Finite Group Databasebeta

← C113×#18751 #43286771

Subgroups — C113×#18751 #43286771

Order 28928.

986 conjugacy classes of subgroups.

The subgroup lattice has 482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#559×C113C211yesmaximal, characteristic
2C113×#3208C211yesmaximal, characteristic
3C113×#3104C211yesmaximal, characteristic, complemented
4C113×#3078C211yesmaximal, characteristic, complemented
5C113×#1640C214yesmaximal, complemented
6C113×#1630C214yesmaximal, complemented
7C113×#1545C211yesmaximal, characteristic
8C113×#1487C211yesmaximal, characteristic, complemented
9C113×#1479C211yesmaximal, characteristic, complemented
10#559×C113—22no—
11#559×C113—22no—
12#559×C113—22no—
13#559×C113C2214yes—
14#533×C113C2211yescharacteristic
15C2×#127×C113C2211yescharacteristic
16C2×#124×C113—21no—
17C2×#124×C113—21no—
18C2×#123×C113—22no—
19C2×C4×Q8×C113C2211yescharacteristic
20C2×C4×Q8×C113C2211yescharacteristic
21C2×C4×D4×C113—21no—
22C2×C4×D4×C113—21no—
23#492×C113C2212yes—
24#486×C113C2212yes—
25#484×C113—21no—
26#479×C113—22no—
27#477×C113C2212yescomplemented
28#477×C113C2212yescomplemented
29#475×C113C2212yescomplemented
30#462×C113C2212yescomplemented
31#460×C113—22no—
32#451×C113—21no—
33#450×C113—22no—
34C4×Q16×C113—22no—
35#431×C113C2211yescharacteristic
36#431×C113C2211yescharacteristic
37#428×C113—21no—
38#423×C113C2211yescharacteristic
39#419×C113—21no—
40#331×C113C2214yes—
41Q8⋊C8×C113C2214yescomplemented
42Q8⋊C8×C113C2214yescomplemented
43C22×Q8×C113D411yescharacteristic
44C22×Q8×C113D411yescharacteristic
45C22×D4×C113—21no—
46C22×D4×C113—21no—
47C22×D4×C113D412yes—
48C23×C4×C113—22no—
49C2×Q16×C113—22no—
50C2×SD16×C113—24no—
51C2×M16×C113—21no—
52C4⋊Q8×C113C2311yescharacteristic
53C4⋊Q8×C113C2311yescharacteristic
54#127×C113—21no—
55#127×C113—21no—
56#127×C113D412yes—
57#127×C113C2312yes—
58#125×C113—21no—
59#124×C113—24no—
60#124×C113—24no—
61#124×C113—24no—
62#124×C113—24no—
63#123×C113—28no—
64#123×C113—28no—
65C22⋊Q8×C113—21no—
66C22⋊Q8×C113—21no—
67C4×Q8×C113—21no—
68C4×Q8×C113—21no—
69C4×Q8×C113—21no—
70C4×Q8×C113—21no—
71C4×Q8×C113—21no—
72C4×Q8×C113—21no—
73C4×Q8×C113D412yes—
74C4×Q8×C113D412yes—
75C4×Q8×C113C2312yes—
76C4×Q8×C113C2312yes—
77C4×D4×C113—24no—
78C4×D4×C113—24no—
79C4×D4×C113—24no—
80C4×D4×C113—24no—
81#117×C113—21no—
82C2×C4⋊C4×C113—21no—
83C2×C4⋊C4×C113—21no—
84C2×C4⋊C4×C113D411yescharacteristic
85C2×C4⋊C4×C113D411yescharacteristic
86C2×C22⋊C4×C113—22no—
87C2×C22⋊C4×C113—22no—
88C2×C22⋊C4×C113—22no—
89C2×C42×C113—21no—
90C2×C42×C113—21no—
91C2×C42×C113C2311yescharacteristic
92#107×C113—22no—
93#107×C113—22no—
94#106×C113—22no—
95C4⋊C8×C113—21no—
96C4⋊C8×C113—21no—
97C4⋊C8×C113C2312yes—
98C4⋊C8×C113C2312yes—
99#103×C113—22no—
100#103×C113—22no—
101#103×C113—22no—
102#103×C113—22no—
103#102×C113—24no—
104C22⋊C8×C113—21no—
105C22⋊C8×C113—21no—
106C4×C8×C113—21no—
107C4×C8×C113C2312yes—
108C24×C113—22no—
109C2×Q8×C113—21no—
110C2×Q8×C113—21no—
111C2×Q8×C113—22no—
112C2×Q8×C113—22no—
113C2×Q8×C113—21no—
114C2×Q8×C113—21no—
115C2×Q8×C113—42no—
116C2×Q8×C113C2×D412yes—
117C2×Q8×C113C2×D412yes—
118C2×D4×C113—22no—
119C2×D4×C113—22no—
120C2×D4×C113—22no—
121C2×D4×C113—22no—
122C2×D4×C113—22no—
123C2×D4×C113—44no—
124C2×D4×C113—42no—
125C2×D4×C113—42no—
126C2×D4×C113—82no—
127C2×D4×C113C2×D414yes—
128C22×C4×C113—21no—
129C22×C4×C113—21no—
130C22×C4×C113—21no—
131C22×C4×C113—21no—
132C22×C4×C113—28no—
133C22×C4×C113—84no—
134C22×C4×C113C2×D411yescharacteristic
135C22×C4×C113C2×D411yescharacteristic
136C22×C4×C113C2×D411yescharacteristic
137Q16×C113—44no—
138SD16×C113—84no—
139M16×C113—42no—
140C2×C8×C113—22no—
141C2×C8×C113—22no—
142C2×C8×C113—22no—
143C4⋊C4×C113—22no—
144C4⋊C4×C113—22no—
145C4⋊C4×C113—21no—
146C4⋊C4×C113—21no—
147C4⋊C4×C113—22no—
148C4⋊C4×C113—22no—
149C4⋊C4×C113—21no—
150C4⋊C4×C113—21no—
151C4⋊C4×C113—21no—
152C4⋊C4×C113—21no—
153C4⋊C4×C113—41no—
154C4⋊C4×C113—41no—
155C4⋊C4×C113C2×D412yes—
156C4⋊C4×C113C2×D412yes—
157C22⋊C4×C113—28no—
158C22⋊C4×C113—28no—
159C22⋊C4×C113—28no—
160C22⋊C4×C113—41no—
161C42×C113—22no—
162C42×C113—22no—
163C42×C113—22no—
164C42×C113—22no—
165C42×C113—41no—
166C42×C113C2×D411yescharacteristic
167C42×C113C2×D411yescharacteristic
168C42×C113C2×D411yescharacteristic
169C42×C113C2411yescharacteristic
170C23×C113—24no—
171C23×C113—44no—
172C23×C113—44no—
173C23×C113—44no—
174C23×C113#12011yescharacteristic
175Q8×C113—22no—
176Q8×C113—22no—
177Q8×C113—22no—
178Q8×C113—22no—
179Q8×C113—42no—
180Q8×C113—42no—
181Q8×C113—42no—
182Q8×C113—42no—
183D4×C113—44no—
184D4×C113—44no—
185D4×C113—42no—
186D4×C113—42no—
187D4×C113—44no—
188D4×C113—44no—
189D4×C113—82no—
190C2×C4×C113—22no—
191C2×C4×C113—22no—
192C2×C4×C113—22no—
193C2×C4×C113—22no—
194C2×C4×C113—22no—
195C2×C4×C113—41no—
196C2×C4×C113—42no—
197C2×C4×C113—42no—
198C2×C4×C113—42no—
199C2×C4×C113—42no—
200C2×C4×C113—41no—
201C2×C4×C113—41no—
202C2×C4×C113—88no—
203C2×C4×C113#12011yescharacteristic
204C2×C4×C113#12011yescharacteristic
205C2×C4×C113#12011yescharacteristic
206C2×C4×C113#13512yes—
207C2×C4×C113#13712yes—
208C2×C4×C113C22×D411yescharacteristic
209C2×C4×C113C22×D411yescharacteristic
210C2×C4×C113C22×D411yescharacteristic
211C8×C113—42no—
212C8×C113—42no—
213C8×C113—42no—
214C22×C113—21no—
215C22×C113—21no—
216C22×C113—44no—
217C22×C113—44no—
218C22×C113—44no—
219C22×C113—88no—
220C22×C113#45212yes—
221C22×C113C2×#12011yescharacteristic
222C4×C113—21no—
223C4×C113—21no—
224C4×C113—21no—
225C4×C113—42no—
226C4×C113—42no—
227C4×C113—42no—
228C4×C113—42no—
229C4×C113—81no—
230C4×C113—81no—
231C4×C113#45212yes—
232C4×C113C2×#13511yescharacteristic
233C4×C113C2×#13711yescharacteristic
234C4×C113#57512yes—
235#18751C11311yesmaximal, characteristic, direct product factor, Sylow
236C2×C113—22no—
237C2×C113—84no—
238C2×C113C2×#45211yescharacteristic
239C2×C113#300511yescharacteristic
240C2×C113#301911yescharacteristic
241C2×#559C2×C11311yescharacteristic
242#3208C2×C11311yescharacteristic
243#3104C2×C11311yescharacteristic, complemented
244#3078C2×C11311yescharacteristic, complemented
245#1640C2×C11314yescomplemented
246#1630C2×C11314yescomplemented
247#1545C2×C11311yescharacteristic
248#1487C2×C11311yescharacteristic, complemented
249#1479C2×C11311yescharacteristic, complemented
250C113#1875111yescharacteristic, direct product factor, Sylow
251#559—22no—
252#559—22no—
253#559—22no—
254#559C22×C11314yes—
255#533C22×C11311yescharacteristic
256C2×#127C22×C11311yescharacteristic
257C2×#124—21no—
258C2×#124—21no—
259C2×#123—22no—
260C2×C4×Q8C22×C11311yescharacteristic
261C2×C4×Q8C22×C11311yescharacteristic
262C2×C4×D4—21no—
263C2×C4×D4—21no—
264#492C22×C11312yes—
265#486C22×C11312yes—
266#484—21no—
267#479—22no—
268#477C22×C11312yescomplemented
269#477C22×C11312yescomplemented
270#475C22×C11312yescomplemented
271#462C22×C11312yescomplemented
272#460—22no—
273#451—21no—
274#450—22no—
275C4×Q16—22no—
276#431C22×C11311yescharacteristic
277#431C22×C11311yescharacteristic
278#428—21no—
279#423C22×C11311yescharacteristic
280#419—21no—
281#331C22×C11314yes—
282Q8⋊C8C22×C11314yescomplemented
283Q8⋊C8C22×C11314yescomplemented
284C22×Q8D4×C11311yescharacteristic
285C22×Q8D4×C11311yescharacteristic
286C22×D4—21no—
287C22×D4—21no—
288C22×D4D4×C11312yes—
289C23×C4—22no—
290C2×Q16—22no—
291C2×SD16—24no—
292C2×M16—21no—
293C4⋊Q8C23×C11311yescharacteristic
294C4⋊Q8C23×C11311yescharacteristic
295#127—21no—
296#127—21no—
297#127D4×C11312yes—
298#127C23×C11312yes—
299#125—21no—
300#124—24no—
301#124—24no—
302#124—24no—
303#124—24no—
304#123—28no—
305#123—28no—
306C22⋊Q8—21no—
307C22⋊Q8—21no—
308C4×Q8—21no—
309C4×Q8—21no—
310C4×Q8—21no—
311C4×Q8—21no—
312C4×Q8—21no—
313C4×Q8—21no—
314C4×Q8D4×C11312yes—
315C4×Q8D4×C11312yes—
316C4×Q8C23×C11312yes—
317C4×Q8C23×C11312yes—
318C4×D4—24no—
319C4×D4—24no—
320C4×D4—24no—
321C4×D4—24no—
322#117—21no—
323C2×C4⋊C4—21no—
324C2×C4⋊C4—21no—
325C2×C4⋊C4D4×C11311yescharacteristic
326C2×C4⋊C4D4×C11311yescharacteristic
327C2×C22⋊C4—22no—
328C2×C22⋊C4—22no—
329C2×C22⋊C4—22no—
330C2×C42—21no—
331C2×C42—21no—
332C2×C42C23×C11311yescharacteristic
333#107—22no—
334#107—22no—
335#106—22no—
336C4⋊C8—21no—
337C4⋊C8—21no—
338C4⋊C8C23×C11312yes—
339C4⋊C8C23×C11312yes—
340#103—22no—
341#103—22no—
342#103—22no—
343#103—22no—
344#102—24no—
345C22⋊C8—21no—
346C22⋊C8—21no—
347C4×C8—21no—
348C4×C8C23×C11312yes—
349C24—22no—
350C2×Q8—21no—
351C2×Q8—21no—
352C2×Q8—22no—
353C2×Q8—22no—
354C2×Q8—21no—
355C2×Q8—21no—
356C2×Q8—42no—
357C2×Q8C2×D4×C11312yes—
358C2×Q8C2×D4×C11312yes—
359C2×D4—22no—
360C2×D4—22no—
361C2×D4—22no—
362C2×D4—22no—
363C2×D4—22no—
364C2×D4—44no—
365C2×D4—42no—
366C2×D4—42no—
367C2×D4—82no—
368C2×D4C2×D4×C11314yes—
369C22×C4—21no—
370C22×C4—21no—
371C22×C4—21no—
372C22×C4—21no—
373C22×C4—28no—
374C22×C4—84no—
375C22×C4C2×D4×C11311yescharacteristic
376C22×C4C2×D4×C11311yescharacteristic
377C22×C4C2×D4×C11311yescharacteristic
378Q16—44no—
379SD16—84no—
380M16—42no—
381C2×C8—22no—
382C2×C8—22no—
383C2×C8—22no—
384C4⋊C4—22no—
385C4⋊C4—22no—
386C4⋊C4—21no—
387C4⋊C4—21no—
388C4⋊C4—22no—
389C4⋊C4—22no—
390C4⋊C4—21no—
391C4⋊C4—21no—
392C4⋊C4—21no—
393C4⋊C4—21no—
394C4⋊C4—41no—
395C4⋊C4—41no—
396C4⋊C4C2×D4×C11312yes—
397C4⋊C4C2×D4×C11312yes—
398C22⋊C4—28no—
399C22⋊C4—28no—
400C22⋊C4—28no—
401C22⋊C4—41no—
402C42—22no—
403C42—22no—
404C42—22no—
405C42—22no—
406C42—41no—
407C42C2×D4×C11311yescharacteristic
408C42C2×D4×C11311yescharacteristic
409C42C2×D4×C11311yescharacteristic
410C42C24×C11311yescharacteristic
411C23—24no—
412C23—44no—
413C23—44no—
414C23—44no—
415C23#120×C11311yescharacteristic
416Q8—22no—
417Q8—22no—
418Q8—22no—
419Q8—22no—
420Q8—42no—
421Q8—42no—
422Q8—42no—
423Q8—42no—
424D4—44no—
425D4—44no—
426D4—42no—
427D4—42no—
428D4—44no—
429D4—44no—
430D4—82no—
431C2×C4—22no—
432C2×C4—22no—
433C2×C4—22no—
434C2×C4—22no—
435C2×C4—22no—
436C2×C4—41no—
437C2×C4—42no—
438C2×C4—42no—
439C2×C4—42no—
440C2×C4—42no—
441C2×C4—41no—
442C2×C4—41no—
443C2×C4—88no—
444C2×C4#120×C11311yescharacteristic
445C2×C4#120×C11311yescharacteristic
446C2×C4#120×C11311yescharacteristic
447C2×C4#135×C11312yes—
448C2×C4#137×C11312yes—
449C2×C4C22×D4×C11311yescharacteristic
450C2×C4C22×D4×C11311yescharacteristic
451C2×C4C22×D4×C11311yescharacteristic
452C8—42no—
453C8—42no—
454C8—42no—
455C22—21no—
456C22—21no—
457C22—44no—
458C22—44no—
459C22—44no—
460C22—88no—
461C22#452×C11312yes—
462C22C2×#120×C11311yescharacteristic
463C4—21no—
464C4—21no—
465C4—21no—
466C4—42no—
467C4—42no—
468C4—42no—
469C4—42no—
470C4—81no—
471C4—81no—
472C4#452×C11312yes—
473C4C2×#135×C11311yescharacteristic
474C4C2×#137×C11311yescharacteristic
475C4#575×C11312yes—
476C2—22no—
477C2—84no—
478C2C2×#452×C11311yescharacteristic
479C2C113×#300511yescharacteristic
480C2C113×#301911yescharacteristic
subgroupG/H
center, socleC22×C113C2×#120
commutator, Frattini, cosocleC42C24×C113
prime radicalC2×#127×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
3. C113×#3104C2semidirect
4. C113×#3078C2semidirect
5. C113×#1640C2semidirect
6. C113×#1630C2semidirect
8. C113×#1487C2semidirect
9. C113×#1479C2semidirect
27. #477×C113C22semidirect
28. #477×C113C22semidirect
29. #475×C113C22semidirect
30. #462×C113C22semidirect
41. Q8⋊C8×C113C22semidirect
42. Q8⋊C8×C113C22semidirect
235. #18751C113direct (N × H)
243. #3104C2×C113semidirect
244. #3078C2×C113semidirect
245. #1640C2×C113semidirect
246. #1630C2×C113semidirect
248. #1487C2×C113semidirect
249. #1479C2×C113semidirect
250. C113#18751direct (N × H)
268. #477C22×C113semidirect
269. #477C22×C113semidirect
270. #475C22×C113semidirect
271. #462C22×C113semidirect
282. Q8⋊C8C22×C113semidirect
283. Q8⋊C8C22×C113semidirect

Maximal subgroups

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

subgroupindex
C2×#559×C1132
C113×#32082
C113×#31042
C113×#30782
C113×#16402
C113×#16302
C113×#15452
C113×#14872
C113×#14792
#18751113