Finite Group Databasebeta

← C2×#13071759 #14916355

Subgroups — C2×#13071759 #14916355

Order 2816.

2870 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
1C22×#66988C211yesmaximal, characteristic
2#13071759C2116yesmaximal, direct product factor
3C2×#10622834C211yesmaximal, characteristic
4C2×#10622260C212yesmaximal, complemented
5C2×#10622558C212yesmaximal, complemented
6C2×#10622557C212yesmaximal, complemented
7C2×#10622265C212yesmaximal, complemented
8C2×#10622823C212yesmaximal, complemented
9C2×#10622555C212yesmaximal, complemented
10C2×C11×#386C211yesmaximal, characteristic
11C23×D4×C11C2211yescharacteristic
12C24×C4×C11C2211yescharacteristic
13C24×Dic11C2211yescharacteristic
14C22×C11×C22⋊C4C2212yes—
15C22×C11×C22⋊C4C2211yescharacteristic
16C22×C22⋊Dic11C2212yes—
17C22×C22⋊Dic11C2212yes—
18C22×C22⋊Dic11C2212yes—
19C22×C22⋊Dic11C2211yescharacteristic
20C2×#66988C4116yescomplemented
21C2×#66988C2218yes—
22C22×C4⋊Dic11C2211yescharacteristic
23C22×Dic11⋊C4C2212yes—
24C22×Dic11⋊C4C2212yes—
25C22×Dic11⋊C4C2212yes—
26C22×Dic11⋊C4C2212yes—
27C22×C4×Dic11C2211yescharacteristic
28C22×C4×Dic11C2212yes—
29C11×#386C2218yes—
30C2×C11×#95C2212yes—
31#10622834C2218yes—
32#10622823C22116yescomplemented
33C2×C11⋊#95C2212yes—
34C2×C11⋊#95C2212yes—
35C2×C11⋊#95C2212yes—
36C2×C11⋊#95C2212yes—
37#10622558C22116yescomplemented
38#10622557C22116yescomplemented
39#10622555C22116yescomplemented
40#10622265C22116yescomplemented
41#10622260C22116yescomplemented
42C25×C11C2311yescharacteristic
43C25×C11C2311yescharacteristic
44C22×D4×C11—42no—
45C22×D4×C11—42no—
46C22×D4×C11C2×C418yes—
47C22×D4×C11C2314yes—
48C23×C4×C11—42no—
49C23×C4×C11—44no—
50C23×C4×C11C2312yes—
51C23×C4×C11C2312yes—
52C23×C4×C11C2311yescharacteristic
53C23×C4×C11C2314yes—
54C23×Dic11—42no—
55C23×Dic11—42no—
56C23×Dic11C2×C418yescomplemented
57C23×Dic11C2312yes—
58C23×Dic11C2312yes—
59C23×Dic11C2312yes—
60C23×Dic11C2312yes—
61C23×Dic11C2314yes—
62C2×C11×C22⋊C4—44no—
63C2×C11×C22⋊C4—42no—
64C2×C11×C22⋊C4C2318yes—
65C2×C11×C22⋊C4C2314yes—
66C2×C22⋊Dic11—44no—
67C2×C22⋊Dic11—44no—
68C2×C22⋊Dic11C2×C4116yes—
69C2×C22⋊Dic11C2×C418yescomplemented
70C2×C22⋊Dic11C2318yes—
71C2×C22⋊Dic11C2318yes—
72C2×C22⋊Dic11C2318yes—
73C2×C22⋊Dic11C2314yes—
74#66988C2×C4164yescomplemented
75C2×C4⋊Dic11—42no—
76C2×C4⋊Dic11C2314yes—
77C2×Dic11⋊C4—44no—
78C2×Dic11⋊C4—44no—
79C2×Dic11⋊C4—44no—
80C2×Dic11⋊C4C2×C4116yescomplemented
81C2×Dic11⋊C4C2318yes—
82C2×Dic11⋊C4C2318yes—
83C2×Dic11⋊C4C2318yes—
84C2×Dic11⋊C4C2318yes—
85C2×C4×Dic11—44no—
86C2×C4×Dic11—42no—
87C2×C4×Dic11C2318yes—
88C2×C4×Dic11C2314yes—
89C11×#95C2318yes—
90C11⋊#95C2318yes—
91C11⋊#95C2318yes—
92C11⋊#95C2318yes—
93C11⋊#95C2318yes—
94C2×#2376—111nomaximal, Sylow
95C24×C11—24no—
96C24×C11—24no—
97C24×C11—22no—
98C24×C11—22no—
99C24×C11—22no—
100C24×C11—22no—
101C24×C11—24no—
102C24×C11—24no—
103C24×C11C22×C414yes—
104C24×C11C22×C414yes—
105C24×C11C2412yes—
106C24×C11C2412yes—
107C24×C11C2411yescharacteristic
108C2×D4×C11—416no—
109C2×D4×C11—44no—
110C2×D4×C11—44no—
111C2×D4×C11C22×C4116yes—
112C22×C4×C11—22no—
113C22×C4×C11—22no—
114C22×C4×C11—24no—
115C22×C4×C11—24no—
116C22×C4×C11—24no—
117C22×C4×C11—24no—
118C22×C4×C11—24no—
119C22×C4×C11—24no—
120C22×C4×C11—44no—
121C22×C4×C11—48no—
122C22×C4×C11—416no—
123C22×C4×C11C22×C414yes—
124C22×C4×C11C2414yes—
125C22×C4×C11C2414yes—
126C22×C4×C11C2412yes—
127C22×Dic11—24no—
128C22×Dic11—24no—
129C22×Dic11—24no—
130C22×Dic11—24no—
131C22×Dic11—24no—
132C22×Dic11—24no—
133C22×Dic11—24no—
134C22×Dic11—24no—
135C22×Dic11—24no—
136C22×Dic11—24no—
137C22×Dic11—416no—
138C22×Dic11—44no—
139C22×Dic11—44no—
140C22×Dic11C22×C418yes—
141C22×Dic11C22×C418yes—
142C22×Dic11C22×C4116yescomplemented
143C22×Dic11C2414yes—
144C22×Dic11C2414yes—
145C22×Dic11C2414yes—
146C22×Dic11C2414yes—
147C11×C22⋊C4—48no—
148C11×C22⋊C4—44no—
149C22⋊Dic11—48no—
150C22⋊Dic11—48no—
151C22⋊Dic11C22×C4132yes—
152C22⋊Dic11C22×C4116yescomplemented
153C4⋊Dic11—44no—
154Dic11⋊C4—48no—
155Dic11⋊C4—48no—
156Dic11⋊C4—48no—
157Dic11⋊C4C22×C4132yescomplemented
158C4×Dic11—44no—
159C4×Dic11—48no—
160C22×#123—111no—
161#2376—1116no—
162C2×#390—111no—
163C2×#389—112no—
164C2×#388—112no—
165C2×#388—112no—
166C2×#387—112no—
167C2×#386D1111yescharacteristic
168C2×#385—112no—
169C2×#380—112no—
170C23×C11—28no—
171C23×C11—28no—
172C23×C11—216no—
173C23×C11—216no—
174C23×C11—24no—
175C23×C11—24no—
176C23×C11—22no—
177C23×C11—22no—
178C23×C11—22no—
179C23×C11—22no—
180C23×C11—24no—
181C23×C11—24no—
182C23×C11—44no—
183C23×C11—44no—
184C23×C11—48no—
185C23×C11—48no—
186C23×C11—44no—
187C23×C11—44no—
188C23×C11C23×C414yes—
189C23×C11C23×C414yes—
190C23×C11C23×C412yes—
191C23×C11H(5,𝔽2)12yes—
192C23×C11H(5,𝔽2)12yes—
193C23×C11H(5,𝔽2)14yes—
194C23×C112−1+414yes—
195C23×C11C2511yescharacteristic
196D4×C11—416no—
197C2×C4×C11—28no—
198C2×C4×C11—22no—
199C2×C4×C11—22no—
200C2×C4×C11—24no—
201C2×C4×C11—24no—
202C2×C4×C11—24no—
203C2×C4×C11—24no—
204C2×C4×C11—24no—
205C2×C4×C11—24no—
206C2×C4×C11—416no—
207C2×C4×C11—48no—
208C2×C4×C11—48no—
209C2×C4×C11C23×C414yes—
210C2×Dic11—216no—
211C2×Dic11—216no—
212C2×Dic11—24no—
213C2×Dic11—24no—
214C2×Dic11—24no—
215C2×Dic11—24no—
216C2×Dic11—24no—
217C2×Dic11—24no—
218C2×Dic11—24no—
219C2×Dic11—24no—
220C2×Dic11—24no—
221C2×Dic11—24no—
222C2×Dic11—416no—
223C2×Dic11—48no—
224C2×Dic11—48no—
225C2×Dic11C23×C418yes—
226C2×Dic11C23×C418yes—
227C23×D4C2×D1111yescharacteristic
228C24×C4—111no—
229C24×C4C2×D1111yescharacteristic
230C2×#123—118no—
231C2×#123—1116no—
232C22×C4⋊C4—112no—
233C22×C4⋊C4—112no—
234C22×C4⋊C4—112no—
235C22×C4⋊C4—112no—
236C22×C4⋊C4—111no—
237C22×C22⋊C4—112no—
238C22×C22⋊C4—111no—
239C22×C22⋊C4—112no—
240C22×C22⋊C4—112no—
241C22×C22⋊C4C2×D1112yes—
242C22×C22⋊C4C2×D1111yescharacteristic
243C22×C42—111no—
244C22×C42—112no—
245#390—118no—
246#389—1116no—
247#388—1116no—
248#388—1116no—
249#387—1116no—
250#386C2×D1118yes—
251#385—1116no—
252#380—1116no—
253C2×#95—112no—
254C2×#95—112no—
255C2×#95—112no—
256C2×#95—112no—
257C2×#95C2×D1112yes—
258C22×C11—24no—
259C22×C11—24no—
260C22×C11—28no—
261C22×C11—28no—
262C22×C11—416no—
263C22×C11—416no—
264C22×C11—42no—
265C22×C11—42no—
266C22×C11—44no—
267C22×C11—44no—
268C22×C11—42no—
269C22×C11—42no—
270C22×C11#51814yes—
271C22×C11#52018yes—
272C22×C11#56014yes—
273C22×C11#56218yes—
274C22×C11#56314yes—
275C22×C11C24×C411yescharacteristic
276C22×C11C2×H(5,𝔽2)11yescharacteristic
277C22×C11C2×H(5,𝔽2)11yescharacteristic
278C22×C11C2×H(5,𝔽2)12yes—
279C22×C11C2×2−1+412yes—
280C4×C11—24no—
281C4×C11—44no—
282C4×C11—44no—
283Dic11—28no—
284Dic11—28no—
285Dic11—44no—
286Dic11—44no—
287C25C22×D1111yescharacteristic
288C25C22×D1111yescharacteristic
289C22×D4—42no—
290C22×D4—42no—
291C22×D4C4×D1118yes—
292C22×D4C22×D1114yes—
293C23×C4—44no—
294C23×C4—42no—
295C23×C4—112no—
296C23×C4—112no—
297C23×C4—118no—
298C23×C4—114no—
299C23×C4—112no—
300C23×C4—112no—
301C23×C4—442no—
302C23×C4—442no—
303C23×C4C22×D1112yes—
304C23×C4C22×D1112yes—
305C23×C4C22×D1111yescharacteristic
306C23×C4C22×D1114yes—
307#123—1164no—
308C2×C4⋊C4—1116no—
309C2×C4⋊C4—118no—
310C2×C4⋊C4—118no—
311C2×C4⋊C4—118no—
312C2×C4⋊C4—118no—
313C2×C4⋊C4—114no—
314C2×C4⋊C4—444no—
315C2×C4⋊C4—444no—
316C2×C4⋊C4—444no—
317C2×C4⋊C4—442no—
318C2×C22⋊C4—44no—
319C2×C22⋊C4—42no—
320C2×C22⋊C4—1116no—
321C2×C22⋊C4—118no—
322C2×C22⋊C4—118no—
323C2×C22⋊C4—114no—
324C2×C22⋊C4—118no—
325C2×C22⋊C4—118no—
326C2×C22⋊C4—444no—
327C2×C22⋊C4—444no—
328C2×C22⋊C4C22×D1118yes—
329C2×C22⋊C4C22×D1114yes—
330C2×C42—114no—
331C2×C42—118no—
332C2×C42—442no—
333C2×C42—444no—
334#95—118no—
335#95—118no—
336#95—118no—
337#95—118no—
338#95C22×D1118yes—
339C2×C11—44no—
340C2×C11—44no—
341C2×C11#237618yescomplemented
342C2×C11C2×#51811yescharacteristic
343C2×C11C2×#52012yes—
344C2×C11C2×#56011yescharacteristic
345C2×C11C2×#56212yes—
346C2×C11C2×#56311yescharacteristic
347C24—24no—
348C24—22no—
349C24—24no—
350C24—22no—
351C24—22no—
352C24—22no—
353C24—24no—
354C24—24no—
355C24C2×C4×D1114yes—
356C24C2×C4×D1114yes—
357C24C23×D1112yes—
358C24C23×D1112yes—
359C24C23×D1111yescharacteristic
360C2×D4—44no—
361C2×D4—44no—
362C2×D4—416no—
363C2×D4C2×C4×D11116yes—
364C22×C4—22no—
365C22×C4—22no—
366C22×C4—24no—
367C22×C4—24no—
368C22×C4—24no—
369C22×C4—24no—
370C22×C4—24no—
371C22×C4—24no—
372C22×C4—48no—
373C22×C4—44no—
374C22×C4—416no—
375C22×C4—118no—
376C22×C4—118no—
377C22×C4—114no—
378C22×C4—114no—
379C22×C4—1116no—
380C22×C4—114no—
381C22×C4—114no—
382C22×C4—224no—
383C22×C4—224no—
384C22×C4—224no—
385C22×C4—224no—
386C22×C4—224no—
387C22×C4—224no—
388C22×C4—224no—
389C22×C4—224no—
390C22×C4—224no—
391C22×C4—224no—
392C22×C4—4416no—
393C22×C4—444no—
394C22×C4—444no—
395C22×C4C2×C4×D1114yes—
396C22×C4C23×D1114yes—
397C22×C4C23×D1114yes—
398C22×C4C23×D1112yes—
399C4⋊C4—1132no—
400C4⋊C4—448no—
401C4⋊C4—448no—
402C4⋊C4—448no—
403C4⋊C4—444no—
404C22⋊C4—48no—
405C22⋊C4—44no—
406C22⋊C4—1132no—
407C22⋊C4—1116no—
408C22⋊C4—448no—
409C22⋊C4—448no—
410C42—444no—
411C42—448no—
412C11C2×#237611yescharacteristic, complemented, Sylow
413C23—28no—
414C23—28no—
415C23—216no—
416C23—216no—
417C23—24no—
418C23—22no—
419C23—24no—
420C23—22no—
421C23—22no—
422C23—22no—
423C23—24no—
424C23—24no—
425C23—44no—
426C23—44no—
427C23—48no—
428C23—48no—
429C23—44no—
430C23—44no—
431C23C22×C4×D1114yes—
432C23C22×C4×D1114yes—
433C23C22×C4×D1112yes—
434C23#6703712yes—
435C23#6703712yes—
436C23#6703714yes—
437C23#6704314yes—
438C23C24×D1111yescharacteristic
439D4—416no—
440C2×C4—28no—
441C2×C4—22no—
442C2×C4—22no—
443C2×C4—24no—
444C2×C4—24no—
445C2×C4—24no—
446C2×C4—24no—
447C2×C4—24no—
448C2×C4—24no—
449C2×C4—416no—
450C2×C4—48no—
451C2×C4—48no—
452C2×C4—118no—
453C2×C4—118no—
454C2×C4—2216no—
455C2×C4—2216no—
456C2×C4—224no—
457C2×C4—224no—
458C2×C4—224no—
459C2×C4—224no—
460C2×C4—224no—
461C2×C4—224no—
462C2×C4—224no—
463C2×C4—224no—
464C2×C4—224no—
465C2×C4—224no—
466C2×C4—4416no—
467C2×C4—448no—
468C2×C4—448no—
469C2×C4C22×C4×D1114yes—
470C22—24no—
471C22—24no—
472C22—28no—
473C22—28no—
474C22—42no—
475C22—42no—
476C22—44no—
477C22—44no—
478C22—42no—
479C22—42no—
480C22—416no—
481C22—416no—
482C22#1062301714yes—
483C22#1062307718yes—
484C22#1062312614yes—
485C22#1062315218yes—
486C22#1062318214yes—
487C22C23×C4×D1111yescharacteristic
488C22C2×#6703712yes—
489C22C2×#6703711yescharacteristic
490C22C2×#6703711yescharacteristic
491C22C2×#6704312yes—
492C4—24no—
493C4—44no—
494C4—44no—
495C4—228no—
496C4—228no—
497C4—444no—
498C4—444no—
499C2—44no—
500C2—44no—
501C2#1307175918yesdirect product factor
502C2C2×#1062301711yescharacteristic
503C2C2×#1062307712yes—
504C2C2×#1062312611yescharacteristic
505C2C2×#1062315212yes—
506C2C2×#1062318211yescharacteristic
subgroupG/H
centerC24C23×D11
commutatorC22×C11C24×C4
FrattiniC23C24×D11
FittingC2×C11×#386C2
socleC24×C11C24
prime radicalC23×D4×C11C22
cosocleC23×C11C25
hypercenterC2×#386D11
hypocenterC11C2×#2376
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
2. #13071759C2direct (N × H)
4. C2×#10622260C2semidirect
5. C2×#10622558C2semidirect
6. C2×#10622557C2semidirect
7. C2×#10622265C2semidirect
8. C2×#10622823C2semidirect
9. C2×#10622555C2semidirect
20. C2×#66988C4semidirect
32. #10622823C22semidirect
37. #10622558C22semidirect
38. #10622557C22semidirect
39. #10622555C22semidirect
40. #10622265C22semidirect
41. #10622260C22semidirect
56. C23×Dic11C2×C4semidirect
69. C2×C22⋊Dic11C2×C4semidirect
74. #66988C2×C4semidirect
80. C2×Dic11⋊C4C2×C4semidirect
142. C22×Dic11C22×C4semidirect
152. C22⋊Dic11C22×C4semidirect
157. Dic11⋊C4C22×C4semidirect
341. C2×C11#2376semidirect
412. C11C2×#2376semidirect
501. C2#13071759direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669882
#130717592
C2×#106228342
C2×#106222602
C2×#106225582
C2×#106225572
C2×#106222652
C2×#106228232
C2×#106225552
C2×C11×#3862
C2×#237611