Finite Group Databasebeta

← C2×#80023 #11670295

Subgroups — C2×#80023 #11670295

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
1C2×#5806C211yesmaximal, characteristic, complemented
2C22×#932C211yesmaximal, characteristic, complemented
3C22×#911C211yesmaximal, characteristic, complemented
4C2×#5612C211yesmaximal, characteristic, complemented
5C2×C3×#447C211yesmaximal, characteristic, complemented
6C2×#5156C211yesmaximal, characteristic, complemented
7C2×#5155C211yesmaximal, characteristic, complemented
8C2×#5153C211yesmaximal, characteristic, complemented
9C2×#5042C211yesmaximal, characteristic, complemented
10#80023C2116yesmaximal, direct product factor
11C2×#4787C211yesmaximal, characteristic, complemented
12C2×#4780C211yesmaximal, characteristic, complemented
13C2×#4783C211yesmaximal, characteristic, complemented
14C2×#4756C211yesmaximal, characteristic, complemented
15C2×#4733C211yesmaximal, characteristic, complemented
16C2×#4729C211yesmaximal, characteristic, complemented
17C2×#3273—31nomaximal, Sylow
18C23×C3×D4C2211yescharacteristic, complemented
19C22×#237C2211yescharacteristic
20C22×D3×D4C2211yescharacteristic, complemented
21C22×#235C2211yescharacteristic
22C22×C3×D8C2211yescharacteristic
23C22×C3×D8C2211yescharacteristic
24C2×C3×#121C2211yescharacteristic
25C2×#953—21no—
26C22×#217—21no—
27#5806—24no—
28#5806C2218yescomplemented
29C2×#939—21no—
30C2×#938—21no—
31C2×#938C2211yescharacteristic
32C2×#937—21no—
33C2×#936C2211yescharacteristic, complemented
34C2×#936C2211yescharacteristic, complemented
35C2×#935—21no—
36C2×D4×Dic3C2211yescharacteristic, complemented
37C22×#214C2211yescharacteristic, complemented
38C22×#214C2211yescharacteristic, complemented
39C22×#214C2211yescharacteristic, complemented
40C2×#932—28no—
41C2×#932C2218yescomplemented
42C22×#213C2211yescharacteristic
43C22×#213C2211yescharacteristic
44C2×C4×#67C2211yescharacteristic
45C2×#924C2211yescharacteristic, complemented
46C22×#208C2211yescharacteristic, complemented
47C2×#911—28no—
48C2×#911C2218yescomplemented
49C22×Dic12C2211yescharacteristic, complemented
50C22×#204C2211yescharacteristic, complemented
51C22×ΓL(1,𝔽25)C2211yescharacteristic, complemented
52#5612—24no—
53#5612C2218yescomplemented
54C2×#897C2211yescharacteristic, complemented
55C2×#893C2211yescharacteristic, complemented
56C2×#883—21no—
57C2×D3×C22⋊C4—21no—
58C3×#447C2218yescomplemented
59C2×C3×#102C2211yescharacteristic, complemented
60C2×C3×#102C2211yescharacteristic, complemented
61C2×C3×C22⋊C8C2211yescharacteristic, complemented
62C2×#832C2211yescharacteristic, complemented
63#5156C2218yescomplemented
64#5155C2218yescomplemented
65#5153C2218yescomplemented
66C2×#821C2211yescharacteristic, complemented
67C2×(C2×D3)⋊C8C2211yescharacteristic, complemented
68C2×#816C2211yescharacteristic, complemented
69C2×Dic3⋊C8C2211yescharacteristic, complemented
70C2×C8×Dic3C2211yescharacteristic, complemented
71#5042C2218yescomplemented
72C2×#810C2211yescharacteristic, complemented
73C2×#807C2211yescharacteristic, complemented
74#4787C2218yescomplemented
75#4783C2218yescomplemented
76#4780C2218yescomplemented
77#4756C2218yescomplemented
78#4733C2218yescomplemented
79#4729C2218yescomplemented
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×#463—31no—
90C2×#452—31no—
91C2×#452—31no—
92C2×#447—31no—
93C2×#447D311yescharacteristic, complemented
94C2×C4×D8—31no—
95C2×#436—31no—
96C25×C3—21no—
97C24×D3—21no—
98C22×C3×D4—24no—
99C22×C3×D4—21no—
100C22×C3×D4—21no—
101C22×C3×D4—22no—
102C22×C3×D4—42no—
103C22×C3×D4C2311yescharacteristic
104C22×C3×D4C2311yescharacteristic
105C22×C3×D4C2311yescharacteristic
106C22×C3×D4C2314yescomplemented
107C23×C3×C4C2311yescharacteristic
108C22×#67—21no—
109C22×#67—21no—
110C22×#67—21no—
111C22×#67—21no—
112C22×#67D411yescharacteristic
113C23×Dic3—21no—
114C23×Dic3—21no—
115C2×#237—24no—
116C2×#237—22no—
117C2×#237—42no—
118C2×#237C2314yes—
119C2×D3×D4—24no—
120C2×D3×D4—22no—
121C2×D3×D4—42no—
122C2×D3×D4C2314yescomplemented
123C2×#235—22no—
124C2×#235—24no—
125C2×#235—42no—
126C2×#235C2314yes—
127C22×D12C2311yescharacteristic
128C22×C4×D3—21no—
129C22×C4×D3—21no—
130C22×C4×D3C2311yescharacteristic
131C22×Dic6C2311yescharacteristic
132C22×Dic6C2311yescharacteristic
133C2×C3×D8—24no—
134C2×C3×D8—42no—
135C2×C3×D8C2314yes—
136C2×C3×D8C2314yes—
137C22×C3×C8C2311yescharacteristic
138C22×C3×C8C2311yescharacteristic
139C3×#121—22no—
140C3×#121C2314yes—
141C2×C3×C4⋊C4C2311yescharacteristic
142C2×C3×C22⋊C4—21no—
143#953—28no—
144C2×#217—21no—
145C2×#217—21no—
146C2×#217—21no—
147C2×#217—21no—
148C2×#217—21no—
149C2×#217—21no—
150C2×#217—21no—
151C2×#217—28no—
152C2×#217D411yescharacteristic
153#939—28no—
154#938—22no—
155#938—28no—
156#938C2314yes—
157#937—28no—
158#936—22no—
159#936—22no—
160#936C2314yescomplemented
161#936C2314yescomplemented
162#935—28no—
163D4×Dic3—22no—
164D4×Dic3C2314yescomplemented
165C2×#214—24no—
166C2×#214—24no—
167C2×#214—24no—
168C2×#214C2314yescomplemented
169C2×#214C2314yescomplemented
170C2×#214C2314yescomplemented
171#932—232no—
172C2×#213—24no—
173C2×#213D418yescomplemented
174C2×#213C2314yes—
175C2×#213C2314yes—
176C4×#67D414yes—
177C4×#67C2314yes—
178C2×(C2×D3)⋊C4—21no—
179C2×(C2×D3)⋊C4—21no—
180C2×(C2×D3)⋊C4D411yescharacteristic
181C2×C4⋊Dic3—21no—
182C2×C4⋊Dic3C2311yescharacteristic
183#924—22no—
184#924C2314yescomplemented
185C2×Dic3⋊C4—21no—
186C2×Dic3⋊C4D411yescharacteristic
187C2×C4×Dic3C2311yescharacteristic
188C2×#208—24no—
189C2×#208C2314yescomplemented
190C22×C3⋊C8C2311yescharacteristic
191C22×C3⋊C8C2311yescharacteristic
192#911—232no—
193C2×Dic12—42no—
194C2×Dic12C2314yescomplemented
195C2×#204—24no—
196C2×#204C2314yescomplemented
197C2×ΓL(1,𝔽25)—24no—
198C2×ΓL(1,𝔽25)C2314yescomplemented
199#897—22no—
200#897C2314yescomplemented
201#893—22no—
202#893C2314yescomplemented
203#883—28no—
204D3×C22⋊C4—28no—
205C3×#102C2314yescomplemented
206C3×#102C2314yescomplemented
207C3×C22⋊C8C2314yescomplemented
208#832C2314yescomplemented
209#821C2314yescomplemented
210(C2×D3)⋊C8C2314yescomplemented
211#816C2314yescomplemented
212Dic3⋊C8C2314yescomplemented
213C8×Dic3C2314yescomplemented
214#810C2314yescomplemented
215#807C2314yescomplemented
216C22×#41—31no—
217C22×#41—31no—
218C23×D4—31no—
219C23×D4C2×D311yescharacteristic, complemented
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×SD16—31no—
229C22×D8—31no—
230C22×D8—31no—
231C22×D8C2×D311yescharacteristic
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×#124—31no—
241C2×#123—61no—
242C2×#123—61no—
243C2×C22⋊Q8—31no—
244C2×C22⋊Q8—31no—
245C2×#121—31no—
246C2×#121—61no—
247C2×#121—61no—
248C2×#121C2×D311yescharacteristic
249C2×#120—61no—
250C2×#120—61no—
251C2×C4×D4—31no—
252C2×C4×D4—31no—
253C2×C4×D4—31no—
254C22×C22⋊C4—61no—
255C22×C22⋊C4—61no—
256#495—38no—
257#468—38no—
258#468—38no—
259#463—38no—
260#463—38no—
261#452—38no—
262#452—38no—
263#447—38no—
264#447C2×D318yescomplemented
265C4×D8—38no—
266#436—38no—
267C2×#107—31no—
268C2×C4⋊C8—31no—
269C2×#103—31no—
270C2×#103—31no—
271C2×#102—31no—
272C2×#102—31no—
273C2×#102C2×D311yescharacteristic, complemented
274C2×#102C2×D311yescharacteristic, complemented
275C2×C22⋊C8—31no—
276C2×C22⋊C8C2×D311yescharacteristic, complemented
277C2×C4×C8—31no—
278C24×C3—21no—
279C24×C3—21no—
280C24×C3—21no—
281C24×C3—24no—
282C24×C3—44no—
283C24×C3—44no—
284C24×C3—82no—
285C24×C3C2×D411yescharacteristic
286C23×D3—21no—
287C23×D3—24no—
288C23×D3—44no—
289C23×D3—44no—
290C23×D3—82no—
291C23×D3C2×D411yescharacteristic
292C2×C3×D4—28no—
293C2×C3×D4—24no—
294C2×C3×D4—21no—
295C2×C3×D4—22no—
296C2×C3×D4—22no—
297C2×C3×D4—24no—
298C2×C3×D4—21no—
299C2×C3×D4—21no—
300C2×C3×D4—22no—
301C2×C3×D4—22no—
302C2×C3×D4—22no—
303C2×C3×D4—44no—
304C2×C3×D4—48no—
305C2×C3×D4—44no—
306C2×C3×D4—82no—
307C2×C3×D4C2×D414yes—
308C2×C3×D4C2412yes—
309C2×C3×D4C2412yes—
310C2×C3×D4C2412yes—
311C22×C3×C4—22no—
312C22×C3×C4—22no—
313C22×C3×C4—21no—
314C22×C3×C4C2×D411yescharacteristic
315C22×C3×C4C2×D412yes—
316C22×C3×C4C2412yes—
317C22×C3×C4C2411yescharacteristic
318C2×#67—24no—
319C2×#67—24no—
320C2×#67—24no—
321C2×#67—24no—
322C2×#67—42no—
323C2×#67—44no—
324C2×#67—44no—
325C2×#67—44no—
326C2×#67—82no—
327C2×#67C2×D414yes—
328C22×Dic3—21no—
329C22×Dic3—21no—
330C22×Dic3—21no—
331C22×Dic3—24no—
332C22×Dic3—24no—
333C22×Dic3—44no—
334C22×Dic3—82no—
335C22×Dic3C2×D411yescharacteristic
336C22×Dic3C2×D411yescharacteristic
337C22×Dic3C2×D411yescharacteristic
338#237—28no—
339#237—44no—
340#237—48no—
341D3×D4—28no—
342D3×D4—44no—
343D3×D4—48no—
344#235—28no—
345#235—44no—
346#235—48no—
347C2×D12—21no—
348C2×D12—22no—
349C2×D12C2×D414yes—
350C2×D12C2412yes—
351C2×C4×D3—22no—
352C2×C4×D3—22no—
353C2×C4×D3—24no—
354C2×C4×D3—24no—
355C2×C4×D3—44no—
356C2×C4×D3—82no—
357C2×C4×D3C2×D412yes—
358C2×C4×D3C2412yes—
359C2×Dic6—22no—
360C2×Dic6—22no—
361C2×Dic6—22no—
362C2×Dic6—22no—
363C2×Dic6—21no—
364C2×Dic6—21no—
365C2×Dic6C2412yes—
366C2×Dic6C2412yes—
367C3×D8—28no—
368C3×D8—44no—
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—
376#217—24no—
377#217—24no—
378#217—24no—
379#217—24no—
380#217—24no—
381#217—24no—
382#217—24no—
383#217C2×D414yes—
384#214—28no—
385#214—28no—
386#214—28no—
387#213—28no—
388#213C2×D4116yescomplemented
389(C2×D3)⋊C4—24no—
390(C2×D3)⋊C4—24no—
391(C2×D3)⋊C4C2×D414yes—
392C4⋊Dic3—21no—
393C4⋊Dic3—24no—
394C4⋊Dic3C2412yes—
395Dic3⋊C4—24no—
396Dic3⋊C4C2×D414yes—
397C4×Dic3C2×D412yes—
398C4×Dic3C2412yes—
399#208—28no—
400C2×C3⋊C8—22no—
401C2×C3⋊C8C2×D414yes—
402C2×C3⋊C8C2412yes—
403C2×C3⋊C8C2412yes—
404Dic12—44no—
405#204—28no—
406ΓL(1,𝔽25)—28no—
407C25—21no—
408C25—61no—
409C2×#41—34no—
410C2×#41—34no—
411C2×#41—64no—
412C2×#41—62no—
413C2×#41—62no—
414C2×#41—64no—
415C2×#41—122no—
416C2×#41—122no—
417C22×Q8—31no—
418C22×Q8—31no—
419C22×D4—24no—
420C22×D4—21no—
421C22×D4—21no—
422C22×D4—22no—
423C22×D4—31no—
424C22×D4—34no—
425C22×D4—31no—
426C22×D4—42no—
427C22×D4—62no—
428C22×D4—61no—
429C22×D4—64no—
430C22×D4—61no—
431C22×D4—61no—
432C22×D4—61no—
433C22×D4—122no—
434C22×D4C22×D311yescharacteristic
435C22×D4C22×D311yescharacteristic
436C22×D4C22×D311yescharacteristic
437C22×D4C22×D314yescomplemented
438C23×C4—31no—
439C23×C4—61no—
440C23×C4—61no—
441C23×C4—61no—
442C23×C4—61no—
443C23×C4C22×D311yescharacteristic
444AGL(1,ℤ/8)—632no—
445AGL(1,ℤ/8)—632no—
446C2×Q16—34no—
447C2×Q16—122no—
448C2×SD16—34no—
449C2×SD16—34no—
450C2×SD16—34no—
451C2×SD16—34no—
452C2×SD16—64no—
453C2×SD16—64no—
454C2×SD16—64no—
455C2×SD16—64no—
456C2×D8—24no—
457C2×D8—38no—
458C2×D8—34no—
459C2×D8—34no—
460C2×D8—42no—
461C2×D8—64no—
462C2×D8C22×D314yes—
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—34no—
473#124—34no—
474#124—62no—
475#124—62no—
476#123—68no—
477#123—68no—
478C22⋊Q8—34no—
479C22⋊Q8—34no—
480C22⋊Q8—62no—
481C22⋊Q8—62no—
482#121—22no—
483#121—34no—
484#121—68no—
485#121—68no—
486#121—62no—
487#121C22×D314yes—
488#120—68no—
489#120—68no—
490C4×D4—34no—
491C4×D4—34no—
492C4×D4—34no—
493C4×D4—34no—
494C4×D4—62no—
495C4×D4—62no—
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—31no—
503C2×C22⋊C4—31no—
504C2×C22⋊C4—68no—
505C2×C22⋊C4—68no—
506C2×C22⋊C4—61no—
507C2×C22⋊C4—61no—
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×C42—31no—
516#107—34no—
517C4⋊C8—34no—
518#103—34no—
519#103—34no—
520#102—34no—
521#102—34no—
522#102C22×D314yescomplemented
523#102C22×D314yescomplemented
524C22⋊C8—34no—
525C22⋊C8C22×D314yescomplemented
526C4×C8—34no—
527C23×C3—24no—
528C23×C3—22no—
529C23×C3—22no—
530C23×C3—22no—
531C23×C3—22no—
532C23×C3—22no—
533C23×C3—22no—
534C23×C3—48no—
535C23×C3—48no—
536C23×C3—42no—
537C23×C3—42no—
538C23×C3—42no—
539C23×C3—42no—
540C23×C3—42no—
541C23×C3—42no—
542C23×C3—42no—
543C23×C3—42no—
544C23×C3—84no—
545C23×C3—816no—
546C23×C3C22×D412yes—
547C23×C3C22×D411yescharacteristic
548C22×D3—22no—
549C22×D3—24no—
550C22×D3—22no—
551C22×D3—22no—
552C22×D3—22no—
553C22×D3—48no—
554C22×D3—48no—
555C22×D3—42no—
556C22×D3—42no—
557C22×D3—84no—
558C22×D3—816no—
559C22×D3C22×D412yes—
560C3×D4—24no—
561C3×D4—22no—
562C3×D4—22no—
563C3×D4—22no—
564C3×D4—22no—
565C3×D4—22no—
566C3×D4—48no—
567C3×D4—42no—
568C3×D4—42no—
569C3×D4—84no—
570C3×D4C22×D414yes—
571C2×C3×C4—22no—
572C2×C3×C4—24no—
573C2×C3×C4—22no—
574C2×C3×C4—22no—
575C2×C3×C4—22no—
576C2×C3×C4—42no—
577C2×C3×C4C22×D412yes—
578C2×C3×C4C22×D411yescharacteristic
579C2×C3×C4C22×D412yes—
580C2×C3×C4H(5,𝔽2)12yes—
581C2×C3×C4C2511yescharacteristic
582#67—44no—
583#67—48no—
584#67—48no—
585#67—48no—
586#67—84no—
587C2×Dic3—22no—
588C2×Dic3—22no—
589C2×Dic3—22no—
590C2×Dic3—22no—
591C2×Dic3—22no—
592C2×Dic3—22no—
593C2×Dic3—48no—
594C2×Dic3—42no—
595C2×Dic3—42no—
596C2×Dic3—42no—
597C2×Dic3—84no—
598C2×Dic3C22×D412yes—
599C2×Dic3C22×D412yes—
600C2×Dic3C22×D412yes—
601D12—24no—
602D12—22no—
603D12C22×D414yes—
604C4×D3—24no—
605C4×D3—22no—
606C4×D3—22no—
607C4×D3—48no—
608C4×D3—84no—
609Dic6—22no—
610Dic6—22no—
611Dic6—22no—
612Dic6—22no—
613Dic6—42no—
614Dic6—42no—
615C3×C8—22no—
616C3×C8—22no—
617C3⋊C8—22no—
618C3⋊C8C22×D414yes—
619C24—21no—
620C24—21no—
621C24—21no—
622C24—24no—
623C24—31no—
624C24—44no—
625C24—44no—
626C24—64no—
627C24—61no—
628C24—82no—
629C24—124no—
630C24—124no—
631C24—242no—
632C24D3×D411yescharacteristic
633#41—68no—
634#41—68no—
635#41—124no—
636#41—128no—
637#41—124no—
638#41—128no—
639C2×Q8—32no—
640C2×Q8—32no—
641C2×Q8—61no—
642C2×Q8—61no—
643C2×Q8—62no—
644C2×Q8—62no—
645C2×Q8—62no—
646C2×Q8—62no—
647C2×D4—28no—
648C2×D4—24no—
649C2×D4—21no—
650C2×D4—22no—
651C2×D4—22no—
652C2×D4—21no—
653C2×D4—24no—
654C2×D4—21no—
655C2×D4—22no—
656C2×D4—22no—
657C2×D4—22no—
658C2×D4—34no—
659C2×D4—34no—
660C2×D4—32no—
661C2×D4—44no—
662C2×D4—48no—
663C2×D4—44no—
664C2×D4—64no—
665C2×D4—68no—
666C2×D4—64no—
667C2×D4—64no—
668C2×D4—64no—
669C2×D4—61no—
670C2×D4—62no—
671C2×D4—82no—
672C2×D4—124no—
673C2×D4—128no—
674C2×D4—122no—
675C2×D4—124no—
676C2×D4—124no—
677C2×D4—124no—
678C2×D4—242no—
679C2×D4D3×D414yes—
680C2×D4C23×D312yes—
681C2×D4C23×D312yes—
682C2×D4C23×D312yes—
683C22×C4—22no—
684C22×C4—22no—
685C22×C4—21no—
686C22×C4—31no—
687C22×C4—31no—
688C22×C4—31no—
689C22×C4—32no—
690C22×C4—32no—
691C22×C4—64no—
692C22×C4—64no—
693C22×C4—64no—
694C22×C4—62no—
695C22×C4—62no—
696C22×C4—61no—
697C22×C4—61no—
698C22×C4—61no—
699C22×C4—64no—
700C22×C4—124no—
701C22×C4—124no—
702C22×C4—242no—
703C22×C4—242no—
704C22×C4D3×D412yes—
705C22×C4D3×D411yescharacteristic
706C22×C4C23×D312yes—
707C22×C4C23×D311yescharacteristic
708Q16—124no—
709SD16—68no—
710SD16—68no—
711SD16—68no—
712SD16—68no—
713D8—28no—
714D8—316no—
715D8—44no—
716D8—68no—
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—61no—
732C4⋊C4—64no—
733C4⋊C4C23×D312yes—
734C22⋊C4—24no—
735C22⋊C4—34no—
736C22⋊C4—34no—
737C22⋊C4—64no—
738C22⋊C4—64no—
739C22⋊C4—64no—
740C22⋊C4—64no—
741C22⋊C4—64no—
742C22⋊C4—64no—
743C22⋊C4—64no—
744C22⋊C4—64no—
745C22⋊C4—64no—
746C42—32no—
747C42—32no—
748C22×C3—24no—
749C22×C3—22no—
750C22×C3—22no—
751C22×C3—22no—
752C22×C3—44no—
753C22×C3—48no—
754C22×C3—42no—
755C22×C3—42no—
756C22×C3—42no—
757C22×C3—42no—
758C22×C3—42no—
759C22×C3—42no—
760C22×C3—42no—
761C22×C3—42no—
762C22×C3—816no—
763C22×C3—84no—
764C22×C3—84no—
765C22×C3D4212yes—
766C22×C3#57512yes—
767C22×C3#57612yes—
768C22×C3C23×D411yescharacteristic
769C2×D3—22no—
770C2×D3—24no—
771C2×D3—22no—
772C2×D3—22no—
773C2×D3—44no—
774C2×D3—48no—
775C2×D3—42no—
776C2×D3—42no—
777C2×D3—816no—
778C3×C4—22no—
779C3×C4—42no—
780C3×C4D4212yes—
781C3×C4C23×D411yescharacteristic
782C3×C4C2×H(5,𝔽2)11yescharacteristic
783Dic3—22no—
784Dic3—22no—
785Dic3—22no—
786Dic3—42no—
787Dic3—42no—
788Dic3—42no—
789C23—22no—
790C23—22no—
791C23—22no—
792C23—22no—
793C23—24no—
794C23—22no—
795C23—22no—
796C23—32no—
797C23—48no—
798C23—48no—
799C23—42no—
800C23—42no—
801C23—42no—
802C23—42no—
803C23—42no—
804C23—42no—
805C23—42no—
806C23—42no—
807C23—62no—
808C23—62no—
809C23—62no—
810C23—62no—
811C23—64no—
812C23—84no—
813C23—816no—
814C23—128no—
815C23—128no—
816C23—122no—
817C23—122no—
818C23—244no—
819C23—2416no—
820C23C2×D3×D412yes—
821C23C2×D3×D411yescharacteristic
822Q8—62no—
823Q8—62no—
824Q8—62no—
825Q8—62no—
826Q8—122no—
827Q8—122no—
828D4—22no—
829D4—22no—
830D4—22no—
831D4—22no—
832D4—22no—
833D4—24no—
834D4—34no—
835D4—48no—
836D4—42no—
837D4—42no—
838D4—62no—
839D4—64no—
840D4—84no—
841D4—124no—
842D4—128no—
843D4—128no—
844D4—128no—
845D4—244no—
846D4C2×D3×D414yes—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—24no—
851C2×C4—22no—
852C2×C4—32no—
853C2×C4—32no—
854C2×C4—32no—
855C2×C4—42no—
856C2×C4—62no—
857C2×C4—62no—
858C2×C4—62no—
859C2×C4—62no—
860C2×C4—62no—
861C2×C4—64no—
862C2×C4—62no—
863C2×C4—62no—
864C2×C4—62no—
865C2×C4—128no—
866C2×C4—128no—
867C2×C4—122no—
868C2×C4—122no—
869C2×C4—122no—
870C2×C4—244no—
871C2×C4—244no—
872C2×C4C2×D3×D412yes—
873C2×C4C2×D3×D412yes—
874C2×C4C2×D3×D411yescharacteristic
875C2×C4#100412yes—
876C2×C4C24×D311yescharacteristic
877C8—22no—
878C8—22no—
879C8—34no—
880C8—62no—
881C2×C3—42no—
882C2×C3—44no—
883C2×C3—82no—
884C2×C3—82no—
885C2×C3#327314yescomplemented
886C2×C3C2×D4211yescharacteristic
887C2×C3C2×#57511yescharacteristic
888C2×C3C2×#57611yescharacteristic
889D3—42no—
890D3—44no—
891C22—22no—
892C22—22no—
893C22—22no—
894C22—24no—
895C22—42no—
896C22—42no—
897C22—44no—
898C22—48no—
899C22—42no—
900C22—42no—
901C22—42no—
902C22—42no—
903C22—42no—
904C22—42no—
905C22—62no—
906C22—62no—
907C22—62no—
908C22—64no—
909C22—816no—
910C22—84no—
911C22—84no—
912C22—122no—
913C22—122no—
914C22—124no—
915C22—128no—
916C22—2416no—
917C22#559012yes—
918C22#575712yes—
919C22#577312yes—
920C22C22×D3×D411yescharacteristic
921C4—22no—
922C4—42no—
923C4—62no—
924C4—62no—
925C4—62no—
926C4—122no—
927C4—122no—
928C4—122no—
929C4#559012yes—
930C4C22×D3×D411yescharacteristic
931C4C2×#100411yescharacteristic
932C3C2×#327311yescharacteristic, complemented, Sylow
933C2—42no—
934C2—44no—
935C2—82no—
936C2—82no—
937C2—122no—
938C2—124no—
939C2#8002314yesdirect product factor
940C2C2×#559011yescharacteristic
941C2C2×#575711yescharacteristic
942C2C2×#577311yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC2×C3×#447C2
socleC23×C3C22×D4
hypercenterC2×#447D3
hypocenterC3C2×#3273
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#447

Complements

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

NH ≅ G/Ntype
1. C2×#5806C2semidirect
2. C22×#932C2semidirect
3. C22×#911C2semidirect
4. C2×#5612C2semidirect
5. C2×C3×#447C2semidirect
6. C2×#5156C2semidirect
7. C2×#5155C2semidirect
8. C2×#5153C2semidirect
9. C2×#5042C2semidirect
10. #80023C2direct (N × H)
11. C2×#4787C2semidirect
12. C2×#4780C2semidirect
13. C2×#4783C2semidirect
14. C2×#4756C2semidirect
15. C2×#4733C2semidirect
16. C2×#4729C2semidirect
18. C23×C3×D4C22semidirect
20. C22×D3×D4C22semidirect
28. #5806C22semidirect
33. C2×#936C22semidirect
34. C2×#936C22semidirect
36. C2×D4×Dic3C22semidirect
37. C22×#214C22semidirect
38. C22×#214C22semidirect
39. C22×#214C22semidirect
41. C2×#932C22semidirect
45. C2×#924C22semidirect
46. C22×#208C22semidirect
48. C2×#911C22semidirect
49. C22×Dic12C22semidirect
50. C22×#204C22semidirect
51. C22×ΓL(1,𝔽25)C22semidirect
53. #5612C22semidirect
54. C2×#897C22semidirect
55. C2×#893C22semidirect
58. C3×#447C22semidirect
59. C2×C3×#102C22semidirect
60. C2×C3×#102C22semidirect
61. C2×C3×C22⋊C8C22semidirect
62. C2×#832C22semidirect
63. #5156C22semidirect
64. #5155C22semidirect
65. #5153C22semidirect
66. C2×#821C22semidirect
67. C2×(C2×D3)⋊C8C22semidirect
68. C2×#816C22semidirect
69. C2×Dic3⋊C8C22semidirect
70. C2×C8×Dic3C22semidirect
71. #5042C22semidirect
72. C2×#810C22semidirect
73. C2×#807C22semidirect
74. #4787C22semidirect
75. #4783C22semidirect
76. #4780C22semidirect
77. #4756C22semidirect
78. #4733C22semidirect
79. #4729C22semidirect
93. C2×#447D3semidirect
106. C22×C3×D4C23semidirect
122. C2×D3×D4C23semidirect
160. #936C23semidirect
161. #936C23semidirect
164. D4×Dic3C23semidirect
168. C2×#214C23semidirect
169. C2×#214C23semidirect
170. C2×#214C23semidirect
173. C2×#213D4semidirect
184. #924C23semidirect
189. C2×#208C23semidirect
194. C2×Dic12C23semidirect
196. C2×#204C23semidirect
198. C2×ΓL(1,𝔽25)C23semidirect
200. #897C23semidirect
202. #893C23semidirect
205. C3×#102C23semidirect
206. C3×#102C23semidirect
207. C3×C22⋊C8C23semidirect
208. #832C23semidirect
209. #821C23semidirect
210. (C2×D3)⋊C8C23semidirect
211. #816C23semidirect
212. Dic3⋊C8C23semidirect
213. C8×Dic3C23semidirect
214. #810C23semidirect
215. #807C23semidirect
219. C23×D4C2×D3semidirect
264. #447C2×D3semidirect
273. C2×#102C2×D3semidirect
274. C2×#102C2×D3semidirect
276. C2×C22⋊C8C2×D3semidirect
388. #213C2×D4semidirect
437. C22×D4C22×D3semidirect
522. #102C22×D3semidirect
523. #102C22×D3semidirect
525. C22⋊C8C22×D3semidirect
885. C2×C3#3273semidirect
932. C3C2×#3273semidirect
939. C2#80023direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#58062
C22×#9322
C22×#9112
C2×#56122
C2×C3×#4472
C2×#51562
C2×#51552
C2×#51532
C2×#50422
#800232
C2×#47872
C2×#47802
C2×#47832
C2×#47562
C2×#47332
C2×#47292
C2×#32733