Finite Group Databasebeta

← C113×#18906 #43286926

Subgroups — C113×#18906 #43286926

Order 28928.

902 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
1C113×#3507C211yesmaximal, characteristic
2C113×#3229C211yesmaximal, characteristic, complemented
3C113×#3226C211yesmaximal, characteristic
4C2×#462×C113C211yesmaximal, characteristic, complemented
5C113×#1648C214yesmaximal, complemented
6C113×#1640C214yesmaximal, complemented
7C113×#1540C211yesmaximal, characteristic
8C113×#1481C211yesmaximal, characteristic, complemented
9C113×#1479C211yesmaximal, characteristic, complemented
10C22×Q16×C113—21no—
11#559×C113C2212yes—
12#557×C113C2212yes—
13#556×C113—21no—
14#556×C113—22no—
15#554×C113—21no—
16#552×C113—22no—
17#539×C113—22no—
18#536×C113—21no—
19#533×C113C2211yescharacteristic
20#532×C113C2211yescharacteristic
21C2×C4⋊Q8×C113C2211yescharacteristic
22#529×C113—22no—
23#520×C113—21no—
24C2×C4×Q8×C113C2211yescharacteristic
25#500×C113C2212yes—
26#498×C113—21no—
27#487×C113—21no—
28#486×C113C2212yes—
29#483×C113—22no—
30#480×C113—22no—
31#475×C113C2214yes—
32#474×C113—22no—
33#462×C113—22no—
34#462×C113C2214yes—
35#431×C113C2211yescharacteristic
36#431×C113C2211yescharacteristic
37C2×C4⋊C8×C113C2211yescharacteristic
38C2×#103×C113—21no—
39#332×C113C2212yes—
40#331×C113C2212yes—
41Q8⋊C8×C113C2214yes—
42Q8⋊C8×C113C2214yes—
43C2×#41×C113—21no—
44C22×Q8×C113—21no—
45C22×Q8×C113D411yescharacteristic
46C2×Q16×C113—24no—
47C2×Q16×C113—44no—
48C22×C8×C113—21no—
49C4⋊Q8×C113—22no—
50C4⋊Q8×C113—21no—
51C4⋊Q8×C113—21no—
52C4⋊Q8×C113—21no—
53C4⋊Q8×C113D411yescharacteristic
54C4⋊Q8×C113D411yescharacteristic
55C4⋊Q8×C113C2312yes—
56C4⋊Q8×C113C2311yescharacteristic
57#127×C113C2311yescharacteristic
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#123×C113—24no—
67#123×C113—24no—
68C22⋊Q8×C113—22no—
69C22⋊Q8×C113—22no—
70C22⋊Q8×C113—24no—
71C22⋊Q8×C113—21no—
72C22⋊Q8×C113D412yes—
73#121×C113—21no—
74#121×C113D412yes—
75C4×Q8×C113—22no—
76C4×Q8×C113—22no—
77C4×Q8×C113—21no—
78C4×Q8×C113—21no—
79C4×Q8×C113—21no—
80C4×Q8×C113D412yes—
81C4×Q8×C113C2312yes—
82C4×Q8×C113C2312yes—
83C4×D4×C113—24no—
84C4×D4×C113—22no—
85C4×D4×C113—22no—
86C4×D4×C113—21no—
87C4×D4×C113D412yes—
88#117×C113—22no—
89#117×C113—24no—
90#117×C113—21no—
91C2×C4⋊C4×C113—22no—
92C2×C4⋊C4×C113—21no—
93C2×C4⋊C4×C113—21no—
94C2×C4⋊C4×C113—21no—
95C2×C4⋊C4×C113D411yescharacteristic
96C2×C42×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—
111#41×C113—42no—
112#41×C113—42no—
113C2×Q8×C113—21no—
114C2×Q8×C113—21no—
115C2×Q8×C113—21no—
116C2×Q8×C113—22no—
117C2×Q8×C113—22no—
118C2×Q8×C113—22no—
119C2×Q8×C113—41no—
120C2×Q8×C113—42no—
121C2×Q8×C113—42no—
122C2×Q8×C113C2×D412yes—
123C2×Q8×C113C2×D412yes—
124C2×D4×C113—22no—
125C2×D4×C113—21no—
126C2×D4×C113—21no—
127C2×D4×C113C2×D412yes—
128C22×C4×C113—21no—
129C22×C4×C113—24no—
130C22×C4×C113—21no—
131C22×C4×C113—22no—
132C22×C4×C113—41no—
133C22×C4×C113C2×D411yescharacteristic
134C22×C4×C113C2×D411yescharacteristic
135C22×C4×C113C2×D411yescharacteristic
136Q16×C113—48no—
137C2×C8×C113—22no—
138C2×C8×C113—22no—
139C2×C8×C113—22no—
140C2×C8×C113—42no—
141C4⋊C4×C113—24no—
142C4⋊C4×C113—24no—
143C4⋊C4×C113—24no—
144C4⋊C4×C113—21no—
145C4⋊C4×C113—21no—
146C4⋊C4×C113—22no—
147C4⋊C4×C113—21no—
148C4⋊C4×C113—22no—
149C4⋊C4×C113—21no—
150C4⋊C4×C113—22no—
151C4⋊C4×C113—21no—
152C4⋊C4×C113—22no—
153C4⋊C4×C113—22no—
154C4⋊C4×C113—22no—
155C4⋊C4×C113—41no—
156C4⋊C4×C113—41no—
157C4⋊C4×C113C2×D412yes—
158C4⋊C4×C113C2×D412yes—
159C4⋊C4×C113C2×D412yes—
160C22⋊C4×C113—24no—
161C22⋊C4×C113—24no—
162C22⋊C4×C113—24no—
163C22⋊C4×C113—22no—
164C22⋊C4×C113—22no—
165C22⋊C4×C113—22no—
166C42×C113—24no—
167C42×C113—22no—
168C42×C113—22no—
169C42×C113—22no—
170C42×C113C2×D411yescharacteristic
171C42×C113C2×D411yescharacteristic
172C42×C113C2×D411yescharacteristic
173C42×C113C2411yescharacteristic
174C23×C113—22no—
175C23×C113#12011yescharacteristic
176Q8×C113—22no—
177Q8×C113—22no—
178Q8×C113—24no—
179Q8×C113—41no—
180Q8×C113—41no—
181Q8×C113—42no—
182Q8×C113—42no—
183Q8×C113—42no—
184Q8×C113—81no—
185Q8×C113—82no—
186D4×C113—42no—
187D4×C113—44no—
188D4×C113—41no—
189D4×C113—41no—
190D4×C113—42no—
191C2×C4×C113—22no—
192C2×C4×C113—22no—
193C2×C4×C113—22no—
194C2×C4×C113—22no—
195C2×C4×C113—22no—
196C2×C4×C113—22no—
197C2×C4×C113—41no—
198C2×C4×C113—42no—
199C2×C4×C113—44no—
200C2×C4×C113—42no—
201C2×C4×C113—81no—
202C2×C4×C113—84no—
203C2×C4×C113—82no—
204C2×C4×C113#12011yescharacteristic
205C2×C4×C113#12011yescharacteristic
206C2×C4×C113#12011yescharacteristic
207C2×C4×C113#13512yes—
208C2×C4×C113AGL(1,ℤ/8)12yes—
209C2×C4×C113C22×D411yescharacteristic
210C2×C4×C113C22×D411yescharacteristic
211C2×C4×C113C22×D411yescharacteristic
212C8×C113—42no—
213C8×C113—42no—
214C8×C113—42no—
215C22×C113—21no—
216C22×C113—21no—
217C22×C113—42no—
218C22×C113—42no—
219C22×C113—42no—
220C22×C113#44912yes—
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—42no—
230C4×C113—82no—
231C4×C113#44912yes—
232C4×C113C2×#13511yescharacteristic
233C4×C113C2×AGL(1,ℤ/8)11yescharacteristic
234C4×C113#57812yes—
235#18906C11311yesmaximal, characteristic, direct product factor, Sylow
236C2×C113—22no—
237C2×C113—82no—
238C2×C113C2×#44911yescharacteristic
239C2×C113#301111yescharacteristic
240C2×C113#302211yescharacteristic
241#3507C2×C11311yescharacteristic
242#3229C2×C11311yescharacteristic, complemented
243#3226C2×C11311yescharacteristic
244C2×#462C2×C11311yescharacteristic, complemented
245#1648C2×C11314yescomplemented
246#1640C2×C11314yescomplemented
247#1540C2×C11311yescharacteristic
248#1481C2×C11311yescharacteristic, complemented
249#1479C2×C11311yescharacteristic, complemented
250C113#1890611yescharacteristic, direct product factor, Sylow
251C22×Q16—21no—
252#559C22×C11312yes—
253#557C22×C11312yes—
254#556—21no—
255#556—22no—
256#554—21no—
257#552—22no—
258#539—22no—
259#536—21no—
260#533C22×C11311yescharacteristic
261#532C22×C11311yescharacteristic
262C2×C4⋊Q8C22×C11311yescharacteristic
263#529—22no—
264#520—21no—
265C2×C4×Q8C22×C11311yescharacteristic
266#500C22×C11312yes—
267#498—21no—
268#487—21no—
269#486C22×C11312yes—
270#483—22no—
271#480—22no—
272#475C22×C11314yes—
273#474—22no—
274#462—22no—
275#462C22×C11314yes—
276#431C22×C11311yescharacteristic
277#431C22×C11311yescharacteristic
278C2×C4⋊C8C22×C11311yescharacteristic
279C2×#103—21no—
280#332C22×C11312yes—
281#331C22×C11312yes—
282Q8⋊C8C22×C11314yes—
283Q8⋊C8C22×C11314yes—
284C2×#41—21no—
285C22×Q8—21no—
286C22×Q8D4×C11311yescharacteristic
287C2×Q16—24no—
288C2×Q16—44no—
289C22×C8—21no—
290C4⋊Q8—22no—
291C4⋊Q8—21no—
292C4⋊Q8—21no—
293C4⋊Q8—21no—
294C4⋊Q8D4×C11311yescharacteristic
295C4⋊Q8D4×C11311yescharacteristic
296C4⋊Q8C23×C11312yes—
297C4⋊Q8C23×C11311yescharacteristic
298#127C23×C11311yescharacteristic
299#126—24no—
300#126—24no—
301#125—22no—
302#125—24no—
303#125—21no—
304#124—22no—
305#124—22no—
306#124—21no—
307#123—24no—
308#123—24no—
309C22⋊Q8—22no—
310C22⋊Q8—22no—
311C22⋊Q8—24no—
312C22⋊Q8—21no—
313C22⋊Q8D4×C11312yes—
314#121—21no—
315#121D4×C11312yes—
316C4×Q8—22no—
317C4×Q8—22no—
318C4×Q8—21no—
319C4×Q8—21no—
320C4×Q8—21no—
321C4×Q8D4×C11312yes—
322C4×Q8C23×C11312yes—
323C4×Q8C23×C11312yes—
324C4×D4—24no—
325C4×D4—22no—
326C4×D4—22no—
327C4×D4—21no—
328C4×D4D4×C11312yes—
329#117—22no—
330#117—24no—
331#117—21no—
332C2×C4⋊C4—22no—
333C2×C4⋊C4—21no—
334C2×C4⋊C4—21no—
335C2×C4⋊C4—21no—
336C2×C4⋊C4D4×C11311yescharacteristic
337C2×C42—21no—
338C2×C42C23×C11311yescharacteristic
339#107—24no—
340#106—24no—
341C4⋊C8—21no—
342C4⋊C8—21no—
343C4⋊C8C23×C11312yes—
344C4⋊C8C23×C11312yes—
345#103—24no—
346#103—24no—
347#102—24no—
348C22⋊C8—21no—
349C22⋊C8—21no—
350C4×C8—21no—
351C4×C8C23×C11312yes—
352#41—42no—
353#41—42no—
354C2×Q8—21no—
355C2×Q8—21no—
356C2×Q8—21no—
357C2×Q8—22no—
358C2×Q8—22no—
359C2×Q8—22no—
360C2×Q8—41no—
361C2×Q8—42no—
362C2×Q8—42no—
363C2×Q8C2×D4×C11312yes—
364C2×Q8C2×D4×C11312yes—
365C2×D4—22no—
366C2×D4—21no—
367C2×D4—21no—
368C2×D4C2×D4×C11312yes—
369C22×C4—21no—
370C22×C4—24no—
371C22×C4—21no—
372C22×C4—22no—
373C22×C4—41no—
374C22×C4C2×D4×C11311yescharacteristic
375C22×C4C2×D4×C11311yescharacteristic
376C22×C4C2×D4×C11311yescharacteristic
377Q16—48no—
378C2×C8—22no—
379C2×C8—22no—
380C2×C8—22no—
381C2×C8—42no—
382C4⋊C4—24no—
383C4⋊C4—24no—
384C4⋊C4—24no—
385C4⋊C4—21no—
386C4⋊C4—21no—
387C4⋊C4—22no—
388C4⋊C4—21no—
389C4⋊C4—22no—
390C4⋊C4—21no—
391C4⋊C4—22no—
392C4⋊C4—21no—
393C4⋊C4—22no—
394C4⋊C4—22no—
395C4⋊C4—22no—
396C4⋊C4—41no—
397C4⋊C4—41no—
398C4⋊C4C2×D4×C11312yes—
399C4⋊C4C2×D4×C11312yes—
400C4⋊C4C2×D4×C11312yes—
401C22⋊C4—24no—
402C22⋊C4—24no—
403C22⋊C4—24no—
404C22⋊C4—22no—
405C22⋊C4—22no—
406C22⋊C4—22no—
407C42—24no—
408C42—22no—
409C42—22no—
410C42—22no—
411C42C2×D4×C11311yescharacteristic
412C42C2×D4×C11311yescharacteristic
413C42C2×D4×C11311yescharacteristic
414C42C24×C11311yescharacteristic
415C23—22no—
416C23#120×C11311yescharacteristic
417Q8—22no—
418Q8—22no—
419Q8—24no—
420Q8—41no—
421Q8—41no—
422Q8—42no—
423Q8—42no—
424Q8—42no—
425Q8—81no—
426Q8—82no—
427D4—42no—
428D4—44no—
429D4—41no—
430D4—41no—
431D4—42no—
432C2×C4—22no—
433C2×C4—22no—
434C2×C4—22no—
435C2×C4—22no—
436C2×C4—22no—
437C2×C4—22no—
438C2×C4—41no—
439C2×C4—42no—
440C2×C4—44no—
441C2×C4—42no—
442C2×C4—81no—
443C2×C4—84no—
444C2×C4—82no—
445C2×C4#120×C11311yescharacteristic
446C2×C4#120×C11311yescharacteristic
447C2×C4#120×C11311yescharacteristic
448C2×C4#135×C11312yes—
449C2×C4AGL(1,ℤ/8)×C11312yes—
450C2×C4C22×D4×C11311yescharacteristic
451C2×C4C22×D4×C11311yescharacteristic
452C2×C4C22×D4×C11311yescharacteristic
453C8—42no—
454C8—42no—
455C8—42no—
456C22—21no—
457C22—21no—
458C22—42no—
459C22—42no—
460C22—42no—
461C22#449×C11312yes—
462C22C2×#120×C11311yescharacteristic
463C4—21no—
464C4—21no—
465C4—21no—
466C4—42no—
467C4—42no—
468C4—42no—
469C4—42no—
470C4—42no—
471C4—82no—
472C4#449×C11312yes—
473C4C2×#135×C11311yescharacteristic
474C4C2×AGL(1,ℤ/8)×C11311yescharacteristic
475C4#578×C11312yes—
476C2—22no—
477C2—82no—
478C2C2×#449×C11311yescharacteristic
479C2C113×#301111yescharacteristic
480C2C113×#302211yescharacteristic
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×#3229C2semidirect
4. C2×#462×C113C2semidirect
5. C113×#1648C2semidirect
6. C113×#1640C2semidirect
8. C113×#1481C2semidirect
9. C113×#1479C2semidirect
235. #18906C113direct (N × H)
242. #3229C2×C113semidirect
244. C2×#462C2×C113semidirect
245. #1648C2×C113semidirect
246. #1640C2×C113semidirect
248. #1481C2×C113semidirect
249. #1479C2×C113semidirect
250. C113#18906direct (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×#32292
C113×#32262
C2×#462×C1132
C113×#16482
C113×#16402
C113×#15402
C113×#14812
C113×#14792
#18906113