Finite Group Databasebeta

← C113×#18939 #43286959

Subgroups — C113×#18939 #43286959

Order 28928.

858 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C113×#3550C211yesmaximal, characteristic
2C113×#3249C211yesmaximal, characteristic, complemented
3C113×#3237C211yesmaximal, characteristic, complemented
4C113×#3210C211yesmaximal, characteristic
5C113×#1645C212yesmaximal, complemented
6C113×#1640C212yesmaximal, complemented
7C113×#1633C212yesmaximal, complemented
8C113×#1630C212yesmaximal, complemented
9C113×#1551C211yesmaximal, characteristic
10C113×#1497C211yesmaximal, characteristic, complemented
11C113×#1481C211yesmaximal, characteristic, complemented
12#563×C113—22no—
13#559×C113C2212yes—
14Q82×C113C2212yes—
15#556×C113—21no—
16#556×C113—21no—
17D4×Q8×C113—21no—
18D4×Q8×C113—21no—
19#542×C113—22no—
20#542×C113—22no—
21#536×C113—22no—
22#533×C113C2211yescharacteristic
23#533×C113C2211yescharacteristic
24#533×C113C2211yescharacteristic
25#532×C113C2211yescharacteristic
26#501×C113—21no—
27#494×C113C2211yescharacteristic
28#492×C113C2211yescharacteristic
29#491×C113—21no—
30#487×C113C2211yescharacteristic
31#486×C113C2211yescharacteristic
32#485×C113—22no—
33#477×C113—21no—
34#477×C113C2212yes—
35#477×C113C2212yes—
36#475×C113C2212yes—
37#467×C113—22no—
38#464×C113—22no—
39#462×C113—21no—
40#462×C113C2212yes—
41#452×C113—22no—
42#432×C113C2211yescharacteristic
43#431×C113C2211yescharacteristic
44C2×C4⋊C8×C113C2211yescharacteristic
45#333×C113C2212yes—
46#331×C113C2212yes—
47Q8⋊C8×C113C2212yes—
48Q8⋊C8×C113C2212yes—
49Q8⋊C8×C113C2212yes—
50Q8⋊C8×C113C2212yes—
51C2×#41×C113D412yes—
52C22×Q8×C113—22no—
53C2×Q16×C113—22no—
54C2×Q16×C113—22no—
55C2×SD16×C113—22no—
56C22×C8×C113—21no—
57C4⋊Q8×C113—24no—
58C4⋊Q8×C113—22no—
59C4⋊Q8×C113—22no—
60C4⋊Q8×C113D411yescharacteristic
61C4⋊Q8×C113D411yescharacteristic
62C4⋊Q8×C113D411yescharacteristic
63C4⋊Q8×C113D411yescharacteristic
64C4⋊Q8×C113C2311yescharacteristic
65C4⋊Q8×C113C2311yescharacteristic
66C4⋊Q8×C113C2311yescharacteristic
67#127×C113C2311yescharacteristic
68#126×C113—24no—
69#126×C113—24no—
70#125×C113—21no—
71#125×C113—21no—
72#125×C113—21no—
73#124×C113—24no—
74#124×C113—22no—
75#124×C113—22no—
76#124×C113D412yes—
77#123×C113—24no—
78#123×C113—24no—
79C22⋊Q8×C113—22no—
80C22⋊Q8×C113—22no—
81C22⋊Q8×C113—24no—
82C22⋊Q8×C113—24no—
83C22⋊Q8×C113—21no—
84C22⋊Q8×C113—21no—
85C22⋊Q8×C113—21no—
86C22⋊Q8×C113—21no—
87C22⋊Q8×C113D412yes—
88C22⋊Q8×C113D412yes—
89#121×C113—21no—
90#121×C113—21no—
91C4×Q8×C113—22no—
92C4×Q8×C113—22no—
93C4×Q8×C113—21no—
94C4×Q8×C113—21no—
95C4×Q8×C113—21no—
96C4×Q8×C113—21no—
97C4×Q8×C113C2312yes—
98C4×Q8×C113C2312yes—
99C4×D4×C113—22no—
100C4×D4×C113—22no—
101C4×D4×C113—21no—
102C4×D4×C113—21no—
103#117×C113—22no—
104#117×C113—21no—
105#117×C113—21no—
106#117×C113—21no—
107C2×C42×C113C2311yescharacteristic
108#107×C113—22no—
109#107×C113—22no—
110#106×C113—22no—
111C4⋊C8×C113—21no—
112C4⋊C8×C113—21no—
113C4⋊C8×C113C2312yes—
114C4⋊C8×C113C2312yes—
115#103×C113—22no—
116#103×C113—22no—
117#103×C113—22no—
118#103×C113—22no—
119#103×C113—22no—
120#102×C113—22no—
121C22⋊C8×C113—21no—
122C22⋊C8×C113—21no—
123#97×C113—21no—
124C4×C8×C113C2311yescharacteristic
125C4×C8×C113C2311yescharacteristic
126#41×C113—82no—
127C2×Q8×C113—24no—
128C2×Q8×C113—21no—
129C2×Q8×C113—21no—
130C2×Q8×C113—21no—
131C2×Q8×C113—21no—
132C2×Q8×C113—84no—
133C2×Q8×C113C2×D412yes—
134C2×Q8×C113C2×D412yes—
135C2×Q8×C113C2×D412yes—
136C2×D4×C113—22no—
137C2×D4×C113—21no—
138C2×D4×C113—21no—
139C2×D4×C113C2×D412yes—
140C22×C4×C113—24no—
141C22×C4×C113—22no—
142C22×C4×C113C2×D411yescharacteristic
143C22×C4×C113C2×D411yescharacteristic
144C22×C4×C113C2×D411yescharacteristic
145Q16×C113—82no—
146Q16×C113—82no—
147SD16×C113—82no—
148C2×C8×C113—21no—
149C2×C8×C113—21no—
150C2×C8×C113—22no—
151C2×C8×C113—22no—
152C2×C8×C113—81no—
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—21no—
160C4⋊C4×C113—21no—
161C4⋊C4×C113—22no—
162C4⋊C4×C113—22no—
163C4⋊C4×C113—21no—
164C4⋊C4×C113—21no—
165C4⋊C4×C113—22no—
166C4⋊C4×C113—22no—
167C4⋊C4×C113—21no—
168C4⋊C4×C113—21no—
169C4⋊C4×C113—21no—
170C4⋊C4×C113—21no—
171C4⋊C4×C113—41no—
172C4⋊C4×C113—41no—
173C4⋊C4×C113C2×D412yes—
174C4⋊C4×C113C2×D412yes—
175C22⋊C4×C113—24no—
176C22⋊C4×C113—24no—
177C22⋊C4×C113—24no—
178C22⋊C4×C113—22no—
179C22⋊C4×C113—22no—
180C22⋊C4×C113—22no—
181C22⋊C4×C113—22no—
182C22⋊C4×C113—41no—
183C42×C113—24no—
184C42×C113—22no—
185C42×C113—22no—
186C42×C113—41no—
187C42×C113C2×D411yescharacteristic
188C42×C113C2×D411yescharacteristic
189C42×C113C2×D411yescharacteristic
190C42×C113C2411yescharacteristic
191C23×C113—22no—
192C23×C113#12011yescharacteristic
193Q8×C113—22no—
194Q8×C113—24no—
195Q8×C113—22no—
196Q8×C113—42no—
197Q8×C113—42no—
198Q8×C113—42no—
199Q8×C113—42no—
200Q8×C113—41no—
201Q8×C113—41no—
202Q8×C113—84no—
203D4×C113—42no—
204D4×C113—41no—
205D4×C113—42no—
206D4×C113—41no—
207D4×C113—82no—
208C2×C4×C113—21no—
209C2×C4×C113—22no—
210C2×C4×C113—21no—
211C2×C4×C113—22no—
212C2×C4×C113—22no—
213C2×C4×C113—22no—
214C2×C4×C113—22no—
215C2×C4×C113—22no—
216C2×C4×C113—41no—
217C2×C4×C113—44no—
218C2×C4×C113—41no—
219C2×C4×C113—41no—
220C2×C4×C113—84no—
221C2×C4×C113#12011yescharacteristic
222C2×C4×C113#12011yescharacteristic
223C2×C4×C113#12011yescharacteristic
224C2×C4×C113C22×D411yescharacteristic
225C2×C4×C113C22×D411yescharacteristic
226C2×C4×C113C22×D411yescharacteristic
227C8×C113—41no—
228C8×C113—41no—
229C8×C113—42no—
230C8×C113—42no—
231C22×C113—21no—
232C22×C113—21no—
233C22×C113—21no—
234C22×C113—42no—
235C22×C113—42no—
236C22×C113—42no—
237C22×C113C2×#12011yescharacteristic
238C4×C113—21no—
239C4×C113—21no—
240C4×C113—21no—
241C4×C113—21no—
242C4×C113—42no—
243C4×C113—42no—
244C4×C113—42no—
245C4×C113—42no—
246C4×C113—42no—
247C4×C113—81no—
248C4×C113—81no—
249C4×C113#57711yescharacteristic
250C4×C113#57812yes—
251C4×C113#57811yescharacteristic
252#18939C11311yesmaximal, characteristic, direct product factor, Sylow
253C2×C113—41no—
254C2×C113—82no—
255C2×C113#301111yescharacteristic
256C2×C113#301311yescharacteristic
257C2×C113#301911yescharacteristic
258#3550C2×C11311yescharacteristic
259#3249C2×C11311yescharacteristic, complemented
260#3237C2×C11311yescharacteristic, complemented
261#3210C2×C11311yescharacteristic
262#1645C2×C11312yescomplemented
263#1640C2×C11312yescomplemented
264#1633C2×C11312yescomplemented
265#1630C2×C11312yescomplemented
266#1551C2×C11311yescharacteristic
267#1497C2×C11311yescharacteristic, complemented
268#1481C2×C11311yescharacteristic, complemented
269C113#1893911yescharacteristic, direct product factor, Sylow
270#563—22no—
271#559C22×C11312yes—
272Q82C22×C11312yes—
273#556—21no—
274#556—21no—
275D4×Q8—21no—
276D4×Q8—21no—
277#542—22no—
278#542—22no—
279#536—22no—
280#533C22×C11311yescharacteristic
281#533C22×C11311yescharacteristic
282#533C22×C11311yescharacteristic
283#532C22×C11311yescharacteristic
284#501—21no—
285#494C22×C11311yescharacteristic
286#492C22×C11311yescharacteristic
287#491—21no—
288#487C22×C11311yescharacteristic
289#486C22×C11311yescharacteristic
290#485—22no—
291#477—21no—
292#477C22×C11312yes—
293#477C22×C11312yes—
294#475C22×C11312yes—
295#467—22no—
296#464—22no—
297#462—21no—
298#462C22×C11312yes—
299#452—22no—
300#432C22×C11311yescharacteristic
301#431C22×C11311yescharacteristic
302C2×C4⋊C8C22×C11311yescharacteristic
303#333C22×C11312yes—
304#331C22×C11312yes—
305Q8⋊C8C22×C11312yes—
306Q8⋊C8C22×C11312yes—
307Q8⋊C8C22×C11312yes—
308Q8⋊C8C22×C11312yes—
309C2×#41D4×C11312yes—
310C22×Q8—22no—
311C2×Q16—22no—
312C2×Q16—22no—
313C2×SD16—22no—
314C22×C8—21no—
315C4⋊Q8—24no—
316C4⋊Q8—22no—
317C4⋊Q8—22no—
318C4⋊Q8D4×C11311yescharacteristic
319C4⋊Q8D4×C11311yescharacteristic
320C4⋊Q8D4×C11311yescharacteristic
321C4⋊Q8D4×C11311yescharacteristic
322C4⋊Q8C23×C11311yescharacteristic
323C4⋊Q8C23×C11311yescharacteristic
324C4⋊Q8C23×C11311yescharacteristic
325#127C23×C11311yescharacteristic
326#126—24no—
327#126—24no—
328#125—21no—
329#125—21no—
330#125—21no—
331#124—24no—
332#124—22no—
333#124—22no—
334#124D4×C11312yes—
335#123—24no—
336#123—24no—
337C22⋊Q8—22no—
338C22⋊Q8—22no—
339C22⋊Q8—24no—
340C22⋊Q8—24no—
341C22⋊Q8—21no—
342C22⋊Q8—21no—
343C22⋊Q8—21no—
344C22⋊Q8—21no—
345C22⋊Q8D4×C11312yes—
346C22⋊Q8D4×C11312yes—
347#121—21no—
348#121—21no—
349C4×Q8—22no—
350C4×Q8—22no—
351C4×Q8—21no—
352C4×Q8—21no—
353C4×Q8—21no—
354C4×Q8—21no—
355C4×Q8C23×C11312yes—
356C4×Q8C23×C11312yes—
357C4×D4—22no—
358C4×D4—22no—
359C4×D4—21no—
360C4×D4—21no—
361#117—22no—
362#117—21no—
363#117—21no—
364#117—21no—
365C2×C42C23×C11311yescharacteristic
366#107—22no—
367#107—22no—
368#106—22no—
369C4⋊C8—21no—
370C4⋊C8—21no—
371C4⋊C8C23×C11312yes—
372C4⋊C8C23×C11312yes—
373#103—22no—
374#103—22no—
375#103—22no—
376#103—22no—
377#103—22no—
378#102—22no—
379C22⋊C8—21no—
380C22⋊C8—21no—
381#97—21no—
382C4×C8C23×C11311yescharacteristic
383C4×C8C23×C11311yescharacteristic
384#41—82no—
385C2×Q8—24no—
386C2×Q8—21no—
387C2×Q8—21no—
388C2×Q8—21no—
389C2×Q8—21no—
390C2×Q8—84no—
391C2×Q8C2×D4×C11312yes—
392C2×Q8C2×D4×C11312yes—
393C2×Q8C2×D4×C11312yes—
394C2×D4—22no—
395C2×D4—21no—
396C2×D4—21no—
397C2×D4C2×D4×C11312yes—
398C22×C4—24no—
399C22×C4—22no—
400C22×C4C2×D4×C11311yescharacteristic
401C22×C4C2×D4×C11311yescharacteristic
402C22×C4C2×D4×C11311yescharacteristic
403Q16—82no—
404Q16—82no—
405SD16—82no—
406C2×C8—21no—
407C2×C8—21no—
408C2×C8—22no—
409C2×C8—22no—
410C2×C8—81no—
411C4⋊C4—24no—
412C4⋊C4—24no—
413C4⋊C4—21no—
414C4⋊C4—21no—
415C4⋊C4—21no—
416C4⋊C4—21no—
417C4⋊C4—21no—
418C4⋊C4—21no—
419C4⋊C4—22no—
420C4⋊C4—22no—
421C4⋊C4—21no—
422C4⋊C4—21no—
423C4⋊C4—22no—
424C4⋊C4—22no—
425C4⋊C4—21no—
426C4⋊C4—21no—
427C4⋊C4—21no—
428C4⋊C4—21no—
429C4⋊C4—41no—
430C4⋊C4—41no—
431C4⋊C4C2×D4×C11312yes—
432C4⋊C4C2×D4×C11312yes—
433C22⋊C4—24no—
434C22⋊C4—24no—
435C22⋊C4—24no—
436C22⋊C4—22no—
437C22⋊C4—22no—
438C22⋊C4—22no—
439C22⋊C4—22no—
440C22⋊C4—41no—
441C42—24no—
442C42—22no—
443C42—22no—
444C42—41no—
445C42C2×D4×C11311yescharacteristic
446C42C2×D4×C11311yescharacteristic
447C42C2×D4×C11311yescharacteristic
448C42C24×C11311yescharacteristic
449C23—22no—
450C23#120×C11311yescharacteristic
451Q8—22no—
452Q8—24no—
453Q8—22no—
454Q8—42no—
455Q8—42no—
456Q8—42no—
457Q8—42no—
458Q8—41no—
459Q8—41no—
460Q8—84no—
461D4—42no—
462D4—41no—
463D4—42no—
464D4—41no—
465D4—82no—
466C2×C4—21no—
467C2×C4—22no—
468C2×C4—21no—
469C2×C4—22no—
470C2×C4—22no—
471C2×C4—22no—
472C2×C4—22no—
473C2×C4—22no—
474C2×C4—41no—
475C2×C4—44no—
476C2×C4—41no—
477C2×C4—41no—
478C2×C4—84no—
479C2×C4#120×C11311yescharacteristic
480C2×C4#120×C11311yescharacteristic
481C2×C4#120×C11311yescharacteristic
482C2×C4C22×D4×C11311yescharacteristic
483C2×C4C22×D4×C11311yescharacteristic
484C2×C4C22×D4×C11311yescharacteristic
485C8—41no—
486C8—41no—
487C8—42no—
488C8—42no—
489C22—21no—
490C22—21no—
491C22—21no—
492C22—42no—
493C22—42no—
494C22—42no—
495C22C2×#120×C11311yescharacteristic
496C4—21no—
497C4—21no—
498C4—21no—
499C4—21no—
500C4—42no—
501C4—42no—
502C4—42no—
503C4—42no—
504C4—42no—
505C4—81no—
506C4—81no—
507C4#577×C11311yescharacteristic
508C4#578×C11312yes—
509C4#578×C11311yescharacteristic
510C2—41no—
511C2—82no—
512C2C113×#301111yescharacteristic
513C2C113×#301311yescharacteristic
514C2C113×#301911yescharacteristic
subgroupG/H
center, socleC22×C113C2×#120
commutator, Frattini, cosocleC42C24×C113
prime radical#532×C113C22
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×#3249C2semidirect
3. C113×#3237C2semidirect
5. C113×#1645C2semidirect
6. C113×#1640C2semidirect
7. C113×#1633C2semidirect
8. C113×#1630C2semidirect
10. C113×#1497C2semidirect
11. C113×#1481C2semidirect
252. #18939C113direct (N × H)
259. #3249C2×C113semidirect
260. #3237C2×C113semidirect
262. #1645C2×C113semidirect
263. #1640C2×C113semidirect
264. #1633C2×C113semidirect
265. #1630C2×C113semidirect
267. #1497C2×C113semidirect
268. #1481C2×C113semidirect
269. C113#18939direct (N × H)

Maximal subgroups

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

subgroupindex
C113×#35502
C113×#32492
C113×#32372
C113×#32102
C113×#16452
C113×#16402
C113×#16332
C113×#16302
C113×#15512
C113×#14972
C113×#14812
#18939113