Finite Group Databasebeta

← C113×#24284 #43292304

Subgroups — C113×#24284 #43292304

Order 28928.

1432 conjugacy classes of subgroups.

The subgroup lattice has 792 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×AGL(1,ℤ/8)×C113C211yesmaximal, characteristic, complemented
2C2×#472×C113C211yesmaximal, characteristic, complemented
3C2×#471×C113C211yesmaximal, characteristic, complemented
4C113×#3005C211yesmaximal, characteristic, complemented
5C113×#3003C211yesmaximal, characteristic, complemented
6C113×#2930C211yesmaximal, characteristic, complemented
7C113×#2046C211yesmaximal, characteristic, complemented
8C113×#2045C211yesmaximal, characteristic, complemented
9C113×#2019C211yesmaximal, characteristic, complemented
10C113×#2018C211yesmaximal, characteristic, complemented
11C113×#1978C211yesmaximal, characteristic, complemented
12C113×#1977C211yesmaximal, characteristic, complemented
13C113×#1811C211yesmaximal, characteristic, complemented
14C113×#1785C211yesmaximal, characteristic, complemented
15C113×#1783C211yesmaximal, characteristic, complemented
16C22×#41×C113C2211yescharacteristic
17C23×D4×C113C2211yescharacteristic
18C2×#137×C113C2211yescharacteristic, complemented
19C2×AGL(1,ℤ/8)×C113—24no—
20C2×AGL(1,ℤ/8)×C113—24no—
21C2×AGL(1,ℤ/8)×C113—22no—
22C2×AGL(1,ℤ/8)×C113—22no—
23C2×AGL(1,ℤ/8)×C113C2211yescharacteristic
24C2×AGL(1,ℤ/8)×C113C2211yescharacteristic
25C2×AGL(1,ℤ/8)×C113C2211yescharacteristic, complemented
26C22×SD16×C113C2211yescharacteristic
27C22×SD16×C113C2211yescharacteristic
28C22×D8×C113C2211yescharacteristic
29C22×D8×C113C2211yescharacteristic
30C2×#131×C113C2211yescharacteristic, complemented
31C22×M16×C113C2211yescharacteristic
32#525×C113C2211yescharacteristic
33#472×C113—24no—
34#471×C113—24no—
35#452×C113—22no—
36#450×C113—22no—
37#449×C113—22no—
38#447×C113—22no—
39#436×C113—22no—
40#435×C113—22no—
41C2×#108×C113C2211yescharacteristic, complemented
42C2×#108×C113C2211yescharacteristic, complemented
43#424×C113C2211yescharacteristic, complemented
44#419×C113C2211yescharacteristic, complemented
45#418×C113C2211yescharacteristic
46#418×C113C2211yescharacteristic
47#418×C113C2211yescharacteristic, complemented
48C2×#101×C113C2211yescharacteristic, complemented
49C2×#101×C113C2211yescharacteristic, complemented
50C2×#100×C113C2211yescharacteristic
51C2×#100×C113C2211yescharacteristic
52C2×#100×C113C2211yescharacteristic
53C2×#100×C113C2211yescharacteristic
54C2×#100×C113C2211yescharacteristic, complemented
55C2×#100×C113C2211yescharacteristic, complemented
56#408×C113C2211yescharacteristic, complemented
57#407×C113C2211yescharacteristic
58#407×C113C2211yescharacteristic
59#407×C113C2211yescharacteristic
60#405×C113C2211yescharacteristic, complemented
61#341×C113C2211yescharacteristic, complemented
62#341×C113C2211yescharacteristic, complemented
63C25×C113—21no—
64C2×#41×C113—22no—
65C2×#41×C113—22no—
66C2×#41×C113—22no—
67C2×#41×C113—22no—
68C2×#41×C113—41no—
69C2×#41×C113—41no—
70C2×#41×C113C2311yescharacteristic
71C22×Q8×C113C2311yescharacteristic
72C22×D4×C113—22no—
73C22×D4×C113—22no—
74C22×D4×C113—21no—
75C22×D4×C113—22no—
76C22×D4×C113—22no—
77C22×D4×C113—21no—
78C22×D4×C113—41no—
79C22×D4×C113—41no—
80C22×D4×C113C2311yescharacteristic
81C22×D4×C113C2311yescharacteristic
82C22×D4×C113C2311yescharacteristic
83C23×C4×C113—21no—
84C23×C4×C113C2311yescharacteristic
85#137×C113—22no—
86#137×C113—41no—
87AGL(1,ℤ/8)×C113—216no—
88AGL(1,ℤ/8)×C113—216no—
89AGL(1,ℤ/8)×C113—22no—
90AGL(1,ℤ/8)×C113—22no—
91AGL(1,ℤ/8)×C113—22no—
92AGL(1,ℤ/8)×C113—41no—
93AGL(1,ℤ/8)×C113—41no—
94AGL(1,ℤ/8)×C113—41no—
95C2×Q16×C113—21no—
96C2×SD16×C113—22no—
97C2×SD16×C113—22no—
98C2×SD16×C113—21no—
99C2×SD16×C113—21no—
100C2×SD16×C113—21no—
101C2×SD16×C113—21no—
102C2×SD16×C113—22no—
103C2×SD16×C113—21no—
104C2×SD16×C113—21no—
105C2×SD16×C113—22no—
106C2×SD16×C113D414yescomplemented
107C2×D8×C113—22no—
108C2×D8×C113—22no—
109C2×D8×C113—21no—
110C2×D8×C113—21no—
111C2×D8×C113—21no—
112C2×D8×C113—22no—
113C2×D8×C113—21no—
114C2×D8×C113—21no—
115C2×D8×C113—22no—
116C2×D8×C113D414yescomplemented
117#131×C113—22no—
118#131×C113—22no—
119C2×M16×C113—22no—
120C2×M16×C113—22no—
121C2×M16×C113—21no—
122C2×M16×C113D412yes—
123C2×M16×C113D412yes—
124C2×M16×C113C2311yescharacteristic
125C2×M16×C113C2311yescharacteristic
126C2×M16×C113C2311yescharacteristic
127C2×M16×C113C2311yescharacteristic
128C2×M16×C113C2311yescharacteristic
129C2×M16×C113C2311yescharacteristic
130C22×C8×C113—21no—
131C22×C8×C113C2311yescharacteristic
132C22×C8×C113C2311yescharacteristic
133#123×C113—21no—
134C22⋊Q8×C113D412yes—
135#121×C113D412yes—
136#120×C113—21no—
137C4×D4×C113—22no—
138#117×C113C2311yescharacteristic
139#108×C113—22no—
140#108×C113—22no—
141C4⋊C8×C113—22no—
142#103×C113—22no—
143#102×C113—22no—
144#102×C113—22no—
145#102×C113—22no—
146#101×C113—22no—
147#101×C113—41no—
148#100×C113—22no—
149#100×C113—22no—
150#100×C113—22no—
151#100×C113—41no—
152#100×C113—41no—
153#100×C113—41no—
154C22⋊C8×C113—22no—
155C22⋊C8×C113—22no—
156C22⋊C8×C113—22no—
157C22⋊C8×C113—22no—
158#97×C113—21no—
159C4×C8×C113—21no—
160C24×C113—21no—
161C24×C113—21no—
162C24×C113—21no—
163C24×C113—42no—
164C24×C113—42no—
165C24×C113—42no—
166C24×C113—84no—
167C24×C113#4111yescharacteristic
168#41×C113—28no—
169#41×C113—21no—
170#41×C113—21no—
171#41×C113—21no—
172#41×C113—21no—
173#41×C113—44no—
174#41×C113—44no—
175#41×C113—44no—
176C2×Q8×C113—21no—
177C2×Q8×C113—21no—
178C2×Q8×C113—21no—
179C2×Q8×C113—21no—
180C2×Q8×C113—21no—
181C2×Q8×C113C2×D412yes—
182C2×Q8×C113C2×D411yescharacteristic
183C2×D4×C113—28no—
184C2×D4×C113—21no—
185C2×D4×C113—22no—
186C2×D4×C113—21no—
187C2×D4×C113—21no—
188C2×D4×C113—21no—
189C2×D4×C113—21no—
190C2×D4×C113—21no—
191C2×D4×C113—21no—
192C2×D4×C113—21no—
193C2×D4×C113—21no—
194C2×D4×C113—21no—
195C2×D4×C113—21no—
196C2×D4×C113—21no—
197C2×D4×C113—21no—
198C2×D4×C113—21no—
199C2×D4×C113—21no—
200C2×D4×C113—21no—
201C2×D4×C113—44no—
202C2×D4×C113—44no—
203C2×D4×C113—42no—
204C2×D4×C113—42no—
205C2×D4×C113—42no—
206C2×D4×C113—44no—
207C2×D4×C113—42no—
208C2×D4×C113—42no—
209C2×D4×C113—42no—
210C2×D4×C113C2×D412yes—
211C2×D4×C113C2×D412yes—
212C2×D4×C113C2×D412yes—
213C2×D4×C113C2×D411yescharacteristic
214C22×C4×C113—21no—
215C22×C4×C113—21no—
216C22×C4×C113—21no—
217C22×C4×C113—21no—
218C22×C4×C113—21no—
219C22×C4×C113—21no—
220C22×C4×C113—42no—
221C22×C4×C113—42no—
222C22×C4×C113—42no—
223C22×C4×C113C2×D412yes—
224C22×C4×C113C2×D412yes—
225C22×C4×C113#4111yescharacteristic
226C22×C4×C113C2411yescharacteristic
227Q16×C113—42no—
228SD16×C113—28no—
229SD16×C113—24no—
230SD16×C113—24no—
231SD16×C113—42no—
232SD16×C113—42no—
233SD16×C113—42no—
234SD16×C113—42no—
235D8×C113—28no—
236D8×C113—24no—
237D8×C113—24no—
238D8×C113—42no—
239D8×C113—42no—
240D8×C113—42no—
241M16×C113—24no—
242M16×C113—24no—
243M16×C113—21no—
244M16×C113—21no—
245M16×C113—21no—
246M16×C113—21no—
247M16×C113—21no—
248M16×C113—21no—
249M16×C113—21no—
250M16×C113—21no—
251M16×C113—21no—
252M16×C113—21no—
253M16×C113—21no—
254M16×C113—21no—
255M16×C113—42no—
256C2×C8×C113—21no—
257C2×C8×C113—21no—
258C2×C8×C113—21no—
259C2×C8×C113—21no—
260C2×C8×C113—21no—
261C2×C8×C113—21no—
262C2×C8×C113—21no—
263C2×C8×C113—21no—
264C2×C8×C113—42no—
265C2×C8×C113C2×D412yes—
266C2×C8×C113C2×D411yescharacteristic
267C2×C8×C113C2×D411yescharacteristic
268C2×C8×C113C2×D412yes—
269C2×C8×C113C2×D412yes—
270C4⋊C4×C113—22no—
271C4⋊C4×C113C2×D412yes—
272C22⋊C4×C113—22no—
273C22⋊C4×C113—21no—
274C22⋊C4×C113—22no—
275C42×C113—21no—
276C23×C113—21no—
277C23×C113—21no—
278C23×C113—21no—
279C23×C113—22no—
280C23×C113—22no—
281C23×C113—22no—
282C23×C113—42no—
283C23×C113—48no—
284C23×C113—41no—
285C23×C113—41no—
286C23×C113—41no—
287C23×C113—41no—
288C23×C113—41no—
289C23×C113—41no—
290C23×C113—82no—
291C23×C113—82no—
292C23×C113—82no—
293C23×C113—84no—
294C23×C113—84no—
295C23×C113—88no—
296C23×C113—88no—
297C23×C113#12112yes—
298C23×C113C2×#4111yescharacteristic
299Q8×C113—22no—
300Q8×C113—21no—
301Q8×C113—21no—
302Q8×C113—22no—
303Q8×C113—41no—
304Q8×C113—41no—
305D4×C113—22no—
306D4×C113—22no—
307D4×C113—22no—
308D4×C113—21no—
309D4×C113—21no—
310D4×C113—22no—
311D4×C113—22no—
312D4×C113—22no—
313D4×C113—48no—
314D4×C113—48no—
315D4×C113—41no—
316D4×C113—41no—
317D4×C113—41no—
318D4×C113—41no—
319D4×C113—41no—
320D4×C113—41no—
321D4×C113—41no—
322D4×C113—41no—
323D4×C113—82no—
324C2×C4×C113—21no—
325C2×C4×C113—21no—
326C2×C4×C113—22no—
327C2×C4×C113—22no—
328C2×C4×C113—22no—
329C2×C4×C113—22no—
330C2×C4×C113—22no—
331C2×C4×C113—21no—
332C2×C4×C113—22no—
333C2×C4×C113—48no—
334C2×C4×C113—41no—
335C2×C4×C113—41no—
336C2×C4×C113—41no—
337C2×C4×C113—41no—
338C2×C4×C113#12112yes—
339C2×C4×C113C22×D411yescharacteristic
340C2×C4×C113C22×D411yescharacteristic
341C2×C4×C113C22×D411yescharacteristic
342C2×C4×C113C22×D411yescharacteristic
343C2×C4×C113H(5,𝔽2)11yescharacteristic
344C2×C4×C113H(5,𝔽2)11yescharacteristic
345C8×C113—22no—
346C8×C113—41no—
347C8×C113—41no—
348C8×C113—41no—
349C8×C113—41no—
350C8×C113—41no—
351C8×C113—41no—
352C8×C113#12012yes—
353C8×C113#12012yes—
354C22×C113—22no—
355C22×C113—22no—
356C22×C113—22no—
357C22×C113—22no—
358C22×C113—42no—
359C22×C113—42no—
360C22×C113—42no—
361C22×C113—41no—
362C22×C113—42no—
363C22×C113—42no—
364C22×C113—42no—
365C22×C113—82no—
366C22×C113—82no—
367C22×C113—82no—
368C22×C113—82no—
369C22×C113—82no—
370C22×C113—82no—
371C22×C113—816no—
372C22×C113—82no—
373C22×C113—82no—
374C22×C113—82no—
375C22×C113C2×#12111yescharacteristic
376C22×C113#54611yescharacteristic
377C22×C113#54611yescharacteristic
378C4×C113—22no—
379C4×C113—42no—
380C4×C113—41no—
381C4×C113—42no—
382C4×C113C2×#12011yescharacteristic
383C4×C113#53511yescharacteristic
384C4×C113D4211yescharacteristic
385C4×C113D4211yescharacteristic
386#24284C11311yesmaximal, characteristic, direct product factor, Sylow
387C2×C113—21no—
388C2×C113—21no—
389C2×C113—42no—
390C2×C113—81no—
391C2×C113—82no—
392C2×C113—82no—
393C2×C113—82no—
394C2×C113#240811yescharacteristic
395C2×C113#306812yes—
396C22×AGL(1,ℤ/8)C2×C11311yescharacteristic, complemented
397C2×#472C2×C11311yescharacteristic, complemented
398C2×#471C2×C11311yescharacteristic, complemented
399#3005C2×C11311yescharacteristic, complemented
400#3003C2×C11311yescharacteristic, complemented
401#2930C2×C11311yescharacteristic, complemented
402#2046C2×C11311yescharacteristic, complemented
403#2045C2×C11311yescharacteristic, complemented
404#2019C2×C11311yescharacteristic, complemented
405#2018C2×C11311yescharacteristic, complemented
406#1978C2×C11311yescharacteristic, complemented
407#1977C2×C11311yescharacteristic, complemented
408#1811C2×C11311yescharacteristic, complemented
409#1785C2×C11311yescharacteristic, complemented
410#1783C2×C11311yescharacteristic, complemented
411C113#2428411yescharacteristic, direct product factor, Sylow
412C22×#41C22×C11311yescharacteristic
413C23×D4C22×C11311yescharacteristic
414C2×#137C22×C11311yescharacteristic, complemented
415C2×AGL(1,ℤ/8)—24no—
416C2×AGL(1,ℤ/8)—24no—
417C2×AGL(1,ℤ/8)—22no—
418C2×AGL(1,ℤ/8)—22no—
419C2×AGL(1,ℤ/8)C22×C11311yescharacteristic
420C2×AGL(1,ℤ/8)C22×C11311yescharacteristic
421C2×AGL(1,ℤ/8)C22×C11311yescharacteristic, complemented
422C22×SD16C22×C11311yescharacteristic
423C22×SD16C22×C11311yescharacteristic
424C22×D8C22×C11311yescharacteristic
425C22×D8C22×C11311yescharacteristic
426C2×#131C22×C11311yescharacteristic, complemented
427C22×M16C22×C11311yescharacteristic
428#525C22×C11311yescharacteristic
429#472—24no—
430#471—24no—
431#452—22no—
432#450—22no—
433#449—22no—
434#447—22no—
435#436—22no—
436#435—22no—
437C2×#108C22×C11311yescharacteristic, complemented
438C2×#108C22×C11311yescharacteristic, complemented
439#424C22×C11311yescharacteristic, complemented
440#419C22×C11311yescharacteristic, complemented
441#418C22×C11311yescharacteristic
442#418C22×C11311yescharacteristic
443#418C22×C11311yescharacteristic, complemented
444C2×#101C22×C11311yescharacteristic, complemented
445C2×#101C22×C11311yescharacteristic, complemented
446C2×#100C22×C11311yescharacteristic
447C2×#100C22×C11311yescharacteristic
448C2×#100C22×C11311yescharacteristic
449C2×#100C22×C11311yescharacteristic
450C2×#100C22×C11311yescharacteristic, complemented
451C2×#100C22×C11311yescharacteristic, complemented
452#408C22×C11311yescharacteristic, complemented
453#407C22×C11311yescharacteristic
454#407C22×C11311yescharacteristic
455#407C22×C11311yescharacteristic
456#405C22×C11311yescharacteristic, complemented
457#341C22×C11311yescharacteristic, complemented
458#341C22×C11311yescharacteristic, complemented
459C25—21no—
460C2×#41—22no—
461C2×#41—22no—
462C2×#41—22no—
463C2×#41—22no—
464C2×#41—41no—
465C2×#41—41no—
466C2×#41C23×C11311yescharacteristic
467C22×Q8C23×C11311yescharacteristic
468C22×D4—22no—
469C22×D4—22no—
470C22×D4—21no—
471C22×D4—22no—
472C22×D4—22no—
473C22×D4—21no—
474C22×D4—41no—
475C22×D4—41no—
476C22×D4C23×C11311yescharacteristic
477C22×D4C23×C11311yescharacteristic
478C22×D4C23×C11311yescharacteristic
479C23×C4—21no—
480C23×C4C23×C11311yescharacteristic
481#137—22no—
482#137—41no—
483AGL(1,ℤ/8)—216no—
484AGL(1,ℤ/8)—216no—
485AGL(1,ℤ/8)—22no—
486AGL(1,ℤ/8)—22no—
487AGL(1,ℤ/8)—22no—
488AGL(1,ℤ/8)—41no—
489AGL(1,ℤ/8)—41no—
490AGL(1,ℤ/8)—41no—
491C2×Q16—21no—
492C2×SD16—22no—
493C2×SD16—22no—
494C2×SD16—21no—
495C2×SD16—21no—
496C2×SD16—21no—
497C2×SD16—21no—
498C2×SD16—22no—
499C2×SD16—21no—
500C2×SD16—21no—
501C2×SD16—22no—
502C2×SD16D4×C11314yescomplemented
503C2×D8—22no—
504C2×D8—22no—
505C2×D8—21no—
506C2×D8—21no—
507C2×D8—21no—
508C2×D8—22no—
509C2×D8—21no—
510C2×D8—21no—
511C2×D8—22no—
512C2×D8D4×C11314yescomplemented
513#131—22no—
514#131—22no—
515C2×M16—22no—
516C2×M16—22no—
517C2×M16—21no—
518C2×M16D4×C11312yes—
519C2×M16D4×C11312yes—
520C2×M16C23×C11311yescharacteristic
521C2×M16C23×C11311yescharacteristic
522C2×M16C23×C11311yescharacteristic
523C2×M16C23×C11311yescharacteristic
524C2×M16C23×C11311yescharacteristic
525C2×M16C23×C11311yescharacteristic
526C22×C8—21no—
527C22×C8C23×C11311yescharacteristic
528C22×C8C23×C11311yescharacteristic
529#123—21no—
530C22⋊Q8D4×C11312yes—
531#121D4×C11312yes—
532#120—21no—
533C4×D4—22no—
534#117C23×C11311yescharacteristic
535#108—22no—
536#108—22no—
537C4⋊C8—22no—
538#103—22no—
539#102—22no—
540#102—22no—
541#102—22no—
542#101—22no—
543#101—41no—
544#100—22no—
545#100—22no—
546#100—22no—
547#100—41no—
548#100—41no—
549#100—41no—
550C22⋊C8—22no—
551C22⋊C8—22no—
552C22⋊C8—22no—
553C22⋊C8—22no—
554#97—21no—
555C4×C8—21no—
556C24—21no—
557C24—21no—
558C24—21no—
559C24—42no—
560C24—42no—
561C24—42no—
562C24—84no—
563C24#41×C11311yescharacteristic
564#41—28no—
565#41—21no—
566#41—21no—
567#41—21no—
568#41—21no—
569#41—44no—
570#41—44no—
571#41—44no—
572C2×Q8—21no—
573C2×Q8—21no—
574C2×Q8—21no—
575C2×Q8—21no—
576C2×Q8—21no—
577C2×Q8C2×D4×C11312yes—
578C2×Q8C2×D4×C11311yescharacteristic
579C2×D4—28no—
580C2×D4—21no—
581C2×D4—22no—
582C2×D4—21no—
583C2×D4—21no—
584C2×D4—21no—
585C2×D4—21no—
586C2×D4—21no—
587C2×D4—21no—
588C2×D4—21no—
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—21no—
595C2×D4—21no—
596C2×D4—21no—
597C2×D4—44no—
598C2×D4—44no—
599C2×D4—42no—
600C2×D4—42no—
601C2×D4—42no—
602C2×D4—44no—
603C2×D4—42no—
604C2×D4—42no—
605C2×D4—42no—
606C2×D4C2×D4×C11312yes—
607C2×D4C2×D4×C11312yes—
608C2×D4C2×D4×C11312yes—
609C2×D4C2×D4×C11311yescharacteristic
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—42no—
617C22×C4—42no—
618C22×C4—42no—
619C22×C4C2×D4×C11312yes—
620C22×C4C2×D4×C11312yes—
621C22×C4#41×C11311yescharacteristic
622C22×C4C24×C11311yescharacteristic
623Q16—42no—
624SD16—28no—
625SD16—24no—
626SD16—24no—
627SD16—42no—
628SD16—42no—
629SD16—42no—
630SD16—42no—
631D8—28no—
632D8—24no—
633D8—24no—
634D8—42no—
635D8—42no—
636D8—42no—
637M16—24no—
638M16—24no—
639M16—21no—
640M16—21no—
641M16—21no—
642M16—21no—
643M16—21no—
644M16—21no—
645M16—21no—
646M16—21no—
647M16—21no—
648M16—21no—
649M16—21no—
650M16—21no—
651M16—42no—
652C2×C8—21no—
653C2×C8—21no—
654C2×C8—21no—
655C2×C8—21no—
656C2×C8—21no—
657C2×C8—21no—
658C2×C8—21no—
659C2×C8—21no—
660C2×C8—42no—
661C2×C8C2×D4×C11312yes—
662C2×C8C2×D4×C11311yescharacteristic
663C2×C8C2×D4×C11311yescharacteristic
664C2×C8C2×D4×C11312yes—
665C2×C8C2×D4×C11312yes—
666C4⋊C4—22no—
667C4⋊C4C2×D4×C11312yes—
668C22⋊C4—22no—
669C22⋊C4—21no—
670C22⋊C4—22no—
671C42—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—22no—
676C23—22no—
677C23—22no—
678C23—42no—
679C23—48no—
680C23—41no—
681C23—41no—
682C23—41no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—82no—
687C23—82no—
688C23—82no—
689C23—84no—
690C23—84no—
691C23—88no—
692C23—88no—
693C23#121×C11312yes—
694C23C2×#41×C11311yescharacteristic
695Q8—22no—
696Q8—21no—
697Q8—21no—
698Q8—22no—
699Q8—41no—
700Q8—41no—
701D4—22no—
702D4—22no—
703D4—22no—
704D4—21no—
705D4—21no—
706D4—22no—
707D4—22no—
708D4—22no—
709D4—48no—
710D4—48no—
711D4—41no—
712D4—41no—
713D4—41no—
714D4—41no—
715D4—41no—
716D4—41no—
717D4—41no—
718D4—41no—
719D4—82no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—21no—
728C2×C4—22no—
729C2×C4—48no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4#121×C11312yes—
735C2×C4C22×D4×C11311yescharacteristic
736C2×C4C22×D4×C11311yescharacteristic
737C2×C4C22×D4×C11311yescharacteristic
738C2×C4C22×D4×C11311yescharacteristic
739C2×C4H(5,𝔽2)×C11311yescharacteristic
740C2×C4H(5,𝔽2)×C11311yescharacteristic
741C8—22no—
742C8—41no—
743C8—41no—
744C8—41no—
745C8—41no—
746C8—41no—
747C8—41no—
748C8#120×C11312yes—
749C8#120×C11312yes—
750C22—22no—
751C22—22no—
752C22—22no—
753C22—22no—
754C22—42no—
755C22—42no—
756C22—42no—
757C22—42no—
758C22—41no—
759C22—42no—
760C22—42no—
761C22—82no—
762C22—82no—
763C22—82no—
764C22—82no—
765C22—82no—
766C22—82no—
767C22—816no—
768C22—82no—
769C22—82no—
770C22—82no—
771C22C2×#121×C11311yescharacteristic
772C22#546×C11311yescharacteristic
773C22#546×C11311yescharacteristic
774C4—22no—
775C4—42no—
776C4—42no—
777C4—41no—
778C4C2×#120×C11311yescharacteristic
779C4#535×C11311yescharacteristic
780C4D42×C11311yescharacteristic
781C4D42×C11311yescharacteristic
782C2—21no—
783C2—21no—
784C2—42no—
785C2—81no—
786C2—82no—
787C2—82no—
788C2—82no—
789C2C113×#240811yescharacteristic
790C2C113×#306812yes—
subgroupG/H
center, socleC22×C113C2×#121
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. C2×#472×C113C2semidirect
3. C2×#471×C113C2semidirect
4. C113×#3005C2semidirect
5. C113×#3003C2semidirect
6. C113×#2930C2semidirect
7. C113×#2046C2semidirect
8. C113×#2045C2semidirect
9. C113×#2019C2semidirect
10. C113×#2018C2semidirect
11. C113×#1978C2semidirect
12. C113×#1977C2semidirect
13. C113×#1811C2semidirect
14. C113×#1785C2semidirect
15. C113×#1783C2semidirect
18. C2×#137×C113C22semidirect
25. C2×AGL(1,ℤ/8)×C113C22semidirect
30. C2×#131×C113C22semidirect
41. C2×#108×C113C22semidirect
42. C2×#108×C113C22semidirect
43. #424×C113C22semidirect
44. #419×C113C22semidirect
47. #418×C113C22semidirect
48. C2×#101×C113C22semidirect
49. C2×#101×C113C22semidirect
54. C2×#100×C113C22semidirect
55. C2×#100×C113C22semidirect
56. #408×C113C22semidirect
60. #405×C113C22semidirect
61. #341×C113C22semidirect
62. #341×C113C22semidirect
106. C2×SD16×C113D4semidirect
116. C2×D8×C113D4semidirect
386. #24284C113direct (N × H)
396. C22×AGL(1,ℤ/8)C2×C113semidirect
397. C2×#472C2×C113semidirect
398. C2×#471C2×C113semidirect
399. #3005C2×C113semidirect
400. #3003C2×C113semidirect
401. #2930C2×C113semidirect
402. #2046C2×C113semidirect
403. #2045C2×C113semidirect
404. #2019C2×C113semidirect
405. #2018C2×C113semidirect
406. #1978C2×C113semidirect
407. #1977C2×C113semidirect
408. #1811C2×C113semidirect
409. #1785C2×C113semidirect
410. #1783C2×C113semidirect
411. C113#24284direct (N × H)
414. C2×#137C22×C113semidirect
421. C2×AGL(1,ℤ/8)C22×C113semidirect
426. C2×#131C22×C113semidirect
437. C2×#108C22×C113semidirect
438. C2×#108C22×C113semidirect
439. #424C22×C113semidirect
440. #419C22×C113semidirect
443. #418C22×C113semidirect
444. C2×#101C22×C113semidirect
445. C2×#101C22×C113semidirect
450. C2×#100C22×C113semidirect
451. C2×#100C22×C113semidirect
452. #408C22×C113semidirect
456. #405C22×C113semidirect
457. #341C22×C113semidirect
458. #341C22×C113semidirect
502. C2×SD16D4×C113semidirect
512. C2×D8D4×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
C2×#472×C1132
C2×#471×C1132
C113×#30052
C113×#30032
C113×#29302
C113×#20462
C113×#20452
C113×#20192
C113×#20182
C113×#19782
C113×#19772
C113×#18112
C113×#17852
C113×#17832
#24284113