Finite Group Databasebeta

← C113×#2418 #28387214

Subgroups — C113×#2418 #28387214

Order 14464.

800 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#123×C113C211yesmaximal, characteristic, complemented
2C2×#120×C113C211yesmaximal, characteristic
3C2×C4×D4×C113C211yesmaximal, characteristic, complemented
4C22×C22⋊C4×C113C211yesmaximal, characteristic, complemented
5#399×C113C211yesmaximal, characteristic, complemented
6#397×C113C211yesmaximal, characteristic, complemented
7#394×C113C211yesmaximal, characteristic, complemented
8#394×C113C211yesmaximal, characteristic, complemented
9#388×C113C211yesmaximal, characteristic, complemented
10#388×C113C211yesmaximal, characteristic, complemented
11#386×C113C211yesmaximal, characteristic, complemented
12#386×C113C211yesmaximal, characteristic, complemented
13#385×C113C211yesmaximal, characteristic, complemented
14#380×C113C211yesmaximal, characteristic, complemented
15#379×C113C211yesmaximal, characteristic, complemented
16C25×C113C2211yescharacteristic
17C22×D4×C113C2211yescharacteristic
18C22×D4×C113C2211yescharacteristic
19C22×D4×C113C2211yescharacteristic
20C23×C4×C113C2211yescharacteristic
21C23×C4×C113C2211yescharacteristic
22C23×C4×C113C2211yescharacteristic, complemented
23#123×C113—24no—
24#120×C113—24no—
25C4×D4×C113—24no—
26C2×C4⋊C4×C113C2211yescharacteristic, complemented
27C2×C4⋊C4×C113C2211yescharacteristic, complemented
28C2×C4⋊C4×C113C2211yescharacteristic, complemented
29C2×C4⋊C4×C113C2211yescharacteristic, complemented
30C2×C4⋊C4×C113C2211yescharacteristic, complemented
31C2×C22⋊C4×C113—24no—
32C2×C22⋊C4×C113C2211yescharacteristic
33C2×C22⋊C4×C113C2211yescharacteristic
34C2×C22⋊C4×C113C2211yescharacteristic
35C2×C22⋊C4×C113C2211yescharacteristic
36C2×C22⋊C4×C113C2211yescharacteristic
37C2×C22⋊C4×C113C2211yescharacteristic
38C2×C22⋊C4×C113C2211yescharacteristic
39C2×C22⋊C4×C113C2211yescharacteristic
40C2×C22⋊C4×C113C2211yescharacteristic
41C2×C22⋊C4×C113C2211yescharacteristic
42C2×C22⋊C4×C113C2211yescharacteristic
43C2×C22⋊C4×C113C2211yescharacteristic
44C2×C22⋊C4×C113C2211yescharacteristic
45C2×C22⋊C4×C113C2211yescharacteristic, complemented
46C2×C22⋊C4×C113C2211yescharacteristic, complemented
47C2×C22⋊C4×C113C2211yescharacteristic, complemented
48C2×C42×C113C2211yescharacteristic, complemented
49#95×C113C2211yescharacteristic, complemented
50#95×C113C2211yescharacteristic, complemented
51#95×C113C2211yescharacteristic, complemented
52#95×C113C2211yescharacteristic, complemented
53#95×C113C2211yescharacteristic, complemented
54#95×C113C2211yescharacteristic, complemented
55C24×C113—22no—
56C24×C113—22no—
57C24×C113—22no—
58C24×C113—22no—
59C24×C113—22no—
60C24×C113—41no—
61C24×C113—41no—
62C24×C113C2311yescharacteristic
63C24×C113C2311yescharacteristic
64C24×C113C2311yescharacteristic
65C24×C113C2311yescharacteristic
66C2×D4×C113—22no—
67C2×D4×C113—22no—
68C2×D4×C113—22no—
69C2×D4×C113—22no—
70C2×D4×C113—22no—
71C2×D4×C113—22no—
72C2×D4×C113—41no—
73C2×D4×C113—41no—
74C2×D4×C113D414yes—
75C22×C4×C113—22no—
76C22×C4×C113—22no—
77C22×C4×C113—22no—
78C22×C4×C113—22no—
79C22×C4×C113—22no—
80C22×C4×C113—22no—
81C22×C4×C113—41no—
82C22×C4×C113—41no—
83C22×C4×C113—41no—
84C22×C4×C113C2311yescharacteristic
85C22×C4×C113C2311yescharacteristic
86C22×C4×C113C2311yescharacteristic
87C22×C4×C113C2311yescharacteristic
88C22×C4×C113C2311yescharacteristic
89C22×C4×C113C2311yescharacteristic
90C22×C4×C113C2311yescharacteristic
91C22×C4×C113C2311yescharacteristic
92C22×C4×C113C2311yescharacteristic
93C22×C4×C113C2311yescharacteristic
94C22×C4×C113C2311yescharacteristic
95C4⋊C4×C113—22no—
96C4⋊C4×C113—22no—
97C4⋊C4×C113—22no—
98C4⋊C4×C113—41no—
99C4⋊C4×C113—41no—
100C22⋊C4×C113—22no—
101C22⋊C4×C113—22no—
102C22⋊C4×C113—22no—
103C22⋊C4×C113—22no—
104C22⋊C4×C113—22no—
105C22⋊C4×C113—22no—
106C22⋊C4×C113—22no—
107C22⋊C4×C113—22no—
108C22⋊C4×C113—22no—
109C22⋊C4×C113—22no—
110C22⋊C4×C113—22no—
111C22⋊C4×C113—22no—
112C22⋊C4×C113—41no—
113C22⋊C4×C113—41no—
114C22⋊C4×C113—41no—
115C22⋊C4×C113D414yescomplemented
116C42×C113—22no—
117C23×C113—21no—
118C23×C113—21no—
119C23×C113—21no—
120C23×C113—21no—
121C23×C113—28no—
122C23×C113—21no—
123C23×C113—21no—
124C23×C113—21no—
125C23×C113—21no—
126C23×C113—21no—
127C23×C113—21no—
128C23×C113—21no—
129C23×C113—21no—
130C23×C113—21no—
131C23×C113—21no—
132C23×C113—21no—
133C23×C113—21no—
134C23×C113—21no—
135C23×C113—21no—
136C23×C113—21no—
137C23×C113—21no—
138C23×C113—21no—
139C23×C113—21no—
140C23×C113—44no—
141C23×C113—44no—
142C23×C113—44no—
143C23×C113—44no—
144C23×C113—44no—
145C23×C113—44no—
146C23×C113C2×D412yes—
147C23×C113C2×D412yes—
148C23×C113C2×D412yes—
149C23×C113#4112yes—
150C23×C113#4112yes—
151C23×C113#4112yes—
152C23×C113C2411yescharacteristic
153D4×C113—28no—
154D4×C113—44no—
155D4×C113—44no—
156C2×C4×C113—21no—
157C2×C4×C113—21no—
158C2×C4×C113—21no—
159C2×C4×C113—21no—
160C2×C4×C113—21no—
161C2×C4×C113—21no—
162C2×C4×C113—21no—
163C2×C4×C113—21no—
164C2×C4×C113—21no—
165C2×C4×C113—21no—
166C2×C4×C113—21no—
167C2×C4×C113—21no—
168C2×C4×C113—21no—
169C2×C4×C113—21no—
170C2×C4×C113—21no—
171C2×C4×C113—21no—
172C2×C4×C113—21no—
173C2×C4×C113—21no—
174C2×C4×C113—21no—
175C2×C4×C113—21no—
176C2×C4×C113—21no—
177C2×C4×C113—21no—
178C2×C4×C113—21no—
179C2×C4×C113—21no—
180C2×C4×C113—21no—
181C2×C4×C113—21no—
182C2×C4×C113—21no—
183C2×C4×C113—21no—
184C2×C4×C113—21no—
185C2×C4×C113—21no—
186C2×C4×C113—44no—
187C2×C4×C113—44no—
188C2×C4×C113—44no—
189C2×C4×C113C2×D412yes—
190C2×C4×C113C2×D412yes—
191C2×C4×C113C2×D412yes—
192C22×C113—22no—
193C22×C113—22no—
194C22×C113—22no—
195C22×C113—22no—
196C22×C113—22no—
197C22×C113—22no—
198C22×C113—22no—
199C22×C113—22no—
200C22×C113—22no—
201C22×C113—22no—
202C22×C113—22no—
203C22×C113—22no—
204C22×C113—22no—
205C22×C113—22no—
206C22×C113—22no—
207C22×C113—416no—
208C22×C113—41no—
209C22×C113—41no—
210C22×C113—41no—
211C22×C113—41no—
212C22×C113—41no—
213C22×C113—41no—
214C22×C113—41no—
215C22×C113—41no—
216C22×C113—41no—
217C22×C113—41no—
218C22×C113—41no—
219C22×C113—41no—
220C22×C113#12314yescomplemented
221C22×C113C22×D411yescharacteristic
222C22×C113C22×D411yescharacteristic
223C22×C113C2×#4111yescharacteristic
224C22×C113C2×#4111yescharacteristic
225C22×C113C2×#4111yescharacteristic
226C22×C113H(5,𝔽2)11yescharacteristic
227C22×C113H(5,𝔽2)11yescharacteristic
228C4×C113—22no—
229C4×C113—22no—
230C4×C113—22no—
231C4×C113—41no—
232C4×C113—41no—
233C4×C113—41no—
234C4×C113—41no—
235C4×C113—41no—
236C4×C113—41no—
237C4×C113—41no—
238C4×C113—41no—
239C2×C113—24no—
240C2×C113—42no—
241C2×C113—42no—
242C2×C113—42no—
243C2×C113C2×#12311yescharacteristic
244C2×C113#52511yescharacteristic
245C2×C113#53811yescharacteristic
246C2×C113D4211yescharacteristic
247C2×C113#54611yescharacteristic
248C2×C113#54611yescharacteristic
249C2×C113#55111yescharacteristic
250#2418C11311yesmaximal, characteristic, direct product factor, Sylow
251C113#241811yescharacteristic, direct product factor, Sylow
252C2×#123C2×C11311yescharacteristic, complemented
253C2×#120C2×C11311yescharacteristic
254C2×C4×D4C2×C11311yescharacteristic, complemented
255C22×C22⋊C4C2×C11311yescharacteristic, complemented
256#399C2×C11311yescharacteristic, complemented
257#397C2×C11311yescharacteristic, complemented
258#394C2×C11311yescharacteristic, complemented
259#394C2×C11311yescharacteristic, complemented
260#388C2×C11311yescharacteristic, complemented
261#388C2×C11311yescharacteristic, complemented
262#386C2×C11311yescharacteristic, complemented
263#386C2×C11311yescharacteristic, complemented
264#385C2×C11311yescharacteristic, complemented
265#380C2×C11311yescharacteristic, complemented
266#379C2×C11311yescharacteristic, complemented
267C25C22×C11311yescharacteristic
268C22×D4C22×C11311yescharacteristic
269C22×D4C22×C11311yescharacteristic
270C22×D4C22×C11311yescharacteristic
271C23×C4C22×C11311yescharacteristic
272C23×C4C22×C11311yescharacteristic
273C23×C4C22×C11311yescharacteristic, complemented
274#123—24no—
275#120—24no—
276C4×D4—24no—
277C2×C4⋊C4C22×C11311yescharacteristic, complemented
278C2×C4⋊C4C22×C11311yescharacteristic, complemented
279C2×C4⋊C4C22×C11311yescharacteristic, complemented
280C2×C4⋊C4C22×C11311yescharacteristic, complemented
281C2×C4⋊C4C22×C11311yescharacteristic, complemented
282C2×C22⋊C4—24no—
283C2×C22⋊C4C22×C11311yescharacteristic
284C2×C22⋊C4C22×C11311yescharacteristic
285C2×C22⋊C4C22×C11311yescharacteristic
286C2×C22⋊C4C22×C11311yescharacteristic
287C2×C22⋊C4C22×C11311yescharacteristic
288C2×C22⋊C4C22×C11311yescharacteristic
289C2×C22⋊C4C22×C11311yescharacteristic
290C2×C22⋊C4C22×C11311yescharacteristic
291C2×C22⋊C4C22×C11311yescharacteristic
292C2×C22⋊C4C22×C11311yescharacteristic
293C2×C22⋊C4C22×C11311yescharacteristic
294C2×C22⋊C4C22×C11311yescharacteristic
295C2×C22⋊C4C22×C11311yescharacteristic
296C2×C22⋊C4C22×C11311yescharacteristic, complemented
297C2×C22⋊C4C22×C11311yescharacteristic, complemented
298C2×C22⋊C4C22×C11311yescharacteristic, complemented
299C2×C42C22×C11311yescharacteristic, complemented
300#95C22×C11311yescharacteristic, complemented
301#95C22×C11311yescharacteristic, complemented
302#95C22×C11311yescharacteristic, complemented
303#95C22×C11311yescharacteristic, complemented
304#95C22×C11311yescharacteristic, complemented
305#95C22×C11311yescharacteristic, complemented
306C24—22no—
307C24—22no—
308C24—22no—
309C24—22no—
310C24—22no—
311C24—41no—
312C24—41no—
313C24C23×C11311yescharacteristic
314C24C23×C11311yescharacteristic
315C24C23×C11311yescharacteristic
316C24C23×C11311yescharacteristic
317C2×D4—22no—
318C2×D4—22no—
319C2×D4—22no—
320C2×D4—22no—
321C2×D4—22no—
322C2×D4—22no—
323C2×D4—41no—
324C2×D4—41no—
325C2×D4D4×C11314yes—
326C22×C4—22no—
327C22×C4—22no—
328C22×C4—22no—
329C22×C4—22no—
330C22×C4—22no—
331C22×C4—22no—
332C22×C4—41no—
333C22×C4—41no—
334C22×C4—41no—
335C22×C4C23×C11311yescharacteristic
336C22×C4C23×C11311yescharacteristic
337C22×C4C23×C11311yescharacteristic
338C22×C4C23×C11311yescharacteristic
339C22×C4C23×C11311yescharacteristic
340C22×C4C23×C11311yescharacteristic
341C22×C4C23×C11311yescharacteristic
342C22×C4C23×C11311yescharacteristic
343C22×C4C23×C11311yescharacteristic
344C22×C4C23×C11311yescharacteristic
345C22×C4C23×C11311yescharacteristic
346C4⋊C4—22no—
347C4⋊C4—22no—
348C4⋊C4—22no—
349C4⋊C4—41no—
350C4⋊C4—41no—
351C22⋊C4—22no—
352C22⋊C4—22no—
353C22⋊C4—22no—
354C22⋊C4—22no—
355C22⋊C4—22no—
356C22⋊C4—22no—
357C22⋊C4—22no—
358C22⋊C4—22no—
359C22⋊C4—22no—
360C22⋊C4—22no—
361C22⋊C4—22no—
362C22⋊C4—22no—
363C22⋊C4—41no—
364C22⋊C4—41no—
365C22⋊C4—41no—
366C22⋊C4D4×C11314yescomplemented
367C42—22no—
368C23—21no—
369C23—21no—
370C23—21no—
371C23—21no—
372C23—28no—
373C23—21no—
374C23—21no—
375C23—21no—
376C23—21no—
377C23—21no—
378C23—21no—
379C23—21no—
380C23—21no—
381C23—21no—
382C23—21no—
383C23—21no—
384C23—21no—
385C23—21no—
386C23—21no—
387C23—21no—
388C23—21no—
389C23—21no—
390C23—21no—
391C23—44no—
392C23—44no—
393C23—44no—
394C23—44no—
395C23—44no—
396C23—44no—
397C23C2×D4×C11312yes—
398C23C2×D4×C11312yes—
399C23C2×D4×C11312yes—
400C23#41×C11312yes—
401C23#41×C11312yes—
402C23#41×C11312yes—
403C23C24×C11311yescharacteristic
404D4—28no—
405D4—44no—
406D4—44no—
407C2×C4—21no—
408C2×C4—21no—
409C2×C4—21no—
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—21no—
414C2×C4—21no—
415C2×C4—21no—
416C2×C4—21no—
417C2×C4—21no—
418C2×C4—21no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—21no—
422C2×C4—21no—
423C2×C4—21no—
424C2×C4—21no—
425C2×C4—21no—
426C2×C4—21no—
427C2×C4—21no—
428C2×C4—21no—
429C2×C4—21no—
430C2×C4—21no—
431C2×C4—21no—
432C2×C4—21no—
433C2×C4—21no—
434C2×C4—21no—
435C2×C4—21no—
436C2×C4—21no—
437C2×C4—44no—
438C2×C4—44no—
439C2×C4—44no—
440C2×C4C2×D4×C11312yes—
441C2×C4C2×D4×C11312yes—
442C2×C4C2×D4×C11312yes—
443C22—22no—
444C22—22no—
445C22—22no—
446C22—22no—
447C22—22no—
448C22—22no—
449C22—22no—
450C22—22no—
451C22—22no—
452C22—22no—
453C22—22no—
454C22—22no—
455C22—22no—
456C22—22no—
457C22—22no—
458C22—416no—
459C22—41no—
460C22—41no—
461C22—41no—
462C22—41no—
463C22—41no—
464C22—41no—
465C22—41no—
466C22—41no—
467C22—41no—
468C22—41no—
469C22—41no—
470C22—41no—
471C22#123×C11314yescomplemented
472C22C22×D4×C11311yescharacteristic
473C22C22×D4×C11311yescharacteristic
474C22C2×#41×C11311yescharacteristic
475C22C2×#41×C11311yescharacteristic
476C22C2×#41×C11311yescharacteristic
477C22H(5,𝔽2)×C11311yescharacteristic
478C22H(5,𝔽2)×C11311yescharacteristic
479C4—22no—
480C4—22no—
481C4—22no—
482C4—41no—
483C4—41no—
484C4—41no—
485C4—41no—
486C4—41no—
487C4—41no—
488C4—41no—
489C4—41no—
490C2—24no—
491C2—42no—
492C2—42no—
493C2—42no—
494C2C2×#123×C11311yescharacteristic
495C2#525×C11311yescharacteristic
496C2#538×C11311yescharacteristic
497C2D42×C11311yescharacteristic
498C2#546×C11311yescharacteristic
499C2#546×C11311yescharacteristic
500C2#551×C11311yescharacteristic
subgroupG/H
center, socleC23×C113C24
commutator, Frattini, cosocleC23C24×C113
prime radicalC2×#120×C113C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C113 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#123×C113C2semidirect
3. C2×C4×D4×C113C2semidirect
4. C22×C22⋊C4×C113C2semidirect
5. #399×C113C2semidirect
6. #397×C113C2semidirect
7. #394×C113C2semidirect
8. #394×C113C2semidirect
9. #388×C113C2semidirect
10. #388×C113C2semidirect
11. #386×C113C2semidirect
12. #386×C113C2semidirect
13. #385×C113C2semidirect
14. #380×C113C2semidirect
15. #379×C113C2semidirect
22. C23×C4×C113C22semidirect
26. C2×C4⋊C4×C113C22semidirect
27. C2×C4⋊C4×C113C22semidirect
28. C2×C4⋊C4×C113C22semidirect
29. C2×C4⋊C4×C113C22semidirect
30. C2×C4⋊C4×C113C22semidirect
45. C2×C22⋊C4×C113C22semidirect
46. C2×C22⋊C4×C113C22semidirect
47. C2×C22⋊C4×C113C22semidirect
48. C2×C42×C113C22semidirect
49. #95×C113C22semidirect
50. #95×C113C22semidirect
51. #95×C113C22semidirect
52. #95×C113C22semidirect
53. #95×C113C22semidirect
54. #95×C113C22semidirect
115. C22⋊C4×C113D4semidirect
220. C22×C113#123semidirect
250. #2418C113direct (N × H)
251. C113#2418direct (N × H)
252. C2×#123C2×C113semidirect
254. C2×C4×D4C2×C113semidirect
255. C22×C22⋊C4C2×C113semidirect
256. #399C2×C113semidirect
257. #397C2×C113semidirect
258. #394C2×C113semidirect
259. #394C2×C113semidirect
260. #388C2×C113semidirect
261. #388C2×C113semidirect
262. #386C2×C113semidirect
263. #386C2×C113semidirect
264. #385C2×C113semidirect
265. #380C2×C113semidirect
266. #379C2×C113semidirect
273. C23×C4C22×C113semidirect
277. C2×C4⋊C4C22×C113semidirect
278. C2×C4⋊C4C22×C113semidirect
279. C2×C4⋊C4C22×C113semidirect
280. C2×C4⋊C4C22×C113semidirect
281. C2×C4⋊C4C22×C113semidirect
296. C2×C22⋊C4C22×C113semidirect
297. C2×C22⋊C4C22×C113semidirect
298. C2×C22⋊C4C22×C113semidirect
299. C2×C42C22×C113semidirect
300. #95C22×C113semidirect
301. #95C22×C113semidirect
302. #95C22×C113semidirect
303. #95C22×C113semidirect
304. #95C22×C113semidirect
305. #95C22×C113semidirect
366. C22⋊C4D4×C113semidirect
471. C22#123×C113semidirect

Maximal subgroups

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

subgroupindex
C2×#123×C1132
C2×#120×C1132
C2×C4×D4×C1132
C22×C22⋊C4×C1132
#399×C1132
#397×C1132
#394×C1132
#388×C1132
#386×C1132
#385×C1132
#380×C1132
#379×C1132
#2418113