Finite Group Databasebeta

← C2×#13079542 #15624957

Subgroups — C2×#13079542 #15624957

Order 2816.

2414 conjugacy classes of subgroups.

The subgroup lattice has 514 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623256C211yesmaximal, characteristic
2C2×D11×C4⋊Q8C211yesmaximal, characteristic, complemented
3#13079542C2116yesmaximal, direct product factor
4C2×#10622698C211yesmaximal, characteristic, complemented
5C2×#10622306C211yesmaximal, characteristic, complemented
6C2×#10622706C211yesmaximal, characteristic, complemented
7C2×#10622431C214yesmaximal, complemented
8C2×#10622419C214yesmaximal, complemented
9C2×#10622298C211yesmaximal, characteristic, complemented
10C2×C11×#487C211yesmaximal, characteristic, complemented
11C22×#4343—21no—
12C22×Q8×D11C2212yes—
13C2×C11×C4⋊Q8C2211yescharacteristic
14C2×C11×C4⋊Q8C2211yescharacteristic
15C2×#67000—21no—
16C2×#66997C2212yes—
17C22×#4325C2214yes—
18C22×#4314C2214yes—
19#10623256—24no—
20#10623256C2218yes—
21D11×C4⋊Q8—24no—
22D11×C4⋊Q8C2218yescomplemented
23C2×#66948—21no—
24C2×#66948C2212yes—
25C2×#66946—21no—
26C2×#66946C2212yes—
27C2×C4⋊C4×D11—21no—
28C2×C4⋊C4×D11—21no—
29C2×#66941—21no—
30C2×#66941—21no—
31C2×#66927C2211yescharacteristic
32C2×C42×D11C2211yescharacteristic
33C2×#66922C2211yescharacteristic
34C11×#487C2218yescomplemented
35C2×C11×#103C2214yes—
36C2×C4×C8×C11C2211yescharacteristic
37C2×(C2×D11)⋊C8C2212yes—
38C2×Dic11⋊C8C2212yes—
39#10622706C2218yescomplemented
40#10622698C2218yescomplemented
41C2×#66874C2214yes—
42C2×C4×C11⋊C8C2211yescharacteristic
43#10622431C22132yescomplemented
44#10622419C22132yescomplemented
45#10622306C2218yescomplemented
46#10622298C2218yescomplemented
47C22×Q8×C11—21no—
48C22×Q8×C11C2312yes—
49C2×#4343—28no—
50C2×#4343—48no—
51C2×Q8×D11—24no—
52C2×Q8×D11—48no—
53C2×Q8×D11C2318yes—
54C22×D44—22no—
55C22×D44—21no—
56C22×D44—21no—
57C22×D44C2312yes—
58C22×C4×D11—22no—
59C22×C4×D11—22no—
60C22×C4×D11D411yescharacteristic
61C22×C4×D11D411yescharacteristic
62C22×C4×D11C2311yescharacteristic
63C22×Dic22—22no—
64C22×Dic22C2312yes—
65C22×C8×C11C2312yes—
66C11×C4⋊Q8—22no—
67C11×C4⋊Q8—22no—
68C11×C4⋊Q8C2314yes—
69C11×C4⋊Q8C2314yes—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4C2312yes—
74C2×C42×C11C2311yescharacteristic
75#67000—28no—
76#66997—24no—
77#66997C2318yes—
78C2×#4325—48no—
79C2×#4325C23116yes—
80C2×(C2×D11)⋊C4—22no—
81C2×(C2×D11)⋊C4—22no—
82C2×C4⋊Dic11—21no—
83C2×C4⋊Dic11—21no—
84C2×Dic11⋊C4—22no—
85C2×Dic11⋊C4—22no—
86C2×C4×Dic11D411yescharacteristic
87C2×C4×Dic11D411yescharacteristic
88C2×C4×Dic11C2311yescharacteristic
89C22×C11⋊C8C2312yes—
90C2×#4314—48no—
91C2×#4314C23116yes—
92#66948—24no—
93#66948—28no—
94#66948C2318yes—
95#66946—24no—
96#66946—28no—
97#66946C2318yes—
98C4⋊C4×D11—28no—
99C4⋊C4×D11—28no—
100#66941—28no—
101#66941—28no—
102#66927—22no—
103#66927C2314yes—
104C42×D11D414yes—
105C42×D11C2314yes—
106#66922—22no—
107#66922C2314yes—
108C11×#103C23116yes—
109C4×C8×C11C2314yes—
110(C2×D11)⋊C8C2318yes—
111Dic11⋊C8C2318yes—
112#66874C23116yes—
113C4×C11⋊C8C2314yes—
114C2×#3206—111nomaximal, Sylow
115C23×D11—22no—
116C23×D11C2×D411yescharacteristic
117C2×Q8×C11—22no—
118C2×Q8×C11—24no—
119C2×Q8×C11—28no—
120C2×Q8×C11—44no—
121C2×Q8×C11C2414yes—
122C22×C4×C11—22no—
123C22×C4×C11—22no—
124C22×C4×C11C2×D411yescharacteristic
125C22×C4×C11C2×D411yescharacteristic
126C22×C4×C11C2411yescharacteristic
127C22×Dic11—22no—
128C22×Dic11C2×D411yescharacteristic
129C22×Dic11C2×D411yescharacteristic
130C22×Dic11C2×D411yescharacteristic
131#4343—432no—
132Q8×D11—416no—
133Q8×D11—416no—
134C2×D44—28no—
135C2×D44—22no—
136C2×D44—24no—
137C2×D44—24no—
138C2×D44—28no—
139C2×D44—48no—
140C2×D44—44no—
141C2×D44—44no—
142C2×D44C2414yes—
143C2×C4×D11—28no—
144C2×C4×D11—28no—
145C2×C4×D11—24no—
146C2×C4×D11—24no—
147C2×C4×D11—48no—
148C2×C4×D11—48no—
149C2×C4×D11SD1618yescomplemented
150C2×C4×D11C2×D412yes—
151C2×C4×D11C2×D414yes—
152C2×C4×D11C2×D414yes—
153C2×C4×D11C2412yes—
154C2×Dic22—28no—
155C2×Dic22—22no—
156C2×Dic22—28no—
157C2×Dic22—48no—
158C2×Dic22C2414yes—
159C2×C8×C11—24no—
160C2×C8×C11C2414yes—
161C11×C4⋊C4—24no—
162C11×C4⋊C4—24no—
163C11×C4⋊C4—24no—
164C11×C4⋊C4—22no—
165C11×C4⋊C4C2414yes—
166C42×C11C2×D412yes—
167C42×C11C2412yes—
168#4325—416no—
169(C2×D11)⋊C4—28no—
170(C2×D11)⋊C4—28no—
171C4⋊Dic11—24no—
172C4⋊Dic11—24no—
173Dic11⋊C4—28no—
174Dic11⋊C4—28no—
175C4×Dic11C2×D412yes—
176C4×Dic11C2×D414yes—
177C4×Dic11C2×D414yes—
178C4×Dic11C2412yes—
179C2×C11⋊C8—24no—
180C2×C11⋊C8C2414yes—
181#4314—416no—
182C2×#532—111no—
183C22×C4⋊Q8—111no—
184#3206—1116no—
185C2×#492—111no—
186C2×#492—111no—
187C2×#487—111no—
188C2×#487D1111yescharacteristic, complemented
189C2×#461—114no—
190C2×#448—114no—
191C2×#431—111no—
192C23×C11C22×D411yescharacteristic
193C22×D11—22no—
194C22×D11—22no—
195C22×D11—24no—
196C22×D11—44no—
197C22×D11—44no—
198C22×D11—44no—
199C22×D11C2×SD1614yes—
200C22×D11C22×D412yes—
201Q8×C11—28no—
202Q8×C11—44no—
203Q8×C11—48no—
204C2×C4×C11—24no—
205C2×C4×C11—24no—
206C2×C4×C11—44no—
207C2×C4×C11—44no—
208C2×C4×C11C2×SD1614yes—
209C2×C4×C11#13714yes—
210C2×C4×C11C22×D411yescharacteristic
211C2×C4×C11C22×D412yes—
212C2×C4×C11C22×D412yes—
213C2×C4×C11H(5,𝔽2)14yes—
214C2×C4×C11C2511yescharacteristic
215C2×Dic11—22no—
216C2×Dic11—22no—
217C2×Dic11—24no—
218C2×Dic11—44no—
219C2×Dic11C2×SD1614yes—
220C2×Dic11C22×D412yes—
221C2×Dic11C22×D412yes—
222C2×Dic11C22×D412yes—
223D44—28no—
224D44—416no—
225D44—44no—
226D44—48no—
227D44—48no—
228C4×D11—24no—
229C4×D11—28no—
230C4×D11—24no—
231C4×D11—416no—
232C4×D11—416no—
233C4×D11C2×SD16116yescomplemented
234Dic22—28no—
235Dic22—416no—
236Dic22—44no—
237C8×C11—24no—
238C11⋊C8—24no—
239C22×#41—221no—
240C23×Q8—112no—
241C22×SD16—114no—
242C22×SD16—114no—
243#532—118no—
244#532—224no—
245C2×C4⋊Q8—112no—
246C2×C4⋊Q8—118no—
247C2×C4⋊Q8—111no—
248C2×C4⋊Q8—221no—
249C2×C4⋊Q8—221no—
250C2×C4⋊Q8—224no—
251C2×C4⋊Q8C2×D1111yescharacteristic
252C2×C4⋊Q8C2×D1111yescharacteristic
253C2×#127—111no—
254C2×#124—221no—
255C2×#121—112no—
256C2×#121—221no—
257C2×C4×D4—112no—
258C2×C4×D4—221no—
259C22×C4⋊C4—221no—
260C22×C4⋊C4—221no—
261C22×C42—111no—
262#492—118no—
263#492—118no—
264#487—118no—
265#487C2×D1118yescomplemented
266#461—1132no—
267#448—1132no—
268#431—118no—
269C2×C4⋊C8—112no—
270C2×#103—114no—
271C2×#103C2×D1114yes—
272C2×C22⋊C8—112no—
273C2×C4×C8—111no—
274C2×C4×C8C2×D1111yescharacteristic
275C22×C11#53512yes—
276C22×C11C22×SD1612yes—
277C22×C11C2×#13712yes—
278C22×C11C23×D411yescharacteristic
279C2×D11—22no—
280C2×D11—28no—
281C2×D11—22no—
282C2×D11—44no—
283C2×D11—44no—
284C2×D11—44no—
285C2×D11—88no—
286C2×D11C22×SD1614yes—
287C4×C11—44no—
288C4×C11—44no—
289C4×C11#53512yes—
290C4×C11C22×SD1614yes—
291C4×C11C2×#13714yes—
292C4×C11C2×H(5,𝔽2)12yes—
293Dic11—22no—
294Dic11—22no—
295Dic11—44no—
296Dic11C22×SD1614yes—
297C2×#41—228no—
298C2×#41—448no—
299C22×Q8—21no—
300C22×Q8—118no—
301C22×Q8—112no—
302C22×Q8—222no—
303C22×Q8—224no—
304C22×Q8—448no—
305C22×Q8C22×D1112yes—
306C22×D4—112no—
307C22×D4—222no—
308C22×D4—221no—
309C22×D4—221no—
310C23×C4—111no—
311C23×C4—111no—
312C23×C4—111no—
313C23×C4—222no—
314C23×C4—222no—
315C2×SD16—1116no—
316C2×SD16—1116no—
317C2×SD16—448no—
318C2×SD16—448no—
319C22×C8—112no—
320C22×C8C22×D1112yes—
321C4⋊Q8—22no—
322C4⋊Q8—22no—
323C4⋊Q8—118no—
324C4⋊Q8—114no—
325C4⋊Q8—228no—
326C4⋊Q8—228no—
327C4⋊Q8—224no—
328C4⋊Q8—222no—
329C4⋊Q8C22×D1114yes—
330C4⋊Q8C22×D1114yes—
331#127—114no—
332#127—222no—
333#124—228no—
334#121—118no—
335#121—224no—
336#121—228no—
337C4×D4—118no—
338C4×D4—224no—
339C4×D4—228no—
340C2×C4⋊C4—21no—
341C2×C4⋊C4—21no—
342C2×C4⋊C4—21no—
343C2×C4⋊C4—228no—
344C2×C4⋊C4—228no—
345C2×C4⋊C4—222no—
346C2×C4⋊C4—222no—
347C2×C4⋊C4—221no—
348C2×C4⋊C4—221no—
349C2×C4⋊C4C22×D1112yes—
350C2×C22⋊C4—222no—
351C2×C22⋊C4—222no—
352C2×C42—111no—
353C2×C42—111no—
354C2×C42—111no—
355C2×C42—114no—
356C2×C42—114no—
357C2×C42C22×D1111yescharacteristic
358C4⋊C8—118no—
359#103—1116no—
360#103C22×D11116yes—
361C22⋊C8—118no—
362C4×C8—114no—
363C4×C8C22×D1114yes—
364C2×C11#320614yescomplemented
365C2×C11C2×#53511yescharacteristic
366C2×C11C23×SD1611yescharacteristic
367C2×C11C22×#13711yescharacteristic
368D11—24no—
369D11—84no—
370C24—111no—
371C24—222no—
372#41—4432no—
373C2×Q8—24no—
374C2×Q8—22no—
375C2×Q8—28no—
376C2×Q8—44no—
377C2×Q8—114no—
378C2×Q8—228no—
379C2×Q8—222no—
380C2×Q8—228no—
381C2×Q8—448no—
382C2×Q8—4416no—
383C2×Q8—4416no—
384C2×Q8C23×D1114yes—
385C2×D4—114no—
386C2×D4—228no—
387C2×D4—224no—
388C2×D4—222no—
389C2×D4—224no—
390C2×D4—228no—
391C2×D4—448no—
392C2×D4—444no—
393C2×D4—444no—
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—111no—
397C22×C4—118no—
398C22×C4—114no—
399C22×C4—111no—
400C22×C4—111no—
401C22×C4—114no—
402C22×C4—112no—
403C22×C4—112no—
404C22×C4—228no—
405C22×C4—228no—
406C22×C4—224no—
407C22×C4—224no—
408C22×C4—222no—
409C22×C4—448no—
410C22×C4—448no—
411C22×C4D4×D1111yescharacteristic
412C22×C4D4×D1111yescharacteristic
413C22×C4C23×D1111yescharacteristic
414SD16—4416no—
415SD16—4416no—
416C2×C8—24no—
417C2×C8—114no—
418C2×C8—224no—
419C2×C8C23×D1114yes—
420C4⋊C4—24no—
421C4⋊C4—24no—
422C4⋊C4—24no—
423C4⋊C4—22no—
424C4⋊C4—228no—
425C4⋊C4—228no—
426C4⋊C4—224no—
427C4⋊C4—224no—
428C4⋊C4C23×D1114yes—
429C22⋊C4—228no—
430C22⋊C4—228no—
431C42—112no—
432C42—114no—
433C42—114no—
434C42—112no—
435C42D4×D1112yes—
436C42C23×D1112yes—
437C11C2×#320611yescharacteristic, complemented, Sylow
438C23—114no—
439C23—112no—
440C23—222no—
441C23—222no—
442C23—224no—
443C23—444no—
444C23—444no—
445C23—444no—
446C23C2×D4×D1111yescharacteristic
447Q8—28no—
448Q8—48no—
449Q8—44no—
450Q8—228no—
451Q8—4416no—
452Q8—444no—
453D4—228no—
454D4—4416no—
455D4—448no—
456D4—448no—
457D4—444no—
458C2×C4—24no—
459C2×C4—24no—
460C2×C4—44no—
461C2×C4—44no—
462C2×C4—114no—
463C2×C4—112no—
464C2×C4—1116no—
465C2×C4—112no—
466C2×C4—112no—
467C2×C4—222no—
468C2×C4—222no—
469C2×C4—228no—
470C2×C4—224no—
471C2×C4—224no—
472C2×C4—224no—
473C2×C4—4416no—
474C2×C4—4416no—
475C2×C4—444no—
476C2×C4SD16×D1114yes—
477C2×C4#6697114yes—
478C2×C4C2×D4×D1112yes—
479C2×C4C2×D4×D1112yes—
480C2×C4C2×D4×D1111yescharacteristic
481C2×C4#6704214yes—
482C2×C4C24×D1111yescharacteristic
483C8—24no—
484C8—224no—
485C22—114no—
486C22—222no—
487C22—222no—
488C22—228no—
489C22—444no—
490C22—444no—
491C22—444no—
492C22—888no—
493C22#1062320512yes—
494C22C2×SD16×D1112yes—
495C22C2×#6697112yes—
496C22C22×D4×D1111yescharacteristic
497C4—44no—
498C4—44no—
499C4—114no—
500C4—222no—
501C4—222no—
502C4—444no—
503C4#1062320512yes—
504C4C2×SD16×D1114yes—
505C4C2×#6697114yes—
506C4C2×#6704212yes—
507C2—224no—
508C2—884no—
509C2#1307954214yesdirect product factor
510C2C2×#1062320511yescharacteristic
511C2C22×SD16×D1111yescharacteristic
512C2C22×#6697111yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#487C2
socleC23×C11C22×D4
prime radicalC2×#10623256C2
hypercenterC2×#487D11
hypocenterC11C2×#3206
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#487

Complements

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

NH ≅ G/Ntype
2. C2×D11×C4⋊Q8C2semidirect
3. #13079542C2direct (N × H)
4. C2×#10622698C2semidirect
5. C2×#10622306C2semidirect
6. C2×#10622706C2semidirect
7. C2×#10622431C2semidirect
8. C2×#10622419C2semidirect
9. C2×#10622298C2semidirect
10. C2×C11×#487C2semidirect
22. D11×C4⋊Q8C22semidirect
34. C11×#487C22semidirect
39. #10622706C22semidirect
40. #10622698C22semidirect
43. #10622431C22semidirect
44. #10622419C22semidirect
45. #10622306C22semidirect
46. #10622298C22semidirect
149. C2×C4×D11SD16semidirect
188. C2×#487D11semidirect
233. C4×D11C2×SD16semidirect
265. #487C2×D11semidirect
364. C2×C11#3206semidirect
437. C11C2×#3206semidirect
509. C2#13079542direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106232562
C2×D11×C4⋊Q82
#130795422
C2×#106226982
C2×#106223062
C2×#106227062
C2×#106224312
C2×#106224192
C2×#106222982
C2×C11×#4872
C2×#320611