Finite Group Databasebeta

← C113×#24459 #43292479

Subgroups — C113×#24459 #43292479

Order 28928.

1362 conjugacy classes of subgroups.

The subgroup lattice has 920 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#576×C113C211yesmaximal, characteristic
2C2×#471×C113C211yesmaximal, characteristic, complemented
3C113×#3046C211yesmaximal, characteristic, complemented
4C2×#455×C113C211yesmaximal, characteristic, complemented
5C113×#3009C211yesmaximal, characteristic, complemented
6C113×#2897C211yesmaximal, characteristic, complemented
7C113×#2051C211yesmaximal, characteristic, complemented
8C113×#2045C211yesmaximal, characteristic, complemented
9C113×#2012C211yesmaximal, characteristic, complemented
10C113×#2003C211yesmaximal, characteristic, complemented
11C113×#1908C211yesmaximal, characteristic, complemented
12C113×#1883C211yesmaximal, characteristic, complemented
13C113×#1876C211yesmaximal, characteristic, complemented
14C113×#1866C211yesmaximal, characteristic, complemented
15C113×#1792C211yesmaximal, characteristic, complemented
16C2×H(5,𝔽2)×C113C2211yescharacteristic
17C2×H(5,𝔽2)×C113C2211yescharacteristic
18#576×C113—24no—
19#576×C113—24no—
20C2×#137×C113C2211yescharacteristic
21C2×#137×C113C2211yescharacteristic, complemented
22C2×AGL(1,ℤ/8)×C113—21no—
23C2×AGL(1,ℤ/8)×C113—21no—
24C2×AGL(1,ℤ/8)×C113C2211yescharacteristic
25C2×AGL(1,ℤ/8)×C113C2211yescharacteristic
26C2×#135×C113—21no—
27C2×#135×C113C2211yescharacteristic
28C22×SD16×C113C2211yescharacteristic, complemented
29C22×D8×C113—21no—
30C22×D8×C113C2211yescharacteristic
31C2×#131×C113C2211yescharacteristic
32C2×#131×C113C2211yescharacteristic, complemented
33#536×C113C2211yescharacteristic, complemented
34C2×#124×C113C2211yescharacteristic, complemented
35#520×C113C2211yescharacteristic, complemented
36#471×C113—24no—
37#464×C113—21no—
38#463×C113—21no—
39#462×C113—21no—
40#461×C113—21no—
41#455×C113—24no—
42#452×C113—21no—
43#452×C113—21no—
44#450×C113—21no—
45#450×C113—21no—
46C2×#108×C113C2211yescharacteristic, complemented
47#424×C113C2211yescharacteristic, complemented
48C2×#104×C113C2211yescharacteristic
49C2×#104×C113C2211yescharacteristic, complemented
50C2×#104×C113C2211yescharacteristic, complemented
51#418×C113—21no—
52#418×C113C2211yescharacteristic, complemented
53#418×C113C2211yescharacteristic, complemented
54#417×C113—21no—
55#417×C113C2211yescharacteristic
56#417×C113C2211yescharacteristic, complemented
57#416×C113—21no—
58#416×C113C2211yescharacteristic
59C2×#103×C113C2211yescharacteristic, complemented
60C2×#102×C113—21no—
61C2×#102×C113C2211yescharacteristic, complemented
62C2×#101×C113C2211yescharacteristic, complemented
63C2×#100×C113C2211yescharacteristic, complemented
64C2×#100×C113C2211yescharacteristic, complemented
65#408×C113C2211yescharacteristic, complemented
66#390×C113C2211yescharacteristic, complemented
67#343×C113C2211yescharacteristic, complemented
68#341×C113C2211yescharacteristic, complemented
69#339×C113C2211yescharacteristic, complemented
70#336×C113C2211yescharacteristic, complemented
71H(5,𝔽2)×C113—22no—
72H(5,𝔽2)×C113—22no—
73H(5,𝔽2)×C113—22no—
74H(5,𝔽2)×C113—22no—
75H(5,𝔽2)×C113—22no—
76H(5,𝔽2)×C113—41no—
77H(5,𝔽2)×C113—41no—
78H(5,𝔽2)×C113D414yes—
79C2×#41×C113—21no—
80C2×#41×C113—21no—
81C2×#41×C113—21no—
82C2×#41×C113—21no—
83C2×#41×C113C2311yescharacteristic
84C2×#41×C113C2311yescharacteristic
85C2×#41×C113C2311yescharacteristic
86C22×Q8×C113C2311yescharacteristic
87C22×D4×C113—21no—
88C22×D4×C113—21no—
89C22×D4×C113—21no—
90C22×D4×C113—21no—
91C22×D4×C113—41no—
92C22×D4×C113—41no—
93C22×D4×C113C2311yescharacteristic
94C22×D4×C113C2311yescharacteristic
95#137×C113—22no—
96#137×C113—22no—
97#137×C113—22no—
98#137×C113—22no—
99AGL(1,ℤ/8)×C113—28no—
100AGL(1,ℤ/8)×C113—28no—
101AGL(1,ℤ/8)×C113—22no—
102AGL(1,ℤ/8)×C113—22no—
103AGL(1,ℤ/8)×C113—22no—
104AGL(1,ℤ/8)×C113D414yes—
105#135×C113—28no—
106#135×C113—22no—
107#135×C113—22no—
108C2×Q16×C113—21no—
109C2×Q16×C113—21no—
110C2×Q16×C113D411yescharacteristic
111C2×SD16×C113—21no—
112C2×SD16×C113—21no—
113C2×SD16×C113—22no—
114C2×SD16×C113—21no—
115C2×SD16×C113—21no—
116C2×SD16×C113—21no—
117C2×SD16×C113—21no—
118C2×SD16×C113—41no—
119C2×SD16×C113D411yescharacteristic
120C2×SD16×C113D411yescharacteristic
121C2×D8×C113—28no—
122C2×D8×C113—21no—
123C2×D8×C113—21no—
124C2×D8×C113—22no—
125C2×D8×C113—22no—
126C2×D8×C113—21no—
127C2×D8×C113—21no—
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
143C4⋊Q8×C113—21no—
144#124×C113—22no—
145#124×C113—21no—
146#124×C113—41no—
147#123×C113—41no—
148C22⋊Q8×C113—21no—
149C22⋊Q8×C113—21no—
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×C113D411yescharacteristic
171#103×C113D411yescharacteristic
172#102×C113—21no—
173#102×C113—21no—
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—
190C24×C113—41no—
191#41×C113—21no—
192#41×C113—21no—
193#41×C113—21no—
194#41×C113—21no—
195#41×C113—24no—
196#41×C113—24no—
197#41×C113—24no—
198#41×C113—21no—
199#41×C113—21no—
200#41×C113—21no—
201#41×C113—21no—
202#41×C113—42no—
203#41×C113—42no—
204#41×C113—42no—
205#41×C113—42no—
206#41×C113—42no—
207#41×C113C2×D412yes—
208#41×C113C2×D412yes—
209#41×C113C2×D412yes—
210#41×C113#4112yes—
211C2×Q8×C113—21no—
212C2×Q8×C113—21no—
213C2×Q8×C113—21no—
214C2×Q8×C113—21no—
215C2×Q8×C113—21no—
216C2×Q8×C113—21no—
217C2×Q8×C113C2×D411yescharacteristic
218C2×Q8×C113C2×D411yescharacteristic
219C2×Q8×C113C2×D411yescharacteristic
220C2×D4×C113—21no—
221C2×D4×C113—21no—
222C2×D4×C113—24no—
223C2×D4×C113—24no—
224C2×D4×C113—24no—
225C2×D4×C113—21no—
226C2×D4×C113—21no—
227C2×D4×C113—21no—
228C2×D4×C113—21no—
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—42no—
237C2×D4×C113—42no—
238C2×D4×C113—42no—
239C2×D4×C113—41no—
240C2×D4×C113—41no—
241C2×D4×C113—41no—
242C2×D4×C113—41no—
243C2×D4×C113—44no—
244C2×D4×C113—42no—
245C2×D4×C113—44no—
246C2×D4×C113—44no—
247C2×D4×C113—44no—
248C2×D4×C113—42no—
249C2×D4×C113C2×D412yes—
250C2×D4×C113C2×D412yes—
251C2×D4×C113C2×D411yescharacteristic
252C2×D4×C113C2×D411yescharacteristic
253C2×D4×C113C2×D411yescharacteristic
254C22×C4×C113—21no—
255C22×C4×C113—21no—
256C22×C4×C113—21no—
257C22×C4×C113—21no—
258C22×C4×C113—21no—
259C22×C4×C113—21no—
260C22×C4×C113—41no—
261C22×C4×C113—41no—
262C22×C4×C113—41no—
263C22×C4×C113C2411yescharacteristic
264Q16×C113—22no—
265Q16×C113—42no—
266Q16×C113—42no—
267SD16×C113—24no—
268SD16×C113—24no—
269SD16×C113—22no—
270SD16×C113—22no—
271SD16×C113—42no—
272SD16×C113—42no—
273SD16×C113—42no—
274SD16×C113—42no—
275D8×C113—24no—
276D8×C113—24no—
277D8×C113—24no—
278D8×C113—22no—
279D8×C113—24no—
280M16×C113—24no—
281M16×C113—21no—
282M16×C113—21no—
283M16×C113—21no—
284M16×C113—21no—
285M16×C113—21no—
286M16×C113—21no—
287M16×C113—21no—
288M16×C113—42no—
289M16×C113C2×D412yes—
290C2×C8×C113—24no—
291C2×C8×C113—21no—
292C2×C8×C113—21no—
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—42no—
300C2×C8×C113C2×D411yescharacteristic
301C2×C8×C113C2×D411yescharacteristic
302C2×C8×C113C2×D411yescharacteristic
303C2×C8×C113C2×D411yescharacteristic
304C4⋊C4×C113—21no—
305C4⋊C4×C113—21no—
306C4⋊C4×C113—41no—
307C4⋊C4×C113—41no—
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—22no—
326C23×C113—44no—
327C23×C113—44no—
328C23×C113—41no—
329C23×C113—41no—
330C23×C113—41no—
331C23×C113—41no—
332C23×C113—81no—
333C23×C113—81no—
334C23×C113—81no—
335C23×C113—81no—
336C23×C113—161no—
337C23×C113—161no—
338C23×C113—161no—
339C23×C113—161no—
340C23×C113H(5,𝔽2)11yescharacteristic
341Q8×C113—21no—
342Q8×C113—21no—
343Q8×C113—21no—
344Q8×C113—21no—
345Q8×C113—41no—
346Q8×C113—41no—
347Q8×C113—41no—
348Q8×C113—41no—
349Q8×C113#12012yes—
350Q8×C113#12112yes—
351D4×C113—22no—
352D4×C113—22no—
353D4×C113—22no—
354D4×C113—22no—
355D4×C113—22no—
356D4×C113—22no—
357D4×C113—21no—
358D4×C113—22no—
359D4×C113—21no—
360D4×C113—22no—
361D4×C113—21no—
362D4×C113—21no—
363D4×C113—44no—
364D4×C113—44no—
365D4×C113—44no—
366D4×C113—44no—
367D4×C113—41no—
368D4×C113—41no—
369D4×C113—41no—
370D4×C113—41no—
371D4×C113—41no—
372D4×C113—41no—
373D4×C113#12012yes—
374D4×C113#12112yes—
375C2×C4×C113—21no—
376C2×C4×C113—21no—
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—41no—
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—42no—
422C22×C113—41no—
423C22×C113—41no—
424C22×C113—82no—
425C22×C113—82no—
426C22×C113—81no—
427C22×C113—81no—
428C22×C113—81no—
429C22×C113—81no—
430C22×C113—161no—
431C22×C113—161no—
432C22×C113—164no—
433C22×C113—164no—
434C22×C113#53411yescharacteristic
435C22×C113D4211yescharacteristic
436C22×C113#54611yescharacteristic
437C4×C113—22no—
438C4×C113—22no—
439C4×C113—41no—
440C4×C113—41no—
441C4×C113—41no—
442C4×C113—81no—
443C4×C113—81no—
444C4×C113—81no—
445C4×C113C2×#12011yescharacteristic
446C4×C113C2×#12111yescharacteristic
447C4×C113D4211yescharacteristic
448C4×C113#54611yescharacteristic
449#24459C11311yesmaximal, characteristic, direct product factor, Sylow
450C2×C113—21no—
451C2×C113—21no—
452C2×C113—42no—
453C2×C113—42no—
454C2×C113—81no—
455C2×C113—82no—
456C2×C113—82no—
457C2×C113#241011yescharacteristic
458C2×C113#328811yescharacteristic
459C2×C113#329011yescharacteristic
460C2×#576C2×C11311yescharacteristic
461C2×#471C2×C11311yescharacteristic, complemented
462#3046C2×C11311yescharacteristic, complemented
463C2×#455C2×C11311yescharacteristic, complemented
464#3009C2×C11311yescharacteristic, complemented
465#2897C2×C11311yescharacteristic, complemented
466#2051C2×C11311yescharacteristic, complemented
467#2045C2×C11311yescharacteristic, complemented
468#2012C2×C11311yescharacteristic, complemented
469#2003C2×C11311yescharacteristic, complemented
470#1908C2×C11311yescharacteristic, complemented
471#1883C2×C11311yescharacteristic, complemented
472#1876C2×C11311yescharacteristic, complemented
473#1866C2×C11311yescharacteristic, complemented
474#1792C2×C11311yescharacteristic, complemented
475C113#2445911yescharacteristic, direct product factor, Sylow
476C2×H(5,𝔽2)C22×C11311yescharacteristic
477C2×H(5,𝔽2)C22×C11311yescharacteristic
478#576—24no—
479#576—24no—
480C2×#137C22×C11311yescharacteristic
481C2×#137C22×C11311yescharacteristic, complemented
482C2×AGL(1,ℤ/8)—21no—
483C2×AGL(1,ℤ/8)—21no—
484C2×AGL(1,ℤ/8)C22×C11311yescharacteristic
485C2×AGL(1,ℤ/8)C22×C11311yescharacteristic
486C2×#135—21no—
487C2×#135C22×C11311yescharacteristic
488C22×SD16C22×C11311yescharacteristic, complemented
489C22×D8—21no—
490C22×D8C22×C11311yescharacteristic
491C2×#131C22×C11311yescharacteristic
492C2×#131C22×C11311yescharacteristic, complemented
493#536C22×C11311yescharacteristic, complemented
494C2×#124C22×C11311yescharacteristic, complemented
495#520C22×C11311yescharacteristic, complemented
496#471—24no—
497#464—21no—
498#463—21no—
499#462—21no—
500#461—21no—
501#455—24no—
502#452—21no—
503#452—21no—
504#450—21no—
505#450—21no—
506C2×#108C22×C11311yescharacteristic, complemented
507#424C22×C11311yescharacteristic, complemented
508C2×#104C22×C11311yescharacteristic
509C2×#104C22×C11311yescharacteristic, complemented
510C2×#104C22×C11311yescharacteristic, complemented
511#418—21no—
512#418C22×C11311yescharacteristic, complemented
513#418C22×C11311yescharacteristic, complemented
514#417—21no—
515#417C22×C11311yescharacteristic
516#417C22×C11311yescharacteristic, complemented
517#416—21no—
518#416C22×C11311yescharacteristic
519C2×#103C22×C11311yescharacteristic, complemented
520C2×#102—21no—
521C2×#102C22×C11311yescharacteristic, complemented
522C2×#101C22×C11311yescharacteristic, complemented
523C2×#100C22×C11311yescharacteristic, complemented
524C2×#100C22×C11311yescharacteristic, complemented
525#408C22×C11311yescharacteristic, complemented
526#390C22×C11311yescharacteristic, complemented
527#343C22×C11311yescharacteristic, complemented
528#341C22×C11311yescharacteristic, complemented
529#339C22×C11311yescharacteristic, complemented
530#336C22×C11311yescharacteristic, complemented
531H(5,𝔽2)—22no—
532H(5,𝔽2)—22no—
533H(5,𝔽2)—22no—
534H(5,𝔽2)—22no—
535H(5,𝔽2)—22no—
536H(5,𝔽2)—41no—
537H(5,𝔽2)—41no—
538H(5,𝔽2)D4×C11314yes—
539C2×#41—21no—
540C2×#41—21no—
541C2×#41—21no—
542C2×#41—21no—
543C2×#41C23×C11311yescharacteristic
544C2×#41C23×C11311yescharacteristic
545C2×#41C23×C11311yescharacteristic
546C22×Q8C23×C11311yescharacteristic
547C22×D4—21no—
548C22×D4—21no—
549C22×D4—21no—
550C22×D4—21no—
551C22×D4—41no—
552C22×D4—41no—
553C22×D4C23×C11311yescharacteristic
554C22×D4C23×C11311yescharacteristic
555#137—22no—
556#137—22no—
557#137—22no—
558#137—22no—
559AGL(1,ℤ/8)—28no—
560AGL(1,ℤ/8)—28no—
561AGL(1,ℤ/8)—22no—
562AGL(1,ℤ/8)—22no—
563AGL(1,ℤ/8)—22no—
564AGL(1,ℤ/8)D4×C11314yes—
565#135—28no—
566#135—22no—
567#135—22no—
568C2×Q16—21no—
569C2×Q16—21no—
570C2×Q16D4×C11311yescharacteristic
571C2×SD16—21no—
572C2×SD16—21no—
573C2×SD16—22no—
574C2×SD16—21no—
575C2×SD16—21no—
576C2×SD16—21no—
577C2×SD16—21no—
578C2×SD16—41no—
579C2×SD16D4×C11311yescharacteristic
580C2×SD16D4×C11311yescharacteristic
581C2×D8—28no—
582C2×D8—21no—
583C2×D8—21no—
584C2×D8—22no—
585C2×D8—22no—
586C2×D8—21no—
587C2×D8—21no—
588C2×D8D4×C11311yescharacteristic
589#131—22no—
590#131—22no—
591#131—22no—
592#131—41no—
593C2×M16—21no—
594C2×M16—21no—
595C2×M16C23×C11311yescharacteristic
596C2×M16C23×C11311yescharacteristic
597C2×M16C23×C11311yescharacteristic
598C2×M16C23×C11311yescharacteristic
599C22×C8—21no—
600C22×C8—21no—
601C22×C8C23×C11311yescharacteristic
602C22×C8C23×C11311yescharacteristic
603C4⋊Q8—21no—
604#124—22no—
605#124—21no—
606#124—41no—
607#123—41no—
608C22⋊Q8—21no—
609C22⋊Q8—21no—
610C4×Q8—21no—
611C4×D4—21no—
612C4×D4—41no—
613#117—21no—
614#117C23×C11311yescharacteristic
615C2×C4⋊C4—21no—
616C2×C4⋊C4C23×C11311yescharacteristic
617C2×C22⋊C4—41no—
618C2×C22⋊C4—41no—
619C2×C42C23×C11311yescharacteristic
620#108—22no—
621C4⋊C8—21no—
622C4⋊C8—21no—
623#104—22no—
624#104—22no—
625#104—41no—
626#103—21no—
627#103—21no—
628#103—21no—
629#103—21no—
630#103D4×C11311yescharacteristic
631#103D4×C11311yescharacteristic
632#102—21no—
633#102—21no—
634#102—21no—
635#102—21no—
636#102—21no—
637#102—21no—
638#102—21no—
639#102—21no—
640#102D4×C11311yescharacteristic
641#102D4×C11311yescharacteristic
642#101—22no—
643#100—22no—
644#100—22no—
645C22⋊C8—21no—
646C22⋊C8—21no—
647C24—21no—
648C24—21no—
649C24—41no—
650C24—41no—
651#41—21no—
652#41—21no—
653#41—21no—
654#41—21no—
655#41—24no—
656#41—24no—
657#41—24no—
658#41—21no—
659#41—21no—
660#41—21no—
661#41—21no—
662#41—42no—
663#41—42no—
664#41—42no—
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—21no—
673C2×Q8—21no—
674C2×Q8—21no—
675C2×Q8—21no—
676C2×Q8—21no—
677C2×Q8C2×D4×C11311yescharacteristic
678C2×Q8C2×D4×C11311yescharacteristic
679C2×Q8C2×D4×C11311yescharacteristic
680C2×D4—21no—
681C2×D4—21no—
682C2×D4—24no—
683C2×D4—24no—
684C2×D4—24no—
685C2×D4—21no—
686C2×D4—21no—
687C2×D4—21no—
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—42no—
697C2×D4—42no—
698C2×D4—42no—
699C2×D4—41no—
700C2×D4—41no—
701C2×D4—41no—
702C2×D4—41no—
703C2×D4—44no—
704C2×D4—42no—
705C2×D4—44no—
706C2×D4—44no—
707C2×D4—44no—
708C2×D4—42no—
709C2×D4C2×D4×C11312yes—
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×C4C24×C11311yescharacteristic
724Q16—22no—
725Q16—42no—
726Q16—42no—
727SD16—24no—
728SD16—24no—
729SD16—22no—
730SD16—22no—
731SD16—42no—
732SD16—42no—
733SD16—42no—
734SD16—42no—
735D8—24no—
736D8—24no—
737D8—24no—
738D8—22no—
739D8—24no—
740M16—24no—
741M16—21no—
742M16—21no—
743M16—21no—
744M16—21no—
745M16—21no—
746M16—21no—
747M16—21no—
748M16—42no—
749M16C2×D4×C11312yes—
750C2×C8—24no—
751C2×C8—21no—
752C2×C8—21no—
753C2×C8—21no—
754C2×C8—21no—
755C2×C8—21no—
756C2×C8—21no—
757C2×C8—21no—
758C2×C8—21no—
759C2×C8—42no—
760C2×C8C2×D4×C11311yescharacteristic
761C2×C8C2×D4×C11311yescharacteristic
762C2×C8C2×D4×C11311yescharacteristic
763C2×C8C2×D4×C11311yescharacteristic
764C4⋊C4—21no—
765C4⋊C4—21no—
766C4⋊C4—41no—
767C4⋊C4—41no—
768C4⋊C4—41no—
769C4⋊C4C2×D4×C11311yescharacteristic
770C4⋊C4C2×D4×C11311yescharacteristic
771C22⋊C4—21no—
772C22⋊C4—41no—
773C22⋊C4—41no—
774C22⋊C4—41no—
775C22⋊C4—44no—
776C22⋊C4—82no—
777C42—21no—
778C42—21no—
779C42—21no—
780C42—41no—
781C23—21no—
782C23—21no—
783C23—21no—
784C23—22no—
785C23—22no—
786C23—44no—
787C23—44no—
788C23—41no—
789C23—41no—
790C23—41no—
791C23—41no—
792C23—81no—
793C23—81no—
794C23—81no—
795C23—81no—
796C23—161no—
797C23—161no—
798C23—161no—
799C23—161no—
800C23H(5,𝔽2)×C11311yescharacteristic
801Q8—21no—
802Q8—21no—
803Q8—21no—
804Q8—21no—
805Q8—41no—
806Q8—41no—
807Q8—41no—
808Q8—41no—
809Q8#120×C11312yes—
810Q8#121×C11312yes—
811D4—22no—
812D4—22no—
813D4—22no—
814D4—22no—
815D4—22no—
816D4—22no—
817D4—21no—
818D4—22no—
819D4—21no—
820D4—22no—
821D4—21no—
822D4—21no—
823D4—44no—
824D4—44no—
825D4—44no—
826D4—44no—
827D4—41no—
828D4—41no—
829D4—41no—
830D4—41no—
831D4—41no—
832D4—41no—
833D4#120×C11312yes—
834D4#121×C11312yes—
835C2×C4—21no—
836C2×C4—21no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—21no—
842C2×C4—21no—
843C2×C4—21no—
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—41no—
855C2×C4—81no—
856C2×C4—161no—
857C2×C4C22×D4×C11311yescharacteristic
858C2×C4C22×D4×C11311yescharacteristic
859C2×C4C22×D4×C11311yescharacteristic
860C2×C4C22×D4×C11311yescharacteristic
861C2×C4C2×#41×C11311yescharacteristic
862C2×C4H(5,𝔽2)×C11311yescharacteristic
863C8—21no—
864C8—22no—
865C8—21no—
866C8—21no—
867C8—21no—
868C8—41no—
869C8—41no—
870C8—41no—
871C22—21no—
872C22—21no—
873C22—22no—
874C22—22no—
875C22—41no—
876C22—41no—
877C22—41no—
878C22—41no—
879C22—41no—
880C22—42no—
881C22—42no—
882C22—41no—
883C22—41no—
884C22—82no—
885C22—82no—
886C22—81no—
887C22—81no—
888C22—81no—
889C22—81no—
890C22—161no—
891C22—161no—
892C22—164no—
893C22—164no—
894C22#534×C11311yescharacteristic
895C22D42×C11311yescharacteristic
896C22#546×C11311yescharacteristic
897C4—22no—
898C4—22no—
899C4—41no—
900C4—41no—
901C4—41no—
902C4—81no—
903C4—81no—
904C4—81no—
905C4C2×#120×C11311yescharacteristic
906C4C2×#121×C11311yescharacteristic
907C4D42×C11311yescharacteristic
908C4#546×C11311yescharacteristic
909C2—21no—
910C2—21no—
911C2—42no—
912C2—42no—
913C2—81no—
914C2—82no—
915C2—82no—
916C2C113×#241011yescharacteristic
917C2C113×#328811yescharacteristic
918C2C113×#329011yescharacteristic
subgroupG/H
center, socleC22×C113D42
commutator, Frattini, cosocleC22×C4C24×C113
prime radicalC2×#576×C113C2
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
2. C2×#471×C113C2semidirect
3. C113×#3046C2semidirect
4. C2×#455×C113C2semidirect
5. C113×#3009C2semidirect
6. C113×#2897C2semidirect
7. C113×#2051C2semidirect
8. C113×#2045C2semidirect
9. C113×#2012C2semidirect
10. C113×#2003C2semidirect
11. C113×#1908C2semidirect
12. C113×#1883C2semidirect
13. C113×#1876C2semidirect
14. C113×#1866C2semidirect
15. C113×#1792C2semidirect
21. C2×#137×C113C22semidirect
28. C22×SD16×C113C22semidirect
32. C2×#131×C113C22semidirect
33. #536×C113C22semidirect
34. C2×#124×C113C22semidirect
35. #520×C113C22semidirect
46. C2×#108×C113C22semidirect
47. #424×C113C22semidirect
49. C2×#104×C113C22semidirect
50. C2×#104×C113C22semidirect
52. #418×C113C22semidirect
53. #418×C113C22semidirect
56. #417×C113C22semidirect
59. C2×#103×C113C22semidirect
61. C2×#102×C113C22semidirect
62. C2×#101×C113C22semidirect
63. C2×#100×C113C22semidirect
64. C2×#100×C113C22semidirect
65. #408×C113C22semidirect
66. #390×C113C22semidirect
67. #343×C113C22semidirect
68. #341×C113C22semidirect
69. #339×C113C22semidirect
70. #336×C113C22semidirect
449. #24459C113direct (N × H)
461. C2×#471C2×C113semidirect
462. #3046C2×C113semidirect
463. C2×#455C2×C113semidirect
464. #3009C2×C113semidirect
465. #2897C2×C113semidirect
466. #2051C2×C113semidirect
467. #2045C2×C113semidirect
468. #2012C2×C113semidirect
469. #2003C2×C113semidirect
470. #1908C2×C113semidirect
471. #1883C2×C113semidirect
472. #1876C2×C113semidirect
473. #1866C2×C113semidirect
474. #1792C2×C113semidirect
475. C113#24459direct (N × H)
481. C2×#137C22×C113semidirect
488. C22×SD16C22×C113semidirect
492. C2×#131C22×C113semidirect
493. #536C22×C113semidirect
494. C2×#124C22×C113semidirect
495. #520C22×C113semidirect
506. C2×#108C22×C113semidirect
507. #424C22×C113semidirect
509. C2×#104C22×C113semidirect
510. C2×#104C22×C113semidirect
512. #418C22×C113semidirect
513. #418C22×C113semidirect
516. #417C22×C113semidirect
519. C2×#103C22×C113semidirect
521. C2×#102C22×C113semidirect
522. C2×#101C22×C113semidirect
523. C2×#100C22×C113semidirect
524. C2×#100C22×C113semidirect
525. #408C22×C113semidirect
526. #390C22×C113semidirect
527. #343C22×C113semidirect
528. #341C22×C113semidirect
529. #339C22×C113semidirect
530. #336C22×C113semidirect

Maximal subgroups

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

subgroupindex
C2×#576×C1132
C2×#471×C1132
C113×#30462
C2×#455×C1132
C113×#30092
C113×#28972
C113×#20512
C113×#20452
C113×#20122
C113×#20032
C113×#19082
C113×#18832
C113×#18762
C113×#18662
C113×#17922
#24459113