Finite Group Databasebeta

← C2×#14360 #520658

Subgroups — C2×#14360 #520658

Order 512.

7134 conjugacy classes of subgroups.

The subgroup lattice has 1176 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#123C211yesmaximal, characteristic
2C22×#390C211yesmaximal, characteristic
3C22×#389C211yesmaximal, characteristic, complemented
4C22×#387C211yesmaximal, characteristic, complemented
5C22×#380C211yesmaximal, characteristic, complemented
6#14360C2116yesmaximal, direct product factor
7C2×#1441C211yesmaximal, characteristic, complemented
8C2×#1439C211yesmaximal, characteristic, complemented
9C2×#1439C211yesmaximal, characteristic, complemented
10C2×#1439C211yesmaximal, characteristic, complemented
11C2×#1439C211yesmaximal, characteristic, complemented
12C2×#1438C211yesmaximal, characteristic
13C2×#1437C211yesmaximal, characteristic, complemented
14C2×#1437C211yesmaximal, characteristic, complemented
15C2×#1436C211yesmaximal, characteristic, complemented
16C2×C22⋊#95C211yesmaximal, characteristic, complemented
17C24×D4C2211yescharacteristic
18C25×C4C2211yescharacteristic
19C22×#123—28no—
20C22×#123—28no—
21C22×#123C4116yescomplemented
22C22×#123C2218yes—
23C23×C4⋊C4C2211yescharacteristic
24C23×C4⋊C4C2211yescharacteristic
25C23×C4⋊C4C2211yescharacteristic
26C23×C4⋊C4C2211yescharacteristic
27C23×C4⋊C4C2211yescharacteristic
28C23×C4⋊C4C2211yescharacteristic
29C23×C22⋊C4C2211yescharacteristic
30C23×C22⋊C4C2211yescharacteristic
31C23×C22⋊C4C2211yescharacteristic
32C23×C22⋊C4C2211yescharacteristic
33C23×C22⋊C4C2211yescharacteristic
34C23×C22⋊C4C2211yescharacteristic
35C23×C22⋊C4C2211yescharacteristic
36C23×C22⋊C4C2211yescharacteristic
37C23×C22⋊C4C2211yescharacteristic
38C23×C22⋊C4C2211yescharacteristic
39C23×C22⋊C4C2211yescharacteristic
40C23×C42C2211yescharacteristic
41C23×C42C2211yescharacteristic
42C2×#390—28no—
43C2×#390C2218yes—
44C2×#389—28no—
45C2×#389C2218yescomplemented
46C2×#387—28no—
47C2×#387C2218yescomplemented
48C2×#380—28no—
49C2×#380C2218yescomplemented
50C22×#95C2211yescharacteristic
51C22×#95C2211yescharacteristic
52C22×#95C2211yescharacteristic
53C22×#95C2211yescharacteristic
54C22×#95C2211yescharacteristic
55C22×#95C2211yescharacteristic
56C22×#95C2211yescharacteristic
57C22×#95C2211yescharacteristic
58C22×#95C2211yescharacteristic
59C22×#95C2211yescharacteristic
60C22×#95C2211yescharacteristic
61C22×#95C2211yescharacteristic
62C22×#95C2211yescharacteristic
63C22×#95C2211yescharacteristic
64#1441C2218yescomplemented
65#1439C2218yescomplemented
66#1439C2218yescomplemented
67#1439C2218yescomplemented
68#1439C2218yescomplemented
69#1438C2218yes—
70#1437C2218yescomplemented
71#1437C2218yescomplemented
72#1436C2218yescomplemented
73C22⋊#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×C4C2311yescharacteristic
101C24×C4C2314yes—
102C24×C4C2311yescharacteristic
103C24×C4C2311yescharacteristic
104C24×C4C2311yescharacteristic
105C2×#123—2128no—
106C2×#123—232no—
107C2×#123—232no—
108C2×#123C2×C4164yescomplemented
109C22×C4⋊C4—24no—
110C22×C4⋊C4—24no—
111C22×C4⋊C4—24no—
112C22×C4⋊C4—24no—
113C22×C4⋊C4—24no—
114C22×C4⋊C4—24no—
115C22×C4⋊C4—24no—
116C22×C4⋊C4—24no—
117C22×C4⋊C4—24no—
118C22×C4⋊C4—42no—
119C22×C4⋊C4—42no—
120C22×C4⋊C4—42no—
121C22×C4⋊C4—42no—
122C22×C4⋊C4—42no—
123C22×C4⋊C4C2×C418yes—
124C22×C4⋊C4C2×C418yes—
125C22×C4⋊C4D418yes—
126C22×C4⋊C4D418yes—
127C22×C4⋊C4C2314yes—
128C22×C4⋊C4C2314yes—
129C22×C4⋊C4C2314yes—
130C22×C4⋊C4C2314yes—
131C22×C4⋊C4C2314yes—
132C22×C4⋊C4C2314yes—
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—24no—
145C22×C22⋊C4—24no—
146C22×C22⋊C4—24no—
147C22×C22⋊C4—24no—
148C22×C22⋊C4—42no—
149C22×C22⋊C4—42no—
150C22×C22⋊C4—42no—
151C22×C22⋊C4—42no—
152C22×C22⋊C4—42no—
153C22×C22⋊C4—42no—
154C22×C22⋊C4—42no—
155C22×C22⋊C4—42no—
156C22×C22⋊C4—42no—
157C22×C22⋊C4—42no—
158C22×C22⋊C4—42no—
159C22×C22⋊C4—42no—
160C22×C22⋊C4—42no—
161C22×C22⋊C4—42no—
162C22×C22⋊C4C2×C418yes—
163C22×C22⋊C4C2×C418yes—
164C22×C22⋊C4C2×C418yes—
165C22×C22⋊C4D418yes—
166C22×C22⋊C4C2314yes—
167C22×C22⋊C4C2314yes—
168C22×C22⋊C4C2314yes—
169C22×C22⋊C4C2314yes—
170C22×C22⋊C4C2314yes—
171C22×C22⋊C4C2314yes—
172C22×C22⋊C4C2314yes—
173C22×C22⋊C4C2314yes—
174C22×C22⋊C4C2314yes—
175C22×C22⋊C4C2314yes—
176C22×C22⋊C4C2314yes—
177C22×C42—24no—
178C22×C42—24no—
179C22×C42—24no—
180C22×C42—42no—
181C22×C42—42no—
182C22×C42—42no—
183C22×C42C2314yes—
184C22×C42C2314yes—
185#390—232no—
186#389—232no—
187#387—232no—
188#380—232no—
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—24no—
198C2×#95—24no—
199C2×#95—42no—
200C2×#95—42no—
201C2×#95—42no—
202C2×#95—42no—
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—
216C2×#95C2314yes—
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—
242C25—22no—
243C25C22×C414yes—
244C25C22×C414yes—
245C25C2×D414yes—
246C25#4114yes—
247C25C2412yes—
248C25C2412yes—
249C25C2411yescharacteristic
250C22×D4—232no—
251C22×D4—28no—
252C22×D4—28no—
253C22×D4—232no—
254C22×D4—28no—
255C22×D4—28no—
256C22×D4—416no—
257C22×D4—44no—
258C22×D4—44no—
259C22×D4—416no—
260C22×D4—416no—
261C22×D4—416no—
262C22×D4—416no—
263C22×D4C22×C4116yes—
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—232no—
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—28no—
286C23×C4—22no—
287C23×C4—22no—
288C23×C4—22no—
289C23×C4—22no—
290C23×C4—28no—
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—232no—
316C23×C4—28no—
317C23×C4—28no—
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×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—22no—
342C23×C4—22no—
343C23×C4—22no—
344C23×C4—22no—
345C23×C4—22no—
346C23×C4—416no—
347C23×C4—44no—
348C23×C4—44no—
349C23×C4—416no—
350C23×C4—416no—
351C23×C4—416no—
352C23×C4—416no—
353C23×C4C22×C414yes—
354C23×C4C22×C414yes—
355C23×C4C22×C4116yes—
356C23×C4C22×C414yes—
357C23×C4C22×C414yes—
358C23×C4C22×C414yes—
359C23×C4C2×D414yes—
360C23×C4C2×D414yes—
361C23×C4C2×D414yes—
362C23×C4C2×D414yes—
363C23×C4C2×D414yes—
364C23×C4C2×D414yes—
365C23×C4C2×D414yes—
366C23×C4C2×D414yes—
367C23×C4#4114yes—
368C23×C4#4114yes—
369C23×C4C2412yes—
370C23×C4C2412yes—
371C23×C4C2412yes—
372C23×C4C2412yes—
373C23×C4C2412yes—
374C23×C4C2412yes—
375C23×C4C2412yes—
376C23×C4C2412yes—
377C23×C4C2412yes—
378C23×C4C2412yes—
379C23×C4C2412yes—
380C23×C4C2412yes—
381C23×C4C2412yes—
382#123—2256no—
383C2×C4⋊C4—232no—
384C2×C4⋊C4—28no—
385C2×C4⋊C4—28no—
386C2×C4⋊C4—28no—
387C2×C4⋊C4—28no—
388C2×C4⋊C4—28no—
389C2×C4⋊C4—28no—
390C2×C4⋊C4—28no—
391C2×C4⋊C4—28no—
392C2×C4⋊C4—28no—
393C2×C4⋊C4—44no—
394C2×C4⋊C4—44no—
395C2×C4⋊C4—44no—
396C2×C4⋊C4—44no—
397C2×C4⋊C4—44no—
398C2×C4⋊C4—416no—
399C2×C4⋊C4—416no—
400C2×C4⋊C4—416no—
401C2×C4⋊C4—416no—
402C2×C4⋊C4C22⋊C4164yescomplemented
403C2×C4⋊C4C22×C4116yes—
404C2×C4⋊C4C22×C4116yes—
405C2×C4⋊C4C2×D4116yes—
406C2×C4⋊C4C2×D4116yes—
407C2×C22⋊C4—232no—
408C2×C22⋊C4—232no—
409C2×C22⋊C4—232no—
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—416no—
426C2×C22⋊C4—44no—
427C2×C22⋊C4—44no—
428C2×C22⋊C4—44no—
429C2×C22⋊C4—44no—
430C2×C22⋊C4—44no—
431C2×C22⋊C4—44no—
432C2×C22⋊C4—44no—
433C2×C22⋊C4—44no—
434C2×C22⋊C4—44no—
435C2×C22⋊C4—44no—
436C2×C22⋊C4—44no—
437C2×C22⋊C4—44no—
438C2×C22⋊C4—44no—
439C2×C22⋊C4—44no—
440C2×C22⋊C4—416no—
441C2×C22⋊C4—416no—
442C2×C22⋊C4—416no—
443C2×C22⋊C4—416no—
444C2×C22⋊C4—416no—
445C2×C22⋊C4—416no—
446C2×C22⋊C4—416no—
447C2×C22⋊C4C22×C4116yes—
448C2×C22⋊C4C22×C4116yes—
449C2×C22⋊C4C22×C4116yes—
450C2×C22⋊C4C2×D4116yes—
451C2×C42—28no—
452C2×C42—28no—
453C2×C42—28no—
454C2×C42—44no—
455C2×C42—44no—
456C2×C42—44no—
457C2×C42—416no—
458C2×C42—416no—
459#95—28no—
460#95—28no—
461#95—28no—
462#95—28no—
463#95—28no—
464#95—28no—
465#95—28no—
466#95—28no—
467#95—28no—
468#95—28no—
469#95—44no—
470#95—44no—
471#95—44no—
472#95—44no—
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—28no—
490C24—28no—
491C24—22no—
492C24—22no—
493C24—22no—
494C24—22no—
495C24—22no—
496C24—22no—
497C24—22no—
498C24—22no—
499C24—22no—
500C24—22no—
501C24—22no—
502C24—22no—
503C24—28no—
504C24—28no—
505C24—28no—
506C24—28no—
507C24—28no—
508C24—28no—
509C24—28no—
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—22no—
523C24—22no—
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—
566C24—44no—
567C24—44no—
568C24C4×D4116yes—
569C24C23×C414yes—
570C24C23×C414yes—
571C24C23×C412yes—
572C24C22×D414yes—
573C24C22×D412yes—
574C24C22×D412yes—
575C24C22×D412yes—
576C24C2×#4114yes—
577C24C2×#4112yes—
578C24C2×#4112yes—
579C24C2×#4112yes—
580C24H(5,𝔽2)12yes—
581C24H(5,𝔽2)12yes—
582C24H(5,𝔽2)12yes—
583C24H(5,𝔽2)12yes—
584C24H(5,𝔽2)12yes—
585C242−1+412yes—
586C242−1+412yes—
587C242−1+412yes—
588C24C2511yescharacteristic
589C2×D4—232no—
590C2×D4—232no—
591C2×D4—416no—
592C2×D4—4128no—
593C2×D4—416no—
594C2×D4—416no—
595C2×D4—416no—
596C2×D4—416no—
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—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—28no—
628C22×C4—28no—
629C22×C4—232no—
630C22×C4—28no—
631C22×C4—28no—
632C22×C4—28no—
633C22×C4—28no—
634C22×C4—28no—
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—22no—
647C22×C4—22no—
648C22×C4—22no—
649C22×C4—22no—
650C22×C4—22no—
651C22×C4—22no—
652C22×C4—22no—
653C22×C4—22no—
654C22×C4—22no—
655C22×C4—22no—
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—232no—
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—22no—
699C22×C4—22no—
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—416no—
712C22×C4—4128no—
713C22×C4—416no—
714C22×C4—416no—
715C22×C4—416no—
716C22×C4—416no—
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×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—44no—
763C22×C4—44no—
764C22×C4—44no—
765C22×C4—44no—
766C22×C4—44no—
767C22×C4—44no—
768C22×C4—44no—
769C22×C4C2×C22⋊C4116yes—
770C22×C4C2×C22⋊C4116yes—
771C22×C4C2×C22⋊C4116yes—
772C22×C4C23×C414yes—
773C22×C4C23×C414yes—
774C22×C4C23×C414yes—
775C22×C4C23×C414yes—
776C22×C4C23×C414yes—
777C22×C4C22×D414yes—
778C22×C4C22×D414yes—
779C22×C4C22×D414yes—
780C22×C4C22×D414yes—
781C22×C4C22×D414yes—
782C22×C4C22×D414yes—
783C22×C4C22×D414yes—
784C22×C4C22×D414yes—
785C22×C4C2×#4114yes—
786C22×C4C2×#4114yes—
787C4⋊C4—232no—
788C4⋊C4—416no—
789C4⋊C4—416no—
790C4⋊C4—416no—
791C4⋊C4—416no—
792C4⋊C4C2×C22⋊C4164yescomplemented
793C22⋊C4—232no—
794C22⋊C4—232no—
795C22⋊C4—232no—
796C22⋊C4—416no—
797C22⋊C4—416no—
798C22⋊C4—416no—
799C22⋊C4—416no—
800C22⋊C4—416no—
801C22⋊C4—416no—
802C22⋊C4—416no—
803C22⋊C4—416no—
804C42—416no—
805C42—416no—
806C23—232no—
807C23—232no—
808C23—232no—
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—24no—
825C23—24no—
826C23—24no—
827C23—24no—
828C23—24no—
829C23—24no—
830C23—24no—
831C23—24no—
832C23—24no—
833C23—24no—
834C23—416no—
835C23—416no—
836C23—416no—
837C23—416no—
838C23—416no—
839C23—416no—
840C23—42no—
841C23—42no—
842C23—42no—
843C23—42no—
844C23—416no—
845C23—416no—
846C23—42no—
847C23—42no—
848C23—42no—
849C23—42no—
850C23—416no—
851C23—416no—
852C23—42no—
853C23—42no—
854C23—42no—
855C23—42no—
856C23—416no—
857C23—416no—
858C23—42no—
859C23—42no—
860C23—42no—
861C23—42no—
862C23—416no—
863C23—416no—
864C23—416no—
865C23—416no—
866C23—416no—
867C23—416no—
868C23—416no—
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—42no—
894C23—42no—
895C23—42no—
896C23—42no—
897C23—88no—
898C23—88no—
899C23—88no—
900C23—88no—
901C23—88no—
902C23—88no—
903C23—88no—
904C23—88no—
905C23C22×C22⋊C414yes—
906C23C2×C4×D418yes—
907C23C2×C4×D414yes—
908C23C4×#4114yes—
909C23#51814yes—
910C23#52014yes—
911C23#52014yes—
912C23#52014yes—
913C23#53414yes—
914C23#53514yes—
915C23#53614yes—
916C23#53614yes—
917C23#53714yes—
918C23#53714yes—
919C23#53814yes—
920C23#53914yes—
921C23#53914yes—
922C23#53914yes—
923C23#54014yes—
924C23#54214yes—
925C23D4214yes—
926C23D4214yes—
927C23#54614yes—
928C23#54614yes—
929C23#54614yes—
930C23#54714yes—
931C23#54814yes—
932C23#54814yes—
933C23#55014yes—
934C23#55014yes—
935C23#55114yes—
936C23#55214yes—
937C23#56014yes—
938C23#56214yes—
939C23#56214yes—
940C23#56314yes—
941C23C24×C411yescharacteristic
942C23C23×D411yescharacteristic
943C23C23×D411yescharacteristic
944C23C23×D411yescharacteristic
945C23C22×#4111yescharacteristic
946C23C22×#4111yescharacteristic
947C23C22×#4111yescharacteristic
948C23C2×H(5,𝔽2)11yescharacteristic
949C23C2×H(5,𝔽2)11yescharacteristic
950C23C2×H(5,𝔽2)11yescharacteristic
951C23C2×H(5,𝔽2)11yescharacteristic
952C23C2×H(5,𝔽2)11yescharacteristic
953C23C2×2−1+411yescharacteristic
954C23C2×2−1+411yescharacteristic
955C23C2×2−1+411yescharacteristic
956D4—464no—
957C2×C4—232no—
958C2×C4—232no—
959C2×C4—232no—
960C2×C4—24no—
961C2×C4—24no—
962C2×C4—24no—
963C2×C4—24no—
964C2×C4—24no—
965C2×C4—24no—
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—464no—
997C2×C4—416no—
998C2×C4—416no—
999C2×C4—416no—
1000C2×C4—42no—
1001C2×C4—42no—
1002C2×C4—42no—
1003C2×C4—42no—
1004C2×C4—42no—
1005C2×C4—416no—
1006C2×C4—416no—
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—42no—
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—42no—
1037C2×C4—42no—
1038C2×C4—42no—
1039C2×C4—42no—
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—42no—
1055C2×C4—88no—
1056C2×C4—88no—
1057C2×C4—88no—
1058C2×C4—88no—
1059C2×C4C22×C22⋊C418yes—
1060C2×C4C22×C22⋊C418yes—
1061C2×C4C22×C22⋊C418yes—
1062C22—28no—
1063C22—28no—
1064C22—28no—
1065C22—464no—
1066C22—44no—
1067C22—44no—
1068C22—44no—
1069C22—44no—
1070C22—44no—
1071C22—44no—
1072C22—44no—
1073C22—44no—
1074C22—44no—
1075C22—44no—
1076C22—44no—
1077C22—44no—
1078C22—44no—
1079C22—44no—
1080C22—44no—
1081C22—44no—
1082C22—44no—
1083C22—44no—
1084C22—44no—
1085C22—832no—
1086C22—82no—
1087C22—82no—
1088C22—82no—
1089C22—82no—
1090C22—82no—
1091C22—82no—
1092C22—82no—
1093C22—82no—
1094C22#231118yes—
1095C22#232218yes—
1096C22#233518yes—
1097C22D4×C22⋊C418yes—
1098C22#234118yes—
1099C22#235918yes—
1100C22#237618yes—
1101C22#267318yes—
1102C22#267418yes—
1103C22#268118yes—
1104C22#268218yes—
1105C22#269418yes—
1106C22#269618yes—
1107C22#270518yes—
1108C22#270718yes—
1109C22C23×C22⋊C411yescharacteristic
1110C22C22×C4×D411yescharacteristic
1111C22C2×C4×#4111yescharacteristic
1112C22C2×#51811yescharacteristic
1113C22C2×#52011yescharacteristic
1114C22C2×#52011yescharacteristic
1115C22C2×#52011yescharacteristic
1116C22C2×#53411yescharacteristic
1117C22C2×#53511yescharacteristic
1118C22C2×#53611yescharacteristic
1119C22C2×#53611yescharacteristic
1120C22C2×#53711yescharacteristic
1121C22C2×#53711yescharacteristic
1122C22C2×#53811yescharacteristic
1123C22C2×#53911yescharacteristic
1124C22C2×#53911yescharacteristic
1125C22C2×#53911yescharacteristic
1126C22C2×#54011yescharacteristic
1127C22C2×#54211yescharacteristic
1128C22C2×D4211yescharacteristic
1129C22C2×D4211yescharacteristic
1130C22C2×#54611yescharacteristic
1131C22C2×#54611yescharacteristic
1132C22C2×#54611yescharacteristic
1133C22C2×#54711yescharacteristic
1134C22C2×#54811yescharacteristic
1135C22C2×#54811yescharacteristic
1136C22C2×#55011yescharacteristic
1137C22C2×#55011yescharacteristic
1138C22C2×#55111yescharacteristic
1139C22C2×#55211yescharacteristic
1140C22C2×#56011yescharacteristic
1141C22C2×#56211yescharacteristic
1142C22C2×#56211yescharacteristic
1143C22C2×#56311yescharacteristic
1144C4—28no—
1145C4—28no—
1146C4—28no—
1147C4—44no—
1148C4—44no—
1149C4—44no—
1150C4—44no—
1151C4—44no—
1152C4—44no—
1153C4—82no—
1154C4—82no—
1155C4—82no—
1156C4—82no—
1157C2—48no—
1158C2—84no—
1159C2#14360116yesdirect product factor
1160C2C2×#231111yescharacteristic
1161C2C2×#232211yescharacteristic
1162C2C2×#233511yescharacteristic
1163C2C2×D4×C22⋊C411yescharacteristic
1164C2C2×#234111yescharacteristic
1165C2C2×#235911yescharacteristic
1166C2C2×#237611yescharacteristic
1167C2C2×#267311yescharacteristic
1168C2C2×#267411yescharacteristic
1169C2C2×#268111yescharacteristic
1170C2C2×#268211yescharacteristic
1171C2C2×#269411yescharacteristic
1172C2C2×#269611yescharacteristic
1173C2C2×#270511yescharacteristic
1174C2C2×#270711yescharacteristic
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
3. C22×#389C2semidirect
4. C22×#387C2semidirect
5. C22×#380C2semidirect
6. #14360C2direct (N × H)
7. C2×#1441C2semidirect
8. C2×#1439C2semidirect
9. C2×#1439C2semidirect
10. C2×#1439C2semidirect
11. C2×#1439C2semidirect
13. C2×#1437C2semidirect
14. C2×#1437C2semidirect
15. C2×#1436C2semidirect
16. C2×C22⋊#95C2semidirect
21. C22×#123C4semidirect
45. C2×#389C22semidirect
47. C2×#387C22semidirect
49. C2×#380C22semidirect
64. #1441C22semidirect
65. #1439C22semidirect
66. #1439C22semidirect
67. #1439C22semidirect
68. #1439C22semidirect
70. #1437C22semidirect
71. #1437C22semidirect
72. #1436C22semidirect
73. C22⋊#95C22semidirect
108. C2×#123C2×C4semidirect
402. C2×C4⋊C4C22⋊C4semidirect
792. C4⋊C4C2×C22⋊C4semidirect
1159. C2#14360direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#1232
C22×#3902
C22×#3892
C22×#3872
C22×#3802
#143602
C2×#14412
C2×#14392
C2×#14382
C2×#14372
C2×#14362
C2×C22⋊#952