Finite Group Databasebeta

← C113×#23043 #43291063

Subgroups — C113×#23043 #43291063

Order 28928.

820 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C113×#3067C211yesmaximal, characteristic
2C113×#2957C211yesmaximal, characteristic, complemented
3C113×#2956C212yesmaximal, complemented
4C113×#2916C211yesmaximal, characteristic, complemented
5C113×#1975C211yesmaximal, characteristic, complemented
6C113×#1953C211yesmaximal, characteristic, complemented
7C113×#1932C212yesmaximal, complemented
8C113×#1881C212yesmaximal, complemented
9C113×#1858C212yesmaximal, complemented
10C113×#1778C211yesmaximal, characteristic, complemented
11C113×#1765C211yesmaximal, characteristic, complemented
12#575×C113C2212yes—
13C2×#135×C113C2211yescharacteristic
14#568×C113C2212yes—
15#568×C113C2212yes—
16C2×#131×C113C2211yescharacteristic
17#473×C113C412yescomplemented
18#472×C113C412yescomplemented
19#471×C113C414yescomplemented
20#444×C113—22no—
21#444×C113—24no—
22#443×C113—22no—
23#443×C113—24no—
24#430×C113—22no—
25#430×C113C2212yes—
26#430×C113C2212yes—
27C2×#108×C113—22no—
28C2×#108×C113C2211yescharacteristic
29C2×#108×C113C2211yescharacteristic
30C2×#108×C113C2211yescharacteristic
31#421×C113C2212yes—
32C2×#104×C113C2212yes—
33C2×#104×C113C2211yescharacteristic
34#416×C113C2211yescharacteristic
35#413×C113C2212yes—
36#408×C113C2212yes—
37#405×C113C2211yescharacteristic
38C4×M16×C113C2212yes—
39C2×#97×C113C2211yescharacteristic
40#344×C113C2212yes—
41#341×C113C2211yescharacteristic
42#341×C113C2212yes—
43#339×C113C2211yescharacteristic
44C2×#41×C113C2312yes—
45C2×#41×C113C2311yescharacteristic
46#137×C113—22no—
47#137×C113C2×C414yes—
48AGL(1,ℤ/8)×C113—22no—
49AGL(1,ℤ/8)×C113C2×C414yes—
50#135×C113—24no—
51#135×C113—21no—
52#135×C113—21no—
53#135×C113—21no—
54#135×C113—21no—
55C2×Q16×C113C2×C411yescharacteristic
56C2×SD16×C113C2×C412yes—
57C2×D8×C113C2×C411yescharacteristic
58#131×C113—21no—
59#131×C113—21no—
60#131×C113—24no—
61#131×C113—24no—
62#131×C113—24no—
63#131×C113—42no—
64#131×C113C2×C412yes—
65#131×C113C2×C412yes—
66C2×M16×C113—21no—
67C2×M16×C113—24no—
68C2×M16×C113—42no—
69C2×M16×C113C2312yes—
70C2×M16×C113C2311yescharacteristic
71C2×M16×C113C2312yes—
72C2×M16×C113C2312yes—
73C2×M16×C113C2311yescharacteristic
74C22×C8×C113—21no—
75C22×C8×C113C2311yescharacteristic
76C22×C8×C113C2311yescharacteristic
77#117×C113C2311yescharacteristic
78C2×C42×C113C2311yescharacteristic
79#108×C113—24no—
80#108×C113—24no—
81#108×C113—21no—
82#108×C113—21no—
83#108×C113C2×C412yes—
84#108×C113C2×C412yes—
85#108×C113D412yes—
86#108×C113D412yes—
87#104×C113—24no—
88#104×C113—22no—
89#104×C113—22no—
90#104×C113D414yes—
91#103×C113—21no—
92#102×C113—21no—
93#101×C113C2×C414yes—
94#100×C113C2×C414yes—
95C22⋊C8×C113—42no—
96#97×C113—21no—
97#97×C113—21no—
98#97×C113—21no—
99#97×C113—22no—
100C4×C8×C113—21no—
101C4×C8×C113—22no—
102#41×C113—21no—
103#41×C113—21no—
104#41×C113—22no—
105#41×C113—22no—
106#41×C113—22no—
107#41×C113—22no—
108#41×C113C22×C412yes—
109#41×C113C2×D412yes—
110C2×Q8×C113C22×C412yes—
111C2×Q8×C113#4111yescharacteristic
112C2×D4×C113—21no—
113C2×D4×C113—22no—
114C2×D4×C113C22×C412yes—
115C2×D4×C113#4111yescharacteristic
116C22×C4×C113—21no—
117C22×C4×C113—21no—
118C22×C4×C113—22no—
119C22×C4×C113C2411yescharacteristic
120Q16×C113—24no—
121Q16×C113—21no—
122Q16×C113—21no—
123SD16×C113—24no—
124SD16×C113—24no—
125SD16×C113—22no—
126SD16×C113—22no—
127D8×C113—24no—
128D8×C113—21no—
129D8×C113—21no—
130M16×C113—21no—
131M16×C113—22no—
132M16×C113—21no—
133M16×C113—22no—
134M16×C113—22no—
135M16×C113—22no—
136M16×C113—22no—
137M16×C113—22no—
138M16×C113—44no—
139M16×C113—44no—
140M16×C113C22×C412yes—
141M16×C113C22×C414yes—
142M16×C113C2×D414yes—
143M16×C113C2×D412yes—
144C2×C8×C113—22no—
145C2×C8×C113—22no—
146C2×C8×C113—21no—
147C2×C8×C113—21no—
148C2×C8×C113—22no—
149C2×C8×C113—22no—
150C2×C8×C113—21no—
151C2×C8×C113—21no—
152C2×C8×C113—21no—
153C2×C8×C113—22no—
154C2×C8×C113—44no—
155C2×C8×C113—44no—
156C2×C8×C113C22×C411yescharacteristic
157C2×C8×C113C22×C411yescharacteristic
158C2×C8×C113C2×D411yescharacteristic
159C2×C8×C113C2×D411yescharacteristic
160C2×C8×C113#4111yescharacteristic
161C2×C8×C113#4111yescharacteristic
162C4⋊C4×C113—21no—
163C22⋊C4×C113—21no—
164C42×C113—21no—
165C42×C113—21no—
166C42×C113C2×D412yes—
167C23×C113—21no—
168C23×C113—22no—
169C23×C1132−1+411yescharacteristic
170Q8×C113—21no—
171Q8×C113—22no—
172Q8×C113—22no—
173Q8×C113C4×D412yes—
174D4×C113—22no—
175D4×C113—22no—
176D4×C113—22no—
177D4×C113—22no—
178D4×C113—21no—
179D4×C113—42no—
180D4×C113—42no—
181D4×C113C4×D412yes—
182C2×C4×C113—21no—
183C2×C4×C113—22no—
184C2×C4×C113—22no—
185C2×C4×C113—22no—
186C2×C4×C113—22no—
187C2×C4×C113—42no—
188C2×C4×C113—42no—
189C2×C4×C113—41no—
190C2×C4×C113—81no—
191C2×C4×C113C23×C411yescharacteristic
192C2×C4×C113C22×D411yescharacteristic
193C2×C4×C113C22×D411yescharacteristic
194C2×C4×C113C2×#4111yescharacteristic
195C2×C4×C113C2×#4111yescharacteristic
196C2×C4×C113H(5,𝔽2)11yescharacteristic
197C8×C113—22no—
198C8×C113—24no—
199C8×C113—22no—
200C8×C113—24no—
201C8×C113—42no—
202C8×C113—41no—
203C8×C113C4×D411yescharacteristic
204C8×C113C4×D411yescharacteristic
205C8×C113C4×D411yescharacteristic
206C8×C113C4×D411yescharacteristic
207C22×C113—22no—
208C22×C113—41no—
209C22×C113—42no—
210C22×C113—81no—
211C22×C113—82no—
212C22×C113#52011yescharacteristic
213C22×C113#54711yescharacteristic
214C22×C113#54811yescharacteristic
215C4×C113—22no—
216C4×C113—42no—
217C4×C113—42no—
218C4×C113—81no—
219C4×C113C2×C4×D411yescharacteristic
220C4×C113C2×C4×D411yescharacteristic
221C4×C113D4211yescharacteristic
222C4×C113#55311yescharacteristic
223#23043C11311yesmaximal, characteristic, direct product factor, Sylow
224C2×C113—21no—
225C2×C113—21no—
226C2×C113—21no—
227C2×C113—42no—
228C2×C113—82no—
229C2×C113#236111yescharacteristic
230#3067C2×C11311yescharacteristic
231#2957C2×C11311yescharacteristic, complemented
232#2956C2×C11312yescomplemented
233#2916C2×C11311yescharacteristic, complemented
234#1975C2×C11311yescharacteristic, complemented
235#1953C2×C11311yescharacteristic, complemented
236#1932C2×C11312yescomplemented
237#1881C2×C11312yescomplemented
238#1858C2×C11312yescomplemented
239#1778C2×C11311yescharacteristic, complemented
240#1765C2×C11311yescharacteristic, complemented
241C113#2304311yescharacteristic, direct product factor, Sylow
242#575C22×C11312yes—
243C2×#135C22×C11311yescharacteristic
244#568C22×C11312yes—
245#568C22×C11312yes—
246C2×#131C22×C11311yescharacteristic
247#473C4×C11312yescomplemented
248#472C4×C11312yescomplemented
249#471C4×C11314yescomplemented
250#444—22no—
251#444—24no—
252#443—22no—
253#443—24no—
254#430—22no—
255#430C22×C11312yes—
256#430C22×C11312yes—
257C2×#108—22no—
258C2×#108C22×C11311yescharacteristic
259C2×#108C22×C11311yescharacteristic
260C2×#108C22×C11311yescharacteristic
261#421C22×C11312yes—
262C2×#104C22×C11312yes—
263C2×#104C22×C11311yescharacteristic
264#416C22×C11311yescharacteristic
265#413C22×C11312yes—
266#408C22×C11312yes—
267#405C22×C11311yescharacteristic
268C4×M16C22×C11312yes—
269C2×#97C22×C11311yescharacteristic
270#344C22×C11312yes—
271#341C22×C11311yescharacteristic
272#341C22×C11312yes—
273#339C22×C11311yescharacteristic
274C2×#41C23×C11312yes—
275C2×#41C23×C11311yescharacteristic
276#137—22no—
277#137C2×C4×C11314yes—
278AGL(1,ℤ/8)—22no—
279AGL(1,ℤ/8)C2×C4×C11314yes—
280#135—24no—
281#135—21no—
282#135—21no—
283#135—21no—
284#135—21no—
285C2×Q16C2×C4×C11311yescharacteristic
286C2×SD16C2×C4×C11312yes—
287C2×D8C2×C4×C11311yescharacteristic
288#131—21no—
289#131—21no—
290#131—24no—
291#131—24no—
292#131—24no—
293#131—42no—
294#131C2×C4×C11312yes—
295#131C2×C4×C11312yes—
296C2×M16—21no—
297C2×M16—24no—
298C2×M16—42no—
299C2×M16C23×C11312yes—
300C2×M16C23×C11311yescharacteristic
301C2×M16C23×C11312yes—
302C2×M16C23×C11312yes—
303C2×M16C23×C11311yescharacteristic
304C22×C8—21no—
305C22×C8C23×C11311yescharacteristic
306C22×C8C23×C11311yescharacteristic
307#117C23×C11311yescharacteristic
308C2×C42C23×C11311yescharacteristic
309#108—24no—
310#108—24no—
311#108—21no—
312#108—21no—
313#108C2×C4×C11312yes—
314#108C2×C4×C11312yes—
315#108D4×C11312yes—
316#108D4×C11312yes—
317#104—24no—
318#104—22no—
319#104—22no—
320#104D4×C11314yes—
321#103—21no—
322#102—21no—
323#101C2×C4×C11314yes—
324#100C2×C4×C11314yes—
325C22⋊C8—42no—
326#97—21no—
327#97—21no—
328#97—21no—
329#97—22no—
330C4×C8—21no—
331C4×C8—22no—
332#41—21no—
333#41—21no—
334#41—22no—
335#41—22no—
336#41—22no—
337#41—22no—
338#41C22×C4×C11312yes—
339#41C2×D4×C11312yes—
340C2×Q8C22×C4×C11312yes—
341C2×Q8#41×C11311yescharacteristic
342C2×D4—21no—
343C2×D4—22no—
344C2×D4C22×C4×C11312yes—
345C2×D4#41×C11311yescharacteristic
346C22×C4—21no—
347C22×C4—21no—
348C22×C4—22no—
349C22×C4C24×C11311yescharacteristic
350Q16—24no—
351Q16—21no—
352Q16—21no—
353SD16—24no—
354SD16—24no—
355SD16—22no—
356SD16—22no—
357D8—24no—
358D8—21no—
359D8—21no—
360M16—21no—
361M16—22no—
362M16—21no—
363M16—22no—
364M16—22no—
365M16—22no—
366M16—22no—
367M16—22no—
368M16—44no—
369M16—44no—
370M16C22×C4×C11312yes—
371M16C22×C4×C11314yes—
372M16C2×D4×C11314yes—
373M16C2×D4×C11312yes—
374C2×C8—22no—
375C2×C8—22no—
376C2×C8—21no—
377C2×C8—21no—
378C2×C8—22no—
379C2×C8—22no—
380C2×C8—21no—
381C2×C8—21no—
382C2×C8—21no—
383C2×C8—22no—
384C2×C8—44no—
385C2×C8—44no—
386C2×C8C22×C4×C11311yescharacteristic
387C2×C8C22×C4×C11311yescharacteristic
388C2×C8C2×D4×C11311yescharacteristic
389C2×C8C2×D4×C11311yescharacteristic
390C2×C8#41×C11311yescharacteristic
391C2×C8#41×C11311yescharacteristic
392C4⋊C4—21no—
393C22⋊C4—21no—
394C42—21no—
395C42—21no—
396C42C2×D4×C11312yes—
397C23—21no—
398C23—22no—
399C232−1+4×C11311yescharacteristic
400Q8—21no—
401Q8—22no—
402Q8—22no—
403Q8C4×D4×C11312yes—
404D4—22no—
405D4—22no—
406D4—22no—
407D4—22no—
408D4—21no—
409D4—42no—
410D4—42no—
411D4C4×D4×C11312yes—
412C2×C4—21no—
413C2×C4—22no—
414C2×C4—22no—
415C2×C4—22no—
416C2×C4—22no—
417C2×C4—42no—
418C2×C4—42no—
419C2×C4—41no—
420C2×C4—81no—
421C2×C4C23×C4×C11311yescharacteristic
422C2×C4C22×D4×C11311yescharacteristic
423C2×C4C22×D4×C11311yescharacteristic
424C2×C4C2×#41×C11311yescharacteristic
425C2×C4C2×#41×C11311yescharacteristic
426C2×C4H(5,𝔽2)×C11311yescharacteristic
427C8—22no—
428C8—24no—
429C8—22no—
430C8—24no—
431C8—42no—
432C8—41no—
433C8C4×D4×C11311yescharacteristic
434C8C4×D4×C11311yescharacteristic
435C8C4×D4×C11311yescharacteristic
436C8C4×D4×C11311yescharacteristic
437C22—22no—
438C22—41no—
439C22—42no—
440C22—81no—
441C22—82no—
442C22#520×C11311yescharacteristic
443C22#547×C11311yescharacteristic
444C22#548×C11311yescharacteristic
445C4—22no—
446C4—42no—
447C4—42no—
448C4—81no—
449C4C2×C4×D4×C11311yescharacteristic
450C4C2×C4×D4×C11311yescharacteristic
451C4D42×C11311yescharacteristic
452C4#553×C11311yescharacteristic
453C2—21no—
454C2—21no—
455C2—21no—
456C2—42no—
457C2—82no—
458C2C113×#236111yescharacteristic
subgroupG/H
centerC4×C113D42
commutatorC2×C4C23×C4×C113
Frattini, cosocleC22×C4C24×C113
socleC2×C113#2361
prime radicalC113×#3067C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C4×C113 ◁ C22×C4×C113 ◁ G

Complements

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

NH ≅ G/Ntype
2. C113×#2957C2semidirect
3. C113×#2956C2semidirect
4. C113×#2916C2semidirect
5. C113×#1975C2semidirect
6. C113×#1953C2semidirect
7. C113×#1932C2semidirect
8. C113×#1881C2semidirect
9. C113×#1858C2semidirect
10. C113×#1778C2semidirect
11. C113×#1765C2semidirect
17. #473×C113C4semidirect
18. #472×C113C4semidirect
19. #471×C113C4semidirect
223. #23043C113direct (N × H)
231. #2957C2×C113semidirect
232. #2956C2×C113semidirect
233. #2916C2×C113semidirect
234. #1975C2×C113semidirect
235. #1953C2×C113semidirect
236. #1932C2×C113semidirect
237. #1881C2×C113semidirect
238. #1858C2×C113semidirect
239. #1778C2×C113semidirect
240. #1765C2×C113semidirect
241. C113#23043direct (N × H)
247. #473C4×C113semidirect
248. #472C4×C113semidirect
249. #471C4×C113semidirect

Maximal subgroups

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

subgroupindex
C113×#30672
C113×#29572
C113×#29562
C113×#29162
C113×#19752
C113×#19532
C113×#19322
C113×#18812
C113×#18582
C113×#17782
C113×#17652
#23043113