Finite Group Databasebeta

← C2×#13067553 #14725941

Subgroups — C2×#13067553 #14725941

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×#10622345C212yesmaximal, complemented
3C2×#10622604C211yesmaximal, characteristic, complemented
4#13067553C218yesmaximal, direct product factor
5C2×#10622108C212yesmaximal, complemented
6C2×C11×#324C211yesmaximal, characteristic, complemented
7C22×#4339—21no—
8C23×D44C2211yescharacteristic
9C22×C11×C4⋊C4C2211yescharacteristic
10C2×#66983—21no—
11C2×#66983C2212yes—
12C22×(C2×D11)⋊C4—21no—
13C22×(C2×D11)⋊C4—21no—
14C22×D88—22no—
15#10623041—22no—
16#10623041—24no—
17#10623041C2214yescomplemented
18C2×#66950—22no—
19C2×#66948—22no—
20C2×C11×C22⋊C8C2212yes—
21C2×C11⋊#95C2211yescharacteristic
22C2×#66885—22no—
23#10622604—22no—
24#10622604C2214yescomplemented
25#10622345—24no—
26#10622345C2218yescomplemented
27C11×#324C2214yescomplemented
28#10622108C2218yescomplemented
29C24×D11—21no—
30C23×C4×C11D411yescharacteristic
31C23×C4×C11D411yescharacteristic
32C23×C4×C11C2311yescharacteristic
33C22×C22⋊D11—22no—
34C23×Dic11—21no—
35C2×#4339—24no—
36C2×#4339—24no—
37C2×#4339—44no—
38C2×#4339—44no—
39C22×D44—22no—
40C22×D44—21no—
41C22×D44—21no—
42C22×D44—22no—
43C22×D44—21no—
44C22×D44—44no—
45C22×D44D412yes—
46C22×D44C2312yes—
47C22×C4×D11—22no—
48C22×Dic22—21no—
49C22×C8×C11—22no—
50C2×C11×C4⋊C4—22no—
51C2×C11×C4⋊C4—22no—
52C2×C11×C4⋊C4D412yes—
53C2×C11×C4⋊C4C2312yes—
54#66983—24no—
55#66983—22no—
56#66983—22no—
57#66983—24no—
58#66983D414yes—
59#66983C2314yes—
60C2×(C2×D11)⋊C4—22no—
61C2×(C2×D11)⋊C4—22no—
62C2×(C2×D11)⋊C4—24no—
63C2×(C2×D11)⋊C4—24no—
64C2×(C2×D11)⋊C4—44no—
65C2×(C2×D11)⋊C4—44no—
66C2×C4⋊Dic11—21no—
67C2×C4⋊Dic11D412yes—
68C2×D88—28no—
69C2×D88—48no—
70#66950—28no—
71#66950—28no—
72#66948—28no—
73#66948—28no—
74C11×C22⋊C8—22no—
75C11×C22⋊C8C2314yes—
76C11⋊#95—21no—
77C11⋊#95C2312yes—
78#66885—28no—
79C2×#1598—111nomaximal, Sylow
80C24×C11C2×D411yescharacteristic
81C23×D11—24no—
82C23×D11—22no—
83C23×D11—22no—
84C23×D11—42no—
85C23×D11—42no—
86C23×D11—42no—
87C23×D11—41no—
88C23×D11—41no—
89C23×D11—42no—
90C23×D11—42no—
91C22×C4×C11—21no—
92C22×C4×C11—21no—
93C22×C4×C11—22no—
94C22×C4×C11—21no—
95C22×C4×C11—21no—
96C22×C4×C11—42no—
97C22×C4×C11—42no—
98C22×C4×C11D814yescomplemented
99C22×C4×C11C2×D412yes—
100C22×C4×C11C2×D412yes—
101C22×C4×C11C2×D412yes—
102C22×C4×C11C2×D411yescharacteristic
103C22×C4×C11C2×D412yes—
104C22×C4×C11C2411yescharacteristic
105C2×C22⋊D11—24no—
106C2×C22⋊D11—24no—
107C2×C22⋊D11—44no—
108C2×C22⋊D11—44no—
109C22×Dic11—22no—
110C22×Dic11—22no—
111C22×Dic11—42no—
112C22×Dic11—42no—
113C22×Dic11—42no—
114#4339—48no—
115#4339—416no—
116#4339—48no—
117C2×D44—24no—
118C2×D44—24no—
119C2×D44—28no—
120C2×D44—22no—
121C2×D44—24no—
122C2×D44—44no—
123C2×D44—44no—
124C2×D44—44no—
125C2×D44—44no—
126C2×D44—44no—
127C2×D44—48no—
128C2×D44—42no—
129C2×D44—82no—
130C2×D44C2×D414yes—
131C2×C4×D11—28no—
132C2×C4×D11—48no—
133C2×Dic22—24no—
134C2×Dic22—44no—
135C2×C8×C11—24no—
136C2×C8×C11—44no—
137C11×C4⋊C4—24no—
138C11×C4⋊C4—24no—
139(C2×D11)⋊C4—28no—
140(C2×D11)⋊C4—24no—
141(C2×D11)⋊C4—24no—
142(C2×D11)⋊C4—48no—
143(C2×D11)⋊C4—48no—
144C4⋊Dic11—24no—
145C4⋊Dic11—22no—
146C4⋊Dic11C2×D414yes—
147D88—416no—
148C2×#537—111no—
149C2×#447—112no—
150C2×#394—111no—
151#1598—118no—
152C2×#327—112no—
153C2×#324D1111yescharacteristic, complemented
154C23×C11—22no—
155C23×C11—22no—
156C23×C11#12011yescharacteristic
157C23×C11#12011yescharacteristic
158C23×C11C2×D812yes—
159C23×C11AGL(1,ℤ/8)12yes—
160C23×C11C22×D411yescharacteristic
161C22×D11—24no—
162C22×D11—24no—
163C22×D11—42no—
164C22×D11—44no—
165C22×D11—48no—
166C22×D11—48no—
167C22×D11—42no—
168C22×D11—42no—
169C22×D11—42no—
170C22×D11—42no—
171C22×D11—42no—
172C22×D11—44no—
173C22×D11—44no—
174C22×D11—44no—
175C22×D11—44no—
176C22×D11—84no—
177C22×D11—84no—
178C22×D11—82no—
179C22×D11—82no—
180C22×D11—82no—
181C22×D11—82no—
182C2×C4×C11—22no—
183C2×C4×C11—22no—
184C2×C4×C11—24no—
185C2×C4×C11—24no—
186C2×C4×C11—24no—
187C2×C4×C11—22no—
188C2×C4×C11—41no—
189C2×C4×C11—42no—
190C2×C4×C11—41no—
191C2×C4×C11—42no—
192C2×C4×C11—42no—
193C2×C4×C11—81no—
194C2×C4×C11#12012yes—
195C2×C4×C11C2×D814yescomplemented
196C2×C4×C11C22×D412yes—
197C22⋊D11—44no—
198C22⋊D11—44no—
199C22⋊D11—48no—
200C2×Dic11—24no—
201C2×Dic11—44no—
202C2×Dic11—42no—
203C2×Dic11—42no—
204C2×Dic11—42no—
205C2×Dic11—84no—
206D44—28no—
207D44—44no—
208D44—48no—
209D44—44no—
210D44—48no—
211D44—82no—
212D44—84no—
213C4×D11—416no—
214Dic22—48no—
215C8×C11—44no—
216C22×#41—221no—
217C23×D4—111no—
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—221no—
228C22×C22⋊C4—221no—
229#447—118no—
230#447—224no—
231C2×#102—222no—
232C2×C22⋊C8C2×D1112yes—
233#394—114no—
234#394—222no—
235C2×#95—111no—
236#327—118no—
237#324C2×D1114yescomplemented
238C22×C11—24no—
239C22×C11—24no—
240C22×C11—21no—
241C22×C11—21no—
242C22×C11—21no—
243C22×C11—21no—
244C22×C11#44712yes—
245C22×C11#44712yes—
246C22×C11#45412yes—
247C22×C11B(4,𝔽2)12yes—
248C22×C11C2×#12011yescharacteristic
249C22×C11C22×D811yescharacteristic
250C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
251C2×D11—44no—
252C2×D11—44no—
253C2×D11—44no—
254C2×D11—44no—
255C2×D11—44no—
256C2×D11—44no—
257C2×D11—82no—
258C2×D11—82no—
259C2×D11—88no—
260C2×D11—88no—
261C2×D11—88no—
262C2×D11—82no—
263C2×D11—82no—
264C4×C11—24no—
265C4×C11—22no—
266C4×C11—22no—
267C4×C11—42no—
268Dic11—44no—
269Dic11—82no—
270C25—221no—
271C2×#41—224no—
272C2×#41—224no—
273C2×#41—444no—
274C2×#41—444no—
275C22×Q8—221no—
276C22×D4—112no—
277C22×D4—112no—
278C22×D4—221no—
279C22×D4—221no—
280C22×D4—222no—
281C22×D4—221no—
282C22×D4—222no—
283C22×D4—222no—
284C22×D4—444no—
285C23×C4—222no—
286C23×C4—221no—
287C23×C4D4411yescharacteristic
288C23×C4D4411yescharacteristic
289C23×C4C22×D1111yescharacteristic
290C2×D8—228no—
291C2×D8—448no—
292C22×C8—22no—
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—224no—
302#121—222no—
303C2×C4⋊C4—22no—
304C2×C4⋊C4—22no—
305C2×C4⋊C4—112no—
306C2×C4⋊C4—221no—
307C2×C4⋊C4D4412yes—
308C2×C4⋊C4C22×D1112yes—
309C2×C22⋊C4—222no—
310C2×C22⋊C4—222no—
311C2×C22⋊C4—224no—
312C2×C22⋊C4—224no—
313C2×C22⋊C4—444no—
314C2×C22⋊C4—444no—
315#102—228no—
316C22⋊C8—22no—
317C22⋊C8C22×D1114yes—
318#95—112no—
319#95—221no—
320C2×C11—21no—
321C2×C11—21no—
322C2×C11—22no—
323C2×C11#159814yescomplemented
324C2×C11C2×#44711yescharacteristic
325C2×C11C2×#45411yescharacteristic
326C2×C11C2×B(4,𝔽2)11yescharacteristic
327D11—84no—
328D11—84no—
329C24—224no—
330C24—222no—
331C24—222no—
332C24—442no—
333C24—442no—
334C24—442no—
335C24—441no—
336C24—441no—
337C24—442no—
338C24—442no—
339C24C2×D4411yescharacteristic
340#41—448no—
341#41—4416no—
342#41—448no—
343C2×Q8—224no—
344C2×Q8—444no—
345C2×D4—114no—
346C2×D4—228no—
347C2×D4—224no—
348C2×D4—224no—
349C2×D4—224no—
350C2×D4—224no—
351C2×D4—222no—
352C2×D4—224no—
353C2×D4—444no—
354C2×D4—444no—
355C2×D4—444no—
356C2×D4—444no—
357C2×D4—448no—
358C2×D4—444no—
359C2×D4—444no—
360C2×D4—444no—
361C2×D4—442no—
362C2×D4—882no—
363C22×C4—21no—
364C22×C4—21no—
365C22×C4—22no—
366C22×C4—21no—
367C22×C4—21no—
368C22×C4—42no—
369C22×C4—42no—
370C22×C4—228no—
371C22×C4—222no—
372C22×C4—222no—
373C22×C4—448no—
374C22×C4—442no—
375C22×C4—442no—
376C22×C4—442no—
377C22×C4D8814yescomplemented
378C22×C4C2×D4412yes—
379C22×C4C2×D4412yes—
380C22×C4C2×D4411yescharacteristic
381C22×C4D4×D1112yes—
382C22×C4D4×D1112yes—
383C22×C4C23×D1111yescharacteristic
384D8—4416no—
385C2×C8—24no—
386C2×C8—44no—
387C4⋊C4—24no—
388C4⋊C4—24no—
389C4⋊C4—114no—
390C4⋊C4—224no—
391C4⋊C4—222no—
392C22⋊C4—228no—
393C22⋊C4—224no—
394C22⋊C4—224no—
395C22⋊C4—448no—
396C22⋊C4—448no—
397C11C2×#159811yescharacteristic, complemented, Sylow
398C23—22no—
399C23—22no—
400C23—224no—
401C23—224no—
402C23—442no—
403C23—444no—
404C23—448no—
405C23—448no—
406C23—442no—
407C23—442no—
408C23—442no—
409C23—442no—
410C23—442no—
411C23—444no—
412C23—444no—
413C23—444no—
414C23—444no—
415C23—884no—
416C23—884no—
417C23—882no—
418C23—882no—
419C23—882no—
420C23—882no—
421C23#6693511yescharacteristic
422C23#6693511yescharacteristic
423C23C2×D8812yes—
424C23#6696112yes—
425C23C22×D4411yescharacteristic
426Q8—448no—
427D4—228no—
428D4—444no—
429D4—444no—
430D4—448no—
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—41no—
444C2×C4—42no—
445C2×C4—41no—
446C2×C4—42no—
447C2×C4—42no—
448C2×C4—81no—
449C2×C4—224no—
450C2×C4—4416no—
451C2×C4—444no—
452C2×C4—442no—
453C2×C4—442no—
454C2×C4—442no—
455C2×C4—884no—
456C2×C4#6693512yes—
457C2×C4C2×D8814yescomplemented
458C2×C4C2×D4×D1112yes—
459C8—44no—
460C22—24no—
461C22—24no—
462C22—21no—
463C22—21no—
464C22—21no—
465C22—21no—
466C22—444no—
467C22—444no—
468C22—444no—
469C22—444no—
470C22—444no—
471C22—444no—
472C22—882no—
473C22—882no—
474C22—888no—
475C22—888no—
476C22—888no—
477C22—882no—
478C22—882no—
479C22#1062234512yes—
480C22#1062234512yes—
481C22#1062235412yes—
482C22#1062236612yes—
483C22C2×#6693511yescharacteristic
484C22C22×D8811yescharacteristic
485C22C2×#6696111yescharacteristic
486C4—24no—
487C4—22no—
488C4—22no—
489C4—42no—
490C4—444no—
491C4—882no—
492C2—21no—
493C2—21no—
494C2—22no—
495C2—884no—
496C2—884no—
497C2#1306755314yesdirect product factor
498C2C2×#1062234511yescharacteristic
499C2C2×#1062236611yescharacteristic
500C2C2×#1062235411yescharacteristic
subgroupG/H
centerC23#66935
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#324C2
socleC23×C11#120
hypercenterC2×#324D11
hypocenterC11C2×#1598
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#324

Complements

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

NH ≅ G/Ntype
1. C2×#10623041C2semidirect
2. C2×#10622345C2semidirect
3. C2×#10622604C2semidirect
4. #13067553C2direct (N × H)
5. C2×#10622108C2semidirect
6. C2×C11×#324C2semidirect
17. #10623041C22semidirect
24. #10622604C22semidirect
26. #10622345C22semidirect
27. C11×#324C22semidirect
28. #10622108C22semidirect
98. C22×C4×C11D8semidirect
153. C2×#324D11semidirect
195. C2×C4×C11C2×D8semidirect
237. #324C2×D11semidirect
323. C2×C11#1598semidirect
377. C22×C4D88semidirect
397. C11C2×#1598semidirect
457. C2×C4C2×D88semidirect
497. C2#13067553direct (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×#106223452
C2×#106226042
#130675532
C2×#106221082
C2×C11×#3242
C2×#159811