Finite Group Databasebeta

← #154388

Subgroups — #154388

Order 512.

2950 conjugacy classes of subgroups.

The subgroup lattice has 905 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#1443C214yesmaximal
2C2×C4⋊#95C211yesmaximal, characteristic
3C2×C4⋊#95C211yesmaximal, characteristic
4C2×C4⋊#95C211yesmaximal, characteristic
5C2×C4⋊#95C211yesmaximal, characteristic
6C2×C4⋊#95C211yesmaximal, characteristic
7C2×C4⋊#95C211yesmaximal, characteristic
8C2×C4×#95C211yesmaximal, characteristic
9#7556C214yesmaximal
10C23×C4⋊C4C2211yescharacteristic
11C23×C4⋊C4C2211yescharacteristic
12C23×C4⋊C4C2211yescharacteristic
13C23×C4⋊C4C2211yescharacteristic
14C23×C42C2211yescharacteristic
15C23×C42C2211yescharacteristic
16C23×C42C2211yescharacteristic
17C22×#95C2212yes—
18C22×#95C2212yes—
19C22×#95C2214yes—
20C22×#95C2212yes—
21C22×#95C2212yes—
22C22×#95C2214yes—
23C22×#95C2214yes—
24C22×#95C2214yes—
25C22×#95C2212yes—
26C22×#95C2212yes—
27#1443—216no—
28C4⋊#95—24no—
29C4⋊#95—24no—
30C4⋊#95—24no—
31C4⋊#95—24no—
32C4⋊#95—24no—
33C4⋊#95C418yescomplemented
34C4×#95—24no—
35C24×C4C2312yes—
36C24×C4C2312yes—
37C24×C4C2312yes—
38C24×C4C2312yes—
39C24×C4C2312yes—
40C24×C4C2311yescharacteristic
41C24×C4C2312yes—
42C24×C4C2311yescharacteristic
43C24×C4C2311yescharacteristic
44C22×C4⋊C4—22no—
45C22×C4⋊C4—22no—
46C22×C4⋊C4—22no—
47C22×C4⋊C4—22no—
48C22×C4⋊C4—22no—
49C22×C4⋊C4—22no—
50C22×C4⋊C4—22no—
51C22×C4⋊C4—22no—
52C22×C4⋊C4—22no—
53C22×C4⋊C4—22no—
54C22×C4⋊C4—22no—
55C22×C4⋊C4—22no—
56C22×C4⋊C4—22no—
57C22×C4⋊C4—22no—
58C22×C4⋊C4—22no—
59C22×C4⋊C4—22no—
60C22×C4⋊C4—22no—
61C22×C4⋊C4—22no—
62C22×C4⋊C4—22no—
63C22×C4⋊C4—22no—
64C22×C4⋊C4—22no—
65C22×C4⋊C4—22no—
66C22×C4⋊C4—22no—
67C22×C4⋊C4—22no—
68C22×C4⋊C4C2×C414yes—
69C22×C4⋊C4C2×C414yes—
70C22×C4⋊C4D414yes—
71C22×C4⋊C4Q814yes—
72C22×C42—22no—
73C22×C42—22no—
74C22×C42—22no—
75C22×C42—22no—
76C22×C42—22no—
77C22×C42—22no—
78C22×C42—22no—
79C22×C42—22no—
80C22×C42—22no—
81C22×C42—22no—
82C22×C42—22no—
83C22×C42—22no—
84C22×C42—22no—
85C22×C42—22no—
86C22×C42—22no—
87C22×C42—22no—
88C22×C42—22no—
89C22×C42—22no—
90C22×C42C2×C414yes—
91C22×C42D414yes—
92C22×C42D414yes—
93C2×#95—24no—
94C2×#95—24no—
95C2×#95—28no—
96C2×#95—24no—
97C2×#95—24no—
98C2×#95—28no—
99C2×#95—24no—
100C2×#95—28no—
101C2×#95—28no—
102C2×#95—24no—
103C2×#95—28no—
104C2×#95—24no—
105C2×#95—24no—
106C2×#95—24no—
107C2×#95—28no—
108C2×#95—28no—
109C2×#95—28no—
110C2×#95—28no—
111C2×#95—28no—
112C2×#95—28no—
113C2×#95—28no—
114C2×#95—44no—
115C2×#95—44no—
116C2×#95—44no—
117C2×#95C2×C4116yes—
118C2×#95D418yes—
119C25C2411yescharacteristic
120C23×C4—22no—
121C23×C4—22no—
122C23×C4—21no—
123C23×C4—21no—
124C23×C4—22no—
125C23×C4—22no—
126C23×C4—22no—
127C23×C4—22no—
128C23×C4—22no—
129C23×C4—22no—
130C23×C4—22no—
131C23×C4—22no—
132C23×C4—22no—
133C23×C4—22no—
134C23×C4—22no—
135C23×C4—21no—
136C23×C4—21no—
137C23×C4—22no—
138C23×C4—22no—
139C23×C4—22no—
140C23×C4—21no—
141C23×C4—21no—
142C23×C4—21no—
143C23×C4—21no—
144C23×C4—22no—
145C23×C4—22no—
146C23×C4—21no—
147C23×C4—21no—
148C23×C4—21no—
149C23×C4—21no—
150C23×C4—22no—
151C23×C4—22no—
152C23×C4—22no—
153C23×C4—22no—
154C23×C4—22no—
155C23×C4—22no—
156C23×C4—22no—
157C23×C4—22no—
158C23×C4—22no—
159C23×C4—22no—
160C23×C4—22no—
161C23×C4—22no—
162C23×C4—22no—
163C23×C4—22no—
164C23×C4—22no—
165C23×C4—22no—
166C23×C4—22no—
167C23×C4—22no—
168C23×C4—22no—
169C23×C4—22no—
170C23×C4—24no—
171C23×C4—24no—
172C23×C4—24no—
173C23×C4—24no—
174C23×C4—22no—
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—22no—
187C23×C4—22no—
188C23×C4—22no—
189C23×C4—22no—
190C23×C4—24no—
191C23×C4—24no—
192C23×C4—24no—
193C23×C4—24no—
194C23×C4—24no—
195C23×C4—24no—
196C23×C4—24no—
197C23×C4—24no—
198C23×C4—24no—
199C23×C4—24no—
200C23×C4—24no—
201C23×C4—24no—
202C23×C4C22×C414yes—
203C23×C4C22×C414yes—
204C23×C4C22×C414yes—
205C23×C4C22×C412yes—
206C23×C4C2×D414yes—
207C23×C4C2×D414yes—
208C23×C4C2×D414yes—
209C23×C4C2×D414yes—
210C23×C4C2×D412yes—
211C23×C4C2×D414yes—
212C23×C4C2×D412yes—
213C23×C4C2×D412yes—
214C23×C4C2×D412yes—
215C23×C4C2×D412yes—
216C23×C4C2×Q814yes—
217C23×C4C2×Q812yes—
218C23×C4#4114yes—
219C23×C4#4114yes—
220C23×C4#4114yes—
221C23×C4#4112yes—
222C23×C4#4112yes—
223C23×C4#4112yes—
224C23×C4#4112yes—
225C23×C4#4112yes—
226C23×C4#4112yes—
227C23×C4#4112yes—
228C23×C4#4112yes—
229C23×C4#4112yes—
230C23×C4#4112yes—
231C2×C4⋊C4—28no—
232C2×C4⋊C4—28no—
233C2×C4⋊C4—28no—
234C2×C4⋊C4—28no—
235C2×C4⋊C4—28no—
236C2×C4⋊C4—28no—
237C2×C4⋊C4—28no—
238C2×C4⋊C4—28no—
239C2×C4⋊C4—28no—
240C2×C4⋊C4—28no—
241C2×C4⋊C4—28no—
242C2×C4⋊C4—28no—
243C2×C4⋊C4—44no—
244C2×C4⋊C4—44no—
245C2×C4⋊C4—44no—
246C2×C4⋊C4—44no—
247C2×C4⋊C4—44no—
248C2×C4⋊C4—44no—
249C2×C4⋊C4—44no—
250C2×C4⋊C4—44no—
251C2×C4⋊C4—44no—
252C2×C4⋊C4—44no—
253C2×C4⋊C4—44no—
254C2×C4⋊C4—44no—
255C2×C4⋊C4—44no—
256C2×C4⋊C4—44no—
257C2×C4⋊C4—44no—
258C2×C4⋊C4—44no—
259C2×C42—28no—
260C2×C42—28no—
261C2×C42—28no—
262C2×C42—28no—
263C2×C42—28no—
264C2×C42—28no—
265C2×C42—28no—
266C2×C42—28no—
267C2×C42—28no—
268C2×C42—44no—
269C2×C42—44no—
270C2×C42—44no—
271C2×C42—44no—
272C2×C42—44no—
273C2×C42—44no—
274C2×C42—44no—
275C2×C42—44no—
276C2×C42—44no—
277C2×C42—44no—
278C2×C42—44no—
279C2×C42—44no—
280#95—216no—
281#95—232no—
282#95—216no—
283#95—416no—
284#95—416no—
285#95—48no—
286#95—416no—
287#95—48no—
288#95—48no—
289#95—48no—
290C24C23×C411yescharacteristic
291C24C22×D411yescharacteristic
292C24C22×D411yescharacteristic
293C24C22×D411yescharacteristic
294C24C22×D412yes—
295C24C22×Q811yescharacteristic
296C24C2×#4111yescharacteristic
297C24C2×#4111yescharacteristic
298C24C2×#4111yescharacteristic
299C24C2×#4111yescharacteristic
300C24C2×#4111yescharacteristic
301C24C2×#4111yescharacteristic
302C24C2×#4111yescharacteristic
303C24C2×#4111yescharacteristic
304C24C2×#4111yescharacteristic
305C24C2×#4112yes—
306C24C2×#4111yescharacteristic
307C24C2×#4112yes—
308C24C2×#4112yes—
309C24H(5,𝔽2)12yes—
310C242−1+412yes—
311C242−1+412yes—
312C242−1+412yes—
313C22×C4—24no—
314C22×C4—24no—
315C22×C4—24no—
316C22×C4—24no—
317C22×C4—24no—
318C22×C4—24no—
319C22×C4—24no—
320C22×C4—24no—
321C22×C4—22no—
322C22×C4—22no—
323C22×C4—24no—
324C22×C4—24no—
325C22×C4—24no—
326C22×C4—22no—
327C22×C4—22no—
328C22×C4—22no—
329C22×C4—22no—
330C22×C4—24no—
331C22×C4—24no—
332C22×C4—24no—
333C22×C4—24no—
334C22×C4—24no—
335C22×C4—24no—
336C22×C4—24no—
337C22×C4—22no—
338C22×C4—24no—
339C22×C4—24no—
340C22×C4—24no—
341C22×C4—22no—
342C22×C4—24no—
343C22×C4—22no—
344C22×C4—24no—
345C22×C4—22no—
346C22×C4—22no—
347C22×C4—22no—
348C22×C4—24no—
349C22×C4—24no—
350C22×C4—24no—
351C22×C4—24no—
352C22×C4—24no—
353C22×C4—24no—
354C22×C4—24no—
355C22×C4—24no—
356C22×C4—24no—
357C22×C4—24no—
358C22×C4—24no—
359C22×C4—24no—
360C22×C4—24no—
361C22×C4—24no—
362C22×C4—24no—
363C22×C4—24no—
364C22×C4—24no—
365C22×C4—24no—
366C22×C4—24no—
367C22×C4—24no—
368C22×C4—24no—
369C22×C4—24no—
370C22×C4—24no—
371C22×C4—24no—
372C22×C4—24no—
373C22×C4—24no—
374C22×C4—24no—
375C22×C4—28no—
376C22×C4—28no—
377C22×C4—24no—
378C22×C4—24no—
379C22×C4—24no—
380C22×C4—24no—
381C22×C4—28no—
382C22×C4—28no—
383C22×C4—24no—
384C22×C4—24no—
385C22×C4—24no—
386C22×C4—24no—
387C22×C4—24no—
388C22×C4—24no—
389C22×C4—28no—
390C22×C4—28no—
391C22×C4—28no—
392C22×C4—28no—
393C22×C4—42no—
394C22×C4—42no—
395C22×C4—41no—
396C22×C4—41no—
397C22×C4—42no—
398C22×C4—41no—
399C22×C4—42no—
400C22×C4—42no—
401C22×C4—41no—
402C22×C4—41no—
403C22×C4—42no—
404C22×C4—41no—
405C22×C4—42no—
406C22×C4—41no—
407C22×C4—41no—
408C22×C4—42no—
409C22×C4—42no—
410C22×C4—42no—
411C22×C4—42no—
412C22×C4—42no—
413C22×C4—42no—
414C22×C4—42no—
415C22×C4—42no—
416C22×C4—42no—
417C22×C4—42no—
418C22×C4—42no—
419C22×C4—42no—
420C22×C4—42no—
421C22×C4—42no—
422C22×C4—42no—
423C22×C4—42no—
424C22×C4—42no—
425C22×C4—42no—
426C22×C4—42no—
427C22×C4—42no—
428C22×C4—42no—
429C22×C4—42no—
430C22×C4—42no—
431C22×C4—42no—
432C22×C4—42no—
433C22×C4—42no—
434C22×C4—42no—
435C22×C4—42no—
436C22×C4—42no—
437C22×C4—42no—
438C22×C4—42no—
439C22×C4—42no—
440C22×C4—42no—
441C22×C4—42no—
442C22×C4—42no—
443C22×C4—42no—
444C22×C4—42no—
445C22×C4—44no—
446C22×C4—44no—
447C22×C4—42no—
448C22×C4—42no—
449C22×C4—42no—
450C22×C4—42no—
451C22×C4—42no—
452C22×C4—42no—
453C22×C4—42no—
454C22×C4—42no—
455C22×C4—44no—
456C22×C4—42no—
457C22×C4—42no—
458C22×C4—42no—
459C22×C4—42no—
460C22×C4—42no—
461C22×C4—42no—
462C22×C4—42no—
463C22×C4—42no—
464C22×C4—42no—
465C22×C4—42no—
466C22×C4—44no—
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—44no—
476C22×C4—44no—
477C22×C4—42no—
478C22×C4—42no—
479C22×C4—44no—
480C22×C4—44no—
481C22×C4—44no—
482C22×C4—44no—
483C22×C4—44no—
484C22×C4—44no—
485C22×C4—42no—
486C22×C4—42no—
487C22×C4—42no—
488C22×C4—42no—
489C22×C4—42no—
490C22×C4—42no—
491C22×C4—42no—
492C22×C4—44no—
493C22×C4—44no—
494C22×C4—44no—
495C22×C4—44no—
496C22×C4—44no—
497C22×C4—44no—
498C22×C4—44no—
499C22×C4—44no—
500C22×C4—44no—
501C22×C4—44no—
502C22×C4—44no—
503C22×C4—44no—
504C22×C4—44no—
505C22×C4—44no—
506C22×C4—44no—
507C22×C4—44no—
508C22×C4—44no—
509C22×C4—44no—
510C22×C4—44no—
511C22×C4—44no—
512C22×C4—44no—
513C22×C4—44no—
514C22×C4—44no—
515C22×C4—44no—
516C22×C4—44no—
517C22×C4#11714yes—
518C22×C4#11714yes—
519C22×C4#11714yes—
520C22×C4C4×D418yes—
521C22×C4C4×D414yes—
522C22×C4C4×D414yes—
523C22×C4C4×D414yes—
524C22×C4C4×Q814yes—
525C22×C4#12118yes—
526C22×C4#12114yes—
527C22×C4#12114yes—
528C22×C4#12114yes—
529C22×C4C22⋊Q814yes—
530C22×C4C22⋊Q814yes—
531C22×C4C22⋊Q814yes—
532C22×C4#12314yes—
533C22×C4#12314yes—
534C22×C4#12314yes—
535C22×C4#12314yes—
536C22×C4#12314yes—
537C22×C4#12314yes—
538C22×C4#12414yes—
539C22×C4#12414yes—
540C22×C4#12414yes—
541C22×C4#12414yes—
542C22×C4#12514yes—
543C22×C4#12514yes—
544C22×C4#12514yes—
545C22×C4#12614yes—
546C22×C4#12614yes—
547C22×C4#12614yes—
548C22×C4#12614yes—
549C22×C4#12614yes—
550C22×C4#12614yes—
551C22×C4#12614yes—
552C22×C4#12614yes—
553C22×C4#12614yes—
554C22×C4#12614yes—
555C22×C4#12714yes—
556C4⋊C4—416no—
557C4⋊C4—416no—
558C4⋊C4—416no—
559C4⋊C4—416no—
560C42—416no—
561C42—416no—
562C42—416no—
563C23C2×#11711yescharacteristic
564C23C2×#11711yescharacteristic
565C23C2×#11711yescharacteristic
566C23C2×C4×D411yescharacteristic
567C23C2×C4×D412yes—
568C23C2×C4×D411yescharacteristic
569C23C2×C4×D411yescharacteristic
570C23C2×C4×Q811yescharacteristic
571C23C4×#4112yes—
572C23#51912yes—
573C23#52012yes—
574C23C2×#12111yescharacteristic
575C23C2×#12112yes—
576C23C2×#12111yescharacteristic
577C23C2×#12111yescharacteristic
578C23C2×C22⋊Q811yescharacteristic
579C23C2×C22⋊Q811yescharacteristic
580C23C2×C22⋊Q811yescharacteristic
581C23C2×#12311yescharacteristic
582C23C2×#12311yescharacteristic
583C23C2×#12311yescharacteristic
584C23C2×#12311yescharacteristic
585C23C2×#12311yescharacteristic
586C23C2×#12311yescharacteristic
587C23#52512yes—
588C23C2×#12411yescharacteristic
589C23C2×#12411yescharacteristic
590C23C2×#12411yescharacteristic
591C23C2×#12411yescharacteristic
592C23C2×#12511yescharacteristic
593C23C2×#12511yescharacteristic
594C23C2×#12511yescharacteristic
595C23C2×#12611yescharacteristic
596C23C2×#12611yescharacteristic
597C23C2×#12611yescharacteristic
598C23C2×#12611yescharacteristic
599C23C2×#12611yescharacteristic
600C23C2×#12611yescharacteristic
601C23C2×#12611yescharacteristic
602C23C2×#12611yescharacteristic
603C23C2×#12611yescharacteristic
604C23C2×#12611yescharacteristic
605C23#52912yes—
606C23#52912yes—
607C23#52912yes—
608C23#52912yes—
609C23C2×#12711yescharacteristic
610C23#53211yescharacteristic
611C23#53212yes—
612C23#53211yescharacteristic
613C23#53212yes—
614C23#53212yes—
615C23#53212yes—
616C23#53511yescharacteristic
617C23#53611yescharacteristic
618C23#53611yescharacteristic
619C23#53612yes—
620C23#53611yescharacteristic
621C23#53712yes—
622C23#54112yes—
623C23#54112yes—
624C23#54112yes—
625C23#54112yes—
626C23#54212yes—
627C23#54212yes—
628C23#54212yes—
629C23#54212yes—
630C23D4212yes—
631C23#54712yes—
632C23#54712yes—
633C23#54712yes—
634C23#54712yes—
635C23#54712yes—
636C23#54712yes—
637C23#54812yes—
638C23#54812yes—
639C23D4×Q812yes—
640C23#55012yes—
641C23#55212yes—
642C23#55212yes—
643C23#55212yes—
644C23#55212yes—
645C23#55212yes—
646C23#55212yes—
647C23#55312yes—
648C23#55312yes—
649C23#55312yes—
650C23#55312yes—
651C23#55412yes—
652C23#55512yes—
653C23#55612yes—
654C23#55612yes—
655C23#55612yes—
656C23#55612yes—
657C23#55612yes—
658C23#55612yes—
659C23#55612yes—
660C23#55712yes—
661C23#55712yes—
662C2×C4—24no—
663C2×C4—28no—
664C2×C4—28no—
665C2×C4—24no—
666C2×C4—28no—
667C2×C4—28no—
668C2×C4—28no—
669C2×C4—24no—
670C2×C4—24no—
671C2×C4—24no—
672C2×C4—24no—
673C2×C4—28no—
674C2×C4—44no—
675C2×C4—44no—
676C2×C4—44no—
677C2×C4—44no—
678C2×C4—44no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—44no—
682C2×C4—44no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—44no—
686C2×C4—44no—
687C2×C4—44no—
688C2×C4—44no—
689C2×C4—44no—
690C2×C4—44no—
691C2×C4—44no—
692C2×C4—44no—
693C2×C4—44no—
694C2×C4—44no—
695C2×C4—44no—
696C2×C4—44no—
697C2×C4—44no—
698C2×C4—44no—
699C2×C4—44no—
700C2×C4—44no—
701C2×C4—44no—
702C2×C4—44no—
703C2×C4—44no—
704C2×C4—44no—
705C2×C4—44no—
706C2×C4—44no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—44no—
712C2×C4—44no—
713C2×C4—44no—
714C2×C4—44no—
715C2×C4—44no—
716C2×C4—44no—
717C2×C4—44no—
718C2×C4—48no—
719C2×C4—48no—
720C2×C4—44no—
721C2×C4—44no—
722C2×C4—48no—
723C2×C4—48no—
724C2×C4—48no—
725C2×C4—48no—
726C2×C4—44no—
727C2×C4—44no—
728C2×C4—44no—
729C2×C4—44no—
730C2×C4—44no—
731C2×C4—48no—
732C2×C4—48no—
733C2×C4—44no—
734C2×C4—82no—
735C2×C4—84no—
736C2×C4—82no—
737C2×C4—82no—
738C2×C4—82no—
739C2×C4—82no—
740C2×C4—84no—
741C2×C4—82no—
742C2×C4—82no—
743C2×C4—82no—
744C2×C4—84no—
745C2×C4—84no—
746C2×C4—82no—
747C2×C4—82no—
748C2×C4—82no—
749C2×C4—82no—
750C2×C4—84no—
751C2×C4—84no—
752C2×C4—84no—
753C2×C4—84no—
754C2×C4—82no—
755C2×C4—82no—
756C2×C4—82no—
757C2×C4—82no—
758C2×C4#38318yes—
759C2×C4#38718yes—
760C2×C4#38718yes—
761C2×C4#38718yes—
762C2×C4#38818yes—
763C2×C4#38818yes—
764C2×C4#38818yes—
765C2×C4#39618yes—
766C2×C4#39718yes—
767C2×C4#39718yes—
768C2×C4#39718yes—
769C2×C4#40018yes—
770C2×C4#40018yes—
771C2×C4#40018yes—
772C2×C4#40118yes—
773C22C2×#38311yescharacteristic
774C22C2×#38711yescharacteristic
775C22C2×#38711yescharacteristic
776C22C2×#38711yescharacteristic
777C22C2×#38811yescharacteristic
778C22C2×#38811yescharacteristic
779C22C2×#38811yescharacteristic
780C22#229312yes—
781C22C4×#12112yes—
782C22C4×#12411yescharacteristic
783C22C4×#12711yescharacteristic
784C22#232012yes—
785C22#232312yes—
786C22#232611yescharacteristic
787C22#232711yescharacteristic
788C22#234412yes—
789C22#234712yes—
790C22#235412yes—
791C22#235612yes—
792C22#236112yes—
793C22#236212yes—
794C22#236512yes—
795C22#237012yes—
796C22C2×#39611yescharacteristic
797C22C2×#39711yescharacteristic
798C22C2×#39711yescharacteristic
799C22C2×#39711yescharacteristic
800C22C2×#40011yescharacteristic
801C22C2×#40011yescharacteristic
802C22C2×#40011yescharacteristic
803C22C2×#40111yescharacteristic
804C22#241512yes—
805C22#241612yes—
806C22#242112yes—
807C22#242112yes—
808C22#242212yes—
809C22#242212yes—
810C22#245212yes—
811C22#245312yes—
812C22#248512yes—
813C22#248612yes—
814C22#248912yes—
815C22#249112yes—
816C22#249412yes—
817C22#249412yes—
818C22#249412yes—
819C22#249512yes—
820C22#249512yes—
821C22#249612yes—
822C22#249612yes—
823C22#249612yes—
824C22#249612yes—
825C22#249612yes—
826C22#249911yescharacteristic
827C22#249911yescharacteristic
828C22#249911yescharacteristic
829C22#250011yescharacteristic
830C22#250111yescharacteristic
831C22#250111yescharacteristic
832C22#250311yescharacteristic
833C22#250411yescharacteristic
834C22#250612yes—
835C22#250612yes—
836C22#250612yes—
837C22#250812yes—
838C22#250912yes—
839C22#250912yes—
840C22#251212yes—
841C22#251212yes—
842C22#251212yes—
843C22#251212yes—
844C22#251412yes—
845C22#251412yes—
846C22#251412yes—
847C22#251412yes—
848C22#253812yes—
849C22#254111yescharacteristic
850C22#254211yescharacteristic
851C22#254511yescharacteristic
852C22#254511yescharacteristic
853C22#254711yescharacteristic
854C22#254712yes—
855C22#256212yes—
856C22#256511yescharacteristic
857C22#256611yescharacteristic
858C22#256811yescharacteristic
859C22#258112yes—
860C22#262011yescharacteristic
861C22#262111yescharacteristic
862C22#262512yes—
863C22#264011yescharacteristic
864C22#264211yescharacteristic
865C22#264512yes—
866C22#285011yescharacteristic
867C22#285412yes—
868C22#285611yescharacteristic
869C22#285811yescharacteristic
870C22#286012yes—
871C22#286111yescharacteristic
872C4—48no—
873C4—44no—
874C4—44no—
875C4—48no—
876C4—84no—
877C4—84no—
878C4—84no—
879C4—84no—
880C4#1443116yescomplemented
881C2C2×#144311yescharacteristic
882C2#1392112yes—
883C2#1397412yes—
884C2#1400111yescharacteristic
885C2#1400311yescharacteristic
886C2#1404212yes—
887C2#1404911yescharacteristic
888C2#1405011yescharacteristic
889C2#1413312yes—
890C2#1426111yescharacteristic
891C2#1470011yescharacteristic
892C2#1513212yes—
893C2#1513411yescharacteristic
894C2#1513611yescharacteristic
895C2#1513912yes—
896C2#1515011yescharacteristic
897C2#1515311yescharacteristic
898C2C4⋊#40112yes—
899C2#1515612yes—
900C2#1523311yescharacteristic
901C2#1523711yescharacteristic
902C2#1523911yescharacteristic
903C2#1524111yescharacteristic
subgroupG/H
center, Frattini, socle, prime radical, cosocleC25C24
commutatorC24C23×C4
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C25 ◁ G
LECSG ▷ C25 ▷ C1

Complements

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

NH ≅ G/Ntype
33. C4⋊#95C4semidirect
880. C4#1443semidirect

Maximal subgroups

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

subgroupindex
C2×#14432
C2×C4⋊#952
C2×C4×#952
#75562