Finite Group Databasebeta

← C113×#18903 #43286923

Subgroups — C113×#18903 #43286923

Order 28928.

1206 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C113×#3496C211yesmaximal, characteristic
2C113×#3227C211yesmaximal, characteristic, complemented
3C113×#3206C211yesmaximal, characteristic, complemented
4C2×#474×C113C211yesmaximal, characteristic, complemented
5C113×#1654C214yesmaximal, complemented
6C113×#1639C214yesmaximal, complemented
7C113×#1540C211yesmaximal, characteristic, complemented
8C113×#1480C211yesmaximal, characteristic, complemented
9C113×#1478C211yesmaximal, characteristic, complemented
10C2×H(5,𝔽2)×C113—21no—
11#547×C113—21no—
12#547×C113C2212yes—
13#546×C113—22no—
14#546×C113—22no—
15D42×C113—21no—
16D42×C113C2212yes—
17#537×C113—21no—
18#534×C113—22no—
19#532×C113C2211yescharacteristic
20#532×C113C2211yescharacteristic
21C2×C4⋊Q8×C113C2211yescharacteristic, complemented
22C2×#121×C113—22no—
23C2×C4×D4×C113C2211yescharacteristic
24#498×C113C2212yescomplemented
25#492×C113—21no—
26#487×C113—21no—
27#486×C113C2212yescomplemented
28#481×C113—22no—
29#476×C113—22no—
30#474×C113—22no—
31#474×C113C2214yescomplemented
32#461×C113C2214yescomplemented
33#448×C113—22no—
34#431×C113C2211yescharacteristic, complemented
35#431×C113C2211yescharacteristic, complemented
36C2×#107×C113—21no—
37C2×C4⋊C8×C113C2211yescharacteristic, complemented
38C2×#102×C113—21no—
39#332×C113C2212yescomplemented
40#331×C113C2212yescomplemented
41D4⋊C8×C113C2214yescomplemented
42D4⋊C8×C113C2214yescomplemented
43H(5,𝔽2)×C113—44no—
44H(5,𝔽2)×C113—44no—
45C2×#41×C113—22no—
46C2×#41×C113—22no—
47C2×#41×C113—21no—
48C2×#41×C113—21no—
49C22×Q8×C113—21no—
50C22×D4×C113—24no—
51C22×D4×C113—22no—
52C22×D4×C113—22no—
53C22×D4×C113—22no—
54C22×D4×C113D411yescharacteristic
55C23×C4×C113—21no—
56C2×SD16×C113—24no—
57C22×C8×C113—21no—
58C4⋊Q8×C113—21no—
59C4⋊Q8×C113—21no—
60C4⋊Q8×C113—21no—
61C4⋊Q8×C113D411yescharacteristic
62C4⋊Q8×C113C2312yes—
63C4⋊Q8×C113C2311yescharacteristic
64#127×C113D411yescharacteristic
65#127×C113C2311yescharacteristic
66#124×C113—21no—
67#124×C113—21no—
68#123×C113—24no—
69#123×C113—24no—
70C22⋊Q8×C113—22no—
71C22⋊Q8×C113—22no—
72#121×C113—24no—
73#121×C113—24no—
74#121×C113—22no—
75#121×C113—22no—
76#121×C113—21no—
77#121×C113—21no—
78#121×C113—22no—
79#121×C113—22no—
80#121×C113D412yes—
81#121×C113D412yes—
82#120×C113—24no—
83#120×C113—24no—
84C4×D4×C113—21no—
85C4×D4×C113—21no—
86C4×D4×C113—21no—
87C4×D4×C113—21no—
88C4×D4×C113D412yes—
89C4×D4×C113D412yes—
90C4×D4×C113C2312yes—
91C4×D4×C113C2312yes—
92C2×C4⋊C4×C113—22no—
93C2×C4⋊C4×C113—21no—
94C2×C4⋊C4×C113—21no—
95C2×C4⋊C4×C113D411yescharacteristic
96C2×C22⋊C4×C113—24no—
97C2×C22⋊C4×C113—21no—
98C2×C42×C113C2311yescharacteristic
99#107×C113—24no—
100#106×C113—24no—
101C4⋊C8×C113—21no—
102C4⋊C8×C113—21no—
103C4⋊C8×C113C2312yes—
104C4⋊C8×C113C2312yes—
105#103×C113—24no—
106#102×C113—24no—
107#102×C113—24no—
108C22⋊C8×C113—21no—
109C22⋊C8×C113—21no—
110C4×C8×C113—21no—
111C4×C8×C113C2312yes—
112C24×C113—21no—
113C24×C113—24no—
114#41×C113—44no—
115#41×C113—48no—
116#41×C113—44no—
117#41×C113—42no—
118#41×C113—42no—
119#41×C113—42no—
120#41×C113—42no—
121C2×Q8×C113—21no—
122C2×Q8×C113—21no—
123C2×Q8×C113—22no—
124C2×Q8×C113—41no—
125C2×Q8×C113—82no—
126C2×D4×C113—24no—
127C2×D4×C113—24no—
128C2×D4×C113—22no—
129C2×D4×C113—22no—
130C2×D4×C113—24no—
131C2×D4×C113—21no—
132C2×D4×C113—21no—
133C2×D4×C113—21no—
134C2×D4×C113—22no—
135C2×D4×C113—21no—
136C2×D4×C113—21no—
137C2×D4×C113—44no—
138C2×D4×C113—48no—
139C2×D4×C113—416no—
140C2×D4×C113—44no—
141C2×D4×C113—84no—
142C2×D4×C113SD1614yescomplemented
143C2×D4×C113C2×D412yes—
144C2×D4×C113C2×D412yes—
145C2×D4×C113C2×D412yes—
146C22×C4×C113—24no—
147C22×C4×C113—21no—
148C22×C4×C113—22no—
149C22×C4×C113—22no—
150C22×C4×C113—22no—
151C22×C4×C113—22no—
152C22×C4×C113—41no—
153C22×C4×C113—82no—
154C22×C4×C113C2×D411yescharacteristic
155C22×C4×C113C2×D411yescharacteristic
156C22×C4×C113C2×D411yescharacteristic
157SD16×C113—84no—
158C2×C8×C113—22no—
159C2×C8×C113—22no—
160C2×C8×C113—22no—
161C2×C8×C113—42no—
162C4⋊C4×C113—24no—
163C4⋊C4×C113—21no—
164C4⋊C4×C113—21no—
165C4⋊C4×C113—21no—
166C4⋊C4×C113—22no—
167C4⋊C4×C113—22no—
168C4⋊C4×C113—41no—
169C4⋊C4×C113—41no—
170C4⋊C4×C113C2×D412yes—
171C4⋊C4×C113C2×D412yes—
172C4⋊C4×C113C2×D412yes—
173C22⋊C4×C113—24no—
174C22⋊C4×C113—24no—
175C22⋊C4×C113—22no—
176C22⋊C4×C113—22no—
177C22⋊C4×C113—22no—
178C22⋊C4×C113—22no—
179C22⋊C4×C113—22no—
180C22⋊C4×C113—22no—
181C42×C113C2×D411yescharacteristic
182C42×C113C2×D411yescharacteristic
183C42×C113C2×D411yescharacteristic
184C42×C113C2411yescharacteristic
185C23×C113—22no—
186C23×C113—24no—
187C23×C113—22no—
188C23×C113—22no—
189C23×C113—48no—
190C23×C113—81no—
191C23×C113—81no—
192C23×C113—84no—
193C23×C113—84no—
194C23×C113#12011yescharacteristic
195Q8×C113—41no—
196Q8×C113—41no—
197Q8×C113—42no—
198Q8×C113—44no—
199Q8×C113—82no—
200D4×C113—22no—
201D4×C113—24no—
202D4×C113—24no—
203D4×C113—42no—
204D4×C113—48no—
205D4×C113—48no—
206D4×C113—44no—
207D4×C113—44no—
208D4×C113—41no—
209D4×C113—41no—
210D4×C113—42no—
211D4×C113—42no—
212D4×C113—81no—
213D4×C113—84no—
214D4×C113C2×SD1614yes—
215C2×C4×C113—22no—
216C2×C4×C113—22no—
217C2×C4×C113—22no—
218C2×C4×C113—22no—
219C2×C4×C113—41no—
220C2×C4×C113—48no—
221C2×C4×C113—42no—
222C2×C4×C113—42no—
223C2×C4×C113—44no—
224C2×C4×C113—44no—
225C2×C4×C113—42no—
226C2×C4×C113—82no—
227C2×C4×C113—81no—
228C2×C4×C113—82no—
229C2×C4×C113#12011yescharacteristic
230C2×C4×C113#12011yescharacteristic
231C2×C4×C113#12011yescharacteristic
232C2×C4×C113C2×SD1612yes—
233C2×C4×C113AGL(1,ℤ/8)12yes—
234C2×C4×C113C22×D411yescharacteristic
235C2×C4×C113C22×D411yescharacteristic
236C2×C4×C113C22×D411yescharacteristic
237C8×C113—42no—
238C8×C113—42no—
239C8×C113—42no—
240C22×C113—21no—
241C22×C113—21no—
242C22×C113—24no—
243C22×C113—42no—
244C22×C113—42no—
245C22×C113—42no—
246C22×C113—42no—
247C22×C113—42no—
248C22×C113—42no—
249C22×C113—42no—
250C22×C113—42no—
251C22×C113—84no—
252C22×C113—168no—
253C22×C113#45012yes—
254C22×C113C2×#12011yescharacteristic
255C4×C113—21no—
256C4×C113—21no—
257C4×C113—21no—
258C4×C113—42no—
259C4×C113—42no—
260C4×C113—42no—
261C4×C113—82no—
262C4×C113#45012yes—
263C4×C113C22×SD1611yescharacteristic
264C4×C113C2×AGL(1,ℤ/8)11yescharacteristic
265C4×C113#57612yes—
266#18903C11311yesmaximal, characteristic, direct product factor, Sylow
267C2×C113—22no—
268C2×C113—44no—
269C2×C113—82no—
270C2×C113—82no—
271C2×C113C2×#45011yescharacteristic
272C2×C113#300811yescharacteristic
273C2×C113#302211yescharacteristic
274#3496C2×C11311yescharacteristic
275#3227C2×C11311yescharacteristic, complemented
276#3206C2×C11311yescharacteristic, complemented
277C2×#474C2×C11311yescharacteristic, complemented
278#1654C2×C11314yescomplemented
279#1639C2×C11314yescomplemented
280#1540C2×C11311yescharacteristic, complemented
281#1480C2×C11311yescharacteristic, complemented
282#1478C2×C11311yescharacteristic, complemented
283C113#1890311yescharacteristic, direct product factor, Sylow
284C2×H(5,𝔽2)—21no—
285#547—21no—
286#547C22×C11312yes—
287#546—22no—
288#546—22no—
289D42—21no—
290D42C22×C11312yes—
291#537—21no—
292#534—22no—
293#532C22×C11311yescharacteristic
294#532C22×C11311yescharacteristic
295C2×C4⋊Q8C22×C11311yescharacteristic, complemented
296C2×#121—22no—
297C2×C4×D4C22×C11311yescharacteristic
298#498C22×C11312yescomplemented
299#492—21no—
300#487—21no—
301#486C22×C11312yescomplemented
302#481—22no—
303#476—22no—
304#474—22no—
305#474C22×C11314yescomplemented
306#461C22×C11314yescomplemented
307#448—22no—
308#431C22×C11311yescharacteristic, complemented
309#431C22×C11311yescharacteristic, complemented
310C2×#107—21no—
311C2×C4⋊C8C22×C11311yescharacteristic, complemented
312C2×#102—21no—
313#332C22×C11312yescomplemented
314#331C22×C11312yescomplemented
315D4⋊C8C22×C11314yescomplemented
316D4⋊C8C22×C11314yescomplemented
317H(5,𝔽2)—44no—
318H(5,𝔽2)—44no—
319C2×#41—22no—
320C2×#41—22no—
321C2×#41—21no—
322C2×#41—21no—
323C22×Q8—21no—
324C22×D4—24no—
325C22×D4—22no—
326C22×D4—22no—
327C22×D4—22no—
328C22×D4D4×C11311yescharacteristic
329C23×C4—21no—
330C2×SD16—24no—
331C22×C8—21no—
332C4⋊Q8—21no—
333C4⋊Q8—21no—
334C4⋊Q8—21no—
335C4⋊Q8D4×C11311yescharacteristic
336C4⋊Q8C23×C11312yes—
337C4⋊Q8C23×C11311yescharacteristic
338#127D4×C11311yescharacteristic
339#127C23×C11311yescharacteristic
340#124—21no—
341#124—21no—
342#123—24no—
343#123—24no—
344C22⋊Q8—22no—
345C22⋊Q8—22no—
346#121—24no—
347#121—24no—
348#121—22no—
349#121—22no—
350#121—21no—
351#121—21no—
352#121—22no—
353#121—22no—
354#121D4×C11312yes—
355#121D4×C11312yes—
356#120—24no—
357#120—24no—
358C4×D4—21no—
359C4×D4—21no—
360C4×D4—21no—
361C4×D4—21no—
362C4×D4D4×C11312yes—
363C4×D4D4×C11312yes—
364C4×D4C23×C11312yes—
365C4×D4C23×C11312yes—
366C2×C4⋊C4—22no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4D4×C11311yescharacteristic
370C2×C22⋊C4—24no—
371C2×C22⋊C4—21no—
372C2×C42C23×C11311yescharacteristic
373#107—24no—
374#106—24no—
375C4⋊C8—21no—
376C4⋊C8—21no—
377C4⋊C8C23×C11312yes—
378C4⋊C8C23×C11312yes—
379#103—24no—
380#102—24no—
381#102—24no—
382C22⋊C8—21no—
383C22⋊C8—21no—
384C4×C8—21no—
385C4×C8C23×C11312yes—
386C24—21no—
387C24—24no—
388#41—44no—
389#41—48no—
390#41—44no—
391#41—42no—
392#41—42no—
393#41—42no—
394#41—42no—
395C2×Q8—21no—
396C2×Q8—21no—
397C2×Q8—22no—
398C2×Q8—41no—
399C2×Q8—82no—
400C2×D4—24no—
401C2×D4—24no—
402C2×D4—22no—
403C2×D4—22no—
404C2×D4—24no—
405C2×D4—21no—
406C2×D4—21no—
407C2×D4—21no—
408C2×D4—22no—
409C2×D4—21no—
410C2×D4—21no—
411C2×D4—44no—
412C2×D4—48no—
413C2×D4—416no—
414C2×D4—44no—
415C2×D4—84no—
416C2×D4SD16×C11314yescomplemented
417C2×D4C2×D4×C11312yes—
418C2×D4C2×D4×C11312yes—
419C2×D4C2×D4×C11312yes—
420C22×C4—24no—
421C22×C4—21no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—41no—
427C22×C4—82no—
428C22×C4C2×D4×C11311yescharacteristic
429C22×C4C2×D4×C11311yescharacteristic
430C22×C4C2×D4×C11311yescharacteristic
431SD16—84no—
432C2×C8—22no—
433C2×C8—22no—
434C2×C8—22no—
435C2×C8—42no—
436C4⋊C4—24no—
437C4⋊C4—21no—
438C4⋊C4—21no—
439C4⋊C4—21no—
440C4⋊C4—22no—
441C4⋊C4—22no—
442C4⋊C4—41no—
443C4⋊C4—41no—
444C4⋊C4C2×D4×C11312yes—
445C4⋊C4C2×D4×C11312yes—
446C4⋊C4C2×D4×C11312yes—
447C22⋊C4—24no—
448C22⋊C4—24no—
449C22⋊C4—22no—
450C22⋊C4—22no—
451C22⋊C4—22no—
452C22⋊C4—22no—
453C22⋊C4—22no—
454C22⋊C4—22no—
455C42C2×D4×C11311yescharacteristic
456C42C2×D4×C11311yescharacteristic
457C42C2×D4×C11311yescharacteristic
458C42C24×C11311yescharacteristic
459C23—22no—
460C23—24no—
461C23—22no—
462C23—22no—
463C23—48no—
464C23—81no—
465C23—81no—
466C23—84no—
467C23—84no—
468C23#120×C11311yescharacteristic
469Q8—41no—
470Q8—41no—
471Q8—42no—
472Q8—44no—
473Q8—82no—
474D4—22no—
475D4—24no—
476D4—24no—
477D4—42no—
478D4—48no—
479D4—48no—
480D4—44no—
481D4—44no—
482D4—41no—
483D4—41no—
484D4—42no—
485D4—42no—
486D4—81no—
487D4—84no—
488D4C2×SD16×C11314yes—
489C2×C4—22no—
490C2×C4—22no—
491C2×C4—22no—
492C2×C4—22no—
493C2×C4—41no—
494C2×C4—48no—
495C2×C4—42no—
496C2×C4—42no—
497C2×C4—44no—
498C2×C4—44no—
499C2×C4—42no—
500C2×C4—82no—
501C2×C4—81no—
502C2×C4—82no—
503C2×C4#120×C11311yescharacteristic
504C2×C4#120×C11311yescharacteristic
505C2×C4#120×C11311yescharacteristic
506C2×C4C2×SD16×C11312yes—
507C2×C4AGL(1,ℤ/8)×C11312yes—
508C2×C4C22×D4×C11311yescharacteristic
509C2×C4C22×D4×C11311yescharacteristic
510C2×C4C22×D4×C11311yescharacteristic
511C8—42no—
512C8—42no—
513C8—42no—
514C22—21no—
515C22—21no—
516C22—24no—
517C22—42no—
518C22—42no—
519C22—42no—
520C22—42no—
521C22—42no—
522C22—42no—
523C22—42no—
524C22—42no—
525C22—84no—
526C22—168no—
527C22#450×C11312yes—
528C22C2×#120×C11311yescharacteristic
529C4—21no—
530C4—21no—
531C4—21no—
532C4—42no—
533C4—42no—
534C4—42no—
535C4—82no—
536C4#450×C11312yes—
537C4C22×SD16×C11311yescharacteristic
538C4C2×AGL(1,ℤ/8)×C11311yescharacteristic
539C4#576×C11312yes—
540C2—22no—
541C2—44no—
542C2—82no—
543C2—82no—
544C2C2×#450×C11311yescharacteristic
545C2C113×#300811yescharacteristic
546C2C113×#302211yescharacteristic
subgroupG/H
center, socleC22×C113C2×#120
commutator, Frattini, cosocleC42C24×C113
prime radicalC113×#3496C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C113 ◁ C2×C42×C113 ◁ G

Complements

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

NH ≅ G/Ntype
2. C113×#3227C2semidirect
3. C113×#3206C2semidirect
4. C2×#474×C113C2semidirect
5. C113×#1654C2semidirect
6. C113×#1639C2semidirect
7. C113×#1540C2semidirect
8. C113×#1480C2semidirect
9. C113×#1478C2semidirect
21. C2×C4⋊Q8×C113C22semidirect
24. #498×C113C22semidirect
27. #486×C113C22semidirect
31. #474×C113C22semidirect
32. #461×C113C22semidirect
34. #431×C113C22semidirect
35. #431×C113C22semidirect
37. C2×C4⋊C8×C113C22semidirect
39. #332×C113C22semidirect
40. #331×C113C22semidirect
41. D4⋊C8×C113C22semidirect
42. D4⋊C8×C113C22semidirect
142. C2×D4×C113SD16semidirect
266. #18903C113direct (N × H)
275. #3227C2×C113semidirect
276. #3206C2×C113semidirect
277. C2×#474C2×C113semidirect
278. #1654C2×C113semidirect
279. #1639C2×C113semidirect
280. #1540C2×C113semidirect
281. #1480C2×C113semidirect
282. #1478C2×C113semidirect
283. C113#18903direct (N × H)
295. C2×C4⋊Q8C22×C113semidirect
298. #498C22×C113semidirect
301. #486C22×C113semidirect
305. #474C22×C113semidirect
306. #461C22×C113semidirect
308. #431C22×C113semidirect
309. #431C22×C113semidirect
311. C2×C4⋊C8C22×C113semidirect
313. #332C22×C113semidirect
314. #331C22×C113semidirect
315. D4⋊C8C22×C113semidirect
316. D4⋊C8C22×C113semidirect
416. C2×D4SD16×C113semidirect

Maximal subgroups

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

subgroupindex
C113×#34962
C113×#32272
C113×#32062
C2×#474×C1132
C113×#16542
C113×#16392
C113×#15402
C113×#14802
C113×#14782
#18903113