Finite Group Databasebeta

← C2×#14405 #520709

Subgroups — C2×#14405 #520709

Order 512.

5730 conjugacy classes of subgroups.

The subgroup lattice has 1038 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#389C211yesmaximal, characteristic, complemented
2C22×#388C211yesmaximal, characteristic
3C22×#388C211yesmaximal, characteristic
4C22×#385C211yesmaximal, characteristic
5C22×#385C211yesmaximal, characteristic
6C22×#385C211yesmaximal, characteristic
7C22×#384C211yesmaximal, characteristic, complemented
8#14405C2116yesmaximal, direct product factor
9C2×#1444C211yesmaximal, characteristic, complemented
10C2×#1444C211yesmaximal, characteristic, complemented
11C2×#1442C211yesmaximal, characteristic, complemented
12C2×#1441C211yesmaximal, characteristic, complemented
13C2×#1439C211yesmaximal, characteristic
14C2×#1439C211yesmaximal, characteristic
15C2×#1436C211yesmaximal, characteristic, complemented
16C2×#1434C211yesmaximal, characteristic, complemented
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×C4⋊C4C2211yescharacteristic
27C23×C4⋊C4C2211yescharacteristic
28C23×C22⋊C4C2211yescharacteristic
29C23×C22⋊C4C2211yescharacteristic
30C23×C22⋊C4C2211yescharacteristic
31C23×C22⋊C4C2211yescharacteristic
32C23×C22⋊C4C2211yescharacteristic
33C23×C22⋊C4C2211yescharacteristic
34C23×C42C2211yescharacteristic
35C23×C42C2211yescharacteristic
36C2×#389—28no—
37C2×#389C2218yescomplemented
38C2×#388—28no—
39C2×#388C4116yescomplemented
40C2×#388C2218yes—
41C2×#388C2218yes—
42C2×#385—28no—
43C2×#385—28no—
44C2×#385—28no—
45C2×#385C2218yes—
46C2×#385C2218yes—
47C2×#385C2218yes—
48C2×#384—28no—
49C2×#384C2218yescomplemented
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#1444C2218yescomplemented
68#1442C2218yescomplemented
69#1441C2218yescomplemented
70#1439C2218yes—
71#1439C2218yes—
72#1436C2218yescomplemented
73#1434C2218yescomplemented
74C26C2311yescharacteristic
75C24×C4—24no—
76C24×C4—24no—
77C24×C4—24no—
78C24×C4—42no—
79C24×C4—42no—
80C24×C4—42no—
81C24×C4—42no—
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×C4C2311yescharacteristic
95C24×C4C2311yescharacteristic
96C24×C4C2314yes—
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—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⋊C4—42no—
118C22×C4⋊C4—42no—
119C22×C4⋊C4—42no—
120C22×C4⋊C4—42no—
121C22×C4⋊C4—42no—
122C22×C4⋊C4—42no—
123C22×C4⋊C4—42no—
124C22×C4⋊C4—42no—
125C22×C4⋊C4C2×C418yescomplemented
126C22×C4⋊C4D418yes—
127C22×C4⋊C4C2314yes—
128C22×C4⋊C4C2314yes—
129C22×C4⋊C4C2314yes—
130C22×C4⋊C4C2314yes—
131C22×C4⋊C4C2314yes—
132C22×C4⋊C4C2314yes—
133C22×C4⋊C4C2314yes—
134C22×C4⋊C4C2314yes—
135C22×C4⋊C4C2314yes—
136C22×C4⋊C4C2314yes—
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—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⋊C4Q818yes—
155C22×C22⋊C4C2314yes—
156C22×C22⋊C4C2314yes—
157C22×C22⋊C4C2314yes—
158C22×C22⋊C4C2314yes—
159C22×C22⋊C4C2314yes—
160C22×C22⋊C4C2314yes—
161C22×C42—24no—
162C22×C42—24no—
163C22×C42—24no—
164C22×C42—24no—
165C22×C42—42no—
166C22×C42C2×C418yescomplemented
167C22×C42C2314yes—
168C22×C42C2314yes—
169#389—232no—
170#388—232no—
171#388C2×C4164yescomplemented
172#385—232no—
173#385—232no—
174#385—232no—
175#384—232no—
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—42no—
187C2×#95—42no—
188C2×#95—42no—
189C2×#95C2×C418yescomplemented
190C2×#95C2×C418yescomplemented
191C2×#95D418yes—
192C2×#95C2314yes—
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—
208C25—22no—
209C25—22no—
210C25—22no—
211C25—22no—
212C25—22no—
213C25—22no—
214C25—22no—
215C25—22no—
216C25—22no—
217C25—22no—
218C25—22no—
219C25—22no—
220C25C22×C414yes—
221C25C2×D414yes—
222C25C2×Q814yes—
223C25C2412yes—
224C25C2411yescharacteristic
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—22no—
279C23×C4—22no—
280C23×C4—22no—
281C23×C4—22no—
282C23×C4—22no—
283C23×C4—22no—
284C23×C4—22no—
285C23×C4—22no—
286C23×C4—28no—
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—28no—
307C23×C4—28no—
308C23×C4—44no—
309C23×C4—44no—
310C23×C4—44no—
311C23×C4—44no—
312C23×C4—416no—
313C23×C4—416no—
314C23×C4—416no—
315C23×C4—416no—
316C23×C4—416no—
317C23×C4—416no—
318C23×C4—416no—
319C23×C4C22×C414yes—
320C23×C4C22×C414yes—
321C23×C4C22×C414yes—
322C23×C4C22×C414yes—
323C23×C4C22×C414yes—
324C23×C4C22×C414yes—
325C23×C4C2×D414yes—
326C23×C4C2×D414yes—
327C23×C4C2×D414yes—
328C23×C4C2×D414yes—
329C23×C4C2×D414yes—
330C23×C4C2×D414yes—
331C23×C4C2×D414yes—
332C23×C4C2×D414yes—
333C23×C4C2×Q814yes—
334C23×C4C2×Q814yes—
335C23×C4#4114yes—
336C23×C4#4114yes—
337C23×C4C2412yes—
338C23×C4C2412yes—
339C23×C4C2412yes—
340C23×C4C2412yes—
341C23×C4C2412yes—
342C23×C4C2412yes—
343C23×C4C2412yes—
344C23×C4C2412yes—
345C23×C4C2412yes—
346C23×C4C2412yes—
347C23×C4C2412yes—
348C23×C4C2412yes—
349C23×C4C2412yes—
350C23×C4C2412yes—
351C2×C4⋊C4—232no—
352C2×C4⋊C4—28no—
353C2×C4⋊C4—28no—
354C2×C4⋊C4—28no—
355C2×C4⋊C4—28no—
356C2×C4⋊C4—28no—
357C2×C4⋊C4—28no—
358C2×C4⋊C4—28no—
359C2×C4⋊C4—28no—
360C2×C4⋊C4—28no—
361C2×C4⋊C4—28no—
362C2×C4⋊C4—28no—
363C2×C4⋊C4—28no—
364C2×C4⋊C4—28no—
365C2×C4⋊C4—28no—
366C2×C4⋊C4—28no—
367C2×C4⋊C4—28no—
368C2×C4⋊C4—416no—
369C2×C4⋊C4—44no—
370C2×C4⋊C4—44no—
371C2×C4⋊C4—44no—
372C2×C4⋊C4—44no—
373C2×C4⋊C4—44no—
374C2×C4⋊C4—44no—
375C2×C4⋊C4—44no—
376C2×C4⋊C4—44no—
377C2×C4⋊C4—44no—
378C2×C4⋊C4—44no—
379C2×C4⋊C4—44no—
380C2×C4⋊C4—44no—
381C2×C4⋊C4—416no—
382C2×C4⋊C4—416no—
383C2×C4⋊C4—416no—
384C2×C4⋊C4—416no—
385C2×C4⋊C4—416no—
386C2×C4⋊C4—416no—
387C2×C4⋊C4—416no—
388C2×C4⋊C4—416no—
389C2×C4⋊C4C22×C4116yescomplemented
390C2×C4⋊C4C2×D4116yes—
391C2×C22⋊C4—232no—
392C2×C22⋊C4—232no—
393C2×C22⋊C4—28no—
394C2×C22⋊C4—28no—
395C2×C22⋊C4—28no—
396C2×C22⋊C4—28no—
397C2×C22⋊C4—28no—
398C2×C22⋊C4—28no—
399C2×C22⋊C4—28no—
400C2×C22⋊C4—28no—
401C2×C22⋊C4—28no—
402C2×C22⋊C4—44no—
403C2×C22⋊C4—44no—
404C2×C22⋊C4—44no—
405C2×C22⋊C4—44no—
406C2×C22⋊C4—416no—
407C2×C22⋊C4—416no—
408C2×C22⋊C4—416no—
409C2×C22⋊C4C4⋊C4164yescomplemented
410C2×C22⋊C4C22×C4116yes—
411C2×C22⋊C4C22×C4116yes—
412C2×C22⋊C4C22×C4116yes—
413C2×C22⋊C4C2×D4116yes—
414C2×C22⋊C4C2×Q8116yes—
415C2×C42—232no—
416C2×C42—28no—
417C2×C42—28no—
418C2×C42—28no—
419C2×C42—28no—
420C2×C42—44no—
421C2×C42—416no—
422C2×C42C22×C4116yescomplemented
423#95—28no—
424#95—28no—
425#95—28no—
426#95—28no—
427#95—28no—
428#95—28no—
429#95—28no—
430#95—28no—
431#95—28no—
432#95—28no—
433#95—44no—
434#95—44no—
435#95—44no—
436#95C22×C4116yescomplemented
437#95C22×C4116yescomplemented
438#95C2×D4116yes—
439C24—28no—
440C24—28no—
441C24—28no—
442C24—28no—
443C24—28no—
444C24—28no—
445C24—28no—
446C24—28no—
447C24—28no—
448C24—28no—
449C24—28no—
450C24—28no—
451C24—28no—
452C24—28no—
453C24—28no—
454C24—28no—
455C24—28no—
456C24—28no—
457C24—22no—
458C24—22no—
459C24—22no—
460C24—22no—
461C24—22no—
462C24—22no—
463C24—22no—
464C24—22no—
465C24—22no—
466C24—22no—
467C24—22no—
468C24—22no—
469C24—44no—
470C24—44no—
471C24—44no—
472C24—44no—
473C24—44no—
474C24—44no—
475C24—44no—
476C24—44no—
477C24—44no—
478C24—44no—
479C24—44no—
480C24—44no—
481C24—44no—
482C24—44no—
483C24—44no—
484C24—44no—
485C24C2×C4⋊C4116yes—
486C24C23×C414yes—
487C24C23×C412yes—
488C24C22×D414yes—
489C24C22×D412yes—
490C24C22×D412yes—
491C24C22×D412yes—
492C24C22×Q814yes—
493C24C22×Q812yes—
494C24C2×#4112yes—
495C24C2×#4112yes—
496C24H(5,𝔽2)12yes—
497C24H(5,𝔽2)12yes—
498C24H(5,𝔽2)12yes—
499C24H(5,𝔽2)12yes—
500C242−1+412yes—
501C242−1+412yes—
502C242−1+412yes—
503C242−1+412yes—
504C24C2511yescharacteristic
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—28no—
522C22×C4—28no—
523C22×C4—28no—
524C22×C4—28no—
525C22×C4—28no—
526C22×C4—28no—
527C22×C4—28no—
528C22×C4—28no—
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—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—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—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—416no—
628C22×C4—416no—
629C22×C4—416no—
630C22×C4—416no—
631C22×C4—416no—
632C22×C4—416no—
633C22×C4—4128no—
634C22×C4—416no—
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×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×C4C2×C4⋊C4116yes—
688C22×C4C2×C4⋊C4116yes—
689C22×C4C4×D4116yes—
690C22×C4C4×D4116yes—
691C22×C4C23×C414yes—
692C22×C4C23×C414yes—
693C22×C4C23×C414yes—
694C22×C4C23×C414yes—
695C22×C4C23×C414yes—
696C22×C4C23×C414yes—
697C22×C4C22×D414yes—
698C22×C4C22×D414yes—
699C22×C4C22×D414yes—
700C22×C4C22×D414yes—
701C22×C4C22×D414yes—
702C22×C4C22×D414yes—
703C22×C4C22×D414yes—
704C22×C4C22×D414yes—
705C22×C4C22×Q814yes—
706C22×C4C22×Q814yes—
707C22×C4C2×#4114yes—
708C22×C4C2×#4114yes—
709C4⋊C4—232no—
710C4⋊C4—416no—
711C4⋊C4—416no—
712C4⋊C4—416no—
713C4⋊C4—416no—
714C4⋊C4—416no—
715C4⋊C4—416no—
716C4⋊C4—416no—
717C4⋊C4—416no—
718C4⋊C4—416no—
719C22⋊C4—232no—
720C22⋊C4—232no—
721C22⋊C4—416no—
722C22⋊C4—416no—
723C22⋊C4—416no—
724C22⋊C4C2×C4⋊C4164yescomplemented
725C42—232no—
726C42—416no—
727C23—232no—
728C23—232no—
729C23—232no—
730C23—24no—
731C23—24no—
732C23—24no—
733C23—24no—
734C23—24no—
735C23—24no—
736C23—24no—
737C23—24no—
738C23—24no—
739C23—24no—
740C23—24no—
741C23—24no—
742C23—24no—
743C23—24no—
744C23—24no—
745C23—24no—
746C23—24no—
747C23—24no—
748C23—416no—
749C23—416no—
750C23—416no—
751C23—416no—
752C23—416no—
753C23—416no—
754C23—416no—
755C23—42no—
756C23—42no—
757C23—42no—
758C23—42no—
759C23—416no—
760C23—42no—
761C23—42no—
762C23—42no—
763C23—42no—
764C23—42no—
765C23—42no—
766C23—42no—
767C23—42no—
768C23—416no—
769C23—416no—
770C23—416no—
771C23—42no—
772C23—42no—
773C23—42no—
774C23—42no—
775C23—416no—
776C23C22×C4⋊C418yes—
777C23C22×C4⋊C414yes—
778C23C2×C4×D414yes—
779C23C2×C4×D414yes—
780C23#52014yes—
781C23#52014yes—
782C23#52014yes—
783C23#52014yes—
784C23#53414yes—
785C23#53514yes—
786C23#53514yes—
787C23#53614yes—
788C23#53614yes—
789C23#53614yes—
790C23#53914yes—
791C23#53914yes—
792C23#54214yes—
793C23#54214yes—
794C23#54414yes—
795C23#54414yes—
796C23D4214yes—
797C23D4214yes—
798C23D4214yes—
799C23#54714yes—
800C23#54714yes—
801C23#54714yes—
802C23#54814yes—
803C23D4×Q814yes—
804C23D4×Q814yes—
805C23#55314yes—
806C23#55414yes—
807C23#55414yes—
808C23#56014yes—
809C23#56314yes—
810C23#56314yes—
811C23#56314yes—
812C23C24×C411yescharacteristic
813C23C23×D411yescharacteristic
814C23C23×D411yescharacteristic
815C23C23×D411yescharacteristic
816C23C23×Q811yescharacteristic
817C23C22×#4111yescharacteristic
818C23C22×#4111yescharacteristic
819C23C2×H(5,𝔽2)11yescharacteristic
820C23C2×H(5,𝔽2)11yescharacteristic
821C23C2×H(5,𝔽2)11yescharacteristic
822C23C2×H(5,𝔽2)11yescharacteristic
823C23C2×2−1+411yescharacteristic
824C23C2×2−1+411yescharacteristic
825C23C2×2−1+411yescharacteristic
826C23C2×2−1+411yescharacteristic
827C2×C4—232no—
828C2×C4—232no—
829C2×C4—232no—
830C2×C4—232no—
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—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—464no—
874C2×C4—416no—
875C2×C4—416no—
876C2×C4—416no—
877C2×C4—416no—
878C2×C4—416no—
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—416no—
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—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—42no—
931C2×C4—42no—
932C2×C4—88no—
933C2×C4—88no—
934C2×C4—88no—
935C2×C4—88no—
936C2×C4C22×C4⋊C418yes—
937C2×C4C22×C4⋊C418yes—
938C2×C4C2×C4×D418yes—
939C2×C4C2×C4×D418yes—
940C22—28no—
941C22—28no—
942C22—28no—
943C22—44no—
944C22—44no—
945C22—44no—
946C22—44no—
947C22—464no—
948C22—44no—
949C22—44no—
950C22—44no—
951C22—44no—
952C22—44no—
953C22—44no—
954C22—44no—
955C22—44no—
956C22#231718yes—
957C22#232218yes—
958C22#232618yes—
959C22D4×C4⋊C418yes—
960C22D4×C4⋊C418yes—
961C22#236118yes—
962C22#238318yes—
963C22#266918yes—
964C22#267418yes—
965C22#267718yes—
966C22#268018yes—
967C22#271818yes—
968C22#272018yes—
969C22#272918yes—
970C22#279018yes—
971C22C23×C4⋊C411yescharacteristic
972C22C22×C4×D411yescharacteristic
973C22C22×C4×D411yescharacteristic
974C22C2×#52011yescharacteristic
975C22C2×#52011yescharacteristic
976C22C2×#52011yescharacteristic
977C22C2×#52011yescharacteristic
978C22C2×#53411yescharacteristic
979C22C2×#53511yescharacteristic
980C22C2×#53511yescharacteristic
981C22C2×#53611yescharacteristic
982C22C2×#53611yescharacteristic
983C22C2×#53611yescharacteristic
984C22C2×#53911yescharacteristic
985C22C2×#53911yescharacteristic
986C22C2×#54211yescharacteristic
987C22C2×#54211yescharacteristic
988C22C2×#54411yescharacteristic
989C22C2×#54411yescharacteristic
990C22C2×D4211yescharacteristic
991C22C2×D4211yescharacteristic
992C22C2×D4211yescharacteristic
993C22C2×#54711yescharacteristic
994C22C2×#54711yescharacteristic
995C22C2×#54711yescharacteristic
996C22C2×#54811yescharacteristic
997C22C2×D4×Q811yescharacteristic
998C22C2×D4×Q811yescharacteristic
999C22C2×#55311yescharacteristic
1000C22C2×#55411yescharacteristic
1001C22C2×#55411yescharacteristic
1002C22C2×#56011yescharacteristic
1003C22C2×#56311yescharacteristic
1004C22C2×#56311yescharacteristic
1005C22C2×#56311yescharacteristic
1006C4—28no—
1007C4—28no—
1008C4—28no—
1009C4—28no—
1010C4—44no—
1011C4—44no—
1012C4—44no—
1013C4—44no—
1014C4—44no—
1015C4—44no—
1016C4—82no—
1017C4—82no—
1018C4—82no—
1019C4—82no—
1020C2—48no—
1021C2#14405116yesdirect product factor
1022C2C2×#231711yescharacteristic
1023C2C2×#232211yescharacteristic
1024C2C2×#232611yescharacteristic
1025C2C2×D4×C4⋊C411yescharacteristic
1026C2C2×D4×C4⋊C411yescharacteristic
1027C2C2×#236111yescharacteristic
1028C2C2×#238311yescharacteristic
1029C2C2×#266911yescharacteristic
1030C2C2×#267411yescharacteristic
1031C2C2×#267711yescharacteristic
1032C2C2×#268011yescharacteristic
1033C2C2×#271811yescharacteristic
1034C2C2×#272011yescharacteristic
1035C2C2×#272911yescharacteristic
1036C2C2×#279011yescharacteristic
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
1. C22×#389C2semidirect
7. C22×#384C2semidirect
8. #14405C2direct (N × H)
9. C2×#1444C2semidirect
10. C2×#1444C2semidirect
11. C2×#1442C2semidirect
12. C2×#1441C2semidirect
15. C2×#1436C2semidirect
16. C2×#1434C2semidirect
37. C2×#389C22semidirect
39. C2×#388C4semidirect
49. C2×#384C22semidirect
66. #1444C22semidirect
67. #1444C22semidirect
68. #1442C22semidirect
69. #1441C22semidirect
72. #1436C22semidirect
73. #1434C22semidirect
125. C22×C4⋊C4C2×C4semidirect
166. C22×C42C2×C4semidirect
171. #388C2×C4semidirect
189. C2×#95C2×C4semidirect
190. C2×#95C2×C4semidirect
389. C2×C4⋊C4C22×C4semidirect
409. C2×C22⋊C4C4⋊C4semidirect
422. C2×C42C22×C4semidirect
436. #95C22×C4semidirect
437. #95C22×C4semidirect
724. C22⋊C4C2×C4⋊C4semidirect
1021. C2#14405direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#3892
C22×#3882
C22×#3852
C22×#3842
#144052
C2×#14442
C2×#14422
C2×#14412
C2×#14392
C2×#14362
C2×#14342