Finite Group Databasebeta

← C2×#25610 #6449124

Subgroups — C2×#25610 #6449124

Order 512.

3734 conjugacy classes of subgroups.

The subgroup lattice has 876 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#542C211yesmaximal, characteristic, complemented
2C22×#495C211yesmaximal, characteristic, complemented
3C22×#489C211yesmaximal, characteristic, complemented
4C2×#2620C211yesmaximal, characteristic, complemented
5#25610C2116yesmaximal, direct product factor
6C2×#2001C211yesmaximal, characteristic, complemented
7C2×#2000C211yesmaximal, characteristic, complemented
8C2×#2000C211yesmaximal, characteristic, complemented
9C2×#1999C211yesmaximal, characteristic
10C2×#1990C211yesmaximal, characteristic, complemented
11C2×#1959C211yesmaximal, characteristic, complemented
12C2×#1880C211yesmaximal, characteristic, complemented
13C2×#1878C211yesmaximal, characteristic, complemented
14C2×#1879C211yesmaximal, characteristic, complemented
15C2×#1877C211yesmaximal, characteristic, complemented
16C2×#1750C211yesmaximal, characteristic, complemented
17C23×Q16C2211yescharacteristic
18C23×SD16C2211yescharacteristic
19C23×SD16C2211yescharacteristic
20C23×D8C2211yescharacteristic
21C2×#542—28no—
22C2×#542—28no—
23C2×#542—24no—
24C2×#542C2218yescomplemented
25C22×C4⋊Q8C2211yescharacteristic
26C22×#126—21no—
27C22×#124—21no—
28C22×#124C2211yescharacteristic
29C22×#124C2211yescharacteristic
30C22×#123—21no—
31C22×C22⋊Q8—21no—
32C22×C22⋊Q8C2211yescharacteristic
33C22×C22⋊Q8C2211yescharacteristic
34C22×#121C2211yescharacteristic
35C22×#121C2211yescharacteristic
36C22×C4×Q8C2211yescharacteristic
37C22×C4×D4C2211yescharacteristic
38C22×#117C2211yescharacteristic
39C2×#495—28no—
40C2×#495C2218yescomplemented
41C2×#489—28no—
42C2×#489C2218yescomplemented
43C22×#103C2211yescharacteristic
44C22×#103C2211yescharacteristic
45C22×#103C2211yescharacteristic
46C22×#103C2211yescharacteristic
47C22×#102C2211yescharacteristic
48C22×#102C2211yescharacteristic
49C22×#102C2211yescharacteristic
50C22×#102C2211yescharacteristic
51C22×C22⋊C8C2211yescharacteristic
52C22×C22⋊C8C2211yescharacteristic
53C22×#97C2211yescharacteristic
54C22×C4×C8C2211yescharacteristic
55#2620—24no—
56#2620C2218yescomplemented
57C2×#396—21no—
58C2×#396—21no—
59C2×#394—21no—
60C2×#394—21no—
61C2×#391C2211yescharacteristic
62C2×#390C2211yescharacteristic
63C2×#384C2211yescharacteristic
64#2001C2218yescomplemented
65#2000C2218yescomplemented
66#2000C2218yescomplemented
67#1999C2218yes—
68#1990C2218yescomplemented
69#1959C2218yescomplemented
70#1880C2218yescomplemented
71#1879C2218yescomplemented
72#1878C2218yescomplemented
73#1877C2218yescomplemented
74#1750C2218yescomplemented
75C2×#340C2211yescharacteristic
76C2×#340C2211yescharacteristic
77C2×#340C2211yescharacteristic
78C2×#340C2211yescharacteristic
79C2×#336C2211yescharacteristic
80C2×#336C2211yescharacteristic
81C23×Q8—21no—
82C23×Q8C2311yescharacteristic
83C23×Q8C2311yescharacteristic
84C23×D4—21no—
85C23×D4—21no—
86C23×D4C2311yescharacteristic
87C23×D4C2311yescharacteristic
88C24×C4—21no—
89C24×C4C2311yescharacteristic
90C22×Q16—24no—
91C22×Q16—24no—
92C22×Q16—42no—
93C22×Q16C2314yes—
94C22×SD16—24no—
95C22×SD16—24no—
96C22×SD16—24no—
97C22×SD16—24no—
98C22×SD16—42no—
99C22×SD16—42no—
100C22×SD16C2314yes—
101C22×SD16C2314yes—
102C22×D8—24no—
103C22×D8—24no—
104C22×D8—42no—
105C22×D8C2314yes—
106C23×C8C2311yescharacteristic
107C23×C8C2311yescharacteristic
108C23×C8C2311yescharacteristic
109C23×C8C2311yescharacteristic
110#542—264no—
111#542—232no—
112#542—232no—
113C2×C4⋊Q8—22no—
114C2×C4⋊Q8—24no—
115C2×C4⋊Q8D418yescomplemented
116C2×C4⋊Q8C2314yes—
117C2×#126—216no—
118C2×#126—28no—
119C2×#124—216no—
120C2×#124—28no—
121C2×#124—22no—
122C2×#124—24no—
123C2×#124—22no—
124C2×#124—24no—
125C2×#124—24no—
126C2×#124D418yescomplemented
127C2×#124C2314yes—
128C2×#124C2314yes—
129C2×#123—216no—
130C2×#123—28no—
131C2×C22⋊Q8—216no—
132C2×C22⋊Q8—24no—
133C2×C22⋊Q8—22no—
134C2×C22⋊Q8—22no—
135C2×C22⋊Q8—28no—
136C2×C22⋊Q8—24no—
137C2×C22⋊Q8—42no—
138C2×C22⋊Q8—42no—
139C2×C22⋊Q8C2314yes—
140C2×C22⋊Q8C2314yes—
141C2×#121—24no—
142C2×#121—22no—
143C2×#121—22no—
144C2×#121—24no—
145C2×#121—42no—
146C2×#121—42no—
147C2×#121C2314yes—
148C2×#121C2314yes—
149C2×C4×Q8—24no—
150C2×C4×Q8—24no—
151C2×C4×Q8—22no—
152C2×C4×Q8C2314yes—
153C2×C4×D4—24no—
154C2×C4×D4—24no—
155C2×C4×D4—22no—
156C2×C4×D4C2314yes—
157C2×#117—24no—
158C2×#117—24no—
159C2×#117D414yes—
160C2×#117C2314yes—
161C22×C4⋊C4—21no—
162C22×C4⋊C4—21no—
163C22×C4⋊C4—21no—
164C22×C4⋊C4—21no—
165C22×C4⋊C4—21no—
166C22×C4⋊C4—21no—
167C22×C4⋊C4D411yescharacteristic
168C22×C4⋊C4D411yescharacteristic
169C22×C4⋊C4C2311yescharacteristic
170C22×C4⋊C4C2311yescharacteristic
171C22×C4⋊C4C2311yescharacteristic
172C22×C4⋊C4C2311yescharacteristic
173C22×C22⋊C4—21no—
174C22×C22⋊C4—21no—
175C22×C22⋊C4—21no—
176C22×C22⋊C4—21no—
177C22×C22⋊C4—21no—
178C22×C22⋊C4—21no—
179C22×C22⋊C4—21no—
180C22×C22⋊C4—21no—
181C22×C22⋊C4—21no—
182C22×C22⋊C4—21no—
183C22×C22⋊C4—21no—
184C22×C22⋊C4D411yescharacteristic
185C22×C22⋊C4D411yescharacteristic
186C22×C42—21no—
187C22×C42C2311yescharacteristic
188C22×C42C2311yescharacteristic
189#495—232no—
190#489—232no—
191C2×#103—24no—
192C2×#103—24no—
193C2×#103—42no—
194C2×#103—42no—
195C2×#103C2314yes—
196C2×#103C2314yes—
197C2×#103C2314yes—
198C2×#103C2314yes—
199C2×#102—24no—
200C2×#102—24no—
201C2×#102—42no—
202C2×#102—42no—
203C2×#102C2314yes—
204C2×#102C2314yes—
205C2×#102C2314yes—
206C2×#102C2314yes—
207C2×C22⋊C8—24no—
208C2×C22⋊C8—24no—
209C2×C22⋊C8C2314yes—
210C2×C22⋊C8C2314yes—
211C2×#97—24no—
212C2×#97C2314yes—
213C2×C4×C8—24no—
214C2×C4×C8C2314yes—
215#396—28no—
216#396—28no—
217#394—28no—
218#394—28no—
219#391—22no—
220#391C2314yes—
221#390—22no—
222#390C2314yes—
223#384—22no—
224#384C2314yes—
225C2×#95—21no—
226C2×#95—21no—
227#340C2314yes—
228#340C2314yes—
229#340C2314yes—
230#340C2314yes—
231#336C2314yes—
232#336C2314yes—
233C25—21no—
234C25—21no—
235C25C2×D411yescharacteristic
236C22×Q8—28no—
237C22×Q8—22no—
238C22×Q8—21no—
239C22×Q8—24no—
240C22×Q8—21no—
241C22×Q8—22no—
242C22×Q8—22no—
243C22×Q8—22no—
244C22×Q8—22no—
245C22×Q8—22no—
246C22×Q8—22no—
247C22×Q8—22no—
248C22×Q8—22no—
249C22×Q8—22no—
250C22×Q8—22no—
251C22×Q8—82no—
252C22×Q8—82no—
253C22×Q8C2×D414yes—
254C22×Q8C2412yes—
255C22×Q8C2412yes—
256C22×D4—28no—
257C22×D4—24no—
258C22×D4—24no—
259C22×D4—21no—
260C22×D4—22no—
261C22×D4—22no—
262C22×D4—22no—
263C22×D4—21no—
264C22×D4—22no—
265C22×D4—22no—
266C22×D4—22no—
267C22×D4—22no—
268C22×D4—22no—
269C22×D4—22no—
270C22×D4—22no—
271C22×D4—22no—
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—28no—
284C23×C4—22no—
285C23×C4—22no—
286C23×C4—22no—
287C23×C4—22no—
288C23×C4—22no—
289C23×C4—22no—
290C23×C4—24no—
291C23×C4—21no—
292C23×C4—21no—
293C23×C4—21no—
294C23×C4—82no—
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×Q16—28no—
305C2×Q16—28no—
306C2×Q16—44no—
307C2×Q16—416no—
308C2×SD16—28no—
309C2×SD16—28no—
310C2×SD16—28no—
311C2×SD16—28no—
312C2×SD16—44no—
313C2×SD16—44no—
314C2×SD16—416no—
315C2×SD16—416no—
316C2×D8—28no—
317C2×D8—28no—
318C2×D8—44no—
319C2×D8—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#4114yes—
331C22×C8#4114yes—
332C22×C8C2412yes—
333C22×C8C2412yes—
334C22×C8C2412yes—
335C22×C8C2412yes—
336C4⋊Q8—216no—
337C4⋊Q8—28no—
338C4⋊Q8C2×D4116yescomplemented
339#126—264no—
340#124—264no—
341#124—216no—
342#124—28no—
343#124—28no—
344#124—28no—
345#124—48no—
346#124C2×D4116yescomplemented
347#123—264no—
348C22⋊Q8—264no—
349C22⋊Q8—216no—
350C22⋊Q8—28no—
351C22⋊Q8—28no—
352C22⋊Q8—44no—
353C22⋊Q8—44no—
354C22⋊Q8—48no—
355#121—216no—
356#121—28no—
357#121—28no—
358#121—44no—
359#121—44no—
360#121—48no—
361C4×Q8—216no—
362C4×Q8—28no—
363C4×Q8—28no—
364C4×D4—216no—
365C4×D4—28no—
366C4×D4—28no—
367#117—216no—
368#117—28no—
369#117—28no—
370C2×C4⋊C4—28no—
371C2×C4⋊C4—28no—
372C2×C4⋊C4—28no—
373C2×C4⋊C4—24no—
374C2×C4⋊C4—24no—
375C2×C4⋊C4—24no—
376C2×C4⋊C4—24no—
377C2×C4⋊C4—24no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—22no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—22no—
382C2×C4⋊C4—22no—
383C2×C4⋊C4—22no—
384C2×C4⋊C4—22no—
385C2×C4⋊C4—22no—
386C2×C4⋊C4—24no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—24no—
390C2×C4⋊C4—24no—
391C2×C4⋊C4—44no—
392C2×C4⋊C4—82no—
393C2×C4⋊C4—82no—
394C2×C4⋊C4C2×D414yes—
395C2×C4⋊C4C2×D414yes—
396C2×C4⋊C4C2×D414yes—
397C2×C4⋊C4C2×D414yes—
398C2×C4⋊C4C2412yes—
399C2×C4⋊C4C2412yes—
400C2×C4⋊C4C2412yes—
401C2×C4⋊C4C2412yes—
402C2×C22⋊C4—28no—
403C2×C22⋊C4—28no—
404C2×C22⋊C4—28no—
405C2×C22⋊C4—24no—
406C2×C22⋊C4—28no—
407C2×C22⋊C4—28no—
408C2×C22⋊C4—24no—
409C2×C22⋊C4—24no—
410C2×C22⋊C4—24no—
411C2×C22⋊C4—24no—
412C2×C22⋊C4—24no—
413C2×C22⋊C4—24no—
414C2×C22⋊C4—24no—
415C2×C22⋊C4—24no—
416C2×C22⋊C4—24no—
417C2×C22⋊C4—24no—
418C2×C22⋊C4—24no—
419C2×C22⋊C4—24no—
420C2×C22⋊C4—44no—
421C2×C22⋊C4—44no—
422C2×C22⋊C4—44no—
423C2×C22⋊C4—44no—
424C2×C22⋊C4—82no—
425C2×C22⋊C4—82no—
426C2×C22⋊C4C2×D414yes—
427C2×C22⋊C4C2×D414yes—
428C2×C42—28no—
429C2×C42—22no—
430C2×C42—22no—
431C2×C42—24no—
432C2×C42C2×D412yes—
433C2×C42C2×D412yes—
434C2×C42C2×D414yes—
435C2×C42C2×D414yes—
436C2×C42C2412yes—
437C2×C42C2412yes—
438#103—28no—
439#103—28no—
440#103—44no—
441#103—44no—
442#102—28no—
443#102—28no—
444#102—44no—
445#102—44no—
446C22⋊C8—28no—
447C22⋊C8—28no—
448#97—28no—
449C4×C8—28no—
450#95—24no—
451#95—24no—
452C24—22no—
453C24—24no—
454C24—22no—
455C24—22no—
456C24—22no—
457C24—22no—
458C24—22no—
459C24—22no—
460C24—22no—
461C24—22no—
462C24—42no—
463C24—42no—
464C24—42no—
465C24—42no—
466C24—42no—
467C24—42no—
468C24—42no—
469C24—42no—
470C24—42no—
471C24—42no—
472C24—42no—
473C24—42no—
474C24—42no—
475C24C22×D412yes—
476C24C22×D411yescharacteristic
477C2×Q8—24no—
478C2×Q8—216no—
479C2×Q8—22no—
480C2×Q8—28no—
481C2×Q8—28no—
482C2×Q8—22no—
483C2×Q8—22no—
484C2×Q8—22no—
485C2×Q8—22no—
486C2×Q8—22no—
487C2×Q8—22no—
488C2×Q8—22no—
489C2×Q8—22no—
490C2×Q8—22no—
491C2×Q8—22no—
492C2×Q8—42no—
493C2×Q8—42no—
494C2×Q8—42no—
495C2×Q8—42no—
496C2×Q8—42no—
497C2×Q8—44no—
498C2×Q8—44no—
499C2×Q8—44no—
500C2×Q8—44no—
501C2×Q8—44no—
502C2×Q8—44no—
503C2×Q8—816no—
504C2×Q8—84no—
505C2×Q8—84no—
506C2×Q8C22×D414yes—
507C2×D4—216no—
508C2×D4—24no—
509C2×D4—28no—
510C2×D4—28no—
511C2×D4—22no—
512C2×D4—22no—
513C2×D4—22no—
514C2×D4—22no—
515C2×D4—22no—
516C2×D4—22no—
517C2×D4—22no—
518C2×D4—22no—
519C2×D4—22no—
520C2×D4—22no—
521C2×D4—22no—
522C2×D4—48no—
523C2×D4—42no—
524C2×D4—42no—
525C2×D4—42no—
526C2×D4—42no—
527C2×D4—42no—
528C2×D4—44no—
529C2×D4—44no—
530C2×D4—44no—
531C2×D4—44no—
532C2×D4—44no—
533C2×D4—44no—
534C2×D4—84no—
535C2×D4—84no—
536C2×D4—84no—
537C2×D4—84no—
538C2×D4—816no—
539C2×D4—816no—
540C2×D4C22×D414yes—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—24no—
547C22×C4—22no—
548C22×C4—24no—
549C22×C4—22no—
550C22×C4—24no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—216no—
561C22×C4—24no—
562C22×C4—24no—
563C22×C4—24no—
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—42no—
574C22×C4—42no—
575C22×C4—42no—
576C22×C4—42no—
577C22×C4—42no—
578C22×C4—42no—
579C22×C4—44no—
580C22×C4—44no—
581C22×C4—44no—
582C22×C4—44no—
583C22×C4—42no—
584C22×C4—42no—
585C22×C4—42no—
586C22×C4—42no—
587C22×C4—42no—
588C22×C4—42no—
589C22×C4—42no—
590C22×C4—42no—
591C22×C4—42no—
592C22×C4—84no—
593C22×C4—84no—
594C22×C4—816no—
595C22×C4#12014yes—
596C22×C4#12014yes—
597C22×C4C22×D412yes—
598C22×C4C22×D412yes—
599C22×C4C22×D412yes—
600C22×C4C22×D412yes—
601C22×C4C22×D412yes—
602C22×C4C22×D411yescharacteristic
603C22×C4C22×D412yes—
604C22×C4C22×D412yes—
605C22×C4C2×#4112yes—
606C22×C4C2×#4112yes—
607C22×C4H(5,𝔽2)12yes—
608C22×C4H(5,𝔽2)12yes—
609C22×C4C2511yescharacteristic
610Q16—416no—
611SD16—416no—
612SD16—416no—
613D8—416no—
614C2×C8—28no—
615C2×C8—28no—
616C2×C8—22no—
617C2×C8—22no—
618C2×C8—22no—
619C2×C8—22no—
620C2×C8—22no—
621C2×C8—22no—
622C2×C8—22no—
623C2×C8—22no—
624C2×C8—22no—
625C2×C8—22no—
626C2×C8—44no—
627C2×C8—44no—
628C2×C8C2×#4114yes—
629C2×C8C2×#4114yes—
630C4⋊C4—216no—
631C4⋊C4—216no—
632C4⋊C4—216no—
633C4⋊C4—28no—
634C4⋊C4—28no—
635C4⋊C4—24no—
636C4⋊C4—24no—
637C4⋊C4—22no—
638C4⋊C4—22no—
639C4⋊C4—22no—
640C4⋊C4—22no—
641C4⋊C4—22no—
642C4⋊C4—22no—
643C4⋊C4—48no—
644C4⋊C4—42no—
645C4⋊C4—42no—
646C4⋊C4—84no—
647C4⋊C4—84no—
648C4⋊C4C22×D414yes—
649C4⋊C4C22×D414yes—
650C22⋊C4—216no—
651C22⋊C4—216no—
652C22⋊C4—216no—
653C22⋊C4—216no—
654C22⋊C4—216no—
655C22⋊C4—28no—
656C22⋊C4—28no—
657C22⋊C4—48no—
658C22⋊C4—48no—
659C22⋊C4—48no—
660C22⋊C4—48no—
661C22⋊C4—84no—
662C22⋊C4—84no—
663C42—216no—
664C42—24no—
665C42—22no—
666C42—22no—
667C42#12018yes—
668C42C22×D414yes—
669C42C22×D414yes—
670C23—22no—
671C23—24no—
672C23—22no—
673C23—22no—
674C23—22no—
675C23—22no—
676C23—22no—
677C23—22no—
678C23—44no—
679C23—44no—
680C23—42no—
681C23—42no—
682C23—44no—
683C23—48no—
684C23—44no—
685C23—44no—
686C23—48no—
687C23—44no—
688C23—44no—
689C23—48no—
690C23—42no—
691C23—42no—
692C23—42no—
693C23—42no—
694C23—42no—
695C23—42no—
696C23—42no—
697C23—42no—
698C23—42no—
699C23—42no—
700C23—42no—
701C23—84no—
702C23—84no—
703C23—84no—
704C23—84no—
705C23—84no—
706C23—84no—
707C23—84no—
708C23—84no—
709C23—84no—
710C23—84no—
711C23—84no—
712C23C2×#12012yes—
713C23#53212yes—
714C23#53512yes—
715C23#57612yes—
716C23#57712yes—
717C23#57712yes—
718C23#57812yes—
719C23C23×D411yescharacteristic
720Q8—24no—
721Q8—24no—
722Q8—48no—
723Q8—42no—
724Q8—42no—
725Q8—42no—
726Q8—42no—
727Q8—42no—
728Q8—42no—
729Q8—816no—
730Q8—84no—
731D4—24no—
732D4—24no—
733D4—48no—
734D4—42no—
735D4—42no—
736D4—42no—
737D4—42no—
738D4—42no—
739D4—42no—
740D4—816no—
741D4—816no—
742D4—84no—
743C2×C4—28no—
744C2×C4—28no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—24no—
751C2×C4—22no—
752C2×C4—24no—
753C2×C4—22no—
754C2×C4—24no—
755C2×C4—22no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—44no—
764C2×C4—48no—
765C2×C4—44no—
766C2×C4—48no—
767C2×C4—48no—
768C2×C4—44no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—42no—
772C2×C4—42no—
773C2×C4—48no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—42no—
778C2×C4—42no—
779C2×C4—42no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—42no—
786C2×C4—42no—
787C2×C4—816no—
788C2×C4—84no—
789C2×C4—84no—
790C2×C4—84no—
791C2×C4C2×#12014yes—
792C2×C4C2×#12014yes—
793C2×C4C2×#12012yes—
794C2×C4#53212yes—
795C2×C4#53512yes—
796C2×C4#54614yes—
797C2×C4#54614yes—
798C2×C4#55014yes—
799C2×C4#55014yes—
800C2×C4C23×D411yescharacteristic
801C2×C4C23×D411yescharacteristic
802C2×C4C22×#4111yescharacteristic
803C2×C4C22×#4111yescharacteristic
804C2×C4C2×H(5,𝔽2)11yescharacteristic
805C2×C4C2×H(5,𝔽2)11yescharacteristic
806C8—24no—
807C8—24no—
808C8—42no—
809C8—42no—
810C22—42no—
811C22—42no—
812C22—42no—
813C22—42no—
814C22—42no—
815C22—44no—
816C22—44no—
817C22—42no—
818C22—42no—
819C22—44no—
820C22—82no—
821C22—82no—
822C22—88no—
823C22—816no—
824C22—82no—
825C22—82no—
826C22—82no—
827C22—82no—
828C22—82no—
829C22—82no—
830C22—82no—
831C22—82no—
832C22—82no—
833C22—168no—
834C22#243114yes—
835C22#301214yes—
836C22#301314yes—
837C22#317314yes—
838C22#317514yes—
839C22#322414yes—
840C22#322514yes—
841C22C22×#12011yescharacteristic
842C22C2×#53211yescharacteristic
843C22C2×#53511yescharacteristic
844C22C2×#57611yescharacteristic
845C22C2×#57711yescharacteristic
846C22C2×#57711yescharacteristic
847C22C2×#57811yescharacteristic
848C4—24no—
849C4—24no—
850C4—42no—
851C4—44no—
852C4—42no—
853C4—44no—
854C4—44no—
855C4—42no—
856C4—82no—
857C4—82no—
858C4—82no—
859C4#243114yes—
860C4C2×#54611yescharacteristic
861C4C2×#54611yescharacteristic
862C4C2×#55011yescharacteristic
863C4C2×#55011yescharacteristic
864C2—82no—
865C2—84no—
866C2—162no—
867C2#2561018yesdirect product factor
868C2C2×#243111yescharacteristic
869C2C2×#301211yescharacteristic
870C2C2×#301311yescharacteristic
871C2C2×#317311yescharacteristic
872C2C2×#317511yescharacteristic
873C2C2×#322411yescharacteristic
874C2C2×#322511yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#1999C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C22×#117 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C22×#542C2semidirect
2. C22×#495C2semidirect
3. C22×#489C2semidirect
4. C2×#2620C2semidirect
5. #25610C2direct (N × H)
6. C2×#2001C2semidirect
7. C2×#2000C2semidirect
8. C2×#2000C2semidirect
10. C2×#1990C2semidirect
11. C2×#1959C2semidirect
12. C2×#1880C2semidirect
13. C2×#1878C2semidirect
14. C2×#1879C2semidirect
15. C2×#1877C2semidirect
16. C2×#1750C2semidirect
24. C2×#542C22semidirect
40. C2×#495C22semidirect
42. C2×#489C22semidirect
56. #2620C22semidirect
64. #2001C22semidirect
65. #2000C22semidirect
66. #2000C22semidirect
68. #1990C22semidirect
69. #1959C22semidirect
70. #1880C22semidirect
71. #1879C22semidirect
72. #1878C22semidirect
73. #1877C22semidirect
74. #1750C22semidirect
115. C2×C4⋊Q8D4semidirect
126. C2×#124D4semidirect
338. C4⋊Q8C2×D4semidirect
346. #124C2×D4semidirect
867. C2#25610direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#5422
C22×#4952
C22×#4892
C2×#26202
#256102
C2×#20012
C2×#20002
C2×#19992
C2×#19902
C2×#19592
C2×#18802
C2×#18782
C2×#18792
C2×#18772
C2×#17502