Finite Group Databasebeta

← C113×#18926 #43286946

Subgroups — C113×#18926 #43286946

Order 28928.

966 conjugacy classes of subgroups.

The subgroup lattice has 506 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C113×#3506C211yesmaximal, characteristic
2C113×#3229C211yesmaximal, characteristic, complemented
3C113×#3226C211yesmaximal, characteristic, complemented
4C2×#461×C113C211yesmaximal, characteristic, complemented
5C113×#1650C214yesmaximal, complemented
6C113×#1642C214yesmaximal, complemented
7C113×#1540C211yesmaximal, characteristic, complemented
8C113×#1481C211yesmaximal, characteristic, complemented
9C113×#1478C211yesmaximal, characteristic, complemented
10C22×SD16×C113—21no—
11#559×C113—22no—
12#556×C113C2212yes—
13#555×C113—21no—
14#553×C113—22no—
15#550×C113C2212yes—
16#547×C113—21no—
17#538×C113—22no—
18#535×C113—21no—
19#533×C113C2211yescharacteristic
20#532×C113C2211yescharacteristic
21C2×C4⋊Q8×C113C2211yescharacteristic
22#525×C113—22no—
23#520×C113—21no—
24C2×C4×D4×C113C2211yescharacteristic
25#500×C113C2212yescomplemented
26#498×C113—21no—
27#487×C113—21no—
28#486×C113C2212yescomplemented
29#483×C113—22no—
30#480×C113—22no—
31#475×C113C2214yescomplemented
32#474×C113—22no—
33#461×C113—22no—
34#461×C113C2214yes—
35#431×C113C2211yescharacteristic
36#431×C113C2211yescharacteristic
37C2×C4⋊C8×C113C2211yescharacteristic
38C2×#103×C113—21no—
39#332×C113C2212yescomplemented
40#331×C113C2212yescomplemented
41Q8⋊C8×C113C2214yescomplemented
42D4⋊C8×C113C2214yes—
43C2×#41×C113—22no—
44C2×#41×C113—21no—
45C22×Q8×C113—21no—
46C22×D4×C113D411yescharacteristic
47C23×C4×C113—21no—
48C2×SD16×C113—24no—
49C2×SD16×C113—44no—
50C22×C8×C113—21no—
51C4⋊Q8×C113—21no—
52C4⋊Q8×C113—21no—
53C4⋊Q8×C113—21no—
54C4⋊Q8×C113D411yescharacteristic
55C4⋊Q8×C113D411yescharacteristic
56C4⋊Q8×C113C2312yes—
57C4⋊Q8×C113C2311yescharacteristic
58#127×C113—22no—
59#127×C113C2311yescharacteristic
60#126×C113—24no—
61#125×C113—21no—
62#124×C113—24no—
63#124×C113—22no—
64#124×C113—21no—
65#123×C113—24no—
66#123×C113—24no—
67C22⋊Q8×C113—22no—
68C22⋊Q8×C113—21no—
69C22⋊Q8×C113D412yes—
70#121×C113—22no—
71#121×C113—22no—
72#121×C113—24no—
73#121×C113—21no—
74#121×C113—22no—
75#121×C113D412yes—
76#120×C113—24no—
77C4×Q8×C113—22no—
78C4×Q8×C113—21no—
79C4×Q8×C113C2312yes—
80C4×D4×C113—24no—
81C4×D4×C113—24no—
82C4×D4×C113—22no—
83C4×D4×C113—21no—
84C4×D4×C113—21no—
85C4×D4×C113—21no—
86C4×D4×C113D412yes—
87C4×D4×C113D412yes—
88C4×D4×C113C2312yes—
89#117×C113—22no—
90#117×C113—21no—
91#117×C113—22no—
92C2×C4⋊C4×C113—22no—
93C2×C4⋊C4×C113—21no—
94C2×C4⋊C4×C113—21no—
95C2×C4⋊C4×C113D411yescharacteristic
96C2×C22⋊C4×C113—21no—
97C2×C42×C113C2311yescharacteristic
98#107×C113—24no—
99#106×C113—24no—
100C4⋊C8×C113—21no—
101C4⋊C8×C113—21no—
102C4⋊C8×C113C2312yes—
103C4⋊C8×C113C2312yes—
104#103×C113—24no—
105#103×C113—24no—
106#102×C113—24no—
107C22⋊C8×C113—21no—
108C22⋊C8×C113—21no—
109C4×C8×C113—21no—
110C4×C8×C113C2312yes—
111C24×C113—21no—
112#41×C113—42no—
113#41×C113—42no—
114#41×C113—84no—
115C2×Q8×C113—21no—
116C2×Q8×C113—21no—
117C2×Q8×C113—22no—
118C2×Q8×C113—41no—
119C2×Q8×C113—42no—
120C2×Q8×C113—42no—
121C2×Q8×C113C2×D412yes—
122C2×D4×C113—22no—
123C2×D4×C113—24no—
124C2×D4×C113—24no—
125C2×D4×C113—21no—
126C2×D4×C113—22no—
127C2×D4×C113—22no—
128C2×D4×C113—21no—
129C2×D4×C113—21no—
130C2×D4×C113C2×D412yes—
131C2×D4×C113C2×D412yes—
132C22×C4×C113—24no—
133C22×C4×C113—21no—
134C22×C4×C113—22no—
135C22×C4×C113—22no—
136C22×C4×C113—22no—
137C22×C4×C113—41no—
138C22×C4×C113—82no—
139C22×C4×C113C2×D411yescharacteristic
140C22×C4×C113C2×D411yescharacteristic
141C22×C4×C113C2×D411yescharacteristic
142SD16×C113—48no—
143C2×C8×C113—22no—
144C2×C8×C113—22no—
145C2×C8×C113—22no—
146C2×C8×C113—42no—
147C4⋊C4×C113—24no—
148C4⋊C4×C113—21no—
149C4⋊C4×C113—21no—
150C4⋊C4×C113—21no—
151C4⋊C4×C113—22no—
152C4⋊C4×C113—21no—
153C4⋊C4×C113—21no—
154C4⋊C4×C113—22no—
155C4⋊C4×C113—22no—
156C4⋊C4×C113—22no—
157C4⋊C4×C113—41no—
158C4⋊C4×C113—41no—
159C4⋊C4×C113C2×D412yes—
160C4⋊C4×C113C2×D412yes—
161C4⋊C4×C113C2×D412yes—
162C22⋊C4×C113—24no—
163C22⋊C4×C113—24no—
164C22⋊C4×C113—24no—
165C22⋊C4×C113—22no—
166C22⋊C4×C113—22no—
167C22⋊C4×C113—22no—
168C22⋊C4×C113—22no—
169C22⋊C4×C113—22no—
170C42×C113—24no—
171C42×C113—22no—
172C42×C113C2×D411yescharacteristic
173C42×C113C2×D411yescharacteristic
174C42×C113C2×D411yescharacteristic
175C42×C113C2411yescharacteristic
176C23×C113—22no—
177C23×C113—22no—
178C23×C113—42no—
179C23×C113—81no—
180C23×C113—81no—
181C23×C113#12011yescharacteristic
182Q8×C113—24no—
183Q8×C113—41no—
184Q8×C113—41no—
185Q8×C113—42no—
186Q8×C113—42no—
187Q8×C113—81no—
188Q8×C113—82no—
189D4×C113—22no—
190D4×C113—22no—
191D4×C113—42no—
192D4×C113—44no—
193D4×C113—41no—
194D4×C113—41no—
195D4×C113—42no—
196D4×C113—42no—
197D4×C113—84no—
198D4×C113—84no—
199C2×C4×C113—22no—
200C2×C4×C113—22no—
201C2×C4×C113—22no—
202C2×C4×C113—22no—
203C2×C4×C113—22no—
204C2×C4×C113—41no—
205C2×C4×C113—44no—
206C2×C4×C113—44no—
207C2×C4×C113—42no—
208C2×C4×C113—82no—
209C2×C4×C113—81no—
210C2×C4×C113—84no—
211C2×C4×C113—82no—
212C2×C4×C113#12011yescharacteristic
213C2×C4×C113#12011yescharacteristic
214C2×C4×C113#12011yescharacteristic
215C2×C4×C113#13512yes—
216C2×C4×C113AGL(1,ℤ/8)12yes—
217C2×C4×C113C22×D411yescharacteristic
218C2×C4×C113C22×D411yescharacteristic
219C2×C4×C113C22×D411yescharacteristic
220C8×C113—42no—
221C8×C113—42no—
222C8×C113—42no—
223C22×C113—21no—
224C22×C113—21no—
225C22×C113—42no—
226C22×C113—42no—
227C22×C113—42no—
228C22×C113—42no—
229C22×C113—42no—
230C22×C113—42no—
231C22×C113—84no—
232C22×C113#44912yes—
233C22×C113C2×#12011yescharacteristic
234C4×C113—21no—
235C4×C113—21no—
236C4×C113—21no—
237C4×C113—42no—
238C4×C113—42no—
239C4×C113—42no—
240C4×C113—42no—
241C4×C113—82no—
242C4×C113#44912yes—
243C4×C113C2×#13511yescharacteristic
244C4×C113C2×AGL(1,ℤ/8)11yescharacteristic
245C4×C113#57712yes—
246#18926C11311yesmaximal, characteristic, direct product factor, Sylow
247C2×C113—22no—
248C2×C113—82no—
249C2×C113—82no—
250C2×C113C2×#44911yescharacteristic
251C2×C113#300911yescharacteristic
252C2×C113#302211yescharacteristic
253#3506C2×C11311yescharacteristic
254#3229C2×C11311yescharacteristic, complemented
255#3226C2×C11311yescharacteristic, complemented
256C2×#461C2×C11311yescharacteristic, complemented
257#1650C2×C11314yescomplemented
258#1642C2×C11314yescomplemented
259#1540C2×C11311yescharacteristic, complemented
260#1481C2×C11311yescharacteristic, complemented
261#1478C2×C11311yescharacteristic, complemented
262C113#1892611yescharacteristic, direct product factor, Sylow
263C22×SD16—21no—
264#559—22no—
265#556C22×C11312yes—
266#555—21no—
267#553—22no—
268#550C22×C11312yes—
269#547—21no—
270#538—22no—
271#535—21no—
272#533C22×C11311yescharacteristic
273#532C22×C11311yescharacteristic
274C2×C4⋊Q8C22×C11311yescharacteristic
275#525—22no—
276#520—21no—
277C2×C4×D4C22×C11311yescharacteristic
278#500C22×C11312yescomplemented
279#498—21no—
280#487—21no—
281#486C22×C11312yescomplemented
282#483—22no—
283#480—22no—
284#475C22×C11314yescomplemented
285#474—22no—
286#461—22no—
287#461C22×C11314yes—
288#431C22×C11311yescharacteristic
289#431C22×C11311yescharacteristic
290C2×C4⋊C8C22×C11311yescharacteristic
291C2×#103—21no—
292#332C22×C11312yescomplemented
293#331C22×C11312yescomplemented
294Q8⋊C8C22×C11314yescomplemented
295D4⋊C8C22×C11314yes—
296C2×#41—22no—
297C2×#41—21no—
298C22×Q8—21no—
299C22×D4D4×C11311yescharacteristic
300C23×C4—21no—
301C2×SD16—24no—
302C2×SD16—44no—
303C22×C8—21no—
304C4⋊Q8—21no—
305C4⋊Q8—21no—
306C4⋊Q8—21no—
307C4⋊Q8D4×C11311yescharacteristic
308C4⋊Q8D4×C11311yescharacteristic
309C4⋊Q8C23×C11312yes—
310C4⋊Q8C23×C11311yescharacteristic
311#127—22no—
312#127C23×C11311yescharacteristic
313#126—24no—
314#125—21no—
315#124—24no—
316#124—22no—
317#124—21no—
318#123—24no—
319#123—24no—
320C22⋊Q8—22no—
321C22⋊Q8—21no—
322C22⋊Q8D4×C11312yes—
323#121—22no—
324#121—22no—
325#121—24no—
326#121—21no—
327#121—22no—
328#121D4×C11312yes—
329#120—24no—
330C4×Q8—22no—
331C4×Q8—21no—
332C4×Q8C23×C11312yes—
333C4×D4—24no—
334C4×D4—24no—
335C4×D4—22no—
336C4×D4—21no—
337C4×D4—21no—
338C4×D4—21no—
339C4×D4D4×C11312yes—
340C4×D4D4×C11312yes—
341C4×D4C23×C11312yes—
342#117—22no—
343#117—21no—
344#117—22no—
345C2×C4⋊C4—22no—
346C2×C4⋊C4—21no—
347C2×C4⋊C4—21no—
348C2×C4⋊C4D4×C11311yescharacteristic
349C2×C22⋊C4—21no—
350C2×C42C23×C11311yescharacteristic
351#107—24no—
352#106—24no—
353C4⋊C8—21no—
354C4⋊C8—21no—
355C4⋊C8C23×C11312yes—
356C4⋊C8C23×C11312yes—
357#103—24no—
358#103—24no—
359#102—24no—
360C22⋊C8—21no—
361C22⋊C8—21no—
362C4×C8—21no—
363C4×C8C23×C11312yes—
364C24—21no—
365#41—42no—
366#41—42no—
367#41—84no—
368C2×Q8—21no—
369C2×Q8—21no—
370C2×Q8—22no—
371C2×Q8—41no—
372C2×Q8—42no—
373C2×Q8—42no—
374C2×Q8C2×D4×C11312yes—
375C2×D4—22no—
376C2×D4—24no—
377C2×D4—24no—
378C2×D4—21no—
379C2×D4—22no—
380C2×D4—22no—
381C2×D4—21no—
382C2×D4—21no—
383C2×D4C2×D4×C11312yes—
384C2×D4C2×D4×C11312yes—
385C22×C4—24no—
386C22×C4—21no—
387C22×C4—22no—
388C22×C4—22no—
389C22×C4—22no—
390C22×C4—41no—
391C22×C4—82no—
392C22×C4C2×D4×C11311yescharacteristic
393C22×C4C2×D4×C11311yescharacteristic
394C22×C4C2×D4×C11311yescharacteristic
395SD16—48no—
396C2×C8—22no—
397C2×C8—22no—
398C2×C8—22no—
399C2×C8—42no—
400C4⋊C4—24no—
401C4⋊C4—21no—
402C4⋊C4—21no—
403C4⋊C4—21no—
404C4⋊C4—22no—
405C4⋊C4—21no—
406C4⋊C4—21no—
407C4⋊C4—22no—
408C4⋊C4—22no—
409C4⋊C4—22no—
410C4⋊C4—41no—
411C4⋊C4—41no—
412C4⋊C4C2×D4×C11312yes—
413C4⋊C4C2×D4×C11312yes—
414C4⋊C4C2×D4×C11312yes—
415C22⋊C4—24no—
416C22⋊C4—24no—
417C22⋊C4—24no—
418C22⋊C4—22no—
419C22⋊C4—22no—
420C22⋊C4—22no—
421C22⋊C4—22no—
422C22⋊C4—22no—
423C42—24no—
424C42—22no—
425C42C2×D4×C11311yescharacteristic
426C42C2×D4×C11311yescharacteristic
427C42C2×D4×C11311yescharacteristic
428C42C24×C11311yescharacteristic
429C23—22no—
430C23—22no—
431C23—42no—
432C23—81no—
433C23—81no—
434C23#120×C11311yescharacteristic
435Q8—24no—
436Q8—41no—
437Q8—41no—
438Q8—42no—
439Q8—42no—
440Q8—81no—
441Q8—82no—
442D4—22no—
443D4—22no—
444D4—42no—
445D4—44no—
446D4—41no—
447D4—41no—
448D4—42no—
449D4—42no—
450D4—84no—
451D4—84no—
452C2×C4—22no—
453C2×C4—22no—
454C2×C4—22no—
455C2×C4—22no—
456C2×C4—22no—
457C2×C4—41no—
458C2×C4—44no—
459C2×C4—44no—
460C2×C4—42no—
461C2×C4—82no—
462C2×C4—81no—
463C2×C4—84no—
464C2×C4—82no—
465C2×C4#120×C11311yescharacteristic
466C2×C4#120×C11311yescharacteristic
467C2×C4#120×C11311yescharacteristic
468C2×C4#135×C11312yes—
469C2×C4AGL(1,ℤ/8)×C11312yes—
470C2×C4C22×D4×C11311yescharacteristic
471C2×C4C22×D4×C11311yescharacteristic
472C2×C4C22×D4×C11311yescharacteristic
473C8—42no—
474C8—42no—
475C8—42no—
476C22—21no—
477C22—21no—
478C22—42no—
479C22—42no—
480C22—42no—
481C22—42no—
482C22—42no—
483C22—42no—
484C22—84no—
485C22#449×C11312yes—
486C22C2×#120×C11311yescharacteristic
487C4—21no—
488C4—21no—
489C4—21no—
490C4—42no—
491C4—42no—
492C4—42no—
493C4—42no—
494C4—82no—
495C4#449×C11312yes—
496C4C2×#135×C11311yescharacteristic
497C4C2×AGL(1,ℤ/8)×C11311yescharacteristic
498C4#577×C11312yes—
499C2—22no—
500C2—82no—
501C2—82no—
502C2C2×#449×C11311yescharacteristic
503C2C113×#300911yescharacteristic
504C2C113×#302211yescharacteristic
subgroupG/H
center, socleC22×C113C2×#120
commutator, Frattini, cosocleC42C24×C113
prime radicalC113×#3506C2
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×#3229C2semidirect
3. C113×#3226C2semidirect
4. C2×#461×C113C2semidirect
5. C113×#1650C2semidirect
6. C113×#1642C2semidirect
7. C113×#1540C2semidirect
8. C113×#1481C2semidirect
9. C113×#1478C2semidirect
25. #500×C113C22semidirect
28. #486×C113C22semidirect
31. #475×C113C22semidirect
39. #332×C113C22semidirect
40. #331×C113C22semidirect
41. Q8⋊C8×C113C22semidirect
246. #18926C113direct (N × H)
254. #3229C2×C113semidirect
255. #3226C2×C113semidirect
256. C2×#461C2×C113semidirect
257. #1650C2×C113semidirect
258. #1642C2×C113semidirect
259. #1540C2×C113semidirect
260. #1481C2×C113semidirect
261. #1478C2×C113semidirect
262. C113#18926direct (N × H)
278. #500C22×C113semidirect
281. #486C22×C113semidirect
284. #475C22×C113semidirect
292. #332C22×C113semidirect
293. #331C22×C113semidirect
294. Q8⋊C8C22×C113semidirect

Maximal subgroups

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

subgroupindex
C113×#35062
C113×#32292
C113×#32262
C2×#461×C1132
C113×#16502
C113×#16422
C113×#15402
C113×#14812
C113×#14782
#18926113