Finite Group Databasebeta

← C113×#22419 #43290439

Subgroups — C113×#22419 #43290439

Order 28928.

1670 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#546×C113C211yesmaximal, characteristic
2C2×#435×C113C211yesmaximal, characteristic, complemented
3C2×#417×C113C211yesmaximal, characteristic, complemented
4C22×#102×C113C211yesmaximal, characteristic, complemented
5D4×C4⋊C4×C113C211yesmaximal, characteristic, complemented
6C113×#1983C211yesmaximal, characteristic, complemented
7C113×#1959C211yesmaximal, characteristic, complemented
8C113×#1895C211yesmaximal, characteristic, complemented
9C113×#1892C211yesmaximal, characteristic, complemented
10C113×#1874C211yesmaximal, characteristic, complemented
11C113×#1872C211yesmaximal, characteristic, complemented
12C113×#1802C211yesmaximal, characteristic, complemented
13C113×#1788C211yesmaximal, characteristic, complemented
14C113×#1786C211yesmaximal, characteristic, complemented
15C113×#1762C211yesmaximal, characteristic, complemented
16C22×#41×C113C2211yescharacteristic
17C23×D4×C113C2211yescharacteristic
18C22×M16×C113C2211yescharacteristic, complemented
19C23×C8×C113C2211yescharacteristic
20#546×C113—24no—
21#546×C113C418yescomplemented
22C2×#124×C113C2211yescharacteristic
23C2×#123×C113—21no—
24C2×C22⋊Q8×C113C2211yescharacteristic
25C2×#121×C113—21no—
26C2×#121×C113C2211yescharacteristic
27C2×#120×C113—21no—
28C2×C4×D4×C113—21no—
29C2×C4×D4×C113C2211yescharacteristic
30C2×C4×D4×C113C2211yescharacteristic
31C22×C4⋊C4×C113C2211yescharacteristic
32C22×C4⋊C4×C113C2211yescharacteristic, complemented
33C22×C22⋊C4×C113—21no—
34#435×C113—24no—
35C2×C4⋊C8×C113C2211yescharacteristic, complemented
36#417×C113—24no—
37C2×#103×C113C2211yescharacteristic, complemented
38C2×#103×C113C2211yescharacteristic, complemented
39C2×#103×C113C2211yescharacteristic, complemented
40C2×#103×C113C2211yescharacteristic, complemented
41C2×#102×C113—24no—
42C2×#102×C113C2211yescharacteristic
43C2×#102×C113C2211yescharacteristic
44C2×#102×C113C2211yescharacteristic
45C2×#102×C113C2211yescharacteristic
46C2×#102×C113C2211yescharacteristic
47C2×#102×C113C2211yescharacteristic
48C2×#102×C113C2211yescharacteristic
49C2×#102×C113C2211yescharacteristic
50C2×C22⋊C8×C113C2211yescharacteristic
51C2×C22⋊C8×C113C2211yescharacteristic, complemented
52C2×#97×C113C2211yescharacteristic, complemented
53#389×C113—21no—
54#385×C113—21no—
55#385×C113—21no—
56#384×C113C2211yescharacteristic, complemented
57#380×C113C2211yescharacteristic
58#380×C113C2211yescharacteristic, complemented
59C4×C4⋊C4×C113C2211yescharacteristic, complemented
60#340×C113C2211yescharacteristic, complemented
61#340×C113C2211yescharacteristic, complemented
62#340×C113C2211yescharacteristic, complemented
63#340×C113C2211yescharacteristic, complemented
64C25×C113—21no—
65C2×#41×C113—22no—
66C2×#41×C113—22no—
67C2×#41×C113—22no—
68C2×#41×C113—41no—
69C2×#41×C113—41no—
70C2×#41×C113C2×C414yescomplemented
71C22×Q8×C113C2311yescharacteristic
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—41no—
79C22×D4×C113—41no—
80C22×D4×C113C2×C414yescomplemented
81C22×D4×C113D411yescharacteristic
82C22×D4×C113C2311yescharacteristic
83C22×D4×C113C2311yescharacteristic
84C23×C4×C113—21no—
85C23×C4×C113—21no—
86C23×C4×C113—21no—
87C23×C4×C113—21no—
88C23×C4×C113C2311yescharacteristic
89C23×C4×C113C2311yescharacteristic
90C2×M16×C113—22no—
91C2×M16×C113—22no—
92C2×M16×C113—41no—
93C22×C8×C113—22no—
94C22×C8×C113—22no—
95C22×C8×C113—41no—
96C22×C8×C113C2311yescharacteristic
97C22×C8×C113C2311yescharacteristic
98C22×C8×C113C2311yescharacteristic
99C22×C8×C113C2311yescharacteristic
100#124×C113—22no—
101#124×C113C2×C414yescomplemented
102#123×C113—28no—
103C22⋊Q8×C113—22no—
104C22⋊Q8×C113C2×C414yescomplemented
105#121×C113—22no—
106#121×C113—28no—
107#121×C113C2×C414yescomplemented
108#120×C113—28no—
109C4×D4×C113—22no—
110C4×D4×C113—44no—
111C4×D4×C113C2×C414yes—
112C4×D4×C113C2×C414yescomplemented
113C4×D4×C113D414yes—
114C2×C4⋊C4×C113—21no—
115C2×C4⋊C4×C113—22no—
116C2×C4⋊C4×C113—22no—
117C2×C4⋊C4×C113—21no—
118C2×C4⋊C4×C113—21no—
119C2×C4⋊C4×C113—21no—
120C2×C4⋊C4×C113—21no—
121C2×C4⋊C4×C113—41no—
122C2×C4⋊C4×C113—41no—
123C2×C4⋊C4×C113D411yescharacteristic
124C2×C4⋊C4×C113C2311yescharacteristic
125C2×C4⋊C4×C113C2311yescharacteristic
126C2×C4⋊C4×C113C2311yescharacteristic
127C2×C4⋊C4×C113C2311yescharacteristic
128C2×C4⋊C4×C113C2311yescharacteristic
129C2×C22⋊C4×C113—21no—
130C2×C22⋊C4×C113—21no—
131C2×C22⋊C4×C113—21no—
132C2×C22⋊C4×C113—21no—
133C2×C22⋊C4×C113—21no—
134C2×C22⋊C4×C113—28no—
135C2×C22⋊C4×C113—21no—
136C2×C22⋊C4×C113—21no—
137C2×C22⋊C4×C113D411yescharacteristic
138C2×C22⋊C4×C113D411yescharacteristic
139C2×C42×C113—21no—
140C2×C42×C113C2311yescharacteristic
141C4⋊C8×C113—22no—
142#103×C113—22no—
143#103×C113—22no—
144#103×C113—41no—
145#103×C113—41no—
146#102×C113—22no—
147#102×C113—22no—
148#102×C113—22no—
149#102×C113—22no—
150#102×C113—22no—
151#102×C113—41no—
152#102×C113—41no—
153#102×C113D414yescomplemented
154C22⋊C8×C113—22no—
155C22⋊C8×C113—22no—
156#97×C113—22no—
157#95×C113—21no—
158#95×C113—21no—
159#95×C113—21no—
160C24×C113—21no—
161C24×C113—21no—
162C24×C113—24no—
163C24×C113—42no—
164C24×C113—42no—
165C24×C113—42no—
166C24×C113—42no—
167C24×C113—81no—
168C24×C113—81no—
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—21no—
176C2×Q8×C113—21no—
177C2×Q8×C113—21no—
178C2×Q8×C113—21no—
179C2×Q8×C113—21no—
180C2×Q8×C113C22×C412yes—
181C2×D4×C113—22no—
182C2×D4×C113—22no—
183C2×D4×C113—28no—
184C2×D4×C113—24no—
185C2×D4×C113—24no—
186C2×D4×C113—24no—
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—44no—
196C2×D4×C113—44no—
197C2×D4×C113—44no—
198C2×D4×C113—42no—
199C2×D4×C113—42no—
200C2×D4×C113—42no—
201C2×D4×C113—42no—
202C2×D4×C113—81no—
203C2×D4×C113—81no—
204C2×D4×C113C22⋊C414yes—
205C2×D4×C113C22×C412yes—
206C2×D4×C113C22×C412yes—
207C2×D4×C113C2×D412yes—
208C2×D4×C113#4112yes—
209C22×C4×C113—21no—
210C22×C4×C113—21no—
211C22×C4×C113—21no—
212C22×C4×C113—21no—
213C22×C4×C113—21no—
214C22×C4×C113—21no—
215C22×C4×C113—21no—
216C22×C4×C113—21no—
217C22×C4×C113—21no—
218C22×C4×C113—21no—
219C22×C4×C113—21no—
220C22×C4×C113—24no—
221C22×C4×C113—24no—
222C22×C4×C113—21no—
223C22×C4×C113—21no—
224C22×C4×C113—21no—
225C22×C4×C113—42no—
226C22×C4×C113—42no—
227C22×C4×C113—42no—
228C22×C4×C113—42no—
229C22×C4×C113—42no—
230C22×C4×C113—42no—
231C22×C4×C113—81no—
232C22×C4×C113—81no—
233C22×C4×C113—81no—
234C22×C4×C113—81no—
235C22×C4×C113C22×C412yes—
236C22×C4×C113C22×C412yes—
237C22×C4×C113C2×D411yescharacteristic
238C22×C4×C113C2×D411yescharacteristic
239C22×C4×C113C2×D411yescharacteristic
240C22×C4×C113C2×D411yescharacteristic
241C22×C4×C113C2×D412yes—
242C22×C4×C113C2×D412yes—
243C22×C4×C113C2411yescharacteristic
244M16×C113—44no—
245C2×C8×C113—21no—
246C2×C8×C113—21no—
247C2×C8×C113—21no—
248C2×C8×C113—21no—
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—44no—
257C2×C8×C113C2×D412yes—
258C4⋊C4×C113—24no—
259C4⋊C4×C113—21no—
260C4⋊C4×C113—21no—
261C4⋊C4×C113—21no—
262C4⋊C4×C113—21no—
263C4⋊C4×C113—21no—
264C4⋊C4×C113—21no—
265C4⋊C4×C113—21no—
266C4⋊C4×C113—21no—
267C4⋊C4×C113—42no—
268C4⋊C4×C113—42no—
269C4⋊C4×C113—42no—
270C4⋊C4×C113—81no—
271C4⋊C4×C113C22⋊C414yes—
272C4⋊C4×C113C22×C412yes—
273C4⋊C4×C113C2×D412yes—
274C22⋊C4×C113—24no—
275C22⋊C4×C113—24no—
276C22⋊C4×C113—24no—
277C22⋊C4×C113—24no—
278C22⋊C4×C113—24no—
279C22⋊C4×C113—42no—
280C22⋊C4×C113—42no—
281C22⋊C4×C113C22⋊C414yes—
282C22⋊C4×C113C22⋊C414yes—
283C42×C113—42no—
284C42×C113C22×C412yes—
285C42×C113C2×D412yes—
286C23×C113—21no—
287C23×C113—21no—
288C23×C113—21no—
289C23×C113—21no—
290C23×C113—22no—
291C23×C113—21no—
292C23×C113—22no—
293C23×C113—21no—
294C23×C113—22no—
295C23×C113—21no—
296C23×C113—21no—
297C23×C113—21no—
298C23×C113—21no—
299C23×C113—22no—
300C23×C113—48no—
301C23×C113—41no—
302C23×C113—41no—
303C23×C113—41no—
304C23×C113—41no—
305C23×C113—41no—
306C23×C113—41no—
307C23×C113—41no—
308C23×C113—41no—
309C23×C113—41no—
310C23×C113—41no—
311C23×C113—48no—
312C23×C113—84no—
313C23×C113—84no—
314C23×C113—84no—
315C23×C113—84no—
316C23×C113—84no—
317C23×C113C2×C22⋊C412yes—
318C23×C113C2×C22⋊C412yes—
319C23×C113AGL(1,ℤ/8)12yes—
320C23×C113#13712yes—
321C23×C113C22×D411yescharacteristic
322Q8×C113—22no—
323Q8×C113—22no—
324Q8×C113—41no—
325Q8×C113—41no—
326D4×C113—28no—
327D4×C113—22no—
328D4×C113—22no—
329D4×C113—22no—
330D4×C113—22no—
331D4×C113—22no—
332D4×C113—48no—
333D4×C113—48no—
334D4×C113—41no—
335D4×C113—41no—
336D4×C113—84no—
337D4×C113C4×D414yescomplemented
338C2×C4×C113—21no—
339C2×C4×C113—21no—
340C2×C4×C113—21no—
341C2×C4×C113—21no—
342C2×C4×C113—21no—
343C2×C4×C113—21no—
344C2×C4×C113—21no—
345C2×C4×C113—21no—
346C2×C4×C113—22no—
347C2×C4×C113—22no—
348C2×C4×C113—22no—
349C2×C4×C113—22no—
350C2×C4×C113—22no—
351C2×C4×C113—22no—
352C2×C4×C113—22no—
353C2×C4×C113—22no—
354C2×C4×C113—22no—
355C2×C4×C113—22no—
356C2×C4×C113—22no—
357C2×C4×C113—48no—
358C2×C4×C113—41no—
359C2×C4×C113—41no—
360C2×C4×C113—41no—
361C2×C4×C113—41no—
362C2×C4×C113—41no—
363C2×C4×C113—41no—
364C2×C4×C113—41no—
365C2×C4×C113—41no—
366C2×C4×C113—41no—
367C2×C4×C113—41no—
368C2×C4×C113—41no—
369C2×C4×C113—41no—
370C2×C4×C113—41no—
371C2×C4×C113—41no—
372C2×C4×C113—41no—
373C2×C4×C113—84no—
374C2×C4×C113—84no—
375C2×C4×C113—84no—
376C2×C4×C113C2×C22⋊C412yes—
377C2×C4×C113C2×C22⋊C412yes—
378C2×C4×C113C2×C22⋊C412yes—
379C2×C4×C113C2×C22⋊C412yes—
380C2×C4×C113C23×C411yescharacteristic
381C2×C4×C113C22×D411yescharacteristic
382C2×C4×C113C22×D411yescharacteristic
383C2×C4×C113C2×#4111yescharacteristic
384C2×C4×C113H(5,𝔽2)11yescharacteristic
385C2×C4×C113H(5,𝔽2)11yescharacteristic
386C8×C113—22no—
387C8×C113—41no—
388C8×C113—41no—
389C8×C113—41no—
390C22×C113—22no—
391C22×C113—22no—
392C22×C113—22no—
393C22×C113—22no—
394C22×C113—22no—
395C22×C113—22no—
396C22×C113—22no—
397C22×C113—24no—
398C22×C113—22no—
399C22×C113—22no—
400C22×C113—42no—
401C22×C113—42no—
402C22×C113—41no—
403C22×C113—42no—
404C22×C113—41no—
405C22×C113—42no—
406C22×C113—41no—
407C22×C113—42no—
408C22×C113—41no—
409C22×C113—42no—
410C22×C113—42no—
411C22×C113—42no—
412C22×C113—42no—
413C22×C113—816no—
414C22×C113—81no—
415C22×C113—81no—
416C22×C113—81no—
417C22×C113—81no—
418C22×C113#41714yescomplemented
419C22×C113C22×C22⋊C411yescharacteristic
420C22×C113D4211yescharacteristic
421C22×C113#54611yescharacteristic
422C22×C113C2×AGL(1,ℤ/8)11yescharacteristic
423C22×C113C2×#13711yescharacteristic
424C22×C113#57611yescharacteristic
425C22×C113#57711yescharacteristic
426C4×C113—22no—
427C4×C113—22no—
428C4×C113—22no—
429C4×C113—22no—
430C4×C113—42no—
431C4×C113—42no—
432C4×C113—42no—
433C4×C113—81no—
434C4×C113—81no—
435C4×C113—81no—
436C4×C113C2×C4×D411yescharacteristic
437C4×C113#51811yescharacteristic
438C4×C113D4211yescharacteristic
439C4×C113#54611yescharacteristic
440#22419C11311yesmaximal, characteristic, direct product factor, Sylow
441C2×C113—24no—
442C2×C113—42no—
443C2×C113—44no—
444C2×C113—82no—
445C2×C113D4×C22⋊C411yescharacteristic
446C2×C113C2×#41711yescharacteristic
447C2×C113#289711yescharacteristic
448C2×C113#326411yescharacteristic
449C2×C113#326611yescharacteristic
450C2×C113#330611yescharacteristic
451C2×C113#331411yescharacteristic
452C2×#546C2×C11311yescharacteristic
453C2×#435C2×C11311yescharacteristic, complemented
454C2×#417C2×C11311yescharacteristic, complemented
455C22×#102C2×C11311yescharacteristic, complemented
456D4×C4⋊C4C2×C11311yescharacteristic, complemented
457#1983C2×C11311yescharacteristic, complemented
458#1959C2×C11311yescharacteristic, complemented
459#1895C2×C11311yescharacteristic, complemented
460#1892C2×C11311yescharacteristic, complemented
461#1874C2×C11311yescharacteristic, complemented
462#1872C2×C11311yescharacteristic, complemented
463#1802C2×C11311yescharacteristic, complemented
464#1788C2×C11311yescharacteristic, complemented
465#1786C2×C11311yescharacteristic, complemented
466#1762C2×C11311yescharacteristic, complemented
467C113#2241911yescharacteristic, direct product factor, Sylow
468C22×#41C22×C11311yescharacteristic
469C23×D4C22×C11311yescharacteristic
470C22×M16C22×C11311yescharacteristic, complemented
471C23×C8C22×C11311yescharacteristic
472#546—24no—
473#546C4×C11318yescomplemented
474C2×#124C22×C11311yescharacteristic
475C2×#123—21no—
476C2×C22⋊Q8C22×C11311yescharacteristic
477C2×#121—21no—
478C2×#121C22×C11311yescharacteristic
479C2×#120—21no—
480C2×C4×D4—21no—
481C2×C4×D4C22×C11311yescharacteristic
482C2×C4×D4C22×C11311yescharacteristic
483C22×C4⋊C4C22×C11311yescharacteristic
484C22×C4⋊C4C22×C11311yescharacteristic, complemented
485C22×C22⋊C4—21no—
486#435—24no—
487C2×C4⋊C8C22×C11311yescharacteristic, complemented
488#417—24no—
489C2×#103C22×C11311yescharacteristic, complemented
490C2×#103C22×C11311yescharacteristic, complemented
491C2×#103C22×C11311yescharacteristic, complemented
492C2×#103C22×C11311yescharacteristic, complemented
493C2×#102—24no—
494C2×#102C22×C11311yescharacteristic
495C2×#102C22×C11311yescharacteristic
496C2×#102C22×C11311yescharacteristic
497C2×#102C22×C11311yescharacteristic
498C2×#102C22×C11311yescharacteristic
499C2×#102C22×C11311yescharacteristic
500C2×#102C22×C11311yescharacteristic
501C2×#102C22×C11311yescharacteristic
502C2×C22⋊C8C22×C11311yescharacteristic
503C2×C22⋊C8C22×C11311yescharacteristic, complemented
504C2×#97C22×C11311yescharacteristic, complemented
505#389—21no—
506#385—21no—
507#385—21no—
508#384C22×C11311yescharacteristic, complemented
509#380C22×C11311yescharacteristic
510#380C22×C11311yescharacteristic, complemented
511C4×C4⋊C4C22×C11311yescharacteristic, complemented
512#340C22×C11311yescharacteristic, complemented
513#340C22×C11311yescharacteristic, complemented
514#340C22×C11311yescharacteristic, complemented
515#340C22×C11311yescharacteristic, complemented
516C25—21no—
517C2×#41—22no—
518C2×#41—22no—
519C2×#41—22no—
520C2×#41—41no—
521C2×#41—41no—
522C2×#41C2×C4×C11314yescomplemented
523C22×Q8C23×C11311yescharacteristic
524C22×D4—22no—
525C22×D4—22no—
526C22×D4—21no—
527C22×D4—21no—
528C22×D4—21no—
529C22×D4—22no—
530C22×D4—41no—
531C22×D4—41no—
532C22×D4C2×C4×C11314yescomplemented
533C22×D4D4×C11311yescharacteristic
534C22×D4C23×C11311yescharacteristic
535C22×D4C23×C11311yescharacteristic
536C23×C4—21no—
537C23×C4—21no—
538C23×C4—21no—
539C23×C4—21no—
540C23×C4C23×C11311yescharacteristic
541C23×C4C23×C11311yescharacteristic
542C2×M16—22no—
543C2×M16—22no—
544C2×M16—41no—
545C22×C8—22no—
546C22×C8—22no—
547C22×C8—41no—
548C22×C8C23×C11311yescharacteristic
549C22×C8C23×C11311yescharacteristic
550C22×C8C23×C11311yescharacteristic
551C22×C8C23×C11311yescharacteristic
552#124—22no—
553#124C2×C4×C11314yescomplemented
554#123—28no—
555C22⋊Q8—22no—
556C22⋊Q8C2×C4×C11314yescomplemented
557#121—22no—
558#121—28no—
559#121C2×C4×C11314yescomplemented
560#120—28no—
561C4×D4—22no—
562C4×D4—44no—
563C4×D4C2×C4×C11314yes—
564C4×D4C2×C4×C11314yescomplemented
565C4×D4D4×C11314yes—
566C2×C4⋊C4—21no—
567C2×C4⋊C4—22no—
568C2×C4⋊C4—22no—
569C2×C4⋊C4—21no—
570C2×C4⋊C4—21no—
571C2×C4⋊C4—21no—
572C2×C4⋊C4—21no—
573C2×C4⋊C4—41no—
574C2×C4⋊C4—41no—
575C2×C4⋊C4D4×C11311yescharacteristic
576C2×C4⋊C4C23×C11311yescharacteristic
577C2×C4⋊C4C23×C11311yescharacteristic
578C2×C4⋊C4C23×C11311yescharacteristic
579C2×C4⋊C4C23×C11311yescharacteristic
580C2×C4⋊C4C23×C11311yescharacteristic
581C2×C22⋊C4—21no—
582C2×C22⋊C4—21no—
583C2×C22⋊C4—21no—
584C2×C22⋊C4—21no—
585C2×C22⋊C4—21no—
586C2×C22⋊C4—28no—
587C2×C22⋊C4—21no—
588C2×C22⋊C4—21no—
589C2×C22⋊C4D4×C11311yescharacteristic
590C2×C22⋊C4D4×C11311yescharacteristic
591C2×C42—21no—
592C2×C42C23×C11311yescharacteristic
593C4⋊C8—22no—
594#103—22no—
595#103—22no—
596#103—41no—
597#103—41no—
598#102—22no—
599#102—22no—
600#102—22no—
601#102—22no—
602#102—22no—
603#102—41no—
604#102—41no—
605#102D4×C11314yescomplemented
606C22⋊C8—22no—
607C22⋊C8—22no—
608#97—22no—
609#95—21no—
610#95—21no—
611#95—21no—
612C24—21no—
613C24—21no—
614C24—24no—
615C24—42no—
616C24—42no—
617C24—42no—
618C24—42no—
619C24—81no—
620C24—81no—
621C24C2×D4×C11311yescharacteristic
622C24C2×D4×C11311yescharacteristic
623#41—28no—
624#41—44no—
625#41—44no—
626#41—44no—
627C2×Q8—21no—
628C2×Q8—21no—
629C2×Q8—21no—
630C2×Q8—21no—
631C2×Q8—21no—
632C2×Q8C22×C4×C11312yes—
633C2×D4—22no—
634C2×D4—22no—
635C2×D4—28no—
636C2×D4—24no—
637C2×D4—24no—
638C2×D4—24no—
639C2×D4—21no—
640C2×D4—21no—
641C2×D4—21no—
642C2×D4—21no—
643C2×D4—21no—
644C2×D4—21no—
645C2×D4—21no—
646C2×D4—21no—
647C2×D4—44no—
648C2×D4—44no—
649C2×D4—44no—
650C2×D4—42no—
651C2×D4—42no—
652C2×D4—42no—
653C2×D4—42no—
654C2×D4—81no—
655C2×D4—81no—
656C2×D4C22⋊C4×C11314yes—
657C2×D4C22×C4×C11312yes—
658C2×D4C22×C4×C11312yes—
659C2×D4C2×D4×C11312yes—
660C2×D4#41×C11312yes—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—24no—
673C22×C4—24no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—42no—
678C22×C4—42no—
679C22×C4—42no—
680C22×C4—42no—
681C22×C4—42no—
682C22×C4—42no—
683C22×C4—81no—
684C22×C4—81no—
685C22×C4—81no—
686C22×C4—81no—
687C22×C4C22×C4×C11312yes—
688C22×C4C22×C4×C11312yes—
689C22×C4C2×D4×C11311yescharacteristic
690C22×C4C2×D4×C11311yescharacteristic
691C22×C4C2×D4×C11311yescharacteristic
692C22×C4C2×D4×C11311yescharacteristic
693C22×C4C2×D4×C11312yes—
694C22×C4C2×D4×C11312yes—
695C22×C4C24×C11311yescharacteristic
696M16—44no—
697C2×C8—21no—
698C2×C8—21no—
699C2×C8—21no—
700C2×C8—21no—
701C2×C8—21no—
702C2×C8—21no—
703C2×C8—21no—
704C2×C8—21no—
705C2×C8—21no—
706C2×C8—21no—
707C2×C8—21no—
708C2×C8—44no—
709C2×C8C2×D4×C11312yes—
710C4⋊C4—24no—
711C4⋊C4—21no—
712C4⋊C4—21no—
713C4⋊C4—21no—
714C4⋊C4—21no—
715C4⋊C4—21no—
716C4⋊C4—21no—
717C4⋊C4—21no—
718C4⋊C4—21no—
719C4⋊C4—42no—
720C4⋊C4—42no—
721C4⋊C4—42no—
722C4⋊C4—81no—
723C4⋊C4C22⋊C4×C11314yes—
724C4⋊C4C22×C4×C11312yes—
725C4⋊C4C2×D4×C11312yes—
726C22⋊C4—24no—
727C22⋊C4—24no—
728C22⋊C4—24no—
729C22⋊C4—24no—
730C22⋊C4—24no—
731C22⋊C4—42no—
732C22⋊C4—42no—
733C22⋊C4C22⋊C4×C11314yes—
734C22⋊C4C22⋊C4×C11314yes—
735C42—42no—
736C42C22×C4×C11312yes—
737C42C2×D4×C11312yes—
738C23—21no—
739C23—21no—
740C23—21no—
741C23—21no—
742C23—22no—
743C23—21no—
744C23—22no—
745C23—21no—
746C23—22no—
747C23—21no—
748C23—21no—
749C23—21no—
750C23—21no—
751C23—22no—
752C23—48no—
753C23—41no—
754C23—41no—
755C23—41no—
756C23—41no—
757C23—41no—
758C23—41no—
759C23—41no—
760C23—41no—
761C23—41no—
762C23—41no—
763C23—48no—
764C23—84no—
765C23—84no—
766C23—84no—
767C23—84no—
768C23—84no—
769C23C2×C22⋊C4×C11312yes—
770C23C2×C22⋊C4×C11312yes—
771C23AGL(1,ℤ/8)×C11312yes—
772C23#137×C11312yes—
773C23C22×D4×C11311yescharacteristic
774Q8—22no—
775Q8—22no—
776Q8—41no—
777Q8—41no—
778D4—28no—
779D4—22no—
780D4—22no—
781D4—22no—
782D4—22no—
783D4—22no—
784D4—48no—
785D4—48no—
786D4—41no—
787D4—41no—
788D4—84no—
789D4C4×D4×C11314yescomplemented
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—21no—
796C2×C4—21no—
797C2×C4—21no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—48no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4—41no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—84no—
826C2×C4—84no—
827C2×C4—84no—
828C2×C4C2×C22⋊C4×C11312yes—
829C2×C4C2×C22⋊C4×C11312yes—
830C2×C4C2×C22⋊C4×C11312yes—
831C2×C4C2×C22⋊C4×C11312yes—
832C2×C4C23×C4×C11311yescharacteristic
833C2×C4C22×D4×C11311yescharacteristic
834C2×C4C22×D4×C11311yescharacteristic
835C2×C4C2×#41×C11311yescharacteristic
836C2×C4H(5,𝔽2)×C11311yescharacteristic
837C2×C4H(5,𝔽2)×C11311yescharacteristic
838C8—22no—
839C8—41no—
840C8—41no—
841C8—41no—
842C22—22no—
843C22—22no—
844C22—22no—
845C22—22no—
846C22—22no—
847C22—22no—
848C22—22no—
849C22—24no—
850C22—22no—
851C22—22no—
852C22—41no—
853C22—42no—
854C22—41no—
855C22—42no—
856C22—42no—
857C22—42no—
858C22—41no—
859C22—42no—
860C22—41no—
861C22—42no—
862C22—42no—
863C22—42no—
864C22—42no—
865C22—816no—
866C22—81no—
867C22—81no—
868C22—81no—
869C22—81no—
870C22#417×C11314yescomplemented
871C22C22×C22⋊C4×C11311yescharacteristic
872C22D42×C11311yescharacteristic
873C22#546×C11311yescharacteristic
874C22C2×AGL(1,ℤ/8)×C11311yescharacteristic
875C22C2×#137×C11311yescharacteristic
876C22#576×C11311yescharacteristic
877C22#577×C11311yescharacteristic
878C4—22no—
879C4—22no—
880C4—22no—
881C4—22no—
882C4—42no—
883C4—42no—
884C4—42no—
885C4—81no—
886C4—81no—
887C4—81no—
888C4C2×C4×D4×C11311yescharacteristic
889C4#518×C11311yescharacteristic
890C4D42×C11311yescharacteristic
891C4#546×C11311yescharacteristic
892C2—24no—
893C2—42no—
894C2—44no—
895C2—82no—
896C2D4×C22⋊C4×C11311yescharacteristic
897C2C2×#417×C11311yescharacteristic
898C2C113×#289711yescharacteristic
899C2C113×#326411yescharacteristic
900C2C113×#326611yescharacteristic
901C2C113×#330611yescharacteristic
902C2C113×#331411yescharacteristic
subgroupG/H
center, socleC23×C113C22×D4
commutatorC2×C4C23×C4×C113
Frattini, cosocleC22×C4C24×C113
prime radicalC2×#546×C113C2
LCSG ▷ C2×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×#435×C113C2semidirect
3. C2×#417×C113C2semidirect
4. C22×#102×C113C2semidirect
5. D4×C4⋊C4×C113C2semidirect
6. C113×#1983C2semidirect
7. C113×#1959C2semidirect
8. C113×#1895C2semidirect
9. C113×#1892C2semidirect
10. C113×#1874C2semidirect
11. C113×#1872C2semidirect
12. C113×#1802C2semidirect
13. C113×#1788C2semidirect
14. C113×#1786C2semidirect
15. C113×#1762C2semidirect
18. C22×M16×C113C22semidirect
21. #546×C113C4semidirect
32. C22×C4⋊C4×C113C22semidirect
35. C2×C4⋊C8×C113C22semidirect
37. C2×#103×C113C22semidirect
38. C2×#103×C113C22semidirect
39. C2×#103×C113C22semidirect
40. C2×#103×C113C22semidirect
51. C2×C22⋊C8×C113C22semidirect
52. C2×#97×C113C22semidirect
56. #384×C113C22semidirect
58. #380×C113C22semidirect
59. C4×C4⋊C4×C113C22semidirect
60. #340×C113C22semidirect
61. #340×C113C22semidirect
62. #340×C113C22semidirect
63. #340×C113C22semidirect
70. C2×#41×C113C2×C4semidirect
80. C22×D4×C113C2×C4semidirect
101. #124×C113C2×C4semidirect
104. C22⋊Q8×C113C2×C4semidirect
107. #121×C113C2×C4semidirect
112. C4×D4×C113C2×C4semidirect
153. #102×C113D4semidirect
337. D4×C113C4×D4semidirect
418. C22×C113#417semidirect
440. #22419C113direct (N × H)
453. C2×#435C2×C113semidirect
454. C2×#417C2×C113semidirect
455. C22×#102C2×C113semidirect
456. D4×C4⋊C4C2×C113semidirect
457. #1983C2×C113semidirect
458. #1959C2×C113semidirect
459. #1895C2×C113semidirect
460. #1892C2×C113semidirect
461. #1874C2×C113semidirect
462. #1872C2×C113semidirect
463. #1802C2×C113semidirect
464. #1788C2×C113semidirect
465. #1786C2×C113semidirect
466. #1762C2×C113semidirect
467. C113#22419direct (N × H)
470. C22×M16C22×C113semidirect
473. #546C4×C113semidirect
484. C22×C4⋊C4C22×C113semidirect
487. C2×C4⋊C8C22×C113semidirect
489. C2×#103C22×C113semidirect
490. C2×#103C22×C113semidirect
491. C2×#103C22×C113semidirect
492. C2×#103C22×C113semidirect
503. C2×C22⋊C8C22×C113semidirect
504. C2×#97C22×C113semidirect
508. #384C22×C113semidirect
510. #380C22×C113semidirect
511. C4×C4⋊C4C22×C113semidirect
512. #340C22×C113semidirect
513. #340C22×C113semidirect
514. #340C22×C113semidirect
515. #340C22×C113semidirect
522. C2×#41C2×C4×C113semidirect
532. C22×D4C2×C4×C113semidirect
553. #124C2×C4×C113semidirect
556. C22⋊Q8C2×C4×C113semidirect
559. #121C2×C4×C113semidirect
564. C4×D4C2×C4×C113semidirect
605. #102D4×C113semidirect
789. D4C4×D4×C113semidirect
870. C22#417×C113semidirect

Maximal subgroups

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

subgroupindex
C2×#546×C1132
C2×#435×C1132
C2×#417×C1132
C22×#102×C1132
D4×C4⋊C4×C1132
C113×#19832
C113×#19592
C113×#18952
C113×#18922
C113×#18742
C113×#18722
C113×#18022
C113×#17882
C113×#17862
C113×#17622
#22419113