Finite Group Databasebeta

← #14769524

Subgroups — #14769524

Order 2816.

1438 conjugacy classes of subgroups.

The subgroup lattice has 524 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66972C211yesmaximal, characteristic
2C2×#10622797C211yesmaximal, characteristic, complemented
3#13071454C212yesmaximal, complemented
4#13069492C211yesmaximal, characteristic, complemented
5#13069490C211yesmaximal, characteristic, complemented
6#13068971C212yesmaximal, complemented
7#13068969C212yesmaximal, complemented
8#13068638C211yesmaximal, characteristic, complemented
9#13068555C212yesmaximal, complemented
10#13068393C211yesmaximal, characteristic, complemented
11C2×C11×#441C211yesmaximal, characteristic, complemented
12C22×#4343C2212yes—
13C22×C11×Q16C2211yescharacteristic
14C2×C4×Q8×C11C2212yes—
15C2×Q8×Dic11C2212yes—
16C22×#4325C2212yes—
17C2×#66972—24no—
18C2×#66972—24no—
19C2×#66972C418yescomplemented
20C22×D88C2211yescharacteristic
21C22×C8×D11C2211yescharacteristic
22C11×#441—24no—
23C2×C11×#106C2211yescharacteristic
24C2×C11×#103C2212yes—
25C2×C11×#97C2211yescharacteristic
26C2×#66899C2212yes—
27#10622797—24no—
28C2×#66885C2212yes—
29C2×(C2×D11)⋊C8C2211yescharacteristic
30C2×#66881C2211yescharacteristic
31C2×#66879C2211yescharacteristic
32#10622601—22no—
33#10622601C2212yes—
34#10622600—22no—
35#10622600C2212yes—
36C2×#66873C2212yes—
37#10622552—22no—
38#10622552C2212yes—
39C4×(C2×D11)⋊C4—22no—
40C4×(C2×D11)⋊C4C2211yescharacteristic
41#10622188C2211yescharacteristic
42#10622167C2212yes—
43#10622162C2211yescharacteristic
44C22×Q8×C11C2312yes—
45C2×#4343—24no—
46C2×#4343—24no—
47C2×#4343—24no—
48C2×#4343—42no—
49C2×#4343—42no—
50C2×#4343C2×C418yes—
51C22×D44—22no—
52C22×D44C2312yes—
53C22×C4×D11—22no—
54C22×C4×D11C2311yescharacteristic
55C2×C11×Q16C2×C414yes—
56C2×C11×Q16D414yes—
57C2×C11×Q16D414yes—
58C22×C8×C11C2311yescharacteristic
59C22×C8×C11C2311yescharacteristic
60C4×Q8×C11—24no—
61C4×Q8×C11—42no—
62C2×C11×C4⋊C4—22no—
63C2×C11×C4⋊C4C2312yes—
64C2×C42×C11—22no—
65C2×C42×C11C2311yescharacteristic
66Q8×Dic11—24no—
67Q8×Dic11—42no—
68C2×#4325—24no—
69C2×#4325—24no—
70C2×#4325C2×C418yes—
71C2×(C2×D11)⋊C4—22no—
72C2×(C2×D11)⋊C4—22no—
73C2×(C2×D11)⋊C4—22no—
74C2×(C2×D11)⋊C4—22no—
75C2×(C2×D11)⋊C4—22no—
76C2×(C2×D11)⋊C4D412yes—
77C2×C4⋊Dic11—22no—
78C2×C4⋊Dic11C2312yes—
79C2×C4×Dic11—22no—
80C2×C4×Dic11C2311yescharacteristic
81C22×C11⋊C8C2311yescharacteristic
82C22×C11⋊C8C2311yescharacteristic
83#66972—232no—
84C2×D88—22no—
85C2×D88—22no—
86C2×D88C2×C414yes—
87C2×C8×D11—22no—
88C2×C8×D11—22no—
89C2×C8×D11C2×C414yes—
90C11×#106—22no—
91C11×#103—24no—
92C11×#97—22no—
93#66899—24no—
94C11⋊#95—22no—
95C11⋊#95D412yes—
96#66885—42no—
97(C2×D11)⋊C8—22no—
98#66881—22no—
99#66879—22no—
100#66873—42no—
101#22441—111nomaximal, Sylow
102C23×D11—22no—
103C23×D11C2×D411yescharacteristic
104C2×Q8×C11—22no—
105C2×Q8×C11—22no—
106C2×Q8×C11—22no—
107C2×Q8×C11C22×C414yes—
108C2×Q8×C11C2×D414yes—
109C2×Q8×C11C2×D414yes—
110C22×C4×C11—22no—
111C22×C4×C11—22no—
112C22×C4×C11C2×D412yes—
113C22×C4×C11C2411yescharacteristic
114C22×Dic11—22no—
115C22×Dic11C2×D412yes—
116C22×Dic11C2×D411yescharacteristic
117#4343—216no—
118#4343—48no—
119#4343—48no—
120#4343—48no—
121C2×D44—28no—
122C2×D44—22no—
123C2×D44—22no—
124C2×D44—22no—
125C2×D44—22no—
126C2×D44—22no—
127C2×D44—44no—
128C2×D44—44no—
129C2×D44C22×C414yes—
130C2×C4×D11—28no—
131C2×C4×D11—21no—
132C2×C4×D11—21no—
133C2×C4×D11—21no—
134C2×C4×D11—21no—
135C2×C4×D11—44no—
136C2×C4×D11—44no—
137C2×C4×D11C22×C412yes—
138C2×C4×D11#4112yes—
139C11×Q16C22⋊C4116yescomplemented
140C2×C8×C11—21no—
141C2×C8×C11—21no—
142C2×C8×C11—21no—
143C2×C8×C11C22×C412yes—
144C2×C8×C11C2×D412yes—
145C2×C8×C11C2×D412yes—
146C11×C4⋊C4—22no—
147C11×C4⋊C4—22no—
148C11×C4⋊C4—44no—
149C42×C11—21no—
150C42×C11—21no—
151C42×C11—44no—
152#4325—216no—
153(C2×D11)⋊C4—42no—
154(C2×D11)⋊C4—44no—
155(C2×D11)⋊C4—44no—
156(C2×D11)⋊C4—82no—
157(C2×D11)⋊C4—82no—
158(C2×D11)⋊C4—82no—
159C4⋊Dic11—22no—
160C4⋊Dic11—22no—
161C4⋊Dic11—44no—
162C4×Dic11—21no—
163C4×Dic11—21no—
164C4×Dic11—44no—
165C2×C11⋊C8—21no—
166C2×C11⋊C8—21no—
167C2×C11⋊C8—21no—
168C2×C11⋊C8—21no—
169C2×C11⋊C8—21no—
170C2×C11⋊C8C22×C412yes—
171D88—28no—
172C8×D11—28no—
173C22×#135—111no—
174C2×#441—111no—
175C2×#441D1111yescharacteristic, complemented
176#2341—112no—
177#1972—111no—
178#1972—111no—
179#1880—112no—
180#1880—112no—
181#1807—111no—
182#1788—112no—
183#1752—111no—
184C23×C11C22×D411yescharacteristic
185C22×D11—21no—
186C22×D11—21no—
187C22×D11—22no—
188C22×D11—22no—
189C22×D11—24no—
190C22×D11—42no—
191C22×D11—42no—
192C22×D11—42no—
193C22×D11—42no—
194C22×D11—42no—
195C22×D11—42no—
196C22×D11C4×D412yes—
197Q8×C11—24no—
198Q8×C11—24no—
199Q8×C11—24no—
200Q8×C11C2×C22⋊C418yes—
201C2×C4×C11—24no—
202C2×C4×C11—24no—
203C2×C4×C11—24no—
204C2×C4×C11—22no—
205C2×C4×C11—22no—
206C2×C4×C11—22no—
207C2×C4×C11—42no—
208C2×C4×C11—42no—
209C2×C4×C11—42no—
210C2×C4×C11C23×C411yescharacteristic
211C2×C4×C11C22×D411yescharacteristic
212C2×C4×C11C22×D411yescharacteristic
213C2×C4×C11C2×#4111yescharacteristic
214C2×C4×C11H(5,𝔽2)11yescharacteristic
215C2×C4×C11H(5,𝔽2)11yescharacteristic
216C2×Dic11—21no—
217C2×Dic11—21no—
218C2×Dic11—22no—
219C2×Dic11—22no—
220C2×Dic11—22no—
221C2×Dic11—42no—
222C2×Dic11—42no—
223C2×Dic11—42no—
224C2×Dic11C4×D412yes—
225D44—24no—
226D44—24no—
227D44—416no—
228D44—42no—
229D44—42no—
230C4×D11—22no—
231C4×D11—22no—
232C4×D11—22no—
233C4×D11—22no—
234C4×D11—416no—
235C8×C11—41no—
236C8×C11C2×C22⋊C414yes—
237C11⋊C8—22no—
238C11⋊C8—41no—
239C22×#41—112no—
240C2×#135—118no—
241C2×#135—224no—
242C2×#135—224no—
243C22×Q16C2×D1111yescharacteristic
244C22×SD16—112no—
245C22×D8—111no—
246C23×C8—111no—
247C2×C4×Q8—112no—
248C2×C4×Q8C2×D1112yes—
249#441—24no—
250#441—224no—
251C2×#106—111no—
252C2×#106C2×D1111yescharacteristic
253C2×#103—112no—
254C2×#103C2×D1112yes—
255C2×#102—112no—
256C2×#102—112no—
257C2×C22⋊C8—111no—
258C2×#97—111no—
259C2×#97C2×D1111yescharacteristic
260#390—112no—
261#390—112no—
262#390—222no—
263#390—222no—
264#380—112no—
265#380—222no—
266C4×C22⋊C4—111no—
267C4×C22⋊C4—222no—
268#340—112no—
269#336—111no—
270#336—111no—
271C22×C11C2×C4×D411yescharacteristic
272C22×C11D4211yescharacteristic
273C22×C11D4211yescharacteristic
274C22×C11#57512yes—
275C22×C11#57712yes—
276C2×D11—22no—
277C2×D11—22no—
278C2×D11—22no—
279C2×D11—42no—
280C2×D11—42no—
281C2×D11—44no—
282C2×D11—44no—
283C2×D11—44no—
284C2×D11—82no—
285C2×D11—82no—
286C2×D11—82no—
287C2×D11—82no—
288C4×C11—28no—
289C4×C11—42no—
290C4×C11—82no—
291C4×C11C22×C22⋊C411yescharacteristic
292C4×C11#51811yescharacteristic
293C4×C11#54611yescharacteristic
294C4×C11#54611yescharacteristic
295Dic11—22no—
296Dic11—42no—
297Dic11—82no—
298C2×#41—118no—
299C2×#41—224no—
300C2×#41—224no—
301C2×#41—224no—
302C2×#41—442no—
303C2×#41—442no—
304C22×Q8C22×D1112yes—
305C22×D4—112no—
306C22×D4—222no—
307C23×C4—111no—
308C23×C4—222no—
309#135—2232no—
310C2×Q16C4×D1114yes—
311C2×Q16D4414yes—
312C2×Q16C22⋊D1114yes—
313C2×SD16—118no—
314C2×SD16—224no—
315C2×SD16—224no—
316C2×D8—114no—
317C2×D8—222no—
318C2×D8—222no—
319C22×C8—111no—
320C22×C8—114no—
321C22×C8—111no—
322C22×C8—222no—
323C22×C8—222no—
324C22×C8C22×D1111yescharacteristic
325C22×C8C22×D1111yescharacteristic
326C4×Q8—24no—
327C4×Q8—42no—
328C4×Q8—224no—
329C4×Q8—442no—
330C2×C4⋊C4—22no—
331C2×C4⋊C4—112no—
332C2×C4⋊C4—222no—
333C2×C4⋊C4C22×D1112yes—
334C2×C22⋊C4—112no—
335C2×C22⋊C4—222no—
336C2×C22⋊C4—222no—
337C2×C22⋊C4—222no—
338C2×C22⋊C4—222no—
339C2×C22⋊C4—222no—
340C2×C42—22no—
341C2×C42—111no—
342C2×C42—222no—
343C2×C42C22×D1111yescharacteristic
344#106—22no—
345#106—222no—
346#103—24no—
347#103—224no—
348#102—442no—
349#102—442no—
350C22⋊C8—222no—
351#97—22no—
352#97—222no—
353#95—112no—
354#95—222no—
355C2×C11D4×C22⋊C411yescharacteristic
356C2×C11#294311yescharacteristic
357C2×C11#295211yescharacteristic
358C2×C11#327112yes—
359C2×C11#327112yes—
360D11—42no—
361D11—84no—
362C24—111no—
363C24—222no—
364#41—2216no—
365#41—448no—
366#41—448no—
367#41—448no—
368C2×Q8—22no—
369C2×Q8—22no—
370C2×Q8—22no—
371C2×Q8C2×C4×D1114yes—
372C2×Q8C2×D4414yes—
373C2×Q8C2×C22⋊D1114yes—
374C2×D4—114no—
375C2×D4—228no—
376C2×D4—222no—
377C2×D4—222no—
378C2×D4—222no—
379C2×D4—222no—
380C2×D4—222no—
381C2×D4—444no—
382C2×D4—444no—
383C22×C4—22no—
384C22×C4—22no—
385C22×C4—111no—
386C22×C4—112no—
387C22×C4—112no—
388C22×C4—112no—
389C22×C4—228no—
390C22×C4—221no—
391C22×C4—221no—
392C22×C4—221no—
393C22×C4—221no—
394C22×C4—222no—
395C22×C4—444no—
396C22×C4—444no—
397C22×C4D4×D1112yes—
398C22×C4C23×D1111yescharacteristic
399Q16(C2×D11)⋊C4116yescomplemented
400SD16—2216no—
401D8—228no—
402C2×C8—21no—
403C2×C8—21no—
404C2×C8—21no—
405C2×C8—112no—
406C2×C8—221no—
407C2×C8—221no—
408C2×C8—228no—
409C2×C8—221no—
410C2×C8—221no—
411C2×C8—221no—
412C2×C8C2×C4×D1112yes—
413C2×C8C2×D4412yes—
414C2×C8C2×C22⋊D1112yes—
415C4⋊C4—22no—
416C4⋊C4—22no—
417C4⋊C4—44no—
418C4⋊C4—222no—
419C4⋊C4—222no—
420C4⋊C4—444no—
421C22⋊C4—442no—
422C22⋊C4—444no—
423C22⋊C4—444no—
424C22⋊C4—882no—
425C22⋊C4—882no—
426C22⋊C4—882no—
427C42—21no—
428C42—21no—
429C42—44no—
430C42—221no—
431C42—221no—
432C42—444no—
433C11#2244111yescharacteristic, complemented, Sylow
434C23—112no—
435C23—222no—
436C23—222no—
437C23—221no—
438C23—221no—
439C23—224no—
440C23—442no—
441C23—442no—
442C23—442no—
443C23—442no—
444C23—442no—
445C23—442no—
446C23C2×D4×D1111yescharacteristic
447Q8—24no—
448Q8—24no—
449Q8—24no—
450Q8C2×(C2×D11)⋊C418yes—
451D4—224no—
452D4—224no—
453D4—4416no—
454D4—442no—
455D4—442no—
456C2×C4—24no—
457C2×C4—24no—
458C2×C4—24no—
459C2×C4—22no—
460C2×C4—22no—
461C2×C4—22no—
462C2×C4—42no—
463C2×C4—42no—
464C2×C4—42no—
465C2×C4—112no—
466C2×C4—221no—
467C2×C4—221no—
468C2×C4—222no—
469C2×C4—222no—
470C2×C4—222no—
471C2×C4—222no—
472C2×C4—222no—
473C2×C4—222no—
474C2×C4—222no—
475C2×C4—4416no—
476C2×C4—442no—
477C2×C4—442no—
478C2×C4—442no—
479C2×C4C22×C4×D1111yescharacteristic
480C2×C4C22×D4411yescharacteristic
481C2×C4#6703711yescharacteristic
482C2×C4#41×D1111yescharacteristic
483C2×C4#6704211yescharacteristic
484C2×C4C22×C22⋊D1111yescharacteristic
485C8—41no—
486C8—222no—
487C8—441no—
488C8C2×(C2×D11)⋊C414yes—
489C22—222no—
490C22—222no—
491C22—222no—
492C22—442no—
493C22—442no—
494C22—444no—
495C22—444no—
496C22—444no—
497C22—882no—
498C22—882no—
499C22—882no—
500C22—882no—
501C22C4×D4×D1111yescharacteristic
502C22D4×D4411yescharacteristic
503C22#1062330812yes—
504C22#1062330912yes—
505C22D4×C22⋊D1111yescharacteristic
506C4—28no—
507C4—42no—
508C4—82no—
509C4—222no—
510C4—442no—
511C4—882no—
512C4#1062307611yescharacteristic
513C4#1062308511yescharacteristic
514C4C22×(C2×D11)⋊C411yescharacteristic
515C4#1062336011yescharacteristic
516C2—442no—
517C2—884no—
518C2D4×(C2×D11)⋊C411yescharacteristic
519C2#1307741511yescharacteristic
520C2#1307749611yescharacteristic
521C2#1308019512yes—
522C2#1308020312yes—
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#441C2
socleC23×C11C22×D4
prime radicalC22×#66972C2
cosocleC22×C4×C11C24
hypercenterC2×#441D11
hypocenterC11#22441
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#441

Complements

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

NH ≅ G/Ntype
2. C2×#10622797C2semidirect
3. #13071454C2semidirect
4. #13069492C2semidirect
5. #13069490C2semidirect
6. #13068971C2semidirect
7. #13068969C2semidirect
8. #13068638C2semidirect
9. #13068555C2semidirect
10. #13068393C2semidirect
11. C2×C11×#441C2semidirect
19. C2×#66972C4semidirect
139. C11×Q16C22⋊C4semidirect
175. C2×#441D11semidirect
399. Q16(C2×D11)⋊C4semidirect
433. C11#22441semidirect

Maximal subgroups

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

subgroupindex
C22×#669722
C2×#106227972
#130714542
#130694922
#130694902
#130689712
#130689692
#130686382
#130685552
#130683932
C2×C11×#4412
#2244111