Finite Group Databasebeta

← C2×#14403 #520707

Subgroups — C2×#14403 #520707

Order 512.

5362 conjugacy classes of subgroups.

The subgroup lattice has 1022 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#388C211yesmaximal, characteristic
2C22×#388C211yesmaximal, characteristic
3C22×#385C211yesmaximal, characteristic
4C22×#385C211yesmaximal, characteristic
5C22×#382C211yesmaximal, characteristic, complemented
6#14403C2116yesmaximal, direct product factor
7C2×#1444C211yesmaximal, characteristic, complemented
8C2×#1444C211yesmaximal, characteristic, complemented
9C2×#1442C211yesmaximal, characteristic, complemented
10C2×#1441C211yesmaximal, characteristic, complemented
11C2×#1439C211yesmaximal, characteristic
12C2×#1439C211yesmaximal, characteristic
13C2×#1436C211yesmaximal, characteristic, complemented
14C2×C4⋊#95C211yesmaximal, characteristic, complemented
15C2×C4⋊#95C211yesmaximal, characteristic, complemented
16C2×C22⋊#95C211yesmaximal, characteristic
17C25×C4C2211yescharacteristic
18C23×C4⋊C4C2211yescharacteristic
19C23×C4⋊C4C2211yescharacteristic
20C23×C4⋊C4C2211yescharacteristic
21C23×C4⋊C4C2211yescharacteristic
22C23×C4⋊C4C2211yescharacteristic
23C23×C4⋊C4C2211yescharacteristic
24C23×C4⋊C4C2211yescharacteristic
25C23×C4⋊C4C2211yescharacteristic
26C23×C22⋊C4C2211yescharacteristic
27C23×C22⋊C4C2211yescharacteristic
28C23×C22⋊C4C2211yescharacteristic
29C23×C22⋊C4C2211yescharacteristic
30C23×C22⋊C4C2211yescharacteristic
31C23×C22⋊C4C2211yescharacteristic
32C23×C42C2211yescharacteristic
33C23×C42C2211yescharacteristic
34C2×#388—28no—
35C2×#388C4116yescomplemented
36C2×#388C2218yes—
37C2×#388C2218yes—
38C2×#385—28no—
39C2×#385—28no—
40C2×#385C2218yes—
41C2×#385C2218yes—
42C2×#382—28no—
43C2×#382C2218yescomplemented
44C22×#95C2211yescharacteristic
45C22×#95C2211yescharacteristic
46C22×#95C2211yescharacteristic
47C22×#95C2211yescharacteristic
48C22×#95C2211yescharacteristic
49C22×#95C2211yescharacteristic
50C22×#95C2211yescharacteristic
51C22×#95C2211yescharacteristic
52C22×#95C2211yescharacteristic
53C22×#95C2211yescharacteristic
54C22×#95C2211yescharacteristic
55C22×#95C2211yescharacteristic
56C22×#95C2211yescharacteristic
57C22×#95C2211yescharacteristic
58C22×#95C2211yescharacteristic
59C22×#95C2211yescharacteristic
60C22×#95C2211yescharacteristic
61C22×#95C2211yescharacteristic
62#1444C2218yescomplemented
63#1444C2218yescomplemented
64#1442C2218yescomplemented
65#1441C2218yescomplemented
66#1439C2218yes—
67#1439C2218yes—
68#1436C2218yescomplemented
69C4⋊#95C2218yescomplemented
70C4⋊#95C2218yescomplemented
71C22⋊#95C2218yes—
72C26C2311yescharacteristic
73C24×C4—24no—
74C24×C4—24no—
75C24×C4—24no—
76C24×C4—42no—
77C24×C4—42no—
78C24×C4—42no—
79C24×C4—42no—
80C24×C4C2311yescharacteristic
81C24×C4C2311yescharacteristic
82C24×C4C2311yescharacteristic
83C24×C4C2311yescharacteristic
84C24×C4C2311yescharacteristic
85C24×C4C2311yescharacteristic
86C24×C4C2311yescharacteristic
87C24×C4C2311yescharacteristic
88C24×C4C2311yescharacteristic
89C24×C4C2311yescharacteristic
90C24×C4C2311yescharacteristic
91C24×C4C2311yescharacteristic
92C24×C4C2311yescharacteristic
93C24×C4C2311yescharacteristic
94C24×C4C2314yes—
95C22×C4⋊C4—24no—
96C22×C4⋊C4—24no—
97C22×C4⋊C4—24no—
98C22×C4⋊C4—24no—
99C22×C4⋊C4—24no—
100C22×C4⋊C4—24no—
101C22×C4⋊C4—24no—
102C22×C4⋊C4—24no—
103C22×C4⋊C4—24no—
104C22×C4⋊C4—24no—
105C22×C4⋊C4—24no—
106C22×C4⋊C4—42no—
107C22×C4⋊C4—42no—
108C22×C4⋊C4—42no—
109C22×C4⋊C4—42no—
110C22×C4⋊C4—42no—
111C22×C4⋊C4—42no—
112C22×C4⋊C4—42no—
113C22×C4⋊C4—42no—
114C22×C4⋊C4—42no—
115C22×C4⋊C4—42no—
116C22×C4⋊C4—42no—
117C22×C4⋊C4—42no—
118C22×C4⋊C4C2×C418yescomplemented
119C22×C4⋊C4C2314yes—
120C22×C4⋊C4C2314yes—
121C22×C4⋊C4C2314yes—
122C22×C4⋊C4C2314yes—
123C22×C4⋊C4C2314yes—
124C22×C4⋊C4C2314yes—
125C22×C4⋊C4C2314yes—
126C22×C4⋊C4C2314yes—
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—42no—
135C22×C22⋊C4—42no—
136C22×C22⋊C4—42no—
137C22×C22⋊C4—42no—
138C22×C22⋊C4—42no—
139C22×C22⋊C4—42no—
140C22×C22⋊C4C2×C418yes—
141C22×C22⋊C4C2×C418yes—
142C22×C22⋊C4C2×C418yes—
143C22×C22⋊C4D418yes—
144C22×C22⋊C4Q818yes—
145C22×C22⋊C4C2314yes—
146C22×C22⋊C4C2314yes—
147C22×C22⋊C4C2314yes—
148C22×C22⋊C4C2314yes—
149C22×C22⋊C4C2314yes—
150C22×C22⋊C4C2314yes—
151C22×C42—24no—
152C22×C42—24no—
153C22×C42—24no—
154C22×C42—24no—
155C22×C42—42no—
156C22×C42C2×C418yescomplemented
157C22×C42C2314yes—
158C22×C42C2314yes—
159#388—232no—
160#388C2×C4164yescomplemented
161#385—232no—
162#385—232no—
163#382—232no—
164C2×#95—24no—
165C2×#95—24no—
166C2×#95—24no—
167C2×#95—24no—
168C2×#95—24no—
169C2×#95—24no—
170C2×#95—24no—
171C2×#95—24no—
172C2×#95—42no—
173C2×#95—42no—
174C2×#95—42no—
175C2×#95—42no—
176C2×#95—42no—
177C2×#95—42no—
178C2×#95—42no—
179C2×#95C2×C418yescomplemented
180C2×#95C2×C418yescomplemented
181C2×#95D418yes—
182C2×#95C2314yes—
183C2×#95C2314yes—
184C2×#95C2314yes—
185C2×#95C2314yes—
186C2×#95C2314yes—
187C2×#95C2314yes—
188C2×#95C2314yes—
189C2×#95C2314yes—
190C2×#95C2314yes—
191C2×#95C2314yes—
192C2×#95C2314yes—
193C2×#95C2314yes—
194C2×#95C2314yes—
195C2×#95C2314yes—
196C2×#95C2314yes—
197C2×#95C2314yes—
198C2×#95C2314yes—
199C2×#95C2314yes—
200C25—22no—
201C25—22no—
202C25—22no—
203C25—22no—
204C25—22no—
205C25—22no—
206C25—22no—
207C25—22no—
208C25—22no—
209C25—22no—
210C25—22no—
211C25—22no—
212C25C22×C414yes—
213C25C2×D414yes—
214C25C2×Q814yes—
215C25C2412yes—
216C25C2411yescharacteristic
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×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—28no—
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—28no—
301C23×C4—28no—
302C23×C4—44no—
303C23×C4—44no—
304C23×C4—44no—
305C23×C4—44no—
306C23×C4—416no—
307C23×C4—416no—
308C23×C4—416no—
309C23×C4—416no—
310C23×C4—416no—
311C23×C4—416no—
312C23×C4—416no—
313C23×C4C22×C414yes—
314C23×C4C22×C414yes—
315C23×C4C22×C414yes—
316C23×C4C22×C414yes—
317C23×C4C22×C414yes—
318C23×C4C22×C414yes—
319C23×C4C2×D414yes—
320C23×C4C2×D414yes—
321C23×C4C2×D414yes—
322C23×C4C2×D414yes—
323C23×C4C2×D414yes—
324C23×C4C2×Q814yes—
325C23×C4C2×Q814yes—
326C23×C4#4114yes—
327C23×C4#4114yes—
328C23×C4#4114yes—
329C23×C4C2412yes—
330C23×C4C2412yes—
331C23×C4C2412yes—
332C23×C4C2412yes—
333C23×C4C2412yes—
334C23×C4C2412yes—
335C23×C4C2412yes—
336C23×C4C2412yes—
337C23×C4C2412yes—
338C23×C4C2412yes—
339C23×C4C2412yes—
340C23×C4C2412yes—
341C23×C4C2412yes—
342C23×C4C2412yes—
343C2×C4⋊C4—28no—
344C2×C4⋊C4—28no—
345C2×C4⋊C4—28no—
346C2×C4⋊C4—28no—
347C2×C4⋊C4—28no—
348C2×C4⋊C4—28no—
349C2×C4⋊C4—28no—
350C2×C4⋊C4—28no—
351C2×C4⋊C4—28no—
352C2×C4⋊C4—28no—
353C2×C4⋊C4—28no—
354C2×C4⋊C4—416no—
355C2×C4⋊C4—44no—
356C2×C4⋊C4—44no—
357C2×C4⋊C4—44no—
358C2×C4⋊C4—44no—
359C2×C4⋊C4—44no—
360C2×C4⋊C4—44no—
361C2×C4⋊C4—44no—
362C2×C4⋊C4—44no—
363C2×C4⋊C4—44no—
364C2×C4⋊C4—44no—
365C2×C4⋊C4—44no—
366C2×C4⋊C4—44no—
367C2×C4⋊C4—416no—
368C2×C4⋊C4—416no—
369C2×C4⋊C4—416no—
370C2×C4⋊C4—416no—
371C2×C4⋊C4—416no—
372C2×C4⋊C4—416no—
373C2×C4⋊C4—416no—
374C2×C4⋊C4C22×C4116yescomplemented
375C2×C22⋊C4—232no—
376C2×C22⋊C4—28no—
377C2×C22⋊C4—28no—
378C2×C22⋊C4—28no—
379C2×C22⋊C4—28no—
380C2×C22⋊C4—28no—
381C2×C22⋊C4—28no—
382C2×C22⋊C4—28no—
383C2×C22⋊C4—416no—
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—416no—
391C2×C22⋊C4—416no—
392C2×C22⋊C4—416no—
393C2×C22⋊C4C4⋊C4164yescomplemented
394C2×C22⋊C4C22×C4116yes—
395C2×C22⋊C4C22×C4116yes—
396C2×C22⋊C4C22×C4116yes—
397C2×C22⋊C4C2×D4116yes—
398C2×C22⋊C4C2×Q8116yes—
399C2×C42—232no—
400C2×C42—28no—
401C2×C42—28no—
402C2×C42—28no—
403C2×C42—28no—
404C2×C42—44no—
405C2×C42—416no—
406C2×C42C22×C4116yescomplemented
407#95—28no—
408#95—28no—
409#95—28no—
410#95—28no—
411#95—28no—
412#95—28no—
413#95—28no—
414#95—28no—
415#95—44no—
416#95—44no—
417#95—44no—
418#95—44no—
419#95—44no—
420#95—44no—
421#95—44no—
422#95C22×C4116yescomplemented
423#95C22×C4116yescomplemented
424#95C2×D4116yes—
425C24—28no—
426C24—28no—
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—28no—
442C24—28no—
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—44no—
456C24—44no—
457C24—44no—
458C24—44no—
459C24—44no—
460C24—44no—
461C24—44no—
462C24—44no—
463C24—44no—
464C24—44no—
465C24—44no—
466C24—44no—
467C24—44no—
468C24—44no—
469C24—44no—
470C24—44no—
471C24C2×C4⋊C4116yes—
472C24C23×C414yes—
473C24C23×C412yes—
474C24C22×D414yes—
475C24C22×D412yes—
476C24C22×D412yes—
477C24C22×Q814yes—
478C24C22×Q812yes—
479C24C2×#4112yes—
480C24C2×#4112yes—
481C24C2×#4112yes—
482C24H(5,𝔽2)12yes—
483C24H(5,𝔽2)12yes—
484C24H(5,𝔽2)12yes—
485C24H(5,𝔽2)12yes—
486C24H(5,𝔽2)12yes—
487C242−1+412yes—
488C242−1+412yes—
489C242−1+412yes—
490C24C2511yescharacteristic
491C22×C4—28no—
492C22×C4—28no—
493C22×C4—28no—
494C22×C4—28no—
495C22×C4—28no—
496C22×C4—28no—
497C22×C4—28no—
498C22×C4—28no—
499C22×C4—28no—
500C22×C4—28no—
501C22×C4—28no—
502C22×C4—28no—
503C22×C4—28no—
504C22×C4—28no—
505C22×C4—28no—
506C22×C4—28no—
507C22×C4—28no—
508C22×C4—28no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—28no—
522C22×C4—28no—
523C22×C4—28no—
524C22×C4—28no—
525C22×C4—28no—
526C22×C4—28no—
527C22×C4—28no—
528C22×C4—28no—
529C22×C4—28no—
530C22×C4—28no—
531C22×C4—28no—
532C22×C4—28no—
533C22×C4—28no—
534C22×C4—28no—
535C22×C4—28no—
536C22×C4—28no—
537C22×C4—28no—
538C22×C4—28no—
539C22×C4—28no—
540C22×C4—28no—
541C22×C4—28no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
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—416no—
613C22×C4—416no—
614C22×C4—416no—
615C22×C4—416no—
616C22×C4—416no—
617C22×C4—416no—
618C22×C4—4128no—
619C22×C4—416no—
620C22×C4—44no—
621C22×C4—44no—
622C22×C4—44no—
623C22×C4—44no—
624C22×C4—44no—
625C22×C4—44no—
626C22×C4—44no—
627C22×C4—44no—
628C22×C4—44no—
629C22×C4—44no—
630C22×C4—44no—
631C22×C4—44no—
632C22×C4—44no—
633C22×C4—44no—
634C22×C4—44no—
635C22×C4—44no—
636C22×C4—44no—
637C22×C4—44no—
638C22×C4—44no—
639C22×C4—44no—
640C22×C4—44no—
641C22×C4—44no—
642C22×C4—44no—
643C22×C4—44no—
644C22×C4—44no—
645C22×C4—44no—
646C22×C4—44no—
647C22×C4—44no—
648C22×C4—44no—
649C22×C4—44no—
650C22×C4—44no—
651C22×C4—44no—
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×C4C2×C4⋊C4116yes—
677C22×C4C2×C4⋊C4116yes—
678C22×C4C4×D4116yes—
679C22×C4C23×C414yes—
680C22×C4C23×C414yes—
681C22×C4C23×C414yes—
682C22×C4C23×C414yes—
683C22×C4C23×C414yes—
684C22×C4C23×C414yes—
685C22×C4C22×D414yes—
686C22×C4C22×D414yes—
687C22×C4C22×D414yes—
688C22×C4C22×D414yes—
689C22×C4C22×D414yes—
690C22×C4C22×Q814yes—
691C22×C4C22×Q814yes—
692C22×C4C2×#4114yes—
693C22×C4C2×#4114yes—
694C22×C4C2×#4114yes—
695C4⋊C4—416no—
696C4⋊C4—416no—
697C4⋊C4—416no—
698C4⋊C4—416no—
699C4⋊C4—416no—
700C4⋊C4—416no—
701C4⋊C4—416no—
702C4⋊C4—416no—
703C22⋊C4—232no—
704C22⋊C4—416no—
705C22⋊C4—416no—
706C22⋊C4—416no—
707C22⋊C4—416no—
708C22⋊C4C2×C4⋊C4164yescomplemented
709C42—232no—
710C42—416no—
711C23—232no—
712C23—232no—
713C23—232no—
714C23—24no—
715C23—24no—
716C23—24no—
717C23—24no—
718C23—24no—
719C23—24no—
720C23—24no—
721C23—24no—
722C23—24no—
723C23—24no—
724C23—24no—
725C23—24no—
726C23—24no—
727C23—24no—
728C23—24no—
729C23—24no—
730C23—24no—
731C23—24no—
732C23—416no—
733C23—416no—
734C23—416no—
735C23—416no—
736C23—416no—
737C23—416no—
738C23—42no—
739C23—42no—
740C23—42no—
741C23—42no—
742C23—42no—
743C23—42no—
744C23—42no—
745C23—42no—
746C23—42no—
747C23—42no—
748C23—416no—
749C23—42no—
750C23—42no—
751C23—416no—
752C23—416no—
753C23—416no—
754C23—42no—
755C23—42no—
756C23—42no—
757C23—42no—
758C23—416no—
759C23—416no—
760C23C22×C4⋊C418yes—
761C23C22×C4⋊C414yes—
762C23C2×C4×D414yes—
763C23C4×#4114yes—
764C23#51814yes—
765C23#52014yes—
766C23#52014yes—
767C23#52014yes—
768C23#53514yes—
769C23#53514yes—
770C23#53614yes—
771C23#53714yes—
772C23#53814yes—
773C23#53914yes—
774C23#54014yes—
775C23#54114yes—
776C23#54214yes—
777C23#54214yes—
778C23#54414yes—
779C23#54414yes—
780C23D4214yes—
781C23#54614yes—
782C23#54614yes—
783C23#54614yes—
784C23#54714yes—
785C23#54714yes—
786C23D4×Q814yes—
787C23#55114yes—
788C23#55214yes—
789C23#55414yes—
790C23#55414yes—
791C23#55414yes—
792C23H(3,𝔽4)14yes—
793C23#56214yes—
794C23#56214yes—
795C23#56314yes—
796C23C24×C411yescharacteristic
797C23C23×D411yescharacteristic
798C23C23×D411yescharacteristic
799C23C23×Q811yescharacteristic
800C23C22×#4111yescharacteristic
801C23C22×#4111yescharacteristic
802C23C22×#4111yescharacteristic
803C23C2×H(5,𝔽2)11yescharacteristic
804C23C2×H(5,𝔽2)11yescharacteristic
805C23C2×H(5,𝔽2)11yescharacteristic
806C23C2×H(5,𝔽2)11yescharacteristic
807C23C2×H(5,𝔽2)11yescharacteristic
808C23C2×2−1+411yescharacteristic
809C23C2×2−1+411yescharacteristic
810C23C2×2−1+411yescharacteristic
811C2×C4—232no—
812C2×C4—232no—
813C2×C4—232no—
814C2×C4—24no—
815C2×C4—24no—
816C2×C4—24no—
817C2×C4—24no—
818C2×C4—24no—
819C2×C4—24no—
820C2×C4—24no—
821C2×C4—24no—
822C2×C4—24no—
823C2×C4—24no—
824C2×C4—24no—
825C2×C4—24no—
826C2×C4—24no—
827C2×C4—24no—
828C2×C4—24no—
829C2×C4—24no—
830C2×C4—24no—
831C2×C4—24no—
832C2×C4—24no—
833C2×C4—24no—
834C2×C4—24no—
835C2×C4—24no—
836C2×C4—24no—
837C2×C4—24no—
838C2×C4—24no—
839C2×C4—24no—
840C2×C4—24no—
841C2×C4—24no—
842C2×C4—24no—
843C2×C4—24no—
844C2×C4—24no—
845C2×C4—24no—
846C2×C4—24no—
847C2×C4—24no—
848C2×C4—24no—
849C2×C4—24no—
850C2×C4—24no—
851C2×C4—24no—
852C2×C4—24no—
853C2×C4—464no—
854C2×C4—416no—
855C2×C4—416no—
856C2×C4—416no—
857C2×C4—416no—
858C2×C4—416no—
859C2×C4—416no—
860C2×C4—42no—
861C2×C4—42no—
862C2×C4—42no—
863C2×C4—42no—
864C2×C4—42no—
865C2×C4—42no—
866C2×C4—42no—
867C2×C4—42no—
868C2×C4—42no—
869C2×C4—42no—
870C2×C4—42no—
871C2×C4—42no—
872C2×C4—42no—
873C2×C4—42no—
874C2×C4—42no—
875C2×C4—42no—
876C2×C4—42no—
877C2×C4—42no—
878C2×C4—42no—
879C2×C4—42no—
880C2×C4—416no—
881C2×C4—42no—
882C2×C4—42no—
883C2×C4—42no—
884C2×C4—42no—
885C2×C4—42no—
886C2×C4—42no—
887C2×C4—42no—
888C2×C4—42no—
889C2×C4—42no—
890C2×C4—42no—
891C2×C4—42no—
892C2×C4—42no—
893C2×C4—42no—
894C2×C4—42no—
895C2×C4—42no—
896C2×C4—42no—
897C2×C4—42no—
898C2×C4—42no—
899C2×C4—42no—
900C2×C4—42no—
901C2×C4—42no—
902C2×C4—42no—
903C2×C4—42no—
904C2×C4—42no—
905C2×C4—42no—
906C2×C4—42no—
907C2×C4—42no—
908C2×C4—42no—
909C2×C4—42no—
910C2×C4—42no—
911C2×C4—42no—
912C2×C4—42no—
913C2×C4—42no—
914C2×C4—42no—
915C2×C4—42no—
916C2×C4—42no—
917C2×C4—88no—
918C2×C4—88no—
919C2×C4—88no—
920C2×C4—88no—
921C2×C4C22×C4⋊C418yes—
922C2×C4C22×C4⋊C418yes—
923C2×C4C2×C4×D418yes—
924C22—28no—
925C22—28no—
926C22—28no—
927C22—44no—
928C22—44no—
929C22—44no—
930C22—464no—
931C22—44no—
932C22—44no—
933C22—44no—
934C22—44no—
935C22—44no—
936C22—44no—
937C22—44no—
938C22—44no—
939C22—44no—
940C22#231718yes—
941C22#232418yes—
942C22#233418yes—
943C22D4×C4⋊C418yes—
944C22#234918yes—
945C22#235918yes—
946C22#237918yes—
947C22#267018yes—
948C22#267218yes—
949C22#269818yes—
950C22#270418yes—
951C22#270618yes—
952C22#272018yes—
953C22#276318yes—
954C22#276818yes—
955C22C23×C4⋊C411yescharacteristic
956C22C22×C4×D411yescharacteristic
957C22C2×C4×#4111yescharacteristic
958C22C2×#51811yescharacteristic
959C22C2×#52011yescharacteristic
960C22C2×#52011yescharacteristic
961C22C2×#52011yescharacteristic
962C22C2×#53511yescharacteristic
963C22C2×#53511yescharacteristic
964C22C2×#53611yescharacteristic
965C22C2×#53711yescharacteristic
966C22C2×#53811yescharacteristic
967C22C2×#53911yescharacteristic
968C22C2×#54011yescharacteristic
969C22C2×#54111yescharacteristic
970C22C2×#54211yescharacteristic
971C22C2×#54211yescharacteristic
972C22C2×#54411yescharacteristic
973C22C2×#54411yescharacteristic
974C22C2×D4211yescharacteristic
975C22C2×#54611yescharacteristic
976C22C2×#54611yescharacteristic
977C22C2×#54611yescharacteristic
978C22C2×#54711yescharacteristic
979C22C2×#54711yescharacteristic
980C22C2×D4×Q811yescharacteristic
981C22C2×#55111yescharacteristic
982C22C2×#55211yescharacteristic
983C22C2×#55411yescharacteristic
984C22C2×#55411yescharacteristic
985C22C2×#55411yescharacteristic
986C22C2×H(3,𝔽4)11yescharacteristic
987C22C2×#56211yescharacteristic
988C22C2×#56211yescharacteristic
989C22C2×#56311yescharacteristic
990C4—28no—
991C4—28no—
992C4—28no—
993C4—44no—
994C4—44no—
995C4—44no—
996C4—44no—
997C4—44no—
998C4—44no—
999C4—44no—
1000C4—82no—
1001C4—82no—
1002C4—82no—
1003C4—82no—
1004C2—48no—
1005C2#14403116yesdirect product factor
1006C2C2×#231711yescharacteristic
1007C2C2×#232411yescharacteristic
1008C2C2×#233411yescharacteristic
1009C2C2×D4×C4⋊C411yescharacteristic
1010C2C2×#234911yescharacteristic
1011C2C2×#235911yescharacteristic
1012C2C2×#237911yescharacteristic
1013C2C2×#267011yescharacteristic
1014C2C2×#267211yescharacteristic
1015C2C2×#269811yescharacteristic
1016C2C2×#270411yescharacteristic
1017C2C2×#270611yescharacteristic
1018C2C2×#272011yescharacteristic
1019C2C2×#276311yescharacteristic
1020C2C2×#276811yescharacteristic
subgroupG/H
center, socleC25C24
commutatorC23C24×C4
Frattini, cosocleC24C25
prime radicalC26C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C25 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
5. C22×#382C2semidirect
6. #14403C2direct (N × H)
7. C2×#1444C2semidirect
8. C2×#1444C2semidirect
9. C2×#1442C2semidirect
10. C2×#1441C2semidirect
13. C2×#1436C2semidirect
14. C2×C4⋊#95C2semidirect
15. C2×C4⋊#95C2semidirect
35. C2×#388C4semidirect
43. C2×#382C22semidirect
62. #1444C22semidirect
63. #1444C22semidirect
64. #1442C22semidirect
65. #1441C22semidirect
68. #1436C22semidirect
69. C4⋊#95C22semidirect
70. C4⋊#95C22semidirect
118. C22×C4⋊C4C2×C4semidirect
156. C22×C42C2×C4semidirect
160. #388C2×C4semidirect
179. C2×#95C2×C4semidirect
180. C2×#95C2×C4semidirect
374. C2×C4⋊C4C22×C4semidirect
393. C2×C22⋊C4C4⋊C4semidirect
406. C2×C42C22×C4semidirect
422. #95C22×C4semidirect
423. #95C22×C4semidirect
708. C22⋊C4C2×C4⋊C4semidirect
1005. C2#14403direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#3882
C22×#3852
C22×#3822
#144032
C2×#14442
C2×#14422
C2×#14412
C2×#14392
C2×#14362
C2×C4⋊#952
C2×C22⋊#952