Finite Group Databasebeta

← C2×#13067136 #14720894

Subgroups — C2×#13067136 #14720894

Order 2816.

1554 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622820C211yesmaximal, characteristic
2C2×C4×C22⋊Dic11C211yesmaximal, characteristic
3#13067136C218yesmaximal, direct product factor
4C2×#10622176C214yesmaximal, complemented
5C22×C11×C22⋊Q8C211yesmaximal, characteristic
6C23×Q8×C11C411yescharacteristic, complemented
7C24×C4×C11C2211yescharacteristic
8C2×C11×C22⋊Q8—21no—
9C2×C11×C22⋊Q8—22no—
10C2×C11×C22⋊Q8—21no—
11C2×C11×C22⋊Q8—22no—
12C2×C11×C22⋊Q8C412yescomplemented
13C2×C11×C22⋊Q8C414yescomplemented
14C2×C11×C22⋊Q8C2212yes—
15C2×C11×C22⋊Q8C2214yes—
16C22×C11×C4⋊C4—21no—
17C22×C11×C4⋊C4C411yescharacteristic, complemented
18C22×C11×C22⋊C4—21no—
19C22×C22⋊Dic11—21no—
20C22×C4×Dic11—21no—
21C22×#4318—21no—
22C4×C22⋊Dic11—22no—
23C4×C22⋊Dic11C2214yes—
24C2×C11⋊#95C2212yes—
25#10622820—22no—
26#10622820C2214yes—
27C2×C22⋊(C11⋊C8)—21no—
28C2×C22⋊(C11⋊C8)C2212yes—
29#10622176C22116yescomplemented
30C25×C11D411yescharacteristic
31C22×Q8×C11—21no—
32C22×Q8×C11—22no—
33C22×Q8×C11—44no—
34C22×Q8×C11C2×C412yes—
35C22×Q8×C11C2×C414yescomplemented
36C23×C4×C11—21no—
37C23×C4×C11—21no—
38C23×C4×C11—44no—
39C23×C4×C11C2×C411yescharacteristic
40C23×C4×C11C2×C412yes—
41C23×C4×C11C2×C411yescharacteristic
42C23×C4×C11D411yescharacteristic
43C23×C4×C11D411yescharacteristic
44C23×C4×C11D412yes—
45C23×C4×C11D411yescharacteristic
46C23×C4×C11D412yes—
47C23×C4×C11C2311yescharacteristic
48C23×C4×C11C2312yes—
49C23×Dic11—22no—
50C11×C22⋊Q8—24no—
51C11×C22⋊Q8—24no—
52C11×C22⋊Q8—24no—
53C11×C22⋊Q8—22no—
54C11×C22⋊Q8—24no—
55C11×C22⋊Q8—22no—
56C11×C22⋊Q8—24no—
57C11×C22⋊Q8C2×C414yes—
58C11×C22⋊Q8C2×C418yescomplemented
59C11×C22⋊Q8C2314yes—
60C2×C11×C4⋊C4—24no—
61C2×C11×C4⋊C4—22no—
62C2×C11×C4⋊C4—22no—
63C2×C11×C4⋊C4—21no—
64C2×C11×C4⋊C4—22no—
65C2×C11×C4⋊C4—24no—
66C2×C11×C4⋊C4C2×C412yes—
67C2×C11×C4⋊C4C2×C414yescomplemented
68C2×C11×C22⋊C4—24no—
69C2×C11×C22⋊C4—22no—
70C2×C11×C22⋊C4—22no—
71C2×C11×C22⋊C4—24no—
72C2×C22⋊Dic11—28no—
73C2×C22⋊Dic11—24no—
74C2×C4×Dic11—24no—
75C2×C4×Dic11—44no—
76C2×#4318—24no—
77C2×#4318—44no—
78C22×C11⋊C8—22no—
79C11⋊#95—22no—
80C11⋊#95C2314yes—
81C22⋊(C11⋊C8)—24no—
82C22⋊(C11⋊C8)—22no—
83C22⋊(C11⋊C8)C2314yes—
84C2×#1508—111nomaximal, Sylow
85C24×C11—24no—
86C24×C11—24no—
87C24×C11—42no—
88C24×C11C22⋊C411yescharacteristic
89C24×C11C22⋊C412yes—
90C24×C11C22⋊C411yescharacteristic
91C24×C11C2×D412yes—
92C24×C11C2×D411yescharacteristic
93C2×Q8×C11—22no—
94C2×Q8×C11—24no—
95C2×Q8×C11—48no—
96C2×Q8×C11—48no—
97C2×Q8×C11—44no—
98C2×Q8×C11—44no—
99C2×Q8×C11C22×C414yes—
100C22×C4×C11—24no—
101C22×C4×C11—24no—
102C22×C4×C11—24no—
103C22×C4×C11—22no—
104C22×C4×C11—24no—
105C22×C4×C11—22no—
106C22×C4×C11—24no—
107C22×C4×C11—44no—
108C22×C4×C11—44no—
109C22×C4×C11—44no—
110C22×C4×C11—44no—
111C22×C4×C11—42no—
112C22×C4×C11—42no—
113C22×C4×C11—42no—
114C22×C4×C11—44no—
115C22×C4×C11—44no—
116C22×C4×C11C22⋊C411yescharacteristic
117C22×C4×C11C22⋊C412yes—
118C22×C4×C11C22⋊C412yes—
119C22×C4×C11C22⋊C412yes—
120C22×C4×C11C22⋊C412yes—
121C22×C4×C11C22⋊C412yes—
122C22×C4×C11C22⋊C411yescharacteristic
123C22×C4×C11C22×C411yescharacteristic
124C22×C4×C11C22×C412yes—
125C22×C4×C11C22×C411yescharacteristic
126C22×C4×C11C22×C412yes—
127C22×C4×C11C2×D412yes—
128C22×C4×C11C2×D411yescharacteristic
129C22×C4×C11C2×D412yes—
130C22×C4×C11C2×D411yescharacteristic
131C22×C4×C11C2×D412yes—
132C22×C4×C11C2×D411yescharacteristic
133C22×C4×C11C2411yescharacteristic
134C22×Dic11—28no—
135C22×Dic11—24no—
136C22×Dic11—44no—
137C22×Dic11—44no—
138C11×C4⋊C4—24no—
139C11×C4⋊C4—28no—
140C11×C4⋊C4—22no—
141C11×C4⋊C4—24no—
142C11×C4⋊C4—24no—
143C11×C4⋊C4C22×C414yes—
144C11×C22⋊C4—24no—
145C11×C22⋊C4—28no—
146C11×C22⋊C4—24no—
147C22⋊Dic11—216no—
148C4×Dic11—48no—
149#4318—48no—
150C2×C11⋊C8—24no—
151C2×C11⋊C8—44no—
152C22×C22⋊Q8D1111yescharacteristic
153C2×#407—111no—
154C2×C4×C22⋊C4—111no—
155#1508—118no—
156C2×#328—114no—
157C23×C11—22no—
158C23×C11—22no—
159C23×C11—22no—
160C23×C11—22no—
161C23×C11—24no—
162C23×C11—22no—
163C23×C11—24no—
164C23×C11—22no—
165C23×C11—24no—
166C23×C11—24no—
167C23×C11—22no—
168C23×C11—42no—
169C23×C11—42no—
170C23×C11—416no—
171C23×C11#10414yes—
172C23×C11C2×C22⋊C412yes—
173C23×C11C2×C22⋊C411yescharacteristic
174C23×C11C2×C22⋊C412yes—
175C23×C11C2×C22⋊C411yescharacteristic
176C23×C11#13714yes—
177C23×C11C22×D411yescharacteristic
178Q8×C11—44no—
179Q8×C11—44no—
180Q8×C11—48no—
181C2×C4×C11—22no—
182C2×C4×C11—22no—
183C2×C4×C11—22no—
184C2×C4×C11—24no—
185C2×C4×C11—24no—
186C2×C4×C11—24no—
187C2×C4×C11—24no—
188C2×C4×C11—24no—
189C2×C4×C11—24no—
190C2×C4×C11—24no—
191C2×C4×C11—24no—
192C2×C4×C11—42no—
193C2×C4×C11—42no—
194C2×C4×C11—41no—
195C2×C4×C11—42no—
196C2×C4×C11—41no—
197C2×C4×C11—42no—
198C2×C4×C11—41no—
199C2×C4×C11—41no—
200C2×C4×C11—48no—
201C2×C4×C11—44no—
202C2×C4×C11—48no—
203C2×C4×C11—44no—
204C2×C4×C11#9914yes—
205C2×C4×C11C2×C22⋊C411yescharacteristic
206C2×C4×C11C2×C22⋊C412yes—
207C2×C4×C11C2×C22⋊C411yescharacteristic
208C2×C4×C11C2×C22⋊C412yes—
209C2×C4×C11C23×C411yescharacteristic
210C2×C4×C11C22×D411yescharacteristic
211C2×Dic11—28no—
212C2×Dic11—44no—
213C2×Dic11—416no—
214C2×Dic11—44no—
215C11⋊C8—44no—
216C23×Q8Dic1111yescharacteristic, complemented
217C24×C4C2×D1111yescharacteristic
218C22×M16—221no—
219C2×C22⋊Q8—21no—
220C2×C22⋊Q8—22no—
221C2×C22⋊Q8—21no—
222C2×C22⋊Q8—22no—
223C2×C22⋊Q8Dic1112yescomplemented
224C2×C22⋊Q8Dic1114yescomplemented
225C2×C22⋊Q8C2×D1112yes—
226C2×C22⋊Q8C2×D1114yes—
227C22×C4⋊C4—21no—
228C22×C4⋊C4Dic1111yescharacteristic, complemented
229C22×C22⋊C4—21no—
230C22×C22⋊C4—221no—
231C22×C42—221no—
232#407—114no—
233#407—222no—
234C2×C22⋊C8—112no—
235C2×C22⋊C8—221no—
236C4×C22⋊C4—114no—
237C4×C22⋊C4—222no—
238C2×#95—112no—
239#328—1116no—
240C22×C11—22no—
241C22×C11—21no—
242C22×C11—21no—
243C22×C11—22no—
244C22×C11—21no—
245C22×C11—21no—
246C22×C11—28no—
247C22×C11—28no—
248C22×C11—22no—
249C22×C11—22no—
250C22×C11—22no—
251C22×C11—48no—
252C22×C11—48no—
253C22×C11—44no—
254C22×C11C2×#9912yes—
255C22×C11#41912yes—
256C22×C11#41912yes—
257C22×C11C2×#10414yes—
258C22×C11C2×#10412yes—
259C22×C11C22×C22⋊C411yescharacteristic
260C22×C11C2×#13712yes—
261C4×C11—21no—
262C4×C11—22no—
263C4×C11—21no—
264C4×C11—21no—
265C4×C11—21no—
266C4×C11—44no—
267C4×C11—44no—
268C4×C11C2×#9914yes—
269Dic11—48no—
270C25C22⋊D1111yescharacteristic
271C22×Q8—22no—
272C22×Q8—21no—
273C22×Q8—44no—
274C22×Q8C2×Dic1112yes—
275C22×Q8C2×Dic1114yescomplemented
276C23×C4—21no—
277C23×C4—21no—
278C23×C4—44no—
279C23×C4—222no—
280C23×C4C2×Dic1111yescharacteristic
281C23×C4C2×Dic1112yes—
282C23×C4C2×Dic1111yescharacteristic
283C23×C4C22⋊D1111yescharacteristic
284C23×C4C22⋊D1111yescharacteristic
285C23×C4C22⋊D1112yes—
286C23×C4C22⋊D1111yescharacteristic
287C23×C4C22⋊D1112yes—
288C23×C4C22×D1111yescharacteristic
289C23×C4C22×D1112yes—
290C2×M16—224no—
291C2×M16—444no—
292C22×C8—222no—
293C22⋊Q8—24no—
294C22⋊Q8—24no—
295C22⋊Q8—24no—
296C22⋊Q8—22no—
297C22⋊Q8—24no—
298C22⋊Q8—22no—
299C22⋊Q8—24no—
300C22⋊Q8C2×Dic1114yes—
301C22⋊Q8C2×Dic1118yescomplemented
302C22⋊Q8C22×D1114yes—
303C2×C4⋊C4—24no—
304C2×C4⋊C4—22no—
305C2×C4⋊C4—22no—
306C2×C4⋊C4—21no—
307C2×C4⋊C4—22no—
308C2×C4⋊C4—24no—
309C2×C4⋊C4C2×Dic1112yes—
310C2×C4⋊C4C2×Dic1114yescomplemented
311C2×C22⋊C4—24no—
312C2×C22⋊C4—22no—
313C2×C22⋊C4—22no—
314C2×C22⋊C4—24no—
315C2×C22⋊C4—228no—
316C2×C22⋊C4—224no—
317C2×C42—224no—
318C2×C42—444no—
319C22⋊C8—114no—
320C22⋊C8—222no—
321C22⋊C8—224no—
322#95—114no—
323#95—222no—
324C2×C11—22no—
325C2×C11—22no—
326C2×C11—24no—
327C2×C11—42no—
328C2×C11#150814yescomplemented
329C2×C11C22×#9911yescharacteristic
330C2×C11C2×#41911yescharacteristic
331C2×C11C22×#10411yescharacteristic
332C24—24no—
333C24—24no—
334C24—42no—
335C24C22⋊Dic1111yescharacteristic
336C24C22⋊Dic1112yes—
337C24C22⋊Dic1111yescharacteristic
338C24C2×C22⋊D1112yes—
339C24C2×C22⋊D1111yescharacteristic
340C2×Q8—22no—
341C2×Q8—24no—
342C2×Q8—48no—
343C2×Q8—48no—
344C2×Q8—44no—
345C2×Q8—44no—
346C2×Q8C22×Dic1114yes—
347C22×C4—24no—
348C22×C4—24no—
349C22×C4—24no—
350C22×C4—24no—
351C22×C4—24no—
352C22×C4—22no—
353C22×C4—22no—
354C22×C4—44no—
355C22×C4—44no—
356C22×C4—44no—
357C22×C4—44no—
358C22×C4—42no—
359C22×C4—42no—
360C22×C4—42no—
361C22×C4—44no—
362C22×C4—44no—
363C22×C4—228no—
364C22×C4—224no—
365C22×C4—444no—
366C22×C4—444no—
367C22×C4C22⋊Dic1112yes—
368C22×C4C22⋊Dic1112yes—
369C22×C4C22⋊Dic1112yes—
370C22×C4C22⋊Dic1111yescharacteristic
371C22×C4C22⋊Dic1112yes—
372C22×C4C22⋊Dic1112yes—
373C22×C4C22⋊Dic1111yescharacteristic
374C22×C4C22×Dic1112yes—
375C22×C4C22×Dic1111yescharacteristic
376C22×C4C22×Dic1111yescharacteristic
377C22×C4C22×Dic1112yes—
378C22×C4C2×C22⋊D1112yes—
379C22×C4C2×C22⋊D1112yes—
380C22×C4C2×C22⋊D1111yescharacteristic
381C22×C4C2×C22⋊D1111yescharacteristic
382C22×C4C2×C22⋊D1112yes—
383C22×C4C2×C22⋊D1111yescharacteristic
384C22×C4C23×D1111yescharacteristic
385M16—448no—
386C2×C8—224no—
387C2×C8—444no—
388C4⋊C4—24no—
389C4⋊C4—28no—
390C4⋊C4—22no—
391C4⋊C4—24no—
392C4⋊C4—24no—
393C4⋊C4C22×Dic1114yes—
394C22⋊C4—24no—
395C22⋊C4—28no—
396C22⋊C4—24no—
397C22⋊C4—2216no—
398C42—448no—
399C11C2×#150811yescharacteristic, complemented, Sylow
400C23—22no—
401C23—22no—
402C23—22no—
403C23—22no—
404C23—24no—
405C23—22no—
406C23—24no—
407C23—22no—
408C23—24no—
409C23—24no—
410C23—22no—
411C23—42no—
412C23—42no—
413C23—416no—
414C23#6690114yes—
415C23#6699514yes—
416C23C2×C22⋊Dic1112yes—
417C23C2×C22⋊Dic1111yescharacteristic
418C23C2×C22⋊Dic1112yes—
419C23C2×C22⋊Dic1111yescharacteristic
420C23C22×C22⋊D1111yescharacteristic
421Q8—44no—
422Q8—44no—
423Q8—48no—
424C2×C4—22no—
425C2×C4—22no—
426C2×C4—22no—
427C2×C4—24no—
428C2×C4—24no—
429C2×C4—24no—
430C2×C4—24no—
431C2×C4—24no—
432C2×C4—24no—
433C2×C4—24no—
434C2×C4—24no—
435C2×C4—42no—
436C2×C4—42no—
437C2×C4—41no—
438C2×C4—42no—
439C2×C4—41no—
440C2×C4—42no—
441C2×C4—41no—
442C2×C4—41no—
443C2×C4—48no—
444C2×C4—44no—
445C2×C4—48no—
446C2×C4—44no—
447C2×C4—228no—
448C2×C4—444no—
449C2×C4—4416no—
450C2×C4—444no—
451C2×C4#6689814yes—
452C2×C4C2×C22⋊Dic1111yescharacteristic
453C2×C4C2×C22⋊Dic1112yes—
454C2×C4C2×C22⋊Dic1111yescharacteristic
455C2×C4C2×C22⋊Dic1112yes—
456C2×C4C23×Dic1111yescharacteristic
457C2×C4C22×C22⋊D1111yescharacteristic
458C8—444no—
459C22—22no—
460C22—21no—
461C22—21no—
462C22—28no—
463C22—28no—
464C22—22no—
465C22—21no—
466C22—21no—
467C22—22no—
468C22—22no—
469C22—22no—
470C22—48no—
471C22—48no—
472C22—44no—
473C22C2×#6689812yes—
474C22#1062283812yes—
475C22#1062283812yes—
476C22C2×#6690114yes—
477C22C2×#6690112yes—
478C22C2×#6699512yes—
479C22C22×C22⋊Dic1111yescharacteristic
480C4—21no—
481C4—21no—
482C4—21no—
483C4—22no—
484C4—21no—
485C4—44no—
486C4—44no—
487C4—448no—
488C4C2×#6689814yes—
489C2—22no—
490C2—22no—
491C2—24no—
492C2—42no—
493C2#1306713614yesdirect product factor
494C2C22×#6689811yescharacteristic
495C2C2×#1062283811yescharacteristic
496C2C22×#6690111yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC22×C11×C22⋊Q8C2
socleC23×C11C2×C22⋊C4
prime radicalC25×C11D4
cosocleC22×C4×C11C24
hypercenterC22×C22⋊Q8D11
hypocenterC11C2×#1508
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C24×C4 ◁ C22×C22⋊Q8

Complements

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

NH ≅ G/Ntype
3. #13067136C2direct (N × H)
4. C2×#10622176C2semidirect
6. C23×Q8×C11C4semidirect
12. C2×C11×C22⋊Q8C4semidirect
13. C2×C11×C22⋊Q8C4semidirect
17. C22×C11×C4⋊C4C4semidirect
29. #10622176C22semidirect
35. C22×Q8×C11C2×C4semidirect
58. C11×C22⋊Q8C2×C4semidirect
67. C2×C11×C4⋊C4C2×C4semidirect
216. C23×Q8Dic11semidirect
223. C2×C22⋊Q8Dic11semidirect
224. C2×C22⋊Q8Dic11semidirect
228. C22×C4⋊C4Dic11semidirect
275. C22×Q8C2×Dic11semidirect
301. C22⋊Q8C2×Dic11semidirect
310. C2×C4⋊C4C2×Dic11semidirect
328. C2×C11#1508semidirect
399. C11C2×#1508semidirect
493. C2#13067136direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106228202
C2×C4×C22⋊Dic112
#130671362
C2×#106221762
C22×C11×C22⋊Q82
C2×#150811