Finite Group Databasebeta

← #123790

Subgroups — #123790

Order 512.

1582 conjugacy classes of subgroups.

The subgroup lattice has 974 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#1742C211yesmaximal, characteristic
2C2×#1742C211yesmaximal, characteristic
3#20347C211yesmaximal, characteristic
4C22×#339C211yesmaximal, characteristic
5C22×#339C211yesmaximal, characteristic
6C22×#338C211yesmaximal, characteristic
7C2×#1728C211yesmaximal, characteristic
8C23×M16C2211yescharacteristic
9C23×M16C2211yescharacteristic
10C23×M16C2211yescharacteristic
11C23×M16C2211yescharacteristic
12C22×#117C2211yescharacteristic
13C22×#117C2211yescharacteristic
14C23×C42C2211yescharacteristic
15#1742—22no—
16#1742—22no—
17#1742—22no—
18#1742C414yescomplemented
19C2×#343—22no—
20C2×#343—22no—
21#1736—22no—
22#1736—22no—
23#1735—22no—
24C2×#339—22no—
25C2×#339—22no—
26C2×#339—22no—
27C2×#339—22no—
28C2×#339—22no—
29C2×#339C414yescomplemented
30C2×#338—22no—
31C2×#338—22no—
32C2×#338C414yescomplemented
33#1728—22no—
34#1728—22no—
35C2×#336—22no—
36C24×C4—21no—
37C24×C4C2311yescharacteristic
38C22×M16—21no—
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×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×M16Q812yes—
93C22×M16Q812yes—
94C23×C8—21no—
95C23×C8—21no—
96C23×C8—21no—
97C23×C8D412yes—
98C2×#117—21no—
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×#117C2×C412yes—
119C2×#117C2×C412yes—
120C2×#117D412yes—
121C2×#117Q812yes—
122C22×C4⋊C4D412yes—
123C22×C4⋊C4D412yes—
124C22×C22⋊C4—21no—
125C22×C22⋊C4—21no—
126C22×C42—21no—
127C22×C42—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×C42C2×C412yes—
140C22×C42D412yes—
141C22×C42D412yes—
142#343—28no—
143#343—28no—
144#340—28no—
145#339—28no—
146#339—28no—
147#338—28no—
148#336—28no—
149C25#4111yescharacteristic
150C23×C4—22no—
151C23×C4—22no—
152C23×C4—22no—
153C23×C4—22no—
154C23×C4—22no—
155C23×C4—48no—
156C23×C4—41no—
157C23×C4—41no—
158C23×C4—41no—
159C23×C4—41no—
160C23×C4C22×C411yescharacteristic
161C23×C4C22×C411yescharacteristic
162C23×C4C22×C411yescharacteristic
163C23×C4C2×D411yescharacteristic
164C23×C4C2×D411yescharacteristic
165C23×C4C2×D411yescharacteristic
166C23×C4C2×D411yescharacteristic
167C23×C4C2×D411yescharacteristic
168C23×C4C2×D411yescharacteristic
169C23×C4C2×D411yescharacteristic
170C23×C4C2×D411yescharacteristic
171C23×C4C2×D411yescharacteristic
172C23×C4C2×Q811yescharacteristic
173C23×C4C2×Q811yescharacteristic
174C23×C4C2×Q811yescharacteristic
175C23×C4#4111yescharacteristic
176C23×C4#4111yescharacteristic
177C23×C4#4111yescharacteristic
178C23×C4#4111yescharacteristic
179C23×C4#4111yescharacteristic
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
190C2×M16—22no—
191C2×M16—22no—
192C2×M16—22no—
193C2×M16—22no—
194C2×M16—22no—
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—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—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×M16—41no—
257C2×M16—41no—
258C2×M16—41no—
259C2×M16—41no—
260C2×M16—41no—
261C2×M16—41no—
262C2×M16—41no—
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×M16C4214yes—
300C2×M16C22⋊C414yes—
301C2×M16C4⋊C414yes—
302C22×C8—22no—
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—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×C8C4⋊C414yes—
330#117—22no—
331#117—22no—
332#117—22no—
333#117—22no—
334#117—22no—
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—41no—
347#117—41no—
348#117—41no—
349#117—41no—
350#117—41no—
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—
362C2×C4⋊C4—22no—
363C2×C4⋊C4—22no—
364C2×C4⋊C4—22no—
365C2×C4⋊C4—22no—
366C2×C4⋊C4—22no—
367C2×C4⋊C4—22no—
368C2×C4⋊C4—22no—
369C2×C4⋊C4—22no—
370C2×C4⋊C4—22no—
371C2×C4⋊C4—22no—
372C2×C4⋊C4C22⋊C414yes—
373C2×C4⋊C4C4⋊C414yes—
374C2×C22⋊C4—22no—
375C2×C22⋊C4—22no—
376C2×C22⋊C4—22no—
377C2×C22⋊C4—22no—
378C2×C22⋊C4—41no—
379C2×C22⋊C4—41no—
380C2×C22⋊C4—41no—
381C2×C22⋊C4—41no—
382C2×C22⋊C4—41no—
383C2×C22⋊C4—41no—
384C2×C22⋊C4—41no—
385C2×C22⋊C4—41no—
386C2×C42—22no—
387C2×C42—22no—
388C2×C42—22no—
389C2×C42—22no—
390C2×C42—22no—
391C2×C42—22no—
392C2×C42—22no—
393C2×C42—22no—
394C2×C42—22no—
395C2×C42—22no—
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—41no—
406C2×C42—41no—
407C2×C42—41no—
408C2×C42—41no—
409C2×C42—41no—
410C2×C42—41no—
411C2×C42—41no—
412C2×C42—41no—
413C2×C42—41no—
414C2×C42—41no—
415C2×C42—41no—
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×C42C22⋊C414yes—
426C24—44no—
427C24#11711yescharacteristic
428C24C4×D411yescharacteristic
429C24C4×Q811yescharacteristic
430C24#12111yescharacteristic
431C24C22⋊Q811yescharacteristic
432C24#12311yescharacteristic
433C24#12311yescharacteristic
434C24#12311yescharacteristic
435C24#12311yescharacteristic
436C24#12411yescharacteristic
437C24#12511yescharacteristic
438C24#12611yescharacteristic
439C24#12611yescharacteristic
440C24#12611yescharacteristic
441C24#12611yescharacteristic
442C22×C4—28no—
443C22×C4—24no—
444C22×C4—24no—
445C22×C4—24no—
446C22×C4—48no—
447C22×C4—48no—
448C22×C4—44no—
449C22×C4—48no—
450C22×C4—48no—
451C22×C4—48no—
452C22×C4—48no—
453C22×C4—42no—
454C22×C4—42no—
455C22×C4—42no—
456C22×C4—42no—
457C22×C4—42no—
458C22×C4—42no—
459C22×C4—42no—
460C22×C4—42no—
461C22×C4—42no—
462C22×C4—42no—
463C22×C4—84no—
464C22×C4—84no—
465C22×C4C2×C4211yescharacteristic
466C22×C4C2×C22⋊C411yescharacteristic
467C22×C4C2×C22⋊C411yescharacteristic
468C22×C4C2×C22⋊C411yescharacteristic
469C22×C4C2×C4⋊C411yescharacteristic
470C22×C4C2×C4⋊C411yescharacteristic
471C22×C4C2×C4⋊C411yescharacteristic
472C22×C4#11711yescharacteristic
473C22×C4#11711yescharacteristic
474C22×C4#11711yescharacteristic
475C22×C4#11711yescharacteristic
476C22×C4#11711yescharacteristic
477C22×C4#11711yescharacteristic
478C22×C4#11711yescharacteristic
479C22×C4#11711yescharacteristic
480C22×C4#11711yescharacteristic
481C22×C4#11711yescharacteristic
482C22×C4#11711yescharacteristic
483C22×C4C4×D411yescharacteristic
484C22×C4C4×D411yescharacteristic
485C22×C4C4×D411yescharacteristic
486C22×C4C4×D411yescharacteristic
487C22×C4C4×D411yescharacteristic
488C22×C4C4×D411yescharacteristic
489C22×C4C4×D411yescharacteristic
490C22×C4C4×D411yescharacteristic
491C22×C4C4×D411yescharacteristic
492C22×C4C4×D411yescharacteristic
493C22×C4C4×D411yescharacteristic
494C22×C4C4×D411yescharacteristic
495C22×C4C4×D411yescharacteristic
496C22×C4C4×D411yescharacteristic
497C22×C4C4×D411yescharacteristic
498C22×C4C4×D411yescharacteristic
499C22×C4C4×D411yescharacteristic
500C22×C4C4×Q811yescharacteristic
501C22×C4C4×Q811yescharacteristic
502C22×C4C4×Q811yescharacteristic
503C22×C4C4×Q811yescharacteristic
504C22×C4C4×Q811yescharacteristic
505C22×C4#12011yescharacteristic
506C22×C4#12011yescharacteristic
507C22×C4#12011yescharacteristic
508C22×C4#12011yescharacteristic
509C22×C4#12111yescharacteristic
510C22×C4#12111yescharacteristic
511C22×C4#12111yescharacteristic
512C22×C4#12111yescharacteristic
513C22×C4#12111yescharacteristic
514C22×C4#12111yescharacteristic
515C22×C4#12111yescharacteristic
516C22×C4#12111yescharacteristic
517C22×C4#12111yescharacteristic
518C22×C4#12111yescharacteristic
519C22×C4#12111yescharacteristic
520C22×C4#12111yescharacteristic
521C22×C4#12111yescharacteristic
522C22×C4#12111yescharacteristic
523C22×C4#12111yescharacteristic
524C22×C4#12111yescharacteristic
525C22×C4#12111yescharacteristic
526C22×C4C22⋊Q811yescharacteristic
527C22×C4C22⋊Q811yescharacteristic
528C22×C4C22⋊Q811yescharacteristic
529C22×C4C22⋊Q811yescharacteristic
530C22×C4C22⋊Q811yescharacteristic
531C22×C4C22⋊Q811yescharacteristic
532C22×C4C22⋊Q811yescharacteristic
533C22×C4C22⋊Q811yescharacteristic
534C22×C4C22⋊Q811yescharacteristic
535C22×C4C22⋊Q811yescharacteristic
536C22×C4C22⋊Q811yescharacteristic
537C22×C4C22⋊Q811yescharacteristic
538C22×C4C22⋊Q811yescharacteristic
539C22×C4C22⋊Q811yescharacteristic
540C22×C4C22⋊Q811yescharacteristic
541C22×C4C22⋊Q811yescharacteristic
542C22×C4C22⋊Q811yescharacteristic
543C22×C4#12311yescharacteristic
544C22×C4#12311yescharacteristic
545C22×C4#12311yescharacteristic
546C22×C4#12311yescharacteristic
547C22×C4#12311yescharacteristic
548C22×C4#12311yescharacteristic
549C22×C4#12311yescharacteristic
550C22×C4#12311yescharacteristic
551C22×C4#12311yescharacteristic
552C22×C4#12311yescharacteristic
553C22×C4#12311yescharacteristic
554C22×C4#12311yescharacteristic
555C22×C4#12311yescharacteristic
556C22×C4#12311yescharacteristic
557C22×C4#12311yescharacteristic
558C22×C4#12311yescharacteristic
559C22×C4#12311yescharacteristic
560C22×C4#12311yescharacteristic
561C22×C4#12311yescharacteristic
562C22×C4#12311yescharacteristic
563C22×C4#12411yescharacteristic
564C22×C4#12411yescharacteristic
565C22×C4#12411yescharacteristic
566C22×C4#12411yescharacteristic
567C22×C4#12411yescharacteristic
568C22×C4#12411yescharacteristic
569C22×C4#12411yescharacteristic
570C22×C4#12411yescharacteristic
571C22×C4#12411yescharacteristic
572C22×C4#12411yescharacteristic
573C22×C4#12411yescharacteristic
574C22×C4#12511yescharacteristic
575C22×C4#12511yescharacteristic
576C22×C4#12511yescharacteristic
577C22×C4#12511yescharacteristic
578C22×C4#12511yescharacteristic
579C22×C4#12511yescharacteristic
580C22×C4#12511yescharacteristic
581C22×C4#12511yescharacteristic
582C22×C4#12511yescharacteristic
583C22×C4#12511yescharacteristic
584C22×C4#12511yescharacteristic
585C22×C4#12611yescharacteristic
586C22×C4#12611yescharacteristic
587C22×C4#12611yescharacteristic
588C22×C4#12611yescharacteristic
589C22×C4#12611yescharacteristic
590C22×C4#12611yescharacteristic
591C22×C4#12611yescharacteristic
592C22×C4#12611yescharacteristic
593C22×C4#12611yescharacteristic
594C22×C4#12611yescharacteristic
595C22×C4#12611yescharacteristic
596C22×C4#12611yescharacteristic
597C22×C4#12611yescharacteristic
598C22×C4#12611yescharacteristic
599C22×C4#12611yescharacteristic
600C22×C4#12611yescharacteristic
601C22×C4#12711yescharacteristic
602C22×C4C4⋊Q811yescharacteristic
603C22×C4C4⋊Q811yescharacteristic
604C22×C4C4⋊Q811yescharacteristic
605M16—24no—
606M16—24no—
607M16—24no—
608M16—24no—
609M16—24no—
610M16—24no—
611M16—42no—
612M16—42no—
613M16—42no—
614M16—42no—
615M16—42no—
616M16—42no—
617M16—42no—
618M16—42no—
619M16—42no—
620M16—42no—
621M16—42no—
622M16—42no—
623M16—42no—
624M16—42no—
625M16—42no—
626M16—42no—
627M16—42no—
628M16—42no—
629M16—42no—
630M16—42no—
631M16—42no—
632M16—42no—
633M16—42no—
634M16—42no—
635M16—42no—
636M16—42no—
637C2×C8—24no—
638C2×C8—24no—
639C2×C8—24no—
640C2×C8—24no—
641C2×C8—24no—
642C2×C8—24no—
643C2×C8—42no—
644C2×C8—42no—
645C2×C8—42no—
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—
665C4⋊C4—24no—
666C4⋊C4—24no—
667C4⋊C4—24no—
668C4⋊C4—24no—
669C4⋊C4—42no—
670C4⋊C4—42no—
671C4⋊C4—42no—
672C4⋊C4—42no—
673C22⋊C4—42no—
674C22⋊C4—42no—
675C22⋊C4—42no—
676C22⋊C4—42no—
677C22⋊C4—42no—
678C22⋊C4—42no—
679C22⋊C4—42no—
680C22⋊C4—42no—
681C42—24no—
682C42—24no—
683C42—42no—
684C42—42no—
685C42—42no—
686C42—42no—
687C42—42no—
688C42—42no—
689C42—42no—
690C42—42no—
691C42—42no—
692C42—42no—
693C42—42no—
694C42—42no—
695C42—42no—
696C42—42no—
697C23—24no—
698C23—24no—
699C23—24no—
700C23—42no—
701C23—42no—
702C23—42no—
703C23—42no—
704C23—42no—
705C23—42no—
706C23—42no—
707C23—42no—
708C23—42no—
709C23—42no—
710C23—42no—
711C23—42no—
712C23C4×C4⋊C411yescharacteristic
713C23#38111yescharacteristic
714C23#38311yescharacteristic
715C23#38511yescharacteristic
716C23#38611yescharacteristic
717C23#38711yescharacteristic
718C23#38711yescharacteristic
719C23#38711yescharacteristic
720C23#38711yescharacteristic
721C23#38711yescharacteristic
722C23#38711yescharacteristic
723C23#38711yescharacteristic
724C23#38811yescharacteristic
725C23#38811yescharacteristic
726C23#38811yescharacteristic
727C23#38811yescharacteristic
728C23#38811yescharacteristic
729C23#38911yescharacteristic
730C23#39111yescharacteristic
731C23#39411yescharacteristic
732C23#39411yescharacteristic
733C23#39611yescharacteristic
734C23#39711yescharacteristic
735C23#39711yescharacteristic
736C23#39711yescharacteristic
737C23#39711yescharacteristic
738C23#39711yescharacteristic
739C23#39711yescharacteristic
740C23#39811yescharacteristic
741C23#39911yescharacteristic
742C23#40011yescharacteristic
743C23#40011yescharacteristic
744C23#40011yescharacteristic
745C23#40011yescharacteristic
746C23#40111yescharacteristic
747C2×C4—28no—
748C2×C4—48no—
749C2×C4—44no—
750C2×C4—48no—
751C2×C4—48no—
752C2×C4—48no—
753C2×C4—48no—
754C2×C4—48no—
755C2×C4—44no—
756C2×C4—44no—
757C2×C4—44no—
758C2×C4—84no—
759C2×C4—84no—
760C2×C4—84no—
761C2×C4—84no—
762C2×C4—84no—
763C2×C4—84no—
764C2×C4#37611yescharacteristic
765C2×C4C4×C22⋊C411yescharacteristic
766C2×C4C4×C22⋊C411yescharacteristic
767C2×C4C4×C22⋊C411yescharacteristic
768C2×C4C4×C4⋊C411yescharacteristic
769C2×C4C4×C4⋊C411yescharacteristic
770C2×C4#38011yescharacteristic
771C2×C4#38011yescharacteristic
772C2×C4#38011yescharacteristic
773C2×C4#38111yescharacteristic
774C2×C4#38111yescharacteristic
775C2×C4#38211yescharacteristic
776C2×C4#38211yescharacteristic
777C2×C4#38211yescharacteristic
778C2×C4#38311yescharacteristic
779C2×C4#38311yescharacteristic
780C2×C4#38511yescharacteristic
781C2×C4#38511yescharacteristic
782C2×C4#38511yescharacteristic
783C2×C4#38511yescharacteristic
784C2×C4#38511yescharacteristic
785C2×C4#38611yescharacteristic
786C2×C4#38611yescharacteristic
787C2×C4#38611yescharacteristic
788C2×C4#38611yescharacteristic
789C2×C4#38611yescharacteristic
790C2×C4#38711yescharacteristic
791C2×C4#38711yescharacteristic
792C2×C4#38711yescharacteristic
793C2×C4#38711yescharacteristic
794C2×C4#38711yescharacteristic
795C2×C4#38711yescharacteristic
796C2×C4#38711yescharacteristic
797C2×C4#38711yescharacteristic
798C2×C4#38711yescharacteristic
799C2×C4#38711yescharacteristic
800C2×C4#38711yescharacteristic
801C2×C4#38711yescharacteristic
802C2×C4#38711yescharacteristic
803C2×C4#38711yescharacteristic
804C2×C4#38711yescharacteristic
805C2×C4#38711yescharacteristic
806C2×C4#38711yescharacteristic
807C2×C4#38811yescharacteristic
808C2×C4#38811yescharacteristic
809C2×C4#38811yescharacteristic
810C2×C4#38811yescharacteristic
811C2×C4#38811yescharacteristic
812C2×C4#38811yescharacteristic
813C2×C4#38811yescharacteristic
814C2×C4#38811yescharacteristic
815C2×C4#38811yescharacteristic
816C2×C4#38811yescharacteristic
817C2×C4#38811yescharacteristic
818C2×C4#38811yescharacteristic
819C2×C4#38811yescharacteristic
820C2×C4#38811yescharacteristic
821C2×C4#38811yescharacteristic
822C2×C4#38811yescharacteristic
823C2×C4#38811yescharacteristic
824C2×C4#38811yescharacteristic
825C2×C4#38811yescharacteristic
826C2×C4#38911yescharacteristic
827C2×C4#38911yescharacteristic
828C2×C4#38911yescharacteristic
829C2×C4#38911yescharacteristic
830C2×C4#38911yescharacteristic
831C2×C4#39011yescharacteristic
832C2×C4#39011yescharacteristic
833C2×C4#39011yescharacteristic
834C2×C4#39111yescharacteristic
835C2×C4#39111yescharacteristic
836C2×C4#39211yescharacteristic
837C2×C4#39311yescharacteristic
838C2×C4#39311yescharacteristic
839C2×C4#39311yescharacteristic
840C2×C4#39411yescharacteristic
841C2×C4#39411yescharacteristic
842C2×C4#39411yescharacteristic
843C2×C4#39411yescharacteristic
844C2×C4#39411yescharacteristic
845C2×C4#39411yescharacteristic
846C2×C4#39411yescharacteristic
847C2×C4#39511yescharacteristic
848C2×C4#39611yescharacteristic
849C2×C4#39611yescharacteristic
850C2×C4#39611yescharacteristic
851C2×C4#39611yescharacteristic
852C2×C4#39611yescharacteristic
853C2×C4#39711yescharacteristic
854C2×C4#39711yescharacteristic
855C2×C4#39711yescharacteristic
856C2×C4#39711yescharacteristic
857C2×C4#39711yescharacteristic
858C2×C4#39711yescharacteristic
859C2×C4#39711yescharacteristic
860C2×C4#39711yescharacteristic
861C2×C4#39711yescharacteristic
862C2×C4#39811yescharacteristic
863C2×C4#39811yescharacteristic
864C2×C4#39811yescharacteristic
865C2×C4#39811yescharacteristic
866C2×C4#39811yescharacteristic
867C2×C4#39811yescharacteristic
868C2×C4#39811yescharacteristic
869C2×C4#39811yescharacteristic
870C2×C4#39911yescharacteristic
871C2×C4#39911yescharacteristic
872C2×C4#40011yescharacteristic
873C2×C4#40011yescharacteristic
874C2×C4#40011yescharacteristic
875C2×C4#40011yescharacteristic
876C2×C4#40011yescharacteristic
877C2×C4#40011yescharacteristic
878C2×C4#40011yescharacteristic
879C2×C4#40011yescharacteristic
880C2×C4#40011yescharacteristic
881C2×C4#40011yescharacteristic
882C2×C4#40011yescharacteristic
883C2×C4#40111yescharacteristic
884C8—44no—
885C8—44no—
886C8—44no—
887C8—44no—
888C22—22no—
889C22—22no—
890C22—22no—
891C22—22no—
892C22—22no—
893C22—22no—
894C22—22no—
895C22—22no—
896C22—22no—
897C22—22no—
898C22—22no—
899C22—22no—
900C22—22no—
901C22—22no—
902C22—22no—
903C22—22no—
904C22—22no—
905C22—22no—
906C22—41no—
907C22—41no—
908C22—41no—
909C22—41no—
910C22—41no—
911C22—41no—
912C22—41no—
913C22—41no—
914C22—41no—
915C22—41no—
916C22—41no—
917C22—41no—
918C22—41no—
919C22—41no—
920C22—41no—
921C22—41no—
922C22#143411yescharacteristic
923C22#143611yescharacteristic
924C22#143611yescharacteristic
925C22#143911yescharacteristic
926C22#144011yescharacteristic
927C22#144011yescharacteristic
928C22#144111yescharacteristic
929C22#144211yescharacteristic
930C22#144211yescharacteristic
931C22#144311yescharacteristic
932C22#144311yescharacteristic
933C22#144311yescharacteristic
934C22#144311yescharacteristic
935C22#144511yescharacteristic
936C22#144511yescharacteristic
937C22#205014yes—
938C4—48no—
939C4—84no—
940C4—84no—
941C4#143411yescharacteristic
942C4#143411yescharacteristic
943C4#143611yescharacteristic
944C4#143711yescharacteristic
945C4#143911yescharacteristic
946C4#143911yescharacteristic
947C4#144011yescharacteristic
948C4#144111yescharacteristic
949C4#144111yescharacteristic
950C4#144211yescharacteristic
951C4#144211yescharacteristic
952C4#144211yescharacteristic
953C4#144211yescharacteristic
954C4#144311yescharacteristic
955C4#144311yescharacteristic
956C4#144511yescharacteristic
957C2—21no—
958C2—21no—
959C2—21no—
960C2—21no—
961C2—21no—
962C2—21no—
963C2—21no—
964C2—21no—
965C2—21no—
966C2—21no—
967C2—21no—
968C2—21no—
969C2#755611yescharacteristic
970C2#1108212yes—
971C2#1115112yes—
972C2#1129412yes—
subgroupG/H
centerC22×C4#124
commutatorC22×C4C2×C42
Frattini, cosocleC24×C4C23
socleC23#394
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
18. #1742C4semidirect
29. C2×#339C4semidirect
32. C2×#338C4semidirect

Maximal subgroups

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

subgroupindex
C2×#17422
#203472
C22×#3392
C22×#3382
C2×#17282