Finite Group Databasebeta

← C2×#80500 #11670211

Subgroups — C2×#80500 #11670211

Order 768.

2774 conjugacy classes of subgroups.

The subgroup lattice has 888 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#918C211yesmaximal, characteristic, complemented
2C22×#919C211yesmaximal, characteristic, complemented
3C2×#5726C211yesmaximal, characteristic, complemented
4C2×#5576C211yesmaximal, characteristic, complemented
5C2×C3×#462C211yesmaximal, characteristic, complemented
6C2×#5187C211yesmaximal, characteristic, complemented
7C2×#5186C211yesmaximal, characteristic, complemented
8C2×#5086C211yesmaximal, characteristic, complemented
9C2×#5026C211yesmaximal, characteristic, complemented
10#80500C2116yesmaximal, direct product factor
11C2×#4844C211yesmaximal, characteristic, complemented
12C2×#4836C211yesmaximal, characteristic, complemented
13C2×#4812C211yesmaximal, characteristic, complemented
14C2×#4813C211yesmaximal, characteristic, complemented
15C2×#4808C211yesmaximal, characteristic, complemented
16C2×#4810C211yesmaximal, characteristic, complemented
17C2×#3269—31nomaximal, Sylow
18C22×#239C2211yescharacteristic
19C22×#239C2211yescharacteristic
20C22×#239C2211yescharacteristic
21C22×D3×Q8C2211yescharacteristic
22C22×C3×Q16C2211yescharacteristic
23C22×C3×Q16C2211yescharacteristic
24C2×C3×C4⋊Q8C2211yescharacteristic
25C2×C3×C4×Q8C2211yescharacteristic
26C2×#946C2211yescharacteristic
27C2×#946C2211yescharacteristic
28C22×#216C2211yescharacteristic
29C22×#216C2211yescharacteristic
30C22×#215C2211yescharacteristic
31C22×#215C2211yescharacteristic
32C22×#215C2211yescharacteristic
33C2×#919—28no—
34C2×#919C2218yescomplemented
35C2×#918—28no—
36C2×#918C2218yescomplemented
37C22×D24C2211yescharacteristic
38C22×#204C2211yescharacteristic
39C22×ΓL(1,𝔽25)C2211yescharacteristic
40C22×D3×C8C2211yescharacteristic
41#5726—24no—
42#5726C2218yescomplemented
43#5576—24no—
44#5576C2218yescomplemented
45C2×#897—21no—
46C2×#897C2211yescharacteristic
47C2×#895—21no—
48C2×#895—21no—
49C2×#895C2211yescharacteristic
50C2×#894—21no—
51C2×#894—21no—
52C2×D3×C4⋊C4—21no—
53C2×#875—21no—
54C2×#875C2211yescharacteristic
55C2×C4×D12—21no—
56C2×C4×D12C2211yescharacteristic
57C2×C4×D12C2211yescharacteristic
58C3×#462C2218yescomplemented
59C2×C3×C4⋊C8C2211yescharacteristic
60C2×C3×#103C2211yescharacteristic
61C2×C3×#103C2211yescharacteristic
62C2×#835C2211yescharacteristic
63#5187C2218yescomplemented
64#5186C2218yescomplemented
65C2×#821C2211yescharacteristic
66C2×(C2×D3)⋊C8C2211yescharacteristic
67C2×(C2×D3)⋊C8C2211yescharacteristic
68C2×#816C2211yescharacteristic
69#5086C2218yescomplemented
70#5026C2218yescomplemented
71C2×#809C2211yescharacteristic
72C2×#807C2211yescharacteristic
73C2×#803C2211yescharacteristic
74#4844C2218yescomplemented
75#4836C2218yescomplemented
76#4813C2218yescomplemented
77#4812C2218yescomplemented
78#4810C2218yescomplemented
79#4808C2218yescomplemented
80C22×#137—31no—
81C22×#135—31no—
82C2×#548—31no—
83C2×#547—31no—
84#3269—316no—
85C2×#497—31no—
86C2×#468—31no—
87C2×#467—31no—
88C2×#462D311yescharacteristic, complemented
89C2×#463—31no—
90C2×#452—31no—
91C2×#452—31no—
92C2×#449—31no—
93C2×#451—31no—
94C2×#440—31no—
95C2×#435—31no—
96C22×C3×Q8C2311yescharacteristic
97C22×C3×Q8C2311yescharacteristic
98C22×C3×Q8C2311yescharacteristic
99C2×#239—22no—
100C2×#239—22no—
101C2×#239—22no—
102C2×#239—24no—
103C2×#239—24no—
104C2×#239—24no—
105C2×#239—42no—
106C2×#239—42no—
107C2×#239—42no—
108C2×#239C2314yes—
109C2×#239C2314yes—
110C2×#239C2314yes—
111C2×D3×Q8—22no—
112C2×D3×Q8—24no—
113C2×D3×Q8—42no—
114C2×D3×Q8C2314yes—
115C22×D12—21no—
116C22×D12—21no—
117C22×D12—21no—
118C22×D12—21no—
119C22×D12D411yescharacteristic
120C22×D12C2311yescharacteristic
121C22×D12C2311yescharacteristic
122C22×C4×D3—21no—
123C22×C4×D3—21no—
124C22×C4×D3—21no—
125C22×C4×D3—21no—
126C22×C4×D3—21no—
127C22×C4×D3C2311yescharacteristic
128C22×C4×D3C2311yescharacteristic
129C22×Dic6—21no—
130C22×Dic6C2311yescharacteristic
131C2×C3×Q16—24no—
132C2×C3×Q16—24no—
133C2×C3×Q16C2314yes—
134C2×C3×Q16C2314yes—
135C22×C3×C8C2311yescharacteristic
136C22×C3×C8C2311yescharacteristic
137C3×C4⋊Q8—22no—
138C3×C4⋊Q8C2314yes—
139C3×C4×Q8—22no—
140C3×C4×Q8C2314yes—
141C2×C3×C4⋊C4—21no—
142C2×C3×C4⋊C4—21no—
143C2×C3×C4⋊C4—21no—
144C2×C3×C4⋊C4C2311yescharacteristic
145C2×C3×C42—21no—
146C2×C3×C42C2311yescharacteristic
147#946—22no—
148#946—22no—
149#946C2314yes—
150#946C2314yes—
151C2×#216—24no—
152C2×#216—42no—
153C2×#216C2314yes—
154C2×#216C2314yes—
155C2×#215—24no—
156C2×#215—42no—
157C2×#215D418yescomplemented
158C2×#215C2314yes—
159C2×#215C2314yes—
160C2×#215C2314yes—
161C2×(C2×D3)⋊C4—21no—
162C2×(C2×D3)⋊C4—21no—
163C2×(C2×D3)⋊C4—21no—
164C2×(C2×D3)⋊C4—21no—
165C2×(C2×D3)⋊C4—21no—
166C2×(C2×D3)⋊C4—21no—
167C2×(C2×D3)⋊C4—21no—
168C2×(C2×D3)⋊C4D411yescharacteristic
169C2×(C2×D3)⋊C4D411yescharacteristic
170C2×C4⋊Dic3—21no—
171C2×C4⋊Dic3D411yescharacteristic
172C2×C4⋊Dic3C2311yescharacteristic
173C2×Dic3⋊C4—21no—
174C2×Dic3⋊C4—21no—
175C22×C3⋊C8C2311yescharacteristic
176C22×C3⋊C8C2311yescharacteristic
177#919—232no—
178#918—232no—
179C2×D24—24no—
180C2×D24C2314yes—
181C2×#204—24no—
182C2×#204C2314yes—
183C2×ΓL(1,𝔽25)—24no—
184C2×ΓL(1,𝔽25)C2314yes—
185C2×D3×C8—24no—
186C2×D3×C8C2314yes—
187#897—22no—
188#897—28no—
189#897C2314yes—
190#895—28no—
191#895—28no—
192#895—22no—
193#895C2314yes—
194#894—28no—
195#894—28no—
196D3×C4⋊C4—28no—
197#875—22no—
198#875—28no—
199#875C2314yes—
200C4×D12—22no—
201C4×D12—28no—
202C4×D12D414yes—
203C4×D12C2314yes—
204C4×D12C2314yes—
205C3×C4⋊C8C2314yes—
206C3×#103C2314yes—
207C3×#103C2314yes—
208#835C2314yes—
209#821C2314yes—
210(C2×D3)⋊C8C2314yes—
211(C2×D3)⋊C8C2314yes—
212#816C2314yes—
213#809C2314yes—
214#807C2314yes—
215#803C2314yes—
216C22×#41—31no—
217C22×#41—31no—
218C22×#41—31no—
219C23×Q8—31no—
220C2×#137—38no—
221C2×#137—68no—
222C2×#135—38no—
223C2×#135—68no—
224C22×Q16—31no—
225C22×Q16—31no—
226C22×Q16C2×D311yescharacteristic
227C22×Q16C2×D311yescharacteristic
228C22×SD16—31no—
229C22×SD16—31no—
230C22×SD16—31no—
231C22×SD16—31no—
232C22×D8—31no—
233C22×M16—31no—
234C23×C8—31no—
235#548—38no—
236#548—64no—
237#547—38no—
238#547—64no—
239C2×C4⋊Q8C2×D311yescharacteristic
240C2×#124—31no—
241C2×#124—61no—
242C2×#123—61no—
243C2×#123—61no—
244C2×C22⋊Q8—31no—
245C2×C22⋊Q8—31no—
246C2×C22⋊Q8—31no—
247C2×C22⋊Q8—61no—
248C2×#121—31no—
249C2×#121—61no—
250C2×#121—61no—
251C2×C4×Q8C2×D311yescharacteristic
252C2×C4×D4—31no—
253C2×C4×D4—31no—
254C2×C4×D4—61no—
255C22×C4⋊C4—61no—
256#497—38no—
257#468—38no—
258#467—38no—
259#463—38no—
260#462C2×D318yescomplemented
261#452—38no—
262#452—38no—
263#451—38no—
264#449—38no—
265#440—38no—
266#435—38no—
267C2×#107—31no—
268C2×C4⋊C8C2×D311yescharacteristic
269C2×#103—31no—
270C2×#103—31no—
271C2×#103C2×D311yescharacteristic
272C2×#103C2×D311yescharacteristic
273C2×#102—31no—
274C2×#102—31no—
275C2×C22⋊C8—31no—
276C2×C22⋊C8—31no—
277C2×#97—31no—
278C23×D3—21no—
279C23×D3—21no—
280C23×D3C2×D411yescharacteristic
281C23×D3C2×D411yescharacteristic
282C2×C3×Q8—21no—
283C2×C3×Q8—21no—
284C2×C3×Q8—21no—
285C2×C3×Q8—22no—
286C2×C3×Q8—22no—
287C2×C3×Q8—22no—
288C2×C3×Q8—22no—
289C2×C3×Q8—22no—
290C2×C3×Q8C2×D414yes—
291C2×C3×Q8C2412yes—
292C2×C3×Q8C2412yes—
293C2×C3×Q8C2412yes—
294C22×C3×C4—21no—
295C22×C3×C4—21no—
296C22×C3×C4—21no—
297C22×C3×C4—21no—
298C22×C3×C4C2×D411yescharacteristic
299C22×C3×C4C2×D411yescharacteristic
300C22×C3×C4C2411yescharacteristic
301C22×Dic3—21no—
302C22×Dic3—21no—
303C22×Dic3C2×D411yescharacteristic
304C22×Dic3C2×D411yescharacteristic
305#239—28no—
306#239—28no—
307#239—28no—
308#239—44no—
309#239—44no—
310#239—44no—
311#239—48no—
312#239—48no—
313#239—48no—
314D3×Q8—28no—
315D3×Q8—44no—
316D3×Q8—48no—
317C2×D12—21no—
318C2×D12—22no—
319C2×D12—22no—
320C2×D12—22no—
321C2×D12—24no—
322C2×D12—24no—
323C2×D12—24no—
324C2×D12—24no—
325C2×D12—21no—
326C2×D12—42no—
327C2×D12—44no—
328C2×D12—44no—
329C2×D12—44no—
330C2×D12—44no—
331C2×D12C2×D414yes—
332C2×D12C2×D414yes—
333C2×D12C2412yes—
334C2×D12C2412yes—
335C2×C4×D3—22no—
336C2×C4×D3—22no—
337C2×C4×D3—22no—
338C2×C4×D3—22no—
339C2×C4×D3—24no—
340C2×C4×D3—24no—
341C2×C4×D3—24no—
342C2×C4×D3—24no—
343C2×C4×D3—24no—
344C2×C4×D3—44no—
345C2×C4×D3—44no—
346C2×C4×D3—44no—
347C2×C4×D3—44no—
348C2×C4×D3—44no—
349C2×C4×D3C2×D412yes—
350C2×C4×D3C2×D412yes—
351C2×C4×D3C2412yes—
352C2×C4×D3C2412yes—
353C2×Dic6—22no—
354C2×Dic6—22no—
355C2×Dic6—21no—
356C2×Dic6—24no—
357C2×Dic6—44no—
358C2×Dic6C2412yes—
359C3×Q16—28no—
360C3×Q16—28no—
361C2×C3×C8—22no—
362C2×C3×C8—22no—
363C2×C3×C8C2412yes—
364C2×C3×C8C2412yes—
365C3×C4⋊C4—24no—
366C3×C4⋊C4—24no—
367C3×C4⋊C4—24no—
368C3×C4⋊C4—21no—
369C3×C4⋊C4C2412yes—
370C3×C42—24no—
371C3×C42C2×D412yes—
372C3×C42C2412yes—
373#216—28no—
374#216—44no—
375#215—28no—
376#215—44no—
377#215C2×D4116yescomplemented
378(C2×D3)⋊C4—24no—
379(C2×D3)⋊C4—24no—
380(C2×D3)⋊C4—24no—
381(C2×D3)⋊C4—24no—
382(C2×D3)⋊C4—24no—
383(C2×D3)⋊C4—24no—
384(C2×D3)⋊C4—24no—
385(C2×D3)⋊C4C2×D414yes—
386(C2×D3)⋊C4C2×D414yes—
387C4⋊Dic3—21no—
388C4⋊Dic3—24no—
389C4⋊Dic3C2×D414yes—
390C4⋊Dic3C2412yes—
391Dic3⋊C4—24no—
392Dic3⋊C4—24no—
393C2×C3⋊C8—22no—
394C2×C3⋊C8C2×D414yes—
395C2×C3⋊C8C2412yes—
396C2×C3⋊C8C2412yes—
397D24—28no—
398#204—28no—
399ΓL(1,𝔽25)—28no—
400D3×C8—28no—
401C2×#41—34no—
402C2×#41—34no—
403C2×#41—34no—
404C2×#41—62no—
405C2×#41—62no—
406C2×#41—62no—
407C2×#41—64no—
408C2×#41—64no—
409C2×#41—64no—
410C2×#41—122no—
411C2×#41—122no—
412C2×#41—122no—
413C22×Q8—34no—
414C22×Q8—31no—
415C22×Q8—61no—
416C22×Q8—62no—
417C22×Q8—64no—
418C22×Q8—122no—
419C22×Q8C22×D311yescharacteristic
420C22×Q8C22×D311yescharacteristic
421C22×Q8C22×D311yescharacteristic
422C22×D4—31no—
423C22×D4—31no—
424C22×D4—31no—
425C22×D4—61no—
426C22×D4—61no—
427C22×D4—61no—
428C22×D4—61no—
429C23×C4—31no—
430C23×C4—31no—
431C23×C4—61no—
432C23×C4—61no—
433C23×C4—61no—
434C23×C4—61no—
435C23×C4—61no—
436#137—632no—
437#135—632no—
438C2×Q16—24no—
439C2×Q16—24no—
440C2×Q16—34no—
441C2×Q16—34no—
442C2×Q16—64no—
443C2×Q16—122no—
444C2×Q16C22×D314yes—
445C2×Q16C22×D314yes—
446C2×SD16—38no—
447C2×SD16—34no—
448C2×SD16—34no—
449C2×SD16—34no—
450C2×SD16—34no—
451C2×SD16—64no—
452C2×SD16—64no—
453C2×SD16—122no—
454C2×D8—34no—
455C2×D8—64no—
456C2×M16—34no—
457C2×M16—64no—
458C22×C8—31no—
459C22×C8—31no—
460C22×C8—34no—
461C22×C8—64no—
462C22×C8C22×D311yescharacteristic
463C22×C8C22×D311yescharacteristic
464C4⋊Q8—22no—
465C4⋊Q8C22×D314yes—
466#124—34no—
467#124—68no—
468#124—62no—
469#123—68no—
470#123—68no—
471C22⋊Q8—34no—
472C22⋊Q8—34no—
473C22⋊Q8—34no—
474C22⋊Q8—68no—
475C22⋊Q8—62no—
476C22⋊Q8—62no—
477C22⋊Q8—62no—
478#121—34no—
479#121—62no—
480#121—68no—
481#121—68no—
482C4×Q8—22no—
483C4×Q8C22×D314yes—
484C4×D4—34no—
485C4×D4—34no—
486C4×D4—34no—
487C4×D4—68no—
488C4×D4—62no—
489C2×C4⋊C4—21no—
490C2×C4⋊C4—21no—
491C2×C4⋊C4—21no—
492C2×C4⋊C4—31no—
493C2×C4⋊C4—31no—
494C2×C4⋊C4—68no—
495C2×C4⋊C4—61no—
496C2×C4⋊C4—61no—
497C2×C4⋊C4—61no—
498C2×C4⋊C4C22×D311yescharacteristic
499C2×C22⋊C4—31no—
500C2×C22⋊C4—31no—
501C2×C22⋊C4—61no—
502C2×C22⋊C4—61no—
503C2×C22⋊C4—61no—
504C2×C22⋊C4—61no—
505C2×C22⋊C4—61no—
506C2×C22⋊C4—61no—
507C2×C22⋊C4—61no—
508C2×C42—21no—
509C2×C42C22×D311yescharacteristic
510#107—34no—
511C4⋊C8C22×D314yes—
512#103—34no—
513#103—34no—
514#103C22×D314yes—
515#103C22×D314yes—
516#102—34no—
517#102—34no—
518C22⋊C8—34no—
519C22⋊C8—34no—
520#97—34no—
521C23×C3C22×D411yescharacteristic
522C22×D3—22no—
523C22×D3—22no—
524C22×D3—24no—
525C22×D3—22no—
526C22×D3—22no—
527C22×D3—22no—
528C22×D3—22no—
529C22×D3—22no—
530C22×D3—22no—
531C22×D3—42no—
532C22×D3—42no—
533C22×D3—42no—
534C22×D3—42no—
535C22×D3—42no—
536C22×D3C22×D412yes—
537C22×D3C22×D412yes—
538C3×Q8—24no—
539C3×Q8—22no—
540C3×Q8—22no—
541C3×Q8—22no—
542C3×Q8—22no—
543C3×Q8—22no—
544C3×Q8—42no—
545C3×Q8—42no—
546C3×Q8C22×D414yes—
547C2×C3×C4—24no—
548C2×C3×C4—22no—
549C2×C3×C4—22no—
550C2×C3×C4—22no—
551C2×C3×C4—22no—
552C2×C3×C4—22no—
553C2×C3×C4—22no—
554C2×C3×C4—42no—
555C2×C3×C4—42no—
556C2×C3×C4—42no—
557C2×C3×C4C22×D412yes—
558C2×C3×C4C22×D412yes—
559C2×C3×C4C22×D411yescharacteristic
560C2×C3×C4C22×D412yes—
561C2×C3×C4H(5,𝔽2)12yes—
562C2×C3×C4C2511yescharacteristic
563C2×Dic3—22no—
564C2×Dic3—22no—
565C2×Dic3—22no—
566C2×Dic3—22no—
567C2×Dic3—42no—
568C2×Dic3—42no—
569C2×Dic3C22×D412yes—
570C2×Dic3C22×D412yes—
571D12—24no—
572D12—22no—
573D12—22no—
574D12—22no—
575D12—44no—
576D12—48no—
577D12—48no—
578D12—48no—
579D12—48no—
580D12—42no—
581D12C22×D414yes—
582C4×D3—24no—
583C4×D3—24no—
584C4×D3—22no—
585C4×D3—22no—
586C4×D3—22no—
587C4×D3—22no—
588C4×D3—48no—
589C4×D3—48no—
590C4×D3—48no—
591C4×D3—48no—
592C4×D3—48no—
593Dic6—22no—
594Dic6—22no—
595Dic6—48no—
596Dic6—42no—
597C3×C8—22no—
598C3×C8—22no—
599C3⋊C8—22no—
600C3⋊C8C22×D414yes—
601C24—31no—
602C24—31no—
603C24—61no—
604C24—61no—
605#41—68no—
606#41—68no—
607#41—68no—
608#41—124no—
609#41—124no—
610#41—124no—
611#41—128no—
612#41—128no—
613#41—128no—
614C2×Q8—21no—
615C2×Q8—21no—
616C2×Q8—21no—
617C2×Q8—22no—
618C2×Q8—22no—
619C2×Q8—22no—
620C2×Q8—22no—
621C2×Q8—22no—
622C2×Q8—32no—
623C2×Q8—64no—
624C2×Q8—61no—
625C2×Q8—68no—
626C2×Q8—62no—
627C2×Q8—62no—
628C2×Q8—124no—
629C2×Q8—124no—
630C2×Q8—128no—
631C2×Q8D3×D414yes—
632C2×Q8C23×D312yes—
633C2×Q8C23×D312yes—
634C2×Q8C23×D312yes—
635C2×D4—34no—
636C2×D4—34no—
637C2×D4—32no—
638C2×D4—32no—
639C2×D4—64no—
640C2×D4—64no—
641C2×D4—64no—
642C2×D4—64no—
643C2×D4—61no—
644C2×D4—62no—
645C2×D4—61no—
646C2×D4—62no—
647C2×D4—62no—
648C2×D4—122no—
649C2×D4—124no—
650C2×D4—124no—
651C2×D4—124no—
652C2×D4—124no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—31no—
658C22×C4—31no—
659C22×C4—32no—
660C22×C4—32no—
661C22×C4—32no—
662C22×C4—32no—
663C22×C4—64no—
664C22×C4—64no—
665C22×C4—64no—
666C22×C4—64no—
667C22×C4—62no—
668C22×C4—62no—
669C22×C4—62no—
670C22×C4—62no—
671C22×C4—61no—
672C22×C4—61no—
673C22×C4—64no—
674C22×C4—124no—
675C22×C4—124no—
676C22×C4—124no—
677C22×C4—124no—
678C22×C4—124no—
679C22×C4D3×D411yescharacteristic
680C22×C4D3×D411yescharacteristic
681C22×C4C23×D311yescharacteristic
682Q16—28no—
683Q16—28no—
684Q16—68no—
685Q16—124no—
686SD16—316no—
687SD16—68no—
688SD16—68no—
689SD16—124no—
690D8—68no—
691M16—68no—
692C2×C8—22no—
693C2×C8—22no—
694C2×C8—34no—
695C2×C8—32no—
696C2×C8—32no—
697C2×C8—68no—
698C2×C8—62no—
699C2×C8C23×D312yes—
700C2×C8C23×D312yes—
701C4⋊C4—24no—
702C4⋊C4—24no—
703C4⋊C4—24no—
704C4⋊C4—21no—
705C4⋊C4—34no—
706C4⋊C4—32no—
707C4⋊C4—64no—
708C4⋊C4—64no—
709C4⋊C4—64no—
710C4⋊C4—61no—
711C4⋊C4C23×D312yes—
712C22⋊C4—34no—
713C22⋊C4—34no—
714C22⋊C4—64no—
715C22⋊C4—64no—
716C22⋊C4—64no—
717C22⋊C4—64no—
718C22⋊C4—64no—
719C22⋊C4—64no—
720C22⋊C4—64no—
721C42—24no—
722C42D3×D412yes—
723C42C23×D312yes—
724C22×C3D4212yes—
725C22×C3#57512yes—
726C22×C3#57812yes—
727C22×C3C23×D411yescharacteristic
728C2×D3—22no—
729C2×D3—22no—
730C2×D3—24no—
731C2×D3—22no—
732C2×D3—22no—
733C2×D3—22no—
734C2×D3—22no—
735C2×D3—44no—
736C2×D3—44no—
737C2×D3—48no—
738C2×D3—42no—
739C2×D3—42no—
740C2×D3—42no—
741C2×D3—42no—
742C2×D3—42no—
743C2×D3—84no—
744C3×C4—24no—
745C3×C4—22no—
746C3×C4—22no—
747C3×C4—42no—
748C3×C4—42no—
749C3×C4—42no—
750C3×C4D4212yes—
751C3×C4C23×D411yescharacteristic
752C3×C4C2×H(5,𝔽2)11yescharacteristic
753Dic3—22no—
754Dic3—22no—
755Dic3—42no—
756Dic3—42no—
757C23—32no—
758C23—32no—
759C23—62no—
760C23—62no—
761C23—62no—
762C23—62no—
763C23—62no—
764C23—62no—
765C23—62no—
766C23—64no—
767C23—62no—
768C23—122no—
769C23—122no—
770C23—122no—
771C23—122no—
772C23—122no—
773C23C2×D3×D411yescharacteristic
774Q8—22no—
775Q8—24no—
776Q8—22no—
777Q8—22no—
778Q8—22no—
779Q8—22no—
780Q8—42no—
781Q8—42no—
782Q8—62no—
783Q8—62no—
784Q8—128no—
785Q8—122no—
786Q8C2×D3×D414yes—
787D4—34no—
788D4—62no—
789D4—62no—
790D4—62no—
791D4—64no—
792D4—124no—
793D4—128no—
794D4—128no—
795D4—128no—
796D4—128no—
797D4—122no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—24no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—32no—
806C2×C4—32no—
807C2×C4—42no—
808C2×C4—42no—
809C2×C4—42no—
810C2×C4—62no—
811C2×C4—62no—
812C2×C4—62no—
813C2×C4—62no—
814C2×C4—62no—
815C2×C4—62no—
816C2×C4—64no—
817C2×C4—64no—
818C2×C4—62no—
819C2×C4—62no—
820C2×C4—128no—
821C2×C4—128no—
822C2×C4—128no—
823C2×C4—128no—
824C2×C4—128no—
825C2×C4—122no—
826C2×C4—122no—
827C2×C4C2×D3×D412yes—
828C2×C4C2×D3×D412yes—
829C2×C4C2×D3×D412yes—
830C2×C4C2×D3×D411yescharacteristic
831C2×C4#100912yes—
832C2×C4C24×D311yescharacteristic
833C8—22no—
834C8—22no—
835C8—34no—
836C8—62no—
837C2×C3#326914yescomplemented
838C2×C3C2×D4211yescharacteristic
839C2×C3C2×#57511yescharacteristic
840C2×C3C2×#57811yescharacteristic
841D3—42no—
842D3—42no—
843D3—44no—
844D3—82no—
845C22—62no—
846C22—62no—
847C22—62no—
848C22—62no—
849C22—62no—
850C22—62no—
851C22—64no—
852C22—124no—
853C22—124no—
854C22—128no—
855C22—122no—
856C22—122no—
857C22—122no—
858C22—122no—
859C22—122no—
860C22—244no—
861C22#560912yes—
862C22#576612yes—
863C22#577712yes—
864C22C22×D3×D411yescharacteristic
865C4—22no—
866C4—22no—
867C4—24no—
868C4—42no—
869C4—42no—
870C4—42no—
871C4—62no—
872C4—62no—
873C4—122no—
874C4—122no—
875C4#560912yes—
876C4C22×D3×D411yescharacteristic
877C4C2×#100911yescharacteristic
878C3C2×#326911yescharacteristic, complemented, Sylow
879C2—122no—
880C2—122no—
881C2—124no—
882C2—242no—
883C2#8050014yesdirect product factor
884C2C2×#560911yescharacteristic
885C2C2×#576611yescharacteristic
886C2C2×#577711yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC2×C3×#462C2
socleC23×C3C22×D4
hypercenterC2×#462D3
hypocenterC3C2×#3269
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#462

Complements

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

NH ≅ G/Ntype
1. C22×#918C2semidirect
2. C22×#919C2semidirect
3. C2×#5726C2semidirect
4. C2×#5576C2semidirect
5. C2×C3×#462C2semidirect
6. C2×#5187C2semidirect
7. C2×#5186C2semidirect
8. C2×#5086C2semidirect
9. C2×#5026C2semidirect
10. #80500C2direct (N × H)
11. C2×#4844C2semidirect
12. C2×#4836C2semidirect
13. C2×#4812C2semidirect
14. C2×#4813C2semidirect
15. C2×#4808C2semidirect
16. C2×#4810C2semidirect
34. C2×#919C22semidirect
36. C2×#918C22semidirect
42. #5726C22semidirect
44. #5576C22semidirect
58. C3×#462C22semidirect
63. #5187C22semidirect
64. #5186C22semidirect
69. #5086C22semidirect
70. #5026C22semidirect
74. #4844C22semidirect
75. #4836C22semidirect
76. #4813C22semidirect
77. #4812C22semidirect
78. #4810C22semidirect
79. #4808C22semidirect
88. C2×#462D3semidirect
157. C2×#215D4semidirect
260. #462C2×D3semidirect
377. #215C2×D4semidirect
837. C2×C3#3269semidirect
878. C3C2×#3269semidirect
883. C2#80500direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#9182
C22×#9192
C2×#57262
C2×#55762
C2×C3×#4622
C2×#51872
C2×#51862
C2×#50862
C2×#50262
#805002
C2×#48442
C2×#48362
C2×#48122
C2×#48132
C2×#48082
C2×#48102
C2×#32693