Finite Group Databasebeta

← C113×#2678 #28387474

Subgroups — C113×#2678 #28387474

Order 14464.

802 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#123×C113C211yesmaximal, characteristic, complemented
2C2×#121×C113C211yesmaximal, characteristic, complemented
3C2×#120×C113C211yesmaximal, characteristic, complemented
4C2×#120×C113C211yesmaximal, characteristic, complemented
5#397×C113C211yesmaximal, characteristic, complemented
6#396×C113C211yesmaximal, characteristic, complemented
7#394×C113C211yesmaximal, characteristic, complemented
8#394×C113C211yesmaximal, characteristic, complemented
9#392×C113C211yesmaximal, characteristic, complemented
10#392×C113C211yesmaximal, characteristic, complemented
11#390×C113C211yesmaximal, characteristic, complemented
12#390×C113C211yesmaximal, characteristic, complemented
13#388×C113C211yesmaximal, characteristic, complemented
14#386×C113C211yesmaximal, characteristic, complemented
15#379×C113C211yesmaximal, characteristic, complemented
16C25×C113C2211yescharacteristic
17C22×D4×C113C2211yescharacteristic
18C22×D4×C113C2211yescharacteristic
19C22×D4×C113C2211yescharacteristic
20C22×D4×C113C2211yescharacteristic
21C22×D4×C113C2211yescharacteristic
22C22×D4×C113C2211yescharacteristic
23C22×D4×C113C2211yescharacteristic, complemented
24C23×C4×C113C2211yescharacteristic, complemented
25#123×C113—24no—
26#121×C113—24no—
27#120×C113—24no—
28#120×C113—24no—
29C2×C4⋊C4×C113C2211yescharacteristic, complemented
30C2×C4⋊C4×C113C2211yescharacteristic, complemented
31C2×C4⋊C4×C113C2211yescharacteristic, complemented
32C2×C4⋊C4×C113C2211yescharacteristic, complemented
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×C22⋊C4×C113C2211yescharacteristic, complemented
49C2×C22⋊C4×C113C2211yescharacteristic, complemented
50C2×C42×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—41no—
59C24×C113—41no—
60C24×C113—41no—
61C24×C113—41no—
62C24×C113C2311yescharacteristic
63C24×C113C2311yescharacteristic
64C24×C113C2311yescharacteristic
65C24×C113C2311yescharacteristic
66C24×C113C2311yescharacteristic
67C2×D4×C113—22no—
68C2×D4×C113—22no—
69C2×D4×C113—22no—
70C2×D4×C113—22no—
71C2×D4×C113—22no—
72C2×D4×C113—22no—
73C2×D4×C113—22no—
74C2×D4×C113—22no—
75C2×D4×C113—22no—
76C2×D4×C113—22no—
77C2×D4×C113—41no—
78C2×D4×C113—41no—
79C2×D4×C113—41no—
80C2×D4×C113—41no—
81C2×D4×C113—41no—
82C2×D4×C113—41no—
83C2×D4×C113—41no—
84C2×D4×C113—41no—
85C2×D4×C113—41no—
86C2×D4×C113—41no—
87C2×D4×C113D414yescomplemented
88C22×C4×C113—22no—
89C22×C4×C113—22no—
90C22×C4×C113—41no—
91C22×C4×C113C2311yescharacteristic
92C22×C4×C113C2311yescharacteristic
93C22×C4×C113C2311yescharacteristic
94C22×C4×C113C2311yescharacteristic
95C22×C4×C113C2311yescharacteristic
96C22×C4×C113C2311yescharacteristic
97C22×C4×C113C2311yescharacteristic
98C22×C4×C113C2311yescharacteristic
99C22×C4×C113C2311yescharacteristic
100C22×C4×C113C2311yescharacteristic
101C4⋊C4×C113—22no—
102C4⋊C4×C113—22no—
103C4⋊C4×C113—22no—
104C4⋊C4×C113—41no—
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—22no—
113C22⋊C4×C113—22no—
114C22⋊C4×C113—41no—
115C22⋊C4×C113—41no—
116C22⋊C4×C113—41no—
117C22⋊C4×C113—41no—
118C22⋊C4×C113—41no—
119C22⋊C4×C113—41no—
120C22⋊C4×C113—41no—
121C22⋊C4×C113D414yescomplemented
122C42×C113—41no—
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—21no—
141C23×C113—21no—
142C23×C113—21no—
143C23×C113—21no—
144C23×C113—21no—
145C23×C113—21no—
146C23×C113—21no—
147C23×C113—21no—
148C23×C113—21no—
149C23×C113—21no—
150C23×C113—21no—
151C23×C113—21no—
152C23×C113—21no—
153C23×C113—21no—
154C23×C113—44no—
155C23×C113—44no—
156C23×C113—44no—
157C23×C113—44no—
158C23×C113—44no—
159C23×C113—44no—
160C23×C113—44no—
161C23×C113C2×D412yes—
162C23×C113C2×D412yes—
163C23×C113C2×D412yes—
164C23×C113#4112yes—
165C23×C113C2411yescharacteristic
166D4×C113—44no—
167D4×C113—44no—
168D4×C113—44no—
169D4×C113—44no—
170D4×C113—44no—
171D4×C113—44no—
172D4×C113—44no—
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—21no—
187C2×C4×C113—21no—
188C2×C4×C113—21no—
189C2×C4×C113—21no—
190C2×C4×C113—21no—
191C2×C4×C113—21no—
192C2×C4×C113—21no—
193C2×C4×C113—21no—
194C2×C4×C113—21no—
195C2×C4×C113—21no—
196C2×C4×C113—21no—
197C2×C4×C113—21no—
198C2×C4×C113—21no—
199C2×C4×C113—21no—
200C2×C4×C113—44no—
201C2×C4×C113C2×D412yes—
202C2×C4×C113C2×D412yes—
203C2×C4×C113C2×D412yes—
204C22×C113—22no—
205C22×C113—22no—
206C22×C113—22no—
207C22×C113—22no—
208C22×C113—22no—
209C22×C113—22no—
210C22×C113—22no—
211C22×C113—22no—
212C22×C113—22no—
213C22×C113—22no—
214C22×C113—22no—
215C22×C113—22no—
216C22×C113—416no—
217C22×C113—41no—
218C22×C113—41no—
219C22×C113—41no—
220C22×C113—41no—
221C22×C113—41no—
222C22×C113—41no—
223C22×C113—41no—
224C22×C113—41no—
225C22×C113—41no—
226C22×C113—41no—
227C22×C113—41no—
228C22×C113—41no—
229C22×C113—41no—
230C22×C113—41no—
231C22×C113—41no—
232C22×C113—41no—
233C22×C113—41no—
234C22×C113—41no—
235C22×C113—41no—
236C22×C113—41no—
237C22×C113—41no—
238C22×C113—41no—
239C22×C113—41no—
240C22×C113C22×D411yescharacteristic
241C22×C113C22×D411yescharacteristic
242C22×C113C2×#4111yescharacteristic
243C22×C113H(5,𝔽2)11yescharacteristic
244C22×C113H(5,𝔽2)11yescharacteristic
245C22×C113H(5,𝔽2)11yescharacteristic
246C22×C113H(5,𝔽2)11yescharacteristic
247C4×C113—22no—
248C4×C113—22no—
249C4×C113—22no—
250C4×C113—41no—
251C4×C113—41no—
252C4×C113—41no—
253C4×C113—41no—
254C4×C113—41no—
255C4×C113—41no—
256C4×C113—41no—
257C2×C113—42no—
258C2×C113—42no—
259C2×C113—42no—
260C2×C113—42no—
261C2×C113—81no—
262C2×C113#53411yescharacteristic
263C2×C113#53511yescharacteristic
264C2×C113#53811yescharacteristic
265C2×C113D4211yescharacteristic
266C2×C113#54611yescharacteristic
267C2×C113#54611yescharacteristic
268C2×C113#56011yescharacteristic
269#2678C11311yesmaximal, characteristic, direct product factor, Sylow
270C113#267811yescharacteristic, direct product factor, Sylow
271C2×#123C2×C11311yescharacteristic, complemented
272C2×#121C2×C11311yescharacteristic, complemented
273C2×#120C2×C11311yescharacteristic, complemented
274C2×#120C2×C11311yescharacteristic, complemented
275#397C2×C11311yescharacteristic, complemented
276#396C2×C11311yescharacteristic, complemented
277#394C2×C11311yescharacteristic, complemented
278#394C2×C11311yescharacteristic, complemented
279#392C2×C11311yescharacteristic, complemented
280#392C2×C11311yescharacteristic, complemented
281#390C2×C11311yescharacteristic, complemented
282#390C2×C11311yescharacteristic, complemented
283#388C2×C11311yescharacteristic, complemented
284#386C2×C11311yescharacteristic, complemented
285#379C2×C11311yescharacteristic, complemented
286C25C22×C11311yescharacteristic
287C22×D4C22×C11311yescharacteristic
288C22×D4C22×C11311yescharacteristic
289C22×D4C22×C11311yescharacteristic
290C22×D4C22×C11311yescharacteristic
291C22×D4C22×C11311yescharacteristic
292C22×D4C22×C11311yescharacteristic
293C22×D4C22×C11311yescharacteristic, complemented
294C23×C4C22×C11311yescharacteristic, complemented
295#123—24no—
296#121—24no—
297#120—24no—
298#120—24no—
299C2×C4⋊C4C22×C11311yescharacteristic, complemented
300C2×C4⋊C4C22×C11311yescharacteristic, complemented
301C2×C4⋊C4C22×C11311yescharacteristic, complemented
302C2×C4⋊C4C22×C11311yescharacteristic, complemented
303C2×C22⋊C4C22×C11311yescharacteristic
304C2×C22⋊C4C22×C11311yescharacteristic
305C2×C22⋊C4C22×C11311yescharacteristic
306C2×C22⋊C4C22×C11311yescharacteristic
307C2×C22⋊C4C22×C11311yescharacteristic
308C2×C22⋊C4C22×C11311yescharacteristic
309C2×C22⋊C4C22×C11311yescharacteristic
310C2×C22⋊C4C22×C11311yescharacteristic
311C2×C22⋊C4C22×C11311yescharacteristic
312C2×C22⋊C4C22×C11311yescharacteristic
313C2×C22⋊C4C22×C11311yescharacteristic
314C2×C22⋊C4C22×C11311yescharacteristic
315C2×C22⋊C4C22×C11311yescharacteristic, complemented
316C2×C22⋊C4C22×C11311yescharacteristic, complemented
317C2×C22⋊C4C22×C11311yescharacteristic, complemented
318C2×C22⋊C4C22×C11311yescharacteristic, complemented
319C2×C22⋊C4C22×C11311yescharacteristic, complemented
320C2×C42C22×C11311yescharacteristic, complemented
321#95C22×C11311yescharacteristic, complemented
322#95C22×C11311yescharacteristic, complemented
323#95C22×C11311yescharacteristic, complemented
324#95C22×C11311yescharacteristic, complemented
325C24—22no—
326C24—22no—
327C24—22no—
328C24—41no—
329C24—41no—
330C24—41no—
331C24—41no—
332C24C23×C11311yescharacteristic
333C24C23×C11311yescharacteristic
334C24C23×C11311yescharacteristic
335C24C23×C11311yescharacteristic
336C24C23×C11311yescharacteristic
337C2×D4—22no—
338C2×D4—22no—
339C2×D4—22no—
340C2×D4—22no—
341C2×D4—22no—
342C2×D4—22no—
343C2×D4—22no—
344C2×D4—22no—
345C2×D4—22no—
346C2×D4—22no—
347C2×D4—41no—
348C2×D4—41no—
349C2×D4—41no—
350C2×D4—41no—
351C2×D4—41no—
352C2×D4—41no—
353C2×D4—41no—
354C2×D4—41no—
355C2×D4—41no—
356C2×D4—41no—
357C2×D4D4×C11314yescomplemented
358C22×C4—22no—
359C22×C4—22no—
360C22×C4—41no—
361C22×C4C23×C11311yescharacteristic
362C22×C4C23×C11311yescharacteristic
363C22×C4C23×C11311yescharacteristic
364C22×C4C23×C11311yescharacteristic
365C22×C4C23×C11311yescharacteristic
366C22×C4C23×C11311yescharacteristic
367C22×C4C23×C11311yescharacteristic
368C22×C4C23×C11311yescharacteristic
369C22×C4C23×C11311yescharacteristic
370C22×C4C23×C11311yescharacteristic
371C4⋊C4—22no—
372C4⋊C4—22no—
373C4⋊C4—22no—
374C4⋊C4—41no—
375C22⋊C4—22no—
376C22⋊C4—22no—
377C22⋊C4—22no—
378C22⋊C4—22no—
379C22⋊C4—22no—
380C22⋊C4—22no—
381C22⋊C4—22no—
382C22⋊C4—22no—
383C22⋊C4—22no—
384C22⋊C4—41no—
385C22⋊C4—41no—
386C22⋊C4—41no—
387C22⋊C4—41no—
388C22⋊C4—41no—
389C22⋊C4—41no—
390C22⋊C4—41no—
391C22⋊C4D4×C11314yescomplemented
392C42—41no—
393C23—21no—
394C23—21no—
395C23—21no—
396C23—21no—
397C23—21no—
398C23—21no—
399C23—21no—
400C23—21no—
401C23—21no—
402C23—21no—
403C23—21no—
404C23—21no—
405C23—21no—
406C23—21no—
407C23—21no—
408C23—21no—
409C23—21no—
410C23—21no—
411C23—21no—
412C23—21no—
413C23—21no—
414C23—21no—
415C23—21no—
416C23—21no—
417C23—21no—
418C23—21no—
419C23—21no—
420C23—21no—
421C23—21no—
422C23—21no—
423C23—21no—
424C23—44no—
425C23—44no—
426C23—44no—
427C23—44no—
428C23—44no—
429C23—44no—
430C23—44no—
431C23C2×D4×C11312yes—
432C23C2×D4×C11312yes—
433C23C2×D4×C11312yes—
434C23#41×C11312yes—
435C23C24×C11311yescharacteristic
436D4—44no—
437D4—44no—
438D4—44no—
439D4—44no—
440D4—44no—
441D4—44no—
442D4—44no—
443C2×C4—21no—
444C2×C4—21no—
445C2×C4—21no—
446C2×C4—21no—
447C2×C4—21no—
448C2×C4—21no—
449C2×C4—21no—
450C2×C4—21no—
451C2×C4—21no—
452C2×C4—21no—
453C2×C4—21no—
454C2×C4—21no—
455C2×C4—21no—
456C2×C4—21no—
457C2×C4—21no—
458C2×C4—21no—
459C2×C4—21no—
460C2×C4—21no—
461C2×C4—21no—
462C2×C4—21no—
463C2×C4—21no—
464C2×C4—21no—
465C2×C4—21no—
466C2×C4—21no—
467C2×C4—21no—
468C2×C4—21no—
469C2×C4—21no—
470C2×C4—44no—
471C2×C4C2×D4×C11312yes—
472C2×C4C2×D4×C11312yes—
473C2×C4C2×D4×C11312yes—
474C22—22no—
475C22—22no—
476C22—22no—
477C22—22no—
478C22—22no—
479C22—22no—
480C22—22no—
481C22—22no—
482C22—22no—
483C22—22no—
484C22—22no—
485C22—22no—
486C22—416no—
487C22—41no—
488C22—41no—
489C22—41no—
490C22—41no—
491C22—41no—
492C22—41no—
493C22—41no—
494C22—41no—
495C22—41no—
496C22—41no—
497C22—41no—
498C22—41no—
499C22—41no—
500C22—41no—
501C22—41no—
502C22—41no—
503C22—41no—
504C22—41no—
505C22—41no—
506C22—41no—
507C22—41no—
508C22—41no—
509C22—41no—
510C22C22×D4×C11311yescharacteristic
511C22C22×D4×C11311yescharacteristic
512C22C2×#41×C11311yescharacteristic
513C22H(5,𝔽2)×C11311yescharacteristic
514C22H(5,𝔽2)×C11311yescharacteristic
515C22H(5,𝔽2)×C11311yescharacteristic
516C22H(5,𝔽2)×C11311yescharacteristic
517C4—22no—
518C4—22no—
519C4—22no—
520C4—41no—
521C4—41no—
522C4—41no—
523C4—41no—
524C4—41no—
525C4—41no—
526C4—41no—
527C2—42no—
528C2—42no—
529C2—42no—
530C2—42no—
531C2—81no—
532C2#534×C11311yescharacteristic
533C2#535×C11311yescharacteristic
534C2#538×C11311yescharacteristic
535C2D42×C11311yescharacteristic
536C2#546×C11311yescharacteristic
537C2#546×C11311yescharacteristic
538C2#560×C11311yescharacteristic
subgroupG/H
center, socleC23×C113C24
commutator, Frattini, cosocleC23C24×C113
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
2. C2×#121×C113C2semidirect
3. C2×#120×C113C2semidirect
4. C2×#120×C113C2semidirect
5. #397×C113C2semidirect
6. #396×C113C2semidirect
7. #394×C113C2semidirect
8. #394×C113C2semidirect
9. #392×C113C2semidirect
10. #392×C113C2semidirect
11. #390×C113C2semidirect
12. #390×C113C2semidirect
13. #388×C113C2semidirect
14. #386×C113C2semidirect
15. #379×C113C2semidirect
23. C22×D4×C113C22semidirect
24. C23×C4×C113C22semidirect
29. C2×C4⋊C4×C113C22semidirect
30. C2×C4⋊C4×C113C22semidirect
31. C2×C4⋊C4×C113C22semidirect
32. C2×C4⋊C4×C113C22semidirect
45. C2×C22⋊C4×C113C22semidirect
46. C2×C22⋊C4×C113C22semidirect
47. C2×C22⋊C4×C113C22semidirect
48. C2×C22⋊C4×C113C22semidirect
49. C2×C22⋊C4×C113C22semidirect
50. C2×C42×C113C22semidirect
51. #95×C113C22semidirect
52. #95×C113C22semidirect
53. #95×C113C22semidirect
54. #95×C113C22semidirect
87. C2×D4×C113D4semidirect
121. C22⋊C4×C113D4semidirect
269. #2678C113direct (N × H)
270. C113#2678direct (N × H)
271. C2×#123C2×C113semidirect
272. C2×#121C2×C113semidirect
273. C2×#120C2×C113semidirect
274. C2×#120C2×C113semidirect
275. #397C2×C113semidirect
276. #396C2×C113semidirect
277. #394C2×C113semidirect
278. #394C2×C113semidirect
279. #392C2×C113semidirect
280. #392C2×C113semidirect
281. #390C2×C113semidirect
282. #390C2×C113semidirect
283. #388C2×C113semidirect
284. #386C2×C113semidirect
285. #379C2×C113semidirect
293. C22×D4C22×C113semidirect
294. C23×C4C22×C113semidirect
299. C2×C4⋊C4C22×C113semidirect
300. C2×C4⋊C4C22×C113semidirect
301. C2×C4⋊C4C22×C113semidirect
302. C2×C4⋊C4C22×C113semidirect
315. C2×C22⋊C4C22×C113semidirect
316. C2×C22⋊C4C22×C113semidirect
317. C2×C22⋊C4C22×C113semidirect
318. C2×C22⋊C4C22×C113semidirect
319. C2×C22⋊C4C22×C113semidirect
320. C2×C42C22×C113semidirect
321. #95C22×C113semidirect
322. #95C22×C113semidirect
323. #95C22×C113semidirect
324. #95C22×C113semidirect
357. C2×D4D4×C113semidirect
391. C22⋊C4D4×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×#121×C1132
C2×#120×C1132
#397×C1132
#396×C1132
#394×C1132
#392×C1132
#390×C1132
#388×C1132
#386×C1132
#379×C1132
#2678113