Finite Group Databasebeta

← C2×#13070561 #14907656

Subgroups — C2×#13070561 #14907656

Order 2816.

1180 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623279C211yesmaximal, characteristic, complemented
2C2×#10622760C212yesmaximal, complemented
3#13070561C218yesmaximal, direct product factor
4C2×#10622126C212yesmaximal, complemented
5C2×#10622191C211yesmaximal, characteristic, complemented
6C2×C11×#469C211yesmaximal, characteristic, complemented
7C22×#4339—21no—
8C22×C11×D8C2211yescharacteristic, complemented
9C22×C11×M16C2211yescharacteristic
10C2×C11×#121—21no—
11#10623279—22no—
12#10623279—24no—
13#10623279C2214yescomplemented
14C2×#66962—22no—
15C2×#66961—22no—
16C2×#66957—21no—
17C2×#66957C2212yes—
18C11×#469—22no—
19C11×#469C2214yescomplemented
20C2×C11×#106C2211yescharacteristic, complemented
21C2×C11×#102—21no—
22C2×#66891—22no—
23#10622760—24no—
24#10622760C2218yescomplemented
25C2×#66890—22no—
26C2×#66876C2212yescomplemented
27#10622191C2214yescomplemented
28#10622126C2218yescomplemented
29C22×D4×C11—21no—
30C22×D4×C11—41no—
31C23×C4×C11D411yescharacteristic
32C22×C22⋊D11—41no—
33C2×#4339—22no—
34C2×#4339—24no—
35C2×#4339—22no—
36C2×#4339—24no—
37C2×#4339—42no—
38C2×#4339—41no—
39C2×#4339—41no—
40C2×#4339—42no—
41C22×D44—21no—
42C22×C4×D11—41no—
43C22×Dic22—21no—
44C2×C11×D8—22no—
45C2×C11×D8—22no—
46C2×C11×D8—21no—
47C2×C11×D8C2312yescomplemented
48C2×C11×M16—22no—
49C2×C11×M16—22no—
50C2×C11×M16D412yes—
51C2×C11×M16C2312yes—
52C22×C8×C11D411yescharacteristic
53C22×C8×C11C2311yescharacteristic
54C11×#121—24no—
55C11×#121—42no—
56C2×C11×C4⋊C4—21no—
57C2×C11×C22⋊C4—41no—
58#66962—28no—
59#66962—28no—
60#66961—28no—
61#66961—28no—
62C2×Dic44—21no—
63C2×Dic44D412yescomplemented
64#66957—24no—
65#66957—24no—
66#66957—22no—
67#66957—22no—
68#66957D414yescomplemented
69#66957C2314yes—
70C2×D88—21no—
71C2×D88D412yescomplemented
72C2×#4314—22no—
73C2×#4314—22no—
74C11×#106—21no—
75C11×#106C2312yescomplemented
76C11×#102—24no—
77#66891—28no—
78#66890—28no—
79#66876—22no—
80#66876C2314yescomplemented
81C2×C11⋊C16—22no—
82C2×#2190—111nomaximal, Sylow
83C24×C11—41no—
84C24×C11D811yescharacteristic
85C23×D11—41no—
86C2×D4×C11—22no—
87C2×D4×C11—44no—
88C2×D4×C11—41no—
89C2×D4×C11—41no—
90C2×D4×C11—41no—
91C2×D4×C11—41no—
92C2×D4×C11—41no—
93C2×D4×C11—84no—
94C22×C4×C11—21no—
95C22×C4×C11—21no—
96C22×C4×C11—21no—
97C22×C4×C11—21no—
98C22×C4×C11—41no—
99C22×C4×C11D811yescharacteristic
100C22×C4×C11D812yes—
101C22×C4×C11C2×D412yes—
102C22×C4×C11C2×D411yescharacteristic
103C2×C22⋊D11—44no—
104C2×C22⋊D11—42no—
105C2×C22⋊D11—44no—
106C2×C22⋊D11—42no—
107C22×Dic11—41no—
108#4339—28no—
109#4339—24no—
110#4339—24no—
111#4339—44no—
112#4339—44no—
113#4339—44no—
114#4339—44no—
115#4339—44no—
116#4339—42no—
117#4339—42no—
118C2×D44—24no—
119C2×D44—22no—
120C2×D44—41no—
121C2×D44—42no—
122C2×C4×D11—42no—
123C2×C4×D11—44no—
124C2×C4×D11—44no—
125C2×C4×D11—42no—
126C2×Dic22—24no—
127C2×Dic22—22no—
128C2×Dic22—41no—
129C2×Dic22—42no—
130C11×D8—24no—
131C11×D8—42no—
132C11×M16—24no—
133C11×M16—24no—
134C2×C8×C11—21no—
135C2×C8×C11—21no—
136C2×C8×C11C2×D412yes—
137C2×C8×C11C2×D412yes—
138C2×C8×C11C2×D412yes—
139C2×C8×C11C2×D411yescharacteristic
140C2×C8×C11C2411yescharacteristic
141C11×C4⋊C4—22no—
142C11×C4⋊C4—41no—
143C11×C22⋊C4—44no—
144Dic44—24no—
145Dic44—22no—
146Dic44C2×D414yescomplemented
147D88—24no—
148D88—22no—
149D88C2×D414yescomplemented
150#4314—28no—
151#4314—24no—
152#4314—24no—
153C11⋊C16—24no—
154C2×#575—111no—
155C2×#509—112no—
156C2×#469D1111yescharacteristic, complemented
157#2190—118no—
158C2×#360—112no—
159C2×#349—111no—
160C23×C11—21no—
161C23×C11—21no—
162C23×C11—42no—
163C23×C11—42no—
164C23×C11—82no—
165C23×C11—82no—
166C23×C11—81no—
167C23×C11—81no—
168C23×C11C2×D811yescharacteristic
169C23×C11C2×D812yes—
170C22×D11—44no—
171C22×D11—42no—
172C22×D11—84no—
173D4×C11—42no—
174D4×C11—42no—
175D4×C11—88no—
176D4×C11—81no—
177D4×C11—81no—
178C2×C4×C11—21no—
179C2×C4×C11—21no—
180C2×C4×C11—22no—
181C2×C4×C11—22no—
182C2×C4×C11—22no—
183C2×C4×C11—22no—
184C2×C4×C11—42no—
185C2×C4×C11—82no—
186C2×C4×C11#12011yescharacteristic
187C2×C4×C11#12011yescharacteristic
188C2×C4×C11C2×D812yes—
189C2×C4×C11C2×D811yescharacteristic
190C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
191C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
192C2×C4×C11C22×D411yescharacteristic
193C22⋊D11—48no—
194C22⋊D11—44no—
195C22⋊D11—44no—
196C2×Dic11—44no—
197C2×Dic11—42no—
198D44—24no—
199D44—44no—
200D44—42no—
201C4×D11—48no—
202C4×D11—44no—
203C4×D11—44no—
204Dic22—24no—
205Dic22—44no—
206Dic22—42no—
207C8×C11—22no—
208C8×C11#12012yes—
209C8×C11C22×D412yes—
210C22×#41—221no—
211#575—114no—
212#575—224no—
213#575—222no—
214C2×#137—222no—
215C2×AGL(1,ℤ/8)—222no—
216C2×#135—112no—
217C2×#135—221no—
218C22×D8C2×D1111yescharacteristic, complemented
219C22×M16C2×D1111yescharacteristic
220C2×#121—21no—
221#509—118no—
222#509—224no—
223C2×SD32—222no—
224C2×D16—222no—
225C2×M32—112no—
226#469—22no—
227#469C2×D1114yescomplemented
228C2×#106C2×D1111yescharacteristic, complemented
229C2×#102—21no—
230#360—118no—
231#349—114no—
232C22×C11—22no—
233C22×C11—22no—
234C22×C11—42no—
235C22×C11—42no—
236C22×C11—81no—
237C22×C11—82no—
238C22×C11—82no—
239C22×C11—82no—
240C22×C11—162no—
241C22×C11—162no—
242C22×C11#44711yescharacteristic
243C22×C11#44711yescharacteristic
244C22×C11C22×D811yescharacteristic
245C2×D11—44no—
246C2×D11—88no—
247C2×D11—84no—
248C4×C11—22no—
249C4×C11—82no—
250C4×C11#44711yescharacteristic
251C4×C11#44711yescharacteristic
252C4×C11C2×#12011yescharacteristic
253C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
254Dic11—44no—
255C2×#41—222no—
256C2×#41—224no—
257C2×#41—224no—
258C2×#41—222no—
259C2×#41—441no—
260C2×#41—442no—
261C2×#41—441no—
262C2×#41—442no—
263C22×Q8—221no—
264C22×D4—21no—
265C22×D4—41no—
266C22×D4—221no—
267C22×D4—441no—
268C23×C4—441no—
269C23×C4C22⋊D1111yescharacteristic
270#137—228no—
271#137—228no—
272AGL(1,ℤ/8)—228no—
273AGL(1,ℤ/8)—228no—
274#135—114no—
275#135—114no—
276#135—224no—
277#135—222no—
278#135—222no—
279#135—224no—
280C2×Q16—112no—
281C2×Q16—221no—
282C2×SD16—222no—
283C2×SD16—222no—
284C2×D8—22no—
285C2×D8—22no—
286C2×D8—21no—
287C2×D8—112no—
288C2×D8—221no—
289C2×D8C22×D1112yescomplemented
290C2×M16—22no—
291C2×M16—22no—
292C2×M16C22⋊D1112yes—
293C2×M16C22×D1112yes—
294C22×C8C22⋊D1111yescharacteristic
295C22×C8C22×D1111yescharacteristic
296#121—24no—
297#121—42no—
298C2×C4⋊C4—21no—
299C2×C22⋊C4—41no—
300SD32—228no—
301D16—228no—
302M32—114no—
303M32—222no—
304C2×C16—222no—
305#106—21no—
306#106C22×D1112yescomplemented
307#102—24no—
308C2×C11—21no—
309C2×C11—21no—
310C2×C11—42no—
311C2×C11—162no—
312C2×C11#219012yescomplemented
313C2×C11C2×#44711yescharacteristic
314D11—84no—
315C24—41no—
316C24—441no—
317C24#432311yescharacteristic
318#41—228no—
319#41—224no—
320#41—224no—
321#41—444no—
322#41—444no—
323#41—444no—
324#41—444no—
325#41—444no—
326#41—442no—
327#41—442no—
328C2×Q8—224no—
329C2×Q8—222no—
330C2×Q8—441no—
331C2×Q8—442no—
332C2×D4—22no—
333C2×D4—44no—
334C2×D4—41no—
335C2×D4—41no—
336C2×D4—41no—
337C2×D4—41no—
338C2×D4—41no—
339C2×D4—84no—
340C2×D4—224no—
341C2×D4—222no—
342C2×D4—441no—
343C2×D4—442no—
344C2×D4—444no—
345C2×D4—442no—
346C2×D4—444no—
347C2×D4—442no—
348C22×C4—21no—
349C22×C4—21no—
350C22×C4—21no—
351C22×C4—21no—
352C22×C4—41no—
353C22×C4—442no—
354C22×C4—444no—
355C22×C4—444no—
356C22×C4—441no—
357C22×C4—442no—
358C22×C4#432311yescharacteristic
359C22×C4#432312yes—
360C22×C4C2×C22⋊D1112yes—
361C22×C4C2×C22⋊D1111yescharacteristic
362Q16—114no—
363Q16—224no—
364Q16—222no—
365SD16—228no—
366SD16—224no—
367SD16—224no—
368D8—24no—
369D8—42no—
370D8—114no—
371D8—224no—
372D8—222no—
373M16—24no—
374M16—24no—
375C2×C8—21no—
376C2×C8—21no—
377C2×C8D4×D1112yes—
378C2×C8D4×D1112yes—
379C2×C8C2×C22⋊D1112yes—
380C2×C8C2×C22⋊D1111yescharacteristic
381C2×C8C23×D1111yescharacteristic
382C4⋊C4—22no—
383C4⋊C4—41no—
384C22⋊C4—44no—
385C16—224no—
386C11C2×#219011yescharacteristic, complemented, Sylow
387C23—21no—
388C23—21no—
389C23—42no—
390C23—42no—
391C23—82no—
392C23—82no—
393C23—81no—
394C23—81no—
395C23—444no—
396C23—442no—
397C23—884no—
398C23C2×#432311yescharacteristic
399C23C2×#432312yes—
400Q8—224no—
401Q8—444no—
402Q8—442no—
403D4—42no—
404D4—42no—
405D4—88no—
406D4—81no—
407D4—81no—
408D4—224no—
409D4—444no—
410D4—448no—
411D4—444no—
412D4—444no—
413D4—442no—
414C2×C4—21no—
415C2×C4—21no—
416C2×C4—22no—
417C2×C4—22no—
418C2×C4—22no—
419C2×C4—22no—
420C2×C4—42no—
421C2×C4—82no—
422C2×C4—448no—
423C2×C4—444no—
424C2×C4—442no—
425C2×C4—444no—
426C2×C4—444no—
427C2×C4C2×#432312yes—
428C2×C4C2×#432311yescharacteristic
429C2×C4#6699011yescharacteristic
430C2×C4#6699011yescharacteristic
431C2×C4#6700211yescharacteristic
432C2×C4#6700211yescharacteristic
433C2×C4C22×C22⋊D1111yescharacteristic
434C8—22no—
435C8#6699012yes—
436C8C2×D4×D1112yes—
437C22—22no—
438C22—22no—
439C22—42no—
440C22—42no—
441C22—81no—
442C22—82no—
443C22—82no—
444C22—82no—
445C22—162no—
446C22—162no—
447C22—444no—
448C22—888no—
449C22—884no—
450C22#1062264911yescharacteristic
451C22#1062264911yescharacteristic
452C22C22×#432311yescharacteristic
453C4—22no—
454C4—82no—
455C4—444no—
456C4#1062264911yescharacteristic
457C4#1062264911yescharacteristic
458C4C2×#6699011yescharacteristic
459C4C2×#6700211yescharacteristic
460C2—21no—
461C2—21no—
462C2—42no—
463C2—162no—
464C2—884no—
465C2#1307056112yesdirect product factor
466C2C2×#1062264911yescharacteristic
subgroupG/H
centerC22#10622649
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC2×C11×#469C2
socleC22×C11#447
hypercenterC2×#469D11
hypocenterC11C2×#2190
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×M16 ◁ C2×#469

Complements

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

NH ≅ G/Ntype
1. C2×#10623279C2semidirect
2. C2×#10622760C2semidirect
3. #13070561C2direct (N × H)
4. C2×#10622126C2semidirect
5. C2×#10622191C2semidirect
6. C2×C11×#469C2semidirect
8. C22×C11×D8C22semidirect
13. #10623279C22semidirect
19. C11×#469C22semidirect
20. C2×C11×#106C22semidirect
24. #10622760C22semidirect
26. C2×#66876C22semidirect
27. #10622191C22semidirect
28. #10622126C22semidirect
47. C2×C11×D8C23semidirect
63. C2×Dic44D4semidirect
68. #66957D4semidirect
71. C2×D88D4semidirect
75. C11×#106C23semidirect
80. #66876C23semidirect
146. Dic44C2×D4semidirect
149. D88C2×D4semidirect
156. C2×#469D11semidirect
218. C22×D8C2×D11semidirect
227. #469C2×D11semidirect
228. C2×#106C2×D11semidirect
289. C2×D8C22×D11semidirect
306. #106C22×D11semidirect
312. C2×C11#2190semidirect
386. C11C2×#2190semidirect
465. C2#13070561direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106232792
C2×#106227602
#130705612
C2×#106221262
C2×#106221912
C2×C11×#4692
C2×#219011