Finite Group Databasebeta

← C113×#24044 #43292064

Subgroups — C113×#24044 #43292064

Order 28928.

1768 conjugacy classes of subgroups.

The subgroup lattice has 942 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D42×C113C211yesmaximal, characteristic
2C2×#482×C113C211yesmaximal, characteristic, complemented
3C2×#418×C113C211yesmaximal, characteristic, complemented
4C113×#2485C211yesmaximal, characteristic, complemented
5C113×#2041C211yesmaximal, characteristic, complemented
6C113×#2041C211yesmaximal, characteristic, complemented
7C113×#2034C211yesmaximal, characteristic, complemented
8C113×#2033C211yesmaximal, characteristic, complemented
9C113×#1895C211yesmaximal, characteristic, complemented
10C113×#1870C211yesmaximal, characteristic, complemented
11C113×#1864C211yesmaximal, characteristic, complemented
12C113×#1862C211yesmaximal, characteristic, complemented
13C113×#1786C211yesmaximal, characteristic, complemented
14C113×#1786C211yesmaximal, characteristic, complemented
15C113×#1786C211yesmaximal, characteristic, complemented
16C23×D4×C113—21no—
17C23×D4×C113C2211yescharacteristic
18C23×D4×C113C2211yescharacteristic
19C22×M16×C113C2211yescharacteristic, complemented
20D42×C113—24no—
21D42×C113—24no—
22C2×#127×C113C2211yescharacteristic
23C2×#121×C113—21no—
24C2×#121×C113C2211yescharacteristic
25C2×#121×C113C2211yescharacteristic
26C2×#120×C113—21no—
27C2×#120×C113—21no—
28C2×C4×D4×C113C2211yescharacteristic
29C2×C4×D4×C113C2211yescharacteristic
30C2×#117×C113C2211yescharacteristic, complemented
31#482×C113—24no—
32C2×#107×C113C2211yescharacteristic, complemented
33C2×#106×C113C2211yescharacteristic, complemented
34#418×C113—24no—
35C2×#102×C113C2211yescharacteristic
36C2×#102×C113C2211yescharacteristic
37C2×#102×C113C2211yescharacteristic
38C2×#102×C113C2211yescharacteristic
39C2×#102×C113C2211yescharacteristic, complemented
40C2×#102×C113C2211yescharacteristic, complemented
41C2×#102×C113C2211yescharacteristic, complemented
42C2×#102×C113C2211yescharacteristic, complemented
43C2×#102×C113C2211yescharacteristic, complemented
44C2×#102×C113C2211yescharacteristic, complemented
45C2×#102×C113C2211yescharacteristic, complemented
46C2×#102×C113C2211yescharacteristic, complemented
47C2×C22⋊C8×C113C2211yescharacteristic, complemented
48C2×C22⋊C8×C113C2211yescharacteristic, complemented
49C2×C22⋊C8×C113C2211yescharacteristic, complemented
50#397×C113—21no—
51#394×C113—21no—
52#389×C113C2211yescharacteristic, complemented
53#389×C113C2211yescharacteristic, complemented
54#388×C113—21no—
55#387×C113—21no—
56#380×C113C2211yescharacteristic, complemented
57#380×C113C2211yescharacteristic, complemented
58#380×C113C2211yescharacteristic, complemented
59#340×C113C2211yescharacteristic, complemented
60#340×C113C2211yescharacteristic, complemented
61#336×C113C2211yescharacteristic, complemented
62#336×C113C2211yescharacteristic, complemented
63C25×C113—21no—
64C25×C113—21no—
65C22×D4×C113—22no—
66C22×D4×C113—22no—
67C22×D4×C113—28no—
68C22×D4×C113—21no—
69C22×D4×C113—21no—
70C22×D4×C113—22no—
71C22×D4×C113—22no—
72C22×D4×C113—22no—
73C22×D4×C113—22no—
74C22×D4×C113—21no—
75C22×D4×C113—21no—
76C22×D4×C113—21no—
77C22×D4×C113—22no—
78C22×D4×C113—21no—
79C22×D4×C113—41no—
80C22×D4×C113—41no—
81C22×D4×C113—41no—
82C22×D4×C113—41no—
83C22×D4×C113—44no—
84C22×D4×C113—44no—
85C22×D4×C113D411yescharacteristic
86C22×D4×C113D414yes—
87C22×D4×C113C2311yescharacteristic
88C22×D4×C113C2311yescharacteristic
89C22×D4×C113C2311yescharacteristic
90C23×C4×C113—21no—
91C23×C4×C113C2311yescharacteristic
92C23×C4×C113C2311yescharacteristic
93C2×M16×C113—22no—
94C2×M16×C113—41no—
95C2×M16×C113—41no—
96C22×C8×C113C2311yescharacteristic
97C22×C8×C113C2311yescharacteristic
98C22×C8×C113C2311yescharacteristic
99C22×C8×C113C2311yescharacteristic
100#127×C113—22no—
101#127×C113—22no—
102#121×C113—28no—
103#121×C113—22no—
104#121×C113—22no—
105#121×C113—22no—
106#121×C113D414yes—
107#120×C113—28no—
108#120×C113—28no—
109C4×D4×C113—22no—
110C4×D4×C113—22no—
111C4×D4×C113—22no—
112C4×D4×C113—22no—
113#117×C113—22no—
114#117×C113—22no—
115C2×C4⋊C4×C113—21no—
116C2×C4⋊C4×C113—21no—
117C2×C4⋊C4×C113D411yescharacteristic
118C2×C4⋊C4×C113C2311yescharacteristic
119C2×C4⋊C4×C113C2311yescharacteristic
120C2×C4⋊C4×C113C2311yescharacteristic
121C2×C4⋊C4×C113C2311yescharacteristic
122C2×C4⋊C4×C113C2311yescharacteristic
123C2×C22⋊C4×C113—21no—
124C2×C22⋊C4×C113—21no—
125C2×C22⋊C4×C113—21no—
126C2×C22⋊C4×C113—21no—
127C2×C22⋊C4×C113—21no—
128C2×C22⋊C4×C113—21no—
129C2×C22⋊C4×C113—21no—
130C2×C22⋊C4×C113D411yescharacteristic
131C2×C22⋊C4×C113D411yescharacteristic
132C2×C42×C113—21no—
133C2×C42×C113C2311yescharacteristic
134#107×C113—22no—
135#106×C113—22no—
136#102×C113—22no—
137#102×C113—22no—
138#102×C113—22no—
139#102×C113—22no—
140#102×C113—22no—
141#102×C113—22no—
142#102×C113—22no—
143#102×C113—22no—
144#102×C113—41no—
145#102×C113—41no—
146#102×C113—41no—
147#102×C113—41no—
148C22⋊C8×C113—22no—
149C22⋊C8×C113—41no—
150C22⋊C8×C113—41no—
151#95×C113—21no—
152#95×C113—21no—
153#95×C113—21no—
154#95×C113—21no—
155#95×C113—21no—
156C24×C113—21no—
157C24×C113—24no—
158C24×C113—21no—
159C24×C113—21no—
160C24×C113—24no—
161C24×C113—42no—
162C24×C113—42no—
163C24×C113—42no—
164C24×C113—42no—
165C24×C113—42no—
166C24×C113—42no—
167C24×C113—42no—
168C24×C113—42no—
169C24×C113—81no—
170C24×C113—81no—
171C24×C113—81no—
172C24×C113—81no—
173C24×C113C2×D411yescharacteristic
174C24×C113C2×D411yescharacteristic
175C2×D4×C113—22no—
176C2×D4×C113—22no—
177C2×D4×C113—28no—
178C2×D4×C113—24no—
179C2×D4×C113—24no—
180C2×D4×C113—24no—
181C2×D4×C113—24no—
182C2×D4×C113—24no—
183C2×D4×C113—24no—
184C2×D4×C113—22no—
185C2×D4×C113—21no—
186C2×D4×C113—21no—
187C2×D4×C113—21no—
188C2×D4×C113—21no—
189C2×D4×C113—21no—
190C2×D4×C113—21no—
191C2×D4×C113—21no—
192C2×D4×C113—21no—
193C2×D4×C113—21no—
194C2×D4×C113—21no—
195C2×D4×C113—21no—
196C2×D4×C113—21no—
197C2×D4×C113—21no—
198C2×D4×C113—44no—
199C2×D4×C113—44no—
200C2×D4×C113—44no—
201C2×D4×C113—42no—
202C2×D4×C113—42no—
203C2×D4×C113—42no—
204C2×D4×C113—42no—
205C2×D4×C113—42no—
206C2×D4×C113—44no—
207C2×D4×C113—44no—
208C2×D4×C113—432no—
209C2×D4×C113—44no—
210C2×D4×C113—42no—
211C2×D4×C113—42no—
212C2×D4×C113—42no—
213C2×D4×C113—42no—
214C2×D4×C113—44no—
215C2×D4×C113—42no—
216C2×D4×C113—81no—
217C2×D4×C113—81no—
218C2×D4×C113C2×D412yes—
219C2×D4×C113C2×D412yes—
220C2×D4×C113C2×D412yes—
221C2×D4×C113#4112yes—
222C2×D4×C113#4112yes—
223C22×C4×C113—21no—
224C22×C4×C113—21no—
225C22×C4×C113—21no—
226C22×C4×C113—21no—
227C22×C4×C113—24no—
228C22×C4×C113—21no—
229C22×C4×C113—21no—
230C22×C4×C113—21no—
231C22×C4×C113—21no—
232C22×C4×C113—21no—
233C22×C4×C113—21no—
234C22×C4×C113—21no—
235C22×C4×C113—21no—
236C22×C4×C113—21no—
237C22×C4×C113—21no—
238C22×C4×C113—21no—
239C22×C4×C113—42no—
240C22×C4×C113—42no—
241C22×C4×C113C2×D411yescharacteristic
242C22×C4×C113C2×D411yescharacteristic
243C22×C4×C113C2×D411yescharacteristic
244C22×C4×C113C2×D412yes—
245C22×C4×C113C2×D412yes—
246C22×C4×C113C2×D411yescharacteristic
247C22×C4×C113C2411yescharacteristic
248M16×C113—44no—
249C2×C8×C113—21no—
250C2×C8×C113—21no—
251C2×C8×C113—21no—
252C2×C8×C113—21no—
253C2×C8×C113—21no—
254C2×C8×C113—21no—
255C2×C8×C113—21no—
256C2×C8×C113—21no—
257C2×C8×C113—21no—
258C2×C8×C113—21no—
259C2×C8×C113—21no—
260C2×C8×C113—21no—
261C4⋊C4×C113—22no—
262C4⋊C4×C113—21no—
263C4⋊C4×C113—21no—
264C4⋊C4×C113—21no—
265C4⋊C4×C113—21no—
266C4⋊C4×C113—21no—
267C4⋊C4×C113—21no—
268C4⋊C4×C113—21no—
269C4⋊C4×C113—21no—
270C4⋊C4×C113—21no—
271C4⋊C4×C113—42no—
272C4⋊C4×C113—81no—
273C4⋊C4×C113C2×D412yes—
274C22⋊C4×C113—24no—
275C22⋊C4×C113—24no—
276C22⋊C4×C113—22no—
277C22⋊C4×C113—24no—
278C22⋊C4×C113—22no—
279C22⋊C4×C113—42no—
280C22⋊C4×C113—42no—
281C22⋊C4×C113—81no—
282C22⋊C4×C113—81no—
283C42×C113—21no—
284C42×C113—21no—
285C42×C113—42no—
286C23×C113—21no—
287C23×C113—22no—
288C23×C113—21no—
289C23×C113—21no—
290C23×C113—21no—
291C23×C113—21no—
292C23×C113—22no—
293C23×C113—22no—
294C23×C113—21no—
295C23×C113—21no—
296C23×C113—21no—
297C23×C113—21no—
298C23×C113—21no—
299C23×C113—21no—
300C23×C113—21no—
301C23×C113—22no—
302C23×C113—22no—
303C23×C113—48no—
304C23×C113—48no—
305C23×C113—48no—
306C23×C113—48no—
307C23×C113—41no—
308C23×C113—41no—
309C23×C113—41no—
310C23×C113—41no—
311C23×C113—41no—
312C23×C113—41no—
313C23×C113—41no—
314C23×C113—41no—
315C23×C113—41no—
316C23×C113—41no—
317C23×C113—41no—
318C23×C113—41no—
319C23×C113—41no—
320C23×C113—41no—
321C23×C113—41no—
322C23×C113—41no—
323C23×C113—84no—
324C23×C113—84no—
325C23×C113—84no—
326C23×C113—84no—
327C23×C113—84no—
328C23×C113—84no—
329C23×C113—84no—
330C23×C113—84no—
331C23×C113—84no—
332C23×C113—84no—
333C23×C113#12012yes—
334C23×C113AGL(1,ℤ/8)12yes—
335C23×C113C22×D411yescharacteristic
336D4×C113—28no—
337D4×C113—22no—
338D4×C113—22no—
339D4×C113—22no—
340D4×C113—22no—
341D4×C113—22no—
342D4×C113—22no—
343D4×C113—22no—
344D4×C113—48no—
345D4×C113—48no—
346D4×C113—48no—
347D4×C113—48no—
348D4×C113—48no—
349D4×C113—41no—
350D4×C113—41no—
351D4×C113—41no—
352D4×C113—41no—
353D4×C113—84no—
354D4×C113#12314yes—
355C2×C4×C113—21no—
356C2×C4×C113—21no—
357C2×C4×C113—21no—
358C2×C4×C113—21no—
359C2×C4×C113—22no—
360C2×C4×C113—22no—
361C2×C4×C113—22no—
362C2×C4×C113—22no—
363C2×C4×C113—21no—
364C2×C4×C113—21no—
365C2×C4×C113—22no—
366C2×C4×C113—21no—
367C2×C4×C113—21no—
368C2×C4×C113—21no—
369C2×C4×C113—21no—
370C2×C4×C113—48no—
371C2×C4×C113—41no—
372C2×C4×C113—41no—
373C2×C4×C113—41no—
374C2×C4×C113—41no—
375C2×C4×C113—41no—
376C2×C4×C113—41no—
377C2×C4×C113—41no—
378C2×C4×C113—41no—
379C2×C4×C113—41no—
380C2×C4×C113—41no—
381C2×C4×C113—41no—
382C2×C4×C113—41no—
383C2×C4×C113—41no—
384C2×C4×C113—41no—
385C2×C4×C113—41no—
386C2×C4×C113—41no—
387C2×C4×C113—41no—
388C2×C4×C113—41no—
389C2×C4×C113#12012yes—
390C2×C4×C113AGL(1,ℤ/8)12yes—
391C2×C4×C113C22×D411yescharacteristic
392C2×C4×C113C22×D411yescharacteristic
393C2×C4×C113C2×#4111yescharacteristic
394C2×C4×C113C2×#4111yescharacteristic
395C2×C4×C113H(5,𝔽2)11yescharacteristic
396C2×C4×C113H(5,𝔽2)11yescharacteristic
397C8×C113—41no—
398C8×C113—41no—
399C8×C113—41no—
400C8×C113—41no—
401C22×C113—22no—
402C22×C113—24no—
403C22×C113—22no—
404C22×C113—22no—
405C22×C113—22no—
406C22×C113—22no—
407C22×C113—22no—
408C22×C113—41no—
409C22×C113—42no—
410C22×C113—41no—
411C22×C113—42no—
412C22×C113—41no—
413C22×C113—42no—
414C22×C113—41no—
415C22×C113—42no—
416C22×C113—41no—
417C22×C113—41no—
418C22×C113—42no—
419C22×C113—41no—
420C22×C113—41no—
421C22×C113—42no—
422C22×C113—42no—
423C22×C113—42no—
424C22×C113—42no—
425C22×C113—42no—
426C22×C113—42no—
427C22×C113—42no—
428C22×C113—816no—
429C22×C113—816no—
430C22×C113—81no—
431C22×C113—81no—
432C22×C113—81no—
433C22×C113—81no—
434C22×C113—81no—
435C22×C113—81no—
436C22×C113—81no—
437C22×C113—81no—
438C22×C113C2×#12011yescharacteristic
439C22×C113#54611yescharacteristic
440C22×C113#54611yescharacteristic
441C22×C113C2×AGL(1,ℤ/8)11yescharacteristic
442C22×C113C2×AGL(1,ℤ/8)11yescharacteristic
443C22×C113#57611yescharacteristic
444C22×C113#57711yescharacteristic
445C4×C113—22no—
446C4×C113—22no—
447C4×C113—41no—
448C4×C113—42no—
449C4×C113—41no—
450C4×C113—81no—
451C4×C113—81no—
452C4×C113—81no—
453C4×C113—81no—
454C4×C113C2×#12311yescharacteristic
455C4×C113#53411yescharacteristic
456C4×C113#54611yescharacteristic
457C4×C113#54611yescharacteristic
458#24044C11311yesmaximal, characteristic, direct product factor, Sylow
459C2×C113—42no—
460C2×C113—42no—
461C2×C113—44no—
462C2×C113—82no—
463C2×C113—82no—
464C2×C113#240511yescharacteristic
465C2×C113#300311yescharacteristic
466C2×C113#301211yescharacteristic
467C2×C113#331011yescharacteristic
468C2×C113#331811yescharacteristic
469C2×C113#332411yescharacteristic
470C2×C113#332511yescharacteristic
471C2×D42C2×C11311yescharacteristic
472C2×#482C2×C11311yescharacteristic, complemented
473C2×#418C2×C11311yescharacteristic, complemented
474#2485C2×C11311yescharacteristic, complemented
475#2041C2×C11311yescharacteristic, complemented
476#2041C2×C11311yescharacteristic, complemented
477#2034C2×C11311yescharacteristic, complemented
478#2033C2×C11311yescharacteristic, complemented
479#1895C2×C11311yescharacteristic, complemented
480#1870C2×C11311yescharacteristic, complemented
481#1864C2×C11311yescharacteristic, complemented
482#1862C2×C11311yescharacteristic, complemented
483#1786C2×C11311yescharacteristic, complemented
484#1786C2×C11311yescharacteristic, complemented
485#1786C2×C11311yescharacteristic, complemented
486C113#2404411yescharacteristic, direct product factor, Sylow
487C23×D4—21no—
488C23×D4C22×C11311yescharacteristic
489C23×D4C22×C11311yescharacteristic
490C22×M16C22×C11311yescharacteristic, complemented
491D42—24no—
492D42—24no—
493C2×#127C22×C11311yescharacteristic
494C2×#121—21no—
495C2×#121C22×C11311yescharacteristic
496C2×#121C22×C11311yescharacteristic
497C2×#120—21no—
498C2×#120—21no—
499C2×C4×D4C22×C11311yescharacteristic
500C2×C4×D4C22×C11311yescharacteristic
501C2×#117C22×C11311yescharacteristic, complemented
502#482—24no—
503C2×#107C22×C11311yescharacteristic, complemented
504C2×#106C22×C11311yescharacteristic, complemented
505#418—24no—
506C2×#102C22×C11311yescharacteristic
507C2×#102C22×C11311yescharacteristic
508C2×#102C22×C11311yescharacteristic
509C2×#102C22×C11311yescharacteristic
510C2×#102C22×C11311yescharacteristic, complemented
511C2×#102C22×C11311yescharacteristic, complemented
512C2×#102C22×C11311yescharacteristic, complemented
513C2×#102C22×C11311yescharacteristic, complemented
514C2×#102C22×C11311yescharacteristic, complemented
515C2×#102C22×C11311yescharacteristic, complemented
516C2×#102C22×C11311yescharacteristic, complemented
517C2×#102C22×C11311yescharacteristic, complemented
518C2×C22⋊C8C22×C11311yescharacteristic, complemented
519C2×C22⋊C8C22×C11311yescharacteristic, complemented
520C2×C22⋊C8C22×C11311yescharacteristic, complemented
521#397—21no—
522#394—21no—
523#389C22×C11311yescharacteristic, complemented
524#389C22×C11311yescharacteristic, complemented
525#388—21no—
526#387—21no—
527#380C22×C11311yescharacteristic, complemented
528#380C22×C11311yescharacteristic, complemented
529#380C22×C11311yescharacteristic, complemented
530#340C22×C11311yescharacteristic, complemented
531#340C22×C11311yescharacteristic, complemented
532#336C22×C11311yescharacteristic, complemented
533#336C22×C11311yescharacteristic, complemented
534C25—21no—
535C25—21no—
536C22×D4—22no—
537C22×D4—22no—
538C22×D4—28no—
539C22×D4—21no—
540C22×D4—21no—
541C22×D4—22no—
542C22×D4—22no—
543C22×D4—22no—
544C22×D4—22no—
545C22×D4—21no—
546C22×D4—21no—
547C22×D4—21no—
548C22×D4—22no—
549C22×D4—21no—
550C22×D4—41no—
551C22×D4—41no—
552C22×D4—41no—
553C22×D4—41no—
554C22×D4—44no—
555C22×D4—44no—
556C22×D4D4×C11311yescharacteristic
557C22×D4D4×C11314yes—
558C22×D4C23×C11311yescharacteristic
559C22×D4C23×C11311yescharacteristic
560C22×D4C23×C11311yescharacteristic
561C23×C4—21no—
562C23×C4C23×C11311yescharacteristic
563C23×C4C23×C11311yescharacteristic
564C2×M16—22no—
565C2×M16—41no—
566C2×M16—41no—
567C22×C8C23×C11311yescharacteristic
568C22×C8C23×C11311yescharacteristic
569C22×C8C23×C11311yescharacteristic
570C22×C8C23×C11311yescharacteristic
571#127—22no—
572#127—22no—
573#121—28no—
574#121—22no—
575#121—22no—
576#121—22no—
577#121D4×C11314yes—
578#120—28no—
579#120—28no—
580C4×D4—22no—
581C4×D4—22no—
582C4×D4—22no—
583C4×D4—22no—
584#117—22no—
585#117—22no—
586C2×C4⋊C4—21no—
587C2×C4⋊C4—21no—
588C2×C4⋊C4D4×C11311yescharacteristic
589C2×C4⋊C4C23×C11311yescharacteristic
590C2×C4⋊C4C23×C11311yescharacteristic
591C2×C4⋊C4C23×C11311yescharacteristic
592C2×C4⋊C4C23×C11311yescharacteristic
593C2×C4⋊C4C23×C11311yescharacteristic
594C2×C22⋊C4—21no—
595C2×C22⋊C4—21no—
596C2×C22⋊C4—21no—
597C2×C22⋊C4—21no—
598C2×C22⋊C4—21no—
599C2×C22⋊C4—21no—
600C2×C22⋊C4—21no—
601C2×C22⋊C4D4×C11311yescharacteristic
602C2×C22⋊C4D4×C11311yescharacteristic
603C2×C42—21no—
604C2×C42C23×C11311yescharacteristic
605#107—22no—
606#106—22no—
607#102—22no—
608#102—22no—
609#102—22no—
610#102—22no—
611#102—22no—
612#102—22no—
613#102—22no—
614#102—22no—
615#102—41no—
616#102—41no—
617#102—41no—
618#102—41no—
619C22⋊C8—22no—
620C22⋊C8—41no—
621C22⋊C8—41no—
622#95—21no—
623#95—21no—
624#95—21no—
625#95—21no—
626#95—21no—
627C24—21no—
628C24—24no—
629C24—21no—
630C24—21no—
631C24—24no—
632C24—42no—
633C24—42no—
634C24—42no—
635C24—42no—
636C24—42no—
637C24—42no—
638C24—42no—
639C24—42no—
640C24—81no—
641C24—81no—
642C24—81no—
643C24—81no—
644C24C2×D4×C11311yescharacteristic
645C24C2×D4×C11311yescharacteristic
646C2×D4—22no—
647C2×D4—22no—
648C2×D4—28no—
649C2×D4—24no—
650C2×D4—24no—
651C2×D4—24no—
652C2×D4—24no—
653C2×D4—24no—
654C2×D4—24no—
655C2×D4—22no—
656C2×D4—21no—
657C2×D4—21no—
658C2×D4—21no—
659C2×D4—21no—
660C2×D4—21no—
661C2×D4—21no—
662C2×D4—21no—
663C2×D4—21no—
664C2×D4—21no—
665C2×D4—21no—
666C2×D4—21no—
667C2×D4—21no—
668C2×D4—21no—
669C2×D4—44no—
670C2×D4—44no—
671C2×D4—44no—
672C2×D4—42no—
673C2×D4—42no—
674C2×D4—42no—
675C2×D4—42no—
676C2×D4—42no—
677C2×D4—44no—
678C2×D4—44no—
679C2×D4—432no—
680C2×D4—44no—
681C2×D4—42no—
682C2×D4—42no—
683C2×D4—42no—
684C2×D4—42no—
685C2×D4—44no—
686C2×D4—42no—
687C2×D4—81no—
688C2×D4—81no—
689C2×D4C2×D4×C11312yes—
690C2×D4C2×D4×C11312yes—
691C2×D4C2×D4×C11312yes—
692C2×D4#41×C11312yes—
693C2×D4#41×C11312yes—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—24no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—42no—
711C22×C4—42no—
712C22×C4C2×D4×C11311yescharacteristic
713C22×C4C2×D4×C11311yescharacteristic
714C22×C4C2×D4×C11311yescharacteristic
715C22×C4C2×D4×C11312yes—
716C22×C4C2×D4×C11312yes—
717C22×C4C2×D4×C11311yescharacteristic
718C22×C4C24×C11311yescharacteristic
719M16—44no—
720C2×C8—21no—
721C2×C8—21no—
722C2×C8—21no—
723C2×C8—21no—
724C2×C8—21no—
725C2×C8—21no—
726C2×C8—21no—
727C2×C8—21no—
728C2×C8—21no—
729C2×C8—21no—
730C2×C8—21no—
731C2×C8—21no—
732C4⋊C4—22no—
733C4⋊C4—21no—
734C4⋊C4—21no—
735C4⋊C4—21no—
736C4⋊C4—21no—
737C4⋊C4—21no—
738C4⋊C4—21no—
739C4⋊C4—21no—
740C4⋊C4—21no—
741C4⋊C4—21no—
742C4⋊C4—42no—
743C4⋊C4—81no—
744C4⋊C4C2×D4×C11312yes—
745C22⋊C4—24no—
746C22⋊C4—24no—
747C22⋊C4—22no—
748C22⋊C4—24no—
749C22⋊C4—22no—
750C22⋊C4—42no—
751C22⋊C4—42no—
752C22⋊C4—81no—
753C22⋊C4—81no—
754C42—21no—
755C42—21no—
756C42—42no—
757C23—21no—
758C23—22no—
759C23—21no—
760C23—21no—
761C23—21no—
762C23—21no—
763C23—22no—
764C23—22no—
765C23—21no—
766C23—21no—
767C23—21no—
768C23—21no—
769C23—21no—
770C23—21no—
771C23—21no—
772C23—22no—
773C23—22no—
774C23—48no—
775C23—48no—
776C23—48no—
777C23—48no—
778C23—41no—
779C23—41no—
780C23—41no—
781C23—41no—
782C23—41no—
783C23—41no—
784C23—41no—
785C23—41no—
786C23—41no—
787C23—41no—
788C23—41no—
789C23—41no—
790C23—41no—
791C23—41no—
792C23—41no—
793C23—41no—
794C23—84no—
795C23—84no—
796C23—84no—
797C23—84no—
798C23—84no—
799C23—84no—
800C23—84no—
801C23—84no—
802C23—84no—
803C23—84no—
804C23#120×C11312yes—
805C23AGL(1,ℤ/8)×C11312yes—
806C23C22×D4×C11311yescharacteristic
807D4—28no—
808D4—22no—
809D4—22no—
810D4—22no—
811D4—22no—
812D4—22no—
813D4—22no—
814D4—22no—
815D4—48no—
816D4—48no—
817D4—48no—
818D4—48no—
819D4—48no—
820D4—41no—
821D4—41no—
822D4—41no—
823D4—41no—
824D4—84no—
825D4#123×C11314yes—
826C2×C4—21no—
827C2×C4—21no—
828C2×C4—21no—
829C2×C4—21no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—21no—
835C2×C4—21no—
836C2×C4—22no—
837C2×C4—21no—
838C2×C4—21no—
839C2×C4—21no—
840C2×C4—21no—
841C2×C4—48no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—41no—
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—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4#120×C11312yes—
861C2×C4AGL(1,ℤ/8)×C11312yes—
862C2×C4C22×D4×C11311yescharacteristic
863C2×C4C22×D4×C11311yescharacteristic
864C2×C4C2×#41×C11311yescharacteristic
865C2×C4C2×#41×C11311yescharacteristic
866C2×C4H(5,𝔽2)×C11311yescharacteristic
867C2×C4H(5,𝔽2)×C11311yescharacteristic
868C8—41no—
869C8—41no—
870C8—41no—
871C8—41no—
872C22—22no—
873C22—22no—
874C22—22no—
875C22—24no—
876C22—22no—
877C22—22no—
878C22—22no—
879C22—41no—
880C22—42no—
881C22—41no—
882C22—42no—
883C22—41no—
884C22—41no—
885C22—42no—
886C22—41no—
887C22—41no—
888C22—42no—
889C22—41no—
890C22—42no—
891C22—41no—
892C22—42no—
893C22—42no—
894C22—42no—
895C22—42no—
896C22—42no—
897C22—42no—
898C22—42no—
899C22—816no—
900C22—816no—
901C22—81no—
902C22—81no—
903C22—81no—
904C22—81no—
905C22—81no—
906C22—81no—
907C22—81no—
908C22—81no—
909C22C2×#120×C11311yescharacteristic
910C22#546×C11311yescharacteristic
911C22#546×C11311yescharacteristic
912C22C2×AGL(1,ℤ/8)×C11311yescharacteristic
913C22C2×AGL(1,ℤ/8)×C11311yescharacteristic
914C22#576×C11311yescharacteristic
915C22#577×C11311yescharacteristic
916C4—22no—
917C4—22no—
918C4—41no—
919C4—42no—
920C4—41no—
921C4—81no—
922C4—81no—
923C4—81no—
924C4—81no—
925C4C2×#123×C11311yescharacteristic
926C4#534×C11311yescharacteristic
927C4#546×C11311yescharacteristic
928C4#546×C11311yescharacteristic
929C2—42no—
930C2—42no—
931C2—44no—
932C2—82no—
933C2—82no—
934C2C113×#240511yescharacteristic
935C2C113×#300311yescharacteristic
936C2C113×#301211yescharacteristic
937C2C113×#331011yescharacteristic
938C2C113×#331811yescharacteristic
939C2C113×#332411yescharacteristic
940C2C113×#332511yescharacteristic
subgroupG/H
center, socleC23×C113C22×D4
commutator, Frattini, cosocleC22×C4C24×C113
prime radicalC2×D42×C113C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C113 ◁ C2×C4×D4×C113 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#482×C113C2semidirect
3. C2×#418×C113C2semidirect
4. C113×#2485C2semidirect
5. C113×#2041C2semidirect
6. C113×#2041C2semidirect
7. C113×#2034C2semidirect
8. C113×#2033C2semidirect
9. C113×#1895C2semidirect
10. C113×#1870C2semidirect
11. C113×#1864C2semidirect
12. C113×#1862C2semidirect
13. C113×#1786C2semidirect
14. C113×#1786C2semidirect
15. C113×#1786C2semidirect
19. C22×M16×C113C22semidirect
30. C2×#117×C113C22semidirect
32. C2×#107×C113C22semidirect
33. C2×#106×C113C22semidirect
39. C2×#102×C113C22semidirect
40. C2×#102×C113C22semidirect
41. C2×#102×C113C22semidirect
42. C2×#102×C113C22semidirect
43. C2×#102×C113C22semidirect
44. C2×#102×C113C22semidirect
45. C2×#102×C113C22semidirect
46. C2×#102×C113C22semidirect
47. C2×C22⋊C8×C113C22semidirect
48. C2×C22⋊C8×C113C22semidirect
49. C2×C22⋊C8×C113C22semidirect
52. #389×C113C22semidirect
53. #389×C113C22semidirect
56. #380×C113C22semidirect
57. #380×C113C22semidirect
58. #380×C113C22semidirect
59. #340×C113C22semidirect
60. #340×C113C22semidirect
61. #336×C113C22semidirect
62. #336×C113C22semidirect
458. #24044C113direct (N × H)
472. C2×#482C2×C113semidirect
473. C2×#418C2×C113semidirect
474. #2485C2×C113semidirect
475. #2041C2×C113semidirect
476. #2041C2×C113semidirect
477. #2034C2×C113semidirect
478. #2033C2×C113semidirect
479. #1895C2×C113semidirect
480. #1870C2×C113semidirect
481. #1864C2×C113semidirect
482. #1862C2×C113semidirect
483. #1786C2×C113semidirect
484. #1786C2×C113semidirect
485. #1786C2×C113semidirect
486. C113#24044direct (N × H)
490. C22×M16C22×C113semidirect
501. C2×#117C22×C113semidirect
503. C2×#107C22×C113semidirect
504. C2×#106C22×C113semidirect
510. C2×#102C22×C113semidirect
511. C2×#102C22×C113semidirect
512. C2×#102C22×C113semidirect
513. C2×#102C22×C113semidirect
514. C2×#102C22×C113semidirect
515. C2×#102C22×C113semidirect
516. C2×#102C22×C113semidirect
517. C2×#102C22×C113semidirect
518. C2×C22⋊C8C22×C113semidirect
519. C2×C22⋊C8C22×C113semidirect
520. C2×C22⋊C8C22×C113semidirect
523. #389C22×C113semidirect
524. #389C22×C113semidirect
527. #380C22×C113semidirect
528. #380C22×C113semidirect
529. #380C22×C113semidirect
530. #340C22×C113semidirect
531. #340C22×C113semidirect
532. #336C22×C113semidirect
533. #336C22×C113semidirect

Maximal subgroups

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

subgroupindex
C2×D42×C1132
C2×#482×C1132
C2×#418×C1132
C113×#24852
C113×#20412
C113×#20342
C113×#20332
C113×#18952
C113×#18702
C113×#18642
C113×#18622
C113×#17862
#24044113