Finite Group Databasebeta

← C2×#13067550 #14725938

Subgroups — C2×#13067550 #14725938

Order 2816.

1652 conjugacy classes of subgroups; only the 203 normal subgroups are shown.

normal subgroups only

This group has 1652 conjugacy classes of subgroups — too many to draw. Only its 203 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623041C211yesmaximal, characteristic, complemented
2C2×#10622830C212yesmaximal, complemented
3#13067550C218yesmaximal, direct product factor
4C2×#10622089C212yesmaximal, complemented
5C2×#10622166C211yesmaximal, characteristic, complemented
6C2×C11×#394C211yesmaximal, characteristic, complemented
7C23×D4×C11C2211yescharacteristic
8C22×#4339—21no—
9C22×C11×C4⋊C4C2211yescharacteristic
10C22×C11×C22⋊C4—21no—
11C22×C11×C22⋊C4—21no—
12C22×#4323—22no—
13C2×#66983—21no—
14C2×#66983C2212yes—
15#10623041—22no—
16#10623041—24no—
17#10623041C2214yescomplemented
18C2×#66950—22no—
19C2×#66948—22no—
20C11×#394—22no—
21C11×#394C2214yescomplemented
22C2×C11×#95C2211yescharacteristic
23#10622830—24no—
24#10622830C2218yescomplemented
25C2×#66896—22no—
26C2×C22⋊(C11⋊C8)C2212yes—
27#10622166C2214yescomplemented
28#10622089C2218yescomplemented
29C25×C11—21no—
30C22×D4×C11—22no—
31C22×D4×C11—22no—
32C22×D4×C11—21no—
33C22×D4×C11—44no—
34C22×D4×C11C2312yes—
35C23×C4×C11—21no—
36C23×C4×C11D411yescharacteristic
37C23×C4×C11D411yescharacteristic
38C23×C4×C11C2311yescharacteristic
39C22×C22⋊D11—22no—
40C2×#4339—24no—
41C2×#4339—24no—
42C2×#4339—44no—
43C2×#4339—44no—
44C22×D44—21no—
45C22×D44—21no—
46C22×D44D412yes—
47C22×C4×D11—22no—
48C22×Dic22—21no—
49C2×C11×C4⋊C4—22no—
50C2×C11×C4⋊C4—22no—
51C2×C11×C4⋊C4D412yes—
52C2×C11×C4⋊C4C2312yes—
53C2×C11×C22⋊C4—24no—
54C2×C11×C22⋊C4—24no—
55C2×C11×C22⋊C4—44no—
56C2×C11×C22⋊C4—44no—
57C2×#4323—28no—
58C2×#4323—48no—
59#66983—24no—
60#66983—22no—
61#66983—22no—
62#66983—24no—
63#66983D414yes—
64#66983C2314yes—
65C2×(C2×D11)⋊C4—22no—
66C2×(C2×D11)⋊C4—22no—
67C2×C4⋊Dic11—21no—
68C2×C4⋊Dic11D412yes—
69C22×C11⋊C8—22no—
70#66950—28no—
71#66950—28no—
72#66948—28no—
73#66948—28no—
74C11×#95—21no—
75C11×#95C2312yes—
76#66896—28no—
77C22⋊(C11⋊C8)—22no—
78C22⋊(C11⋊C8)C2314yes—
79C2×#1598—111nomaximal, Sylow
80C24×C11—24no—
81C24×C11—22no—
82C24×C11—42no—
83C24×C11—42no—
84C24×C11—42no—
85C24×C11—41no—
86C24×C11—41no—
87C24×C11—42no—
88C24×C11—42no—
89C24×C11C2×D411yescharacteristic
90C23×D11—22no—
91C2×D4×C11—28no—
92C2×D4×C11—24no—
93C2×D4×C11—44no—
94C2×D4×C11—44no—
95C2×D4×C11—48no—
96C2×D4×C11—44no—
97C2×D4×C11—42no—
98C22×C4×C11—21no—
99C22×C4×C11—21no—
100C22×C4×C11—22no—
101C22×C4×C11—21no—
102C22×C4×C11—21no—
103C22×C4×C11—22no—
104C22×C4×C11—42no—
105C22×C4×C11—42no—
106C22×C4×C11—42no—
107C22×C4×C11—42no—
108C22×C4×C11—42no—
109C22×C4×C11D814yescomplemented
110C22×C4×C11C2×D412yes—
111C22×C4×C11C2×D412yes—
112C22×C4×C11C2×D412yes—
113C22×C4×C11C2×D411yescharacteristic
114C22×C4×C11C2×D412yes—
115C22×C4×C11C2411yescharacteristic
116C2×C22⋊D11—24no—
117C2×C22⋊D11—24no—
118C2×C22⋊D11—44no—
119C2×C22⋊D11—44no—
120C22×Dic11—22no—
121#4339—48no—
122#4339—416no—
123#4339—48no—
124C2×D44—24no—
125C2×D44—24no—
126C2×D44—22no—
127C2×D44—44no—
128C2×D44—44no—
129C2×D44—82no—
130C2×D44C2×D414yes—
131C2×C4×D11—28no—
132C2×C4×D11—48no—
133C2×Dic22—24no—
134C2×Dic22—44no—
135C11×C4⋊C4—24no—
136C11×C4⋊C4—24no—
137C11×C22⋊C4—48no—
138C11×C22⋊C4—48no—
139#4323—416no—
140(C2×D11)⋊C4—28no—
141(C2×D11)⋊C4—24no—
142(C2×D11)⋊C4—24no—
143C4⋊Dic11—24no—
144C4⋊Dic11—22no—
145C4⋊Dic11C2×D414yes—
146C2×C11⋊C8—24no—
147C2×C11⋊C8—44no—
148C2×#537—111no—
149C2×#447—112no—
150C2×#394D1111yescharacteristic, complemented
151#1598—118no—
152C2×#327—112no—
153C2×#324—111no—
154C23×C11—22no—
155C23×C11—22no—
156C23×C11—24no—
157C23×C11—42no—
158C23×C11—44no—
159C23×C11—48no—
160C23×C11—48no—
161C23×C11—42no—
162C23×C11—42no—
163C23×C11—42no—
164C23×C11—42no—
165C23×C11—42no—
166C23×C11—44no—
167C23×C11—84no—
168C23×C11—84no—
169C23×C11—82no—
170C23×C11—82no—
171C23×C11—82no—
172C23×C11—82no—
173C23×C11#12011yescharacteristic
174C23×C11#12011yescharacteristic
175C23×C11C2×D812yes—
176C23×C11AGL(1,ℤ/8)12yes—
177C23×C11C22×D411yescharacteristic
178C22×D11—24no—
179C22×D11—44no—
180C22×D11—44no—
181C22×D11—44no—
182D4×C11—28no—
183D4×C11—48no—
184D4×C11—44no—
185C2×C4×C11—22no—
186C2×C4×C11—22no—
187C2×C4×C11—24no—
188C2×C4×C11—24no—
189C2×C4×C11—24no—
190C2×C4×C11—22no—
191C2×C4×C11—42no—
192C2×C4×C11—41no—
193C2×C4×C11—41no—
194C2×C4×C11—42no—
195C2×C4×C11—42no—
196C2×C4×C11—42no—
197C2×C4×C11—42no—
198C2×C4×C11—42no—
199C2×C4×C11—81no—
200C2×C4×C11—84no—
201C2×C4×C11#12012yes—
202C2×C4×C11C2×D814yescomplemented
203C2×C4×C11C22×D412yes—
204C22⋊D11—44no—
205C22⋊D11—44no—
206C22⋊D11—48no—
207C2×Dic11—24no—
208C2×Dic11—44no—
209D44—44no—
210D44—48no—
211D44—82no—
212D44—84no—
213C4×D11—416no—
214Dic22—48no—
215C11⋊C8—44no—
216C22×#41—221no—
217C23×D4C2×D1111yescharacteristic
218C22×D8—222no—
219#537—114no—
220#537—224no—
221#537—222no—
222C2×C22⋊Q8—222no—
223C2×#121—112no—
224C2×#121—222no—
225C2×#121—221no—
226C22×C4⋊C4C2×D1111yescharacteristic
227C22×C22⋊C4—21no—
228C22×C22⋊C4—21no—
229#447—118no—
230#447—224no—
231C2×#102—222no—
232C2×C22⋊C8—112no—
233#394—22no—
234#394C2×D1114yescomplemented
235C2×#95C2×D1111yescharacteristic
236#327—118no—
237#324—114no—
238C22×C11—24no—
239C22×C11—24no—
240C22×C11—21no—
241C22×C11—21no—
242C22×C11—21no—
243C22×C11—21no—
244C22×C11—44no—
245C22×C11—44no—
246C22×C11—44no—
247C22×C11—82no—
248C22×C11—82no—
249C22×C11—88no—
250C22×C11—88no—
251C22×C11—82no—
252C22×C11—82no—
253C22×C11#44712yes—
254C22×C11#44712yes—
255C22×C11#45412yes—
256C22×C11B(4,𝔽2)12yes—
257C22×C11C2×#12011yescharacteristic
258C22×C11C22×D811yescharacteristic
259C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
260C2×D11—44no—
261C2×D11—44no—
262C2×D11—44no—
263C2×D11—88no—
264C4×C11—24no—
265C4×C11—22no—
266C4×C11—22no—
267C4×C11—42no—
268C4×C11—82no—
269Dic11—44no—
270C25—21no—
271C2×#41—224no—
272C2×#41—224no—
273C2×#41—444no—
274C2×#41—444no—
275C22×Q8—221no—
276C22×D4—22no—
277C22×D4—22no—
278C22×D4—21no—
279C22×D4—44no—
280C22×D4—112no—
281C22×D4—221no—
282C22×D4—221no—
283C22×D4—222no—
284C22×D4C22×D1112yes—
285C23×C4—21no—
286C23×C4—222no—
287C23×C4C22⋊D1111yescharacteristic
288C23×C4C22⋊D1111yescharacteristic
289C23×C4C22×D1111yescharacteristic
290C2×D8—228no—
291C2×D8—448no—
292C22×C8—222no—
293C22⋊Q8—228no—
294C22⋊Q8—228no—
295#121—114no—
296#121—114no—
297#121—228no—
298#121—228no—
299#121—224no—
300#121—222no—
301#121—222no—
302#121—224no—
303C2×C4⋊C4—22no—
304C2×C4⋊C4—22no—
305C2×C4⋊C4—112no—
306C2×C4⋊C4—221no—
307C2×C4⋊C4C22⋊D1112yes—
308C2×C4⋊C4C22×D1112yes—
309C2×C22⋊C4—24no—
310C2×C22⋊C4—24no—
311C2×C22⋊C4—44no—
312C2×C22⋊C4—44no—
313C2×C22⋊C4—222no—
314C2×C22⋊C4—222no—
315#102—228no—
316C22⋊C8—114no—
317C22⋊C8—222no—
318#95—21no—
319#95C22×D1112yes—
320C2×C11—21no—
321C2×C11—21no—
322C2×C11—22no—
323C2×C11—84no—
324C2×C11#159814yescomplemented
325C2×C11C2×#44711yescharacteristic
326C2×C11C2×#45411yescharacteristic
327C2×C11C2×B(4,𝔽2)11yescharacteristic
328D11—84no—
329C24—24no—
330C24—22no—
331C24—42no—
332C24—42no—
333C24—42no—
334C24—42no—
335C24—41no—
336C24—41no—
337C24—42no—
338C24—222no—
339C24C2×C22⋊D1111yescharacteristic
340#41—448no—
341#41—4416no—
342#41—448no—
343C2×Q8—224no—
344C2×Q8—444no—
345C2×D4—28no—
346C2×D4—24no—
347C2×D4—44no—
348C2×D4—44no—
349C2×D4—48no—
350C2×D4—44no—
351C2×D4—42no—
352C2×D4—114no—
353C2×D4—224no—
354C2×D4—224no—
355C2×D4—224no—
356C2×D4—224no—
357C2×D4—222no—
358C2×D4—444no—
359C2×D4—444no—
360C2×D4—444no—
361C2×D4—444no—
362C2×D4—882no—
363C22×C4—21no—
364C22×C4—21no—
365C22×C4—22no—
366C22×C4—21no—
367C22×C4—21no—
368C22×C4—22no—
369C22×C4—42no—
370C22×C4—42no—
371C22×C4—42no—
372C22×C4—42no—
373C22×C4—42no—
374C22×C4—228no—
375C22×C4—222no—
376C22×C4—448no—
377C22×C4#432314yescomplemented
378C22×C4D4×D1112yes—
379C22×C4D4×D1112yes—
380C22×C4C2×C22⋊D1112yes—
381C22×C4C2×C22⋊D1112yes—
382C22×C4C2×C22⋊D1111yescharacteristic
383C22×C4C23×D1111yescharacteristic
384D8—4416no—
385C2×C8—224no—
386C2×C8—444no—
387C4⋊C4—24no—
388C4⋊C4—24no—
389C4⋊C4—114no—
390C4⋊C4—224no—
391C4⋊C4—222no—
392C22⋊C4—48no—
393C22⋊C4—48no—
394C22⋊C4—228no—
395C22⋊C4—224no—
396C22⋊C4—224no—
397C11C2×#159811yescharacteristic, complemented, Sylow
398C23—22no—
399C23—22no—
400C23—24no—
401C23—42no—
402C23—44no—
403C23—48no—
404C23—48no—
405C23—42no—
406C23—42no—
407C23—42no—
408C23—42no—
409C23—42no—
410C23—44no—
411C23—84no—
412C23—84no—
413C23—82no—
414C23—82no—
415C23—82no—
416C23—82no—
417C23—224no—
418C23—444no—
419C23—444no—
420C23—444no—
421C23C2×#432312yes—
422C23#6699011yescharacteristic
423C23#6699011yescharacteristic
424C23#6700212yes—
425C23C22×C22⋊D1111yescharacteristic
426Q8—448no—
427D4—28no—
428D4—44no—
429D4—48no—
430D4—444no—
431D4—448no—
432D4—444no—
433D4—444no—
434D4—448no—
435D4—882no—
436D4—884no—
437C2×C4—22no—
438C2×C4—22no—
439C2×C4—24no—
440C2×C4—24no—
441C2×C4—24no—
442C2×C4—22no—
443C2×C4—42no—
444C2×C4—41no—
445C2×C4—41no—
446C2×C4—42no—
447C2×C4—42no—
448C2×C4—42no—
449C2×C4—42no—
450C2×C4—42no—
451C2×C4—81no—
452C2×C4—84no—
453C2×C4—224no—
454C2×C4—4416no—
455C2×C4—444no—
456C2×C4C2×#432314yescomplemented
457C2×C4#6699012yes—
458C2×C4C2×D4×D1112yes—
459C8—444no—
460C22—24no—
461C22—24no—
462C22—21no—
463C22—21no—
464C22—21no—
465C22—21no—
466C22—44no—
467C22—44no—
468C22—44no—
469C22—82no—
470C22—82no—
471C22—88no—
472C22—88no—
473C22—82no—
474C22—82no—
475C22—444no—
476C22—444no—
477C22—444no—
478C22—888no—
479C22#1062264512yes—
480C22#1062264912yes—
481C22#1062264912yes—
482C22#1062267512yes—
483C22C22×#432311yescharacteristic
484C22C2×#6699011yescharacteristic
485C22C2×#6700211yescharacteristic
486C4—24no—
487C4—22no—
488C4—22no—
489C4—42no—
490C4—82no—
491C4—444no—
492C2—21no—
493C2—21no—
494C2—22no—
495C2—84no—
496C2—884no—
497C2#1306755014yesdirect product factor
498C2C2×#1062264911yescharacteristic
499C2C2×#1062267511yescharacteristic
500C2C2×#1062264511yescharacteristic
subgroupG/H
centerC23#66990
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#394C2
socleC23×C11#120
hypercenterC2×#394D11
hypocenterC11C2×#1598
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#394

Complements

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

NH ≅ G/Ntype
1. C2×#10623041C2semidirect
2. C2×#10622830C2semidirect
3. #13067550C2direct (N × H)
4. C2×#10622089C2semidirect
5. C2×#10622166C2semidirect
6. C2×C11×#394C2semidirect
17. #10623041C22semidirect
21. C11×#394C22semidirect
24. #10622830C22semidirect
27. #10622166C22semidirect
28. #10622089C22semidirect
109. C22×C4×C11D8semidirect
150. C2×#394D11semidirect
202. C2×C4×C11C2×D8semidirect
234. #394C2×D11semidirect
324. C2×C11#1598semidirect
377. C22×C4#4323semidirect
397. C11C2×#1598semidirect
456. C2×C4C2×#4323semidirect
497. C2#13067550direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230412
C2×#106228302
#130675502
C2×#106220892
C2×#106221662
C2×C11×#3942
C2×#159811