Finite Group Databasebeta

← C2×#80555 #11670290

Subgroups — C2×#80555 #11670290

Order 768.

3042 conjugacy classes of subgroups.

The subgroup lattice has 944 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#914C211yesmaximal, characteristic, complemented
2C22×#911C211yesmaximal, characteristic, complemented
3C2×#5676C211yesmaximal, characteristic, complemented
4C2×#5554C211yesmaximal, characteristic, complemented
5C2×C3×#463C211yesmaximal, characteristic, complemented
6C2×#5173C211yesmaximal, characteristic, complemented
7C2×#5156C211yesmaximal, characteristic, complemented
8C2×#5059C211yesmaximal, characteristic, complemented
9C2×C4×#213C211yesmaximal, characteristic, complemented
10#80555C2116yesmaximal, direct product factor
11C2×#4844C211yesmaximal, characteristic, complemented
12C2×#4838C211yesmaximal, characteristic, complemented
13C2×#4812C211yesmaximal, characteristic, complemented
14C2×#4808C211yesmaximal, characteristic, complemented
15C2×#4780C211yesmaximal, characteristic, complemented
16C2×#4773C211yesmaximal, characteristic, complemented
17C2×#3273—31nomaximal, Sylow
18C22×#239C2211yescharacteristic
19C22×#237C2211yescharacteristic
20C22×D3×D4C2211yescharacteristic, complemented
21C22×D3×D4C2211yescharacteristic, complemented
22C22×C3×SD16C2211yescharacteristic, complemented
23C22×C3×D8C2211yescharacteristic
24C2×C3×#124C2211yescharacteristic, complemented
25C2×C3×C4×D4C2211yescharacteristic, complemented
26C2×#946C2211yescharacteristic, complemented
27C22×#216C2211yescharacteristic, complemented
28C22×#215C2211yescharacteristic, complemented
29C2×#938C2211yescharacteristic
30C22×#214C2211yescharacteristic, complemented
31C22×#213C2211yescharacteristic
32C22×#213C2211yescharacteristic
33C2×#930—21no—
34C22×(C2×D3)⋊C4—21no—
35C2×#914—28no—
36C2×#914C2218yescomplemented
37C2×#911—28no—
38C2×#911C2218yescomplemented
39C22×D24C2211yescharacteristic
40C22×#204C2211yescharacteristic, complemented
41C22×ΓL(1,𝔽25)C2211yescharacteristic, complemented
42C22×ΓL(1,𝔽25)C2211yescharacteristic, complemented
43#5676—24no—
44#5676C2218yescomplemented
45#5554—24no—
46#5554C2218yescomplemented
47C2×#897C2211yescharacteristic, complemented
48C2×#895C2211yescharacteristic
49C2×#886—21no—
50C2×#884—21no—
51C2×#883—21no—
52C2×#882—21no—
53C2×#882—21no—
54C2×D3×C22⋊C4—21no—
55C2×#875C2211yescharacteristic, complemented
56C2×C4×D12C2211yescharacteristic
57C2×C4×D12C2211yescharacteristic, complemented
58C3×#463C2218yescomplemented
59C2×C3×C4⋊C8C2211yescharacteristic, complemented
60C2×C3×#103C2211yescharacteristic, complemented
61C2×C3×#102C2211yescharacteristic, complemented
62C2×#832C2211yescharacteristic, complemented
63#5173C2218yescomplemented
64#5156C2218yescomplemented
65C2×#821C2211yescharacteristic, complemented
66C2×(C2×D3)⋊C8C2211yescharacteristic, complemented
67C2×(C2×D3)⋊C8C2211yescharacteristic, complemented
68C2×#816C2211yescharacteristic, complemented
69#5059C2218yescomplemented
70C4×#213C2218yescomplemented
71C2×#809C2211yescharacteristic, complemented
72C2×#807C2211yescharacteristic, complemented
73C2×C4×C3⋊C8C2211yescharacteristic, complemented
74#4844C2218yescomplemented
75#4838C2218yescomplemented
76#4812C2218yescomplemented
77#4808C2218yescomplemented
78#4780C2218yescomplemented
79#4773C2218yescomplemented
80C22×AGL(1,ℤ/8)—31no—
81C22×AGL(1,ℤ/8)—31no—
82C2×#546—31no—
83C2×#546—31no—
84#3273—316no—
85C2×#495—31no—
86C2×#468—31no—
87C2×#468—31no—
88C2×#463—31no—
89C2×#463D311yescharacteristic, complemented
90C2×#452—31no—
91C2×#452—31no—
92C2×#447—31no—
93C2×#447—31no—
94C2×C4×D8—31no—
95C2×#436—31no—
96C24×D3—21no—
97C24×D3—21no—
98C22×C3×Q8C2311yescharacteristic
99C22×C3×D4C2311yescharacteristic
100C22×C3×D4C2311yescharacteristic
101C23×C3×C4—21no—
102C22×#67—21no—
103C22×#67—21no—
104C22×#67—21no—
105C22×#67—21no—
106C23×Dic3—21no—
107C2×#239—22no—
108C2×#239—24no—
109C2×#239—42no—
110C2×#239C2314yes—
111C2×#237—24no—
112C2×#237—22no—
113C2×#237—42no—
114C2×#237C2314yes—
115C2×D3×D4—24no—
116C2×D3×D4—24no—
117C2×D3×D4—22no—
118C2×D3×D4—22no—
119C2×D3×D4—42no—
120C2×D3×D4—42no—
121C2×D3×D4C2314yescomplemented
122C2×D3×D4C2314yescomplemented
123C22×D12—21no—
124C22×D12—21no—
125C22×D12D411yescharacteristic
126C22×D12C2311yescharacteristic
127C22×D12C2311yescharacteristic
128C22×C4×D3—21no—
129C22×C4×D3—21no—
130C22×C4×D3C2311yescharacteristic
131C22×C4×D3C2311yescharacteristic
132C22×Dic6C2311yescharacteristic
133C2×C3×SD16—24no—
134C2×C3×SD16C2314yescomplemented
135C2×C3×D8—24no—
136C2×C3×D8C2314yes—
137C22×C3×C8C2311yescharacteristic
138C22×C3×C8C2311yescharacteristic
139C3×#124—22no—
140C3×#124C2314yescomplemented
141C3×C4×D4—22no—
142C3×C4×D4C2314yescomplemented
143C2×C3×C4⋊C4C2311yescharacteristic
144C2×C3×C22⋊C4—21no—
145C2×C3×C22⋊C4—21no—
146C2×C3×C22⋊C4—21no—
147C2×C3×C42C2311yescharacteristic
148C2×#217—21no—
149#946—22no—
150#946C2314yescomplemented
151C2×#216—42no—
152C2×#216C2314yescomplemented
153C2×#215—24no—
154C2×#215C2314yescomplemented
155#938—22no—
156#938C2314yes—
157C2×#214—24no—
158C2×#214C2314yescomplemented
159C2×#213—42no—
160C2×#213D418yescomplemented
161C2×#213C2314yes—
162C2×#213C2314yes—
163#930—28no—
164C2×(C2×D3)⋊C4—21no—
165C2×(C2×D3)⋊C4—21no—
166C2×(C2×D3)⋊C4—21no—
167C2×(C2×D3)⋊C4—21no—
168C2×(C2×D3)⋊C4—21no—
169C2×(C2×D3)⋊C4—21no—
170C2×(C2×D3)⋊C4—28no—
171C2×(C2×D3)⋊C4D411yescharacteristic
172C2×(C2×D3)⋊C4D411yescharacteristic
173C2×C4⋊Dic3—21no—
174C2×C4⋊Dic3D411yescharacteristic
175C2×C4⋊Dic3C2311yescharacteristic
176C2×Dic3⋊C4—21no—
177C22×C3⋊C8C2311yescharacteristic
178C22×C3⋊C8C2311yescharacteristic
179#914—232no—
180#911—232no—
181C2×D24—24no—
182C2×D24C2314yes—
183C2×#204—24no—
184C2×#204C2314yescomplemented
185C2×ΓL(1,𝔽25)—24no—
186C2×ΓL(1,𝔽25)—24no—
187C2×ΓL(1,𝔽25)C2314yescomplemented
188C2×ΓL(1,𝔽25)C2314yescomplemented
189#897—22no—
190#897C2314yescomplemented
191#895—22no—
192#895C2314yes—
193#886—28no—
194#884—28no—
195#883—28no—
196#882—28no—
197#882—28no—
198D3×C22⋊C4—28no—
199#875—22no—
200#875C2314yescomplemented
201C4×D12—22no—
202C4×D12D414yes—
203C4×D12C2314yes—
204C4×D12C2314yescomplemented
205C3×C4⋊C8C2314yescomplemented
206C3×#103C2314yescomplemented
207C3×#102C2314yescomplemented
208#832C2314yescomplemented
209#821C2314yescomplemented
210(C2×D3)⋊C8C2314yescomplemented
211(C2×D3)⋊C8C2314yescomplemented
212#816C2314yescomplemented
213#809C2314yescomplemented
214#807C2314yescomplemented
215C4×C3⋊C8C2314yescomplemented
216C22×#41—31no—
217C22×#41—31no—
218C23×D4—31no—
219C23×D4—31no—
220C2×AGL(1,ℤ/8)—38no—
221C2×AGL(1,ℤ/8)—38no—
222C2×AGL(1,ℤ/8)—68no—
223C2×AGL(1,ℤ/8)—68no—
224C22×Q16—31no—
225C22×SD16—31no—
226C22×SD16—31no—
227C22×SD16—31no—
228C22×SD16C2×D311yescharacteristic, complemented
229C22×D8—31no—
230C22×D8—31no—
231C22×D8—31no—
232C22×D8C2×D311yescharacteristic
233C22×M16—31no—
234C22×M16—31no—
235#546—38no—
236#546—38no—
237#546—64no—
238#546—64no—
239C2×#124—31no—
240C2×#124C2×D311yescharacteristic, complemented
241C2×#123—61no—
242C2×#123—61no—
243C2×C22⋊Q8—31no—
244C2×C22⋊Q8—31no—
245C2×#121—31no—
246C2×#121—31no—
247C2×#121—61no—
248C2×#121—61no—
249C2×#120—61no—
250C2×#120—61no—
251C2×C4×D4—31no—
252C2×C4×D4—31no—
253C2×C4×D4C2×D311yescharacteristic, complemented
254C22×C22⋊C4—61no—
255C22×C22⋊C4—61no—
256#495—38no—
257#468—38no—
258#468—38no—
259#463—38no—
260#463C2×D318yescomplemented
261#452—38no—
262#452—38no—
263#447—38no—
264#447—38no—
265C4×D8—38no—
266#436—38no—
267C2×#107—31no—
268C2×C4⋊C8C2×D311yescharacteristic, complemented
269C2×#103—31no—
270C2×#103C2×D311yescharacteristic, complemented
271C2×#102—31no—
272C2×#102—31no—
273C2×#102—31no—
274C2×#102C2×D311yescharacteristic, complemented
275C2×C22⋊C8—31no—
276C2×C22⋊C8—31no—
277C2×C4×C8—31no—
278C24×C3—21no—
279C24×C3—21no—
280C23×D3—21no—
281C23×D3—21no—
282C23×D3—24no—
283C23×D3—24no—
284C23×D3—44no—
285C23×D3—44no—
286C23×D3—44no—
287C23×D3—44no—
288C23×D3—82no—
289C23×D3—82no—
290C23×D3C2×D411yescharacteristic
291C23×D3C2×D411yescharacteristic
292C2×C3×Q8—21no—
293C2×C3×Q8—22no—
294C2×C3×Q8—22no—
295C2×C3×Q8C2412yes—
296C2×C3×D4—21no—
297C2×C3×D4—22no—
298C2×C3×D4—21no—
299C2×C3×D4—22no—
300C2×C3×D4—22no—
301C2×C3×D4C2×D414yes—
302C2×C3×D4C2412yes—
303C2×C3×D4C2412yes—
304C22×C3×C4—21no—
305C22×C3×C4—21no—
306C22×C3×C4—24no—
307C22×C3×C4—82no—
308C22×C3×C4C2×D411yescharacteristic
309C22×C3×C4C2×D411yescharacteristic
310C22×C3×C4C2411yescharacteristic
311C2×#67—24no—
312C2×#67—24no—
313C2×#67—24no—
314C2×#67—24no—
315C2×#67—44no—
316C2×#67—44no—
317C2×#67—44no—
318C2×#67—82no—
319C22×Dic3—21no—
320C22×Dic3—21no—
321C22×Dic3—24no—
322C22×Dic3—44no—
323C22×Dic3C2×D411yescharacteristic
324C22×Dic3C2×D411yescharacteristic
325#239—28no—
326#239—44no—
327#239—48no—
328#237—28no—
329#237—44no—
330#237—48no—
331D3×D4—28no—
332D3×D4—28no—
333D3×D4—44no—
334D3×D4—44no—
335D3×D4—48no—
336D3×D4—48no—
337C2×D12—21no—
338C2×D12—22no—
339C2×D12—22no—
340C2×D12—22no—
341C2×D12—24no—
342C2×D12—21no—
343C2×D12—24no—
344C2×D12—42no—
345C2×D12—44no—
346C2×D12—82no—
347C2×D12C2×D414yes—
348C2×D12C2×D414yes—
349C2×D12C2412yes—
350C2×D12C2412yes—
351C2×C4×D3—22no—
352C2×C4×D3—22no—
353C2×C4×D3—22no—
354C2×C4×D3—22no—
355C2×C4×D3—24no—
356C2×C4×D3—24no—
357C2×C4×D3—44no—
358C2×C4×D3—82no—
359C2×C4×D3C2×D412yes—
360C2×C4×D3C2×D412yes—
361C2×C4×D3C2412yes—
362C2×C4×D3C2412yes—
363C2×Dic6—22no—
364C2×Dic6—22no—
365C2×Dic6—21no—
366C2×Dic6C2412yes—
367C3×SD16—28no—
368C3×D8—28no—
369C2×C3×C8—22no—
370C2×C3×C8—22no—
371C2×C3×C8C2412yes—
372C2×C3×C8C2412yes—
373C3×C4⋊C4—21no—
374C3×C4⋊C4C2412yes—
375C3×C22⋊C4—24no—
376C3×C22⋊C4—24no—
377C3×C22⋊C4—24no—
378C3×C42C2×D412yes—
379C3×C42C2412yes—
380#217—24no—
381#216—44no—
382#215—28no—
383#214—28no—
384#213—44no—
385#213C2×D4116yescomplemented
386(C2×D3)⋊C4—24no—
387(C2×D3)⋊C4—24no—
388(C2×D3)⋊C4—24no—
389(C2×D3)⋊C4—24no—
390(C2×D3)⋊C4—24no—
391(C2×D3)⋊C4—24no—
392(C2×D3)⋊C4C2×D414yes—
393(C2×D3)⋊C4C2×D414yes—
394C4⋊Dic3—21no—
395C4⋊Dic3—24no—
396C4⋊Dic3C2×D414yes—
397C4⋊Dic3C2412yes—
398Dic3⋊C4—24no—
399C2×C3⋊C8—22no—
400C2×C3⋊C8C2×D414yes—
401C2×C3⋊C8C2412yes—
402C2×C3⋊C8C2412yes—
403D24—28no—
404#204—28no—
405ΓL(1,𝔽25)—28no—
406ΓL(1,𝔽25)—28no—
407C25—61no—
408C25—61no—
409C2×#41—34no—
410C2×#41—34no—
411C2×#41—62no—
412C2×#41—62no—
413C2×#41—64no—
414C2×#41—64no—
415C2×#41—122no—
416C2×#41—122no—
417C22×Q8—31no—
418C22×Q8C22×D311yescharacteristic
419C22×D4—34no—
420C22×D4—34no—
421C22×D4—31no—
422C22×D4—31no—
423C22×D4—31no—
424C22×D4—61no—
425C22×D4—61no—
426C22×D4—62no—
427C22×D4—62no—
428C22×D4—61no—
429C22×D4—61no—
430C22×D4—64no—
431C22×D4—64no—
432C22×D4—61no—
433C22×D4—61no—
434C22×D4—122no—
435C22×D4—122no—
436C22×D4C22×D311yescharacteristic
437C22×D4C22×D311yescharacteristic
438C23×C4—21no—
439C23×C4—31no—
440C23×C4—31no—
441C23×C4—61no—
442C23×C4—61no—
443C23×C4—61no—
444AGL(1,ℤ/8)—632no—
445AGL(1,ℤ/8)—632no—
446C2×Q16—34no—
447C2×Q16—122no—
448C2×SD16—24no—
449C2×SD16—34no—
450C2×SD16—34no—
451C2×SD16—34no—
452C2×SD16—64no—
453C2×SD16—64no—
454C2×SD16—64no—
455C2×SD16C22×D314yescomplemented
456C2×D8—24no—
457C2×D8—38no—
458C2×D8—34no—
459C2×D8—34no—
460C2×D8—34no—
461C2×D8—64no—
462C2×D8—122no—
463C2×D8C22×D314yes—
464C2×M16—34no—
465C2×M16—34no—
466C2×M16—64no—
467C2×M16—64no—
468C22×C8—31no—
469C22×C8—31no—
470C22×C8C22×D311yescharacteristic
471C22×C8C22×D311yescharacteristic
472#124—22no—
473#124—34no—
474#124—62no—
475#124C22×D314yescomplemented
476#123—68no—
477#123—68no—
478C22⋊Q8—34no—
479C22⋊Q8—34no—
480C22⋊Q8—62no—
481C22⋊Q8—62no—
482#121—34no—
483#121—34no—
484#121—68no—
485#121—68no—
486#121—62no—
487#121—62no—
488#120—68no—
489#120—68no—
490C4×D4—22no—
491C4×D4—34no—
492C4×D4—34no—
493C4×D4—34no—
494C4×D4—62no—
495C4×D4C22×D314yescomplemented
496C2×C4⋊C4—31no—
497C2×C4⋊C4—31no—
498C2×C4⋊C4—61no—
499C2×C4⋊C4—61no—
500C2×C4⋊C4C22×D311yescharacteristic
501C2×C22⋊C4—21no—
502C2×C22⋊C4—21no—
503C2×C22⋊C4—21no—
504C2×C22⋊C4—31no—
505C2×C22⋊C4—31no—
506C2×C22⋊C4—68no—
507C2×C22⋊C4—68no—
508C2×C22⋊C4—61no—
509C2×C22⋊C4—61no—
510C2×C22⋊C4—61no—
511C2×C22⋊C4—61no—
512C2×C22⋊C4—61no—
513C2×C22⋊C4—61no—
514C2×C22⋊C4—61no—
515C2×C42C22×D311yescharacteristic
516#107—34no—
517C4⋊C8C22×D314yescomplemented
518#103—34no—
519#103C22×D314yescomplemented
520#102—34no—
521#102—34no—
522#102—34no—
523#102C22×D314yescomplemented
524C22⋊C8—34no—
525C22⋊C8—34no—
526C4×C8—34no—
527C23×C3—24no—
528C23×C3—22no—
529C23×C3—22no—
530C23×C3—42no—
531C23×C3—42no—
532C23×C3—42no—
533C23×C3—42no—
534C23×C3—42no—
535C23×C3C22×D411yescharacteristic
536C22×D3—22no—
537C22×D3—22no—
538C22×D3—24no—
539C22×D3—22no—
540C22×D3—22no—
541C22×D3—22no—
542C22×D3—22no—
543C22×D3—22no—
544C22×D3—22no—
545C22×D3—48no—
546C22×D3—48no—
547C22×D3—48no—
548C22×D3—48no—
549C22×D3—42no—
550C22×D3—42no—
551C22×D3—42no—
552C22×D3—42no—
553C22×D3—42no—
554C22×D3—84no—
555C22×D3—84no—
556C22×D3—816no—
557C22×D3—816no—
558C22×D3C22×D412yes—
559C22×D3C22×D412yes—
560C3×Q8—22no—
561C3×Q8—22no—
562C3×Q8—42no—
563C3×D4—24no—
564C3×D4—22no—
565C3×D4—22no—
566C3×D4—22no—
567C3×D4—42no—
568C3×D4C22×D414yes—
569C2×C3×C4—22no—
570C2×C3×C4—22no—
571C2×C3×C4—22no—
572C2×C3×C4—22no—
573C2×C3×C4—42no—
574C2×C3×C4—42no—
575C2×C3×C4—84no—
576C2×C3×C4C22×D412yes—
577C2×C3×C4C22×D412yes—
578C2×C3×C4C22×D411yescharacteristic
579C2×C3×C4C22×D412yes—
580C2×C3×C4H(5,𝔽2)12yes—
581C2×C3×C4C2511yescharacteristic
582#67—48no—
583#67—48no—
584#67—48no—
585#67—84no—
586C2×Dic3—22no—
587C2×Dic3—22no—
588C2×Dic3—22no—
589C2×Dic3—22no—
590C2×Dic3—48no—
591C2×Dic3—42no—
592C2×Dic3—42no—
593C2×Dic3C22×D412yes—
594C2×Dic3C22×D412yes—
595D12—24no—
596D12—22no—
597D12—22no—
598D12—22no—
599D12—44no—
600D12—48no—
601D12—42no—
602D12—84no—
603D12C22×D414yes—
604C4×D3—24no—
605C4×D3—24no—
606C4×D3—22no—
607C4×D3—22no—
608C4×D3—22no—
609C4×D3—22no—
610C4×D3—48no—
611C4×D3—84no—
612Dic6—22no—
613Dic6—22no—
614Dic6—42no—
615C3×C8—22no—
616C3×C8—22no—
617C3⋊C8—22no—
618C3⋊C8C22×D414yes—
619C24—21no—
620C24—21no—
621C24—31no—
622C24—31no—
623C24—64no—
624C24—64no—
625C24—61no—
626C24—61no—
627C24—124no—
628C24—124no—
629C24—124no—
630C24—124no—
631C24—242no—
632C24—242no—
633#41—68no—
634#41—68no—
635#41—124no—
636#41—128no—
637#41—124no—
638#41—128no—
639C2×Q8—21no—
640C2×Q8—22no—
641C2×Q8—22no—
642C2×Q8—32no—
643C2×Q8—61no—
644C2×Q8—62no—
645C2×Q8—62no—
646C2×Q8C23×D312yes—
647C2×D4—21no—
648C2×D4—22no—
649C2×D4—21no—
650C2×D4—22no—
651C2×D4—22no—
652C2×D4—34no—
653C2×D4—34no—
654C2×D4—32no—
655C2×D4—32no—
656C2×D4—64no—
657C2×D4—64no—
658C2×D4—64no—
659C2×D4—64no—
660C2×D4—68no—
661C2×D4—68no—
662C2×D4—64no—
663C2×D4—64no—
664C2×D4—61no—
665C2×D4—62no—
666C2×D4—61no—
667C2×D4—62no—
668C2×D4—62no—
669C2×D4—122no—
670C2×D4—124no—
671C2×D4—124no—
672C2×D4—124no—
673C2×D4—128no—
674C2×D4—128no—
675C2×D4—124no—
676C2×D4—124no—
677C2×D4—124no—
678C2×D4—242no—
679C2×D4—242no—
680C2×D4D3×D414yes—
681C2×D4C23×D312yes—
682C2×D4C23×D312yes—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—24no—
686C22×C4—31no—
687C22×C4—31no—
688C22×C4—32no—
689C22×C4—32no—
690C22×C4—32no—
691C22×C4—32no—
692C22×C4—64no—
693C22×C4—64no—
694C22×C4—62no—
695C22×C4—62no—
696C22×C4—62no—
697C22×C4—62no—
698C22×C4—61no—
699C22×C4—61no—
700C22×C4—64no—
701C22×C4—82no—
702C22×C4—124no—
703C22×C4—124no—
704C22×C4—242no—
705C22×C4D3×D411yescharacteristic
706C22×C4D3×D411yescharacteristic
707C22×C4C23×D311yescharacteristic
708Q16—124no—
709SD16—28no—
710SD16—68no—
711SD16—68no—
712SD16—68no—
713D8—28no—
714D8—316no—
715D8—68no—
716D8—124no—
717M16—68no—
718M16—68no—
719C2×C8—22no—
720C2×C8—22no—
721C2×C8—34no—
722C2×C8—32no—
723C2×C8—32no—
724C2×C8—62no—
725C2×C8C23×D312yes—
726C2×C8C23×D312yes—
727C4⋊C4—21no—
728C4⋊C4—34no—
729C4⋊C4—32no—
730C4⋊C4—64no—
731C4⋊C4—64no—
732C4⋊C4—61no—
733C4⋊C4C23×D312yes—
734C22⋊C4—24no—
735C22⋊C4—24no—
736C22⋊C4—24no—
737C22⋊C4—34no—
738C22⋊C4—34no—
739C22⋊C4—64no—
740C22⋊C4—64no—
741C22⋊C4—64no—
742C22⋊C4—64no—
743C22⋊C4—64no—
744C22⋊C4—64no—
745C22⋊C4—64no—
746C42D3×D412yes—
747C42C23×D312yes—
748C22×C3—24no—
749C22×C3—48no—
750C22×C3—42no—
751C22×C3—42no—
752C22×C3—42no—
753C22×C3—42no—
754C22×C3—42no—
755C22×C3—84no—
756C22×C3D4212yes—
757C22×C3#57512yes—
758C22×C3#57612yes—
759C22×C3C23×D411yescharacteristic
760C2×D3—22no—
761C2×D3—22no—
762C2×D3—24no—
763C2×D3—22no—
764C2×D3—22no—
765C2×D3—22no—
766C2×D3—22no—
767C2×D3—44no—
768C2×D3—44no—
769C2×D3—48no—
770C2×D3—42no—
771C2×D3—42no—
772C2×D3—42no—
773C2×D3—42no—
774C2×D3—42no—
775C2×D3—816no—
776C2×D3—816no—
777C2×D3—84no—
778C3×C4—22no—
779C3×C4—22no—
780C3×C4—42no—
781C3×C4—42no—
782C3×C4D4212yes—
783C3×C4C23×D411yescharacteristic
784C3×C4C2×H(5,𝔽2)11yescharacteristic
785Dic3—22no—
786Dic3—22no—
787Dic3—42no—
788Dic3—42no—
789C23—22no—
790C23—24no—
791C23—22no—
792C23—32no—
793C23—32no—
794C23—42no—
795C23—42no—
796C23—42no—
797C23—42no—
798C23—42no—
799C23—62no—
800C23—62no—
801C23—62no—
802C23—62no—
803C23—62no—
804C23—62no—
805C23—62no—
806C23—64no—
807C23—62no—
808C23—128no—
809C23—128no—
810C23—128no—
811C23—128no—
812C23—122no—
813C23—122no—
814C23—122no—
815C23—122no—
816C23—122no—
817C23—244no—
818C23—244no—
819C23—2416no—
820C23—2416no—
821C23C2×D3×D411yescharacteristic
822Q8—22no—
823Q8—22no—
824Q8—42no—
825Q8—62no—
826Q8—62no—
827Q8—122no—
828D4—22no—
829D4—22no—
830D4—22no—
831D4—24no—
832D4—34no—
833D4—42no—
834D4—62no—
835D4—62no—
836D4—62no—
837D4—64no—
838D4—124no—
839D4—128no—
840D4—128no—
841D4—128no—
842D4—128no—
843D4—122no—
844D4—244no—
845D4—244no—
846D4C2×D3×D414yes—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—32no—
852C2×C4—32no—
853C2×C4—42no—
854C2×C4—42no—
855C2×C4—62no—
856C2×C4—62no—
857C2×C4—62no—
858C2×C4—62no—
859C2×C4—62no—
860C2×C4—62no—
861C2×C4—64no—
862C2×C4—64no—
863C2×C4—62no—
864C2×C4—62no—
865C2×C4—84no—
866C2×C4—128no—
867C2×C4—128no—
868C2×C4—122no—
869C2×C4—122no—
870C2×C4—244no—
871C2×C4C2×D3×D412yes—
872C2×C4C2×D3×D412yes—
873C2×C4C2×D3×D412yes—
874C2×C4C2×D3×D411yescharacteristic
875C2×C4#100912yes—
876C2×C4C24×D311yescharacteristic
877C8—22no—
878C8—22no—
879C8—34no—
880C8—62no—
881C2×C3—44no—
882C2×C3—82no—
883C2×C3#327314yescomplemented
884C2×C3C2×D4211yescharacteristic
885C2×C3C2×#57511yescharacteristic
886C2×C3C2×#57611yescharacteristic
887D3—42no—
888D3—42no—
889D3—44no—
890D3—82no—
891C22—24no—
892C22—42no—
893C22—42no—
894C22—48no—
895C22—42no—
896C22—42no—
897C22—42no—
898C22—62no—
899C22—62no—
900C22—62no—
901C22—62no—
902C22—62no—
903C22—62no—
904C22—64no—
905C22—84no—
906C22—122no—
907C22—122no—
908C22—124no—
909C22—124no—
910C22—128no—
911C22—122no—
912C22—122no—
913C22—122no—
914C22—2416no—
915C22—2416no—
916C22—244no—
917C22#560912yes—
918C22#576812yes—
919C22#577412yes—
920C22C22×D3×D411yescharacteristic
921C4—22no—
922C4—22no—
923C4—42no—
924C4—42no—
925C4—62no—
926C4—62no—
927C4—122no—
928C4—122no—
929C4#560912yes—
930C4C22×D3×D411yescharacteristic
931C4C2×#100911yescharacteristic
932C3C2×#327311yescharacteristic, complemented, Sylow
933C2—44no—
934C2—82no—
935C2—122no—
936C2—122no—
937C2—124no—
938C2—242no—
939C2#8055514yesdirect product factor
940C2C2×#560911yescharacteristic
941C2C2×#576811yescharacteristic
942C2C2×#577411yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC2×C3×#463C2
socleC23×C3C22×D4
hypercenterC2×#463D3
hypocenterC3C2×#3273
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#463

Complements

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

NH ≅ G/Ntype
1. C22×#914C2semidirect
2. C22×#911C2semidirect
3. C2×#5676C2semidirect
4. C2×#5554C2semidirect
5. C2×C3×#463C2semidirect
6. C2×#5173C2semidirect
7. C2×#5156C2semidirect
8. C2×#5059C2semidirect
9. C2×C4×#213C2semidirect
10. #80555C2direct (N × H)
11. C2×#4844C2semidirect
12. C2×#4838C2semidirect
13. C2×#4812C2semidirect
14. C2×#4808C2semidirect
15. C2×#4780C2semidirect
16. C2×#4773C2semidirect
20. C22×D3×D4C22semidirect
21. C22×D3×D4C22semidirect
22. C22×C3×SD16C22semidirect
24. C2×C3×#124C22semidirect
25. C2×C3×C4×D4C22semidirect
26. C2×#946C22semidirect
27. C22×#216C22semidirect
28. C22×#215C22semidirect
30. C22×#214C22semidirect
36. C2×#914C22semidirect
38. C2×#911C22semidirect
40. C22×#204C22semidirect
41. C22×ΓL(1,𝔽25)C22semidirect
42. C22×ΓL(1,𝔽25)C22semidirect
44. #5676C22semidirect
46. #5554C22semidirect
47. C2×#897C22semidirect
55. C2×#875C22semidirect
57. C2×C4×D12C22semidirect
58. C3×#463C22semidirect
59. C2×C3×C4⋊C8C22semidirect
60. C2×C3×#103C22semidirect
61. C2×C3×#102C22semidirect
62. C2×#832C22semidirect
63. #5173C22semidirect
64. #5156C22semidirect
65. C2×#821C22semidirect
66. C2×(C2×D3)⋊C8C22semidirect
67. C2×(C2×D3)⋊C8C22semidirect
68. C2×#816C22semidirect
69. #5059C22semidirect
70. C4×#213C22semidirect
71. C2×#809C22semidirect
72. C2×#807C22semidirect
73. C2×C4×C3⋊C8C22semidirect
74. #4844C22semidirect
75. #4838C22semidirect
76. #4812C22semidirect
77. #4808C22semidirect
78. #4780C22semidirect
79. #4773C22semidirect
89. C2×#463D3semidirect
121. C2×D3×D4C23semidirect
122. C2×D3×D4C23semidirect
134. C2×C3×SD16C23semidirect
140. C3×#124C23semidirect
142. C3×C4×D4C23semidirect
150. #946C23semidirect
152. C2×#216C23semidirect
154. C2×#215C23semidirect
158. C2×#214C23semidirect
160. C2×#213D4semidirect
184. C2×#204C23semidirect
187. C2×ΓL(1,𝔽25)C23semidirect
188. C2×ΓL(1,𝔽25)C23semidirect
190. #897C23semidirect
200. #875C23semidirect
204. C4×D12C23semidirect
205. C3×C4⋊C8C23semidirect
206. C3×#103C23semidirect
207. C3×#102C23semidirect
208. #832C23semidirect
209. #821C23semidirect
210. (C2×D3)⋊C8C23semidirect
211. (C2×D3)⋊C8C23semidirect
212. #816C23semidirect
213. #809C23semidirect
214. #807C23semidirect
215. C4×C3⋊C8C23semidirect
228. C22×SD16C2×D3semidirect
240. C2×#124C2×D3semidirect
253. C2×C4×D4C2×D3semidirect
260. #463C2×D3semidirect
268. C2×C4⋊C8C2×D3semidirect
270. C2×#103C2×D3semidirect
274. C2×#102C2×D3semidirect
385. #213C2×D4semidirect
455. C2×SD16C22×D3semidirect
475. #124C22×D3semidirect
495. C4×D4C22×D3semidirect
517. C4⋊C8C22×D3semidirect
519. #103C22×D3semidirect
523. #102C22×D3semidirect
883. C2×C3#3273semidirect
932. C3C2×#3273semidirect
939. C2#80555direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#9142
C22×#9112
C2×#56762
C2×#55542
C2×C3×#4632
C2×#51732
C2×#51562
C2×#50592
C2×C4×#2132
#805552
C2×#48442
C2×#48382
C2×#48122
C2×#48082
C2×#47802
C2×#47732
C2×#32733