Finite Group Databasebeta

← C2×#13074733 #14920319

Subgroups — C2×#13074733 #14920319

Order 2816.

2982 conjugacy classes of subgroups.

The subgroup lattice has 524 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66931C212yesmaximal
2#13074733C2116yesmaximal, direct product factor
3C2×#10622270C212yesmaximal, complemented
4C2×#10622597C212yesmaximal, complemented
5C2×#10622269C212yesmaximal, complemented
6C2×#10622592C212yesmaximal, complemented
7C2×#10622825C211yesmaximal, characteristic
8C2×#10622555C212yesmaximal
9C22×C11⋊#95C211yesmaximal, characteristic
10C2×C11×#380C211yesmaximal, characteristic
11C24×C4×C11C2211yescharacteristic
12C24×Dic11C2211yescharacteristic
13C24×Dic11C2211yescharacteristic
14C23×Dic22C2212yes—
15C22×C11×C4⋊C4C2211yescharacteristic
16C22×C11×C4⋊C4C2211yescharacteristic
17C22×C11×C22⋊C4C2212yes—
18C22×C22⋊Dic11C2212yes—
19C22×C4⋊Dic11C2212yes—
20C22×C4⋊Dic11C2211yescharacteristic
21C22×C4⋊Dic11C2211yescharacteristic
22C22×Dic11⋊C4C2212yes—
23C22×Dic11⋊C4C2212yes—
24C22×Dic11⋊C4C2212yes—
25C22×Dic11⋊C4C2212yes—
26C2×#66931—216no—
27C2×#66931C22116yes—
28C11×#380C2218yes—
29C2×C11×#95C2212yes—
30#10622825C2218yes—
31C2×C11⋊#95C2218yes—
32C2×C11⋊#95C2212yes—
33C2×C11⋊#95C2212yes—
34C2×C11⋊#95C2212yes—
35C2×C11⋊#95C2212yes—
36C2×C11⋊#95C2212yes—
37#10622597C22116yescomplemented
38#10622592C22116yescomplemented
39#10622555C22116yes—
40#10622270C22116yescomplemented
41#10622269C22116yescomplemented
42C25×C11C2311yescharacteristic
43C23×C4×C11—42no—
44C23×C4×C11—42no—
45C23×C4×C11Q818yescomplemented
46C23×C4×C11C2312yes—
47C23×C4×C11C2312yes—
48C23×C4×C11C2311yescharacteristic
49C23×C4×C11C2311yescharacteristic
50C23×C4×C11C2314yes—
51C23×Dic11—42no—
52C23×Dic11—42no—
53C23×Dic11—42no—
54C23×Dic11—42no—
55C23×Dic11D418yes—
56C23×Dic11Q818yescomplemented
57C23×Dic11C2312yes—
58C23×Dic11C2312yes—
59C23×Dic11C2312yes—
60C23×Dic11C2312yes—
61C23×Dic11C2314yes—
62C23×Dic11C2314yes—
63C22×Dic22—28no—
64C22×Dic22—44no—
65C22×Dic22—44no—
66C22×Dic22C2318yes—
67C2×C11×C4⋊C4—42no—
68C2×C11×C4⋊C4—42no—
69C2×C11×C4⋊C4C2314yes—
70C2×C11×C4⋊C4C2314yes—
71C2×C11×C22⋊C4—28no—
72C2×C11×C22⋊C4C2318yes—
73C2×C22⋊Dic11—28no—
74C2×C22⋊Dic11C2318yes—
75C2×C4⋊Dic11—28no—
76C2×C4⋊Dic11—42no—
77C2×C4⋊Dic11—42no—
78C2×C4⋊Dic11C2318yes—
79C2×C4⋊Dic11C2314yes—
80C2×C4⋊Dic11C2314yes—
81C2×Dic11⋊C4—28no—
82C2×Dic11⋊C4—28no—
83C2×Dic11⋊C4—44no—
84C2×Dic11⋊C4—44no—
85C2×Dic11⋊C4C2318yes—
86C2×Dic11⋊C4C2318yes—
87C2×Dic11⋊C4C2318yes—
88C2×Dic11⋊C4C2318yes—
89#66931—264no—
90C11×#95C2318yes—
91C11⋊#95C2318yes—
92C11⋊#95C2318yes—
93C11⋊#95C2318yes—
94C11⋊#95C2318yes—
95C11⋊#95C2318yes—
96C2×#2659—111nomaximal, Sylow
97C24×C11—22no—
98C24×C11—22no—
99C24×C11—22no—
100C24×C11—22no—
101C24×C11C2×D414yes—
102C24×C11C2×Q814yes—
103C24×C11C2×Q814yes—
104C24×C11C2412yes—
105C24×C11C2411yescharacteristic
106C22×C4×C11—22no—
107C22×C4×C11—22no—
108C22×C4×C11—22no—
109C22×C4×C11—22no—
110C22×C4×C11—24no—
111C22×C4×C11—24no—
112C22×C4×C11—24no—
113C22×C4×C11—24no—
114C22×C4×C11—24no—
115C22×C4×C11—24no—
116C22×C4×C11—416no—
117C22×C4×C11—44no—
118C22×C4×C11—44no—
119C22×C4×C11C2×Q814yes—
120C22×C4×C11C2×Q814yes—
121C22×C4×C11C2×Q8116yescomplemented
122C22×C4×C11C2414yes—
123C22×C4×C11C2414yes—
124C22×C4×C11C2412yes—
125C22×C4×C11C2412yes—
126C22×Dic11—24no—
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—416no—
137C22×Dic11—416no—
138C22×Dic11—44no—
139C22×Dic11—44no—
140C22×Dic11—44no—
141C22×Dic11—44no—
142C22×Dic11C2×D418yes—
143C22×Dic11C2×D4116yes—
144C22×Dic11C2×Q818yes—
145C22×Dic11C2×Q8116yescomplemented
146C22×Dic11C2414yes—
147C22×Dic11C2414yes—
148C22×Dic11C2414yes—
149C22×Dic11C2414yes—
150C2×Dic22—216no—
151C2×Dic22—48no—
152C2×Dic22—48no—
153C2×Dic22—432no—
154C11×C4⋊C4—44no—
155C11×C4⋊C4—44no—
156C11×C22⋊C4—216no—
157C22⋊Dic11—216no—
158C4⋊Dic11—216no—
159C4⋊Dic11—44no—
160C4⋊Dic11—44no—
161Dic11⋊C4—216no—
162Dic11⋊C4—216no—
163Dic11⋊C4—48no—
164Dic11⋊C4—48no—
165C22×C22⋊Q8—112no—
166#2659—1116no—
167C2×#398—112no—
168C2×#398—112no—
169C2×#395—112no—
170C2×#395—112no—
171C2×#380—111no—
172C2×#380—112no—
173C2×#380D1111yescharacteristic
174C22×#95—111no—
175C23×C11—28no—
176C23×C11—28no—
177C23×C11—28no—
178C23×C11—28no—
179C23×C11—28no—
180C23×C11—28no—
181C23×C11—22no—
182C23×C11—22no—
183C23×C11—22no—
184C23×C11—22no—
185C23×C11C4⋊Q8116yes—
186C23×C11C22×D414yes—
187C23×C11C22×D412yes—
188C23×C11C22×Q814yes—
189C23×C11C22×Q812yes—
190C23×C11C22×Q814yes—
191C23×C11C22×Q812yes—
192C23×C11H(5,𝔽2)12yes—
193C23×C11H(5,𝔽2)12yes—
194C23×C11H(5,𝔽2)12yes—
195C23×C112−1+412yes—
196C23×C11C2511yescharacteristic
197C2×C4×C11—28no—
198C2×C4×C11—28no—
199C2×C4×C11—22no—
200C2×C4×C11—22no—
201C2×C4×C11—22no—
202C2×C4×C11—22no—
203C2×C4×C11—24no—
204C2×C4×C11—24no—
205C2×C4×C11—24no—
206C2×C4×C11—24no—
207C2×C4×C11—24no—
208C2×C4×C11—24no—
209C2×C4×C11—416no—
210C2×C4×C11—48no—
211C2×C4×C11—48no—
212C2×C4×C11C22×Q814yes—
213C2×C4×C11C22×Q814yes—
214C2×Dic11—216no—
215C2×Dic11—216no—
216C2×Dic11—24no—
217C2×Dic11—24no—
218C2×Dic11—24no—
219C2×Dic11—24no—
220C2×Dic11—24no—
221C2×Dic11—24no—
222C2×Dic11—24no—
223C2×Dic11—24no—
224C2×Dic11—24no—
225C2×Dic11—24no—
226C2×Dic11—416no—
227C2×Dic11—416no—
228C2×Dic11—48no—
229C2×Dic11—48no—
230C2×Dic11C22×D418yes—
231C2×Dic11C22×Q818yes—
232Dic22—432no—
233C23×Q8—112no—
234C24×C4—111no—
235C24×C4—111no—
236C24×C4C2×D1111yescharacteristic
237C2×C22⋊Q8—1116no—
238C2×C22⋊Q8—2216no—
239C22×C4⋊C4—112no—
240C22×C4⋊C4—112no—
241C22×C4⋊C4—112no—
242C22×C4⋊C4—112no—
243C22×C4⋊C4—112no—
244C22×C4⋊C4—111no—
245C22×C4⋊C4—111no—
246C22×C4⋊C4C2×D1111yescharacteristic
247C22×C4⋊C4C2×D1111yescharacteristic
248C22×C22⋊C4—112no—
249C22×C22⋊C4C2×D1112yes—
250#398—1116no—
251#398—1116no—
252#395—1116no—
253#395—1116no—
254#380—118no—
255#380—1116no—
256#380C2×D1118yes—
257C2×#95—112no—
258C2×#95—112no—
259C2×#95—112no—
260C2×#95—112no—
261C2×#95—112no—
262C2×#95—118no—
263C2×#95C2×D1112yes—
264C22×C11—232no—
265C22×C11—24no—
266C22×C11—24no—
267C22×C11—24no—
268C22×C11—24no—
269C22×C11—24no—
270C22×C11—24no—
271C22×C11C2×C4⋊Q818yes—
272C22×C11C2×C4⋊Q814yes—
273C22×C11#53414yes—
274C22×C11#53714yes—
275C22×C11#54314yes—
276C22×C11#54314yes—
277C22×C11#54414yes—
278C22×C11#54414yes—
279C22×C11C23×D411yescharacteristic
280C22×C11C23×Q811yescharacteristic
281C22×C11C23×Q811yescharacteristic
282C22×C11C2×H(5,𝔽2)11yescharacteristic
283C22×C11C2×H(5,𝔽2)11yescharacteristic
284C22×C11C2×H(5,𝔽2)11yescharacteristic
285C22×C11C2×2−1+411yescharacteristic
286C4×C11—24no—
287C4×C11—24no—
288C4×C11—44no—
289C4×C11—44no—
290Dic11—28no—
291Dic11—28no—
292Dic11—44no—
293Dic11—44no—
294C25C22×D1111yescharacteristic
295C22×Q8—118no—
296C22×Q8—228no—
297C22×Q8—444no—
298C22×Q8—444no—
299C23×C4—42no—
300C23×C4—42no—
301C23×C4—112no—
302C23×C4—112no—
303C23×C4—118no—
304C23×C4—118no—
305C23×C4—114no—
306C23×C4—114no—
307C23×C4—112no—
308C23×C4—112no—
309C23×C4—442no—
310C23×C4—442no—
311C23×C4—442no—
312C23×C4—442no—
313C23×C4Dic2218yescomplemented
314C23×C4C22×D1112yes—
315C23×C4C22×D1112yes—
316C23×C4C22×D1111yescharacteristic
317C23×C4C22×D1111yescharacteristic
318C23×C4C22×D1114yes—
319C22⋊Q8—2264no—
320C2×C4⋊C4—42no—
321C2×C4⋊C4—42no—
322C2×C4⋊C4—118no—
323C2×C4⋊C4—118no—
324C2×C4⋊C4—118no—
325C2×C4⋊C4—118no—
326C2×C4⋊C4—114no—
327C2×C4⋊C4—118no—
328C2×C4⋊C4—114no—
329C2×C4⋊C4—228no—
330C2×C4⋊C4—228no—
331C2×C4⋊C4—228no—
332C2×C4⋊C4—444no—
333C2×C4⋊C4—444no—
334C2×C4⋊C4—442no—
335C2×C4⋊C4—442no—
336C2×C4⋊C4C22×D1114yes—
337C2×C4⋊C4C22×D1114yes—
338C2×C22⋊C4—28no—
339C2×C22⋊C4—118no—
340C2×C22⋊C4—228no—
341C2×C22⋊C4C22×D1118yes—
342#95—118no—
343#95—118no—
344#95—118no—
345#95—118no—
346#95—118no—
347#95C22×D1118yes—
348C2×C11—28no—
349C2×C11#265918yescomplemented
350C2×C11C22×C4⋊Q811yescharacteristic
351C2×C11C2×#53411yescharacteristic
352C2×C11C2×#53711yescharacteristic
353C2×C11C2×#54311yescharacteristic
354C2×C11C2×#54311yescharacteristic
355C2×C11C2×#54411yescharacteristic
356C2×C11C2×#54411yescharacteristic
357C24—22no—
358C24—22no—
359C24—22no—
360C24—22no—
361C24C2×Dic2214yes—
362C24D4×D1114yes—
363C24Q8×D1114yes—
364C24C23×D1112yes—
365C24C23×D1111yescharacteristic
366C2×Q8—2216no—
367C2×Q8—448no—
368C2×Q8—448no—
369C2×Q8—4432no—
370C22×C4—22no—
371C22×C4—22no—
372C22×C4—22no—
373C22×C4—22no—
374C22×C4—24no—
375C22×C4—24no—
376C22×C4—24no—
377C22×C4—24no—
378C22×C4—24no—
379C22×C4—24no—
380C22×C4—44no—
381C22×C4—44no—
382C22×C4—416no—
383C22×C4—118no—
384C22×C4—118no—
385C22×C4—114no—
386C22×C4—114no—
387C22×C4—1116no—
388C22×C4—1116no—
389C22×C4—114no—
390C22×C4—114no—
391C22×C4—224no—
392C22×C4—224no—
393C22×C4—224no—
394C22×C4—224no—
395C22×C4—224no—
396C22×C4—224no—
397C22×C4—224no—
398C22×C4—224no—
399C22×C4—224no—
400C22×C4—224no—
401C22×C4—4416no—
402C22×C4—4416no—
403C22×C4—444no—
404C22×C4—444no—
405C22×C4—444no—
406C22×C4—444no—
407C22×C4C2×Dic2214yes—
408C22×C4C2×Dic2214yes—
409C22×C4C2×Dic22116yescomplemented
410C22×C4C23×D1114yes—
411C22×C4C23×D1114yes—
412C22×C4C23×D1112yes—
413C22×C4C23×D1112yes—
414C4⋊C4—44no—
415C4⋊C4—44no—
416C4⋊C4—2216no—
417C4⋊C4—2216no—
418C4⋊C4—2216no—
419C4⋊C4—448no—
420C4⋊C4—448no—
421C4⋊C4—444no—
422C4⋊C4—444no—
423C22⋊C4—216no—
424C22⋊C4—2216no—
425C11C2×#265911yescharacteristic, complemented, Sylow
426C23—28no—
427C23—28no—
428C23—28no—
429C23—28no—
430C23—28no—
431C23—28no—
432C23—22no—
433C23—22no—
434C23—22no—
435C23—22no—
436C23#66941116yes—
437C23C22×Dic2214yes—
438C23C22×Dic2212yes—
439C23C2×D4×D1114yes—
440C23C2×D4×D1112yes—
441C23#6703712yes—
442C23#6703712yes—
443C23C2×Q8×D1114yes—
444C23C2×Q8×D1112yes—
445C23#6704212yes—
446C23#6704312yes—
447C23C24×D1111yescharacteristic
448Q8—4432no—
449C2×C4—28no—
450C2×C4—28no—
451C2×C4—22no—
452C2×C4—22no—
453C2×C4—22no—
454C2×C4—22no—
455C2×C4—24no—
456C2×C4—24no—
457C2×C4—24no—
458C2×C4—24no—
459C2×C4—24no—
460C2×C4—24no—
461C2×C4—416no—
462C2×C4—48no—
463C2×C4—48no—
464C2×C4—118no—
465C2×C4—118no—
466C2×C4—2216no—
467C2×C4—2216no—
468C2×C4—224no—
469C2×C4—224no—
470C2×C4—224no—
471C2×C4—224no—
472C2×C4—224no—
473C2×C4—224no—
474C2×C4—224no—
475C2×C4—224no—
476C2×C4—224no—
477C2×C4—224no—
478C2×C4—4416no—
479C2×C4—4416no—
480C2×C4—448no—
481C2×C4—448no—
482C2×C4C22×Dic2214yes—
483C2×C4C22×Dic2214yes—
484C22—232no—
485C22—24no—
486C22—24no—
487C22—24no—
488C22—24no—
489C22—24no—
490C22—24no—
491C22#1062301414yes—
492C22C2×#6694118yes—
493C22C2×#6694114yes—
494C22#1062305014yes—
495C22#1062312814yes—
496C22#1062313614yes—
497C22#1062315414yes—
498C22#1062316514yes—
499C22C23×Dic2211yescharacteristic
500C22C22×D4×D1111yescharacteristic
501C22C2×#6703711yescharacteristic
502C22C2×#6703711yescharacteristic
503C22C22×Q8×D1111yescharacteristic
504C22C2×#6704211yescharacteristic
505C22C2×#6704311yescharacteristic
506C4—24no—
507C4—24no—
508C4—44no—
509C4—44no—
510C4—228no—
511C4—228no—
512C4—444no—
513C4—444no—
514C2—28no—
515C2#1307473318yesdirect product factor
516C2C22×#6694111yescharacteristic
517C2C2×#1062313611yescharacteristic
518C2C2×#1062312811yescharacteristic
519C2C2×#1062316511yescharacteristic
520C2C2×#1062301411yescharacteristic
521C2C2×#1062305011yescharacteristic
522C2C2×#1062315411yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#380C2
socleC24×C11C24
prime radicalC25×C11C23
hypercenterC2×#380D11
hypocenterC11C2×#2659
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#380

Complements

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

NH ≅ G/Ntype
2. #13074733C2direct (N × H)
3. C2×#10622270C2semidirect
4. C2×#10622597C2semidirect
5. C2×#10622269C2semidirect
6. C2×#10622592C2semidirect
37. #10622597C22semidirect
38. #10622592C22semidirect
40. #10622270C22semidirect
41. #10622269C22semidirect
45. C23×C4×C11Q8semidirect
56. C23×Dic11Q8semidirect
121. C22×C4×C11C2×Q8semidirect
145. C22×Dic11C2×Q8semidirect
313. C23×C4Dic22semidirect
349. C2×C11#2659semidirect
409. C22×C4C2×Dic22semidirect
425. C11C2×#2659semidirect
515. C2#13074733direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669312
#130747332
C2×#106222702
C2×#106225972
C2×#106222692
C2×#106225922
C2×#106228252
C2×#106225552
C22×C11⋊#952
C2×C11×#3802
C2×#265911