Finite Group Databasebeta

← #123688

Subgroups — #123688

Order 512.

1674 conjugacy classes of subgroups.

The subgroup lattice has 1018 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#341C211yesmaximal, characteristic
2C2×#1735C211yesmaximal, characteristic
3C22×#339C211yesmaximal, characteristic
4C22×#339C211yesmaximal, characteristic
5C2×#1729C211yesmaximal, characteristic
6C2×#1729C211yesmaximal, characteristic
7C22×#336C211yesmaximal, characteristic
8C23×M16C2211yescharacteristic
9C23×M16C2211yescharacteristic
10C24×C8C2211yescharacteristic
11C24×C8C2211yescharacteristic
12C22×#117C2211yescharacteristic
13C22×#117C2211yescharacteristic
14C23×C42C2211yescharacteristic
15C2×#341—22no—
16C2×#341—22no—
17C2×#341—22no—
18#1735—22no—
19#1735—22no—
20C2×#340C412yescomplemented
21C2×#340C412yescomplemented
22C2×#339—22no—
23C2×#339—22no—
24C2×#339—22no—
25C2×#339—22no—
26C2×#339—22no—
27C2×#339C414yescomplemented
28#1729—22no—
29#1729—22no—
30#1729—22no—
31#1729C414yescomplemented
32C2×#336—22no—
33C2×#336—22no—
34C2×#336—22no—
35C2×#336—22no—
36C2×#336—22no—
37C24×C4—21no—
38C24×C4C2311yescharacteristic
39C22×M16—21no—
40C22×M16—21no—
41C22×M16—21no—
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×M16C2×C412yes—
62C22×M16C2×C412yes—
63C22×M16D412yes—
64C22×M16D412yes—
65C22×M16Q812yes—
66C22×M16Q812yes—
67C23×C8—21no—
68C23×C8—21no—
69C23×C8—21no—
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×C8C2×C412yes—
94C23×C8C2×C412yes—
95C23×C8D412yes—
96C23×C8D412yes—
97C23×C8D412yes—
98C23×C8D412yes—
99C2×#117—21no—
100C2×#117—21no—
101C2×#117—21no—
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×#117—21no—
119C2×#117C2×C412yes—
120C2×#117C2×C412yes—
121C2×#117D412yes—
122C2×#117Q812yes—
123C22×C4⋊C4C2×C411yescharacteristic
124C22×C4⋊C4C2×C411yescharacteristic
125C22×C4⋊C4C2×C412yes—
126C22×C22⋊C4—21no—
127C22×C22⋊C4—21no—
128C22×C42—21no—
129C22×C42—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×C42C2×C412yes—
142C22×C42D412yes—
143C22×C42D412yes—
144#341—28no—
145#340—24no—
146#340—24no—
147#339—28no—
148#339—28no—
149#336—28no—
150#336—28no—
151#336—28no—
152C25#4111yescharacteristic
153C23×C4—28no—
154C23×C4—22no—
155C23×C4—22no—
156C23×C4—22no—
157C23×C4—21no—
158C23×C4—21no—
159C23×C4—22no—
160C23×C4—44no—
161C23×C4—41no—
162C23×C4—41no—
163C23×C4—41no—
164C23×C4—41no—
165C23×C4C22×C411yescharacteristic
166C23×C4C22×C411yescharacteristic
167C23×C4C22×C411yescharacteristic
168C23×C4C2×D411yescharacteristic
169C23×C4C2×D411yescharacteristic
170C23×C4C2×D411yescharacteristic
171C23×C4C2×D411yescharacteristic
172C23×C4C2×D411yescharacteristic
173C23×C4C2×D411yescharacteristic
174C23×C4C2×D411yescharacteristic
175C23×C4C2×D411yescharacteristic
176C23×C4C2×D411yescharacteristic
177C23×C4C2×Q811yescharacteristic
178C23×C4C2×Q811yescharacteristic
179C23×C4C2×Q811yescharacteristic
180C23×C4#4111yescharacteristic
181C23×C4#4111yescharacteristic
182C23×C4#4111yescharacteristic
183C23×C4#4111yescharacteristic
184C23×C4#4111yescharacteristic
185C23×C4#4111yescharacteristic
186C23×C4#4111yescharacteristic
187C23×C4#4111yescharacteristic
188C23×C4#4111yescharacteristic
189C23×C4#4111yescharacteristic
190C23×C4#4111yescharacteristic
191C23×C4#4111yescharacteristic
192C23×C4#4111yescharacteristic
193C23×C4#4111yescharacteristic
194C23×C4#4111yescharacteristic
195C2×M16—22no—
196C2×M16—22no—
197C2×M16—22no—
198C2×M16—22no—
199C2×M16—22no—
200C2×M16—22no—
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—41no—
226C2×M16—41no—
227C2×M16—41no—
228C2×M16—41no—
229C2×M16—41no—
230C2×M16—41no—
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×M16C4⋊C414yes—
250C2×M16C4⋊C414yes—
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—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—41no—
294C22×C8—41no—
295C22×C8—41no—
296C22×C8—41no—
297C22×C8—41no—
298C22×C8—41no—
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×C8C22⋊C414yes—
334C22×C8C22⋊C414yes—
335#117—22no—
336#117—22no—
337#117—22no—
338#117—22no—
339#117—22no—
340#117—22no—
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—41no—
352#117—41no—
353#117—41no—
354#117—41no—
355#117—41no—
356#117—41no—
357#117—41no—
358#117—41no—
359#117—41no—
360#117—41no—
361#117—41no—
362#117—41no—
363#117—41no—
364#117—41no—
365#117—41no—
366#117—41no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—22no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—22no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—22no—
378C2×C4⋊C4—22no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—22no—
382C2×C4⋊C4C4212yes—
383C2×C4⋊C4C4212yes—
384C2×C4⋊C4C4⋊C414yes—
385C2×C22⋊C4—22no—
386C2×C22⋊C4—22no—
387C2×C22⋊C4—22no—
388C2×C22⋊C4—22no—
389C2×C22⋊C4—41no—
390C2×C22⋊C4—41no—
391C2×C22⋊C4—41no—
392C2×C22⋊C4—41no—
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—41no—
417C2×C42—41no—
418C2×C42—41no—
419C2×C42—41no—
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×C42C22⋊C414yes—
437C24—24no—
438C24—24no—
439C24#11711yescharacteristic
440C24C4×D411yescharacteristic
441C24C4×D411yescharacteristic
442C24#12111yescharacteristic
443C24C22⋊Q811yescharacteristic
444C24#12311yescharacteristic
445C24#12311yescharacteristic
446C24#12411yescharacteristic
447C24#12411yescharacteristic
448C24#12511yescharacteristic
449C24#12511yescharacteristic
450C24#12611yescharacteristic
451C24#12611yescharacteristic
452C24#12611yescharacteristic
453C24#12611yescharacteristic
454C22×C4—28no—
455C22×C4—28no—
456C22×C4—28no—
457C22×C4—24no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—24no—
461C22×C4—48no—
462C22×C4—48no—
463C22×C4—48no—
464C22×C4—48no—
465C22×C4—44no—
466C22×C4—44no—
467C22×C4—44no—
468C22×C4—42no—
469C22×C4—42no—
470C22×C4—42no—
471C22×C4—42no—
472C22×C4—42no—
473C22×C4—42no—
474C22×C4—41no—
475C22×C4—41no—
476C22×C4—42no—
477C22×C4—41no—
478C22×C4—41no—
479C22×C4—42no—
480C22×C4—44no—
481C22×C4—44no—
482C22×C4—44no—
483C22×C4—44no—
484C22×C4C2×C4211yescharacteristic
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×C4#11711yescharacteristic
492C22×C4#11711yescharacteristic
493C22×C4#11711yescharacteristic
494C22×C4#11711yescharacteristic
495C22×C4#11711yescharacteristic
496C22×C4#11711yescharacteristic
497C22×C4#11711yescharacteristic
498C22×C4#11711yescharacteristic
499C22×C4#11711yescharacteristic
500C22×C4#11711yescharacteristic
501C22×C4#11711yescharacteristic
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×D411yescharacteristic
515C22×C4C4×D411yescharacteristic
516C22×C4C4×D411yescharacteristic
517C22×C4C4×D411yescharacteristic
518C22×C4C4×Q811yescharacteristic
519C22×C4C4×Q811yescharacteristic
520C22×C4C4×Q811yescharacteristic
521C22×C4C4×Q811yescharacteristic
522C22×C4C4×Q811yescharacteristic
523C22×C4C4×Q811yescharacteristic
524C22×C4#12011yescharacteristic
525C22×C4#12011yescharacteristic
526C22×C4#12011yescharacteristic
527C22×C4#12011yescharacteristic
528C22×C4#12111yescharacteristic
529C22×C4#12111yescharacteristic
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×C4C22⋊Q811yescharacteristic
546C22×C4C22⋊Q811yescharacteristic
547C22×C4C22⋊Q811yescharacteristic
548C22×C4C22⋊Q811yescharacteristic
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×C4#12311yescharacteristic
563C22×C4#12311yescharacteristic
564C22×C4#12311yescharacteristic
565C22×C4#12311yescharacteristic
566C22×C4#12311yescharacteristic
567C22×C4#12311yescharacteristic
568C22×C4#12311yescharacteristic
569C22×C4#12311yescharacteristic
570C22×C4#12311yescharacteristic
571C22×C4#12311yescharacteristic
572C22×C4#12311yescharacteristic
573C22×C4#12311yescharacteristic
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#12411yescharacteristic
585C22×C4#12411yescharacteristic
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#12611yescharacteristic
611C22×C4#12611yescharacteristic
612C22×C4#12611yescharacteristic
613C22×C4#12611yescharacteristic
614C22×C4#12611yescharacteristic
615C22×C4#12611yescharacteristic
616C22×C4#12611yescharacteristic
617C22×C4#12611yescharacteristic
618C22×C4#12611yescharacteristic
619C22×C4#12611yescharacteristic
620C22×C4#12711yescharacteristic
621C22×C4C4⋊Q811yescharacteristic
622C22×C4C4⋊Q811yescharacteristic
623C22×C4C4⋊Q811yescharacteristic
624M16—24no—
625M16—24no—
626M16—24no—
627M16—24no—
628M16—42no—
629M16—42no—
630M16—42no—
631M16—42no—
632M16—42no—
633M16—42no—
634M16—42no—
635M16—42no—
636M16—42no—
637M16—42no—
638M16—42no—
639M16—42no—
640C2×C8—24no—
641C2×C8—24no—
642C2×C8—24no—
643C2×C8—24no—
644C2×C8—24no—
645C2×C8—24no—
646C2×C8—24no—
647C2×C8—24no—
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—
682C2×C8—42no—
683C2×C8—42no—
684C4⋊C4—22no—
685C4⋊C4—22no—
686C4⋊C4—22no—
687C4⋊C4—22no—
688C4⋊C4—24no—
689C4⋊C4—24no—
690C4⋊C4—41no—
691C4⋊C4—41no—
692C4⋊C4—42no—
693C4⋊C4—41no—
694C4⋊C4—41no—
695C4⋊C4—42no—
696C22⋊C4—42no—
697C22⋊C4—42no—
698C22⋊C4—42no—
699C22⋊C4—42no—
700C22⋊C4—42no—
701C22⋊C4—42no—
702C22⋊C4—42no—
703C22⋊C4—42no—
704C42—24no—
705C42—24no—
706C42—42no—
707C42—42no—
708C42—42no—
709C42—42no—
710C42—42no—
711C42—42no—
712C42—42no—
713C42—42no—
714C42—42no—
715C42—42no—
716C42—42no—
717C42—42no—
718C42—42no—
719C42—42no—
720C23—24no—
721C23—24no—
722C23—24no—
723C23—24no—
724C23—24no—
725C23—24no—
726C23—24no—
727C23—24no—
728C23—22no—
729C23—22no—
730C23—22no—
731C23—22no—
732C23—22no—
733C23—22no—
734C23—22no—
735C23—22no—
736C23—22no—
737C23—22no—
738C23—22no—
739C23—22no—
740C23C4×C22⋊C411yescharacteristic
741C23#38211yescharacteristic
742C23#38311yescharacteristic
743C23#38511yescharacteristic
744C23#38611yescharacteristic
745C23#38711yescharacteristic
746C23#38711yescharacteristic
747C23#38711yescharacteristic
748C23#38711yescharacteristic
749C23#38711yescharacteristic
750C23#38811yescharacteristic
751C23#38811yescharacteristic
752C23#38811yescharacteristic
753C23#38811yescharacteristic
754C23#38811yescharacteristic
755C23#38811yescharacteristic
756C23#38811yescharacteristic
757C23#38911yescharacteristic
758C23#39011yescharacteristic
759C23#39311yescharacteristic
760C23#39411yescharacteristic
761C23#39611yescharacteristic
762C23#39711yescharacteristic
763C23#39711yescharacteristic
764C23#39711yescharacteristic
765C23#39711yescharacteristic
766C23#39811yescharacteristic
767C23#39811yescharacteristic
768C23#40011yescharacteristic
769C23#40011yescharacteristic
770C23#40011yescharacteristic
771C23#40011yescharacteristic
772C23#40011yescharacteristic
773C23#40011yescharacteristic
774C23#40111yescharacteristic
775C23#44314yes—
776C23#44414yes—
777C2×C4—28no—
778C2×C4—48no—
779C2×C4—48no—
780C2×C4—48no—
781C2×C4—48no—
782C2×C4—48no—
783C2×C4—48no—
784C2×C4—44no—
785C2×C4—44no—
786C2×C4—48no—
787C2×C4—42no—
788C2×C4—42no—
789C2×C4—44no—
790C2×C4—44no—
791C2×C4—44no—
792C2×C4—84no—
793C2×C4—82no—
794C2×C4—82no—
795C2×C4—82no—
796C2×C4—82no—
797C2×C4—82no—
798C2×C4—82no—
799C2×C4#37611yescharacteristic
800C2×C4C4×C22⋊C411yescharacteristic
801C2×C4C4×C22⋊C411yescharacteristic
802C2×C4C4×C4⋊C411yescharacteristic
803C2×C4C4×C4⋊C411yescharacteristic
804C2×C4C4×C4⋊C411yescharacteristic
805C2×C4#38011yescharacteristic
806C2×C4#38011yescharacteristic
807C2×C4#38011yescharacteristic
808C2×C4#38111yescharacteristic
809C2×C4#38111yescharacteristic
810C2×C4#38111yescharacteristic
811C2×C4#38211yescharacteristic
812C2×C4#38211yescharacteristic
813C2×C4#38311yescharacteristic
814C2×C4#38311yescharacteristic
815C2×C4#38511yescharacteristic
816C2×C4#38511yescharacteristic
817C2×C4#38511yescharacteristic
818C2×C4#38511yescharacteristic
819C2×C4#38511yescharacteristic
820C2×C4#38611yescharacteristic
821C2×C4#38611yescharacteristic
822C2×C4#38611yescharacteristic
823C2×C4#38611yescharacteristic
824C2×C4#38611yescharacteristic
825C2×C4#38711yescharacteristic
826C2×C4#38711yescharacteristic
827C2×C4#38711yescharacteristic
828C2×C4#38711yescharacteristic
829C2×C4#38711yescharacteristic
830C2×C4#38711yescharacteristic
831C2×C4#38711yescharacteristic
832C2×C4#38711yescharacteristic
833C2×C4#38711yescharacteristic
834C2×C4#38711yescharacteristic
835C2×C4#38711yescharacteristic
836C2×C4#38711yescharacteristic
837C2×C4#38711yescharacteristic
838C2×C4#38711yescharacteristic
839C2×C4#38711yescharacteristic
840C2×C4#38711yescharacteristic
841C2×C4#38711yescharacteristic
842C2×C4#38711yescharacteristic
843C2×C4#38711yescharacteristic
844C2×C4#38811yescharacteristic
845C2×C4#38811yescharacteristic
846C2×C4#38811yescharacteristic
847C2×C4#38811yescharacteristic
848C2×C4#38811yescharacteristic
849C2×C4#38811yescharacteristic
850C2×C4#38811yescharacteristic
851C2×C4#38811yescharacteristic
852C2×C4#38811yescharacteristic
853C2×C4#38811yescharacteristic
854C2×C4#38811yescharacteristic
855C2×C4#38811yescharacteristic
856C2×C4#38811yescharacteristic
857C2×C4#38811yescharacteristic
858C2×C4#38811yescharacteristic
859C2×C4#38811yescharacteristic
860C2×C4#38811yescharacteristic
861C2×C4#38911yescharacteristic
862C2×C4#38911yescharacteristic
863C2×C4#38911yescharacteristic
864C2×C4#38911yescharacteristic
865C2×C4#38911yescharacteristic
866C2×C4#39011yescharacteristic
867C2×C4#39011yescharacteristic
868C2×C4#39111yescharacteristic
869C2×C4#39111yescharacteristic
870C2×C4#39111yescharacteristic
871C2×C4#39211yescharacteristic
872C2×C4#39311yescharacteristic
873C2×C4#39311yescharacteristic
874C2×C4#39411yescharacteristic
875C2×C4#39411yescharacteristic
876C2×C4#39411yescharacteristic
877C2×C4#39411yescharacteristic
878C2×C4#39411yescharacteristic
879C2×C4#39411yescharacteristic
880C2×C4#39411yescharacteristic
881C2×C4#39411yescharacteristic
882C2×C4#39511yescharacteristic
883C2×C4#39611yescharacteristic
884C2×C4#39611yescharacteristic
885C2×C4#39611yescharacteristic
886C2×C4#39611yescharacteristic
887C2×C4#39611yescharacteristic
888C2×C4#39711yescharacteristic
889C2×C4#39711yescharacteristic
890C2×C4#39711yescharacteristic
891C2×C4#39711yescharacteristic
892C2×C4#39711yescharacteristic
893C2×C4#39711yescharacteristic
894C2×C4#39711yescharacteristic
895C2×C4#39711yescharacteristic
896C2×C4#39711yescharacteristic
897C2×C4#39711yescharacteristic
898C2×C4#39711yescharacteristic
899C2×C4#39811yescharacteristic
900C2×C4#39811yescharacteristic
901C2×C4#39811yescharacteristic
902C2×C4#39811yescharacteristic
903C2×C4#39811yescharacteristic
904C2×C4#39811yescharacteristic
905C2×C4#39811yescharacteristic
906C2×C4#39911yescharacteristic
907C2×C4#39911yescharacteristic
908C2×C4#39911yescharacteristic
909C2×C4#40011yescharacteristic
910C2×C4#40011yescharacteristic
911C2×C4#40011yescharacteristic
912C2×C4#40011yescharacteristic
913C2×C4#40011yescharacteristic
914C2×C4#40011yescharacteristic
915C2×C4#40011yescharacteristic
916C2×C4#40011yescharacteristic
917C2×C4#40011yescharacteristic
918C2×C4#40111yescharacteristic
919C8—44no—
920C8—44no—
921C8—44no—
922C8—44no—
923C22—22no—
924C22—22no—
925C22—22no—
926C22—22no—
927C22—22no—
928C22—22no—
929C22—22no—
930C22—22no—
931C22—22no—
932C22—22no—
933C22—22no—
934C22—22no—
935C22—22no—
936C22—22no—
937C22—22no—
938C22—22no—
939C22—22no—
940C22—22no—
941C22—22no—
942C22—22no—
943C22—22no—
944C22—22no—
945C22—22no—
946C22—22no—
947C22—21no—
948C22—21no—
949C22—21no—
950C22—21no—
951C22—21no—
952C22—21no—
953C22—21no—
954C22—21no—
955C22#143411yescharacteristic
956C22#143611yescharacteristic
957C22#143711yescharacteristic
958C22#143911yescharacteristic
959C22#144011yescharacteristic
960C22#144111yescharacteristic
961C22#144211yescharacteristic
962C22#144211yescharacteristic
963C22#144211yescharacteristic
964C22#144211yescharacteristic
965C22#144311yescharacteristic
966C22#144311yescharacteristic
967C22#144311yescharacteristic
968C22#144311yescharacteristic
969C22#144511yescharacteristic
970C22#176412yes—
971C22#176512yes—
972C22#186614yes—
973C22#192214yes—
974C22#192214yes—
975C22#192914yes—
976C22#193712yes—
977C22#193812yes—
978C22#197412yes—
979C22#197512yes—
980C4—48no—
981C4—84no—
982C4—82no—
983C4—82no—
984C4#143411yescharacteristic
985C4#143411yescharacteristic
986C4#143611yescharacteristic
987C4#143611yescharacteristic
988C4#143911yescharacteristic
989C4#143911yescharacteristic
990C4#144011yescharacteristic
991C4#144011yescharacteristic
992C4#144111yescharacteristic
993C4#144111yescharacteristic
994C4#144211yescharacteristic
995C4#144211yescharacteristic
996C4#144311yescharacteristic
997C4#144311yescharacteristic
998C4#144511yescharacteristic
999C4#144511yescharacteristic
1000C2—21no—
1001C2—21no—
1002C2—21no—
1003C2—21no—
1004C2—21no—
1005C2—21no—
1006C2—21no—
1007C2—21no—
1008C2#755611yescharacteristic
1009C2#1080912yes—
1010C2#1088712yes—
1011C2#1092911yescharacteristic
1012C2#1093011yescharacteristic
1013C2#1112512yes—
1014C2#1129112yes—
1015C2#1131712yes—
1016C2#1137612yes—
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×#340C4semidirect
21. C2×#340C4semidirect
27. C2×#339C4semidirect
31. #1729C4semidirect

Maximal subgroups

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

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