Finite Group Databasebeta

← C113×#25164 #43293184

Subgroups — C113×#25164 #43293184

Order 28928.

1296 conjugacy classes of subgroups.

The subgroup lattice has 856 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#463×C113C211yesmaximal, characteristic, complemented
2C2×#450×C113C211yesmaximal, characteristic, complemented
3C2×#447×C113C211yesmaximal, characteristic
4C2×#440×C113C211yesmaximal, characteristic, complemented
5C113×#2426C211yesmaximal, characteristic, complemented
6D4×C22⋊C4×C113C211yesmaximal, characteristic, complemented
7C113×#2067C211yesmaximal, characteristic, complemented
8C113×#2035C211yesmaximal, characteristic, complemented
9C113×#2033C211yesmaximal, characteristic, complemented
10C113×#2012C211yesmaximal, characteristic, complemented
11C113×#1972C211yesmaximal, characteristic, complemented
12C113×#1924C211yesmaximal, characteristic, complemented
13C113×#1880C211yesmaximal, characteristic, complemented
14C113×#1879C211yesmaximal, characteristic, complemented
15C113×#1864C211yesmaximal, characteristic, complemented
16C23×D4×C113C2211yescharacteristic
17C22×SD16×C113C2211yescharacteristic
18C22×SD16×C113C2211yescharacteristic
19C22×D8×C113C2211yescharacteristic
20C22×D8×C113C2211yescharacteristic
21C2×#124×C113C2211yescharacteristic, complemented
22C2×C22⋊Q8×C113C2211yescharacteristic
23C2×#121×C113C2211yescharacteristic
24C2×C4×Q8×C113C2211yescharacteristic, complemented
25C2×C4×D4×C113C2211yescharacteristic
26C2×C4×D4×C113C2211yescharacteristic
27C22×C22⋊C4×C113—21no—
28#463×C113—24no—
29#450×C113—24no—
30#447×C113—24no—
31#440×C113—24no—
32C2×#107×C113C2211yescharacteristic, complemented
33C2×#106×C113C2211yescharacteristic, complemented
34C2×C4⋊C8×C113C2211yescharacteristic, complemented
35C2×#103×C113C2211yescharacteristic, complemented
36C2×#103×C113C2211yescharacteristic, complemented
37C2×#102×C113C2211yescharacteristic
38C2×#102×C113C2211yescharacteristic
39C2×#102×C113C2211yescharacteristic
40C2×#102×C113C2211yescharacteristic
41C2×#102×C113C2211yescharacteristic, complemented
42C2×#102×C113C2211yescharacteristic, complemented
43C2×C22⋊C8×C113C2211yescharacteristic
44C2×C22⋊C8×C113C2211yescharacteristic
45C2×#97×C113C2211yescharacteristic, complemented
46#396×C113—21no—
47#394×C113—21no—
48#390×C113—21no—
49#390×C113C2211yescharacteristic
50#390×C113C2211yescharacteristic
51#390×C113C2211yescharacteristic, complemented
52#389×C113C2211yescharacteristic, complemented
53#388×C113—21no—
54#386×C113—21no—
55#386×C113—21no—
56#380×C113C2211yescharacteristic
57#379×C113—21no—
58C4×C22⋊C4×C113C2211yescharacteristic
59#340×C113C2211yescharacteristic, complemented
60#340×C113C2211yescharacteristic, complemented
61#336×C113C2211yescharacteristic, complemented
62#336×C113C2211yescharacteristic, complemented
63C25×C113—21no—
64C22×Q8×C113C2311yescharacteristic
65C22×D4×C113—22no—
66C22×D4×C113—22no—
67C22×D4×C113—22no—
68C22×D4×C113—22no—
69C22×D4×C113—21no—
70C22×D4×C113—21no—
71C22×D4×C113—41no—
72C22×D4×C113—41no—
73C22×D4×C113C2311yescharacteristic
74C22×D4×C113C2311yescharacteristic
75C22×D4×C113C2311yescharacteristic
76C23×C4×C113—21no—
77C23×C4×C113—21no—
78C23×C4×C113C2311yescharacteristic
79C2×SD16×C113—22no—
80C2×SD16×C113—22no—
81C2×SD16×C113—22no—
82C2×SD16×C113—22no—
83C2×SD16×C113—41no—
84C2×SD16×C113D414yescomplemented
85C2×D8×C113—22no—
86C2×D8×C113—22no—
87C2×D8×C113—22no—
88C2×D8×C113—22no—
89C2×D8×C113—22no—
90C2×D8×C113—41no—
91C22×C8×C113C2311yescharacteristic
92C22×C8×C113C2311yescharacteristic
93C22×C8×C113C2311yescharacteristic
94C22×C8×C113C2311yescharacteristic
95#124×C113—22no—
96#124×C113—41no—
97C22⋊Q8×C113—22no—
98C22⋊Q8×C113—41no—
99#121×C113—22no—
100#121×C113—41no—
101C4×Q8×C113—22no—
102C4×Q8×C113—41no—
103C4×D4×C113—22no—
104C4×D4×C113—22no—
105C4×D4×C113—41no—
106C4×D4×C113—41no—
107C2×C4⋊C4×C113—21no—
108C2×C4⋊C4×C113—21no—
109C2×C4⋊C4×C113—21no—
110C2×C4⋊C4×C113C2311yescharacteristic
111C2×C4⋊C4×C113C2311yescharacteristic
112C2×C4⋊C4×C113C2311yescharacteristic
113C2×C4⋊C4×C113C2311yescharacteristic
114C2×C22⋊C4×C113—21no—
115C2×C22⋊C4×C113—21no—
116C2×C22⋊C4×C113—21no—
117C2×C22⋊C4×C113—21no—
118C2×C22⋊C4×C113—21no—
119C2×C22⋊C4×C113—21no—
120C2×C22⋊C4×C113—21no—
121C2×C22⋊C4×C113—21no—
122C2×C22⋊C4×C113—21no—
123C2×C22⋊C4×C113—21no—
124C2×C22⋊C4×C113—21no—
125C2×C22⋊C4×C113—21no—
126C2×C22⋊C4×C113—21no—
127C2×C22⋊C4×C113—44no—
128C2×C22⋊C4×C113D411yescharacteristic
129C2×C22⋊C4×C113D411yescharacteristic
130C2×C42×C113—21no—
131C2×C42×C113C2311yescharacteristic
132C2×C42×C113C2311yescharacteristic
133#107×C113—22no—
134#106×C113—41no—
135C4⋊C8×C113—22no—
136#103×C113—22no—
137#103×C113—22no—
138#102×C113—22no—
139#102×C113—22no—
140#102×C113—22no—
141#102×C113—22no—
142#102×C113—41no—
143#102×C113D414yes—
144C22⋊C8×C113—22no—
145C22⋊C8×C113—22no—
146#97×C113—22no—
147#95×C113—21no—
148#95×C113—21no—
149#95×C113D411yescharacteristic
150#95×C113D411yescharacteristic
151C24×C113—21no—
152C24×C113—24no—
153C24×C113—21no—
154C24×C113—21no—
155C24×C113—42no—
156C24×C113—42no—
157C24×C113—42no—
158C24×C113—42no—
159C24×C113—81no—
160C24×C113—81no—
161C24×C113C2×D411yescharacteristic
162C2×Q8×C113—21no—
163C2×Q8×C113—21no—
164C2×Q8×C113—21no—
165C2×Q8×C113—21no—
166C2×Q8×C113—21no—
167C2×Q8×C113C2×D412yes—
168C2×D4×C113—24no—
169C2×D4×C113—21no—
170C2×D4×C113—21no—
171C2×D4×C113—21no—
172C2×D4×C113—21no—
173C2×D4×C113—21no—
174C2×D4×C113—21no—
175C2×D4×C113—21no—
176C2×D4×C113—21no—
177C2×D4×C113—21no—
178C2×D4×C113—21no—
179C2×D4×C113—21no—
180C2×D4×C113—21no—
181C2×D4×C113—21no—
182C2×D4×C113—21no—
183C2×D4×C113—42no—
184C2×D4×C113—42no—
185C2×D4×C113—42no—
186C2×D4×C113—44no—
187C2×D4×C113—44no—
188C2×D4×C113—44no—
189C2×D4×C113—44no—
190C2×D4×C113—42no—
191C2×D4×C113—81no—
192C2×D4×C113C2×D412yes—
193C2×D4×C113C2×D412yes—
194C2×D4×C113#4112yes—
195C2×D4×C113#4112yes—
196C22×C4×C113—21no—
197C22×C4×C113—21no—
198C22×C4×C113—21no—
199C22×C4×C113—21no—
200C22×C4×C113—21no—
201C22×C4×C113—21no—
202C22×C4×C113—21no—
203C22×C4×C113—21no—
204C22×C4×C113—21no—
205C22×C4×C113—21no—
206C22×C4×C113—21no—
207C22×C4×C113—42no—
208C22×C4×C113—42no—
209C22×C4×C113—42no—
210C22×C4×C113—42no—
211C22×C4×C113—81no—
212C22×C4×C113—81no—
213C22×C4×C113C2×D411yescharacteristic
214C22×C4×C113C2×D411yescharacteristic
215C22×C4×C113C2×D411yescharacteristic
216C22×C4×C113C2×D411yescharacteristic
217C22×C4×C113C2×D411yescharacteristic
218C22×C4×C113C2411yescharacteristic
219SD16×C113—28no—
220SD16×C113—44no—
221D8×C113—44no—
222D8×C113—44no—
223C2×C8×C113—21no—
224C2×C8×C113—21no—
225C2×C8×C113—21no—
226C2×C8×C113—21no—
227C2×C8×C113—21no—
228C2×C8×C113—21no—
229C2×C8×C113—21no—
230C2×C8×C113—21no—
231C2×C8×C113—21no—
232C2×C8×C113—21no—
233C2×C8×C113C2×D412yes—
234C2×C8×C113C2×D412yes—
235C4⋊C4×C113—21no—
236C4⋊C4×C113—21no—
237C4⋊C4×C113—21no—
238C4⋊C4×C113—21no—
239C4⋊C4×C113—21no—
240C4⋊C4×C113—21no—
241C4⋊C4×C113—21no—
242C4⋊C4×C113—42no—
243C4⋊C4×C113—42no—
244C4⋊C4×C113—81no—
245C4⋊C4×C113C2×D412yes—
246C22⋊C4×C113—22no—
247C22⋊C4×C113—41no—
248C22⋊C4×C113—42no—
249C22⋊C4×C113—42no—
250C22⋊C4×C113—42no—
251C22⋊C4×C113—42no—
252C22⋊C4×C113—42no—
253C22⋊C4×C113—42no—
254C22⋊C4×C113—42no—
255C22⋊C4×C113—42no—
256C22⋊C4×C113—42no—
257C22⋊C4×C113—42no—
258C22⋊C4×C113—81no—
259C22⋊C4×C113—81no—
260C22⋊C4×C113—81no—
261C42×C113—21no—
262C42×C113—21no—
263C42×C113—21no—
264C42×C113—21no—
265C42×C113—42no—
266C23×C113—21no—
267C23×C113—22no—
268C23×C113—21no—
269C23×C113—22no—
270C23×C113—22no—
271C23×C113—21no—
272C23×C113—21no—
273C23×C113—21no—
274C23×C113—21no—
275C23×C113—22no—
276C23×C113—48no—
277C23×C113—48no—
278C23×C113—41no—
279C23×C113—41no—
280C23×C113—41no—
281C23×C113—41no—
282C23×C113—41no—
283C23×C113—41no—
284C23×C113—41no—
285C23×C113—41no—
286C23×C113—41no—
287C23×C113—41no—
288C23×C113—41no—
289C23×C113—41no—
290C23×C113—41no—
291C23×C113—41no—
292C23×C113—41no—
293C23×C113—41no—
294C23×C113—41no—
295C23×C113—84no—
296C23×C113—84no—
297C23×C113—84no—
298C23×C113—84no—
299C23×C113—84no—
300C23×C113AGL(1,ℤ/8)12yes—
301C23×C113C22×D411yescharacteristic
302Q8×C113—22no—
303Q8×C113—22no—
304Q8×C113—41no—
305Q8×C113—41no—
306D4×C113—22no—
307D4×C113—22no—
308D4×C113—22no—
309D4×C113—22no—
310D4×C113—22no—
311D4×C113—48no—
312D4×C113—41no—
313D4×C113—41no—
314D4×C113—41no—
315D4×C113—41no—
316D4×C113—41no—
317D4×C113—41no—
318D4×C113—84no—
319D4×C113#12114yes—
320C2×C4×C113—21no—
321C2×C4×C113—21no—
322C2×C4×C113—21no—
323C2×C4×C113—21no—
324C2×C4×C113—21no—
325C2×C4×C113—22no—
326C2×C4×C113—22no—
327C2×C4×C113—21no—
328C2×C4×C113—21no—
329C2×C4×C113—21no—
330C2×C4×C113—21no—
331C2×C4×C113—21no—
332C2×C4×C113—21no—
333C2×C4×C113—21no—
334C2×C4×C113—21no—
335C2×C4×C113—21no—
336C2×C4×C113—21no—
337C2×C4×C113—41no—
338C2×C4×C113—41no—
339C2×C4×C113—41no—
340C2×C4×C113—41no—
341C2×C4×C113—41no—
342C2×C4×C113—41no—
343C2×C4×C113—41no—
344C2×C4×C113—41no—
345C2×C4×C113—41no—
346C2×C4×C113—41no—
347C2×C4×C113—41no—
348C2×C4×C113—41no—
349C2×C4×C113—41no—
350C2×C4×C113—41no—
351C2×C4×C113—41no—
352C2×C4×C113—41no—
353C2×C4×C113—41no—
354C2×C4×C113—84no—
355C2×C4×C113—84no—
356C2×C4×C113C22×D411yescharacteristic
357C2×C4×C113C22×D411yescharacteristic
358C2×C4×C113C2×#4111yescharacteristic
359C2×C4×C113C2×#4111yescharacteristic
360C2×C4×C113H(5,𝔽2)11yescharacteristic
361C2×C4×C113H(5,𝔽2)11yescharacteristic
362C8×C113—22no—
363C8×C113—22no—
364C8×C113—41no—
365C8×C113—41no—
366C22×C113—22no—
367C22×C113—24no—
368C22×C113—22no—
369C22×C113—22no—
370C22×C113—42no—
371C22×C113—41no—
372C22×C113—42no—
373C22×C113—41no—
374C22×C113—42no—
375C22×C113—42no—
376C22×C113—41no—
377C22×C113—42no—
378C22×C113—41no—
379C22×C113—42no—
380C22×C113—42no—
381C22×C113—42no—
382C22×C113—42no—
383C22×C113—816no—
384C22×C113—81no—
385C22×C113—81no—
386C22×C113—81no—
387C22×C113—81no—
388C22×C113—81no—
389C22×C113—81no—
390C22×C113—81no—
391C22×C113—81no—
392C22×C113—81no—
393C22×C113—81no—
394C22×C113—81no—
395C22×C113#52511yescharacteristic
396C22×C113D4211yescharacteristic
397C22×C113D4211yescharacteristic
398C22×C113C2×AGL(1,ℤ/8)11yescharacteristic
399C22×C113#57511yescharacteristic
400C22×C113#57611yescharacteristic
401C22×C113#57711yescharacteristic
402C4×C113—41no—
403C4×C113—42no—
404C4×C113—41no—
405C4×C113—42no—
406C4×C113—41no—
407C4×C113—41no—
408C4×C113—41no—
409C4×C113—81no—
410C4×C113—81no—
411C4×C113—81no—
412C4×C113C2×#12111yescharacteristic
413C4×C113#53811yescharacteristic
414C4×C113#54611yescharacteristic
415C4×C113#54611yescharacteristic
416#25164C11311yesmaximal, characteristic, direct product factor, Sylow
417C2×C113—42no—
418C2×C113—44no—
419C2×C113—82no—
420C2×C113—161no—
421C2×C113#242411yescharacteristic
422C2×C113#311411yescharacteristic
423C2×C113#311811yescharacteristic
424C2×C113#326411yescharacteristic
425C2×C113#326511yescharacteristic
426C2×C113#326811yescharacteristic
427C2×C113#327511yescharacteristic
428C2×#463C2×C11311yescharacteristic, complemented
429C2×#450C2×C11311yescharacteristic, complemented
430C2×#447C2×C11311yescharacteristic
431C2×#440C2×C11311yescharacteristic, complemented
432#2426C2×C11311yescharacteristic, complemented
433D4×C22⋊C4C2×C11311yescharacteristic, complemented
434#2067C2×C11311yescharacteristic, complemented
435#2035C2×C11311yescharacteristic, complemented
436#2033C2×C11311yescharacteristic, complemented
437#2012C2×C11311yescharacteristic, complemented
438#1972C2×C11311yescharacteristic, complemented
439#1924C2×C11311yescharacteristic, complemented
440#1880C2×C11311yescharacteristic, complemented
441#1879C2×C11311yescharacteristic, complemented
442#1864C2×C11311yescharacteristic, complemented
443C113#2516411yescharacteristic, direct product factor, Sylow
444C23×D4C22×C11311yescharacteristic
445C22×SD16C22×C11311yescharacteristic
446C22×SD16C22×C11311yescharacteristic
447C22×D8C22×C11311yescharacteristic
448C22×D8C22×C11311yescharacteristic
449C2×#124C22×C11311yescharacteristic, complemented
450C2×C22⋊Q8C22×C11311yescharacteristic
451C2×#121C22×C11311yescharacteristic
452C2×C4×Q8C22×C11311yescharacteristic, complemented
453C2×C4×D4C22×C11311yescharacteristic
454C2×C4×D4C22×C11311yescharacteristic
455C22×C22⋊C4—21no—
456#463—24no—
457#450—24no—
458#447—24no—
459#440—24no—
460C2×#107C22×C11311yescharacteristic, complemented
461C2×#106C22×C11311yescharacteristic, complemented
462C2×C4⋊C8C22×C11311yescharacteristic, complemented
463C2×#103C22×C11311yescharacteristic, complemented
464C2×#103C22×C11311yescharacteristic, complemented
465C2×#102C22×C11311yescharacteristic
466C2×#102C22×C11311yescharacteristic
467C2×#102C22×C11311yescharacteristic
468C2×#102C22×C11311yescharacteristic
469C2×#102C22×C11311yescharacteristic, complemented
470C2×#102C22×C11311yescharacteristic, complemented
471C2×C22⋊C8C22×C11311yescharacteristic
472C2×C22⋊C8C22×C11311yescharacteristic
473C2×#97C22×C11311yescharacteristic, complemented
474#396—21no—
475#394—21no—
476#390—21no—
477#390C22×C11311yescharacteristic
478#390C22×C11311yescharacteristic
479#390C22×C11311yescharacteristic, complemented
480#389C22×C11311yescharacteristic, complemented
481#388—21no—
482#386—21no—
483#386—21no—
484#380C22×C11311yescharacteristic
485#379—21no—
486C4×C22⋊C4C22×C11311yescharacteristic
487#340C22×C11311yescharacteristic, complemented
488#340C22×C11311yescharacteristic, complemented
489#336C22×C11311yescharacteristic, complemented
490#336C22×C11311yescharacteristic, complemented
491C25—21no—
492C22×Q8C23×C11311yescharacteristic
493C22×D4—22no—
494C22×D4—22no—
495C22×D4—22no—
496C22×D4—22no—
497C22×D4—21no—
498C22×D4—21no—
499C22×D4—41no—
500C22×D4—41no—
501C22×D4C23×C11311yescharacteristic
502C22×D4C23×C11311yescharacteristic
503C22×D4C23×C11311yescharacteristic
504C23×C4—21no—
505C23×C4—21no—
506C23×C4C23×C11311yescharacteristic
507C2×SD16—22no—
508C2×SD16—22no—
509C2×SD16—22no—
510C2×SD16—22no—
511C2×SD16—41no—
512C2×SD16D4×C11314yescomplemented
513C2×D8—22no—
514C2×D8—22no—
515C2×D8—22no—
516C2×D8—22no—
517C2×D8—22no—
518C2×D8—41no—
519C22×C8C23×C11311yescharacteristic
520C22×C8C23×C11311yescharacteristic
521C22×C8C23×C11311yescharacteristic
522C22×C8C23×C11311yescharacteristic
523#124—22no—
524#124—41no—
525C22⋊Q8—22no—
526C22⋊Q8—41no—
527#121—22no—
528#121—41no—
529C4×Q8—22no—
530C4×Q8—41no—
531C4×D4—22no—
532C4×D4—22no—
533C4×D4—41no—
534C4×D4—41no—
535C2×C4⋊C4—21no—
536C2×C4⋊C4—21no—
537C2×C4⋊C4—21no—
538C2×C4⋊C4C23×C11311yescharacteristic
539C2×C4⋊C4C23×C11311yescharacteristic
540C2×C4⋊C4C23×C11311yescharacteristic
541C2×C4⋊C4C23×C11311yescharacteristic
542C2×C22⋊C4—21no—
543C2×C22⋊C4—21no—
544C2×C22⋊C4—21no—
545C2×C22⋊C4—21no—
546C2×C22⋊C4—21no—
547C2×C22⋊C4—21no—
548C2×C22⋊C4—21no—
549C2×C22⋊C4—21no—
550C2×C22⋊C4—21no—
551C2×C22⋊C4—21no—
552C2×C22⋊C4—21no—
553C2×C22⋊C4—21no—
554C2×C22⋊C4—21no—
555C2×C22⋊C4—44no—
556C2×C22⋊C4D4×C11311yescharacteristic
557C2×C22⋊C4D4×C11311yescharacteristic
558C2×C42—21no—
559C2×C42C23×C11311yescharacteristic
560C2×C42C23×C11311yescharacteristic
561#107—22no—
562#106—41no—
563C4⋊C8—22no—
564#103—22no—
565#103—22no—
566#102—22no—
567#102—22no—
568#102—22no—
569#102—22no—
570#102—41no—
571#102D4×C11314yes—
572C22⋊C8—22no—
573C22⋊C8—22no—
574#97—22no—
575#95—21no—
576#95—21no—
577#95D4×C11311yescharacteristic
578#95D4×C11311yescharacteristic
579C24—21no—
580C24—24no—
581C24—21no—
582C24—21no—
583C24—42no—
584C24—42no—
585C24—42no—
586C24—42no—
587C24—81no—
588C24—81no—
589C24C2×D4×C11311yescharacteristic
590C2×Q8—21no—
591C2×Q8—21no—
592C2×Q8—21no—
593C2×Q8—21no—
594C2×Q8—21no—
595C2×Q8C2×D4×C11312yes—
596C2×D4—24no—
597C2×D4—21no—
598C2×D4—21no—
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—21no—
605C2×D4—21no—
606C2×D4—21no—
607C2×D4—21no—
608C2×D4—21no—
609C2×D4—21no—
610C2×D4—21no—
611C2×D4—42no—
612C2×D4—42no—
613C2×D4—42no—
614C2×D4—44no—
615C2×D4—44no—
616C2×D4—44no—
617C2×D4—44no—
618C2×D4—42no—
619C2×D4—81no—
620C2×D4C2×D4×C11312yes—
621C2×D4C2×D4×C11312yes—
622C2×D4#41×C11312yes—
623C2×D4#41×C11312yes—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—42no—
636C22×C4—42no—
637C22×C4—42no—
638C22×C4—42no—
639C22×C4—81no—
640C22×C4—81no—
641C22×C4C2×D4×C11311yescharacteristic
642C22×C4C2×D4×C11311yescharacteristic
643C22×C4C2×D4×C11311yescharacteristic
644C22×C4C2×D4×C11311yescharacteristic
645C22×C4C2×D4×C11311yescharacteristic
646C22×C4C24×C11311yescharacteristic
647SD16—28no—
648SD16—44no—
649D8—44no—
650D8—44no—
651C2×C8—21no—
652C2×C8—21no—
653C2×C8—21no—
654C2×C8—21no—
655C2×C8—21no—
656C2×C8—21no—
657C2×C8—21no—
658C2×C8—21no—
659C2×C8—21no—
660C2×C8—21no—
661C2×C8C2×D4×C11312yes—
662C2×C8C2×D4×C11312yes—
663C4⋊C4—21no—
664C4⋊C4—21no—
665C4⋊C4—21no—
666C4⋊C4—21no—
667C4⋊C4—21no—
668C4⋊C4—21no—
669C4⋊C4—21no—
670C4⋊C4—42no—
671C4⋊C4—42no—
672C4⋊C4—81no—
673C4⋊C4C2×D4×C11312yes—
674C22⋊C4—22no—
675C22⋊C4—41no—
676C22⋊C4—42no—
677C22⋊C4—42no—
678C22⋊C4—42no—
679C22⋊C4—42no—
680C22⋊C4—42no—
681C22⋊C4—42no—
682C22⋊C4—42no—
683C22⋊C4—42no—
684C22⋊C4—42no—
685C22⋊C4—42no—
686C22⋊C4—81no—
687C22⋊C4—81no—
688C22⋊C4—81no—
689C42—21no—
690C42—21no—
691C42—21no—
692C42—21no—
693C42—42no—
694C23—21no—
695C23—22no—
696C23—21no—
697C23—22no—
698C23—22no—
699C23—21no—
700C23—21no—
701C23—21no—
702C23—21no—
703C23—22no—
704C23—48no—
705C23—48no—
706C23—41no—
707C23—41no—
708C23—41no—
709C23—41no—
710C23—41no—
711C23—41no—
712C23—41no—
713C23—41no—
714C23—41no—
715C23—41no—
716C23—41no—
717C23—41no—
718C23—41no—
719C23—41no—
720C23—41no—
721C23—41no—
722C23—41no—
723C23—84no—
724C23—84no—
725C23—84no—
726C23—84no—
727C23—84no—
728C23AGL(1,ℤ/8)×C11312yes—
729C23C22×D4×C11311yescharacteristic
730Q8—22no—
731Q8—22no—
732Q8—41no—
733Q8—41no—
734D4—22no—
735D4—22no—
736D4—22no—
737D4—22no—
738D4—22no—
739D4—48no—
740D4—41no—
741D4—41no—
742D4—41no—
743D4—41no—
744D4—41no—
745D4—41no—
746D4—84no—
747D4#121×C11314yes—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—84no—
783C2×C4—84no—
784C2×C4C22×D4×C11311yescharacteristic
785C2×C4C22×D4×C11311yescharacteristic
786C2×C4C2×#41×C11311yescharacteristic
787C2×C4C2×#41×C11311yescharacteristic
788C2×C4H(5,𝔽2)×C11311yescharacteristic
789C2×C4H(5,𝔽2)×C11311yescharacteristic
790C8—22no—
791C8—22no—
792C8—41no—
793C8—41no—
794C22—22no—
795C22—24no—
796C22—22no—
797C22—22no—
798C22—42no—
799C22—41no—
800C22—42no—
801C22—41no—
802C22—42no—
803C22—42no—
804C22—41no—
805C22—42no—
806C22—41no—
807C22—42no—
808C22—42no—
809C22—42no—
810C22—42no—
811C22—816no—
812C22—81no—
813C22—81no—
814C22—81no—
815C22—81no—
816C22—81no—
817C22—81no—
818C22—81no—
819C22—81no—
820C22—81no—
821C22—81no—
822C22—81no—
823C22#525×C11311yescharacteristic
824C22D42×C11311yescharacteristic
825C22D42×C11311yescharacteristic
826C22C2×AGL(1,ℤ/8)×C11311yescharacteristic
827C22#575×C11311yescharacteristic
828C22#576×C11311yescharacteristic
829C22#577×C11311yescharacteristic
830C4—41no—
831C4—42no—
832C4—41no—
833C4—42no—
834C4—41no—
835C4—41no—
836C4—41no—
837C4—81no—
838C4—81no—
839C4—81no—
840C4C2×#121×C11311yescharacteristic
841C4#538×C11311yescharacteristic
842C4#546×C11311yescharacteristic
843C4#546×C11311yescharacteristic
844C2—42no—
845C2—44no—
846C2—82no—
847C2—161no—
848C2C113×#242411yescharacteristic
849C2C113×#311411yescharacteristic
850C2C113×#311811yescharacteristic
851C2C113×#326411yescharacteristic
852C2C113×#326511yescharacteristic
853C2C113×#326811yescharacteristic
854C2C113×#327511yescharacteristic
subgroupG/H
center, socleC23×C113C22×D4
commutator, Frattini, cosocleC22×C4C24×C113
prime radicalC2×#447×C113C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C113 ◁ C4×C22⋊C4×C113 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#463×C113C2semidirect
2. C2×#450×C113C2semidirect
4. C2×#440×C113C2semidirect
5. C113×#2426C2semidirect
6. D4×C22⋊C4×C113C2semidirect
7. C113×#2067C2semidirect
8. C113×#2035C2semidirect
9. C113×#2033C2semidirect
10. C113×#2012C2semidirect
11. C113×#1972C2semidirect
12. C113×#1924C2semidirect
13. C113×#1880C2semidirect
14. C113×#1879C2semidirect
15. C113×#1864C2semidirect
21. C2×#124×C113C22semidirect
24. C2×C4×Q8×C113C22semidirect
32. C2×#107×C113C22semidirect
33. C2×#106×C113C22semidirect
34. C2×C4⋊C8×C113C22semidirect
35. C2×#103×C113C22semidirect
36. C2×#103×C113C22semidirect
41. C2×#102×C113C22semidirect
42. C2×#102×C113C22semidirect
45. C2×#97×C113C22semidirect
51. #390×C113C22semidirect
52. #389×C113C22semidirect
59. #340×C113C22semidirect
60. #340×C113C22semidirect
61. #336×C113C22semidirect
62. #336×C113C22semidirect
84. C2×SD16×C113D4semidirect
416. #25164C113direct (N × H)
428. C2×#463C2×C113semidirect
429. C2×#450C2×C113semidirect
431. C2×#440C2×C113semidirect
432. #2426C2×C113semidirect
433. D4×C22⋊C4C2×C113semidirect
434. #2067C2×C113semidirect
435. #2035C2×C113semidirect
436. #2033C2×C113semidirect
437. #2012C2×C113semidirect
438. #1972C2×C113semidirect
439. #1924C2×C113semidirect
440. #1880C2×C113semidirect
441. #1879C2×C113semidirect
442. #1864C2×C113semidirect
443. C113#25164direct (N × H)
449. C2×#124C22×C113semidirect
452. C2×C4×Q8C22×C113semidirect
460. C2×#107C22×C113semidirect
461. C2×#106C22×C113semidirect
462. C2×C4⋊C8C22×C113semidirect
463. C2×#103C22×C113semidirect
464. C2×#103C22×C113semidirect
469. C2×#102C22×C113semidirect
470. C2×#102C22×C113semidirect
473. C2×#97C22×C113semidirect
479. #390C22×C113semidirect
480. #389C22×C113semidirect
487. #340C22×C113semidirect
488. #340C22×C113semidirect
489. #336C22×C113semidirect
490. #336C22×C113semidirect
512. C2×SD16D4×C113semidirect

Maximal subgroups

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

subgroupindex
C2×#463×C1132
C2×#450×C1132
C2×#447×C1132
C2×#440×C1132
C113×#24262
D4×C22⋊C4×C1132
C113×#20672
C113×#20352
C113×#20332
C113×#20122
C113×#19722
C113×#19242
C113×#18802
C113×#18792
C113×#18642
#25164113