Finite Group Databasebeta

← C113×#23863 #43291883

Subgroups — C113×#23863 #43291883

Order 28928.

1922 conjugacy classes of subgroups.

The subgroup lattice has 1020 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×AGL(1,ℤ/8)×C113C211yesmaximal, characteristic, complemented
2C2×#546×C113C211yesmaximal, characteristic, complemented
3C2×#452×C113C211yesmaximal, characteristic, complemented
4C2×#452×C113C211yesmaximal, characteristic, complemented
5C2×#449×C113C211yesmaximal, characteristic, complemented
6C113×#2407C211yesmaximal, characteristic, complemented
7C113×#2015C211yesmaximal, characteristic, complemented
8C113×#2012C211yesmaximal, characteristic, complemented
9C113×#2000C211yesmaximal, characteristic, complemented
10C113×#1999C211yesmaximal, characteristic, complemented
11C113×#1894C211yesmaximal, characteristic, complemented
12C113×#1879C211yesmaximal, characteristic, complemented
13C113×#1877C211yesmaximal, characteristic, complemented
14C113×#1870C211yesmaximal, characteristic, complemented
15C113×#1786C211yesmaximal, characteristic, complemented
16C22×#41×C113C2211yescharacteristic
17C22×#41×C113C2211yescharacteristic
18C23×D4×C113C2211yescharacteristic
19C2×AGL(1,ℤ/8)×C113—24no—
20C2×AGL(1,ℤ/8)×C113—24no—
21C2×AGL(1,ℤ/8)×C113—24no—
22C22×Q16×C113C2211yescharacteristic, complemented
23C22×SD16×C113C2211yescharacteristic
24C22×SD16×C113C2211yescharacteristic
25C22×SD16×C113C2211yescharacteristic, complemented
26C22×D8×C113C2211yescharacteristic
27C22×D8×C113C2211yescharacteristic
28C22×M16×C113C2211yescharacteristic
29#546×C113—24no—
30#546×C113—24no—
31C2×#124×C113C2211yescharacteristic
32C2×#123×C113—21no—
33C2×C22⋊Q8×C113C2211yescharacteristic
34C2×C22⋊Q8×C113C2211yescharacteristic, complemented
35C2×#121×C113—21no—
36C2×#121×C113C2211yescharacteristic
37C2×#121×C113C2211yescharacteristic, complemented
38C2×#120×C113—21no—
39C2×C4×D4×C113C2211yescharacteristic
40C2×C4×D4×C113C2211yescharacteristic
41C22×C22⋊C4×C113—21no—
42#452×C113—24no—
43#452×C113—24no—
44#449×C113—24no—
45C2×#103×C113C2211yescharacteristic, complemented
46C2×#103×C113C2211yescharacteristic, complemented
47C2×#103×C113C2211yescharacteristic, complemented
48C2×#102×C113C2211yescharacteristic
49C2×#102×C113C2211yescharacteristic
50C2×#102×C113C2211yescharacteristic
51C2×#102×C113C2211yescharacteristic
52C2×#102×C113C2211yescharacteristic, complemented
53C2×C22⋊C8×C113C2211yescharacteristic
54C2×C22⋊C8×C113C2211yescharacteristic, complemented
55C2×C22⋊C8×C113C2211yescharacteristic, complemented
56#394×C113—21no—
57#392×C113—21no—
58#391×C113C2211yescharacteristic, complemented
59#390×C113C2211yescharacteristic, complemented
60#386×C113—21no—
61#385×C113—21no—
62#380×C113C2211yescharacteristic
63#340×C113C2211yescharacteristic, complemented
64#340×C113C2211yescharacteristic, complemented
65#336×C113C2211yescharacteristic, complemented
66#336×C113C2211yescharacteristic, complemented
67C25×C113—21no—
68C2×#41×C113—22no—
69C2×#41×C113—22no—
70C2×#41×C113—22no—
71C2×#41×C113—22no—
72C2×#41×C113—22no—
73C2×#41×C113—22no—
74C2×#41×C113—22no—
75C2×#41×C113—22no—
76C2×#41×C113—41no—
77C2×#41×C113—41no—
78C2×#41×C113—41no—
79C2×#41×C113—41no—
80C22×Q8×C113C2311yescharacteristic
81C22×Q8×C113C2311yescharacteristic
82C22×D4×C113—22no—
83C22×D4×C113—22no—
84C22×D4×C113—21no—
85C22×D4×C113—21no—
86C22×D4×C113—21no—
87C22×D4×C113—21no—
88C22×D4×C113—21no—
89C22×D4×C113—22no—
90C22×D4×C113—41no—
91C22×D4×C113—41no—
92C22×D4×C113D411yescharacteristic
93C22×D4×C113D414yescomplemented
94C22×D4×C113C2311yescharacteristic
95C22×D4×C113C2311yescharacteristic
96C22×D4×C113C2311yescharacteristic
97C23×C4×C113—21no—
98C23×C4×C113—21no—
99C23×C4×C113—21no—
100C23×C4×C113C2311yescharacteristic
101C23×C4×C113C2311yescharacteristic
102AGL(1,ℤ/8)×C113—232no—
103C2×Q16×C113—22no—
104C2×Q16×C113—22no—
105C2×Q16×C113—41no—
106C2×SD16×C113—22no—
107C2×SD16×C113—22no—
108C2×SD16×C113—22no—
109C2×SD16×C113—22no—
110C2×SD16×C113—22no—
111C2×SD16×C113—22no—
112C2×SD16×C113—22no—
113C2×SD16×C113—41no—
114C2×SD16×C113D414yescomplemented
115C2×D8×C113—22no—
116C2×D8×C113—22no—
117C2×D8×C113—22no—
118C2×D8×C113—22no—
119C2×D8×C113—22no—
120C2×D8×C113D414yescomplemented
121C2×M16×C113—22no—
122C2×M16×C113—22no—
123C2×M16×C113—22no—
124C22×C8×C113C2311yescharacteristic
125C22×C8×C113C2311yescharacteristic
126C22×C8×C113C2311yescharacteristic
127C22×C8×C113C2311yescharacteristic
128#124×C113—22no—
129#124×C113—22no—
130#123×C113—28no—
131C22⋊Q8×C113—22no—
132C22⋊Q8×C113—22no—
133C22⋊Q8×C113—41no—
134C22⋊Q8×C113D414yescomplemented
135#121×C113—28no—
136#121×C113—22no—
137#121×C113—22no—
138#121×C113—22no—
139#121×C113—41no—
140#120×C113—28no—
141C4×D4×C113—22no—
142C4×D4×C113—22no—
143C4×D4×C113—22no—
144C4×D4×C113—22no—
145C2×C4⋊C4×C113—21no—
146C2×C4⋊C4×C113—21no—
147C2×C4⋊C4×C113D411yescharacteristic
148C2×C4⋊C4×C113C2311yescharacteristic
149C2×C4⋊C4×C113C2311yescharacteristic
150C2×C4⋊C4×C113C2311yescharacteristic
151C2×C22⋊C4×C113—28no—
152C2×C22⋊C4×C113—21no—
153C2×C22⋊C4×C113—21no—
154C2×C22⋊C4×C113—21no—
155C2×C22⋊C4×C113—21no—
156C2×C22⋊C4×C113—21no—
157C2×C22⋊C4×C113—21no—
158C2×C22⋊C4×C113—21no—
159C2×C22⋊C4×C113—21no—
160C2×C22⋊C4×C113—21no—
161C2×C22⋊C4×C113—21no—
162C2×C22⋊C4×C113D411yescharacteristic
163C2×C22⋊C4×C113D411yescharacteristic
164C2×C42×C113C2311yescharacteristic
165#103×C113—22no—
166#103×C113—22no—
167#103×C113—22no—
168#102×C113—22no—
169#102×C113—22no—
170#102×C113—22no—
171#102×C113—41no—
172#102×C113—41no—
173C22⋊C8×C113—22no—
174C22⋊C8×C113—22no—
175C22⋊C8×C113—22no—
176#95×C113—21no—
177#95×C113—21no—
178#95×C113—21no—
179C24×C113—21no—
180C24×C113—21no—
181C24×C113—21no—
182C24×C113—24no—
183C24×C113—42no—
184C24×C113—42no—
185C24×C113—42no—
186C24×C113—42no—
187C24×C113—81no—
188C24×C113—81no—
189C24×C113C2×D411yescharacteristic
190C24×C113C2×D411yescharacteristic
191#41×C113—28no—
192#41×C113—44no—
193#41×C113—44no—
194#41×C113—44no—
195#41×C113—44no—
196#41×C113—44no—
197#41×C113—44no—
198#41×C113—44no—
199C2×Q8×C113—21no—
200C2×Q8×C113—21no—
201C2×Q8×C113—21no—
202C2×Q8×C113—21no—
203C2×Q8×C113—21no—
204C2×Q8×C113—21no—
205C2×Q8×C113—21no—
206C2×Q8×C113—21no—
207C2×Q8×C113—21no—
208C2×Q8×C113—21no—
209C2×Q8×C113C2×D412yes—
210C2×Q8×C113C2×D412yes—
211C2×D4×C113—28no—
212C2×D4×C113—24no—
213C2×D4×C113—22no—
214C2×D4×C113—24no—
215C2×D4×C113—24no—
216C2×D4×C113—21no—
217C2×D4×C113—21no—
218C2×D4×C113—21no—
219C2×D4×C113—21no—
220C2×D4×C113—21no—
221C2×D4×C113—21no—
222C2×D4×C113—21no—
223C2×D4×C113—21no—
224C2×D4×C113—21no—
225C2×D4×C113—21no—
226C2×D4×C113—21no—
227C2×D4×C113—21no—
228C2×D4×C113—21no—
229C2×D4×C113—44no—
230C2×D4×C113—44no—
231C2×D4×C113—44no—
232C2×D4×C113—41no—
233C2×D4×C113—41no—
234C2×D4×C113—42no—
235C2×D4×C113—42no—
236C2×D4×C113—42no—
237C2×D4×C113—42no—
238C2×D4×C113—42no—
239C2×D4×C113—42no—
240C2×D4×C113—42no—
241C2×D4×C113—42no—
242C2×D4×C113—42no—
243C2×D4×C113—81no—
244C2×D4×C113—81no—
245C2×D4×C113—81no—
246C2×D4×C113C2×D412yes—
247C2×D4×C113C2×D412yes—
248C2×D4×C113C2×D412yes—
249C2×D4×C113C2×D412yes—
250C2×D4×C113C2×D412yes—
251C22×C4×C113—21no—
252C22×C4×C113—21no—
253C22×C4×C113—21no—
254C22×C4×C113—21no—
255C22×C4×C113—24no—
256C22×C4×C113—21no—
257C22×C4×C113—21no—
258C22×C4×C113—21no—
259C22×C4×C113—24no—
260C22×C4×C113—21no—
261C22×C4×C113—21no—
262C22×C4×C113—21no—
263C22×C4×C113—21no—
264C22×C4×C113—21no—
265C22×C4×C113—21no—
266C22×C4×C113—21no—
267C22×C4×C113—21no—
268C22×C4×C113—42no—
269C22×C4×C113—42no—
270C22×C4×C113—42no—
271C22×C4×C113—42no—
272C22×C4×C113—42no—
273C22×C4×C113—81no—
274C22×C4×C113—81no—
275C22×C4×C113C2×D411yescharacteristic
276C22×C4×C113C2×D411yescharacteristic
277C22×C4×C113C2×D411yescharacteristic
278C22×C4×C113C2×D411yescharacteristic
279C22×C4×C113C2×D412yes—
280C22×C4×C113C2×D412yes—
281C22×C4×C113C2411yescharacteristic
282Q16×C113—44no—
283SD16×C113—28no—
284SD16×C113—28no—
285SD16×C113—44no—
286D8×C113—28no—
287D8×C113—28no—
288M16×C113—28no—
289C2×C8×C113—21no—
290C2×C8×C113—21no—
291C2×C8×C113—21no—
292C2×C8×C113—21no—
293C2×C8×C113—21no—
294C2×C8×C113—21no—
295C2×C8×C113—21no—
296C2×C8×C113—21no—
297C2×C8×C113—21no—
298C2×C8×C113—21no—
299C2×C8×C113C2×D412yes—
300C2×C8×C113C2×D412yes—
301C4⋊C4×C113—24no—
302C4⋊C4×C113—22no—
303C4⋊C4×C113—21no—
304C4⋊C4×C113—21no—
305C4⋊C4×C113—21no—
306C4⋊C4×C113—21no—
307C4⋊C4×C113—21no—
308C4⋊C4×C113—42no—
309C4⋊C4×C113C2×D412yes—
310C22⋊C4×C113—24no—
311C22⋊C4×C113—24no—
312C22⋊C4×C113—24no—
313C22⋊C4×C113—24no—
314C22⋊C4×C113—22no—
315C22⋊C4×C113—24no—
316C22⋊C4×C113—22no—
317C22⋊C4×C113—42no—
318C22⋊C4×C113—42no—
319C22⋊C4×C113—42no—
320C22⋊C4×C113—81no—
321C22⋊C4×C113—81no—
322C42×C113—21no—
323C42×C113—21no—
324C23×C113—22no—
325C23×C113—21no—
326C23×C113—21no—
327C23×C113—22no—
328C23×C113—22no—
329C23×C113—21no—
330C23×C113—21no—
331C23×C113—21no—
332C23×C113—21no—
333C23×C113—22no—
334C23×C113—21no—
335C23×C113—21no—
336C23×C113—22no—
337C23×C113—21no—
338C23×C113—21no—
339C23×C113—21no—
340C23×C113—21no—
341C23×C113—21no—
342C23×C113—48no—
343C23×C113—48no—
344C23×C113—41no—
345C23×C113—41no—
346C23×C113—41no—
347C23×C113—41no—
348C23×C113—41no—
349C23×C113—41no—
350C23×C113—41no—
351C23×C113—41no—
352C23×C113—41no—
353C23×C113—41no—
354C23×C113—41no—
355C23×C113—41no—
356C23×C113—41no—
357C23×C113—41no—
358C23×C113—41no—
359C23×C113—41no—
360C23×C113—84no—
361C23×C113—84no—
362C23×C113—84no—
363C23×C113—84no—
364C23×C113—84no—
365C23×C113#12012yes—
366C23×C113C22×D411yescharacteristic
367Q8×C113—22no—
368Q8×C113—22no—
369Q8×C113—22no—
370Q8×C113—22no—
371Q8×C113—41no—
372Q8×C113—41no—
373Q8×C113—41no—
374Q8×C113—41no—
375D4×C113—22no—
376D4×C113—22no—
377D4×C113—22no—
378D4×C113—22no—
379D4×C113—22no—
380D4×C113—22no—
381D4×C113—22no—
382D4×C113—48no—
383D4×C113—44no—
384D4×C113—48no—
385D4×C113—48no—
386D4×C113—41no—
387D4×C113—41no—
388D4×C113—41no—
389D4×C113—41no—
390D4×C113—84no—
391D4×C113—84no—
392D4×C113#12014yes—
393C2×C4×C113—21no—
394C2×C4×C113—21no—
395C2×C4×C113—22no—
396C2×C4×C113—22no—
397C2×C4×C113—22no—
398C2×C4×C113—22no—
399C2×C4×C113—21no—
400C2×C4×C113—21no—
401C2×C4×C113—22no—
402C2×C4×C113—21no—
403C2×C4×C113—22no—
404C2×C4×C113—21no—
405C2×C4×C113—22no—
406C2×C4×C113—21no—
407C2×C4×C113—21no—
408C2×C4×C113—21no—
409C2×C4×C113—21no—
410C2×C4×C113—21no—
411C2×C4×C113—48no—
412C2×C4×C113—48no—
413C2×C4×C113—41no—
414C2×C4×C113—41no—
415C2×C4×C113—41no—
416C2×C4×C113—41no—
417C2×C4×C113—41no—
418C2×C4×C113—41no—
419C2×C4×C113—41no—
420C2×C4×C113—41no—
421C2×C4×C113—41no—
422C2×C4×C113—41no—
423C2×C4×C113—41no—
424C2×C4×C113—41no—
425C2×C4×C113—41no—
426C2×C4×C113—41no—
427C2×C4×C113—41no—
428C2×C4×C113—41no—
429C2×C4×C113—84no—
430C2×C4×C113#12012yes—
431C2×C4×C113C22×D411yescharacteristic
432C2×C4×C113C22×D411yescharacteristic
433C2×C4×C113C22×D411yescharacteristic
434C2×C4×C113C22×D411yescharacteristic
435C2×C4×C113H(5,𝔽2)11yescharacteristic
436C2×C4×C113H(5,𝔽2)11yescharacteristic
437C8×C113—22no—
438C8×C113—22no—
439C8×C113—41no—
440C8×C113—41no—
441C22×C113—22no—
442C22×C113—24no—
443C22×C113—22no—
444C22×C113—22no—
445C22×C113—42no—
446C22×C113—41no—
447C22×C113—42no—
448C22×C113—42no—
449C22×C113—41no—
450C22×C113—42no—
451C22×C113—41no—
452C22×C113—42no—
453C22×C113—41no—
454C22×C113—42no—
455C22×C113—42no—
456C22×C113—41no—
457C22×C113—42no—
458C22×C113—41no—
459C22×C113—42no—
460C22×C113—41no—
461C22×C113—42no—
462C22×C113—41no—
463C22×C113—42no—
464C22×C113—41no—
465C22×C113—41no—
466C22×C113—42no—
467C22×C113—41no—
468C22×C113—816no—
469C22×C113—81no—
470C22×C113—81no—
471C22×C113—81no—
472C22×C113—81no—
473C22×C113—81no—
474C22×C113—81no—
475C22×C113—81no—
476C22×C113—81no—
477C22×C113C2×#12011yescharacteristic
478C22×C113D4211yescharacteristic
479C22×C113D4211yescharacteristic
480C22×C113#57511yescharacteristic
481C22×C113#57511yescharacteristic
482C22×C113#57611yescharacteristic
483C22×C113#57711yescharacteristic
484C4×C113—22no—
485C4×C113—41no—
486C4×C113—42no—
487C4×C113—42no—
488C4×C113—41no—
489C4×C113—41no—
490C4×C113—42no—
491C4×C113—81no—
492C4×C113—81no—
493C4×C113C2×#12011yescharacteristic
494C4×C113#53411yescharacteristic
495C4×C113D4211yescharacteristic
496C4×C113D4211yescharacteristic
497#23863C11311yesmaximal, characteristic, direct product factor, Sylow
498C2×C113—42no—
499C2×C113—44no—
500C2×C113—81no—
501C2×C113—82no—
502C2×C113—82no—
503C2×C113#240311yescharacteristic
504C2×C113#300511yescharacteristic
505C2×C113#301211yescharacteristic
506C2×C113#326711yescharacteristic
507C2×C113#326811yescharacteristic
508C2×C113#327311yescharacteristic
509C2×C113#327511yescharacteristic
510C22×AGL(1,ℤ/8)C2×C11311yescharacteristic, complemented
511C2×#546C2×C11311yescharacteristic, complemented
512C2×#452C2×C11311yescharacteristic, complemented
513C2×#452C2×C11311yescharacteristic, complemented
514C2×#449C2×C11311yescharacteristic, complemented
515#2407C2×C11311yescharacteristic, complemented
516#2015C2×C11311yescharacteristic, complemented
517#2012C2×C11311yescharacteristic, complemented
518#2000C2×C11311yescharacteristic, complemented
519#1999C2×C11311yescharacteristic, complemented
520#1894C2×C11311yescharacteristic, complemented
521#1879C2×C11311yescharacteristic, complemented
522#1877C2×C11311yescharacteristic, complemented
523#1870C2×C11311yescharacteristic, complemented
524#1786C2×C11311yescharacteristic, complemented
525C113#2386311yescharacteristic, direct product factor, Sylow
526C22×#41C22×C11311yescharacteristic
527C22×#41C22×C11311yescharacteristic
528C23×D4C22×C11311yescharacteristic
529C2×AGL(1,ℤ/8)—24no—
530C2×AGL(1,ℤ/8)—24no—
531C2×AGL(1,ℤ/8)—24no—
532C22×Q16C22×C11311yescharacteristic, complemented
533C22×SD16C22×C11311yescharacteristic
534C22×SD16C22×C11311yescharacteristic
535C22×SD16C22×C11311yescharacteristic, complemented
536C22×D8C22×C11311yescharacteristic
537C22×D8C22×C11311yescharacteristic
538C22×M16C22×C11311yescharacteristic
539#546—24no—
540#546—24no—
541C2×#124C22×C11311yescharacteristic
542C2×#123—21no—
543C2×C22⋊Q8C22×C11311yescharacteristic
544C2×C22⋊Q8C22×C11311yescharacteristic, complemented
545C2×#121—21no—
546C2×#121C22×C11311yescharacteristic
547C2×#121C22×C11311yescharacteristic, complemented
548C2×#120—21no—
549C2×C4×D4C22×C11311yescharacteristic
550C2×C4×D4C22×C11311yescharacteristic
551C22×C22⋊C4—21no—
552#452—24no—
553#452—24no—
554#449—24no—
555C2×#103C22×C11311yescharacteristic, complemented
556C2×#103C22×C11311yescharacteristic, complemented
557C2×#103C22×C11311yescharacteristic, complemented
558C2×#102C22×C11311yescharacteristic
559C2×#102C22×C11311yescharacteristic
560C2×#102C22×C11311yescharacteristic
561C2×#102C22×C11311yescharacteristic
562C2×#102C22×C11311yescharacteristic, complemented
563C2×C22⋊C8C22×C11311yescharacteristic
564C2×C22⋊C8C22×C11311yescharacteristic, complemented
565C2×C22⋊C8C22×C11311yescharacteristic, complemented
566#394—21no—
567#392—21no—
568#391C22×C11311yescharacteristic, complemented
569#390C22×C11311yescharacteristic, complemented
570#386—21no—
571#385—21no—
572#380C22×C11311yescharacteristic
573#340C22×C11311yescharacteristic, complemented
574#340C22×C11311yescharacteristic, complemented
575#336C22×C11311yescharacteristic, complemented
576#336C22×C11311yescharacteristic, complemented
577C25—21no—
578C2×#41—22no—
579C2×#41—22no—
580C2×#41—22no—
581C2×#41—22no—
582C2×#41—22no—
583C2×#41—22no—
584C2×#41—22no—
585C2×#41—22no—
586C2×#41—41no—
587C2×#41—41no—
588C2×#41—41no—
589C2×#41—41no—
590C22×Q8C23×C11311yescharacteristic
591C22×Q8C23×C11311yescharacteristic
592C22×D4—22no—
593C22×D4—22no—
594C22×D4—21no—
595C22×D4—21no—
596C22×D4—21no—
597C22×D4—21no—
598C22×D4—21no—
599C22×D4—22no—
600C22×D4—41no—
601C22×D4—41no—
602C22×D4D4×C11311yescharacteristic
603C22×D4D4×C11314yescomplemented
604C22×D4C23×C11311yescharacteristic
605C22×D4C23×C11311yescharacteristic
606C22×D4C23×C11311yescharacteristic
607C23×C4—21no—
608C23×C4—21no—
609C23×C4—21no—
610C23×C4C23×C11311yescharacteristic
611C23×C4C23×C11311yescharacteristic
612AGL(1,ℤ/8)—232no—
613C2×Q16—22no—
614C2×Q16—22no—
615C2×Q16—41no—
616C2×SD16—22no—
617C2×SD16—22no—
618C2×SD16—22no—
619C2×SD16—22no—
620C2×SD16—22no—
621C2×SD16—22no—
622C2×SD16—22no—
623C2×SD16—41no—
624C2×SD16D4×C11314yescomplemented
625C2×D8—22no—
626C2×D8—22no—
627C2×D8—22no—
628C2×D8—22no—
629C2×D8—22no—
630C2×D8D4×C11314yescomplemented
631C2×M16—22no—
632C2×M16—22no—
633C2×M16—22no—
634C22×C8C23×C11311yescharacteristic
635C22×C8C23×C11311yescharacteristic
636C22×C8C23×C11311yescharacteristic
637C22×C8C23×C11311yescharacteristic
638#124—22no—
639#124—22no—
640#123—28no—
641C22⋊Q8—22no—
642C22⋊Q8—22no—
643C22⋊Q8—41no—
644C22⋊Q8D4×C11314yescomplemented
645#121—28no—
646#121—22no—
647#121—22no—
648#121—22no—
649#121—41no—
650#120—28no—
651C4×D4—22no—
652C4×D4—22no—
653C4×D4—22no—
654C4×D4—22no—
655C2×C4⋊C4—21no—
656C2×C4⋊C4—21no—
657C2×C4⋊C4D4×C11311yescharacteristic
658C2×C4⋊C4C23×C11311yescharacteristic
659C2×C4⋊C4C23×C11311yescharacteristic
660C2×C4⋊C4C23×C11311yescharacteristic
661C2×C22⋊C4—28no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4—21no—
664C2×C22⋊C4—21no—
665C2×C22⋊C4—21no—
666C2×C22⋊C4—21no—
667C2×C22⋊C4—21no—
668C2×C22⋊C4—21no—
669C2×C22⋊C4—21no—
670C2×C22⋊C4—21no—
671C2×C22⋊C4—21no—
672C2×C22⋊C4D4×C11311yescharacteristic
673C2×C22⋊C4D4×C11311yescharacteristic
674C2×C42C23×C11311yescharacteristic
675#103—22no—
676#103—22no—
677#103—22no—
678#102—22no—
679#102—22no—
680#102—22no—
681#102—41no—
682#102—41no—
683C22⋊C8—22no—
684C22⋊C8—22no—
685C22⋊C8—22no—
686#95—21no—
687#95—21no—
688#95—21no—
689C24—21no—
690C24—21no—
691C24—21no—
692C24—24no—
693C24—42no—
694C24—42no—
695C24—42no—
696C24—42no—
697C24—81no—
698C24—81no—
699C24C2×D4×C11311yescharacteristic
700C24C2×D4×C11311yescharacteristic
701#41—28no—
702#41—44no—
703#41—44no—
704#41—44no—
705#41—44no—
706#41—44no—
707#41—44no—
708#41—44no—
709C2×Q8—21no—
710C2×Q8—21no—
711C2×Q8—21no—
712C2×Q8—21no—
713C2×Q8—21no—
714C2×Q8—21no—
715C2×Q8—21no—
716C2×Q8—21no—
717C2×Q8—21no—
718C2×Q8—21no—
719C2×Q8C2×D4×C11312yes—
720C2×Q8C2×D4×C11312yes—
721C2×D4—28no—
722C2×D4—24no—
723C2×D4—22no—
724C2×D4—24no—
725C2×D4—24no—
726C2×D4—21no—
727C2×D4—21no—
728C2×D4—21no—
729C2×D4—21no—
730C2×D4—21no—
731C2×D4—21no—
732C2×D4—21no—
733C2×D4—21no—
734C2×D4—21no—
735C2×D4—21no—
736C2×D4—21no—
737C2×D4—21no—
738C2×D4—21no—
739C2×D4—44no—
740C2×D4—44no—
741C2×D4—44no—
742C2×D4—41no—
743C2×D4—41no—
744C2×D4—42no—
745C2×D4—42no—
746C2×D4—42no—
747C2×D4—42no—
748C2×D4—42no—
749C2×D4—42no—
750C2×D4—42no—
751C2×D4—42no—
752C2×D4—42no—
753C2×D4—81no—
754C2×D4—81no—
755C2×D4—81no—
756C2×D4C2×D4×C11312yes—
757C2×D4C2×D4×C11312yes—
758C2×D4C2×D4×C11312yes—
759C2×D4C2×D4×C11312yes—
760C2×D4C2×D4×C11312yes—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—24no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—24no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—42no—
779C22×C4—42no—
780C22×C4—42no—
781C22×C4—42no—
782C22×C4—42no—
783C22×C4—81no—
784C22×C4—81no—
785C22×C4C2×D4×C11311yescharacteristic
786C22×C4C2×D4×C11311yescharacteristic
787C22×C4C2×D4×C11311yescharacteristic
788C22×C4C2×D4×C11311yescharacteristic
789C22×C4C2×D4×C11312yes—
790C22×C4C2×D4×C11312yes—
791C22×C4C24×C11311yescharacteristic
792Q16—44no—
793SD16—28no—
794SD16—28no—
795SD16—44no—
796D8—28no—
797D8—28no—
798M16—28no—
799C2×C8—21no—
800C2×C8—21no—
801C2×C8—21no—
802C2×C8—21no—
803C2×C8—21no—
804C2×C8—21no—
805C2×C8—21no—
806C2×C8—21no—
807C2×C8—21no—
808C2×C8—21no—
809C2×C8C2×D4×C11312yes—
810C2×C8C2×D4×C11312yes—
811C4⋊C4—24no—
812C4⋊C4—22no—
813C4⋊C4—21no—
814C4⋊C4—21no—
815C4⋊C4—21no—
816C4⋊C4—21no—
817C4⋊C4—21no—
818C4⋊C4—42no—
819C4⋊C4C2×D4×C11312yes—
820C22⋊C4—24no—
821C22⋊C4—24no—
822C22⋊C4—24no—
823C22⋊C4—24no—
824C22⋊C4—22no—
825C22⋊C4—24no—
826C22⋊C4—22no—
827C22⋊C4—42no—
828C22⋊C4—42no—
829C22⋊C4—42no—
830C22⋊C4—81no—
831C22⋊C4—81no—
832C42—21no—
833C42—21no—
834C23—22no—
835C23—21no—
836C23—21no—
837C23—22no—
838C23—22no—
839C23—21no—
840C23—21no—
841C23—21no—
842C23—21no—
843C23—22no—
844C23—21no—
845C23—21no—
846C23—22no—
847C23—21no—
848C23—21no—
849C23—21no—
850C23—21no—
851C23—21no—
852C23—48no—
853C23—48no—
854C23—41no—
855C23—41no—
856C23—41no—
857C23—41no—
858C23—41no—
859C23—41no—
860C23—41no—
861C23—41no—
862C23—41no—
863C23—41no—
864C23—41no—
865C23—41no—
866C23—41no—
867C23—41no—
868C23—41no—
869C23—41no—
870C23—84no—
871C23—84no—
872C23—84no—
873C23—84no—
874C23—84no—
875C23#120×C11312yes—
876C23C22×D4×C11311yescharacteristic
877Q8—22no—
878Q8—22no—
879Q8—22no—
880Q8—22no—
881Q8—41no—
882Q8—41no—
883Q8—41no—
884Q8—41no—
885D4—22no—
886D4—22no—
887D4—22no—
888D4—22no—
889D4—22no—
890D4—22no—
891D4—22no—
892D4—48no—
893D4—48no—
894D4—44no—
895D4—48no—
896D4—41no—
897D4—41no—
898D4—41no—
899D4—41no—
900D4—84no—
901D4—84no—
902D4#120×C11314yes—
903C2×C4—21no—
904C2×C4—21no—
905C2×C4—22no—
906C2×C4—22no—
907C2×C4—22no—
908C2×C4—22no—
909C2×C4—21no—
910C2×C4—21no—
911C2×C4—22no—
912C2×C4—21no—
913C2×C4—22no—
914C2×C4—21no—
915C2×C4—22no—
916C2×C4—21no—
917C2×C4—21no—
918C2×C4—21no—
919C2×C4—21no—
920C2×C4—21no—
921C2×C4—48no—
922C2×C4—48no—
923C2×C4—41no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—41no—
930C2×C4—41no—
931C2×C4—41no—
932C2×C4—41no—
933C2×C4—41no—
934C2×C4—41no—
935C2×C4—41no—
936C2×C4—41no—
937C2×C4—41no—
938C2×C4—41no—
939C2×C4—84no—
940C2×C4#120×C11312yes—
941C2×C4C22×D4×C11311yescharacteristic
942C2×C4C22×D4×C11311yescharacteristic
943C2×C4C22×D4×C11311yescharacteristic
944C2×C4C22×D4×C11311yescharacteristic
945C2×C4H(5,𝔽2)×C11311yescharacteristic
946C2×C4H(5,𝔽2)×C11311yescharacteristic
947C8—22no—
948C8—22no—
949C8—41no—
950C8—41no—
951C22—22no—
952C22—24no—
953C22—22no—
954C22—22no—
955C22—42no—
956C22—41no—
957C22—42no—
958C22—42no—
959C22—41no—
960C22—42no—
961C22—41no—
962C22—42no—
963C22—41no—
964C22—42no—
965C22—42no—
966C22—41no—
967C22—42no—
968C22—41no—
969C22—42no—
970C22—41no—
971C22—42no—
972C22—41no—
973C22—42no—
974C22—41no—
975C22—41no—
976C22—42no—
977C22—41no—
978C22—816no—
979C22—81no—
980C22—81no—
981C22—81no—
982C22—81no—
983C22—81no—
984C22—81no—
985C22—81no—
986C22—81no—
987C22C2×#120×C11311yescharacteristic
988C22D42×C11311yescharacteristic
989C22D42×C11311yescharacteristic
990C22#575×C11311yescharacteristic
991C22#575×C11311yescharacteristic
992C22#576×C11311yescharacteristic
993C22#577×C11311yescharacteristic
994C4—22no—
995C4—41no—
996C4—42no—
997C4—42no—
998C4—41no—
999C4—41no—
1000C4—42no—
1001C4—81no—
1002C4—81no—
1003C4C2×#120×C11311yescharacteristic
1004C4#534×C11311yescharacteristic
1005C4D42×C11311yescharacteristic
1006C4D42×C11311yescharacteristic
1007C2—42no—
1008C2—44no—
1009C2—81no—
1010C2—82no—
1011C2—82no—
1012C2C113×#240311yescharacteristic
1013C2C113×#300511yescharacteristic
1014C2C113×#301211yescharacteristic
1015C2C113×#326711yescharacteristic
1016C2C113×#326811yescharacteristic
1017C2C113×#327311yescharacteristic
1018C2C113×#327511yescharacteristic
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. C22×AGL(1,ℤ/8)×C113C2semidirect
2. C2×#546×C113C2semidirect
3. C2×#452×C113C2semidirect
4. C2×#452×C113C2semidirect
5. C2×#449×C113C2semidirect
6. C113×#2407C2semidirect
7. C113×#2015C2semidirect
8. C113×#2012C2semidirect
9. C113×#2000C2semidirect
10. C113×#1999C2semidirect
11. C113×#1894C2semidirect
12. C113×#1879C2semidirect
13. C113×#1877C2semidirect
14. C113×#1870C2semidirect
15. C113×#1786C2semidirect
22. C22×Q16×C113C22semidirect
25. C22×SD16×C113C22semidirect
34. C2×C22⋊Q8×C113C22semidirect
37. C2×#121×C113C22semidirect
45. C2×#103×C113C22semidirect
46. C2×#103×C113C22semidirect
47. C2×#103×C113C22semidirect
52. C2×#102×C113C22semidirect
54. C2×C22⋊C8×C113C22semidirect
55. C2×C22⋊C8×C113C22semidirect
58. #391×C113C22semidirect
59. #390×C113C22semidirect
63. #340×C113C22semidirect
64. #340×C113C22semidirect
65. #336×C113C22semidirect
66. #336×C113C22semidirect
93. C22×D4×C113D4semidirect
114. C2×SD16×C113D4semidirect
120. C2×D8×C113D4semidirect
134. C22⋊Q8×C113D4semidirect
497. #23863C113direct (N × H)
510. C22×AGL(1,ℤ/8)C2×C113semidirect
511. C2×#546C2×C113semidirect
512. C2×#452C2×C113semidirect
513. C2×#452C2×C113semidirect
514. C2×#449C2×C113semidirect
515. #2407C2×C113semidirect
516. #2015C2×C113semidirect
517. #2012C2×C113semidirect
518. #2000C2×C113semidirect
519. #1999C2×C113semidirect
520. #1894C2×C113semidirect
521. #1879C2×C113semidirect
522. #1877C2×C113semidirect
523. #1870C2×C113semidirect
524. #1786C2×C113semidirect
525. C113#23863direct (N × H)
532. C22×Q16C22×C113semidirect
535. C22×SD16C22×C113semidirect
544. C2×C22⋊Q8C22×C113semidirect
547. C2×#121C22×C113semidirect
555. C2×#103C22×C113semidirect
556. C2×#103C22×C113semidirect
557. C2×#103C22×C113semidirect
562. C2×#102C22×C113semidirect
564. C2×C22⋊C8C22×C113semidirect
565. C2×C22⋊C8C22×C113semidirect
568. #391C22×C113semidirect
569. #390C22×C113semidirect
573. #340C22×C113semidirect
574. #340C22×C113semidirect
575. #336C22×C113semidirect
576. #336C22×C113semidirect
603. C22×D4D4×C113semidirect
624. C2×SD16D4×C113semidirect
630. C2×D8D4×C113semidirect
644. C22⋊Q8D4×C113semidirect

Maximal subgroups

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

subgroupindex
C22×AGL(1,ℤ/8)×C1132
C2×#546×C1132
C2×#452×C1132
C2×#449×C1132
C113×#24072
C113×#20152
C113×#20122
C113×#20002
C113×#19992
C113×#18942
C113×#18792
C113×#18772
C113×#18702
C113×#17862
#23863113