Finite Group Databasebeta

← C113×#21072 #43289092

Subgroups — C113×#21072 #43289092

Order 28928.

1018 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#108×C113C211yesmaximal, characteristic, complemented
2C2×#421×C113C211yesmaximal, characteristic
3C2×#416×C113C211yesmaximal, characteristic
4C113×#2879C211yesmaximal, characteristic
5C113×#2873C211yesmaximal, characteristic, complemented
6C113×#1929C218yesmaximal, complemented
7C113×#1733C211yesmaximal, characteristic, complemented
8C113×#1729C211yesmaximal, characteristic, complemented
9C22×#41×C113C2211yescharacteristic
10C22×M16×C113C2211yescharacteristic
11C22×M16×C113C2211yescharacteristic
12C22×M16×C113C2211yescharacteristic
13C23×C8×C113C2211yescharacteristic
14C2×#117×C113C2211yescharacteristic
15C2×#117×C113C2211yescharacteristic
16C2×#108×C113—24no—
17C2×#108×C113C2214yescomplemented
18#421×C113—24no—
19C2×#104×C113C2214yes—
20#416×C113C414yescomplemented
21#416×C113C2214yes—
22C2×#103×C113C412yescomplemented
23C2×#102×C113C412yescomplemented
24#408×C113—22no—
25#408×C113C2214yes—
26#407×C113—22no—
27#405×C113—22no—
28#405×C113C2214yescomplemented
29C4×M16×C113—22no—
30#339×C113C2214yescomplemented
31#336×C113C2214yescomplemented
32C2×#41×C113—21no—
33C2×#41×C113—21no—
34C2×#41×C113—22no—
35C2×#41×C113—22no—
36C2×#41×C113—22no—
37C2×#41×C113—22no—
38C2×#41×C113C2×C412yes—
39C2×#41×C113C2312yes—
40C22×Q8×C113C2×C411yescharacteristic
41C22×D4×C113—21no—
42C22×D4×C113C2×C411yescharacteristic
43C23×C4×C113—21no—
44C23×C4×C113C2311yescharacteristic
45C2×M16×C113—21no—
46C2×M16×C113—22no—
47C2×M16×C113—22no—
48C2×M16×C113—22no—
49C2×M16×C113—21no—
50C2×M16×C113—22no—
51C2×M16×C113—22no—
52C2×M16×C113D414yes—
53C2×M16×C113D412yes—
54C2×M16×C113D412yes—
55C2×M16×C113C2312yes—
56C2×M16×C113C2312yes—
57C22×C8×C113—22no—
58C22×C8×C113—21no—
59C22×C8×C113—22no—
60C22×C8×C113—21no—
61C22×C8×C113C2×C412yes—
62C22×C8×C113C2×C412yes—
63C22×C8×C113C2312yes—
64C22×C8×C113C2312yes—
65#117×C113—21no—
66#117×C113—21no—
67#117×C113—22no—
68#117×C113—22no—
69#117×C113C2×C412yes—
70#117×C113C2312yes—
71C2×C4⋊C4×C113—21no—
72C2×C4⋊C4×C113C2×C412yes—
73C2×C22⋊C4×C113—21no—
74C2×C22⋊C4×C113—21no—
75C2×C42×C113—21no—
76C2×C42×C113C2312yes—
77#108×C113—28no—
78#104×C113—28no—
79#103×C113C2×C418yes—
80#102×C113C2×C418yes—
81C22⋊C8×C113—28no—
82#97×C113—24no—
83C4×C8×C113—24no—
84C24×C113—21no—
85C24×C113#4111yescharacteristic
86#41×C113—24no—
87#41×C113—24no—
88#41×C113—22no—
89#41×C113—22no—
90#41×C113—22no—
91#41×C113—22no—
92#41×C113—42no—
93#41×C113—42no—
94#41×C113—42no—
95#41×C113—42no—
96C2×Q8×C113—21no—
97C2×Q8×C113—22no—
98C2×Q8×C113—22no—
99C2×Q8×C113C22×C412yes—
100C2×D4×C113—22no—
101C2×D4×C113—22no—
102C2×D4×C113—22no—
103C2×D4×C113—22no—
104C2×D4×C113—21no—
105C2×D4×C113—42no—
106C2×D4×C113—42no—
107C2×D4×C113C22×C412yes—
108C22×C4×C113—21no—
109C22×C4×C113—22no—
110C22×C4×C113—22no—
111C22×C4×C113—22no—
112C22×C4×C113—22no—
113C22×C4×C113—42no—
114C22×C4×C113—42no—
115C22×C4×C113C22×C411yescharacteristic
116C22×C4×C113C22×C411yescharacteristic
117C22×C4×C113C2×D412yes—
118C22×C4×C113C2×D411yescharacteristic
119C22×C4×C113C2×D411yescharacteristic
120C22×C4×C113#4112yes—
121C22×C4×C113#4112yes—
122C22×C4×C113#4112yes—
123C22×C4×C113#4111yescharacteristic
124C22×C4×C113C2411yescharacteristic
125M16×C113—24no—
126M16×C113—24no—
127M16×C113—24no—
128M16×C113—22no—
129M16×C113—22no—
130M16×C113—22no—
131M16×C113—42no—
132M16×C113C2×D414yes—
133C2×C8×C113—24no—
134C2×C8×C113—24no—
135C2×C8×C113—24no—
136C2×C8×C113—22no—
137C2×C8×C113—22no—
138C2×C8×C113—22no—
139C2×C8×C113—22no—
140C2×C8×C113—22no—
141C2×C8×C113—22no—
142C2×C8×C113—42no—
143C2×C8×C113C22×C414yes—
144C2×C8×C113C2×D414yes—
145C4⋊C4×C113—22no—
146C4⋊C4×C113—42no—
147C4⋊C4×C113C22×C414yes—
148C22⋊C4×C113—22no—
149C22⋊C4×C113—22no—
150C22⋊C4×C113—42no—
151C42×C113—22no—
152C42×C113—22no—
153C42×C113—22no—
154C42×C113—22no—
155C23×C113—22no—
156C23×C113—42no—
157C23×C113—42no—
158C23×C113—82no—
159C23×C113C4×D411yescharacteristic
160C23×C113C4×D411yescharacteristic
161C23×C113#12412yes—
162C23×C113#12612yes—
163C23×C113C2×#4111yescharacteristic
164Q8×C113—22no—
165Q8×C113—22no—
166Q8×C113—42no—
167D4×C113—22no—
168D4×C113—22no—
169D4×C113—42no—
170D4×C113—42no—
171D4×C113—44no—
172D4×C113—42no—
173C2×C4×C113—24no—
174C2×C4×C113—22no—
175C2×C4×C113—42no—
176C2×C4×C113—42no—
177C2×C4×C113—42no—
178C2×C4×C113—44no—
179C2×C4×C113—44no—
180C2×C4×C113—42no—
181C2×C4×C113—82no—
182C2×C4×C113#11712yes—
183C2×C4×C113#11712yes—
184C2×C4×C113C4×D412yes—
185C2×C4×C113C4×D412yes—
186C2×C4×C113C4×D411yescharacteristic
187C2×C4×C113C4×D411yescharacteristic
188C2×C4×C113#12112yes—
189C2×C4×C113#12112yes—
190C2×C4×C113#12312yes—
191C2×C4×C113#12312yes—
192C2×C4×C113#12412yes—
193C2×C4×C113#12612yes—
194C2×C4×C113C23×C411yescharacteristic
195C2×C4×C113C22×D411yescharacteristic
196C2×C4×C113C22×D411yescharacteristic
197C2×C4×C113C2×#4111yescharacteristic
198C2×C4×C113C2×#4111yescharacteristic
199C2×C4×C113C2×#4111yescharacteristic
200C8×C113—24no—
201C8×C113—24no—
202C8×C113—24no—
203C8×C113—42no—
204C22×C113—22no—
205C22×C113—22no—
206C22×C113—22no—
207C22×C113—42no—
208C22×C113—42no—
209C22×C113—44no—
210C22×C113—42no—
211C22×C113—84no—
212C22×C113#38812yes—
213C22×C113#38812yes—
214C22×C113C2×C4×D411yescharacteristic
215C22×C113C2×#12411yescharacteristic
216C22×C113C2×#12611yescharacteristic
217C4×C113—44no—
218C4×C113—42no—
219C4×C113—82no—
220C4×C113#38812yes—
221C4×C113#38812yes—
222C4×C113C2×#11711yescharacteristic
223C4×C113C2×C4×D411yescharacteristic
224C4×C113C2×#12111yescharacteristic
225C4×C113C2×#12311yescharacteristic
226#21072C11311yesmaximal, characteristic, direct product factor, Sylow
227C2×C113—21no—
228C2×C113—22no—
229C2×C113—21no—
230C2×C113—22no—
231C2×C113—82no—
232C2×C113C2×#38811yescharacteristic
233C2×C113#295712yes—
234C22×#108C2×C11311yescharacteristic, complemented
235C2×#421C2×C11311yescharacteristic
236C2×#416C2×C11311yescharacteristic
237#2879C2×C11311yescharacteristic
238#2873C2×C11311yescharacteristic, complemented
239#1929C2×C11318yescomplemented
240#1733C2×C11311yescharacteristic, complemented
241#1729C2×C11311yescharacteristic, complemented
242C113#2107211yescharacteristic, direct product factor, Sylow
243C22×#41C22×C11311yescharacteristic
244C22×M16C22×C11311yescharacteristic
245C22×M16C22×C11311yescharacteristic
246C22×M16C22×C11311yescharacteristic
247C23×C8C22×C11311yescharacteristic
248C2×#117C22×C11311yescharacteristic
249C2×#117C22×C11311yescharacteristic
250C2×#108—24no—
251C2×#108C22×C11314yescomplemented
252#421—24no—
253C2×#104C22×C11314yes—
254#416C4×C11314yescomplemented
255#416C22×C11314yes—
256C2×#103C4×C11312yescomplemented
257C2×#102C4×C11312yescomplemented
258#408—22no—
259#408C22×C11314yes—
260#407—22no—
261#405—22no—
262#405C22×C11314yescomplemented
263C4×M16—22no—
264#339C22×C11314yescomplemented
265#336C22×C11314yescomplemented
266C2×#41—21no—
267C2×#41—21no—
268C2×#41—22no—
269C2×#41—22no—
270C2×#41—22no—
271C2×#41—22no—
272C2×#41C2×C4×C11312yes—
273C2×#41C23×C11312yes—
274C22×Q8C2×C4×C11311yescharacteristic
275C22×D4—21no—
276C22×D4C2×C4×C11311yescharacteristic
277C23×C4—21no—
278C23×C4C23×C11311yescharacteristic
279C2×M16—21no—
280C2×M16—22no—
281C2×M16—22no—
282C2×M16—22no—
283C2×M16—21no—
284C2×M16—22no—
285C2×M16—22no—
286C2×M16D4×C11314yes—
287C2×M16D4×C11312yes—
288C2×M16D4×C11312yes—
289C2×M16C23×C11312yes—
290C2×M16C23×C11312yes—
291C22×C8—22no—
292C22×C8—21no—
293C22×C8—22no—
294C22×C8—21no—
295C22×C8C2×C4×C11312yes—
296C22×C8C2×C4×C11312yes—
297C22×C8C23×C11312yes—
298C22×C8C23×C11312yes—
299#117—21no—
300#117—21no—
301#117—22no—
302#117—22no—
303#117C2×C4×C11312yes—
304#117C23×C11312yes—
305C2×C4⋊C4—21no—
306C2×C4⋊C4C2×C4×C11312yes—
307C2×C22⋊C4—21no—
308C2×C22⋊C4—21no—
309C2×C42—21no—
310C2×C42C23×C11312yes—
311#108—28no—
312#104—28no—
313#103C2×C4×C11318yes—
314#102C2×C4×C11318yes—
315C22⋊C8—28no—
316#97—24no—
317C4×C8—24no—
318C24—21no—
319C24#41×C11311yescharacteristic
320#41—24no—
321#41—24no—
322#41—22no—
323#41—22no—
324#41—22no—
325#41—22no—
326#41—42no—
327#41—42no—
328#41—42no—
329#41—42no—
330C2×Q8—21no—
331C2×Q8—22no—
332C2×Q8—22no—
333C2×Q8C22×C4×C11312yes—
334C2×D4—22no—
335C2×D4—22no—
336C2×D4—22no—
337C2×D4—22no—
338C2×D4—21no—
339C2×D4—42no—
340C2×D4—42no—
341C2×D4C22×C4×C11312yes—
342C22×C4—21no—
343C22×C4—22no—
344C22×C4—22no—
345C22×C4—22no—
346C22×C4—22no—
347C22×C4—42no—
348C22×C4—42no—
349C22×C4C22×C4×C11311yescharacteristic
350C22×C4C22×C4×C11311yescharacteristic
351C22×C4C2×D4×C11312yes—
352C22×C4C2×D4×C11311yescharacteristic
353C22×C4C2×D4×C11311yescharacteristic
354C22×C4#41×C11312yes—
355C22×C4#41×C11312yes—
356C22×C4#41×C11312yes—
357C22×C4#41×C11311yescharacteristic
358C22×C4C24×C11311yescharacteristic
359M16—24no—
360M16—24no—
361M16—24no—
362M16—22no—
363M16—22no—
364M16—22no—
365M16—42no—
366M16C2×D4×C11314yes—
367C2×C8—24no—
368C2×C8—24no—
369C2×C8—24no—
370C2×C8—22no—
371C2×C8—22no—
372C2×C8—22no—
373C2×C8—22no—
374C2×C8—22no—
375C2×C8—22no—
376C2×C8—42no—
377C2×C8C22×C4×C11314yes—
378C2×C8C2×D4×C11314yes—
379C4⋊C4—22no—
380C4⋊C4—42no—
381C4⋊C4C22×C4×C11314yes—
382C22⋊C4—22no—
383C22⋊C4—22no—
384C22⋊C4—42no—
385C42—22no—
386C42—22no—
387C42—22no—
388C42—22no—
389C23—22no—
390C23—42no—
391C23—42no—
392C23—82no—
393C23C4×D4×C11311yescharacteristic
394C23C4×D4×C11311yescharacteristic
395C23#124×C11312yes—
396C23#126×C11312yes—
397C23C2×#41×C11311yescharacteristic
398Q8—22no—
399Q8—22no—
400Q8—42no—
401D4—22no—
402D4—22no—
403D4—42no—
404D4—42no—
405D4—44no—
406D4—42no—
407C2×C4—24no—
408C2×C4—22no—
409C2×C4—42no—
410C2×C4—42no—
411C2×C4—42no—
412C2×C4—44no—
413C2×C4—44no—
414C2×C4—42no—
415C2×C4—82no—
416C2×C4#117×C11312yes—
417C2×C4#117×C11312yes—
418C2×C4C4×D4×C11312yes—
419C2×C4C4×D4×C11312yes—
420C2×C4C4×D4×C11311yescharacteristic
421C2×C4C4×D4×C11311yescharacteristic
422C2×C4#121×C11312yes—
423C2×C4#121×C11312yes—
424C2×C4#123×C11312yes—
425C2×C4#123×C11312yes—
426C2×C4#124×C11312yes—
427C2×C4#126×C11312yes—
428C2×C4C23×C4×C11311yescharacteristic
429C2×C4C22×D4×C11311yescharacteristic
430C2×C4C22×D4×C11311yescharacteristic
431C2×C4C2×#41×C11311yescharacteristic
432C2×C4C2×#41×C11311yescharacteristic
433C2×C4C2×#41×C11311yescharacteristic
434C8—24no—
435C8—24no—
436C8—24no—
437C8—42no—
438C22—22no—
439C22—22no—
440C22—22no—
441C22—42no—
442C22—42no—
443C22—42no—
444C22—44no—
445C22—84no—
446C22#388×C11312yes—
447C22#388×C11312yes—
448C22C2×C4×D4×C11311yescharacteristic
449C22C2×#124×C11311yescharacteristic
450C22C2×#126×C11311yescharacteristic
451C4—42no—
452C4—44no—
453C4—82no—
454C4#388×C11312yes—
455C4#388×C11312yes—
456C4C2×#117×C11311yescharacteristic
457C4C2×C4×D4×C11311yescharacteristic
458C4C2×#121×C11311yescharacteristic
459C4C2×#123×C11311yescharacteristic
460C2—21no—
461C2—22no—
462C2—21no—
463C2—22no—
464C2—82no—
465C2C2×#388×C11311yescharacteristic
466C2C113×#295712yes—
subgroupG/H
centerC2×C4×C113C22×D4
commutatorC2×C4C23×C4×C113
Frattini, cosocleC22×C4C24×C113
socleC22×C113C2×C4×D4
prime radicalC22×#41×C113C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C113 ◁ C22×M16×C113 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×#108×C113C2semidirect
5. C113×#2873C2semidirect
6. C113×#1929C2semidirect
7. C113×#1733C2semidirect
8. C113×#1729C2semidirect
17. C2×#108×C113C22semidirect
20. #416×C113C4semidirect
22. C2×#103×C113C4semidirect
23. C2×#102×C113C4semidirect
28. #405×C113C22semidirect
30. #339×C113C22semidirect
31. #336×C113C22semidirect
226. #21072C113direct (N × H)
234. C22×#108C2×C113semidirect
238. #2873C2×C113semidirect
239. #1929C2×C113semidirect
240. #1733C2×C113semidirect
241. #1729C2×C113semidirect
242. C113#21072direct (N × H)
251. C2×#108C22×C113semidirect
254. #416C4×C113semidirect
256. C2×#103C4×C113semidirect
257. C2×#102C4×C113semidirect
262. #405C22×C113semidirect
264. #339C22×C113semidirect
265. #336C22×C113semidirect

Maximal subgroups

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

subgroupindex
C22×#108×C1132
C2×#421×C1132
C2×#416×C1132
C113×#28792
C113×#28732
C113×#19292
C113×#17332
C113×#17292
#21072113