Finite Group Databasebeta

← C2×#30860 #7502095

Subgroups — C2×#30860 #7502095

Order 512.

3202 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×#468C211yesmaximal, characteristic, complemented
2C22×#468C211yesmaximal, characteristic, complemented
3C22×#460C211yesmaximal, characteristic, complemented
4C22×#461C211yesmaximal, characteristic, complemented
5C2×#2429C211yesmaximal, characteristic, complemented
6C2×#2428C211yesmaximal, characteristic
7#30860C2116yesmaximal, direct product factor
8C2×#2068C211yesmaximal, characteristic, complemented
9C2×#2067C211yesmaximal, characteristic, complemented
10C2×#2013C211yesmaximal, characteristic, complemented
11C2×#2014C211yesmaximal, characteristic, complemented
12C2×#2000C211yesmaximal, characteristic, complemented
13C2×#2000C211yesmaximal, characteristic, complemented
14C2×#1863C211yesmaximal, characteristic, complemented
15C2×#1862C211yesmaximal, characteristic, complemented
16C2×#1851C211yesmaximal, characteristic, complemented
17C23×SD16C2211yescharacteristic
18C23×SD16C2211yescharacteristic
19C23×SD16C2211yescharacteristic
20C23×SD16C2211yescharacteristic
21C23×M16C2211yescharacteristic
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×#468—28no—
32C2×#468—28no—
33C2×#468C2218yescomplemented
34C2×#468C2218yescomplemented
35C2×#460—28no—
36C2×#460C2218yescomplemented
37C2×#461—28no—
38C2×#461C2218yescomplemented
39C22×#107C2211yescharacteristic
40C22×#107C2211yescharacteristic
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#2068C2218yescomplemented
69#2067C2218yescomplemented
70#2014C2218yescomplemented
71#2013C2218yescomplemented
72#2000C2218yescomplemented
73#2000C2218yescomplemented
74#1863C2218yescomplemented
75#1862C2218yescomplemented
76#1851C2218yescomplemented
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—
107C22×M16—24no—
108C22×M16—24no—
109C22×M16—42no—
110C22×M16C2314yes—
111C23×C8C2311yescharacteristic
112C23×C8C2311yescharacteristic
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—48no—
137C2×#121—42no—
138C2×#121—42no—
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#468—232no—
173#468—232no—
174#461—232no—
175#460—232no—
176C2×#107—24no—
177C2×#107—24no—
178C2×#107C2314yes—
179C2×#107C2314yes—
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—
320C2×M16—28no—
321C2×M16—28no—
322C2×M16—44no—
323C2×M16—416no—
324C22×C8—22no—
325C22×C8—22no—
326C22×C8—22no—
327C22×C8—22no—
328C22×C8—22no—
329C22×C8—22no—
330C22×C8—22no—
331C22×C8—22no—
332C22×C8—22no—
333C22×C8—22no—
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—432no—
355#121—44no—
356#121—44no—
357#121—48no—
358#121—48no—
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—24no—
403C2×C22⋊C4—24no—
404C2×C22⋊C4—44no—
405C2×C22⋊C4—44no—
406C2×C22⋊C4—44no—
407C2×C22⋊C4—44no—
408C2×C22⋊C4—44no—
409C2×C22⋊C4—44no—
410C2×C22⋊C4—82no—
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#107—28no—
424#107—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—24no—
446C24—22no—
447C24—22no—
448C24—22no—
449C24—22no—
450C24—22no—
451C24—22no—
452C24—42no—
453C24—42no—
454C24—42no—
455C24—42no—
456C24—42no—
457C24—42no—
458C24—42no—
459C24—42no—
460C24—42no—
461C24—42no—
462C24—42no—
463C24—42no—
464C24—42no—
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×C4AGL(1,ℤ/8)14yes—
590C22×C4#13714yes—
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—
608M16—416no—
609C2×C8—28no—
610C2×C8—28no—
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—22no—
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—28no—
645C22⋊C4—28no—
646C22⋊C4—48no—
647C22⋊C4—48no—
648C22⋊C4—48no—
649C22⋊C4—48no—
650C22⋊C4—48no—
651C22⋊C4—48no—
652C22⋊C4—84no—
653C42—24no—
654C42—24no—
655C42—22no—
656C42—22no—
657C42—22no—
658C42—22no—
659C42—48no—
660C23—22no—
661C23—22no—
662C23—22no—
663C23—24no—
664C23—22no—
665C23—22no—
666C23—22no—
667C23—22no—
668C23—44no—
669C23—48no—
670C23—42no—
671C23—42no—
672C23—44no—
673C23—44no—
674C23—44no—
675C23—48no—
676C23—44no—
677C23—44no—
678C23—48no—
679C23—44no—
680C23—42no—
681C23—42no—
682C23—42no—
683C23—42no—
684C23—42no—
685C23—42no—
686C23—42no—
687C23—42no—
688C23—42no—
689C23—42no—
690C23—42no—
691C23—84no—
692C23—84no—
693C23—84no—
694C23—84no—
695C23—84no—
696C23—84no—
697C23—84no—
698C23—84no—
699C23—84no—
700C23—84no—
701C23—84no—
702C23#53712yes—
703C23D4212yes—
704C23D4212yes—
705C23C2×AGL(1,ℤ/8)12yes—
706C23C2×#13712yes—
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—48no—
757C2×C4—44no—
758C2×C4—48no—
759C2×C4—44no—
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×C4C2×AGL(1,ℤ/8)14yes—
790C2×C4C2×#13714yes—
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—42no—
802C22—44no—
803C22—42no—
804C22—42no—
805C22—44no—
806C22—42no—
807C22—42no—
808C22—44no—
809C22—42no—
810C22—42no—
811C22—82no—
812C22—82no—
813C22—88no—
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#325414yes—
827C22#326014yes—
828C22#326514yes—
829C22#326614yes—
830C22#327214yes—
831C22#327814yes—
832C22C2×#53711yescharacteristic
833C22C2×D4211yescharacteristic
834C22C2×D4211yescharacteristic
835C22C22×AGL(1,ℤ/8)11yescharacteristic
836C22C22×#13711yescharacteristic
837C22C2×#57711yescharacteristic
838C22C2×#57711yescharacteristic
839C4—24no—
840C4—24no—
841C4—44no—
842C4—42no—
843C4—44no—
844C4—42no—
845C4—42no—
846C4—44no—
847C4—82no—
848C4—82no—
849C4—82no—
850C4#267514yes—
851C4C2×#53711yescharacteristic
852C4C2×#53711yescharacteristic
853C4C2×D4211yescharacteristic
854C4C2×#56011yescharacteristic
855C2—82no—
856C2—84no—
857C2—162no—
858C2#3086018yesdirect product factor
859C2C2×#267511yescharacteristic
860C2C2×#325411yescharacteristic
861C2C2×#326011yescharacteristic
862C2C2×#326511yescharacteristic
863C2C2×#326611yescharacteristic
864C2C2×#327211yescharacteristic
865C2C2×#327811yescharacteristic
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×#468C2semidirect
2. C22×#468C2semidirect
3. C22×#460C2semidirect
4. C22×#461C2semidirect
5. C2×#2429C2semidirect
7. #30860C2direct (N × H)
8. C2×#2068C2semidirect
9. C2×#2067C2semidirect
10. C2×#2013C2semidirect
11. C2×#2014C2semidirect
12. C2×#2000C2semidirect
13. C2×#2000C2semidirect
14. C2×#1863C2semidirect
15. C2×#1862C2semidirect
16. C2×#1851C2semidirect
33. C2×#468C22semidirect
34. C2×#468C22semidirect
36. C2×#460C22semidirect
38. C2×#461C22semidirect
53. #2429C22semidirect
68. #2068C22semidirect
69. #2067C22semidirect
70. #2014C22semidirect
71. #2013C22semidirect
72. #2000C22semidirect
73. #2000C22semidirect
74. #1863C22semidirect
75. #1862C22semidirect
76. #1851C22semidirect
187. C2×#103D4semidirect
195. C2×#102D4semidirect
430. #103C2×D4semidirect
434. #102C2×D4semidirect
858. C2#30860direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#4682
C22×#4602
C22×#4612
C2×#24292
C2×#24282
#308602
C2×#20682
C2×#20672
C2×#20132
C2×#20142
C2×#20002
C2×#18632
C2×#18622
C2×#18512