Finite Group Databasebeta

← C2×#13069224 #14756051

Subgroups — C2×#13069224 #14756051

Order 2816.

1462 conjugacy classes of subgroups.

The subgroup lattice has 522 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4⋊(C11⋊C8)C211yesmaximal, characteristic, complemented
2C22×C22⋊(C11⋊C8)C211yesmaximal, characteristic
3C22×C22⋊(C11⋊C8)C211yesmaximal, characteristic
4C22×C4×C11⋊C8C211yesmaximal, characteristic, complemented
5#13069224C218yesmaximal, direct product factor
6C2×#10622162C211yesmaximal, characteristic, complemented
7C2×#10622162C211yesmaximal, characteristic, complemented
8C2×C4×C11×C22⋊C4C211yesmaximal, characteristic
9C24×C4×C11C2211yescharacteristic
10C22×C11×C22⋊C4C411yescharacteristic
11C22×C11×C22⋊C4C411yescharacteristic
12C22×C42×C11C2211yescharacteristic
13C22×C42×C11C2211yescharacteristic
14C23×C11⋊C8C2211yescharacteristic
15C23×C11⋊C8C2211yescharacteristic
16C23×C11⋊C8C2211yescharacteristic
17C23×C11⋊C8C2211yescharacteristic
18C4×C11×C22⋊C4C414yes—
19C4×C11×C22⋊C4C2214yes—
20C2×C11×#95C411yescharacteristic
21C2×C11×#95C411yescharacteristic
22C2×C22⋊(C11⋊C8)—24no—
23C2×C22⋊(C11⋊C8)—24no—
24C2×C22⋊(C11⋊C8)C2214yes—
25C2×C22⋊(C11⋊C8)C2214yes—
26C2×C4⋊(C11⋊C8)—24no—
27C2×C4⋊(C11⋊C8)C2214yescomplemented
28C2×C4×C11⋊C8—24no—
29C2×C4×C11⋊C8C2214yescomplemented
30#10622162C2214yescomplemented
31#10622162C2214yescomplemented
32C25×C11C2×C411yescharacteristic
33C23×C4×C11—22no—
34C23×C4×C11—22no—
35C23×C4×C11—22no—
36C23×C4×C11—22no—
37C23×C4×C11—22no—
38C23×C4×C11—22no—
39C23×C4×C11C2×C411yescharacteristic
40C23×C4×C11C2×C411yescharacteristic
41C23×C4×C11C2×C412yes—
42C23×C4×C11C2×C411yescharacteristic
43C23×C4×C11C2×C411yescharacteristic
44C23×C4×C11C2×C411yescharacteristic
45C23×C4×C11C2312yes—
46C23×C4×C11C2311yescharacteristic
47C2×C11×C22⋊C4—24no—
48C2×C11×C22⋊C4C818yescomplemented
49C2×C11×C22⋊C4C2×C414yes—
50C2×C11×C22⋊C4C2×C414yes—
51C2×C42×C11—22no—
52C2×C42×C11—22no—
53C2×C42×C11—22no—
54C2×C42×C11—22no—
55C2×C42×C11C2×C412yes—
56C2×C42×C11C2×C412yes—
57C2×C42×C11C2312yes—
58C2×C42×C11C2312yes—
59C22×C11⋊C8—22no—
60C22×C11⋊C8—22no—
61C22×C11⋊C8—22no—
62C22×C11⋊C8—22no—
63C22×C11⋊C8—22no—
64C22×C11⋊C8—22no—
65C22×C11⋊C8—22no—
66C22×C11⋊C8—22no—
67C22×C11⋊C8—22no—
68C22×C11⋊C8—22no—
69C22×C11⋊C8D414yes—
70C22×C11⋊C8D414yes—
71C22×C11⋊C8C2312yes—
72C22×C11⋊C8C2312yes—
73C22×C11⋊C8C2312yes—
74C22×C11⋊C8C2312yes—
75C11×#95C2×C414yes—
76C11×#95C2×C414yes—
77C22⋊(C11⋊C8)—28no—
78C22⋊(C11⋊C8)—28no—
79C4⋊(C11⋊C8)—28no—
80C4×C11⋊C8—28no—
81C2×#1923—111nomaximal, Sylow
82C24×C11—22no—
83C24×C11—22no—
84C24×C11—22no—
85C24×C11—22no—
86C24×C11—22no—
87C24×C11—22no—
88C24×C11C2×C814yes—
89C24×C11C22×C412yes—
90C24×C11C22×C411yescharacteristic
91C22×C4×C11—22no—
92C22×C4×C11—22no—
93C22×C4×C11—22no—
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—22no—
103C22×C4×C11—24no—
104C22×C4×C11—24no—
105C22×C4×C11—24no—
106C22×C4×C11—22no—
107C22×C4×C11—22no—
108C22×C4×C11—22no—
109C22×C4×C11—22no—
110C22×C4×C11—22no—
111C22×C4×C11—22no—
112C22×C4×C11—44no—
113C22×C4×C11—44no—
114C22×C4×C11—44no—
115C22×C4×C11—44no—
116C22×C4×C11C2×C814yes—
117C22×C4×C11C2×C814yes—
118C22×C4×C11M1614yes—
119C22×C4×C11C22×C412yes—
120C22×C4×C11C22×C412yes—
121C22×C4×C11C22×C412yes—
122C22×C4×C11C22×C412yes—
123C22×C4×C11C22×C412yes—
124C22×C4×C11C22×C411yescharacteristic
125C22×C4×C11C2×D412yes—
126C22×C4×C11C2×D412yes—
127C22×C4×C11#4112yes—
128C22×C4×C11#4112yes—
129C22×C4×C11#4112yes—
130C22×C4×C11#4112yes—
131C22×C4×C11C2411yescharacteristic
132C11×C22⋊C4—28no—
133C11×C22⋊C4C2×C8116yescomplemented
134C42×C11—24no—
135C42×C11—24no—
136C42×C11—22no—
137C42×C11—22no—
138C42×C11—22no—
139C42×C11—22no—
140C2×C11⋊C8—28no—
141C2×C11⋊C8—28no—
142C2×C11⋊C8—22no—
143C2×C11⋊C8—22no—
144C2×C11⋊C8—22no—
145C2×C11⋊C8—22no—
146C2×C11⋊C8—22no—
147C2×C11⋊C8—22no—
148C2×C11⋊C8—22no—
149C2×C11⋊C8—22no—
150C2×C11⋊C8—22no—
151C2×C11⋊C8—22no—
152C2×C11⋊C8—44no—
153C2×C11⋊C8—44no—
154C2×C11⋊C8C2×D414yes—
155C2×C11⋊C8C2×D414yes—
156C22×C4⋊C8—111no—
157C22×C22⋊C8—111no—
158C22×C22⋊C8—111no—
159C22×C4×C8—111no—
160C2×C4×C22⋊C4D1111yescharacteristic
161#1923—118no—
162C2×#336—111no—
163C2×#336—111no—
164C23×C11—22no—
165C23×C11—22no—
166C23×C11—22no—
167C23×C11—22no—
168C23×C11—22no—
169C23×C11—22no—
170C23×C11—28no—
171C23×C11—28no—
172C23×C11—28no—
173C23×C11—44no—
174C23×C11—44no—
175C23×C11—44no—
176C23×C11—44no—
177C23×C11#11712yes—
178C23×C11C4×D412yes—
179C23×C11C4×D412yes—
180C23×C11C22×C814yes—
181C23×C11C22×C812yes—
182C23×C11C2×M1612yes—
183C23×C11#13112yes—
184C23×C11#13112yes—
185C23×C11C23×C411yescharacteristic
186C2×C4×C11—22no—
187C2×C4×C11—22no—
188C2×C4×C11—22no—
189C2×C4×C11—22no—
190C2×C4×C11—22no—
191C2×C4×C11—22no—
192C2×C4×C11—28no—
193C2×C4×C11—28no—
194C2×C4×C11—28no—
195C2×C4×C11—22no—
196C2×C4×C11—22no—
197C2×C4×C11—22no—
198C2×C4×C11—22no—
199C2×C4×C11—22no—
200C2×C4×C11—22no—
201C2×C4×C11—44no—
202C2×C4×C11—44no—
203C2×C4×C11—42no—
204C2×C4×C11—42no—
205C2×C4×C11—42no—
206C2×C4×C11—42no—
207C2×C4×C11—48no—
208C2×C4×C11#11712yes—
209C2×C4×C11C4×D412yes—
210C2×C4×C11C4×D412yes—
211C2×C4×C11#12114yes—
212C2×C4×C11#12314yes—
213C2×C4×C11#12414yes—
214C2×C4×C11#12614yes—
215C2×C4×C11C22×C814yes—
216C2×C4×C11C22×C814yes—
217C2×C4×C11C2×M1614yes—
218C2×C4×C11C22×D411yescharacteristic
219C2×C4×C11C22×D411yescharacteristic
220C2×C4×C11C2×#4111yescharacteristic
221C2×C4×C11C2×#4111yescharacteristic
222C2×C4×C11C2×#4111yescharacteristic
223C2×C4×C11C2×#4111yescharacteristic
224C11⋊C8—24no—
225C11⋊C8—24no—
226C11⋊C8—42no—
227C11⋊C8—42no—
228C24×C4C2×D1111yescharacteristic
229C23×C8—111no—
230C23×C8—111no—
231C23×C8—111no—
232C23×C8—111no—
233C22×C22⋊C4Dic1111yescharacteristic
234C22×C22⋊C4Dic1111yescharacteristic
235C22×C42C2×D1111yescharacteristic
236C22×C42C2×D1111yescharacteristic
237C2×C4⋊C8—114no—
238C2×C4⋊C8—224no—
239C2×C22⋊C8—114no—
240C2×C22⋊C8—114no—
241C2×C22⋊C8—224no—
242C2×C22⋊C8—224no—
243C2×C4×C8—114no—
244C2×C4×C8—224no—
245C4×C22⋊C4Dic1114yes—
246C4×C22⋊C4C2×D1114yes—
247C2×#95Dic1111yescharacteristic
248C2×#95Dic1111yescharacteristic
249#336—114no—
250#336—114no—
251C22×C11—24no—
252C22×C11—24no—
253C22×C11—24no—
254C22×C11—42no—
255C22×C11—42no—
256C22×C11—42no—
257C22×C11—416no—
258C22×C11—42no—
259C22×C11#38814yes—
260C22×C11#43114yes—
261C22×C11#43314yes—
262C22×C11C8×D414yes—
263C22×C11C8×D414yes—
264C22×C11#43514yes—
265C22×C11#43614yes—
266C22×C11C2×#11711yescharacteristic
267C22×C11C2×C4×D411yescharacteristic
268C22×C11C2×C4×D411yescharacteristic
269C22×C11C23×C811yescharacteristic
270C22×C11C22×M1611yescharacteristic
271C22×C11C2×#13111yescharacteristic
272C22×C11C2×#13111yescharacteristic
273C4×C11—24no—
274C4×C11—24no—
275C4×C11—24no—
276C4×C11—42no—
277C4×C11—42no—
278C4×C11#38814yes—
279C4×C11C2×#12111yescharacteristic
280C4×C11C2×#12311yescharacteristic
281C4×C11C2×#12411yescharacteristic
282C4×C11C2×#12611yescharacteristic
283C25C2×Dic1111yescharacteristic
284C23×C4—22no—
285C23×C4—22no—
286C23×C4—22no—
287C23×C4—22no—
288C23×C4—22no—
289C23×C4—22no—
290C23×C4C2×Dic1111yescharacteristic
291C23×C4C2×Dic1111yescharacteristic
292C23×C4C2×Dic1112yes—
293C23×C4C2×Dic1111yescharacteristic
294C23×C4C2×Dic1111yescharacteristic
295C23×C4C2×Dic1111yescharacteristic
296C23×C4C22×D1112yes—
297C23×C4C22×D1111yescharacteristic
298C22×C8—114no—
299C22×C8—114no—
300C22×C8—112no—
301C22×C8—112no—
302C22×C8—112no—
303C22×C8—112no—
304C22×C8—222no—
305C22×C8—222no—
306C22×C8—222no—
307C22×C8—222no—
308C22×C8—222no—
309C22×C8—222no—
310C22×C8—222no—
311C22×C8—222no—
312C22×C8—222no—
313C22×C8—222no—
314C2×C22⋊C4—24no—
315C2×C22⋊C4C11⋊C818yescomplemented
316C2×C22⋊C4C2×Dic1114yes—
317C2×C22⋊C4C2×Dic1114yes—
318C2×C42—22no—
319C2×C42—22no—
320C2×C42—22no—
321C2×C42—22no—
322C2×C42C2×Dic1112yes—
323C2×C42C2×Dic1112yes—
324C2×C42C22×D1112yes—
325C2×C42C22×D1112yes—
326C4⋊C8—228no—
327C22⋊C8—228no—
328C22⋊C8—228no—
329C4×C8—228no—
330#95C2×Dic1114yes—
331#95C2×Dic1114yes—
332C2×C11—44no—
333C2×C11#192318yescomplemented
334C2×C11C2×#38811yescharacteristic
335C2×C11C2×#43111yescharacteristic
336C2×C11C2×#43311yescharacteristic
337C2×C11C2×C8×D411yescharacteristic
338C2×C11C2×C8×D411yescharacteristic
339C2×C11C2×#43511yescharacteristic
340C2×C11C2×#43611yescharacteristic
341C24—22no—
342C24—22no—
343C24—22no—
344C24—22no—
345C24—22no—
346C24—22no—
347C24C2×C11⋊C814yes—
348C24C22×Dic1112yes—
349C24C22×Dic1111yescharacteristic
350C22×C4—22no—
351C22×C4—22no—
352C22×C4—22no—
353C22×C4—22no—
354C22×C4—22no—
355C22×C4—22no—
356C22×C4—22no—
357C22×C4—22no—
358C22×C4—22no—
359C22×C4—22no—
360C22×C4—22no—
361C22×C4—22no—
362C22×C4—24no—
363C22×C4—24no—
364C22×C4—24no—
365C22×C4—22no—
366C22×C4—22no—
367C22×C4—22no—
368C22×C4—22no—
369C22×C4—22no—
370C22×C4—22no—
371C22×C4—44no—
372C22×C4—44no—
373C22×C4—44no—
374C22×C4—44no—
375C22×C4C2×C11⋊C814yes—
376C22×C4C2×C11⋊C814yes—
377C22×C4#431814yes—
378C22×C4#433912yes—
379C22×C4#433912yes—
380C22×C4D4×D1112yes—
381C22×C4D4×D1112yes—
382C22×C4#434112yes—
383C22×C4#434112yes—
384C22×C4C22×Dic1112yes—
385C22×C4C22×Dic1112yes—
386C22×C4C22×Dic1112yes—
387C22×C4C22×Dic1112yes—
388C22×C4C22×Dic1112yes—
389C22×C4C22×Dic1111yescharacteristic
390C22×C4C23×D1111yescharacteristic
391C2×C8—114no—
392C2×C8—114no—
393C2×C8—228no—
394C2×C8—228no—
395C2×C8—222no—
396C2×C8—222no—
397C2×C8—222no—
398C2×C8—222no—
399C2×C8—222no—
400C2×C8—222no—
401C2×C8—222no—
402C2×C8—222no—
403C2×C8—222no—
404C2×C8—222no—
405C2×C8—444no—
406C2×C8—444no—
407C22⋊C4—28no—
408C22⋊C4C2×C11⋊C8116yescomplemented
409C42—24no—
410C42—24no—
411C42—22no—
412C42—22no—
413C42—22no—
414C42—22no—
415C11C2×#192311yescharacteristic, complemented, Sylow
416C23—28no—
417C23—22no—
418C23—22no—
419C23—22no—
420C23—22no—
421C23—22no—
422C23—22no—
423C23—28no—
424C23—28no—
425C23—44no—
426C23—44no—
427C23—44no—
428C23—44no—
429C23C22×C11⋊C814yes—
430C23C22×C11⋊C812yes—
431C23C2×#431812yes—
432C23#6697912yes—
433C23D4×Dic1112yes—
434C23D4×Dic1112yes—
435C23#6700112yes—
436C23#6700112yes—
437C23C23×Dic1111yescharacteristic
438C2×C4—22no—
439C2×C4—22no—
440C2×C4—22no—
441C2×C4—22no—
442C2×C4—22no—
443C2×C4—22no—
444C2×C4—28no—
445C2×C4—28no—
446C2×C4—28no—
447C2×C4—22no—
448C2×C4—22no—
449C2×C4—22no—
450C2×C4—22no—
451C2×C4—22no—
452C2×C4—22no—
453C2×C4—44no—
454C2×C4—44no—
455C2×C4—42no—
456C2×C4—42no—
457C2×C4—42no—
458C2×C4—42no—
459C2×C4—48no—
460C2×C4#6693214yes—
461C2×C4#6693614yes—
462C2×C4#6693714yes—
463C2×C4#6693814yes—
464C2×C4C22×C11⋊C814yes—
465C2×C4C22×C11⋊C814yes—
466C2×C4C2×#431814yes—
467C2×C4#6697912yes—
468C2×C4D4×Dic1112yes—
469C2×C4D4×Dic1112yes—
470C2×C4C2×#433911yescharacteristic
471C2×C4C2×#433911yescharacteristic
472C2×C4C2×D4×D1111yescharacteristic
473C2×C4C2×D4×D1111yescharacteristic
474C2×C4C2×#434111yescharacteristic
475C2×C4C2×#434111yescharacteristic
476C8—224no—
477C8—224no—
478C8—442no—
479C8—442no—
480C22—24no—
481C22—24no—
482C22—24no—
483C22—42no—
484C22—42no—
485C22—416no—
486C22—42no—
487C22—42no—
488C22#1062253814yes—
489C22#1062256414yes—
490C22#1062261314yes—
491C22D4×C11⋊C814yes—
492C22D4×C11⋊C814yes—
493C22#1062262414yes—
494C22#1062262514yes—
495C22C23×C11⋊C811yescharacteristic
496C22C22×#431811yescharacteristic
497C22C2×#6697911yescharacteristic
498C22C2×D4×Dic1111yescharacteristic
499C22C2×D4×Dic1111yescharacteristic
500C22C2×#6700111yescharacteristic
501C22C2×#6700111yescharacteristic
502C4—24no—
503C4—24no—
504C4—24no—
505C4—42no—
506C4—42no—
507C4#1062256414yes—
508C4C2×#6693211yescharacteristic
509C4C2×#6693611yescharacteristic
510C4C2×#6693711yescharacteristic
511C4C2×#6693811yescharacteristic
512C2—44no—
513C2#1306922418yesdirect product factor
514C2C2×#1062256411yescharacteristic
515C2C2×#1062253811yescharacteristic
516C2C2×#1062261311yescharacteristic
517C2C2×D4×C11⋊C811yescharacteristic
518C2C2×D4×C11⋊C811yescharacteristic
519C2C2×#1062262411yescharacteristic
520C2C2×#1062262511yescharacteristic
subgroupG/H
centerC23×C4C22×D11
commutatorC22×C11C23×C8
FrattiniC22×C4C23×D11
FittingC2×C4×C11×C22⋊C4C2
socleC24×C11C22×C4
prime radicalC25×C11C2×C4
cosocleC22×C4×C11C24
hypercenterC2×C4×C22⋊C4D11
hypocenterC11C2×#1923
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23×C4 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×C4⋊(C11⋊C8)C2semidirect
4. C22×C4×C11⋊C8C2semidirect
5. #13069224C2direct (N × H)
6. C2×#10622162C2semidirect
7. C2×#10622162C2semidirect
27. C2×C4⋊(C11⋊C8)C22semidirect
29. C2×C4×C11⋊C8C22semidirect
30. #10622162C22semidirect
31. #10622162C22semidirect
48. C2×C11×C22⋊C4C8semidirect
133. C11×C22⋊C4C2×C8semidirect
315. C2×C22⋊C4C11⋊C8semidirect
333. C2×C11#1923semidirect
408. C22⋊C4C2×C11⋊C8semidirect
415. C11C2×#1923semidirect
513. C2#13069224direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4⋊(C11⋊C8)2
C22×C22⋊(C11⋊C8)2
C22×C4×C11⋊C82
#130692242
C2×#106221622
C2×C4×C11×C22⋊C42
C2×#192311