Finite Group Databasebeta

← C22×#135908 #72320060

Subgroups — C22×#135908 #72320060

Order 2048.

15280 conjugacy classes of subgroups.

The subgroup lattice has 1077 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#9595C211yesmaximal, characteristic, complemented
2C22×#7178C211yesmaximal, characteristic, complemented
3C22×#12637C211yesmaximal, characteristic
4C22×#7137C211yesmaximal, characteristic, complemented
5C2×#135908C2124yesmaximal, direct product factor
6C23×#1333C211yesmaximal, characteristic
7C23×#1580C211yesmaximal, characteristic
8C23×#1368C211yesmaximal, characteristic, complemented
9C23×C8×D4—21no—
10C23×C4×D8C2211yescharacteristic
11C23×#357C411yescharacteristic
12C23×#357C411yescharacteristic
13C23×#346C2211yescharacteristic
14C23×#346C2211yescharacteristic
15C22×#1939—21no—
16C22×C4×#107C2211yescharacteristic
17C22×#1580—28no—
18C22×#1580—26no—
19C22×#1580—28no—
20C22×#1580C22112yes—
21C23×#334C2211yescharacteristic
22C23×#334C2211yescharacteristic
23C23×D4⋊C8—21no—
24C23×#322C2211yescharacteristic
25C2×#12637C4112yes—
26C2×#12637C22112yes—
27C22×#1380C411yescharacteristic
28C22×#1380C411yescharacteristic
29C22×#1368—28no—
30C22×#1368C22112yescomplemented
31C22×#1333—28no—
32C22×#1333C22112yes—
33C2×#9595—26no—
34C2×#9595C22112yescomplemented
35C22×#1279—21no—
36#135908C22164yesdirect product factor
37C2×#7178C22112yescomplemented
38C2×#7137C22112yescomplemented
39C24×D8C2×C411yescharacteristic
40C25×C8—41no—
41C23×C4×D4—21no—
42C24×C16—21no—
43C24×C16C2×C411yescharacteristic
44C24×C16C2×C411yescharacteristic
45C22×C4×D8—23no—
46C22×C4×D8—24no—
47C22×C4×D8—24no—
48C22×C4×D8—23no—
49C22×C4×D8C2×C416yes—
50C22×C4×D8D418yes—
51C22×C4×D8Q818yes—
52C22×C4×D8C2316yes—
53C22×C8×D4—216no—
54C22×C8×D4—212no—
55C22×C8×D4—46no—
56C22×C8×D4—48no—
57C23×#107C2×C411yescharacteristic
58C23×#107C2×C411yescharacteristic
59C23×#107C2×C411yescharacteristic
60C23×C4⋊C8—21no—
61C23×C4⋊C8—21no—
62C23×C4⋊C8—41no—
63C23×#102—21no—
64C23×C22⋊C8—41no—
65C23×C4×C8D411yescharacteristic
66C23×C4×C8D411yescharacteristic
67C23×C4×C8C2311yescharacteristic
68C22×C4×C4⋊C4—21no—
69C22×#357—28no—
70C22×#357C8116yescomplemented
71C22×#357C2×C4112yes—
72C22×#357C2×C4112yes—
73C22×#346—24no—
74C22×#346—24no—
75C22×#346—24no—
76C22×#346—24no—
77C22×#346—23no—
78C22×#346C2×C416yes—
79C22×#346C2316yes—
80C22×#346C2316yes—
81C2×#1939—212no—
82C2×#1939—46no—
83C2×C4×#107—23no—
84C2×C4×#107—23no—
85C2×C4×#107C2×C416yes—
86C2×C4×#107C2316yes—
87C22×#340—21no—
88C22×#336—41no—
89C2×#1580—296no—
90C2×#1580—224no—
91C2×#1580—248no—
92C2×#1580—248no—
93C2×#1580C23116yes—
94C22×#334—23no—
95C22×#334—24no—
96C22×#334—24no—
97C22×#334—24no—
98C22×#334—23no—
99C22×#334D418yes—
100C22×#334C2316yes—
101C22×#334C2316yes—
102C22×D4⋊C8—216no—
103C22×D4⋊C8—212no—
104C22×#322—24no—
105C22×#322—24no—
106C22×#322D416yes—
107C22×#322C2316yes—
108#12637C2×C4148yes—
109#12637C23116yes—
110C2×#1380C2×C4112yes—
111C2×#1380C2×C4112yes—
112C2×#1368—248no—
113C2×#1368C23116yescomplemented
114C2×#1333—248no—
115C2×#1333C23116yes—
116#9595—224no—
117#9595C23116yescomplemented
118C2×#1279—212no—
119#7178C23116yescomplemented
120#7137C23116yescomplemented
121C24×D4—21no—
122C25×C4—41no—
123C23×D8—24no—
124C23×D8—23no—
125C23×D8—24no—
126C23×D8—24no—
127C23×D8C4⋊C418yes—
128C23×D8C2×C818yes—
129C23×D8M1618yes—
130C23×D8C22×C416yes—
131C24×C8—21no—
132C24×C8—21no—
133C24×C8—412no—
134C24×C8—416no—
135C24×C8—41no—
136C24×C8—41no—
137C24×C8—88no—
138C24×C8—88no—
139C24×C8C22×C411yescharacteristic
140C24×C8#4111yescharacteristic
141C22×C4×D4—26no—
142C22×C4×D4—28no—
143C22×C4×D4—28no—
144C22×C4×D4—26no—
145C22×C4×D4—44no—
146C22×C4×D4—44no—
147C22×C4×D4—43no—
148C22×C4×D4—43no—
149C23×C4⋊C4—21no—
150C23×C4⋊C4—21no—
151C23×C4⋊C4—21no—
152C23×C22⋊C4—41no—
153C23×C42—41no—
154C23×C42C2×D411yescharacteristic
155C23×C16—28no—
156C23×C16—24no—
157C23×C16—24no—
158C23×C16—24no—
159C23×C16—24no—
160C23×C16—24no—
161C23×C16—26no—
162C23×C16—44no—
163C23×C16—44no—
164C23×C16C2×C818yescomplemented
165C23×C16C22×C416yes—
166C23×C16C22×C416yes—
167C2×C4×D8—212no—
168C2×C4×D8—224no—
169C2×C4×D8—224no—
170C2×C4×D8—224no—
171C2×C4×D8—224no—
172C2×C4×D8—224no—
173C2×C4×D8—212no—
174C2×C4×D8—26no—
175C2×C4×D8—26no—
176C2×C4×D8—212no—
177C2×C4×D8C4⋊C4148yes—
178C2×C4×D8C22×C4112yes—
179C2×C4×D8C2×D4124yes—
180C2×C4×D8C2×Q8124yes—
181C2×C4×D8C2414yes—
182C2×C8×D4—296no—
183C2×C8×D4—216no—
184C2×C8×D4—424no—
185C2×C8×D4—496no—
186C2×C8×D4—448no—
187C22×#107—23no—
188C22×#107—23no—
189C22×#107—24no—
190C22×#107—23no—
191C22×#107—24no—
192C22×#107—24no—
193C22×#107—24no—
194C22×#107C4⋊C418yes—
195C22×#107C2×C818yescomplemented
196C22×#107C22×C416yes—
197C22×#107C22×C416yes—
198C22×#107C22×C416yes—
199C22×C4⋊C8—28no—
200C22×C4⋊C8—26no—
201C22×C4⋊C8—26no—
202C22×C4⋊C8—412no—
203C22×C4⋊C8—44no—
204C22×C4⋊C8—43no—
205C22×C4⋊C8—43no—
206C22×C4⋊C8—44no—
207C22×C4⋊C8—44no—
208C22×C4⋊C8—88no—
209C22×#102—26no—
210C22×#102—28no—
211C22×#102—28no—
212C22×#102—26no—
213C22×C22⋊C8—412no—
214C22×C22⋊C8—416no—
215C22×C4×C8—24no—
216C22×C4×C8—23no—
217C22×C4×C8—23no—
218C22×C4×C8—24no—
219C22×C4×C8—24no—
220C22×C4×C8SD1618yes—
221C22×C4×C8C22×C413yes—
222C22×C4×C8C2×D416yes—
223C22×C4×C8C2×D416yes—
224C22×C4×C8C2×D414yes—
225C22×C4×C8C2×D413yes—
226C22×C4×C8C2×D414yes—
227C22×C4×C8C2×Q814yes—
228C22×C4×C8#4114yes—
229C22×C4×C8#4113yes—
230C22×C4×C8C2413yes—
231C2×C4×C4⋊C4—26no—
232C2×C4×C4⋊C4—26no—
233C2×C4×C4⋊C4—43no—
234C2×C4×C4⋊C4—43no—
235C22×#95—41no—
236C2×#357—248no—
237C2×#357C2×C8196yescomplemented
238C2×#357C22×C4116yes—
239C2×#357C22×C4116yes—
240C2×#346—224no—
241C2×#346—212no—
242C2×#346—212no—
243C2×#346—212no—
244C2×#346—212no—
245C2×#346—26no—
246C2×#346—412no—
247C2×#346C22×C4112yes—
248C2×#346C2414yes—
249C2×#346C2414yes—
250#1939—216no—
251#1939—424no—
252C4×#107—212no—
253C4×#107—26no—
254C4×#107—26no—
255C4×#107C22×C4112yes—
256C4×#107C2414yes—
257C2×#340—26no—
258C2×#340—26no—
259C2×#336—412no—
260#1580—2192no—
261#1580—232no—
262#1580—232no—
263C2×#334—224no—
264C2×#334—26no—
265C2×#334—212no—
266C2×#334—212no—
267C2×#334—212no—
268C2×#334—26no—
269C2×#334—412no—
270C2×#334C2×D4124yes—
271C2×#334C2414yes—
272C2×#334C2414yes—
273C2×D4⋊C8—296no—
274C2×D4⋊C8—216no—
275C2×#322—224no—
276C2×#322—212no—
277C2×#322—212no—
278C2×#322C2×D4112yes—
279C2×#322C2414yes—
280#1380C22×C4116yes—
281#1380C22×C4116yes—
282#1368—232no—
283#1333—232no—
284#1279—216no—
285C26—41no—
286C23×D4—26no—
287C23×D4—28no—
288C23×D4—28no—
289C23×D4—28no—
290C23×D4—44no—
291C23×D4—43no—
292C23×D4—44no—
293C23×D4—44no—
294C24×C4—41no—
295C24×C4—41no—
296C24×C4—46no—
297C24×C4—46no—
298C24×C4—48no—
299C24×C4—48no—
300C24×C4—41no—
301C24×C4—84no—
302C24×C4—84no—
303C24×C4—84no—
304C24×C4—84no—
305C24×C4C4×D411yescharacteristic
306C24×C4AGL(1,ℤ/8)11yescharacteristic
307C24×C4AGL(1,ℤ/8)11yescharacteristic
308C22×D8—212no—
309C22×D8—26no—
310C22×D8—212no—
311C22×D8—212no—
312C22×D8—224no—
313C22×D8—232no—
314C22×D8—224no—
315C22×D8—232no—
316C22×D8—224no—
317C22×D8—232no—
318C22×D8C4⋊C8164yescomplemented
319C22×D8C2×C4⋊C4124yes—
320C22×D8C22×C8124yes—
321C22×D8C2×M16124yes—
322C22×D8C23×C414yes—
323C23×C8—24no—
324C23×C8—24no—
325C23×C8—26no—
326C23×C8—28no—
327C23×C8—26no—
328C23×C8—496no—
329C23×C8—416no—
330C23×C8—44no—
331C23×C8—44no—
332C23×C8—44no—
333C23×C8—44no—
334C23×C8—46no—
335C23×C8—44no—
336C23×C8—48no—
337C23×C8—46no—
338C23×C8—8128no—
339C23×C8—848no—
340C23×C8—848no—
341C23×C8—84no—
342C23×C8—84no—
343C23×C8—84no—
344C23×C8—84no—
345C23×C8—84no—
346C23×C8C2×C4⋊C414yes—
347C23×C8C4×D413yes—
348C23×C8C4×D414yes—
349C23×C8C4×D413yes—
350C23×C8C22⋊Q814yes—
351C23×C8#12314yes—
352C23×C8C22×C814yes—
353C23×C8C2×M1614yes—
354C23×C8#13114yes—
355C23×C8#13114yes—
356C23×C8C23×C413yes—
357C23×C8C2×#4113yes—
358C2×C4×D4—212no—
359C2×C4×D4—224no—
360C2×C4×D4—224no—
361C2×C4×D4—24no—
362C2×C4×D4—248no—
363C2×C4×D4—412no—
364C2×C4×D4—412no—
365C2×C4×D4—46no—
366C2×C4×D4—46no—
367C2×C4×D4—424no—
368C2×C4×D4—412no—
369C2×C4×D4—424no—
370C2×C4×D4—424no—
371C2×C4×D4—424no—
372C2×C4×D4—424no—
373C22×C4⋊C4—26no—
374C22×C4⋊C4—26no—
375C22×C4⋊C4—28no—
376C22×C4⋊C4—28no—
377C22×C4⋊C4—26no—
378C22×C4⋊C4—44no—
379C22×C4⋊C4—43no—
380C22×C4⋊C4—43no—
381C22×C4⋊C4—44no—
382C22×C4⋊C4—44no—
383C22×C4⋊C4—44no—
384C22×C4⋊C4—43no—
385C22×C22⋊C4—46no—
386C22×C22⋊C4—46no—
387C22×C22⋊C4—48no—
388C22×C22⋊C4—48no—
389C22×C42—46no—
390C22×C42—46no—
391C22×C42—84no—
392C22×C42—84no—
393C22×C42C4×D413yes—
394C22×C42#12014yes—
395C22×C42C22⋊Q814yes—
396C22×C42C2×SD1614yes—
397C22×C42#13514yes—
398C22×C42AGL(1,ℤ/8)13yes—
399C22×C42AGL(1,ℤ/8)13yes—
400C22×C42C22×D413yes—
401C22×C16—212no—
402C22×C16—212no—
403C22×C16—232no—
404C22×C16—224no—
405C22×C16—212no—
406C22×C16—212no—
407C22×C16—212no—
408C22×C16—24no—
409C22×C16—432no—
410C22×C16—412no—
411C22×C16—412no—
412C22×C16—416no—
413C22×C16C22×C8124yescomplemented
414C22×C16C23×C414yes—
415C22×C16C23×C414yes—
416C4×D8—224no—
417C4×D8—224no—
418C4×D8—224no—
419C4×D8—224no—
420C4×D8—224no—
421C4×D8—24no—
422C4×D8—24no—
423C4×D8—296no—
424C4×D8C2×C4⋊C4148yes—
425C4×D8C22×D418yes—
426C4×D8C22×Q818yes—
427C8×D4—264no—
428C8×D4—4192no—
429C8×D4—432no—
430C2×#107—212no—
431C2×#107—26no—
432C2×#107—26no—
433C2×#107—212no—
434C2×#107—224no—
435C2×#107—224no—
436C2×#107—212no—
437C2×#107—212no—
438C2×#107—26no—
439C2×#107—412no—
440C2×#107C2×C4⋊C4124yes—
441C2×#107C22×C8124yescomplemented
442C2×#107C23×C414yes—
443C2×#107C23×C414yes—
444C2×#107C23×C414yes—
445C2×C4⋊C8—224no—
446C2×C4⋊C8—24no—
447C2×C4⋊C8—24no—
448C2×C4⋊C8—412no—
449C2×C4⋊C8—46no—
450C2×C4⋊C8—424no—
451C2×C4⋊C8—412no—
452C2×C4⋊C8—412no—
453C2×C4⋊C8—416no—
454C2×C4⋊C8—46no—
455C2×C4⋊C8—848no—
456C2×C4⋊C8—812no—
457C2×#102—212no—
458C2×#102—224no—
459C2×#102—224no—
460C2×#102—24no—
461C2×#102—248no—
462C2×C22⋊C8—496no—
463C2×C22⋊C8—416no—
464C2×C4×C8—212no—
465C2×C4×C8—26no—
466C2×C4×C8—224no—
467C2×C4×C8—212no—
468C2×C4×C8—212no—
469C2×C4×C8—26no—
470C2×C4×C8—412no—
471C2×C4×C8C2×C4⋊C4112yes—
472C2×C4×C8C4×D4112yes—
473C2×C4×C8C4×D416yes—
474C2×C4×C8#120112yes—
475C2×C4×C8C22⋊Q8112yes—
476C2×C4×C8C22⋊Q8112yes—
477C2×C4×C8#123112yes—
478C2×C4×C8C2×SD16124yes—
479C2×C4×C8C23×C413yes—
480C2×C4×C8C22×D414yes—
481C2×C4×C8C22×D414yes—
482C2×C4×C8C22×D416yes—
483C2×C4×C8C22×D416yes—
484C2×C4×C8C22×D413yes—
485C2×C4×C8C22×Q816yes—
486C2×C4×C8C2×#4116yes—
487C2×C4×C8C2×#4113yes—
488C2×C4×C8C2511yescharacteristic
489C4×C4⋊C4—212no—
490C4×C4⋊C4—24no—
491C4×C4⋊C4—46no—
492C4×C4⋊C4—46no—
493C4×C4⋊C4—412no—
494C2×#95—46no—
495C2×#95—46no—
496#357—232no—
497#357C22×C8164yescomplemented
498#346—224no—
499#346—24no—
500#346—24no—
501#346—24no—
502#346—24no—
503#346—412no—
504#340—212no—
505#340—24no—
506#336—416no—
507#334—224no—
508#334—24no—
509#334—24no—
510#334—24no—
511#334—412no—
512#334C22×D418yes—
513D4⋊C8—264no—
514#322—224no—
515#322—24no—
516#322—24no—
517C25—48no—
518C25—48no—
519C25—48no—
520C25—46no—
521C25—84no—
522C25—84no—
523C25—84no—
524C25—84no—
525C25#44211yescharacteristic
526C22×D4—264no—
527C22×D4—24no—
528C22×D4—224no—
529C22×D4—224no—
530C22×D4—224no—
531C22×D4—432no—
532C22×D4—424no—
533C22×D4—432no—
534C22×D4—424no—
535C22×D4—424no—
536C22×D4—432no—
537C22×D4—412no—
538C22×D4—46no—
539C22×D4—412no—
540C22×D4—412no—
541C23×C4—24no—
542C23×C4—24no—
543C23×C4—24no—
544C23×C4—24no—
545C23×C4—48no—
546C23×C4—48no—
547C23×C4—46no—
548C23×C4—46no—
549C23×C4—424no—
550C23×C4—448no—
551C23×C4—412no—
552C23×C4—424no—
553C23×C4—44no—
554C23×C4—46no—
555C23×C4—832no—
556C23×C4—812no—
557C23×C4—812no—
558C23×C4—832no—
559C23×C4—832no—
560C23×C4—832no—
561C23×C4—812no—
562C23×C4—812no—
563C23×C4—824no—
564C23×C4—824no—
565C23×C4—84no—
566C23×C4—84no—
567C23×C4—84no—
568C23×C4—84no—
569C23×C4—84no—
570C23×C4—84no—
571C23×C4—84no—
572C23×C4#38514yes—
573C23×C4C8×D414yes—
574C23×C4#43514yes—
575C23×C4C4×SD1614yes—
576C23×C4#44213yes—
577C23×C4#44213yes—
578C23×C4#44213yes—
579C23×C4#44314yes—
580C23×C4#44414yes—
581C23×C4#44914yes—
582C23×C4#45014yes—
583C23×C4#47614yes—
584C23×C4#47814yes—
585C23×C4C2×C4×D413yes—
586C23×C4C2×AGL(1,ℤ/8)13yes—
587C23×C4C2×AGL(1,ℤ/8)13yes—
588C2×D8—2192no—
589C2×D8—248no—
590C2×D8—24no—
591C2×D8—224no—
592C2×D8—248no—
593C2×D8—224no—
594C2×D8—248no—
595C2×D8—224no—
596C2×D8—24no—
597C2×D8—24no—
598C2×D8C2×C4⋊C8196yescomplemented
599C2×D8C22×C4⋊C418yes—
600C2×D8C23×C818yes—
601C2×D8C22×M1618yes—
602C22×C8—216no—
603C22×C8—216no—
604C22×C8—26no—
605C22×C8—26no—
606C22×C8—26no—
607C22×C8—26no—
608C22×C8—224no—
609C22×C8—24no—
610C22×C8—24no—
611C22×C8—464no—
612C22×C8—432no—
613C22×C8—412no—
614C22×C8—412no—
615C22×C8—412no—
616C22×C8—412no—
617C22×C8—424no—
618C22×C8—412no—
619C22×C8—44no—
620C22×C8—44no—
621C22×C8—8384no—
622C22×C8—832no—
623C22×C8—832no—
624C22×C8—816no—
625C22×C8—832no—
626C22×C8—812no—
627C22×C8—812no—
628C22×C8—812no—
629C22×C8—812no—
630C22×C8—812no—
631C22×C8—1616no—
632C22×C8#385112yes—
633C22×C8#385112yes—
634C22×C8C2×C4⋊C8116yes—
635C22×C8#424116yes—
636C22×C8C8×D4112yes—
637C22×C8C8×D4116yes—
638C22×C8#435112yes—
639C22×C8#435116yes—
640C22×C8C22×C4⋊C416yes—
641C22×C8C2×C4×D413yes—
642C22×C8C2×C4×D416yes—
643C22×C8C2×C4×D413yes—
644C22×C8C2×C22⋊Q816yes—
645C22×C8C2×#12316yes—
646C22×C8C23×C816yes—
647C22×C8C22×M1616yes—
648C22×C8C2×#13116yes—
649C22×C8C2×#13116yes—
650C22×C8C24×C411yescharacteristic
651C22×C8C22×#4111yescharacteristic
652C4×D4—28no—
653C4×D4—28no—
654C4×D4—248no—
655C4×D4—424no—
656C4×D4—496no—
657C4×D4—424no—
658C4×D4—424no—
659C4×D4—424no—
660C4×D4—44no—
661C4×D4—44no—
662C4×D4—424no—
663C2×C4⋊C4—24no—
664C2×C4⋊C4—24no—
665C2×C4⋊C4—224no—
666C2×C4⋊C4—224no—
667C2×C4⋊C4—24no—
668C2×C4⋊C4—424no—
669C2×C4⋊C4—424no—
670C2×C4⋊C4—412no—
671C2×C4⋊C4—46no—
672C2×C4⋊C4—46no—
673C2×C4⋊C4—412no—
674C2×C4⋊C4—412no—
675C2×C4⋊C4—412no—
676C2×C4⋊C4—46no—
677C2×C4⋊C4—812no—
678C2×C22⋊C4—448no—
679C2×C22⋊C4—412no—
680C2×C22⋊C4—424no—
681C2×C22⋊C4—44no—
682C2×C22⋊C4—424no—
683C2×C42—412no—
684C2×C42—44no—
685C2×C42—812no—
686C2×C42—812no—
687C2×C42—824no—
688C2×C42#385112yes—
689C2×C42C4×SD16112yes—
690C2×C42#44216yes—
691C2×C42#449112yes—
692C2×C42#450112yes—
693C2×C42#476112yes—
694C2×C42#478112yes—
695C2×C42C2×C4×D413yes—
696C2×C42C2×#12016yes—
697C2×C42C2×C22⋊Q816yes—
698C2×C42C22×SD1616yes—
699C2×C42C2×#13516yes—
700C2×C42C2×AGL(1,ℤ/8)13yes—
701C2×C42C2×AGL(1,ℤ/8)13yes—
702C2×C42C23×D411yescharacteristic
703C2×C16—24no—
704C2×C16—248no—
705C2×C16—24no—
706C2×C16—28no—
707C2×C16—24no—
708C2×C16—24no—
709C2×C16—24no—
710C2×C16—44no—
711C2×C16—448no—
712C2×C16—44no—
713C2×C16—424no—
714C2×C16C23×C818yescomplemented
715#107—24no—
716#107—224no—
717#107—224no—
718#107—24no—
719#107—24no—
720#107—24no—
721#107—412no—
722#107C22×C4⋊C418yes—
723#107C23×C818yescomplemented
724C4⋊C8—28no—
725C4⋊C8—44no—
726C4⋊C8—424no—
727C4⋊C8—44no—
728C4⋊C8—44no—
729C4⋊C8—832no—
730C4⋊C8—812no—
731#102—28no—
732#102—28no—
733#102—248no—
734C22⋊C8—464no—
735C4×C8—24no—
736C4×C8—24no—
737C4×C8—224no—
738C4×C8—24no—
739C4×C8—412no—
740C4×C8#385124yes—
741C4×C8C22×C4⋊C416yes—
742C4×C8C2×C4×D416yes—
743C4×C8C2×#12016yes—
744C4×C8C2×C22⋊Q816yes—
745C4×C8C2×C22⋊Q816yes—
746C4×C8C2×#12316yes—
747C4×C8C22×SD1618yes—
748C4×C8C23×D411yescharacteristic
749C4×C8C23×D411yescharacteristic
750C4×C8C23×Q811yescharacteristic
751C4×C8C22×#4111yescharacteristic
752#95—412no—
753#95—44no—
754C24—424no—
755C24—464no—
756C24—424no—
757C24—424no—
758C24—44no—
759C24—832no—
760C24—832no—
761C24—832no—
762C24—832no—
763C24—832no—
764C24—832no—
765C24—812no—
766C24—812no—
767C24—812no—
768C24—812no—
769C24#158014yes—
770C24#158614yes—
771C24#186414yes—
772C24#218014yes—
773C24AGL(1,ℤ/16)14yes—
774C24AGL(1,ℤ/16)14yes—
775C24AGL(1,ℤ/16)14yes—
776C24C2×#44213yes—
777C2×D4—296no—
778C2×D4—28no—
779C2×D4—28no—
780C2×D4—28no—
781C2×D4—44no—
782C2×D4—44no—
783C2×D4—424no—
784C2×D4—4192no—
785C2×D4—448no—
786C2×D4—448no—
787C2×D4—424no—
788C2×D4—448no—
789C2×D4—424no—
790C2×D4—44no—
791C22×C4—216no—
792C22×C4—216no—
793C22×C4—216no—
794C22×C4—216no—
795C22×C4—26no—
796C22×C4—26no—
797C22×C4—26no—
798C22×C4—26no—
799C22×C4—26no—
800C22×C4—26no—
801C22×C4—26no—
802C22×C4—26no—
803C22×C4—424no—
804C22×C4—424no—
805C22×C4—44no—
806C22×C4—44no—
807C22×C4—48no—
808C22×C4—448no—
809C22×C4—48no—
810C22×C4—44no—
811C22×C4—848no—
812C22×C4—84no—
813C22×C4—84no—
814C22×C4—848no—
815C22×C4—848no—
816C22×C4—848no—
817C22×C4—8192no—
818C22×C4—84no—
819C22×C4—84no—
820C22×C4—824no—
821C22×C4—824no—
822C22×C4—832no—
823C22×C4—832no—
824C22×C4—812no—
825C22×C4—812no—
826C22×C4—812no—
827C22×C4—812no—
828C22×C4—812no—
829C22×C4—812no—
830C22×C4—812no—
831C22×C4—1616no—
832C22×C4C8×SD16116yes—
833C22×C4#1580112yes—
834C22×C4#1582116yes—
835C22×C4#1586112yes—
836C22×C4#1850116yes—
837C22×C4#1864112yes—
838C22×C4#1864112yes—
839C22×C4#1864112yes—
840C22×C4#1866116yes—
841C22×C4C2×#38516yes—
842C22×C4C2×C8×D416yes—
843C22×C4C2×#43516yes—
844C22×C4C2×C4×SD1616yes—
845C22×C4C2×#44213yes—
846C22×C4C2×#44213yes—
847C22×C4C2×#44213yes—
848C22×C4C2×#44316yes—
849C22×C4C2×#44416yes—
850C22×C4C2×#45016yes—
851C22×C4C2×#44916yes—
852C22×C4C2×#47616yes—
853C22×C4C2×#47816yes—
854C22×C4C22×C4×D411yescharacteristic
855C22×C4C22×AGL(1,ℤ/8)11yescharacteristic
856C22×C4C22×AGL(1,ℤ/8)11yescharacteristic
857D8—296no—
858D8—28no—
859D8—28no—
860D8—28no—
861D8C22×C4⋊C8116yescomplemented
862C2×C8—21no—
863C2×C8—23no—
864C2×C8—21no—
865C2×C8—23no—
866C2×C8—212no—
867C2×C8—212no—
868C2×C8—224no—
869C2×C8—28no—
870C2×C8—448no—
871C2×C8—44no—
872C2×C8—44no—
873C2×C8—44no—
874C2×C8—44no—
875C2×C8—48no—
876C2×C8—44no—
877C2×C8—8128no—
878C2×C8—824no—
879C2×C8—848no—
880C2×C8—84no—
881C2×C8—84no—
882C2×C8—84no—
883C2×C8—84no—
884C2×C8—84no—
885C2×C8—1624no—
886C2×C8#1850148yes—
887C2×C8C2×#38516yes—
888C2×C8C2×#38516yes—
889C2×C8C22×C4⋊C8112yes—
890C2×C8C2×#424112yes—
891C2×C8C2×C8×D416yes—
892C2×C8C2×C8×D4112yes—
893C2×C8C2×#43516yes—
894C2×C8C2×#435112yes—
895C2×C8C23×C4⋊C411yescharacteristic
896C2×C8C22×C4×D411yescharacteristic
897C2×C8C22×C22⋊Q811yescharacteristic
898C2×C8C22×#12311yescharacteristic
899C2×C8C24×C811yescharacteristic
900C2×C8C23×M1611yescharacteristic
901C2×C8C22×#13111yescharacteristic
902C2×C8C22×#13111yescharacteristic
903C4⋊C4—28no—
904C4⋊C4—28no—
905C4⋊C4—44no—
906C4⋊C4—424no—
907C4⋊C4—424no—
908C4⋊C4—44no—
909C4⋊C4—44no—
910C4⋊C4—44no—
911C4⋊C4—812no—
912C22⋊C4—48no—
913C22⋊C4—448no—
914C22⋊C4—48no—
915C42—84no—
916C42—84no—
917C42—824no—
918C42#1864124yes—
919C42C2×#38516yes—
920C42C2×C4×SD1616yes—
921C42C2×#45016yes—
922C42C2×#44916yes—
923C42C2×#47616yes—
924C42C2×#47816yes—
925C42C22×#12011yescharacteristic
926C42C22×C22⋊Q811yescharacteristic
927C42C23×SD1611yescharacteristic
928C42C22×#13511yescharacteristic
929C16—28no—
930C16—48no—
931C16—44no—
932C23—48no—
933C23—48no—
934C23—496no—
935C23—48no—
936C23—848no—
937C23—848no—
938C23—848no—
939C23—848no—
940C23—848no—
941C23—8256no—
942C23—84no—
943C23—84no—
944C23—84no—
945C23—84no—
946C23—848no—
947C23#8845116yes—
948C23#12065116yes—
949C23#12067116yes—
950C23#12077116yes—
951C23#12078116yes—
952C23#12955116yes—
953C23#12956116yes—
954C23C2×#158016yes—
955C23C2×#158616yes—
956C23C2×#186416yes—
957C23C2×#218016yes—
958C23C2×AGL(1,ℤ/16)16yes—
959C23C2×AGL(1,ℤ/16)16yes—
960C23C2×AGL(1,ℤ/16)16yes—
961C23C22×#44211yescharacteristic
962D4—216no—
963D4—48no—
964D4—48no—
965D4—496no—
966D4—48no—
967C2×C4—212no—
968C2×C4—212no—
969C2×C4—224no—
970C2×C4—21no—
971C2×C4—23no—
972C2×C4—21no—
973C2×C4—23no—
974C2×C4—21no—
975C2×C4—21no—
976C2×C4—23no—
977C2×C4—23no—
978C2×C4—212no—
979C2×C4—224no—
980C2×C4—212no—
981C2×C4—48no—
982C2×C4—48no—
983C2×C4—88no—
984C2×C4—88no—
985C2×C4—88no—
986C2×C4—88no—
987C2×C4—896no—
988C2×C4—848no—
989C2×C4—848no—
990C2×C4—84no—
991C2×C4—84no—
992C2×C4—84no—
993C2×C4—84no—
994C2×C4—84no—
995C2×C4—84no—
996C2×C4—84no—
997C2×C4—1624no—
998C2×C4#8845148yes—
999C2×C4C2×C8×SD16112yes—
1000C2×C4C2×#158016yes—
1001C2×C4C2×#1582112yes—
1002C2×C4C2×#158616yes—
1003C2×C4C2×#1850112yes—
1004C2×C4C2×#186416yes—
1005C2×C4C2×#186416yes—
1006C2×C4C2×#186416yes—
1007C2×C4C2×#1866112yes—
1008C2×C4C22×#38511yescharacteristic
1009C2×C4C22×C8×D411yescharacteristic
1010C2×C4C22×#43511yescharacteristic
1011C2×C4C22×C4×SD1611yescharacteristic
1012C2×C4C22×#44311yescharacteristic
1013C2×C4C22×#44411yescharacteristic
1014C2×C4C22×#45011yescharacteristic
1015C2×C4C22×#44911yescharacteristic
1016C2×C4C22×#47611yescharacteristic
1017C2×C4C22×#47811yescharacteristic
1018C8—21no—
1019C8—21no—
1020C8—26no—
1021C8—48no—
1022C8—84no—
1023C8—88no—
1024C8—164no—
1025C8C2×#1850112yes—
1026C8C23×C4⋊C811yescharacteristic
1027C8C22×#42411yescharacteristic
1028C8C22×C8×D411yescharacteristic
1029C8C22×#43511yescharacteristic
1030C22—416no—
1031C22—88no—
1032C22—8192no—
1033C22—88no—
1034C22—88no—
1035C22—88no—
1036C22—88no—
1037C22—88no—
1038C22#135908164yesdirect product factor
1039C22C2×#8845112yes—
1040C22C2×#12065112yes—
1041C22C2×#12067112yes—
1042C22C2×#12077112yes—
1043C22C2×#12078112yes—
1044C22C2×#12955112yes—
1045C22C2×#12956112yes—
1046C22C22×#158011yescharacteristic
1047C22C22×#158611yescharacteristic
1048C22C22×#186411yescharacteristic
1049C22C22×#218011yescharacteristic
1050C22C22×AGL(1,ℤ/16)11yescharacteristic
1051C22C22×AGL(1,ℤ/16)11yescharacteristic
1052C22C22×AGL(1,ℤ/16)11yescharacteristic
1053C4—21no—
1054C4—21no—
1055C4—26no—
1056C4—21no—
1057C4—21no—
1058C4—26no—
1059C4—88no—
1060C4—88no—
1061C4—164no—
1062C4C2×#8845112yes—
1063C4C22×C8×SD1611yescharacteristic
1064C4C22×#158211yescharacteristic
1065C4C22×#185011yescharacteristic
1066C4C22×#186611yescharacteristic
1067C2—816no—
1068C2C22×#1206711yescharacteristic
1069C2C22×#1295611yescharacteristic
1070C2C22×#1207811yescharacteristic
1071C2C2×#135908124yesdirect product factor
1072C2C22×#1207711yescharacteristic
1073C2C22×#1206511yescharacteristic
1074C2C22×#1295511yescharacteristic
1075C2C22×#884511yescharacteristic
subgroupG/H
center, socleC25#442
commutatorC2×C8C24×C8
Frattini, cosocleC2×C4×C8C25
prime radicalC24×D8C2×C4
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C25 ◁ C23×C42 ◁ C23×#322 ◁ G
LECSG ▷ C2×C4×C8 ▷ C2×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C22×#9595C2semidirect
2. C22×#7178C2semidirect
4. C22×#7137C2semidirect
5. C2×#135908C2direct (N × H)
8. C23×#1368C2semidirect
30. C22×#1368C22semidirect
34. C2×#9595C22semidirect
36. #135908C22direct (N × H)
37. C2×#7178C22semidirect
38. C2×#7137C22semidirect
70. C22×#357C8semidirect
113. C2×#1368C23semidirect
117. #9595C23semidirect
119. #7178C23semidirect
120. #7137C23semidirect
164. C23×C16C2×C8semidirect
195. C22×#107C2×C8semidirect
237. C2×#357C2×C8semidirect
318. C22×D8C4⋊C8semidirect
413. C22×C16C22×C8semidirect
441. C2×#107C22×C8semidirect
497. #357C22×C8semidirect
598. C2×D8C2×C4⋊C8semidirect
714. C2×C16C23×C8semidirect
723. #107C23×C8semidirect
861. D8C22×C4⋊C8semidirect
1038. C22#135908direct (N × H)
1071. C2C2×#135908direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#95952
C22×#71782
C22×#126372
C22×#71372
C2×#1359082
C23×#13332
C23×#15802
C23×#13682