Finite Group Databasebeta

← C2×#13074729 #14920317

Subgroups — C2×#13074729 #14920317

Order 2816.

2982 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66949C211yesmaximal, characteristic
2C22×#66999C211yesmaximal, characteristic
3#13074729C2116yesmaximal, direct product factor
4C2×#10622270C212yesmaximal, complemented
5C2×#10622274C211yesmaximal, characteristic, complemented
6C2×#10622596C211yesmaximal, characteristic, complemented
7C2×#10622592C212yesmaximal, complemented
8C2×#10622842C211yesmaximal, characteristic, complemented
9C2×#10622280C212yesmaximal
10C2×#10622600C212yesmaximal
11C2×D11×#95C211yesmaximal, characteristic
12C2×C11×#395C211yesmaximal, characteristic, complemented
13C23×Q8×C11C2211yescharacteristic
14C23×C4×D11C2211yescharacteristic
15C23×C4×D11C2212yes—
16C23×Dic22C2211yescharacteristic
17C22×C11×C4⋊C4C2211yescharacteristic
18C22×C11×C4⋊C4C2212yes—
19C2×#66999—28no—
20C2×#66999C2218yes—
21C22×(C2×D11)⋊C4C2211yescharacteristic
22C22×(C2×D11)⋊C4C2212yes—
23C22×(C2×D11)⋊C4C2211yescharacteristic
24C22×C4⋊Dic11C2211yescharacteristic
25C22×C4⋊Dic11C2212yes—
26C22×Dic11⋊C4C2211yescharacteristic
27C22×Dic11⋊C4C2212yes—
28C22×Dic11⋊C4C2211yescharacteristic
29C22×Dic11⋊C4C2212yes—
30C22×Dic11⋊C4C2212yes—
31C2×#66949—28no—
32C2×#66949C2218yes—
33C11×#395C2218yescomplemented
34C2×C11×#95C2211yescharacteristic
35C2×C11×#95C2212yes—
36#10622842C2218yescomplemented
37C2×C11⋊#95C2211yescharacteristic
38C2×C11⋊#95C2212yes—
39C2×C11⋊#95C2212yes—
40C2×C11⋊#95C2212yes—
41C2×C11⋊#95C2212yes—
42#10622600C22116yes—
43#10622596C2218yescomplemented
44#10622592C22116yescomplemented
45#10622280C22116yes—
46D11×#95C2218yes—
47#10622274C2218yescomplemented
48#10622270C22116yescomplemented
49C24×D11C2311yescharacteristic
50C22×Q8×C11—24no—
51C22×Q8×C11—44no—
52C22×Q8×C11C2314yes—
53C23×C4×C11C2311yescharacteristic
54C23×C4×C11C2312yes—
55C23×C4×C11C2311yescharacteristic
56C23×C4×C11C2311yescharacteristic
57C23×C4×C11C2312yes—
58C23×Dic11C2311yescharacteristic
59C23×Dic11C2311yescharacteristic
60C23×Dic11C2312yes—
61C23×Dic11C2311yescharacteristic
62C23×Dic11C2312yes—
63C22×C4×D11—44no—
64C22×C4×D11—44no—
65C22×C4×D11—44no—
66C22×C4×D11D418yes—
67C22×C4×D11Q8116yescomplemented
68C22×C4×D11C2314yes—
69C22×C4×D11C2318yes—
70C22×Dic22—24no—
71C22×Dic22—44no—
72C22×Dic22C2314yes—
73C2×C11×C4⋊C4—24no—
74C2×C11×C4⋊C4—44no—
75C2×C11×C4⋊C4C2314yes—
76C2×C11×C4⋊C4C2318yes—
77#66999—232no—
78C2×(C2×D11)⋊C4—24no—
79C2×(C2×D11)⋊C4—24no—
80C2×(C2×D11)⋊C4—28no—
81C2×(C2×D11)⋊C4C2314yes—
82C2×(C2×D11)⋊C4C2314yes—
83C2×(C2×D11)⋊C4C2318yes—
84C2×C4⋊Dic11—24no—
85C2×C4⋊Dic11—44no—
86C2×C4⋊Dic11C2314yes—
87C2×C4⋊Dic11C2318yes—
88C2×Dic11⋊C4—24no—
89C2×Dic11⋊C4—24no—
90C2×Dic11⋊C4—28no—
91C2×Dic11⋊C4—44no—
92C2×Dic11⋊C4—44no—
93C2×Dic11⋊C4C2314yes—
94C2×Dic11⋊C4C2318yes—
95C2×Dic11⋊C4C2314yes—
96C2×Dic11⋊C4C2318yes—
97C2×Dic11⋊C4C2318yes—
98#66949—232no—
99C11×#95C2318yes—
100C11×#95C2314yes—
101C11⋊#95C2318yes—
102C11⋊#95C2318yes—
103C11⋊#95C2318yes—
104C11⋊#95C2314yes—
105C11⋊#95C2318yes—
106C2×#2659—111nomaximal, Sylow
107C24×C11C2411yescharacteristic
108C23×D11—24no—
109C23×D11—22no—
110C23×D11—22no—
111C23×D11C2×D414yes—
112C23×D11C2×Q818yes—
113C23×D11C2412yes—
114C2×Q8×C11—28no—
115C2×Q8×C11—48no—
116C2×Q8×C11—416no—
117C22×C4×C11—24no—
118C22×C4×C11—24no—
119C22×C4×C11—24no—
120C22×C4×C11—22no—
121C22×C4×C11—24no—
122C22×C4×C11—22no—
123C22×C4×C11—22no—
124C22×C4×C11—24no—
125C22×C4×C11—24no—
126C22×C4×C11—24no—
127C22×C4×C11—22no—
128C22×C4×C11C2×D414yes—
129C22×C4×C11C2×Q818yes—
130C22×C4×C11C2412yes—
131C22×C4×C11C2414yes—
132C22×C4×C11C2412yes—
133C22×C4×C11C2412yes—
134C22×C4×C11C2414yes—
135C22×Dic11—22no—
136C22×Dic11—24no—
137C22×Dic11—22no—
138C22×Dic11—24no—
139C22×Dic11—24no—
140C22×Dic11—24no—
141C22×Dic11—24no—
142C22×Dic11—24no—
143C22×Dic11—22no—
144C22×Dic11—22no—
145C22×Dic11—24no—
146C22×Dic11C2×D414yes—
147C22×Dic11C2×Q818yes—
148C22×Dic11C2412yes—
149C22×Dic11C2412yes—
150C22×Dic11C2414yes—
151C22×Dic11C2412yes—
152C22×Dic11C2414yes—
153C2×C4×D11—416no—
154C2×C4×D11—432no—
155C2×C4×D11—48no—
156C2×C4×D11—48no—
157C2×C4×D11—48no—
158C2×C4×D11C2×D4116yes—
159C2×C4×D11C2×Q8132yescomplemented
160C2×Dic22—28no—
161C2×Dic22—48no—
162C2×Dic22—416no—
163C11×C4⋊C4—28no—
164C11×C4⋊C4—48no—
165(C2×D11)⋊C4—28no—
166(C2×D11)⋊C4—28no—
167(C2×D11)⋊C4—216no—
168C4⋊Dic11—28no—
169C4⋊Dic11—48no—
170Dic11⋊C4—28no—
171Dic11⋊C4—216no—
172Dic11⋊C4—28no—
173Dic11⋊C4—48no—
174Dic11⋊C4—48no—
175C22×C22⋊Q8—111no—
176C22×C22⋊Q8—111no—
177#2659—1116no—
178C2×#398—111no—
179C2×#398—112no—
180C2×#398—111no—
181C2×#395—111no—
182C2×#395—112no—
183C2×#395D1111yescharacteristic, complemented
184C2×#380—112no—
185C2×#380—112no—
186C22×#95—111no—
187C23×C11C22×D412yes—
188C23×C11C22×Q814yes—
189C23×C11H(5,𝔽2)14yes—
190C23×C11H(5,𝔽2)12yes—
191C23×C112−1+412yes—
192C23×C11C2511yescharacteristic
193C22×D11—28no—
194C22×D11—28no—
195C22×D11—216no—
196C22×D11—216no—
197C22×D11—24no—
198C22×D11—22no—
199C22×D11—22no—
200C22×D11C4⋊Q8116yes—
201C22×D11C22×D414yes—
202C22×D11C22×Q818yes—
203Q8×C11—416no—
204C2×C4×C11—28no—
205C2×C4×C11—216no—
206C2×C4×C11—24no—
207C2×C4×C11—24no—
208C2×C4×C11—24no—
209C2×C4×C11—22no—
210C2×C4×C11—24no—
211C2×C4×C11—22no—
212C2×C4×C11—22no—
213C2×C4×C11—24no—
214C2×C4×C11—24no—
215C2×C4×C11—24no—
216C2×C4×C11—22no—
217C2×C4×C11—44no—
218C2×C4×C11—48no—
219C2×C4×C11—44no—
220C2×C4×C11C22×D414yes—
221C2×C4×C11C22×Q818yes—
222C2×Dic11—28no—
223C2×Dic11—216no—
224C2×Dic11—24no—
225C2×Dic11—24no—
226C2×Dic11—24no—
227C2×Dic11—22no—
228C2×Dic11—24no—
229C2×Dic11—22no—
230C2×Dic11—24no—
231C2×Dic11—24no—
232C2×Dic11—22no—
233C2×Dic11—22no—
234C2×Dic11—24no—
235C2×Dic11—44no—
236C2×Dic11—44no—
237C2×Dic11—48no—
238C2×Dic11C22×D414yes—
239C2×Dic11C22×Q818yes—
240C4×D11—416no—
241C4×D11—432no—
242Dic22—416no—
243C23×Q8—111no—
244C23×Q8C2×D1111yescharacteristic
245C24×C4—111no—
246C24×C4—112no—
247C2×C22⋊Q8—118no—
248C2×C22⋊Q8—118no—
249C2×C22⋊Q8—228no—
250C2×C22⋊Q8—228no—
251C22×C4⋊C4—112no—
252C22×C4⋊C4—111no—
253C22×C4⋊C4—111no—
254C22×C4⋊C4—111no—
255C22×C4⋊C4—112no—
256C22×C4⋊C4—112no—
257C22×C4⋊C4—112no—
258C22×C4⋊C4C2×D1111yescharacteristic
259C22×C4⋊C4C2×D1112yes—
260C22×C22⋊C4—112no—
261C22×C22⋊C4—111no—
262C22×C22⋊C4—111no—
263#398—118no—
264#398—1116no—
265#398—118no—
266#395—118no—
267#395—1116no—
268#395C2×D1118yescomplemented
269#380—1116no—
270#380—1116no—
271C2×#95—112no—
272C2×#95—111no—
273C2×#95—112no—
274C2×#95—112no—
275C2×#95—112no—
276C2×#95—118no—
277C2×#95C2×D1111yescharacteristic
278C2×#95C2×D1112yes—
279C22×C11C2×C4⋊Q814yes—
280C22×C11#53414yes—
281C22×C11#53714yes—
282C22×C11#54318yes—
283C22×C11#54418yes—
284C22×C11C23×D411yescharacteristic
285C22×C11C23×Q812yes—
286C22×C11C2×H(5,𝔽2)12yes—
287C22×C11C2×H(5,𝔽2)11yescharacteristic
288C22×C11C2×2−1+411yescharacteristic
289C2×D11—232no—
290C2×D11—24no—
291C2×D11—24no—
292C2×D11—28no—
293C2×D11—28no—
294C2×D11C2×C4⋊Q818yes—
295C4×C11—24no—
296C4×C11—28no—
297C4×C11—44no—
298C4×C11—42no—
299C4×C11—42no—
300Dic11—24no—
301Dic11—28no—
302Dic11—42no—
303Dic11—42no—
304Dic11—44no—
305C25—111no—
306C22×Q8—24no—
307C22×Q8—44no—
308C22×Q8—114no—
309C22×Q8—224no—
310C22×Q8—444no—
311C22×Q8C22×D1114yes—
312C23×C4—111no—
313C23×C4—112no—
314C23×C4—118no—
315C23×C4—1116no—
316C23×C4—114no—
317C23×C4—118no—
318C23×C4—111no—
319C23×C4—112no—
320C23×C4—111no—
321C23×C4—444no—
322C23×C4—444no—
323C23×C4—444no—
324C23×C4C22×D1111yescharacteristic
325C23×C4C22×D1112yes—
326C23×C4C22×D1111yescharacteristic
327C23×C4C22×D1111yescharacteristic
328C23×C4C22×D1112yes—
329C22⋊Q8—2232no—
330C22⋊Q8—2232no—
331C2×C4⋊C4—24no—
332C2×C4⋊C4—44no—
333C2×C4⋊C4—118no—
334C2×C4⋊C4—114no—
335C2×C4⋊C4—114no—
336C2×C4⋊C4—114no—
337C2×C4⋊C4—118no—
338C2×C4⋊C4—118no—
339C2×C4⋊C4—118no—
340C2×C4⋊C4—224no—
341C2×C4⋊C4—228no—
342C2×C4⋊C4—224no—
343C2×C4⋊C4—224no—
344C2×C4⋊C4—444no—
345C2×C4⋊C4—444no—
346C2×C4⋊C4—444no—
347C2×C4⋊C4C22×D1114yes—
348C2×C4⋊C4C22×D1118yes—
349C2×C22⋊C4—114no—
350C2×C22⋊C4—118no—
351C2×C22⋊C4—114no—
352C2×C22⋊C4—224no—
353C2×C22⋊C4—224no—
354C2×C22⋊C4—228no—
355#95—114no—
356#95—118no—
357#95—118no—
358#95—118no—
359#95—118no—
360#95C22×D1114yes—
361#95C22×D1118yes—
362C2×C11#265918yescomplemented
363C2×C11C22×C4⋊Q811yescharacteristic
364C2×C11C2×#53411yescharacteristic
365C2×C11C2×#53711yescharacteristic
366C2×C11C2×#54312yes—
367C2×C11C2×#54412yes—
368D11—28no—
369C24—114no—
370C24—118no—
371C24—112no—
372C24—224no—
373C24—222no—
374C24—222no—
375C24C23×D1111yescharacteristic
376C2×Q8—28no—
377C2×Q8—48no—
378C2×Q8—416no—
379C2×Q8—228no—
380C2×Q8—448no—
381C2×Q8—4416no—
382C22×C4—24no—
383C22×C4—24no—
384C22×C4—24no—
385C22×C4—22no—
386C22×C4—22no—
387C22×C4—24no—
388C22×C4—24no—
389C22×C4—24no—
390C22×C4—24no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—114no—
394C22×C4—118no—
395C22×C4—114no—
396C22×C4—112no—
397C22×C4—1116no—
398C22×C4—1132no—
399C22×C4—112no—
400C22×C4—114no—
401C22×C4—112no—
402C22×C4—224no—
403C22×C4—224no—
404C22×C4—224no—
405C22×C4—222no—
406C22×C4—224no—
407C22×C4—222no—
408C22×C4—224no—
409C22×C4—222no—
410C22×C4—224no—
411C22×C4—224no—
412C22×C4—222no—
413C22×C4—4416no—
414C22×C4—4432no—
415C22×C4—448no—
416C22×C4—448no—
417C22×C4—448no—
418C22×C4D4×D1114yes—
419C22×C4Q8×D1118yes—
420C22×C4C23×D1112yes—
421C22×C4C23×D1114yes—
422C22×C4C23×D1112yes—
423C22×C4C23×D1112yes—
424C22×C4C23×D1114yes—
425C4⋊C4—28no—
426C4⋊C4—48no—
427C4⋊C4—228no—
428C4⋊C4—2216no—
429C4⋊C4—228no—
430C4⋊C4—228no—
431C4⋊C4—448no—
432C4⋊C4—448no—
433C4⋊C4—448no—
434C22⋊C4—228no—
435C22⋊C4—228no—
436C22⋊C4—2216no—
437C11C2×#265911yescharacteristic, complemented, Sylow
438C23—1116no—
439C23—114no—
440C23—118no—
441C23—2216no—
442C23—228no—
443C23—228no—
444C23—2216no—
445C23—224no—
446C23—222no—
447C23—222no—
448C23C2×D4×D1112yes—
449C23#6703714yes—
450C23C2×Q8×D1114yes—
451C23#6704012yes—
452C23#6704212yes—
453C23C24×D1111yescharacteristic
454Q8—416no—
455Q8—4416no—
456C2×C4—28no—
457C2×C4—216no—
458C2×C4—24no—
459C2×C4—24no—
460C2×C4—24no—
461C2×C4—22no—
462C2×C4—22no—
463C2×C4—24no—
464C2×C4—24no—
465C2×C4—24no—
466C2×C4—24no—
467C2×C4—22no—
468C2×C4—22no—
469C2×C4—48no—
470C2×C4—44no—
471C2×C4—44no—
472C2×C4—114no—
473C2×C4—118no—
474C2×C4—228no—
475C2×C4—2216no—
476C2×C4—224no—
477C2×C4—224no—
478C2×C4—224no—
479C2×C4—222no—
480C2×C4—224no—
481C2×C4—222no—
482C2×C4—224no—
483C2×C4—222no—
484C2×C4—224no—
485C2×C4—224no—
486C2×C4—222no—
487C2×C4—4416no—
488C2×C4—4432no—
489C2×C4—444no—
490C2×C4—444no—
491C2×C4—448no—
492C2×C4C2×D4×D1114yes—
493C2×C4C2×Q8×D1118yes—
494C22—118no—
495C22—2232no—
496C22—224no—
497C22—224no—
498C22—228no—
499C22—228no—
500C22#1062312014yes—
501C22#1062316014yes—
502C22#1062316518yes—
503C22D11×C4⋊Q814yes—
504C22#1062326018yes—
505C22C22×D4×D1111yescharacteristic
506C22C2×#6703712yes—
507C22C22×Q8×D1112yes—
508C22C2×#6704011yescharacteristic
509C22C2×#6704211yescharacteristic
510C4—24no—
511C4—28no—
512C4—44no—
513C4—42no—
514C4—42no—
515C4—224no—
516C4—228no—
517C4—442no—
518C4—442no—
519C4—444no—
520C2—228no—
521C2#1307472918yesdirect product factor
522C2C2×D11×C4⋊Q811yescharacteristic
523C2C2×#1062312011yescharacteristic
524C2C2×#1062316011yescharacteristic
525C2C2×#1062316512yes—
526C2C2×#1062326012yes—
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#395C2
socleC24×C11C24
prime radicalC24×D11C23
hypercenterC2×#395D11
hypocenterC11C2×#2659
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#395

Complements

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

NH ≅ G/Ntype
3. #13074729C2direct (N × H)
4. C2×#10622270C2semidirect
5. C2×#10622274C2semidirect
6. C2×#10622596C2semidirect
7. C2×#10622592C2semidirect
8. C2×#10622842C2semidirect
12. C2×C11×#395C2semidirect
33. C11×#395C22semidirect
36. #10622842C22semidirect
43. #10622596C22semidirect
44. #10622592C22semidirect
47. #10622274C22semidirect
48. #10622270C22semidirect
67. C22×C4×D11Q8semidirect
159. C2×C4×D11C2×Q8semidirect
183. C2×#395D11semidirect
268. #395C2×D11semidirect
362. C2×C11#2659semidirect
437. C11C2×#2659semidirect
521. C2#13074729direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669492
C22×#669992
#130747292
C2×#106222702
C2×#106222742
C2×#106225962
C2×#106225922
C2×#106228422
C2×#106222802
C2×#106226002
C2×D11×#952
C2×C11×#3952
C2×#265911