Finite Group Databasebeta

← C113×#23888 #43291908

Subgroups — C113×#23888 #43291908

Order 28928.

1682 conjugacy classes of subgroups.

The subgroup lattice has 1026 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#577×C113C211yesmaximal, characteristic, complemented
2C2×#576×C113C211yesmaximal, characteristic, complemented
3C2×#454×C113C211yesmaximal, characteristic, complemented
4C2×#455×C113C211yesmaximal, characteristic, complemented
5C113×#3013C211yesmaximal, characteristic, complemented
6C113×#3012C211yesmaximal, characteristic, complemented
7C113×#2019C211yesmaximal, characteristic, complemented
8C113×#2018C211yesmaximal, characteristic, complemented
9C113×#2012C211yesmaximal, characteristic, complemented
10C113×#2006C211yesmaximal, characteristic, complemented
11C113×#1908C211yesmaximal, characteristic, complemented
12C113×#1907C211yesmaximal, characteristic, complemented
13C113×#1876C211yesmaximal, characteristic, complemented
14C113×#1876C211yesmaximal, characteristic, complemented
15C113×#1792C211yesmaximal, characteristic, complemented
16C2×2−1+4×C113C2211yescharacteristic, complemented
17C2×H(5,𝔽2)×C113C2211yescharacteristic
18C2×H(5,𝔽2)×C113C2211yescharacteristic
19#577×C113—24no—
20#577×C113—24no—
21#576×C113—24no—
22#576×C113—24no—
23C2×#137×C113—21no—
24C2×#137×C113C2211yescharacteristic
25C2×#137×C113C2211yescharacteristic, complemented
26C2×AGL(1,ℤ/8)×C113—21no—
27C2×AGL(1,ℤ/8)×C113—21no—
28C2×AGL(1,ℤ/8)×C113—21no—
29C2×AGL(1,ℤ/8)×C113C2211yescharacteristic
30C2×AGL(1,ℤ/8)×C113C2211yescharacteristic
31C2×AGL(1,ℤ/8)×C113C2211yescharacteristic, complemented
32C2×AGL(1,ℤ/8)×C113C2211yescharacteristic, complemented
33C2×#135×C113—21no—
34C2×#135×C113—21no—
35C2×#135×C113C2211yescharacteristic
36C2×#135×C113C2211yescharacteristic
37C22×SD16×C113—21no—
38C22×SD16×C113C2211yescharacteristic, complemented
39C22×D8×C113—21no—
40C22×D8×C113C2211yescharacteristic
41C2×#131×C113C2211yescharacteristic
42C2×#131×C113C2211yescharacteristic, complemented
43#537×C113C2211yescharacteristic, complemented
44C2×#124×C113C2211yescharacteristic, complemented
45#455×C113—24no—
46#454×C113—24no—
47#452×C113—21no—
48#452×C113—21no—
49#451×C113—21no—
50#450×C113—21no—
51#449×C113—21no—
52#449×C113—21no—
53#448×C113—21no—
54#447×C113—21no—
55C2×#104×C113C2211yescharacteristic
56C2×#104×C113C2211yescharacteristic, complemented
57C2×#104×C113C2211yescharacteristic, complemented
58C2×#104×C113C2211yescharacteristic, complemented
59#417×C113C2211yescharacteristic
60#417×C113C2211yescharacteristic, complemented
61C2×#103×C113C2211yescharacteristic, complemented
62C2×#102×C113C2211yescharacteristic, complemented
63C2×#101×C113C2211yescharacteristic, complemented
64C2×#100×C113C2211yescharacteristic, complemented
65C2×#100×C113C2211yescharacteristic, complemented
66#408×C113C2211yescharacteristic, complemented
67#408×C113C2211yescharacteristic, complemented
68#390×C113C2211yescharacteristic, complemented
69#343×C113C2211yescharacteristic, complemented
70#341×C113C2211yescharacteristic, complemented
71#341×C113C2211yescharacteristic, complemented
72#336×C113C2211yescharacteristic, complemented
732−1+4×C113—22no—
742−1+4×C113—22no—
752−1+4×C113—22no—
762−1+4×C113—41no—
77H(5,𝔽2)×C113—22no—
78H(5,𝔽2)×C113—22no—
79H(5,𝔽2)×C113—22no—
80H(5,𝔽2)×C113—22no—
81H(5,𝔽2)×C113—22no—
82H(5,𝔽2)×C113—41no—
83H(5,𝔽2)×C113—41no—
84H(5,𝔽2)×C113D414yescomplemented
85C2×#41×C113—21no—
86C2×#41×C113—21no—
87C2×#41×C113—21no—
88C2×#41×C113—21no—
89C2×#41×C113—21no—
90C2×#41×C113—21no—
91C2×#41×C113—41no—
92C2×#41×C113C2311yescharacteristic
93C2×#41×C113C2311yescharacteristic
94C2×#41×C113C2311yescharacteristic
95C2×#41×C113C2311yescharacteristic
96C22×Q8×C113—21no—
97C22×Q8×C113—21no—
98C22×Q8×C113C2311yescharacteristic
99C22×D4×C113—21no—
100C22×D4×C113—21no—
101C22×D4×C113—21no—
102C22×D4×C113—21no—
103C22×D4×C113—41no—
104C22×D4×C113—41no—
105C22×D4×C113C2311yescharacteristic
106C22×D4×C113C2311yescharacteristic
107#137×C113—28no—
108#137×C113—22no—
109#137×C113—22no—
110#137×C113—41no—
111#137×C113D414yescomplemented
112AGL(1,ℤ/8)×C113—28no—
113AGL(1,ℤ/8)×C113—28no—
114AGL(1,ℤ/8)×C113—28no—
115AGL(1,ℤ/8)×C113—22no—
116AGL(1,ℤ/8)×C113—22no—
117AGL(1,ℤ/8)×C113—22no—
118AGL(1,ℤ/8)×C113—22no—
119AGL(1,ℤ/8)×C113—22no—
120AGL(1,ℤ/8)×C113—22no—
121AGL(1,ℤ/8)×C113—41no—
122AGL(1,ℤ/8)×C113D414yescomplemented
123#135×C113—28no—
124#135×C113—28no—
125#135×C113—22no—
126#135×C113—22no—
127#135×C113—22no—
128#135×C113—22no—
129C2×Q16×C113—21no—
130C2×Q16×C113—21no—
131C2×Q16×C113D411yescharacteristic
132C2×Q16×C113D411yescharacteristic
133C2×SD16×C113—28no—
134C2×SD16×C113—21no—
135C2×SD16×C113—22no—
136C2×SD16×C113—21no—
137C2×SD16×C113—21no—
138C2×SD16×C113—21no—
139C2×SD16×C113—22no—
140C2×SD16×C113—21no—
141C2×SD16×C113—21no—
142C2×SD16×C113—21no—
143C2×SD16×C113—21no—
144C2×SD16×C113D411yescharacteristic
145C2×SD16×C113D411yescharacteristic
146C2×SD16×C113D411yescharacteristic
147C2×SD16×C113D411yescharacteristic
148C2×D8×C113—28no—
149C2×D8×C113—21no—
150C2×D8×C113—21no—
151C2×D8×C113—22no—
152C2×D8×C113—22no—
153C2×D8×C113—21no—
154C2×D8×C113—21no—
155C2×D8×C113—21no—
156C2×D8×C113—21no—
157C2×D8×C113D411yescharacteristic
158C2×D8×C113D411yescharacteristic
159#131×C113—22no—
160#131×C113—22no—
161#131×C113—22no—
162#131×C113—22no—
163C2×M16×C113—21no—
164C2×M16×C113—21no—
165C2×M16×C113C2311yescharacteristic
166C2×M16×C113C2311yescharacteristic
167C2×M16×C113C2311yescharacteristic
168C2×M16×C113C2311yescharacteristic
169C22×C8×C113—21no—
170C22×C8×C113—21no—
171C22×C8×C113C2311yescharacteristic
172C22×C8×C113C2311yescharacteristic
173#124×C113—22no—
174#124×C113—22no—
175C22⋊Q8×C113—21no—
176C22⋊Q8×C113—21no—
177#121×C113—21no—
178#121×C113—21no—
179#121×C113—41no—
180C2×C4⋊C4×C113C2311yescharacteristic
181C2×C22⋊C4×C113—41no—
182C2×C22⋊C4×C113—41no—
183C2×C42×C113C2311yescharacteristic
184#104×C113—22no—
185#104×C113—22no—
186#104×C113—22no—
187#104×C113—22no—
188#103×C113—21no—
189#103×C113—21no—
190#103×C113—21no—
191#103×C113—21no—
192#102×C113—21no—
193#102×C113—21no—
194#102×C113—21no—
195#102×C113—21no—
196#101×C113—22no—
197#100×C113—22no—
198#100×C113—41no—
199C22⋊C8×C113—21no—
200C22⋊C8×C113—21no—
201C22⋊C8×C113—21no—
202C22⋊C8×C113—21no—
203C24×C113—21no—
204C24×C113—21no—
205C24×C113—41no—
206C24×C113—41no—
207#41×C113—21no—
208#41×C113—21no—
209#41×C113—21no—
210#41×C113—21no—
211#41×C113—24no—
212#41×C113—24no—
213#41×C113—24no—
214#41×C113—24no—
215#41×C113—21no—
216#41×C113—21no—
217#41×C113—21no—
218#41×C113—21no—
219#41×C113—21no—
220#41×C113—21no—
221#41×C113—21no—
222#41×C113—21no—
223#41×C113—42no—
224#41×C113—44no—
225#41×C113—42no—
226#41×C113—42no—
227#41×C113—42no—
228#41×C113—42no—
229#41×C113—42no—
230#41×C113—44no—
231#41×C113—42no—
232#41×C113—42no—
233#41×C113C2×D412yes—
234#41×C113C2×D412yes—
235#41×C113C2×D412yes—
236#41×C113C2×D412yes—
237C2×Q8×C113—21no—
238C2×Q8×C113—24no—
239C2×Q8×C113—21no—
240C2×Q8×C113—21no—
241C2×Q8×C113—21no—
242C2×Q8×C113—21no—
243C2×Q8×C113—41no—
244C2×Q8×C113—42no—
245C2×Q8×C113—42no—
246C2×Q8×C113—42no—
247C2×Q8×C113C2×D411yescharacteristic
248C2×Q8×C113C2×D411yescharacteristic
249C2×Q8×C113C2×D412yes—
250C2×Q8×C113C2×D411yescharacteristic
251C2×Q8×C113C2×D411yescharacteristic
252C2×D4×C113—21no—
253C2×D4×C113—21no—
254C2×D4×C113—24no—
255C2×D4×C113—24no—
256C2×D4×C113—24no—
257C2×D4×C113—21no—
258C2×D4×C113—21no—
259C2×D4×C113—21no—
260C2×D4×C113—21no—
261C2×D4×C113—21no—
262C2×D4×C113—21no—
263C2×D4×C113—21no—
264C2×D4×C113—21no—
265C2×D4×C113—21no—
266C2×D4×C113—21no—
267C2×D4×C113—21no—
268C2×D4×C113—21no—
269C2×D4×C113—42no—
270C2×D4×C113—42no—
271C2×D4×C113—42no—
272C2×D4×C113—41no—
273C2×D4×C113—41no—
274C2×D4×C113—41no—
275C2×D4×C113—41no—
276C2×D4×C113—44no—
277C2×D4×C113—42no—
278C2×D4×C113—44no—
279C2×D4×C113—44no—
280C2×D4×C113—44no—
281C2×D4×C113—41no—
282C2×D4×C113—42no—
283C2×D4×C113—41no—
284C2×D4×C113C2×D411yescharacteristic
285C2×D4×C113C2×D411yescharacteristic
286C2×D4×C113C2×D412yes—
287C2×D4×C113C2×D412yes—
288C2×D4×C113C2×D411yescharacteristic
289C2×D4×C113C2×D411yescharacteristic
290C22×C4×C113—21no—
291C22×C4×C113—21no—
292C22×C4×C113—21no—
293C22×C4×C113—21no—
294C22×C4×C113—21no—
295C22×C4×C113—21no—
296C22×C4×C113—21no—
297C22×C4×C113—41no—
298C22×C4×C113—41no—
299C22×C4×C113—41no—
300C22×C4×C113—41no—
301C22×C4×C113C2411yescharacteristic
302Q16×C113—24no—
303Q16×C113—22no—
304Q16×C113—22no—
305Q16×C113—42no—
306SD16×C113—24no—
307SD16×C113—24no—
308SD16×C113—24no—
309SD16×C113—24no—
310SD16×C113—24no—
311SD16×C113—22no—
312SD16×C113—22no—
313SD16×C113—22no—
314SD16×C113—24no—
315SD16×C113—22no—
316SD16×C113—42no—
317SD16×C113—42no—
318D8×C113—24no—
319D8×C113—24no—
320D8×C113—24no—
321D8×C113—24no—
322D8×C113—22no—
323D8×C113—24no—
324D8×C113—22no—
325D8×C113—42no—
326M16×C113—24no—
327M16×C113—24no—
328M16×C113—21no—
329M16×C113—21no—
330M16×C113—21no—
331M16×C113—21no—
332M16×C113—21no—
333M16×C113—21no—
334M16×C113C2×D412yes—
335M16×C113C2×D412yes—
336C2×C8×C113—24no—
337C2×C8×C113—24no—
338C2×C8×C113—21no—
339C2×C8×C113—21no—
340C2×C8×C113—21no—
341C2×C8×C113—21no—
342C2×C8×C113—21no—
343C2×C8×C113—21no—
344C2×C8×C113—21no—
345C2×C8×C113—21no—
346C2×C8×C113C2×D411yescharacteristic
347C2×C8×C113C2×D411yescharacteristic
348C2×C8×C113C2×D411yescharacteristic
349C2×C8×C113C2×D411yescharacteristic
350C4⋊C4×C113—21no—
351C4⋊C4×C113—21no—
352C4⋊C4×C113—41no—
353C22⋊C4×C113—44no—
354C22⋊C4×C113—41no—
355C22⋊C4×C113—41no—
356C22⋊C4×C113—82no—
357C42×C113—21no—
358C42×C113—21no—
359C23×C113—21no—
360C23×C113—21no—
361C23×C113—21no—
362C23×C113—21no—
363C23×C113—22no—
364C23×C113—22no—
365C23×C113—44no—
366C23×C113—44no—
367C23×C113—41no—
368C23×C113—41no—
369C23×C113—41no—
370C23×C113—41no—
371C23×C113—81no—
372C23×C113—81no—
373C23×C113—81no—
374C23×C113—81no—
375C23×C113—161no—
376C23×C113—161no—
377C23×C113—161no—
378C23×C113—161no—
379C23×C113H(5,𝔽2)11yescharacteristic
380Q8×C113—21no—
381Q8×C113—21no—
382Q8×C113—22no—
383Q8×C113—21no—
384Q8×C113—21no—
385Q8×C113—21no—
386Q8×C113—22no—
387Q8×C113—21no—
388Q8×C113—44no—
389Q8×C113—41no—
390Q8×C113—41no—
391Q8×C113#12012yes—
392Q8×C113#12012yes—
393D4×C113—22no—
394D4×C113—22no—
395D4×C113—22no—
396D4×C113—22no—
397D4×C113—22no—
398D4×C113—22no—
399D4×C113—21no—
400D4×C113—21no—
401D4×C113—22no—
402D4×C113—21no—
403D4×C113—21no—
404D4×C113—21no—
405D4×C113—22no—
406D4×C113—21no—
407D4×C113—44no—
408D4×C113—44no—
409D4×C113—44no—
410D4×C113—44no—
411D4×C113—44no—
412D4×C113—41no—
413D4×C113—41no—
414D4×C113—41no—
415D4×C113—41no—
416D4×C113—41no—
417D4×C113—41no—
418D4×C113—41no—
419D4×C113—41no—
420D4×C113—161no—
421D4×C113#12012yes—
422D4×C113#12012yes—
423C2×C4×C113—21no—
424C2×C4×C113—21no—
425C2×C4×C113—22no—
426C2×C4×C113—22no—
427C2×C4×C113—22no—
428C2×C4×C113—22no—
429C2×C4×C113—22no—
430C2×C4×C113—21no—
431C2×C4×C113—21no—
432C2×C4×C113—44no—
433C2×C4×C113—44no—
434C2×C4×C113—44no—
435C2×C4×C113—44no—
436C2×C4×C113—41no—
437C2×C4×C113—41no—
438C2×C4×C113—41no—
439C2×C4×C113—41no—
440C2×C4×C113—41no—
441C2×C4×C113—41no—
442C2×C4×C113—41no—
443C2×C4×C113—41no—
444C2×C4×C113—41no—
445C2×C4×C113—41no—
446C2×C4×C113—81no—
447C2×C4×C113C22×D411yescharacteristic
448C2×C4×C113C22×D411yescharacteristic
449C2×C4×C113C22×D411yescharacteristic
450C2×C4×C113C22×D411yescharacteristic
451C2×C4×C113C22×D411yescharacteristic
452C2×C4×C113H(5,𝔽2)11yescharacteristic
453C8×C113—21no—
454C8×C113—21no—
455C8×C113—22no—
456C8×C113—22no—
457C8×C113—21no—
458C8×C113—21no—
459C8×C113—41no—
460C8×C113—41no—
461C22×C113—21no—
462C22×C113—21no—
463C22×C113—22no—
464C22×C113—22no—
465C22×C113—41no—
466C22×C113—41no—
467C22×C113—41no—
468C22×C113—41no—
469C22×C113—41no—
470C22×C113—41no—
471C22×C113—42no—
472C22×C113—42no—
473C22×C113—41no—
474C22×C113—41no—
475C22×C113—41no—
476C22×C113—41no—
477C22×C113—82no—
478C22×C113—82no—
479C22×C113—81no—
480C22×C113—81no—
481C22×C113—81no—
482C22×C113—81no—
483C22×C113—161no—
484C22×C113—161no—
485C22×C113—164no—
486C22×C113—164no—
487C22×C113#53411yescharacteristic
488C22×C113D4211yescharacteristic
489C22×C113D4211yescharacteristic
490C4×C113—22no—
491C4×C113—22no—
492C4×C113—41no—
493C4×C113—42no—
494C4×C113—41no—
495C4×C113—81no—
496C4×C113—81no—
497C4×C113C2×#12011yescharacteristic
498C4×C113C2×#12011yescharacteristic
499C4×C113D4211yescharacteristic
500C4×C113D4211yescharacteristic
501#23888C11311yesmaximal, characteristic, direct product factor, Sylow
502C2×C113—21no—
503C2×C113—21no—
504C2×C113—42no—
505C2×C113—42no—
506C2×C113—81no—
507C2×C113—81no—
508C2×C113—82no—
509C2×C113—82no—
510C2×C113#240311yescharacteristic
511C2×C113#328811yescharacteristic
512C2×C113#329011yescharacteristic
513C2×#577C2×C11311yescharacteristic, complemented
514C2×#576C2×C11311yescharacteristic, complemented
515C2×#454C2×C11311yescharacteristic, complemented
516C2×#455C2×C11311yescharacteristic, complemented
517#3013C2×C11311yescharacteristic, complemented
518#3012C2×C11311yescharacteristic, complemented
519#2019C2×C11311yescharacteristic, complemented
520#2018C2×C11311yescharacteristic, complemented
521#2012C2×C11311yescharacteristic, complemented
522#2006C2×C11311yescharacteristic, complemented
523#1908C2×C11311yescharacteristic, complemented
524#1907C2×C11311yescharacteristic, complemented
525#1876C2×C11311yescharacteristic, complemented
526#1876C2×C11311yescharacteristic, complemented
527#1792C2×C11311yescharacteristic, complemented
528C113#2388811yescharacteristic, direct product factor, Sylow
529C2×2−1+4C22×C11311yescharacteristic, complemented
530C2×H(5,𝔽2)C22×C11311yescharacteristic
531C2×H(5,𝔽2)C22×C11311yescharacteristic
532#577—24no—
533#577—24no—
534#576—24no—
535#576—24no—
536C2×#137—21no—
537C2×#137C22×C11311yescharacteristic
538C2×#137C22×C11311yescharacteristic, complemented
539C2×AGL(1,ℤ/8)—21no—
540C2×AGL(1,ℤ/8)—21no—
541C2×AGL(1,ℤ/8)—21no—
542C2×AGL(1,ℤ/8)C22×C11311yescharacteristic
543C2×AGL(1,ℤ/8)C22×C11311yescharacteristic
544C2×AGL(1,ℤ/8)C22×C11311yescharacteristic, complemented
545C2×AGL(1,ℤ/8)C22×C11311yescharacteristic, complemented
546C2×#135—21no—
547C2×#135—21no—
548C2×#135C22×C11311yescharacteristic
549C2×#135C22×C11311yescharacteristic
550C22×SD16—21no—
551C22×SD16C22×C11311yescharacteristic, complemented
552C22×D8—21no—
553C22×D8C22×C11311yescharacteristic
554C2×#131C22×C11311yescharacteristic
555C2×#131C22×C11311yescharacteristic, complemented
556#537C22×C11311yescharacteristic, complemented
557C2×#124C22×C11311yescharacteristic, complemented
558#455—24no—
559#454—24no—
560#452—21no—
561#452—21no—
562#451—21no—
563#450—21no—
564#449—21no—
565#449—21no—
566#448—21no—
567#447—21no—
568C2×#104C22×C11311yescharacteristic
569C2×#104C22×C11311yescharacteristic, complemented
570C2×#104C22×C11311yescharacteristic, complemented
571C2×#104C22×C11311yescharacteristic, complemented
572#417C22×C11311yescharacteristic
573#417C22×C11311yescharacteristic, complemented
574C2×#103C22×C11311yescharacteristic, complemented
575C2×#102C22×C11311yescharacteristic, complemented
576C2×#101C22×C11311yescharacteristic, complemented
577C2×#100C22×C11311yescharacteristic, complemented
578C2×#100C22×C11311yescharacteristic, complemented
579#408C22×C11311yescharacteristic, complemented
580#408C22×C11311yescharacteristic, complemented
581#390C22×C11311yescharacteristic, complemented
582#343C22×C11311yescharacteristic, complemented
583#341C22×C11311yescharacteristic, complemented
584#341C22×C11311yescharacteristic, complemented
585#336C22×C11311yescharacteristic, complemented
5862−1+4—22no—
5872−1+4—22no—
5882−1+4—22no—
5892−1+4—41no—
590H(5,𝔽2)—22no—
591H(5,𝔽2)—22no—
592H(5,𝔽2)—22no—
593H(5,𝔽2)—22no—
594H(5,𝔽2)—22no—
595H(5,𝔽2)—41no—
596H(5,𝔽2)—41no—
597H(5,𝔽2)D4×C11314yescomplemented
598C2×#41—21no—
599C2×#41—21no—
600C2×#41—21no—
601C2×#41—21no—
602C2×#41—21no—
603C2×#41—21no—
604C2×#41—41no—
605C2×#41C23×C11311yescharacteristic
606C2×#41C23×C11311yescharacteristic
607C2×#41C23×C11311yescharacteristic
608C2×#41C23×C11311yescharacteristic
609C22×Q8—21no—
610C22×Q8—21no—
611C22×Q8C23×C11311yescharacteristic
612C22×D4—21no—
613C22×D4—21no—
614C22×D4—21no—
615C22×D4—21no—
616C22×D4—41no—
617C22×D4—41no—
618C22×D4C23×C11311yescharacteristic
619C22×D4C23×C11311yescharacteristic
620#137—28no—
621#137—22no—
622#137—22no—
623#137—41no—
624#137D4×C11314yescomplemented
625AGL(1,ℤ/8)—28no—
626AGL(1,ℤ/8)—28no—
627AGL(1,ℤ/8)—28no—
628AGL(1,ℤ/8)—22no—
629AGL(1,ℤ/8)—22no—
630AGL(1,ℤ/8)—22no—
631AGL(1,ℤ/8)—22no—
632AGL(1,ℤ/8)—22no—
633AGL(1,ℤ/8)—22no—
634AGL(1,ℤ/8)—41no—
635AGL(1,ℤ/8)D4×C11314yescomplemented
636#135—28no—
637#135—28no—
638#135—22no—
639#135—22no—
640#135—22no—
641#135—22no—
642C2×Q16—21no—
643C2×Q16—21no—
644C2×Q16D4×C11311yescharacteristic
645C2×Q16D4×C11311yescharacteristic
646C2×SD16—28no—
647C2×SD16—21no—
648C2×SD16—22no—
649C2×SD16—21no—
650C2×SD16—21no—
651C2×SD16—21no—
652C2×SD16—22no—
653C2×SD16—21no—
654C2×SD16—21no—
655C2×SD16—21no—
656C2×SD16—21no—
657C2×SD16D4×C11311yescharacteristic
658C2×SD16D4×C11311yescharacteristic
659C2×SD16D4×C11311yescharacteristic
660C2×SD16D4×C11311yescharacteristic
661C2×D8—28no—
662C2×D8—21no—
663C2×D8—21no—
664C2×D8—22no—
665C2×D8—22no—
666C2×D8—21no—
667C2×D8—21no—
668C2×D8—21no—
669C2×D8—21no—
670C2×D8D4×C11311yescharacteristic
671C2×D8D4×C11311yescharacteristic
672#131—22no—
673#131—22no—
674#131—22no—
675#131—22no—
676C2×M16—21no—
677C2×M16—21no—
678C2×M16C23×C11311yescharacteristic
679C2×M16C23×C11311yescharacteristic
680C2×M16C23×C11311yescharacteristic
681C2×M16C23×C11311yescharacteristic
682C22×C8—21no—
683C22×C8—21no—
684C22×C8C23×C11311yescharacteristic
685C22×C8C23×C11311yescharacteristic
686#124—22no—
687#124—22no—
688C22⋊Q8—21no—
689C22⋊Q8—21no—
690#121—21no—
691#121—21no—
692#121—41no—
693C2×C4⋊C4C23×C11311yescharacteristic
694C2×C22⋊C4—41no—
695C2×C22⋊C4—41no—
696C2×C42C23×C11311yescharacteristic
697#104—22no—
698#104—22no—
699#104—22no—
700#104—22no—
701#103—21no—
702#103—21no—
703#103—21no—
704#103—21no—
705#102—21no—
706#102—21no—
707#102—21no—
708#102—21no—
709#101—22no—
710#100—22no—
711#100—41no—
712C22⋊C8—21no—
713C22⋊C8—21no—
714C22⋊C8—21no—
715C22⋊C8—21no—
716C24—21no—
717C24—21no—
718C24—41no—
719C24—41no—
720#41—21no—
721#41—21no—
722#41—21no—
723#41—21no—
724#41—24no—
725#41—24no—
726#41—24no—
727#41—24no—
728#41—21no—
729#41—21no—
730#41—21no—
731#41—21no—
732#41—21no—
733#41—21no—
734#41—21no—
735#41—21no—
736#41—42no—
737#41—44no—
738#41—42no—
739#41—42no—
740#41—42no—
741#41—42no—
742#41—42no—
743#41—44no—
744#41—42no—
745#41—42no—
746#41C2×D4×C11312yes—
747#41C2×D4×C11312yes—
748#41C2×D4×C11312yes—
749#41C2×D4×C11312yes—
750C2×Q8—21no—
751C2×Q8—24no—
752C2×Q8—21no—
753C2×Q8—21no—
754C2×Q8—21no—
755C2×Q8—21no—
756C2×Q8—41no—
757C2×Q8—42no—
758C2×Q8—42no—
759C2×Q8—42no—
760C2×Q8C2×D4×C11311yescharacteristic
761C2×Q8C2×D4×C11311yescharacteristic
762C2×Q8C2×D4×C11312yes—
763C2×Q8C2×D4×C11311yescharacteristic
764C2×Q8C2×D4×C11311yescharacteristic
765C2×D4—21no—
766C2×D4—21no—
767C2×D4—24no—
768C2×D4—24no—
769C2×D4—24no—
770C2×D4—21no—
771C2×D4—21no—
772C2×D4—21no—
773C2×D4—21no—
774C2×D4—21no—
775C2×D4—21no—
776C2×D4—21no—
777C2×D4—21no—
778C2×D4—21no—
779C2×D4—21no—
780C2×D4—21no—
781C2×D4—21no—
782C2×D4—42no—
783C2×D4—42no—
784C2×D4—42no—
785C2×D4—41no—
786C2×D4—41no—
787C2×D4—41no—
788C2×D4—41no—
789C2×D4—44no—
790C2×D4—42no—
791C2×D4—44no—
792C2×D4—44no—
793C2×D4—44no—
794C2×D4—41no—
795C2×D4—42no—
796C2×D4—41no—
797C2×D4C2×D4×C11311yescharacteristic
798C2×D4C2×D4×C11311yescharacteristic
799C2×D4C2×D4×C11312yes—
800C2×D4C2×D4×C11312yes—
801C2×D4C2×D4×C11311yescharacteristic
802C2×D4C2×D4×C11311yescharacteristic
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—41no—
811C22×C4—41no—
812C22×C4—41no—
813C22×C4—41no—
814C22×C4C24×C11311yescharacteristic
815Q16—24no—
816Q16—22no—
817Q16—22no—
818Q16—42no—
819SD16—24no—
820SD16—24no—
821SD16—24no—
822SD16—24no—
823SD16—24no—
824SD16—22no—
825SD16—22no—
826SD16—22no—
827SD16—24no—
828SD16—22no—
829SD16—42no—
830SD16—42no—
831D8—24no—
832D8—24no—
833D8—24no—
834D8—24no—
835D8—22no—
836D8—24no—
837D8—22no—
838D8—42no—
839M16—24no—
840M16—24no—
841M16—21no—
842M16—21no—
843M16—21no—
844M16—21no—
845M16—21no—
846M16—21no—
847M16C2×D4×C11312yes—
848M16C2×D4×C11312yes—
849C2×C8—24no—
850C2×C8—24no—
851C2×C8—21no—
852C2×C8—21no—
853C2×C8—21no—
854C2×C8—21no—
855C2×C8—21no—
856C2×C8—21no—
857C2×C8—21no—
858C2×C8—21no—
859C2×C8C2×D4×C11311yescharacteristic
860C2×C8C2×D4×C11311yescharacteristic
861C2×C8C2×D4×C11311yescharacteristic
862C2×C8C2×D4×C11311yescharacteristic
863C4⋊C4—21no—
864C4⋊C4—21no—
865C4⋊C4—41no—
866C22⋊C4—44no—
867C22⋊C4—41no—
868C22⋊C4—41no—
869C22⋊C4—82no—
870C42—21no—
871C42—21no—
872C23—21no—
873C23—21no—
874C23—21no—
875C23—21no—
876C23—22no—
877C23—22no—
878C23—44no—
879C23—44no—
880C23—41no—
881C23—41no—
882C23—41no—
883C23—41no—
884C23—81no—
885C23—81no—
886C23—81no—
887C23—81no—
888C23—161no—
889C23—161no—
890C23—161no—
891C23—161no—
892C23H(5,𝔽2)×C11311yescharacteristic
893Q8—21no—
894Q8—21no—
895Q8—22no—
896Q8—21no—
897Q8—21no—
898Q8—21no—
899Q8—22no—
900Q8—21no—
901Q8—44no—
902Q8—41no—
903Q8—41no—
904Q8#120×C11312yes—
905Q8#120×C11312yes—
906D4—22no—
907D4—22no—
908D4—22no—
909D4—22no—
910D4—22no—
911D4—22no—
912D4—21no—
913D4—21no—
914D4—22no—
915D4—21no—
916D4—21no—
917D4—21no—
918D4—22no—
919D4—21no—
920D4—44no—
921D4—44no—
922D4—44no—
923D4—44no—
924D4—44no—
925D4—41no—
926D4—41no—
927D4—41no—
928D4—41no—
929D4—41no—
930D4—41no—
931D4—41no—
932D4—41no—
933D4—161no—
934D4#120×C11312yes—
935D4#120×C11312yes—
936C2×C4—21no—
937C2×C4—21no—
938C2×C4—22no—
939C2×C4—22no—
940C2×C4—22no—
941C2×C4—22no—
942C2×C4—22no—
943C2×C4—21no—
944C2×C4—21no—
945C2×C4—44no—
946C2×C4—44no—
947C2×C4—44no—
948C2×C4—44no—
949C2×C4—41no—
950C2×C4—41no—
951C2×C4—41no—
952C2×C4—41no—
953C2×C4—41no—
954C2×C4—41no—
955C2×C4—41no—
956C2×C4—41no—
957C2×C4—41no—
958C2×C4—41no—
959C2×C4—81no—
960C2×C4C22×D4×C11311yescharacteristic
961C2×C4C22×D4×C11311yescharacteristic
962C2×C4C22×D4×C11311yescharacteristic
963C2×C4C22×D4×C11311yescharacteristic
964C2×C4C22×D4×C11311yescharacteristic
965C2×C4H(5,𝔽2)×C11311yescharacteristic
966C8—21no—
967C8—21no—
968C8—22no—
969C8—22no—
970C8—21no—
971C8—21no—
972C8—41no—
973C8—41no—
974C22—21no—
975C22—21no—
976C22—22no—
977C22—22no—
978C22—41no—
979C22—41no—
980C22—41no—
981C22—41no—
982C22—41no—
983C22—41no—
984C22—42no—
985C22—42no—
986C22—41no—
987C22—41no—
988C22—41no—
989C22—41no—
990C22—82no—
991C22—82no—
992C22—81no—
993C22—81no—
994C22—81no—
995C22—81no—
996C22—161no—
997C22—161no—
998C22—164no—
999C22—164no—
1000C22#534×C11311yescharacteristic
1001C22D42×C11311yescharacteristic
1002C22D42×C11311yescharacteristic
1003C4—22no—
1004C4—22no—
1005C4—41no—
1006C4—42no—
1007C4—41no—
1008C4—81no—
1009C4—81no—
1010C4C2×#120×C11311yescharacteristic
1011C4C2×#120×C11311yescharacteristic
1012C4D42×C11311yescharacteristic
1013C4D42×C11311yescharacteristic
1014C2—21no—
1015C2—21no—
1016C2—42no—
1017C2—42no—
1018C2—81no—
1019C2—81no—
1020C2—82no—
1021C2—82no—
1022C2C113×#240311yescharacteristic
1023C2C113×#328811yescharacteristic
1024C2C113×#329011yescharacteristic
subgroupG/H
center, socleC22×C113D42
commutator, Frattini, cosocleC22×C4C24×C113
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C113 ◁ C22×C4×C113 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#577×C113C2semidirect
2. C2×#576×C113C2semidirect
3. C2×#454×C113C2semidirect
4. C2×#455×C113C2semidirect
5. C113×#3013C2semidirect
6. C113×#3012C2semidirect
7. C113×#2019C2semidirect
8. C113×#2018C2semidirect
9. C113×#2012C2semidirect
10. C113×#2006C2semidirect
11. C113×#1908C2semidirect
12. C113×#1907C2semidirect
13. C113×#1876C2semidirect
14. C113×#1876C2semidirect
15. C113×#1792C2semidirect
16. C2×2−1+4×C113C22semidirect
25. C2×#137×C113C22semidirect
31. C2×AGL(1,ℤ/8)×C113C22semidirect
32. C2×AGL(1,ℤ/8)×C113C22semidirect
38. C22×SD16×C113C22semidirect
42. C2×#131×C113C22semidirect
43. #537×C113C22semidirect
44. C2×#124×C113C22semidirect
56. C2×#104×C113C22semidirect
57. C2×#104×C113C22semidirect
58. C2×#104×C113C22semidirect
60. #417×C113C22semidirect
61. C2×#103×C113C22semidirect
62. C2×#102×C113C22semidirect
63. C2×#101×C113C22semidirect
64. C2×#100×C113C22semidirect
65. C2×#100×C113C22semidirect
66. #408×C113C22semidirect
67. #408×C113C22semidirect
68. #390×C113C22semidirect
69. #343×C113C22semidirect
70. #341×C113C22semidirect
71. #341×C113C22semidirect
72. #336×C113C22semidirect
84. H(5,𝔽2)×C113D4semidirect
111. #137×C113D4semidirect
122. AGL(1,ℤ/8)×C113D4semidirect
501. #23888C113direct (N × H)
513. C2×#577C2×C113semidirect
514. C2×#576C2×C113semidirect
515. C2×#454C2×C113semidirect
516. C2×#455C2×C113semidirect
517. #3013C2×C113semidirect
518. #3012C2×C113semidirect
519. #2019C2×C113semidirect
520. #2018C2×C113semidirect
521. #2012C2×C113semidirect
522. #2006C2×C113semidirect
523. #1908C2×C113semidirect
524. #1907C2×C113semidirect
525. #1876C2×C113semidirect
526. #1876C2×C113semidirect
527. #1792C2×C113semidirect
528. C113#23888direct (N × H)
529. C2×2−1+4C22×C113semidirect
538. C2×#137C22×C113semidirect
544. C2×AGL(1,ℤ/8)C22×C113semidirect
545. C2×AGL(1,ℤ/8)C22×C113semidirect
551. C22×SD16C22×C113semidirect
555. C2×#131C22×C113semidirect
556. #537C22×C113semidirect
557. C2×#124C22×C113semidirect
569. C2×#104C22×C113semidirect
570. C2×#104C22×C113semidirect
571. C2×#104C22×C113semidirect
573. #417C22×C113semidirect
574. C2×#103C22×C113semidirect
575. C2×#102C22×C113semidirect
576. C2×#101C22×C113semidirect
577. C2×#100C22×C113semidirect
578. C2×#100C22×C113semidirect
579. #408C22×C113semidirect
580. #408C22×C113semidirect
581. #390C22×C113semidirect
582. #343C22×C113semidirect
583. #341C22×C113semidirect
584. #341C22×C113semidirect
585. #336C22×C113semidirect
597. H(5,𝔽2)D4×C113semidirect
624. #137D4×C113semidirect
635. AGL(1,ℤ/8)D4×C113semidirect

Maximal subgroups

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

subgroupindex
C2×#577×C1132
C2×#576×C1132
C2×#454×C1132
C2×#455×C1132
C113×#30132
C113×#30122
C113×#20192
C113×#20182
C113×#20122
C113×#20062
C113×#19082
C113×#19072
C113×#18762
C113×#17922
#23888113