Finite Group Databasebeta

← C2×#14012 #514306

Subgroups — C2×#14012 #514306

Order 512.

6886 conjugacy classes of subgroups.

The subgroup lattice has 1174 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#390C211yesmaximal, characteristic
2C22×#388C211yesmaximal, characteristic, complemented
3C22×#388C211yesmaximal, characteristic, complemented
4C22×#388C211yesmaximal, characteristic, complemented
5C22×#386C211yesmaximal, characteristic
6C22×#380C211yesmaximal, characteristic, complemented
7C22×C4×C22⋊C4C211yesmaximal, characteristic, complemented
8#14012C2116yesmaximal, direct product factor
9C2×#1444C211yesmaximal, characteristic, complemented
10C2×#1440C211yesmaximal, characteristic, complemented
11C2×#1439C211yesmaximal, characteristic, complemented
12C2×#1438C211yesmaximal, characteristic
13C2×#1437C211yesmaximal, characteristic, complemented
14C2×#1436C211yesmaximal, characteristic, complemented
15C2×#1436C211yesmaximal, characteristic, complemented
16C2×C4×#95C211yesmaximal, characteristic, complemented
17C24×D4C2211yescharacteristic
18C25×C4C2211yescharacteristic
19C23×C4⋊C4C2211yescharacteristic
20C23×C4⋊C4C2211yescharacteristic
21C23×C4⋊C4C2211yescharacteristic
22C23×C4⋊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
34C23×C42C2211yescharacteristic
35C23×C42C2211yescharacteristic
36C23×C42C2211yescharacteristic
37C23×C42C2211yescharacteristic
38C2×#390—28no—
39C2×#390C2218yes—
40C2×#388—28no—
41C2×#388—28no—
42C2×#388—28no—
43C2×#388C2218yescomplemented
44C2×#388C2218yescomplemented
45C2×#388C2218yescomplemented
46C2×#386C4116yescomplemented
47C2×#386C2218yes—
48C2×#380—28no—
49C2×#380C2218yescomplemented
50C2×C4×C22⋊C4—28no—
51C2×C4×C22⋊C4C2218yescomplemented
52C22×#95C2211yescharacteristic
53C22×#95C2211yescharacteristic
54C22×#95C2211yescharacteristic
55C22×#95C2211yescharacteristic
56C22×#95C2211yescharacteristic
57C22×#95C2211yescharacteristic
58C22×#95C2211yescharacteristic
59C22×#95C2211yescharacteristic
60C22×#95C2211yescharacteristic
61C22×#95C2211yescharacteristic
62C22×#95C2211yescharacteristic
63C22×#95C2211yescharacteristic
64C22×#95C2211yescharacteristic
65C22×#95C2211yescharacteristic
66#1444C2218yescomplemented
67#1440C2218yescomplemented
68#1439C2218yescomplemented
69#1438C2218yes—
70#1437C2218yescomplemented
71#1436C2218yescomplemented
72#1436C2218yescomplemented
73C4×#95C2218yescomplemented
74C26C2311yescharacteristic
75C26C2311yescharacteristic
76C23×D4—24no—
77C23×D4—24no—
78C23×D4—24no—
79C23×D4—24no—
80C23×D4—42no—
81C23×D4—42no—
82C23×D4C2×C418yes—
83C23×D4C2314yes—
84C24×C4—24no—
85C24×C4—24no—
86C24×C4—24no—
87C24×C4—24no—
88C24×C4—42no—
89C24×C4—42no—
90C24×C4C2×C418yes—
91C24×C4C2311yescharacteristic
92C24×C4C2311yescharacteristic
93C24×C4C2311yescharacteristic
94C24×C4C2311yescharacteristic
95C24×C4C2311yescharacteristic
96C24×C4C2311yescharacteristic
97C24×C4C2311yescharacteristic
98C24×C4C2311yescharacteristic
99C24×C4C2311yescharacteristic
100C24×C4C2314yes—
101C24×C4C2311yescharacteristic
102C24×C4C2311yescharacteristic
103C24×C4C2311yescharacteristic
104C24×C4C2311yescharacteristic
105C22×C4⋊C4—24no—
106C22×C4⋊C4—24no—
107C22×C4⋊C4—24no—
108C22×C4⋊C4—24no—
109C22×C4⋊C4—24no—
110C22×C4⋊C4—24no—
111C22×C4⋊C4—24no—
112C22×C4⋊C4—24no—
113C22×C4⋊C4—42no—
114C22×C4⋊C4—42no—
115C22×C4⋊C4—42no—
116C22×C4⋊C4—42no—
117C22×C4⋊C4C2314yes—
118C22×C4⋊C4C2314yes—
119C22×C4⋊C4C2314yes—
120C22×C4⋊C4C2314yes—
121C22×C22⋊C4—24no—
122C22×C22⋊C4—24no—
123C22×C22⋊C4—24no—
124C22×C22⋊C4—24no—
125C22×C22⋊C4—24no—
126C22×C22⋊C4—24no—
127C22×C22⋊C4—24no—
128C22×C22⋊C4—24no—
129C22×C22⋊C4—24no—
130C22×C22⋊C4—24no—
131C22×C22⋊C4—24no—
132C22×C22⋊C4—24no—
133C22×C22⋊C4—24no—
134C22×C22⋊C4—24no—
135C22×C22⋊C4—24no—
136C22×C22⋊C4—24no—
137C22×C22⋊C4—24no—
138C22×C22⋊C4—24no—
139C22×C22⋊C4—24no—
140C22×C22⋊C4—24no—
141C22×C22⋊C4—24no—
142C22×C22⋊C4—24no—
143C22×C22⋊C4—24no—
144C22×C22⋊C4—42no—
145C22×C22⋊C4—42no—
146C22×C22⋊C4—42no—
147C22×C22⋊C4—42no—
148C22×C22⋊C4—42no—
149C22×C22⋊C4—42no—
150C22×C22⋊C4C2×C418yes—
151C22×C22⋊C4C2×C418yes—
152C22×C22⋊C4C2×C418yes—
153C22×C22⋊C4D418yes—
154C22×C22⋊C4C2314yes—
155C22×C22⋊C4C2314yes—
156C22×C22⋊C4C2314yes—
157C22×C22⋊C4C2314yes—
158C22×C22⋊C4C2314yes—
159C22×C22⋊C4C2314yes—
160C22×C22⋊C4C2314yes—
161C22×C22⋊C4C2314yes—
162C22×C22⋊C4C2314yes—
163C22×C22⋊C4C2314yes—
164C22×C22⋊C4C2314yes—
165C22×C42—24no—
166C22×C42—24no—
167C22×C42—24no—
168C22×C42—24no—
169C22×C42—24no—
170C22×C42—24no—
171C22×C42—24no—
172C22×C42—24no—
173C22×C42—24no—
174C22×C42—42no—
175C22×C42—42no—
176C22×C42—42no—
177C22×C42C2314yes—
178C22×C42C2314yes—
179C22×C42C2314yes—
180C22×C42C2314yes—
181#390—232no—
182#388—232no—
183#388—232no—
184#388—232no—
185#386C2×C4164yescomplemented
186#380—232no—
187C4×C22⋊C4—232no—
188C2×#95—24no—
189C2×#95—24no—
190C2×#95—24no—
191C2×#95—24no—
192C2×#95—24no—
193C2×#95—24no—
194C2×#95—24no—
195C2×#95—24no—
196C2×#95—24no—
197C2×#95—42no—
198C2×#95C2×C418yes—
199C2×#95C2×C418yes—
200C2×#95D418yescomplemented
201C2×#95D418yescomplemented
202C2×#95C2314yes—
203C2×#95C2314yes—
204C2×#95C2314yes—
205C2×#95C2314yes—
206C2×#95C2314yes—
207C2×#95C2314yes—
208C2×#95C2314yes—
209C2×#95C2314yes—
210C2×#95C2314yes—
211C2×#95C2314yes—
212C2×#95C2314yes—
213C2×#95C2314yes—
214C2×#95C2314yes—
215C2×#95C2314yes—
216C25—22no—
217C25—22no—
218C25—22no—
219C25—22no—
220C25—22no—
221C25—22no—
222C25—22no—
223C25—22no—
224C25—22no—
225C25—22no—
226C25—22no—
227C25—22no—
228C25—22no—
229C25—22no—
230C25—22no—
231C25—22no—
232C25—22no—
233C25—22no—
234C25—22no—
235C25—22no—
236C25—22no—
237C25—22no—
238C25—22no—
239C25—22no—
240C25—22no—
241C25—22no—
242C25C22×C414yes—
243C25C22×C414yes—
244C25C2×D414yes—
245C25#4114yes—
246C25C2412yes—
247C25C2412yes—
248C25C2411yescharacteristic
249C22×D4—232no—
250C22×D4—28no—
251C22×D4—28no—
252C22×D4—232no—
253C22×D4—28no—
254C22×D4—28no—
255C22×D4—416no—
256C22×D4—44no—
257C22×D4—44no—
258C22×D4—416no—
259C22×D4—416no—
260C22×D4—416no—
261C22×D4—416no—
262C22×D4C22×C4116yes—
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—232no—
322C23×C4—232no—
323C23×C4—28no—
324C23×C4—28no—
325C23×C4—28no—
326C23×C4—28no—
327C23×C4—22no—
328C23×C4—22no—
329C23×C4—22no—
330C23×C4—22no—
331C23×C4—22no—
332C23×C4—22no—
333C23×C4—22no—
334C23×C4—22no—
335C23×C4—22no—
336C23×C4—22no—
337C23×C4—22no—
338C23×C4—22no—
339C23×C4—22no—
340C23×C4—22no—
341C23×C4—416no—
342C23×C4—44no—
343C23×C4—44no—
344C23×C4—416no—
345C23×C4—416no—
346C23×C4—416no—
347C23×C4—416no—
348C23×C4C22×C414yes—
349C23×C4C22×C414yes—
350C23×C4C22×C4116yes—
351C23×C4C22×C414yes—
352C23×C4C22×C414yes—
353C23×C4C22×C414yes—
354C23×C4C2×D414yes—
355C23×C4C2×D414yes—
356C23×C4C2×D414yes—
357C23×C4C2×D414yes—
358C23×C4C2×D414yes—
359C23×C4C2×D414yes—
360C23×C4C2×D414yes—
361C23×C4C2×D414yes—
362C23×C4#4114yes—
363C23×C4#4114yes—
364C23×C4#4114yes—
365C23×C4#4114yes—
366C23×C4#4114yes—
367C23×C4#4114yes—
368C23×C4C2412yes—
369C23×C4C2412yes—
370C23×C4C2412yes—
371C23×C4C2412yes—
372C23×C4C2412yes—
373C23×C4C2412yes—
374C23×C4C2412yes—
375C23×C4C2412yes—
376C23×C4C2412yes—
377C23×C4C2412yes—
378C23×C4C2412yes—
379C23×C4C2412yes—
380C23×C4C2412yes—
381C2×C4⋊C4—28no—
382C2×C4⋊C4—28no—
383C2×C4⋊C4—28no—
384C2×C4⋊C4—28no—
385C2×C4⋊C4—28no—
386C2×C4⋊C4—28no—
387C2×C4⋊C4—28no—
388C2×C4⋊C4—28no—
389C2×C4⋊C4—44no—
390C2×C4⋊C4—44no—
391C2×C4⋊C4—44no—
392C2×C4⋊C4—44no—
393C2×C4⋊C4—416no—
394C2×C4⋊C4—416no—
395C2×C4⋊C4—416no—
396C2×C4⋊C4—416no—
397C2×C22⋊C4—232no—
398C2×C22⋊C4—232no—
399C2×C22⋊C4—28no—
400C2×C22⋊C4—28no—
401C2×C22⋊C4—28no—
402C2×C22⋊C4—232no—
403C2×C22⋊C4—232no—
404C2×C22⋊C4—232no—
405C2×C22⋊C4—28no—
406C2×C22⋊C4—28no—
407C2×C22⋊C4—28no—
408C2×C22⋊C4—28no—
409C2×C22⋊C4—28no—
410C2×C22⋊C4—28no—
411C2×C22⋊C4—28no—
412C2×C22⋊C4—28no—
413C2×C22⋊C4—28no—
414C2×C22⋊C4—28no—
415C2×C22⋊C4—28no—
416C2×C22⋊C4—28no—
417C2×C22⋊C4—28no—
418C2×C22⋊C4—28no—
419C2×C22⋊C4—28no—
420C2×C22⋊C4—28no—
421C2×C22⋊C4—28no—
422C2×C22⋊C4—28no—
423C2×C22⋊C4—28no—
424C2×C22⋊C4—28no—
425C2×C22⋊C4—44no—
426C2×C22⋊C4—44no—
427C2×C22⋊C4—44no—
428C2×C22⋊C4—44no—
429C2×C22⋊C4—44no—
430C2×C22⋊C4—44no—
431C2×C22⋊C4—416no—
432C2×C22⋊C4—416no—
433C2×C22⋊C4—416no—
434C2×C22⋊C4—416no—
435C2×C22⋊C4—416no—
436C2×C22⋊C4—416no—
437C2×C22⋊C4C22×C4116yes—
438C2×C22⋊C4C22×C4116yes—
439C2×C22⋊C4C22×C4116yes—
440C2×C22⋊C4C2×D4116yes—
441C2×C42—28no—
442C2×C42—28no—
443C2×C42—28no—
444C2×C42—28no—
445C2×C42—28no—
446C2×C42—28no—
447C2×C42—28no—
448C2×C42—28no—
449C2×C42—28no—
450C2×C42—44no—
451C2×C42—44no—
452C2×C42—44no—
453C2×C42—416no—
454C2×C42—416no—
455C2×C42—416no—
456C2×C42—416no—
457#95—28no—
458#95—28no—
459#95—28no—
460#95—28no—
461#95—28no—
462#95—28no—
463#95—28no—
464#95—28no—
465#95—28no—
466#95—44no—
467#95C22×C4116yes—
468#95C22×C4116yes—
469#95C2×D4116yescomplemented
470#95C2×D4116yescomplemented
471C24—28no—
472C24—28no—
473C24—28no—
474C24—28no—
475C24—28no—
476C24—28no—
477C24—28no—
478C24—28no—
479C24—28no—
480C24—28no—
481C24—28no—
482C24—28no—
483C24—28no—
484C24—28no—
485C24—28no—
486C24—28no—
487C24—28no—
488C24—28no—
489C24—22no—
490C24—22no—
491C24—22no—
492C24—22no—
493C24—22no—
494C24—22no—
495C24—22no—
496C24—22no—
497C24—22no—
498C24—22no—
499C24—22no—
500C24—22no—
501C24—28no—
502C24—28no—
503C24—28no—
504C24—28no—
505C24—28no—
506C24—28no—
507C24—28no—
508C24—22no—
509C24—22no—
510C24—22no—
511C24—22no—
512C24—22no—
513C24—22no—
514C24—22no—
515C24—22no—
516C24—22no—
517C24—22no—
518C24—22no—
519C24—22no—
520C24—22no—
521C24—22no—
522C24—44no—
523C24—44no—
524C24—44no—
525C24—44no—
526C24—44no—
527C24—44no—
528C24—44no—
529C24—44no—
530C24—44no—
531C24—44no—
532C24—44no—
533C24—44no—
534C24—44no—
535C24—44no—
536C24—44no—
537C24—44no—
538C24—44no—
539C24—44no—
540C24—44no—
541C24—44no—
542C24—44no—
543C24—44no—
544C24—44no—
545C24—44no—
546C24—44no—
547C24—44no—
548C24—44no—
549C24—44no—
550C24—44no—
551C24—44no—
552C24—44no—
553C24—44no—
554C24—44no—
555C24—44no—
556C24—44no—
557C24—44no—
558C24—44no—
559C24—44no—
560C24—44no—
561C24—44no—
562C24—44no—
563C24—44no—
564C24—44no—
565C24—44no—
566C24C4×D4116yes—
567C24C23×C414yes—
568C24C23×C414yes—
569C24C23×C412yes—
570C24C22×D414yes—
571C24C22×D412yes—
572C24C22×D412yes—
573C24C22×D412yes—
574C24C2×#4114yes—
575C24C2×#4112yes—
576C24C2×#4112yes—
577C24C2×#4112yes—
578C24C2×#4112yes—
579C24C2×#4112yes—
580C24C2×#4112yes—
581C24C2×#4112yes—
582C24H(5,𝔽2)12yes—
583C24H(5,𝔽2)12yes—
584C24H(5,𝔽2)12yes—
585C242−1+412yes—
586C24C2511yescharacteristic
587C2×D4—232no—
588C2×D4—232no—
589C2×D4—416no—
590C2×D4—4128no—
591C2×D4—416no—
592C2×D4—416no—
593C2×D4—416no—
594C2×D4—416no—
595C22×C4—28no—
596C22×C4—28no—
597C22×C4—28no—
598C22×C4—28no—
599C22×C4—28no—
600C22×C4—28no—
601C22×C4—28no—
602C22×C4—28no—
603C22×C4—28no—
604C22×C4—28no—
605C22×C4—28no—
606C22×C4—28no—
607C22×C4—28no—
608C22×C4—28no—
609C22×C4—28no—
610C22×C4—28no—
611C22×C4—28no—
612C22×C4—28no—
613C22×C4—28no—
614C22×C4—28no—
615C22×C4—28no—
616C22×C4—28no—
617C22×C4—28no—
618C22×C4—28no—
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—28no—
636C22×C4—28no—
637C22×C4—28no—
638C22×C4—28no—
639C22×C4—28no—
640C22×C4—28no—
641C22×C4—28no—
642C22×C4—28no—
643C22×C4—28no—
644C22×C4—28no—
645C22×C4—28no—
646C22×C4—28no—
647C22×C4—28no—
648C22×C4—28no—
649C22×C4—28no—
650C22×C4—28no—
651C22×C4—28no—
652C22×C4—28no—
653C22×C4—28no—
654C22×C4—28no—
655C22×C4—28no—
656C22×C4—22no—
657C22×C4—22no—
658C22×C4—22no—
659C22×C4—22no—
660C22×C4—22no—
661C22×C4—22no—
662C22×C4—22no—
663C22×C4—22no—
664C22×C4—22no—
665C22×C4—22no—
666C22×C4—22no—
667C22×C4—22no—
668C22×C4—22no—
669C22×C4—22no—
670C22×C4—22no—
671C22×C4—22no—
672C22×C4—22no—
673C22×C4—22no—
674C22×C4—22no—
675C22×C4—22no—
676C22×C4—22no—
677C22×C4—22no—
678C22×C4—22no—
679C22×C4—22no—
680C22×C4—22no—
681C22×C4—22no—
682C22×C4—22no—
683C22×C4—22no—
684C22×C4—22no—
685C22×C4—22no—
686C22×C4—22no—
687C22×C4—22no—
688C22×C4—22no—
689C22×C4—22no—
690C22×C4—22no—
691C22×C4—22no—
692C22×C4—22no—
693C22×C4—22no—
694C22×C4—22no—
695C22×C4—22no—
696C22×C4—22no—
697C22×C4—22no—
698C22×C4—232no—
699C22×C4—232no—
700C22×C4—22no—
701C22×C4—22no—
702C22×C4—22no—
703C22×C4—22no—
704C22×C4—22no—
705C22×C4—22no—
706C22×C4—22no—
707C22×C4—22no—
708C22×C4—22no—
709C22×C4—22no—
710C22×C4—22no—
711C22×C4—22no—
712C22×C4—22no—
713C22×C4—22no—
714C22×C4—416no—
715C22×C4—4128no—
716C22×C4—416no—
717C22×C4—416no—
718C22×C4—416no—
719C22×C4—416no—
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×C4—44no—
729C22×C4—44no—
730C22×C4—44no—
731C22×C4—44no—
732C22×C4—44no—
733C22×C4—44no—
734C22×C4—44no—
735C22×C4—44no—
736C22×C4—44no—
737C22×C4—44no—
738C22×C4—44no—
739C22×C4—44no—
740C22×C4—44no—
741C22×C4—44no—
742C22×C4—44no—
743C22×C4—44no—
744C22×C4—44no—
745C22×C4—44no—
746C22×C4—44no—
747C22×C4—44no—
748C22×C4—44no—
749C22×C4—44no—
750C22×C4—44no—
751C22×C4—44no—
752C22×C4—44no—
753C22×C4—44no—
754C22×C4—44no—
755C22×C4—44no—
756C22×C4—44no—
757C22×C4—44no—
758C22×C4—44no—
759C22×C4—44no—
760C22×C4—44no—
761C22×C4—44no—
762C22×C4#117116yes—
763C22×C4C4×D4116yes—
764C22×C4C4×D4116yes—
765C22×C4#121116yes—
766C22×C4C23×C414yes—
767C22×C4C23×C414yes—
768C22×C4C23×C414yes—
769C22×C4C23×C414yes—
770C22×C4C23×C414yes—
771C22×C4C22×D414yes—
772C22×C4C22×D414yes—
773C22×C4C22×D414yes—
774C22×C4C22×D414yes—
775C22×C4C22×D414yes—
776C22×C4C22×D414yes—
777C22×C4C22×D414yes—
778C22×C4C22×D414yes—
779C22×C4C2×#4114yes—
780C22×C4C2×#4114yes—
781C22×C4C2×#4114yes—
782C22×C4C2×#4114yes—
783C22×C4C2×#4114yes—
784C22×C4C2×#4114yes—
785C4⋊C4—416no—
786C4⋊C4—416no—
787C4⋊C4—416no—
788C4⋊C4—416no—
789C22⋊C4—232no—
790C22⋊C4—232no—
791C22⋊C4—232no—
792C22⋊C4—232no—
793C22⋊C4—232no—
794C22⋊C4—416no—
795C22⋊C4—416no—
796C22⋊C4—416no—
797C22⋊C4—416no—
798C22⋊C4—416no—
799C22⋊C4—416no—
800C42—416no—
801C42—416no—
802C42—416no—
803C42—416no—
804C23—232no—
805C23—232no—
806C23—24no—
807C23—24no—
808C23—24no—
809C23—24no—
810C23—24no—
811C23—24no—
812C23—24no—
813C23—24no—
814C23—24no—
815C23—24no—
816C23—24no—
817C23—24no—
818C23—24no—
819C23—24no—
820C23—24no—
821C23—24no—
822C23—24no—
823C23—24no—
824C23—232no—
825C23—24no—
826C23—24no—
827C23—24no—
828C23—24no—
829C23—24no—
830C23—24no—
831C23—24no—
832C23—416no—
833C23—416no—
834C23—416no—
835C23—416no—
836C23—42no—
837C23—42no—
838C23—42no—
839C23—42no—
840C23—416no—
841C23—42no—
842C23—42no—
843C23—416no—
844C23—42no—
845C23—42no—
846C23—42no—
847C23—42no—
848C23—42no—
849C23—42no—
850C23—42no—
851C23—42no—
852C23—42no—
853C23—42no—
854C23—416no—
855C23—416no—
856C23—416no—
857C23—416no—
858C23—416no—
859C23—416no—
860C23—416no—
861C23—416no—
862C23—416no—
863C23—416no—
864C23—416no—
865C23—42no—
866C23—42no—
867C23—42no—
868C23—42no—
869C23—42no—
870C23—42no—
871C23—42no—
872C23—42no—
873C23—42no—
874C23—42no—
875C23—42no—
876C23—42no—
877C23—42no—
878C23—42no—
879C23—42no—
880C23—42no—
881C23—42no—
882C23—42no—
883C23—42no—
884C23—42no—
885C23—42no—
886C23—42no—
887C23—42no—
888C23—42no—
889C23—42no—
890C23—42no—
891C23—42no—
892C23—42no—
893C23—416no—
894C23—416no—
895C23—88no—
896C23—88no—
897C23—88no—
898C23—88no—
899C23—88no—
900C23—88no—
901C23—88no—
902C23—88no—
903C23C2×#11714yes—
904C23C2×C4×D418yes—
905C23C2×C4×D414yes—
906C23C2×C4×D414yes—
907C23C2×C4×D414yes—
908C23C4×#4114yes—
909C23#51814yes—
910C23#52014yes—
911C23C2×#12114yes—
912C23#52514yes—
913C23#52914yes—
914C23#52914yes—
915C23#52914yes—
916C23#53214yes—
917C23#53214yes—
918C23#53214yes—
919C23#53814yes—
920C23#53914yes—
921C23#54014yes—
922C23#54214yes—
923C23D4214yes—
924C23D4214yes—
925C23#54614yes—
926C23#54614yes—
927C23#54614yes—
928C23#54614yes—
929C23#54714yes—
930C23#54714yes—
931C23#54814yes—
932C23#55014yes—
933C23#55114yes—
934C23#55114yes—
935C23#55114yes—
936C23#55314yes—
937C23#55514yes—
938C23#55614yes—
939C23C24×C411yescharacteristic
940C23C23×D411yescharacteristic
941C23C23×D411yescharacteristic
942C23C23×D411yescharacteristic
943C23C22×#4111yescharacteristic
944C23C22×#4111yescharacteristic
945C23C22×#4111yescharacteristic
946C23C22×#4111yescharacteristic
947C23C22×#4111yescharacteristic
948C23C22×#4111yescharacteristic
949C23C22×#4111yescharacteristic
950C23C2×H(5,𝔽2)11yescharacteristic
951C23C2×H(5,𝔽2)11yescharacteristic
952C23C2×H(5,𝔽2)11yescharacteristic
953C23C2×2−1+411yescharacteristic
954D4—464no—
955C2×C4—232no—
956C2×C4—232no—
957C2×C4—232no—
958C2×C4—24no—
959C2×C4—24no—
960C2×C4—24no—
961C2×C4—24no—
962C2×C4—24no—
963C2×C4—24no—
964C2×C4—24no—
965C2×C4—232no—
966C2×C4—24no—
967C2×C4—24no—
968C2×C4—24no—
969C2×C4—24no—
970C2×C4—24no—
971C2×C4—24no—
972C2×C4—24no—
973C2×C4—24no—
974C2×C4—24no—
975C2×C4—24no—
976C2×C4—24no—
977C2×C4—24no—
978C2×C4—24no—
979C2×C4—24no—
980C2×C4—24no—
981C2×C4—24no—
982C2×C4—24no—
983C2×C4—24no—
984C2×C4—24no—
985C2×C4—24no—
986C2×C4—24no—
987C2×C4—24no—
988C2×C4—24no—
989C2×C4—24no—
990C2×C4—24no—
991C2×C4—24no—
992C2×C4—24no—
993C2×C4—24no—
994C2×C4—24no—
995C2×C4—24no—
996C2×C4—24no—
997C2×C4—24no—
998C2×C4—24no—
999C2×C4—24no—
1000C2×C4—24no—
1001C2×C4—24no—
1002C2×C4—24no—
1003C2×C4—24no—
1004C2×C4—464no—
1005C2×C4—416no—
1006C2×C4—42no—
1007C2×C4—42no—
1008C2×C4—42no—
1009C2×C4—42no—
1010C2×C4—42no—
1011C2×C4—42no—
1012C2×C4—42no—
1013C2×C4—42no—
1014C2×C4—42no—
1015C2×C4—416no—
1016C2×C4—416no—
1017C2×C4—42no—
1018C2×C4—42no—
1019C2×C4—42no—
1020C2×C4—42no—
1021C2×C4—42no—
1022C2×C4—42no—
1023C2×C4—42no—
1024C2×C4—42no—
1025C2×C4—42no—
1026C2×C4—42no—
1027C2×C4—42no—
1028C2×C4—42no—
1029C2×C4—42no—
1030C2×C4—42no—
1031C2×C4—42no—
1032C2×C4—42no—
1033C2×C4—42no—
1034C2×C4—42no—
1035C2×C4—42no—
1036C2×C4—416no—
1037C2×C4—416no—
1038C2×C4—416no—
1039C2×C4—416no—
1040C2×C4—42no—
1041C2×C4—42no—
1042C2×C4—42no—
1043C2×C4—42no—
1044C2×C4—42no—
1045C2×C4—42no—
1046C2×C4—42no—
1047C2×C4—42no—
1048C2×C4—42no—
1049C2×C4—42no—
1050C2×C4—42no—
1051C2×C4—42no—
1052C2×C4—42no—
1053C2×C4—42no—
1054C2×C4—88no—
1055C2×C4—88no—
1056C2×C4C2×#11718yes—
1057C2×C4C2×C4×D418yes—
1058C2×C4C2×C4×D418yes—
1059C2×C4C2×#12118yes—
1060C22—28no—
1061C22—28no—
1062C22—28no—
1063C22—44no—
1064C22—44no—
1065C22—44no—
1066C22—44no—
1067C22—44no—
1068C22—44no—
1069C22—44no—
1070C22—44no—
1071C22—44no—
1072C22—464no—
1073C22—44no—
1074C22—44no—
1075C22—44no—
1076C22—44no—
1077C22—44no—
1078C22—44no—
1079C22—44no—
1080C22—44no—
1081C22—44no—
1082C22—44no—
1083C22—82no—
1084C22—82no—
1085C22—82no—
1086C22—82no—
1087C22—82no—
1088C22—82no—
1089C22—832no—
1090C22—82no—
1091C22—82no—
1092C22#229318yes—
1093C22C4×#12118yes—
1094C22#233518yes—
1095C22#234218yes—
1096C22#235418yes—
1097C22#235818yes—
1098C22#236118yes—
1099C22#242518yes—
1100C22#242818yes—
1101C22#246118yes—
1102C22#246718yes—
1103C22#252118yes—
1104C22#253118yes—
1105C22#255518yes—
1106C22#256018yes—
1107C22C22×#11711yescharacteristic
1108C22C22×C4×D411yescharacteristic
1109C22C22×C4×D411yescharacteristic
1110C22C22×C4×D411yescharacteristic
1111C22C2×C4×#4111yescharacteristic
1112C22C2×#51811yescharacteristic
1113C22C2×#52011yescharacteristic
1114C22C22×#12111yescharacteristic
1115C22C2×#52511yescharacteristic
1116C22C2×#52911yescharacteristic
1117C22C2×#52911yescharacteristic
1118C22C2×#52911yescharacteristic
1119C22C2×#53211yescharacteristic
1120C22C2×#53211yescharacteristic
1121C22C2×#53211yescharacteristic
1122C22C2×#53811yescharacteristic
1123C22C2×#53911yescharacteristic
1124C22C2×#54011yescharacteristic
1125C22C2×#54211yescharacteristic
1126C22C2×D4211yescharacteristic
1127C22C2×D4211yescharacteristic
1128C22C2×#54611yescharacteristic
1129C22C2×#54611yescharacteristic
1130C22C2×#54611yescharacteristic
1131C22C2×#54611yescharacteristic
1132C22C2×#54711yescharacteristic
1133C22C2×#54711yescharacteristic
1134C22C2×#54811yescharacteristic
1135C22C2×#55011yescharacteristic
1136C22C2×#55111yescharacteristic
1137C22C2×#55111yescharacteristic
1138C22C2×#55111yescharacteristic
1139C22C2×#55311yescharacteristic
1140C22C2×#55511yescharacteristic
1141C22C2×#55611yescharacteristic
1142C4—28no—
1143C4—28no—
1144C4—28no—
1145C4—28no—
1146C4—44no—
1147C4—44no—
1148C4—44no—
1149C4—44no—
1150C4—44no—
1151C4—44no—
1152C4—44no—
1153C4—82no—
1154C4—82no—
1155C2—48no—
1156C2—84no—
1157C2#14012116yesdirect product factor
1158C2C2×#229311yescharacteristic
1159C2C2×C4×#12111yescharacteristic
1160C2C2×#233511yescharacteristic
1161C2C2×#234211yescharacteristic
1162C2C2×#235411yescharacteristic
1163C2C2×#235811yescharacteristic
1164C2C2×#236111yescharacteristic
1165C2C2×#246711yescharacteristic
1166C2C2×#242511yescharacteristic
1167C2C2×#246111yescharacteristic
1168C2C2×#242811yescharacteristic
1169C2C2×#252111yescharacteristic
1170C2C2×#253111yescharacteristic
1171C2C2×#255511yescharacteristic
1172C2C2×#256011yescharacteristic
subgroupG/H
center, socleC25C24
commutatorC23C24×C4
Frattini, cosocleC24C25
prime radicalC24×D4C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C25 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C22×#388C2semidirect
3. C22×#388C2semidirect
4. C22×#388C2semidirect
6. C22×#380C2semidirect
7. C22×C4×C22⋊C4C2semidirect
8. #14012C2direct (N × H)
9. C2×#1444C2semidirect
10. C2×#1440C2semidirect
11. C2×#1439C2semidirect
13. C2×#1437C2semidirect
14. C2×#1436C2semidirect
15. C2×#1436C2semidirect
16. C2×C4×#95C2semidirect
43. C2×#388C22semidirect
44. C2×#388C22semidirect
45. C2×#388C22semidirect
46. C2×#386C4semidirect
49. C2×#380C22semidirect
51. C2×C4×C22⋊C4C22semidirect
66. #1444C22semidirect
67. #1440C22semidirect
68. #1439C22semidirect
70. #1437C22semidirect
71. #1436C22semidirect
72. #1436C22semidirect
73. C4×#95C22semidirect
185. #386C2×C4semidirect
200. C2×#95D4semidirect
201. C2×#95D4semidirect
469. #95C2×D4semidirect
470. #95C2×D4semidirect
1157. C2#14012direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#3902
C22×#3882
C22×#3862
C22×#3802
C22×C4×C22⋊C42
#140122
C2×#14442
C2×#14402
C2×#14392
C2×#14382
C2×#14372
C2×#14362
C2×C4×#952