Finite Group Databasebeta

← C2×#13067585 #14725945

Subgroups — C2×#13067585 #14725945

Order 2816.

1480 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622653C212yesmaximal, complemented
2C2×#10622592C211yesmaximal, characteristic, complemented
3#13067585C218yesmaximal, direct product factor
4C2×#10622175C212yesmaximal, complemented
5C2×#10622166C211yesmaximal, characteristic, complemented
6C2×C11×#537C211yesmaximal, characteristic
7C22×C11×#41—21no—
8C23×Dic22C2211yescharacteristic
9C11×#537—24no—
10C11×#537—22no—
11C11×#537C2214yes—
12C2×C11×C22⋊Q8—22no—
13C2×C11×#121—22no—
14C2×C11×#121—21no—
15C2×C11×#121C2212yes—
16C22×C11×C4⋊C4C2211yescharacteristic
17C22×#4324—22no—
18C22×Dic11⋊C4—21no—
19C2×C11⋊#95—21no—
20C2×C11⋊#95C2211yescharacteristic
21C2×C22⋊(C11⋊C8)C2212yes—
22#10622653—24no—
23#10622653C2218yescomplemented
24#10622592—22no—
25#10622592C2214yescomplemented
26C2×#66874—22no—
27#10622175C2218yescomplemented
28#10622166C2214yescomplemented
29C2×C11×#41—24no—
30C2×C11×#41—24no—
31C2×C11×#41—44no—
32C2×C11×#41—44no—
33C22×Q8×C11—21no—
34C22×D4×C11—21no—
35C22×D4×C11—22no—
36C22×D4×C11—21no—
37C22×D4×C11D412yes—
38C23×C4×C11—22no—
39C23×C4×C11D411yescharacteristic
40C23×C4×C11D411yescharacteristic
41C23×C4×C11C2311yescharacteristic
42C23×Dic11—21no—
43C23×Dic11—21no—
44C22×Dic22—22no—
45C22×Dic22—22no—
46C22×Dic22—21no—
47C22×Dic22—44no—
48C22×Dic22C2312yes—
49C11×C22⋊Q8—28no—
50C11×C22⋊Q8—28no—
51C11×#121—24no—
52C11×#121—28no—
53C11×#121—28no—
54C11×#121—24no—
55C11×#121—22no—
56C11×#121—22no—
57C11×#121D414yes—
58C11×#121C2314yes—
59C2×C11×C4⋊C4—21no—
60C2×C11×C4⋊C4—22no—
61C2×C11×C4⋊C4—22no—
62C2×C11×C4⋊C4D412yes—
63C2×C11×C4⋊C4D412yes—
64C2×C11×C4⋊C4C2312yes—
65C2×C11×C22⋊C4—22no—
66C2×C11×C22⋊C4—22no—
67C2×#4324—28no—
68C2×#4324—48no—
69C2×Dic11⋊C4—24no—
70C2×Dic11⋊C4—44no—
71C22×C11⋊C8—22no—
72C11⋊#95—24no—
73C11⋊#95—21no—
74C11⋊#95C2312yes—
75C22⋊(C11⋊C8)—22no—
76C22⋊(C11⋊C8)C2314yes—
77#66874—28no—
78C2×#1604—111nomaximal, Sylow
79C24×C11—22no—
80C24×C11C2×D411yescharacteristic
81C11×#41—48no—
82C11×#41—416no—
83C11×#41—48no—
84C2×Q8×C11—24no—
85C2×Q8×C11—44no—
86C2×D4×C11—24no—
87C2×D4×C11—24no—
88C2×D4×C11—24no—
89C2×D4×C11—24no—
90C2×D4×C11—22no—
91C2×D4×C11—44no—
92C2×D4×C11—44no—
93C2×D4×C11—44no—
94C2×D4×C11—44no—
95C2×D4×C11—82no—
96C2×D4×C11C2×D414yes—
97C22×C4×C11—21no—
98C22×C4×C11—21no—
99C22×C4×C11—22no—
100C22×C4×C11—28no—
101C22×C4×C11—21no—
102C22×C4×C11—22no—
103C22×C4×C11—21no—
104C22×C4×C11—42no—
105C22×C4×C11—48no—
106C22×C4×C11—42no—
107C22×C4×C11SD1614yescomplemented
108C22×C4×C11C2×D412yes—
109C22×C4×C11C2×D412yes—
110C22×C4×C11C2×D412yes—
111C22×C4×C11C2×D411yescharacteristic
112C22×C4×C11C2×D412yes—
113C22×C4×C11C2411yescharacteristic
114C22×Dic11—24no—
115C22×Dic11—24no—
116C22×Dic11—22no—
117C22×Dic11—22no—
118C22×Dic11—42no—
119C22×Dic11—42no—
120C22×Dic11—41no—
121C22×Dic11—41no—
122C22×Dic11—42no—
123C2×Dic22—28no—
124C2×Dic22—24no—
125C2×Dic22—44no—
126C2×Dic22—44no—
127C2×Dic22—48no—
128C2×Dic22—44no—
129C2×Dic22—42no—
130C11×C4⋊C4—24no—
131C11×C4⋊C4—24no—
132C11×C4⋊C4—22no—
133C11×C4⋊C4—24no—
134C11×C4⋊C4C2×D414yes—
135C11×C22⋊C4—28no—
136C11×C22⋊C4—24no—
137C11×C22⋊C4—24no—
138#4324—416no—
139Dic11⋊C4—48no—
140C2×C11⋊C8—24no—
141C2×C11⋊C8—44no—
142C2×#537D1111yescharacteristic
143C2×#448—112no—
144C2×#395—111no—
145#1604—118no—
146C2×#327—112no—
147C2×#324—111no—
148C23×C11—22no—
149C23×C11—22no—
150C23×C11—24no—
151C23×C11—44no—
152C23×C11—44no—
153C23×C11—44no—
154C23×C11#12011yescharacteristic
155C23×C11#12011yescharacteristic
156C23×C11C2×SD1612yes—
157C23×C11AGL(1,ℤ/8)12yes—
158C23×C11C22×D411yescharacteristic
159Q8×C11—48no—
160D4×C11—44no—
161D4×C11—48no—
162D4×C11—44no—
163D4×C11—44no—
164D4×C11—48no—
165D4×C11—82no—
166D4×C11—84no—
167C2×C4×C11—22no—
168C2×C4×C11—22no—
169C2×C4×C11—24no—
170C2×C4×C11—24no—
171C2×C4×C11—24no—
172C2×C4×C11—22no—
173C2×C4×C11—24no—
174C2×C4×C11—41no—
175C2×C4×C11—42no—
176C2×C4×C11—41no—
177C2×C4×C11—416no—
178C2×C4×C11—44no—
179C2×C4×C11—42no—
180C2×C4×C11—42no—
181C2×C4×C11—81no—
182C2×C4×C11#12012yes—
183C2×C4×C11C2×SD1614yescomplemented
184C2×C4×C11C22×D412yes—
185C2×Dic11—24no—
186C2×Dic11—24no—
187C2×Dic11—42no—
188C2×Dic11—42no—
189C2×Dic11—44no—
190C2×Dic11—48no—
191C2×Dic11—42no—
192C2×Dic11—42no—
193C2×Dic11—44no—
194Dic22—28no—
195Dic22—48no—
196Dic22—44no—
197C11⋊C8—44no—
198C22×#41—21no—
199C23×Q8—111no—
200C22×SD16—222no—
201#537—24no—
202#537—22no—
203#537C2×D1114yes—
204C2×C22⋊Q8—22no—
205C2×#121—22no—
206C2×#121—21no—
207C2×#121C2×D1112yes—
208C22×C4⋊C4—221no—
209C22×C4⋊C4C2×D1111yescharacteristic
210#448—118no—
211#448—224no—
212C2×#103—222no—
213C2×C22⋊C8—112no—
214#395—114no—
215#395—222no—
216C2×#95—111no—
217C2×#95—221no—
218#327—118no—
219#324—114no—
220C22×C11—24no—
221C22×C11—24no—
222C22×C11—21no—
223C22×C11—21no—
224C22×C11—21no—
225C22×C11—21no—
226C22×C11—44no—
227C22×C11—44no—
228C22×C11—44no—
229C22×C11—88no—
230C22×C11#45012yes—
231C22×C11#45012yes—
232C22×C11#45612yes—
233C22×C11B(4,𝔽2)12yes—
234C22×C11C2×#12011yescharacteristic
235C22×C11C22×SD1611yescharacteristic
236C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
237C4×C11—24no—
238C4×C11—22no—
239C4×C11—22no—
240C4×C11—44no—
241C4×C11—42no—
242Dic11—44no—
243Dic11—44no—
244C2×#41—24no—
245C2×#41—24no—
246C2×#41—44no—
247C2×#41—44no—
248C22×Q8—21no—
249C22×Q8—112no—
250C22×Q8—221no—
251C22×Q8—222no—
252C22×Q8—222no—
253C22×Q8—444no—
254C22×D4—21no—
255C22×D4—22no—
256C22×D4—21no—
257C22×D4C22⋊D1112yes—
258C23×C4—22no—
259C23×C4—221no—
260C23×C4—221no—
261C23×C4C22⋊D1111yescharacteristic
262C23×C4C22⋊D1111yescharacteristic
263C23×C4C22×D1111yescharacteristic
264C2×SD16—228no—
265C2×SD16—448no—
266C22×C8—222no—
267C22⋊Q8—28no—
268C22⋊Q8—28no—
269#121—24no—
270#121—28no—
271#121—28no—
272#121—24no—
273#121—22no—
274#121—22no—
275#121C22⋊D1114yes—
276#121C22×D1114yes—
277C2×C4⋊C4—21no—
278C2×C4⋊C4—22no—
279C2×C4⋊C4—22no—
280C2×C4⋊C4—224no—
281C2×C4⋊C4—444no—
282C2×C4⋊C4C22⋊D1112yes—
283C2×C4⋊C4C22⋊D1112yes—
284C2×C4⋊C4C22×D1112yes—
285C2×C22⋊C4—22no—
286C2×C22⋊C4—22no—
287#103—228no—
288C22⋊C8—114no—
289C22⋊C8—222no—
290#95—112no—
291#95—221no—
292#95—224no—
293C2×C11—21no—
294C2×C11—21no—
295C2×C11—22no—
296C2×C11—84no—
297C2×C11#160414yescomplemented
298C2×C11C2×#45011yescharacteristic
299C2×C11C2×#45611yescharacteristic
300C2×C11C2×B(4,𝔽2)11yescharacteristic
301C24—22no—
302C24C2×C22⋊D1111yescharacteristic
303#41—48no—
304#41—416no—
305#41—48no—
306C2×Q8—24no—
307C2×Q8—44no—
308C2×Q8—228no—
309C2×Q8—224no—
310C2×Q8—444no—
311C2×Q8—444no—
312C2×Q8—444no—
313C2×Q8—448no—
314C2×Q8—442no—
315C2×D4—24no—
316C2×D4—24no—
317C2×D4—24no—
318C2×D4—24no—
319C2×D4—22no—
320C2×D4—44no—
321C2×D4—44no—
322C2×D4—44no—
323C2×D4—44no—
324C2×D4—82no—
325C2×D4C2×C22⋊D1114yes—
326C22×C4—22no—
327C22×C4—21no—
328C22×C4—21no—
329C22×C4—28no—
330C22×C4—21no—
331C22×C4—22no—
332C22×C4—21no—
333C22×C4—42no—
334C22×C4—48no—
335C22×C4—42no—
336C22×C4—224no—
337C22×C4—224no—
338C22×C4—222no—
339C22×C4—222no—
340C22×C4—442no—
341C22×C4—442no—
342C22×C4—442no—
343C22×C4—441no—
344C22×C4—441no—
345C22×C4#432414yescomplemented
346C22×C4C2×C22⋊D1112yes—
347C22×C4C2×C22⋊D1112yes—
348C22×C4C2×C22⋊D1112yes—
349C22×C4C2×C22⋊D1111yescharacteristic
350C22×C4C2×C22⋊D1112yes—
351C22×C4C23×D1111yescharacteristic
352SD16—4416no—
353C2×C8—224no—
354C2×C8—444no—
355C4⋊C4—24no—
356C4⋊C4—24no—
357C4⋊C4—22no—
358C4⋊C4—24no—
359C4⋊C4—448no—
360C4⋊C4C2×C22⋊D1114yes—
361C22⋊C4—28no—
362C22⋊C4—24no—
363C22⋊C4—24no—
364C11C2×#160411yescharacteristic, complemented, Sylow
365C23—22no—
366C23—22no—
367C23—24no—
368C23—44no—
369C23—44no—
370C23—44no—
371C23#6698512yes—
372C23C2×#432412yes—
373C23#6700611yescharacteristic
374C23#6700611yescharacteristic
375C23C22×C22⋊D1111yescharacteristic
376Q8—48no—
377Q8—228no—
378Q8—444no—
379Q8—448no—
380D4—44no—
381D4—48no—
382D4—44no—
383D4—44no—
384D4—48no—
385D4—82no—
386D4—84no—
387C2×C4—22no—
388C2×C4—24no—
389C2×C4—24no—
390C2×C4—24no—
391C2×C4—22no—
392C2×C4—22no—
393C2×C4—24no—
394C2×C4—42no—
395C2×C4—41no—
396C2×C4—41no—
397C2×C4—416no—
398C2×C4—44no—
399C2×C4—42no—
400C2×C4—42no—
401C2×C4—81no—
402C2×C4—224no—
403C2×C4—224no—
404C2×C4—442no—
405C2×C4—442no—
406C2×C4—444no—
407C2×C4—448no—
408C2×C4—442no—
409C2×C4—444no—
410C2×C4—442no—
411C2×C4C2×#432414yescomplemented
412C2×C4#6700612yes—
413C2×C4C22×C22⋊D1112yes—
414C8—444no—
415C22—24no—
416C22—24no—
417C22—21no—
418C22—21no—
419C22—21no—
420C22—21no—
421C22—44no—
422C22—44no—
423C22—44no—
424C22—88no—
425C22#1062283112yes—
426C22#1062283112yes—
427C22#1062285712yes—
428C22#1062285912yes—
429C22C2×#6698511yescharacteristic
430C22C22×#432411yescharacteristic
431C22C2×#6700611yescharacteristic
432C4—24no—
433C4—22no—
434C4—22no—
435C4—44no—
436C4—42no—
437C4—444no—
438C4—444no—
439C2—21no—
440C2—21no—
441C2—22no—
442C2—84no—
443C2#1306758514yesdirect product factor
444C2C2×#1062283111yescharacteristic
445C2C2×#1062285911yescharacteristic
446C2C2×#1062285711yescharacteristic
subgroupG/H
centerC23#67006
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
Fitting, prime radicalC2×C11×#537C2
socleC23×C11#120
hypercenterC2×#537D11
hypocenterC11C2×#1604
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#537

Complements

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

NH ≅ G/Ntype
1. C2×#10622653C2semidirect
2. C2×#10622592C2semidirect
3. #13067585C2direct (N × H)
4. C2×#10622175C2semidirect
5. C2×#10622166C2semidirect
23. #10622653C22semidirect
25. #10622592C22semidirect
27. #10622175C22semidirect
28. #10622166C22semidirect
107. C22×C4×C11SD16semidirect
183. C2×C4×C11C2×SD16semidirect
297. C2×C11#1604semidirect
345. C22×C4#4324semidirect
364. C11C2×#1604semidirect
411. C2×C4C2×#4324semidirect
443. C2#13067585direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106226532
C2×#106225922
#130675852
C2×#106221752
C2×#106221662
C2×C11×#5372
C2×#160411