Finite Group Databasebeta

← C2×#30449 #7500775

Subgroups — C2×#30449 #7500775

Order 512.

3306 conjugacy classes of subgroups.

The subgroup lattice has 841 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#494C211yesmaximal, characteristic, complemented
2C22×#462C211yesmaximal, characteristic, complemented
3C22×#451C211yesmaximal, characteristic
4C22×#451C211yesmaximal, characteristic
5C2×#2429C211yesmaximal, characteristic
6C2×#2434C211yesmaximal, characteristic
7#30449C2116yesmaximal, direct product factor
8C2×#2056C211yesmaximal, characteristic, complemented
9C2×#2043C211yesmaximal, characteristic, complemented
10C2×#2016C211yesmaximal, characteristic, complemented
11C2×#2016C211yesmaximal, characteristic, complemented
12C2×#2001C211yesmaximal, characteristic
13C2×#2001C211yesmaximal, characteristic
14C2×#1933C211yesmaximal, characteristic, complemented
15C2×#1923C211yesmaximal, characteristic
16C2×#1878C211yesmaximal, characteristic, complemented
17C24×Q8C2211yescharacteristic
18C23×Q16C2211yescharacteristic
19C23×Q16C2211yescharacteristic
20C23×Q16C2211yescharacteristic
21C23×Q16C2211yescharacteristic
22C23×Q16C2211yescharacteristic
23C23×Q16C2211yescharacteristic
24C22×C4⋊Q8C2211yescharacteristic
25C22×C4⋊Q8C2211yescharacteristic
26C22×C4⋊Q8C2211yescharacteristic
27C22×C22⋊Q8C2211yescharacteristic
28C22×C22⋊Q8C2211yescharacteristic
29C22×C22⋊Q8C2211yescharacteristic
30C22×C4×Q8C2211yescharacteristic
31C2×#494—28no—
32C2×#494C2218yescomplemented
33C2×#462—28no—
34C2×#462C2218yescomplemented
35C2×#451—28no—
36C2×#451—28no—
37C2×#451C2218yes—
38C2×#451C2218yes—
39C22×C4⋊C8C2211yescharacteristic
40C22×#103C2211yescharacteristic
41C22×#103C2211yescharacteristic
42C22×#103C2211yescharacteristic
43C22×#103C2211yescharacteristic
44C22×#103C2211yescharacteristic
45C22×#103C2211yescharacteristic
46C22×#103C2211yescharacteristic
47C22×#103C2211yescharacteristic
48C22×C22⋊C8C2211yescharacteristic
49C22×C22⋊C8C2211yescharacteristic
50C22×C4×C8C2211yescharacteristic
51#2434—24no—
52#2434C2218yes—
53#2429—24no—
54#2429C2218yes—
55C2×#398—21no—
56C2×#396—21no—
57C2×#395—21no—
58C2×#395—21no—
59C2×#391C2211yescharacteristic
60C2×#391C2211yescharacteristic
61C2×#391C2211yescharacteristic
62C2×#389—21no—
63C2×#389C2211yescharacteristic
64C2×#388—21no—
65C2×#385—21no—
66C2×#385—21no—
67C2×C4×C22⋊C4C2211yescharacteristic
68#2056C2218yescomplemented
69#2043C2218yescomplemented
70#2016C2218yescomplemented
71#2016C2218yescomplemented
72#2001C2218yes—
73#2001C2218yes—
74#1933C2218yescomplemented
75#1923C2218yes—
76#1878C2218yescomplemented
77C2×#340C2211yescharacteristic
78C2×#340C2211yescharacteristic
79C2×#336C2211yescharacteristic
80C2×#336C2211yescharacteristic
81C23×Q8—21no—
82C23×Q8—22no—
83C23×Q8—24no—
84C23×Q8—24no—
85C23×Q8—42no—
86C23×Q8—42no—
87C23×Q8—42no—
88C23×Q8—42no—
89C23×Q8C2311yescharacteristic
90C23×Q8C2311yescharacteristic
91C23×Q8C2311yescharacteristic
92C23×Q8C2311yescharacteristic
93C23×Q8C2311yescharacteristic
94C23×Q8C2314yes—
95C24×C4—21no—
96C24×C4C2311yescharacteristic
97C22×Q16—24no—
98C22×Q16—24no—
99C22×Q16—24no—
100C22×Q16—24no—
101C22×Q16—24no—
102C22×Q16—24no—
103C22×Q16—24no—
104C22×Q16—24no—
105C22×Q16—42no—
106C22×Q16—42no—
107C22×Q16—42no—
108C22×Q16—42no—
109C22×Q16—42no—
110C22×Q16—42no—
111C22×Q16—42no—
112C22×Q16—42no—
113C22×Q16—42no—
114C22×Q16D418yes—
115C22×Q16C2314yes—
116C22×Q16C2314yes—
117C22×Q16C2314yes—
118C22×Q16C2314yes—
119C22×Q16C2314yes—
120C22×Q16C2314yes—
121C23×C8C2311yescharacteristic
122C23×C8C2311yescharacteristic
123C23×C8C2311yescharacteristic
124C23×C8C2311yescharacteristic
125C2×C4⋊Q8—24no—
126C2×C4⋊Q8—24no—
127C2×C4⋊Q8—24no—
128C2×C4⋊Q8—22no—
129C2×C4⋊Q8—22no—
130C2×C4⋊Q8—22no—
131C2×C4⋊Q8—42no—
132C2×C4⋊Q8—42no—
133C2×C4⋊Q8—42no—
134C2×C4⋊Q8C2314yes—
135C2×C4⋊Q8C2314yes—
136C2×C4⋊Q8C2314yes—
137C2×C22⋊Q8—22no—
138C2×C22⋊Q8—22no—
139C2×C22⋊Q8—22no—
140C2×C22⋊Q8—24no—
141C2×C22⋊Q8—24no—
142C2×C22⋊Q8—42no—
143C2×C22⋊Q8—42no—
144C2×C22⋊Q8—42no—
145C2×C22⋊Q8—42no—
146C2×C22⋊Q8C2314yes—
147C2×C22⋊Q8C2314yes—
148C2×C22⋊Q8C2314yes—
149C2×C4×Q8—22no—
150C2×C4×Q8—24no—
151C2×C4×Q8—42no—
152C2×C4×Q8C2314yes—
153C22×C4⋊C4—21no—
154C22×C4⋊C4—21no—
155C22×C4⋊C4—21no—
156C22×C4⋊C4—21no—
157C22×C4⋊C4—21no—
158C22×C4⋊C4—21no—
159C22×C4⋊C4—21no—
160C22×C4⋊C4—21no—
161C22×C4⋊C4—21no—
162C22×C4⋊C4—21no—
163C22×C4⋊C4—21no—
164C22×C4⋊C4C2311yescharacteristic
165C22×C4⋊C4C2311yescharacteristic
166C22×C4⋊C4C2311yescharacteristic
167C22×C22⋊C4—21no—
168C22×C22⋊C4—21no—
169C22×C22⋊C4—21no—
170C22×C22⋊C4D411yescharacteristic
171C22×C22⋊C4D411yescharacteristic
172C22×C42—21no—
173C22×C42C2311yescharacteristic
174C22×C42C2311yescharacteristic
175#494—232no—
176#462—232no—
177#451—232no—
178#451—232no—
179C2×C4⋊C8—24no—
180C2×C4⋊C8C2314yes—
181C2×#103—24no—
182C2×#103—24no—
183C2×#103—24no—
184C2×#103—24no—
185C2×#103—42no—
186C2×#103—42no—
187C2×#103—42no—
188C2×#103D418yes—
189C2×#103C2314yes—
190C2×#103C2314yes—
191C2×#103C2314yes—
192C2×#103C2314yes—
193C2×#103C2314yes—
194C2×#103C2314yes—
195C2×#103C2314yes—
196C2×#103C2314yes—
197C2×C22⋊C8—24no—
198C2×C22⋊C8—24no—
199C2×C22⋊C8C2314yes—
200C2×C22⋊C8C2314yes—
201C2×C4×C8—24no—
202C2×C4×C8C2314yes—
203#398—28no—
204#396—28no—
205#395—28no—
206#395—28no—
207#391—22no—
208#391—22no—
209#391—22no—
210#391C2314yes—
211#391C2314yes—
212#391C2314yes—
213#389—22no—
214#389—28no—
215#389C2314yes—
216#388—28no—
217#385—28no—
218#385—28no—
219C4×C22⋊C4D414yes—
220C4×C22⋊C4C2314yes—
221C2×#95—21no—
222C2×#95—21no—
223C2×#95—21no—
224C2×#95—21no—
225C2×#95—21no—
226C2×#95—21no—
227C2×#95—21no—
228C2×#95D411yescharacteristic
229C2×#95D411yescharacteristic
230#340C2314yes—
231#340C2314yes—
232#336C2314yes—
233#336C2314yes—
234C25C2×D411yescharacteristic
235C22×Q8—21no—
236C22×Q8—21no—
237C22×Q8—21no—
238C22×Q8—21no—
239C22×Q8—21no—
240C22×Q8—24no—
241C22×Q8—22no—
242C22×Q8—22no—
243C22×Q8—22no—
244C22×Q8—28no—
245C22×Q8—28no—
246C22×Q8—22no—
247C22×Q8—22no—
248C22×Q8—22no—
249C22×Q8—22no—
250C22×Q8—22no—
251C22×Q8—22no—
252C22×Q8—22no—
253C22×Q8—22no—
254C22×Q8—22no—
255C22×Q8—22no—
256C22×Q8—22no—
257C22×Q8—22no—
258C22×Q8—22no—
259C22×Q8—22no—
260C22×Q8—22no—
261C22×Q8—22no—
262C22×Q8—22no—
263C22×Q8—22no—
264C22×Q8—22no—
265C22×Q8—22no—
266C22×Q8—22no—
267C22×Q8—22no—
268C22×Q8—22no—
269C22×Q8—22no—
270C22×Q8—44no—
271C22×Q8—44no—
272C22×Q8—44no—
273C22×Q8—44no—
274C22×Q8—44no—
275C22×Q8—44no—
276C22×Q8—48no—
277C22×Q8—48no—
278C22×Q8—44no—
279C22×Q8—48no—
280C22×Q8—416no—
281C22×Q8—416no—
282C22×Q8—416no—
283C22×Q8—416no—
284C22×Q8C2×D414yes—
285C22×Q8C2×D414yes—
286C22×Q8C2×D414yes—
287C22×Q8C2412yes—
288C22×Q8C2412yes—
289C22×Q8C2412yes—
290C22×Q8C2412yes—
291C22×Q8C2412yes—
292C23×C4—21no—
293C23×C4—21no—
294C23×C4—21no—
295C23×C4—21no—
296C23×C4—22no—
297C23×C4—22no—
298C23×C4—22no—
299C23×C4—22no—
300C23×C4—22no—
301C23×C4—22no—
302C23×C4—24no—
303C23×C4—21no—
304C23×C4—21no—
305C23×C4—21no—
306C23×C4—21no—
307C23×C4—44no—
308C23×C4—44no—
309C23×C4—44no—
310C23×C4C2×D412yes—
311C23×C4C2×D411yescharacteristic
312C23×C4C2×D411yescharacteristic
313C23×C4C2×D411yescharacteristic
314C23×C4C2×D411yescharacteristic
315C23×C4C2×D411yescharacteristic
316C23×C4C2412yes—
317C23×C4C2411yescharacteristic
318C2×Q16—28no—
319C2×Q16—28no—
320C2×Q16—28no—
321C2×Q16—28no—
322C2×Q16—28no—
323C2×Q16—28no—
324C2×Q16—28no—
325C2×Q16—28no—
326C2×Q16—416no—
327C2×Q16—44no—
328C2×Q16—44no—
329C2×Q16—44no—
330C2×Q16—44no—
331C2×Q16—44no—
332C2×Q16—44no—
333C2×Q16—44no—
334C2×Q16—44no—
335C2×Q16—44no—
336C2×Q16—416no—
337C2×Q16—416no—
338C2×Q16—416no—
339C2×Q16—416no—
340C2×Q16—416no—
341C2×Q16C2×D4116yes—
342C22×C8—22no—
343C22×C8—22no—
344C22×C8—22no—
345C22×C8—22no—
346C22×C8—22no—
347C22×C8—22no—
348C22×C8—22no—
349C22×C8—22no—
350C22×C8—22no—
351C22×C8—22no—
352C22×C8C2×D414yes—
353C22×C8C2×D414yes—
354C22×C8C2412yes—
355C22×C8C2412yes—
356C22×C8C2412yes—
357C22×C8C2412yes—
358C4⋊Q8—28no—
359C4⋊Q8—28no—
360C4⋊Q8—28no—
361C4⋊Q8—44no—
362C4⋊Q8—44no—
363C4⋊Q8—44no—
364C4⋊Q8—48no—
365C4⋊Q8—48no—
366C4⋊Q8—48no—
367C22⋊Q8—28no—
368C22⋊Q8—28no—
369C22⋊Q8—44no—
370C22⋊Q8—44no—
371C22⋊Q8—44no—
372C22⋊Q8—44no—
373C22⋊Q8—48no—
374C22⋊Q8—48no—
375C22⋊Q8—48no—
376C4×Q8—28no—
377C4×Q8—44no—
378C4×Q8—48no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—22no—
381C2×C4⋊C4—22no—
382C2×C4⋊C4—22no—
383C2×C4⋊C4—22no—
384C2×C4⋊C4—22no—
385C2×C4⋊C4—24no—
386C2×C4⋊C4—24no—
387C2×C4⋊C4—24no—
388C2×C4⋊C4—24no—
389C2×C4⋊C4—24no—
390C2×C4⋊C4—24no—
391C2×C4⋊C4—24no—
392C2×C4⋊C4—24no—
393C2×C4⋊C4—24no—
394C2×C4⋊C4—24no—
395C2×C4⋊C4—24no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—44no—
399C2×C4⋊C4—44no—
400C2×C4⋊C4—44no—
401C2×C4⋊C4—44no—
402C2×C4⋊C4—44no—
403C2×C4⋊C4—44no—
404C2×C4⋊C4—44no—
405C2×C4⋊C4—44no—
406C2×C4⋊C4—44no—
407C2×C4⋊C4—44no—
408C2×C4⋊C4—44no—
409C2×C4⋊C4C2×D414yes—
410C2×C4⋊C4C2412yes—
411C2×C4⋊C4C2412yes—
412C2×C4⋊C4C2412yes—
413C2×C22⋊C4—24no—
414C2×C22⋊C4—24no—
415C2×C22⋊C4—24no—
416C2×C22⋊C4—24no—
417C2×C22⋊C4—44no—
418C2×C22⋊C4—44no—
419C2×C22⋊C4—44no—
420C2×C22⋊C4Q1618yescomplemented
421C2×C22⋊C4C2×D414yes—
422C2×C22⋊C4C2×D414yes—
423C2×C42—22no—
424C2×C42—22no—
425C2×C42—22no—
426C2×C42—22no—
427C2×C42—24no—
428C2×C42—44no—
429C2×C42C2×D412yes—
430C2×C42C2×D412yes—
431C2×C42C2412yes—
432C2×C42C2412yes—
433C4⋊C8—28no—
434#103—28no—
435#103—28no—
436#103—28no—
437#103—28no—
438#103—44no—
439#103—44no—
440#103—44no—
441#103C2×D4116yes—
442C22⋊C8—28no—
443C22⋊C8—28no—
444C4×C8—28no—
445#95—24no—
446#95—24no—
447#95—24no—
448#95—24no—
449#95—24no—
450#95—24no—
451#95—24no—
452#95C2×D414yes—
453#95C2×D414yes—
454C24—22no—
455C24—22no—
456C24—22no—
457C24—22no—
458C24—22no—
459C24—22no—
460C24C2×Q1614yes—
461C24C22×D412yes—
462C24C22×D411yescharacteristic
463C2×Q8—24no—
464C2×Q8—24no—
465C2×Q8—24no—
466C2×Q8—22no—
467C2×Q8—22no—
468C2×Q8—22no—
469C2×Q8—28no—
470C2×Q8—28no—
471C2×Q8—28no—
472C2×Q8—28no—
473C2×Q8—28no—
474C2×Q8—28no—
475C2×Q8—22no—
476C2×Q8—22no—
477C2×Q8—22no—
478C2×Q8—22no—
479C2×Q8—22no—
480C2×Q8—22no—
481C2×Q8—22no—
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—22no—
493C2×Q8—22no—
494C2×Q8—22no—
495C2×Q8—22no—
496C2×Q8—22no—
497C2×Q8—22no—
498C2×Q8—22no—
499C2×Q8—48no—
500C2×Q8—48no—
501C2×Q8—48no—
502C2×Q8—416no—
503C2×Q8—416no—
504C2×Q8—416no—
505C2×Q8—464no—
506C2×Q8—416no—
507C2×Q8—432no—
508C2×Q8—44no—
509C2×Q8—44no—
510C2×Q8—42no—
511C2×Q8—44no—
512C2×Q8—42no—
513C2×Q8—42no—
514C2×Q8—42no—
515C2×Q8—42no—
516C2×Q8—42no—
517C2×Q8—42no—
518C2×Q8—42no—
519C2×Q8—42no—
520C2×Q8—42no—
521C2×Q8—42no—
522C2×Q8—42no—
523C2×Q8—44no—
524C2×Q8—44no—
525C2×Q8—44no—
526C2×Q8—44no—
527C2×Q8—44no—
528C2×Q8—44no—
529C2×Q8—44no—
530C2×Q8—44no—
531C2×Q8—44no—
532C2×Q8—44no—
533C2×Q8—44no—
534C2×Q8C22×D414yes—
535C2×Q8C22×D414yes—
536C2×Q8C22×D414yes—
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—24no—
546C22×C4—24no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—24no—
550C22×C4—24no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—24no—
558C22×C4—24no—
559C22×C4—24no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—48no—
571C22×C4—48no—
572C22×C4—48no—
573C22×C4—432no—
574C22×C4—42no—
575C22×C4—42no—
576C22×C4—42no—
577C22×C4—42no—
578C22×C4—42no—
579C22×C4—42no—
580C22×C4—42no—
581C22×C4—42no—
582C22×C4—44no—
583C22×C4—44no—
584C22×C4—44no—
585C22×C4—44no—
586C22×C4—42no—
587C22×C4—42no—
588C22×C4—42no—
589C22×C4—42no—
590C22×C4—42no—
591C22×C4—42no—
592C22×C4—42no—
593C22×C4—42no—
594C22×C4—42no—
595C22×C4—42no—
596C22×C4—42no—
597C22×C4—42no—
598C22×C4C2×Q1614yes—
599C22×C4C2×Q1614yes—
600C22×C4#13714yes—
601C22×C4C22×D412yes—
602C22×C4C22×D412yes—
603C22×C4C22×D412yes—
604C22×C4C22×D412yes—
605C22×C4C22×D412yes—
606C22×C4C22×D412yes—
607C22×C4C22×D411yescharacteristic
608C22×C4C22×D412yes—
609C22×C4H(5,𝔽2)12yes—
610C22×C4H(5,𝔽2)12yes—
611C22×C4H(5,𝔽2)12yes—
612C22×C4H(5,𝔽2)12yes—
613C22×C4C2511yescharacteristic
614Q16—416no—
615Q16—416no—
616Q16—416no—
617Q16—416no—
618Q16—416no—
619Q16—416no—
620C2×C8—28no—
621C2×C8—28no—
622C2×C8—22no—
623C2×C8—22no—
624C2×C8—22no—
625C2×C8—22no—
626C2×C8—22no—
627C2×C8—22no—
628C2×C8—22no—
629C2×C8—22no—
630C2×C8—22no—
631C2×C8—22no—
632C2×C8—44no—
633C2×C8—44no—
634C2×C8C22×D414yes—
635C2×C8C22×D414yes—
636C4⋊C4—24no—
637C4⋊C4—22no—
638C4⋊C4—22no—
639C4⋊C4—22no—
640C4⋊C4—22no—
641C4⋊C4—22no—
642C4⋊C4—48no—
643C4⋊C4—48no—
644C4⋊C4—48no—
645C4⋊C4—48no—
646C4⋊C4—48no—
647C4⋊C4—48no—
648C4⋊C4—48no—
649C4⋊C4—48no—
650C4⋊C4—48no—
651C4⋊C4—48no—
652C4⋊C4—42no—
653C4⋊C4—42no—
654C4⋊C4—48no—
655C4⋊C4C22×D414yes—
656C22⋊C4—28no—
657C22⋊C4—48no—
658C22⋊C4—48no—
659C22⋊C4—48no—
660C22⋊C4C2×Q16116yescomplemented
661C42—24no—
662C42—24no—
663C42—22no—
664C42—22no—
665C42—22no—
666C42—22no—
667C42—48no—
668C23—22no—
669C23—22no—
670C23—22no—
671C23—28no—
672C23—28no—
673C23—28no—
674C23—22no—
675C23—22no—
676C23—22no—
677C23—44no—
678C23—44no—
679C23—44no—
680C23—44no—
681C23#53512yes—
682C23D4212yes—
683C23D4212yes—
684C23C22×Q1614yes—
685C23C22×Q1612yes—
686C23C2×#13712yes—
687C23#57812yes—
688C23#57812yes—
689C23C23×D411yescharacteristic
690Q8—24no—
691Q8—24no—
692Q8—24no—
693Q8—24no—
694Q8—24no—
695Q8—24no—
696Q8—432no—
697Q8—48no—
698Q8—48no—
699Q8—48no—
700Q8—42no—
701Q8—42no—
702Q8—42no—
703Q8—42no—
704Q8—42no—
705Q8—42no—
706Q8—42no—
707Q8—42no—
708Q8—42no—
709Q8—42no—
710Q8—42no—
711Q8—42no—
712Q8—42no—
713Q8—42no—
714Q8—84no—
715Q8—84no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—28no—
720C2×C4—28no—
721C2×C4—28no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—24no—
728C2×C4—24no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—24no—
732C2×C4—24no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—432no—
736C2×C4—44no—
737C2×C4—48no—
738C2×C4—48no—
739C2×C4—48no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—44no—
747C2×C4—48no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—48no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
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—42no—
767C2×C4—84no—
768C2×C4—84no—
769C2×C4—84no—
770C2×C4—84no—
771C2×C4#53414yes—
772C2×C4#53512yes—
773C2×C4#53514yes—
774C2×C4D4212yes—
775C2×C4D4212yes—
776C2×C4D4214yes—
777C2×C4#56014yes—
778C2×C4C22×Q1614yes—
779C2×C4C22×Q1614yes—
780C2×C4C2×#13714yes—
781C2×C4C23×D411yescharacteristic
782C2×C4C23×D411yescharacteristic
783C2×C4C2×H(5,𝔽2)11yescharacteristic
784C2×C4C2×H(5,𝔽2)11yescharacteristic
785C2×C4C2×H(5,𝔽2)11yescharacteristic
786C2×C4C2×H(5,𝔽2)11yescharacteristic
787C8—24no—
788C8—24no—
789C8—42no—
790C8—42no—
791C22—24no—
792C22—24no—
793C22—24no—
794C22—42no—
795C22—42no—
796C22—42no—
797C22—42no—
798C22—416no—
799C22#266914yes—
800C22#320914yes—
801C22#322314yes—
802C22#327014yes—
803C22#327614yes—
804C22D4×Q1614yes—
805C22D4×Q1614yes—
806C22C2×#53511yescharacteristic
807C22C2×D4211yescharacteristic
808C22C2×D4211yescharacteristic
809C22C23×Q1611yescharacteristic
810C22C22×#13711yescharacteristic
811C22C2×#57811yescharacteristic
812C22C2×#57811yescharacteristic
813C4—24no—
814C4—24no—
815C4—24no—
816C4—42no—
817C4—44no—
818C4—42no—
819C4—44no—
820C4—44no—
821C4—44no—
822C4—82no—
823C4—82no—
824C4—82no—
825C4—82no—
826C4#266914yes—
827C4C2×#53411yescharacteristic
828C4C2×#53511yescharacteristic
829C4C2×D4211yescharacteristic
830C4C2×#56011yescharacteristic
831C2—44no—
832C2#3044918yesdirect product factor
833C2C2×#266911yescharacteristic
834C2C2×#320911yescharacteristic
835C2C2×#322311yescharacteristic
836C2C2×#327011yescharacteristic
837C2C2×#327611yescharacteristic
838C2C2×D4×Q1611yescharacteristic
839C2C2×D4×Q1611yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC25C2×D4
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×#494C2semidirect
2. C22×#462C2semidirect
7. #30449C2direct (N × H)
8. C2×#2056C2semidirect
9. C2×#2043C2semidirect
10. C2×#2016C2semidirect
11. C2×#2016C2semidirect
14. C2×#1933C2semidirect
16. C2×#1878C2semidirect
32. C2×#494C22semidirect
34. C2×#462C22semidirect
68. #2056C22semidirect
69. #2043C22semidirect
70. #2016C22semidirect
71. #2016C22semidirect
74. #1933C22semidirect
76. #1878C22semidirect
420. C2×C22⋊C4Q16semidirect
660. C22⋊C4C2×Q16semidirect
832. C2#30449direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#4942
C22×#4622
C22×#4512
C2×#24292
C2×#24342
#304492
C2×#20562
C2×#20432
C2×#20162
C2×#20012
C2×#19332
C2×#19232
C2×#18782