Finite Group Databasebeta

← #153756

Subgroups — #153756

Order 512.

3178 conjugacy classes of subgroups.

The subgroup lattice has 1044 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#382C211yesmaximal, characteristic
2C2×#1436C212yesmaximal
3C2×#1434C211yesmaximal, characteristic
4C2×#1434C211yesmaximal, characteristic
5C2×C4×#95C211yesmaximal, characteristic
6C2×C4×#95C211yesmaximal, characteristic
7#7557C212yesmaximal
8#7556C212yesmaximal
9#7554C212yesmaximal
10#7554C211yesmaximal, characteristic
11#7554C211yesmaximal, characteristic
12C23×C4⋊C4C2212yes—
13C23×C42C2212yes—
14C23×C42C2211yescharacteristic
15C23×C42C2211yescharacteristic
16C23×C42C2211yescharacteristic
17C2×#382—24no—
18C2×#382—24no—
19C2×#382C418yescomplemented
20C22×#95C2212yes—
21C22×#95C2212yes—
22C22×#95C2212yes—
23C22×#95C2212yes—
24C22×#95C2212yes—
25C22×#95C2212yes—
26C22×#95C2211yescharacteristic
27C22×#95C2211yescharacteristic
28C22×#95C2212yes—
29C22×#95C2212yes—
30C22×#95C2211yescharacteristic
31C22×#95C2211yescharacteristic
32C22×#95C2211yescharacteristic
33C22×#95C2211yescharacteristic
34C22×#95C2212yes—
35C22×#95C2212yes—
36C22×#95C2211yescharacteristic
37C22×#95C2211yescharacteristic
38#1436—28no—
39#1434—24no—
40#1434C418yescomplemented
41C4×#95—24no—
42C4×#95C418yescomplemented
43C24×C4C2312yes—
44C24×C4C2312yes—
45C24×C4C2311yescharacteristic
46C24×C4C2312yes—
47C24×C4C2311yescharacteristic
48C24×C4C2312yes—
49C24×C4C2311yescharacteristic
50C24×C4C2311yescharacteristic
51C24×C4C2311yescharacteristic
52C24×C4C2311yescharacteristic
53C24×C4C2311yescharacteristic
54C22×C4⋊C4—24no—
55C22×C4⋊C4—24no—
56C22×C4⋊C4—24no—
57C22×C4⋊C4—24no—
58C22×C4⋊C4—42no—
59C22×C4⋊C4—42no—
60C22×C4⋊C4C2×C418yes—
61C22×C42—22no—
62C22×C42—22no—
63C22×C42—22no—
64C22×C42—22no—
65C22×C42—24no—
66C22×C42—22no—
67C22×C42—22no—
68C22×C42—24no—
69C22×C42—24no—
70C22×C42—24no—
71C22×C42—24no—
72C22×C42—22no—
73C22×C42—22no—
74C22×C42—24no—
75C22×C42—24no—
76C22×C42—42no—
77C22×C42—42no—
78C22×C42—42no—
79C22×C42—42no—
80C22×C42C2×C414yes—
81C22×C42C2×C414yes—
82C22×C42C2×C414yes—
83C22×C42C2×C414yes—
84C22×C42C2×C414yes—
85#382—232no—
86C2×#95—24no—
87C2×#95—22no—
88C2×#95—22no—
89C2×#95—24no—
90C2×#95—24no—
91C2×#95—24no—
92C2×#95—22no—
93C2×#95—22no—
94C2×#95—24no—
95C2×#95—24no—
96C2×#95—24no—
97C2×#95—22no—
98C2×#95—22no—
99C2×#95—24no—
100C2×#95—24no—
101C2×#95—24no—
102C2×#95—22no—
103C2×#95—24no—
104C2×#95—22no—
105C2×#95—24no—
106C2×#95—24no—
107C2×#95—24no—
108C2×#95—24no—
109C2×#95—24no—
110C2×#95—24no—
111C2×#95—24no—
112C2×#95—24no—
113C2×#95—24no—
114C2×#95—24no—
115C2×#95—24no—
116C2×#95—24no—
117C2×#95—42no—
118C2×#95—42no—
119C2×#95—42no—
120C2×#95—42no—
121C2×#95—42no—
122C2×#95—42no—
123C2×#95C2×C414yes—
124C2×#95C2×C414yes—
125C2×#95C2×C414yes—
126C2×#95C2×C418yes—
127C2×#95C2×C414yes—
128C2×#95C2×C418yes—
129C2×#95C2×C414yes—
130C2×#95C2×C414yes—
131C2×#95C2×C418yes—
132C2×#95C2×C414yes—
133C2×#95C2×C414yes—
134C2×#95D414yes—
135C2×#95D414yes—
136C2×#95D414yes—
137C2×#95Q814yes—
138C25C2411yescharacteristic
139C23×C4—21no—
140C23×C4—21no—
141C23×C4—21no—
142C23×C4—21no—
143C23×C4—21no—
144C23×C4—22no—
145C23×C4—22no—
146C23×C4—21no—
147C23×C4—22no—
148C23×C4—21no—
149C23×C4—21no—
150C23×C4—22no—
151C23×C4—22no—
152C23×C4—21no—
153C23×C4—22no—
154C23×C4—21no—
155C23×C4—21no—
156C23×C4—21no—
157C23×C4—22no—
158C23×C4—21no—
159C23×C4—21no—
160C23×C4—22no—
161C23×C4—22no—
162C23×C4—21no—
163C23×C4—21no—
164C23×C4—21no—
165C23×C4—22no—
166C23×C4—22no—
167C23×C4—22no—
168C23×C4—22no—
169C23×C4—22no—
170C23×C4—22no—
171C23×C4—21no—
172C23×C4—21no—
173C23×C4—21no—
174C23×C4—21no—
175C23×C4—22no—
176C23×C4—22no—
177C23×C4—22no—
178C23×C4—22no—
179C23×C4—22no—
180C23×C4—22no—
181C23×C4—22no—
182C23×C4—22no—
183C23×C4—22no—
184C23×C4—22no—
185C23×C4—22no—
186C23×C4—21no—
187C23×C4—21no—
188C23×C4—22no—
189C23×C4—22no—
190C23×C4—21no—
191C23×C4—21no—
192C23×C4—21no—
193C23×C4—22no—
194C23×C4—22no—
195C23×C4—22no—
196C23×C4—22no—
197C23×C4—22no—
198C23×C4—22no—
199C23×C4—22no—
200C23×C4—21no—
201C23×C4—21no—
202C23×C4—21no—
203C23×C4—22no—
204C23×C4—22no—
205C23×C4—22no—
206C23×C4—22no—
207C23×C4—22no—
208C23×C4—22no—
209C23×C4—21no—
210C23×C4—22no—
211C23×C4—21no—
212C23×C4—22no—
213C23×C4—21no—
214C23×C4—22no—
215C23×C4—22no—
216C23×C4—22no—
217C23×C4—22no—
218C23×C4—22no—
219C23×C4—22no—
220C23×C4—22no—
221C23×C4—22no—
222C23×C4—22no—
223C23×C4—22no—
224C23×C4—22no—
225C23×C4—22no—
226C23×C4—22no—
227C23×C4—22no—
228C23×C4—22no—
229C23×C4—22no—
230C23×C4—22no—
231C23×C4—22no—
232C23×C4—22no—
233C23×C4—22no—
234C23×C4—22no—
235C23×C4—22no—
236C23×C4—22no—
237C23×C4—22no—
238C23×C4—22no—
239C23×C4—22no—
240C23×C4—22no—
241C23×C4—22no—
242C23×C4—22no—
243C23×C4C22×C414yes—
244C23×C4C22×C414yes—
245C23×C4C22×C412yes—
246C23×C4C22×C412yes—
247C23×C4C22×C412yes—
248C23×C4C22×C414yes—
249C23×C4C22×C412yes—
250C23×C4C22×C414yes—
251C23×C4C22×C412yes—
252C23×C4C22×C412yes—
253C23×C4C22×C412yes—
254C23×C4C22×C412yes—
255C23×C4C22×C412yes—
256C23×C4C22×C412yes—
257C23×C4C22×C412yes—
258C23×C4C22×C412yes—
259C23×C4C22×C412yes—
260C23×C4C2×D414yes—
261C23×C4C2×D414yes—
262C23×C4C2×D412yes—
263C23×C4C2×D412yes—
264C23×C4C2×D412yes—
265C23×C4C2×D412yes—
266C23×C4C2×D412yes—
267C23×C4C2×Q812yes—
268C23×C4C2×Q812yes—
269C23×C4C2×Q812yes—
270C23×C4#4114yes—
271C23×C4#4114yes—
272C23×C4#4114yes—
273C23×C4#4114yes—
274C23×C4#4112yes—
275C23×C4#4112yes—
276C23×C4#4112yes—
277C23×C4#4112yes—
278C23×C4#4114yes—
279C23×C4#4114yes—
280C2×C4⋊C4—216no—
281C2×C4⋊C4—216no—
282C2×C4⋊C4—48no—
283C2×C4⋊C4—48no—
284C2×C4⋊C4—48no—
285C2×C4⋊C4—48no—
286C2×C4⋊C4—48no—
287C2×C42—28no—
288C2×C42—28no—
289C2×C42—28no—
290C2×C42—28no—
291C2×C42—28no—
292C2×C42—28no—
293C2×C42—216no—
294C2×C42—28no—
295C2×C42—28no—
296C2×C42—28no—
297C2×C42—28no—
298C2×C42—44no—
299C2×C42—44no—
300C2×C42—48no—
301C2×C42—48no—
302C2×C42—48no—
303C2×C42—48no—
304C2×C42—48no—
305C2×C42—48no—
306C2×C42—48no—
307C2×C42—48no—
308C2×C42—48no—
309C2×C42—48no—
310C2×C42C42116yescomplemented
311#95—216no—
312#95—216no—
313#95—28no—
314#95—28no—
315#95—28no—
316#95—28no—
317#95—216no—
318#95—28no—
319#95—216no—
320#95—28no—
321#95—48no—
322#95—48no—
323#95—48no—
324#95—48no—
325#95—48no—
326#95—48no—
327#95C22⋊C4116yes—
328#95C4⋊C4116yes—
329C24C23×C411yescharacteristic
330C24C23×C411yescharacteristic
331C24C23×C411yescharacteristic
332C24C22×D411yescharacteristic
333C24C22×D411yescharacteristic
334C24C22×D411yescharacteristic
335C24C22×Q811yescharacteristic
336C24C2×#4111yescharacteristic
337C24C2×#4111yescharacteristic
338C24C2×#4111yescharacteristic
339C24C2×#4111yescharacteristic
340C24C2×#4112yes—
341C24C2×#4112yes—
342C24C2×#4112yes—
343C24C2×#4112yes—
344C24C2×#4112yes—
345C24C2×#4112yes—
346C24H(5,𝔽2)12yes—
347C24H(5,𝔽2)11yescharacteristic
348C24H(5,𝔽2)11yescharacteristic
349C242−1+411yescharacteristic
350C242−1+411yescharacteristic
351C242−1+412yes—
352C22×C4—22no—
353C22×C4—22no—
354C22×C4—22no—
355C22×C4—22no—
356C22×C4—22no—
357C22×C4—22no—
358C22×C4—22no—
359C22×C4—22no—
360C22×C4—22no—
361C22×C4—24no—
362C22×C4—22no—
363C22×C4—24no—
364C22×C4—22no—
365C22×C4—22no—
366C22×C4—22no—
367C22×C4—22no—
368C22×C4—22no—
369C22×C4—22no—
370C22×C4—24no—
371C22×C4—22no—
372C22×C4—22no—
373C22×C4—24no—
374C22×C4—22no—
375C22×C4—22no—
376C22×C4—24no—
377C22×C4—24no—
378C22×C4—24no—
379C22×C4—24no—
380C22×C4—22no—
381C22×C4—22no—
382C22×C4—22no—
383C22×C4—24no—
384C22×C4—24no—
385C22×C4—24no—
386C22×C4—24no—
387C22×C4—22no—
388C22×C4—22no—
389C22×C4—24no—
390C22×C4—24no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—22no—
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—24no—
400C22×C4—24no—
401C22×C4—24no—
402C22×C4—24no—
403C22×C4—24no—
404C22×C4—24no—
405C22×C4—24no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—24no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—24no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—24no—
426C22×C4—24no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—24no—
435C22×C4—24no—
436C22×C4—22no—
437C22×C4—24no—
438C22×C4—22no—
439C22×C4—24no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—24no—
443C22×C4—24no—
444C22×C4—24no—
445C22×C4—22no—
446C22×C4—24no—
447C22×C4—24no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—24no—
452C22×C4—22no—
453C22×C4—24no—
454C22×C4—22no—
455C22×C4—24no—
456C22×C4—22no—
457C22×C4—24no—
458C22×C4—24no—
459C22×C4—24no—
460C22×C4—24no—
461C22×C4—24no—
462C22×C4—24no—
463C22×C4—24no—
464C22×C4—24no—
465C22×C4—24no—
466C22×C4—24no—
467C22×C4—24no—
468C22×C4—24no—
469C22×C4—24no—
470C22×C4—24no—
471C22×C4—24no—
472C22×C4—24no—
473C22×C4—24no—
474C22×C4—24no—
475C22×C4—24no—
476C22×C4—22no—
477C22×C4—24no—
478C22×C4—24no—
479C22×C4—24no—
480C22×C4—24no—
481C22×C4—24no—
482C22×C4—24no—
483C22×C4—24no—
484C22×C4—24no—
485C22×C4—24no—
486C22×C4—24no—
487C22×C4—24no—
488C22×C4—22no—
489C22×C4—24no—
490C22×C4—22no—
491C22×C4—24no—
492C22×C4—24no—
493C22×C4—24no—
494C22×C4—24no—
495C22×C4—24no—
496C22×C4—24no—
497C22×C4—24no—
498C22×C4—24no—
499C22×C4—24no—
500C22×C4—22no—
501C22×C4—24no—
502C22×C4—24no—
503C22×C4—24no—
504C22×C4—24no—
505C22×C4—24no—
506C22×C4—24no—
507C22×C4—24no—
508C22×C4—24no—
509C22×C4—24no—
510C22×C4—24no—
511C22×C4—24no—
512C22×C4—24no—
513C22×C4—24no—
514C22×C4—24no—
515C22×C4—24no—
516C22×C4—42no—
517C22×C4—42no—
518C22×C4—42no—
519C22×C4—42no—
520C22×C4—42no—
521C22×C4—42no—
522C22×C4—42no—
523C22×C4—42no—
524C22×C4—42no—
525C22×C4—42no—
526C22×C4—42no—
527C22×C4—42no—
528C22×C4—42no—
529C22×C4—42no—
530C22×C4—42no—
531C22×C4—42no—
532C22×C4—42no—
533C22×C4—42no—
534C22×C4—42no—
535C22×C4—42no—
536C22×C4—42no—
537C22×C4—42no—
538C22×C4—42no—
539C22×C4—42no—
540C22×C4—42no—
541C22×C4—42no—
542C22×C4—42no—
543C22×C4—42no—
544C22×C4—42no—
545C22×C4—42no—
546C22×C4—42no—
547C22×C4—42no—
548C22×C4—42no—
549C22×C4—42no—
550C22×C4—42no—
551C22×C4—42no—
552C22×C4—42no—
553C22×C4—41no—
554C22×C4—41no—
555C22×C4—42no—
556C22×C4—42no—
557C22×C4—41no—
558C22×C4—41no—
559C22×C4—42no—
560C22×C4—42no—
561C22×C4—42no—
562C22×C4—42no—
563C22×C4—42no—
564C22×C4—42no—
565C22×C4—42no—
566C22×C4—41no—
567C22×C4—42no—
568C22×C4—42no—
569C22×C4—41no—
570C22×C4—42no—
571C22×C4—41no—
572C22×C4—42no—
573C22×C4—42no—
574C22×C4—41no—
575C22×C4—42no—
576C22×C4—42no—
577C22×C4—42no—
578C22×C4—42no—
579C22×C4—42no—
580C22×C4—42no—
581C22×C4—42no—
582C22×C4—42no—
583C22×C4—42no—
584C22×C4—42no—
585C22×C4—42no—
586C22×C4—42no—
587C22×C4—42no—
588C22×C4—42no—
589C22×C4—42no—
590C22×C4—42no—
591C22×C4—42no—
592C22×C4—42no—
593C22×C4—42no—
594C22×C4—42no—
595C22×C4—42no—
596C22×C4—42no—
597C22×C4—42no—
598C22×C4—42no—
599C22×C4—42no—
600C22×C4—42no—
601C22×C4—42no—
602C22×C4—42no—
603C22×C4—42no—
604C22×C4—42no—
605C22×C4—42no—
606C22×C4—42no—
607C22×C4—42no—
608C22×C4—42no—
609C22×C4—42no—
610C22×C4—42no—
611C22×C4—42no—
612C22×C4—42no—
613C22×C4—42no—
614C22×C4—42no—
615C22×C4—42no—
616C22×C4—42no—
617C22×C4—42no—
618C22×C4—42no—
619C22×C4—42no—
620C22×C4—42no—
621C22×C4—42no—
622C22×C4—42no—
623C22×C4—42no—
624C22×C4—42no—
625C22×C4—42no—
626C22×C4—42no—
627C22×C4—42no—
628C22×C4—42no—
629C22×C4—42no—
630C22×C4—42no—
631C22×C4—42no—
632C22×C4—42no—
633C22×C4—42no—
634C22×C4—42no—
635C22×C4—42no—
636C22×C4—42no—
637C22×C4—42no—
638C22×C4—42no—
639C22×C4—42no—
640C22×C4C2×C4214yes—
641C22×C4C2×C4214yes—
642C22×C4C2×C4214yes—
643C22×C4C2×C22⋊C418yes—
644C22×C4C2×C22⋊C414yes—
645C22×C4C2×C4⋊C414yes—
646C22×C4C2×C4⋊C414yes—
647C22×C4C2×C4⋊C414yes—
648C22×C4#11714yes—
649C22×C4#11718yes—
650C22×C4#11714yes—
651C22×C4#11714yes—
652C22×C4#11714yes—
653C22×C4#11714yes—
654C22×C4#11714yes—
655C22×C4C4×D414yes—
656C22×C4C4×D414yes—
657C22×C4C4×D414yes—
658C22×C4C4×D414yes—
659C22×C4C4×D414yes—
660C22×C4C4×D414yes—
661C22×C4C4×Q814yes—
662C22×C4C4×Q814yes—
663C22×C4#12418yes—
664C22×C4#12518yes—
665C4⋊C4—432no—
666C42—232no—
667C42—416no—
668C42—416no—
669C42—432no—
670C23C22×C4211yescharacteristic
671C23C22×C22⋊C411yescharacteristic
672C23C22×C4⋊C411yescharacteristic
673C23C2×#11711yescharacteristic
674C23C2×#11711yescharacteristic
675C23C2×#11711yescharacteristic
676C23C2×#11711yescharacteristic
677C23C2×#11711yescharacteristic
678C23C2×#11712yes—
679C23C2×#11711yescharacteristic
680C23C2×C4×D411yescharacteristic
681C23C2×C4×D411yescharacteristic
682C23C2×C4×D411yescharacteristic
683C23C2×C4×D411yescharacteristic
684C23C2×C4×D411yescharacteristic
685C23C2×C4×D411yescharacteristic
686C23C2×C4×Q811yescharacteristic
687C23C2×C4×Q811yescharacteristic
688C23C4×#4112yes—
689C23C4×#4112yes—
690C23C4×#4112yes—
691C23C4×#4112yes—
692C23C4×#4111yescharacteristic
693C23C4×#4111yescharacteristic
694C23C4×#4112yes—
695C23#51811yescharacteristic
696C23#51811yescharacteristic
697C23#51911yescharacteristic
698C23#51911yescharacteristic
699C23#52011yescharacteristic
700C23#52011yescharacteristic
701C23#52011yescharacteristic
702C23#52011yescharacteristic
703C23#52012yes—
704C23#52012yes—
705C23#52512yes—
706C23#52512yes—
707C23C2×#12412yes—
708C23C2×#12512yes—
709C23#52912yes—
710C23#52912yes—
711C23#52912yes—
712C23#52912yes—
713C23#52912yes—
714C23#52912yes—
715C23#52912yes—
716C23#52912yes—
717C23#53212yes—
718C23#53212yes—
719C23#53212yes—
720C23#53312yes—
721C23#53812yes—
722C23#53812yes—
723C23#53912yes—
724C23#53912yes—
725C23#54112yes—
726C23#54112yes—
727C23#54212yes—
728C23#54212yes—
729C23D4211yescharacteristic
730C23D4211yescharacteristic
731C23#54611yescharacteristic
732C23#54611yescharacteristic
733C23#54612yes—
734C23#54612yes—
735C23#54612yes—
736C23#54712yes—
737C23#54712yes—
738C23#54711yescharacteristic
739C23#54711yescharacteristic
740C23#54811yescharacteristic
741C23#54811yescharacteristic
742C23#54812yes—
743C23D4×Q811yescharacteristic
744C23D4×Q811yescharacteristic
745C23#55112yes—
746C23#55112yes—
747C23#55112yes—
748C23#55112yes—
749C23#55211yescharacteristic
750C23#55212yes—
751C23#55212yes—
752C23#55212yes—
753C23#55212yes—
754C23#55212yes—
755C23#55212yes—
756C23#55211yescharacteristic
757C23#55212yes—
758C23#55311yescharacteristic
759C23#55312yes—
760C23#55311yescharacteristic
761C23#55411yescharacteristic
762C23#55412yes—
763C23#55411yescharacteristic
764C23#55512yes—
765C23#55512yes—
766C23#55612yes—
767C23#55712yes—
768C23#55912yes—
769C2×C4—24no—
770C2×C4—24no—
771C2×C4—28no—
772C2×C4—24no—
773C2×C4—24no—
774C2×C4—24no—
775C2×C4—24no—
776C2×C4—24no—
777C2×C4—28no—
778C2×C4—24no—
779C2×C4—24no—
780C2×C4—24no—
781C2×C4—24no—
782C2×C4—24no—
783C2×C4—24no—
784C2×C4—24no—
785C2×C4—24no—
786C2×C4—24no—
787C2×C4—24no—
788C2×C4—28no—
789C2×C4—28no—
790C2×C4—24no—
791C2×C4—24no—
792C2×C4—24no—
793C2×C4—24no—
794C2×C4—28no—
795C2×C4—28no—
796C2×C4—28no—
797C2×C4—28no—
798C2×C4—24no—
799C2×C4—24no—
800C2×C4—24no—
801C2×C4—24no—
802C2×C4—24no—
803C2×C4—24no—
804C2×C4—28no—
805C2×C4—28no—
806C2×C4—24no—
807C2×C4—24no—
808C2×C4—28no—
809C2×C4—24no—
810C2×C4—24no—
811C2×C4—28no—
812C2×C4—24no—
813C2×C4—24no—
814C2×C4—24no—
815C2×C4—24no—
816C2×C4—24no—
817C2×C4—24no—
818C2×C4—24no—
819C2×C4—28no—
820C2×C4—28no—
821C2×C4—42no—
822C2×C4—42no—
823C2×C4—44no—
824C2×C4—44no—
825C2×C4—44no—
826C2×C4—44no—
827C2×C4—44no—
828C2×C4—44no—
829C2×C4—42no—
830C2×C4—42no—
831C2×C4—42no—
832C2×C4—42no—
833C2×C4—42no—
834C2×C4—42no—
835C2×C4—42no—
836C2×C4—42no—
837C2×C4—44no—
838C2×C4—44no—
839C2×C4—44no—
840C2×C4—44no—
841C2×C4—44no—
842C2×C4—44no—
843C2×C4—44no—
844C2×C4—44no—
845C2×C4—44no—
846C2×C4—44no—
847C2×C4—44no—
848C2×C4—44no—
849C2×C4—44no—
850C2×C4—44no—
851C2×C4—44no—
852C2×C4—44no—
853C2×C4—44no—
854C2×C4—44no—
855C2×C4—44no—
856C2×C4—44no—
857C2×C4—42no—
858C2×C4—42no—
859C2×C4—44no—
860C2×C4—42no—
861C2×C4—42no—
862C2×C4—42no—
863C2×C4—42no—
864C2×C4—44no—
865C2×C4—44no—
866C2×C4—44no—
867C2×C4—44no—
868C2×C4—44no—
869C2×C4—44no—
870C2×C4—44no—
871C2×C4—44no—
872C2×C4—44no—
873C2×C4—44no—
874C2×C4—44no—
875C2×C4—44no—
876C2×C4—44no—
877C2×C4—44no—
878C2×C4—44no—
879C2×C4—44no—
880C2×C4—44no—
881C2×C4—44no—
882C2×C4—44no—
883C2×C4—44no—
884C2×C4—44no—
885C2×C4—44no—
886C2×C4—44no—
887C2×C4—44no—
888C2×C4—44no—
889C2×C4—44no—
890C2×C4—44no—
891C2×C4—82no—
892C2×C4—82no—
893C2×C4—82no—
894C2×C4—82no—
895C2×C4—82no—
896C2×C4—82no—
897C2×C4—82no—
898C2×C4—82no—
899C2×C4—82no—
900C2×C4—82no—
901C2×C4—82no—
902C2×C4—82no—
903C2×C4—82no—
904C2×C4—82no—
905C2×C4—82no—
906C2×C4—82no—
907C2×C4C4×C22⋊C418yes—
908C2×C4C4×C4⋊C418yes—
909C2×C4#38218yescomplemented
910C22C2×C4×C22⋊C411yescharacteristic
911C22C2×C4×C4⋊C411yescharacteristic
912C22C4×#11711yescharacteristic
913C22C4×#11711yescharacteristic
914C22C4×#11711yescharacteristic
915C22#227411yescharacteristic
916C22#227411yescharacteristic
917C22C2×#38211yescharacteristic
918C22#228311yescharacteristic
919C22#228311yescharacteristic
920C22#228511yescharacteristic
921C22#229011yescharacteristic
922C22#229011yescharacteristic
923C22#229012yes—
924C22#229311yescharacteristic
925C22#229311yescharacteristic
926C22#229312yes—
927C22#229712yes—
928C22#229812yes—
929C22C4×#12412yes—
930C22C4×#12412yes—
931C22C4×#12512yes—
932C22C4×#12512yes—
933C22#231811yescharacteristic
934C22#231811yescharacteristic
935C22#232011yescharacteristic
936C22#232011yescharacteristic
937C22#233412yes—
938C22#233412yes—
939C22#233612yes—
940C22#233712yes—
941C22D4×C22⋊C411yescharacteristic
942C22#233912yes—
943C22Q8×C22⋊C411yescharacteristic
944C22#234211yescharacteristic
945C22#234211yescharacteristic
946C22#234312yes—
947C22#234311yescharacteristic
948C22#234311yescharacteristic
949C22#234312yes—
950C22#234411yescharacteristic
951C22#234411yescharacteristic
952C22#234411yescharacteristic
953C22#234511yescharacteristic
954C22#234611yescharacteristic
955C22#234611yescharacteristic
956C22#234612yes—
957C22D4×C4⋊C411yescharacteristic
958C22D4×C4⋊C411yescharacteristic
959C22#234911yescharacteristic
960C22#235111yescharacteristic
961C22#235211yescharacteristic
962C22#235211yescharacteristic
963C22#235212yes—
964C22#235512yes—
965C22#235611yescharacteristic
966C22#235711yescharacteristic
967C22#235912yes—
968C22#235912yes—
969C22#236011yescharacteristic
970C22#236011yescharacteristic
971C22#236111yescharacteristic
972C22#236111yescharacteristic
973C22#236712yes—
974C22#237012yes—
975C22#237112yes—
976C22#237212yes—
977C22#245912yes—
978C22#246012yes—
979C22#246112yes—
980C22#246212yes—
981C22#247212yes—
982C22#247312yes—
983C22#247412yes—
984C22#247512yes—
985C22#248812yes—
986C22#248912yes—
987C22#249112yes—
988C22#250512yes—
989C22#250612yes—
990C22#250812yes—
991C22#251512yes—
992C22#251712yes—
993C22#251812yes—
994C22#251912yes—
995C22#251912yes—
996C22#252012yes—
997C22#252112yes—
998C22#252412yes—
999C22#252812yes—
1000C22#252912yes—
1001C22#255312yes—
1002C22#255512yes—
1003C22#255612yes—
1004C22#255712yes—
1005C22#255812yes—
1006C22#257412yes—
1007C22#257512yes—
1008C22#257612yes—
1009C4—28no—
1010C4—28no—
1011C4—28no—
1012C4—48no—
1013C4—44no—
1014C4—44no—
1015C4—44no—
1016C4—48no—
1017C4—44no—
1018C4—84no—
1019C4—84no—
1020C2#1376111yescharacteristic
1021C2C4×#38211yescharacteristic
1022C2#1378111yescharacteristic
1023C2#1379911yescharacteristic
1024C2C22⋊C4×C4⋊C411yescharacteristic
1025C2#1380411yescharacteristic
1026C2#1380511yescharacteristic
1027C2#1388811yescharacteristic
1028C2#1388911yescharacteristic
1029C2#1389611yescharacteristic
1030C2#1389711yescharacteristic
1031C2#1391411yescharacteristic
1032C2#1391511yescharacteristic
1033C2#1391711yescharacteristic
1034C2#1391811yescharacteristic
1035C2#1398512yes—
1036C2#1398612yes—
1037C2#1400912yes—
1038C2#1401012yes—
1039C2#1409712yes—
1040C2#1409812yes—
1041C2#1410512yes—
1042C2#1410612yes—
subgroupG/H
center, Frattini, socle, prime radical, cosocleC25C24
commutatorC23C22×C42
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C25 ◁ G
LECSG ▷ C25 ▷ C1

Complements

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

NH ≅ G/Ntype
19. C2×#382C4semidirect
40. #1434C4semidirect
42. C4×#95C4semidirect
310. C2×C42C42semidirect
909. C2×C4#382semidirect

Maximal subgroups

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

subgroupindex
C22×#3822
C2×#14362
C2×#14342
C2×C4×#952
#75572
#75562
#75542