Finite Group Databasebeta

← C2×#15279 #608805

Subgroups — C2×#15279 #608805

Order 512.

6466 conjugacy classes of subgroups.

The subgroup lattice has 1052 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C22⋊Q8C211yesmaximal, characteristic
2C22×#398C211yesmaximal, characteristic, complemented
3C22×#395C211yesmaximal, characteristic, complemented
4C22×#391C211yesmaximal, characteristic, complemented
5C22×#388C211yesmaximal, characteristic
6C22×#385C211yesmaximal, characteristic
7#15279C2116yesmaximal, direct product factor
8C2×#1444C211yesmaximal, characteristic, complemented
9C2×#1442C211yesmaximal, characteristic, complemented
10C2×#1442C211yesmaximal, characteristic, complemented
11C2×#1441C211yesmaximal, characteristic, complemented
12C2×#1440C211yesmaximal, characteristic
13C2×#1439C211yesmaximal, characteristic
14C2×#1439C211yesmaximal, characteristic
15C2×#1436C211yesmaximal, characteristic, complemented
16C2×C22⋊#95C211yesmaximal, characteristic
17C24×Q8C2211yescharacteristic
18C25×C4C2211yescharacteristic
19C22×C22⋊Q8—28no—
20C22×C22⋊Q8—28no—
21C22×C22⋊Q8—28no—
22C22×C22⋊Q8C2218yes—
23C23×C4⋊C4C2211yescharacteristic
24C23×C4⋊C4C2211yescharacteristic
25C23×C4⋊C4C2211yescharacteristic
26C23×C4⋊C4C2211yescharacteristic
27C23×C4⋊C4C2211yescharacteristic
28C23×C4⋊C4C2211yescharacteristic
29C23×C4⋊C4C2211yescharacteristic
30C23×C4⋊C4C2211yescharacteristic
31C23×C22⋊C4C2211yescharacteristic
32C23×C22⋊C4C2211yescharacteristic
33C23×C22⋊C4C2211yescharacteristic
34C23×C22⋊C4C2211yescharacteristic
35C23×C22⋊C4C2211yescharacteristic
36C23×C22⋊C4C2211yescharacteristic
37C23×C42C2211yescharacteristic
38C2×#398—28no—
39C2×#398C2218yescomplemented
40C2×#395—28no—
41C2×#395C2218yescomplemented
42C2×#391—28no—
43C2×#391C2218yescomplemented
44C2×#388—28no—
45C2×#388C2218yes—
46C2×#385—28no—
47C2×#385C2218yes—
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
62C22×#95C2211yescharacteristic
63C22×#95C2211yescharacteristic
64C22×#95C2211yescharacteristic
65C22×#95C2211yescharacteristic
66#1444C2218yescomplemented
67#1442C2218yescomplemented
68#1442C2218yescomplemented
69#1441C2218yescomplemented
70#1440C2218yes—
71#1439C2218yes—
72#1439C2218yes—
73#1436C2218yescomplemented
74C22⋊#95C2218yes—
75C26C2311yescharacteristic
76C23×Q8—24no—
77C23×Q8—24no—
78C23×Q8—24no—
79C23×Q8—24no—
80C23×Q8—42no—
81C23×Q8—42no—
82C23×Q8D418yes—
83C23×Q8C2314yes—
84C24×C4—24no—
85C24×C4—24no—
86C24×C4—24no—
87C24×C4—24no—
88C24×C4—24no—
89C24×C4—42no—
90C24×C4—42no—
91C24×C4C2311yescharacteristic
92C24×C4C2311yescharacteristic
93C24×C4C2311yescharacteristic
94C24×C4C2311yescharacteristic
95C24×C4C2311yescharacteristic
96C24×C4C2311yescharacteristic
97C24×C4C2311yescharacteristic
98C24×C4C2311yescharacteristic
99C24×C4C2311yescharacteristic
100C24×C4C2311yescharacteristic
101C24×C4C2311yescharacteristic
102C24×C4C2311yescharacteristic
103C24×C4C2314yes—
104C24×C4C2311yescharacteristic
105C24×C4C2311yescharacteristic
106C2×C22⋊Q8—2128no—
107C2×C22⋊Q8—232no—
108C2×C22⋊Q8—232no—
109C2×C22⋊Q8—232no—
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—24no—
119C22×C4⋊C4—24no—
120C22×C4⋊C4—24no—
121C22×C4⋊C4—24no—
122C22×C4⋊C4—24no—
123C22×C4⋊C4—24no—
124C22×C4⋊C4—24no—
125C22×C4⋊C4—24no—
126C22×C4⋊C4—24no—
127C22×C4⋊C4—24no—
128C22×C4⋊C4—24no—
129C22×C4⋊C4—42no—
130C22×C4⋊C4—42no—
131C22×C4⋊C4—42no—
132C22×C4⋊C4—42no—
133C22×C4⋊C4D418yes—
134C22×C4⋊C4C2314yes—
135C22×C4⋊C4C2314yes—
136C22×C4⋊C4C2314yes—
137C22×C4⋊C4C2314yes—
138C22×C4⋊C4C2314yes—
139C22×C4⋊C4C2314yes—
140C22×C4⋊C4C2314yes—
141C22×C4⋊C4C2314yes—
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—24no—
149C22×C22⋊C4—24no—
150C22×C22⋊C4—24no—
151C22×C22⋊C4—24no—
152C22×C22⋊C4—24no—
153C22×C22⋊C4—24no—
154C22×C22⋊C4—24no—
155C22×C22⋊C4—24no—
156C22×C22⋊C4—42no—
157C22×C22⋊C4—42no—
158C22×C22⋊C4D418yes—
159C22×C22⋊C4Q818yescomplemented
160C22×C22⋊C4C2314yes—
161C22×C22⋊C4C2314yes—
162C22×C22⋊C4C2314yes—
163C22×C22⋊C4C2314yes—
164C22×C22⋊C4C2314yes—
165C22×C22⋊C4C2314yes—
166C22×C42—24no—
167C22×C42—24no—
168C22×C42—42no—
169C22×C42C2314yes—
170#398—232no—
171#395—232no—
172#391—232no—
173#388—232no—
174#385—232no—
175C2×#95—24no—
176C2×#95—24no—
177C2×#95—24no—
178C2×#95—24no—
179C2×#95—24no—
180C2×#95—24no—
181C2×#95—24no—
182C2×#95—24no—
183C2×#95—24no—
184C2×#95—24no—
185C2×#95—24no—
186C2×#95—24no—
187C2×#95—24no—
188C2×#95—24no—
189C2×#95—24no—
190C2×#95—24no—
191C2×#95—42no—
192C2×#95D418yes—
193C2×#95C2314yes—
194C2×#95C2314yes—
195C2×#95C2314yes—
196C2×#95C2314yes—
197C2×#95C2314yes—
198C2×#95C2314yes—
199C2×#95C2314yes—
200C2×#95C2314yes—
201C2×#95C2314yes—
202C2×#95C2314yes—
203C2×#95C2314yes—
204C2×#95C2314yes—
205C2×#95C2314yes—
206C2×#95C2314yes—
207C2×#95C2314yes—
208C2×#95C2314yes—
209C2×#95C2314yes—
210C2×#95C2314yes—
211C25—22no—
212C25—22no—
213C25—22no—
214C25—22no—
215C25—22no—
216C25—22no—
217C25—22no—
218C25—22no—
219C25—22no—
220C25—22no—
221C25—22no—
222C25—22no—
223C25C2×D414yes—
224C25C2×Q814yes—
225C25#4114yes—
226C25C2412yes—
227C25C2411yescharacteristic
228C22×Q8—232no—
229C22×Q8—232no—
230C22×Q8—28no—
231C22×Q8—28no—
232C22×Q8—28no—
233C22×Q8—28no—
234C22×Q8—416no—
235C22×Q8—44no—
236C22×Q8—44no—
237C22×Q8—416no—
238C22×Q8—416no—
239C22×Q8—416no—
240C22×Q8—416no—
241C22×Q8C2×D4116yes—
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—232no—
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—28no—
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—28no—
313C23×C4—28no—
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×C4—22no—
328C23×C4—28no—
329C23×C4—28no—
330C23×C4—44no—
331C23×C4—44no—
332C23×C4—416no—
333C23×C4—416no—
334C23×C4—416no—
335C23×C4—416no—
336C23×C4—416no—
337C23×C4—416no—
338C23×C4C2×D414yes—
339C23×C4C2×D414yes—
340C23×C4C2×D414yes—
341C23×C4C2×D414yes—
342C23×C4C2×D414yes—
343C23×C4C2×D414yes—
344C23×C4C2×D414yes—
345C23×C4C2×D414yes—
346C23×C4C2×D414yes—
347C23×C4C2×D414yes—
348C23×C4C2×D414yes—
349C23×C4C2×Q814yes—
350C23×C4C2×Q814yes—
351C23×C4#4114yes—
352C23×C4#4114yes—
353C23×C4#4114yes—
354C23×C4C2412yes—
355C23×C4C2412yes—
356C23×C4C2412yes—
357C23×C4C2412yes—
358C23×C4C2412yes—
359C23×C4C2412yes—
360C23×C4C2412yes—
361C23×C4C2412yes—
362C23×C4C2412yes—
363C23×C4C2412yes—
364C23×C4C2412yes—
365C23×C4C2412yes—
366C23×C4C2412yes—
367C23×C4C2412yes—
368C22⋊Q8—2256no—
369C2×C4⋊C4—232no—
370C2×C4⋊C4—232no—
371C2×C4⋊C4—232no—
372C2×C4⋊C4—28no—
373C2×C4⋊C4—28no—
374C2×C4⋊C4—28no—
375C2×C4⋊C4—28no—
376C2×C4⋊C4—28no—
377C2×C4⋊C4—28no—
378C2×C4⋊C4—28no—
379C2×C4⋊C4—28no—
380C2×C4⋊C4—28no—
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—28no—
390C2×C4⋊C4—28no—
391C2×C4⋊C4—44no—
392C2×C4⋊C4—44no—
393C2×C4⋊C4—44no—
394C2×C4⋊C4—44no—
395C2×C4⋊C4—416no—
396C2×C4⋊C4—416no—
397C2×C4⋊C4—416no—
398C2×C4⋊C4—416no—
399C2×C4⋊C4—416no—
400C2×C4⋊C4C2×D4116yes—
401C2×C22⋊C4—232no—
402C2×C22⋊C4—232no—
403C2×C22⋊C4—232no—
404C2×C22⋊C4—28no—
405C2×C22⋊C4—28no—
406C2×C22⋊C4—28no—
407C2×C22⋊C4—28no—
408C2×C22⋊C4—232no—
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—44no—
420C2×C22⋊C4—44no—
421C2×C22⋊C4—416no—
422C2×C22⋊C4—416no—
423C2×C22⋊C4C2×D4116yes—
424C2×C22⋊C4C2×Q8116yescomplemented
425C2×C42—28no—
426C2×C42—28no—
427C2×C42—44no—
428C2×C42—416no—
429#95—28no—
430#95—28no—
431#95—28no—
432#95—28no—
433#95—28no—
434#95—28no—
435#95—28no—
436#95—28no—
437#95—28no—
438#95—28no—
439#95—28no—
440#95—28no—
441#95—28no—
442#95—28no—
443#95—28no—
444#95—28no—
445#95—44no—
446#95C2×D4116yes—
447C24—28no—
448C24—28no—
449C24—28no—
450C24—28no—
451C24—28no—
452C24—28no—
453C24—28no—
454C24—28no—
455C24—28no—
456C24—28no—
457C24—28no—
458C24—28no—
459C24—28no—
460C24—28no—
461C24—28no—
462C24—28no—
463C24—28no—
464C24—28no—
465C24—22no—
466C24—22no—
467C24—22no—
468C24—22no—
469C24—22no—
470C24—22no—
471C24—22no—
472C24—22no—
473C24—22no—
474C24—22no—
475C24—22no—
476C24—22no—
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—
493C24C22⋊Q8116yes—
494C24C22×D414yes—
495C24C22×D412yes—
496C24C22×D412yes—
497C24C22×D412yes—
498C24C22×D412yes—
499C24C22×Q814yes—
500C24C22×Q812yes—
501C24C2×#4114yes—
502C24C2×#4112yes—
503C24C2×#4112yes—
504C24C2×#4112yes—
505C24C2×#4112yes—
506C24H(5,𝔽2)12yes—
507C24H(5,𝔽2)12yes—
508C242−1+412yes—
509C242−1+412yes—
510C242−1+412yes—
511C242−1+412yes—
512C24C2511yescharacteristic
513C2×Q8—232no—
514C2×Q8—232no—
515C2×Q8—416no—
516C2×Q8—4128no—
517C2×Q8—416no—
518C2×Q8—416no—
519C2×Q8—416no—
520C2×Q8—416no—
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—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—232no—
542C22×C4—28no—
543C22×C4—28no—
544C22×C4—28no—
545C22×C4—28no—
546C22×C4—28no—
547C22×C4—28no—
548C22×C4—28no—
549C22×C4—28no—
550C22×C4—28no—
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—28no—
567C22×C4—28no—
568C22×C4—28no—
569C22×C4—28no—
570C22×C4—28no—
571C22×C4—28no—
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—416no—
647C22×C4—416no—
648C22×C4—416no—
649C22×C4—416no—
650C22×C4—4128no—
651C22×C4—416no—
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—416no—
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#120116yes—
708C22×C4#121116yes—
709C22×C4C22×D414yes—
710C22×C4C22×D414yes—
711C22×C4C22×D414yes—
712C22×C4C22×D414yes—
713C22×C4C22×D414yes—
714C22×C4C22×D414yes—
715C22×C4C22×D414yes—
716C22×C4C22×D414yes—
717C22×C4C22×D414yes—
718C22×C4C22×D414yes—
719C22×C4C22×D414yes—
720C22×C4C22×Q814yes—
721C22×C4C22×Q814yes—
722C22×C4C2×#4114yes—
723C22×C4C2×#4114yes—
724C22×C4C2×#4114yes—
725C4⋊C4—232no—
726C4⋊C4—232no—
727C4⋊C4—232no—
728C4⋊C4—416no—
729C4⋊C4—416no—
730C4⋊C4—416no—
731C4⋊C4—416no—
732C4⋊C4—416no—
733C22⋊C4—232no—
734C22⋊C4—232no—
735C22⋊C4—232no—
736C22⋊C4—232no—
737C22⋊C4—416no—
738C22⋊C4—416no—
739C42—416no—
740C23—24no—
741C23—232no—
742C23—24no—
743C23—24no—
744C23—24no—
745C23—24no—
746C23—24no—
747C23—232no—
748C23—24no—
749C23—24no—
750C23—24no—
751C23—24no—
752C23—24no—
753C23—24no—
754C23—24no—
755C23—24no—
756C23—24no—
757C23—24no—
758C23—24no—
759C23—24no—
760C23—232no—
761C23—42no—
762C23—416no—
763C23—42no—
764C23—416no—
765C23—42no—
766C23—42no—
767C23—42no—
768C23—416no—
769C23—42no—
770C23—416no—
771C23—42no—
772C23—42no—
773C23—416no—
774C23—416no—
775C23—42no—
776C23—42no—
777C23—42no—
778C23—42no—
779C23—42no—
780C23—416no—
781C23—42no—
782C23—416no—
783C23—416no—
784C23—416no—
785C23—42no—
786C23—42no—
787C23—416no—
788C23—416no—
789C23C2×#12014yes—
790C23C2×#12114yes—
791C23C2×C22⋊Q818yes—
792C23C2×C22⋊Q814yes—
793C23#52514yes—
794C23#53214yes—
795C23#53314yes—
796C23#53414yes—
797C23#53614yes—
798C23#53614yes—
799C23#53614yes—
800C23#53914yes—
801C23#53914yes—
802C23#54114yes—
803C23#54214yes—
804C23#54414yes—
805C23D4214yes—
806C23D4214yes—
807C23#54614yes—
808C23#54614yes—
809C23#54714yes—
810C23#54714yes—
811C23#54714yes—
812C23#54814yes—
813C23#54814yes—
814C23#54814yes—
815C23#54814yes—
816C23D4×Q814yes—
817C23D4×Q814yes—
818C23D4×Q814yes—
819C23#55114yes—
820C23#55214yes—
821C23#55214yes—
822C23#55414yes—
823C23#56314yes—
824C23#56314yes—
825C23C23×D411yescharacteristic
826C23C23×D411yescharacteristic
827C23C23×D411yescharacteristic
828C23C23×D411yescharacteristic
829C23C23×Q811yescharacteristic
830C23C22×#4111yescharacteristic
831C23C22×#4111yescharacteristic
832C23C22×#4111yescharacteristic
833C23C22×#4111yescharacteristic
834C23C2×H(5,𝔽2)11yescharacteristic
835C23C2×H(5,𝔽2)11yescharacteristic
836C23C2×2−1+411yescharacteristic
837C23C2×2−1+411yescharacteristic
838C23C2×2−1+411yescharacteristic
839C23C2×2−1+411yescharacteristic
840Q8—464no—
841C2×C4—24no—
842C2×C4—24no—
843C2×C4—232no—
844C2×C4—232no—
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—24no—
854C2×C4—24no—
855C2×C4—24no—
856C2×C4—24no—
857C2×C4—24no—
858C2×C4—24no—
859C2×C4—24no—
860C2×C4—24no—
861C2×C4—24no—
862C2×C4—24no—
863C2×C4—24no—
864C2×C4—24no—
865C2×C4—24no—
866C2×C4—24no—
867C2×C4—24no—
868C2×C4—24no—
869C2×C4—24no—
870C2×C4—24no—
871C2×C4—24no—
872C2×C4—24no—
873C2×C4—24no—
874C2×C4—24no—
875C2×C4—24no—
876C2×C4—24no—
877C2×C4—24no—
878C2×C4—24no—
879C2×C4—24no—
880C2×C4—24no—
881C2×C4—24no—
882C2×C4—24no—
883C2×C4—24no—
884C2×C4—24no—
885C2×C4—464no—
886C2×C4—42no—
887C2×C4—42no—
888C2×C4—42no—
889C2×C4—416no—
890C2×C4—416no—
891C2×C4—416no—
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—416no—
902C2×C4—42no—
903C2×C4—42no—
904C2×C4—42no—
905C2×C4—42no—
906C2×C4—416no—
907C2×C4—416no—
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—42no—
918C2×C4—42no—
919C2×C4—42no—
920C2×C4—42no—
921C2×C4—42no—
922C2×C4—42no—
923C2×C4—42no—
924C2×C4—42no—
925C2×C4—42no—
926C2×C4—42no—
927C2×C4—42no—
928C2×C4—42no—
929C2×C4—42no—
930C2×C4—416no—
931C2×C4—416no—
932C2×C4—416no—
933C2×C4—42no—
934C2×C4—42no—
935C2×C4—416no—
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—88no—
951C2×C4—88no—
952C2×C4C2×#12018yes—
953C2×C4C2×#12118yes—
954C22—28no—
955C22—28no—
956C22—28no—
957C22—44no—
958C22—44no—
959C22—44no—
960C22—44no—
961C22—44no—
962C22—44no—
963C22—44no—
964C22—44no—
965C22—44no—
966C22—44no—
967C22—464no—
968C22—44no—
969C22—44no—
970C22#240918yes—
971C22#241018yes—
972C22#242918yes—
973C22#243218yes—
974C22#243818yes—
975C22#244918yes—
976C22#246118yes—
977C22#253618yes—
978C22#255618yes—
979C22#267718yes—
980C22#268018yes—
981C22#269018yes—
982C22#269818yes—
983C22#272818yes—
984C22#272918yes—
985C22C22×#12011yescharacteristic
986C22C22×#12111yescharacteristic
987C22C22×C22⋊Q811yescharacteristic
988C22C2×#52511yescharacteristic
989C22C2×#53211yescharacteristic
990C22C2×#53311yescharacteristic
991C22C2×#53411yescharacteristic
992C22C2×#53611yescharacteristic
993C22C2×#53611yescharacteristic
994C22C2×#53611yescharacteristic
995C22C2×#53911yescharacteristic
996C22C2×#53911yescharacteristic
997C22C2×#54111yescharacteristic
998C22C2×#54211yescharacteristic
999C22C2×#54411yescharacteristic
1000C22C2×D4211yescharacteristic
1001C22C2×D4211yescharacteristic
1002C22C2×#54611yescharacteristic
1003C22C2×#54611yescharacteristic
1004C22C2×#54711yescharacteristic
1005C22C2×#54711yescharacteristic
1006C22C2×#54711yescharacteristic
1007C22C2×#54811yescharacteristic
1008C22C2×#54811yescharacteristic
1009C22C2×#54811yescharacteristic
1010C22C2×#54811yescharacteristic
1011C22C2×D4×Q811yescharacteristic
1012C22C2×D4×Q811yescharacteristic
1013C22C2×D4×Q811yescharacteristic
1014C22C2×#55111yescharacteristic
1015C22C2×#55211yescharacteristic
1016C22C2×#55211yescharacteristic
1017C22C2×#55411yescharacteristic
1018C22C2×#56311yescharacteristic
1019C22C2×#56311yescharacteristic
1020C4—28no—
1021C4—28no—
1022C4—44no—
1023C4—44no—
1024C4—44no—
1025C4—44no—
1026C4—44no—
1027C4—44no—
1028C4—44no—
1029C4—44no—
1030C4—44no—
1031C4—44no—
1032C4—82no—
1033C4—82no—
1034C2—48no—
1035C2#15279116yesdirect product factor
1036C2C2×#241011yescharacteristic
1037C2C2×#244911yescharacteristic
1038C2C2×#246111yescharacteristic
1039C2C2×#240911yescharacteristic
1040C2C2×#242911yescharacteristic
1041C2C2×#243211yescharacteristic
1042C2C2×#243811yescharacteristic
1043C2C2×#255611yescharacteristic
1044C2C2×#253611yescharacteristic
1045C2C2×#267711yescharacteristic
1046C2C2×#268011yescharacteristic
1047C2C2×#269011yescharacteristic
1048C2C2×#269811yescharacteristic
1049C2C2×#272811yescharacteristic
1050C2C2×#272911yescharacteristic
subgroupG/H
center, socleC25C24
commutator, Frattini, cosocleC24C25
prime radicalC26C23
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C25 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C22×#398C2semidirect
3. C22×#395C2semidirect
4. C22×#391C2semidirect
7. #15279C2direct (N × H)
8. C2×#1444C2semidirect
9. C2×#1442C2semidirect
10. C2×#1442C2semidirect
11. C2×#1441C2semidirect
15. C2×#1436C2semidirect
39. C2×#398C22semidirect
41. C2×#395C22semidirect
43. C2×#391C22semidirect
66. #1444C22semidirect
67. #1442C22semidirect
68. #1442C22semidirect
69. #1441C22semidirect
73. #1436C22semidirect
159. C22×C22⋊C4Q8semidirect
424. C2×C22⋊C4C2×Q8semidirect
1035. C2#15279direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C22⋊Q82
C22×#3982
C22×#3952
C22×#3912
C22×#3882
C22×#3852
#152792
C2×#14442
C2×#14422
C2×#14412
C2×#14402
C2×#14392
C2×#14362
C2×C22⋊#952