Finite Group Databasebeta

← C113×#24460 #43292480

Subgroups — C113×#24460 #43292480

Order 28928.

1352 conjugacy classes of subgroups.

The subgroup lattice has 918 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#577×C113C211yesmaximal, characteristic, complemented
2C2×#472×C113C211yesmaximal, characteristic, complemented
3C113×#3045C211yesmaximal, characteristic, complemented
4C2×#454×C113C211yesmaximal, characteristic, complemented
5C113×#3008C211yesmaximal, characteristic, complemented
6C113×#2898C211yesmaximal, characteristic, complemented
7C113×#2052C211yesmaximal, characteristic, complemented
8C113×#2046C211yesmaximal, characteristic, complemented
9C113×#2012C211yesmaximal, characteristic, complemented
10C113×#2004C211yesmaximal, characteristic, complemented
11C113×#1907C211yesmaximal, characteristic, complemented
12C113×#1883C211yesmaximal, characteristic, complemented
13C113×#1876C211yesmaximal, characteristic, complemented
14C113×#1866C211yesmaximal, characteristic, complemented
15C113×#1792C211yesmaximal, characteristic, complemented
16C2×2−1+4×C113C2211yescharacteristic
17C2×H(5,𝔽2)×C113C2211yescharacteristic
18#577×C113—24no—
19#577×C113—24no—
20C2×#137×C113—21no—
21C2×#137×C113C2211yescharacteristic
22C2×AGL(1,ℤ/8)×C113—21no—
23C2×AGL(1,ℤ/8)×C113C2211yescharacteristic
24C2×AGL(1,ℤ/8)×C113C2211yescharacteristic
25C2×AGL(1,ℤ/8)×C113C2211yescharacteristic, complemented
26C2×#135×C113—21no—
27C2×#135×C113C2211yescharacteristic
28C22×SD16×C113—21no—
29C22×SD16×C113C2211yescharacteristic
30C22×D8×C113C2211yescharacteristic
31C2×#131×C113C2211yescharacteristic
32C2×#131×C113C2211yescharacteristic, complemented
33#535×C113C2211yescharacteristic
34C2×#124×C113C2211yescharacteristic, complemented
35#520×C113C2211yescharacteristic, complemented
36#472×C113—24no—
37#464×C113—21no—
38#463×C113—21no—
39#460×C113—21no—
40#459×C113—21no—
41#454×C113—24no—
42#449×C113—21no—
43#449×C113—21no—
44#447×C113—21no—
45#447×C113—21no—
46C2×#108×C113C2211yescharacteristic, complemented
47#424×C113C2211yescharacteristic, complemented
48C2×#104×C113C2211yescharacteristic
49C2×#104×C113C2211yescharacteristic
50C2×#104×C113C2211yescharacteristic, complemented
51#419×C113—21no—
52#419×C113C2211yescharacteristic, complemented
53#418×C113C2211yescharacteristic
54#417×C113—21no—
55#417×C113C2211yescharacteristic
56#417×C113C2211yescharacteristic
57#416×C113—21no—
58#416×C113C2211yescharacteristic
59C2×#103×C113—21no—
60C2×#103×C113C2211yescharacteristic, complemented
61C2×#102×C113C2211yescharacteristic, complemented
62C2×#101×C113C2211yescharacteristic, complemented
63C2×#100×C113C2211yescharacteristic
64C2×#100×C113C2211yescharacteristic, complemented
65#408×C113C2211yescharacteristic
66#390×C113C2211yescharacteristic
67#343×C113C2211yescharacteristic, complemented
68#341×C113C2211yescharacteristic, complemented
69#339×C113C2211yescharacteristic, complemented
70#336×C113C2211yescharacteristic, complemented
712−1+4×C113—22no—
722−1+4×C113—22no—
732−1+4×C113—41no—
742−1+4×C113D414yescomplemented
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
87C22×Q8×C113—21no—
88C22×Q8×C113—21no—
89C22×Q8×C113C2311yescharacteristic
90C22×D4×C113—21no—
91C22×D4×C113—21no—
92C22×D4×C113—41no—
93C22×D4×C113C2311yescharacteristic
94C22×D4×C113C2311yescharacteristic
95#137×C113—28no—
96#137×C113—22no—
97#137×C113—22no—
98AGL(1,ℤ/8)×C113—28no—
99AGL(1,ℤ/8)×C113—22no—
100AGL(1,ℤ/8)×C113—22no—
101AGL(1,ℤ/8)×C113—22no—
102AGL(1,ℤ/8)×C113—22no—
103AGL(1,ℤ/8)×C113—22no—
104AGL(1,ℤ/8)×C113D414yescomplemented
105#135×C113—28no—
106#135×C113—22no—
107#135×C113—22no—
108C2×Q16×C113—21no—
109C2×Q16×C113D411yescharacteristic
110C2×SD16×C113—28no—
111C2×SD16×C113—21no—
112C2×SD16×C113—22no—
113C2×SD16×C113—21no—
114C2×SD16×C113—22no—
115C2×SD16×C113—21no—
116C2×SD16×C113—21no—
117C2×SD16×C113—21no—
118C2×SD16×C113—21no—
119C2×SD16×C113D411yescharacteristic
120C2×SD16×C113D411yescharacteristic
121C2×D8×C113—21no—
122C2×D8×C113—22no—
123C2×D8×C113—21no—
124C2×D8×C113—21no—
125C2×D8×C113—21no—
126C2×D8×C113—21no—
127C2×D8×C113—41no—
128C2×D8×C113D411yescharacteristic
129#131×C113—22no—
130#131×C113—22no—
131#131×C113—22no—
132#131×C113—41no—
133C2×M16×C113—21no—
134C2×M16×C113—21no—
135C2×M16×C113C2311yescharacteristic
136C2×M16×C113C2311yescharacteristic
137C2×M16×C113C2311yescharacteristic
138C2×M16×C113C2311yescharacteristic
139C22×C8×C113—21no—
140C22×C8×C113—21no—
141C22×C8×C113C2311yescharacteristic
142C22×C8×C113C2311yescharacteristic
143#127×C113—21no—
144#124×C113—22no—
145#124×C113—21no—
146#124×C113—41no—
147#121×C113—21no—
148#121×C113—21no—
149#120×C113—41no—
150C4×Q8×C113—21no—
151C4×D4×C113—21no—
152C4×D4×C113—41no—
153#117×C113—21no—
154#117×C113C2311yescharacteristic
155C2×C4⋊C4×C113—21no—
156C2×C4⋊C4×C113C2311yescharacteristic
157C2×C22⋊C4×C113—41no—
158C2×C22⋊C4×C113—41no—
159C2×C42×C113C2311yescharacteristic
160#108×C113—22no—
161C4⋊C8×C113—21no—
162C4⋊C8×C113—21no—
163#104×C113—22no—
164#104×C113—22no—
165#104×C113—41no—
166#103×C113—21no—
167#103×C113—21no—
168#103×C113—21no—
169#103×C113—21no—
170#103×C113—21no—
171#103×C113—21no—
172#103×C113D411yescharacteristic
173#103×C113D411yescharacteristic
174#102×C113—21no—
175#102×C113—21no—
176#102×C113—21no—
177#102×C113—21no—
178#102×C113—21no—
179#102×C113—21no—
180#102×C113D411yescharacteristic
181#102×C113D411yescharacteristic
182#101×C113—22no—
183#100×C113—22no—
184#100×C113—22no—
185C22⋊C8×C113—21no—
186C22⋊C8×C113—21no—
187C24×C113—21no—
188C24×C113—21no—
189C24×C113—41no—
190#41×C113—21no—
191#41×C113—21no—
192#41×C113—21no—
193#41×C113—21no—
194#41×C113—24no—
195#41×C113—24no—
196#41×C113—24no—
197#41×C113—21no—
198#41×C113—21no—
199#41×C113—21no—
200#41×C113—21no—
201#41×C113—44no—
202#41×C113—42no—
203#41×C113—42no—
204#41×C113—42no—
205#41×C113—44no—
206#41×C113—42no—
207#41×C113—42no—
208#41×C113C2×D412yes—
209#41×C113C2×D412yes—
210#41×C113C2×D412yes—
211#41×C113#4112yes—
212C2×Q8×C113—21no—
213C2×Q8×C113—24no—
214C2×Q8×C113—24no—
215C2×Q8×C113—21no—
216C2×Q8×C113—21no—
217C2×Q8×C113—21no—
218C2×Q8×C113—21no—
219C2×Q8×C113—41no—
220C2×Q8×C113—42no—
221C2×Q8×C113—42no—
222C2×Q8×C113C2×D412yes—
223C2×Q8×C113C2×D411yescharacteristic
224C2×Q8×C113C2×D411yescharacteristic
225C2×Q8×C113C2×D411yescharacteristic
226C2×D4×C113—21no—
227C2×D4×C113—21no—
228C2×D4×C113—24no—
229C2×D4×C113—21no—
230C2×D4×C113—21no—
231C2×D4×C113—21no—
232C2×D4×C113—21no—
233C2×D4×C113—21no—
234C2×D4×C113—21no—
235C2×D4×C113—21no—
236C2×D4×C113—21no—
237C2×D4×C113—21no—
238C2×D4×C113—21no—
239C2×D4×C113—21no—
240C2×D4×C113—21no—
241C2×D4×C113—42no—
242C2×D4×C113—41no—
243C2×D4×C113—41no—
244C2×D4×C113—41no—
245C2×D4×C113—41no—
246C2×D4×C113—42no—
247C2×D4×C113—44no—
248C2×D4×C113—44no—
249C2×D4×C113—41no—
250C2×D4×C113—42no—
251C2×D4×C113C2×D412yes—
252C2×D4×C113C2×D411yescharacteristic
253C2×D4×C113C2×D411yescharacteristic
254C2×D4×C113C2×D411yescharacteristic
255C22×C4×C113—21no—
256C22×C4×C113—21no—
257C22×C4×C113—21no—
258C22×C4×C113—21no—
259C22×C4×C113—21no—
260C22×C4×C113—21no—
261C22×C4×C113—41no—
262C22×C4×C113—41no—
263C22×C4×C113—41no—
264C22×C4×C113—41no—
265C22×C4×C113C2411yescharacteristic
266Q16×C113—24no—
267Q16×C113—22no—
268SD16×C113—24no—
269SD16×C113—24no—
270SD16×C113—24no—
271SD16×C113—22no—
272SD16×C113—24no—
273SD16×C113—22no—
274SD16×C113—42no—
275SD16×C113—42no—
276D8×C113—24no—
277D8×C113—22no—
278D8×C113—42no—
279D8×C113—42no—
280D8×C113—42no—
281D8×C113—42no—
282M16×C113—24no—
283M16×C113—21no—
284M16×C113—21no—
285M16×C113—21no—
286M16×C113—21no—
287M16×C113—21no—
288M16×C113—21no—
289M16×C113—21no—
290M16×C113—42no—
291M16×C113C2×D412yes—
292C2×C8×C113—24no—
293C2×C8×C113—21no—
294C2×C8×C113—21no—
295C2×C8×C113—21no—
296C2×C8×C113—21no—
297C2×C8×C113—21no—
298C2×C8×C113—21no—
299C2×C8×C113—21no—
300C2×C8×C113—21no—
301C2×C8×C113—42no—
302C2×C8×C113C2×D411yescharacteristic
303C2×C8×C113C2×D411yescharacteristic
304C2×C8×C113C2×D411yescharacteristic
305C2×C8×C113C2×D411yescharacteristic
306C4⋊C4×C113—21no—
307C4⋊C4×C113—21no—
308C4⋊C4×C113—41no—
309C4⋊C4×C113C2×D411yescharacteristic
310C4⋊C4×C113C2×D411yescharacteristic
311C22⋊C4×C113—21no—
312C22⋊C4×C113—41no—
313C22⋊C4×C113—41no—
314C22⋊C4×C113—41no—
315C22⋊C4×C113—44no—
316C22⋊C4×C113—82no—
317C42×C113—21no—
318C42×C113—21no—
319C42×C113—21no—
320C42×C113—41no—
321C23×C113—21no—
322C23×C113—21no—
323C23×C113—21no—
324C23×C113—22no—
325C23×C113—44no—
326C23×C113—41no—
327C23×C113—41no—
328C23×C113—41no—
329C23×C113—41no—
330C23×C113—41no—
331C23×C113—81no—
332C23×C113—81no—
333C23×C113—81no—
334C23×C113—81no—
335C23×C113—161no—
336C23×C113—161no—
337C23×C113H(5,𝔽2)11yescharacteristic
338Q8×C113—21no—
339Q8×C113—21no—
340Q8×C113—22no—
341Q8×C113—21no—
342Q8×C113—22no—
343Q8×C113—21no—
344Q8×C113—44no—
345Q8×C113—41no—
346Q8×C113—41no—
347Q8×C113#12012yes—
348Q8×C113#12112yes—
349D4×C113—22no—
350D4×C113—22no—
351D4×C113—22no—
352D4×C113—22no—
353D4×C113—22no—
354D4×C113—21no—
355D4×C113—21no—
356D4×C113—22no—
357D4×C113—21no—
358D4×C113—21no—
359D4×C113—44no—
360D4×C113—44no—
361D4×C113—44no—
362D4×C113—41no—
363D4×C113—41no—
364D4×C113—41no—
365D4×C113—41no—
366D4×C113—41no—
367D4×C113—41no—
368D4×C113—41no—
369D4×C113—41no—
370D4×C113—161no—
371D4×C113—161no—
372D4×C113#12012yes—
373D4×C113#12112yes—
374C2×C4×C113—21no—
375C2×C4×C113—21no—
376C2×C4×C113—22no—
377C2×C4×C113—22no—
378C2×C4×C113—22no—
379C2×C4×C113—22no—
380C2×C4×C113—22no—
381C2×C4×C113—21no—
382C2×C4×C113—21no—
383C2×C4×C113—21no—
384C2×C4×C113—44no—
385C2×C4×C113—44no—
386C2×C4×C113—44no—
387C2×C4×C113—41no—
388C2×C4×C113—41no—
389C2×C4×C113—41no—
390C2×C4×C113—41no—
391C2×C4×C113—41no—
392C2×C4×C113—41no—
393C2×C4×C113—41no—
394C2×C4×C113—41no—
395C2×C4×C113—81no—
396C2×C4×C113—161no—
397C2×C4×C113C22×D411yescharacteristic
398C2×C4×C113C22×D411yescharacteristic
399C2×C4×C113C22×D411yescharacteristic
400C2×C4×C113C22×D411yescharacteristic
401C2×C4×C113C2×#4111yescharacteristic
402C2×C4×C113H(5,𝔽2)11yescharacteristic
403C8×C113—21no—
404C8×C113—22no—
405C8×C113—21no—
406C8×C113—21no—
407C8×C113—21no—
408C8×C113—41no—
409C8×C113—41no—
410C8×C113—41no—
411C22×C113—21no—
412C22×C113—21no—
413C22×C113—22no—
414C22×C113—22no—
415C22×C113—41no—
416C22×C113—41no—
417C22×C113—41no—
418C22×C113—41no—
419C22×C113—41no—
420C22×C113—42no—
421C22×C113—41no—
422C22×C113—41no—
423C22×C113—82no—
424C22×C113—82no—
425C22×C113—81no—
426C22×C113—81no—
427C22×C113—81no—
428C22×C113—81no—
429C22×C113—81no—
430C22×C113—161no—
431C22×C113—161no—
432C22×C113—164no—
433C22×C113#53411yescharacteristic
434C22×C113D4211yescharacteristic
435C22×C113#54611yescharacteristic
436C4×C113—22no—
437C4×C113—22no—
438C4×C113—41no—
439C4×C113—42no—
440C4×C113—41no—
441C4×C113—41no—
442C4×C113—81no—
443C4×C113—81no—
444C4×C113C2×#12011yescharacteristic
445C4×C113C2×#12111yescharacteristic
446C4×C113D4211yescharacteristic
447C4×C113#54611yescharacteristic
448#24460C11311yesmaximal, characteristic, direct product factor, Sylow
449C2×C113—21no—
450C2×C113—21no—
451C2×C113—42no—
452C2×C113—42no—
453C2×C113—81no—
454C2×C113—82no—
455C2×C113—161no—
456C2×C113#241011yescharacteristic
457C2×C113#328811yescharacteristic
458C2×C113#329011yescharacteristic
459C2×#577C2×C11311yescharacteristic, complemented
460C2×#472C2×C11311yescharacteristic, complemented
461#3045C2×C11311yescharacteristic, complemented
462C2×#454C2×C11311yescharacteristic, complemented
463#3008C2×C11311yescharacteristic, complemented
464#2898C2×C11311yescharacteristic, complemented
465#2052C2×C11311yescharacteristic, complemented
466#2046C2×C11311yescharacteristic, complemented
467#2012C2×C11311yescharacteristic, complemented
468#2004C2×C11311yescharacteristic, complemented
469#1907C2×C11311yescharacteristic, complemented
470#1883C2×C11311yescharacteristic, complemented
471#1876C2×C11311yescharacteristic, complemented
472#1866C2×C11311yescharacteristic, complemented
473#1792C2×C11311yescharacteristic, complemented
474C113#2446011yescharacteristic, direct product factor, Sylow
475C2×2−1+4C22×C11311yescharacteristic
476C2×H(5,𝔽2)C22×C11311yescharacteristic
477#577—24no—
478#577—24no—
479C2×#137—21no—
480C2×#137C22×C11311yescharacteristic
481C2×AGL(1,ℤ/8)—21no—
482C2×AGL(1,ℤ/8)C22×C11311yescharacteristic
483C2×AGL(1,ℤ/8)C22×C11311yescharacteristic
484C2×AGL(1,ℤ/8)C22×C11311yescharacteristic, complemented
485C2×#135—21no—
486C2×#135C22×C11311yescharacteristic
487C22×SD16—21no—
488C22×SD16C22×C11311yescharacteristic
489C22×D8C22×C11311yescharacteristic
490C2×#131C22×C11311yescharacteristic
491C2×#131C22×C11311yescharacteristic, complemented
492#535C22×C11311yescharacteristic
493C2×#124C22×C11311yescharacteristic, complemented
494#520C22×C11311yescharacteristic, complemented
495#472—24no—
496#464—21no—
497#463—21no—
498#460—21no—
499#459—21no—
500#454—24no—
501#449—21no—
502#449—21no—
503#447—21no—
504#447—21no—
505C2×#108C22×C11311yescharacteristic, complemented
506#424C22×C11311yescharacteristic, complemented
507C2×#104C22×C11311yescharacteristic
508C2×#104C22×C11311yescharacteristic
509C2×#104C22×C11311yescharacteristic, complemented
510#419—21no—
511#419C22×C11311yescharacteristic, complemented
512#418C22×C11311yescharacteristic
513#417—21no—
514#417C22×C11311yescharacteristic
515#417C22×C11311yescharacteristic
516#416—21no—
517#416C22×C11311yescharacteristic
518C2×#103—21no—
519C2×#103C22×C11311yescharacteristic, complemented
520C2×#102C22×C11311yescharacteristic, complemented
521C2×#101C22×C11311yescharacteristic, complemented
522C2×#100C22×C11311yescharacteristic
523C2×#100C22×C11311yescharacteristic, complemented
524#408C22×C11311yescharacteristic
525#390C22×C11311yescharacteristic
526#343C22×C11311yescharacteristic, complemented
527#341C22×C11311yescharacteristic, complemented
528#339C22×C11311yescharacteristic, complemented
529#336C22×C11311yescharacteristic, complemented
5302−1+4—22no—
5312−1+4—22no—
5322−1+4—41no—
5332−1+4D4×C11314yescomplemented
534H(5,𝔽2)—22no—
535H(5,𝔽2)—22no—
536H(5,𝔽2)—22no—
537H(5,𝔽2)—41no—
538C2×#41—21no—
539C2×#41—21no—
540C2×#41—21no—
541C2×#41—21no—
542C2×#41—41no—
543C2×#41C23×C11311yescharacteristic
544C2×#41C23×C11311yescharacteristic
545C2×#41C23×C11311yescharacteristic
546C22×Q8—21no—
547C22×Q8—21no—
548C22×Q8C23×C11311yescharacteristic
549C22×D4—21no—
550C22×D4—21no—
551C22×D4—41no—
552C22×D4C23×C11311yescharacteristic
553C22×D4C23×C11311yescharacteristic
554#137—28no—
555#137—22no—
556#137—22no—
557AGL(1,ℤ/8)—28no—
558AGL(1,ℤ/8)—22no—
559AGL(1,ℤ/8)—22no—
560AGL(1,ℤ/8)—22no—
561AGL(1,ℤ/8)—22no—
562AGL(1,ℤ/8)—22no—
563AGL(1,ℤ/8)D4×C11314yescomplemented
564#135—28no—
565#135—22no—
566#135—22no—
567C2×Q16—21no—
568C2×Q16D4×C11311yescharacteristic
569C2×SD16—28no—
570C2×SD16—21no—
571C2×SD16—22no—
572C2×SD16—21no—
573C2×SD16—22no—
574C2×SD16—21no—
575C2×SD16—21no—
576C2×SD16—21no—
577C2×SD16—21no—
578C2×SD16D4×C11311yescharacteristic
579C2×SD16D4×C11311yescharacteristic
580C2×D8—21no—
581C2×D8—22no—
582C2×D8—21no—
583C2×D8—21no—
584C2×D8—21no—
585C2×D8—21no—
586C2×D8—41no—
587C2×D8D4×C11311yescharacteristic
588#131—22no—
589#131—22no—
590#131—22no—
591#131—41no—
592C2×M16—21no—
593C2×M16—21no—
594C2×M16C23×C11311yescharacteristic
595C2×M16C23×C11311yescharacteristic
596C2×M16C23×C11311yescharacteristic
597C2×M16C23×C11311yescharacteristic
598C22×C8—21no—
599C22×C8—21no—
600C22×C8C23×C11311yescharacteristic
601C22×C8C23×C11311yescharacteristic
602#127—21no—
603#124—22no—
604#124—21no—
605#124—41no—
606#121—21no—
607#121—21no—
608#120—41no—
609C4×Q8—21no—
610C4×D4—21no—
611C4×D4—41no—
612#117—21no—
613#117C23×C11311yescharacteristic
614C2×C4⋊C4—21no—
615C2×C4⋊C4C23×C11311yescharacteristic
616C2×C22⋊C4—41no—
617C2×C22⋊C4—41no—
618C2×C42C23×C11311yescharacteristic
619#108—22no—
620C4⋊C8—21no—
621C4⋊C8—21no—
622#104—22no—
623#104—22no—
624#104—41no—
625#103—21no—
626#103—21no—
627#103—21no—
628#103—21no—
629#103—21no—
630#103—21no—
631#103D4×C11311yescharacteristic
632#103D4×C11311yescharacteristic
633#102—21no—
634#102—21no—
635#102—21no—
636#102—21no—
637#102—21no—
638#102—21no—
639#102D4×C11311yescharacteristic
640#102D4×C11311yescharacteristic
641#101—22no—
642#100—22no—
643#100—22no—
644C22⋊C8—21no—
645C22⋊C8—21no—
646C24—21no—
647C24—21no—
648C24—41no—
649#41—21no—
650#41—21no—
651#41—21no—
652#41—21no—
653#41—24no—
654#41—24no—
655#41—24no—
656#41—21no—
657#41—21no—
658#41—21no—
659#41—21no—
660#41—44no—
661#41—42no—
662#41—42no—
663#41—42no—
664#41—44no—
665#41—42no—
666#41—42no—
667#41C2×D4×C11312yes—
668#41C2×D4×C11312yes—
669#41C2×D4×C11312yes—
670#41#41×C11312yes—
671C2×Q8—21no—
672C2×Q8—24no—
673C2×Q8—24no—
674C2×Q8—21no—
675C2×Q8—21no—
676C2×Q8—21no—
677C2×Q8—21no—
678C2×Q8—41no—
679C2×Q8—42no—
680C2×Q8—42no—
681C2×Q8C2×D4×C11312yes—
682C2×Q8C2×D4×C11311yescharacteristic
683C2×Q8C2×D4×C11311yescharacteristic
684C2×Q8C2×D4×C11311yescharacteristic
685C2×D4—21no—
686C2×D4—21no—
687C2×D4—24no—
688C2×D4—21no—
689C2×D4—21no—
690C2×D4—21no—
691C2×D4—21no—
692C2×D4—21no—
693C2×D4—21no—
694C2×D4—21no—
695C2×D4—21no—
696C2×D4—21no—
697C2×D4—21no—
698C2×D4—21no—
699C2×D4—21no—
700C2×D4—42no—
701C2×D4—41no—
702C2×D4—41no—
703C2×D4—41no—
704C2×D4—41no—
705C2×D4—42no—
706C2×D4—44no—
707C2×D4—44no—
708C2×D4—41no—
709C2×D4—42no—
710C2×D4C2×D4×C11312yes—
711C2×D4C2×D4×C11311yescharacteristic
712C2×D4C2×D4×C11311yescharacteristic
713C2×D4C2×D4×C11311yescharacteristic
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—41no—
721C22×C4—41no—
722C22×C4—41no—
723C22×C4—41no—
724C22×C4C24×C11311yescharacteristic
725Q16—24no—
726Q16—22no—
727SD16—24no—
728SD16—24no—
729SD16—24no—
730SD16—22no—
731SD16—24no—
732SD16—22no—
733SD16—42no—
734SD16—42no—
735D8—24no—
736D8—22no—
737D8—42no—
738D8—42no—
739D8—42no—
740D8—42no—
741M16—24no—
742M16—21no—
743M16—21no—
744M16—21no—
745M16—21no—
746M16—21no—
747M16—21no—
748M16—21no—
749M16—42no—
750M16C2×D4×C11312yes—
751C2×C8—24no—
752C2×C8—21no—
753C2×C8—21no—
754C2×C8—21no—
755C2×C8—21no—
756C2×C8—21no—
757C2×C8—21no—
758C2×C8—21no—
759C2×C8—21no—
760C2×C8—42no—
761C2×C8C2×D4×C11311yescharacteristic
762C2×C8C2×D4×C11311yescharacteristic
763C2×C8C2×D4×C11311yescharacteristic
764C2×C8C2×D4×C11311yescharacteristic
765C4⋊C4—21no—
766C4⋊C4—21no—
767C4⋊C4—41no—
768C4⋊C4C2×D4×C11311yescharacteristic
769C4⋊C4C2×D4×C11311yescharacteristic
770C22⋊C4—21no—
771C22⋊C4—41no—
772C22⋊C4—41no—
773C22⋊C4—41no—
774C22⋊C4—44no—
775C22⋊C4—82no—
776C42—21no—
777C42—21no—
778C42—21no—
779C42—41no—
780C23—21no—
781C23—21no—
782C23—21no—
783C23—22no—
784C23—44no—
785C23—41no—
786C23—41no—
787C23—41no—
788C23—41no—
789C23—41no—
790C23—81no—
791C23—81no—
792C23—81no—
793C23—81no—
794C23—161no—
795C23—161no—
796C23H(5,𝔽2)×C11311yescharacteristic
797Q8—21no—
798Q8—21no—
799Q8—22no—
800Q8—21no—
801Q8—22no—
802Q8—21no—
803Q8—44no—
804Q8—41no—
805Q8—41no—
806Q8#120×C11312yes—
807Q8#121×C11312yes—
808D4—22no—
809D4—22no—
810D4—22no—
811D4—22no—
812D4—22no—
813D4—21no—
814D4—21no—
815D4—22no—
816D4—21no—
817D4—21no—
818D4—44no—
819D4—44no—
820D4—44no—
821D4—41no—
822D4—41no—
823D4—41no—
824D4—41no—
825D4—41no—
826D4—41no—
827D4—41no—
828D4—41no—
829D4—161no—
830D4—161no—
831D4#120×C11312yes—
832D4#121×C11312yes—
833C2×C4—21no—
834C2×C4—21no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—21no—
841C2×C4—21no—
842C2×C4—21no—
843C2×C4—44no—
844C2×C4—44no—
845C2×C4—44no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—81no—
855C2×C4—161no—
856C2×C4C22×D4×C11311yescharacteristic
857C2×C4C22×D4×C11311yescharacteristic
858C2×C4C22×D4×C11311yescharacteristic
859C2×C4C22×D4×C11311yescharacteristic
860C2×C4C2×#41×C11311yescharacteristic
861C2×C4H(5,𝔽2)×C11311yescharacteristic
862C8—21no—
863C8—22no—
864C8—21no—
865C8—21no—
866C8—21no—
867C8—41no—
868C8—41no—
869C8—41no—
870C22—21no—
871C22—21no—
872C22—22no—
873C22—22no—
874C22—41no—
875C22—41no—
876C22—41no—
877C22—41no—
878C22—41no—
879C22—42no—
880C22—41no—
881C22—41no—
882C22—82no—
883C22—82no—
884C22—81no—
885C22—81no—
886C22—81no—
887C22—81no—
888C22—81no—
889C22—161no—
890C22—161no—
891C22—164no—
892C22#534×C11311yescharacteristic
893C22D42×C11311yescharacteristic
894C22#546×C11311yescharacteristic
895C4—22no—
896C4—22no—
897C4—41no—
898C4—42no—
899C4—41no—
900C4—41no—
901C4—81no—
902C4—81no—
903C4C2×#120×C11311yescharacteristic
904C4C2×#121×C11311yescharacteristic
905C4D42×C11311yescharacteristic
906C4#546×C11311yescharacteristic
907C2—21no—
908C2—21no—
909C2—42no—
910C2—42no—
911C2—81no—
912C2—82no—
913C2—161no—
914C2C113×#241011yescharacteristic
915C2C113×#328811yescharacteristic
916C2C113×#329011yescharacteristic
subgroupG/H
center, socleC22×C113D42
commutator, Frattini, cosocleC22×C4C24×C113
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C113 ◁ C22×C4×C113 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#577×C113C2semidirect
2. C2×#472×C113C2semidirect
3. C113×#3045C2semidirect
4. C2×#454×C113C2semidirect
5. C113×#3008C2semidirect
6. C113×#2898C2semidirect
7. C113×#2052C2semidirect
8. C113×#2046C2semidirect
9. C113×#2012C2semidirect
10. C113×#2004C2semidirect
11. C113×#1907C2semidirect
12. C113×#1883C2semidirect
13. C113×#1876C2semidirect
14. C113×#1866C2semidirect
15. C113×#1792C2semidirect
25. C2×AGL(1,ℤ/8)×C113C22semidirect
32. C2×#131×C113C22semidirect
34. C2×#124×C113C22semidirect
35. #520×C113C22semidirect
46. C2×#108×C113C22semidirect
47. #424×C113C22semidirect
50. C2×#104×C113C22semidirect
52. #419×C113C22semidirect
60. C2×#103×C113C22semidirect
61. C2×#102×C113C22semidirect
62. C2×#101×C113C22semidirect
64. C2×#100×C113C22semidirect
67. #343×C113C22semidirect
68. #341×C113C22semidirect
69. #339×C113C22semidirect
70. #336×C113C22semidirect
74. 2−1+4×C113D4semidirect
104. AGL(1,ℤ/8)×C113D4semidirect
448. #24460C113direct (N × H)
459. C2×#577C2×C113semidirect
460. C2×#472C2×C113semidirect
461. #3045C2×C113semidirect
462. C2×#454C2×C113semidirect
463. #3008C2×C113semidirect
464. #2898C2×C113semidirect
465. #2052C2×C113semidirect
466. #2046C2×C113semidirect
467. #2012C2×C113semidirect
468. #2004C2×C113semidirect
469. #1907C2×C113semidirect
470. #1883C2×C113semidirect
471. #1876C2×C113semidirect
472. #1866C2×C113semidirect
473. #1792C2×C113semidirect
474. C113#24460direct (N × H)
484. C2×AGL(1,ℤ/8)C22×C113semidirect
491. C2×#131C22×C113semidirect
493. C2×#124C22×C113semidirect
494. #520C22×C113semidirect
505. C2×#108C22×C113semidirect
506. #424C22×C113semidirect
509. C2×#104C22×C113semidirect
511. #419C22×C113semidirect
519. C2×#103C22×C113semidirect
520. C2×#102C22×C113semidirect
521. C2×#101C22×C113semidirect
523. C2×#100C22×C113semidirect
526. #343C22×C113semidirect
527. #341C22×C113semidirect
528. #339C22×C113semidirect
529. #336C22×C113semidirect
533. 2−1+4D4×C113semidirect
563. AGL(1,ℤ/8)D4×C113semidirect

Maximal subgroups

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

subgroupindex
C2×#577×C1132
C2×#472×C1132
C113×#30452
C2×#454×C1132
C113×#30082
C113×#28982
C113×#20522
C113×#20462
C113×#20122
C113×#20042
C113×#19072
C113×#18832
C113×#18762
C113×#18662
C113×#17922
#24460113