Finite Group Databasebeta

← C2×#13067866 #14729574

Subgroups — C2×#13067866 #14729574

Order 2816.

1206 conjugacy classes of subgroups.

The subgroup lattice has 482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623258C211yesmaximal, characteristic
2C2×#10622691C211yesmaximal, characteristic, complemented
3C2×#10622459C211yesmaximal, characteristic
4C2×#10622462C211yesmaximal, characteristic, complemented
5#13067866C218yesmaximal, direct product factor
6C2×#10622122C211yesmaximal, characteristic, complemented
7C2×#10622121C211yesmaximal, characteristic
8C2×C11×#332C211yesmaximal, characteristic, complemented
9C22×Q8×D11—21no—
10C2×C11×C4⋊Q8C2211yescharacteristic
11C2×#66999—21no—
12C22×Dic44—21no—
13#10623258—22no—
14#10623258—22no—
15#10623258—22no—
16#10623258C2214yes—
17C2×#66949—22no—
18C2×#66946—21no—
19C2×#66941—21no—
20C2×C4×D44C2211yescharacteristic
21C2×#66922C2211yescharacteristic
22C2×C4×Dic22C2211yescharacteristic
23C2×C11×C4⋊C8C2211yescharacteristic
24C2×C11×C4⋊C8C2211yescharacteristic
25C2×#66885—21no—
26C2×#66882—21no—
27C2×#66880—21no—
28#10622691—22no—
29#10622691C2214yescomplemented
30C2×#66871—22no—
31C2×C4×C11⋊C8C2211yescharacteristic
32#10622462—22no—
33#10622462C2214yescomplemented
34#10622459—22no—
35#10622459C2214yes—
36C11×#332C2214yescomplemented
37#10622122C2214yescomplemented
38#10622121C2214yes—
39C22×Q8×C11—21no—
40C2×Q8×D11—24no—
41C2×Q8×D11—24no—
42C2×Q8×D11—44no—
43C2×Q8×D11—44no—
44C22×D44D411yescharacteristic
45C22×C4×D11—22no—
46C22×C4×D11—21no—
47C22×Dic22—22no—
48C22×Dic22—21no—
49C22×Dic22D411yescharacteristic
50C22×C8×C11—21no—
51C22×C8×C11—21no—
52C11×C4⋊Q8—21no—
53C11×C4⋊Q8—21no—
54C11×C4⋊Q8D412yes—
55C11×C4⋊Q8C2312yes—
56C2×C11×C4⋊C4—21no—
57C2×C11×C4⋊C4D412yes—
58C2×C42×C11C2311yescharacteristic
59#66999—24no—
60#66999—24no—
61C2×(C2×D11)⋊C4—22no—
62C2×(C2×D11)⋊C4—21no—
63C2×C4⋊Dic11—21no—
64C2×C4⋊Dic11—21no—
65C2×C4⋊Dic11D411yescharacteristic
66C2×C4⋊Dic11D411yescharacteristic
67C2×Dic11⋊C4—22no—
68C2×Dic11⋊C4—21no—
69C2×C4×Dic11—21no—
70C22×C11⋊C8—21no—
71C2×Dic44—24no—
72C2×Dic44—44no—
73#66949—28no—
74#66949—28no—
75#66946—24no—
76#66946—24no—
77#66941—24no—
78#66941—24no—
79C4×D44—21no—
80C4×D44—21no—
81C4×D44D412yes—
82C4×D44C2312yes—
83#66922—21no—
84#66922—21no—
85#66922—21no—
86#66922C2312yes—
87C4×Dic22—21no—
88C4×Dic22—21no—
89C4×Dic22D412yes—
90C4×Dic22C2312yes—
91C11×C4⋊C8—21no—
92C11×C4⋊C8—21no—
93C11×C4⋊C8C2312yes—
94C11×C4⋊C8C2312yes—
95#66885—24no—
96#66882—24no—
97#66880—24no—
98#66871—28no—
99C4×C11⋊C8—21no—
100C4×C11⋊C8C2312yes—
101C2×#1649—111nomaximal, Sylow
102C23×D11—21no—
103C2×Q8×C11—22no—
104C2×Q8×C11—22no—
105C2×Q8×C11—42no—
106C2×Q8×C11—42no—
107C22×C4×C11—22no—
108C22×C4×C11C2×D411yescharacteristic
109C22×C4×C11C2×D411yescharacteristic
110C22×C4×C11C2×D411yescharacteristic
111C22×Dic11—21no—
112C22×Dic11—21no—
113C22×Dic11—21no—
114C22×Dic11—41no—
115Q8×D11—48no—
116Q8×D11—416no—
117Q8×D11—48no—
118C2×D44—21no—
119C2×D44—22no—
120C2×D44Q1614yescomplemented
121C2×D44C2×D412yes—
122C2×C4×D11—28no—
123C2×C4×D11—22no—
124C2×C4×D11—22no—
125C2×C4×D11—48no—
126C2×C4×D11—42no—
127C2×C4×D11—42no—
128C2×Dic22—28no—
129C2×Dic22—21no—
130C2×Dic22—22no—
131C2×Dic22—22no—
132C2×Dic22—48no—
133C2×Dic22—41no—
134C2×Dic22—42no—
135C2×Dic22—42no—
136C2×Dic22D814yes—
137C2×Dic22C2×D412yes—
138C2×C8×C11—22no—
139C2×C8×C11—22no—
140C2×C8×C11—42no—
141C2×C8×C11—42no—
142C11×C4⋊C4—22no—
143C11×C4⋊C4—22no—
144C11×C4⋊C4—22no—
145C11×C4⋊C4C2×D414yes—
146C42×C11C2×D411yescharacteristic
147C42×C11C2×D411yescharacteristic
148C42×C11C2×D411yescharacteristic
149C42×C11C2411yescharacteristic
150(C2×D11)⋊C4—28no—
151(C2×D11)⋊C4—22no—
152(C2×D11)⋊C4—22no—
153C4⋊Dic11—21no—
154C4⋊Dic11—21no—
155C4⋊Dic11—22no—
156C4⋊Dic11—22no—
157C4⋊Dic11—41no—
158C4⋊Dic11—41no—
159C4⋊Dic11C2×D412yes—
160C4⋊Dic11C2×D412yes—
161Dic11⋊C4—28no—
162Dic11⋊C4—22no—
163Dic11⋊C4—22no—
164C4×Dic11—22no—
165C4×Dic11—22no—
166C2×C11⋊C8—24no—
167C2×C11⋊C8—22no—
168Dic44—48no—
169C2×D4×Q8—111no—
170C2×#500—111no—
171C2×#474—111no—
172C2×#462—111no—
173#1649—118no—
174C2×#332D1111yescharacteristic, complemented
175C2×Q8⋊C8—111no—
176C2×D4⋊C8—111no—
177C23×C11#12011yescharacteristic
178C22×D11—22no—
179C22×D11—24no—
180C22×D11—42no—
181C22×D11—42no—
182Q8×C11—42no—
183Q8×C11—42no—
184Q8×C11—44no—
185C2×C4×C11—22no—
186C2×C4×C11—24no—
187C2×C4×C11—44no—
188C2×C4×C11#12011yescharacteristic
189C2×C4×C11#12011yescharacteristic
190C2×C4×C11#12011yescharacteristic
191C2×C4×C11C2×D812yes—
192C2×C4×C11C2×Q1612yes—
193C2×C4×C11AGL(1,ℤ/8)12yes—
194C2×C4×C11#13712yes—
195C2×C4×C11C22×D411yescharacteristic
196C2×C4×C11C22×D411yescharacteristic
197C2×C4×C11C22×D411yescharacteristic
198C2×Dic11—22no—
199C2×Dic11—24no—
200C2×Dic11—22no—
201C2×Dic11—22no—
202C2×Dic11—42no—
203C2×Dic11—42no—
204C2×Dic11—42no—
205C2×Dic11—82no—
206D44—22no—
207D44—24no—
208D44C2×Q1614yescomplemented
209C4×D11—416no—
210C4×D11—42no—
211C4×D11—42no—
212C4×D11—44no—
213Dic22—22no—
214Dic22—24no—
215Dic22—416no—
216Dic22—42no—
217Dic22—42no—
218Dic22—82no—
219Dic22C2×D814yes—
220C8×C11—42no—
221C8×C11—42no—
222C11⋊C8—24no—
223C23×Q8—221no—
224C22×Q16—221no—
225D4×Q8—114no—
226D4×Q8—222no—
227D4×Q8—222no—
228D4×Q8—222no—
229C2×C4⋊Q8—111no—
230C2×C4⋊Q8—221no—
231C2×C4⋊Q8C2×D1111yescharacteristic
232C2×C22⋊Q8—221no—
233C2×C22⋊Q8—222no—
234C2×C4×Q8—111no—
235C2×C4×D4—111no—
236C2×C4×D4—221no—
237#500—114no—
238#500—222no—
239#474—114no—
240#474—222no—
241#462—114no—
242#462—222no—
243C2×#107—221no—
244C2×#107—222no—
245C2×C4⋊C8C2×D1111yescharacteristic
246C2×C4⋊C8C2×D1111yescharacteristic
247C2×#103—221no—
248C2×#102—221no—
249C2×C4×C8—111no—
250#332C2×D1114yescomplemented
251Q8⋊C8—114no—
252D4⋊C8—114no—
253C22×C11#44712yes—
254C22×C11#45112yes—
255C22×C11#45612yes—
256C22×C11C2×#12011yescharacteristic
257C2×D11—24no—
258C2×D11—48no—
259C2×D11—42no—
260C2×D11—42no—
261C4×C11—21no—
262C4×C11—21no—
263C4×C11—44no—
264C4×C11#44712yes—
265C4×C11#45112yes—
266C4×C11C22×D811yescharacteristic
267C4×C11C22×Q1611yescharacteristic
268C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
269C4×C11C2×#13711yescharacteristic
270Dic11—24no—
271Dic11—42no—
272Dic11—42no—
273Dic11—82no—
274C22×Q8—21no—
275C22×Q8—111no—
276C22×Q8—222no—
277C22×Q8—224no—
278C22×Q8—224no—
279C22×Q8—221no—
280C22×Q8—444no—
281C22×Q8—444no—
282C22×D4—111no—
283C23×C4—222no—
284C23×C4—221no—
285C2×Q16—224no—
286C2×Q16—444no—
287C22×C8—21no—
288C22×C8—21no—
289C22×C8—221no—
290C4⋊Q8—21no—
291C4⋊Q8—21no—
292C4⋊Q8—112no—
293C4⋊Q8—224no—
294C4⋊Q8—224no—
295C4⋊Q8—221no—
296C4⋊Q8—221no—
297C4⋊Q8—221no—
298C4⋊Q8D4412yes—
299C4⋊Q8C22×D1112yes—
300C22⋊Q8—228no—
301C22⋊Q8—224no—
302C22⋊Q8—224no—
303C22⋊Q8—228no—
304C4×Q8—112no—
305C4×Q8—112no—
306C4×Q8—221no—
307C4×Q8—221no—
308C4×D4—112no—
309C4×D4—112no—
310C4×D4—224no—
311C4×D4—224no—
312C4×D4—221no—
313C4×D4—221no—
314C2×C4⋊C4—21no—
315C2×C4⋊C4—111no—
316C2×C4⋊C4—111no—
317C2×C4⋊C4—222no—
318C2×C4⋊C4—221no—
319C2×C4⋊C4—221no—
320C2×C4⋊C4—221no—
321C2×C4⋊C4D4412yes—
322C2×C22⋊C4—222no—
323C2×C22⋊C4—221no—
324C2×C42—221no—
325C2×C42C22×D1111yescharacteristic
326#107—224no—
327#107—228no—
328C4⋊C8—21no—
329C4⋊C8—21no—
330C4⋊C8C22×D1112yes—
331C4⋊C8C22×D1112yes—
332#103—224no—
333#102—224no—
334C4×C8—112no—
335C4×C8—221no—
336C2×C11#164914yescomplemented
337C2×C11C2×#44711yescharacteristic
338C2×C11C2×#45111yescharacteristic
339C2×C11C2×#45611yescharacteristic
340D11—44no—
341C24—221no—
342C2×Q8—22no—
343C2×Q8—22no—
344C2×Q8—42no—
345C2×Q8—42no—
346C2×Q8—114no—
347C2×Q8—112no—
348C2×Q8—228no—
349C2×Q8—221no—
350C2×Q8—222no—
351C2×Q8—222no—
352C2×Q8—448no—
353C2×Q8—448no—
354C2×Q8—448no—
355C2×Q8—4416no—
356C2×Q8—441no—
357C2×Q8—442no—
358C2×Q8—442no—
359C2×D4—114no—
360C2×D4—112no—
361C2×D4—221no—
362C2×D4—222no—
363C22×C4—22no—
364C22×C4—228no—
365C22×C4—221no—
366C22×C4—221no—
367C22×C4—221no—
368C22×C4—222no—
369C22×C4—222no—
370C22×C4—448no—
371C22×C4—442no—
372C22×C4—442no—
373C22×C4—441no—
374C22×C4C2×D4411yescharacteristic
375C22×C4D4×D1111yescharacteristic
376C22×C4D4×D1111yescharacteristic
377Q16—448no—
378C2×C8—22no—
379C2×C8—22no—
380C2×C8—42no—
381C2×C8—42no—
382C2×C8—224no—
383C2×C8—222no—
384C4⋊C4—22no—
385C4⋊C4—22no—
386C4⋊C4—22no—
387C4⋊C4—112no—
388C4⋊C4—112no—
389C4⋊C4—228no—
390C4⋊C4—221no—
391C4⋊C4—221no—
392C4⋊C4—222no—
393C4⋊C4—222no—
394C4⋊C4—222no—
395C4⋊C4—222no—
396C4⋊C4—441no—
397C4⋊C4—441no—
398C4⋊C4C2×D4414yes—
399C22⋊C4—228no—
400C22⋊C4—222no—
401C22⋊C4—222no—
402C42—222no—
403C42—222no—
404C42C2×D4411yescharacteristic
405C42D4×D1111yescharacteristic
406C42D4×D1111yescharacteristic
407C42C23×D1111yescharacteristic
408C11C2×#164911yescharacteristic, complemented, Sylow
409C23—222no—
410C23—224no—
411C23—442no—
412C23—442no—
413C23#6693511yescharacteristic
414Q8—42no—
415Q8—42no—
416Q8—44no—
417Q8—114no—
418Q8—222no—
419Q8—224no—
420Q8—4416no—
421Q8—442no—
422Q8—442no—
423Q8—882no—
424D4—114no—
425D4—222no—
426D4—224no—
427C2×C4—22no—
428C2×C4—24no—
429C2×C4—44no—
430C2×C4—222no—
431C2×C4—224no—
432C2×C4—222no—
433C2×C4—222no—
434C2×C4—4416no—
435C2×C4—442no—
436C2×C4—442no—
437C2×C4—442no—
438C2×C4—442no—
439C2×C4—444no—
440C2×C4—442no—
441C2×C4—882no—
442C2×C4#6693511yescharacteristic
443C2×C4#6693511yescharacteristic
444C2×C4#6693511yescharacteristic
445C2×C4D8×D1112yes—
446C2×C4#6696712yes—
447C2×C4#6696812yes—
448C2×C4Q16×D1112yes—
449C2×C4C22×D4411yescharacteristic
450C2×C4C2×D4×D1111yescharacteristic
451C2×C4C2×D4×D1111yescharacteristic
452C8—42no—
453C8—42no—
454C8—224no—
455C22—224no—
456C22—442no—
457C22—448no—
458C22—442no—
459C22#1062236512yes—
460C22#1062238612yes—
461C22#1062242112yes—
462C22C2×#6693511yescharacteristic
463C4—21no—
464C4—21no—
465C4—44no—
466C4—224no—
467C4—442no—
468C4—442no—
469C4—882no—
470C4#1062238612yes—
471C4#1062242112yes—
472C4C2×D8×D1111yescharacteristic
473C4C2×#6696711yescharacteristic
474C4C2×#6696811yescharacteristic
475C4C2×Q16×D1111yescharacteristic
476C2—444no—
477C2#1306786614yesdirect product factor
478C2C2×#1062238611yescharacteristic
479C2C2×#1062242111yescharacteristic
480C2C2×#1062236511yescharacteristic
subgroupG/H
centerC23#66935
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC2×C11×#332C2
socleC23×C11#120
prime radicalC22×D44D4
hypercenterC2×#332D11
hypocenterC11C2×#1649
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#332

Complements

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

NH ≅ G/Ntype
2. C2×#10622691C2semidirect
4. C2×#10622462C2semidirect
5. #13067866C2direct (N × H)
6. C2×#10622122C2semidirect
8. C2×C11×#332C2semidirect
29. #10622691C22semidirect
33. #10622462C22semidirect
36. C11×#332C22semidirect
37. #10622122C22semidirect
120. C2×D44Q16semidirect
174. C2×#332D11semidirect
208. D44C2×Q16semidirect
250. #332C2×D11semidirect
336. C2×C11#1649semidirect
408. C11C2×#1649semidirect
477. C2#13067866direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106232582
C2×#106226912
C2×#106224592
C2×#106224622
#130678662
C2×#106221222
C2×#106221212
C2×C11×#3322
C2×#164911