Finite Group Databasebeta

← C2×#17156 #844934

Subgroups — C2×#17156 #844934

Order 512.

4698 conjugacy classes of subgroups.

The subgroup lattice has 1118 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#399C211yesmaximal, characteristic, complemented
2C22×#397C211yesmaximal, characteristic, complemented
3#17156C2116yesmaximal, direct product factor
4C2×#1443C211yesmaximal, characteristic, complemented
5C2×#1442C211yesmaximal, characteristic, complemented
6C2×#1442C211yesmaximal, characteristic, complemented
7C2×#1441C211yesmaximal, characteristic, complemented
8C2×#1440C211yesmaximal, characteristic, complemented
9C2×#1440C211yesmaximal, characteristic, complemented
10C2×#1439C211yesmaximal, characteristic, complemented
11C2×#1439C211yesmaximal, characteristic, complemented
12C2×#1439C211yesmaximal, characteristic, complemented
13C2×#1439C211yesmaximal, characteristic, complemented
14C2×#1438C211yesmaximal, characteristic
15C2×#1438C211yesmaximal, characteristic
16C2×#1438C211yesmaximal, characteristic
17C24×D4C2211yescharacteristic
18C23×C4⋊C4C2211yescharacteristic
19C23×C4⋊C4C2211yescharacteristic
20C23×C4⋊C4C2211yescharacteristic
21C23×C4⋊C4C2211yescharacteristic
22C23×C22⋊C4C2211yescharacteristic
23C23×C22⋊C4C2211yescharacteristic
24C23×C22⋊C4C2211yescharacteristic
25C23×C22⋊C4C2211yescharacteristic
26C23×C22⋊C4C2211yescharacteristic
27C23×C22⋊C4C2211yescharacteristic
28C23×C22⋊C4C2211yescharacteristic
29C23×C22⋊C4C2211yescharacteristic
30C23×C22⋊C4C2211yescharacteristic
31C23×C22⋊C4C2211yescharacteristic
32C23×C22⋊C4C2211yescharacteristic
33C23×C22⋊C4C2211yescharacteristic
34C2×#399—28no—
35C2×#399C2218yescomplemented
36C2×#397—28no—
37C2×#397C2218yescomplemented
38C22×#95C2211yescharacteristic
39C22×#95C2211yescharacteristic
40C22×#95C2211yescharacteristic
41C22×#95C2211yescharacteristic
42C22×#95C2211yescharacteristic
43C22×#95C2211yescharacteristic
44C22×#95C2211yescharacteristic
45C22×#95C2211yescharacteristic
46C22×#95C2211yescharacteristic
47C22×#95C2211yescharacteristic
48C22×#95C2211yescharacteristic
49C22×#95C2211yescharacteristic
50C22×#95C2211yescharacteristic
51C22×#95C2211yescharacteristic
52C22×#95C2211yescharacteristic
53C22×#95C2211yescharacteristic
54C22×#95C2211yescharacteristic
55C22×#95C2211yescharacteristic
56#1443C2218yescomplemented
57#1442C2218yescomplemented
58#1442C2218yescomplemented
59#1441C2218yescomplemented
60#1440C2218yescomplemented
61#1440C2218yescomplemented
62#1439C2218yescomplemented
63#1439C2218yescomplemented
64#1439C2218yescomplemented
65#1439C2218yescomplemented
66#1438C2218yes—
67#1438C2218yes—
68#1438C2218yes—
69C26C2311yescharacteristic
70C26C2311yescharacteristic
71C23×D4—24no—
72C23×D4—24no—
73C23×D4—24no—
74C23×D4—42no—
75C23×D4—42no—
76C23×D4—42no—
77C23×D4—42no—
78C23×D4C2314yes—
79C24×C4C2311yescharacteristic
80C24×C4C2311yescharacteristic
81C24×C4C2311yescharacteristic
82C24×C4C2311yescharacteristic
83C24×C4C2311yescharacteristic
84C24×C4C2311yescharacteristic
85C24×C4C2311yescharacteristic
86C24×C4C2311yescharacteristic
87C24×C4C2311yescharacteristic
88C24×C4C2311yescharacteristic
89C24×C4C2311yescharacteristic
90C24×C4C2311yescharacteristic
91C24×C4C2311yescharacteristic
92C22×C4⋊C4—24no—
93C22×C4⋊C4—24no—
94C22×C4⋊C4—24no—
95C22×C4⋊C4—24no—
96C22×C4⋊C4—24no—
97C22×C4⋊C4—42no—
98C22×C4⋊C4—42no—
99C22×C4⋊C4—42no—
100C22×C4⋊C4—42no—
101C22×C4⋊C4—42no—
102C22×C4⋊C4—42no—
103C22×C4⋊C4—42no—
104C22×C4⋊C4C2314yes—
105C22×C4⋊C4C2314yes—
106C22×C4⋊C4C2314yes—
107C22×C4⋊C4C2314yes—
108C22×C22⋊C4—24no—
109C22×C22⋊C4—24no—
110C22×C22⋊C4—24no—
111C22×C22⋊C4—24no—
112C22×C22⋊C4—24no—
113C22×C22⋊C4—24no—
114C22×C22⋊C4—24no—
115C22×C22⋊C4—24no—
116C22×C22⋊C4—24no—
117C22×C22⋊C4—24no—
118C22×C22⋊C4—24no—
119C22×C22⋊C4—24no—
120C22×C22⋊C4—42no—
121C22×C22⋊C4—42no—
122C22×C22⋊C4—42no—
123C22×C22⋊C4—42no—
124C22×C22⋊C4—42no—
125C22×C22⋊C4—42no—
126C22×C22⋊C4—42no—
127C22×C22⋊C4—42no—
128C22×C22⋊C4—42no—
129C22×C22⋊C4—42no—
130C22×C22⋊C4—42no—
131C22×C22⋊C4—42no—
132C22×C22⋊C4—42no—
133C22×C22⋊C4—42no—
134C22×C22⋊C4—42no—
135C22×C22⋊C4—42no—
136C22×C22⋊C4—42no—
137C22×C22⋊C4—42no—
138C22×C22⋊C4—42no—
139C22×C22⋊C4—42no—
140C22×C22⋊C4—42no—
141C22×C22⋊C4—42no—
142C22×C22⋊C4—42no—
143C22×C22⋊C4—42no—
144C22×C22⋊C4C2314yes—
145C22×C22⋊C4C2314yes—
146C22×C22⋊C4C2314yes—
147C22×C22⋊C4C2314yes—
148C22×C22⋊C4C2314yes—
149C22×C22⋊C4C2314yes—
150C22×C22⋊C4C2314yes—
151C22×C22⋊C4C2314yes—
152C22×C22⋊C4C2314yes—
153C22×C22⋊C4C2314yes—
154C22×C22⋊C4C2314yes—
155C22×C22⋊C4C2314yes—
156#399—232no—
157#397—232no—
158C2×#95—24no—
159C2×#95—24no—
160C2×#95—24no—
161C2×#95—24no—
162C2×#95—42no—
163C2×#95—42no—
164C2×#95—42no—
165C2×#95—42no—
166C2×#95—42no—
167C2×#95—42no—
168C2×#95—42no—
169C2×#95—42no—
170C2×#95—42no—
171C2×#95—42no—
172C2×#95—42no—
173C2×#95—42no—
174C2×#95—42no—
175C2×#95D418yescomplemented
176C2×#95C2314yes—
177C2×#95C2314yes—
178C2×#95C2314yes—
179C2×#95C2314yes—
180C2×#95C2314yes—
181C2×#95C2314yes—
182C2×#95C2314yes—
183C2×#95C2314yes—
184C2×#95C2314yes—
185C2×#95C2314yes—
186C2×#95C2314yes—
187C2×#95C2314yes—
188C2×#95C2314yes—
189C2×#95C2314yes—
190C2×#95C2314yes—
191C2×#95C2314yes—
192C2×#95C2314yes—
193C2×#95C2314yes—
194C25—22no—
195C25—22no—
196C25—22no—
197C25—22no—
198C25—22no—
199C25—22no—
200C25—22no—
201C25—22no—
202C25—22no—
203C25—22no—
204C25—22no—
205C25—22no—
206C25—22no—
207C25—22no—
208C25—22no—
209C25—22no—
210C25—22no—
211C25—22no—
212C25—22no—
213C25—22no—
214C25—22no—
215C25—22no—
216C25—22no—
217C25—22no—
218C25—22no—
219C25—22no—
220C25—22no—
221C25—22no—
222C25#4114yes—
223C25#4114yes—
224C25C2412yes—
225C25C2412yes—
226C25C2411yescharacteristic
227C22×D4—28no—
228C22×D4—28no—
229C22×D4—28no—
230C22×D4—44no—
231C22×D4—44no—
232C22×D4—44no—
233C22×D4—44no—
234C22×D4—416no—
235C22×D4—416no—
236C22×D4—416no—
237C22×D4—416no—
238C22×D4—416no—
239C22×D4—416no—
240C22×D4—416no—
241C23×C4—22no—
242C23×C4—22no—
243C23×C4—22no—
244C23×C4—22no—
245C23×C4—22no—
246C23×C4—22no—
247C23×C4—22no—
248C23×C4—22no—
249C23×C4—22no—
250C23×C4—22no—
251C23×C4—22no—
252C23×C4—22no—
253C23×C4—22no—
254C23×C4—22no—
255C23×C4—22no—
256C23×C4—22no—
257C23×C4—22no—
258C23×C4—22no—
259C23×C4—22no—
260C23×C4—22no—
261C23×C4—22no—
262C23×C4—22no—
263C23×C4—22no—
264C23×C4—22no—
265C23×C4—22no—
266C23×C4—22no—
267C23×C4—22no—
268C23×C4—22no—
269C23×C4—22no—
270C23×C4—22no—
271C23×C4—22no—
272C23×C4—22no—
273C23×C4—22no—
274C23×C4—22no—
275C23×C4—22no—
276C23×C4—22no—
277C23×C4—22no—
278C23×C4—22no—
279C23×C4—22no—
280C23×C4—22no—
281C23×C4—22no—
282C23×C4—22no—
283C23×C4—22no—
284C23×C4—22no—
285C23×C4—22no—
286C23×C4—22no—
287C23×C4—22no—
288C23×C4—22no—
289C23×C4—22no—
290C23×C4—22no—
291C23×C4—22no—
292C23×C4—22no—
293C23×C4—22no—
294C23×C4—22no—
295C23×C4—22no—
296C23×C4—22no—
297C23×C4—22no—
298C23×C4—22no—
299C23×C4—22no—
300C23×C4—22no—
301C23×C4—22no—
302C23×C4—22no—
303C23×C4—22no—
304C23×C4—22no—
305C23×C4—22no—
306C23×C4—22no—
307C23×C4—22no—
308C23×C4—22no—
309C23×C4—22no—
310C23×C4—22no—
311C23×C4—22no—
312C23×C4—22no—
313C23×C4—22no—
314C23×C4—22no—
315C23×C4—22no—
316C23×C4—22no—
317C23×C4—22no—
318C23×C4—22no—
319C23×C4—22no—
320C23×C4—22no—
321C23×C4—22no—
322C23×C4—22no—
323C23×C4—22no—
324C23×C4—22no—
325C23×C4—22no—
326C23×C4—22no—
327C23×C4C2×D414yes—
328C23×C4C2×D414yes—
329C23×C4C2×D414yes—
330C23×C4#4114yes—
331C23×C4#4114yes—
332C23×C4C2412yes—
333C23×C4C2412yes—
334C23×C4C2412yes—
335C23×C4C2412yes—
336C23×C4C2412yes—
337C23×C4C2412yes—
338C23×C4C2412yes—
339C23×C4C2412yes—
340C23×C4C2412yes—
341C23×C4C2412yes—
342C23×C4C2412yes—
343C23×C4C2412yes—
344C23×C4C2412yes—
345C2×C4⋊C4—28no—
346C2×C4⋊C4—28no—
347C2×C4⋊C4—28no—
348C2×C4⋊C4—28no—
349C2×C4⋊C4—28no—
350C2×C4⋊C4—44no—
351C2×C4⋊C4—44no—
352C2×C4⋊C4—44no—
353C2×C4⋊C4—44no—
354C2×C4⋊C4—44no—
355C2×C4⋊C4—44no—
356C2×C4⋊C4—44no—
357C2×C4⋊C4—416no—
358C2×C4⋊C4—416no—
359C2×C4⋊C4—416no—
360C2×C4⋊C4—416no—
361C2×C22⋊C4—28no—
362C2×C22⋊C4—28no—
363C2×C22⋊C4—28no—
364C2×C22⋊C4—28no—
365C2×C22⋊C4—28no—
366C2×C22⋊C4—28no—
367C2×C22⋊C4—28no—
368C2×C22⋊C4—28no—
369C2×C22⋊C4—28no—
370C2×C22⋊C4—28no—
371C2×C22⋊C4—28no—
372C2×C22⋊C4—28no—
373C2×C22⋊C4—44no—
374C2×C22⋊C4—44no—
375C2×C22⋊C4—44no—
376C2×C22⋊C4—44no—
377C2×C22⋊C4—44no—
378C2×C22⋊C4—44no—
379C2×C22⋊C4—44no—
380C2×C22⋊C4—44no—
381C2×C22⋊C4—44no—
382C2×C22⋊C4—44no—
383C2×C22⋊C4—44no—
384C2×C22⋊C4—44no—
385C2×C22⋊C4—44no—
386C2×C22⋊C4—44no—
387C2×C22⋊C4—44no—
388C2×C22⋊C4—44no—
389C2×C22⋊C4—44no—
390C2×C22⋊C4—44no—
391C2×C22⋊C4—44no—
392C2×C22⋊C4—44no—
393C2×C22⋊C4—44no—
394C2×C22⋊C4—44no—
395C2×C22⋊C4—44no—
396C2×C22⋊C4—44no—
397C2×C22⋊C4—416no—
398C2×C22⋊C4—416no—
399C2×C22⋊C4—416no—
400C2×C22⋊C4—416no—
401C2×C22⋊C4—416no—
402C2×C22⋊C4—416no—
403C2×C22⋊C4—416no—
404C2×C22⋊C4—416no—
405C2×C22⋊C4—416no—
406C2×C22⋊C4—416no—
407C2×C22⋊C4—416no—
408C2×C22⋊C4—416no—
409#95—28no—
410#95—28no—
411#95—28no—
412#95—28no—
413#95—44no—
414#95—44no—
415#95—44no—
416#95—44no—
417#95—44no—
418#95—44no—
419#95—44no—
420#95—44no—
421#95—44no—
422#95—44no—
423#95—44no—
424#95—44no—
425#95—44no—
426#95C2×D4116yescomplemented
427C24—28no—
428C24—28no—
429C24—28no—
430C24—28no—
431C24—28no—
432C24—28no—
433C24—28no—
434C24—28no—
435C24—28no—
436C24—28no—
437C24—28no—
438C24—28no—
439C24—28no—
440C24—28no—
441C24—22no—
442C24—22no—
443C24—22no—
444C24—22no—
445C24—22no—
446C24—22no—
447C24—22no—
448C24—22no—
449C24—22no—
450C24—22no—
451C24—22no—
452C24—22no—
453C24—22no—
454C24—22no—
455C24—22no—
456C24—22no—
457C24—22no—
458C24—22no—
459C24—22no—
460C24—22no—
461C24—22no—
462C24—22no—
463C24—22no—
464C24—22no—
465C24—22no—
466C24—22no—
467C24—22no—
468C24—22no—
469C24—44no—
470C24—44no—
471C24—44no—
472C24—44no—
473C24—44no—
474C24—44no—
475C24—44no—
476C24—44no—
477C24—44no—
478C24—44no—
479C24—44no—
480C24—44no—
481C24—44no—
482C24—44no—
483C24—44no—
484C24—44no—
485C24—44no—
486C24—44no—
487C24—44no—
488C24—44no—
489C24—44no—
490C24—44no—
491C24—44no—
492C24—44no—
493C24—44no—
494C24—44no—
495C24—44no—
496C24—44no—
497C24—44no—
498C24—44no—
499C24—44no—
500C24—44no—
501C24—44no—
502C24—44no—
503C24—44no—
504C24—44no—
505C24—44no—
506C24—44no—
507C24—44no—
508C24—44no—
509C24—44no—
510C24—44no—
511C24—44no—
512C24—44no—
513C24—44no—
514C24—44no—
515C24—44no—
516C24—44no—
517C24—44no—
518C24—44no—
519C24—44no—
520C24—44no—
521C24—44no—
522C24—44no—
523C24—44no—
524C24—44no—
525C24C22×D412yes—
526C24C2×#4114yes—
527C24C2×#4114yes—
528C24C2×#4112yes—
529C24C2×#4112yes—
530C24C2×#4112yes—
531C24C2×#4112yes—
532C24H(5,𝔽2)12yes—
533C24H(5,𝔽2)12yes—
534C24H(5,𝔽2)12yes—
535C24H(5,𝔽2)12yes—
536C24H(5,𝔽2)12yes—
537C24H(5,𝔽2)12yes—
538C24H(5,𝔽2)12yes—
539C24H(5,𝔽2)12yes—
540C242−1+412yes—
541C242−1+412yes—
542C24C2511yescharacteristic
543C2×D4—416no—
544C2×D4—416no—
545C2×D4—416no—
546C2×D4—416no—
547C2×D4—416no—
548C2×D4—416no—
549C2×D4—4128no—
550C2×D4—416no—
551C22×C4—28no—
552C22×C4—28no—
553C22×C4—28no—
554C22×C4—28no—
555C22×C4—28no—
556C22×C4—28no—
557C22×C4—28no—
558C22×C4—28no—
559C22×C4—28no—
560C22×C4—28no—
561C22×C4—28no—
562C22×C4—28no—
563C22×C4—28no—
564C22×C4—28no—
565C22×C4—28no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—22no—
611C22×C4—22no—
612C22×C4—22no—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—22no—
616C22×C4—22no—
617C22×C4—22no—
618C22×C4—22no—
619C22×C4—22no—
620C22×C4—22no—
621C22×C4—22no—
622C22×C4—22no—
623C22×C4—22no—
624C22×C4—22no—
625C22×C4—22no—
626C22×C4—22no—
627C22×C4—22no—
628C22×C4—22no—
629C22×C4—22no—
630C22×C4—22no—
631C22×C4—22no—
632C22×C4—22no—
633C22×C4—22no—
634C22×C4—22no—
635C22×C4—22no—
636C22×C4—22no—
637C22×C4—22no—
638C22×C4—22no—
639C22×C4—22no—
640C22×C4—22no—
641C22×C4—22no—
642C22×C4—22no—
643C22×C4—22no—
644C22×C4—22no—
645C22×C4—22no—
646C22×C4—22no—
647C22×C4—22no—
648C22×C4—22no—
649C22×C4—22no—
650C22×C4—22no—
651C22×C4—22no—
652C22×C4—44no—
653C22×C4—44no—
654C22×C4—44no—
655C22×C4—44no—
656C22×C4—44no—
657C22×C4—44no—
658C22×C4—44no—
659C22×C4—44no—
660C22×C4—44no—
661C22×C4—44no—
662C22×C4—44no—
663C22×C4—44no—
664C22×C4—44no—
665C22×C4—44no—
666C22×C4—44no—
667C22×C4—44no—
668C22×C4—44no—
669C22×C4—44no—
670C22×C4—44no—
671C22×C4—44no—
672C22×C4—44no—
673C22×C4—44no—
674C22×C4—44no—
675C22×C4—44no—
676C22×C4—44no—
677C22×C4—44no—
678C22×C4—44no—
679C22×C4—44no—
680C22×C4—44no—
681C22×C4—44no—
682C22×C4—44no—
683C22×C4—44no—
684C22×C4—44no—
685C22×C4—44no—
686C22×C4—44no—
687C22×C4—44no—
688C22×C4—44no—
689C22×C4—44no—
690C22×C4—44no—
691C22×C4—44no—
692C22×C4—44no—
693C22×C4—44no—
694C22×C4—44no—
695C22×C4—44no—
696C22×C4—44no—
697C22×C4—44no—
698C22×C4—44no—
699C22×C4—44no—
700C22×C4—44no—
701C22×C4—44no—
702C22×C4—44no—
703C22×C4—44no—
704C22×C4—44no—
705C22×C4—44no—
706C22×C4—44no—
707C22×C4—44no—
708C22×C4—44no—
709C22×C4—44no—
710C22×C4—44no—
711C22×C4—44no—
712C22×C4—44no—
713C22×C4—44no—
714C22×C4—44no—
715C22×C4—44no—
716C22×C4—44no—
717C22×C4—44no—
718C22×C4—44no—
719C22×C4—44no—
720C22×C4—44no—
721C22×C4—44no—
722C22×C4—44no—
723C22×C4—44no—
724C22×C4—44no—
725C22×C4—44no—
726C22×C4—44no—
727C22×C4—44no—
728C22×C4C22×D414yes—
729C22×C4C22×D414yes—
730C22×C4C22×D414yes—
731C22×C4C2×#4114yes—
732C22×C4C2×#4114yes—
733C4⋊C4—416no—
734C4⋊C4—416no—
735C4⋊C4—416no—
736C4⋊C4—416no—
737C22⋊C4—416no—
738C22⋊C4—416no—
739C22⋊C4—416no—
740C22⋊C4—416no—
741C22⋊C4—416no—
742C22⋊C4—416no—
743C22⋊C4—416no—
744C22⋊C4—416no—
745C22⋊C4—416no—
746C22⋊C4—416no—
747C22⋊C4—416no—
748C22⋊C4—416no—
749C23—24no—
750C23—24no—
751C23—24no—
752C23—24no—
753C23—24no—
754C23—24no—
755C23—24no—
756C23—24no—
757C23—24no—
758C23—24no—
759C23—24no—
760C23—24no—
761C23—24no—
762C23—24no—
763C23—416no—
764C23—416no—
765C23—42no—
766C23—42no—
767C23—42no—
768C23—42no—
769C23—42no—
770C23—42no—
771C23—42no—
772C23—42no—
773C23—42no—
774C23—42no—
775C23—42no—
776C23—42no—
777C23—42no—
778C23—42no—
779C23—42no—
780C23—42no—
781C23—42no—
782C23—42no—
783C23—42no—
784C23—42no—
785C23—42no—
786C23—42no—
787C23—42no—
788C23—42no—
789C23—42no—
790C23—42no—
791C23—42no—
792C23—416no—
793C23—416no—
794C23—416no—
795C23—42no—
796C23—42no—
797C23—42no—
798C23—42no—
799C23—42no—
800C23—42no—
801C23—416no—
802C23—42no—
803C23—416no—
804C23—42no—
805C23—42no—
806C23—416no—
807C23—416no—
808C23—416no—
809C23—416no—
810C23—416no—
811C23—416no—
812C23—42no—
813C23—42no—
814C23—42no—
815C23—42no—
816C23—42no—
817C23—42no—
818C23—42no—
819C23—42no—
820C23—42no—
821C23—42no—
822C23—42no—
823C23—42no—
824C23—42no—
825C23—42no—
826C23—42no—
827C23—42no—
828C23—42no—
829C23—42no—
830C23—42no—
831C23—42no—
832C23—416no—
833C23—88no—
834C23—88no—
835C23—88no—
836C23—88no—
837C23—88no—
838C23—88no—
839C23—88no—
840C23—88no—
841C23—88no—
842C23—88no—
843C23—88no—
844C23—88no—
845C23—88no—
846C23—88no—
847C23—88no—
848C23—88no—
849C23#53514yes—
850C23#53514yes—
851C23#53514yes—
852C23#53814yes—
853C23#53814yes—
854C23#53814yes—
855C23#53814yes—
856C23#53914yes—
857C23#53914yes—
858C23#53914yes—
859C23#53914yes—
860C23#54014yes—
861C23#54014yes—
862C23#54214yes—
863C23#54214yes—
864C23#54614yes—
865C23#54614yes—
866C23#54714yes—
867C23#54814yes—
868C23#55114yes—
869C23#55114yes—
870C23#55114yes—
871C23#55114yes—
872C23#55314yes—
873C23#55914yes—
874C23#56014yes—
875C23#56014yes—
876C23#56014yes—
877C23#56014yes—
878C23#56014yes—
879C23#56214yes—
880C23#56214yes—
881C23#56214yes—
882C23#56214yes—
883C23#56314yes—
884C23C23×D411yescharacteristic
885C23C22×#4111yescharacteristic
886C23C22×#4111yescharacteristic
887C23C22×#4111yescharacteristic
888C23C22×#4111yescharacteristic
889C23C2×H(5,𝔽2)11yescharacteristic
890C23C2×H(5,𝔽2)11yescharacteristic
891C23C2×H(5,𝔽2)11yescharacteristic
892C23C2×H(5,𝔽2)11yescharacteristic
893C23C2×H(5,𝔽2)11yescharacteristic
894C23C2×H(5,𝔽2)11yescharacteristic
895C23C2×H(5,𝔽2)11yescharacteristic
896C23C2×H(5,𝔽2)11yescharacteristic
897C23C2×2−1+411yescharacteristic
898C23C2×2−1+411yescharacteristic
899D4—464no—
900C2×C4—24no—
901C2×C4—24no—
902C2×C4—24no—
903C2×C4—24no—
904C2×C4—24no—
905C2×C4—24no—
906C2×C4—24no—
907C2×C4—24no—
908C2×C4—24no—
909C2×C4—24no—
910C2×C4—24no—
911C2×C4—24no—
912C2×C4—24no—
913C2×C4—24no—
914C2×C4—24no—
915C2×C4—42no—
916C2×C4—42no—
917C2×C4—42no—
918C2×C4—42no—
919C2×C4—42no—
920C2×C4—42no—
921C2×C4—42no—
922C2×C4—42no—
923C2×C4—42no—
924C2×C4—42no—
925C2×C4—416no—
926C2×C4—42no—
927C2×C4—42no—
928C2×C4—42no—
929C2×C4—416no—
930C2×C4—42no—
931C2×C4—416no—
932C2×C4—416no—
933C2×C4—42no—
934C2×C4—416no—
935C2×C4—42no—
936C2×C4—42no—
937C2×C4—42no—
938C2×C4—42no—
939C2×C4—42no—
940C2×C4—42no—
941C2×C4—42no—
942C2×C4—42no—
943C2×C4—42no—
944C2×C4—42no—
945C2×C4—42no—
946C2×C4—42no—
947C2×C4—42no—
948C2×C4—42no—
949C2×C4—42no—
950C2×C4—42no—
951C2×C4—42no—
952C2×C4—42no—
953C2×C4—42no—
954C2×C4—42no—
955C2×C4—42no—
956C2×C4—42no—
957C2×C4—42no—
958C2×C4—42no—
959C2×C4—42no—
960C2×C4—42no—
961C2×C4—42no—
962C2×C4—42no—
963C2×C4—42no—
964C2×C4—42no—
965C2×C4—42no—
966C2×C4—42no—
967C2×C4—42no—
968C2×C4—42no—
969C2×C4—42no—
970C2×C4—42no—
971C2×C4—42no—
972C2×C4—42no—
973C2×C4—42no—
974C2×C4—42no—
975C2×C4—42no—
976C2×C4—42no—
977C2×C4—42no—
978C2×C4—42no—
979C2×C4—42no—
980C2×C4—42no—
981C2×C4—42no—
982C2×C4—42no—
983C2×C4—42no—
984C2×C4—42no—
985C2×C4—42no—
986C2×C4—42no—
987C2×C4—42no—
988C2×C4—42no—
989C2×C4—42no—
990C2×C4—42no—
991C2×C4—42no—
992C2×C4—42no—
993C2×C4—42no—
994C2×C4—42no—
995C2×C4—42no—
996C2×C4—88no—
997C2×C4—88no—
998C2×C4—88no—
999C2×C4—88no—
1000C2×C4—88no—
1001C2×C4—88no—
1002C2×C4—88no—
1003C2×C4—88no—
1004C22—44no—
1005C22—44no—
1006C22—44no—
1007C22—44no—
1008C22—44no—
1009C22—44no—
1010C22—44no—
1011C22—44no—
1012C22—44no—
1013C22—44no—
1014C22—44no—
1015C22—44no—
1016C22—44no—
1017C22—44no—
1018C22—832no—
1019C22—832no—
1020C22—82no—
1021C22—82no—
1022C22—82no—
1023C22—82no—
1024C22—82no—
1025C22—82no—
1026C22—82no—
1027C22—82no—
1028C22—82no—
1029C22—82no—
1030C22—82no—
1031C22—82no—
1032C22—82no—
1033C22—82no—
1034C22—82no—
1035C22—82no—
1036C22#269618yes—
1037C22#269618yes—
1038C22#270318yes—
1039C22#270618yes—
1040C22#271018yes—
1041C22#272318yes—
1042C22#273518yes—
1043C22#274618yes—
1044C22#275218yes—
1045C22#279618yes—
1046C22#281818yes—
1047C22#282618yes—
1048C22#282718yes—
1049C22#282918yes—
1050C22#283718yes—
1051C22C2×#53511yescharacteristic
1052C22C2×#53511yescharacteristic
1053C22C2×#53511yescharacteristic
1054C22C2×#53811yescharacteristic
1055C22C2×#53811yescharacteristic
1056C22C2×#53811yescharacteristic
1057C22C2×#53811yescharacteristic
1058C22C2×#53911yescharacteristic
1059C22C2×#53911yescharacteristic
1060C22C2×#53911yescharacteristic
1061C22C2×#53911yescharacteristic
1062C22C2×#54011yescharacteristic
1063C22C2×#54011yescharacteristic
1064C22C2×#54211yescharacteristic
1065C22C2×#54211yescharacteristic
1066C22C2×#54611yescharacteristic
1067C22C2×#54611yescharacteristic
1068C22C2×#54711yescharacteristic
1069C22C2×#54811yescharacteristic
1070C22C2×#55111yescharacteristic
1071C22C2×#55111yescharacteristic
1072C22C2×#55111yescharacteristic
1073C22C2×#55111yescharacteristic
1074C22C2×#55311yescharacteristic
1075C22C2×#55911yescharacteristic
1076C22C2×#56011yescharacteristic
1077C22C2×#56011yescharacteristic
1078C22C2×#56011yescharacteristic
1079C22C2×#56011yescharacteristic
1080C22C2×#56011yescharacteristic
1081C22C2×#56211yescharacteristic
1082C22C2×#56211yescharacteristic
1083C22C2×#56211yescharacteristic
1084C22C2×#56211yescharacteristic
1085C22C2×#56311yescharacteristic
1086C4—44no—
1087C4—44no—
1088C4—44no—
1089C4—44no—
1090C4—44no—
1091C4—82no—
1092C4—82no—
1093C4—82no—
1094C4—82no—
1095C4—82no—
1096C4—82no—
1097C4—82no—
1098C4—82no—
1099C2—84no—
1100C2—84no—
1101C2#17156116yesdirect product factor
1102C2C2×#282711yescharacteristic
1103C2C2×#282611yescharacteristic
1104C2C2×#283711yescharacteristic
1105C2C2×#282911yescharacteristic
1106C2C2×#281811yescharacteristic
1107C2C2×#269611yescharacteristic
1108C2C2×#269611yescharacteristic
1109C2C2×#270311yescharacteristic
1110C2C2×#270611yescharacteristic
1111C2C2×#271011yescharacteristic
1112C2C2×#272311yescharacteristic
1113C2C2×#273511yescharacteristic
1114C2C2×#274611yescharacteristic
1115C2C2×#275211yescharacteristic
1116C2C2×#279611yescharacteristic
subgroupG/H
center, socleC25C24
commutator, Frattini, cosocleC24C25
prime radicalC24×D4C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C25 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C22×#399C2semidirect
2. C22×#397C2semidirect
3. #17156C2direct (N × H)
4. C2×#1443C2semidirect
5. C2×#1442C2semidirect
6. C2×#1442C2semidirect
7. C2×#1441C2semidirect
8. C2×#1440C2semidirect
9. C2×#1440C2semidirect
10. C2×#1439C2semidirect
11. C2×#1439C2semidirect
12. C2×#1439C2semidirect
13. C2×#1439C2semidirect
35. C2×#399C22semidirect
37. C2×#397C22semidirect
56. #1443C22semidirect
57. #1442C22semidirect
58. #1442C22semidirect
59. #1441C22semidirect
60. #1440C22semidirect
61. #1440C22semidirect
62. #1439C22semidirect
63. #1439C22semidirect
64. #1439C22semidirect
65. #1439C22semidirect
175. C2×#95D4semidirect
426. #95C2×D4semidirect
1101. C2#17156direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#3992
C22×#3972
#171562
C2×#14432
C2×#14422
C2×#14412
C2×#14402
C2×#14392
C2×#14382