Finite Group Databasebeta

← C2×#13066976 #14719739

Subgroups — C2×#13066976 #14719739

Order 2816.

1770 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622820C211yesmaximal, characteristic, complemented
2C22×C22⋊(C11⋊C8)C211yesmaximal, characteristic, complemented
3#13066976C218yesmaximal, direct product factor
4C2×#10622163C214yesmaximal, complemented
5C22×C11×#121C211yesmaximal, characteristic
6C23×D4×C11C411yescharacteristic
7C23×D4×C11C412yes—
8C24×C4×C11C2211yescharacteristic
9C2×C11×#121—21no—
10C2×C11×#121—21no—
11C2×C11×#121—21no—
12C2×C11×#121—21no—
13C2×C11×#121—22no—
14C2×C11×#121—22no—
15C2×C11×#121C414yes—
16C2×C11×#121C2214yes—
17C22×C11×C4⋊C4C411yescharacteristic
18C22×C11×C22⋊C4C2212yes—
19C22×#4318—21no—
20C23×C11⋊C8—21no—
21#10622820—22no—
22#10622820C2214yescomplemented
23C2×C22⋊(C11⋊C8)—22no—
24C2×C22⋊(C11⋊C8)—21no—
25C2×C22⋊(C11⋊C8)—21no—
26C2×C22⋊(C11⋊C8)C2212yes—
27C2×C22⋊(C11⋊C8)C2212yes—
28C2×C22⋊(C11⋊C8)C2214yescomplemented
29#10622163C22116yescomplemented
30C25×C11C2×C411yescharacteristic
31C25×C11C2×C412yes—
32C22×D4×C11—22no—
33C22×D4×C11—24no—
34C22×D4×C11—22no—
35C22×D4×C11—22no—
36C22×D4×C11—21no—
37C22×D4×C11—21no—
38C22×D4×C11—44no—
39C22×D4×C11—48no—
40C22×D4×C11C2×C414yes—
41C22×D4×C11C2×C418yes—
42C23×C4×C11—44no—
43C23×C4×C11C2×C411yescharacteristic
44C23×C4×C11C2×C412yes—
45C23×C4×C11C2×C412yes—
46C23×C4×C11D411yescharacteristic
47C23×C4×C11D411yescharacteristic
48C23×C4×C11D412yes—
49C23×C4×C11D411yescharacteristic
50C23×C4×C11D411yescharacteristic
51C23×C4×C11D412yes—
52C23×C4×C11C2311yescharacteristic
53C23×C4×C11C2312yes—
54C11×#121—24no—
55C11×#121—24no—
56C11×#121—24no—
57C11×#121—24no—
58C11×#121—24no—
59C11×#121—24no—
60C11×#121—24no—
61C11×#121—24no—
62C2×C11×C4⋊C4—22no—
63C2×C11×C4⋊C4—21no—
64C2×C11×C4⋊C4—21no—
65C2×C11×C4⋊C4C2×C414yes—
66C2×C11×C22⋊C4—22no—
67C2×C11×C22⋊C4—22no—
68C2×C11×C22⋊C4—22no—
69C2×C11×C22⋊C4—22no—
70C2×C11×C22⋊C4C2×C414yes—
71C2×C11×C22⋊C4C2314yes—
72C2×#4318—24no—
73C2×#4318—44no—
74C22×C11⋊C8—22no—
75C22×C11⋊C8—24no—
76C22×C11⋊C8—22no—
77C22×C11⋊C8—44no—
78C22⋊(C11⋊C8)—22no—
79C22⋊(C11⋊C8)—24no—
80C22⋊(C11⋊C8)—24no—
81C22⋊(C11⋊C8)—22no—
82C22⋊(C11⋊C8)C2314yes—
83C22⋊(C11⋊C8)C2314yes—
84C2×#1471—111nomaximal, Sylow
85C24×C11—24no—
86C24×C11—24no—
87C24×C11—22no—
88C24×C11—22no—
89C24×C11—28no—
90C24×C11—42no—
91C24×C11—44no—
92C24×C11—44no—
93C24×C11C22⋊C411yescharacteristic
94C24×C11C22⋊C412yes—
95C24×C11C22⋊C411yescharacteristic
96C24×C11C22×C412yes—
97C24×C11C22×C411yescharacteristic
98C24×C11C22×C414yes—
99C2×D4×C11—28no—
100C2×D4×C11—28no—
101C2×D4×C11—24no—
102C2×D4×C11—24no—
103C2×D4×C11—44no—
104C2×D4×C11—48no—
105C2×D4×C11—48no—
106C2×D4×C11—416no—
107C2×D4×C11—48no—
108C2×D4×C11—48no—
109C2×D4×C11—416no—
110C2×D4×C11—44no—
111C22×C4×C11—24no—
112C22×C4×C11—24no—
113C22×C4×C11—24no—
114C22×C4×C11—22no—
115C22×C4×C11—22no—
116C22×C4×C11—44no—
117C22×C4×C11—44no—
118C22×C4×C11—44no—
119C22×C4×C11—44no—
120C22×C4×C11—42no—
121C22×C4×C11—42no—
122C22×C4×C11—42no—
123C22×C4×C11—44no—
124C22×C4×C11C22⋊C411yescharacteristic
125C22×C4×C11C22⋊C412yes—
126C22×C4×C11C22⋊C412yes—
127C22×C4×C11C22⋊C412yes—
128C22×C4×C11C22⋊C412yes—
129C22×C4×C11C22⋊C412yes—
130C22×C4×C11C22⋊C411yescharacteristic
131C22×C4×C11C22×C412yes—
132C22×C4×C11C22×C414yes—
133C22×C4×C11C22×C411yescharacteristic
134C22×C4×C11C2×D411yescharacteristic
135C22×C4×C11C2×D411yescharacteristic
136C22×C4×C11C2×D412yes—
137C22×C4×C11C2×D412yes—
138C22×C4×C11C2×D411yescharacteristic
139C22×C4×C11C2×D411yescharacteristic
140C22×C4×C11C2×D412yes—
141C22×C4×C11C2×D412yes—
142C22×C4×C11C2411yescharacteristic
143C11×C4⋊C4—24no—
144C11×C4⋊C4—24no—
145C11×C22⋊C4—24no—
146C11×C22⋊C4—24no—
147C11×C22⋊C4—24no—
148C11×C22⋊C4—24no—
149#4318—48no—
150C2×C11⋊C8—24no—
151C2×C11⋊C8—24no—
152C2×C11⋊C8—44no—
153C2×C11⋊C8—48no—
154C2×C11⋊C8—44no—
155C22×#121D1111yescharacteristic
156C2×#407—111no—
157C22×C22⋊C8—111no—
158#1471—118no—
159C2×#323—114no—
160C23×C11—22no—
161C23×C11—22no—
162C23×C11—22no—
163C23×C11—22no—
164C23×C11—24no—
165C23×C11—24no—
166C23×C11—22no—
167C23×C11—22no—
168C23×C11—24no—
169C23×C11—22no—
170C23×C11—24no—
171C23×C11—24no—
172C23×C11—28no—
173C23×C11—42no—
174C23×C11—42no—
175C23×C11—416no—
176C23×C11—44no—
177C23×C11—44no—
178C23×C11—44no—
179C23×C11—44no—
180C23×C11—44no—
181C23×C11—44no—
182C23×C11—44no—
183C23×C11—44no—
184C23×C11—816no—
185C23×C11#10014yes—
186C23×C11C2×C22⋊C412yes—
187C23×C11C2×C22⋊C411yescharacteristic
188C23×C11C2×C22⋊C412yes—
189C23×C11C2×C22⋊C411yescharacteristic
190C23×C11#13114yes—
191C23×C11C23×C411yescharacteristic
192D4×C11—48no—
193D4×C11—416no—
194D4×C11—416no—
195D4×C11—48no—
196C2×C4×C11—22no—
197C2×C4×C11—22no—
198C2×C4×C11—22no—
199C2×C4×C11—24no—
200C2×C4×C11—24no—
201C2×C4×C11—24no—
202C2×C4×C11—24no—
203C2×C4×C11—24no—
204C2×C4×C11—24no—
205C2×C4×C11—24no—
206C2×C4×C11—42no—
207C2×C4×C11—42no—
208C2×C4×C11—41no—
209C2×C4×C11—41no—
210C2×C4×C11—41no—
211C2×C4×C11—42no—
212C2×C4×C11—42no—
213C2×C4×C11—41no—
214C2×C4×C11—44no—
215C2×C4×C11—44no—
216C2×C4×C11—44no—
217C2×C4×C11#9914yes—
218C2×C4×C11C2×C22⋊C411yescharacteristic
219C2×C4×C11C2×C22⋊C411yescharacteristic
220C2×C4×C11C2×C22⋊C412yes—
221C2×C4×C11C2×C22⋊C412yes—
222C2×C4×C11C22×D411yescharacteristic
223C2×C4×C11C22×D411yescharacteristic
224C11⋊C8—44no—
225C11⋊C8—44no—
226C23×D4Dic1111yescharacteristic
227C23×D4Dic1112yes—
228C24×C4C2×D1111yescharacteristic
229C22×M16—221no—
230C23×C8—221no—
231C2×#121—21no—
232C2×#121—21no—
233C2×#121—22no—
234C2×#121—21no—
235C2×#121—21no—
236C2×#121—22no—
237C2×#121Dic1114yes—
238C2×#121C2×D1114yes—
239C22×C4⋊C4Dic1111yescharacteristic
240C22×C22⋊C4C2×D1112yes—
241#407—114no—
242#407—222no—
243C2×C22⋊C8—112no—
244C2×C22⋊C8—114no—
245C2×C22⋊C8—112no—
246C2×C22⋊C8—222no—
247C2×C22⋊C8—221no—
248C2×C22⋊C8—221no—
249#323—1116no—
250C22×C11—22no—
251C22×C11—21no—
252C22×C11—21no—
253C22×C11—22no—
254C22×C11—21no—
255C22×C11—21no—
256C22×C11—28no—
257C22×C11—28no—
258C22×C11—22no—
259C22×C11—22no—
260C22×C11—22no—
261C22×C11—48no—
262C22×C11—48no—
263C22×C11—44no—
264C22×C11—44no—
265C22×C11—44no—
266C22×C11—44no—
267C22×C11—88no—
268C22×C11—88no—
269C22×C11—88no—
270C22×C11#40812yes—
271C22×C11#40812yes—
272C22×C11C2×#9912yes—
273C22×C11C2×#10014yes—
274C22×C11C2×#10012yes—
275C22×C11C22×C22⋊C411yescharacteristic
276C22×C11C2×#13112yes—
277C4×C11—21no—
278C4×C11—21no—
279C4×C11—22no—
280C4×C11—21no—
281C4×C11—21no—
282C4×C11—44no—
283C4×C11C2×#9914yes—
284C25C2×Dic1111yescharacteristic
285C25C2×Dic1112yes—
286C22×D4—24no—
287C22×D4—22no—
288C22×D4—22no—
289C22×D4—22no—
290C22×D4—21no—
291C22×D4—21no—
292C22×D4—44no—
293C22×D4—48no—
294C22×D4C2×Dic1114yes—
295C22×D4C2×Dic1118yes—
296C23×C4—44no—
297C23×C4C2×Dic1111yescharacteristic
298C23×C4C2×Dic1112yes—
299C23×C4C2×Dic1112yes—
300C23×C4C22⋊D1111yescharacteristic
301C23×C4C22⋊D1111yescharacteristic
302C23×C4C22⋊D1112yes—
303C23×C4C22⋊D1111yescharacteristic
304C23×C4C22⋊D1111yescharacteristic
305C23×C4C22⋊D1112yes—
306C23×C4C22×D1111yescharacteristic
307C23×C4C22×D1112yes—
308C2×M16—224no—
309C2×M16—444no—
310C22×C8—224no—
311C22×C8—222no—
312C22×C8—222no—
313C22×C8—444no—
314#121—24no—
315#121—24no—
316#121—24no—
317#121—24no—
318#121—24no—
319#121—24no—
320#121—24no—
321#121—24no—
322C2×C4⋊C4—22no—
323C2×C4⋊C4—21no—
324C2×C4⋊C4—21no—
325C2×C4⋊C4C2×Dic1114yes—
326C2×C22⋊C4—22no—
327C2×C22⋊C4—22no—
328C2×C22⋊C4—22no—
329C2×C22⋊C4—22no—
330C2×C22⋊C4C2×Dic1114yes—
331C2×C22⋊C4C22×D1114yes—
332C22⋊C8—114no—
333C22⋊C8—114no—
334C22⋊C8—222no—
335C22⋊C8—224no—
336C22⋊C8—222no—
337C22⋊C8—224no—
338C2×C11—22no—
339C2×C11—22no—
340C2×C11—24no—
341C2×C11—42no—
342C2×C11—84no—
343C2×C11#147114yescomplemented
344C2×C11C2×#40811yescharacteristic
345C2×C11C22×#9911yescharacteristic
346C2×C11C22×#10011yescharacteristic
347C24—24no—
348C24—24no—
349C24—22no—
350C24—22no—
351C24—28no—
352C24—42no—
353C24—44no—
354C24—44no—
355C24C22⋊Dic1111yescharacteristic
356C24C22⋊Dic1112yes—
357C24C22⋊Dic1111yescharacteristic
358C24C22×Dic1112yes—
359C24C22×Dic1111yescharacteristic
360C24C22×Dic1114yes—
361C2×D4—28no—
362C2×D4—28no—
363C2×D4—24no—
364C2×D4—24no—
365C2×D4—44no—
366C2×D4—48no—
367C2×D4—48no—
368C2×D4—416no—
369C2×D4—48no—
370C2×D4—48no—
371C2×D4—416no—
372C2×D4—44no—
373C22×C4—24no—
374C22×C4—24no—
375C22×C4—24no—
376C22×C4—22no—
377C22×C4—22no—
378C22×C4—44no—
379C22×C4—44no—
380C22×C4—44no—
381C22×C4—44no—
382C22×C4—42no—
383C22×C4—42no—
384C22×C4—42no—
385C22×C4—44no—
386C22×C4C22⋊Dic1112yes—
387C22×C4C22⋊Dic1112yes—
388C22×C4C22⋊Dic1112yes—
389C22×C4C22⋊Dic1111yescharacteristic
390C22×C4C22⋊Dic1112yes—
391C22×C4C22⋊Dic1112yes—
392C22×C4C22⋊Dic1111yescharacteristic
393C22×C4C22×Dic1112yes—
394C22×C4C22×Dic1114yes—
395C22×C4C22×Dic1111yescharacteristic
396C22×C4C2×C22⋊D1112yes—
397C22×C4C2×C22⋊D1112yes—
398C22×C4C2×C22⋊D1111yescharacteristic
399C22×C4C2×C22⋊D1111yescharacteristic
400C22×C4C2×C22⋊D1111yescharacteristic
401C22×C4C2×C22⋊D1111yescharacteristic
402C22×C4C2×C22⋊D1112yes—
403C22×C4C2×C22⋊D1112yes—
404C22×C4C23×D1111yescharacteristic
405M16—448no—
406C2×C8—224no—
407C2×C8—224no—
408C2×C8—444no—
409C2×C8—448no—
410C2×C8—444no—
411C4⋊C4—24no—
412C4⋊C4—24no—
413C22⋊C4—24no—
414C22⋊C4—24no—
415C22⋊C4—24no—
416C22⋊C4—24no—
417C11C2×#147111yescharacteristic, complemented, Sylow
418C23—22no—
419C23—22no—
420C23—22no—
421C23—22no—
422C23—24no—
423C23—22no—
424C23—24no—
425C23—22no—
426C23—24no—
427C23—24no—
428C23—22no—
429C23—24no—
430C23—28no—
431C23—42no—
432C23—42no—
433C23—416no—
434C23—44no—
435C23—44no—
436C23—44no—
437C23—44no—
438C23—44no—
439C23—44no—
440C23—44no—
441C23—44no—
442C23—816no—
443C23#6689714yes—
444C23#6700114yes—
445C23C2×C22⋊Dic1112yes—
446C23C2×C22⋊Dic1112yes—
447C23C2×C22⋊Dic1111yescharacteristic
448C23C2×C22⋊Dic1111yescharacteristic
449C23C23×Dic1111yescharacteristic
450D4—48no—
451D4—416no—
452D4—416no—
453D4—48no—
454C2×C4—22no—
455C2×C4—22no—
456C2×C4—22no—
457C2×C4—24no—
458C2×C4—24no—
459C2×C4—24no—
460C2×C4—24no—
461C2×C4—24no—
462C2×C4—24no—
463C2×C4—24no—
464C2×C4—42no—
465C2×C4—42no—
466C2×C4—41no—
467C2×C4—42no—
468C2×C4—42no—
469C2×C4—41no—
470C2×C4—41no—
471C2×C4—41no—
472C2×C4—44no—
473C2×C4—44no—
474C2×C4—44no—
475C2×C4#6689814yes—
476C2×C4C2×C22⋊Dic1111yescharacteristic
477C2×C4C2×C22⋊Dic1111yescharacteristic
478C2×C4C2×C22⋊Dic1112yes—
479C2×C4C2×C22⋊Dic1112yes—
480C2×C4C22×C22⋊D1111yescharacteristic
481C2×C4C22×C22⋊D1111yescharacteristic
482C8—444no—
483C8—444no—
484C22—22no—
485C22—21no—
486C22—21no—
487C22—22no—
488C22—21no—
489C22—21no—
490C22—28no—
491C22—28no—
492C22—22no—
493C22—22no—
494C22—22no—
495C22—48no—
496C22—48no—
497C22—44no—
498C22—44no—
499C22—44no—
500C22—44no—
501C22—88no—
502C22—88no—
503C22—88no—
504C22C2×#6689714yes—
505C22C2×#6689712yes—
506C22C2×#6689812yes—
507C22#1062284712yes—
508C22#1062284712yes—
509C22C2×#6700112yes—
510C22C22×C22⋊Dic1111yescharacteristic
511C4—21no—
512C4—21no—
513C4—22no—
514C4—21no—
515C4—21no—
516C4—44no—
517C4C2×#6689814yes—
518C2—22no—
519C2—22no—
520C2—24no—
521C2—42no—
522C2—84no—
523C2#1306697614yesdirect product factor
524C2C2×#1062284711yescharacteristic
525C2C22×#6689811yescharacteristic
526C2C22×#6689711yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic11
commutatorC23×C11C23×C4
FrattiniC22×C4C23×D11
Fitting, prime radicalC22×C11×#121C2
socleC23×C11C2×C22⋊C4
cosocleC22×C4×C11C24
hypercenterC22×#121D11
hypocenterC11C2×#1471
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C24×C4 ◁ C22×#121

Complements

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

NH ≅ G/Ntype
1. C2×#10622820C2semidirect
2. C22×C22⋊(C11⋊C8)C2semidirect
3. #13066976C2direct (N × H)
4. C2×#10622163C2semidirect
22. #10622820C22semidirect
28. C2×C22⋊(C11⋊C8)C22semidirect
29. #10622163C22semidirect
343. C2×C11#1471semidirect
417. C11C2×#1471semidirect
523. C2#13066976direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106228202
C22×C22⋊(C11⋊C8)2
#130669762
C2×#106221632
C22×C11×#1212
C2×#147111