Finite Group Databasebeta

← #123961

Subgroups — #123961

Order 512.

1838 conjugacy classes of subgroups.

The subgroup lattice has 1008 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#424C211yesmaximal, 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×#424—22no—
16C2×#424—22no—
17C2×#424—22no—
18C2×#424—22no—
19C2×#424—22no—
20C2×#424C414yescomplemented
21C22×C4⋊C8—22no—
22C2×#341—22no—
23C2×#341—22no—
24C2×#341—22no—
25#1735—22no—
26#1735—22no—
27C2×#340C414yescomplemented
28C2×#339—22no—
29C2×#339—22no—
30C2×#339—22no—
31C2×#339—22no—
32C2×#339—22no—
33C2×#339C414yescomplemented
34#1729—22no—
35#1729—22no—
36C2×#336—22no—
37C2×#336—22no—
38C2×#336—22no—
39C2×#336—22no—
40C24×C4—21no—
41C24×C4C2311yescharacteristic
42C22×M16—21no—
43C22×M16—21no—
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×M16—21no—
63C22×M16—21no—
64C22×M16C2×C412yes—
65C22×M16C2×C412yes—
66C22×M16D412yes—
67C22×M16D412yes—
68C22×M16D412yes—
69C22×M16Q812yes—
70C23×C8—21no—
71C23×C8—21no—
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×C8—21no—
95C23×C8—21no—
96C23×C8C2×C412yes—
97C23×C8C2×C412yes—
98C23×C8D412yes—
99C23×C8D412yes—
100C23×C8D412yes—
101C23×C8Q812yes—
102C2×#117—21no—
103C2×#117—21no—
104C2×#117—21no—
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×#117C2×C412yes—
119C2×#117C2×C412yes—
120C2×#117D412yes—
121C2×#117D412yes—
122C2×#117D412yes—
123C2×#117D412yes—
124C2×#117Q812yes—
125C2×#117Q812yes—
126C22×C4⋊C4C2×C412yes—
127C22×C4⋊C4C2×C412yes—
128C22×C22⋊C4—21no—
129C22×C22⋊C4—21no—
130C22×C42—21no—
131C22×C42—21no—
132C22×C42—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×C42C2×C412yes—
144C22×C42D412yes—
145C22×C42Q812yes—
146#424—28no—
147#424—28no—
148#424—28no—
149#424—28no—
150C2×C4⋊C8—28no—
151C2×C4⋊C8—28no—
152C2×C4⋊C8—28no—
153#341—28no—
154#340—28no—
155#339—28no—
156#339—28no—
157#336—28no—
158#336—28no—
159C25#4111yescharacteristic
160C23×C4—28no—
161C23×C4—22no—
162C23×C4—22no—
163C23×C4—22no—
164C23×C4—22no—
165C23×C4—22no—
166C23×C4—44no—
167C23×C4—41no—
168C23×C4—41no—
169C23×C4—41no—
170C23×C4—41no—
171C23×C4C22×C411yescharacteristic
172C23×C4C22×C411yescharacteristic
173C23×C4C22×C411yescharacteristic
174C23×C4C2×D411yescharacteristic
175C23×C4C2×D411yescharacteristic
176C23×C4C2×D411yescharacteristic
177C23×C4C2×D411yescharacteristic
178C23×C4C2×D411yescharacteristic
179C23×C4C2×D411yescharacteristic
180C23×C4C2×D411yescharacteristic
181C23×C4C2×D411yescharacteristic
182C23×C4C2×D411yescharacteristic
183C23×C4C2×D411yescharacteristic
184C23×C4C2×D411yescharacteristic
185C23×C4C2×Q811yescharacteristic
186C23×C4C2×Q811yescharacteristic
187C23×C4C2×Q811yescharacteristic
188C23×C4C2×Q811yescharacteristic
189C23×C4C2×Q811yescharacteristic
190C23×C4#4111yescharacteristic
191C23×C4#4111yescharacteristic
192C23×C4#4111yescharacteristic
193C23×C4#4111yescharacteristic
194C23×C4#4111yescharacteristic
195C23×C4#4111yescharacteristic
196C23×C4#4111yescharacteristic
197C23×C4#4111yescharacteristic
198C23×C4#4111yescharacteristic
199C23×C4#4111yescharacteristic
200C23×C4#4111yescharacteristic
201C2×M16—22no—
202C2×M16—22no—
203C2×M16—22no—
204C2×M16—22no—
205C2×M16—22no—
206C2×M16—22no—
207C2×M16—22no—
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—41no—
232C2×M16—41no—
233C2×M16—41no—
234C2×M16—41no—
235C2×M16—41no—
236C2×M16—41no—
237C2×M16—41no—
238C2×M16—41no—
239C2×M16—41no—
240C2×M16—41no—
241C2×M16—41no—
242C2×M16—41no—
243C2×M16—41no—
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×M16C22⋊C414yes—
256C2×M16C4⋊C414yes—
257C22×C8—22no—
258C22×C8—22no—
259C22×C8—22no—
260C22×C8—22no—
261C22×C8—22no—
262C22×C8—22no—
263C22×C8—22no—
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—22no—
280C22×C8—22no—
281C22×C8—22no—
282C22×C8—22no—
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—22no—
299C22×C8—41no—
300C22×C8—41no—
301C22×C8—41no—
302C22×C8—41no—
303C22×C8—41no—
304C22×C8—41no—
305C22×C8—41no—
306C22×C8—41no—
307C22×C8—41no—
308C22×C8—41no—
309C22×C8—41no—
310C22×C8—41no—
311C22×C8—41no—
312C22×C8—41no—
313C22×C8—41no—
314C22×C8—41no—
315C22×C8—41no—
316C22×C8—41no—
317C22×C8—41no—
318C22×C8—41no—
319C22×C8—41no—
320C22×C8—41no—
321C22×C8—41no—
322C22×C8—41no—
323C22×C8—41no—
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×C8C22⋊C414yes—
340C22×C8C4⋊C414yes—
341#117—22no—
342#117—22no—
343#117—22no—
344#117—22no—
345#117—22no—
346#117—22no—
347#117—22no—
348#117—22no—
349#117—22no—
350#117—22no—
351#117—22no—
352#117—22no—
353#117—22no—
354#117—22no—
355#117—22no—
356#117—22no—
357#117—22no—
358#117—22no—
359#117—22no—
360#117—22no—
361#117—41no—
362#117—41no—
363#117—41no—
364#117—41no—
365#117—41no—
366#117—41no—
367#117—41no—
368#117—41no—
369#117C22⋊C414yes—
370#117C22⋊C414yes—
371#117C4⋊C414yes—
372#117C4⋊C414yes—
373C2×C4⋊C4—22no—
374C2×C4⋊C4—22no—
375C2×C4⋊C4—22no—
376C2×C4⋊C4—22no—
377C2×C4⋊C4—22no—
378C2×C4⋊C4—22no—
379C2×C4⋊C4—22no—
380C2×C4⋊C4—22no—
381C2×C4⋊C4C4214yes—
382C2×C4⋊C4C22⋊C414yes—
383C2×C4⋊C4C4⋊C414yes—
384C2×C4⋊C4C4⋊C414yes—
385C2×C22⋊C4—22no—
386C2×C22⋊C4—22no—
387C2×C22⋊C4—22no—
388C2×C22⋊C4—22no—
389C2×C22⋊C4—22no—
390C2×C22⋊C4—22no—
391C2×C22⋊C4—22no—
392C2×C22⋊C4—22no—
393C2×C22⋊C4—41no—
394C2×C22⋊C4—41no—
395C2×C22⋊C4—41no—
396C2×C22⋊C4—41no—
397C2×C42—22no—
398C2×C42—22no—
399C2×C42—22no—
400C2×C42—22no—
401C2×C42—22no—
402C2×C42—22no—
403C2×C42—22no—
404C2×C42—22no—
405C2×C42—22no—
406C2×C42—22no—
407C2×C42—22no—
408C2×C42—22no—
409C2×C42—22no—
410C2×C42—22no—
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—41no—
421C2×C42—41no—
422C2×C42—41no—
423C2×C42—41no—
424C2×C42—41no—
425C2×C42—41no—
426C2×C42—41no—
427C2×C42—41no—
428C2×C42—41no—
429C2×C42—41no—
430C2×C42—41no—
431C2×C42—41no—
432C2×C42—41no—
433C2×C42—41no—
434C2×C42—41no—
435C2×C42—41no—
436C2×C42C4⋊C414yes—
437C4⋊C8—232no—
438C24—24no—
439C24—24no—
440C24#11711yescharacteristic
441C24C4×D411yescharacteristic
442C24C4×D411yescharacteristic
443C24#12111yescharacteristic
444C24C22⋊Q811yescharacteristic
445C24C22⋊Q811yescharacteristic
446C24C22⋊Q811yescharacteristic
447C24#12311yescharacteristic
448C24#12311yescharacteristic
449C24#12311yescharacteristic
450C24#12311yescharacteristic
451C24#12511yescharacteristic
452C24#12511yescharacteristic
453C24#12611yescharacteristic
454C24#12611yescharacteristic
455C22×C4—28no—
456C22×C4—28no—
457C22×C4—28no—
458C22×C4—24no—
459C22×C4—24no—
460C22×C4—24no—
461C22×C4—24no—
462C22×C4—24no—
463C22×C4—48no—
464C22×C4—48no—
465C22×C4—48no—
466C22×C4—48no—
467C22×C4—44no—
468C22×C4—44no—
469C22×C4—44no—
470C22×C4—42no—
471C22×C4—42no—
472C22×C4—42no—
473C22×C4—42no—
474C22×C4—42no—
475C22×C4—42no—
476C22×C4—44no—
477C22×C4—44no—
478C22×C4—42no—
479C22×C4—42no—
480C22×C4—44no—
481C22×C4—44no—
482C22×C4C2×C4211yescharacteristic
483C22×C4C2×C22⋊C411yescharacteristic
484C22×C4C2×C22⋊C411yescharacteristic
485C22×C4C2×C22⋊C411yescharacteristic
486C22×C4C2×C22⋊C411yescharacteristic
487C22×C4C2×C22⋊C411yescharacteristic
488C22×C4C2×C4⋊C411yescharacteristic
489C22×C4C2×C4⋊C411yescharacteristic
490C22×C4C2×C4⋊C411yescharacteristic
491C22×C4C2×C4⋊C411yescharacteristic
492C22×C4C2×C4⋊C411yescharacteristic
493C22×C4C2×C4⋊C411yescharacteristic
494C22×C4C2×C4⋊C411yescharacteristic
495C22×C4#11711yescharacteristic
496C22×C4#11711yescharacteristic
497C22×C4#11711yescharacteristic
498C22×C4#11711yescharacteristic
499C22×C4#11711yescharacteristic
500C22×C4C4×D411yescharacteristic
501C22×C4C4×D411yescharacteristic
502C22×C4C4×D411yescharacteristic
503C22×C4C4×D411yescharacteristic
504C22×C4C4×D411yescharacteristic
505C22×C4C4×D411yescharacteristic
506C22×C4C4×D411yescharacteristic
507C22×C4C4×D411yescharacteristic
508C22×C4C4×D411yescharacteristic
509C22×C4C4×D411yescharacteristic
510C22×C4C4×D411yescharacteristic
511C22×C4C4×D411yescharacteristic
512C22×C4C4×D411yescharacteristic
513C22×C4C4×D411yescharacteristic
514C22×C4C4×Q811yescharacteristic
515C22×C4C4×Q811yescharacteristic
516C22×C4C4×Q811yescharacteristic
517C22×C4C4×Q811yescharacteristic
518C22×C4C4×Q811yescharacteristic
519C22×C4C4×Q811yescharacteristic
520C22×C4C4×Q811yescharacteristic
521C22×C4C4×Q811yescharacteristic
522C22×C4#12011yescharacteristic
523C22×C4#12011yescharacteristic
524C22×C4#12011yescharacteristic
525C22×C4#12011yescharacteristic
526C22×C4#12011yescharacteristic
527C22×C4#12011yescharacteristic
528C22×C4#12011yescharacteristic
529C22×C4#12011yescharacteristic
530C22×C4#12111yescharacteristic
531C22×C4#12111yescharacteristic
532C22×C4#12111yescharacteristic
533C22×C4#12111yescharacteristic
534C22×C4#12111yescharacteristic
535C22×C4#12111yescharacteristic
536C22×C4#12111yescharacteristic
537C22×C4#12111yescharacteristic
538C22×C4#12111yescharacteristic
539C22×C4#12111yescharacteristic
540C22×C4#12111yescharacteristic
541C22×C4#12111yescharacteristic
542C22×C4#12111yescharacteristic
543C22×C4#12111yescharacteristic
544C22×C4#12111yescharacteristic
545C22×C4#12111yescharacteristic
546C22×C4#12111yescharacteristic
547C22×C4#12111yescharacteristic
548C22×C4#12111yescharacteristic
549C22×C4C22⋊Q811yescharacteristic
550C22×C4C22⋊Q811yescharacteristic
551C22×C4C22⋊Q811yescharacteristic
552C22×C4C22⋊Q811yescharacteristic
553C22×C4C22⋊Q811yescharacteristic
554C22×C4C22⋊Q811yescharacteristic
555C22×C4C22⋊Q811yescharacteristic
556C22×C4C22⋊Q811yescharacteristic
557C22×C4C22⋊Q811yescharacteristic
558C22×C4C22⋊Q811yescharacteristic
559C22×C4C22⋊Q811yescharacteristic
560C22×C4C22⋊Q811yescharacteristic
561C22×C4C22⋊Q811yescharacteristic
562C22×C4C22⋊Q811yescharacteristic
563C22×C4C22⋊Q811yescharacteristic
564C22×C4C22⋊Q811yescharacteristic
565C22×C4C22⋊Q811yescharacteristic
566C22×C4C22⋊Q811yescharacteristic
567C22×C4C22⋊Q811yescharacteristic
568C22×C4C22⋊Q811yescharacteristic
569C22×C4C22⋊Q811yescharacteristic
570C22×C4C22⋊Q811yescharacteristic
571C22×C4C22⋊Q811yescharacteristic
572C22×C4C22⋊Q811yescharacteristic
573C22×C4C22⋊Q811yescharacteristic
574C22×C4#12311yescharacteristic
575C22×C4#12311yescharacteristic
576C22×C4#12311yescharacteristic
577C22×C4#12311yescharacteristic
578C22×C4#12311yescharacteristic
579C22×C4#12311yescharacteristic
580C22×C4#12311yescharacteristic
581C22×C4#12311yescharacteristic
582C22×C4#12311yescharacteristic
583C22×C4#12311yescharacteristic
584C22×C4#12311yescharacteristic
585C22×C4#12311yescharacteristic
586C22×C4#12411yescharacteristic
587C22×C4#12411yescharacteristic
588C22×C4#12411yescharacteristic
589C22×C4#12411yescharacteristic
590C22×C4#12411yescharacteristic
591C22×C4#12411yescharacteristic
592C22×C4#12411yescharacteristic
593C22×C4#12411yescharacteristic
594C22×C4#12511yescharacteristic
595C22×C4#12511yescharacteristic
596C22×C4#12511yescharacteristic
597C22×C4#12511yescharacteristic
598C22×C4#12511yescharacteristic
599C22×C4#12511yescharacteristic
600C22×C4#12511yescharacteristic
601C22×C4#12511yescharacteristic
602C22×C4#12511yescharacteristic
603C22×C4#12511yescharacteristic
604C22×C4#12611yescharacteristic
605C22×C4#12611yescharacteristic
606C22×C4#12611yescharacteristic
607C22×C4#12611yescharacteristic
608C22×C4#12611yescharacteristic
609C22×C4#12611yescharacteristic
610C22×C4#12711yescharacteristic
611C22×C4#12711yescharacteristic
612C22×C4C4⋊Q811yescharacteristic
613C22×C4C4⋊Q811yescharacteristic
614C22×C4C4⋊Q811yescharacteristic
615C22×C4C4⋊Q811yescharacteristic
616C22×C4C4⋊Q811yescharacteristic
617C22×C4C4⋊Q811yescharacteristic
618C22×C4C4⋊Q811yescharacteristic
619C22×C4C4⋊Q811yescharacteristic
620C22×C4C4⋊Q811yescharacteristic
621C22×C4C4⋊Q811yescharacteristic
622M16—24no—
623M16—24no—
624M16—24no—
625M16—24no—
626M16—42no—
627M16—42no—
628M16—42no—
629M16—42no—
630M16—42no—
631M16—42no—
632M16—42no—
633M16—42no—
634M16—42no—
635M16—42no—
636M16—42no—
637M16—42no—
638C2×C8—24no—
639C2×C8—24no—
640C2×C8—24no—
641C2×C8—24no—
642C2×C8—24no—
643C2×C8—24no—
644C2×C8—24no—
645C2×C8—24no—
646C2×C8—42no—
647C2×C8—42no—
648C2×C8—42no—
649C2×C8—42no—
650C2×C8—42no—
651C2×C8—42no—
652C2×C8—42no—
653C2×C8—42no—
654C2×C8—42no—
655C2×C8—42no—
656C2×C8—42no—
657C2×C8—42no—
658C2×C8—42no—
659C2×C8—42no—
660C2×C8—42no—
661C2×C8—42no—
662C2×C8—42no—
663C2×C8—42no—
664C2×C8—42no—
665C2×C8—42no—
666C2×C8—42no—
667C2×C8—42no—
668C2×C8—42no—
669C2×C8—42no—
670C2×C8—42no—
671C2×C8—42no—
672C2×C8—42no—
673C2×C8—42no—
674C2×C8—42no—
675C2×C8—42no—
676C2×C8—42no—
677C2×C8—42no—
678C2×C8—42no—
679C2×C8—42no—
680C2×C8—42no—
681C2×C8—42no—
682C4⋊C4—24no—
683C4⋊C4—24no—
684C4⋊C4—24no—
685C4⋊C4—24no—
686C4⋊C4—24no—
687C4⋊C4—42no—
688C4⋊C4—42no—
689C4⋊C4#9518yes—
690C22⋊C4—24no—
691C22⋊C4—24no—
692C22⋊C4—24no—
693C22⋊C4—24no—
694C22⋊C4—42no—
695C22⋊C4—42no—
696C22⋊C4—42no—
697C22⋊C4—42no—
698C42—24no—
699C42—24no—
700C42—24no—
701C42—24no—
702C42—24no—
703C42—24no—
704C42—42no—
705C42—42no—
706C42—42no—
707C42—42no—
708C42—42no—
709C42—42no—
710C42—42no—
711C42—42no—
712C42—42no—
713C42—42no—
714C23—24no—
715C23—24no—
716C23—24no—
717C23—24no—
718C23—24no—
719C23—24no—
720C23—24no—
721C23—24no—
722C23—22no—
723C23—22no—
724C23—22no—
725C23—22no—
726C23—22no—
727C23—22no—
728C23—22no—
729C23—22no—
730C23—22no—
731C23—22no—
732C23—22no—
733C23—22no—
734C23C4×C22⋊C411yescharacteristic
735C23#38011yescharacteristic
736C23#38111yescharacteristic
737C23#38511yescharacteristic
738C23#38511yescharacteristic
739C23#38511yescharacteristic
740C23#38511yescharacteristic
741C23#38611yescharacteristic
742C23#38611yescharacteristic
743C23#38711yescharacteristic
744C23#38711yescharacteristic
745C23#38711yescharacteristic
746C23#38711yescharacteristic
747C23#38711yescharacteristic
748C23#38711yescharacteristic
749C23#38811yescharacteristic
750C23#38811yescharacteristic
751C23#38911yescharacteristic
752C23#38911yescharacteristic
753C23#39411yescharacteristic
754C23#39511yescharacteristic
755C23#39611yescharacteristic
756C23#39611yescharacteristic
757C23#39711yescharacteristic
758C23#39711yescharacteristic
759C23#39811yescharacteristic
760C23#39811yescharacteristic
761C23#39811yescharacteristic
762C23#39811yescharacteristic
763C23#39811yescharacteristic
764C23#39911yescharacteristic
765C23#39911yescharacteristic
766C23#40011yescharacteristic
767C23#40011yescharacteristic
768C23#40011yescharacteristic
769C23#44314yes—
770C23#44414yes—
771C2×C4—28no—
772C2×C4—28no—
773C2×C4—48no—
774C2×C4—48no—
775C2×C4—48no—
776C2×C4—48no—
777C2×C4—44no—
778C2×C4—48no—
779C2×C4—48no—
780C2×C4—48no—
781C2×C4—48no—
782C2×C4—44no—
783C2×C4—44no—
784C2×C4—44no—
785C2×C4—48no—
786C2×C4—44no—
787C2×C4—84no—
788C2×C4—82no—
789C2×C4—82no—
790C2×C4C2×#9511yescharacteristic
791C2×C4C4×C22⋊C411yescharacteristic
792C2×C4C4×C4⋊C411yescharacteristic
793C2×C4C4×C4⋊C411yescharacteristic
794C2×C4C4×C4⋊C411yescharacteristic
795C2×C4C4×C4⋊C411yescharacteristic
796C2×C4#37911yescharacteristic
797C2×C4#38011yescharacteristic
798C2×C4#38011yescharacteristic
799C2×C4#38011yescharacteristic
800C2×C4#38011yescharacteristic
801C2×C4#38011yescharacteristic
802C2×C4#38211yescharacteristic
803C2×C4#38211yescharacteristic
804C2×C4#38411yescharacteristic
805C2×C4#38411yescharacteristic
806C2×C4#38511yescharacteristic
807C2×C4#38511yescharacteristic
808C2×C4#38511yescharacteristic
809C2×C4#38511yescharacteristic
810C2×C4#38511yescharacteristic
811C2×C4#38511yescharacteristic
812C2×C4#38511yescharacteristic
813C2×C4#38511yescharacteristic
814C2×C4#38611yescharacteristic
815C2×C4#38611yescharacteristic
816C2×C4#38611yescharacteristic
817C2×C4#38611yescharacteristic
818C2×C4#38611yescharacteristic
819C2×C4#38611yescharacteristic
820C2×C4#38711yescharacteristic
821C2×C4#38711yescharacteristic
822C2×C4#38711yescharacteristic
823C2×C4#38711yescharacteristic
824C2×C4#38711yescharacteristic
825C2×C4#38711yescharacteristic
826C2×C4#38711yescharacteristic
827C2×C4#38711yescharacteristic
828C2×C4#38711yescharacteristic
829C2×C4#38711yescharacteristic
830C2×C4#38811yescharacteristic
831C2×C4#38811yescharacteristic
832C2×C4#38811yescharacteristic
833C2×C4#38811yescharacteristic
834C2×C4#38811yescharacteristic
835C2×C4#38811yescharacteristic
836C2×C4#38911yescharacteristic
837C2×C4#38911yescharacteristic
838C2×C4#38911yescharacteristic
839C2×C4#38911yescharacteristic
840C2×C4#38911yescharacteristic
841C2×C4#38911yescharacteristic
842C2×C4#38911yescharacteristic
843C2×C4#38911yescharacteristic
844C2×C4#38911yescharacteristic
845C2×C4#38911yescharacteristic
846C2×C4#38911yescharacteristic
847C2×C4#38911yescharacteristic
848C2×C4#38911yescharacteristic
849C2×C4#38911yescharacteristic
850C2×C4#39011yescharacteristic
851C2×C4#39011yescharacteristic
852C2×C4#39011yescharacteristic
853C2×C4#39011yescharacteristic
854C2×C4#39111yescharacteristic
855C2×C4#39111yescharacteristic
856C2×C4#39111yescharacteristic
857C2×C4#39111yescharacteristic
858C2×C4#39111yescharacteristic
859C2×C4#39111yescharacteristic
860C2×C4#39111yescharacteristic
861C2×C4#39111yescharacteristic
862C2×C4#39211yescharacteristic
863C2×C4#39211yescharacteristic
864C2×C4#39211yescharacteristic
865C2×C4#39211yescharacteristic
866C2×C4#39311yescharacteristic
867C2×C4#39311yescharacteristic
868C2×C4#39311yescharacteristic
869C2×C4#39311yescharacteristic
870C2×C4#39411yescharacteristic
871C2×C4#39411yescharacteristic
872C2×C4#39411yescharacteristic
873C2×C4#39411yescharacteristic
874C2×C4#39411yescharacteristic
875C2×C4#39411yescharacteristic
876C2×C4#39411yescharacteristic
877C2×C4#39511yescharacteristic
878C2×C4#39511yescharacteristic
879C2×C4#39511yescharacteristic
880C2×C4#39511yescharacteristic
881C2×C4#39511yescharacteristic
882C2×C4#39511yescharacteristic
883C2×C4#39511yescharacteristic
884C2×C4#39611yescharacteristic
885C2×C4#39611yescharacteristic
886C2×C4#39611yescharacteristic
887C2×C4#39611yescharacteristic
888C2×C4#39611yescharacteristic
889C2×C4#39611yescharacteristic
890C2×C4#39711yescharacteristic
891C2×C4#39711yescharacteristic
892C2×C4#39811yescharacteristic
893C2×C4#39811yescharacteristic
894C2×C4#39811yescharacteristic
895C2×C4#39811yescharacteristic
896C2×C4#39811yescharacteristic
897C2×C4#39811yescharacteristic
898C2×C4#39811yescharacteristic
899C2×C4#39811yescharacteristic
900C2×C4#39811yescharacteristic
901C2×C4#39811yescharacteristic
902C2×C4#39811yescharacteristic
903C2×C4#39911yescharacteristic
904C2×C4#39911yescharacteristic
905C2×C4#40011yescharacteristic
906C2×C4#40011yescharacteristic
907C2×C4#40011yescharacteristic
908C2×C4#40011yescharacteristic
909C2×C4#40011yescharacteristic
910C8—44no—
911C8—44no—
912C8—44no—
913C8—44no—
914C22—22no—
915C22—22no—
916C22—22no—
917C22—22no—
918C22—22no—
919C22—22no—
920C22—22no—
921C22—22no—
922C22—22no—
923C22—22no—
924C22—22no—
925C22—22no—
926C22—22no—
927C22—22no—
928C22—22no—
929C22—22no—
930C22—21no—
931C22—21no—
932C22—21no—
933C22—21no—
934C22—21no—
935C22—21no—
936C22—21no—
937C22—21no—
938C22—22no—
939C22—22no—
940C22—22no—
941C22—22no—
942C22—22no—
943C22—22no—
944C22—22no—
945C22—22no—
946C22C22⋊#9511yescharacteristic
947C22#143611yescharacteristic
948C22#143611yescharacteristic
949C22#143911yescharacteristic
950C22#143911yescharacteristic
951C22#144111yescharacteristic
952C22#144111yescharacteristic
953C22#144111yescharacteristic
954C22#144111yescharacteristic
955C22#144211yescharacteristic
956C22#144211yescharacteristic
957C22#144411yescharacteristic
958C22#144411yescharacteristic
959C22#144511yescharacteristic
960C22#144511yescharacteristic
961C22#176412yes—
962C22#176512yes—
963C22#186614yes—
964C22#186614yes—
965C22#187614yes—
966C22#192214yes—
967C22#193712yes—
968C22#193812yes—
969C22#194512yes—
970C22#194612yes—
971C4—48no—
972C4—48no—
973C4—84no—
974C4C4⋊#9511yescharacteristic
975C4C4⋊#9511yescharacteristic
976C4#143611yescharacteristic
977C4#143611yescharacteristic
978C4#143811yescharacteristic
979C4#143911yescharacteristic
980C4#143911yescharacteristic
981C4#144111yescharacteristic
982C4#144111yescharacteristic
983C4#144111yescharacteristic
984C4#144111yescharacteristic
985C4#144211yescharacteristic
986C4#144211yescharacteristic
987C4#144411yescharacteristic
988C4#144411yescharacteristic
989C4#144611yescharacteristic
990C2—21no—
991C2—21no—
992C2—21no—
993C2—21no—
994C2—21no—
995C2—21no—
996C2—21no—
997C2—21no—
998C2#755711yescharacteristic
999C2#1079112yes—
1000C2#1088211yescharacteristic
1001C2#1088311yescharacteristic
1002C2#1088712yes—
1003C2#1106812yes—
1004C2#1122112yes—
1005C2#1129112yes—
1006C2#1132912yes—
subgroupG/H
centerC23×C4C2×D4
commutatorC22×C4C2×C42
Frattini, cosocleC24×C4C23
socleC24C4×D4
prime radicalC25#41
LCSG ▷ C22×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×#424C4semidirect
27. C2×#340C4semidirect
33. C2×#339C4semidirect

Maximal subgroups

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

subgroupindex
C22×#4242
C22×#3412
C2×#17352
C22×#3392
C2×#17292
C22×#3362