Finite Group Databasebeta

← #14755016

Subgroups — #14755016

Order 2816.

1934 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66979C211yesmaximal, characteristic
2C2×#10622838C212yesmaximal, complemented
3C2×#10622820C211yesmaximal, characteristic
4#13068929C214yesmaximal, complemented
5#13068924C214yesmaximal, complemented
6#13068335C212yesmaximal, complemented
7C22×C11×C22⋊Q8C211yesmaximal, characteristic
8C23×Q8×C11C2211yescharacteristic
9C24×C4×C11C2211yescharacteristic
10C2×C11×C22⋊Q8—24no—
11C2×C11×C22⋊Q8—21no—
12C2×C11×C22⋊Q8—21no—
13C2×C11×C22⋊Q8C418yescomplemented
14C2×C11×C22⋊Q8C2212yes—
15C2×C11×C22⋊Q8C2212yes—
16C22×C11×C4⋊C4—21no—
17C22×C11×C4⋊C4C2211yescharacteristic
18C22×C11×C22⋊C4—21no—
19C22×C22⋊Dic11—21no—
20C2×#66979—21no—
21C2×#66979—21no—
22C2×#66979—28no—
23C2×#66979C2212yes—
24C2×#66979C2212yes—
25C22×C4⋊Dic11C2212yes—
26C22×C4×Dic11—21no—
27C22×#4318C2212yes—
28#10622838—28no—
29C2×#66899C2218yescomplemented
30#10622820—24no—
31C2×C22⋊(C11⋊C8)C2212yes—
32C2×C22⋊(C11⋊C8)C2212yes—
33#10622167C2218yescomplemented
34C25×C11D411yescharacteristic
35C22×Q8×C11—22no—
36C22×Q8×C11—21no—
37C22×Q8×C11—24no—
38C22×Q8×C11—24no—
39C22×Q8×C11C2×C414yescomplemented
40C22×Q8×C11C2312yes—
41C23×C4×C11—24no—
42C23×C4×C11—24no—
43C23×C4×C11—21no—
44C23×C4×C11—21no—
45C23×C4×C11C2×C414yes—
46C23×C4×C11D411yescharacteristic
47C23×C4×C11D411yescharacteristic
48C23×C4×C11D411yescharacteristic
49C23×C4×C11D414yes—
50C23×C4×C11C2311yescharacteristic
51C23×C4×C11C2311yescharacteristic
52C23×C4×C11C2311yescharacteristic
53C23×Dic11—22no—
54C11×C22⋊Q8—28no—
55C11×C22⋊Q8—28no—
56C11×C22⋊Q8—24no—
57C11×C22⋊Q8—24no—
58C11×C22⋊Q8C2×C418yes—
59C11×C22⋊Q8C2×C418yescomplemented
60C2×C11×C4⋊C4—28no—
61C2×C11×C4⋊C4—22no—
62C2×C11×C4⋊C4—22no—
63C2×C11×C4⋊C4—21no—
64C2×C11×C4⋊C4—22no—
65C2×C11×C4⋊C4C2×C414yescomplemented
66C2×C11×C4⋊C4C2312yes—
67C2×C11×C22⋊C4—28no—
68C2×C11×C22⋊C4—22no—
69C2×C11×C22⋊C4—22no—
70C2×C22⋊Dic11—28no—
71C2×C22⋊Dic11—22no—
72C2×C22⋊Dic11—22no—
73#66979—28no—
74#66979—28no—
75#66979—24no—
76#66979—28no—
77#66979D418yes—
78C2×C4⋊Dic11—22no—
79C2×C4⋊Dic11—28no—
80C2×C4⋊Dic11C2314yes—
81C2×C4×Dic11—28no—
82C2×C4×Dic11—22no—
83C2×C4×Dic11—22no—
84C2×#4318—24no—
85C2×#4318—24no—
86C2×#4318—24no—
87C22×C11⋊C8C2314yes—
88#66899—216no—
89C22⋊(C11⋊C8)—24no—
90C22⋊(C11⋊C8)—24no—
91#20911—111nomaximal, Sylow
92C24×C11—22no—
93C24×C11—22no—
94C24×C11—24no—
95C24×C11—42no—
96C24×C11C22⋊C414yes—
97C24×C11C2×D411yescharacteristic
98C24×C11C2×D411yescharacteristic
99C24×C11C2×D411yescharacteristic
100C2×Q8×C11—24no—
101C2×Q8×C11—22no—
102C2×Q8×C11—216no—
103C2×Q8×C11—24no—
104C2×Q8×C11—24no—
105C2×Q8×C11—42no—
106C2×Q8×C11—48no—
107C2×Q8×C11—42no—
108C2×Q8×C11C22×C414yes—
109C22×C4×C11—22no—
110C22×C4×C11—22no—
111C22×C4×C11—216no—
112C22×C4×C11—22no—
113C22×C4×C11—22no—
114C22×C4×C11—216no—
115C22×C4×C11—22no—
116C22×C4×C11—22no—
117C22×C4×C11—22no—
118C22×C4×C11—22no—
119C22×C4×C11—22no—
120C22×C4×C11—22no—
121C22×C4×C11—24no—
122C22×C4×C11—24no—
123C22×C4×C11—22no—
124C22×C4×C11—22no—
125C22×C4×C11—44no—
126C22×C4×C11—42no—
127C22×C4×C11—42no—
128C22×C4×C11C22⋊C414yes—
129C22×C4×C11C22⋊C414yes—
130C22×C4×C11C22⋊C414yes—
131C22×C4×C11C22×C412yes—
132C22×C4×C11C22×C412yes—
133C22×C4×C11C22×C412yes—
134C22×C4×C11C2×D411yescharacteristic
135C22×C4×C11C2×D411yescharacteristic
136C22×C4×C11C2×D412yes—
137C22×C4×C11C2×D412yes—
138C22×C4×C11C2×D411yescharacteristic
139C22×C4×C11C2×D412yes—
140C22×C4×C11C2×D414yes—
141C22×C4×C11#4114yes—
142C22×C4×C11C2411yescharacteristic
143C22×Dic11—28no—
144C22×Dic11—24no—
145C22×Dic11—44no—
146C22×Dic11—44no—
147C11×C4⋊C4—28no—
148C11×C4⋊C4—28no—
149C11×C4⋊C4—24no—
150C11×C4⋊C4—22no—
151C11×C4⋊C4C22×C414yes—
152C11×C22⋊C4—28no—
153C11×C22⋊C4—28no—
154C22⋊Dic11—28no—
155C22⋊Dic11—28no—
156C4⋊Dic11—28no—
157C4⋊Dic11—24no—
158C4⋊Dic11C2×D418yes—
159C4×Dic11—28no—
160C4×Dic11—28no—
161#4318—48no—
162C2×C11⋊C8—24no—
163C2×C11⋊C8—24no—
164C2×C11⋊C8—24no—
165C22×C22⋊Q8D1111yescharacteristic
166C22×#117—111no—
167C2×#419—112no—
168C2×#407—111no—
169#1873—114no—
170#1872—114no—
171#1736—112no—
172C23×C11—21no—
173C23×C11—21no—
174C23×C11—22no—
175C23×C11—22no—
176C23×C11—22no—
177C23×C11—21no—
178C23×C11—21no—
179C23×C11—22no—
180C23×C11—22no—
181C23×C11—28no—
182C23×C11—28no—
183C23×C11—44no—
184C23×C11—48no—
185C23×C11—48no—
186C23×C11C2×C22⋊C412yes—
187C23×C11C2×C22⋊C412yes—
188C23×C11C2×C22⋊C412yes—
189C23×C11#12012yes—
190C23×C11#12312yes—
191C23×C11#13714yes—
192C23×C11C22×D411yescharacteristic
193Q8×C11—28no—
194Q8×C11—44no—
195Q8×C11—48no—
196C2×C4×C11—21no—
197C2×C4×C11—21no—
198C2×C4×C11—21no—
199C2×C4×C11—21no—
200C2×C4×C11—28no—
201C2×C4×C11—24no—
202C2×C4×C11—24no—
203C2×C4×C11—24no—
204C2×C4×C11—24no—
205C2×C4×C11—28no—
206C2×C4×C11—28no—
207C2×C4×C11—24no—
208C2×C4×C11—24no—
209C2×C4×C11—48no—
210C2×C4×C11—42no—
211C2×C4×C11—42no—
212C2×C4×C11—44no—
213C2×C4×C11—48no—
214C2×C4×C11C2×C22⋊C412yes—
215C2×C4×C11C2×C22⋊C412yes—
216C2×C4×C11C2×C22⋊C412yes—
217C2×C4×C11C4×D418yes—
218C2×C4×C11#12012yes—
219C2×C4×C11#12118yes—
220C2×C4×C11#12312yes—
221C2×C4×C11C23×C411yescharacteristic
222C2×C4×C11C22×D412yes—
223C2×C4×C11C22×D411yescharacteristic
224C2×C4×C11C2×#4112yes—
225C2×Dic11—28no—
226C2×Dic11—416no—
227C2×Dic11—44no—
228C2×Dic11—44no—
229C11⋊C8—44no—
230C23×Q8C2×D1111yescharacteristic
231C24×C4C2×D1111yescharacteristic
232C22×M16—112no—
233C2×C22⋊Q8—24no—
234C2×C22⋊Q8—21no—
235C2×C22⋊Q8—21no—
236C2×C22⋊Q8Dic1118yescomplemented
237C2×C22⋊Q8C2×D1112yes—
238C2×C22⋊Q8C2×D1112yes—
239C2×#117—112no—
240C2×#117—112no—
241C2×#117—228no—
242C2×#117—221no—
243C2×#117—221no—
244C22×C4⋊C4—21no—
245C22×C4⋊C4—112no—
246C22×C4⋊C4C2×D1111yescharacteristic
247C22×C22⋊C4—21no—
248C22×C22⋊C4—221no—
249C22×C42—221no—
250#419—228no—
251C2×#103—118no—
252#407—224no—
253C2×C22⋊C8—112no—
254C2×C22⋊C8—112no—
255#340—118no—
256C22×C11—24no—
257C22×C11—24no—
258C22×C11—22no—
259C22×C11—22no—
260C22×C11—22no—
261C22×C11—24no—
262C22×C11—24no—
263C22×C11—22no—
264C22×C11—22no—
265C22×C11—22no—
266C22×C11—22no—
267C22×C11—416no—
268C22×C11—42no—
269C22×C11—42no—
270C22×C11#38614yes—
271C22×C11#41914yescomplemented
272C22×C11C22×C22⋊C411yescharacteristic
273C22×C11C2×#12011yescharacteristic
274C22×C11C2×#12311yescharacteristic
275C22×C11C2×#13712yes—
276C22×C11#57512yes—
277C4×C11—22no—
278C4×C11—22no—
279C4×C11—44no—
280C4×C11—44no—
281C4×C11#38614yes—
282C4×C11C2×C4×D412yes—
283C4×C11C2×#12112yes—
284Dic11—48no—
285C25C22⋊D1111yescharacteristic
286C22×Q8—22no—
287C22×Q8—21no—
288C22×Q8—24no—
289C22×Q8—24no—
290C22×Q8C2×Dic1114yescomplemented
291C22×Q8C22×D1112yes—
292C23×C4—24no—
293C23×C4—24no—
294C23×C4—21no—
295C23×C4—21no—
296C23×C4—222no—
297C23×C4C2×Dic1114yes—
298C23×C4C22⋊D1111yescharacteristic
299C23×C4C22⋊D1111yescharacteristic
300C23×C4C22⋊D1111yescharacteristic
301C23×C4C22⋊D1114yes—
302C23×C4C22×D1111yescharacteristic
303C23×C4C22×D1111yescharacteristic
304C23×C4C22×D1111yescharacteristic
305C2×M16—224no—
306C2×M16—224no—
307C2×M16—224no—
308C22×C8—114no—
309C22⋊Q8—28no—
310C22⋊Q8—28no—
311C22⋊Q8—24no—
312C22⋊Q8—24no—
313C22⋊Q8C2×Dic1118yes—
314C22⋊Q8C2×Dic1118yescomplemented
315#117—118no—
316#117—228no—
317#117—228no—
318#117—228no—
319#117—224no—
320C2×C4⋊C4—28no—
321C2×C4⋊C4—22no—
322C2×C4⋊C4—22no—
323C2×C4⋊C4—21no—
324C2×C4⋊C4—22no—
325C2×C4⋊C4—114no—
326C2×C4⋊C4—228no—
327C2×C4⋊C4—222no—
328C2×C4⋊C4C2×Dic1114yescomplemented
329C2×C4⋊C4C22×D1112yes—
330C2×C22⋊C4—28no—
331C2×C22⋊C4—22no—
332C2×C22⋊C4—22no—
333C2×C22⋊C4—228no—
334C2×C22⋊C4—222no—
335C2×C22⋊C4—222no—
336C2×C42—228no—
337C2×C42—222no—
338C2×C42—222no—
339#103—2216no—
340C22⋊C8—224no—
341C22⋊C8—224no—
342C2×C11—24no—
343C2×C11—24no—
344C2×C11—42no—
345C2×C11C2×#38611yescharacteristic
346C2×C11C2×#41911yescharacteristic
347C2×C11#289611yescharacteristic
348C2×C11#300712yes—
349C2×C11#309512yes—
350C24—22no—
351C24—22no—
352C24—24no—
353C24—42no—
354C24C22⋊Dic1114yes—
355C24C2×C22⋊D1111yescharacteristic
356C24C2×C22⋊D1111yescharacteristic
357C24C2×C22⋊D1111yescharacteristic
358C2×Q8—24no—
359C2×Q8—22no—
360C2×Q8—216no—
361C2×Q8—24no—
362C2×Q8—24no—
363C2×Q8—42no—
364C2×Q8—42no—
365C2×Q8—48no—
366C2×Q8C22×Dic1114yes—
367C22×C4—22no—
368C22×C4—22no—
369C22×C4—216no—
370C22×C4—22no—
371C22×C4—22no—
372C22×C4—22no—
373C22×C4—22no—
374C22×C4—216no—
375C22×C4—22no—
376C22×C4—22no—
377C22×C4—22no—
378C22×C4—22no—
379C22×C4—24no—
380C22×C4—24no—
381C22×C4—22no—
382C22×C4—22no—
383C22×C4—44no—
384C22×C4—42no—
385C22×C4—42no—
386C22×C4—228no—
387C22×C4—224no—
388C22×C4—444no—
389C22×C4—444no—
390C22×C4C22⋊Dic1114yes—
391C22×C4C22⋊Dic1114yes—
392C22×C4C22⋊Dic1114yes—
393C22×C4D4×D1114yes—
394C22×C4#434114yes—
395C22×C4C22×Dic1112yes—
396C22×C4C22×Dic1112yes—
397C22×C4C22×Dic1112yes—
398C22×C4C2×C22⋊D1111yescharacteristic
399C22×C4C2×C22⋊D1111yescharacteristic
400C22×C4C2×C22⋊D1112yes—
401C22×C4C2×C22⋊D1112yes—
402C22×C4C2×C22⋊D1111yescharacteristic
403C22×C4C2×C22⋊D1112yes—
404C22×C4C23×D1111yescharacteristic
405M16—448no—
406C2×C8—224no—
407C2×C8—224no—
408C2×C8—224no—
409C4⋊C4—28no—
410C4⋊C4—28no—
411C4⋊C4—24no—
412C4⋊C4—22no—
413C4⋊C4—118no—
414C4⋊C4—228no—
415C4⋊C4—224no—
416C4⋊C4C22×Dic1114yes—
417C22⋊C4—28no—
418C22⋊C4—28no—
419C22⋊C4—228no—
420C22⋊C4—228no—
421C42—228no—
422C42—228no—
423C11#2091111yescharacteristic, complemented, Sylow
424C23—21no—
425C23—21no—
426C23—22no—
427C23—22no—
428C23—22no—
429C23—21no—
430C23—21no—
431C23—22no—
432C23—28no—
433C23—28no—
434C23—22no—
435C23—44no—
436C23—48no—
437C23—48no—
438C23#6698812yes—
439C23#6699012yes—
440C23#6699514yes—
441C23C2×C22⋊Dic1112yes—
442C23C2×C22⋊Dic1112yes—
443C23C2×C22⋊Dic1112yes—
444C23C22×C22⋊D1111yescharacteristic
445Q8—28no—
446Q8—44no—
447Q8—48no—
448C2×C4—21no—
449C2×C4—21no—
450C2×C4—21no—
451C2×C4—21no—
452C2×C4—28no—
453C2×C4—24no—
454C2×C4—24no—
455C2×C4—24no—
456C2×C4—24no—
457C2×C4—28no—
458C2×C4—28no—
459C2×C4—24no—
460C2×C4—24no—
461C2×C4—48no—
462C2×C4—42no—
463C2×C4—42no—
464C2×C4—48no—
465C2×C4—44no—
466C2×C4—228no—
467C2×C4—4416no—
468C2×C4—444no—
469C2×C4—444no—
470C2×C4D4×Dic1118yes—
471C2×C4#6698812yes—
472C2×C4#6699012yes—
473C2×C4#6699218yes—
474C2×C4C2×C22⋊Dic1112yes—
475C2×C4C2×C22⋊Dic1112yes—
476C2×C4C2×C22⋊Dic1112yes—
477C2×C4C2×D4×D1112yes—
478C2×C4C2×#434112yes—
479C2×C4C23×Dic1111yescharacteristic
480C2×C4C22×C22⋊D1111yescharacteristic
481C8—444no—
482C22—24no—
483C22—24no—
484C22—24no—
485C22—24no—
486C22—22no—
487C22—22no—
488C22—22no—
489C22—22no—
490C22—22no—
491C22—22no—
492C22—22no—
493C22—416no—
494C22—42no—
495C22—42no—
496C22#1062283314yes—
497C22#1062283814yescomplemented
498C22C2×#6698811yescharacteristic
499C22C2×#6699011yescharacteristic
500C22C2×#6699512yes—
501C22#1062335312yes—
502C22C22×C22⋊Dic1111yescharacteristic
503C4—22no—
504C4—22no—
505C4—44no—
506C4—44no—
507C4—448no—
508C4#1062283314yes—
509C4C2×D4×Dic1112yes—
510C4C2×#6699212yes—
511C2—24no—
512C2—24no—
513C2—42no—
514C2C2×#1062283311yescharacteristic
515C2C2×#1062283811yescharacteristic
516C2#1307713511yescharacteristic
517C2#1307787412yes—
518C2#1307856012yes—
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC22×C11×C22⋊Q8C2
socleC23×C11C22×D4
prime radicalC25×C11D4
cosocleC22×C4×C11C24
hypercenterC22×C22⋊Q8D11
hypocenterC11#20911
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C24×C4 ◁ C22×C22⋊Q8

Complements

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

NH ≅ G/Ntype
2. C2×#10622838C2semidirect
4. #13068929C2semidirect
5. #13068924C2semidirect
6. #13068335C2semidirect
13. C2×C11×C22⋊Q8C4semidirect
29. C2×#66899C22semidirect
33. #10622167C22semidirect
39. C22×Q8×C11C2×C4semidirect
59. C11×C22⋊Q8C2×C4semidirect
65. C2×C11×C4⋊C4C2×C4semidirect
236. C2×C22⋊Q8Dic11semidirect
271. C22×C11#419semidirect
290. C22×Q8C2×Dic11semidirect
314. C22⋊Q8C2×Dic11semidirect
328. C2×C4⋊C4C2×Dic11semidirect
423. C11#20911semidirect
497. C22#10622838semidirect

Maximal subgroups

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

subgroupindex
C22×#669792
C2×#106228382
C2×#106228202
#130689292
#130689242
#130683352
C22×C11×C22⋊Q82
#2091111