Finite Group Databasebeta

← C2×#13067851 #14729549

Subgroups — C2×#13067851 #14729549

Order 2816.

1238 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622691C211yesmaximal, characteristic, complemented
2C2×#10622620C211yesmaximal, characteristic, complemented
3C2×#10622632C211yesmaximal, characteristic, complemented
4#13067851C218yesmaximal, direct product factor
5C2×#10622185C211yesmaximal, characteristic, complemented
6C2×D4⋊(C11⋊C8)C211yesmaximal, characteristic, complemented
7C2×D4⋊(C11⋊C8)C211yesmaximal, characteristic, complemented
8C2×C11×#547C211yesmaximal, characteristic
9C22×C11×#41—21no—
10C11×#547—22no—
11C11×#547—22no—
12C11×#547—22no—
13C11×#547C2214yes—
14C2×C11×C4⋊Q8C2211yescharacteristic
15C2×C11×#123—22no—
16C2×C11×C22⋊Q8—21no—
17C2×C11×#121—21no—
18C2×C4×D4×C11C2211yescharacteristic
19C2×C4×D4×C11C2211yescharacteristic
20C22×C11×C4⋊C4—21no—
21C22×#4324—21no—
22C2×#66922C2211yescharacteristic
23C2×#66896—21no—
24#10622691—22no—
25#10622691C2214yescomplemented
26#10622632—22no—
27#10622632C2214yescomplemented
28#10622620—22no—
29#10622620C2214yescomplemented
30C2×#66874—21no—
31C2×#66871—22no—
32C2×#66871—21no—
33C2×C4⋊(C11⋊C8)C2211yescharacteristic
34C2×C4⋊(C11⋊C8)C2211yescharacteristic
35C2×C4×C11⋊C8C2211yescharacteristic
36#10622185C2214yescomplemented
37D4⋊(C11⋊C8)C2214yescomplemented
38D4⋊(C11⋊C8)C2214yescomplemented
39C2×C11×#41—24no—
40C2×C11×#41—24no—
41C2×C11×#41—44no—
42C2×C11×#41—44no—
43C22×Q8×C11—21no—
44C22×D4×C11—22no—
45C22×D4×C11D411yescharacteristic
46C22×D4×C11D411yescharacteristic
47C23×C4×C11—22no—
48C23×C4×C11—21no—
49C23×C4×C11—21no—
50C22×Dic22—21no—
51C11×C4⋊Q8—21no—
52C11×C4⋊Q8—21no—
53C11×C4⋊Q8D412yes—
54C11×C4⋊Q8C2312yes—
55C11×#123—28no—
56C11×#123—28no—
57C11×C22⋊Q8—24no—
58C11×C22⋊Q8—24no—
59C11×#121—24no—
60C11×#121—24no—
61C4×D4×C11—21no—
62C4×D4×C11—21no—
63C4×D4×C11—21no—
64C4×D4×C11—21no—
65C4×D4×C11D412yes—
66C4×D4×C11D412yes—
67C4×D4×C11C2312yes—
68C4×D4×C11C2312yes—
69C2×C11×C4⋊C4—22no—
70C2×C11×C4⋊C4—24no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4—24no—
73C2×C11×C4⋊C4D411yescharacteristic
74C2×C11×C4⋊C4D412yes—
75C2×C11×C4⋊C4D411yescharacteristic
76C2×C11×C22⋊C4—22no—
77C2×C11×C22⋊C4—21no—
78C2×C11×C22⋊C4—21no—
79C2×C42×C11C2311yescharacteristic
80C2×#4324—24no—
81C2×#4324—44no—
82C2×C4⋊Dic11—21no—
83C2×C4⋊Dic11—21no—
84C22×C11⋊C8—21no—
85C22×C11⋊C8—21no—
86C22×C11⋊C8—21no—
87#66922—21no—
88#66922—21no—
89#66922—21no—
90#66922C2312yes—
91#66896—24no—
92#66874—24no—
93#66871—24no—
94#66871—28no—
95C4⋊(C11⋊C8)—21no—
96C4⋊(C11⋊C8)—21no—
97C4⋊(C11⋊C8)C2312yes—
98C4⋊(C11⋊C8)C2312yes—
99C4×C11⋊C8—21no—
100C4×C11⋊C8C2312yes—
101C2×#1647—111nomaximal, Sylow
102C24×C11—21no—
103C24×C11—21no—
104C11×#41—48no—
105C11×#41—416no—
106C11×#41—48no—
107C2×Q8×C11—22no—
108C2×Q8×C11—22no—
109C2×Q8×C11—42no—
110C2×Q8×C11—42no—
111C2×D4×C11—28no—
112C2×D4×C11—21no—
113C2×D4×C11—21no—
114C2×D4×C11—22no—
115C2×D4×C11—22no—
116C2×D4×C11—22no—
117C2×D4×C11—48no—
118C2×D4×C11D814yes—
119C2×D4×C11C2×D412yes—
120C2×D4×C11C2×D412yes—
121C22×C4×C11—28no—
122C22×C4×C11—21no—
123C22×C4×C11—21no—
124C22×C4×C11—22no—
125C22×C4×C11—22no—
126C22×C4×C11—22no—
127C22×C4×C11—22no—
128C22×C4×C11—22no—
129C22×C4×C11—48no—
130C22×C4×C11—42no—
131C22×C4×C11—42no—
132C22×C4×C11—42no—
133C22×C4×C11—42no—
134C22×C4×C11C2×D411yescharacteristic
135C22×C4×C11C2×D411yescharacteristic
136C22×C4×C11C2×D411yescharacteristic
137C22×Dic11—41no—
138C2×Dic22—22no—
139C2×Dic22—41no—
140C2×Dic22—42no—
141C2×Dic22—42no—
142C11×C4⋊C4—28no—
143C11×C4⋊C4—21no—
144C11×C4⋊C4—22no—
145C11×C4⋊C4—21no—
146C11×C4⋊C4—22no—
147C11×C4⋊C4—22no—
148C11×C4⋊C4C2×D412yes—
149C11×C4⋊C4C2×D414yes—
150C11×C4⋊C4C2×D412yes—
151C11×C22⋊C4—28no—
152C11×C22⋊C4—22no—
153C11×C22⋊C4—22no—
154C11×C22⋊C4—22no—
155C11×C22⋊C4—22no—
156C42×C11C2×D411yescharacteristic
157C42×C11C2×D411yescharacteristic
158C42×C11C2×D411yescharacteristic
159C42×C11C2411yescharacteristic
160#4324—48no—
161C4⋊Dic11—22no—
162C4⋊Dic11—22no—
163C4⋊Dic11—41no—
164C4⋊Dic11—41no—
165C2×C11⋊C8—24no—
166C2×C11⋊C8—22no—
167C2×C11⋊C8—22no—
168C2×C11⋊C8—22no—
169C2×C11⋊C8—42no—
170C2×C11⋊C8—42no—
171C2×#547D1111yescharacteristic
172C2×#500—111no—
173C2×#474—111no—
174C2×#461—111no—
175#1647—118no—
176C2×#332—111no—
177C2×D4⋊C8—111no—
178C2×D4⋊C8—111no—
179C23×C11—22no—
180C23×C11—24no—
181C23×C11—22no—
182C23×C11—42no—
183C23×C11—42no—
184C23×C11—42no—
185C23×C11—42no—
186C23×C11—42no—
187C23×C11#12011yescharacteristic
188Q8×C11—42no—
189Q8×C11—42no—
190Q8×C11—44no—
191D4×C11—22no—
192D4×C11—22no—
193D4×C11—22no—
194D4×C11—24no—
195D4×C11—416no—
196D4×C11—42no—
197D4×C11C2×D814yes—
198C2×C4×C11—22no—
199C2×C4×C11—22no—
200C2×C4×C11—22no—
201C2×C4×C11—24no—
202C2×C4×C11—416no—
203C2×C4×C11—42no—
204C2×C4×C11—44no—
205C2×C4×C11—42no—
206C2×C4×C11—42no—
207C2×C4×C11—42no—
208C2×C4×C11—42no—
209C2×C4×C11—42no—
210C2×C4×C11—44no—
211C2×C4×C11—44no—
212C2×C4×C11#12011yescharacteristic
213C2×C4×C11#12011yescharacteristic
214C2×C4×C11#12011yescharacteristic
215C2×C4×C11C2×D812yes—
216C2×C4×C11#13512yes—
217C2×C4×C11AGL(1,ℤ/8)12yes—
218C2×C4×C11#13712yes—
219C2×C4×C11C22×D411yescharacteristic
220C2×C4×C11C22×D411yescharacteristic
221C2×C4×C11C22×D411yescharacteristic
222C2×Dic11—42no—
223C2×Dic11—82no—
224Dic22—42no—
225Dic22—42no—
226Dic22—82no—
227C11⋊C8—24no—
228C11⋊C8—42no—
229C11⋊C8—42no—
230C22×#41—21no—
231C22×SD16—221no—
232#547—22no—
233#547—22no—
234#547—22no—
235#547C2×D1114yes—
236C2×C4⋊Q8—111no—
237C2×C4⋊Q8C2×D1111yescharacteristic
238C2×#123—22no—
239C2×C22⋊Q8—21no—
240C2×#121—21no—
241C2×C4×D4C2×D1111yescharacteristic
242C2×C4×D4C2×D1111yescharacteristic
243C22×C4⋊C4—21no—
244#500—114no—
245#500—222no—
246#474—114no—
247#474—222no—
248#461—114no—
249#461—222no—
250C2×#107—222no—
251C2×#107—221no—
252C2×C4⋊C8—111no—
253C2×C4⋊C8—111no—
254C2×#103—221no—
255C2×#102—221no—
256C2×C4×C8—111no—
257#332—114no—
258D4⋊C8—114no—
259D4⋊C8—114no—
260C22×C11—24no—
261C22×C11—48no—
262C22×C11—42no—
263C22×C11—42no—
264C22×C11—42no—
265C22×C11—42no—
266C22×C11—42no—
267C22×C11—84no—
268C22×C11#44712yes—
269C22×C11#45212yes—
270C22×C11#45612yes—
271C22×C11C2×#12011yescharacteristic
272C4×C11—21no—
273C4×C11—21no—
274C4×C11—42no—
275C4×C11—44no—
276C4×C11—42no—
277C4×C11#44712yes—
278C4×C11#45212yes—
279C4×C11C22×D811yescharacteristic
280C4×C11C2×#13511yescharacteristic
281C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
282C4×C11C2×#13711yescharacteristic
283Dic11—82no—
284C2×#41—24no—
285C2×#41—24no—
286C2×#41—44no—
287C2×#41—44no—
288C22×Q8—21no—
289C22×Q8—221no—
290C22×D4—22no—
291C22×D4C22⋊D1111yescharacteristic
292C22×D4C22⋊D1111yescharacteristic
293C23×C4—22no—
294C23×C4—21no—
295C23×C4—21no—
296C2×SD16—224no—
297C2×SD16—444no—
298C22×C8—221no—
299C22×C8—221no—
300C22×C8—221no—
301C4⋊Q8—21no—
302C4⋊Q8—21no—
303C4⋊Q8—112no—
304C4⋊Q8—221no—
305C4⋊Q8—221no—
306C4⋊Q8—221no—
307C4⋊Q8C22⋊D1112yes—
308C4⋊Q8C22×D1112yes—
309#123—28no—
310#123—28no—
311C22⋊Q8—24no—
312C22⋊Q8—24no—
313#121—24no—
314#121—24no—
315C4×D4—21no—
316C4×D4—21no—
317C4×D4—21no—
318C4×D4—21no—
319C4×D4C22⋊D1112yes—
320C4×D4C22⋊D1112yes—
321C4×D4C22×D1112yes—
322C4×D4C22×D1112yes—
323C2×C4⋊C4—22no—
324C2×C4⋊C4—24no—
325C2×C4⋊C4—21no—
326C2×C4⋊C4—24no—
327C2×C4⋊C4—221no—
328C2×C4⋊C4—221no—
329C2×C4⋊C4C22⋊D1111yescharacteristic
330C2×C4⋊C4C22⋊D1111yescharacteristic
331C2×C4⋊C4C22⋊D1112yes—
332C2×C22⋊C4—22no—
333C2×C22⋊C4—21no—
334C2×C22⋊C4—21no—
335C2×C42C22×D1111yescharacteristic
336#107—224no—
337#107—228no—
338C4⋊C8—112no—
339C4⋊C8—112no—
340C4⋊C8—221no—
341C4⋊C8—221no—
342#103—224no—
343#102—224no—
344C4×C8—112no—
345C4×C8—221no—
346C2×C11—44no—
347C2×C11—82no—
348C2×C11#164714yescomplemented
349C2×C11C2×#44711yescharacteristic
350C2×C11C2×#45211yescharacteristic
351C2×C11C2×#45611yescharacteristic
352C24—21no—
353C24—21no—
354#41—48no—
355#41—416no—
356#41—48no—
357C2×Q8—22no—
358C2×Q8—22no—
359C2×Q8—42no—
360C2×Q8—42no—
361C2×Q8—222no—
362C2×Q8—441no—
363C2×Q8—442no—
364C2×Q8—442no—
365C2×D4—28no—
366C2×D4—22no—
367C2×D4—22no—
368C2×D4—22no—
369C2×D4—21no—
370C2×D4—21no—
371C2×D4—48no—
372C2×D4#432314yes—
373C2×D4C2×C22⋊D1112yes—
374C2×D4C2×C22⋊D1112yes—
375C22×C4—28no—
376C22×C4—21no—
377C22×C4—21no—
378C22×C4—22no—
379C22×C4—22no—
380C22×C4—22no—
381C22×C4—22no—
382C22×C4—22no—
383C22×C4—48no—
384C22×C4—42no—
385C22×C4—42no—
386C22×C4—42no—
387C22×C4—42no—
388C22×C4—441no—
389C22×C4C2×C22⋊D1111yescharacteristic
390C22×C4C2×C22⋊D1111yescharacteristic
391C22×C4C2×C22⋊D1111yescharacteristic
392SD16—448no—
393C2×C8—224no—
394C2×C8—222no—
395C2×C8—222no—
396C2×C8—222no—
397C2×C8—442no—
398C2×C8—442no—
399C4⋊C4—28no—
400C4⋊C4—21no—
401C4⋊C4—22no—
402C4⋊C4—21no—
403C4⋊C4—22no—
404C4⋊C4—22no—
405C4⋊C4—222no—
406C4⋊C4—222no—
407C4⋊C4—441no—
408C4⋊C4—441no—
409C4⋊C4C2×C22⋊D1112yes—
410C4⋊C4C2×C22⋊D1112yes—
411C4⋊C4C2×C22⋊D1114yes—
412C22⋊C4—28no—
413C22⋊C4—22no—
414C22⋊C4—22no—
415C22⋊C4—22no—
416C22⋊C4—22no—
417C42C2×C22⋊D1111yescharacteristic
418C42C2×C22⋊D1111yescharacteristic
419C42C2×C22⋊D1111yescharacteristic
420C42C23×D1111yescharacteristic
421C11C2×#164711yescharacteristic, complemented, Sylow
422C23—24no—
423C23—22no—
424C23—22no—
425C23—42no—
426C23—42no—
427C23—42no—
428C23—42no—
429C23—42no—
430C23#6700611yescharacteristic
431Q8—42no—
432Q8—42no—
433Q8—44no—
434Q8—442no—
435Q8—442no—
436Q8—882no—
437D4—22no—
438D4—24no—
439D4—22no—
440D4—22no—
441D4—416no—
442D4—42no—
443D4C2×#432314yes—
444C2×C4—22no—
445C2×C4—22no—
446C2×C4—22no—
447C2×C4—24no—
448C2×C4—416no—
449C2×C4—42no—
450C2×C4—44no—
451C2×C4—42no—
452C2×C4—42no—
453C2×C4—42no—
454C2×C4—44no—
455C2×C4—42no—
456C2×C4—42no—
457C2×C4—44no—
458C2×C4—442no—
459C2×C4—882no—
460C2×C4C2×#432312yes—
461C2×C4#6698512yes—
462C2×C4#6700312yes—
463C2×C4#6700412yes—
464C2×C4#6700611yescharacteristic
465C2×C4#6700611yescharacteristic
466C2×C4#6700611yescharacteristic
467C2×C4C22×C22⋊D1111yescharacteristic
468C2×C4C22×C22⋊D1111yescharacteristic
469C2×C4C22×C22⋊D1111yescharacteristic
470C8—224no—
471C8—442no—
472C8—442no—
473C22—24no—
474C22—42no—
475C22—48no—
476C22—42no—
477C22—42no—
478C22—42no—
479C22—42no—
480C22—84no—
481C22#1062283012yes—
482C22#1062285212yes—
483C22#1062285912yes—
484C22C2×#6700611yescharacteristic
485C4—21no—
486C4—21no—
487C4—42no—
488C4—44no—
489C4—42no—
490C4—882no—
491C4#1062283012yes—
492C4#1062285212yes—
493C4C22×#432311yescharacteristic
494C4C2×#6698511yescharacteristic
495C4C2×#6700311yescharacteristic
496C4C2×#6700411yescharacteristic
497C2—44no—
498C2—82no—
499C2#1306785114yesdirect product factor
500C2C2×#1062283011yescharacteristic
501C2C2×#1062285211yescharacteristic
502C2C2×#1062285911yescharacteristic
subgroupG/H
centerC23#67006
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
Fitting, prime radicalC2×C11×#547C2
socleC23×C11#120
hypercenterC2×#547D11
hypocenterC11C2×#1647
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#547

Complements

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

NH ≅ G/Ntype
1. C2×#10622691C2semidirect
2. C2×#10622620C2semidirect
3. C2×#10622632C2semidirect
4. #13067851C2direct (N × H)
5. C2×#10622185C2semidirect
6. C2×D4⋊(C11⋊C8)C2semidirect
7. C2×D4⋊(C11⋊C8)C2semidirect
25. #10622691C22semidirect
27. #10622632C22semidirect
29. #10622620C22semidirect
36. #10622185C22semidirect
37. D4⋊(C11⋊C8)C22semidirect
38. D4⋊(C11⋊C8)C22semidirect
348. C2×C11#1647semidirect
421. C11C2×#1647semidirect
499. C2#13067851direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106226912
C2×#106226202
C2×#106226322
#130678512
C2×#106221852
C2×D4⋊(C11⋊C8)2
C2×C11×#5472
C2×#164711