Finite Group Databasebeta

← C113×#24441 #43292461

Subgroups — C113×#24441 #43292461

Order 28928.

1522 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×#548×C113C211yesmaximal, characteristic, complemented
2C2×#468×C113C211yesmaximal, characteristic, complemented
3C2×#449×C113C211yesmaximal, characteristic, complemented
4C2×#448×C113C211yesmaximal, characteristic, complemented
5C2×#417×C113C211yesmaximal, characteristic, complemented
6C113×#2416C211yesmaximal, characteristic, complemented
7C113×#2042C211yesmaximal, characteristic, complemented
8C113×#2033C211yesmaximal, characteristic, complemented
9C113×#2012C211yesmaximal, characteristic, complemented
10C113×#1999C211yesmaximal, characteristic, complemented
11C113×#1880C211yesmaximal, characteristic, complemented
12C113×#1872C211yesmaximal, characteristic, complemented
13C113×#1870C211yesmaximal, characteristic, complemented
14C113×#1863C211yesmaximal, characteristic, complemented
15C113×#1787C211yesmaximal, characteristic, complemented
16C22×#41×C113C2211yescharacteristic
17C23×Q8×C113C2211yescharacteristic
18C22×SD16×C113C2211yescharacteristic
19C22×SD16×C113C2211yescharacteristic
20C22×D8×C113C2211yescharacteristic
21C22×M16×C113C2211yescharacteristic
22#548×C113—24no—
23#548×C113—24no—
24C2×#124×C113—21no—
25C2×#124×C113C2211yescharacteristic
26C2×C22⋊Q8×C113—21no—
27C2×C22⋊Q8×C113C2211yescharacteristic
28C2×#121×C113—21no—
29C2×#121×C113—21no—
30C2×#121×C113C2211yescharacteristic
31C2×#121×C113C2211yescharacteristic
32C2×#121×C113C2211yescharacteristic
33C2×C4×Q8×C113C2211yescharacteristic
34C2×C4×D4×C113—21no—
35C2×C4×D4×C113C2211yescharacteristic
36C22×C4⋊C4×C113C2211yescharacteristic
37#468×C113—24no—
38#449×C113—24no—
39#448×C113—24no—
40C2×#107×C113C2211yescharacteristic
41#417×C113—24no—
42C2×#103×C113C2211yescharacteristic
43C2×#103×C113C2211yescharacteristic
44C2×#103×C113C2211yescharacteristic
45C2×#103×C113C2211yescharacteristic
46C2×#103×C113C2211yescharacteristic
47C2×#103×C113C2211yescharacteristic
48C2×#102×C113C2211yescharacteristic
49C2×#102×C113C2211yescharacteristic
50C2×#102×C113C2211yescharacteristic
51C2×#102×C113C2211yescharacteristic
52C2×C22⋊C8×C113C2211yescharacteristic
53C2×C22⋊C8×C113C2211yescharacteristic
54C2×C22⋊C8×C113C2211yescharacteristic
55#396×C113—21no—
56#394×C113—21no—
57#390×C113C2211yescharacteristic
58#389×C113C2211yescharacteristic
59#386×C113—21no—
60#380×C113C2211yescharacteristic
61#340×C113C2211yescharacteristic
62#340×C113C2211yescharacteristic
63#336×C113C2211yescharacteristic
64#336×C113C2211yescharacteristic
65C2×#41×C113—22no—
66C2×#41×C113—22no—
67C2×#41×C113—22no—
68C2×#41×C113—41no—
69C2×#41×C113—41no—
70C2×#41×C113D414yescomplemented
71C22×Q8×C113—22no—
72C22×Q8×C113—22no—
73C22×Q8×C113—21no—
74C22×Q8×C113—22no—
75C22×Q8×C113—22no—
76C22×Q8×C113—41no—
77C22×Q8×C113—41no—
78C22×Q8×C113C2311yescharacteristic
79C22×Q8×C113C2311yescharacteristic
80C22×D4×C113—21no—
81C22×D4×C113—21no—
82C22×D4×C113—21no—
83C22×D4×C113—21no—
84C22×D4×C113D411yescharacteristic
85C22×D4×C113C2311yescharacteristic
86C22×D4×C113C2311yescharacteristic
87C23×C4×C113—21no—
88C23×C4×C113—21no—
89C23×C4×C113—21no—
90C23×C4×C113C2311yescharacteristic
91C23×C4×C113C2311yescharacteristic
92C2×SD16×C113—22no—
93C2×SD16×C113—22no—
94C2×SD16×C113—22no—
95C2×SD16×C113—22no—
96C2×SD16×C113—22no—
97C2×SD16×C113—41no—
98C2×D8×C113—22no—
99C2×D8×C113—41no—
100C2×D8×C113—41no—
101C2×M16×C113—22no—
102C2×M16×C113—22no—
103C2×M16×C113—41no—
104C22×C8×C113C2311yescharacteristic
105C22×C8×C113C2311yescharacteristic
106C22×C8×C113C2311yescharacteristic
107C22×C8×C113C2311yescharacteristic
108#124×C113—28no—
109#124×C113—22no—
110#124×C113—22no—
111C22⋊Q8×C113—28no—
112C22⋊Q8×C113—22no—
113C22⋊Q8×C113D414yescomplemented
114#121×C113—28no—
115#121×C113—22no—
116#121×C113—22no—
117#121×C113—22no—
118#121×C113—22no—
119#121×C113—22no—
120#121×C113—41no—
121#121×C113—44no—
122C4×Q8×C113—22no—
123C4×Q8×C113—22no—
124C4×D4×C113—28no—
125C4×D4×C113—22no—
126C4×D4×C113—22no—
127C2×C4⋊C4×C113—21no—
128C2×C4⋊C4×C113—21no—
129C2×C4⋊C4×C113—22no—
130C2×C4⋊C4×C113—21no—
131C2×C4⋊C4×C113—21no—
132C2×C4⋊C4×C113—41no—
133C2×C4⋊C4×C113D411yescharacteristic
134C2×C4⋊C4×C113C2311yescharacteristic
135C2×C4⋊C4×C113C2311yescharacteristic
136C2×C4⋊C4×C113C2311yescharacteristic
137C2×C4⋊C4×C113C2311yescharacteristic
138C2×C22⋊C4×C113—21no—
139C2×C22⋊C4×C113—21no—
140C2×C22⋊C4×C113—21no—
141C2×C22⋊C4×C113—21no—
142C2×C22⋊C4×C113—21no—
143C2×C22⋊C4×C113—21no—
144C2×C22⋊C4×C113—21no—
145C2×C22⋊C4×C113—21no—
146C2×C22⋊C4×C113—21no—
147C2×C22⋊C4×C113D411yescharacteristic
148C2×C22⋊C4×C113D411yescharacteristic
149C2×C42×C113—21no—
150C2×C42×C113C2311yescharacteristic
151#107×C113—22no—
152#103×C113—22no—
153#103×C113—22no—
154#103×C113—22no—
155#103×C113—22no—
156#103×C113—41no—
157#103×C113D414yescomplemented
158#102×C113—22no—
159#102×C113—22no—
160#102×C113—22no—
161#102×C113—22no—
162C22⋊C8×C113—22no—
163C22⋊C8×C113—22no—
164C22⋊C8×C113—41no—
165#95×C113—21no—
166#95×C113—21no—
167C24×C113—21no—
168C24×C113—21no—
169C24×C113C2×D411yescharacteristic
170C24×C113C2×D411yescharacteristic
171#41×C113—28no—
172#41×C113—44no—
173#41×C113—44no—
174#41×C113—44no—
175C2×Q8×C113—24no—
176C2×Q8×C113—21no—
177C2×Q8×C113—21no—
178C2×Q8×C113—21no—
179C2×Q8×C113—21no—
180C2×Q8×C113—21no—
181C2×Q8×C113—21no—
182C2×Q8×C113—21no—
183C2×Q8×C113—21no—
184C2×Q8×C113—42no—
185C2×Q8×C113—42no—
186C2×Q8×C113—44no—
187C2×Q8×C113—44no—
188C2×Q8×C113—44no—
189C2×Q8×C113—44no—
190C2×Q8×C113C2×D412yes—
191C2×Q8×C113C2×D412yes—
192C2×Q8×C113C2×D412yes—
193C2×Q8×C113#4112yes—
194C2×D4×C113—24no—
195C2×D4×C113—22no—
196C2×D4×C113—24no—
197C2×D4×C113—22no—
198C2×D4×C113—21no—
199C2×D4×C113—21no—
200C2×D4×C113—21no—
201C2×D4×C113—21no—
202C2×D4×C113—21no—
203C2×D4×C113—21no—
204C2×D4×C113—21no—
205C2×D4×C113—21no—
206C2×D4×C113—21no—
207C2×D4×C113—21no—
208C2×D4×C113—21no—
209C2×D4×C113—41no—
210C2×D4×C113—42no—
211C2×D4×C113—42no—
212C2×D4×C113—42no—
213C2×D4×C113—42no—
214C2×D4×C113—42no—
215C2×D4×C113—42no—
216C2×D4×C113—42no—
217C2×D4×C113—42no—
218C2×D4×C113—42no—
219C2×D4×C113—81no—
220C2×D4×C113C2×D412yes—
221C22×C4×C113—21no—
222C22×C4×C113—21no—
223C22×C4×C113—21no—
224C22×C4×C113—21no—
225C22×C4×C113—21no—
226C22×C4×C113—24no—
227C22×C4×C113—21no—
228C22×C4×C113—21no—
229C22×C4×C113—21no—
230C22×C4×C113—24no—
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×C113—42no—
242C22×C4×C113—42no—
243C22×C4×C113—42no—
244C22×C4×C113—42no—
245C22×C4×C113—81no—
246C22×C4×C113C2×D411yescharacteristic
247C22×C4×C113C2×D411yescharacteristic
248C22×C4×C113C2×D411yescharacteristic
249C22×C4×C113C2×D411yescharacteristic
250C22×C4×C113C2×D412yes—
251C22×C4×C113C2×D412yes—
252C22×C4×C113C2411yescharacteristic
253SD16×C113—44no—
254SD16×C113—44no—
255D8×C113—44no—
256M16×C113—44no—
257C2×C8×C113—21no—
258C2×C8×C113—21no—
259C2×C8×C113—21no—
260C2×C8×C113—21no—
261C2×C8×C113—21no—
262C2×C8×C113—21no—
263C2×C8×C113—21no—
264C2×C8×C113—21no—
265C2×C8×C113—21no—
266C2×C8×C113—21no—
267C2×C8×C113—21no—
268C2×C8×C113C2×D412yes—
269C4⋊C4×C113—24no—
270C4⋊C4×C113—24no—
271C4⋊C4×C113—22no—
272C4⋊C4×C113—21no—
273C4⋊C4×C113—21no—
274C4⋊C4×C113—21no—
275C4⋊C4×C113—21no—
276C4⋊C4×C113—21no—
277C4⋊C4×C113—21no—
278C4⋊C4×C113—42no—
279C4⋊C4×C113—42no—
280C4⋊C4×C113C2×D412yes—
281C4⋊C4×C113C2×D412yes—
282C22⋊C4×C113—24no—
283C22⋊C4×C113—24no—
284C22⋊C4×C113—24no—
285C22⋊C4×C113—24no—
286C22⋊C4×C113—22no—
287C22⋊C4×C113—22no—
288C22⋊C4×C113—42no—
289C22⋊C4×C113—42no—
290C22⋊C4×C113—42no—
291C22⋊C4×C113—42no—
292C22⋊C4×C113—81no—
293C42×C113—24no—
294C42×C113—21no—
295C42×C113—21no—
296C23×C113—21no—
297C23×C113—21no—
298C23×C113—21no—
299C23×C113—21no—
300C23×C113—21no—
301C23×C113—21no—
302C23×C113—21no—
303C23×C113—21no—
304C23×C113—21no—
305C23×C113—21no—
306C23×C113—21no—
307C23×C113—21no—
308C23×C113—22no—
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#12012yes—
323C23×C113AGL(1,ℤ/8)12yes—
324C23×C113C22×D411yescharacteristic
325Q8×C113—22no—
326Q8×C113—22no—
327Q8×C113—22no—
328Q8×C113—22no—
329Q8×C113—22no—
330Q8×C113—48no—
331Q8×C113—41no—
332Q8×C113—41no—
333Q8×C113#12114yescomplemented
334D4×C113—22no—
335D4×C113—22no—
336D4×C113—48no—
337D4×C113—44no—
338D4×C113—48no—
339D4×C113—41no—
340D4×C113—41no—
341D4×C113—41no—
342D4×C113—41no—
343D4×C113—41no—
344D4×C113—41no—
345D4×C113—84no—
346D4×C113—84no—
347C2×C4×C113—22no—
348C2×C4×C113—21no—
349C2×C4×C113—22no—
350C2×C4×C113—21no—
351C2×C4×C113—22no—
352C2×C4×C113—22no—
353C2×C4×C113—22no—
354C2×C4×C113—22no—
355C2×C4×C113—22no—
356C2×C4×C113—21no—
357C2×C4×C113—21no—
358C2×C4×C113—22no—
359C2×C4×C113—22no—
360C2×C4×C113—21no—
361C2×C4×C113—21no—
362C2×C4×C113—22no—
363C2×C4×C113—21no—
364C2×C4×C113—21no—
365C2×C4×C113—21no—
366C2×C4×C113—21no—
367C2×C4×C113—21no—
368C2×C4×C113—48no—
369C2×C4×C113—48no—
370C2×C4×C113—41no—
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—84no—
387C2×C4×C113#12012yes—
388C2×C4×C113C22×D411yescharacteristic
389C2×C4×C113C22×D411yescharacteristic
390C2×C4×C113C22×D411yescharacteristic
391C2×C4×C113C2×#4111yescharacteristic
392C2×C4×C113H(5,𝔽2)11yescharacteristic
393C2×C4×C113H(5,𝔽2)11yescharacteristic
394C8×C113—22no—
395C8×C113—41no—
396C8×C113—41no—
397C8×C113—41no—
398C22×C113—22no—
399C22×C113—22no—
400C22×C113—22no—
401C22×C113—22no—
402C22×C113—22no—
403C22×C113—22no—
404C22×C113—41no—
405C22×C113—41no—
406C22×C113—41no—
407C22×C113—41no—
408C22×C113—41no—
409C22×C113—41no—
410C22×C113—41no—
411C22×C113—41no—
412C22×C113—42no—
413C22×C113—42no—
414C22×C113—42no—
415C22×C113—81no—
416C22×C113—81no—
417C22×C113—81no—
418C22×C113—81no—
419C22×C113—81no—
420C22×C113—81no—
421C22×C113—81no—
422C22×C113—81no—
423C22×C113—81no—
424C22×C113—81no—
425C22×C113—81no—
426C22×C113C2×#12011yescharacteristic
427C22×C113D4211yescharacteristic
428C22×C113#54611yescharacteristic
429C22×C113C2×AGL(1,ℤ/8)11yescharacteristic
430C22×C113#57511yescharacteristic
431C22×C113#57711yescharacteristic
432C22×C113#57811yescharacteristic
433C4×C113—22no—
434C4×C113—24no—
435C4×C113—41no—
436C4×C113—42no—
437C4×C113—41no—
438C4×C113—42no—
439C4×C113—42no—
440C4×C113—41no—
441C4×C113—81no—
442C4×C113—81no—
443C4×C113C2×#12111yescharacteristic
444C4×C113#53411yescharacteristic
445C4×C113D4211yescharacteristic
446C4×C113#54611yescharacteristic
447#24441C11311yesmaximal, characteristic, direct product factor, Sylow
448C2×C113—42no—
449C2×C113—42no—
450C2×C113—82no—
451C2×C113—161no—
452C2×C113#241011yescharacteristic
453C2×C113#300611yescharacteristic
454C2×C113#301311yescharacteristic
455C2×C113#326511yescharacteristic
456C2×C113#327711yescharacteristic
457C2×C113#330811yescharacteristic
458C2×C113#332611yescharacteristic
459C2×#548C2×C11311yescharacteristic, complemented
460C2×#468C2×C11311yescharacteristic, complemented
461C2×#449C2×C11311yescharacteristic, complemented
462C2×#448C2×C11311yescharacteristic, complemented
463C2×#417C2×C11311yescharacteristic, complemented
464#2416C2×C11311yescharacteristic, complemented
465#2042C2×C11311yescharacteristic, complemented
466#2033C2×C11311yescharacteristic, complemented
467#2012C2×C11311yescharacteristic, complemented
468#1999C2×C11311yescharacteristic, complemented
469#1880C2×C11311yescharacteristic, complemented
470#1872C2×C11311yescharacteristic, complemented
471#1870C2×C11311yescharacteristic, complemented
472#1863C2×C11311yescharacteristic, complemented
473#1787C2×C11311yescharacteristic, complemented
474C113#2444111yescharacteristic, direct product factor, Sylow
475C22×#41C22×C11311yescharacteristic
476C23×Q8C22×C11311yescharacteristic
477C22×SD16C22×C11311yescharacteristic
478C22×SD16C22×C11311yescharacteristic
479C22×D8C22×C11311yescharacteristic
480C22×M16C22×C11311yescharacteristic
481#548—24no—
482#548—24no—
483C2×#124—21no—
484C2×#124C22×C11311yescharacteristic
485C2×C22⋊Q8—21no—
486C2×C22⋊Q8C22×C11311yescharacteristic
487C2×#121—21no—
488C2×#121—21no—
489C2×#121C22×C11311yescharacteristic
490C2×#121C22×C11311yescharacteristic
491C2×#121C22×C11311yescharacteristic
492C2×C4×Q8C22×C11311yescharacteristic
493C2×C4×D4—21no—
494C2×C4×D4C22×C11311yescharacteristic
495C22×C4⋊C4C22×C11311yescharacteristic
496#468—24no—
497#449—24no—
498#448—24no—
499C2×#107C22×C11311yescharacteristic
500#417—24no—
501C2×#103C22×C11311yescharacteristic
502C2×#103C22×C11311yescharacteristic
503C2×#103C22×C11311yescharacteristic
504C2×#103C22×C11311yescharacteristic
505C2×#103C22×C11311yescharacteristic
506C2×#103C22×C11311yescharacteristic
507C2×#102C22×C11311yescharacteristic
508C2×#102C22×C11311yescharacteristic
509C2×#102C22×C11311yescharacteristic
510C2×#102C22×C11311yescharacteristic
511C2×C22⋊C8C22×C11311yescharacteristic
512C2×C22⋊C8C22×C11311yescharacteristic
513C2×C22⋊C8C22×C11311yescharacteristic
514#396—21no—
515#394—21no—
516#390C22×C11311yescharacteristic
517#389C22×C11311yescharacteristic
518#386—21no—
519#380C22×C11311yescharacteristic
520#340C22×C11311yescharacteristic
521#340C22×C11311yescharacteristic
522#336C22×C11311yescharacteristic
523#336C22×C11311yescharacteristic
524C2×#41—22no—
525C2×#41—22no—
526C2×#41—22no—
527C2×#41—41no—
528C2×#41—41no—
529C2×#41D4×C11314yescomplemented
530C22×Q8—22no—
531C22×Q8—22no—
532C22×Q8—21no—
533C22×Q8—22no—
534C22×Q8—22no—
535C22×Q8—41no—
536C22×Q8—41no—
537C22×Q8C23×C11311yescharacteristic
538C22×Q8C23×C11311yescharacteristic
539C22×D4—21no—
540C22×D4—21no—
541C22×D4—21no—
542C22×D4—21no—
543C22×D4D4×C11311yescharacteristic
544C22×D4C23×C11311yescharacteristic
545C22×D4C23×C11311yescharacteristic
546C23×C4—21no—
547C23×C4—21no—
548C23×C4—21no—
549C23×C4C23×C11311yescharacteristic
550C23×C4C23×C11311yescharacteristic
551C2×SD16—22no—
552C2×SD16—22no—
553C2×SD16—22no—
554C2×SD16—22no—
555C2×SD16—22no—
556C2×SD16—41no—
557C2×D8—22no—
558C2×D8—41no—
559C2×D8—41no—
560C2×M16—22no—
561C2×M16—22no—
562C2×M16—41no—
563C22×C8C23×C11311yescharacteristic
564C22×C8C23×C11311yescharacteristic
565C22×C8C23×C11311yescharacteristic
566C22×C8C23×C11311yescharacteristic
567#124—28no—
568#124—22no—
569#124—22no—
570C22⋊Q8—28no—
571C22⋊Q8—22no—
572C22⋊Q8D4×C11314yescomplemented
573#121—28no—
574#121—22no—
575#121—22no—
576#121—22no—
577#121—22no—
578#121—22no—
579#121—41no—
580#121—44no—
581C4×Q8—22no—
582C4×Q8—22no—
583C4×D4—28no—
584C4×D4—22no—
585C4×D4—22no—
586C2×C4⋊C4—21no—
587C2×C4⋊C4—21no—
588C2×C4⋊C4—22no—
589C2×C4⋊C4—21no—
590C2×C4⋊C4—21no—
591C2×C4⋊C4—41no—
592C2×C4⋊C4D4×C11311yescharacteristic
593C2×C4⋊C4C23×C11311yescharacteristic
594C2×C4⋊C4C23×C11311yescharacteristic
595C2×C4⋊C4C23×C11311yescharacteristic
596C2×C4⋊C4C23×C11311yescharacteristic
597C2×C22⋊C4—21no—
598C2×C22⋊C4—21no—
599C2×C22⋊C4—21no—
600C2×C22⋊C4—21no—
601C2×C22⋊C4—21no—
602C2×C22⋊C4—21no—
603C2×C22⋊C4—21no—
604C2×C22⋊C4—21no—
605C2×C22⋊C4—21no—
606C2×C22⋊C4D4×C11311yescharacteristic
607C2×C22⋊C4D4×C11311yescharacteristic
608C2×C42—21no—
609C2×C42C23×C11311yescharacteristic
610#107—22no—
611#103—22no—
612#103—22no—
613#103—22no—
614#103—22no—
615#103—41no—
616#103D4×C11314yescomplemented
617#102—22no—
618#102—22no—
619#102—22no—
620#102—22no—
621C22⋊C8—22no—
622C22⋊C8—22no—
623C22⋊C8—41no—
624#95—21no—
625#95—21no—
626C24—21no—
627C24—21no—
628C24C2×D4×C11311yescharacteristic
629C24C2×D4×C11311yescharacteristic
630#41—28no—
631#41—44no—
632#41—44no—
633#41—44no—
634C2×Q8—24no—
635C2×Q8—21no—
636C2×Q8—21no—
637C2×Q8—21no—
638C2×Q8—21no—
639C2×Q8—21no—
640C2×Q8—21no—
641C2×Q8—21no—
642C2×Q8—21no—
643C2×Q8—42no—
644C2×Q8—42no—
645C2×Q8—44no—
646C2×Q8—44no—
647C2×Q8—44no—
648C2×Q8—44no—
649C2×Q8C2×D4×C11312yes—
650C2×Q8C2×D4×C11312yes—
651C2×Q8C2×D4×C11312yes—
652C2×Q8#41×C11312yes—
653C2×D4—24no—
654C2×D4—22no—
655C2×D4—24no—
656C2×D4—22no—
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—41no—
669C2×D4—42no—
670C2×D4—42no—
671C2×D4—42no—
672C2×D4—42no—
673C2×D4—42no—
674C2×D4—42no—
675C2×D4—42no—
676C2×D4—42no—
677C2×D4—42no—
678C2×D4—81no—
679C2×D4C2×D4×C11312yes—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—24no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—24no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—42no—
699C22×C4—42no—
700C22×C4—42no—
701C22×C4—42no—
702C22×C4—42no—
703C22×C4—42no—
704C22×C4—81no—
705C22×C4C2×D4×C11311yescharacteristic
706C22×C4C2×D4×C11311yescharacteristic
707C22×C4C2×D4×C11311yescharacteristic
708C22×C4C2×D4×C11311yescharacteristic
709C22×C4C2×D4×C11312yes—
710C22×C4C2×D4×C11312yes—
711C22×C4C24×C11311yescharacteristic
712SD16—44no—
713SD16—44no—
714D8—44no—
715M16—44no—
716C2×C8—21no—
717C2×C8—21no—
718C2×C8—21no—
719C2×C8—21no—
720C2×C8—21no—
721C2×C8—21no—
722C2×C8—21no—
723C2×C8—21no—
724C2×C8—21no—
725C2×C8—21no—
726C2×C8—21no—
727C2×C8C2×D4×C11312yes—
728C4⋊C4—24no—
729C4⋊C4—24no—
730C4⋊C4—22no—
731C4⋊C4—21no—
732C4⋊C4—21no—
733C4⋊C4—21no—
734C4⋊C4—21no—
735C4⋊C4—21no—
736C4⋊C4—21no—
737C4⋊C4—42no—
738C4⋊C4—42no—
739C4⋊C4C2×D4×C11312yes—
740C4⋊C4C2×D4×C11312yes—
741C22⋊C4—24no—
742C22⋊C4—24no—
743C22⋊C4—24no—
744C22⋊C4—24no—
745C22⋊C4—22no—
746C22⋊C4—22no—
747C22⋊C4—42no—
748C22⋊C4—42no—
749C22⋊C4—42no—
750C22⋊C4—42no—
751C22⋊C4—81no—
752C42—24no—
753C42—21no—
754C42—21no—
755C23—21no—
756C23—21no—
757C23—21no—
758C23—21no—
759C23—21no—
760C23—21no—
761C23—21no—
762C23—21no—
763C23—21no—
764C23—21no—
765C23—21no—
766C23—21no—
767C23—22no—
768C23—41no—
769C23—41no—
770C23—41no—
771C23—41no—
772C23—41no—
773C23—41no—
774C23—41no—
775C23—41no—
776C23—41no—
777C23—41no—
778C23—41no—
779C23—41no—
780C23—41no—
781C23#120×C11312yes—
782C23AGL(1,ℤ/8)×C11312yes—
783C23C22×D4×C11311yescharacteristic
784Q8—22no—
785Q8—22no—
786Q8—22no—
787Q8—22no—
788Q8—22no—
789Q8—48no—
790Q8—41no—
791Q8—41no—
792Q8#121×C11314yescomplemented
793D4—22no—
794D4—22no—
795D4—48no—
796D4—44no—
797D4—48no—
798D4—41no—
799D4—41no—
800D4—41no—
801D4—41no—
802D4—41no—
803D4—41no—
804D4—84no—
805D4—84no—
806C2×C4—22no—
807C2×C4—21no—
808C2×C4—22no—
809C2×C4—21no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—21no—
816C2×C4—21no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—21no—
820C2×C4—21no—
821C2×C4—22no—
822C2×C4—21no—
823C2×C4—21no—
824C2×C4—21no—
825C2×C4—21no—
826C2×C4—21no—
827C2×C4—48no—
828C2×C4—48no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—41no—
841C2×C4—41no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—84no—
846C2×C4#120×C11312yes—
847C2×C4C22×D4×C11311yescharacteristic
848C2×C4C22×D4×C11311yescharacteristic
849C2×C4C22×D4×C11311yescharacteristic
850C2×C4C2×#41×C11311yescharacteristic
851C2×C4H(5,𝔽2)×C11311yescharacteristic
852C2×C4H(5,𝔽2)×C11311yescharacteristic
853C8—22no—
854C8—41no—
855C8—41no—
856C8—41no—
857C22—22no—
858C22—22no—
859C22—22no—
860C22—22no—
861C22—22no—
862C22—22no—
863C22—41no—
864C22—41no—
865C22—41no—
866C22—41no—
867C22—41no—
868C22—41no—
869C22—41no—
870C22—41no—
871C22—42no—
872C22—42no—
873C22—42no—
874C22—81no—
875C22—81no—
876C22—81no—
877C22—81no—
878C22—81no—
879C22—81no—
880C22—81no—
881C22—81no—
882C22—81no—
883C22—81no—
884C22—81no—
885C22C2×#120×C11311yescharacteristic
886C22D42×C11311yescharacteristic
887C22#546×C11311yescharacteristic
888C22C2×AGL(1,ℤ/8)×C11311yescharacteristic
889C22#575×C11311yescharacteristic
890C22#577×C11311yescharacteristic
891C22#578×C11311yescharacteristic
892C4—22no—
893C4—24no—
894C4—41no—
895C4—42no—
896C4—41no—
897C4—42no—
898C4—42no—
899C4—41no—
900C4—81no—
901C4—81no—
902C4C2×#121×C11311yescharacteristic
903C4#534×C11311yescharacteristic
904C4D42×C11311yescharacteristic
905C4#546×C11311yescharacteristic
906C2—42no—
907C2—42no—
908C2—82no—
909C2—161no—
910C2C113×#241011yescharacteristic
911C2C113×#300611yescharacteristic
912C2C113×#301311yescharacteristic
913C2C113×#326511yescharacteristic
914C2C113×#327711yescharacteristic
915C2C113×#330811yescharacteristic
916C2C113×#332611yescharacteristic
subgroupG/H
center, socleC23×C113C22×D4
commutator, Frattini, cosocleC22×C4C24×C113
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
1. C2×#548×C113C2semidirect
2. C2×#468×C113C2semidirect
3. C2×#449×C113C2semidirect
4. C2×#448×C113C2semidirect
5. C2×#417×C113C2semidirect
6. C113×#2416C2semidirect
7. C113×#2042C2semidirect
8. C113×#2033C2semidirect
9. C113×#2012C2semidirect
10. C113×#1999C2semidirect
11. C113×#1880C2semidirect
12. C113×#1872C2semidirect
13. C113×#1870C2semidirect
14. C113×#1863C2semidirect
15. C113×#1787C2semidirect
70. C2×#41×C113D4semidirect
113. C22⋊Q8×C113D4semidirect
157. #103×C113D4semidirect
333. Q8×C113#121semidirect
447. #24441C113direct (N × H)
459. C2×#548C2×C113semidirect
460. C2×#468C2×C113semidirect
461. C2×#449C2×C113semidirect
462. C2×#448C2×C113semidirect
463. C2×#417C2×C113semidirect
464. #2416C2×C113semidirect
465. #2042C2×C113semidirect
466. #2033C2×C113semidirect
467. #2012C2×C113semidirect
468. #1999C2×C113semidirect
469. #1880C2×C113semidirect
470. #1872C2×C113semidirect
471. #1870C2×C113semidirect
472. #1863C2×C113semidirect
473. #1787C2×C113semidirect
474. C113#24441direct (N × H)
529. C2×#41D4×C113semidirect
572. C22⋊Q8D4×C113semidirect
616. #103D4×C113semidirect
792. Q8#121×C113semidirect

Maximal subgroups

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

subgroupindex
C2×#548×C1132
C2×#468×C1132
C2×#449×C1132
C2×#448×C1132
C2×#417×C1132
C113×#24162
C113×#20422
C113×#20332
C113×#20122
C113×#19992
C113×#18802
C113×#18722
C113×#18702
C113×#18632
C113×#17872
#24441113