Finite Group Databasebeta

← C113×#18898 #43286918

Subgroups — C113×#18898 #43286918

Order 28928.

978 conjugacy classes of subgroups.

The subgroup lattice has 508 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C113×#3507C211yesmaximal, characteristic, complemented
2C113×#3208C211yesmaximal, characteristic, complemented
3C113×#3205C211yesmaximal, characteristic
4C2×#460×C113C211yesmaximal, characteristic, complemented
5C113×#1628C214yesmaximal, complemented
6C113×#1622C214yesmaximal, complemented
7C113×#1542C211yesmaximal, characteristic, complemented
8C113×#1480C211yesmaximal, characteristic, complemented
9C113×#1479C211yesmaximal, characteristic, complemented
10C22×SD16×C113—21no—
11#559×C113—21no—
12#557×C113—21no—
13#556×C113—22no—
14#556×C113C2212yescomplemented
15#554×C113C2212yescomplemented
16#552×C113—22no—
17#539×C113—22no—
18#536×C113—21no—
19#533×C113C2211yescharacteristic
20#532×C113C2211yescharacteristic
21C2×#127×C113C2211yescharacteristic
22#529×C113—22no—
23#520×C113—21no—
24C2×C4×Q8×C113C2211yescharacteristic
25#493×C113—21no—
26#492×C113C2212yes—
27#486×C113—21no—
28#486×C113C2212yes—
29#460×C113—22no—
30#460×C113—22no—
31#460×C113C2214yes—
32#459×C113C2214yes—
33#450×C113—22no—
34#447×C113—22no—
35#431×C113C2211yescharacteristic
36#431×C113C2211yescharacteristic
37C2×C4⋊C8×C113C2211yescharacteristic
38C2×#102×C113—21no—
39#333×C113C2212yescomplemented
40#332×C113C2212yescomplemented
41Q8⋊C8×C113C2214yescomplemented
42D4⋊C8×C113C2214yescomplemented
43C2×#41×C113—21no—
44C22×Q8×C113D411yescharacteristic
45C22×D4×C113—21no—
46C22×D4×C113—21no—
47C22×D4×C113—21no—
48C2×SD16×C113—24no—
49C2×SD16×C113—24no—
50C2×SD16×C113—44no—
51C2×D8×C113—24no—
52C22×C8×C113—21no—
53C4⋊Q8×C113—22no—
54C4⋊Q8×C113D411yescharacteristic
55C4⋊Q8×C113C2311yescharacteristic
56C4⋊Q8×C113C2311yescharacteristic
57#127×C113—21no—
58#127×C113—21no—
59#127×C113—21no—
60#127×C113D411yescharacteristic
61#127×C113C2312yes—
62#126×C113—24no—
63#126×C113—24no—
64#125×C113—24no—
65#125×C113—22no—
66#125×C113—21no—
67#124×C113—22no—
68#124×C113—22no—
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×C113D412yes—
77#121×C113—21no—
78#121×C113D412yes—
79C4×Q8×C113—22no—
80C4×Q8×C113—22no—
81C4×Q8×C113—21no—
82C4×Q8×C113—21no—
83C4×Q8×C113—21no—
84C4×Q8×C113D412yes—
85C4×Q8×C113D412yes—
86C4×Q8×C113C2312yes—
87C4×D4×C113—24no—
88C4×D4×C113—22no—
89C4×D4×C113—22no—
90C4×D4×C113—21no—
91C4×D4×C113C2312yes—
92#117×C113—24no—
93#117×C113—21no—
94#117×C113—22no—
95C2×C4⋊C4×C113—21no—
96C2×C4⋊C4×C113—22no—
97C2×C4⋊C4×C113D411yescharacteristic
98C2×C42×C113—21no—
99C2×C42×C113C2311yescharacteristic
100C4⋊C8×C113—21no—
101C4⋊C8×C113—21no—
102C4⋊C8×C113C2312yes—
103C4⋊C8×C113C2312yes—
104#102×C113—24no—
105#102×C113—24no—
106#102×C113—24no—
107C22⋊C8×C113—21no—
108C22⋊C8×C113—21no—
109C4×C8×C113—21no—
110C4×C8×C113C2312yes—
111C24×C113—41no—
112#41×C113—42no—
113#41×C113—42no—
114C2×Q8×C113—21no—
115C2×Q8×C113—21no—
116C2×Q8×C113—21no—
117C2×Q8×C113—22no—
118C2×Q8×C113—22no—
119C2×Q8×C113C2×D412yes—
120C2×Q8×C113C2×D412yes—
121C2×D4×C113—22no—
122C2×D4×C113—21no—
123C2×D4×C113—21no—
124C2×D4×C113—22no—
125C2×D4×C113—22no—
126C2×D4×C113—22no—
127C2×D4×C113—41no—
128C2×D4×C113—41no—
129C2×D4×C113—41no—
130C2×D4×C113—42no—
131C2×D4×C113—42no—
132C2×D4×C113—82no—
133C2×D4×C113—82no—
134C2×D4×C113C2×D412yes—
135C22×C4×C113—21no—
136C22×C4×C113—24no—
137C22×C4×C113—21no—
138C22×C4×C113—22no—
139C22×C4×C113C2×D411yescharacteristic
140C22×C4×C113C2×D411yescharacteristic
141C22×C4×C113C2×D411yescharacteristic
142SD16×C113—48no—
143SD16×C113—84no—
144D8×C113—84no—
145C2×C8×C113—22no—
146C2×C8×C113—22no—
147C2×C8×C113—22no—
148C2×C8×C113—42no—
149C4⋊C4×C113—24no—
150C4⋊C4×C113—24no—
151C4⋊C4×C113—24no—
152C4⋊C4×C113—22no—
153C4⋊C4×C113—21no—
154C4⋊C4×C113—22no—
155C4⋊C4×C113—21no—
156C4⋊C4×C113—22no—
157C4⋊C4×C113—21no—
158C4⋊C4×C113—22no—
159C4⋊C4×C113—21no—
160C4⋊C4×C113—21no—
161C4⋊C4×C113C2×D412yes—
162C4⋊C4×C113C2×D412yes—
163C4⋊C4×C113C2×D412yes—
164C22⋊C4×C113—24no—
165C22⋊C4×C113—24no—
166C22⋊C4×C113—24no—
167C22⋊C4×C113—22no—
168C22⋊C4×C113—22no—
169C22⋊C4×C113—22no—
170C42×C113—24no—
171C42×C113—22no—
172C42×C113—22no—
173C42×C113—22no—
174C42×C113C2×D411yescharacteristic
175C42×C113C2×D411yescharacteristic
176C42×C113C2×D411yescharacteristic
177C42×C113C2411yescharacteristic
178C23×C113—22no—
179C23×C113—42no—
180C23×C113—82no—
181C23×C113—82no—
182C23×C113—82no—
183C23×C113#12011yescharacteristic
184Q8×C113—22no—
185Q8×C113—22no—
186Q8×C113—42no—
187Q8×C113—42no—
188Q8×C113—42no—
189Q8×C113—42no—
190D4×C113—24no—
191D4×C113—44no—
192D4×C113—44no—
193D4×C113—42no—
194D4×C113—42no—
195D4×C113—44no—
196D4×C113—42no—
197D4×C113—81no—
198D4×C113—82no—
199D4×C113—82no—
200D4×C113—82no—
201C2×C4×C113—22no—
202C2×C4×C113—22no—
203C2×C4×C113—22no—
204C2×C4×C113—22no—
205C2×C4×C113—22no—
206C2×C4×C113—22no—
207C2×C4×C113—41no—
208C2×C4×C113—42no—
209C2×C4×C113—42no—
210C2×C4×C113—42no—
211C2×C4×C113—81no—
212C2×C4×C113—84no—
213C2×C4×C113#12011yescharacteristic
214C2×C4×C113#12011yescharacteristic
215C2×C4×C113#12011yescharacteristic
216C2×C4×C113#13512yes—
217C2×C4×C113AGL(1,ℤ/8)12yes—
218C2×C4×C113C22×D411yescharacteristic
219C2×C4×C113C22×D411yescharacteristic
220C2×C4×C113C22×D411yescharacteristic
221C8×C113—42no—
222C8×C113—42no—
223C8×C113—42no—
224C22×C113—21no—
225C22×C113—21no—
226C22×C113—42no—
227C22×C113—42no—
228C22×C113—42no—
229C22×C113—82no—
230C22×C113—82no—
231C22×C113—82no—
232C22×C113—164no—
233C22×C113#44912yes—
234C22×C113C2×#12011yescharacteristic
235C4×C113—21no—
236C4×C113—21no—
237C4×C113—21no—
238C4×C113—42no—
239C4×C113—42no—
240C4×C113—42no—
241C4×C113—42no—
242C4×C113—42no—
243C4×C113#44912yes—
244C4×C113C2×#13511yescharacteristic
245C4×C113C2×AGL(1,ℤ/8)11yescharacteristic
246C4×C113#57712yes—
247#18898C11311yesmaximal, characteristic, direct product factor, Sylow
248C2×C113—22no—
249C2×C113—82no—
250C2×C113—162no—
251C2×C113C2×#44911yescharacteristic
252C2×C113#301011yescharacteristic
253C2×C113#302111yescharacteristic
254#3507C2×C11311yescharacteristic, complemented
255#3208C2×C11311yescharacteristic, complemented
256#3205C2×C11311yescharacteristic
257C2×#460C2×C11311yescharacteristic, complemented
258#1628C2×C11314yescomplemented
259#1622C2×C11314yescomplemented
260#1542C2×C11311yescharacteristic, complemented
261#1480C2×C11311yescharacteristic, complemented
262#1479C2×C11311yescharacteristic, complemented
263C113#1889811yescharacteristic, direct product factor, Sylow
264C22×SD16—21no—
265#559—21no—
266#557—21no—
267#556—22no—
268#556C22×C11312yescomplemented
269#554C22×C11312yescomplemented
270#552—22no—
271#539—22no—
272#536—21no—
273#533C22×C11311yescharacteristic
274#532C22×C11311yescharacteristic
275C2×#127C22×C11311yescharacteristic
276#529—22no—
277#520—21no—
278C2×C4×Q8C22×C11311yescharacteristic
279#493—21no—
280#492C22×C11312yes—
281#486—21no—
282#486C22×C11312yes—
283#460—22no—
284#460—22no—
285#460C22×C11314yes—
286#459C22×C11314yes—
287#450—22no—
288#447—22no—
289#431C22×C11311yescharacteristic
290#431C22×C11311yescharacteristic
291C2×C4⋊C8C22×C11311yescharacteristic
292C2×#102—21no—
293#333C22×C11312yescomplemented
294#332C22×C11312yescomplemented
295Q8⋊C8C22×C11314yescomplemented
296D4⋊C8C22×C11314yescomplemented
297C2×#41—21no—
298C22×Q8D4×C11311yescharacteristic
299C22×D4—21no—
300C22×D4—21no—
301C22×D4—21no—
302C2×SD16—24no—
303C2×SD16—24no—
304C2×SD16—44no—
305C2×D8—24no—
306C22×C8—21no—
307C4⋊Q8—22no—
308C4⋊Q8D4×C11311yescharacteristic
309C4⋊Q8C23×C11311yescharacteristic
310C4⋊Q8C23×C11311yescharacteristic
311#127—21no—
312#127—21no—
313#127—21no—
314#127D4×C11311yescharacteristic
315#127C23×C11312yes—
316#126—24no—
317#126—24no—
318#125—24no—
319#125—22no—
320#125—21no—
321#124—22no—
322#124—22no—
323#124—21no—
324#123—24no—
325#123—24no—
326C22⋊Q8—22no—
327C22⋊Q8—22no—
328C22⋊Q8—24no—
329C22⋊Q8—21no—
330C22⋊Q8D4×C11312yes—
331#121—21no—
332#121D4×C11312yes—
333C4×Q8—22no—
334C4×Q8—22no—
335C4×Q8—21no—
336C4×Q8—21no—
337C4×Q8—21no—
338C4×Q8D4×C11312yes—
339C4×Q8D4×C11312yes—
340C4×Q8C23×C11312yes—
341C4×D4—24no—
342C4×D4—22no—
343C4×D4—22no—
344C4×D4—21no—
345C4×D4C23×C11312yes—
346#117—24no—
347#117—21no—
348#117—22no—
349C2×C4⋊C4—21no—
350C2×C4⋊C4—22no—
351C2×C4⋊C4D4×C11311yescharacteristic
352C2×C42—21no—
353C2×C42C23×C11311yescharacteristic
354C4⋊C8—21no—
355C4⋊C8—21no—
356C4⋊C8C23×C11312yes—
357C4⋊C8C23×C11312yes—
358#102—24no—
359#102—24no—
360#102—24no—
361C22⋊C8—21no—
362C22⋊C8—21no—
363C4×C8—21no—
364C4×C8C23×C11312yes—
365C24—41no—
366#41—42no—
367#41—42no—
368C2×Q8—21no—
369C2×Q8—21no—
370C2×Q8—21no—
371C2×Q8—22no—
372C2×Q8—22no—
373C2×Q8C2×D4×C11312yes—
374C2×Q8C2×D4×C11312yes—
375C2×D4—22no—
376C2×D4—21no—
377C2×D4—21no—
378C2×D4—22no—
379C2×D4—22no—
380C2×D4—22no—
381C2×D4—41no—
382C2×D4—41no—
383C2×D4—41no—
384C2×D4—42no—
385C2×D4—42no—
386C2×D4—82no—
387C2×D4—82no—
388C2×D4C2×D4×C11312yes—
389C22×C4—21no—
390C22×C4—24no—
391C22×C4—21no—
392C22×C4—22no—
393C22×C4C2×D4×C11311yescharacteristic
394C22×C4C2×D4×C11311yescharacteristic
395C22×C4C2×D4×C11311yescharacteristic
396SD16—48no—
397SD16—84no—
398D8—84no—
399C2×C8—22no—
400C2×C8—22no—
401C2×C8—22no—
402C2×C8—42no—
403C4⋊C4—24no—
404C4⋊C4—24no—
405C4⋊C4—24no—
406C4⋊C4—22no—
407C4⋊C4—21no—
408C4⋊C4—22no—
409C4⋊C4—21no—
410C4⋊C4—22no—
411C4⋊C4—21no—
412C4⋊C4—22no—
413C4⋊C4—21no—
414C4⋊C4—21no—
415C4⋊C4C2×D4×C11312yes—
416C4⋊C4C2×D4×C11312yes—
417C4⋊C4C2×D4×C11312yes—
418C22⋊C4—24no—
419C22⋊C4—24no—
420C22⋊C4—24no—
421C22⋊C4—22no—
422C22⋊C4—22no—
423C22⋊C4—22no—
424C42—24no—
425C42—22no—
426C42—22no—
427C42—22no—
428C42C2×D4×C11311yescharacteristic
429C42C2×D4×C11311yescharacteristic
430C42C2×D4×C11311yescharacteristic
431C42C24×C11311yescharacteristic
432C23—22no—
433C23—42no—
434C23—82no—
435C23—82no—
436C23—82no—
437C23#120×C11311yescharacteristic
438Q8—22no—
439Q8—22no—
440Q8—42no—
441Q8—42no—
442Q8—42no—
443Q8—42no—
444D4—24no—
445D4—44no—
446D4—44no—
447D4—42no—
448D4—42no—
449D4—44no—
450D4—42no—
451D4—81no—
452D4—82no—
453D4—82no—
454D4—82no—
455C2×C4—22no—
456C2×C4—22no—
457C2×C4—22no—
458C2×C4—22no—
459C2×C4—22no—
460C2×C4—22no—
461C2×C4—41no—
462C2×C4—42no—
463C2×C4—42no—
464C2×C4—42no—
465C2×C4—81no—
466C2×C4—84no—
467C2×C4#120×C11311yescharacteristic
468C2×C4#120×C11311yescharacteristic
469C2×C4#120×C11311yescharacteristic
470C2×C4#135×C11312yes—
471C2×C4AGL(1,ℤ/8)×C11312yes—
472C2×C4C22×D4×C11311yescharacteristic
473C2×C4C22×D4×C11311yescharacteristic
474C2×C4C22×D4×C11311yescharacteristic
475C8—42no—
476C8—42no—
477C8—42no—
478C22—21no—
479C22—21no—
480C22—42no—
481C22—42no—
482C22—42no—
483C22—82no—
484C22—82no—
485C22—82no—
486C22—164no—
487C22#449×C11312yes—
488C22C2×#120×C11311yescharacteristic
489C4—21no—
490C4—21no—
491C4—21no—
492C4—42no—
493C4—42no—
494C4—42no—
495C4—42no—
496C4—42no—
497C4#449×C11312yes—
498C4C2×#135×C11311yescharacteristic
499C4C2×AGL(1,ℤ/8)×C11311yescharacteristic
500C4#577×C11312yes—
501C2—22no—
502C2—82no—
503C2—162no—
504C2C2×#449×C11311yescharacteristic
505C2C113×#301011yescharacteristic
506C2C113×#302111yescharacteristic
subgroupG/H
center, socleC22×C113C2×#120
commutator, Frattini, cosocleC42C24×C113
prime radicalC113×#3205C2
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
1. C113×#3507C2semidirect
2. C113×#3208C2semidirect
4. C2×#460×C113C2semidirect
5. C113×#1628C2semidirect
6. C113×#1622C2semidirect
7. C113×#1542C2semidirect
8. C113×#1480C2semidirect
9. C113×#1479C2semidirect
14. #556×C113C22semidirect
15. #554×C113C22semidirect
39. #333×C113C22semidirect
40. #332×C113C22semidirect
41. Q8⋊C8×C113C22semidirect
42. D4⋊C8×C113C22semidirect
247. #18898C113direct (N × H)
254. #3507C2×C113semidirect
255. #3208C2×C113semidirect
257. C2×#460C2×C113semidirect
258. #1628C2×C113semidirect
259. #1622C2×C113semidirect
260. #1542C2×C113semidirect
261. #1480C2×C113semidirect
262. #1479C2×C113semidirect
263. C113#18898direct (N × H)
268. #556C22×C113semidirect
269. #554C22×C113semidirect
293. #333C22×C113semidirect
294. #332C22×C113semidirect
295. Q8⋊C8C22×C113semidirect
296. D4⋊C8C22×C113semidirect

Maximal subgroups

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

subgroupindex
C113×#35072
C113×#32082
C113×#32052
C2×#460×C1132
C113×#16282
C113×#16222
C113×#15422
C113×#14802
C113×#14792
#18898113