Finite Group Databasebeta

← C113×#18132 #43286152

Subgroups — C113×#18132 #43286152

Order 28928.

1654 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#534×C113C211yesmaximal, characteristic, complemented
2C113×#3006C212yesmaximal, complemented
3C113×#2404C211yesmaximal, characteristic, complemented
4C113×#1601C214yesmaximal, complemented
5C113×#1595C214yesmaximal, complemented
6C113×#1510C212yesmaximal, complemented
7C113×#1462C211yesmaximal, characteristic, complemented
8C22×#41×C113C2211yescharacteristic, complemented
9C23×D4×C113—21no—
10C2×AGL(1,ℤ/8)×C113—22no—
11#534×C113—24no—
12#534×C113—22no—
13#534×C113C2214yes—
14C2×#123×C113—22no—
15C2×#121×C113—21no—
16C2×#121×C113C2212yes—
17C2×#120×C113—22no—
18C2×#120×C113—21no—
19C22×C22⋊C4×C113C2211yescharacteristic
20#449×C113—24no—
21#448×C113C2214yescomplemented
22#447×C113C2214yescomplemented
23#417×C113—22no—
24#407×C113C2212yescomplemented
25#393×C113C2212yescomplemented
26#392×C113C2212yescomplemented
27#386×C113—21no—
28#386×C113—22no—
29#381×C113C2211yescharacteristic, complemented
30#327×C113C2218yescomplemented
31#323×C113C2214yescomplemented
32C25×C113—21no—
33C25×C113D411yescharacteristic
34C2×#41×C113—22no—
35C2×#41×C113—22no—
36C2×#41×C113—44no—
37C22×Q8×C113C2311yescharacteristic, complemented
38C22×D4×C113—22no—
39C22×D4×C113—24no—
40C22×D4×C113—21no—
41C22×D4×C113—22no—
42C22×D4×C113—24no—
43C22×D4×C113—21no—
44C22×D4×C113—22no—
45C22×D4×C113—48no—
46C22×D4×C113D412yescomplemented
47C22×D4×C113C2311yescharacteristic, complemented
48C23×C4×C113—21no—
49C23×C4×C113—21no—
50C23×C4×C113D411yescharacteristic
51C23×C4×C113C2311yescharacteristic
52AGL(1,ℤ/8)×C113—48no—
53C2×SD16×C113—24no—
54C2×D8×C113—24no—
55C2×M16×C113—22no—
56#123×C113—28no—
57#123×C113—28no—
58#121×C113—24no—
59#121×C113—24no—
60#121×C113—22no—
61#121×C113—22no—
62#121×C113D414yescomplemented
63#121×C113C2314yes—
64#120×C113—28no—
65#120×C113—28no—
66#120×C113—44no—
67C2×C4⋊C4×C113—21no—
68C2×C4⋊C4×C113D412yescomplemented
69C2×C22⋊C4×C113—22no—
70C2×C22⋊C4×C113—22no—
71C2×C22⋊C4×C113—22no—
72C2×C22⋊C4×C113—22no—
73C2×C22⋊C4×C113—21no—
74C2×C22⋊C4×C113—22no—
75C2×C22⋊C4×C113—22no—
76C2×C22⋊C4×C113D412yes—
77C2×C22⋊C4×C113C2312yes—
78#103×C113—24no—
79#102×C113—24no—
80C22⋊C8×C113—22no—
81C22⋊C8×C113C2314yescomplemented
82#95×C113—21no—
83#95×C113—22no—
84#95×C113C2312yescomplemented
85C24×C113—21no—
86C24×C113—21no—
87C24×C113—24no—
88C24×C113—24no—
89C24×C113—22no—
90C24×C113—21no—
91C24×C113—44no—
92C24×C113—42no—
93C24×C113—81no—
94C24×C113—82no—
95C24×C113—82no—
96C24×C113C2×D411yescharacteristic
97C24×C113C2×D412yes—
98#41×C113—28no—
99#41×C113—44no—
100#41×C113—44no—
101#41×C113—44no—
102C2×Q8×C113—22no—
103C2×Q8×C113—42no—
104C2×D4×C113—28no—
105C2×D4×C113—24no—
106C2×D4×C113—24no—
107C2×D4×C113—24no—
108C2×D4×C113—24no—
109C2×D4×C113—22no—
110C2×D4×C113—22no—
111C2×D4×C113—44no—
112C2×D4×C113—42no—
113C2×D4×C113—48no—
114C2×D4×C113—416no—
115C2×D4×C113—48no—
116C2×D4×C113—48no—
117C2×D4×C113—42no—
118C2×D4×C113—41no—
119C2×D4×C113—41no—
120C2×D4×C113—48no—
121C2×D4×C113—44no—
122C2×D4×C113—44no—
123C2×D4×C113—82no—
124C2×D4×C113—82no—
125C2×D4×C113C2×D414yes—
126C22×C4×C113—24no—
127C22×C4×C113—21no—
128C22×C4×C113—22no—
129C22×C4×C113—21no—
130C22×C4×C113—21no—
131C22×C4×C113—22no—
132C22×C4×C113—42no—
133C22×C4×C113—42no—
134C22×C4×C113—44no—
135C22×C4×C113—42no—
136C22×C4×C113—42no—
137C22×C4×C113—81no—
138C22×C4×C113C2×D412yes—
139C22×C4×C113C2×D412yes—
140C22×C4×C113C2×D411yescharacteristic
141C22×C4×C113C2×D412yes—
142C22×C4×C113C2411yescharacteristic
143SD16×C113—48no—
144D8×C113—48no—
145M16×C113—44no—
146C2×C8×C113—24no—
147C4⋊C4×C113—24no—
148C4⋊C4×C113—22no—
149C4⋊C4×C113C2×D414yes—
150C22⋊C4×C113—28no—
151C22⋊C4×C113—24no—
152C22⋊C4×C113—24no—
153C22⋊C4×C113—24no—
154C22⋊C4×C113—24no—
155C22⋊C4×C113—44no—
156C22⋊C4×C113—42no—
157C22⋊C4×C113—82no—
158C23×C113—24no—
159C23×C113—24no—
160C23×C113—22no—
161C23×C113—22no—
162C23×C113—22no—
163C23×C113—22no—
164C23×C113—22no—
165C23×C113—24no—
166C23×C113—41no—
167C23×C113—42no—
168C23×C113—42no—
169C23×C113—42no—
170C23×C113—42no—
171C23×C113—41no—
172C23×C113—44no—
173C23×C113—48no—
174C23×C113—44no—
175C23×C113—42no—
176C23×C113—41no—
177C23×C113—42no—
178C23×C113—44no—
179C23×C113—81no—
180C23×C113—81no—
181C23×C113—88no—
182C23×C113—84no—
183C23×C113—84no—
184C23×C113—816no—
185C23×C113#12011yescharacteristic
186C23×C113#12011yescharacteristic
187C23×C113AGL(1,ℤ/8)14yescomplemented
188C23×C113C22×D411yescharacteristic
189Q8×C113—24no—
190Q8×C113—42no—
191D4×C113—24no—
192D4×C113—44no—
193D4×C113—42no—
194D4×C113—416no—
195D4×C113—48no—
196D4×C113—44no—
197D4×C113—48no—
198D4×C113—44no—
199D4×C113—82no—
200D4×C113—84no—
201D4×C113—88no—
202C2×C4×C113—24no—
203C2×C4×C113—22no—
204C2×C4×C113—22no—
205C2×C4×C113—24no—
206C2×C4×C113—41no—
207C2×C4×C113—42no—
208C2×C4×C113—41no—
209C2×C4×C113—48no—
210C2×C4×C113—44no—
211C2×C4×C113—48no—
212C2×C4×C113—41no—
213C2×C4×C113—42no—
214C2×C4×C113—41no—
215C2×C4×C113—42no—
216C2×C4×C113—42no—
217C2×C4×C113—42no—
218C2×C4×C113—42no—
219C2×C4×C113—81no—
220C2×C4×C113#12012yes—
221C2×C4×C113C22×D412yes—
222C8×C113—44no—
223C22×C113—21no—
224C22×C113—21no—
225C22×C113—21no—
226C22×C113—21no—
227C22×C113—24no—
228C22×C113—21no—
229C22×C113—21no—
230C22×C113—21no—
231C22×C113—44no—
232C22×C113—44no—
233C22×C113—48no—
234C22×C113—44no—
235C22×C113—42no—
236C22×C113—42no—
237C22×C113—44no—
238C22×C113—44no—
239C22×C113—42no—
240C22×C113—44no—
241C22×C113—82no—
242C22×C113—82no—
243C22×C113—88no—
244C22×C113—84no—
245C22×C113—816no—
246C22×C113—81no—
247C22×C113—81no—
248C22×C113B(4,𝔽2)12yes—
249C22×C113C2×#12011yescharacteristic
250C22×C113C2×AGL(1,ℤ/8)12yes—
251C4×C113—22no—
252C4×C113—22no—
253C4×C113—44no—
254C4×C113—42no—
255C4×C113—42no—
256C4×C113—82no—
257#18132C11311yesmaximal, characteristic, direct product factor, Sylow
258C2×C113—22no—
259C2×C113—22no—
260C2×C113—41no—
261C2×C113—44no—
262C2×C113—82no—
263C2×C113—84no—
264C2×C113#300311yescharacteristic
265C2×C113#301911yescharacteristic
266C2×C113C2×B(4,𝔽2)11yescharacteristic
267C2×#534C2×C11311yescharacteristic, complemented
268#3006C2×C11312yescomplemented
269#2404C2×C11311yescharacteristic, complemented
270#1601C2×C11314yescomplemented
271#1595C2×C11314yescomplemented
272#1510C2×C11312yescomplemented
273#1462C2×C11311yescharacteristic, complemented
274C113#1813211yescharacteristic, direct product factor, Sylow
275C22×#41C22×C11311yescharacteristic, complemented
276C23×D4—21no—
277C2×AGL(1,ℤ/8)—22no—
278#534—24no—
279#534—22no—
280#534C22×C11314yes—
281C2×#123—22no—
282C2×#121—21no—
283C2×#121C22×C11312yes—
284C2×#120—22no—
285C2×#120—21no—
286C22×C22⋊C4C22×C11311yescharacteristic
287#449—24no—
288#448C22×C11314yescomplemented
289#447C22×C11314yescomplemented
290#417—22no—
291#407C22×C11312yescomplemented
292#393C22×C11312yescomplemented
293#392C22×C11312yescomplemented
294#386—21no—
295#386—22no—
296#381C22×C11311yescharacteristic, complemented
297#327C22×C11318yescomplemented
298#323C22×C11314yescomplemented
299C25—21no—
300C25D4×C11311yescharacteristic
301C2×#41—22no—
302C2×#41—22no—
303C2×#41—44no—
304C22×Q8C23×C11311yescharacteristic, complemented
305C22×D4—22no—
306C22×D4—24no—
307C22×D4—21no—
308C22×D4—22no—
309C22×D4—24no—
310C22×D4—21no—
311C22×D4—22no—
312C22×D4—48no—
313C22×D4D4×C11312yescomplemented
314C22×D4C23×C11311yescharacteristic, complemented
315C23×C4—21no—
316C23×C4—21no—
317C23×C4D4×C11311yescharacteristic
318C23×C4C23×C11311yescharacteristic
319AGL(1,ℤ/8)—48no—
320C2×SD16—24no—
321C2×D8—24no—
322C2×M16—22no—
323#123—28no—
324#123—28no—
325#121—24no—
326#121—24no—
327#121—22no—
328#121—22no—
329#121D4×C11314yescomplemented
330#121C23×C11314yes—
331#120—28no—
332#120—28no—
333#120—44no—
334C2×C4⋊C4—21no—
335C2×C4⋊C4D4×C11312yescomplemented
336C2×C22⋊C4—22no—
337C2×C22⋊C4—22no—
338C2×C22⋊C4—22no—
339C2×C22⋊C4—22no—
340C2×C22⋊C4—21no—
341C2×C22⋊C4—22no—
342C2×C22⋊C4—22no—
343C2×C22⋊C4D4×C11312yes—
344C2×C22⋊C4C23×C11312yes—
345#103—24no—
346#102—24no—
347C22⋊C8—22no—
348C22⋊C8C23×C11314yescomplemented
349#95—21no—
350#95—22no—
351#95C23×C11312yescomplemented
352C24—21no—
353C24—21no—
354C24—24no—
355C24—24no—
356C24—22no—
357C24—21no—
358C24—44no—
359C24—42no—
360C24—81no—
361C24—82no—
362C24—82no—
363C24C2×D4×C11311yescharacteristic
364C24C2×D4×C11312yes—
365#41—28no—
366#41—44no—
367#41—44no—
368#41—44no—
369C2×Q8—22no—
370C2×Q8—42no—
371C2×D4—28no—
372C2×D4—24no—
373C2×D4—24no—
374C2×D4—24no—
375C2×D4—24no—
376C2×D4—22no—
377C2×D4—22no—
378C2×D4—44no—
379C2×D4—42no—
380C2×D4—48no—
381C2×D4—416no—
382C2×D4—48no—
383C2×D4—48no—
384C2×D4—42no—
385C2×D4—41no—
386C2×D4—41no—
387C2×D4—48no—
388C2×D4—44no—
389C2×D4—44no—
390C2×D4—82no—
391C2×D4—82no—
392C2×D4C2×D4×C11314yes—
393C22×C4—24no—
394C22×C4—21no—
395C22×C4—22no—
396C22×C4—21no—
397C22×C4—21no—
398C22×C4—22no—
399C22×C4—42no—
400C22×C4—42no—
401C22×C4—44no—
402C22×C4—42no—
403C22×C4—42no—
404C22×C4—81no—
405C22×C4C2×D4×C11312yes—
406C22×C4C2×D4×C11312yes—
407C22×C4C2×D4×C11311yescharacteristic
408C22×C4C2×D4×C11312yes—
409C22×C4C24×C11311yescharacteristic
410SD16—48no—
411D8—48no—
412M16—44no—
413C2×C8—24no—
414C4⋊C4—24no—
415C4⋊C4—22no—
416C4⋊C4C2×D4×C11314yes—
417C22⋊C4—28no—
418C22⋊C4—24no—
419C22⋊C4—24no—
420C22⋊C4—24no—
421C22⋊C4—24no—
422C22⋊C4—44no—
423C22⋊C4—42no—
424C22⋊C4—82no—
425C23—24no—
426C23—24no—
427C23—22no—
428C23—22no—
429C23—22no—
430C23—22no—
431C23—22no—
432C23—24no—
433C23—41no—
434C23—42no—
435C23—42no—
436C23—42no—
437C23—42no—
438C23—41no—
439C23—44no—
440C23—48no—
441C23—44no—
442C23—42no—
443C23—41no—
444C23—42no—
445C23—44no—
446C23—81no—
447C23—81no—
448C23—88no—
449C23—84no—
450C23—84no—
451C23—816no—
452C23#120×C11311yescharacteristic
453C23#120×C11311yescharacteristic
454C23AGL(1,ℤ/8)×C11314yescomplemented
455C23C22×D4×C11311yescharacteristic
456Q8—24no—
457Q8—42no—
458D4—24no—
459D4—44no—
460D4—42no—
461D4—416no—
462D4—48no—
463D4—44no—
464D4—48no—
465D4—44no—
466D4—82no—
467D4—84no—
468D4—88no—
469C2×C4—24no—
470C2×C4—22no—
471C2×C4—22no—
472C2×C4—24no—
473C2×C4—41no—
474C2×C4—42no—
475C2×C4—41no—
476C2×C4—48no—
477C2×C4—44no—
478C2×C4—48no—
479C2×C4—41no—
480C2×C4—42no—
481C2×C4—41no—
482C2×C4—42no—
483C2×C4—42no—
484C2×C4—42no—
485C2×C4—42no—
486C2×C4—81no—
487C2×C4#120×C11312yes—
488C2×C4C22×D4×C11312yes—
489C8—44no—
490C22—21no—
491C22—21no—
492C22—21no—
493C22—21no—
494C22—24no—
495C22—21no—
496C22—21no—
497C22—21no—
498C22—44no—
499C22—44no—
500C22—48no—
501C22—44no—
502C22—42no—
503C22—42no—
504C22—44no—
505C22—44no—
506C22—42no—
507C22—44no—
508C22—82no—
509C22—88no—
510C22—82no—
511C22—84no—
512C22—816no—
513C22—81no—
514C22—81no—
515C22B(4,𝔽2)×C11312yes—
516C22C2×#120×C11311yescharacteristic
517C22C2×AGL(1,ℤ/8)×C11312yes—
518C4—22no—
519C4—22no—
520C4—44no—
521C4—42no—
522C4—42no—
523C4—82no—
524C2—22no—
525C2—22no—
526C2—41no—
527C2—44no—
528C2—84no—
529C2—82no—
530C2C113×#300311yescharacteristic
531C2C113×#301911yescharacteristic
532C2C2×B(4,𝔽2)×C11311yescharacteristic
subgroupG/H
center, socleC22×C113C2×#120
commutator, Frattini, cosocleC22×C4C24×C113
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C113 ◁ C23×C4×C113 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#534×C113C2semidirect
2. C113×#3006C2semidirect
3. C113×#2404C2semidirect
4. C113×#1601C2semidirect
5. C113×#1595C2semidirect
6. C113×#1510C2semidirect
7. C113×#1462C2semidirect
8. C22×#41×C113C22semidirect
21. #448×C113C22semidirect
22. #447×C113C22semidirect
24. #407×C113C22semidirect
25. #393×C113C22semidirect
26. #392×C113C22semidirect
29. #381×C113C22semidirect
30. #327×C113C22semidirect
31. #323×C113C22semidirect
37. C22×Q8×C113C23semidirect
46. C22×D4×C113D4semidirect
47. C22×D4×C113C23semidirect
62. #121×C113D4semidirect
68. C2×C4⋊C4×C113D4semidirect
81. C22⋊C8×C113C23semidirect
84. #95×C113C23semidirect
187. C23×C113AGL(1,ℤ/8)semidirect
257. #18132C113direct (N × H)
267. C2×#534C2×C113semidirect
268. #3006C2×C113semidirect
269. #2404C2×C113semidirect
270. #1601C2×C113semidirect
271. #1595C2×C113semidirect
272. #1510C2×C113semidirect
273. #1462C2×C113semidirect
274. C113#18132direct (N × H)
275. C22×#41C22×C113semidirect
288. #448C22×C113semidirect
289. #447C22×C113semidirect
291. #407C22×C113semidirect
292. #393C22×C113semidirect
293. #392C22×C113semidirect
296. #381C22×C113semidirect
297. #327C22×C113semidirect
298. #323C22×C113semidirect
304. C22×Q8C23×C113semidirect
313. C22×D4D4×C113semidirect
314. C22×D4C23×C113semidirect
329. #121D4×C113semidirect
335. C2×C4⋊C4D4×C113semidirect
348. C22⋊C8C23×C113semidirect
351. #95C23×C113semidirect
454. C23AGL(1,ℤ/8)×C113semidirect

Maximal subgroups

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

subgroupindex
C2×#534×C1132
C113×#30062
C113×#24042
C113×#16012
C113×#15952
C113×#15102
C113×#14622
#18132113