Finite Group Databasebeta

← C2×#13067570 #14725845

Subgroups — C2×#13067570 #14725845

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×#10623024C211yesmaximal, characteristic
2C2×#10622351C212yesmaximal, complemented
3C2×#10622560C211yesmaximal, characteristic, complemented
4#13067570C218yesmaximal, direct product factor
5C2×#10622108C212yesmaximal, complemented
6C2×C11×#323C211yesmaximal, characteristic, complemented
7C23×C22⋊D11—21no—
8C23×Dic22C2211yescharacteristic, complemented
9C22×C11×C22⋊C4C2211yescharacteristic
10C22×C22⋊Dic11—21no—
11C2×#66983—21no—
12C2×#66983C2212yes—
13C22×#4314—22no—
14#10623024—22no—
15#10623024—24no—
16#10623024C2214yes—
17C2×#66939—22no—
18C2×#66935—22no—
19C2×C11×C22⋊C8C2212yescomplemented
20C2×C11⋊#95—21no—
21C2×C11⋊#95C2211yescharacteristic, complemented
22C2×#66880—22no—
23#10622560—22no—
24#10622560C2214yescomplemented
25#10622351—24no—
26#10622351C2218yescomplemented
27C11×#323C2214yescomplemented
28#10622108C2218yescomplemented
29C25×C11D411yescharacteristic
30C24×D11—21no—
31C23×C4×C11D411yescharacteristic
32C23×C4×C11C2311yescharacteristic
33C22×C22⋊D11—22no—
34C22×C22⋊D11—24no—
35C22×C22⋊D11—24no—
36C22×C22⋊D11—22no—
37C22×C22⋊D11—44no—
38C22×C22⋊D11—44no—
39C23×Dic11—21no—
40C23×Dic11—21no—
41C23×Dic11—21no—
42C22×D44—21no—
43C22×D44D412yes—
44C22×Dic22—22no—
45C22×Dic22—22no—
46C22×Dic22—21no—
47C22×Dic22—44no—
48C22×Dic22C2312yescomplemented
49C22×C8×C11—22no—
50C2×C11×C22⋊C4—22no—
51C2×C11×C22⋊C4—22no—
52C2×C11×C22⋊C4D412yes—
53C2×C11×C22⋊C4C2312yes—
54C2×C22⋊Dic11—24no—
55C2×C22⋊Dic11—44no—
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—
66C2×#4314—28no—
67C2×#4314—48no—
68#66939—28no—
69#66939—28no—
70#66935—28no—
71#66935—28no—
72C11×C22⋊C8—22no—
73C11×C22⋊C8C2314yescomplemented
74C11⋊#95—21no—
75C11⋊#95—24no—
76C11⋊#95C2312yescomplemented
77#66880—28no—
78C2×#1601—111nomaximal, Sylow
79C24×C11—21no—
80C24×C11—21no—
81C24×C11—22no—
82C24×C11—42no—
83C24×C11—42no—
84C24×C11SD1614yescomplemented
85C24×C11C2×D411yescharacteristic
86C24×C11C2×D412yes—
87C23×D11—22no—
88C23×D11—24no—
89C23×D11—44no—
90C23×D11—82no—
91C23×D11—82no—
92C22×C4×C11—21no—
93C22×C4×C11—21no—
94C22×C4×C11—42no—
95C22×C4×C11—42no—
96C22×C4×C11C2×D412yes—
97C22×C4×C11C2×D412yes—
98C22×C4×C11C2×D411yescharacteristic
99C22×C4×C11C2×D412yes—
100C22×C4×C11C2411yescharacteristic
101C2×C22⋊D11—28no—
102C2×C22⋊D11—24no—
103C2×C22⋊D11—24no—
104C2×C22⋊D11—48no—
105C2×C22⋊D11—416no—
106C2×C22⋊D11—48no—
107C2×C22⋊D11—44no—
108C2×C22⋊D11—48no—
109C2×C22⋊D11—44no—
110C22×Dic11—24no—
111C22×Dic11—24no—
112C22×Dic11—22no—
113C22×Dic11—22no—
114C22×Dic11—22no—
115C22×Dic11—42no—
116C22×Dic11—44no—
117C22×Dic11—42no—
118C22×Dic11—42no—
119C22×Dic11—41no—
120C22×Dic11—41no—
121C22×Dic11—42no—
122C2×D44—24no—
123C2×D44—22no—
124C2×D44—44no—
125C2×D44—82no—
126C2×D44C2×D414yes—
127C2×Dic22—28no—
128C2×Dic22—24no—
129C2×Dic22—44no—
130C2×Dic22—44no—
131C2×Dic22—48no—
132C2×Dic22—44no—
133C2×Dic22—42no—
134C2×C8×C11—24no—
135C2×C8×C11—44no—
136C11×C22⋊C4—24no—
137C11×C22⋊C4—24no—
138C22⋊Dic11—48no—
139(C2×D11)⋊C4—28no—
140(C2×D11)⋊C4—24no—
141(C2×D11)⋊C4—24no—
142C4⋊Dic11—24no—
143C4⋊Dic11—22no—
144C4⋊Dic11C2×D414yes—
145#4314—416no—
146C2×#534—111no—
147C2×#448—112no—
148C2×#393—111no—
149#1601—118no—
150C2×#327—112no—
151C2×#323D1111yescharacteristic, complemented
152C23×C11—22no—
153C23×C11—22no—
154C23×C11—22no—
155C23×C11—24no—
156C23×C11—22no—
157C23×C11—24no—
158C23×C11—42no—
159C23×C11—48no—
160C23×C11—42no—
161C23×C11—42no—
162C23×C11—42no—
163C23×C11—84no—
164C23×C11—81no—
165C23×C11—81no—
166C23×C11#12011yescharacteristic
167C23×C11#12011yescharacteristic
168C23×C11C2×SD1612yes—
169C23×C11C2×SD1614yescomplemented
170C23×C11AGL(1,ℤ/8)12yes—
171C23×C11C22×D411yescharacteristic
172C22×D11—24no—
173C22×D11—48no—
174C22×D11—44no—
175C22×D11—44no—
176C22×D11—44no—
177C22×D11—84no—
178C22×D11—84no—
179C22×D11—816no—
180C2×C4×C11—24no—
181C2×C4×C11—22no—
182C2×C4×C11—41no—
183C2×C4×C11—42no—
184C2×C4×C11—41no—
185C2×C4×C11—42no—
186C2×C4×C11—42no—
187C2×C4×C11—81no—
188C2×C4×C11#12012yes—
189C2×C4×C11C22×D412yes—
190C22⋊D11—416no—
191C22⋊D11—44no—
192C22⋊D11—44no—
193C22⋊D11—48no—
194C2×Dic11—24no—
195C2×Dic11—24no—
196C2×Dic11—42no—
197C2×Dic11—44no—
198C2×Dic11—48no—
199C2×Dic11—42no—
200C2×Dic11—44no—
201C2×Dic11—44no—
202C2×Dic11—42no—
203C2×Dic11—42no—
204C2×Dic11—42no—
205C2×Dic11—84no—
206D44—44no—
207D44—82no—
208D44—84no—
209Dic22—28no—
210Dic22—48no—
211Dic22—44no—
212C8×C11—44no—
213C23×Q8—111no—
214C23×D4—221no—
215C22×SD16—222no—
216#534—114no—
217#534—224no—
218#534—222no—
219C2×#123—222no—
220C2×#121—112no—
221C2×#121—221no—
222C2×#120—222no—
223C22×C22⋊C4—221no—
224C22×C22⋊C4C2×D1111yescharacteristic
225#448—118no—
226#448—224no—
227C2×#103—222no—
228C2×C22⋊C8C2×D1112yescomplemented
229#393—114no—
230#393—222no—
231C2×#95—111no—
232C2×#95—221no—
233#327—118no—
234#323C2×D1114yescomplemented
235C22×C11—24no—
236C22×C11—24no—
237C22×C11—21no—
238C22×C11—21no—
239C22×C11—21no—
240C22×C11—21no—
241C22×C11—24no—
242C22×C11—44no—
243C22×C11—48no—
244C22×C11—42no—
245C22×C11—42no—
246C22×C11—82no—
247C22×C11—84no—
248C22×C11#45012yes—
249C22×C11#45012yes—
250C22×C11#45512yes—
251C22×C11B(4,𝔽2)12yes—
252C22×C11C2×#12011yescharacteristic
253C22×C11C22×SD1611yescharacteristic
254C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
255C2×D11—44no—
256C2×D11—44no—
257C2×D11—44no—
258C2×D11—816no—
259C2×D11—88no—
260C4×C11—22no—
261C4×C11—22no—
262C4×C11—42no—
263Dic11—44no—
264Dic11—44no—
265Dic11—82no—
266C25—221no—
267C25D4411yescharacteristic
268C22×Q8—112no—
269C22×Q8—221no—
270C22×Q8—222no—
271C22×Q8—222no—
272C22×Q8—444no—
273C22×D4—112no—
274C22×D4—221no—
275C22×D4—222no—
276C22×D4—224no—
277C22×D4—222no—
278C22×D4—224no—
279C22×D4—444no—
280C22×D4—444no—
281C23×C4—221no—
282C23×C4—221no—
283C23×C4—221no—
284C23×C4D4411yescharacteristic
285C23×C4C22×D1111yescharacteristic
286C2×SD16—228no—
287C2×SD16—448no—
288C22×C8—22no—
289#123—228no—
290#123—228no—
291#121—114no—
292#121—114no—
293#121—224no—
294#121—222no—
295#121—224no—
296#121—222no—
297#120—228no—
298#120—228no—
299C2×C4⋊C4—112no—
300C2×C4⋊C4—221no—
301C2×C22⋊C4—22no—
302C2×C22⋊C4—22no—
303C2×C22⋊C4—222no—
304C2×C22⋊C4—222no—
305C2×C22⋊C4—224no—
306C2×C22⋊C4—444no—
307C2×C22⋊C4D4412yes—
308C2×C22⋊C4C22×D1112yes—
309#103—228no—
310C22⋊C8—22no—
311C22⋊C8C22×D1114yescomplemented
312#95—112no—
313#95—221no—
314#95—224no—
315C2×C11—21no—
316C2×C11—21no—
317C2×C11—22no—
318C2×C11—44no—
319C2×C11#160114yescomplemented
320C2×C11C2×#45011yescharacteristic
321C2×C11C2×#45511yescharacteristic
322C2×C11C2×B(4,𝔽2)11yescharacteristic
323D11—84no—
324C24—21no—
325C24—21no—
326C24—22no—
327C24—42no—
328C24—42no—
329C24—224no—
330C24—222no—
331C24—444no—
332C24—882no—
333C24—882no—
334C24#431414yescomplemented
335C24C2×D4411yescharacteristic
336C24C2×D4412yes—
337C2×Q8—228no—
338C2×Q8—224no—
339C2×Q8—444no—
340C2×Q8—444no—
341C2×Q8—444no—
342C2×Q8—448no—
343C2×Q8—442no—
344C2×D4—114no—
345C2×D4—224no—
346C2×D4—228no—
347C2×D4—224no—
348C2×D4—224no—
349C2×D4—222no—
350C2×D4—444no—
351C2×D4—448no—
352C2×D4—4416no—
353C2×D4—448no—
354C2×D4—444no—
355C2×D4—448no—
356C2×D4—444no—
357C2×D4—882no—
358C22×C4—21no—
359C22×C4—21no—
360C22×C4—42no—
361C22×C4—42no—
362C22×C4—224no—
363C22×C4—224no—
364C22×C4—222no—
365C22×C4—222no—
366C22×C4—222no—
367C22×C4—444no—
368C22×C4—442no—
369C22×C4—441no—
370C22×C4—441no—
371C22×C4—442no—
372C22×C4—442no—
373C22×C4—442no—
374C22×C4C2×D4412yes—
375C22×C4C2×D4411yescharacteristic
376C22×C4D4×D1112yes—
377C22×C4D4×D1112yes—
378C22×C4C23×D1111yescharacteristic
379SD16—4416no—
380C2×C8—24no—
381C2×C8—44no—
382C4⋊C4—114no—
383C4⋊C4—224no—
384C4⋊C4—222no—
385C22⋊C4—24no—
386C22⋊C4—24no—
387C22⋊C4—228no—
388C22⋊C4—224no—
389C22⋊C4—224no—
390C22⋊C4—448no—
391C11C2×#160111yescharacteristic, complemented, Sylow
392C23—22no—
393C23—22no—
394C23—22no—
395C23—24no—
396C23—22no—
397C23—24no—
398C23—42no—
399C23—48no—
400C23—42no—
401C23—42no—
402C23—42no—
403C23—84no—
404C23—81no—
405C23—81no—
406C23—224no—
407C23—448no—
408C23—444no—
409C23—444no—
410C23—444no—
411C23—884no—
412C23—884no—
413C23—8816no—
414C23#6693511yescharacteristic
415C23#6693511yescharacteristic
416C23C2×#431412yes—
417C23C2×#431414yescomplemented
418C23#6696112yes—
419C23C22×D4411yescharacteristic
420Q8—228no—
421Q8—444no—
422Q8—448no—
423D4—444no—
424D4—4416no—
425D4—444no—
426D4—444no—
427D4—448no—
428D4—882no—
429D4—884no—
430C2×C4—24no—
431C2×C4—22no—
432C2×C4—41no—
433C2×C4—42no—
434C2×C4—41no—
435C2×C4—42no—
436C2×C4—42no—
437C2×C4—81no—
438C2×C4—224no—
439C2×C4—224no—
440C2×C4—448no—
441C2×C4—442no—
442C2×C4—444no—
443C2×C4—442no—
444C2×C4—444no—
445C2×C4—444no—
446C2×C4—442no—
447C2×C4—442no—
448C2×C4—442no—
449C2×C4—884no—
450C2×C4#6693512yes—
451C2×C4C2×D4×D1112yes—
452C8—44no—
453C22—24no—
454C22—24no—
455C22—21no—
456C22—21no—
457C22—21no—
458C22—21no—
459C22—24no—
460C22—44no—
461C22—48no—
462C22—42no—
463C22—42no—
464C22—82no—
465C22—84no—
466C22—444no—
467C22—444no—
468C22—444no—
469C22—8816no—
470C22—888no—
471C22#1062234412yes—
472C22#1062234412yes—
473C22#1062235412yes—
474C22#1062235912yes—
475C22C2×#6693511yescharacteristic
476C22C22×#431411yescharacteristic
477C22C2×#6696111yescharacteristic
478C4—22no—
479C4—22no—
480C4—42no—
481C4—444no—
482C4—444no—
483C4—882no—
484C2—21no—
485C2—21no—
486C2—22no—
487C2—44no—
488C2—884no—
489C2#1306757014yesdirect product factor
490C2C2×#1062234411yescharacteristic
491C2C2×#1062235911yescharacteristic
492C2C2×#1062235411yescharacteristic
subgroupG/H
centerC23#66935
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#323C2
socleC23×C11#120
prime radicalC2×#10623024C2
hypercenterC2×#323D11
hypocenterC11C2×#1601
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#323

Complements

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

NH ≅ G/Ntype
2. C2×#10622351C2semidirect
3. C2×#10622560C2semidirect
4. #13067570C2direct (N × H)
5. C2×#10622108C2semidirect
6. C2×C11×#323C2semidirect
8. C23×Dic22C22semidirect
19. C2×C11×C22⋊C8C22semidirect
21. C2×C11⋊#95C22semidirect
24. #10622560C22semidirect
26. #10622351C22semidirect
27. C11×#323C22semidirect
28. #10622108C22semidirect
48. C22×Dic22C23semidirect
73. C11×C22⋊C8C23semidirect
76. C11⋊#95C23semidirect
84. C24×C11SD16semidirect
151. C2×#323D11semidirect
169. C23×C11C2×SD16semidirect
228. C2×C22⋊C8C2×D11semidirect
234. #323C2×D11semidirect
311. C22⋊C8C22×D11semidirect
319. C2×C11#1601semidirect
334. C24#4314semidirect
391. C11C2×#1601semidirect
417. C23C2×#4314semidirect
489. C2#13067570direct (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×#106223512
C2×#106225602
#130675702
C2×#106221082
C2×C11×#3232
C2×#160111