Finite Group Databasebeta

← C2×#14315 #515136

Subgroups — C2×#14315 #515136

Order 512.

5026 conjugacy classes of subgroups.

The subgroup lattice has 1006 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#396C211yesmaximal, characteristic
2C22×#387C211yesmaximal, characteristic, complemented
3C22×C4×C22⋊C4C211yesmaximal, characteristic
4#14315C2116yesmaximal, direct product factor
5C2×#1445C211yesmaximal, characteristic, complemented
6C2×#1442C211yesmaximal, characteristic, complemented
7C2×#1441C211yesmaximal, characteristic, complemented
8C2×#1441C211yesmaximal, characteristic, complemented
9C2×#1439C211yesmaximal, characteristic
10C2×#1439C211yesmaximal, characteristic
11C2×#1439C211yesmaximal, characteristic
12C2×#1436C211yesmaximal, characteristic, complemented
13C2×#1436C211yesmaximal, characteristic, complemented
14C2×C4⋊#95C211yesmaximal, characteristic, complemented
15C2×C22⋊#95C211yesmaximal, characteristic
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×C22⋊C4C2211yescharacteristic
25C23×C22⋊C4C2211yescharacteristic
26C23×C22⋊C4C2211yescharacteristic
27C23×C22⋊C4C2211yescharacteristic
28C23×C22⋊C4C2211yescharacteristic
29C23×C22⋊C4C2211yescharacteristic
30C23×C42C2211yescharacteristic
31C23×C42C2211yescharacteristic
32C2×#396C4116yescomplemented
33C2×#396C2218yes—
34C2×#387—28no—
35C2×#387C2218yescomplemented
36C2×C4×C22⋊C4—28no—
37C2×C4×C22⋊C4C2218yes—
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
56C22×#95C2211yescharacteristic
57C22×#95C2211yescharacteristic
58#1445C2218yescomplemented
59#1442C2218yescomplemented
60#1441C2218yescomplemented
61#1441C2218yescomplemented
62#1439C2218yes—
63#1439C2218yes—
64#1439C2218yes—
65#1436C2218yescomplemented
66#1436C2218yescomplemented
67C4⋊#95C2218yescomplemented
68C22⋊#95C2218yes—
69C22⋊#95C2218yes—
70C26C2311yescharacteristic
71C24×C4—24no—
72C24×C4—24no—
73C24×C4—42no—
74C24×C4—42no—
75C24×C4—42no—
76C24×C4—42no—
77C24×C4Q818yes—
78C24×C4C2311yescharacteristic
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
92C24×C4C2314yes—
93C22×C4⋊C4—24no—
94C22×C4⋊C4—24no—
95C22×C4⋊C4—24no—
96C22×C4⋊C4—24no—
97C22×C4⋊C4—24no—
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⋊C4—42no—
105C22×C4⋊C4—42no—
106C22×C4⋊C4—42no—
107C22×C4⋊C4—42no—
108C22×C4⋊C4C2×C418yescomplemented
109C22×C4⋊C4C2×C418yescomplemented
110C22×C4⋊C4C2×C418yescomplemented
111C22×C4⋊C4C2314yes—
112C22×C4⋊C4C2314yes—
113C22×C4⋊C4C2314yes—
114C22×C4⋊C4C2314yes—
115C22×C4⋊C4C2314yes—
116C22×C4⋊C4C2314yes—
117C22×C22⋊C4—24no—
118C22×C22⋊C4—24no—
119C22×C22⋊C4—24no—
120C22×C22⋊C4—24no—
121C22×C22⋊C4—24no—
122C22×C22⋊C4—24no—
123C22×C22⋊C4—24no—
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⋊C4C2×C418yes—
133C22×C22⋊C4C2×C418yes—
134C22×C22⋊C4C2×C418yes—
135C22×C22⋊C4C2314yes—
136C22×C22⋊C4C2314yes—
137C22×C22⋊C4C2314yes—
138C22×C22⋊C4C2314yes—
139C22×C22⋊C4C2314yes—
140C22×C22⋊C4C2314yes—
141C22×C42—24no—
142C22×C42—42no—
143C22×C42—42no—
144C22×C42—42no—
145C22×C42—42no—
146C22×C42D418yes—
147C22×C42C2314yes—
148C22×C42C2314yes—
149#396C2×C4164yescomplemented
150#387—232no—
151C4×C22⋊C4—232no—
152C2×#95—24no—
153C2×#95—24no—
154C2×#95—24no—
155C2×#95—24no—
156C2×#95—24no—
157C2×#95—24no—
158C2×#95—24no—
159C2×#95—24no—
160C2×#95—24no—
161C2×#95—42no—
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×#95C2×C418yescomplemented
172C2×#95C2314yes—
173C2×#95C2314yes—
174C2×#95C2314yes—
175C2×#95C2314yes—
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—
192C25—22no—
193C25—22no—
194C25—22no—
195C25—22no—
196C25—22no—
197C25—22no—
198C25—22no—
199C25—22no—
200C25—22no—
201C25—22no—
202C25—22no—
203C25—22no—
204C25C22×C414yes—
205C25C2×Q814yes—
206C25#4114yes—
207C25C2412yes—
208C25C2411yescharacteristic
209C23×C4—22no—
210C23×C4—22no—
211C23×C4—22no—
212C23×C4—22no—
213C23×C4—22no—
214C23×C4—22no—
215C23×C4—22no—
216C23×C4—22no—
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—232no—
266C23×C4—28no—
267C23×C4—28no—
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—416no—
297C23×C4—416no—
298C23×C4—44no—
299C23×C4—44no—
300C23×C4—44no—
301C23×C4—44no—
302C23×C4—416no—
303C23×C4—416no—
304C23×C4—416no—
305C23×C4—416no—
306C23×C4C22×C414yes—
307C23×C4C22×C414yes—
308C23×C4C22×C414yes—
309C23×C4C22×C414yes—
310C23×C4C22×C414yes—
311C23×C4C22×C414yes—
312C23×C4C2×D414yes—
313C23×C4C2×D414yes—
314C23×C4C2×D414yes—
315C23×C4C2×Q814yes—
316C23×C4C2×Q814yes—
317C23×C4C2×Q8116yes—
318C23×C4#4114yes—
319C23×C4#4114yes—
320C23×C4#4114yes—
321C23×C4C2412yes—
322C23×C4C2412yes—
323C23×C4C2412yes—
324C23×C4C2412yes—
325C23×C4C2412yes—
326C23×C4C2412yes—
327C23×C4C2412yes—
328C23×C4C2412yes—
329C23×C4C2412yes—
330C23×C4C2412yes—
331C23×C4C2412yes—
332C23×C4C2412yes—
333C23×C4C2412yes—
334C23×C4C2412yes—
335C2×C4⋊C4—232no—
336C2×C4⋊C4—28no—
337C2×C4⋊C4—28no—
338C2×C4⋊C4—28no—
339C2×C4⋊C4—28no—
340C2×C4⋊C4—28no—
341C2×C4⋊C4—416no—
342C2×C4⋊C4—416no—
343C2×C4⋊C4—44no—
344C2×C4⋊C4—44no—
345C2×C4⋊C4—44no—
346C2×C4⋊C4—44no—
347C2×C4⋊C4—44no—
348C2×C4⋊C4—44no—
349C2×C4⋊C4—44no—
350C2×C4⋊C4—44no—
351C2×C4⋊C4—44no—
352C2×C4⋊C4—44no—
353C2×C4⋊C4—416no—
354C2×C4⋊C4—416no—
355C2×C4⋊C4—416no—
356C2×C4⋊C4C22×C4116yescomplemented
357C2×C4⋊C4C22×C4116yescomplemented
358C2×C4⋊C4C22×C4116yescomplemented
359C2×C22⋊C4—232no—
360C2×C22⋊C4—28no—
361C2×C22⋊C4—232no—
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—416no—
369C2×C22⋊C4—416no—
370C2×C22⋊C4—44no—
371C2×C22⋊C4—44no—
372C2×C22⋊C4—44no—
373C2×C22⋊C4—44no—
374C2×C22⋊C4—44no—
375C2×C22⋊C4—44no—
376C2×C22⋊C4—44no—
377C2×C22⋊C4—44no—
378C2×C22⋊C4—416no—
379C2×C22⋊C4—416no—
380C2×C22⋊C4C22×C4116yes—
381C2×C22⋊C4C22×C4116yes—
382C2×C22⋊C4C22×C4116yes—
383C2×C42—28no—
384C2×C42—416no—
385C2×C42—44no—
386C2×C42—44no—
387C2×C42—44no—
388C2×C42—44no—
389C2×C42—416no—
390C2×C42C2×D4116yes—
391#95—28no—
392#95—28no—
393#95—28no—
394#95—28no—
395#95—28no—
396#95—28no—
397#95—28no—
398#95—28no—
399#95—28no—
400#95—44no—
401#95—44no—
402#95—44no—
403#95—44no—
404#95—44no—
405#95—44no—
406#95—44no—
407#95—44no—
408#95—44no—
409#95—44no—
410#95C22×C4116yescomplemented
411C24—28no—
412C24—28no—
413C24—28no—
414C24—28no—
415C24—28no—
416C24—28no—
417C24—28no—
418C24—28no—
419C24—28no—
420C24—28no—
421C24—28no—
422C24—28no—
423C24—28no—
424C24—28no—
425C24—28no—
426C24—28no—
427C24—28no—
428C24—28no—
429C24—22no—
430C24—22no—
431C24—22no—
432C24—22no—
433C24—22no—
434C24—22no—
435C24—22no—
436C24—22no—
437C24—22no—
438C24—22no—
439C24—22no—
440C24—22no—
441C24—44no—
442C24—44no—
443C24—44no—
444C24—44no—
445C24—44no—
446C24—44no—
447C24—44no—
448C24—44no—
449C24—44no—
450C24—44no—
451C24—44no—
452C24—44no—
453C24—44no—
454C24—44no—
455C24—44no—
456C24—44no—
457C24C4×Q8116yes—
458C24C23×C414yes—
459C24C23×C412yes—
460C24C22×D412yes—
461C24C22×Q814yes—
462C24C22×Q812yes—
463C24C2×#4114yes—
464C24C2×#4112yes—
465C24C2×#4112yes—
466C24C2×#4112yes—
467C24C2×#4112yes—
468C24H(5,𝔽2)12yes—
469C24H(5,𝔽2)12yes—
470C24H(5,𝔽2)12yes—
471C24H(5,𝔽2)12yes—
472C24H(5,𝔽2)12yes—
473C24H(5,𝔽2)12yes—
474C242−1+412yes—
475C242−1+412yes—
476C24C2511yescharacteristic
477C22×C4—28no—
478C22×C4—28no—
479C22×C4—28no—
480C22×C4—28no—
481C22×C4—28no—
482C22×C4—28no—
483C22×C4—28no—
484C22×C4—28no—
485C22×C4—28no—
486C22×C4—28no—
487C22×C4—28no—
488C22×C4—28no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
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—28no—
510C22×C4—28no—
511C22×C4—28no—
512C22×C4—28no—
513C22×C4—28no—
514C22×C4—28no—
515C22×C4—28no—
516C22×C4—28no—
517C22×C4—28no—
518C22×C4—28no—
519C22×C4—28no—
520C22×C4—28no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
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—232no—
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—416no—
599C22×C4—416no—
600C22×C4—4128no—
601C22×C4—416no—
602C22×C4—416no—
603C22×C4—416no—
604C22×C4—416no—
605C22×C4—44no—
606C22×C4—44no—
607C22×C4—44no—
608C22×C4—44no—
609C22×C4—44no—
610C22×C4—44no—
611C22×C4—44no—
612C22×C4—44no—
613C22×C4—44no—
614C22×C4—44no—
615C22×C4—44no—
616C22×C4—44no—
617C22×C4—44no—
618C22×C4—44no—
619C22×C4—44no—
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×C4C4×D4116yes—
666C22×C4C22⋊Q8116yes—
667C22×C4C23×C414yes—
668C22×C4C23×C414yes—
669C22×C4C23×C414yes—
670C22×C4C23×C414yes—
671C22×C4C23×C414yes—
672C22×C4C23×C414yes—
673C22×C4C22×D414yes—
674C22×C4C22×D414yes—
675C22×C4C22×D414yes—
676C22×C4C22×Q814yes—
677C22×C4C22×Q814yes—
678C22×C4C2×#4114yes—
679C22×C4C2×#4114yes—
680C22×C4C2×#4114yes—
681C4⋊C4—232no—
682C4⋊C4—416no—
683C4⋊C4—416no—
684C4⋊C4—416no—
685C4⋊C4—416no—
686C4⋊C4—416no—
687C22⋊C4—232no—
688C22⋊C4—232no—
689C22⋊C4—416no—
690C22⋊C4—416no—
691C22⋊C4—416no—
692C22⋊C4—416no—
693C42—416no—
694C42—416no—
695C23—232no—
696C23—232no—
697C23—24no—
698C23—24no—
699C23—24no—
700C23—24no—
701C23—24no—
702C23—24no—
703C23—24no—
704C23—24no—
705C23—24no—
706C23—24no—
707C23—24no—
708C23—24no—
709C23—24no—
710C23—24no—
711C23—24no—
712C23—24no—
713C23—24no—
714C23—24no—
715C23—232no—
716C23—416no—
717C23—416no—
718C23—416no—
719C23—416no—
720C23—416no—
721C23—416no—
722C23—416no—
723C23—416no—
724C23—416no—
725C23—416no—
726C23—416no—
727C23—416no—
728C23—42no—
729C23—42no—
730C23—42no—
731C23—42no—
732C23—42no—
733C23—42no—
734C23—42no—
735C23—42no—
736C23—42no—
737C23—42no—
738C23—42no—
739C23—42no—
740C23—42no—
741C23—42no—
742C23—42no—
743C23—42no—
744C23C2×C4×D414yes—
745C23C2×C4×Q818yes—
746C23C2×C4×Q814yes—
747C23C4×#4114yes—
748C23#51814yes—
749C23#51814yes—
750C23#52014yes—
751C23#52014yes—
752C23C2×C22⋊Q814yes—
753C23#52514yes—
754C23#52914yes—
755C23#53314yes—
756C23#53414yes—
757C23#53514yes—
758C23#53714yes—
759C23#53714yes—
760C23#53814yes—
761C23#53814yes—
762C23#53814yes—
763C23#53814yes—
764C23#53814yes—
765C23#53814yes—
766C23#53914yes—
767C23#53914yes—
768C23#53914yes—
769C23#53914yes—
770C23#54014yes—
771C23#54014yes—
772C23#54014yes—
773C23#54114yes—
774C23#54214yes—
775C23#54214yes—
776C23#54314yes—
777C23#54314yes—
778C23#54414yes—
779C23#54414yes—
780C23C24×C411yescharacteristic
781C23C23×D411yescharacteristic
782C23C23×Q811yescharacteristic
783C23C22×#4111yescharacteristic
784C23C22×#4111yescharacteristic
785C23C22×#4111yescharacteristic
786C23C22×#4111yescharacteristic
787C23C2×H(5,𝔽2)11yescharacteristic
788C23C2×H(5,𝔽2)11yescharacteristic
789C23C2×H(5,𝔽2)11yescharacteristic
790C23C2×H(5,𝔽2)11yescharacteristic
791C23C2×H(5,𝔽2)11yescharacteristic
792C23C2×H(5,𝔽2)11yescharacteristic
793C23C2×2−1+411yescharacteristic
794C23C2×2−1+411yescharacteristic
795C2×C4—232no—
796C2×C4—232no—
797C2×C4—24no—
798C2×C4—24no—
799C2×C4—24no—
800C2×C4—24no—
801C2×C4—24no—
802C2×C4—24no—
803C2×C4—24no—
804C2×C4—24no—
805C2×C4—24no—
806C2×C4—24no—
807C2×C4—24no—
808C2×C4—24no—
809C2×C4—24no—
810C2×C4—24no—
811C2×C4—24no—
812C2×C4—24no—
813C2×C4—24no—
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—464no—
834C2×C4—416no—
835C2×C4—416no—
836C2×C4—416no—
837C2×C4—416no—
838C2×C4—416no—
839C2×C4—416no—
840C2×C4—416no—
841C2×C4—416no—
842C2×C4—42no—
843C2×C4—42no—
844C2×C4—42no—
845C2×C4—42no—
846C2×C4—42no—
847C2×C4—42no—
848C2×C4—42no—
849C2×C4—42no—
850C2×C4—42no—
851C2×C4—42no—
852C2×C4—42no—
853C2×C4—42no—
854C2×C4—42no—
855C2×C4—42no—
856C2×C4—42no—
857C2×C4—42no—
858C2×C4—42no—
859C2×C4—42no—
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—42no—
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—88no—
903C2×C4—88no—
904C2×C4—88no—
905C2×C4—88no—
906C2×C4C2×C4×D418yes—
907C2×C4C2×C22⋊Q818yes—
908C22—28no—
909C22—28no—
910C22—28no—
911C22—44no—
912C22—44no—
913C22—44no—
914C22—44no—
915C22—44no—
916C22—44no—
917C22—44no—
918C22—44no—
919C22—44no—
920C22—44no—
921C22—464no—
922C22—44no—
923C22—44no—
924C22C4×C22⋊Q818yes—
925C22#232418yes—
926C22#232518yes—
927C22#232918yes—
928C22#232918yes—
929C22#233318yes—
930C22#233418yes—
931C22#262618yes—
932C22#262918yes—
933C22#263018yes—
934C22#263618yes—
935C22#264818yes—
936C22#265218yes—
937C22#266518yes—
938C22#266718yes—
939C22C22×C4×D411yescharacteristic
940C22C22×C4×Q811yescharacteristic
941C22C2×C4×#4111yescharacteristic
942C22C2×#51811yescharacteristic
943C22C2×#51811yescharacteristic
944C22C2×#52011yescharacteristic
945C22C2×#52011yescharacteristic
946C22C22×C22⋊Q811yescharacteristic
947C22C2×#52511yescharacteristic
948C22C2×#52911yescharacteristic
949C22C2×#53311yescharacteristic
950C22C2×#53411yescharacteristic
951C22C2×#53511yescharacteristic
952C22C2×#53711yescharacteristic
953C22C2×#53711yescharacteristic
954C22C2×#53811yescharacteristic
955C22C2×#53811yescharacteristic
956C22C2×#53811yescharacteristic
957C22C2×#53811yescharacteristic
958C22C2×#53811yescharacteristic
959C22C2×#53811yescharacteristic
960C22C2×#53911yescharacteristic
961C22C2×#53911yescharacteristic
962C22C2×#53911yescharacteristic
963C22C2×#53911yescharacteristic
964C22C2×#54011yescharacteristic
965C22C2×#54011yescharacteristic
966C22C2×#54011yescharacteristic
967C22C2×#54111yescharacteristic
968C22C2×#54211yescharacteristic
969C22C2×#54211yescharacteristic
970C22C2×#54311yescharacteristic
971C22C2×#54311yescharacteristic
972C22C2×#54411yescharacteristic
973C22C2×#54411yescharacteristic
974C4—28no—
975C4—28no—
976C4—44no—
977C4—44no—
978C4—44no—
979C4—44no—
980C4—44no—
981C4—44no—
982C4—44no—
983C4—44no—
984C4—82no—
985C4—82no—
986C4—82no—
987C4—82no—
988C2—48no—
989C2#14315116yesdirect product factor
990C2C2×C4×C22⋊Q811yescharacteristic
991C2C2×#232411yescharacteristic
992C2C2×#232511yescharacteristic
993C2C2×#232911yescharacteristic
994C2C2×#232911yescharacteristic
995C2C2×#233311yescharacteristic
996C2C2×#233411yescharacteristic
997C2C2×#262611yescharacteristic
998C2C2×#263011yescharacteristic
999C2C2×#264811yescharacteristic
1000C2C2×#265211yescharacteristic
1001C2C2×#266511yescharacteristic
1002C2C2×#266711yescharacteristic
1003C2C2×#263611yescharacteristic
1004C2C2×#262911yescharacteristic
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
2. C22×#387C2semidirect
4. #14315C2direct (N × H)
5. C2×#1445C2semidirect
6. C2×#1442C2semidirect
7. C2×#1441C2semidirect
8. C2×#1441C2semidirect
12. C2×#1436C2semidirect
13. C2×#1436C2semidirect
14. C2×C4⋊#95C2semidirect
32. C2×#396C4semidirect
35. C2×#387C22semidirect
58. #1445C22semidirect
59. #1442C22semidirect
60. #1441C22semidirect
61. #1441C22semidirect
65. #1436C22semidirect
66. #1436C22semidirect
67. C4⋊#95C22semidirect
108. C22×C4⋊C4C2×C4semidirect
109. C22×C4⋊C4C2×C4semidirect
110. C22×C4⋊C4C2×C4semidirect
149. #396C2×C4semidirect
171. C2×#95C2×C4semidirect
356. C2×C4⋊C4C22×C4semidirect
357. C2×C4⋊C4C22×C4semidirect
358. C2×C4⋊C4C22×C4semidirect
410. #95C22×C4semidirect
989. C2#14315direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#3962
C22×#3872
C22×C4×C22⋊C42
#143152
C2×#14452
C2×#14422
C2×#14412
C2×#14392
C2×#14362
C2×C4⋊#952
C2×C22⋊#952