Finite Group Databasebeta

← C113×#24283 #43292303

Subgroups — C113×#24283 #43292303

Order 28928.

1304 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#137×C113C211yesmaximal, characteristic, complemented
2C2×#473×C113C211yesmaximal, characteristic, complemented
3C2×#471×C113C211yesmaximal, characteristic, complemented
4C113×#3005C211yesmaximal, characteristic
5C113×#3004C211yesmaximal, characteristic, complemented
6C113×#2930C211yesmaximal, characteristic, complemented
7C113×#2047C211yesmaximal, characteristic, complemented
8C113×#2046C211yesmaximal, characteristic, complemented
9C113×#2020C211yesmaximal, characteristic, complemented
10C113×#2019C211yesmaximal, characteristic, complemented
11C113×#1979C211yesmaximal, characteristic, complemented
12C113×#1977C211yesmaximal, characteristic, complemented
13C113×#1811C211yesmaximal, characteristic, complemented
14C113×#1785C211yesmaximal, characteristic, complemented
15C113×#1784C211yesmaximal, characteristic, complemented
16C22×#41×C113C2211yescharacteristic
17C23×Q8×C113C2211yescharacteristic
18C2×#137×C113—24no—
19C2×#137×C113—24no—
20C2×#137×C113—22no—
21C2×#137×C113—22no—
22C2×#137×C113C2211yescharacteristic
23C2×#137×C113C2211yescharacteristic
24C2×#137×C113C2211yescharacteristic
25C2×AGL(1,ℤ/8)×C113C2211yescharacteristic
26C22×Q16×C113C2211yescharacteristic
27C22×Q16×C113C2211yescharacteristic
28C22×SD16×C113C2211yescharacteristic
29C22×SD16×C113C2211yescharacteristic
30C2×#131×C113C2211yescharacteristic
31C22×M16×C113C2211yescharacteristic
32#525×C113C2211yescharacteristic
33#473×C113—24no—
34#471×C113—24no—
35#452×C113—22no—
36#451×C113—22no—
37#449×C113—22no—
38#448×C113—22no—
39#436×C113—22no—
40#435×C113—22no—
41C2×#108×C113C2211yescharacteristic
42C2×#108×C113C2211yescharacteristic
43#424×C113C2211yescharacteristic
44#419×C113C2211yescharacteristic
45#419×C113C2211yescharacteristic
46#419×C113C2211yescharacteristic
47#418×C113C2211yescharacteristic
48C2×#101×C113C2211yescharacteristic
49C2×#101×C113C2211yescharacteristic
50C2×#101×C113C2211yescharacteristic
51C2×#101×C113C2211yescharacteristic
52C2×#101×C113C2211yescharacteristic
53C2×#101×C113C2211yescharacteristic
54C2×#100×C113C2211yescharacteristic
55C2×#100×C113C2211yescharacteristic
56#408×C113C2211yescharacteristic
57#407×C113C2211yescharacteristic
58#407×C113C2211yescharacteristic
59#407×C113C2211yescharacteristic
60#405×C113C2211yescharacteristic
61#341×C113C2211yescharacteristic
62#341×C113C2211yescharacteristic
63C2×#41×C113—22no—
64C2×#41×C113—22no—
65C2×#41×C113—22no—
66C2×#41×C113—22no—
67C2×#41×C113—41no—
68C2×#41×C113—41no—
69C2×#41×C113C2311yescharacteristic
70C22×Q8×C113—21no—
71C22×Q8×C113—22no—
72C22×Q8×C113—22no—
73C22×Q8×C113—22no—
74C22×Q8×C113—22no—
75C22×Q8×C113—41no—
76C22×Q8×C113—41no—
77C22×Q8×C113C2311yescharacteristic
78C22×Q8×C113C2311yescharacteristic
79C22×Q8×C113C2311yescharacteristic
80C22×D4×C113—21no—
81C22×D4×C113C2311yescharacteristic
82C23×C4×C113—21no—
83C23×C4×C113—21no—
84C23×C4×C113C2311yescharacteristic
85#137×C113—216no—
86#137×C113—216no—
87#137×C113—22no—
88#137×C113—22no—
89#137×C113—22no—
90#137×C113—41no—
91#137×C113—41no—
92#137×C113—41no—
93AGL(1,ℤ/8)×C113—22no—
94AGL(1,ℤ/8)×C113—41no—
95C2×Q16×C113—22no—
96C2×Q16×C113—22no—
97C2×Q16×C113—21no—
98C2×Q16×C113—21no—
99C2×Q16×C113—21no—
100C2×Q16×C113—22no—
101C2×Q16×C113—21no—
102C2×Q16×C113—21no—
103C2×Q16×C113—22no—
104C2×Q16×C113D414yescomplemented
105C2×SD16×C113—22no—
106C2×SD16×C113—22no—
107C2×SD16×C113—21no—
108C2×SD16×C113—21no—
109C2×SD16×C113—21no—
110C2×SD16×C113—21no—
111C2×SD16×C113—22no—
112C2×SD16×C113—21no—
113C2×SD16×C113—21no—
114C2×SD16×C113—22no—
115C2×SD16×C113D414yescomplemented
116C2×D8×C113—21no—
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#103×C113—22no—
144#103×C113—22no—
145#102×C113—22no—
146#101×C113—22no—
147#101×C113—22no—
148#101×C113—22no—
149#101×C113—41no—
150#101×C113—41no—
151#101×C113—41no—
152#100×C113—22no—
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#4111yescharacteristic
162#41×C113—28no—
163#41×C113—21no—
164#41×C113—21no—
165#41×C113—21no—
166#41×C113—21no—
167#41×C113—44no—
168#41×C113—44no—
169#41×C113—44no—
170C2×Q8×C113—21no—
171C2×Q8×C113—21no—
172C2×Q8×C113—21no—
173C2×Q8×C113—28no—
174C2×Q8×C113—21no—
175C2×Q8×C113—21no—
176C2×Q8×C113—21no—
177C2×Q8×C113—21no—
178C2×Q8×C113—21no—
179C2×Q8×C113—21no—
180C2×Q8×C113—21no—
181C2×Q8×C113—21no—
182C2×Q8×C113—21no—
183C2×Q8×C113—21no—
184C2×Q8×C113—21no—
185C2×Q8×C113—21no—
186C2×Q8×C113—42no—
187C2×Q8×C113—42no—
188C2×Q8×C113—44no—
189C2×Q8×C113—44no—
190C2×Q8×C113—44no—
191C2×Q8×C113—42no—
192C2×Q8×C113C2×D412yes—
193C2×Q8×C113C2×D412yes—
194C2×Q8×C113C2×D412yes—
195C2×Q8×C113C2×D411yescharacteristic
196C2×D4×C113—21no—
197C2×D4×C113—22no—
198C2×D4×C113—21no—
199C2×D4×C113—21no—
200C2×D4×C113—21no—
201C2×D4×C113—21no—
202C2×D4×C113—21no—
203C2×D4×C113—42no—
204C2×D4×C113—42no—
205C2×D4×C113—42no—
206C2×D4×C113C2×D412yes—
207C2×D4×C113C2×D411yescharacteristic
208C22×C4×C113—21no—
209C22×C4×C113—21no—
210C22×C4×C113—21no—
211C22×C4×C113—21no—
212C22×C4×C113—21no—
213C22×C4×C113—21no—
214C22×C4×C113—21no—
215C22×C4×C113—21no—
216C22×C4×C113—42no—
217C22×C4×C113—42no—
218C22×C4×C113—42no—
219C22×C4×C113—42no—
220C22×C4×C113—42no—
221C22×C4×C113—42no—
222C22×C4×C113C2×D412yes—
223C22×C4×C113C2×D412yes—
224C22×C4×C113#4111yescharacteristic
225C22×C4×C113C2411yescharacteristic
226Q16×C113—28no—
227Q16×C113—24no—
228Q16×C113—24no—
229Q16×C113—42no—
230Q16×C113—42no—
231Q16×C113—42no—
232SD16×C113—28no—
233SD16×C113—24no—
234SD16×C113—24no—
235SD16×C113—42no—
236SD16×C113—42no—
237SD16×C113—42no—
238SD16×C113—42no—
239D8×C113—42no—
240M16×C113—24no—
241M16×C113—24no—
242M16×C113—21no—
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—42no—
255C2×C8×C113—21no—
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—42no—
264C2×C8×C113C2×D412yes—
265C2×C8×C113C2×D411yescharacteristic
266C2×C8×C113C2×D411yescharacteristic
267C2×C8×C113C2×D412yes—
268C2×C8×C113C2×D412yes—
269C4⋊C4×C113—22no—
270C4⋊C4×C113C2×D412yes—
271C22⋊C4×C113—22no—
272C22⋊C4×C113—21no—
273C22⋊C4×C113—22no—
274C42×C113—21no—
275C23×C113—21no—
276C23×C113—21no—
277C23×C113—21no—
278C23×C113—22no—
279C23×C113—42no—
280C23×C113—41no—
281C23×C113—41no—
282C23×C113—82no—
283C23×C113#12112yes—
284C23×C113C2×#4111yescharacteristic
285Q8×C113—22no—
286Q8×C113—22no—
287Q8×C113—22no—
288Q8×C113—21no—
289Q8×C113—22no—
290Q8×C113—22no—
291Q8×C113—22no—
292Q8×C113—21no—
293Q8×C113—48no—
294Q8×C113—41no—
295Q8×C113—41no—
296Q8×C113—41no—
297Q8×C113—41no—
298Q8×C113—41no—
299Q8×C113—41no—
300D4×C113—22no—
301D4×C113—21no—
302D4×C113—22no—
303D4×C113—21no—
304D4×C113—48no—
305D4×C113—41no—
306D4×C113—41no—
307D4×C113—41no—
308D4×C113—41no—
309D4×C113—82no—
310C2×C4×C113—21no—
311C2×C4×C113—21no—
312C2×C4×C113—22no—
313C2×C4×C113—22no—
314C2×C4×C113—22no—
315C2×C4×C113—22no—
316C2×C4×C113—22no—
317C2×C4×C113—21no—
318C2×C4×C113—22no—
319C2×C4×C113—22no—
320C2×C4×C113—22no—
321C2×C4×C113—48no—
322C2×C4×C113—48no—
323C2×C4×C113—41no—
324C2×C4×C113—41no—
325C2×C4×C113—41no—
326C2×C4×C113—41no—
327C2×C4×C113—41no—
328C2×C4×C113—41no—
329C2×C4×C113—41no—
330C2×C4×C113—41no—
331C2×C4×C113#12112yes—
332C2×C4×C113C22×D411yescharacteristic
333C2×C4×C113C22×D411yescharacteristic
334C2×C4×C113C22×D411yescharacteristic
335C2×C4×C113C22×D411yescharacteristic
336C2×C4×C113H(5,𝔽2)11yescharacteristic
337C2×C4×C113H(5,𝔽2)11yescharacteristic
338C8×C113—22no—
339C8×C113—41no—
340C8×C113—41no—
341C8×C113—41no—
342C8×C113—41no—
343C8×C113—41no—
344C8×C113—41no—
345C8×C113#12012yes—
346C8×C113#12012yes—
347C22×C113—22no—
348C22×C113—22no—
349C22×C113—22no—
350C22×C113—22no—
351C22×C113—42no—
352C22×C113—42no—
353C22×C113—42no—
354C22×C113—41no—
355C22×C113—42no—
356C22×C113—82no—
357C22×C113—82no—
358C22×C113—82no—
359C22×C113C2×#12111yescharacteristic
360C22×C113#54611yescharacteristic
361C22×C113#54611yescharacteristic
362C4×C113—22no—
363C4×C113—42no—
364C4×C113—42no—
365C4×C113—42no—
366C4×C113—41no—
367C4×C113—42no—
368C4×C113C2×#12011yescharacteristic
369C4×C113#53511yescharacteristic
370C4×C113D4211yescharacteristic
371C4×C113D4211yescharacteristic
372#24283C11311yesmaximal, characteristic, direct product factor, Sylow
373C2×C113—21no—
374C2×C113—21no—
375C2×C113—42no—
376C2×C113—81no—
377C2×C113—82no—
378C2×C113#240811yescharacteristic
379C2×C113#306912yes—
380C22×#137C2×C11311yescharacteristic, complemented
381C2×#473C2×C11311yescharacteristic, complemented
382C2×#471C2×C11311yescharacteristic, complemented
383#3005C2×C11311yescharacteristic
384#3004C2×C11311yescharacteristic, complemented
385#2930C2×C11311yescharacteristic, complemented
386#2047C2×C11311yescharacteristic, complemented
387#2046C2×C11311yescharacteristic, complemented
388#2020C2×C11311yescharacteristic, complemented
389#2019C2×C11311yescharacteristic, complemented
390#1979C2×C11311yescharacteristic, complemented
391#1977C2×C11311yescharacteristic, complemented
392#1811C2×C11311yescharacteristic, complemented
393#1785C2×C11311yescharacteristic, complemented
394#1784C2×C11311yescharacteristic, complemented
395C113#2428311yescharacteristic, direct product factor, Sylow
396C22×#41C22×C11311yescharacteristic
397C23×Q8C22×C11311yescharacteristic
398C2×#137—24no—
399C2×#137—24no—
400C2×#137—22no—
401C2×#137—22no—
402C2×#137C22×C11311yescharacteristic
403C2×#137C22×C11311yescharacteristic
404C2×#137C22×C11311yescharacteristic
405C2×AGL(1,ℤ/8)C22×C11311yescharacteristic
406C22×Q16C22×C11311yescharacteristic
407C22×Q16C22×C11311yescharacteristic
408C22×SD16C22×C11311yescharacteristic
409C22×SD16C22×C11311yescharacteristic
410C2×#131C22×C11311yescharacteristic
411C22×M16C22×C11311yescharacteristic
412#525C22×C11311yescharacteristic
413#473—24no—
414#471—24no—
415#452—22no—
416#451—22no—
417#449—22no—
418#448—22no—
419#436—22no—
420#435—22no—
421C2×#108C22×C11311yescharacteristic
422C2×#108C22×C11311yescharacteristic
423#424C22×C11311yescharacteristic
424#419C22×C11311yescharacteristic
425#419C22×C11311yescharacteristic
426#419C22×C11311yescharacteristic
427#418C22×C11311yescharacteristic
428C2×#101C22×C11311yescharacteristic
429C2×#101C22×C11311yescharacteristic
430C2×#101C22×C11311yescharacteristic
431C2×#101C22×C11311yescharacteristic
432C2×#101C22×C11311yescharacteristic
433C2×#101C22×C11311yescharacteristic
434C2×#100C22×C11311yescharacteristic
435C2×#100C22×C11311yescharacteristic
436#408C22×C11311yescharacteristic
437#407C22×C11311yescharacteristic
438#407C22×C11311yescharacteristic
439#407C22×C11311yescharacteristic
440#405C22×C11311yescharacteristic
441#341C22×C11311yescharacteristic
442#341C22×C11311yescharacteristic
443C2×#41—22no—
444C2×#41—22no—
445C2×#41—22no—
446C2×#41—22no—
447C2×#41—41no—
448C2×#41—41no—
449C2×#41C23×C11311yescharacteristic
450C22×Q8—21no—
451C22×Q8—22no—
452C22×Q8—22no—
453C22×Q8—22no—
454C22×Q8—22no—
455C22×Q8—41no—
456C22×Q8—41no—
457C22×Q8C23×C11311yescharacteristic
458C22×Q8C23×C11311yescharacteristic
459C22×Q8C23×C11311yescharacteristic
460C22×D4—21no—
461C22×D4C23×C11311yescharacteristic
462C23×C4—21no—
463C23×C4—21no—
464C23×C4C23×C11311yescharacteristic
465#137—216no—
466#137—216no—
467#137—22no—
468#137—22no—
469#137—22no—
470#137—41no—
471#137—41no—
472#137—41no—
473AGL(1,ℤ/8)—22no—
474AGL(1,ℤ/8)—41no—
475C2×Q16—22no—
476C2×Q16—22no—
477C2×Q16—21no—
478C2×Q16—21no—
479C2×Q16—21no—
480C2×Q16—22no—
481C2×Q16—21no—
482C2×Q16—21no—
483C2×Q16—22no—
484C2×Q16D4×C11314yescomplemented
485C2×SD16—22no—
486C2×SD16—22no—
487C2×SD16—21no—
488C2×SD16—21no—
489C2×SD16—21no—
490C2×SD16—21no—
491C2×SD16—22no—
492C2×SD16—21no—
493C2×SD16—21no—
494C2×SD16—22no—
495C2×SD16D4×C11314yescomplemented
496C2×D8—21no—
497#131—22no—
498#131—22no—
499C2×M16—22no—
500C2×M16—22no—
501C2×M16—21no—
502C2×M16D4×C11312yes—
503C2×M16D4×C11312yes—
504C2×M16C23×C11311yescharacteristic
505C2×M16C23×C11311yescharacteristic
506C2×M16C23×C11311yescharacteristic
507C2×M16C23×C11311yescharacteristic
508C2×M16C23×C11311yescharacteristic
509C2×M16C23×C11311yescharacteristic
510C22×C8—21no—
511C22×C8C23×C11311yescharacteristic
512C22×C8C23×C11311yescharacteristic
513#123—21no—
514C22⋊Q8D4×C11312yes—
515#121D4×C11312yes—
516#120—21no—
517C4×D4—22no—
518#117C23×C11311yescharacteristic
519#108—22no—
520#108—22no—
521C4⋊C8—22no—
522#103—22no—
523#103—22no—
524#103—22no—
525#102—22no—
526#101—22no—
527#101—22no—
528#101—22no—
529#101—41no—
530#101—41no—
531#101—41no—
532#100—22no—
533#100—41no—
534C22⋊C8—22no—
535C22⋊C8—22no—
536C22⋊C8—22no—
537C22⋊C8—22no—
538#97—21no—
539C4×C8—21no—
540C24—21no—
541C24#41×C11311yescharacteristic
542#41—28no—
543#41—21no—
544#41—21no—
545#41—21no—
546#41—21no—
547#41—44no—
548#41—44no—
549#41—44no—
550C2×Q8—21no—
551C2×Q8—21no—
552C2×Q8—21no—
553C2×Q8—28no—
554C2×Q8—21no—
555C2×Q8—21no—
556C2×Q8—21no—
557C2×Q8—21no—
558C2×Q8—21no—
559C2×Q8—21no—
560C2×Q8—21no—
561C2×Q8—21no—
562C2×Q8—21no—
563C2×Q8—21no—
564C2×Q8—21no—
565C2×Q8—21no—
566C2×Q8—42no—
567C2×Q8—42no—
568C2×Q8—44no—
569C2×Q8—44no—
570C2×Q8—44no—
571C2×Q8—42no—
572C2×Q8C2×D4×C11312yes—
573C2×Q8C2×D4×C11312yes—
574C2×Q8C2×D4×C11312yes—
575C2×Q8C2×D4×C11311yescharacteristic
576C2×D4—21no—
577C2×D4—22no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—21no—
583C2×D4—42no—
584C2×D4—42no—
585C2×D4—42no—
586C2×D4C2×D4×C11312yes—
587C2×D4C2×D4×C11311yescharacteristic
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—42no—
597C22×C4—42no—
598C22×C4—42no—
599C22×C4—42no—
600C22×C4—42no—
601C22×C4—42no—
602C22×C4C2×D4×C11312yes—
603C22×C4C2×D4×C11312yes—
604C22×C4#41×C11311yescharacteristic
605C22×C4C24×C11311yescharacteristic
606Q16—28no—
607Q16—24no—
608Q16—24no—
609Q16—42no—
610Q16—42no—
611Q16—42no—
612SD16—28no—
613SD16—24no—
614SD16—24no—
615SD16—42no—
616SD16—42no—
617SD16—42no—
618SD16—42no—
619D8—42no—
620M16—24no—
621M16—24no—
622M16—21no—
623M16—21no—
624M16—21no—
625M16—21no—
626M16—21no—
627M16—21no—
628M16—21no—
629M16—21no—
630M16—21no—
631M16—21no—
632M16—21no—
633M16—21no—
634M16—42no—
635C2×C8—21no—
636C2×C8—21no—
637C2×C8—21no—
638C2×C8—21no—
639C2×C8—21no—
640C2×C8—21no—
641C2×C8—21no—
642C2×C8—21no—
643C2×C8—42no—
644C2×C8C2×D4×C11312yes—
645C2×C8C2×D4×C11311yescharacteristic
646C2×C8C2×D4×C11311yescharacteristic
647C2×C8C2×D4×C11312yes—
648C2×C8C2×D4×C11312yes—
649C4⋊C4—22no—
650C4⋊C4C2×D4×C11312yes—
651C22⋊C4—22no—
652C22⋊C4—21no—
653C22⋊C4—22no—
654C42—21no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—22no—
659C23—42no—
660C23—41no—
661C23—41no—
662C23—82no—
663C23#121×C11312yes—
664C23C2×#41×C11311yescharacteristic
665Q8—22no—
666Q8—22no—
667Q8—22no—
668Q8—21no—
669Q8—22no—
670Q8—22no—
671Q8—22no—
672Q8—21no—
673Q8—48no—
674Q8—41no—
675Q8—41no—
676Q8—41no—
677Q8—41no—
678Q8—41no—
679Q8—41no—
680D4—22no—
681D4—21no—
682D4—22no—
683D4—21no—
684D4—48no—
685D4—41no—
686D4—41no—
687D4—41no—
688D4—41no—
689D4—82no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—21no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—48no—
702C2×C4—48no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4#121×C11312yes—
712C2×C4C22×D4×C11311yescharacteristic
713C2×C4C22×D4×C11311yescharacteristic
714C2×C4C22×D4×C11311yescharacteristic
715C2×C4C22×D4×C11311yescharacteristic
716C2×C4H(5,𝔽2)×C11311yescharacteristic
717C2×C4H(5,𝔽2)×C11311yescharacteristic
718C8—22no—
719C8—41no—
720C8—41no—
721C8—41no—
722C8—41no—
723C8—41no—
724C8—41no—
725C8#120×C11312yes—
726C8#120×C11312yes—
727C22—22no—
728C22—22no—
729C22—22no—
730C22—22no—
731C22—42no—
732C22—42no—
733C22—42no—
734C22—42no—
735C22—41no—
736C22—82no—
737C22—82no—
738C22—82no—
739C22C2×#121×C11311yescharacteristic
740C22#546×C11311yescharacteristic
741C22#546×C11311yescharacteristic
742C4—22no—
743C4—42no—
744C4—42no—
745C4—42no—
746C4—42no—
747C4—41no—
748C4C2×#120×C11311yescharacteristic
749C4#535×C11311yescharacteristic
750C4D42×C11311yescharacteristic
751C4D42×C11311yescharacteristic
752C2—21no—
753C2—21no—
754C2—42no—
755C2—81no—
756C2—82no—
757C2C113×#240811yescharacteristic
758C2C113×#306912yes—
subgroupG/H
center, socleC22×C113C2×#121
commutator, Frattini, cosocleC22×C4C24×C113
prime radicalC113×#3005C2
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×#137×C113C2semidirect
2. C2×#473×C113C2semidirect
3. C2×#471×C113C2semidirect
5. C113×#3004C2semidirect
6. C113×#2930C2semidirect
7. C113×#2047C2semidirect
8. C113×#2046C2semidirect
9. C113×#2020C2semidirect
10. C113×#2019C2semidirect
11. C113×#1979C2semidirect
12. C113×#1977C2semidirect
13. C113×#1811C2semidirect
14. C113×#1785C2semidirect
15. C113×#1784C2semidirect
104. C2×Q16×C113D4semidirect
115. C2×SD16×C113D4semidirect
372. #24283C113direct (N × H)
380. C22×#137C2×C113semidirect
381. C2×#473C2×C113semidirect
382. C2×#471C2×C113semidirect
384. #3004C2×C113semidirect
385. #2930C2×C113semidirect
386. #2047C2×C113semidirect
387. #2046C2×C113semidirect
388. #2020C2×C113semidirect
389. #2019C2×C113semidirect
390. #1979C2×C113semidirect
391. #1977C2×C113semidirect
392. #1811C2×C113semidirect
393. #1785C2×C113semidirect
394. #1784C2×C113semidirect
395. C113#24283direct (N × H)
484. C2×Q16D4×C113semidirect
495. C2×SD16D4×C113semidirect

Maximal subgroups

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

subgroupindex
C22×#137×C1132
C2×#473×C1132
C2×#471×C1132
C113×#30052
C113×#30042
C113×#29302
C113×#20472
C113×#20462
C113×#20202
C113×#20192
C113×#19792
C113×#19772
C113×#18112
C113×#17852
C113×#17842
#24283113