—
414C2×C42—22no—
415C2×C42—22no—
416C2×C42—22no—
417C2×C42—22no—
418C2×C42—22no—
419C2×C42—22no—
420C2×C42—22no—
421C2×C42—22no—
422C2×C42—22no—
423C2×C42—22no—
424C2×C42—22no—
425C2×C42—22no—
426C2×C42—22no—
427C2×C42—22no—
428C2×C42—22no—
429C2×C42—22no—
430C2×C42—22no—
431C2×C42—22no—
432C2×C42—22no—
433C2×C42—22no—
434C2×C42—41no—
435C2×C42—41no—
436C2×C42—41no—
437C2×C42—41no—
438C2×C42—41no—
439C2×C42—41no—
440C2×C42—41no—
441C2×C42—41no—
442C2×C42—41no—
443C2×C42—41no—
444C2×C42—41no—
445C2×C42—41no—
446C2×C42—41no—
447C2×C42—41no—
448C2×C42—41no—
449C2×C42—41no—
450C2×C42C4214yes—
451#97—216no—
452C4×C8—216no—
453C24—24no—
454C24—24no—
455C24#11711yescharacteristic
456C24#11711yescharacteristic
457C24#11711yescharacteristic
458C24C4×D411yescharacteristic
459C24C4×D411yescharacteristic
460C24C4×D411yescharacteristic
461C24C4×Q811yescharacteristic
462C24#12111yescharacteristic
463C24C22⋊Q811yescharacteristic
464C24#12311yescharacteristic
465C24#12311yescharacteristic
466C24#12411yescharacteristic
467C24#12511yescharacteristic
468C24#12611yescharacteristic
469C24#12611yescharacteristic
470C22×C4—28no—
471C22×C4—28no—
472C22×C4—28no—
473C22×C4—24no—
474C22×C4—24no—
475C22×C4—24no—
476C22×C4—24no—
477C22×C4—24no—
478C22×C4—48no—
479C22×C4—48no—
480C22×C4—48no—
481C22×C4—48no—
482C22×C4—44no—
483C22×C4—44no—
484C22×C4—44no—
485C22×C4—42no—
486C22×C4—42no—
487C22×C4—42no—
488C22×C4—42no—
489C22×C4—42no—
490C22×C4—42no—
491C22×C4—44no—
492C22×C4—44no—
493C22×C4—42no—
494C22×C4—42no—
495C22×C4—44no—
496C22×C4—44no—
497C22×C4C2×C4211yescharacteristic
498C22×C4C2×C4211yescharacteristic
499C22×C4C2×C4211yescharacteristic
500C22×C4C2×C4211yescharacteristic
501C22×C4C2×C4211yescharacteristic
502C22×C4C2×C4211yescharacteristic
503C22×C4C2×C4211yescharacteristic
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×C22⋊C411yescharacteristic
511C22×C4C2×C22⋊C411yescharacteristic
512C22×C4C2×C22⋊C411yescharacteristic
513C22×C4C2×C4⋊C411yescharacteristic
514C22×C4C2×C4⋊C411yescharacteristic
515C22×C4C2×C4⋊C411yescharacteristic
516C22×C4C2×C4⋊C411yescharacteristic
517C22×C4C2×C4⋊C411yescharacteristic
518C22×C4C2×C4⋊C411yescharacteristic
519C22×C4C2×C4⋊C411yescharacteristic
520C22×C4C2×C4⋊C411yescharacteristic
521C22×C4C2×C4⋊C411yescharacteristic
522C22×C4#11711yescharacteristic
523C22×C4#11711yescharacteristic
524C22×C4#11711yescharacteristic
525C22×C4#11711yescharacteristic
526C22×C4#11711yescharacteristic
527C22×C4#11711yescharacteristic
528C22×C4#11711yescharacteristic
529C22×C4#11711yescharacteristic
530C22×C4#11711yescharacteristic
531C22×C4#11711yescharacteristic
532C22×C4#11711yescharacteristic
533C22×C4#11711yescharacteristic
534C22×C4#11711yescharacteristic
535C22×C4#11711yescharacteristic
536C22×C4#11711yescharacteristic
537C22×C4C4×D411yescharacteristic
538C22×C4C4×D411yescharacteristic
539C22×C4C4×D411yescharacteristic
540C22×C4C4×D411yescharacteristic
541C22×C4C4×D411yescharacteristic
542C22×C4C4×D411yescharacteristic
543C22×C4C4×D411yescharacteristic
544C22×C4C4×D411yescharacteristic
545C22×C4C4×D411yescharacteristic
546C22×C4C4×D411yescharacteristic
547C22×C4C4×D411yescharacteristic
548C22×C4C4×D411yescharacteristic
549C22×C4C4×D411yescharacteristic
550C22×C4C4×D411yescharacteristic
551C22×C4C4×D411yescharacteristic
552C22×C4C4×D411yescharacteristic
553C22×C4C4×D411yescharacteristic
554C22×C4C4×D411yescharacteristic
555C22×C4C4×D411yescharacteristic
556C22×C4C4×D411yescharacteristic
557C22×C4C4×D411yescharacteristic
558C22×C4C4×D411yescharacteristic
559C22×C4C4×D411yescharacteristic
560C22×C4C4×D411yescharacteristic
561C22×C4C4×D411yescharacteristic
562C22×C4C4×D411yescharacteristic
563C22×C4C4×D411yescharacteristic
564C22×C4C4×D411yescharacteristic
565C22×C4C4×D411yescharacteristic
566C22×C4C4×D411yescharacteristic
567C22×C4C4×D411yescharacteristic
568C22×C4C4×D411yescharacteristic
569C22×C4C4×D411yescharacteristic
570C22×C4C4×Q811yescharacteristic
571C22×C4C4×Q811yescharacteristic
572C22×C4C4×Q811yescharacteristic
573C22×C4C4×Q811yescharacteristic
574C22×C4C4×Q811yescharacteristic
575C22×C4C4×Q811yescharacteristic
576C22×C4C4×Q811yescharacteristic
577C22×C4C4×Q811yescharacteristic
578C22×C4C4×Q811yescharacteristic
579C22×C4C4×Q811yescharacteristic
580C22×C4C4×Q811yescharacteristic
581C22×C4#12011yescharacteristic
582C22×C4#12011yescharacteristic
583C22×C4#12011yescharacteristic
584C22×C4#12011yescharacteristic
585C22×C4#12111yescharacteristic
586C22×C4#12111yescharacteristic
587C22×C4#12111yescharacteristic
588C22×C4#12111yescharacteristic
589C22×C4#12111yescharacteristic
590C22×C4#12111yescharacteristic
591C22×C4#12111yescharacteristic
592C22×C4#12111yescharacteristic
593C22×C4#12111yescharacteristic
594C22×C4#12111yescharacteristic
595C22×C4#12111yescharacteristic
596C22×C4C22⋊Q811yescharacteristic
597C22×C4C22⋊Q811yescharacteristic
598C22×C4C22⋊Q811yescharacteristic
599C22×C4C22⋊Q811yescharacteristic
600C22×C4C22⋊Q811yescharacteristic
601C22×C4C22⋊Q811yescharacteristic
602C22×C4C22⋊Q811yescharacteristic
603C22×C4C22⋊Q811yescharacteristic
604C22×C4C22⋊Q811yescharacteristic
605C22×C4C22⋊Q811yescharacteristic
606C22×C4C22⋊Q811yescharacteristic
607C22×C4#12311yescharacteristic
608C22×C4#12311yescharacteristic
609C22×C4#12311yescharacteristic
610C22×C4#12311yescharacteristic
611C22×C4#12311yescharacteristic
612C22×C4#12311yescharacteristic
613C22×C4#12311yescharacteristic
614C22×C4#12311yescharacteristic
615C22×C4#12311yescharacteristic
616C22×C4#12311yescharacteristic
617C22×C4#12411yescharacteristic
618C22×C4#12411yescharacteristic
619C22×C4#12411yescharacteristic
620C22×C4#12411yescharacteristic
621C22×C4#12411yescharacteristic
622C22×C4#12511yescharacteristic
623C22×C4#12511yescharacteristic
624C22×C4#12511yescharacteristic
625C22×C4#12511yescharacteristic
626C22×C4#12511yescharacteristic
627C22×C4#12611yescharacteristic
628C22×C4#12611yescharacteristic
629C22×C4#12611yescharacteristic
630C22×C4#12611yescharacteristic
631C22×C4#12611yescharacteristic
632C22×C4#12611yescharacteristic
633C22×C4#12711yescharacteristic
634C22×C4C4⋊Q811yescharacteristic
635C22×C4C4⋊Q811yescharacteristic
636C22×C4C4⋊Q811yescharacteristic
637M16—24no—
638M16—24no—
639M16—24no—
640M16—24no—
641M16—24no—
642M16—24no—
643M16—24no—
644M16—24no—
645M16—24no—
646M16—42no—
647M16—42no—
648M16—42no—
649M16—42no—
650M16—42no—
651M16—42no—
652M16#9518yes—
653C2×C8—24no—
654C2×C8—24no—
655C2×C8—24no—
656C2×C8—22no—
657C2×C8—24no—
658C2×C8—22no—
659C2×C8—24no—
660C2×C8—24no—
661C2×C8—24no—
662C2×C8—22no—
663C2×C8—22no—
664C2×C8—22no—
665C2×C8—22no—
666C2×C8—22no—
667C2×C8—22no—
668C2×C8—24no—
669C2×C8—24no—
670C2×C8—24no—
671C2×C8—24no—
672C2×C8—22no—
673C2×C8—22no—
674C2×C8—24no—
675C2×C8—22no—
676C2×C8—22no—
677C2×C8—24no—
678C2×C8—24no—
679C2×C8—24no—
680C2×C8—24no—
681C2×C8—24no—
682C2×C8—24no—
683C2×C8—24no—
684C2×C8—42no—
685C2×C8—42no—
686C2×C8—42no—
687C2×C8—42no—
688C2×C8—42no—
689C2×C8—42no—
690C2×C8—42no—
691C2×C8—42no—
692C2×C8—42no—
693C2×C8—42no—
694C2×C8—42no—
695C2×C8—42no—
696C2×C8—42no—
697C2×C8—42no—
698C2×C8—42no—
699C2×C8—42no—
700C2×C8—42no—
701C2×C8—42no—
702C2×C8#9514yes—
703C2×C8#9514yes—
704C4⋊C4—24no—
705C4⋊C4—24no—
706C4⋊C4—24no—
707C4⋊C4—24no—
708C4⋊C4—24no—
709C4⋊C4—42no—
710C4⋊C4—42no—
711C4⋊C4#9518yes—
712C22⋊C4—24no—
713C22⋊C4—24no—
714C22⋊C4—24no—
715C22⋊C4—24no—
716C22⋊C4—42no—
717C22⋊C4—42no—
718C22⋊C4—42no—
719C22⋊C4—42no—
720C42—24no—
721C42—24no—
722C42—24no—
723C42—24no—
724C42—24no—
725C42—24no—
726C42—42no—
727C42—42no—
728C42—42no—
729C42—42no—
730C42—42no—
731C42—42no—
732C42—42no—
733C42—42no—
734C42—42no—
735C42—42no—
736C23—24no—
737C23—24no—
738C23—24no—
739C23—24no—
740C23—24no—
741C23—24no—
742C23—24no—
743C23—24no—
744C23—22no—
745C23—22no—
746C23—22no—
747C23—22no—
748C23—22no—
749C23—22no—
750C23—22no—
751C23—22no—
752C23—22no—
753C23—22no—
754C23—22no—
755C23—22no—
756C23#37611yescharacteristic
757C23C4×C22⋊C411yescharacteristic
758C23C4×C22⋊C411yescharacteristic
759C23C4×C22⋊C411yescharacteristic
760C23C4×C4⋊C411yescharacteristic
761C23C4×C4⋊C411yescharacteristic
762C23C4×C4⋊C411yescharacteristic
763C23#38011yescharacteristic
764C23#38111yescharacteristic
765C23#38211yescharacteristic
766C23#38311yescharacteristic
767C23#38511yescharacteristic
768C23#38511yescharacteristic
769C23#38611yescharacteristic
770C23#38611yescharacteristic
771C23#38711yescharacteristic
772C23#38711yescharacteristic
773C23#38711yescharacteristic
774C23#38711yescharacteristic
775C23#38711yescharacteristic
776C23#38711yescharacteristic
777C23#38711yescharacteristic
778C23#38711yescharacteristic
779C23#38811yescharacteristic
780C23#38811yescharacteristic
781C23#38811yescharacteristic
782C23#38811yescharacteristic
783C23#38811yescharacteristic
784C23#38811yescharacteristic
785C23#38811yescharacteristic
786C23#38811yescharacteristic
787C23#38911yescharacteristic
788C23#38911yescharacteristic
789C23#39011yescharacteristic
790C23#39111yescharacteristic
791C23#44314yes—
792C23#44414yes—
793C2×C4—28no—
794C2×C4—28no—
795C2×C4—48no—
796C2×C4—48no—
797C2×C4—48no—
798C2×C4—48no—
799C2×C4—48no—
800C2×C4—48no—
801C2×C4—44no—
802C2×C4—48no—
803C2×C4—48no—
804C2×C4—44no—
805C2×C4—44no—
806C2×C4—44no—
807C2×C4—44no—
808C2×C4—44no—
809C2×C4—44no—
810C2×C4—84no—
811C2×C4—84no—
812C2×C4C4311yescharacteristic
813C2×C4C2×#9511yescharacteristic
814C2×C4C2×#9511yescharacteristic
815C2×C4C2×#9511yescharacteristic
816C2×C4#37611yescharacteristic
817C2×C4#37611yescharacteristic
818C2×C4C4×C22⋊C411yescharacteristic
819C2×C4C4×C22⋊C411yescharacteristic
820C2×C4C4×C22⋊C411yescharacteristic
821C2×C4C4×C22⋊C411yescharacteristic
822C2×C4C4×C22⋊C411yescharacteristic
823C2×C4C4×C22⋊C411yescharacteristic
824C2×C4C4×C22⋊C411yescharacteristic
825C2×C4C4×C22⋊C411yescharacteristic
826C2×C4C4×C22⋊C411yescharacteristic
827C2×C4C4×C22⋊C411yescharacteristic
828C2×C4C4×C22⋊C411yescharacteristic
829C2×C4C4×C22⋊C411yescharacteristic
830C2×C4C4×C22⋊C411yescharacteristic
831C2×C4C4×C22⋊C411yescharacteristic
832C2×C4C4×C22⋊C411yescharacteristic
833C2×C4C4×C4⋊C411yescharacteristic
834C2×C4C4×C4⋊C411yescharacteristic
835C2×C4C4×C4⋊C411yescharacteristic
836C2×C4C4×C4⋊C411yescharacteristic
837C2×C4C4×C4⋊C411yescharacteristic
838C2×C4C4×C4⋊C411yescharacteristic
839C2×C4C4×C4⋊C411yescharacteristic
840C2×C4C4×C4⋊C411yescharacteristic
841C2×C4C4×C4⋊C411yescharacteristic
842C2×C4C4×C4⋊C411yescharacteristic
843C2×C4C4×C4⋊C411yescharacteristic
844C2×C4C4×C4⋊C411yescharacteristic
845C2×C4C4×C4⋊C411yescharacteristic
846C2×C4C4×C4⋊C411yescharacteristic
847C2×C4C4×C4⋊C411yescharacteristic
848C2×C4#37911yescharacteristic
849C2×C4#38011yescharacteristic
850C2×C4#38011yescharacteristic
851C2×C4#38011yescharacteristic
852C2×C4#38011yescharacteristic
853C2×C4#38011yescharacteristic
854C2×C4#38111yescharacteristic
855C2×C4#38111yescharacteristic
856C2×C4#38211yescharacteristic
857C2×C4#38211yescharacteristic
858C2×C4#38311yescharacteristic
859C2×C4#38411yescharacteristic
860C2×C4#38511yescharacteristic
861C2×C4#38511yescharacteristic
862C2×C4#38511yescharacteristic
863C2×C4#38511yescharacteristic
864C2×C4#38511yescharacteristic
865C2×C4#38511yescharacteristic
866C2×C4#38511yescharacteristic
867C2×C4#38511yescharacteristic
868C2×C4#38511yescharacteristic
869C2×C4#38511yescharacteristic
870C2×C4#38611yescharacteristic
871C2×C4#38611yescharacteristic
872C2×C4#38611yescharacteristic
873C2×C4#38611yescharacteristic
874C2×C4#38611yescharacteristic
875C2×C4#38611yescharacteristic
876C2×C4#38611yescharacteristic
877C2×C4#38611yescharacteristic
878C2×C4#38611yescharacteristic
879C2×C4#38611yescharacteristic
880C2×C4#38711yescharacteristic
881C2×C4#38711yescharacteristic
882C2×C4#38711yescharacteristic
883C2×C4#38711yescharacteristic
884C2×C4#38711yescharacteristic
885C2×C4#38711yescharacteristic
886C2×C4#38711yescharacteristic
887C2×C4#38711yescharacteristic
888C2×C4#38711yescharacteristic
889C2×C4#38711yescharacteristic
890C2×C4#38711yescharacteristic
891C2×C4#38711yescharacteristic
892C2×C4#38711yescharacteristic
893C2×C4#38711yescharacteristic
894C2×C4#38711yescharacteristic
895C2×C4#38711yescharacteristic
896C2×C4#38811yescharacteristic
897C2×C4#38811yescharacteristic
898C2×C4#38811yescharacteristic
899C2×C4#38811yescharacteristic
900C2×C4#38811yescharacteristic
901C2×C4#38811yescharacteristic
902C2×C4#38811yescharacteristic
903C2×C4#38811yescharacteristic
904C2×C4#38811yescharacteristic
905C2×C4#38811yescharacteristic
906C2×C4#38811yescharacteristic
907C2×C4#38811yescharacteristic
908C2×C4#38811yescharacteristic
909C2×C4#38811yescharacteristic
910C2×C4#38811yescharacteristic
911C2×C4#38811yescharacteristic
912C2×C4#38911yescharacteristic
913C2×C4#38911yescharacteristic
914C2×C4#38911yescharacteristic
915C2×C4#38911yescharacteristic
916C2×C4#38911yescharacteristic
917C2×C4#38911yescharacteristic
918C2×C4#38911yescharacteristic
919C2×C4#38911yescharacteristic
920C2×C4#38911yescharacteristic
921C2×C4#38911yescharacteristic
922C2×C4#39011yescharacteristic
923C2×C4#39011yescharacteristic
924C2×C4#39011yescharacteristic
925C2×C4#39011yescharacteristic
926C2×C4#39011yescharacteristic
927C2×C4#39111yescharacteristic
928C2×C4#39111yescharacteristic
929C2×C4#39111yescharacteristic
930C2×C4#39111yescharacteristic
931C2×C4#39111yescharacteristic
932C8—24no—
933C8—24no—
934C8—28no—
935C8—44no—
936C8—44no—
937C22—22no—
938C22—22no—
939C22—22no—
940C22—22no—
941C22—22no—
942C22—22no—
943C22—22no—
944C22—22no—
945C22—22no—
946C22—22no—
947C22—22no—
948C22—22no—
949C22—22no—
950C22—22no—
951C22—22no—
952C22—22no—
953C22—22no—
954C22—22no—
955C22—22no—
956C22—22no—
957C22—22no—
958C22—22no—
959C22—22no—
960C22—22no—
961C22—21no—
962C22—21no—
963C22—21no—
964C22—21no—
965C22—21no—
966C22—21no—
967C22—21no—
968C22—21no—
969C22C4×#9511yescharacteristic
970C22C22⋊#9511yescharacteristic
971C22#143411yescharacteristic
972C22#143411yescharacteristic
973C22#143411yescharacteristic
974C22#143411yescharacteristic
975C22C4⋊#9511yescharacteristic
976C22#143611yescharacteristic
977C22#143611yescharacteristic
978C22#143611yescharacteristic
979C22#143611yescharacteristic
980C22#143611yescharacteristic
981C22#143611yescharacteristic
982C22#143711yescharacteristic
983C22#143711yescharacteristic
984C22#176412yes—
985C22#176412yes—
986C22#176512yes—
987C22#176512yes—
988C22#177212yes—
989C22#177312yes—
990C22#186614yes—
991C22#187614yes—
992C22#192214yes—
993C22#192914yes—
994C4—48no—
995C4—48no—
996C4—84no—
997C4C4×#9511yescharacteristic
998C4C4×#9511yescharacteristic
999C4C22⋊#9511yescharacteristic
1000C4C22⋊#9511yescharacteristic
1001C4#143411yescharacteristic
1002C4#143411yescharacteristic
1003C4C4⋊#9511yescharacteristic
1004C4C4⋊#9511yescharacteristic
1005C4#143611yescharacteristic
1006C4#143611yescharacteristic
1007C4#143611yescharacteristic
1008C4#143611yescharacteristic
1009C4#143611yescharacteristic
1010C4#143611yescharacteristic
1011C4#143711yescharacteristic
1012C4#143711yescharacteristic
1013C2—21no—
1014C2—21no—
1015C2—21no—
1016C2—21no—
1017C2—21no—
1018C2—21no—
1019C2—21no—
1020C2—21no—
1021C2#755411yescharacteristic
1022C2#1070611yescharacteristic
1023C2#1070711yescharacteristic
1024C2#1079112yes—
1025C2#1080912yes—
1026C2#1088712yes—
1027C2#1090912yes—
1028C2#1091012yes—
1029C2#1093412yes—
subgroupG/H
centerC23×C4C2×D4
commutatorC2×C4C43
Frattini, cosocleC24×C4C23
socleC24C4×D4
prime radicalC25#41
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C4 ◁ C24×C8 ◁ G
LECSG ▷ C24×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
20. C2×#405C4semidirect
25. C2×#341C4semidirect
28. C2×#340C4semidirect
33. C2×#339C4semidirect
34. C2×#339C4semidirect
36. #1729C4semidirect
41. C2×#336C4semidirect

Maximal subgroups

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

subgroupindex
C22×#4052
C22×#3412
C2×#17352
C22×#3392
C2×#17292
C22×#3362