Finite Group Databasebeta

← C113×#25563 #43293583

Subgroups — C113×#25563 #43293583

Order 28928.

1608 conjugacy classes of subgroups.

The subgroup lattice has 876 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C113×#3490C211yesmaximal, characteristic, complemented
2C113×#2410C212yesmaximal, complemented
3C113×#2405C211yesmaximal, characteristic, complemented
4C113×#2062C211yesmaximal, characteristic, complemented
5C113×#2044C211yesmaximal, characteristic, complemented
6C113×#2029C211yesmaximal, characteristic, complemented
7C113×#2021C211yesmaximal, characteristic, complemented
8C113×#1898C212yesmaximal, complemented
9C113×#1889C212yesmaximal, complemented
10C113×#1867C212yesmaximal, complemented
11C2×#342×C113C211yesmaximal, characteristic, complemented
12C23×D4×C113C2211yescharacteristic
13#551×C113—22no—
14#551×C113—22no—
15#546×C113—22no—
16#546×C113—22no—
17#543×C113C2211yescharacteristic
18#538×C113—21no—
19#538×C113—21no—
20#534×C113C2211yescharacteristic
21#525×C113—21no—
22#525×C113—21no—
23C2×#123×C113—21no—
24C2×#121×C113—22no—
25C2×#120×C113C2212yes—
26C2×#120×C113C2212yes—
27#518×C113C2212yes—
28C22×C22⋊C4×C113C2211yescharacteristic
29C22×C22⋊C4×C113C2212yes—
30C2×#99×C113C2212yes—
31C2×#99×C113C2212yes—
32#394×C113—21no—
33#394×C113—21no—
34#394×C113—22no—
35#392×C113—22no—
36#386×C113—21no—
37#386×C113—22no—
38#386×C113C2212yes—
39#385×C113C2211yescharacteristic
40#385×C113C2212yes—
41#385×C113C2211yescharacteristic
42#379×C113C2211yescharacteristic
43#379×C113C2212yes—
44#379×C113C2211yescharacteristic
45#379×C113C2211yescharacteristic
46#342×C113C2211yescharacteristic
47#342×C113C2211yescharacteristic
48#342×C113C2212yes—
49#342×C113C2212yes—
50#342×C113C2212yes—
51C25×C113C2311yescharacteristic
52C25×C113C2311yescharacteristic
53C2×#41×C113—21no—
54C2×#41×C113—21no—
55C22×D4×C113—22no—
56C22×D4×C113—21no—
57C22×D4×C113—22no—
58C22×D4×C113—21no—
59C22×D4×C113—22no—
60C22×D4×C113—44no—
61C22×D4×C113D412yescomplemented
62C22×D4×C113D412yescomplemented
63C22×D4×C113C2312yes—
64C23×C4×C113—22no—
65C23×C4×C113D411yescharacteristic, complemented
66C23×C4×C113D411yescharacteristic, complemented
67C23×C4×C113C2311yescharacteristic
68#126×C113—22no—
69#126×C113—22no—
70#124×C113—22no—
71#124×C113—22no—
72#123×C113—22no—
73#123×C113—22no—
74#123×C113—22no—
75#123×C113—22no—
76#123×C113—22no—
77#123×C113—44no—
78C22⋊Q8×C113—21no—
79C22⋊Q8×C113—21no—
80C22⋊Q8×C113—21no—
81C22⋊Q8×C113—21no—
82C22⋊Q8×C113—22no—
83C22⋊Q8×C113—22no—
84#121×C113—21no—
85#121×C113—21no—
86#121×C113—22no—
87#121×C113—22no—
88#121×C113—21no—
89#121×C113—21no—
90#121×C113—48no—
91#120×C113—22no—
92#120×C113—22no—
93#120×C113—22no—
94#120×C113—22no—
95#120×C113—22no—
96#120×C113—24no—
97#120×C113—42no—
98C4×D4×C113—22no—
99C4×D4×C113—22no—
100C4×D4×C113—22no—
101C4×D4×C113—22no—
102C4×D4×C113—22no—
103C4×D4×C113—22no—
104#117×C113—21no—
105#117×C113—21no—
106#117×C113—22no—
107C2×C4⋊C4×C113—22no—
108C2×C4⋊C4×C113—21no—
109C2×C4⋊C4×C113—21no—
110C2×C22⋊C4×C113—22no—
111C2×C22⋊C4×C113—22no—
112C2×C22⋊C4×C113—22no—
113C2×C22⋊C4×C113—24no—
114C2×C22⋊C4×C113—22no—
115C2×C22⋊C4×C113—22no—
116C2×C22⋊C4×C113—21no—
117C2×C22⋊C4×C113—22no—
118C2×C22⋊C4×C113—22no—
119C2×C22⋊C4×C113—21no—
120C2×C22⋊C4×C113—21no—
121C2×C22⋊C4×C113—21no—
122C2×C22⋊C4×C113—22no—
123C2×C22⋊C4×C113—21no—
124C2×C22⋊C4×C113—21no—
125C2×C22⋊C4×C113—42no—
126C2×C22⋊C4×C113D411yescharacteristic, complemented
127C2×C22⋊C4×C113D411yescharacteristic, complemented
128C2×C22⋊C4×C113D412yescomplemented
129C2×C22⋊C4×C113D412yescomplemented
130C2×C22⋊C4×C113C2312yes—
131C2×C22⋊C4×C113C2311yescharacteristic
132C2×C22⋊C4×C113C2311yescharacteristic
133C2×C22⋊C4×C113C2311yescharacteristic
134C2×C22⋊C4×C113C2311yescharacteristic
135C2×C22⋊C4×C113C2312yes—
136C2×C22⋊C4×C113C2312yes—
137#99×C113—24no—
138#99×C113—42no—
139#95×C113—22no—
140#95×C113—21no—
141#95×C113—21no—
142#95×C113—22no—
143C24×C113—22no—
144C24×C113—21no—
145C24×C113—21no—
146C24×C113—21no—
147C24×C113—22no—
148C24×C113—22no—
149C24×C113—21no—
150C24×C113—21no—
151C24×C113—42no—
152C24×C113—42no—
153C24×C113—81no—
154C24×C113—81no—
155C24×C113C2×D412yes—
156C24×C113C2×D411yescharacteristic
157C24×C113C2×D412yes—
158C24×C113C2×D412yes—
159C24×C113C2×D411yescharacteristic
160C24×C113C2411yescharacteristic
161#41×C113—82no—
162#41×C113—82no—
163C2×Q8×C113—21no—
164C2×Q8×C113—21no—
165C2×D4×C113—28no—
166C2×D4×C113—24no—
167C2×D4×C113—22no—
168C2×D4×C113—22no—
169C2×D4×C113—22no—
170C2×D4×C113—22no—
171C2×D4×C113—22no—
172C2×D4×C113—22no—
173C2×D4×C113—22no—
174C2×D4×C113—22no—
175C2×D4×C113—21no—
176C2×D4×C113—21no—
177C2×D4×C113—22no—
178C2×D4×C113—22no—
179C2×D4×C113—44no—
180C2×D4×C113—42no—
181C2×D4×C113—44no—
182C2×D4×C113—42no—
183C2×D4×C113—44no—
184C2×D4×C113—42no—
185C2×D4×C113—44no—
186C2×D4×C113—42no—
187C2×D4×C113—41no—
188C2×D4×C113—41no—
189C2×D4×C113—44no—
190C2×D4×C113—44no—
191C2×D4×C113—82no—
192C2×D4×C113—82no—
193C22×C4×C113—21no—
194C22×C4×C113—21no—
195C22×C4×C113—22no—
196C22×C4×C113—21no—
197C22×C4×C113—22no—
198C22×C4×C113—22no—
199C22×C4×C113—22no—
200C22×C4×C113—21no—
201C22×C4×C113—21no—
202C22×C4×C113—21no—
203C22×C4×C113—21no—
204C22×C4×C113—22no—
205C22×C4×C113—42no—
206C22×C4×C113—44no—
207C22×C4×C113—42no—
208C22×C4×C113—44no—
209C22×C4×C113—81no—
210C22×C4×C113—82no—
211C22×C4×C113C2×D412yes—
212C22×C4×C113C2×D411yescharacteristic
213C22×C4×C113C2×D412yes—
214C22×C4×C113C2×D411yescharacteristic
215C22×C4×C113C2×D411yescharacteristic
216C22×C4×C113C2×D412yes—
217C22×C4×C113C2×D411yescharacteristic
218C4⋊C4×C113—22no—
219C4⋊C4×C113—22no—
220C4⋊C4×C113—21no—
221C4⋊C4×C113—21no—
222C4⋊C4×C113—21no—
223C4⋊C4×C113—21no—
224C4⋊C4×C113—22no—
225C4⋊C4×C113—22no—
226C4⋊C4×C113—44no—
227C4⋊C4×C113—42no—
228C4⋊C4×C113—42no—
229C22⋊C4×C113—22no—
230C22⋊C4×C113—22no—
231C22⋊C4×C113—22no—
232C22⋊C4×C113—22no—
233C22⋊C4×C113—22no—
234C22⋊C4×C113—22no—
235C22⋊C4×C113—22no—
236C22⋊C4×C113—22no—
237C22⋊C4×C113—22no—
238C22⋊C4×C113—22no—
239C22⋊C4×C113—22no—
240C22⋊C4×C113—22no—
241C22⋊C4×C113—22no—
242C22⋊C4×C113—22no—
243C22⋊C4×C113—22no—
244C22⋊C4×C113—22no—
245C22⋊C4×C113—22no—
246C22⋊C4×C113—21no—
247C22⋊C4×C113—22no—
248C22⋊C4×C113—21no—
249C22⋊C4×C113—44no—
250C22⋊C4×C113—44no—
251C22⋊C4×C113—44no—
252C22⋊C4×C113—44no—
253C22⋊C4×C113—42no—
254C22⋊C4×C113—42no—
255C22⋊C4×C113—42no—
256C22⋊C4×C113—81no—
257C22⋊C4×C113—81no—
258C22⋊C4×C113—82no—
259C22⋊C4×C113—81no—
260C22⋊C4×C113#4114yescomplemented
261C42×C113—22no—
262C42×C113—22no—
263C23×C113—21no—
264C23×C113—21no—
265C23×C113—22no—
266C23×C113—22no—
267C23×C113—22no—
268C23×C113—24no—
269C23×C113—21no—
270C23×C113—21no—
271C23×C113—22no—
272C23×C113—22no—
273C23×C113—22no—
274C23×C113—24no—
275C23×C113—22no—
276C23×C113—22no—
277C23×C113—22no—
278C23×C113—41no—
279C23×C113—41no—
280C23×C113—42no—
281C23×C113—41no—
282C23×C113—41no—
283C23×C113—41no—
284C23×C113—42no—
285C23×C113—42no—
286C23×C113—41no—
287C23×C113—41no—
288C23×C113—42no—
289C23×C113—41no—
290C23×C113—42no—
291C23×C113—42no—
292C23×C113—42no—
293C23×C113—42no—
294C23×C113—41no—
295C23×C113—41no—
296C23×C113—41no—
297C23×C113—42no—
298C23×C113—42no—
299C23×C113—84no—
300C23×C113—84no—
301C23×C113—82no—
302C23×C113—82no—
303C23×C113—82no—
304C23×C113—82no—
305C23×C113#12012yes—
306C23×C113#12011yescharacteristic
307C23×C113#12011yescharacteristic
308C23×C113C22×D411yescharacteristic
309C23×C113C22×D412yes—
310C23×C113C2×#4112yes—
311C23×C113H(5,𝔽2)11yescharacteristic
312C23×C1132−1+411yescharacteristic
313Q8×C113—81no—
314Q8×C113—81no—
315D4×C113—44no—
316D4×C113—48no—
317D4×C113—44no—
318D4×C113—42no—
319D4×C113—42no—
320D4×C113—42no—
321D4×C113—42no—
322D4×C113—44no—
323D4×C113—44no—
324D4×C113—82no—
325D4×C113—82no—
326D4×C113—81no—
327D4×C113—81no—
328D4×C113—88no—
329C2×C4×C113—24no—
330C2×C4×C113—22no—
331C2×C4×C113—22no—
332C2×C4×C113—21no—
333C2×C4×C113—21no—
334C2×C4×C113—22no—
335C2×C4×C113—22no—
336C2×C4×C113—21no—
337C2×C4×C113—21no—
338C2×C4×C113—24no—
339C2×C4×C113—22no—
340C2×C4×C113—22no—
341C2×C4×C113—42no—
342C2×C4×C113—41no—
343C2×C4×C113—42no—
344C2×C4×C113—42no—
345C2×C4×C113—42no—
346C2×C4×C113—41no—
347C2×C4×C113—42no—
348C2×C4×C113—41no—
349C2×C4×C113—41no—
350C2×C4×C113—42no—
351C2×C4×C113—41no—
352C2×C4×C113—41no—
353C2×C4×C113—42no—
354C2×C4×C113—41no—
355C2×C4×C113—41no—
356C2×C4×C113—42no—
357C2×C4×C113—41no—
358C2×C4×C113—41no—
359C2×C4×C113—42no—
360C2×C4×C113—41no—
361C2×C4×C113—41no—
362C2×C4×C113—42no—
363C2×C4×C113—81no—
364C2×C4×C113—81no—
365C2×C4×C113—82no—
366C2×C4×C113—82no—
367C2×C4×C113—88no—
368C22×C113—21no—
369C22×C113—21no—
370C22×C113—22no—
371C22×C113—21no—
372C22×C113—22no—
373C22×C113—21no—
374C22×C113—21no—
375C22×C113—22no—
376C22×C113—21no—
377C22×C113—22no—
378C22×C113—21no—
379C22×C113—22no—
380C22×C113—42no—
381C22×C113—41no—
382C22×C113—41no—
383C22×C113—44no—
384C22×C113—42no—
385C22×C113—42no—
386C22×C113—44no—
387C22×C113—44no—
388C22×C113—42no—
389C22×C113—42no—
390C22×C113—44no—
391C22×C113—42no—
392C22×C113—42no—
393C22×C113—42no—
394C22×C113—42no—
395C22×C113—82no—
396C22×C113—81no—
397C22×C113—81no—
398C22×C113—82no—
399C22×C113—82no—
400C22×C113—82no—
401C22×C113—82no—
402C22×C113—81no—
403C22×C113—81no—
404C22×C113—82no—
405C22×C113—81no—
406C22×C113—81no—
407C22×C113B(4,𝔽2)12yes—
408C22×C113C2×#12011yescharacteristic
409C22×C113#53211yescharacteristic
410C22×C113#53711yescharacteristic
411C22×C113#54612yes—
412C22×C113#54712yes—
413C4×C113—44no—
414C4×C113—42no—
415C4×C113—42no—
416C4×C113—41no—
417C4×C113—41no—
418C4×C113—42no—
419C4×C113—41no—
420C4×C113—41no—
421C4×C113—42no—
422C4×C113—81no—
423C4×C113—81no—
424C4×C113—82no—
425#25563C11311yesmaximal, characteristic, direct product factor, Sylow
426C2×C113—22no—
427C2×C113—21no—
428C2×C113—21no—
429C2×C113—22no—
430C2×C113—22no—
431C2×C113—41no—
432C2×C113—42no—
433C2×C113—82no—
434C2×C113—82no—
435C2×C113#243011yescharacteristic
436C2×C113C2×B(4,𝔽2)11yescharacteristic
437C2×C113#302611yescharacteristic
438#3490C2×C11311yescharacteristic, complemented
439#2410C2×C11312yescomplemented
440#2405C2×C11311yescharacteristic, complemented
441#2062C2×C11311yescharacteristic, complemented
442#2044C2×C11311yescharacteristic, complemented
443#2029C2×C11311yescharacteristic, complemented
444#2021C2×C11311yescharacteristic, complemented
445#1898C2×C11312yescomplemented
446#1889C2×C11312yescomplemented
447#1867C2×C11312yescomplemented
448C2×#342C2×C11311yescharacteristic, complemented
449C113#2556311yescharacteristic, direct product factor, Sylow
450C23×D4C22×C11311yescharacteristic
451#551—22no—
452#551—22no—
453#546—22no—
454#546—22no—
455#543C22×C11311yescharacteristic
456#538—21no—
457#538—21no—
458#534C22×C11311yescharacteristic
459#525—21no—
460#525—21no—
461C2×#123—21no—
462C2×#121—22no—
463C2×#120C22×C11312yes—
464C2×#120C22×C11312yes—
465#518C22×C11312yes—
466C22×C22⋊C4C22×C11311yescharacteristic
467C22×C22⋊C4C22×C11312yes—
468C2×#99C22×C11312yes—
469C2×#99C22×C11312yes—
470#394—21no—
471#394—21no—
472#394—22no—
473#392—22no—
474#386—21no—
475#386—22no—
476#386C22×C11312yes—
477#385C22×C11312yes—
478#385C22×C11311yescharacteristic
479#385C22×C11311yescharacteristic
480#379C22×C11311yescharacteristic
481#379C22×C11312yes—
482#379C22×C11311yescharacteristic
483#379C22×C11311yescharacteristic
484#342C22×C11312yes—
485#342C22×C11311yescharacteristic
486#342C22×C11312yes—
487#342C22×C11312yes—
488#342C22×C11311yescharacteristic
489C25C23×C11311yescharacteristic
490C25C23×C11311yescharacteristic
491C2×#41—21no—
492C2×#41—21no—
493C22×D4—22no—
494C22×D4—21no—
495C22×D4—22no—
496C22×D4—21no—
497C22×D4—22no—
498C22×D4—44no—
499C22×D4D4×C11312yescomplemented
500C22×D4D4×C11312yescomplemented
501C22×D4C23×C11312yes—
502C23×C4—22no—
503C23×C4D4×C11311yescharacteristic, complemented
504C23×C4D4×C11311yescharacteristic, complemented
505C23×C4C23×C11311yescharacteristic
506#126—22no—
507#126—22no—
508#124—22no—
509#124—22no—
510#123—22no—
511#123—22no—
512#123—22no—
513#123—22no—
514#123—22no—
515#123—44no—
516C22⋊Q8—21no—
517C22⋊Q8—21no—
518C22⋊Q8—21no—
519C22⋊Q8—21no—
520C22⋊Q8—22no—
521C22⋊Q8—22no—
522#121—21no—
523#121—21no—
524#121—22no—
525#121—22no—
526#121—21no—
527#121—21no—
528#121—48no—
529#120—22no—
530#120—22no—
531#120—22no—
532#120—22no—
533#120—22no—
534#120—24no—
535#120—42no—
536C4×D4—22no—
537C4×D4—22no—
538C4×D4—22no—
539C4×D4—22no—
540C4×D4—22no—
541C4×D4—22no—
542#117—21no—
543#117—21no—
544#117—22no—
545C2×C4⋊C4—22no—
546C2×C4⋊C4—21no—
547C2×C4⋊C4—21no—
548C2×C22⋊C4—22no—
549C2×C22⋊C4—22no—
550C2×C22⋊C4—22no—
551C2×C22⋊C4—24no—
552C2×C22⋊C4—22no—
553C2×C22⋊C4—22no—
554C2×C22⋊C4—21no—
555C2×C22⋊C4—22no—
556C2×C22⋊C4—22no—
557C2×C22⋊C4—21no—
558C2×C22⋊C4—21no—
559C2×C22⋊C4—21no—
560C2×C22⋊C4—22no—
561C2×C22⋊C4—21no—
562C2×C22⋊C4—21no—
563C2×C22⋊C4—42no—
564C2×C22⋊C4D4×C11311yescharacteristic, complemented
565C2×C22⋊C4D4×C11311yescharacteristic, complemented
566C2×C22⋊C4D4×C11312yescomplemented
567C2×C22⋊C4D4×C11312yescomplemented
568C2×C22⋊C4C23×C11312yes—
569C2×C22⋊C4C23×C11311yescharacteristic
570C2×C22⋊C4C23×C11311yescharacteristic
571C2×C22⋊C4C23×C11311yescharacteristic
572C2×C22⋊C4C23×C11311yescharacteristic
573C2×C22⋊C4C23×C11312yes—
574C2×C22⋊C4C23×C11312yes—
575#99—24no—
576#99—42no—
577#95—22no—
578#95—21no—
579#95—21no—
580#95—22no—
581C24—22no—
582C24—21no—
583C24—21no—
584C24—21no—
585C24—22no—
586C24—22no—
587C24—21no—
588C24—21no—
589C24—42no—
590C24—42no—
591C24—81no—
592C24—81no—
593C24C2×D4×C11312yes—
594C24C2×D4×C11311yescharacteristic
595C24C2×D4×C11312yes—
596C24C2×D4×C11312yes—
597C24C2×D4×C11311yescharacteristic
598C24C24×C11311yescharacteristic
599#41—82no—
600#41—82no—
601C2×Q8—21no—
602C2×Q8—21no—
603C2×D4—28no—
604C2×D4—24no—
605C2×D4—22no—
606C2×D4—22no—
607C2×D4—22no—
608C2×D4—22no—
609C2×D4—22no—
610C2×D4—22no—
611C2×D4—22no—
612C2×D4—22no—
613C2×D4—21no—
614C2×D4—21no—
615C2×D4—22no—
616C2×D4—22no—
617C2×D4—44no—
618C2×D4—42no—
619C2×D4—44no—
620C2×D4—42no—
621C2×D4—44no—
622C2×D4—42no—
623C2×D4—44no—
624C2×D4—42no—
625C2×D4—41no—
626C2×D4—41no—
627C2×D4—44no—
628C2×D4—44no—
629C2×D4—82no—
630C2×D4—82no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—22no—
634C22×C4—21no—
635C22×C4—22no—
636C22×C4—22no—
637C22×C4—22no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—22no—
643C22×C4—42no—
644C22×C4—44no—
645C22×C4—42no—
646C22×C4—44no—
647C22×C4—81no—
648C22×C4—82no—
649C22×C4C2×D4×C11312yes—
650C22×C4C2×D4×C11311yescharacteristic
651C22×C4C2×D4×C11312yes—
652C22×C4C2×D4×C11311yescharacteristic
653C22×C4C2×D4×C11311yescharacteristic
654C22×C4C2×D4×C11312yes—
655C22×C4C2×D4×C11311yescharacteristic
656C4⋊C4—22no—
657C4⋊C4—22no—
658C4⋊C4—21no—
659C4⋊C4—21no—
660C4⋊C4—21no—
661C4⋊C4—21no—
662C4⋊C4—22no—
663C4⋊C4—22no—
664C4⋊C4—44no—
665C4⋊C4—42no—
666C4⋊C4—42no—
667C22⋊C4—22no—
668C22⋊C4—22no—
669C22⋊C4—22no—
670C22⋊C4—22no—
671C22⋊C4—22no—
672C22⋊C4—22no—
673C22⋊C4—22no—
674C22⋊C4—22no—
675C22⋊C4—22no—
676C22⋊C4—22no—
677C22⋊C4—22no—
678C22⋊C4—22no—
679C22⋊C4—22no—
680C22⋊C4—22no—
681C22⋊C4—22no—
682C22⋊C4—22no—
683C22⋊C4—22no—
684C22⋊C4—21no—
685C22⋊C4—22no—
686C22⋊C4—21no—
687C22⋊C4—44no—
688C22⋊C4—44no—
689C22⋊C4—44no—
690C22⋊C4—44no—
691C22⋊C4—42no—
692C22⋊C4—42no—
693C22⋊C4—42no—
694C22⋊C4—81no—
695C22⋊C4—81no—
696C22⋊C4—82no—
697C22⋊C4—81no—
698C22⋊C4#41×C11314yescomplemented
699C42—22no—
700C42—22no—
701C23—21no—
702C23—21no—
703C23—22no—
704C23—22no—
705C23—22no—
706C23—24no—
707C23—21no—
708C23—21no—
709C23—22no—
710C23—22no—
711C23—22no—
712C23—24no—
713C23—22no—
714C23—22no—
715C23—22no—
716C23—41no—
717C23—41no—
718C23—42no—
719C23—41no—
720C23—41no—
721C23—41no—
722C23—42no—
723C23—42no—
724C23—41no—
725C23—41no—
726C23—42no—
727C23—41no—
728C23—42no—
729C23—42no—
730C23—42no—
731C23—42no—
732C23—41no—
733C23—41no—
734C23—41no—
735C23—42no—
736C23—42no—
737C23—84no—
738C23—84no—
739C23—82no—
740C23—82no—
741C23—82no—
742C23—82no—
743C23#120×C11312yes—
744C23#120×C11311yescharacteristic
745C23#120×C11311yescharacteristic
746C23C22×D4×C11311yescharacteristic
747C23C22×D4×C11312yes—
748C23C2×#41×C11312yes—
749C23H(5,𝔽2)×C11311yescharacteristic
750C232−1+4×C11311yescharacteristic
751Q8—81no—
752Q8—81no—
753D4—44no—
754D4—48no—
755D4—44no—
756D4—42no—
757D4—42no—
758D4—42no—
759D4—42no—
760D4—44no—
761D4—44no—
762D4—82no—
763D4—82no—
764D4—81no—
765D4—81no—
766D4—88no—
767C2×C4—24no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—24no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—42no—
780C2×C4—41no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—41no—
785C2×C4—42no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—42no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—42no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—42no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—42no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—42no—
801C2×C4—81no—
802C2×C4—81no—
803C2×C4—82no—
804C2×C4—82no—
805C2×C4—88no—
806C22—21no—
807C22—21no—
808C22—22no—
809C22—21no—
810C22—22no—
811C22—21no—
812C22—21no—
813C22—22no—
814C22—21no—
815C22—22no—
816C22—21no—
817C22—22no—
818C22—42no—
819C22—41no—
820C22—41no—
821C22—44no—
822C22—42no—
823C22—42no—
824C22—44no—
825C22—44no—
826C22—42no—
827C22—42no—
828C22—44no—
829C22—42no—
830C22—42no—
831C22—42no—
832C22—42no—
833C22—82no—
834C22—81no—
835C22—81no—
836C22—82no—
837C22—82no—
838C22—82no—
839C22—82no—
840C22—81no—
841C22—81no—
842C22—82no—
843C22—81no—
844C22—81no—
845C22B(4,𝔽2)×C11312yes—
846C22C2×#120×C11311yescharacteristic
847C22#532×C11311yescharacteristic
848C22#537×C11311yescharacteristic
849C22#546×C11312yes—
850C22#547×C11312yes—
851C4—44no—
852C4—42no—
853C4—42no—
854C4—41no—
855C4—41no—
856C4—42no—
857C4—41no—
858C4—41no—
859C4—42no—
860C4—82no—
861C4—81no—
862C4—81no—
863C2—22no—
864C2—21no—
865C2—21no—
866C2—22no—
867C2—22no—
868C2—41no—
869C2—42no—
870C2—82no—
871C2—82no—
872C2C113×#243011yescharacteristic
873C2C2×B(4,𝔽2)×C11311yescharacteristic
874C2C113×#302611yescharacteristic
subgroupG/H
center, socleC22×C113C2×#120
commutator, Frattini, cosocleC24C24×C113
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C113 ◁ C25×C113 ◁ G

Complements

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

NH ≅ G/Ntype
1. C113×#3490C2semidirect
2. C113×#2410C2semidirect
3. C113×#2405C2semidirect
4. C113×#2062C2semidirect
5. C113×#2044C2semidirect
6. C113×#2029C2semidirect
7. C113×#2021C2semidirect
8. C113×#1898C2semidirect
9. C113×#1889C2semidirect
10. C113×#1867C2semidirect
11. C2×#342×C113C2semidirect
61. C22×D4×C113D4semidirect
62. C22×D4×C113D4semidirect
65. C23×C4×C113D4semidirect
66. C23×C4×C113D4semidirect
126. C2×C22⋊C4×C113D4semidirect
127. C2×C22⋊C4×C113D4semidirect
128. C2×C22⋊C4×C113D4semidirect
129. C2×C22⋊C4×C113D4semidirect
260. C22⋊C4×C113#41semidirect
425. #25563C113direct (N × H)
438. #3490C2×C113semidirect
439. #2410C2×C113semidirect
440. #2405C2×C113semidirect
441. #2062C2×C113semidirect
442. #2044C2×C113semidirect
443. #2029C2×C113semidirect
444. #2021C2×C113semidirect
445. #1898C2×C113semidirect
446. #1889C2×C113semidirect
447. #1867C2×C113semidirect
448. C2×#342C2×C113semidirect
449. C113#25563direct (N × H)
499. C22×D4D4×C113semidirect
500. C22×D4D4×C113semidirect
503. C23×C4D4×C113semidirect
504. C23×C4D4×C113semidirect
564. C2×C22⋊C4D4×C113semidirect
565. C2×C22⋊C4D4×C113semidirect
566. C2×C22⋊C4D4×C113semidirect
567. C2×C22⋊C4D4×C113semidirect
698. C22⋊C4#41×C113semidirect

Maximal subgroups

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

subgroupindex
C113×#34902
C113×#24102
C113×#24052
C113×#20622
C113×#20442
C113×#20292
C113×#20212
C113×#18982
C113×#18892
C113×#18672
C2×#342×C1132
#25563113