Finite Group Databasebeta

← C113×#18360 #43286380

Subgroups — C113×#18360 #43286380

Order 28928.

928 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C113×#3507C211yesmaximal, characteristic, complemented
2C113×#3215C211yesmaximal, characteristic, complemented
3C113×#3213C211yesmaximal, characteristic
4C113×#2632C211yesmaximal, characteristic, complemented
5C113×#1603C214yesmaximal, complemented
6C113×#1597C214yesmaximal, complemented
7C113×#1515C211yesmaximal, characteristic, complemented
8C113×#1514C211yesmaximal, characteristic, complemented
9C113×#1467C211yesmaximal, characteristic, complemented
10#559×C113—21no—
11#557×C113—21no—
12#556×C113—21no—
13#556×C113—22no—
14#554×C113—21no—
15#552×C113—22no—
16#539×C113C2214yes—
17#536×C113—21no—
18#533×C113C2211yescharacteristic
19#532×C113C2211yescharacteristic
20#529×C113—22no—
21C2×#124×C113C2211yescharacteristic
22#520×C113—21no—
23C2×C4×Q8×C113C2211yescharacteristic
24#497×C113—21no—
25#496×C113—21no—
26#489×C113—21no—
27#489×C113—21no—
28#464×C113—22no—
29#463×C113—22no—
30#451×C113C2212yes—
31#450×C113C2212yes—
32#448×C113C2212yes—
33#447×C113C2212yes—
34#432×C113C2211yescharacteristic
35#432×C113C2211yescharacteristic
36#399×C113—21no—
37#395×C113C2212yes—
38#394×C113C2212yes—
39#393×C113—21no—
40#388×C113—22no—
41#383×C113C2211yescharacteristic
42#328×C113C2214yes—
43#327×C113C2214yes—
44#324×C113C2214yes—
45C2×#41×C113—21no—
46C22×Q8×C113D411yescharacteristic
47C22×Q8×C113C2311yescharacteristic
48C22×D4×C113C2311yescharacteristic
49C2×Q16×C113—22no—
50C2×SD16×C113—22no—
51C2×SD16×C113—22no—
52C2×D8×C113—22no—
53C4⋊Q8×C113—22no—
54C4⋊Q8×C113D411yescharacteristic
55C4⋊Q8×C113D411yescharacteristic
56C4⋊Q8×C113D411yescharacteristic
57#127×C113D411yescharacteristic
58#126×C113—24no—
59#126×C113—24no—
60#125×C113—22no—
61#125×C113—24no—
62#125×C113—21no—
63#124×C113—22no—
64#124×C113—22no—
65#124×C113—21no—
66#124×C113—21no—
67#124×C113—21no—
68#124×C113—21no—
69#124×C113—21no—
70#123×C113—24no—
71#123×C113—24no—
72C22⋊Q8×C113—22no—
73C22⋊Q8×C113—22no—
74C22⋊Q8×C113—24no—
75C22⋊Q8×C113—21no—
76C22⋊Q8×C113C2312yes—
77#121×C113—21no—
78#121×C113C2312yes—
79C4×Q8×C113—22no—
80C4×Q8×C113—22no—
81C4×Q8×C113—21no—
82C4×Q8×C113—21no—
83C4×Q8×C113—21no—
84C4×Q8×C113—21no—
85C4×Q8×C113—21no—
86C4×Q8×C113D412yes—
87C4×D4×C113—22no—
88C4×D4×C113—22no—
89C4×D4×C113—24no—
90C4×D4×C113—21no—
91C4×D4×C113D412yes—
92#117×C113—22no—
93#117×C113—24no—
94#117×C113—21no—
95C2×C4⋊C4×C113—22no—
96C2×C4⋊C4×C113—22no—
97C2×C4⋊C4×C113D411yescharacteristic
98C2×C4⋊C4×C113C2312yes—
99C2×C22⋊C4×C113—21no—
100C2×C22⋊C4×C113—21no—
101C2×C22⋊C4×C113—22no—
102C2×C22⋊C4×C113—22no—
103C2×C42×C113D412yes—
104C2×C42×C113C2311yescharacteristic
105C4⋊C8×C113—21no—
106C4⋊C8×C113—21no—
107#103×C113—22no—
108#103×C113—22no—
109#102×C113—22no—
110#102×C113—22no—
111C22⋊C8×C113C2312yes—
112C22⋊C8×C113C2312yes—
113#97×C113—21no—
114#97×C113—21no—
115#95×C113—21no—
116#95×C113—21no—
117#95×C113—22no—
118#95×C113C2312yes—
119C24×C113—21no—
120#41×C113—44no—
121C2×Q8×C113—21no—
122C2×Q8×C113—21no—
123C2×Q8×C113—21no—
124C2×Q8×C113—21no—
125C2×Q8×C113—21no—
126C2×Q8×C113—21no—
127C2×Q8×C113—42no—
128C2×Q8×C113—81no—
129C2×Q8×C113C2×D412yes—
130C2×D4×C113—22no—
131C2×D4×C113—21no—
132C2×D4×C113—21no—
133C2×D4×C113—21no—
134C2×D4×C113—21no—
135C2×D4×C113—81no—
136C2×D4×C113C2×D412yes—
137C22×C4×C113—24no—
138C22×C4×C113—22no—
139C22×C4×C113—22no—
140C22×C4×C113—21no—
141C22×C4×C113C2×D412yes—
142C22×C4×C113C2×D411yescharacteristic
143C22×C4×C113C2×D412yes—
144C22×C4×C113C2×D411yescharacteristic
145C22×C4×C113C2411yescharacteristic
146Q16×C113—82no—
147SD16×C113—82no—
148SD16×C113—82no—
149D8×C113—82no—
150C2×C8×C113—22no—
151C2×C8×C113—22no—
152C4⋊C4×C113—24no—
153C4⋊C4×C113—24no—
154C4⋊C4×C113—24no—
155C4⋊C4×C113—21no—
156C4⋊C4×C113—21no—
157C4⋊C4×C113—21no—
158C4⋊C4×C113—21no—
159C4⋊C4×C113—22no—
160C4⋊C4×C113—21no—
161C4⋊C4×C113—21no—
162C4⋊C4×C113—22no—
163C4⋊C4×C113—22no—
164C4⋊C4×C113—22no—
165C4⋊C4×C113—82no—
166C4⋊C4×C113C2×D412yes—
167C4⋊C4×C113C2×D412yes—
168C22⋊C4×C113—24no—
169C22⋊C4×C113—24no—
170C22⋊C4×C113—24no—
171C22⋊C4×C113—22no—
172C22⋊C4×C113—22no—
173C22⋊C4×C113—22no—
174C22⋊C4×C113—44no—
175C22⋊C4×C113—41no—
176C22⋊C4×C113—41no—
177C22⋊C4×C113—41no—
178C22⋊C4×C113—41no—
179C22⋊C4×C113—82no—
180C42×C113—24no—
181C42×C113—22no—
182C42×C113—22no—
183C42×C113—22no—
184C42×C113C2×D411yescharacteristic
185C42×C113C2×D411yescharacteristic
186C42×C113C2×D411yescharacteristic
187C42×C113C2×D411yescharacteristic
188C23×C113—22no—
189C23×C113—42no—
190C23×C113—42no—
191C23×C113—41no—
192C23×C113—42no—
193C23×C113C22×D411yescharacteristic
194Q8×C113—42no—
195Q8×C113—42no—
196Q8×C113—42no—
197Q8×C113—42no—
198Q8×C113—42no—
199Q8×C113—42no—
200Q8×C113—42no—
201D4×C113—42no—
202D4×C113—42no—
203D4×C113—42no—
204D4×C113—42no—
205D4×C113—42no—
206D4×C113—44no—
207C2×C4×C113—22no—
208C2×C4×C113—22no—
209C2×C4×C113—22no—
210C2×C4×C113—22no—
211C2×C4×C113—22no—
212C2×C4×C113—22no—
213C2×C4×C113—22no—
214C2×C4×C113—22no—
215C2×C4×C113—41no—
216C2×C4×C113—41no—
217C2×C4×C113—44no—
218C2×C4×C113—42no—
219C2×C4×C113—42no—
220C2×C4×C113—42no—
221C2×C4×C113—42no—
222C2×C4×C113—41no—
223C2×C4×C113—42no—
224C2×C4×C113—84no—
225C2×C4×C113#12011yescharacteristic
226C2×C4×C113#12011yescharacteristic
227C2×C4×C113#12011yescharacteristic
228C2×C4×C113#12011yescharacteristic
229C2×C4×C113C22×D411yescharacteristic
230C2×C4×C113C22×D411yescharacteristic
231C8×C113—42no—
232C8×C113—42no—
233C22×C113—21no—
234C22×C113—21no—
235C22×C113—42no—
236C22×C113—42no—
237C22×C113—42no—
238C22×C113—84no—
239C22×C113—81no—
240C22×C113—81no—
241C22×C113—81no—
242C22×C113C2×#12011yescharacteristic
243C22×C113#57512yes—
244C4×C113—21no—
245C4×C113—21no—
246C4×C113—21no—
247C4×C113—21no—
248C4×C113—21no—
249C4×C113—21no—
250C4×C113—42no—
251C4×C113—42no—
252C4×C113—42no—
253C4×C113—42no—
254C4×C113—42no—
255C4×C113—82no—
256C4×C113—81no—
257#18360C11311yesmaximal, characteristic, direct product factor, Sylow
258C2×C113—22no—
259C2×C113—82no—
260C2×C113—161no—
261C2×C113#300511yescharacteristic
262C2×C113#302011yescharacteristic
263C2×C113#302711yescharacteristic
264#3507C2×C11311yescharacteristic, complemented
265#3215C2×C11311yescharacteristic, complemented
266#3213C2×C11311yescharacteristic
267#2632C2×C11311yescharacteristic, complemented
268#1603C2×C11314yescomplemented
269#1597C2×C11314yescomplemented
270#1515C2×C11311yescharacteristic, complemented
271#1514C2×C11311yescharacteristic, complemented
272#1467C2×C11311yescharacteristic, complemented
273C113#1836011yescharacteristic, direct product factor, Sylow
274#559—21no—
275#557—21no—
276#556—21no—
277#556—22no—
278#554—21no—
279#552—22no—
280#539C22×C11314yes—
281#536—21no—
282#533C22×C11311yescharacteristic
283#532C22×C11311yescharacteristic
284#529—22no—
285C2×#124C22×C11311yescharacteristic
286#520—21no—
287C2×C4×Q8C22×C11311yescharacteristic
288#497—21no—
289#496—21no—
290#489—21no—
291#489—21no—
292#464—22no—
293#463—22no—
294#451C22×C11312yes—
295#450C22×C11312yes—
296#448C22×C11312yes—
297#447C22×C11312yes—
298#432C22×C11311yescharacteristic
299#432C22×C11311yescharacteristic
300#399—21no—
301#395C22×C11312yes—
302#394C22×C11312yes—
303#393—21no—
304#388—22no—
305#383C22×C11311yescharacteristic
306#328C22×C11314yes—
307#327C22×C11314yes—
308#324C22×C11314yes—
309C2×#41—21no—
310C22×Q8D4×C11311yescharacteristic
311C22×Q8C23×C11311yescharacteristic
312C22×D4C23×C11311yescharacteristic
313C2×Q16—22no—
314C2×SD16—22no—
315C2×SD16—22no—
316C2×D8—22no—
317C4⋊Q8—22no—
318C4⋊Q8D4×C11311yescharacteristic
319C4⋊Q8D4×C11311yescharacteristic
320C4⋊Q8D4×C11311yescharacteristic
321#127D4×C11311yescharacteristic
322#126—24no—
323#126—24no—
324#125—22no—
325#125—24no—
326#125—21no—
327#124—22no—
328#124—22no—
329#124—21no—
330#124—21no—
331#124—21no—
332#124—21no—
333#124—21no—
334#123—24no—
335#123—24no—
336C22⋊Q8—22no—
337C22⋊Q8—22no—
338C22⋊Q8—24no—
339C22⋊Q8—21no—
340C22⋊Q8C23×C11312yes—
341#121—21no—
342#121C23×C11312yes—
343C4×Q8—22no—
344C4×Q8—22no—
345C4×Q8—21no—
346C4×Q8—21no—
347C4×Q8—21no—
348C4×Q8—21no—
349C4×Q8—21no—
350C4×Q8D4×C11312yes—
351C4×D4—22no—
352C4×D4—22no—
353C4×D4—24no—
354C4×D4—21no—
355C4×D4D4×C11312yes—
356#117—22no—
357#117—24no—
358#117—21no—
359C2×C4⋊C4—22no—
360C2×C4⋊C4—22no—
361C2×C4⋊C4D4×C11311yescharacteristic
362C2×C4⋊C4C23×C11312yes—
363C2×C22⋊C4—21no—
364C2×C22⋊C4—21no—
365C2×C22⋊C4—22no—
366C2×C22⋊C4—22no—
367C2×C42D4×C11312yes—
368C2×C42C23×C11311yescharacteristic
369C4⋊C8—21no—
370C4⋊C8—21no—
371#103—22no—
372#103—22no—
373#102—22no—
374#102—22no—
375C22⋊C8C23×C11312yes—
376C22⋊C8C23×C11312yes—
377#97—21no—
378#97—21no—
379#95—21no—
380#95—21no—
381#95—22no—
382#95C23×C11312yes—
383C24—21no—
384#41—44no—
385C2×Q8—21no—
386C2×Q8—21no—
387C2×Q8—21no—
388C2×Q8—21no—
389C2×Q8—21no—
390C2×Q8—21no—
391C2×Q8—42no—
392C2×Q8—81no—
393C2×Q8C2×D4×C11312yes—
394C2×D4—22no—
395C2×D4—21no—
396C2×D4—21no—
397C2×D4—21no—
398C2×D4—21no—
399C2×D4—81no—
400C2×D4C2×D4×C11312yes—
401C22×C4—24no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—21no—
405C22×C4C2×D4×C11312yes—
406C22×C4C2×D4×C11311yescharacteristic
407C22×C4C2×D4×C11312yes—
408C22×C4C2×D4×C11311yescharacteristic
409C22×C4C24×C11311yescharacteristic
410Q16—82no—
411SD16—82no—
412SD16—82no—
413D8—82no—
414C2×C8—22no—
415C2×C8—22no—
416C4⋊C4—24no—
417C4⋊C4—24no—
418C4⋊C4—24no—
419C4⋊C4—21no—
420C4⋊C4—21no—
421C4⋊C4—21no—
422C4⋊C4—21no—
423C4⋊C4—22no—
424C4⋊C4—21no—
425C4⋊C4—21no—
426C4⋊C4—22no—
427C4⋊C4—22no—
428C4⋊C4—22no—
429C4⋊C4—82no—
430C4⋊C4C2×D4×C11312yes—
431C4⋊C4C2×D4×C11312yes—
432C22⋊C4—24no—
433C22⋊C4—24no—
434C22⋊C4—24no—
435C22⋊C4—22no—
436C22⋊C4—22no—
437C22⋊C4—22no—
438C22⋊C4—44no—
439C22⋊C4—41no—
440C22⋊C4—41no—
441C22⋊C4—41no—
442C22⋊C4—41no—
443C22⋊C4—82no—
444C42—24no—
445C42—22no—
446C42—22no—
447C42—22no—
448C42C2×D4×C11311yescharacteristic
449C42C2×D4×C11311yescharacteristic
450C42C2×D4×C11311yescharacteristic
451C42C2×D4×C11311yescharacteristic
452C23—22no—
453C23—42no—
454C23—42no—
455C23—41no—
456C23—42no—
457C23C22×D4×C11311yescharacteristic
458Q8—42no—
459Q8—42no—
460Q8—42no—
461Q8—42no—
462Q8—42no—
463Q8—42no—
464Q8—42no—
465D4—42no—
466D4—42no—
467D4—42no—
468D4—42no—
469D4—42no—
470D4—44no—
471C2×C4—22no—
472C2×C4—22no—
473C2×C4—22no—
474C2×C4—22no—
475C2×C4—22no—
476C2×C4—22no—
477C2×C4—22no—
478C2×C4—22no—
479C2×C4—41no—
480C2×C4—41no—
481C2×C4—44no—
482C2×C4—42no—
483C2×C4—42no—
484C2×C4—42no—
485C2×C4—42no—
486C2×C4—41no—
487C2×C4—42no—
488C2×C4—84no—
489C2×C4#120×C11311yescharacteristic
490C2×C4#120×C11311yescharacteristic
491C2×C4#120×C11311yescharacteristic
492C2×C4#120×C11311yescharacteristic
493C2×C4C22×D4×C11311yescharacteristic
494C2×C4C22×D4×C11311yescharacteristic
495C8—42no—
496C8—42no—
497C22—21no—
498C22—21no—
499C22—42no—
500C22—42no—
501C22—42no—
502C22—84no—
503C22—81no—
504C22—81no—
505C22—81no—
506C22C2×#120×C11311yescharacteristic
507C22#575×C11312yes—
508C4—21no—
509C4—21no—
510C4—21no—
511C4—21no—
512C4—21no—
513C4—21no—
514C4—42no—
515C4—42no—
516C4—42no—
517C4—42no—
518C4—42no—
519C4—82no—
520C4—81no—
521C2—22no—
522C2—82no—
523C2—161no—
524C2C113×#300511yescharacteristic
525C2C113×#302011yescharacteristic
526C2C113×#302711yescharacteristic
subgroupG/H
center, socleC22×C113C2×#120
commutator, Frattini, cosocleC22×C4C24×C113
prime radicalC113×#3213C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C113 ◁ C2×C42×C113 ◁ G

Complements

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

NH ≅ G/Ntype
1. C113×#3507C2semidirect
2. C113×#3215C2semidirect
4. C113×#2632C2semidirect
5. C113×#1603C2semidirect
6. C113×#1597C2semidirect
7. C113×#1515C2semidirect
8. C113×#1514C2semidirect
9. C113×#1467C2semidirect
257. #18360C113direct (N × H)
264. #3507C2×C113semidirect
265. #3215C2×C113semidirect
267. #2632C2×C113semidirect
268. #1603C2×C113semidirect
269. #1597C2×C113semidirect
270. #1515C2×C113semidirect
271. #1514C2×C113semidirect
272. #1467C2×C113semidirect
273. C113#18360direct (N × H)

Maximal subgroups

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

subgroupindex
C113×#35072
C113×#32152
C113×#32132
C113×#26322
C113×#16032
C113×#15972
C113×#15152
C113×#15142
C113×#14672
#18360113