Finite Group Databasebeta

← C113×#24295 #43292315

Subgroups — C113×#24295 #43292315

Order 28928.

1302 conjugacy classes of subgroups.

The subgroup lattice has 924 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#577×C113C211yesmaximal, characteristic, complemented
2C113×#3067C211yesmaximal, characteristic, complemented
3C113×#3057C211yesmaximal, characteristic, complemented
4C113×#3020C211yesmaximal, characteristic, complemented
5C113×#3019C211yesmaximal, characteristic, complemented
6C113×#2955C211yesmaximal, characteristic, complemented
7C113×#2049C211yesmaximal, characteristic, complemented
8C113×#2048C211yesmaximal, characteristic, complemented
9C113×#2009C211yesmaximal, characteristic, complemented
10C113×#2008C211yesmaximal, characteristic, complemented
11C113×#1977C211yesmaximal, characteristic, complemented
12C113×#1976C211yesmaximal, characteristic, complemented
13C113×#1814C211yesmaximal, characteristic, complemented
14C113×#1796C211yesmaximal, characteristic, complemented
15C113×#1795C211yesmaximal, characteristic, complemented
16C2×2−1+4×C113C2211yescharacteristic
17C2×H(5,𝔽2)×C113C2211yescharacteristic
18#577×C113—22no—
19#577×C113—22no—
20#577×C113—22no—
21#577×C113—22no—
22#575×C113C2211yescharacteristic
23#575×C113C2211yescharacteristic
24#575×C113C2211yescharacteristic, complemented
25C2×#137×C113—21no—
26C2×#137×C113C2211yescharacteristic
27C2×AGL(1,ℤ/8)×C113—21no—
28C2×AGL(1,ℤ/8)×C113C2211yescharacteristic
29C2×#135×C113—21no—
30C2×#135×C113C2211yescharacteristic
31C22×SD16×C113—21no—
32C22×SD16×C113C2211yescharacteristic
33C2×#131×C113C2211yescharacteristic
34C2×#131×C113C2211yescharacteristic, complemented
35#536×C113C2211yescharacteristic, complemented
36#535×C113C2211yescharacteristic
37#473×C113—21no—
38#472×C113—21no—
39#471×C113—21no—
40#471×C113—21no—
41#468×C113—22no—
42#465×C113—22no—
43#456×C113—22no—
44#455×C113—22no—
45#454×C113—22no—
46#453×C113—22no—
47#444×C113—22no—
48#443×C113—22no—
49#430×C113C2211yescharacteristic, complemented
50C2×#108×C113C2211yescharacteristic, complemented
51#427×C113C2211yescharacteristic, complemented
52#421×C113C2211yescharacteristic
53#421×C113C2211yescharacteristic
54#421×C113C2211yescharacteristic
55#421×C113C2211yescharacteristic
56#421×C113C2211yescharacteristic, complemented
57#421×C113C2211yescharacteristic, complemented
58#419×C113C2211yescharacteristic, complemented
59#419×C113C2211yescharacteristic, complemented
60#418×C113C2211yescharacteristic
61#418×C113C2211yescharacteristic
62#413×C113C2211yescharacteristic
63#413×C113C2211yescharacteristic, complemented
64C2×#101×C113C2211yescharacteristic, complemented
65C2×#100×C113C2211yescharacteristic
66#410×C113C2211yescharacteristic
67#410×C113C2211yescharacteristic, complemented
68#405×C113C2211yescharacteristic, complemented
69#344×C113C2211yescharacteristic, complemented
70#344×C113C2211yescharacteristic, complemented
712−1+4×C113—22no—
722−1+4×C113—22no—
732−1+4×C113—22no—
742−1+4×C113—41no—
75H(5,𝔽2)×C113—22no—
76H(5,𝔽2)×C113—22no—
77H(5,𝔽2)×C113—22no—
78H(5,𝔽2)×C113—41no—
79C2×#41×C113—21no—
80C2×#41×C113—21no—
81C2×#41×C113—21no—
82C2×#41×C113—21no—
83C2×#41×C113—41no—
84C2×#41×C113C2311yescharacteristic
85C2×#41×C113C2311yescharacteristic
86C2×#41×C113C2311yescharacteristic
87C2×#41×C113C2311yescharacteristic
88C22×Q8×C113—21no—
89C22×Q8×C113—21no—
90C22×Q8×C113C2311yescharacteristic
91C22×D4×C113—21no—
92C22×D4×C113—21no—
93C22×D4×C113—41no—
94C22×D4×C113C2311yescharacteristic
95#137×C113—24no—
96#137×C113—24no—
97#137×C113—22no—
98#137×C113—21no—
99#137×C113—21no—
100#137×C113—21no—
101#137×C113—21no—
102#137×C113—21no—
103#137×C113—22no—
104#137×C113D412yes—
105AGL(1,ℤ/8)×C113—24no—
106AGL(1,ℤ/8)×C113—24no—
107AGL(1,ℤ/8)×C113—22no—
108AGL(1,ℤ/8)×C113—21no—
109AGL(1,ℤ/8)×C113—21no—
110AGL(1,ℤ/8)×C113—21no—
111AGL(1,ℤ/8)×C113—21no—
112AGL(1,ℤ/8)×C113—21no—
113AGL(1,ℤ/8)×C113—22no—
114AGL(1,ℤ/8)×C113D412yes—
115#135×C113—24no—
116#135×C113—24no—
117#135×C113—22no—
118#135×C113—21no—
119#135×C113—21no—
120#135×C113—21no—
121#135×C113—21no—
122#135×C113—41no—
123#135×C113—41no—
124C2×Q16×C113—21no—
125C2×Q16×C113D411yescharacteristic, complemented
126C2×SD16×C113—24no—
127C2×SD16×C113—24no—
128C2×SD16×C113—21no—
129C2×SD16×C113—21no—
130C2×SD16×C113—21no—
131C2×SD16×C113—21no—
132C2×SD16×C113—21no—
133C2×SD16×C113—21no—
134C2×SD16×C113D412yes—
135C2×SD16×C113D412yes—
136C2×SD16×C113D411yescharacteristic, complemented
137C2×SD16×C113D411yescharacteristic, complemented
138C2×D8×C113—21no—
139C2×D8×C113D411yescharacteristic, complemented
140#131×C113—21no—
141#131×C113—21no—
142#131×C113—21no—
143#131×C113—21no—
144#131×C113—21no—
145#131×C113—21no—
146#131×C113D412yescomplemented
147#131×C113D412yescomplemented
148C2×M16×C113—21no—
149C2×M16×C113—21no—
150C2×M16×C113C2311yescharacteristic
151C2×M16×C113C2311yescharacteristic
152C2×M16×C113C2311yescharacteristic
153C2×M16×C113C2311yescharacteristic
154C2×M16×C113C2311yescharacteristic
155C22×C8×C113—21no—
156C22×C8×C113—21no—
157C22×C8×C113C2311yescharacteristic
158C4⋊Q8×C113—21no—
159#127×C113—21no—
160#124×C113—21no—
161#124×C113—21no—
162#123×C113—41no—
163C22⋊Q8×C113—22no—
164#121×C113—22no—
165#120×C113—41no—
166#117×C113C2311yescharacteristic
167#117×C113C2311yescharacteristic
168#117×C113C2311yescharacteristic
169#108×C113—22no—
170#108×C113—21no—
171#108×C113—21no—
172#107×C113—21no—
173#106×C113—21no—
174#104×C113—22no—
175#104×C113—22no—
176#104×C113—22no—
177#104×C113—22no—
178#104×C113—22no—
179#104×C113—22no—
180#103×C113—22no—
181#103×C113—41no—
182#102×C113—22no—
183#102×C113—41no—
184#101×C113—21no—
185#101×C113—21no—
186#101×C113—22no—
187#100×C113—21no—
188#100×C113—21no—
189#100×C113—22no—
190#99×C113—41no—
191#99×C113—41no—
192#97×C113—21no—
193C4×C8×C113—21no—
194C24×C113—21no—
195C24×C113—41no—
196#41×C113—21no—
197#41×C113—21no—
198#41×C113—24no—
199#41×C113—24no—
200#41×C113—21no—
201#41×C113—21no—
202#41×C113—21no—
203#41×C113—21no—
204#41×C113—21no—
205#41×C113—21no—
206#41×C113—21no—
207#41×C113—21no—
208#41×C113—21no—
209#41×C113—21no—
210#41×C113—21no—
211#41×C113—21no—
212#41×C113—42no—
213#41×C113—44no—
214#41×C113—42no—
215#41×C113—42no—
216#41×C113—42no—
217#41×C113—44no—
218#41×C113—42no—
219#41×C113—42no—
220#41×C113C2×D412yes—
221#41×C113C2×D412yes—
222C2×Q8×C113—21no—
223C2×Q8×C113—24no—
224C2×Q8×C113—21no—
225C2×Q8×C113—21no—
226C2×Q8×C113—21no—
227C2×Q8×C113—21no—
228C2×Q8×C113—41no—
229C2×Q8×C113—42no—
230C2×Q8×C113—42no—
231C2×Q8×C113—42no—
232C2×Q8×C113C2×D411yescharacteristic
233C2×Q8×C113C2×D411yescharacteristic
234C2×Q8×C113C2×D412yes—
235C2×Q8×C113C2×D411yescharacteristic
236C2×Q8×C113#4111yescharacteristic
237C2×D4×C113—21no—
238C2×D4×C113—24no—
239C2×D4×C113—21no—
240C2×D4×C113—21no—
241C2×D4×C113—21no—
242C2×D4×C113—21no—
243C2×D4×C113—21no—
244C2×D4×C113—21no—
245C2×D4×C113—21no—
246C2×D4×C113—21no—
247C2×D4×C113—42no—
248C2×D4×C113—41no—
249C2×D4×C113—41no—
250C2×D4×C113—42no—
251C2×D4×C113—44no—
252C2×D4×C113—44no—
253C2×D4×C113—41no—
254C2×D4×C113—42no—
255C2×D4×C113—42no—
256C2×D4×C113C2×D411yescharacteristic
257C2×D4×C113C2×D411yescharacteristic
258C2×D4×C113C2×D412yes—
259C2×D4×C113C2×D411yescharacteristic
260C2×D4×C113#4111yescharacteristic
261C22×C4×C113—21no—
262C22×C4×C113—21no—
263C22×C4×C113—21no—
264C22×C4×C113—21no—
265C22×C4×C113—21no—
266C22×C4×C113—41no—
267C22×C4×C113—41no—
268C22×C4×C113—41no—
269C22×C4×C113C2411yescharacteristic
270Q16×C113—24no—
271Q16×C113—22no—
272Q16×C113—21no—
273Q16×C113—21no—
274Q16×C113—41no—
275Q16×C113—41no—
276SD16×C113—24no—
277SD16×C113—24no—
278SD16×C113—22no—
279SD16×C113—22no—
280SD16×C113—22no—
281SD16×C113—22no—
282SD16×C113—21no—
283SD16×C113—21no—
284SD16×C113—22no—
285SD16×C113—22no—
286SD16×C113—21no—
287SD16×C113—21no—
288SD16×C113—41no—
289SD16×C113—41no—
290SD16×C113—41no—
291SD16×C113—41no—
292D8×C113—24no—
293D8×C113—22no—
294D8×C113—21no—
295D8×C113—21no—
296D8×C113—41no—
297D8×C113—41no—
298M16×C113—21no—
299M16×C113—21no—
300M16×C113—22no—
301M16×C113—22no—
302M16×C113—21no—
303M16×C113—21no—
304M16×C113—21no—
305M16×C113—21no—
306M16×C113—21no—
307M16×C113—21no—
308M16×C113—41no—
309M16×C113—41no—
310M16×C113C2×D412yes—
311M16×C113C2×D412yes—
312C2×C8×C113—21no—
313C2×C8×C113—21no—
314C2×C8×C113—22no—
315C2×C8×C113—22no—
316C2×C8×C113—21no—
317C2×C8×C113—21no—
318C2×C8×C113—21no—
319C2×C8×C113—41no—
320C2×C8×C113—41no—
321C2×C8×C113C2×D411yescharacteristic
322C2×C8×C113C2×D411yescharacteristic
323C2×C8×C113C2×D411yescharacteristic
324C2×C8×C113C2×D411yescharacteristic
325C2×C8×C113C2×D411yescharacteristic
326C2×C8×C113C2×D411yescharacteristic
327C4⋊C4×C113—21no—
328C4⋊C4×C113—21no—
329C4⋊C4×C113—21no—
330C4⋊C4×C113—42no—
331C22⋊C4×C113—21no—
332C22⋊C4×C113—21no—
333C22⋊C4×C113—21no—
334C22⋊C4×C113—42no—
335C22⋊C4×C113—42no—
336C42×C113—21no—
337C42×C113—21no—
338C42×C113—21no—
339C23×C113—21no—
340C23×C113—21no—
341C23×C113—22no—
342C23×C113—21no—
343C23×C113—21no—
344C23×C113—44no—
345C23×C113—41no—
346C23×C113—41no—
347C23×C113—161no—
348C23×C113—162no—
349C23×C113H(5,𝔽2)11yescharacteristic
350Q8×C113—21no—
351Q8×C113—21no—
352Q8×C113—22no—
353Q8×C113—21no—
354Q8×C113—21no—
355Q8×C113—21no—
356Q8×C113—21no—
357Q8×C113—21no—
358Q8×C113—22no—
359Q8×C113—44no—
360Q8×C113—41no—
361Q8×C113—41no—
362Q8×C113#12112yes—
363D4×C113—22no—
364D4×C113—22no—
365D4×C113—21no—
366D4×C113—22no—
367D4×C113—21no—
368D4×C113—21no—
369D4×C113—21no—
370D4×C113—21no—
371D4×C113—21no—
372D4×C113—21no—
373D4×C113—22no—
374D4×C113—44no—
375D4×C113—44no—
376D4×C113—44no—
377D4×C113—41no—
378D4×C113—41no—
379D4×C113—41no—
380D4×C113—41no—
381D4×C113—41no—
382D4×C113—41no—
383D4×C113—41no—
384D4×C113—41no—
385D4×C113—162no—
386D4×C113#12112yes—
387C2×C4×C113—21no—
388C2×C4×C113—22no—
389C2×C4×C113—22no—
390C2×C4×C113—21no—
391C2×C4×C113—22no—
392C2×C4×C113—21no—
393C2×C4×C113—21no—
394C2×C4×C113—44no—
395C2×C4×C113—44no—
396C2×C4×C113—44no—
397C2×C4×C113—41no—
398C2×C4×C113—41no—
399C2×C4×C113—41no—
400C2×C4×C113—41no—
401C2×C4×C113—41no—
402C2×C4×C113—41no—
403C2×C4×C113—41no—
404C2×C4×C113—41no—
405C2×C4×C113—41no—
406C2×C4×C113—41no—
407C2×C4×C113—41no—
408C2×C4×C113C22×D411yescharacteristic
409C2×C4×C113C22×D411yescharacteristic
410C2×C4×C113C22×D411yescharacteristic
411C2×C4×C113C22×D411yescharacteristic
412C2×C4×C113C2×#4111yescharacteristic
413C2×C4×C113H(5,𝔽2)11yescharacteristic
414C8×C113—22no—
415C8×C113—22no—
416C8×C113—41no—
417C8×C113—41no—
418C8×C113—41no—
419C8×C113#12011yescharacteristic
420C8×C113#12011yescharacteristic
421C8×C113#12011yescharacteristic
422C8×C113#12011yescharacteristic
423C22×C113—22no—
424C22×C113—41no—
425C22×C113—42no—
426C22×C113—42no—
427C22×C113—41no—
428C22×C113—42no—
429C22×C113—41no—
430C22×C113—41no—
431C22×C113—82no—
432C22×C113—81no—
433C22×C113—81no—
434C22×C113—82no—
435C22×C113—161no—
436C22×C113—164no—
437C22×C113#53511yescharacteristic
438C22×C113D4211yescharacteristic
439C22×C113#54611yescharacteristic
440C4×C113—22no—
441C4×C113—41no—
442C4×C113—42no—
443C4×C113—41no—
444C4×C113—41no—
445C4×C113—81no—
446C4×C113—81no—
447C4×C113—81no—
448C4×C113C2×#12011yescharacteristic
449C4×C113C2×#12111yescharacteristic
450C4×C113D4211yescharacteristic
451C4×C113#54611yescharacteristic
452#24295C11311yesmaximal, characteristic, direct product factor, Sylow
453C2×C113—21no—
454C2×C113—21no—
455C2×C113—21no—
456C2×C113—42no—
457C2×C113—81no—
458C2×C113—81no—
459C2×C113—82no—
460C2×C113—81no—
461C2×C113#240811yescharacteristic
462C2×#577C2×C11311yescharacteristic, complemented
463#3067C2×C11311yescharacteristic, complemented
464#3057C2×C11311yescharacteristic, complemented
465#3020C2×C11311yescharacteristic, complemented
466#3019C2×C11311yescharacteristic, complemented
467#2955C2×C11311yescharacteristic, complemented
468#2049C2×C11311yescharacteristic, complemented
469#2048C2×C11311yescharacteristic, complemented
470#2009C2×C11311yescharacteristic, complemented
471#2008C2×C11311yescharacteristic, complemented
472#1977C2×C11311yescharacteristic, complemented
473#1976C2×C11311yescharacteristic, complemented
474#1814C2×C11311yescharacteristic, complemented
475#1796C2×C11311yescharacteristic, complemented
476#1795C2×C11311yescharacteristic, complemented
477C113#2429511yescharacteristic, direct product factor, Sylow
478C2×2−1+4C22×C11311yescharacteristic
479C2×H(5,𝔽2)C22×C11311yescharacteristic
480#577—22no—
481#577—22no—
482#577—22no—
483#577—22no—
484#575C22×C11311yescharacteristic
485#575C22×C11311yescharacteristic
486#575C22×C11311yescharacteristic, complemented
487C2×#137—21no—
488C2×#137C22×C11311yescharacteristic
489C2×AGL(1,ℤ/8)—21no—
490C2×AGL(1,ℤ/8)C22×C11311yescharacteristic
491C2×#135—21no—
492C2×#135C22×C11311yescharacteristic
493C22×SD16—21no—
494C22×SD16C22×C11311yescharacteristic
495C2×#131C22×C11311yescharacteristic
496C2×#131C22×C11311yescharacteristic, complemented
497#536C22×C11311yescharacteristic, complemented
498#535C22×C11311yescharacteristic
499#473—21no—
500#472—21no—
501#471—21no—
502#471—21no—
503#468—22no—
504#465—22no—
505#456—22no—
506#455—22no—
507#454—22no—
508#453—22no—
509#444—22no—
510#443—22no—
511#430C22×C11311yescharacteristic, complemented
512C2×#108C22×C11311yescharacteristic, complemented
513#427C22×C11311yescharacteristic, complemented
514#421C22×C11311yescharacteristic
515#421C22×C11311yescharacteristic
516#421C22×C11311yescharacteristic
517#421C22×C11311yescharacteristic
518#421C22×C11311yescharacteristic, complemented
519#421C22×C11311yescharacteristic, complemented
520#419C22×C11311yescharacteristic, complemented
521#419C22×C11311yescharacteristic, complemented
522#418C22×C11311yescharacteristic
523#418C22×C11311yescharacteristic
524#413C22×C11311yescharacteristic
525#413C22×C11311yescharacteristic, complemented
526C2×#101C22×C11311yescharacteristic, complemented
527C2×#100C22×C11311yescharacteristic
528#410C22×C11311yescharacteristic
529#410C22×C11311yescharacteristic, complemented
530#405C22×C11311yescharacteristic, complemented
531#344C22×C11311yescharacteristic, complemented
532#344C22×C11311yescharacteristic, complemented
5332−1+4—22no—
5342−1+4—22no—
5352−1+4—22no—
5362−1+4—41no—
537H(5,𝔽2)—22no—
538H(5,𝔽2)—22no—
539H(5,𝔽2)—22no—
540H(5,𝔽2)—41no—
541C2×#41—21no—
542C2×#41—21no—
543C2×#41—21no—
544C2×#41—21no—
545C2×#41—41no—
546C2×#41C23×C11311yescharacteristic
547C2×#41C23×C11311yescharacteristic
548C2×#41C23×C11311yescharacteristic
549C2×#41C23×C11311yescharacteristic
550C22×Q8—21no—
551C22×Q8—21no—
552C22×Q8C23×C11311yescharacteristic
553C22×D4—21no—
554C22×D4—21no—
555C22×D4—41no—
556C22×D4C23×C11311yescharacteristic
557#137—24no—
558#137—24no—
559#137—22no—
560#137—21no—
561#137—21no—
562#137—21no—
563#137—21no—
564#137—21no—
565#137—22no—
566#137D4×C11312yes—
567AGL(1,ℤ/8)—24no—
568AGL(1,ℤ/8)—24no—
569AGL(1,ℤ/8)—22no—
570AGL(1,ℤ/8)—21no—
571AGL(1,ℤ/8)—21no—
572AGL(1,ℤ/8)—21no—
573AGL(1,ℤ/8)—21no—
574AGL(1,ℤ/8)—21no—
575AGL(1,ℤ/8)—22no—
576AGL(1,ℤ/8)D4×C11312yes—
577#135—24no—
578#135—24no—
579#135—22no—
580#135—21no—
581#135—21no—
582#135—21no—
583#135—21no—
584#135—41no—
585#135—41no—
586C2×Q16—21no—
587C2×Q16D4×C11311yescharacteristic, complemented
588C2×SD16—24no—
589C2×SD16—24no—
590C2×SD16—21no—
591C2×SD16—21no—
592C2×SD16—21no—
593C2×SD16—21no—
594C2×SD16—21no—
595C2×SD16—21no—
596C2×SD16D4×C11312yes—
597C2×SD16D4×C11312yes—
598C2×SD16D4×C11311yescharacteristic, complemented
599C2×SD16D4×C11311yescharacteristic, complemented
600C2×D8—21no—
601C2×D8D4×C11311yescharacteristic, complemented
602#131—21no—
603#131—21no—
604#131—21no—
605#131—21no—
606#131—21no—
607#131—21no—
608#131D4×C11312yescomplemented
609#131D4×C11312yescomplemented
610C2×M16—21no—
611C2×M16—21no—
612C2×M16C23×C11311yescharacteristic
613C2×M16C23×C11311yescharacteristic
614C2×M16C23×C11311yescharacteristic
615C2×M16C23×C11311yescharacteristic
616C2×M16C23×C11311yescharacteristic
617C22×C8—21no—
618C22×C8—21no—
619C22×C8C23×C11311yescharacteristic
620C4⋊Q8—21no—
621#127—21no—
622#124—21no—
623#124—21no—
624#123—41no—
625C22⋊Q8—22no—
626#121—22no—
627#120—41no—
628#117C23×C11311yescharacteristic
629#117C23×C11311yescharacteristic
630#117C23×C11311yescharacteristic
631#108—22no—
632#108—21no—
633#108—21no—
634#107—21no—
635#106—21no—
636#104—22no—
637#104—22no—
638#104—22no—
639#104—22no—
640#104—22no—
641#104—22no—
642#103—22no—
643#103—41no—
644#102—22no—
645#102—41no—
646#101—21no—
647#101—21no—
648#101—22no—
649#100—21no—
650#100—21no—
651#100—22no—
652#99—41no—
653#99—41no—
654#97—21no—
655C4×C8—21no—
656C24—21no—
657C24—41no—
658#41—21no—
659#41—21no—
660#41—24no—
661#41—24no—
662#41—21no—
663#41—21no—
664#41—21no—
665#41—21no—
666#41—21no—
667#41—21no—
668#41—21no—
669#41—21no—
670#41—21no—
671#41—21no—
672#41—21no—
673#41—21no—
674#41—42no—
675#41—44no—
676#41—42no—
677#41—42no—
678#41—42no—
679#41—44no—
680#41—42no—
681#41—42no—
682#41C2×D4×C11312yes—
683#41C2×D4×C11312yes—
684C2×Q8—21no—
685C2×Q8—24no—
686C2×Q8—21no—
687C2×Q8—21no—
688C2×Q8—21no—
689C2×Q8—21no—
690C2×Q8—41no—
691C2×Q8—42no—
692C2×Q8—42no—
693C2×Q8—42no—
694C2×Q8C2×D4×C11311yescharacteristic
695C2×Q8C2×D4×C11311yescharacteristic
696C2×Q8C2×D4×C11312yes—
697C2×Q8C2×D4×C11311yescharacteristic
698C2×Q8#41×C11311yescharacteristic
699C2×D4—21no—
700C2×D4—24no—
701C2×D4—21no—
702C2×D4—21no—
703C2×D4—21no—
704C2×D4—21no—
705C2×D4—21no—
706C2×D4—21no—
707C2×D4—21no—
708C2×D4—21no—
709C2×D4—42no—
710C2×D4—41no—
711C2×D4—41no—
712C2×D4—42no—
713C2×D4—44no—
714C2×D4—44no—
715C2×D4—41no—
716C2×D4—42no—
717C2×D4—42no—
718C2×D4C2×D4×C11311yescharacteristic
719C2×D4C2×D4×C11311yescharacteristic
720C2×D4C2×D4×C11312yes—
721C2×D4C2×D4×C11311yescharacteristic
722C2×D4#41×C11311yescharacteristic
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—41no—
729C22×C4—41no—
730C22×C4—41no—
731C22×C4C24×C11311yescharacteristic
732Q16—24no—
733Q16—22no—
734Q16—21no—
735Q16—21no—
736Q16—41no—
737Q16—41no—
738SD16—24no—
739SD16—24no—
740SD16—22no—
741SD16—22no—
742SD16—22no—
743SD16—22no—
744SD16—21no—
745SD16—21no—
746SD16—22no—
747SD16—22no—
748SD16—21no—
749SD16—21no—
750SD16—41no—
751SD16—41no—
752SD16—41no—
753SD16—41no—
754D8—24no—
755D8—22no—
756D8—21no—
757D8—21no—
758D8—41no—
759D8—41no—
760M16—21no—
761M16—21no—
762M16—22no—
763M16—22no—
764M16—21no—
765M16—21no—
766M16—21no—
767M16—21no—
768M16—21no—
769M16—21no—
770M16—41no—
771M16—41no—
772M16C2×D4×C11312yes—
773M16C2×D4×C11312yes—
774C2×C8—21no—
775C2×C8—21no—
776C2×C8—22no—
777C2×C8—22no—
778C2×C8—21no—
779C2×C8—21no—
780C2×C8—21no—
781C2×C8—41no—
782C2×C8—41no—
783C2×C8C2×D4×C11311yescharacteristic
784C2×C8C2×D4×C11311yescharacteristic
785C2×C8C2×D4×C11311yescharacteristic
786C2×C8C2×D4×C11311yescharacteristic
787C2×C8C2×D4×C11311yescharacteristic
788C2×C8C2×D4×C11311yescharacteristic
789C4⋊C4—21no—
790C4⋊C4—21no—
791C4⋊C4—21no—
792C4⋊C4—42no—
793C22⋊C4—21no—
794C22⋊C4—21no—
795C22⋊C4—21no—
796C22⋊C4—42no—
797C22⋊C4—42no—
798C42—21no—
799C42—21no—
800C42—21no—
801C23—21no—
802C23—21no—
803C23—22no—
804C23—21no—
805C23—21no—
806C23—44no—
807C23—41no—
808C23—41no—
809C23—161no—
810C23—162no—
811C23H(5,𝔽2)×C11311yescharacteristic
812Q8—21no—
813Q8—21no—
814Q8—22no—
815Q8—21no—
816Q8—21no—
817Q8—21no—
818Q8—21no—
819Q8—21no—
820Q8—22no—
821Q8—44no—
822Q8—41no—
823Q8—41no—
824Q8#121×C11312yes—
825D4—22no—
826D4—22no—
827D4—21no—
828D4—22no—
829D4—21no—
830D4—21no—
831D4—21no—
832D4—21no—
833D4—21no—
834D4—21no—
835D4—22no—
836D4—44no—
837D4—44no—
838D4—44no—
839D4—41no—
840D4—41no—
841D4—41no—
842D4—41no—
843D4—41no—
844D4—41no—
845D4—41no—
846D4—41no—
847D4—162no—
848D4#121×C11312yes—
849C2×C4—21no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—21no—
853C2×C4—22no—
854C2×C4—21no—
855C2×C4—21no—
856C2×C4—44no—
857C2×C4—44no—
858C2×C4—44no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4C22×D4×C11311yescharacteristic
871C2×C4C22×D4×C11311yescharacteristic
872C2×C4C22×D4×C11311yescharacteristic
873C2×C4C22×D4×C11311yescharacteristic
874C2×C4C2×#41×C11311yescharacteristic
875C2×C4H(5,𝔽2)×C11311yescharacteristic
876C8—22no—
877C8—22no—
878C8—41no—
879C8—41no—
880C8—41no—
881C8#120×C11311yescharacteristic
882C8#120×C11311yescharacteristic
883C8#120×C11311yescharacteristic
884C8#120×C11311yescharacteristic
885C22—22no—
886C22—41no—
887C22—42no—
888C22—42no—
889C22—41no—
890C22—42no—
891C22—41no—
892C22—41no—
893C22—82no—
894C22—81no—
895C22—81no—
896C22—82no—
897C22—161no—
898C22—164no—
899C22#535×C11311yescharacteristic
900C22D42×C11311yescharacteristic
901C22#546×C11311yescharacteristic
902C4—22no—
903C4—41no—
904C4—42no—
905C4—41no—
906C4—41no—
907C4—81no—
908C4—81no—
909C4—81no—
910C4C2×#120×C11311yescharacteristic
911C4C2×#121×C11311yescharacteristic
912C4D42×C11311yescharacteristic
913C4#546×C11311yescharacteristic
914C2—21no—
915C2—21no—
916C2—21no—
917C2—42no—
918C2—81no—
919C2—82no—
920C2—81no—
921C2—81no—
922C2C113×#240811yescharacteristic
subgroupG/H
center, socleC2×C113#2408
commutator, Frattini, cosocleC22×C4C24×C113
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C113 ◁ C22×C4×C113 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#577×C113C2semidirect
2. C113×#3067C2semidirect
3. C113×#3057C2semidirect
4. C113×#3020C2semidirect
5. C113×#3019C2semidirect
6. C113×#2955C2semidirect
7. C113×#2049C2semidirect
8. C113×#2048C2semidirect
9. C113×#2009C2semidirect
10. C113×#2008C2semidirect
11. C113×#1977C2semidirect
12. C113×#1976C2semidirect
13. C113×#1814C2semidirect
14. C113×#1796C2semidirect
15. C113×#1795C2semidirect
24. #575×C113C22semidirect
34. C2×#131×C113C22semidirect
35. #536×C113C22semidirect
49. #430×C113C22semidirect
50. C2×#108×C113C22semidirect
51. #427×C113C22semidirect
56. #421×C113C22semidirect
57. #421×C113C22semidirect
58. #419×C113C22semidirect
59. #419×C113C22semidirect
63. #413×C113C22semidirect
64. C2×#101×C113C22semidirect
67. #410×C113C22semidirect
68. #405×C113C22semidirect
69. #344×C113C22semidirect
70. #344×C113C22semidirect
125. C2×Q16×C113D4semidirect
136. C2×SD16×C113D4semidirect
137. C2×SD16×C113D4semidirect
139. C2×D8×C113D4semidirect
146. #131×C113D4semidirect
147. #131×C113D4semidirect
452. #24295C113direct (N × H)
462. C2×#577C2×C113semidirect
463. #3067C2×C113semidirect
464. #3057C2×C113semidirect
465. #3020C2×C113semidirect
466. #3019C2×C113semidirect
467. #2955C2×C113semidirect
468. #2049C2×C113semidirect
469. #2048C2×C113semidirect
470. #2009C2×C113semidirect
471. #2008C2×C113semidirect
472. #1977C2×C113semidirect
473. #1976C2×C113semidirect
474. #1814C2×C113semidirect
475. #1796C2×C113semidirect
476. #1795C2×C113semidirect
477. C113#24295direct (N × H)
486. #575C22×C113semidirect
496. C2×#131C22×C113semidirect
497. #536C22×C113semidirect
511. #430C22×C113semidirect
512. C2×#108C22×C113semidirect
513. #427C22×C113semidirect
518. #421C22×C113semidirect
519. #421C22×C113semidirect
520. #419C22×C113semidirect
521. #419C22×C113semidirect
525. #413C22×C113semidirect
526. C2×#101C22×C113semidirect
529. #410C22×C113semidirect
530. #405C22×C113semidirect
531. #344C22×C113semidirect
532. #344C22×C113semidirect
587. C2×Q16D4×C113semidirect
598. C2×SD16D4×C113semidirect
599. C2×SD16D4×C113semidirect
601. C2×D8D4×C113semidirect
608. #131D4×C113semidirect
609. #131D4×C113semidirect

Maximal subgroups

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

subgroupindex
C2×#577×C1132
C113×#30672
C113×#30572
C113×#30202
C113×#30192
C113×#29552
C113×#20492
C113×#20482
C113×#20092
C113×#20082
C113×#19772
C113×#19762
C113×#18142
C113×#17962
C113×#17952
#24295113