Finite Group Databasebeta

← C2×#13067865 #14729573

Subgroups — C2×#13067865 #14729573

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×#10622691C211yesmaximal, characteristic, complemented
2C2×#10622620C211yesmaximal, characteristic
3C2×#10622644C211yesmaximal, characteristic, complemented
4#13067865C218yesmaximal, direct product factor
5C2×#10622185C211yesmaximal, characteristic, complemented
6C2×Q8⋊(C11⋊C8)C211yesmaximal, characteristic, complemented
7C2×D4⋊(C11⋊C8)C211yesmaximal, characteristic
8C2×D4×Q8×C11C211yesmaximal, characteristic
9C23×Q8×C11—21no—
10D4×Q8×C11—22no—
11D4×Q8×C11—22no—
12D4×Q8×C11—22no—
13D4×Q8×C11C2214yes—
14C2×C11×C4⋊Q8—21no—
15C2×C11×C4⋊Q8C2211yescharacteristic
16C2×C11×C22⋊Q8—21no—
17C2×C11×C22⋊Q8—22no—
18C2×C4×Q8×C11C2211yescharacteristic
19C2×C4×D4×C11—21no—
20C2×C4×D4×C11C2211yescharacteristic
21C22×#4326—21no—
22C2×#66922C2211yescharacteristic
23C2×#66896—21no—
24#10622691—22no—
25#10622691C2214yescomplemented
26#10622644—22no—
27#10622644C2214yescomplemented
28#10622620—22no—
29#10622620C2214yes—
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
37Q8⋊(C11⋊C8)C2214yescomplemented
38D4⋊(C11⋊C8)C2214yes—
39C22×Q8×C11—22no—
40C22×Q8×C11—24no—
41C22×Q8×C11—24no—
42C22×Q8×C11—21no—
43C22×Q8×C11—44no—
44C22×Q8×C11—44no—
45C22×Q8×C11D411yescharacteristic
46C22×D4×C11D411yescharacteristic
47C23×C4×C11—22no—
48C23×C4×C11—21no—
49C22×Dic22—21no—
50C11×C4⋊Q8—24no—
51C11×C4⋊Q8—24no—
52C11×C4⋊Q8—21no—
53C11×C4⋊Q8—21no—
54C11×C4⋊Q8D412yes—
55C11×C4⋊Q8C2312yes—
56C11×C22⋊Q8—24no—
57C11×C22⋊Q8—28no—
58C11×C22⋊Q8—24no—
59C11×C22⋊Q8—28no—
60C4×Q8×C11—21no—
61C4×Q8×C11—21no—
62C4×Q8×C11D412yes—
63C4×Q8×C11C2312yes—
64C4×D4×C11—24no—
65C4×D4×C11—24no—
66C4×D4×C11—21no—
67C4×D4×C11—21no—
68C4×D4×C11D412yes—
69C4×D4×C11C2312yes—
70C2×C11×C4⋊C4—22no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4D411yescharacteristic
74C2×C11×C4⋊C4D412yes—
75C2×C11×C4⋊C4D411yescharacteristic
76C2×C11×C22⋊C4—22no—
77C2×C11×C22⋊C4—21no—
78C2×C42×C11—21no—
79C2×C42×C11C2311yescharacteristic
80C2×#4326—24no—
81C2×#4326—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×#1649—111nomaximal, Sylow
102C24×C11—21no—
103C2×Q8×C11—28no—
104C2×Q8×C11—21no—
105C2×Q8×C11—22no—
106C2×Q8×C11—22no—
107C2×Q8×C11—22no—
108C2×Q8×C11—48no—
109C2×Q8×C11—48no—
110C2×Q8×C11—416no—
111C2×Q8×C11—48no—
112C2×Q8×C11—42no—
113C2×Q8×C11—42no—
114C2×Q8×C11D814yes—
115C2×Q8×C11C2×D412yes—
116C2×D4×C11—21no—
117C2×D4×C11—22no—
118C2×D4×C11Q1614yescomplemented
119C2×D4×C11C2×D412yes—
120C22×C4×C11—21no—
121C22×C4×C11—28no—
122C22×C4×C11—21no—
123C22×C4×C11—22no—
124C22×C4×C11—21no—
125C22×C4×C11—22no—
126C22×C4×C11—22no—
127C22×C4×C11—48no—
128C22×C4×C11—42no—
129C22×C4×C11—42no—
130C22×C4×C11C2×D411yescharacteristic
131C22×C4×C11C2×D411yescharacteristic
132C22×C4×C11C2×D411yescharacteristic
133C22×Dic11—41no—
134C2×Dic22—22no—
135C2×Dic22—41no—
136C2×Dic22—42no—
137C2×Dic22—42no—
138C11×C4⋊C4—28no—
139C11×C4⋊C4—22no—
140C11×C4⋊C4—22no—
141C11×C4⋊C4—21no—
142C11×C4⋊C4—21no—
143C11×C4⋊C4—22no—
144C11×C4⋊C4—22no—
145C11×C4⋊C4—22no—
146C11×C4⋊C4C2×D412yes—
147C11×C4⋊C4C2×D414yes—
148C11×C4⋊C4C2×D412yes—
149C11×C22⋊C4—28no—
150C11×C22⋊C4—22no—
151C11×C22⋊C4—22no—
152C42×C11—22no—
153C42×C11—22no—
154C42×C11C2×D411yescharacteristic
155C42×C11C2×D411yescharacteristic
156C42×C11C2×D411yescharacteristic
157C42×C11C2411yescharacteristic
158#4326—48no—
159C4⋊Dic11—22no—
160C4⋊Dic11—22no—
161C4⋊Dic11—41no—
162C4⋊Dic11—41no—
163C2×C11⋊C8—24no—
164C2×C11⋊C8—22no—
165C2×C11⋊C8—22no—
166C2×C11⋊C8—22no—
167C2×C11⋊C8—42no—
168C2×C11⋊C8—42no—
169C2×D4×Q8D1111yescharacteristic
170C2×#500—111no—
171C2×#474—111no—
172C2×#462—111no—
173#1649—118no—
174C2×#332—111no—
175C2×Q8⋊C8—111no—
176C2×D4⋊C8—111no—
177C23×C11—22no—
178C23×C11—24no—
179C23×C11—42no—
180C23×C11—42no—
181C23×C11#12011yescharacteristic
182Q8×C11—22no—
183Q8×C11—24no—
184Q8×C11—416no—
185Q8×C11—42no—
186Q8×C11—42no—
187Q8×C11—44no—
188Q8×C11C2×D814yes—
189D4×C11—22no—
190D4×C11—24no—
191D4×C11C2×Q1614yescomplemented
192C2×C4×C11—22no—
193C2×C4×C11—24no—
194C2×C4×C11—22no—
195C2×C4×C11—22no—
196C2×C4×C11—24no—
197C2×C4×C11—22no—
198C2×C4×C11—416no—
199C2×C4×C11—44no—
200C2×C4×C11—42no—
201C2×C4×C11—42no—
202C2×C4×C11—42no—
203C2×C4×C11—42no—
204C2×C4×C11—44no—
205C2×C4×C11#12011yescharacteristic
206C2×C4×C11#12011yescharacteristic
207C2×C4×C11#12011yescharacteristic
208C2×C4×C11C2×D812yes—
209C2×C4×C11C2×Q1612yes—
210C2×C4×C11AGL(1,ℤ/8)12yes—
211C2×C4×C11#13712yes—
212C2×C4×C11C22×D411yescharacteristic
213C2×C4×C11C22×D411yescharacteristic
214C2×C4×C11C22×D411yescharacteristic
215C2×Dic11—42no—
216C2×Dic11—82no—
217Dic22—42no—
218Dic22—42no—
219Dic22—82no—
220C11⋊C8—24no—
221C11⋊C8—42no—
222C11⋊C8—42no—
223C23×Q8—21no—
224C22×Q16—221no—
225D4×Q8—22no—
226D4×Q8—22no—
227D4×Q8—22no—
228D4×Q8C2×D1114yes—
229C2×C4⋊Q8—21no—
230C2×C4⋊Q8—111no—
231C2×C4⋊Q8C2×D1111yescharacteristic
232C2×C22⋊Q8—21no—
233C2×C22⋊Q8—22no—
234C2×C4×Q8C2×D1111yescharacteristic
235C2×C4×D4—21no—
236C2×C4×D4C2×D1111yescharacteristic
237#500—114no—
238#500—222no—
239#474—114no—
240#474—222no—
241#462—114no—
242#462—222no—
243C2×#107—222no—
244C2×#107—221no—
245C2×C4⋊C8—111no—
246C2×C4⋊C8—111no—
247C2×#103—221no—
248C2×#102—221no—
249C2×C4×C8—111no—
250#332—114no—
251Q8⋊C8—114no—
252D4⋊C8—114no—
253C22×C11—24no—
254C22×C11—48no—
255C22×C11—42no—
256C22×C11—42no—
257C22×C11#44712yes—
258C22×C11#45112yes—
259C22×C11#45612yes—
260C22×C11C2×#12011yescharacteristic
261C4×C11—24no—
262C4×C11—21no—
263C4×C11—21no—
264C4×C11—44no—
265C4×C11—42no—
266C4×C11—42no—
267C4×C11#44712yes—
268C4×C11#45112yes—
269C4×C11C22×D811yescharacteristic
270C4×C11C22×Q1611yescharacteristic
271C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
272C4×C11C2×#13711yescharacteristic
273Dic11—82no—
274C22×Q8—22no—
275C22×Q8—24no—
276C22×Q8—24no—
277C22×Q8—21no—
278C22×Q8—44no—
279C22×Q8—44no—
280C22×Q8—221no—
281C22×Q8C22⋊D1111yescharacteristic
282C22×D4C22⋊D1111yescharacteristic
283C23×C4—22no—
284C23×C4—21no—
285C2×Q16—224no—
286C2×Q16—444no—
287C22×C8—221no—
288C22×C8—221no—
289C22×C8—221no—
290C4⋊Q8—24no—
291C4⋊Q8—24no—
292C4⋊Q8—21no—
293C4⋊Q8—21no—
294C4⋊Q8—112no—
295C4⋊Q8—221no—
296C4⋊Q8—221no—
297C4⋊Q8—221no—
298C4⋊Q8C22⋊D1112yes—
299C4⋊Q8C22×D1112yes—
300C22⋊Q8—24no—
301C22⋊Q8—28no—
302C22⋊Q8—24no—
303C22⋊Q8—28no—
304C4×Q8—21no—
305C4×Q8—21no—
306C4×Q8C22⋊D1112yes—
307C4×Q8C22×D1112yes—
308C4×D4—24no—
309C4×D4—24no—
310C4×D4—21no—
311C4×D4—21no—
312C4×D4C22⋊D1112yes—
313C4×D4C22×D1112yes—
314C2×C4⋊C4—22no—
315C2×C4⋊C4—21no—
316C2×C4⋊C4—21no—
317C2×C4⋊C4—221no—
318C2×C4⋊C4—221no—
319C2×C4⋊C4C22⋊D1111yescharacteristic
320C2×C4⋊C4C22⋊D1111yescharacteristic
321C2×C4⋊C4C22⋊D1112yes—
322C2×C22⋊C4—22no—
323C2×C22⋊C4—21no—
324C2×C42—21no—
325C2×C42C22×D1111yescharacteristic
326#107—224no—
327#107—228no—
328C4⋊C8—112no—
329C4⋊C8—112no—
330C4⋊C8—221no—
331C4⋊C8—221no—
332#103—224no—
333#102—224no—
334C4×C8—112no—
335C4×C8—221no—
336C2×C11—44no—
337C2×C11#164914yescomplemented
338C2×C11C2×#44711yescharacteristic
339C2×C11C2×#45111yescharacteristic
340C2×C11C2×#45611yescharacteristic
341C24—21no—
342C2×Q8—28no—
343C2×Q8—22no—
344C2×Q8—21no—
345C2×Q8—22no—
346C2×Q8—22no—
347C2×Q8—48no—
348C2×Q8—48no—
349C2×Q8—416no—
350C2×Q8—48no—
351C2×Q8—42no—
352C2×Q8—42no—
353C2×Q8—222no—
354C2×Q8—441no—
355C2×Q8—442no—
356C2×Q8—442no—
357C2×Q8#432314yes—
358C2×Q8C2×C22⋊D1112yes—
359C2×D4—22no—
360C2×D4—21no—
361C2×D4#432614yescomplemented
362C2×D4C2×C22⋊D1112yes—
363C22×C4—21no—
364C22×C4—28no—
365C22×C4—21no—
366C22×C4—22no—
367C22×C4—21no—
368C22×C4—22no—
369C22×C4—22no—
370C22×C4—48no—
371C22×C4—42no—
372C22×C4—42no—
373C22×C4—441no—
374C22×C4C2×C22⋊D1111yescharacteristic
375C22×C4C2×C22⋊D1111yescharacteristic
376C22×C4C2×C22⋊D1111yescharacteristic
377Q16—448no—
378C2×C8—224no—
379C2×C8—222no—
380C2×C8—222no—
381C2×C8—222no—
382C2×C8—442no—
383C2×C8—442no—
384C4⋊C4—28no—
385C4⋊C4—22no—
386C4⋊C4—22no—
387C4⋊C4—21no—
388C4⋊C4—21no—
389C4⋊C4—22no—
390C4⋊C4—22no—
391C4⋊C4—22no—
392C4⋊C4—222no—
393C4⋊C4—222no—
394C4⋊C4—441no—
395C4⋊C4—441no—
396C4⋊C4C2×C22⋊D1112yes—
397C4⋊C4C2×C22⋊D1112yes—
398C4⋊C4C2×C22⋊D1114yes—
399C22⋊C4—28no—
400C22⋊C4—22no—
401C22⋊C4—22no—
402C42—22no—
403C42—22no—
404C42C2×C22⋊D1111yescharacteristic
405C42C2×C22⋊D1111yescharacteristic
406C42C2×C22⋊D1111yescharacteristic
407C42C23×D1111yescharacteristic
408C11C2×#164911yescharacteristic, complemented, Sylow
409C23—24no—
410C23—22no—
411C23—42no—
412C23—42no—
413C23#6700611yescharacteristic
414Q8—22no—
415Q8—24no—
416Q8—416no—
417Q8—42no—
418Q8—42no—
419Q8—44no—
420Q8—442no—
421Q8—442no—
422Q8—882no—
423Q8C2×#432314yes—
424D4—22no—
425D4—24no—
426D4C2×#432614yescomplemented
427C2×C4—24no—
428C2×C4—22no—
429C2×C4—22no—
430C2×C4—22no—
431C2×C4—24no—
432C2×C4—22no—
433C2×C4—416no—
434C2×C4—44no—
435C2×C4—42no—
436C2×C4—42no—
437C2×C4—42no—
438C2×C4—42no—
439C2×C4—44no—
440C2×C4—442no—
441C2×C4—882no—
442C2×C4C2×#432312yes—
443C2×C4#6698512yes—
444C2×C4#6699512yes—
445C2×C4C2×#432612yes—
446C2×C4#6700611yescharacteristic
447C2×C4#6700611yescharacteristic
448C2×C4#6700611yescharacteristic
449C2×C4C22×C22⋊D1111yescharacteristic
450C2×C4C22×C22⋊D1111yescharacteristic
451C2×C4C22×C22⋊D1111yescharacteristic
452C8—224no—
453C8—442no—
454C8—442no—
455C22—24no—
456C22—42no—
457C22—48no—
458C22—42no—
459C22#1062283012yes—
460C22#1062284112yes—
461C22#1062285912yes—
462C22C2×#6700611yescharacteristic
463C4—24no—
464C4—21no—
465C4—21no—
466C4—44no—
467C4—42no—
468C4—42no—
469C4—882no—
470C4#1062283012yes—
471C4#1062284112yes—
472C4C22×#432311yescharacteristic
473C4C2×#6698511yescharacteristic
474C4C2×#6699511yescharacteristic
475C4C22×#432611yescharacteristic
476C2—44no—
477C2#1306786514yesdirect product factor
478C2C2×#1062283011yescharacteristic
479C2C2×#1062284111yescharacteristic
480C2C2×#1062285911yescharacteristic
subgroupG/H
centerC23#67006
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC2×D4×Q8×C11C2
socleC23×C11#120
prime radicalC22×D4×C11D4
hypercenterC2×D4×Q8D11
hypocenterC11C2×#1649
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×D4×Q8

Complements

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

NH ≅ G/Ntype
1. C2×#10622691C2semidirect
3. C2×#10622644C2semidirect
4. #13067865C2direct (N × H)
5. C2×#10622185C2semidirect
6. C2×Q8⋊(C11⋊C8)C2semidirect
25. #10622691C22semidirect
27. #10622644C22semidirect
36. #10622185C22semidirect
37. Q8⋊(C11⋊C8)C22semidirect
118. C2×D4×C11Q16semidirect
191. D4×C11C2×Q16semidirect
337. C2×C11#1649semidirect
361. C2×D4#4326semidirect
408. C11C2×#1649semidirect
426. D4C2×#4326semidirect
477. C2#13067865direct (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×#106226442
#130678652
C2×#106221852
C2×Q8⋊(C11⋊C8)2
C2×D4⋊(C11⋊C8)2
C2×D4×Q8×C112
C2×#164911