Finite Group Databasebeta

← C2×#30848 #7502080

Subgroups — C2×#30848 #7502080

Order 512.

3240 conjugacy classes of subgroups.

The subgroup lattice has 867 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#465C211yesmaximal, characteristic, complemented
2C22×#465C211yesmaximal, characteristic, complemented
3C22×#460C211yesmaximal, characteristic, complemented
4C22×#461C211yesmaximal, characteristic, complemented
5C2×#2429C211yesmaximal, characteristic, complemented
6C2×#2428C211yesmaximal, characteristic
7#30848C2116yesmaximal, direct product factor
8C2×#2066C211yesmaximal, characteristic, complemented
9C2×#2065C211yesmaximal, characteristic, complemented
10C2×#2013C211yesmaximal, characteristic, complemented
11C2×#2014C211yesmaximal, characteristic, complemented
12C2×#2000C211yesmaximal, characteristic, complemented
13C2×#2000C211yesmaximal, characteristic, complemented
14C2×#1865C211yesmaximal, characteristic, complemented
15C2×#1864C211yesmaximal, characteristic, complemented
16C2×#1850C211yesmaximal, characteristic, complemented
17C23×SD16C2211yescharacteristic
18C23×SD16C2211yescharacteristic
19C23×SD16C2211yescharacteristic
20C23×SD16C2211yescharacteristic
21C24×C8C2211yescharacteristic
22C22×C4⋊Q8C2211yescharacteristic
23C22×#127C2211yescharacteristic
24C22×C22⋊Q8C2211yescharacteristic
25C22×C22⋊Q8C2211yescharacteristic
26C22×#121—21no—
27C22×#121C2211yescharacteristic
28C22×#121C2211yescharacteristic
29C22×C4×Q8C2211yescharacteristic
30C22×C4×D4C2211yescharacteristic
31C2×#465—28no—
32C2×#465—28no—
33C2×#465C2218yescomplemented
34C2×#465C2218yescomplemented
35C2×#460—28no—
36C2×#460C2218yescomplemented
37C2×#461—28no—
38C2×#461C2218yescomplemented
39C22×#106C2211yescharacteristic
40C22×#106C2211yescharacteristic
41C22×C4⋊C8C2211yescharacteristic
42C22×C4⋊C8C2211yescharacteristic
43C22×#103C2211yescharacteristic
44C22×#103C2211yescharacteristic
45C22×#103C2211yescharacteristic
46C22×#103C2211yescharacteristic
47C22×#102C2211yescharacteristic
48C22×#102C2211yescharacteristic
49C22×#102C2211yescharacteristic
50C22×#102C2211yescharacteristic
51C22×C22⋊C8C2211yescharacteristic
52#2429—24no—
53#2429C2218yescomplemented
54#2428—24no—
55#2428C2218yes—
56C2×#398—21no—
57C2×#396—21no—
58C2×#394—21no—
59C2×#392—21no—
60C2×#391C2211yescharacteristic
61C2×#390C2211yescharacteristic
62C2×#389—21no—
63C2×#389C2211yescharacteristic
64C2×#389C2211yescharacteristic
65C2×#388—21no—
66C2×#386—21no—
67C2×C4×C22⋊C4C2211yescharacteristic
68#2066C2218yescomplemented
69#2065C2218yescomplemented
70#2014C2218yescomplemented
71#2013C2218yescomplemented
72#2000C2218yescomplemented
73#2000C2218yescomplemented
74#1865C2218yescomplemented
75#1864C2218yescomplemented
76#1850C2218yescomplemented
77C2×#340C2211yescharacteristic
78C2×#340C2211yescharacteristic
79C2×#336C2211yescharacteristic
80C2×#336C2211yescharacteristic
81C23×Q8C2311yescharacteristic
82C23×Q8C2311yescharacteristic
83C23×D4—21no—
84C23×D4—21no—
85C23×D4—21no—
86C23×D4—21no—
87C23×D4C2311yescharacteristic
88C23×D4C2311yescharacteristic
89C24×C4—21no—
90C24×C4C2311yescharacteristic
91C22×SD16—24no—
92C22×SD16—24no—
93C22×SD16—24no—
94C22×SD16—24no—
95C22×SD16—24no—
96C22×SD16—24no—
97C22×SD16—42no—
98C22×SD16—42no—
99C22×SD16—42no—
100C22×SD16—42no—
101C22×SD16—42no—
102C22×SD16—42no—
103C22×SD16C2314yes—
104C22×SD16C2314yes—
105C22×SD16C2314yes—
106C22×SD16C2314yes—
107C23×C8—24no—
108C23×C8—24no—
109C23×C8—42no—
110C23×C8C2311yescharacteristic
111C23×C8C2311yescharacteristic
112C23×C8C2314yes—
113C23×C8C2311yescharacteristic
114C23×C8C2311yescharacteristic
115C2×C4⋊Q8—24no—
116C2×C4⋊Q8—22no—
117C2×C4⋊Q8—42no—
118C2×C4⋊Q8C2314yes—
119C2×#127—24no—
120C2×#127—22no—
121C2×#127—42no—
122C2×#127C2314yes—
123C2×C22⋊Q8—22no—
124C2×C22⋊Q8—22no—
125C2×C22⋊Q8—24no—
126C2×C22⋊Q8—24no—
127C2×C22⋊Q8—42no—
128C2×C22⋊Q8—42no—
129C2×C22⋊Q8C2314yes—
130C2×C22⋊Q8C2314yes—
131C2×#121—22no—
132C2×#121—22no—
133C2×#121—28no—
134C2×#121—24no—
135C2×#121—24no—
136C2×#121—42no—
137C2×#121—42no—
138C2×#121—48no—
139C2×#121C2314yes—
140C2×#121C2314yes—
141C2×C4×Q8—22no—
142C2×C4×Q8—24no—
143C2×C4×Q8—42no—
144C2×C4×Q8C2314yes—
145C2×C4×D4—24no—
146C2×C4×D4—22no—
147C2×C4×D4—42no—
148C2×C4×D4C2314yes—
149C22×C4⋊C4—21no—
150C22×C4⋊C4—21no—
151C22×C4⋊C4—21no—
152C22×C4⋊C4—21no—
153C22×C4⋊C4—21no—
154C22×C4⋊C4—21no—
155C22×C4⋊C4—21no—
156C22×C4⋊C4C2311yescharacteristic
157C22×C4⋊C4C2311yescharacteristic
158C22×C4⋊C4C2311yescharacteristic
159C22×C4⋊C4C2311yescharacteristic
160C22×C22⋊C4—21no—
161C22×C22⋊C4—21no—
162C22×C22⋊C4—21no—
163C22×C22⋊C4—21no—
164C22×C22⋊C4—21no—
165C22×C22⋊C4—21no—
166C22×C22⋊C4—21no—
167C22×C22⋊C4D411yescharacteristic
168C22×C22⋊C4D411yescharacteristic
169C22×C42—21no—
170C22×C42C2311yescharacteristic
171C22×C42C2311yescharacteristic
172#465—232no—
173#465—232no—
174#461—232no—
175#460—232no—
176C2×#106—24no—
177C2×#106—24no—
178C2×#106C2314yes—
179C2×#106C2314yes—
180C2×C4⋊C8—24no—
181C2×C4⋊C8—24no—
182C2×C4⋊C8C2314yes—
183C2×C4⋊C8C2314yes—
184C2×#103—24no—
185C2×#103—24no—
186C2×#103—42no—
187C2×#103D418yescomplemented
188C2×#103C2314yes—
189C2×#103C2314yes—
190C2×#103C2314yes—
191C2×#103C2314yes—
192C2×#102—24no—
193C2×#102—24no—
194C2×#102—42no—
195C2×#102D418yescomplemented
196C2×#102C2314yes—
197C2×#102C2314yes—
198C2×#102C2314yes—
199C2×#102C2314yes—
200C2×C22⋊C8—42no—
201C2×C22⋊C8C2314yes—
202#398—28no—
203#396—28no—
204#394—28no—
205#392—28no—
206#391—22no—
207#391C2314yes—
208#390—22no—
209#390C2314yes—
210#389—22no—
211#389—22no—
212#389—28no—
213#389C2314yes—
214#389C2314yes—
215#388—28no—
216#386—28no—
217C4×C22⋊C4D414yes—
218C4×C22⋊C4C2314yes—
219C2×#95—21no—
220C2×#95—21no—
221C2×#95—21no—
222C2×#95—21no—
223C2×#95D411yescharacteristic
224C2×#95D411yescharacteristic
225#340C2314yes—
226#340C2314yes—
227#336C2314yes—
228#336C2314yes—
229C25—21no—
230C25—21no—
231C25C2×D411yescharacteristic
232C22×Q8—21no—
233C22×Q8—21no—
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×Q8—22no—
245C22×Q8C2×D414yes—
246C22×Q8C2412yes—
247C22×Q8C2412yes—
248C22×D4—24no—
249C22×D4—24no—
250C22×D4—22no—
251C22×D4—21no—
252C22×D4—22no—
253C22×D4—22no—
254C22×D4—21no—
255C22×D4—24no—
256C22×D4—24no—
257C22×D4—22no—
258C22×D4—22no—
259C22×D4—22no—
260C22×D4—22no—
261C22×D4—22no—
262C22×D4—22no—
263C22×D4—22no—
264C22×D4—22no—
265C22×D4—44no—
266C22×D4—44no—
267C22×D4—44no—
268C22×D4—44no—
269C22×D4—44no—
270C22×D4—44no—
271C22×D4—44no—
272C22×D4—44no—
273C22×D4—82no—
274C22×D4—82no—
275C22×D4—82no—
276C22×D4—82no—
277C22×D4C2×D414yes—
278C22×D4C2412yes—
279C22×D4C2412yes—
280C23×C4—21no—
281C23×C4—21no—
282C23×C4—21no—
283C23×C4—22no—
284C23×C4—22no—
285C23×C4—22no—
286C23×C4—22no—
287C23×C4—22no—
288C23×C4—22no—
289C23×C4—21no—
290C23×C4—21no—
291C23×C4—21no—
292C23×C4—24no—
293C23×C4—44no—
294C23×C4—44no—
295C23×C4—82no—
296C23×C4C2×D412yes—
297C23×C4C2×D411yescharacteristic
298C23×C4C2×D411yescharacteristic
299C23×C4C2×D411yescharacteristic
300C23×C4C2×D411yescharacteristic
301C23×C4C2×D411yescharacteristic
302C23×C4C2412yes—
303C23×C4C2411yescharacteristic
304C2×SD16—28no—
305C2×SD16—28no—
306C2×SD16—28no—
307C2×SD16—28no—
308C2×SD16—28no—
309C2×SD16—28no—
310C2×SD16—44no—
311C2×SD16—44no—
312C2×SD16—44no—
313C2×SD16—44no—
314C2×SD16—44no—
315C2×SD16—44no—
316C2×SD16—416no—
317C2×SD16—416no—
318C2×SD16—416no—
319C2×SD16—416no—
320C22×C8—22no—
321C22×C8—22no—
322C22×C8—22no—
323C22×C8—22no—
324C22×C8—22no—
325C22×C8—22no—
326C22×C8—22no—
327C22×C8—22no—
328C22×C8—22no—
329C22×C8—22no—
330C22×C8—28no—
331C22×C8—28no—
332C22×C8—44no—
333C22×C8—416no—
334C22×C8C2×D414yes—
335C22×C8C2×D414yes—
336C22×C8C2412yes—
337C22×C8C2412yes—
338C22×C8C2412yes—
339C22×C8C2412yes—
340C4⋊Q8—28no—
341C4⋊Q8—44no—
342C4⋊Q8—48no—
343#127—28no—
344#127—44no—
345#127—48no—
346C22⋊Q8—28no—
347C22⋊Q8—28no—
348C22⋊Q8—44no—
349C22⋊Q8—44no—
350C22⋊Q8—48no—
351C22⋊Q8—48no—
352#121—28no—
353#121—28no—
354#121—44no—
355#121—44no—
356#121—48no—
357#121—48no—
358#121—432no—
359C4×Q8—28no—
360C4×Q8—44no—
361C4×Q8—48no—
362C4×D4—28no—
363C4×D4—44no—
364C4×D4—48no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—22no—
368C2×C4⋊C4—22no—
369C2×C4⋊C4—22no—
370C2×C4⋊C4—22no—
371C2×C4⋊C4—22no—
372C2×C4⋊C4—22no—
373C2×C4⋊C4—24no—
374C2×C4⋊C4—24no—
375C2×C4⋊C4—24no—
376C2×C4⋊C4—24no—
377C2×C4⋊C4—24no—
378C2×C4⋊C4—24no—
379C2×C4⋊C4—24no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—44no—
383C2×C4⋊C4—44no—
384C2×C4⋊C4—44no—
385C2×C4⋊C4—44no—
386C2×C4⋊C4—44no—
387C2×C4⋊C4—44no—
388C2×C4⋊C4—44no—
389C2×C4⋊C4C2×D414yes—
390C2×C4⋊C4C2×D414yes—
391C2×C4⋊C4C2412yes—
392C2×C4⋊C4C2412yes—
393C2×C4⋊C4C2412yes—
394C2×C4⋊C4C2412yes—
395C2×C22⋊C4—24no—
396C2×C22⋊C4—24no—
397C2×C22⋊C4—24no—
398C2×C22⋊C4—24no—
399C2×C22⋊C4—24no—
400C2×C22⋊C4—24no—
401C2×C22⋊C4—24no—
402C2×C22⋊C4—42no—
403C2×C22⋊C4—44no—
404C2×C22⋊C4—44no—
405C2×C22⋊C4—44no—
406C2×C22⋊C4—44no—
407C2×C22⋊C4—44no—
408C2×C22⋊C4—44no—
409C2×C22⋊C4—82no—
410C2×C22⋊C4SD1618yescomplemented
411C2×C22⋊C4C2×D414yes—
412C2×C22⋊C4C2×D414yes—
413C2×C42—22no—
414C2×C42—22no—
415C2×C42—22no—
416C2×C42—22no—
417C2×C42—24no—
418C2×C42—44no—
419C2×C42C2×D412yes—
420C2×C42C2×D412yes—
421C2×C42C2412yes—
422C2×C42C2412yes—
423#106—28no—
424#106—28no—
425C4⋊C8—28no—
426C4⋊C8—28no—
427#103—28no—
428#103—28no—
429#103—44no—
430#103C2×D4116yescomplemented
431#102—28no—
432#102—28no—
433#102—44no—
434#102C2×D4116yescomplemented
435C22⋊C8—44no—
436#95—24no—
437#95—24no—
438#95—24no—
439#95—24no—
440#95C2×D414yes—
441#95C2×D414yes—
442C24—22no—
443C24—22no—
444C24—22no—
445C24—22no—
446C24—22no—
447C24—22no—
448C24—24no—
449C24—22no—
450C24—22no—
451C24—42no—
452C24—42no—
453C24—42no—
454C24—42no—
455C24—42no—
456C24—42no—
457C24—42no—
458C24—42no—
459C24—42no—
460C24—42no—
461C24—42no—
462C24—42no—
463C24—42no—
464C24C2×SD1614yes—
465C24C22×D412yes—
466C24C22×D411yescharacteristic
467C2×Q8—24no—
468C2×Q8—22no—
469C2×Q8—28no—
470C2×Q8—28no—
471C2×Q8—22no—
472C2×Q8—22no—
473C2×Q8—22no—
474C2×Q8—22no—
475C2×Q8—22no—
476C2×Q8—22no—
477C2×Q8—22no—
478C2×Q8—22no—
479C2×Q8—22no—
480C2×Q8—22no—
481C2×Q8—44no—
482C2×Q8—42no—
483C2×Q8—42no—
484C2×Q8—42no—
485C2×Q8—42no—
486C2×Q8—42no—
487C2×Q8—44no—
488C2×Q8—44no—
489C2×Q8—44no—
490C2×Q8—44no—
491C2×Q8—44no—
492C2×Q8C22×D414yes—
493C2×D4—28no—
494C2×D4—28no—
495C2×D4—24no—
496C2×D4—22no—
497C2×D4—22no—
498C2×D4—22no—
499C2×D4—22no—
500C2×D4—22no—
501C2×D4—22no—
502C2×D4—22no—
503C2×D4—22no—
504C2×D4—22no—
505C2×D4—22no—
506C2×D4—22no—
507C2×D4—48no—
508C2×D4—48no—
509C2×D4—48no—
510C2×D4—48no—
511C2×D4—48no—
512C2×D4—48no—
513C2×D4—48no—
514C2×D4—42no—
515C2×D4—44no—
516C2×D4—44no—
517C2×D4—44no—
518C2×D4—42no—
519C2×D4—42no—
520C2×D4—44no—
521C2×D4—42no—
522C2×D4—42no—
523C2×D4—44no—
524C2×D4—44no—
525C2×D4—48no—
526C2×D4—84no—
527C2×D4—84no—
528C2×D4—816no—
529C2×D4—84no—
530C2×D4—84no—
531C2×D4—816no—
532C2×D4—816no—
533C2×D4—816no—
534C2×D4C22×D414yes—
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—22no—
545C22×C4—22no—
546C22×C4—24no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—24no—
555C22×C4—24no—
556C22×C4—24no—
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—48no—
567C22×C4—42no—
568C22×C4—42no—
569C22×C4—42no—
570C22×C4—42no—
571C22×C4—42no—
572C22×C4—42no—
573C22×C4—44no—
574C22×C4—44no—
575C22×C4—44no—
576C22×C4—44no—
577C22×C4—42no—
578C22×C4—42no—
579C22×C4—42no—
580C22×C4—42no—
581C22×C4—42no—
582C22×C4—42no—
583C22×C4—42no—
584C22×C4—42no—
585C22×C4—42no—
586C22×C4—48no—
587C22×C4—84no—
588C22×C4—816no—
589C22×C4C2×SD1614yes—
590C22×C4C2×SD1614yes—
591C22×C4C22×D412yes—
592C22×C4C22×D412yes—
593C22×C4C22×D412yes—
594C22×C4C22×D412yes—
595C22×C4C22×D412yes—
596C22×C4C22×D411yescharacteristic
597C22×C4C22×D412yes—
598C22×C4C22×D412yes—
599C22×C4H(5,𝔽2)12yes—
600C22×C4H(5,𝔽2)12yes—
601C22×C4H(5,𝔽2)12yes—
602C22×C42−1+412yes—
603C22×C4C2511yescharacteristic
604SD16—416no—
605SD16—416no—
606SD16—416no—
607SD16—416no—
608C2×C8—28no—
609C2×C8—28no—
610C2×C8—22no—
611C2×C8—22no—
612C2×C8—22no—
613C2×C8—22no—
614C2×C8—22no—
615C2×C8—22no—
616C2×C8—22no—
617C2×C8—22no—
618C2×C8—22no—
619C2×C8—22no—
620C2×C8—416no—
621C2×C8—44no—
622C2×C8—44no—
623C2×C8C22×D414yes—
624C2×C8C22×D414yes—
625C4⋊C4—24no—
626C4⋊C4—24no—
627C4⋊C4—22no—
628C4⋊C4—22no—
629C4⋊C4—22no—
630C4⋊C4—22no—
631C4⋊C4—22no—
632C4⋊C4—22no—
633C4⋊C4—48no—
634C4⋊C4—48no—
635C4⋊C4—48no—
636C4⋊C4—48no—
637C4⋊C4—48no—
638C4⋊C4—48no—
639C4⋊C4—42no—
640C4⋊C4—42no—
641C4⋊C4—48no—
642C4⋊C4C22×D414yes—
643C4⋊C4C22×D414yes—
644C22⋊C4—44no—
645C22⋊C4—48no—
646C22⋊C4—48no—
647C22⋊C4—48no—
648C22⋊C4—48no—
649C22⋊C4—48no—
650C22⋊C4—48no—
651C22⋊C4—84no—
652C22⋊C4C2×SD16116yescomplemented
653C42—24no—
654C42—24no—
655C42—22no—
656C42—22no—
657C42—22no—
658C42—22no—
659C42—48no—
660C23—22no—
661C23—22no—
662C23—22no—
663C23—28no—
664C23—28no—
665C23—28no—
666C23—22no—
667C23—22no—
668C23—22no—
669C23—24no—
670C23—44no—
671C23—44no—
672C23—44no—
673C23—44no—
674C23—48no—
675C23—42no—
676C23—42no—
677C23—48no—
678C23—48no—
679C23—42no—
680C23—42no—
681C23—42no—
682C23—42no—
683C23—42no—
684C23—42no—
685C23—42no—
686C23—42no—
687C23—42no—
688C23—42no—
689C23—42no—
690C23—84no—
691C23—84no—
692C23—84no—
693C23—84no—
694C23—84no—
695C23—84no—
696C23—84no—
697C23—84no—
698C23—84no—
699C23—84no—
700C23—84no—
701C23#53712yes—
702C23D4212yes—
703C23D4212yes—
704C23C22×SD1614yes—
705C23C22×SD1612yes—
706C23#57512yes—
707C23#57712yes—
708C23#57712yes—
709C23C23×D411yescharacteristic
710Q8—24no—
711Q8—24no—
712Q8—48no—
713Q8—42no—
714Q8—42no—
715Q8—42no—
716Q8—42no—
717Q8—42no—
718Q8—42no—
719Q8—84no—
720D4—24no—
721D4—24no—
722D4—48no—
723D4—42no—
724D4—42no—
725D4—42no—
726D4—42no—
727D4—42no—
728D4—42no—
729D4—816no—
730D4—816no—
731D4—816no—
732D4—816no—
733D4—84no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—28no—
737C2×C4—28no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—24no—
744C2×C4—24no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—24no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—44no—
753C2×C4—48no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4—44no—
757C2×C4—48no—
758C2×C4—44no—
759C2×C4—48no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—48no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—42no—
772C2×C4—42no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—42no—
778C2×C4—816no—
779C2×C4—84no—
780C2×C4—84no—
781C2×C4—84no—
782C2×C4#53712yes—
783C2×C4#53714yes—
784C2×C4#53714yes—
785C2×C4D4212yes—
786C2×C4D4212yes—
787C2×C4D4214yes—
788C2×C4#56014yes—
789C2×C4C22×SD1614yes—
790C2×C4C22×SD1614yes—
791C2×C4C23×D411yescharacteristic
792C2×C4C23×D411yescharacteristic
793C2×C4C2×H(5,𝔽2)11yescharacteristic
794C2×C4C2×H(5,𝔽2)11yescharacteristic
795C2×C4C2×H(5,𝔽2)11yescharacteristic
796C2×C4C2×2−1+411yescharacteristic
797C8—24no—
798C8—24no—
799C8—42no—
800C8—42no—
801C22—24no—
802C22—24no—
803C22—24no—
804C22—42no—
805C22—42no—
806C22—42no—
807C22—416no—
808C22—42no—
809C22—44no—
810C22—44no—
811C22—44no—
812C22—82no—
813C22—82no—
814C22—816no—
815C22—82no—
816C22—82no—
817C22—82no—
818C22—82no—
819C22—82no—
820C22—82no—
821C22—82no—
822C22—82no—
823C22—82no—
824C22—168no—
825C22#267514yes—
826C22#324614yes—
827C22#326014yes—
828C22#326714yes—
829C22#327114yes—
830C22D4×SD1614yes—
831C22D4×SD1614yes—
832C22C2×#53711yescharacteristic
833C22C2×D4211yescharacteristic
834C22C2×D4211yescharacteristic
835C22C23×SD1611yescharacteristic
836C22C2×#57511yescharacteristic
837C22C2×#57711yescharacteristic
838C22C2×#57711yescharacteristic
839C4—24no—
840C4—24no—
841C4—42no—
842C4—44no—
843C4—42no—
844C4—44no—
845C4—42no—
846C4—44no—
847C4—82no—
848C4—82no—
849C4—82no—
850C4#267514yes—
851C4C2×#53711yescharacteristic
852C4C2×#53711yescharacteristic
853C4C2×D4211yescharacteristic
854C4C2×#56011yescharacteristic
855C2—44no—
856C2—84no—
857C2—162no—
858C2#3084818yesdirect product factor
859C2C2×#267511yescharacteristic
860C2C2×#324611yescharacteristic
861C2C2×#326011yescharacteristic
862C2C2×#326711yescharacteristic
863C2C2×#327111yescharacteristic
864C2C2×D4×SD1611yescharacteristic
865C2C2×D4×SD1611yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#2428C2
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×#465C2semidirect
2. C22×#465C2semidirect
3. C22×#460C2semidirect
4. C22×#461C2semidirect
5. C2×#2429C2semidirect
7. #30848C2direct (N × H)
8. C2×#2066C2semidirect
9. C2×#2065C2semidirect
10. C2×#2013C2semidirect
11. C2×#2014C2semidirect
12. C2×#2000C2semidirect
13. C2×#2000C2semidirect
14. C2×#1865C2semidirect
15. C2×#1864C2semidirect
16. C2×#1850C2semidirect
33. C2×#465C22semidirect
34. C2×#465C22semidirect
36. C2×#460C22semidirect
38. C2×#461C22semidirect
53. #2429C22semidirect
68. #2066C22semidirect
69. #2065C22semidirect
70. #2014C22semidirect
71. #2013C22semidirect
72. #2000C22semidirect
73. #2000C22semidirect
74. #1865C22semidirect
75. #1864C22semidirect
76. #1850C22semidirect
187. C2×#103D4semidirect
195. C2×#102D4semidirect
410. C2×C22⋊C4SD16semidirect
430. #103C2×D4semidirect
434. #102C2×D4semidirect
652. C22⋊C4C2×SD16semidirect
858. C2#30848direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#4652
C22×#4602
C22×#4612
C2×#24292
C2×#24282
#308482
C2×#20662
C2×#20652
C2×#20132
C2×#20142
C2×#20002
C2×#18652
C2×#18642
C2×#18502