Finite Group Databasebeta

← C2×#13067635 #14725893

Subgroups — C2×#13067635 #14725893

Order 2816.

1524 conjugacy classes of subgroups; only the 203 normal subgroups are shown.

normal subgroups only

This group has 1524 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×#10623024C211yesmaximal, characteristic
2C2×#10622581C212yesmaximal, complemented
3#13067635C218yesmaximal, direct product factor
4C2×#10622089C212yesmaximal, complemented
5C2×#10622163C211yesmaximal, characteristic, complemented
6C2×C11×#399C211yesmaximal, characteristic, complemented
7C23×C22⋊D11—21no—
8C22×C11×C4⋊C4—21no—
9C22×C11×C4⋊C4C2211yescharacteristic, complemented
10C22×C11×C22⋊C4—21no—
11C22×C11×C22⋊C4C2211yescharacteristic
12C2×#66983—21no—
13C2×#66983C2212yes—
14#10623024—22no—
15#10623024—24no—
16#10623024C2214yes—
17C2×#66939—22no—
18C2×#66935—22no—
19C11×#399—22no—
20C11×#399C2214yescomplemented
21C2×C11×#95C2211yescharacteristic, complemented
22C2×C22⋊(C11⋊C8)C2212yescomplemented
23#10622581—24no—
24#10622581C2218yescomplemented
25C2×#66873—22no—
26C2×#66872—22no—
27#10622163C2214yescomplemented
28#10622089C2218yescomplemented
29C25×C11D411yescharacteristic
30C24×D11—21no—
31C23×C4×C11—21no—
32C23×C4×C11—21no—
33C23×C4×C11D411yescharacteristic
34C23×C4×C11C2311yescharacteristic
35C22×C22⋊D11—22no—
36C22×C22⋊D11—24no—
37C22×C22⋊D11—24no—
38C22×C22⋊D11—22no—
39C22×C22⋊D11—44no—
40C22×C22⋊D11—44no—
41C23×Dic11—21no—
42C22×D44—21no—
43C22×D44D412yes—
44C2×C11×C4⋊C4—22no—
45C2×C11×C4⋊C4—22no—
46C2×C11×C4⋊C4—24no—
47C2×C11×C4⋊C4—21no—
48C2×C11×C4⋊C4—44no—
49C2×C11×C4⋊C4C2312yescomplemented
50C2×C11×C22⋊C4—22no—
51C2×C11×C22⋊C4—22no—
52C2×C11×C22⋊C4—24no—
53C2×C11×C22⋊C4—44no—
54C2×C11×C22⋊C4D412yes—
55C2×C11×C22⋊C4C2312yes—
56#66983—24no—
57#66983—22no—
58#66983—22no—
59#66983—24no—
60#66983D414yes—
61#66983C2314yes—
62C2×(C2×D11)⋊C4—22no—
63C2×(C2×D11)⋊C4—22no—
64C2×C4⋊Dic11—21no—
65C2×C4⋊Dic11D412yes—
66C22×C11⋊C8—22no—
67#66939—28no—
68#66939—28no—
69#66935—28no—
70#66935—28no—
71C11×#95—21no—
72C11×#95C2312yescomplemented
73C22⋊(C11⋊C8)—22no—
74C22⋊(C11⋊C8)C2314yescomplemented
75#66873—28no—
76#66872—28no—
77C2×#1613—111nomaximal, Sylow
78C24×C11—21no—
79C24×C11—21no—
80C24×C11—22no—
81C24×C11—42no—
82C24×C11—42no—
83C24×C11SD1614yes—
84C24×C11C2×D411yescharacteristic
85C24×C11C2×D412yes—
86C23×D11—22no—
87C23×D11—24no—
88C23×D11—44no—
89C23×D11—82no—
90C23×D11—82no—
91C22×C4×C11—24no—
92C22×C4×C11—21no—
93C22×C4×C11—22no—
94C22×C4×C11—21no—
95C22×C4×C11—22no—
96C22×C4×C11—42no—
97C22×C4×C11—42no—
98C22×C4×C11—42no—
99C22×C4×C11—42no—
100C22×C4×C11—42no—
101C22×C4×C11—42no—
102C22×C4×C11—41no—
103C22×C4×C11—41no—
104C22×C4×C11C2×D412yes—
105C22×C4×C11C2×D412yes—
106C22×C4×C11C2×D411yescharacteristic
107C22×C4×C11C2×D412yes—
108C22×C4×C11C2411yescharacteristic
109C2×C22⋊D11—28no—
110C2×C22⋊D11—24no—
111C2×C22⋊D11—24no—
112C2×C22⋊D11—48no—
113C2×C22⋊D11—416no—
114C2×C22⋊D11—48no—
115C2×C22⋊D11—48no—
116C2×C22⋊D11—44no—
117C2×C22⋊D11—44no—
118C22×Dic11—24no—
119C22×Dic11—22no—
120C22×Dic11—44no—
121C2×D44—24no—
122C2×D44—22no—
123C2×D44—44no—
124C2×D44—82no—
125C2×D44C2×D414yes—
126C11×C4⋊C4—24no—
127C11×C4⋊C4—48no—
128C11×C4⋊C4—42no—
129C11×C22⋊C4—24no—
130C11×C22⋊C4—24no—
131C11×C22⋊C4—48no—
132(C2×D11)⋊C4—28no—
133(C2×D11)⋊C4—24no—
134(C2×D11)⋊C4—24no—
135C4⋊Dic11—24no—
136C4⋊Dic11—22no—
137C4⋊Dic11C2×D414yes—
138C2×C11⋊C8—24no—
139C2×C11⋊C8—44no—
140C2×#534—111no—
141C2×#481—112no—
142C2×#399D1111yescharacteristic, complemented
143#1613—118no—
144C2×#327—112no—
145C2×#323—111no—
146C23×C11—22no—
147C23×C11—22no—
148C23×C11—22no—
149C23×C11—24no—
150C23×C11—22no—
151C23×C11—24no—
152C23×C11—42no—
153C23×C11—48no—
154C23×C11—42no—
155C23×C11—42no—
156C23×C11—42no—
157C23×C11—84no—
158C23×C11—81no—
159C23×C11—81no—
160C23×C11#12011yescharacteristic
161C23×C11#12011yescharacteristic
162C23×C11C2×SD1612yes—
163C23×C11C2×SD1614yes—
164C23×C11AGL(1,ℤ/8)12yes—
165C23×C11C22×D411yescharacteristic
166C22×D11—24no—
167C22×D11—48no—
168C22×D11—44no—
169C22×D11—44no—
170C22×D11—44no—
171C22×D11—84no—
172C22×D11—84no—
173C22×D11—816no—
174C2×C4×C11—24no—
175C2×C4×C11—24no—
176C2×C4×C11—22no—
177C2×C4×C11—42no—
178C2×C4×C11—41no—
179C2×C4×C11—41no—
180C2×C4×C11—48no—
181C2×C4×C11—42no—
182C2×C4×C11—42no—
183C2×C4×C11—42no—
184C2×C4×C11—42no—
185C2×C4×C11—42no—
186C2×C4×C11—42no—
187C2×C4×C11—42no—
188C2×C4×C11—81no—
189C2×C4×C11—82no—
190C2×C4×C11—82no—
191C2×C4×C11#12012yes—
192C2×C4×C11C22×D412yes—
193C22⋊D11—416no—
194C22⋊D11—44no—
195C22⋊D11—44no—
196C22⋊D11—48no—
197C2×Dic11—24no—
198C2×Dic11—48no—
199C2×Dic11—44no—
200D44—44no—
201D44—82no—
202D44—84no—
203C11⋊C8—44no—
204C23×D4—221no—
205#534—114no—
206#534—224no—
207#534—222no—
208C2×#123—222no—
209C2×#121—112no—
210C2×#121—221no—
211C2×#120—222no—
212C22×C4⋊C4—21no—
213C22×C4⋊C4C2×D1111yescharacteristic, complemented
214C22×C22⋊C4—21no—
215C22×C22⋊C4C2×D1111yescharacteristic
216#481—118no—
217#481—224no—
218C2×#106—222no—
219C2×#102—222no—
220C2×C22⋊C8—112no—
221#399—22no—
222#399C2×D1114yescomplemented
223C2×#95C2×D1111yescharacteristic, complemented
224#327—118no—
225#323—114no—
226C22×C11—24no—
227C22×C11—24no—
228C22×C11—21no—
229C22×C11—21no—
230C22×C11—21no—
231C22×C11—21no—
232C22×C11—24no—
233C22×C11—44no—
234C22×C11—48no—
235C22×C11—42no—
236C22×C11—42no—
237C22×C11—82no—
238C22×C11—84no—
239C22×C11#45012yes—
240C22×C11#45012yes—
241C22×C11#45312yes—
242C22×C11#45812yes—
243C22×C11C2×#12011yescharacteristic
244C22×C11C22×SD1611yescharacteristic
245C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
246C2×D11—44no—
247C2×D11—44no—
248C2×D11—44no—
249C2×D11—816no—
250C2×D11—88no—
251C4×C11—22no—
252C4×C11—22no—
253C4×C11—44no—
254C4×C11—42no—
255C4×C11—82no—
256Dic11—44no—
257C25—221no—
258C25C22⋊D1111yescharacteristic
259C22×D4—112no—
260C22×D4—221no—
261C22×D4—222no—
262C22×D4—224no—
263C22×D4—222no—
264C22×D4—224no—
265C22×D4—444no—
266C22×D4—444no—
267C23×C4—21no—
268C23×C4—21no—
269C23×C4—221no—
270C23×C4C22⋊D1111yescharacteristic
271C23×C4C22×D1111yescharacteristic
272C22×C8—222no—
273#123—228no—
274#123—228no—
275#121—114no—
276#121—114no—
277#121—224no—
278#121—222no—
279#121—222no—
280#121—224no—
281#120—228no—
282#120—228no—
283C2×C4⋊C4—22no—
284C2×C4⋊C4—22no—
285C2×C4⋊C4—24no—
286C2×C4⋊C4—21no—
287C2×C4⋊C4—44no—
288C2×C4⋊C4—112no—
289C2×C4⋊C4—221no—
290C2×C4⋊C4C22×D1112yescomplemented
291C2×C22⋊C4—22no—
292C2×C22⋊C4—22no—
293C2×C22⋊C4—24no—
294C2×C22⋊C4—44no—
295C2×C22⋊C4—222no—
296C2×C22⋊C4—222no—
297C2×C22⋊C4C22⋊D1112yes—
298C2×C22⋊C4C22×D1112yes—
299#106—228no—
300#102—228no—
301C22⋊C8—114no—
302C22⋊C8—222no—
303#95—21no—
304#95C22×D1112yescomplemented
305C2×C11—21no—
306C2×C11—21no—
307C2×C11—22no—
308C2×C11—44no—
309C2×C11#161314yescomplemented
310C2×C11C2×#45011yescharacteristic
311C2×C11C2×#45311yescharacteristic
312C2×C11C2×#45811yescharacteristic
313D11—84no—
314C24—21no—
315C24—21no—
316C24—22no—
317C24—42no—
318C24—42no—
319C24—224no—
320C24—222no—
321C24—444no—
322C24—882no—
323C24—882no—
324C24#432514yes—
325C24C2×C22⋊D1111yescharacteristic
326C24C2×C22⋊D1112yes—
327C2×D4—114no—
328C2×D4—224no—
329C2×D4—228no—
330C2×D4—224no—
331C2×D4—224no—
332C2×D4—222no—
333C2×D4—444no—
334C2×D4—448no—
335C2×D4—4416no—
336C2×D4—448no—
337C2×D4—448no—
338C2×D4—444no—
339C2×D4—444no—
340C2×D4—882no—
341C22×C4—24no—
342C22×C4—21no—
343C22×C4—22no—
344C22×C4—21no—
345C22×C4—22no—
346C22×C4—42no—
347C22×C4—42no—
348C22×C4—42no—
349C22×C4—42no—
350C22×C4—42no—
351C22×C4—42no—
352C22×C4—41no—
353C22×C4—41no—
354C22×C4—224no—
355C22×C4—222no—
356C22×C4—444no—
357C22×C4D4×D1112yes—
358C22×C4D4×D1112yes—
359C22×C4C2×C22⋊D1112yes—
360C22×C4C2×C22⋊D1111yescharacteristic
361C22×C4C23×D1111yescharacteristic
362C2×C8—224no—
363C2×C8—444no—
364C4⋊C4—24no—
365C4⋊C4—48no—
366C4⋊C4—42no—
367C4⋊C4—114no—
368C4⋊C4—224no—
369C4⋊C4—222no—
370C22⋊C4—24no—
371C22⋊C4—24no—
372C22⋊C4—48no—
373C22⋊C4—228no—
374C22⋊C4—224no—
375C22⋊C4—224no—
376C11C2×#161311yescharacteristic, complemented, Sylow
377C23—22no—
378C23—22no—
379C23—22no—
380C23—24no—
381C23—22no—
382C23—24no—
383C23—42no—
384C23—48no—
385C23—42no—
386C23—42no—
387C23—42no—
388C23—84no—
389C23—81no—
390C23—81no—
391C23—224no—
392C23—448no—
393C23—444no—
394C23—444no—
395C23—444no—
396C23—884no—
397C23—884no—
398C23—8816no—
399C23#6699011yescharacteristic
400C23#6699011yescharacteristic
401C23C2×#432512yes—
402C23C2×#432514yes—
403C23#6700212yes—
404C23C22×C22⋊D1111yescharacteristic
405D4—444no—
406D4—4416no—
407D4—444no—
408D4—444no—
409D4—448no—
410D4—882no—
411D4—884no—
412C2×C4—24no—
413C2×C4—24no—
414C2×C4—22no—
415C2×C4—42no—
416C2×C4—41no—
417C2×C4—41no—
418C2×C4—48no—
419C2×C4—42no—
420C2×C4—42no—
421C2×C4—42no—
422C2×C4—42no—
423C2×C4—42no—
424C2×C4—42no—
425C2×C4—42no—
426C2×C4—81no—
427C2×C4—82no—
428C2×C4—82no—
429C2×C4—224no—
430C2×C4—448no—
431C2×C4—444no—
432C2×C4#6699012yes—
433C2×C4C2×D4×D1112yes—
434C8—444no—
435C22—24no—
436C22—24no—
437C22—21no—
438C22—21no—
439C22—21no—
440C22—21no—
441C22—24no—
442C22—44no—
443C22—48no—
444C22—42no—
445C22—42no—
446C22—82no—
447C22—84no—
448C22—444no—
449C22—444no—
450C22—444no—
451C22—8816no—
452C22—888no—
453C22#1062265912yes—
454C22#1062265912yes—
455C22#1062266612yes—
456C22#1062269012yes—
457C22C2×#6699011yescharacteristic
458C22C22×#432511yescharacteristic
459C22C2×#6700211yescharacteristic
460C4—22no—
461C4—22no—
462C4—44no—
463C4—42no—
464C4—82no—
465C4—444no—
466C2—21no—
467C2—21no—
468C2—22no—
469C2—44no—
470C2—884no—
471C2#1306763514yesdirect product factor
472C2C2×#1062265911yescharacteristic
473C2C2×#1062269011yescharacteristic
474C2C2×#1062266611yescharacteristic
subgroupG/H
centerC23#66990
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#399C2
socleC23×C11#120
prime radicalC2×#10623024C2
hypercenterC2×#399D11
hypocenterC11C2×#1613
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#399

Complements

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

NH ≅ G/Ntype
2. C2×#10622581C2semidirect
3. #13067635C2direct (N × H)
4. C2×#10622089C2semidirect
5. C2×#10622163C2semidirect
6. C2×C11×#399C2semidirect
9. C22×C11×C4⋊C4C22semidirect
20. C11×#399C22semidirect
21. C2×C11×#95C22semidirect
22. C2×C22⋊(C11⋊C8)C22semidirect
24. #10622581C22semidirect
27. #10622163C22semidirect
28. #10622089C22semidirect
49. C2×C11×C4⋊C4C23semidirect
72. C11×#95C23semidirect
74. C22⋊(C11⋊C8)C23semidirect
142. C2×#399D11semidirect
213. C22×C4⋊C4C2×D11semidirect
222. #399C2×D11semidirect
223. C2×#95C2×D11semidirect
290. C2×C4⋊C4C22×D11semidirect
304. #95C22×D11semidirect
309. C2×C11#1613semidirect
376. C11C2×#1613semidirect
471. C2#13067635direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230242
C2×#106225812
#130676352
C2×#106220892
C2×#106221632
C2×C11×#3992
C2×#161311