Finite Group Databasebeta

← C113×#23876 #43291896

Subgroups — C113×#23876 #43291896

Order 28928.

2012 conjugacy classes of subgroups.

The subgroup lattice has 938 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×AGL(1,ℤ/8)×C113C211yesmaximal, characteristic, complemented
2C113×#3488C211yesmaximal, characteristic, complemented
3C2×#453×C113C212yesmaximal, complemented
4C113×#3003C211yesmaximal, characteristic, complemented
5C113×#2433C211yesmaximal, characteristic, complemented
6C113×#2006C212yesmaximal, complemented
7C113×#2002C212yesmaximal, complemented
8C113×#1900C211yesmaximal, characteristic, complemented
9C113×#1883C212yesmaximal, complemented
10C113×#1871C211yesmaximal, characteristic, complemented
11C113×#1789C211yesmaximal, characteristic, complemented
12C2×H(5,𝔽2)×C113C2211yescharacteristic, complemented
13C22×#41×C113C2211yescharacteristic
14C23×D4×C113C2211yescharacteristic, complemented
15C2×AGL(1,ℤ/8)×C113—21no—
16C2×AGL(1,ℤ/8)×C113—21no—
17C2×AGL(1,ℤ/8)×C113—28no—
18C2×AGL(1,ℤ/8)×C113C2212yes—
19C2×AGL(1,ℤ/8)×C113C2212yescomplemented
20C2×AGL(1,ℤ/8)×C113C2212yescomplemented
21C22×SD16×C113—21no—
22C22×D8×C113—21no—
23C22×M16×C113C2211yescharacteristic, complemented
24#550×C113—21no—
25#548×C113—21no—
26#546×C113—21no—
27#546×C113—22no—
28D42×C113—22no—
29D42×C113—21no—
30#537×C113—21no—
31#537×C113C2211yescharacteristic, complemented
32#535×C113—21no—
33#535×C113C2211yescharacteristic, complemented
34C2×#127×C113C2212yescomplemented
35#525×C113—21no—
36#525×C113C2211yescharacteristic
37C2×#121×C113—21no—
38C2×#121×C113C2211yescharacteristic
39C2×#120×C113—22no—
40#520×C113C2211yescharacteristic, complemented
41#453×C113—28no—
42#450×C113—21no—
43#450×C113—21no—
44#447×C113—21no—
45#447×C113—21no—
46C2×#104×C113C2212yescomplemented
47C2×#104×C113C2212yescomplemented
48C2×#104×C113C2212yescomplemented
49#418×C113C2212yescomplemented
50C2×#100×C113C2212yescomplemented
51#407×C113C2211yescharacteristic, complemented
52#392×C113—22no—
53#390×C113C2212yescomplemented
54C4×C22⋊C4×C113C2211yescharacteristic, complemented
55#343×C113C2212yescomplemented
56#339×C113C2212yescomplemented
57C25×C113—21no—
58H(5,𝔽2)×C113—24no—
59H(5,𝔽2)×C113—42no—
60C2×#41×C113—21no—
61C2×#41×C113—21no—
62C2×#41×C113—21no—
63C2×#41×C113—21no—
64C2×#41×C113—24no—
65C2×#41×C113—42no—
66C2×#41×C113D411yescharacteristic, complemented
67C2×#41×C113D411yescharacteristic, complemented
68C2×#41×C113C2311yescharacteristic
69C2×#41×C113C2311yescharacteristic
70C2×#41×C113C2311yescharacteristic
71C22×Q8×C113D411yescharacteristic, complemented
72C22×D4×C113—24no—
73C22×D4×C113—21no—
74C22×D4×C113—22no—
75C22×D4×C113—22no—
76C22×D4×C113—21no—
77C22×D4×C113—21no—
78C22×D4×C113—24no—
79C22×D4×C113—21no—
80C22×D4×C113—21no—
81C22×D4×C113—21no—
82C22×D4×C113—21no—
83C22×D4×C113—21no—
84C22×D4×C113—42no—
85C22×D4×C113D412yes—
86C22×D4×C113D411yescharacteristic, complemented
87C22×D4×C113C2311yescharacteristic
88C22×D4×C113C2312yes—
89C23×C4×C113—21no—
90C23×C4×C113C2311yescharacteristic
91AGL(1,ℤ/8)×C113—28no—
92AGL(1,ℤ/8)×C113—28no—
93AGL(1,ℤ/8)×C113—24no—
94AGL(1,ℤ/8)×C113—24no—
95AGL(1,ℤ/8)×C113—24no—
96AGL(1,ℤ/8)×C113—24no—
97AGL(1,ℤ/8)×C113—42no—
98AGL(1,ℤ/8)×C113D418yescomplemented
99C2×SD16×C113—28no—
100C2×SD16×C113—22no—
101C2×SD16×C113—22no—
102C2×SD16×C113—22no—
103C2×D8×C113—28no—
104C2×D8×C113—22no—
105C2×D8×C113—22no—
106C2×D8×C113—22no—
107C2×M16×C113—21no—
108C2×M16×C113—24no—
109C2×M16×C113C2312yes—
110C2×M16×C113C2312yes—
111C22×C8×C113—21no—
112#127×C113—22no—
113#127×C113—21no—
114#127×C113—24no—
115#127×C113—42no—
116#124×C113—22no—
117#124×C113—21no—
118#123×C113—22no—
119#123×C113—21no—
120C22⋊Q8×C113—22no—
121C22⋊Q8×C113—21no—
122C22⋊Q8×C113—21no—
123C22⋊Q8×C113D411yescharacteristic, complemented
124C22⋊Q8×C113D411yescharacteristic, complemented
125#121×C113—22no—
126#121×C113—22no—
127#121×C113—22no—
128#121×C113—22no—
129#121×C113—22no—
130#121×C113—21no—
131#121×C113—21no—
132#121×C113—21no—
133#121×C113—21no—
134#121×C113—21no—
135#121×C113—21no—
136#121×C113—22no—
137#121×C113—21no—
138#121×C113—21no—
139#121×C113D411yescharacteristic, complemented
140#121×C113D411yescharacteristic, complemented
141#120×C113—22no—
142#120×C113—22no—
143#120×C113—22no—
144#120×C113—21no—
145#120×C113—22no—
146#120×C113—48no—
147C4×Q8×C113—21no—
148C4×D4×C113—22no—
149C4×D4×C113—22no—
150C4×D4×C113—21no—
151C4×D4×C113—22no—
152C4×D4×C113—21no—
153C4×D4×C113—21no—
154#117×C113—21no—
155#117×C113C2311yescharacteristic
156C2×C4⋊C4×C113—21no—
157C2×C4⋊C4×C113C2311yescharacteristic
158C2×C22⋊C4×C113—22no—
159C2×C22⋊C4×C113—21no—
160C2×C22⋊C4×C113—24no—
161C2×C22⋊C4×C113D412yes—
162C2×C42×C113C2312yes—
163#104×C113—24no—
164#104×C113—24no—
165#104×C113—42no—
166#102×C113—22no—
167#102×C113—22no—
168#100×C113—24no—
169C22⋊C8×C113—21no—
170C22⋊C8×C113—21no—
171#95×C113—21no—
172C24×C113—22no—
173C24×C113—22no—
174C24×C113—21no—
175C24×C113—44no—
176C24×C113—44no—
177C24×C113—41no—
178C24×C113—41no—
179C24×C113—82no—
180C24×C113C2×D411yescharacteristic
181C24×C113C2×D412yes—
182#41×C113—22no—
183#41×C113—22no—
184#41×C113—22no—
185#41×C113—22no—
186#41×C113—22no—
187#41×C113—22no—
188#41×C113—22no—
189#41×C113—44no—
190#41×C113—41no—
191#41×C113—41no—
192#41×C113—44no—
193#41×C113—44no—
194#41×C113—42no—
195#41×C113—42no—
196#41×C113C2×D414yes—
197C2×Q8×C113—21no—
198C2×Q8×C113—22no—
199C2×Q8×C113—41no—
200C2×Q8×C113C2×D411yescharacteristic
201C2×Q8×C113C2×D411yescharacteristic
202C2×Q8×C113C2×D411yescharacteristic
203C2×D4×C113—21no—
204C2×D4×C113—24no—
205C2×D4×C113—24no—
206C2×D4×C113—22no—
207C2×D4×C113—22no—
208C2×D4×C113—22no—
209C2×D4×C113—22no—
210C2×D4×C113—21no—
211C2×D4×C113—21no—
212C2×D4×C113—21no—
213C2×D4×C113—21no—
214C2×D4×C113—21no—
215C2×D4×C113—22no—
216C2×D4×C113—22no—
217C2×D4×C113—22no—
218C2×D4×C113—21no—
219C2×D4×C113—22no—
220C2×D4×C113—21no—
221C2×D4×C113—22no—
222C2×D4×C113—22no—
223C2×D4×C113—22no—
224C2×D4×C113—22no—
225C2×D4×C113—21no—
226C2×D4×C113—21no—
227C2×D4×C113—22no—
228C2×D4×C113—22no—
229C2×D4×C113—22no—
230C2×D4×C113—41no—
231C2×D4×C113—44no—
232C2×D4×C113—44no—
233C2×D4×C113—44no—
234C2×D4×C113—44no—
235C2×D4×C113—42no—
236C2×D4×C113—42no—
237C2×D4×C113—48no—
238C2×D4×C113—44no—
239C2×D4×C113—48no—
240C2×D4×C113—42no—
241C2×D4×C113—42no—
242C2×D4×C113—44no—
243C2×D4×C113—48no—
244C2×D4×C113—41no—
245C2×D4×C113—41no—
246C2×D4×C113—84no—
247C2×D4×C113—84no—
248C2×D4×C113C2×D411yescharacteristic
249C2×D4×C113C2×D411yescharacteristic
250C2×D4×C113C2×D411yescharacteristic
251C2×D4×C113C2×D414yescomplemented
252C22×C4×C113—21no—
253C22×C4×C113—22no—
254C22×C4×C113—22no—
255C22×C4×C113—22no—
256C22×C4×C113—21no—
257C22×C4×C113—22no—
258C22×C4×C113—22no—
259C22×C4×C113—21no—
260C22×C4×C113—21no—
261C22×C4×C113—21no—
262C22×C4×C113—21no—
263C22×C4×C113—44no—
264C22×C4×C113C2×D411yescharacteristic
265C22×C4×C113C2×D411yescharacteristic
266C22×C4×C113C2×D411yescharacteristic
267C22×C4×C113C2×D411yescharacteristic
268C22×C4×C113C2×D411yescharacteristic
269C22×C4×C113C2×D412yes—
270C22×C4×C113C2411yescharacteristic
271SD16×C113—28no—
272SD16×C113—28no—
273SD16×C113—44no—
274D8×C113—28no—
275D8×C113—28no—
276D8×C113—44no—
277M16×C113—24no—
278M16×C113—22no—
279M16×C113—22no—
280M16×C113—22no—
281M16×C113C2×D414yescomplemented
282C2×C8×C113—24no—
283C2×C8×C113—22no—
284C2×C8×C113—22no—
285C4⋊C4×C113—22no—
286C4⋊C4×C113—22no—
287C4⋊C4×C113—21no—
288C4⋊C4×C113—21no—
289C4⋊C4×C113—21no—
290C4⋊C4×C113—21no—
291C4⋊C4×C113C2×D411yescharacteristic
292C4⋊C4×C113C2×D411yescharacteristic
293C22⋊C4×C113—22no—
294C22⋊C4×C113—22no—
295C22⋊C4×C113—24no—
296C22⋊C4×C113—22no—
297C22⋊C4×C113—22no—
298C22⋊C4×C113—22no—
299C22⋊C4×C113—21no—
300C22⋊C4×C113—21no—
301C22⋊C4×C113—21no—
302C22⋊C4×C113—21no—
303C22⋊C4×C113—22no—
304C22⋊C4×C113—22no—
305C22⋊C4×C113—21no—
306C22⋊C4×C113—48no—
307C42×C113—22no—
308C42×C113—21no—
309C42×C113—22no—
310C42×C113—22no—
311C23×C113—21no—
312C23×C113—22no—
313C23×C113—22no—
314C23×C113—22no—
315C23×C113—21no—
316C23×C113—21no—
317C23×C113—24no—
318C23×C113—24no—
319C23×C113—41no—
320C23×C113—42no—
321C23×C113—44no—
322C23×C113—44no—
323C23×C113—44no—
324C23×C113—44no—
325C23×C113—44no—
326C23×C113—42no—
327C23×C113—42no—
328C23×C113—42no—
329C23×C113—42no—
330C23×C113—42no—
331C23×C113—81no—
332C23×C113—82no—
333C23×C113—82no—
334C23×C113—82no—
335C23×C113—82no—
336C23×C113—82no—
337C23×C113—816no—
338C23×C113—82no—
339C23×C113#12011yescharacteristic
340C23×C113#12011yescharacteristic
341C23×C113C22×D411yescharacteristic
342Q8×C113—21no—
343Q8×C113—21no—
344Q8×C113—21no—
345Q8×C113—22no—
346Q8×C113—42no—
347Q8×C113#12012yescomplemented
348D4×C113—24no—
349D4×C113—21no—
350D4×C113—24no—
351D4×C113—21no—
352D4×C113—21no—
353D4×C113—22no—
354D4×C113—24no—
355D4×C113—42no—
356D4×C113—42no—
357D4×C113—44no—
358D4×C113—44no—
359D4×C113—44no—
360D4×C113—42no—
361D4×C113—44no—
362D4×C113—42no—
363D4×C113—42no—
364D4×C113—44no—
365D4×C113—42no—
366D4×C113—41no—
367D4×C113—42no—
368D4×C113—41no—
369D4×C113—42no—
370D4×C113—42no—
371D4×C113—81no—
372D4×C113—82no—
373D4×C113—82no—
374D4×C113—82no—
375D4×C113—82no—
376D4×C113—816no—
377D4×C113#12012yescomplemented
378C2×C4×C113—21no—
379C2×C4×C113—22no—
380C2×C4×C113—21no—
381C2×C4×C113—21no—
382C2×C4×C113—21no—
383C2×C4×C113—21no—
384C2×C4×C113—22no—
385C2×C4×C113—22no—
386C2×C4×C113—24no—
387C2×C4×C113—24no—
388C2×C4×C113—21no—
389C2×C4×C113—22no—
390C2×C4×C113—21no—
391C2×C4×C113—21no—
392C2×C4×C113—21no—
393C2×C4×C113—42no—
394C2×C4×C113—42no—
395C2×C4×C113—42no—
396C2×C4×C113—44no—
397C2×C4×C113—42no—
398C2×C4×C113—42no—
399C2×C4×C113—41no—
400C2×C4×C113—41no—
401C2×C4×C113—42no—
402C2×C4×C113—42no—
403C2×C4×C113—82no—
404C2×C4×C113#12011yescharacteristic
405C2×C4×C113#12011yescharacteristic
406C2×C4×C113C22×D411yescharacteristic
407C2×C4×C113C22×D412yes—
408C2×C4×C113C22×D411yescharacteristic
409C2×C4×C113H(5,𝔽2)12yes—
410C8×C113—24no—
411C8×C113—42no—
412C22×C113—21no—
413C22×C113—21no—
414C22×C113—21no—
415C22×C113—21no—
416C22×C113—21no—
417C22×C113—22no—
418C22×C113—21no—
419C22×C113—21no—
420C22×C113—44no—
421C22×C113—48no—
422C22×C113—41no—
423C22×C113—41no—
424C22×C113—41no—
425C22×C113—41no—
426C22×C113—42no—
427C22×C113—44no—
428C22×C113—42no—
429C22×C113—41no—
430C22×C113—41no—
431C22×C113—41no—
432C22×C113—42no—
433C22×C113—41no—
434C22×C113—84no—
435C22×C113—84no—
436C22×C113—84no—
437C22×C113—88no—
438C22×C113—88no—
439C22×C113—82no—
440C22×C113—82no—
441C22×C113—164no—
442C22×C113#45312yescomplemented
443C22×C113C2×#12011yescharacteristic
444C22×C113D4212yes—
445C4×C113—21no—
446C4×C113—21no—
447C4×C113—22no—
448C4×C113—44no—
449C4×C113—41no—
450C4×C113—41no—
451C4×C113—42no—
452C4×C113—41no—
453C4×C113—41no—
454C4×C113C2×#12011yescharacteristic
455C4×C113#53411yescharacteristic
456C4×C113D4212yes—
457#23876C11311yesmaximal, characteristic, direct product factor, Sylow
458C2×C113—22no—
459C2×C113—22no—
460C2×C113—41no—
461C2×C113—42no—
462C2×C113—81no—
463C2×C113—84no—
464C2×C113—82no—
465C2×C113—81no—
466C2×C113#240311yescharacteristic
467C2×C113C2×#45311yescharacteristic
468C2×C113#302111yescharacteristic
469C22×AGL(1,ℤ/8)C2×C11311yescharacteristic, complemented
470#3488C2×C11311yescharacteristic, complemented
471C2×#453C2×C11312yescomplemented
472#3003C2×C11311yescharacteristic, complemented
473#2433C2×C11311yescharacteristic, complemented
474#2006C2×C11312yescomplemented
475#2002C2×C11312yescomplemented
476#1900C2×C11311yescharacteristic, complemented
477#1883C2×C11312yescomplemented
478#1871C2×C11311yescharacteristic, complemented
479#1789C2×C11311yescharacteristic, complemented
480C113#2387611yescharacteristic, direct product factor, Sylow
481C2×H(5,𝔽2)C22×C11311yescharacteristic, complemented
482C22×#41C22×C11311yescharacteristic
483C23×D4C22×C11311yescharacteristic, complemented
484C2×AGL(1,ℤ/8)—21no—
485C2×AGL(1,ℤ/8)—21no—
486C2×AGL(1,ℤ/8)—28no—
487C2×AGL(1,ℤ/8)C22×C11312yes—
488C2×AGL(1,ℤ/8)C22×C11312yescomplemented
489C2×AGL(1,ℤ/8)C22×C11312yescomplemented
490C22×SD16—21no—
491C22×D8—21no—
492C22×M16C22×C11311yescharacteristic, complemented
493#550—21no—
494#548—21no—
495#546—21no—
496#546—22no—
497D42—22no—
498D42—21no—
499#537—21no—
500#537C22×C11311yescharacteristic, complemented
501#535—21no—
502#535C22×C11311yescharacteristic, complemented
503C2×#127C22×C11312yescomplemented
504#525—21no—
505#525C22×C11311yescharacteristic
506C2×#121—21no—
507C2×#121C22×C11311yescharacteristic
508C2×#120—22no—
509#520C22×C11311yescharacteristic, complemented
510#453—28no—
511#450—21no—
512#450—21no—
513#447—21no—
514#447—21no—
515C2×#104C22×C11312yescomplemented
516C2×#104C22×C11312yescomplemented
517C2×#104C22×C11312yescomplemented
518#418C22×C11312yescomplemented
519C2×#100C22×C11312yescomplemented
520#407C22×C11311yescharacteristic, complemented
521#392—22no—
522#390C22×C11312yescomplemented
523C4×C22⋊C4C22×C11311yescharacteristic, complemented
524#343C22×C11312yescomplemented
525#339C22×C11312yescomplemented
526C25—21no—
527H(5,𝔽2)—24no—
528H(5,𝔽2)—42no—
529C2×#41—21no—
530C2×#41—21no—
531C2×#41—21no—
532C2×#41—21no—
533C2×#41—24no—
534C2×#41—42no—
535C2×#41D4×C11311yescharacteristic, complemented
536C2×#41D4×C11311yescharacteristic, complemented
537C2×#41C23×C11311yescharacteristic
538C2×#41C23×C11311yescharacteristic
539C2×#41C23×C11311yescharacteristic
540C22×Q8D4×C11311yescharacteristic, complemented
541C22×D4—24no—
542C22×D4—21no—
543C22×D4—22no—
544C22×D4—22no—
545C22×D4—21no—
546C22×D4—21no—
547C22×D4—24no—
548C22×D4—21no—
549C22×D4—21no—
550C22×D4—21no—
551C22×D4—21no—
552C22×D4—21no—
553C22×D4—42no—
554C22×D4D4×C11312yes—
555C22×D4D4×C11311yescharacteristic, complemented
556C22×D4C23×C11311yescharacteristic
557C22×D4C23×C11312yes—
558C23×C4—21no—
559C23×C4C23×C11311yescharacteristic
560AGL(1,ℤ/8)—28no—
561AGL(1,ℤ/8)—28no—
562AGL(1,ℤ/8)—24no—
563AGL(1,ℤ/8)—24no—
564AGL(1,ℤ/8)—24no—
565AGL(1,ℤ/8)—24no—
566AGL(1,ℤ/8)—42no—
567AGL(1,ℤ/8)D4×C11318yescomplemented
568C2×SD16—28no—
569C2×SD16—22no—
570C2×SD16—22no—
571C2×SD16—22no—
572C2×D8—28no—
573C2×D8—22no—
574C2×D8—22no—
575C2×D8—22no—
576C2×M16—21no—
577C2×M16—24no—
578C2×M16C23×C11312yes—
579C2×M16C23×C11312yes—
580C22×C8—21no—
581#127—22no—
582#127—21no—
583#127—24no—
584#127—42no—
585#124—22no—
586#124—21no—
587#123—22no—
588#123—21no—
589C22⋊Q8—22no—
590C22⋊Q8—21no—
591C22⋊Q8—21no—
592C22⋊Q8D4×C11311yescharacteristic, complemented
593C22⋊Q8D4×C11311yescharacteristic, complemented
594#121—22no—
595#121—22no—
596#121—22no—
597#121—22no—
598#121—22no—
599#121—21no—
600#121—21no—
601#121—21no—
602#121—21no—
603#121—21no—
604#121—21no—
605#121—22no—
606#121—21no—
607#121—21no—
608#121D4×C11311yescharacteristic, complemented
609#121D4×C11311yescharacteristic, complemented
610#120—22no—
611#120—22no—
612#120—22no—
613#120—21no—
614#120—22no—
615#120—48no—
616C4×Q8—21no—
617C4×D4—22no—
618C4×D4—22no—
619C4×D4—21no—
620C4×D4—22no—
621C4×D4—21no—
622C4×D4—21no—
623#117—21no—
624#117C23×C11311yescharacteristic
625C2×C4⋊C4—21no—
626C2×C4⋊C4C23×C11311yescharacteristic
627C2×C22⋊C4—22no—
628C2×C22⋊C4—21no—
629C2×C22⋊C4—24no—
630C2×C22⋊C4D4×C11312yes—
631C2×C42C23×C11312yes—
632#104—24no—
633#104—24no—
634#104—42no—
635#102—22no—
636#102—22no—
637#100—24no—
638C22⋊C8—21no—
639C22⋊C8—21no—
640#95—21no—
641C24—22no—
642C24—22no—
643C24—21no—
644C24—44no—
645C24—44no—
646C24—41no—
647C24—41no—
648C24—82no—
649C24C2×D4×C11311yescharacteristic
650C24C2×D4×C11312yes—
651#41—22no—
652#41—22no—
653#41—22no—
654#41—22no—
655#41—22no—
656#41—22no—
657#41—22no—
658#41—44no—
659#41—41no—
660#41—41no—
661#41—44no—
662#41—44no—
663#41—42no—
664#41—42no—
665#41C2×D4×C11314yes—
666C2×Q8—21no—
667C2×Q8—22no—
668C2×Q8—41no—
669C2×Q8C2×D4×C11311yescharacteristic
670C2×Q8C2×D4×C11311yescharacteristic
671C2×Q8C2×D4×C11311yescharacteristic
672C2×D4—21no—
673C2×D4—24no—
674C2×D4—24no—
675C2×D4—22no—
676C2×D4—22no—
677C2×D4—22no—
678C2×D4—22no—
679C2×D4—21no—
680C2×D4—21no—
681C2×D4—21no—
682C2×D4—21no—
683C2×D4—21no—
684C2×D4—22no—
685C2×D4—22no—
686C2×D4—22no—
687C2×D4—21no—
688C2×D4—22no—
689C2×D4—21no—
690C2×D4—22no—
691C2×D4—22no—
692C2×D4—22no—
693C2×D4—22no—
694C2×D4—21no—
695C2×D4—21no—
696C2×D4—22no—
697C2×D4—22no—
698C2×D4—22no—
699C2×D4—41no—
700C2×D4—44no—
701C2×D4—44no—
702C2×D4—44no—
703C2×D4—44no—
704C2×D4—42no—
705C2×D4—42no—
706C2×D4—48no—
707C2×D4—44no—
708C2×D4—48no—
709C2×D4—42no—
710C2×D4—42no—
711C2×D4—44no—
712C2×D4—48no—
713C2×D4—41no—
714C2×D4—41no—
715C2×D4—84no—
716C2×D4—84no—
717C2×D4C2×D4×C11311yescharacteristic
718C2×D4C2×D4×C11311yescharacteristic
719C2×D4C2×D4×C11311yescharacteristic
720C2×D4C2×D4×C11314yescomplemented
721C22×C4—21no—
722C22×C4—22no—
723C22×C4—22no—
724C22×C4—22no—
725C22×C4—21no—
726C22×C4—22no—
727C22×C4—22no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—44no—
733C22×C4C2×D4×C11311yescharacteristic
734C22×C4C2×D4×C11311yescharacteristic
735C22×C4C2×D4×C11311yescharacteristic
736C22×C4C2×D4×C11311yescharacteristic
737C22×C4C2×D4×C11311yescharacteristic
738C22×C4C2×D4×C11312yes—
739C22×C4C24×C11311yescharacteristic
740SD16—28no—
741SD16—28no—
742SD16—44no—
743D8—28no—
744D8—28no—
745D8—44no—
746M16—24no—
747M16—22no—
748M16—22no—
749M16—22no—
750M16C2×D4×C11314yescomplemented
751C2×C8—24no—
752C2×C8—22no—
753C2×C8—22no—
754C4⋊C4—22no—
755C4⋊C4—22no—
756C4⋊C4—21no—
757C4⋊C4—21no—
758C4⋊C4—21no—
759C4⋊C4—21no—
760C4⋊C4C2×D4×C11311yescharacteristic
761C4⋊C4C2×D4×C11311yescharacteristic
762C22⋊C4—22no—
763C22⋊C4—22no—
764C22⋊C4—24no—
765C22⋊C4—22no—
766C22⋊C4—22no—
767C22⋊C4—22no—
768C22⋊C4—21no—
769C22⋊C4—21no—
770C22⋊C4—21no—
771C22⋊C4—21no—
772C22⋊C4—22no—
773C22⋊C4—22no—
774C22⋊C4—21no—
775C22⋊C4—48no—
776C42—22no—
777C42—21no—
778C42—22no—
779C42—22no—
780C23—21no—
781C23—22no—
782C23—22no—
783C23—22no—
784C23—21no—
785C23—21no—
786C23—24no—
787C23—24no—
788C23—41no—
789C23—42no—
790C23—44no—
791C23—44no—
792C23—44no—
793C23—44no—
794C23—44no—
795C23—42no—
796C23—42no—
797C23—42no—
798C23—42no—
799C23—42no—
800C23—81no—
801C23—82no—
802C23—82no—
803C23—82no—
804C23—82no—
805C23—82no—
806C23—816no—
807C23—82no—
808C23#120×C11311yescharacteristic
809C23#120×C11311yescharacteristic
810C23C22×D4×C11311yescharacteristic
811Q8—21no—
812Q8—21no—
813Q8—21no—
814Q8—22no—
815Q8—42no—
816Q8#120×C11312yescomplemented
817D4—24no—
818D4—21no—
819D4—24no—
820D4—21no—
821D4—21no—
822D4—22no—
823D4—24no—
824D4—42no—
825D4—42no—
826D4—44no—
827D4—44no—
828D4—44no—
829D4—42no—
830D4—44no—
831D4—42no—
832D4—42no—
833D4—44no—
834D4—42no—
835D4—41no—
836D4—42no—
837D4—41no—
838D4—42no—
839D4—42no—
840D4—82no—
841D4—81no—
842D4—82no—
843D4—82no—
844D4—82no—
845D4—816no—
846D4#120×C11312yescomplemented
847C2×C4—21no—
848C2×C4—22no—
849C2×C4—21no—
850C2×C4—21no—
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—24no—
856C2×C4—24no—
857C2×C4—21no—
858C2×C4—22no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—21no—
862C2×C4—42no—
863C2×C4—42no—
864C2×C4—42no—
865C2×C4—44no—
866C2×C4—42no—
867C2×C4—42no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—42no—
871C2×C4—42no—
872C2×C4—82no—
873C2×C4#120×C11311yescharacteristic
874C2×C4#120×C11311yescharacteristic
875C2×C4C22×D4×C11311yescharacteristic
876C2×C4C22×D4×C11312yes—
877C2×C4C22×D4×C11311yescharacteristic
878C2×C4H(5,𝔽2)×C11312yes—
879C8—24no—
880C8—42no—
881C22—21no—
882C22—21no—
883C22—21no—
884C22—21no—
885C22—21no—
886C22—22no—
887C22—21no—
888C22—21no—
889C22—44no—
890C22—48no—
891C22—41no—
892C22—41no—
893C22—41no—
894C22—41no—
895C22—42no—
896C22—44no—
897C22—42no—
898C22—41no—
899C22—41no—
900C22—41no—
901C22—42no—
902C22—41no—
903C22—84no—
904C22—84no—
905C22—84no—
906C22—88no—
907C22—88no—
908C22—82no—
909C22—82no—
910C22—164no—
911C22#453×C11312yescomplemented
912C22C2×#120×C11311yescharacteristic
913C22D42×C11312yes—
914C4—21no—
915C4—21no—
916C4—22no—
917C4—44no—
918C4—41no—
919C4—41no—
920C4—42no—
921C4—41no—
922C4—41no—
923C4C2×#120×C11311yescharacteristic
924C4#534×C11311yescharacteristic
925C4D42×C11312yes—
926C2—22no—
927C2—22no—
928C2—41no—
929C2—42no—
930C2—84no—
931C2—81no—
932C2—82no—
933C2—81no—
934C2C113×#240311yescharacteristic
935C2C2×#453×C11311yescharacteristic
936C2C113×#302111yescharacteristic
subgroupG/H
center, socleC22×C113C2×#120
commutator, Frattini, cosocleC22×C4C24×C113
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C113 ◁ C23×C4×C113 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×AGL(1,ℤ/8)×C113C2semidirect
2. C113×#3488C2semidirect
3. C2×#453×C113C2semidirect
4. C113×#3003C2semidirect
5. C113×#2433C2semidirect
6. C113×#2006C2semidirect
7. C113×#2002C2semidirect
8. C113×#1900C2semidirect
9. C113×#1883C2semidirect
10. C113×#1871C2semidirect
11. C113×#1789C2semidirect
12. C2×H(5,𝔽2)×C113C22semidirect
14. C23×D4×C113C22semidirect
19. C2×AGL(1,ℤ/8)×C113C22semidirect
20. C2×AGL(1,ℤ/8)×C113C22semidirect
23. C22×M16×C113C22semidirect
31. #537×C113C22semidirect
33. #535×C113C22semidirect
34. C2×#127×C113C22semidirect
40. #520×C113C22semidirect
46. C2×#104×C113C22semidirect
47. C2×#104×C113C22semidirect
48. C2×#104×C113C22semidirect
49. #418×C113C22semidirect
50. C2×#100×C113C22semidirect
51. #407×C113C22semidirect
53. #390×C113C22semidirect
54. C4×C22⋊C4×C113C22semidirect
55. #343×C113C22semidirect
56. #339×C113C22semidirect
66. C2×#41×C113D4semidirect
67. C2×#41×C113D4semidirect
71. C22×Q8×C113D4semidirect
86. C22×D4×C113D4semidirect
98. AGL(1,ℤ/8)×C113D4semidirect
123. C22⋊Q8×C113D4semidirect
124. C22⋊Q8×C113D4semidirect
139. #121×C113D4semidirect
140. #121×C113D4semidirect
251. C2×D4×C113C2×D4semidirect
281. M16×C113C2×D4semidirect
347. Q8×C113#120semidirect
377. D4×C113#120semidirect
442. C22×C113#453semidirect
457. #23876C113direct (N × H)
469. C22×AGL(1,ℤ/8)C2×C113semidirect
470. #3488C2×C113semidirect
471. C2×#453C2×C113semidirect
472. #3003C2×C113semidirect
473. #2433C2×C113semidirect
474. #2006C2×C113semidirect
475. #2002C2×C113semidirect
476. #1900C2×C113semidirect
477. #1883C2×C113semidirect
478. #1871C2×C113semidirect
479. #1789C2×C113semidirect
480. C113#23876direct (N × H)
481. C2×H(5,𝔽2)C22×C113semidirect
483. C23×D4C22×C113semidirect
488. C2×AGL(1,ℤ/8)C22×C113semidirect
489. C2×AGL(1,ℤ/8)C22×C113semidirect
492. C22×M16C22×C113semidirect
500. #537C22×C113semidirect
502. #535C22×C113semidirect
503. C2×#127C22×C113semidirect
509. #520C22×C113semidirect
515. C2×#104C22×C113semidirect
516. C2×#104C22×C113semidirect
517. C2×#104C22×C113semidirect
518. #418C22×C113semidirect
519. C2×#100C22×C113semidirect
520. #407C22×C113semidirect
522. #390C22×C113semidirect
523. C4×C22⋊C4C22×C113semidirect
524. #343C22×C113semidirect
525. #339C22×C113semidirect
535. C2×#41D4×C113semidirect
536. C2×#41D4×C113semidirect
540. C22×Q8D4×C113semidirect
555. C22×D4D4×C113semidirect
567. AGL(1,ℤ/8)D4×C113semidirect
592. C22⋊Q8D4×C113semidirect
593. C22⋊Q8D4×C113semidirect
608. #121D4×C113semidirect
609. #121D4×C113semidirect
720. C2×D4C2×D4×C113semidirect
750. M16C2×D4×C113semidirect
816. Q8#120×C113semidirect
846. D4#120×C113semidirect
911. C22#453×C113semidirect

Maximal subgroups

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

subgroupindex
C22×AGL(1,ℤ/8)×C1132
C113×#34882
C2×#453×C1132
C113×#30032
C113×#24332
C113×#20062
C113×#20022
C113×#19002
C113×#18832
C113×#18712
C113×#17892
#23876113