Finite Group Databasebeta

← C2×#13070042 #14782595

Subgroups — C2×#13070042 #14782595

Order 2816.

1270 conjugacy classes of subgroups.

The subgroup lattice has 508 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66871C211yesmaximal, characteristic, complemented
2C22×C22⋊(C11⋊C8)C211yesmaximal, characteristic
3C2×#10622825C211yesmaximal, characteristic
4#13070042C218yesmaximal, direct product factor
5C2×#10622167C211yesmaximal, characteristic, complemented
6C2×#10622167C211yesmaximal, characteristic, complemented
7C2×#10622167C211yesmaximal, characteristic, complemented
8C2×C11×#380C211yesmaximal, characteristic
9C24×C4×C11C2211yescharacteristic
10C22×C11×C4⋊C4C2211yescharacteristic
11C22×C11×C4⋊C4C2211yescharacteristic
12C22×C11×C22⋊C4—21no—
13C22×C22⋊Dic11—21no—
14C22×C4⋊Dic11C2211yescharacteristic
15C22×C4⋊Dic11C2211yescharacteristic
16C23×C11⋊C8C2211yescharacteristic
17C23×C11⋊C8C2211yescharacteristic
18C11×#380—22no—
19C11×#380C2214yes—
20C2×C11×#95—21no—
21#10622825—22no—
22#10622825C2214yes—
23C2×C11⋊#95—21no—
24C2×C22⋊(C11⋊C8)—24no—
25C2×C22⋊(C11⋊C8)C2214yes—
26C2×#66871—24no—
27C2×#66871C2214yescomplemented
28#10622167C2214yescomplemented
29#10622167C2214yescomplemented
30#10622167C2214yescomplemented
31C25×C11D411yescharacteristic
32C23×C4×C11—22no—
33C23×C4×C11—22no—
34C23×C4×C11—22no—
35C23×C4×C11—22no—
36C23×C4×C11—22no—
37C23×C4×C11—22no—
38C23×C4×C11—21no—
39C23×C4×C11—21no—
40C23×C4×C11D411yescharacteristic
41C23×C4×C11D412yes—
42C23×C4×C11C2312yes—
43C23×C4×C11C2311yescharacteristic
44C23×Dic11—21no—
45C23×Dic11—21no—
46C2×C11×C4⋊C4—22no—
47C2×C11×C4⋊C4—22no—
48C2×C11×C4⋊C4—22no—
49C2×C11×C4⋊C4—22no—
50C2×C11×C4⋊C4—21no—
51C2×C11×C4⋊C4—21no—
52C2×C11×C4⋊C4C2312yes—
53C2×C11×C4⋊C4C2312yes—
54C2×C11×C22⋊C4—24no—
55C2×C11×C22⋊C4—44no—
56C2×C22⋊Dic11—24no—
57C2×C22⋊Dic11—44no—
58C2×C4⋊Dic11—22no—
59C2×C4⋊Dic11—22no—
60C2×C4⋊Dic11—22no—
61C2×C4⋊Dic11—22no—
62C2×C4⋊Dic11—21no—
63C2×C4⋊Dic11—21no—
64C2×C4⋊Dic11C2312yes—
65C2×C4⋊Dic11C2312yes—
66C22×C11⋊C8—22no—
67C22×C11⋊C8—22no—
68C22×C11⋊C8—22no—
69C22×C11⋊C8—22no—
70C22×C11⋊C8—22no—
71C22×C11⋊C8D414yes—
72C22×C11⋊C8C2312yes—
73C22×C11⋊C8C2312yes—
74C11×#95—24no—
75C11⋊#95—24no—
76C22⋊(C11⋊C8)—28no—
77#66871—28no—
78C2×#2075—111nomaximal, Sylow
79C24×C11—22no—
80C24×C11—22no—
81C24×C11—22no—
82C24×C11—22no—
83C24×C11—22no—
84C24×C11—22no—
85C24×C11D814yes—
86C24×C11C2×D412yes—
87C24×C11C2×D411yescharacteristic
88C22×C4×C11—22no—
89C22×C4×C11—22no—
90C22×C4×C11—22no—
91C22×C4×C11—24no—
92C22×C4×C11—24no—
93C22×C4×C11—24no—
94C22×C4×C11—22no—
95C22×C4×C11—22no—
96C22×C4×C11—22no—
97C22×C4×C11—22no—
98C22×C4×C11—22no—
99C22×C4×C11—22no—
100C22×C4×C11—22no—
101C22×C4×C11—22no—
102C22×C4×C11—44no—
103C22×C4×C11—44no—
104C22×C4×C11—44no—
105C22×C4×C11—44no—
106C22×C4×C11—42no—
107C22×C4×C11—42no—
108C22×C4×C11—42no—
109C22×C4×C11—42no—
110C22×C4×C11—42no—
111C22×C4×C11—42no—
112C22×C4×C11C2×D412yes—
113C22×C4×C11C2×D411yescharacteristic
114C22×C4×C11C2×D412yes—
115C22×C4×C11#4112yes—
116C22×C4×C11#4112yes—
117C22×C4×C11#4112yes—
118C22×C4×C11#4112yes—
119C22×C4×C11#4112yes—
120C22×C4×C11C2411yescharacteristic
121C22×Dic11—22no—
122C22×Dic11—22no—
123C22×Dic11—42no—
124C22×Dic11—42no—
125C22×Dic11—42no—
126C22×Dic11—42no—
127C22×Dic11—42no—
128C22×Dic11—42no—
129C11×C4⋊C4—22no—
130C11×C4⋊C4—22no—
131C11×C4⋊C4—22no—
132C11×C4⋊C4—22no—
133C11×C4⋊C4—42no—
134C11×C4⋊C4—42no—
135C11×C22⋊C4—48no—
136C22⋊Dic11—48no—
137C4⋊Dic11—22no—
138C4⋊Dic11—22no—
139C4⋊Dic11—22no—
140C4⋊Dic11—22no—
141C4⋊Dic11—42no—
142C4⋊Dic11—42no—
143C2×C11⋊C8—28no—
144C2×C11⋊C8—22no—
145C2×C11⋊C8—22no—
146C2×C11⋊C8—22no—
147C2×C11⋊C8—22no—
148C2×C11⋊C8—22no—
149C2×C11⋊C8—44no—
150C2×C11⋊C8C2×D414yes—
151C22×#107—111no—
152C22×C22⋊C8—111no—
153C2×#380—111no—
154C2×#380D1111yescharacteristic
155#2075—118no—
156C2×#340—111no—
157C2×#340—111no—
158C2×#340—111no—
159C23×C11—22no—
160C23×C11—22no—
161C23×C11—22no—
162C23×C11—22no—
163C23×C11—22no—
164C23×C11—22no—
165C23×C11—28no—
166C23×C11—28no—
167C23×C11—28no—
168C23×C11—44no—
169C23×C11—44no—
170C23×C11—44no—
171C23×C11—44no—
172C23×C11#12112yes—
173C23×C11#12312yes—
174C23×C11#12312yes—
175C23×C11C2×D814yes—
176C23×C11C2×D812yes—
177C23×C11#13512yes—
178C23×C11#13712yes—
179C23×C11#13712yes—
180C23×C11C22×D411yescharacteristic
181C2×C4×C11—22no—
182C2×C4×C11—22no—
183C2×C4×C11—22no—
184C2×C4×C11—44no—
185C2×C4×C11—42no—
186C2×C4×C11—42no—
187C2×C4×C11—42no—
188C2×C4×C11—42no—
189C2×C4×C11—48no—
190C2×C4×C11—42no—
191C2×C4×C11—42no—
192C2×C4×C11—42no—
193C2×C4×C11—42no—
194C2×C4×C11—42no—
195C2×C4×C11—42no—
196C2×C4×C11—84no—
197C2×C4×C11—84no—
198C2×C4×C11#12112yes—
199C2×C4×C11#12314yes—
200C2×C4×C11#12312yes—
201C2×C4×C11#12312yes—
202C2×C4×C11#12414yes—
203C2×C4×C11#12614yes—
204C2×C4×C11#12614yes—
205C2×C4×C11C22×D411yescharacteristic
206C2×C4×C11C2×#4111yescharacteristic
207C2×C4×C11C2×#4111yescharacteristic
208C2×C4×C11C2×#4111yescharacteristic
209C2×C4×C11C2×#4111yescharacteristic
210C2×C4×C11C2×#4111yescharacteristic
211C2×Dic11—42no—
212C2×Dic11—42no—
213C2×Dic11—42no—
214C2×Dic11—42no—
215C2×Dic11—42no—
216C2×Dic11—42no—
217C2×Dic11—84no—
218C2×Dic11—84no—
219C11⋊C8—24no—
220C11⋊C8—42no—
221C24×C4C2×D1111yescharacteristic
222C23×C8—111no—
223C23×C8—111no—
224C22×C4⋊C4—111no—
225C22×C4⋊C4—111no—
226C22×C4⋊C4C2×D1111yescharacteristic
227C22×C4⋊C4C2×D1111yescharacteristic
228C22×C22⋊C4—21no—
229C22×C22⋊C4—221no—
230C2×#107—114no—
231C2×#107—224no—
232C2×C22⋊C8—114no—
233C2×C22⋊C8—224no—
234#380—22no—
235#380—114no—
236#380—222no—
237#380C2×D1114yes—
238C2×#95—21no—
239C2×#95—221no—
240#340—114no—
241#340—114no—
242#340—114no—
243C22×C11—24no—
244C22×C11—24no—
245C22×C11—24no—
246C22×C11—42no—
247C22×C11—42no—
248C22×C11—416no—
249C22×C11—42no—
250C22×C11—42no—
251C22×C11#39714yes—
252C22×C11#46614yes—
253C22×C11#47014yes—
254C22×C11#48014yes—
255C22×C11#48014yes—
256C22×C11#48514yes—
257C22×C11#48514yes—
258C22×C11C2×#12111yescharacteristic
259C22×C11C2×#12311yescharacteristic
260C22×C11C2×#12311yescharacteristic
261C22×C11C22×D811yescharacteristic
262C22×C11C2×#13511yescharacteristic
263C22×C11C2×#13711yescharacteristic
264C22×C11C2×#13711yescharacteristic
265C4×C11—42no—
266C4×C11—82no—
267C4×C11—82no—
268C4×C11#39714yes—
269C4×C11C2×#12311yescharacteristic
270C4×C11C2×#12411yescharacteristic
271C4×C11C2×#12611yescharacteristic
272C4×C11C2×#12611yescharacteristic
273Dic11—82no—
274Dic11—82no—
275C25C22⋊D1111yescharacteristic
276C23×C4—22no—
277C23×C4—22no—
278C23×C4—22no—
279C23×C4—22no—
280C23×C4—22no—
281C23×C4—22no—
282C23×C4—21no—
283C23×C4—21no—
284C23×C4—221no—
285C23×C4—221no—
286C23×C4C22⋊D1112yes—
287C23×C4C22⋊D1111yescharacteristic
288C23×C4C22×D1112yes—
289C23×C4C22×D1111yescharacteristic
290C22×C8—114no—
291C22×C8—112no—
292C22×C8—112no—
293C22×C8—222no—
294C22×C8—222no—
295C22×C8—222no—
296C22×C8—222no—
297C22×C8—222no—
298C2×C4⋊C4—22no—
299C2×C4⋊C4—22no—
300C2×C4⋊C4—22no—
301C2×C4⋊C4—22no—
302C2×C4⋊C4—21no—
303C2×C4⋊C4—21no—
304C2×C4⋊C4—112no—
305C2×C4⋊C4—112no—
306C2×C4⋊C4—222no—
307C2×C4⋊C4—222no—
308C2×C4⋊C4—222no—
309C2×C4⋊C4—222no—
310C2×C4⋊C4—221no—
311C2×C4⋊C4—221no—
312C2×C4⋊C4C22×D1112yes—
313C2×C4⋊C4C22×D1112yes—
314C2×C22⋊C4—24no—
315C2×C22⋊C4—44no—
316C2×C22⋊C4—224no—
317C2×C22⋊C4—444no—
318#107—228no—
319C22⋊C8—228no—
320#95—24no—
321#95—224no—
322C2×C11—44no—
323C2×C11#207518yescomplemented
324C2×C11C2×#39711yescharacteristic
325C2×C11C2×#46611yescharacteristic
326C2×C11C2×#47011yescharacteristic
327C2×C11C2×#48011yescharacteristic
328C2×C11C2×#48011yescharacteristic
329C2×C11C2×#48511yescharacteristic
330C2×C11C2×#48511yescharacteristic
331C24—22no—
332C24—22no—
333C24—22no—
334C24—22no—
335C24—22no—
336C24—22no—
337C24#432314yes—
338C24C2×C22⋊D1112yes—
339C24C2×C22⋊D1111yescharacteristic
340C22×C4—22no—
341C22×C4—22no—
342C22×C4—22no—
343C22×C4—24no—
344C22×C4—24no—
345C22×C4—24no—
346C22×C4—22no—
347C22×C4—22no—
348C22×C4—22no—
349C22×C4—22no—
350C22×C4—22no—
351C22×C4—22no—
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—42no—
362C22×C4—42no—
363C22×C4—42no—
364C22×C4—222no—
365C22×C4—222no—
366C22×C4—442no—
367C22×C4—442no—
368C22×C4—442no—
369C22×C4—442no—
370C22×C4—442no—
371C22×C4—442no—
372C22×C4#433912yes—
373C22×C4#433912yes—
374C22×C4D4×D1112yes—
375C22×C4#434112yes—
376C22×C4#434112yes—
377C22×C4#434112yes—
378C22×C4C2×C22⋊D1112yes—
379C22×C4C2×C22⋊D1111yescharacteristic
380C22×C4C23×D1111yescharacteristic
381C2×C8—114no—
382C2×C8—228no—
383C2×C8—222no—
384C2×C8—222no—
385C2×C8—222no—
386C2×C8—222no—
387C2×C8—222no—
388C2×C8—444no—
389C4⋊C4—22no—
390C4⋊C4—22no—
391C4⋊C4—22no—
392C4⋊C4—22no—
393C4⋊C4—42no—
394C4⋊C4—42no—
395C4⋊C4—222no—
396C4⋊C4—222no—
397C4⋊C4—222no—
398C4⋊C4—222no—
399C4⋊C4—442no—
400C4⋊C4—442no—
401C22⋊C4—48no—
402C22⋊C4—448no—
403C11C2×#207511yescharacteristic, complemented, Sylow
404C23—22no—
405C23—22no—
406C23—22no—
407C23—22no—
408C23—28no—
409C23—22no—
410C23—22no—
411C23—28no—
412C23—28no—
413C23—44no—
414C23—44no—
415C23—44no—
416C23—44no—
417C23#6698212yes—
418C23C2×#432314yes—
419C23C2×#432312yes—
420C23#6698812yes—
421C23#6699212yes—
422C23#6699512yes—
423C23#6700312yes—
424C23#6700412yes—
425C23C22×C22⋊D1111yescharacteristic
426C2×C4—22no—
427C2×C4—22no—
428C2×C4—22no—
429C2×C4—44no—
430C2×C4—42no—
431C2×C4—42no—
432C2×C4—42no—
433C2×C4—42no—
434C2×C4—48no—
435C2×C4—42no—
436C2×C4—42no—
437C2×C4—42no—
438C2×C4—42no—
439C2×C4—42no—
440C2×C4—42no—
441C2×C4—84no—
442C2×C4—84no—
443C2×C4—442no—
444C2×C4—442no—
445C2×C4—442no—
446C2×C4—442no—
447C2×C4—442no—
448C2×C4—442no—
449C2×C4—884no—
450C2×C4—884no—
451C2×C4#6693214yes—
452C2×C4#6693214yes—
453C2×C4#6693614yes—
454C2×C4#6693814yes—
455C2×C4#6698212yes—
456C2×C4#6698812yes—
457C2×C4#6699212yes—
458C2×C4C2×#433911yescharacteristic
459C2×C4C2×#433911yescharacteristic
460C2×C4C2×D4×D1111yescharacteristic
461C2×C4C2×#434111yescharacteristic
462C2×C4C2×#434111yescharacteristic
463C2×C4C2×#434111yescharacteristic
464C8—224no—
465C8—442no—
466C22—24no—
467C22—24no—
468C22—24no—
469C22—42no—
470C22—416no—
471C22—42no—
472C22—42no—
473C22—42no—
474C22#1062256514yes—
475C22#1062258014yes—
476C22#1062260914yes—
477C22#1062264614yes—
478C22#1062265114yes—
479C22#1062265814yes—
480C22#1062266514yes—
481C22C2×#6698211yescharacteristic
482C22C22×#432311yescharacteristic
483C22C2×#6698811yescharacteristic
484C22C2×#6699211yescharacteristic
485C22C2×#6699511yescharacteristic
486C22C2×#6700311yescharacteristic
487C22C2×#6700411yescharacteristic
488C4—42no—
489C4—82no—
490C4—82no—
491C4—882no—
492C4—882no—
493C4#1062256514yes—
494C4C2×#6693211yescharacteristic
495C4C2×#6693211yescharacteristic
496C4C2×#6693611yescharacteristic
497C4C2×#6693811yescharacteristic
498C2—44no—
499C2#1307004218yesdirect product factor
500C2C2×#1062256511yescharacteristic
501C2C2×#1062265111yescharacteristic
502C2C2×#1062266511yescharacteristic
503C2C2×#1062264611yescharacteristic
504C2C2×#1062258011yescharacteristic
505C2C2×#1062265811yescharacteristic
506C2C2×#1062260911yescharacteristic
subgroupG/H
centerC24C2×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#380C2
socleC24×C11C2×D4
prime radicalC25×C11D4
hypercenterC2×#380D11
hypocenterC11C2×#2075
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C24 ◁ C24×C4 ◁ C2×#380

Complements

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

NH ≅ G/Ntype
1. C22×#66871C2semidirect
4. #13070042C2direct (N × H)
5. C2×#10622167C2semidirect
6. C2×#10622167C2semidirect
7. C2×#10622167C2semidirect
27. C2×#66871C22semidirect
28. #10622167C22semidirect
29. #10622167C22semidirect
30. #10622167C22semidirect
323. C2×C11#2075semidirect
403. C11C2×#2075semidirect
499. C2#13070042direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#668712
C22×C22⋊(C11⋊C8)2
C2×#106228252
#130700422
C2×#106221672
C2×C11×#3802
C2×#207511