Finite Group Databasebeta

← C2×#13067895 #14729592

Subgroups — C2×#13067895 #14729592

Order 2816.

946 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623101C211yesmaximal, characteristic
2C2×#10622293C211yesmaximal, characteristic
3C2×#10622464C211yesmaximal, characteristic
4C2×#10622644C211yesmaximal, characteristic
5#13067895C218yesmaximal, direct product factor
6C2×#10622120C211yesmaximal, characteristic
7C2×#10622094C211yesmaximal, characteristic
8C2×C11×Q8⋊C8C211yesmaximal, characteristic
9C2×C4×Q8×C11C2211yescharacteristic
10C2×Q8×Dic11—21no—
11C22×#4326—21no—
12#10623101—22no—
13#10623101—22no—
14#10623101—22no—
15#10623101C2214yes—
16C2×#66943—21no—
17C2×#66943—22no—
18C2×#66922—21no—
19C2×#66922C2211yescharacteristic
20C2×#66922C2211yescharacteristic
21C2×C4×Dic22—21no—
22C2×C4×Dic22C2211yescharacteristic
23C2×C11×C4⋊C8C2211yescharacteristic
24C2×C4×C8×C11C2211yescharacteristic
25C2×#66881—22no—
26C2×#66881—21no—
27C2×#66880—21no—
28#10622644—22no—
29#10622644C2214yes—
30C2×#66874—21no—
31C2×C4⋊(C11⋊C8)C2211yescharacteristic
32#10622464—22no—
33#10622464C2214yes—
34#10622293—22no—
35#10622293C2214yes—
36C11×Q8⋊C8C2214yes—
37#10622120C2214yes—
38#10622094C2214yes—
39C22×Q8×C11D411yescharacteristic
40C22×Dic22—21no—
41C22×Dic22—21no—
42C22×Dic22D411yescharacteristic
43C22×C8×C11—21no—
44C22×C8×C11—21no—
45C4×Q8×C11—21no—
46C4×Q8×C11—21no—
47C4×Q8×C11D412yes—
48C4×Q8×C11C2312yes—
49C2×C11×C4⋊C4—21no—
50C2×C11×C4⋊C4D411yescharacteristic
51C2×C42×C11—21no—
52C2×C42×C11C2311yescharacteristic
53Q8×Dic11—24no—
54Q8×Dic11—24no—
55C2×#4326—24no—
56C2×#4326—44no—
57C2×C4⋊Dic11—22no—
58C2×C4⋊Dic11—22no—
59C2×C4⋊Dic11—21no—
60C2×C4⋊Dic11—21no—
61C2×C4⋊Dic11—21no—
62C2×C4⋊Dic11D411yescharacteristic
63C2×C4⋊Dic11D412yes—
64C2×Dic11⋊C4—22no—
65C2×Dic11⋊C4—21no—
66C2×C4×Dic11—22no—
67C2×C4×Dic11—21no—
68C22×C11⋊C8—21no—
69#66943—28no—
70#66943—24no—
71#66943—24no—
72#66943—28no—
73#66922—24no—
74#66922—24no—
75#66922—21no—
76#66922—21no—
77#66922—21no—
78#66922—21no—
79#66922—21no—
80#66922D412yes—
81#66922C2312yes—
82#66922C2312yes—
83C4×Dic22—24no—
84C4×Dic22—21no—
85C4×Dic22—21no—
86C4×Dic22—24no—
87C4×Dic22D412yes—
88C4×Dic22C2312yes—
89C11×C4⋊C8—21no—
90C11×C4⋊C8C2312yes—
91C4×C8×C11—21no—
92C4×C8×C11C2312yes—
93#66881—24no—
94#66881—28no—
95#66880—24no—
96#66874—24no—
97C4⋊(C11⋊C8)—21no—
98C4⋊(C11⋊C8)C2312yes—
99C2×#1653—111nomaximal, Sylow
100C2×Q8×C11—21no—
101C2×Q8×C11—22no—
102C2×Q8×C11SD1614yes—
103C2×Q8×C11C2×D412yes—
104C22×C4×C11—21no—
105C22×C4×C11—21no—
106C22×C4×C11C2×D411yescharacteristic
107C22×C4×C11C2×D411yescharacteristic
108C22×C4×C11C2×D411yescharacteristic
109C22×Dic11—21no—
110C22×Dic11—21no—
111C22×Dic11—22no—
112C22×Dic11—41no—
113C2×Dic22—21no—
114C2×Dic22—22no—
115C2×Dic22—22no—
116C2×Dic22—22no—
117C2×Dic22—22no—
118C2×Dic22—22no—
119C2×Dic22—41no—
120C2×Dic22—42no—
121C2×Dic22—42no—
122C2×Dic22—42no—
123C2×Dic22—42no—
124C2×Dic22C2×D412yes—
125C2×C8×C11—24no—
126C2×C8×C11—22no—
127C2×C8×C11—22no—
128C2×C8×C11—42no—
129C11×C4⋊C4—22no—
130C11×C4⋊C4—21no—
131C11×C4⋊C4—22no—
132C11×C4⋊C4C2×D412yes—
133C42×C11—22no—
134C42×C11—22no—
135C42×C11C2×D411yescharacteristic
136C42×C11C2×D411yescharacteristic
137C42×C11C2×D411yescharacteristic
138C42×C11C2411yescharacteristic
139#4326—48no—
140C4⋊Dic11—28no—
141C4⋊Dic11—28no—
142C4⋊Dic11—21no—
143C4⋊Dic11—22no—
144C4⋊Dic11—22no—
145C4⋊Dic11—22no—
146C4⋊Dic11—22no—
147C4⋊Dic11—22no—
148C4⋊Dic11—41no—
149C4⋊Dic11—41no—
150C4⋊Dic11C2×D412yes—
151C4⋊Dic11C2×D414yes—
152Dic11⋊C4—28no—
153Dic11⋊C4—22no—
154Dic11⋊C4—22no—
155C4×Dic11—28no—
156C4×Dic11—22no—
157C4×Dic11—22no—
158C2×C11⋊C8—22no—
159C2×C11⋊C8—42no—
160C2×#557—111no—
161C2×#498—111no—
162C2×#475—111no—
163C2×#462—111no—
164#1653—118no—
165C2×#332—111no—
166C2×Q8⋊C8—111no—
167C2×Q8⋊C8D1111yescharacteristic
168C23×C11#12011yescharacteristic
169Q8×C11—22no—
170Q8×C11—24no—
171Q8×C11C2×SD1614yes—
172C2×C4×C11—22no—
173C2×C4×C11—24no—
174C2×C4×C11—22no—
175C2×C4×C11—22no—
176C2×C4×C11—42no—
177C2×C4×C11#12011yescharacteristic
178C2×C4×C11#12011yescharacteristic
179C2×C4×C11#12011yescharacteristic
180C2×C4×C11C2×SD1612yes—
181C2×C4×C11#13512yes—
182C2×C4×C11#13712yes—
183C2×C4×C11#13712yes—
184C2×C4×C11C22×D411yescharacteristic
185C2×C4×C11C22×D411yescharacteristic
186C2×C4×C11C22×D411yescharacteristic
187C2×Dic11—22no—
188C2×Dic11—22no—
189C2×Dic11—24no—
190C2×Dic11—42no—
191C2×Dic11—44no—
192C2×Dic11—42no—
193C2×Dic11—42no—
194C2×Dic11—82no—
195Dic22—22no—
196Dic22—22no—
197Dic22—42no—
198Dic22—42no—
199Dic22—42no—
200Dic22—44no—
201Dic22—42no—
202Dic22—42no—
203Dic22—82no—
204C8×C11—24no—
205C8×C11—42no—
206C11⋊C8—42no—
207C22×Q16—221no—
208#557—114no—
209#557—222no—
210#557—222no—
211#557—222no—
212C2×C4⋊Q8—111no—
213C2×C4⋊Q8—111no—
214C2×C4⋊Q8—221no—
215C2×#125—222no—
216C2×#125—221no—
217C2×C4×Q8—111no—
218C2×C4×Q8—221no—
219C2×C4×Q8—221no—
220C2×C4×Q8C2×D1111yescharacteristic
221#498—114no—
222#498—222no—
223#475—114no—
224#475—222no—
225#462—114no—
226#462—222no—
227C2×#106—221no—
228C2×#106—222no—
229C2×C4⋊C8—111no—
230C2×C4⋊C8C2×D1111yescharacteristic
231C2×#103—221no—
232C2×#103—221no—
233C2×C4×C8C2×D1111yescharacteristic
234#332—114no—
235Q8⋊C8—114no—
236Q8⋊C8C2×D1114yes—
237C22×C11#44812yes—
238C22×C11#45212yes—
239C22×C11#45612yes—
240C22×C11C2×#12011yescharacteristic
241C4×C11—24no—
242C4×C11—21no—
243C4×C11—21no—
244C4×C11—42no—
245C4×C11#44812yes—
246C4×C11#45212yes—
247C4×C11C22×SD1611yescharacteristic
248C4×C11C2×#13511yescharacteristic
249C4×C11C2×#13711yescharacteristic
250C4×C11C2×#13711yescharacteristic
251Dic11—42no—
252Dic11—44no—
253Dic11—42no—
254Dic11—82no—
255C22×Q8—111no—
256C22×Q8—221no—
257C22×Q8—221no—
258C22×Q8D4411yescharacteristic
259C2×Q16—224no—
260C2×Q16—444no—
261C22×C8—21no—
262C22×C8—21no—
263C22×C8—221no—
264C4⋊Q8—112no—
265C4⋊Q8—112no—
266C4⋊Q8—112no—
267C4⋊Q8—224no—
268C4⋊Q8—224no—
269C4⋊Q8—221no—
270C4⋊Q8—221no—
271C4⋊Q8—221no—
272C4⋊Q8—221no—
273C4⋊Q8—221no—
274#125—228no—
275#125—228no—
276#125—224no—
277#125—224no—
278C4×Q8—21no—
279C4×Q8—21no—
280C4×Q8—112no—
281C4×Q8—112no—
282C4×Q8—224no—
283C4×Q8—224no—
284C4×Q8—224no—
285C4×Q8—224no—
286C4×Q8—221no—
287C4×Q8—221no—
288C4×Q8D4412yes—
289C4×Q8C22×D1112yes—
290C2×C4⋊C4—21no—
291C2×C4⋊C4—111no—
292C2×C4⋊C4—112no—
293C2×C4⋊C4—222no—
294C2×C4⋊C4—222no—
295C2×C4⋊C4—222no—
296C2×C4⋊C4—221no—
297C2×C4⋊C4—221no—
298C2×C4⋊C4—221no—
299C2×C4⋊C4—221no—
300C2×C4⋊C4D4411yescharacteristic
301C2×C42—21no—
302C2×C42—222no—
303C2×C42—221no—
304C2×C42C22×D1111yescharacteristic
305#106—224no—
306#106—228no—
307C4⋊C8—21no—
308C4⋊C8—112no—
309C4⋊C8—221no—
310C4⋊C8C22×D1112yes—
311#103—224no—
312#103—224no—
313C4×C8—21no—
314C4×C8C22×D1112yes—
315C2×C11#165314yescomplemented
316C2×C11C2×#44811yescharacteristic
317C2×C11C2×#45211yescharacteristic
318C2×C11C2×#45611yescharacteristic
319C2×Q8—21no—
320C2×Q8—22no—
321C2×Q8—112no—
322C2×Q8—222no—
323C2×Q8—221no—
324C2×Q8—222no—
325C2×Q8—222no—
326C2×Q8—222no—
327C2×Q8—222no—
328C2×Q8—441no—
329C2×Q8—442no—
330C2×Q8—442no—
331C2×Q8—442no—
332C2×Q8—442no—
333C2×Q8#431414yes—
334C2×Q8C2×D4412yes—
335C22×C4—21no—
336C22×C4—21no—
337C22×C4—221no—
338C22×C4—222no—
339C22×C4—221no—
340C22×C4—441no—
341C22×C4C2×D4411yescharacteristic
342C22×C4D4×D1111yescharacteristic
343C22×C4D4×D1111yescharacteristic
344Q16—448no—
345C2×C8—24no—
346C2×C8—22no—
347C2×C8—22no—
348C2×C8—42no—
349C2×C8—222no—
350C2×C8—442no—
351C4⋊C4—22no—
352C4⋊C4—21no—
353C4⋊C4—22no—
354C4⋊C4—112no—
355C4⋊C4—114no—
356C4⋊C4—228no—
357C4⋊C4—228no—
358C4⋊C4—228no—
359C4⋊C4—221no—
360C4⋊C4—222no—
361C4⋊C4—222no—
362C4⋊C4—222no—
363C4⋊C4—222no—
364C4⋊C4—222no—
365C4⋊C4—222no—
366C4⋊C4—222no—
367C4⋊C4—441no—
368C4⋊C4—441no—
369C4⋊C4C2×D4412yes—
370C42—22no—
371C42—22no—
372C42—228no—
373C42—222no—
374C42—222no—
375C42C2×D4411yescharacteristic
376C42D4×D1111yescharacteristic
377C42D4×D1111yescharacteristic
378C42C23×D1111yescharacteristic
379C11C2×#165311yescharacteristic, complemented, Sylow
380C23#6693511yescharacteristic
381Q8—22no—
382Q8—24no—
383Q8—222no—
384Q8—222no—
385Q8—442no—
386Q8—442no—
387Q8—442no—
388Q8—444no—
389Q8—442no—
390Q8—442no—
391Q8—882no—
392Q8C2×#431414yes—
393C2×C4—22no—
394C2×C4—24no—
395C2×C4—22no—
396C2×C4—22no—
397C2×C4—42no—
398C2×C4—222no—
399C2×C4—224no—
400C2×C4—222no—
401C2×C4—442no—
402C2×C4—444no—
403C2×C4—442no—
404C2×C4—442no—
405C2×C4—882no—
406C2×C4#6693511yescharacteristic
407C2×C4#6693511yescharacteristic
408C2×C4#6693511yescharacteristic
409C2×C4C2×#431412yes—
410C2×C4#6696212yes—
411C2×C4#6696912yes—
412C2×C4#6697112yes—
413C2×C4C22×D4411yescharacteristic
414C2×C4C2×D4×D1111yescharacteristic
415C2×C4C2×D4×D1111yescharacteristic
416C8—24no—
417C8—42no—
418C8—442no—
419C22#1062235112yes—
420C22#1062242312yes—
421C22#1062243912yes—
422C22C2×#6693511yescharacteristic
423C4—24no—
424C4—21no—
425C4—21no—
426C4—42no—
427C4—442no—
428C4—444no—
429C4—442no—
430C4—882no—
431C4#1062235112yes—
432C4#1062242312yes—
433C4C22×#431411yescharacteristic
434C4C2×#6696211yescharacteristic
435C4C2×#6696911yescharacteristic
436C4C2×#6697111yescharacteristic
437C2#1306789514yesdirect product factor
438C2C2×#1062235111yescharacteristic
439C2C2×#1062242311yescharacteristic
440C2C2×#1062243911yescharacteristic
subgroupG/H
centerC23#66935
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC2×C11×Q8⋊C8C2
socle, prime radicalC23×C11#120
hypercenterC2×Q8⋊C8D11
hypocenterC11C2×#1653
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×Q8⋊C8

Complements

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

NH ≅ G/Ntype
5. #13067895C2direct (N × H)
315. C2×C11#1653semidirect
379. C11C2×#1653semidirect
437. C2#13067895direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231012
C2×#106222932
C2×#106224642
C2×#106226442
#130678952
C2×#106221202
C2×#106220942
C2×C11×Q8⋊C82
C2×#165311