Finite Group Databasebeta

← C2×#25429 #6444227

Subgroups — C2×#25429 #6444227

Order 512.

3106 conjugacy classes of subgroups.

The subgroup lattice has 853 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#495C211yesmaximal, characteristic, complemented
2C22×#468C211yesmaximal, characteristic, complemented
3C22×#468C211yesmaximal, characteristic, complemented
4C22×#440C211yesmaximal, characteristic, complemented
5C2×#2426C211yesmaximal, characteristic, complemented
6C2×#2427C211yesmaximal, characteristic, complemented
7#25429C2116yesmaximal, direct product factor
8C2×#2042C211yesmaximal, characteristic, complemented
9C2×#2042C211yesmaximal, characteristic, complemented
10C2×#2001C211yesmaximal, characteristic, complemented
11C2×#1999C211yesmaximal, characteristic
12C2×#1973C211yesmaximal, characteristic, complemented
13C2×#1942C211yesmaximal, characteristic, complemented
14C2×#1878C211yesmaximal, characteristic, complemented
15C2×#1879C211yesmaximal, characteristic, complemented
16C2×#1753C211yesmaximal, characteristic, complemented
17C23×Q16C2211yescharacteristic
18C23×SD16C2211yescharacteristic
19C23×SD16C2211yescharacteristic
20C23×D8C2211yescharacteristic
21C23×M16C2211yescharacteristic
22C22×#124C2211yescharacteristic
23C22×#124C2211yescharacteristic
24C22×C22⋊Q8C2211yescharacteristic
25C22×C22⋊Q8C2211yescharacteristic
26C22×#121C2211yescharacteristic
27C22×#121C2211yescharacteristic
28C22×C4×Q8C2211yescharacteristic
29C22×C4×D4C2211yescharacteristic
30C2×#495—28no—
31C2×#495C2218yescomplemented
32C2×#468—28no—
33C2×#468—28no—
34C2×#468C2218yescomplemented
35C2×#468C2218yescomplemented
36C2×#440—28no—
37C2×#440C2218yescomplemented
38C22×#107C2211yescharacteristic
39C22×#107C2211yescharacteristic
40C22×#103C2211yescharacteristic
41C22×#103C2211yescharacteristic
42C22×#103C2211yescharacteristic
43C22×#103C2211yescharacteristic
44C22×#102C2211yescharacteristic
45C22×#102C2211yescharacteristic
46C22×#102C2211yescharacteristic
47C22×#102C2211yescharacteristic
48C22×C22⋊C8C2211yescharacteristic
49C22×#97C2211yescharacteristic
50C22×C4×C8C2211yescharacteristic
51#2427—24no—
52#2427C2218yescomplemented
53#2426—24no—
54#2426C2218yescomplemented
55C2×#397—21no—
56C2×#396—21no—
57C2×#394—21no—
58C2×#394—21no—
59C2×#391C2211yescharacteristic
60C2×#390—21no—
61C2×#390C2211yescharacteristic
62C2×#389C2211yescharacteristic
63C2×#389C2211yescharacteristic
64C2×#388—21no—
65C2×#386—21no—
66C2×#380—21no—
67C2×C4×C22⋊C4C2211yescharacteristic
68#2042C2218yescomplemented
69#2042C2218yescomplemented
70#2001C2218yescomplemented
71#1999C2218yes—
72#1973C2218yescomplemented
73#1942C2218yescomplemented
74#1879C2218yescomplemented
75#1878C2218yescomplemented
76#1753C2218yescomplemented
77C2×#340C2211yescharacteristic
78C2×#340C2211yescharacteristic
79C2×#336C2211yescharacteristic
80C2×#336C2211yescharacteristic
81C23×Q8C2311yescharacteristic
82C23×Q8C2311yescharacteristic
83C23×D4—21no—
84C23×D4—21no—
85C23×D4C2311yescharacteristic
86C23×D4C2311yescharacteristic
87C24×C4—21no—
88C24×C4C2311yescharacteristic
89C22×Q16—24no—
90C22×Q16—24no—
91C22×Q16—42no—
92C22×Q16C2314yes—
93C22×SD16—24no—
94C22×SD16—24no—
95C22×SD16—24no—
96C22×SD16—24no—
97C22×SD16—24no—
98C22×SD16D418yescomplemented
99C22×SD16C2314yes—
100C22×SD16C2314yes—
101C22×D8—24no—
102C22×D8—24no—
103C22×D8—42no—
104C22×D8C2314yes—
105C22×M16—24no—
106C22×M16—24no—
107C22×M16—24no—
108C22×M16C2314yes—
109C23×C8C2311yescharacteristic
110C23×C8C2311yescharacteristic
111C23×C8C2311yescharacteristic
112C23×C8C2311yescharacteristic
113C2×#124—24no—
114C2×#124—24no—
115C2×#124—22no—
116C2×#124—22no—
117C2×#124—42no—
118C2×#124—42no—
119C2×#124C2314yes—
120C2×#124C2314yes—
121C2×C22⋊Q8—22no—
122C2×C22⋊Q8—22no—
123C2×C22⋊Q8—24no—
124C2×C22⋊Q8—24no—
125C2×C22⋊Q8—42no—
126C2×C22⋊Q8—42no—
127C2×C22⋊Q8C2314yes—
128C2×C22⋊Q8C2314yes—
129C2×#121—22no—
130C2×#121—22no—
131C2×#121—24no—
132C2×#121—24no—
133C2×#121—42no—
134C2×#121—42no—
135C2×#121C2314yes—
136C2×#121C2314yes—
137C2×C4×Q8—22no—
138C2×C4×Q8—24no—
139C2×C4×Q8—42no—
140C2×C4×Q8C2314yes—
141C2×C4×D4—24no—
142C2×C4×D4—22no—
143C2×C4×D4—42no—
144C2×C4×D4C2314yes—
145C22×C4⋊C4—21no—
146C22×C4⋊C4—21no—
147C22×C4⋊C4—21no—
148C22×C4⋊C4—21no—
149C22×C4⋊C4—21no—
150C22×C4⋊C4C2311yescharacteristic
151C22×C4⋊C4C2311yescharacteristic
152C22×C4⋊C4C2311yescharacteristic
153C22×C4⋊C4C2311yescharacteristic
154C22×C22⋊C4—21no—
155C22×C22⋊C4—21no—
156C22×C22⋊C4—21no—
157C22×C22⋊C4—21no—
158C22×C22⋊C4—21no—
159C22×C22⋊C4—21no—
160C22×C22⋊C4—21no—
161C22×C22⋊C4—21no—
162C22×C22⋊C4—21no—
163C22×C22⋊C4—21no—
164C22×C22⋊C4—21no—
165C22×C22⋊C4D411yescharacteristic
166C22×C22⋊C4D411yescharacteristic
167C22×C42—21no—
168C22×C42C2311yescharacteristic
169C22×C42C2311yescharacteristic
170#495—232no—
171#468—232no—
172#468—232no—
173#440—232no—
174C2×#107—24no—
175C2×#107D418yescomplemented
176C2×#107C2314yes—
177C2×#107C2314yes—
178C2×#103—24no—
179C2×#103—24no—
180C2×#103—24no—
181C2×#103—42no—
182C2×#103C2314yes—
183C2×#103C2314yes—
184C2×#103C2314yes—
185C2×#103C2314yes—
186C2×#102—24no—
187C2×#102—24no—
188C2×#102—24no—
189C2×#102—42no—
190C2×#102C2314yes—
191C2×#102C2314yes—
192C2×#102C2314yes—
193C2×#102C2314yes—
194C2×C22⋊C8—24no—
195C2×C22⋊C8C2314yes—
196C2×#97—24no—
197C2×#97C2314yes—
198C2×C4×C8—24no—
199C2×C4×C8C2314yes—
200#397—28no—
201#396—28no—
202#394—28no—
203#394—28no—
204#391—22no—
205#391C2314yes—
206#390—28no—
207#390—22no—
208#390C2314yes—
209#389—22no—
210#389—22no—
211#389C2314yes—
212#389C2314yes—
213#388—28no—
214#386—28no—
215#380—28no—
216C4×C22⋊C4D414yes—
217C4×C22⋊C4C2314yes—
218C2×#95—21no—
219C2×#95—21no—
220C2×#95—21no—
221C2×#95—21no—
222C2×#95D411yescharacteristic
223C2×#95D411yescharacteristic
224#340C2314yes—
225#340C2314yes—
226#336C2314yes—
227#336C2314yes—
228C25—21no—
229C25—21no—
230C25C2×D411yescharacteristic
231C22×Q8—21no—
232C22×Q8—21no—
233C22×Q8—22no—
234C22×Q8—22no—
235C22×Q8—22no—
236C22×Q8—22no—
237C22×Q8—22no—
238C22×Q8—22no—
239C22×Q8—22no—
240C22×Q8—22no—
241C22×Q8—22no—
242C22×Q8—22no—
243C22×Q8—22no—
244C22×Q8C2×D414yes—
245C22×Q8C2412yes—
246C22×Q8C2412yes—
247C22×D4—24no—
248C22×D4—24no—
249C22×D4—22no—
250C22×D4—21no—
251C22×D4—22no—
252C22×D4—22no—
253C22×D4—21no—
254C22×D4—22no—
255C22×D4—22no—
256C22×D4—22no—
257C22×D4—22no—
258C22×D4—22no—
259C22×D4—22no—
260C22×D4—22no—
261C22×D4—22no—
262C22×D4—44no—
263C22×D4—44no—
264C22×D4—44no—
265C22×D4—44no—
266C22×D4—82no—
267C22×D4—82no—
268C22×D4C2×D414yes—
269C22×D4C2412yes—
270C22×D4C2412yes—
271C23×C4—21no—
272C23×C4—21no—
273C23×C4—21no—
274C23×C4—22no—
275C23×C4—22no—
276C23×C4—22no—
277C23×C4—22no—
278C23×C4—22no—
279C23×C4—22no—
280C23×C4—21no—
281C23×C4—21no—
282C23×C4—21no—
283C23×C4—24no—
284C23×C4—44no—
285C23×C4—44no—
286C23×C4—82no—
287C23×C4C2×D412yes—
288C23×C4C2×D411yescharacteristic
289C23×C4C2×D411yescharacteristic
290C23×C4C2×D411yescharacteristic
291C23×C4C2×D411yescharacteristic
292C23×C4C2×D411yescharacteristic
293C23×C4C2412yes—
294C23×C4C2411yescharacteristic
295C2×Q16—28no—
296C2×Q16—28no—
297C2×Q16—44no—
298C2×Q16—416no—
299C2×SD16—232no—
300C2×SD16—28no—
301C2×SD16—28no—
302C2×SD16—28no—
303C2×SD16—28no—
304C2×SD16—28no—
305C2×SD16—416no—
306C2×SD16C2×D4116yescomplemented
307C2×D8—28no—
308C2×D8—28no—
309C2×D8—44no—
310C2×D8—416no—
311C2×M16—28no—
312C2×M16—28no—
313C2×M16—28no—
314C2×M16—416no—
315C22×C8—22no—
316C22×C8—22no—
317C22×C8—22no—
318C22×C8—22no—
319C22×C8—22no—
320C22×C8—22no—
321C22×C8—22no—
322C22×C8—22no—
323C22×C8C2×D414yes—
324C22×C8C2×D414yes—
325C22×C8#4114yes—
326C22×C8#4114yes—
327C22×C8C2412yes—
328C22×C8C2412yes—
329C22×C8C2412yes—
330C22×C8C2412yes—
331#124—28no—
332#124—28no—
333#124—44no—
334#124—44no—
335#124—48no—
336#124—48no—
337C22⋊Q8—28no—
338C22⋊Q8—28no—
339C22⋊Q8—44no—
340C22⋊Q8—44no—
341C22⋊Q8—48no—
342C22⋊Q8—48no—
343#121—28no—
344#121—28no—
345#121—44no—
346#121—44no—
347#121—48no—
348#121—48no—
349C4×Q8—28no—
350C4×Q8—44no—
351C4×Q8—48no—
352C4×D4—28no—
353C4×D4—44no—
354C4×D4—48no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—22no—
358C2×C4⋊C4—22no—
359C2×C4⋊C4—22no—
360C2×C4⋊C4—22no—
361C2×C4⋊C4—22no—
362C2×C4⋊C4—22no—
363C2×C4⋊C4—24no—
364C2×C4⋊C4—24no—
365C2×C4⋊C4—24no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—24no—
369C2×C4⋊C4—24no—
370C2×C4⋊C4—44no—
371C2×C4⋊C4—44no—
372C2×C4⋊C4—44no—
373C2×C4⋊C4—82no—
374C2×C4⋊C4—82no—
375C2×C4⋊C4C2×D414yes—
376C2×C4⋊C4C2×D414yes—
377C2×C4⋊C4C2412yes—
378C2×C4⋊C4C2412yes—
379C2×C4⋊C4C2412yes—
380C2×C4⋊C4C2412yes—
381C2×C22⋊C4—24no—
382C2×C22⋊C4—24no—
383C2×C22⋊C4—24no—
384C2×C22⋊C4—24no—
385C2×C22⋊C4—24no—
386C2×C22⋊C4—24no—
387C2×C22⋊C4—24no—
388C2×C22⋊C4—24no—
389C2×C22⋊C4—24no—
390C2×C22⋊C4—24no—
391C2×C22⋊C4—24no—
392C2×C22⋊C4—42no—
393C2×C22⋊C4—42no—
394C2×C22⋊C4—44no—
395C2×C22⋊C4—44no—
396C2×C22⋊C4—44no—
397C2×C22⋊C4—44no—
398C2×C22⋊C4—44no—
399C2×C22⋊C4—44no—
400C2×C22⋊C4—44no—
401C2×C22⋊C4—44no—
402C2×C22⋊C4—44no—
403C2×C22⋊C4—44no—
404C2×C22⋊C4—82no—
405C2×C22⋊C4C2×D414yes—
406C2×C22⋊C4C2×D414yes—
407C2×C42—22no—
408C2×C42—22no—
409C2×C42—22no—
410C2×C42—22no—
411C2×C42—24no—
412C2×C42—44no—
413C2×C42C2×D412yes—
414C2×C42C2×D412yes—
415C2×C42C2412yes—
416C2×C42C2412yes—
417#107—28no—
418#107C2×D4116yescomplemented
419#103—28no—
420#103—28no—
421#103—28no—
422#103—44no—
423#102—28no—
424#102—28no—
425#102—28no—
426#102—44no—
427C22⋊C8—28no—
428#97—28no—
429C4×C8—28no—
430#95—24no—
431#95—24no—
432#95—24no—
433#95—24no—
434#95C2×D414yes—
435#95C2×D414yes—
436C24—22no—
437C24—24no—
438C24—22no—
439C24—22no—
440C24—22no—
441C24—22no—
442C24—22no—
443C24—22no—
444C24—22no—
445C24—22no—
446C24—42no—
447C24—42no—
448C24—42no—
449C24—42no—
450C24—42no—
451C24—42no—
452C24—42no—
453C24—42no—
454C24—42no—
455C24—42no—
456C24—42no—
457C24—42no—
458C24—42no—
459C24C22×D412yes—
460C24C22×D411yescharacteristic
461C2×Q8—24no—
462C2×Q8—22no—
463C2×Q8—28no—
464C2×Q8—28no—
465C2×Q8—22no—
466C2×Q8—22no—
467C2×Q8—22no—
468C2×Q8—22no—
469C2×Q8—22no—
470C2×Q8—22no—
471C2×Q8—22no—
472C2×Q8—22no—
473C2×Q8—22no—
474C2×Q8—22no—
475C2×Q8—42no—
476C2×Q8—42no—
477C2×Q8—44no—
478C2×Q8—42no—
479C2×Q8—42no—
480C2×Q8—42no—
481C2×Q8—44no—
482C2×Q8—44no—
483C2×Q8—44no—
484C2×Q8—44no—
485C2×Q8—44no—
486C2×Q8C22×D414yes—
487C2×D4—28no—
488C2×D4—24no—
489C2×D4—28no—
490C2×D4—22no—
491C2×D4—22no—
492C2×D4—22no—
493C2×D4—22no—
494C2×D4—22no—
495C2×D4—22no—
496C2×D4—22no—
497C2×D4—22no—
498C2×D4—22no—
499C2×D4—22no—
500C2×D4—22no—
501C2×D4—48no—
502C2×D4—48no—
503C2×D4—48no—
504C2×D4—48no—
505C2×D4—44no—
506C2×D4—42no—
507C2×D4—42no—
508C2×D4—44no—
509C2×D4—44no—
510C2×D4—42no—
511C2×D4—42no—
512C2×D4—42no—
513C2×D4—44no—
514C2×D4—44no—
515C2×D4—44no—
516C2×D4—84no—
517C2×D4—84no—
518C2×D4—816no—
519C2×D4—816no—
520C2×D4C22×D414yes—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—24no—
527C22×C4—24no—
528C22×C4—24no—
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—24no—
543C22×C4—24no—
544C22×C4—24no—
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—48no—
555C22×C4—48no—
556C22×C4—42no—
557C22×C4—42no—
558C22×C4—42no—
559C22×C4—42no—
560C22×C4—42no—
561C22×C4—42no—
562C22×C4—44no—
563C22×C4—44no—
564C22×C4—44no—
565C22×C4—44no—
566C22×C4—42no—
567C22×C4—42no—
568C22×C4—42no—
569C22×C4—42no—
570C22×C4—42no—
571C22×C4—42no—
572C22×C4—42no—
573C22×C4—42no—
574C22×C4—42no—
575C22×C4—84no—
576C22×C4—816no—
577C22×C4C22×D412yes—
578C22×C4C22×D412yes—
579C22×C4C22×D412yes—
580C22×C4C22×D412yes—
581C22×C4C22×D412yes—
582C22×C4C22×D412yes—
583C22×C4C22×D412yes—
584C22×C4C22×D411yescharacteristic
585C22×C4C2×#4112yes—
586C22×C4C2×#4112yes—
587C22×C4H(5,𝔽2)12yes—
588C22×C4H(5,𝔽2)12yes—
589C22×C4C2511yescharacteristic
590Q16—416no—
591SD16—232no—
592SD16—416no—
593D8—416no—
594M16—416no—
595C2×C8—28no—
596C2×C8—22no—
597C2×C8—22no—
598C2×C8—22no—
599C2×C8—22no—
600C2×C8—22no—
601C2×C8—22no—
602C2×C8—22no—
603C2×C8—22no—
604C2×C8—44no—
605C2×C8—44no—
606C2×C8#121116yes—
607C2×C8C22×D414yes—
608C2×C8C22×D414yes—
609C2×C8C2×#4114yes—
610C2×C8C2×#4114yes—
611C4⋊C4—24no—
612C4⋊C4—24no—
613C4⋊C4—22no—
614C4⋊C4—22no—
615C4⋊C4—22no—
616C4⋊C4—22no—
617C4⋊C4—22no—
618C4⋊C4—22no—
619C4⋊C4—48no—
620C4⋊C4—48no—
621C4⋊C4—48no—
622C4⋊C4—42no—
623C4⋊C4—42no—
624C4⋊C4—84no—
625C4⋊C4—84no—
626C4⋊C4C22×D414yes—
627C4⋊C4C22×D414yes—
628C22⋊C4—44no—
629C22⋊C4—44no—
630C22⋊C4—48no—
631C22⋊C4—48no—
632C22⋊C4—48no—
633C22⋊C4—48no—
634C22⋊C4—48no—
635C22⋊C4—48no—
636C22⋊C4—48no—
637C22⋊C4—48no—
638C22⋊C4—48no—
639C22⋊C4—48no—
640C22⋊C4—84no—
641C42—24no—
642C42—24no—
643C42—22no—
644C42—22no—
645C42—22no—
646C42—22no—
647C42—48no—
648C23—22no—
649C23—24no—
650C23—22no—
651C23—22no—
652C23—22no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—44no—
657C23—44no—
658C23—42no—
659C23—44no—
660C23—48no—
661C23—42no—
662C23—44no—
663C23—48no—
664C23—44no—
665C23—48no—
666C23—44no—
667C23—44no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—42no—
672C23—42no—
673C23—42no—
674C23—42no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23—84no—
680C23—84no—
681C23—84no—
682C23—84no—
683C23—84no—
684C23—84no—
685C23—84no—
686C23—84no—
687C23—84no—
688C23—84no—
689C23—84no—
690C23#53212yes—
691C23D4212yes—
692C23D4212yes—
693C23#57512yes—
694C23#57512yes—
695C23#57612yes—
696C23#57812yes—
697C23C23×D411yescharacteristic
698Q8—24no—
699Q8—24no—
700Q8—48no—
701Q8—42no—
702Q8—42no—
703Q8—42no—
704Q8—42no—
705Q8—42no—
706Q8—42no—
707Q8—84no—
708D4—24no—
709D4—24no—
710D4—42no—
711D4—48no—
712D4—42no—
713D4—42no—
714D4—42no—
715D4—42no—
716D4—42no—
717D4—816no—
718D4—816no—
719D4—84no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—24no—
726C2×C4—24no—
727C2×C4—24no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—42no—
739C2×C4—44no—
740C2×C4—48no—
741C2×C4—42no—
742C2×C4—44no—
743C2×C4—44no—
744C2×C4—44no—
745C2×C4—48no—
746C2×C4—48no—
747C2×C4—44no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—48no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—816no—
767C2×C4—84no—
768C2×C4—84no—
769C2×C4—84no—
770C2×C4C2×#12114yes—
771C2×C4#53212yes—
772C2×C4#54014yes—
773C2×C4D4212yes—
774C2×C4D4212yes—
775C2×C4#54614yes—
776C2×C4#55014yes—
777C2×C4C23×D411yescharacteristic
778C2×C4C23×D411yescharacteristic
779C2×C4C22×#4111yescharacteristic
780C2×C4C22×#4111yescharacteristic
781C2×C4C2×H(5,𝔽2)11yescharacteristic
782C2×C4C2×H(5,𝔽2)11yescharacteristic
783C8—24no—
784C8—42no—
785C8—42no—
786C8C2×#12118yes—
787C22—42no—
788C22—42no—
789C22—42no—
790C22—44no—
791C22—42no—
792C22—44no—
793C22—42no—
794C22—42no—
795C22—42no—
796C22—44no—
797C22—82no—
798C22—82no—
799C22—88no—
800C22—816no—
801C22—82no—
802C22—82no—
803C22—82no—
804C22—82no—
805C22—82no—
806C22—82no—
807C22—82no—
808C22—82no—
809C22—82no—
810C22—168no—
811C22#242814yes—
812C22#317514yes—
813C22#318314yes—
814C22#326814yes—
815C22#326914yes—
816C22#327314yes—
817C22#327714yes—
818C22C2×#53211yescharacteristic
819C22C2×D4211yescharacteristic
820C22C2×D4211yescharacteristic
821C22C2×#57511yescharacteristic
822C22C2×#57511yescharacteristic
823C22C2×#57611yescharacteristic
824C22C2×#57811yescharacteristic
825C4—42no—
826C4—42no—
827C4—42no—
828C4—44no—
829C4—44no—
830C4—42no—
831C4—42no—
832C4—44no—
833C4—82no—
834C4—82no—
835C4—82no—
836C4#242814yes—
837C4C22×#12111yescharacteristic
838C4C2×#54011yescharacteristic
839C4C2×#54611yescharacteristic
840C4C2×#55011yescharacteristic
841C2—82no—
842C2—84no—
843C2—162no—
844C2#2542918yesdirect product factor
845C2C2×#242811yescharacteristic
846C2C2×#317511yescharacteristic
847C2C2×#318311yescharacteristic
848C2C2×#326811yescharacteristic
849C2C2×#326911yescharacteristic
850C2C2×#327311yescharacteristic
851C2C2×#327711yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#1999C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C22×#495C2semidirect
2. C22×#468C2semidirect
3. C22×#468C2semidirect
4. C22×#440C2semidirect
5. C2×#2426C2semidirect
6. C2×#2427C2semidirect
7. #25429C2direct (N × H)
8. C2×#2042C2semidirect
9. C2×#2042C2semidirect
10. C2×#2001C2semidirect
12. C2×#1973C2semidirect
13. C2×#1942C2semidirect
14. C2×#1878C2semidirect
15. C2×#1879C2semidirect
16. C2×#1753C2semidirect
31. C2×#495C22semidirect
34. C2×#468C22semidirect
35. C2×#468C22semidirect
37. C2×#440C22semidirect
52. #2427C22semidirect
54. #2426C22semidirect
68. #2042C22semidirect
69. #2042C22semidirect
70. #2001C22semidirect
72. #1973C22semidirect
73. #1942C22semidirect
74. #1879C22semidirect
75. #1878C22semidirect
76. #1753C22semidirect
98. C22×SD16D4semidirect
175. C2×#107D4semidirect
306. C2×SD16C2×D4semidirect
418. #107C2×D4semidirect
844. C2#25429direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#4952
C22×#4682
C22×#4402
C2×#24262
C2×#24272
#254292
C2×#20422
C2×#20012
C2×#19992
C2×#19732
C2×#19422
C2×#18782
C2×#18792
C2×#17532