Finite Group Databasebeta

← #123973

Subgroups — #123973

Order 512.

1738 conjugacy classes of subgroups.

The subgroup lattice has 985 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#430C211yesmaximal, characteristic
2C22×#344C211yesmaximal, characteristic
3C2×#1733C211yesmaximal, characteristic
4C22×#339C211yesmaximal, characteristic
5C22×#339C211yesmaximal, characteristic
6#20335C211yesmaximal, characteristic
7C2×#1728C211yesmaximal, characteristic
8C23×M16C2211yescharacteristic
9C23×M16C2211yescharacteristic
10C23×M16C2211yescharacteristic
11C23×M16C2211yescharacteristic
12C22×#117C2211yescharacteristic
13C22×#117C2211yescharacteristic
14C23×C42C2211yescharacteristic
15C2×#430—22no—
16C2×#430—22no—
17C2×#430—22no—
18C2×#430—22no—
19C2×#430—22no—
20C2×#430C414yescomplemented
21C22×#108—22no—
22C2×#344—22no—
23C2×#344—22no—
24C2×#344C414yescomplemented
25#1733—22no—
26#1733—22no—
27C2×#339—22no—
28C2×#339—22no—
29C2×#339—22no—
30C2×#339—22no—
31C2×#339—22no—
32C2×#339—22no—
33C2×#339C414yescomplemented
34#1729—22no—
35#1729—22no—
36#1728—22no—
37#1728—22no—
38#1728—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×M16—21no—
65C22×M16—21no—
66C22×M16—21no—
67C22×M16—21no—
68C22×M16—21no—
69C22×M16—21no—
70C22×M16—21no—
71C22×M16—21no—
72C22×M16—21no—
73C22×M16—21no—
74C22×M16—21no—
75C22×M16—21no—
76C22×M16—21no—
77C22×M16—21no—
78C22×M16—21no—
79C22×M16—21no—
80C22×M16—21no—
81C22×M16—21no—
82C22×M16—21no—
83C22×M16C2×C412yes—
84C22×M16C2×C412yes—
85C22×M16C2×C412yes—
86C22×M16C2×C412yes—
87C22×M16C2×C412yes—
88C22×M16C2×C412yes—
89C22×M16D412yes—
90C22×M16D412yes—
91C22×M16D412yes—
92C22×M16D412yes—
93C22×M16D412yes—
94C22×M16D412yes—
95C22×M16D412yes—
96C22×M16Q812yes—
97C22×M16Q812yes—
98C23×C8—21no—
99C23×C8—21no—
100C23×C8—21no—
101C23×C8D412yes—
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×#117—21no—
120C2×#117—21no—
121C2×#117C2×C412yes—
122C2×#117C2×C412yes—
123C2×#117D412yes—
124C2×#117D412yes—
125C2×#117Q812yes—
126C22×C4⋊C4—21no—
127C22×C4⋊C4Q812yes—
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#430—28no—
147#430—28no—
148#430—28no—
149#430—28no—
150C2×#108—28no—
151C2×#108—28no—
152C2×#108—28no—
153#344—28no—
154#339—28no—
155#339—28no—
156#339—28no—
157#336—28no—
158#336—28no—
159C25#4111yescharacteristic
160C23×C4—22no—
161C23×C4—22no—
162C23×C4—22no—
163C23×C4—22no—
164C23×C4—48no—
165C23×C4—41no—
166C23×C4—41no—
167C23×C4—41no—
168C23×C4—41no—
169C23×C4—41no—
170C23×C4C22×C411yescharacteristic
171C23×C4C22×C411yescharacteristic
172C23×C4C22×C411yescharacteristic
173C23×C4C2×D411yescharacteristic
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×Q811yescharacteristic
185C23×C4C2×Q811yescharacteristic
186C23×C4C2×Q811yescharacteristic
187C23×C4C2×Q811yescharacteristic
188C23×C4C2×Q811yescharacteristic
189C23×C4#4111yescharacteristic
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
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—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—22no—
245C2×M16—22no—
246C2×M16—22no—
247C2×M16—22no—
248C2×M16—22no—
249C2×M16—22no—
250C2×M16—22no—
251C2×M16—22no—
252C2×M16—22no—
253C2×M16—22no—
254C2×M16—22no—
255C2×M16—22no—
256C2×M16—22no—
257C2×M16—22no—
258C2×M16—22no—
259C2×M16—22no—
260C2×M16—22no—
261C2×M16—22no—
262C2×M16—22no—
263C2×M16—41no—
264C2×M16—41no—
265C2×M16—41no—
266C2×M16—41no—
267C2×M16—41no—
268C2×M16—41no—
269C2×M16—41no—
270C2×M16—41no—
271C2×M16—41no—
272C2×M16—41no—
273C2×M16—41no—
274C2×M16—41no—
275C2×M16—41no—
276C2×M16—41no—
277C2×M16—41no—
278C2×M16—41no—
279C2×M16—41no—
280C2×M16—41no—
281C2×M16—41no—
282C2×M16—41no—
283C2×M16—41no—
284C2×M16—41no—
285C2×M16—41no—
286C2×M16—41no—
287C2×M16—41no—
288C2×M16—41no—
289C2×M16—41no—
290C2×M16—41no—
291C2×M16—41no—
292C2×M16—41no—
293C2×M16—41no—
294C2×M16—41no—
295C2×M16—41no—
296C2×M16—41no—
297C2×M16—41no—
298C2×M16—41no—
299C2×M16—41no—
300C2×M16—41no—
301C2×M16—41no—
302C2×M16—41no—
303C2×M16C4214yes—
304C2×M16C22⋊C414yes—
305C2×M16C22⋊C414yes—
306C2×M16C22⋊C414yes—
307C2×M16C22⋊C414yes—
308C2×M16C22⋊C414yes—
309C2×M16C4⋊C414yes—
310C2×M16C4⋊C414yes—
311C2×M16C4⋊C414yes—
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—22no—
325C22×C8—22no—
326C22×C8—22no—
327C22×C8—22no—
328C22×C8—22no—
329C22×C8—22no—
330C22×C8—22no—
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×C8C4⋊C414yes—
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—22no—
352#117—22no—
353#117—22no—
354#117—22no—
355#117—22no—
356#117—22no—
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—
367#117—41no—
368#117—41no—
369#117—41no—
370#117—41no—
371#117C4⋊C414yes—
372C2×C4⋊C4—22no—
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—41no—
381C2×C4⋊C4—41no—
382C2×C4⋊C4—41no—
383C2×C4⋊C4C4⋊C414yes—
384C2×C22⋊C4—22no—
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×C42—22no—
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×C42C4⋊C414yes—
436#108—232no—
437C24—44no—
438C24#11711yescharacteristic
439C24C4×D411yescharacteristic
440C24C4×Q811yescharacteristic
441C24#12111yescharacteristic
442C24C22⋊Q811yescharacteristic
443C24C22⋊Q811yescharacteristic
444C24C22⋊Q811yescharacteristic
445C24#12311yescharacteristic
446C24#12311yescharacteristic
447C24#12411yescharacteristic
448C24#12411yescharacteristic
449C24#12411yescharacteristic
450C24#12511yescharacteristic
451C24#12611yescharacteristic
452C24#12611yescharacteristic
453C22×C4—28no—
454C22×C4—24no—
455C22×C4—24no—
456C22×C4—48no—
457C22×C4—48no—
458C22×C4—44no—
459C22×C4—48no—
460C22×C4—48no—
461C22×C4—48no—
462C22×C4—48no—
463C22×C4—42no—
464C22×C4—42no—
465C22×C4—42no—
466C22×C4—42no—
467C22×C4—42no—
468C22×C4—42no—
469C22×C4—42no—
470C22×C4—42no—
471C22×C4—42no—
472C22×C4—42no—
473C22×C4—42no—
474C22×C4—84no—
475C22×C4—84no—
476C22×C4C2×C4211yescharacteristic
477C22×C4C2×C22⋊C411yescharacteristic
478C22×C4C2×C22⋊C411yescharacteristic
479C22×C4C2×C22⋊C411yescharacteristic
480C22×C4C2×C22⋊C411yescharacteristic
481C22×C4C2×C22⋊C411yescharacteristic
482C22×C4C2×C4⋊C411yescharacteristic
483C22×C4C2×C4⋊C411yescharacteristic
484C22×C4C2×C4⋊C411yescharacteristic
485C22×C4C2×C4⋊C411yescharacteristic
486C22×C4C2×C4⋊C411yescharacteristic
487C22×C4C2×C4⋊C411yescharacteristic
488C22×C4C2×C4⋊C411yescharacteristic
489C22×C4#11711yescharacteristic
490C22×C4#11711yescharacteristic
491C22×C4#11711yescharacteristic
492C22×C4#11711yescharacteristic
493C22×C4#11711yescharacteristic
494C22×C4C4×D411yescharacteristic
495C22×C4C4×D411yescharacteristic
496C22×C4C4×D411yescharacteristic
497C22×C4C4×D411yescharacteristic
498C22×C4C4×D411yescharacteristic
499C22×C4C4×D411yescharacteristic
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×Q811yescharacteristic
510C22×C4C4×Q811yescharacteristic
511C22×C4C4×Q811yescharacteristic
512C22×C4C4×Q811yescharacteristic
513C22×C4C4×Q811yescharacteristic
514C22×C4C4×Q811yescharacteristic
515C22×C4C4×Q811yescharacteristic
516C22×C4#12011yescharacteristic
517C22×C4#12011yescharacteristic
518C22×C4#12011yescharacteristic
519C22×C4#12011yescharacteristic
520C22×C4#12011yescharacteristic
521C22×C4#12011yescharacteristic
522C22×C4#12011yescharacteristic
523C22×C4#12011yescharacteristic
524C22×C4#12111yescharacteristic
525C22×C4#12111yescharacteristic
526C22×C4#12111yescharacteristic
527C22×C4#12111yescharacteristic
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×C4C22⋊Q811yescharacteristic
544C22×C4C22⋊Q811yescharacteristic
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×C4C22⋊Q811yescharacteristic
563C22×C4C22⋊Q811yescharacteristic
564C22×C4C22⋊Q811yescharacteristic
565C22×C4C22⋊Q811yescharacteristic
566C22×C4C22⋊Q811yescharacteristic
567C22×C4C22⋊Q811yescharacteristic
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#12411yescharacteristic
583C22×C4#12411yescharacteristic
584C22×C4#12411yescharacteristic
585C22×C4#12411yescharacteristic
586C22×C4#12411yescharacteristic
587C22×C4#12511yescharacteristic
588C22×C4#12511yescharacteristic
589C22×C4#12511yescharacteristic
590C22×C4#12511yescharacteristic
591C22×C4#12511yescharacteristic
592C22×C4#12511yescharacteristic
593C22×C4#12511yescharacteristic
594C22×C4#12511yescharacteristic
595C22×C4#12511yescharacteristic
596C22×C4#12511yescharacteristic
597C22×C4#12511yescharacteristic
598C22×C4#12611yescharacteristic
599C22×C4#12611yescharacteristic
600C22×C4#12611yescharacteristic
601C22×C4#12611yescharacteristic
602C22×C4#12611yescharacteristic
603C22×C4#12611yescharacteristic
604C22×C4#12711yescharacteristic
605C22×C4#12711yescharacteristic
606C22×C4C4⋊Q811yescharacteristic
607C22×C4C4⋊Q811yescharacteristic
608C22×C4C4⋊Q811yescharacteristic
609C22×C4C4⋊Q811yescharacteristic
610C22×C4C4⋊Q811yescharacteristic
611C22×C4C4⋊Q811yescharacteristic
612C22×C4C4⋊Q811yescharacteristic
613C22×C4C4⋊Q811yescharacteristic
614C22×C4C4⋊Q811yescharacteristic
615C22×C4C4⋊Q811yescharacteristic
616M16—24no—
617M16—24no—
618M16—24no—
619M16—24no—
620M16—24no—
621M16—24no—
622M16—24no—
623M16—24no—
624M16—24no—
625M16—24no—
626M16—24no—
627M16—42no—
628M16—42no—
629M16—42no—
630M16—42no—
631M16—42no—
632M16—42no—
633M16—42no—
634M16—42no—
635M16—42no—
636M16—42no—
637M16—42no—
638M16—42no—
639M16—42no—
640M16—42no—
641M16—42no—
642M16—42no—
643M16—42no—
644M16—42no—
645M16—42no—
646M16—42no—
647M16#9518yes—
648C2×C8—24no—
649C2×C8—24no—
650C2×C8—24no—
651C2×C8—24no—
652C2×C8—24no—
653C2×C8—24no—
654C2×C8—24no—
655C2×C8—24no—
656C2×C8—24no—
657C2×C8—24no—
658C2×C8—24no—
659C2×C8—24no—
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—
676C4⋊C4—24no—
677C4⋊C4—24no—
678C4⋊C4—24no—
679C4⋊C4—42no—
680C4⋊C4—42no—
681C4⋊C4—42no—
682C4⋊C4—42no—
683C4⋊C4—42no—
684C22⋊C4—24no—
685C22⋊C4—42no—
686C22⋊C4—42no—
687C22⋊C4—42no—
688C22⋊C4—42no—
689C22⋊C4—42no—
690C22⋊C4—42no—
691C22⋊C4—42no—
692C42—24no—
693C42—24no—
694C42—24no—
695C42—42no—
696C42—42no—
697C42—42no—
698C42—42no—
699C42—42no—
700C42—42no—
701C42—42no—
702C42—42no—
703C42—42no—
704C42—42no—
705C42—42no—
706C42—42no—
707C42—42no—
708C23—24no—
709C23—24no—
710C23—24no—
711C23—42no—
712C23—42no—
713C23—42no—
714C23—42no—
715C23—42no—
716C23—42no—
717C23—42no—
718C23—42no—
719C23—42no—
720C23—42no—
721C23—42no—
722C23—42no—
723C23C4×C4⋊C411yescharacteristic
724C23#38011yescharacteristic
725C23#38211yescharacteristic
726C23#38511yescharacteristic
727C23#38511yescharacteristic
728C23#38711yescharacteristic
729C23#38711yescharacteristic
730C23#38711yescharacteristic
731C23#38711yescharacteristic
732C23#38811yescharacteristic
733C23#38811yescharacteristic
734C23#38811yescharacteristic
735C23#38811yescharacteristic
736C23#38911yescharacteristic
737C23#38911yescharacteristic
738C23#39011yescharacteristic
739C23#39111yescharacteristic
740C23#39111yescharacteristic
741C23#39111yescharacteristic
742C23#39311yescharacteristic
743C23#39311yescharacteristic
744C23#39311yescharacteristic
745C23#39411yescharacteristic
746C23#39411yescharacteristic
747C23#39511yescharacteristic
748C23#39611yescharacteristic
749C23#39611yescharacteristic
750C23#39711yescharacteristic
751C23#39711yescharacteristic
752C23#39811yescharacteristic
753C23#39811yescharacteristic
754C23#39911yescharacteristic
755C23#40011yescharacteristic
756C23#40011yescharacteristic
757C23#40011yescharacteristic
758C2×C4—28no—
759C2×C4—44no—
760C2×C4—48no—
761C2×C4—48no—
762C2×C4—48no—
763C2×C4—48no—
764C2×C4—48no—
765C2×C4—48no—
766C2×C4—44no—
767C2×C4—48no—
768C2×C4—44no—
769C2×C4—44no—
770C2×C4—84no—
771C2×C4—84no—
772C2×C4—84no—
773C2×C4—84no—
774C2×C4—84no—
775C2×C4C2×#9511yescharacteristic
776C2×C4C4×C22⋊C411yescharacteristic
777C2×C4C4×C22⋊C411yescharacteristic
778C2×C4C4×C4⋊C411yescharacteristic
779C2×C4C4×C4⋊C411yescharacteristic
780C2×C4C4×C4⋊C411yescharacteristic
781C2×C4#37911yescharacteristic
782C2×C4#38011yescharacteristic
783C2×C4#38011yescharacteristic
784C2×C4#38011yescharacteristic
785C2×C4#38011yescharacteristic
786C2×C4#38011yescharacteristic
787C2×C4#38111yescharacteristic
788C2×C4#38211yescharacteristic
789C2×C4#38411yescharacteristic
790C2×C4#38411yescharacteristic
791C2×C4#38511yescharacteristic
792C2×C4#38511yescharacteristic
793C2×C4#38511yescharacteristic
794C2×C4#38511yescharacteristic
795C2×C4#38511yescharacteristic
796C2×C4#38511yescharacteristic
797C2×C4#38511yescharacteristic
798C2×C4#38511yescharacteristic
799C2×C4#38511yescharacteristic
800C2×C4#38511yescharacteristic
801C2×C4#38611yescharacteristic
802C2×C4#38611yescharacteristic
803C2×C4#38611yescharacteristic
804C2×C4#38611yescharacteristic
805C2×C4#38611yescharacteristic
806C2×C4#38611yescharacteristic
807C2×C4#38611yescharacteristic
808C2×C4#38611yescharacteristic
809C2×C4#38711yescharacteristic
810C2×C4#38711yescharacteristic
811C2×C4#38711yescharacteristic
812C2×C4#38711yescharacteristic
813C2×C4#38711yescharacteristic
814C2×C4#38711yescharacteristic
815C2×C4#38711yescharacteristic
816C2×C4#38711yescharacteristic
817C2×C4#38711yescharacteristic
818C2×C4#38711yescharacteristic
819C2×C4#38711yescharacteristic
820C2×C4#38711yescharacteristic
821C2×C4#38811yescharacteristic
822C2×C4#38811yescharacteristic
823C2×C4#38811yescharacteristic
824C2×C4#38811yescharacteristic
825C2×C4#38911yescharacteristic
826C2×C4#38911yescharacteristic
827C2×C4#38911yescharacteristic
828C2×C4#38911yescharacteristic
829C2×C4#38911yescharacteristic
830C2×C4#38911yescharacteristic
831C2×C4#38911yescharacteristic
832C2×C4#38911yescharacteristic
833C2×C4#38911yescharacteristic
834C2×C4#38911yescharacteristic
835C2×C4#38911yescharacteristic
836C2×C4#38911yescharacteristic
837C2×C4#38911yescharacteristic
838C2×C4#38911yescharacteristic
839C2×C4#39011yescharacteristic
840C2×C4#39011yescharacteristic
841C2×C4#39011yescharacteristic
842C2×C4#39111yescharacteristic
843C2×C4#39111yescharacteristic
844C2×C4#39111yescharacteristic
845C2×C4#39111yescharacteristic
846C2×C4#39111yescharacteristic
847C2×C4#39211yescharacteristic
848C2×C4#39211yescharacteristic
849C2×C4#39211yescharacteristic
850C2×C4#39211yescharacteristic
851C2×C4#39311yescharacteristic
852C2×C4#39411yescharacteristic
853C2×C4#39411yescharacteristic
854C2×C4#39411yescharacteristic
855C2×C4#39411yescharacteristic
856C2×C4#39411yescharacteristic
857C2×C4#39411yescharacteristic
858C2×C4#39511yescharacteristic
859C2×C4#39511yescharacteristic
860C2×C4#39511yescharacteristic
861C2×C4#39511yescharacteristic
862C2×C4#39511yescharacteristic
863C2×C4#39511yescharacteristic
864C2×C4#39511yescharacteristic
865C2×C4#39611yescharacteristic
866C2×C4#39611yescharacteristic
867C2×C4#39611yescharacteristic
868C2×C4#39611yescharacteristic
869C2×C4#39611yescharacteristic
870C2×C4#39611yescharacteristic
871C2×C4#39711yescharacteristic
872C2×C4#39711yescharacteristic
873C2×C4#39811yescharacteristic
874C2×C4#39811yescharacteristic
875C2×C4#39811yescharacteristic
876C2×C4#39811yescharacteristic
877C2×C4#39811yescharacteristic
878C2×C4#39811yescharacteristic
879C2×C4#39811yescharacteristic
880C2×C4#39811yescharacteristic
881C2×C4#39811yescharacteristic
882C2×C4#39811yescharacteristic
883C2×C4#39811yescharacteristic
884C2×C4#39811yescharacteristic
885C2×C4#39811yescharacteristic
886C2×C4#39811yescharacteristic
887C2×C4#39911yescharacteristic
888C2×C4#39911yescharacteristic
889C2×C4#39911yescharacteristic
890C2×C4#40011yescharacteristic
891C2×C4#40011yescharacteristic
892C2×C4#40011yescharacteristic
893C2×C4#40011yescharacteristic
894C2×C4#40011yescharacteristic
895C8—28no—
896C8—44no—
897C8—44no—
898C8—44no—
899C22—22no—
900C22—22no—
901C22—22no—
902C22—22no—
903C22—22no—
904C22—22no—
905C22—22no—
906C22—22no—
907C22—22no—
908C22—22no—
909C22—22no—
910C22—22no—
911C22—22no—
912C22—22no—
913C22—22no—
914C22—22no—
915C22—22no—
916C22—22no—
917C22—41no—
918C22—41no—
919C22—41no—
920C22—41no—
921C22—41no—
922C22—41no—
923C22—41no—
924C22—41no—
925C22—41no—
926C22—41no—
927C22—41no—
928C22—41no—
929C22—41no—
930C22—41no—
931C22—41no—
932C22—41no—
933C22C4⋊#9511yescharacteristic
934C22#143611yescharacteristic
935C22#143611yescharacteristic
936C22#143911yescharacteristic
937C22#143911yescharacteristic
938C22#143911yescharacteristic
939C22#144111yescharacteristic
940C22#144111yescharacteristic
941C22#144111yescharacteristic
942C22#144211yescharacteristic
943C22#144211yescharacteristic
944C22#144211yescharacteristic
945C22#144411yescharacteristic
946C22#144511yescharacteristic
947C22#144611yescharacteristic
948C22#186114yes—
949C4—48no—
950C4—84no—
951C4—84no—
952C4C22⋊#9511yescharacteristic
953C4C4⋊#9511yescharacteristic
954C4#143611yescharacteristic
955C4#143611yescharacteristic
956C4#143811yescharacteristic
957C4#143911yescharacteristic
958C4#144111yescharacteristic
959C4#144111yescharacteristic
960C4#144111yescharacteristic
961C4#144111yescharacteristic
962C4#144111yescharacteristic
963C4#144211yescharacteristic
964C4#144411yescharacteristic
965C4#144411yescharacteristic
966C4#144411yescharacteristic
967C4#144511yescharacteristic
968C2—21no—
969C2—21no—
970C2—21no—
971C2—21no—
972C2—21no—
973C2—21no—
974C2—21no—
975C2—21no—
976C2—21no—
977C2—21no—
978C2—21no—
979C2—21no—
980C2#755711yescharacteristic
981C2#1090112yes—
982C2#1111412yes—
983C2#1134112yes—
subgroupG/H
centerC22×C4#120
commutatorC22×C4C2×C42
Frattini, cosocleC24×C4C23
socleC23#385
prime radicalC25#41
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4 ◁ C24×C4 ◁ G
LECSG ▷ C24×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
20. C2×#430C4semidirect
24. C2×#344C4semidirect
33. C2×#339C4semidirect

Maximal subgroups

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

subgroupindex
C22×#4302
C22×#3442
C2×#17332
C22×#3392
#203352
C2×#17282