Finite Group Databasebeta

← #14659210

Subgroups — #14659210

Order 2816.

1254 conjugacy classes of subgroups.

The subgroup lattice has 486 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623358C211yesmaximal, characteristic
2C2×#10622850C211yesmaximal, characteristic
3#13068337C212yesmaximal, complemented
4#13068326C212yesmaximal, complemented
5C2×C11×#410C211yesmaximal, characteristic
6C22×C11×#41C2211yescharacteristic
7C2×C11×#117C2212yes—
8#10623358—24no—
9#10623358—24no—
10C2×Q8×Dic11—21no—
11C2×D4×Dic11—21no—
12C2×D4×Dic11—22no—
13C2×#66979C412yescomplemented
14C2×#66979C2211yescharacteristic
15C22×C4⋊Dic11C412yescomplemented
16C22×C4⋊Dic11C2211yescharacteristic
17C22×#4318C2212yes—
18C11×#410—22no—
19C11×#410C414yescomplemented
20C2×C11×#99—22no—
21#10622850—22no—
22#10622850C414yescomplemented
23C2×#66900—21no—
24C2×#66897—21no—
25#10622167—24no—
26#10622161—24no—
27C2×C11×#41—22no—
28C2×C11×#41—22no—
29C2×C11×#41—22no—
30C2×C11×#41—22no—
31C2×C11×#41C2×C412yes—
32C2×C11×#41C2×C412yes—
33C2×C11×#41D412yes—
34C2×C11×#41Q812yes—
35C22×Q8×C11D411yescharacteristic
36C22×D4×C11D411yescharacteristic
37C22×D4×C11D412yes—
38C23×C4×C11C2×C412yes—
39C23×C4×C11C2311yescharacteristic
40C23×Dic11—22no—
41C23×Dic11—21no—
42C11×#117—22no—
43C11×#117—22no—
44C11×#117—22no—
45C11×#117C2×C414yescomplemented
46C2×C11×C4⋊C4—22no—
47C2×C11×C22⋊C4—22no—
48C2×C42×C11—22no—
49C2×C22⋊Dic11—22no—
50C2×C22⋊Dic11—21no—
51Q8×Dic11—28no—
52D4×Dic11—216no—
53D4×Dic11—28no—
54#66979—22no—
55#66979—24no—
56#66979—24no—
57#66979D414yes—
58C2×C4⋊Dic11—22no—
59C2×C4⋊Dic11—21no—
60C2×C4⋊Dic11—22no—
61C2×C4⋊Dic11—24no—
62C2×C4⋊Dic11—24no—
63C2×C4⋊Dic11C2×C411yescharacteristic
64C2×C4⋊Dic11C2×C412yes—
65C2×C4⋊Dic11C2×C411yescharacteristic
66C2×C4⋊Dic11D414yes—
67C2×C4×Dic11—22no—
68C2×C4×Dic11—21no—
69C2×#4318—22no—
70C2×#4318—22no—
71C2×#4318—22no—
72C2×#4318—22no—
73C2×#4318—22no—
74C2×#4318C2×C414yescomplemented
75C22×C11⋊C8—22no—
76C11×#99—28no—
77#66900—24no—
78#66897—24no—
79#10765—111nomaximal, Sylow
80C24×C11C22⋊C412yes—
81C24×C11C2×D411yescharacteristic
82C11×#41—24no—
83C11×#41—24no—
84C11×#41—24no—
85C11×#41—24no—
86C11×#41—24no—
87C11×#41—24no—
88C11×#41—24no—
89C11×#41—24no—
90C2×Q8×C11—22no—
91C2×Q8×C11—22no—
92C2×Q8×C11C22⋊C412yes—
93C2×Q8×C11C4⋊C412yes—
94C2×D4×C11—24no—
95C2×D4×C11—24no—
96C2×D4×C11—22no—
97C2×D4×C11—22no—
98C2×D4×C11C22⋊C414yes—
99C2×D4×C11C22⋊C412yes—
100C2×D4×C11C4⋊C414yes—
101C2×D4×C11C4⋊C412yes—
102C22×C4×C11—22no—
103C22×C4×C11—22no—
104C22×C4×C11—22no—
105C22×C4×C11—22no—
106C22×C4×C11—42no—
107C22×C4×C11C4214yes—
108C22×C4×C11C22⋊C412yes—
109C22×C4×C11C4⋊C414yes—
110C22×C4×C11C22×C411yescharacteristic
111C22×C4×C11C22×C411yescharacteristic
112C22×C4×C11C22×C411yescharacteristic
113C22×C4×C11C2×D411yescharacteristic
114C22×C4×C11C2×D411yescharacteristic
115C22×C4×C11C2×D412yes—
116C22×C4×C11C2×D412yes—
117C22×C4×C11C2×Q811yescharacteristic
118C22×C4×C11#4112yes—
119C22×C4×C11#4112yes—
120C22×Dic11—28no—
121C22×Dic11—21no—
122C22×Dic11—22no—
123C22×Dic11—21no—
124C22×Dic11—24no—
125C22×Dic11—82no—
126C22×Dic11—84no—
127C11×C4⋊C4—24no—
128C11×C4⋊C4—42no—
129C11×C22⋊C4—24no—
130C11×C22⋊C4—42no—
131C42×C11—24no—
132C42×C11—42no—
133C22⋊Dic11—28no—
134C22⋊Dic11—24no—
135C4⋊Dic11—28no—
136C4⋊Dic11—22no—
137C4⋊Dic11—21no—
138C4⋊Dic11—21no—
139C4⋊Dic11—24no—
140C4⋊Dic11C22⋊C412yes—
141C4⋊Dic11C22⋊C414yes—
142C4⋊Dic11C22⋊C412yes—
143C4×Dic11—28no—
144C4×Dic11—24no—
145#4318—24no—
146#4318—24no—
147#4318—42no—
148#4318—42no—
149C2×C11⋊C8—24no—
150C2×C11⋊C8—42no—
151C2×C11⋊C8—42no—
152C2×#520—111no—
153C2×#413—111no—
154C2×#410D1111yescharacteristic
155#1736—112no—
156#1733—112no—
157C23×C11—22no—
158C23×C11—22no—
159C23×C11—41no—
160C23×C11—41no—
161C23×C11—42no—
162C23×C11—42no—
163C23×C11#9514yes—
164C23×C11C2×C22⋊C411yescharacteristic
165C23×C11C2×C22⋊C411yescharacteristic
166C23×C11C2×C4⋊C411yescharacteristic
167C23×C11#12012yes—
168C23×C11#12312yes—
169Q8×C11—24no—
170Q8×C11—24no—
171D4×C11—28no—
172D4×C11—28no—
173D4×C11—24no—
174D4×C11—24no—
175C2×C4×C11—22no—
176C2×C4×C11—22no—
177C2×C4×C11—24no—
178C2×C4×C11—24no—
179C2×C4×C11—24no—
180C2×C4×C11—24no—
181C2×C4×C11—44no—
182C2×C4×C11—82no—
183C2×C4×C11—82no—
184C2×C4×C11#9514yes—
185C2×C4×C11C2×C4211yescharacteristic
186C2×C4×C11C2×C22⋊C411yescharacteristic
187C2×C4×C11C2×C22⋊C411yescharacteristic
188C2×C4×C11C2×C22⋊C411yescharacteristic
189C2×C4×C11C2×C4⋊C411yescharacteristic
190C2×C4×C11C2×C4⋊C411yescharacteristic
191C2×C4×C11#11711yescharacteristic
192C2×C4×C11#11711yescharacteristic
193C2×C4×C11C4×D412yes—
194C2×C4×C11C4×D412yes—
195C2×C4×C11C4×D412yes—
196C2×C4×C11C4×D412yes—
197C2×C4×C11#12012yes—
198C2×C4×C11#12112yes—
199C2×C4×C11#12112yes—
200C2×C4×C11C22⋊Q812yes—
201C2×C4×C11C22⋊Q812yes—
202C2×C4×C11#12312yes—
203C2×Dic11—22no—
204C2×Dic11—24no—
205C2×Dic11—22no—
206C2×Dic11—42no—
207C2×Dic11—44no—
208C2×Dic11—42no—
209C2×Dic11—84no—
210C2×Dic11—88no—
211C11⋊C8—44no—
212C22×#41C2×D1111yescharacteristic
213C22×M16—112no—
214#520—224no—
215#520—224no—
216C2×C4×Q8—221no—
217C2×C4×D4—221no—
218C2×C4×D4—222no—
219C2×#117—111no—
220C2×#117—112no—
221C2×#117C2×D1112yes—
222C22×C4⋊C4—111no—
223C22×C4⋊C4—112no—
224#413—114no—
225#413—222no—
226C2×#101—221no—
227C2×#100—221no—
228#410—22no—
229#410Dic1114yescomplemented
230C2×#99—22no—
231#340—224no—
232#339—224no—
233C22×C11—22no—
234C22×C11—21no—
235C22×C11—22no—
236C22×C11—21no—
237C22×C11—24no—
238C22×C11—41no—
239C22×C11—41no—
240C22×C11—42no—
241C22×C11—44no—
242C22×C11—44no—
243C22×C11—42no—
244C22×C11—42no—
245C22×C11C2×#9511yescharacteristic
246C22×C11#37911yescharacteristic
247C22×C11#38111yescharacteristic
248C22×C11#38512yes—
249C22×C11#38612yes—
250C4×C11—24no—
251C4×C11—84no—
252C4×C11C4×C22⋊C411yescharacteristic
253C4×C11C4×C22⋊C411yescharacteristic
254C4×C11#38011yescharacteristic
255C4×C11#38011yescharacteristic
256C4×C11#38512yes—
257C4×C11#38612yes—
258Dic11—44no—
259Dic11—42no—
260Dic11—42no—
261C2×#41—22no—
262C2×#41—22no—
263C2×#41—22no—
264C2×#41—22no—
265C2×#41Dic2212yes—
266C2×#41C4×D1112yes—
267C2×#41C2×Dic1112yes—
268C2×#41C22⋊D1112yes—
269C22×Q8D4411yescharacteristic
270C22×D4D4411yescharacteristic
271C22×D4C22⋊D1112yes—
272C23×C4—222no—
273C23×C4—221no—
274C23×C4C4×D1112yes—
275C23×C4C22×D1111yescharacteristic
276C2×M16—114no—
277C2×M16—222no—
278C2×M16—222no—
279C2×M16—222no—
280C2×M16—222no—
281C2×M16—222no—
282C22×C8—222no—
283C4×Q8—228no—
284C4×D4—2216no—
285C4×D4—228no—
286#117—22no—
287#117—22no—
288#117—22no—
289#117—114no—
290#117—224no—
291#117—224no—
292#117—222no—
293#117C2×Dic1114yescomplemented
294C2×C4⋊C4—22no—
295C2×C4⋊C4—112no—
296C2×C4⋊C4—111no—
297C2×C4⋊C4—111no—
298C2×C4⋊C4—114no—
299C2×C4⋊C4—224no—
300C2×C4⋊C4—224no—
301C2×C4⋊C4—222no—
302C2×C4⋊C4—221no—
303C2×C4⋊C4—222no—
304C2×C22⋊C4—22no—
305C2×C22⋊C4—222no—
306C2×C22⋊C4—221no—
307C2×C42—22no—
308C2×C42—222no—
309C2×C42—221no—
310#101—224no—
311#100—224no—
312#99—28no—
313C2×C11—22no—
314C2×C11—21no—
315C2×C11—21no—
316C2×C11—22no—
317C2×C11—44no—
318C2×C11C22⋊#9511yescharacteristic
319C2×C11#179511yescharacteristic
320C2×C11#179611yescharacteristic
321C24(C2×D11)⋊C412yes—
322C24C2×C22⋊D1111yescharacteristic
323#41—24no—
324#41—24no—
325#41—24no—
326#41—24no—
327#41—24no—
328#41—24no—
329#41—24no—
330#41—24no—
331C2×Q8—22no—
332C2×Q8—22no—
333C2×Q8C4⋊Dic1112yes—
334C2×Q8(C2×D11)⋊C412yes—
335C2×D4—24no—
336C2×D4—24no—
337C2×D4—22no—
338C2×D4—22no—
339C2×D4Dic11⋊C414yes—
340C2×D4C4⋊Dic1112yes—
341C2×D4(C2×D11)⋊C412yes—
342C2×D4C22⋊Dic1114yes—
343C22×C4—22no—
344C22×C4—22no—
345C22×C4—22no—
346C22×C4—22no—
347C22×C4—42no—
348C22×C4—221no—
349C22×C4—222no—
350C22×C4—221no—
351C22×C4—228no—
352C22×C4—224no—
353C22×C4—882no—
354C22×C4—884no—
355C22×C4C4×Dic1114yes—
356C22×C4Dic11⋊C414yes—
357C22×C4(C2×D11)⋊C412yes—
358C22×C4C2×Dic2211yescharacteristic
359C22×C4C2×C4×D1111yescharacteristic
360C22×C4C2×C4×D1111yescharacteristic
361C22×C4C2×D4411yescharacteristic
362C22×C4D4×D1112yes—
363C22×C4D4×D1112yes—
364C22×C4#434112yes—
365C22×C4#434112yes—
366C22×C4C22×Dic1111yescharacteristic
367C22×C4C2×C22⋊D1111yescharacteristic
368M16—224no—
369M16—224no—
370M16—442no—
371M16—442no—
372C2×C8—224no—
373C2×C8—442no—
374C2×C8—442no—
375C4⋊C4—24no—
376C4⋊C4—42no—
377C4⋊C4—114no—
378C4⋊C4—112no—
379C4⋊C4—112no—
380C4⋊C4—228no—
381C4⋊C4—221no—
382C4⋊C4—222no—
383C4⋊C4—221no—
384C4⋊C4—224no—
385C22⋊C4—24no—
386C22⋊C4—42no—
387C22⋊C4—228no—
388C22⋊C4—224no—
389C42—24no—
390C42—42no—
391C42—228no—
392C42—224no—
393C11#1076511yescharacteristic, complemented, Sylow
394C23—22no—
395C23—22no—
396C23—41no—
397C23—41no—
398C23—42no—
399C23—42no—
400C23C11⋊#9514yes—
401C23C2×Dic11⋊C411yescharacteristic
402C23C2×(C2×D11)⋊C411yescharacteristic
403C23#6698812yes—
404C23#6699012yes—
405C23C2×C22⋊Dic1111yescharacteristic
406Q8—24no—
407Q8—24no—
408D4—28no—
409D4—28no—
410D4—24no—
411D4—24no—
412C2×C4—22no—
413C2×C4—22no—
414C2×C4—24no—
415C2×C4—24no—
416C2×C4—24no—
417C2×C4—24no—
418C2×C4—44no—
419C2×C4—82no—
420C2×C4—82no—
421C2×C4—222no—
422C2×C4—224no—
423C2×C4—222no—
424C2×C4—444no—
425C2×C4—442no—
426C2×C4—442no—
427C2×C4—884no—
428C2×C4—888no—
429C2×C4C11⋊#9514yes—
430C2×C4#6693011yescharacteristic
431C2×C4#6693011yescharacteristic
432C2×C4#6693112yes—
433C2×C4#6693112yes—
434C2×C4C22⋊C4×D1111yescharacteristic
435C2×C4C22⋊C4×D1111yescharacteristic
436C2×C4(C22⋊D11)⋊C412yes—
437C2×C4(C22⋊D11)⋊C412yes—
438C2×C4#6693512yes—
439C2×C4#6693912yes—
440C2×C4C2×C4×Dic1111yescharacteristic
441C2×C4C2×Dic11⋊C411yescharacteristic
442C2×C4C2×C4⋊Dic1111yescharacteristic
443C2×C4C2×(C2×D11)⋊C411yescharacteristic
444C2×C4D4×Dic1112yes—
445C2×C4D4×Dic1112yes—
446C2×C4#6699212yes—
447C2×C4#6699212yes—
448C8—444no—
449C22—22no—
450C22—21no—
451C22—22no—
452C22—21no—
453C22—24no—
454C22—41no—
455C22—42no—
456C22—41no—
457C22—44no—
458C22—44no—
459C22—42no—
460C22—42no—
461C22#1062255611yescharacteristic
462C22#1062255912yes—
463C22#1062256811yescharacteristic
464C22C2×C11⋊#9511yescharacteristic
465C22#1062283312yes—
466C4—24no—
467C4—84no—
468C4—444no—
469C4—442no—
470C4—442no—
471C4C22⋊C4×Dic1111yescharacteristic
472C4C22⋊C4×Dic1111yescharacteristic
473C4#1062255511yescharacteristic
474C4#1062255511yescharacteristic
475C4#1062256312yes—
476C4#1062257112yes—
477C2—22no—
478C2—21no—
479C2—21no—
480C2—22no—
481C2—44no—
482C2#1306683811yescharacteristic
483C2#1306858411yescharacteristic
484C2#1306858911yescharacteristic
subgroupG/H
centerC22#10622568
commutatorC2×C4×C11C2×C42
FrattiniC23×C4C22×D11
FittingC2×C11×#410C2
socleC22×C11#379
prime radicalC22×C11×#41C22
cosocleC23×C4×C11C23
hypercenterC2×#410D11
hypocenterC11#10765
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#410

Complements

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

NH ≅ G/Ntype
3. #13068337C2semidirect
4. #13068326C2semidirect
13. C2×#66979C4semidirect
15. C22×C4⋊Dic11C4semidirect
19. C11×#410C4semidirect
22. #10622850C4semidirect
45. C11×#117C2×C4semidirect
74. C2×#4318C2×C4semidirect
229. #410Dic11semidirect
293. #117C2×Dic11semidirect
393. C11#10765semidirect

Maximal subgroups

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

subgroupindex
C2×#106233582
C2×#106228502
#130683372
#130683262
C2×C11×#4102
#1076511