Finite Group Databasebeta

← C2×#13067538 #14725848

Subgroups — C2×#13067538 #14725848

Order 2816.

1696 conjugacy classes of subgroups; only the 203 normal subgroups are shown.

normal subgroups only

This group has 1696 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×#10623014C211yesmaximal, characteristic, complemented
2C2×#10622831C212yesmaximal, complemented
3#13067538C218yesmaximal, direct product factor
4C2×#10622090C212yesmaximal, complemented
5C2×#10622163C211yesmaximal, characteristic, complemented
6C2×C11×#392C211yesmaximal, characteristic
7C23×D4×C11—21no—
8C23×D4×C11C2211yescharacteristic
9C22×C11×C22⋊C4—21no—
10C22×C11×C22⋊C4C2211yescharacteristic
11C22×C22⋊Dic11—21no—
12C22×#4324—22no—
13C2×#66977—21no—
14C2×#66977C2212yes—
15#10623014—22no—
16#10623014—24no—
17#10623014C2214yescomplemented
18C2×#66931—22no—
19C2×#66931—22no—
20C11×#392—22no—
21C11×#392C2214yes—
22C2×C11×#95C2211yescharacteristic
23#10622831—24no—
24#10622831C2218yescomplemented
25C2×#66896—22no—
26C2×C22⋊(C11⋊C8)C2212yes—
27#10622163C2214yescomplemented
28#10622090C2218yescomplemented
29C25×C11—21no—
30C25×C11D411yescharacteristic
31C22×D4×C11—24no—
32C22×D4×C11—22no—
33C22×D4×C11—22no—
34C22×D4×C11—21no—
35C22×D4×C11—44no—
36C22×D4×C11—44no—
37C22×D4×C11—44no—
38C22×D4×C11—44no—
39C22×D4×C11C2312yes—
40C23×C4×C11—21no—
41C23×C4×C11D411yescharacteristic
42C23×C4×C11C2311yescharacteristic
43C23×Dic11—21no—
44C23×Dic11—21no—
45C22×Dic22—21no—
46C22×Dic22D412yescomplemented
47C2×C11×C22⋊C4—22no—
48C2×C11×C22⋊C4—22no—
49C2×C11×C22⋊C4—24no—
50C2×C11×C22⋊C4—44no—
51C2×C11×C22⋊C4D412yes—
52C2×C11×C22⋊C4C2312yes—
53C2×C22⋊Dic11—22no—
54C2×C22⋊Dic11—24no—
55C2×C22⋊Dic11—24no—
56C2×C22⋊Dic11—22no—
57C2×#4324—28no—
58C2×#4324—48no—
59C2×C4⋊Dic11—21no—
60C2×C4⋊Dic11D412yescomplemented
61#66977—24no—
62#66977—22no—
63#66977—22no—
64#66977—24no—
65#66977D414yescomplemented
66#66977C2314yes—
67C2×Dic11⋊C4—22no—
68C2×Dic11⋊C4—22no—
69C22×C11⋊C8—22no—
70#66931—28no—
71#66931—28no—
72#66931—28no—
73#66931—28no—
74C11×#95—21no—
75C11×#95C2312yes—
76#66896—28no—
77C22⋊(C11⋊C8)—22no—
78C22⋊(C11⋊C8)C2314yes—
79C2×#1596—111nomaximal, Sylow
80C24×C11—21no—
81C24×C11—21no—
82C24×C11—22no—
83C24×C11—24no—
84C24×C11—22no—
85C24×C11—42no—
86C24×C11—42no—
87C24×C11—42no—
88C24×C11—42no—
89C24×C11—42no—
90C24×C11—41no—
91C24×C11—41no—
92C24×C11—42no—
93C24×C11—42no—
94C24×C11SD1614yescomplemented
95C24×C11C2×D411yescharacteristic
96C24×C11C2×D412yes—
97C2×D4×C11—28no—
98C2×D4×C11—24no—
99C2×D4×C11—44no—
100C2×D4×C11—48no—
101C2×D4×C11—44no—
102C2×D4×C11—48no—
103C2×D4×C11—44no—
104C2×D4×C11—48no—
105C2×D4×C11—432no—
106C2×D4×C11—48no—
107C2×D4×C11—42no—
108C22×C4×C11—24no—
109C22×C4×C11—21no—
110C22×C4×C11—22no—
111C22×C4×C11—21no—
112C22×C4×C11—42no—
113C22×C4×C11—42no—
114C22×C4×C11—42no—
115C22×C4×C11—42no—
116C22×C4×C11C2×D412yes—
117C22×C4×C11C2×D412yes—
118C22×C4×C11C2×D411yescharacteristic
119C22×C4×C11C2×D412yes—
120C22×C4×C11C2411yescharacteristic
121C22×Dic11—24no—
122C22×Dic11—24no—
123C22×Dic11—22no—
124C22×Dic11—22no—
125C22×Dic11—82no—
126C22×Dic11—82no—
127C2×Dic22—24no—
128C2×Dic22—22no—
129C2×Dic22—44no—
130C2×Dic22—82no—
131C2×Dic22C2×D414yescomplemented
132C11×C22⋊C4—24no—
133C11×C22⋊C4—24no—
134C11×C22⋊C4—48no—
135C22⋊Dic11—28no—
136C22⋊Dic11—24no—
137C22⋊Dic11—24no—
138#4324—416no—
139C4⋊Dic11—24no—
140C4⋊Dic11—22no—
141C4⋊Dic11C2×D414yescomplemented
142Dic11⋊C4—28no—
143Dic11⋊C4—24no—
144Dic11⋊C4—24no—
145C2×C11⋊C8—24no—
146C2×C11⋊C8—44no—
147C2×#543—111no—
148C2×#450—112no—
149C2×#392D1111yescharacteristic
150#1596—118no—
151C2×#328—112no—
152C2×#323—111no—
153C23×C11—22no—
154C23×C11—22no—
155C23×C11—22no—
156C23×C11—24no—
157C23×C11—22no—
158C23×C11—24no—
159C23×C11—24no—
160C23×C11—48no—
161C23×C11—42no—
162C23×C11—42no—
163C23×C11—42no—
164C23×C11—48no—
165C23×C11—42no—
166C23×C11—42no—
167C23×C11—44no—
168C23×C11—48no—
169C23×C11—42no—
170C23×C11—42no—
171C23×C11—42no—
172C23×C11—42no—
173C23×C11—42no—
174C23×C11—44no—
175C23×C11—84no—
176C23×C11—81no—
177C23×C11—81no—
178C23×C11—84no—
179C23×C11—84no—
180C23×C11—82no—
181C23×C11—82no—
182C23×C11—82no—
183C23×C11—82no—
184C23×C11#12011yescharacteristic
185C23×C11#12011yescharacteristic
186C23×C11C2×SD1612yes—
187C23×C11C2×SD1614yescomplemented
188C23×C11#13712yes—
189C23×C11C22×D411yescharacteristic
190D4×C11—28no—
191D4×C11—48no—
192D4×C11—44no—
193D4×C11—432no—
194C2×C4×C11—24no—
195C2×C4×C11—24no—
196C2×C4×C11—22no—
197C2×C4×C11—42no—
198C2×C4×C11—41no—
199C2×C4×C11—41no—
200C2×C4×C11—48no—
201C2×C4×C11—42no—
202C2×C4×C11—42no—
203C2×C4×C11—42no—
204C2×C4×C11—42no—
205C2×C4×C11—81no—
206C2×C4×C11#12012yes—
207C2×C4×C11C22×D412yes—
208C2×Dic11—24no—
209C2×Dic11—24no—
210C2×Dic11—44no—
211C2×Dic11—44no—
212C2×Dic11—84no—
213C2×Dic11—84no—
214Dic22—44no—
215Dic22—82no—
216Dic22—84no—
217C11⋊C8—44no—
218C23×D4—21no—
219C23×D4C2×D1111yescharacteristic
220C22×SD16—222no—
221#543—114no—
222#543—224no—
223#543—222no—
224C2×C22⋊Q8—112no—
225C2×C22⋊Q8—222no—
226C2×C22⋊Q8—222no—
227C2×C22⋊Q8—221no—
228C22×C22⋊C4—21no—
229C22×C22⋊C4—221no—
230C22×C22⋊C4C2×D1111yescharacteristic
231#450—118no—
232#450—224no—
233C2×#102—222no—
234C2×C22⋊C8—112no—
235#392—22no—
236#392C2×D1114yes—
237C2×#95C2×D1111yescharacteristic
238#328—118no—
239#323—114no—
240C22×C11—24no—
241C22×C11—24no—
242C22×C11—21no—
243C22×C11—21no—
244C22×C11—21no—
245C22×C11—21no—
246C22×C11—24no—
247C22×C11—44no—
248C22×C11—44no—
249C22×C11—44no—
250C22×C11—48no—
251C22×C11—42no—
252C22×C11—42no—
253C22×C11—44no—
254C22×C11—82no—
255C22×C11—84no—
256C22×C11—82no—
257C22×C11—82no—
258C22×C11—88no—
259C22×C11—88no—
260C22×C11—82no—
261C22×C11—82no—
262C22×C11#44812yes—
263C22×C11#44812yes—
264C22×C11#45312yes—
265C22×C11B(4,𝔽2)12yes—
266C22×C11C2×#12011yescharacteristic
267C22×C11C22×SD1611yescharacteristic
268C22×C11C2×#13711yescharacteristic
269C4×C11—22no—
270C4×C11—22no—
271C4×C11—44no—
272C4×C11—42no—
273Dic11—44no—
274Dic11—44no—
275C25—21no—
276C25C22⋊D1111yescharacteristic
277C22×Q8—112no—
278C22×Q8—221no—
279C22×D4—24no—
280C22×D4—22no—
281C22×D4—22no—
282C22×D4—21no—
283C22×D4—44no—
284C22×D4—44no—
285C22×D4—44no—
286C22×D4—44no—
287C22×D4C22×D1112yes—
288C23×C4—21no—
289C23×C4—221no—
290C23×C4—221no—
291C23×C4C22⋊D1111yescharacteristic
292C23×C4C22×D1111yescharacteristic
293C2×SD16—228no—
294C2×SD16—448no—
295C22×C8—222no—
296C22⋊Q8—114no—
297C22⋊Q8—114no—
298C22⋊Q8—228no—
299C22⋊Q8—228no—
300C22⋊Q8—228no—
301C22⋊Q8—228no—
302C22⋊Q8—224no—
303C22⋊Q8—222no—
304C22⋊Q8—222no—
305C22⋊Q8—224no—
306C2×C4⋊C4—112no—
307C2×C4⋊C4—222no—
308C2×C4⋊C4—221no—
309C2×C4⋊C4—222no—
310C2×C22⋊C4—22no—
311C2×C22⋊C4—22no—
312C2×C22⋊C4—24no—
313C2×C22⋊C4—44no—
314C2×C22⋊C4—222no—
315C2×C22⋊C4—224no—
316C2×C22⋊C4—222no—
317C2×C22⋊C4—224no—
318C2×C22⋊C4C22⋊D1112yes—
319C2×C22⋊C4C22×D1112yes—
320#102—228no—
321C22⋊C8—114no—
322C22⋊C8—222no—
323#95—21no—
324#95C22×D1112yes—
325C2×C11—21no—
326C2×C11—21no—
327C2×C11—22no—
328C2×C11—44no—
329C2×C11—84no—
330C2×C11#159614yescomplemented
331C2×C11C2×#44811yescharacteristic
332C2×C11C2×#45311yescharacteristic
333C2×C11C2×B(4,𝔽2)11yescharacteristic
334C24—21no—
335C24—21no—
336C24—22no—
337C24—24no—
338C24—22no—
339C24—42no—
340C24—42no—
341C24—42no—
342C24—42no—
343C24—42no—
344C24—42no—
345C24—41no—
346C24—41no—
347C24—42no—
348C24#432414yescomplemented
349C24C2×C22⋊D1111yescharacteristic
350C24C2×C22⋊D1112yes—
351C2×Q8—114no—
352C2×Q8—224no—
353C2×Q8—222no—
354C2×Q8—444no—
355C2×Q8—882no—
356C2×D4—28no—
357C2×D4—24no—
358C2×D4—44no—
359C2×D4—48no—
360C2×D4—44no—
361C2×D4—48no—
362C2×D4—44no—
363C2×D4—48no—
364C2×D4—432no—
365C2×D4—48no—
366C2×D4—42no—
367C22×C4—24no—
368C22×C4—21no—
369C22×C4—22no—
370C22×C4—21no—
371C22×C4—42no—
372C22×C4—42no—
373C22×C4—42no—
374C22×C4—42no—
375C22×C4—222no—
376C22×C4—222no—
377C22×C4—224no—
378C22×C4—224no—
379C22×C4—882no—
380C22×C4—882no—
381C22×C4D4×D1112yes—
382C22×C4D4×D1112yes—
383C22×C4C2×C22⋊D1112yes—
384C22×C4C2×C22⋊D1111yescharacteristic
385C22×C4C23×D1111yescharacteristic
386SD16—4416no—
387C2×C8—224no—
388C2×C8—444no—
389C4⋊C4—114no—
390C4⋊C4—228no—
391C4⋊C4—224no—
392C4⋊C4—222no—
393C4⋊C4—224no—
394C4⋊C4—224no—
395C22⋊C4—24no—
396C22⋊C4—24no—
397C22⋊C4—48no—
398C22⋊C4—228no—
399C22⋊C4—224no—
400C22⋊C4—224no—
401C11C2×#159611yescharacteristic, complemented, Sylow
402C23—22no—
403C23—22no—
404C23—22no—
405C23—24no—
406C23—22no—
407C23—24no—
408C23—24no—
409C23—48no—
410C23—42no—
411C23—42no—
412C23—42no—
413C23—48no—
414C23—42no—
415C23—42no—
416C23—44no—
417C23—48no—
418C23—42no—
419C23—42no—
420C23—42no—
421C23—42no—
422C23—42no—
423C23—44no—
424C23—84no—
425C23—81no—
426C23—81no—
427C23—84no—
428C23—84no—
429C23—82no—
430C23—82no—
431C23—82no—
432C23—82no—
433C23C2×#432412yes—
434C23C2×#432414yescomplemented
435C23#6699011yescharacteristic
436C23#6699011yescharacteristic
437C23#6700412yes—
438C23C22×C22⋊D1111yescharacteristic
439Q8—444no—
440Q8—882no—
441Q8—884no—
442D4—28no—
443D4—44no—
444D4—48no—
445D4—432no—
446C2×C4—24no—
447C2×C4—24no—
448C2×C4—22no—
449C2×C4—42no—
450C2×C4—41no—
451C2×C4—41no—
452C2×C4—48no—
453C2×C4—42no—
454C2×C4—42no—
455C2×C4—42no—
456C2×C4—42no—
457C2×C4—81no—
458C2×C4—224no—
459C2×C4—224no—
460C2×C4—444no—
461C2×C4—444no—
462C2×C4—884no—
463C2×C4—884no—
464C2×C4#6699012yes—
465C2×C4C2×D4×D1112yes—
466C8—444no—
467C22—24no—
468C22—24no—
469C22—21no—
470C22—21no—
471C22—21no—
472C22—21no—
473C22—24no—
474C22—44no—
475C22—44no—
476C22—44no—
477C22—48no—
478C22—42no—
479C22—42no—
480C22—44no—
481C22—82no—
482C22—84no—
483C22—82no—
484C22—82no—
485C22—88no—
486C22—88no—
487C22—82no—
488C22—82no—
489C22#1062264512yes—
490C22#1062265312yes—
491C22#1062265312yes—
492C22#1062269012yes—
493C22C22×#432411yescharacteristic
494C22C2×#6699011yescharacteristic
495C22C2×#6700411yescharacteristic
496C4—22no—
497C4—22no—
498C4—44no—
499C4—42no—
500C4—444no—
501C4—444no—
502C2—21no—
503C2—21no—
504C2—22no—
505C2—44no—
506C2—84no—
507C2#1306753814yesdirect product factor
508C2C2×#1062265311yescharacteristic
509C2C2×#1062269011yescharacteristic
510C2C2×#1062264511yescharacteristic
subgroupG/H
centerC23#66990
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
Fitting, prime radicalC2×C11×#392C2
socleC23×C11#120
hypercenterC2×#392D11
hypocenterC11C2×#1596
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#392

Complements

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

NH ≅ G/Ntype
1. C2×#10623014C2semidirect
2. C2×#10622831C2semidirect
3. #13067538C2direct (N × H)
4. C2×#10622090C2semidirect
5. C2×#10622163C2semidirect
17. #10623014C22semidirect
24. #10622831C22semidirect
27. #10622163C22semidirect
28. #10622090C22semidirect
46. C22×Dic22D4semidirect
60. C2×C4⋊Dic11D4semidirect
65. #66977D4semidirect
94. C24×C11SD16semidirect
131. C2×Dic22C2×D4semidirect
141. C4⋊Dic11C2×D4semidirect
187. C23×C11C2×SD16semidirect
330. C2×C11#1596semidirect
348. C24#4324semidirect
401. C11C2×#1596semidirect
434. C23C2×#4324semidirect
507. C2#13067538direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230142
C2×#106228312
#130675382
C2×#106220902
C2×#106221632
C2×C11×#3922
C2×#159611