Finite Group Databasebeta

← C2×#13067556 #14725951

Subgroups — C2×#13067556 #14725951

Order 2816.

1372 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622659C212yesmaximal
2C2×#10622604C211yesmaximal, characteristic
3#13067556C218yesmaximal, direct product factor
4C2×#10622176C212yesmaximal, complemented
5C2×#10622166C211yesmaximal, characteristic, complemented
6C2×C11×#544C211yesmaximal, characteristic, complemented
7C23×D44C2211yescharacteristic
8C11×#544—24no—
9C11×#544—22no—
10C11×#544C2214yescomplemented
11C2×C11×C4⋊Q8—22no—
12C2×C11×#125—22no—
13C2×C11×C22⋊Q8—21no—
14C2×C11×C22⋊Q8C2212yes—
15C2×C11×#117—21no—
16C22×C11×C4⋊C4C2211yescharacteristic
17C22×#4325—22no—
18C22×(C2×D11)⋊C4—21no—
19C22×(C2×D11)⋊C4—21no—
20C2×C11⋊#95C2211yescharacteristic
21C2×C22⋊(C11⋊C8)C2212yes—
22#10622659—24no—
23#10622659C2218yes—
24#10622604—22no—
25#10622604C2214yes—
26C2×#66873—22no—
27#10622176C2218yescomplemented
28#10622166C2214yescomplemented
29C24×D11—21no—
30C22×Q8×C11—21no—
31C22×Q8×C11D412yes—
32C23×C4×C11D411yescharacteristic
33C23×C4×C11D411yescharacteristic
34C23×C4×C11C2311yescharacteristic
35C23×Dic11—21no—
36C22×D44—22no—
37C22×D44—22no—
38C22×D44—21no—
39C22×D44—44no—
40C22×D44C2312yes—
41C11×C4⋊Q8—28no—
42C11×C4⋊Q8—28no—
43C11×#125—28no—
44C11×#125—28no—
45C11×C22⋊Q8—24no—
46C11×C22⋊Q8—24no—
47C11×C22⋊Q8—22no—
48C11×C22⋊Q8—22no—
49C11×C22⋊Q8D414yes—
50C11×C22⋊Q8C2314yes—
51C11×#117—24no—
52C11×#117—24no—
53C2×C11×C4⋊C4—21no—
54C2×C11×C4⋊C4—21no—
55C2×C11×C4⋊C4—21no—
56C2×C11×C4⋊C4—22no—
57C2×C11×C4⋊C4—22no—
58C2×C11×C4⋊C4—22no—
59C2×C11×C4⋊C4—22no—
60C2×C11×C4⋊C4D412yes—
61C2×C11×C4⋊C4D412yes—
62C2×C11×C4⋊C4C2312yes—
63C2×C11×C22⋊C4—22no—
64C2×C42×C11—22no—
65C2×#4325—28no—
66C2×#4325—48no—
67C2×(C2×D11)⋊C4—24no—
68C2×(C2×D11)⋊C4—24no—
69C2×(C2×D11)⋊C4—44no—
70C2×(C2×D11)⋊C4—44no—
71C22×C11⋊C8—22no—
72C11⋊#95—21no—
73C11⋊#95C2312yes—
74C22⋊(C11⋊C8)—22no—
75C22⋊(C11⋊C8)C2314yes—
76#66873—28no—
77C2×#1599—111nomaximal, Sylow
78C24×C11C2×D411yescharacteristic
79C23×D11—24no—
80C23×D11—22no—
81C23×D11—42no—
82C23×D11—42no—
83C23×D11—42no—
84C23×D11—41no—
85C23×D11—41no—
86C23×D11—42no—
87C23×D11—42no—
88C2×Q8×C11—24no—
89C2×Q8×C11—22no—
90C2×Q8×C11—44no—
91C2×Q8×C11—82no—
92C2×Q8×C11C2×D414yes—
93C22×C4×C11—21no—
94C22×C4×C11—21no—
95C22×C4×C11—22no—
96C22×C4×C11—22no—
97C22×C4×C11—22no—
98C22×C4×C11—21no—
99C22×C4×C11—21no—
100C22×C4×C11—42no—
101C22×C4×C11—42no—
102C22×C4×C11SD1614yescomplemented
103C22×C4×C11C2×D412yes—
104C22×C4×C11C2×D412yes—
105C22×C4×C11C2×D412yes—
106C22×C4×C11C2×D411yescharacteristic
107C22×C4×C11C2×D412yes—
108C22×C4×C11C2411yescharacteristic
109C22×Dic11—22no—
110C22×Dic11—42no—
111C22×Dic11—42no—
112C22×Dic11—42no—
113C2×D44—28no—
114C2×D44—24no—
115C2×D44—44no—
116C2×D44—44no—
117C2×D44—44no—
118C2×D44—48no—
119C2×D44—42no—
120C11×C4⋊C4—24no—
121C11×C4⋊C4—24no—
122C11×C4⋊C4—24no—
123C11×C4⋊C4—28no—
124C11×C4⋊C4—24no—
125C11×C4⋊C4—24no—
126C11×C4⋊C4—22no—
127C11×C4⋊C4—24no—
128C11×C4⋊C4—24no—
129C11×C4⋊C4C2×D414yes—
130C11×C22⋊C4—24no—
131C11×C22⋊C4—24no—
132C42×C11—28no—
133#4325—416no—
134(C2×D11)⋊C4—48no—
135(C2×D11)⋊C4—48no—
136C2×C11⋊C8—24no—
137C2×C11⋊C8—44no—
138C2×#544D1111yescharacteristic, complemented
139C2×#450—112no—
140C2×#394—111no—
141#1599—118no—
142C2×#328—112no—
143C2×#324—111no—
144C23×C11—22no—
145C23×C11—22no—
146C23×C11#12011yescharacteristic
147C23×C11#12011yescharacteristic
148C23×C11C2×SD1612yes—
149C23×C11#13712yes—
150C23×C11C22×D411yescharacteristic
151C22×D11—24no—
152C22×D11—42no—
153C22×D11—44no—
154C22×D11—48no—
155C22×D11—48no—
156C22×D11—42no—
157C22×D11—42no—
158C22×D11—42no—
159C22×D11—42no—
160C22×D11—42no—
161C22×D11—44no—
162C22×D11—84no—
163C22×D11—84no—
164C22×D11—82no—
165C22×D11—82no—
166C22×D11—82no—
167C22×D11—82no—
168Q8×C11—44no—
169Q8×C11—82no—
170Q8×C11—84no—
171C2×C4×C11—22no—
172C2×C4×C11—22no—
173C2×C4×C11—24no—
174C2×C4×C11—24no—
175C2×C4×C11—24no—
176C2×C4×C11—24no—
177C2×C4×C11—24no—
178C2×C4×C11—22no—
179C2×C4×C11—41no—
180C2×C4×C11—42no—
181C2×C4×C11—41no—
182C2×C4×C11—44no—
183C2×C4×C11—42no—
184C2×C4×C11—44no—
185C2×C4×C11—42no—
186C2×C4×C11—81no—
187C2×C4×C11#12012yes—
188C2×C4×C11C2×SD1614yescomplemented
189C2×C4×C11C22×D412yes—
190C2×Dic11—42no—
191C2×Dic11—42no—
192C2×Dic11—42no—
193C2×Dic11—84no—
194D44—28no—
195D44—48no—
196D44—44no—
197C11⋊C8—44no—
198C23×D4—111no—
199C22×SD16—222no—
200#544—24no—
201#544—22no—
202#544C2×D1114yescomplemented
203C2×C4⋊Q8—22no—
204C2×#125—22no—
205C2×C22⋊Q8—21no—
206C2×C22⋊Q8C2×D1112yes—
207C2×#117—21no—
208C22×C4⋊C4C2×D1111yescharacteristic
209C22×C22⋊C4—221no—
210C22×C22⋊C4—221no—
211#450—118no—
212#450—224no—
213C2×#102—222no—
214C2×C22⋊C8—112no—
215#394—114no—
216#394—222no—
217C2×#95—111no—
218#328—118no—
219#324—114no—
220C22×C11—24no—
221C22×C11—24no—
222C22×C11—21no—
223C22×C11—21no—
224C22×C11—21no—
225C22×C11—21no—
226C22×C11#44812yes—
227C22×C11#44812yes—
228C22×C11#45412yes—
229C22×C11B(4,𝔽2)12yes—
230C22×C11C2×#12011yescharacteristic
231C22×C11C22×SD1611yescharacteristic
232C22×C11C2×#13711yescharacteristic
233C2×D11—44no—
234C2×D11—44no—
235C2×D11—44no—
236C2×D11—82no—
237C2×D11—82no—
238C2×D11—88no—
239C2×D11—88no—
240C2×D11—82no—
241C2×D11—82no—
242C4×C11—24no—
243C4×C11—22no—
244C4×C11—22no—
245C4×C11—44no—
246C4×C11—42no—
247C4×C11—44no—
248Dic11—82no—
249C25—221no—
250C22×Q8—21no—
251C22×Q8C22⋊D1112yes—
252C22×D4—112no—
253C22×D4—222no—
254C22×D4—222no—
255C22×D4—221no—
256C22×D4—444no—
257C23×C4—221no—
258C23×C4C22⋊D1111yescharacteristic
259C23×C4C22⋊D1111yescharacteristic
260C23×C4C22×D1111yescharacteristic
261C2×SD16—228no—
262C2×SD16—448no—
263C22×C8—222no—
264C4⋊Q8—28no—
265C4⋊Q8—28no—
266#125—28no—
267#125—28no—
268C22⋊Q8—24no—
269C22⋊Q8—24no—
270C22⋊Q8—22no—
271C22⋊Q8—22no—
272C22⋊Q8C22⋊D1114yes—
273C22⋊Q8C22×D1114yes—
274#117—24no—
275#117—24no—
276C2×C4⋊C4—21no—
277C2×C4⋊C4—21no—
278C2×C4⋊C4—21no—
279C2×C4⋊C4—22no—
280C2×C4⋊C4—22no—
281C2×C4⋊C4—22no—
282C2×C4⋊C4—22no—
283C2×C4⋊C4C22⋊D1112yes—
284C2×C4⋊C4C22⋊D1112yes—
285C2×C4⋊C4C22×D1112yes—
286C2×C22⋊C4—22no—
287C2×C22⋊C4—224no—
288C2×C22⋊C4—224no—
289C2×C22⋊C4—444no—
290C2×C22⋊C4—444no—
291C2×C42—22no—
292#102—228no—
293C22⋊C8—114no—
294C22⋊C8—222no—
295#95—112no—
296#95—221no—
297C2×C11—21no—
298C2×C11—21no—
299C2×C11—22no—
300C2×C11#159914yescomplemented
301C2×C11C2×#44811yescharacteristic
302C2×C11C2×#45411yescharacteristic
303C2×C11C2×B(4,𝔽2)11yescharacteristic
304D11—84no—
305C24—224no—
306C24—222no—
307C24—442no—
308C24—442no—
309C24—442no—
310C24—442no—
311C24—442no—
312C24—441no—
313C24—441no—
314C24C2×C22⋊D1111yescharacteristic
315C2×Q8—24no—
316C2×Q8—22no—
317C2×Q8—44no—
318C2×Q8—82no—
319C2×Q8C2×C22⋊D1114yes—
320C2×D4—228no—
321C2×D4—224no—
322C2×D4—444no—
323C2×D4—444no—
324C2×D4—448no—
325C2×D4—444no—
326C2×D4—442no—
327C22×C4—22no—
328C22×C4—21no—
329C22×C4—21no—
330C22×C4—22no—
331C22×C4—22no—
332C22×C4—21no—
333C22×C4—21no—
334C22×C4—42no—
335C22×C4—42no—
336C22×C4—222no—
337C22×C4—442no—
338C22×C4—442no—
339C22×C4—442no—
340C22×C4#432514yescomplemented
341C22×C4C2×C22⋊D1112yes—
342C22×C4C2×C22⋊D1112yes—
343C22×C4C2×C22⋊D1112yes—
344C22×C4C2×C22⋊D1111yescharacteristic
345C22×C4C2×C22⋊D1112yes—
346C22×C4C23×D1111yescharacteristic
347SD16—4416no—
348C2×C8—224no—
349C2×C8—444no—
350C4⋊C4—24no—
351C4⋊C4—24no—
352C4⋊C4—24no—
353C4⋊C4—28no—
354C4⋊C4—24no—
355C4⋊C4—24no—
356C4⋊C4—22no—
357C4⋊C4—24no—
358C4⋊C4—24no—
359C4⋊C4C2×C22⋊D1114yes—
360C22⋊C4—24no—
361C22⋊C4—24no—
362C22⋊C4—448no—
363C22⋊C4—448no—
364C42—28no—
365C11C2×#159911yescharacteristic, complemented, Sylow
366C23—22no—
367C23—22no—
368C23—224no—
369C23—442no—
370C23—444no—
371C23—448no—
372C23—448no—
373C23—442no—
374C23—442no—
375C23—442no—
376C23—442no—
377C23—444no—
378C23—442no—
379C23—884no—
380C23—884no—
381C23—882no—
382C23—882no—
383C23—882no—
384C23—882no—
385C23C2×#432512yes—
386C23#6699512yes—
387C23#6700611yescharacteristic
388C23#6700611yescharacteristic
389C23C22×C22⋊D1111yescharacteristic
390Q8—44no—
391Q8—82no—
392Q8—84no—
393D4—228no—
394D4—444no—
395D4—448no—
396C2×C4—22no—
397C2×C4—24no—
398C2×C4—24no—
399C2×C4—24no—
400C2×C4—22no—
401C2×C4—24no—
402C2×C4—24no—
403C2×C4—22no—
404C2×C4—42no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—42no—
408C2×C4—44no—
409C2×C4—44no—
410C2×C4—42no—
411C2×C4—81no—
412C2×C4—442no—
413C2×C4—442no—
414C2×C4—442no—
415C2×C4—884no—
416C2×C4C2×#432514yescomplemented
417C2×C4#6700612yes—
418C2×C4C22×C22⋊D1112yes—
419C8—444no—
420C22—24no—
421C22—24no—
422C22—21no—
423C22—21no—
424C22—21no—
425C22—21no—
426C22—444no—
427C22—444no—
428C22—444no—
429C22—882no—
430C22—882no—
431C22—888no—
432C22—888no—
433C22—882no—
434C22—882no—
435C22#1062284012yes—
436C22#1062284012yes—
437C22#1062285712yes—
438C22#1062285812yes—
439C22C22×#432511yescharacteristic
440C22C2×#6699511yescharacteristic
441C22C2×#6700611yescharacteristic
442C4—24no—
443C4—22no—
444C4—22no—
445C4—44no—
446C4—42no—
447C4—44no—
448C4—882no—
449C2—21no—
450C2—21no—
451C2—22no—
452C2—884no—
453C2#1306755614yesdirect product factor
454C2C2×#1062284011yescharacteristic
455C2C2×#1062285811yescharacteristic
456C2C2×#1062285711yescharacteristic
subgroupG/H
centerC23#67006
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#544C2
socleC23×C11#120
prime radicalC23×D44C22
hypercenterC2×#544D11
hypocenterC11C2×#1599
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#544

Complements

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

NH ≅ G/Ntype
3. #13067556C2direct (N × H)
4. C2×#10622176C2semidirect
5. C2×#10622166C2semidirect
6. C2×C11×#544C2semidirect
10. C11×#544C22semidirect
27. #10622176C22semidirect
28. #10622166C22semidirect
102. C22×C4×C11SD16semidirect
138. C2×#544D11semidirect
188. C2×C4×C11C2×SD16semidirect
202. #544C2×D11semidirect
300. C2×C11#1599semidirect
340. C22×C4#4325semidirect
365. C11C2×#1599semidirect
416. C2×C4C2×#4325semidirect
453. C2#13067556direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106226592
C2×#106226042
#130675562
C2×#106221762
C2×#106221662
C2×C11×#5442
C2×#159911