Finite Group Databasebeta

← C2×#13080899 #15630658

Subgroups — C2×#13080899 #15630658

Order 2816.

2082 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×#10623073C211yesmaximal, characteristic
2#13080899C2116yesmaximal, direct product factor
3C2×#10622694C211yesmaximal, characteristic, complemented
4C2×#10622658C212yesmaximal, complemented
5C2×#10622633C211yesmaximal, characteristic, complemented
6C2×#10622665C212yesmaximal, complemented
7C2×#10622703C211yesmaximal, characteristic, complemented
8C2×#10622841C212yesmaximal, complemented
9C2×C4×#4326C211yesmaximal, characteristic, complemented
10C2×#10622625C211yesmaximal, characteristic
11C2×#10622838C212yesmaximal, complemented
12C2×D4×Q8×C11C211yesmaximal, characteristic
13C23×Q8×C11C2212yes—
14D4×Q8×C11—24no—
15D4×Q8×C11C2218yes—
16C2×C11×C4⋊Q8—21no—
17C2×C11×C4⋊Q8C2211yescharacteristic
18C2×C11×C22⋊Q8—22no—
19C2×C11×C22⋊Q8C2212yes—
20C2×C4×Q8×C11C2211yescharacteristic
21C2×C4×D4×C11—21no—
22C2×C4×D4×C11C2211yescharacteristic
23C22×#4326C2211yescharacteristic
24C22×#4326C2212yes—
25C2×#66989—21no—
26C2×#66979C2212yes—
27C2×#66977C2212yes—
28C22×#4318C2212yes—
29#10623073—24no—
30#10623073C2218yes—
31C2×#66940—21no—
32C2×#66932—22no—
33C2×#66922C2211yescharacteristic
34C2×C4×Dic22C2211yescharacteristic
35#10622841C22116yescomplemented
36#10622838C22116yescomplemented
37C2×#66899C2212yes—
38C2×#66899C2212yes—
39C2×#66899C2212yes—
40C2×#66899C2211yescharacteristic
41C2×#66899C2212yes—
42C2×C22⋊(C11⋊C8)C2212yes—
43#10622703C2218yescomplemented
44#10622694C2218yescomplemented
45#10622665C22116yescomplemented
46#10622658C22116yescomplemented
47C4×#4326C2218yescomplemented
48#10622633C2218yescomplemented
49#10622625C2218yes—
50C2×#66874C2211yescharacteristic
51C2×#66872C2212yes—
52C2×#66871C2211yescharacteristic
53C2×C4⋊(C11⋊C8)C2211yescharacteristic
54C2×C4×C11⋊C8C2211yescharacteristic
55C22×Q8×C11—22no—
56C22×Q8×C11—24no—
57C22×Q8×C11—28no—
58C22×Q8×C11—44no—
59C22×Q8×C11C2312yes—
60C22×Q8×C11C2318yes—
61C22×Q8×C11C2311yescharacteristic
62C22×D4×C11D411yescharacteristic
63C23×C4×C11—22no—
64C23×C4×C11C2312yes—
65C22×Dic22—21no—
66C22×Dic22C2311yescharacteristic
67C11×C4⋊Q8—28no—
68C11×C4⋊Q8—22no—
69C11×C4⋊Q8C2314yes—
70C11×C22⋊Q8—24no—
71C11×C22⋊Q8—216no—
72C11×C22⋊Q8C2318yes—
73C4×Q8×C11—22no—
74C4×Q8×C11C2314yes—
75C4×D4×C11—28no—
76C4×D4×C11D414yes—
77C4×D4×C11C2314yes—
78C2×C11×C4⋊C4—21no—
79C2×C11×C4⋊C4—21no—
80C2×C11×C4⋊C4—21no—
81C2×C11×C4⋊C4—22no—
82C2×C11×C4⋊C4D411yescharacteristic
83C2×C11×C4⋊C4C2311yescharacteristic
84C2×C11×C22⋊C4—22no—
85C2×C11×C22⋊C4D412yes—
86C2×C42×C11—21no—
87C2×C42×C11C2311yescharacteristic
88C2×C22⋊Dic11—22no—
89C2×C22⋊Dic11—22no—
90C2×#4326—24no—
91C2×#4326—44no—
92C2×#4326C2314yes—
93C2×#4326C2318yes—
94#66989—28no—
95#66979—24no—
96#66979C2318yes—
97C2×C4⋊Dic11—21no—
98C2×C4⋊Dic11C2311yescharacteristic
99C2×C4⋊Dic11C2312yes—
100#66977—24no—
101#66977C2318yes—
102C2×Dic11⋊C4—21no—
103C2×Dic11⋊C4—22no—
104C2×C4×Dic11—21no—
105C2×C4×Dic11—22no—
106C2×#4318—44no—
107C2×#4318C2318yes—
108C22×C11⋊C8C2311yescharacteristic
109C22×C11⋊C8C2311yescharacteristic
110C22×C11⋊C8C2312yes—
111#66940—28no—
112#66932—216no—
113#66922—22no—
114#66922C2314yes—
115C4×Dic22—22no—
116C4×Dic22C2314yes—
117#66899C2314yes—
118#66899C2318yes—
119#66899C2318yes—
120#66899C2318yes—
121#66899C2318yes—
122C22⋊(C11⋊C8)C2318yes—
123#66874C2314yes—
124#66872C2318yes—
125#66871C2314yes—
126C4⋊(C11⋊C8)C2314yes—
127C4×C11⋊C8C2314yes—
128C2×#3328—111nomaximal, Sylow
129C24×C11C2×D412yes—
130C2×Q8×C11—21no—
131C2×Q8×C11—28no—
132C2×Q8×C11—22no—
133C2×Q8×C11—22no—
134C2×Q8×C11—216no—
135C2×Q8×C11—24no—
136C2×Q8×C11—24no—
137C2×Q8×C11—48no—
138C2×Q8×C11—48no—
139C2×Q8×C11—416no—
140C2×Q8×C11#4114yes—
141C2×Q8×C11C2414yes—
142C2×Q8×C11C2412yes—
143C2×D4×C11—24no—
144C2×D4×C11C2×D414yes—
145C22×C4×C11—21no—
146C22×C4×C11—24no—
147C22×C4×C11—24no—
148C22×C4×C11—21no—
149C22×C4×C11—22no—
150C22×C4×C11—28no—
151C22×C4×C11—48no—
152C22×C4×C11C2×D412yes—
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11C2×D414yes—
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11C2414yes—
157C22×C4×C11C2411yescharacteristic
158C22×Dic11—21no—
159C22×Dic11—21no—
160C22×Dic11—22no—
161C2×Dic22—21no—
162C2×Dic22—24no—
163C2×Dic22—22no—
164C2×Dic22—22no—
165C2×Dic22—44no—
166C2×Dic22C2412yes—
167C11×C4⋊C4—24no—
168C11×C4⋊C4—24no—
169C11×C4⋊C4—24no—
170C11×C4⋊C4—28no—
171C11×C4⋊C4—21no—
172C11×C4⋊C4C2×D414yes—
173C11×C4⋊C4C2412yes—
174C11×C22⋊C4—28no—
175C11×C22⋊C4C2×D418yes—
176C42×C11—24no—
177C42×C11C2×D412yes—
178C42×C11C2412yes—
179C22⋊Dic11—28no—
180C22⋊Dic11—28no—
181#4326—28no—
182#4326—48no—
183C4⋊Dic11—21no—
184C4⋊Dic11—22no—
185C4⋊Dic11—24no—
186C4⋊Dic11C2412yes—
187C4⋊Dic11C2414yes—
188Dic11⋊C4—24no—
189Dic11⋊C4—28no—
190C4×Dic11—24no—
191C4×Dic11—28no—
192#4318—48no—
193C2×C11⋊C8—22no—
194C2×C11⋊C8—22no—
195C2×C11⋊C8—24no—
196C2×C11⋊C8C2412yes—
197C2×C11⋊C8C2412yes—
198C2×C11⋊C8C2414yes—
199C2×#556—111no—
200C2×D4×Q8D1111yescharacteristic
201#3328—1116no—
202C2×#487—111no—
203C2×#485—112no—
204C2×#475—111no—
205C2×#470—112no—
206C2×#462—111no—
207C2×#451—112no—
208C2×C4×Q16—111no—
209C2×#436—111no—
210C2×#419—112no—
211C23×C11—24no—
212C23×C11—24no—
213C23×C11—24no—
214C23×C11C22×D414yes—
215C23×C11C22×D411yescharacteristic
216Q8×C11—24no—
217Q8×C11—22no—
218Q8×C11—24no—
219Q8×C11—24no—
220Q8×C11—416no—
221Q8×C11—44no—
222Q8×C11C2×#4114yes—
223D4×C11—28no—
224C2×C4×C11—24no—
225C2×C4×C11—24no—
226C2×C4×C11—22no—
227C2×C4×C11—22no—
228C2×C4×C11—28no—
229C2×C4×C11—24no—
230C2×C4×C11—24no—
231C2×C4×C11—22no—
232C2×C4×C11—24no—
233C2×C4×C11—416no—
234C2×C4×C11—44no—
235C2×C4×C11—42no—
236C2×C4×C11#13714yes—
237C2×C4×C11C22×D414yes—
238C2×C4×C11C22×D412yes—
239C2×C4×C11C22×D411yescharacteristic
240C2×C4×C11C22×D412yes—
241C2×C4×C11C2×#4112yes—
242C2×C4×C11H(5,𝔽2)12yes—
243C2×C4×C11C2511yescharacteristic
244C2×Dic11—22no—
245C2×Dic11—22no—
246C2×Dic11—24no—
247C2×Dic11—42no—
248C2×Dic11—44no—
249C2×Dic11—42no—
250Dic22—22no—
251Dic22—22no—
252Dic22—42no—
253Dic22—48no—
254C11⋊C8—22no—
255C11⋊C8—22no—
256C11⋊C8—24no—
257C23×Q8C2×D1112yes—
258C22×Q16—111no—
259C22×Q16—112no—
260C22×M16—112no—
261#556—118no—
262#556—224no—
263D4×Q8—24no—
264D4×Q8C2×D1118yes—
265C2×C4⋊Q8—21no—
266C2×C4⋊Q8—111no—
267C2×C4⋊Q8C2×D1111yescharacteristic
268C2×#126—222no—
269C2×#124—221no—
270C2×C22⋊Q8—22no—
271C2×C22⋊Q8—112no—
272C2×C22⋊Q8C2×D1112yes—
273C2×C4×Q8—111no—
274C2×C4×Q8—221no—
275C2×C4×Q8C2×D1111yescharacteristic
276C2×C4×D4—21no—
277C2×C4×D4C2×D1111yescharacteristic
278C2×#117—112no—
279#487—118no—
280#485—1116no—
281#475—118no—
282#470—1116no—
283#462—118no—
284#451—1116no—
285C4×Q16—118no—
286#436—118no—
287C2×#107—111no—
288C2×#106—112no—
289C2×C4⋊C8—111no—
290#419—1116no—
291C2×#103—112no—
292C2×#103—112no—
293C2×#103—112no—
294C2×#103—112no—
295C2×#103—111no—
296C2×#103—111no—
297C2×C22⋊C8—112no—
298C2×C4×C8—111no—
299C22×C11—24no—
300C22×C11—24no—
301C22×C11—24no—
302C22×C11—48no—
303C22×C11#54612yes—
304C22×C11C2×#13712yes—
305C22×C11#57812yes—
306C22×C11C23×D411yescharacteristic
307C4×C11—24no—
308C4×C11—24no—
309C4×C11—22no—
310C4×C11—44no—
311C4×C11—42no—
312C4×C11#54612yes—
313C4×C11C2×#13714yes—
314C4×C11C22×#4111yescharacteristic
315C4×C11C2×H(5,𝔽2)11yescharacteristic
316Dic11—42no—
317Dic11—44no—
318Dic11—42no—
319C22×Q8—22no—
320C22×Q8—24no—
321C22×Q8—28no—
322C22×Q8—44no—
323C22×Q8—111no—
324C22×Q8—221no—
325C22×Q8C22×D1112yes—
326C22×Q8C22×D1118yes—
327C22×Q8C22×D1111yescharacteristic
328C22×D4C22⋊D1111yescharacteristic
329C23×C4—22no—
330C23×C4C22×D1112yes—
331C2×Q16—114no—
332C2×Q16—118no—
333C2×Q16—224no—
334C2×Q16—444no—
335C2×M16—118no—
336C2×M16—444no—
337C22×C8—111no—
338C22×C8—112no—
339C22×C8—111no—
340C4⋊Q8—28no—
341C4⋊Q8—22no—
342C4⋊Q8—114no—
343C4⋊Q8—222no—
344C4⋊Q8C22×D1114yes—
345#126—2216no—
346#124—228no—
347C22⋊Q8—24no—
348C22⋊Q8—216no—
349C22⋊Q8—118no—
350C22⋊Q8—224no—
351C22⋊Q8C22×D1118yes—
352C4×Q8—22no—
353C4×Q8—114no—
354C4×Q8—228no—
355C4×Q8—222no—
356C4×Q8C22×D1114yes—
357C4×D4—28no—
358C4×D4C22⋊D1114yes—
359C4×D4C22×D1114yes—
360#117—118no—
361#117—224no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—22no—
366C2×C4⋊C4—111no—
367C2×C4⋊C4—112no—
368C2×C4⋊C4—221no—
369C2×C4⋊C4—222no—
370C2×C4⋊C4—221no—
371C2×C4⋊C4C22⋊D1111yescharacteristic
372C2×C4⋊C4C22×D1111yescharacteristic
373C2×C22⋊C4—22no—
374C2×C22⋊C4—222no—
375C2×C22⋊C4—222no—
376C2×C22⋊C4C22⋊D1112yes—
377C2×C42—21no—
378C2×C42—222no—
379C2×C42—221no—
380C2×C42C22×D1111yescharacteristic
381#107—114no—
382#106—118no—
383C4⋊C8—114no—
384#103—114no—
385#103—118no—
386#103—118no—
387#103—118no—
388#103—118no—
389#103—114no—
390C22⋊C8—118no—
391C4×C8—114no—
392C2×C11—44no—
393C2×C11#332814yescomplemented
394C2×C11C2×#54611yescharacteristic
395C2×C11C22×#13711yescharacteristic
396C2×C11C2×#57811yescharacteristic
397C24C2×C22⋊D1112yes—
398C2×Q8—22no—
399C2×Q8—21no—
400C2×Q8—28no—
401C2×Q8—22no—
402C2×Q8—216no—
403C2×Q8—24no—
404C2×Q8—24no—
405C2×Q8—48no—
406C2×Q8—48no—
407C2×Q8—416no—
408C2×Q8—112no—
409C2×Q8—221no—
410C2×Q8—224no—
411C2×Q8—222no—
412C2×Q8—222no—
413C2×Q8—444no—
414C2×Q8#434114yes—
415C2×Q8C23×D1114yes—
416C2×Q8C23×D1112yes—
417C2×D4—24no—
418C2×D4C2×C22⋊D1114yes—
419C22×C4—21no—
420C22×C4—24no—
421C22×C4—24no—
422C22×C4—28no—
423C22×C4—21no—
424C22×C4—22no—
425C22×C4—48no—
426C22×C4—221no—
427C22×C4—222no—
428C22×C4—221no—
429C22×C4C2×C22⋊D1114yes—
430C22×C4C2×C22⋊D1112yes—
431C22×C4C2×C22⋊D1111yescharacteristic
432C22×C4C2×C22⋊D1111yescharacteristic
433C22×C4C23×D1114yes—
434C22×C4C23×D1111yescharacteristic
435Q16—228no—
436Q16—448no—
437M16—448no—
438C2×C8—112no—
439C2×C8—112no—
440C2×C8—114no—
441C2×C8—222no—
442C2×C8—222no—
443C2×C8—224no—
444C4⋊C4—24no—
445C4⋊C4—24no—
446C4⋊C4—24no—
447C4⋊C4—28no—
448C4⋊C4—21no—
449C4⋊C4—114no—
450C4⋊C4—112no—
451C4⋊C4—221no—
452C4⋊C4—222no—
453C4⋊C4—224no—
454C4⋊C4—228no—
455C4⋊C4—224no—
456C4⋊C4C2×C22⋊D1114yes—
457C4⋊C4C23×D1112yes—
458C22⋊C4—28no—
459C22⋊C4—228no—
460C22⋊C4—228no—
461C22⋊C4C2×C22⋊D1118yes—
462C42—24no—
463C42—228no—
464C42—224no—
465C42C2×C22⋊D1112yes—
466C42C23×D1112yes—
467C11C2×#332811yescharacteristic, complemented, Sylow
468C23—24no—
469C23—24no—
470C23—24no—
471C23C22×C22⋊D1114yes—
472C23C22×C22⋊D1111yescharacteristic
473Q8—24no—
474Q8—22no—
475Q8—24no—
476Q8—24no—
477Q8—416no—
478Q8—44no—
479Q8—222no—
480Q8—222no—
481Q8—442no—
482Q8—448no—
483Q8C2×#434114yes—
484D4—28no—
485C2×C4—24no—
486C2×C4—24no—
487C2×C4—22no—
488C2×C4—22no—
489C2×C4—28no—
490C2×C4—24no—
491C2×C4—24no—
492C2×C4—22no—
493C2×C4—24no—
494C2×C4—416no—
495C2×C4—44no—
496C2×C4—42no—
497C2×C4—222no—
498C2×C4—224no—
499C2×C4—222no—
500C2×C4—442no—
501C2×C4—444no—
502C2×C4—442no—
503C2×C4#6699514yes—
504C2×C4C2×#434112yes—
505C2×C4#6703712yes—
506C2×C4C22×C22⋊D1114yes—
507C2×C4C22×C22⋊D1112yes—
508C2×C4C22×C22⋊D1111yescharacteristic
509C2×C4C22×C22⋊D1112yes—
510C2×C4C24×D1111yescharacteristic
511C8—222no—
512C8—222no—
513C8—224no—
514C22—24no—
515C22—24no—
516C22—24no—
517C22—48no—
518C22#1062333712yes—
519C22C2×#6699512yes—
520C22#1062336912yes—
521C22C23×C22⋊D1111yescharacteristic
522C4—24no—
523C4—24no—
524C4—22no—
525C4—44no—
526C4—42no—
527C4—442no—
528C4—444no—
529C4—442no—
530C4#1062333712yes—
531C4C2×#6699514yes—
532C4C22×#434111yescharacteristic
533C4C2×#6703711yescharacteristic
534C2—44no—
535C2#1308089914yesdirect product factor
536C2C2×#1062333711yescharacteristic
537C2C22×#6699511yescharacteristic
538C2C2×#1062336911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×D4×Q8×C11C2
socleC23×C11C22×D4
prime radicalC22×D4×C11D4
hypercenterC2×D4×Q8D11
hypocenterC11C2×#3328
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×D4×Q8

Complements

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

NH ≅ G/Ntype
2. #13080899C2direct (N × H)
3. C2×#10622694C2semidirect
4. C2×#10622658C2semidirect
5. C2×#10622633C2semidirect
6. C2×#10622665C2semidirect
7. C2×#10622703C2semidirect
8. C2×#10622841C2semidirect
9. C2×C4×#4326C2semidirect
11. C2×#10622838C2semidirect
35. #10622841C22semidirect
36. #10622838C22semidirect
43. #10622703C22semidirect
44. #10622694C22semidirect
45. #10622665C22semidirect
46. #10622658C22semidirect
47. C4×#4326C22semidirect
48. #10622633C22semidirect
393. C2×C11#3328semidirect
467. C11C2×#3328semidirect
535. C2#13080899direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230732
#130808992
C2×#106226942
C2×#106226582
C2×#106226332
C2×#106226652
C2×#106227032
C2×#106228412
C2×C4×#43262
C2×#106226252
C2×#106228382
C2×D4×Q8×C112
C2×#332811