Finite Group Databasebeta

← #14909501

Subgroups — #14909501

Order 2816.

694 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622496C211yesmaximal, characteristic, complemented
2D11×#466C211yesmaximal, characteristic, complemented
3#13070798C212yesmaximal, complemented
4#13070796C211yesmaximal, characteristic, complemented
5#13070703C212yesmaximal, complemented
6#13070701C212yesmaximal, complemented
7#13070530C211yesmaximal, characteristic, complemented
8#13070529C212yesmaximal, complemented
9#13070527C211yesmaximal, characteristic, complemented
10D11×C22⋊C16C211yesmaximal, characteristic, complemented
11C11×#2232C211yesmaximal, characteristic, complemented
12C2×D8×D11C2211yescharacteristic, complemented
13C22×D88C2211yescharacteristic, complemented
14C22×C8×D11C2211yescharacteristic
15D11×#121—21no—
16C2×#66948—21no—
17C11×#466C2211yescharacteristic
18C2×C11×#107C2211yescharacteristic, complemented
19#10622770C2211yescharacteristic, complemented
20C2×#66890C2212yescomplemented
21#10622728C2211yescharacteristic
22#10622651—21no—
23C2×#66873—21no—
24C2×D176C2212yescomplemented
25C2×C16×D11C2212yescomplemented
26#10622496—21no—
27#10622496—21no—
28#10622496C2212yes—
29#10622496C2212yescomplemented
30#10622496C2211yescharacteristic, complemented
31D11×#107C2211yescharacteristic, complemented
32#10622388—21no—
33D11×#102—21no—
34C11×#366C2212yescomplemented
35C11×#357C2212yescomplemented
36C11×C22⋊C16C2211yescharacteristic, complemented
37C22⋊(C11⋊C16)C2211yescharacteristic, complemented
38#10622147C2212yescomplemented
39(C2×D11)⋊C16C2212yescomplemented
40#10622129C2212yescomplemented
41#10622129C2212yescomplemented
42#10622127C2212yescomplemented
43C2×D4×D11—21no—
44C2×D4×D11—41no—
45C22×D44—21no—
46C22×D44—41no—
47C22×C4×D11D411yescharacteristic
48C2×C11×D8C2311yescharacteristic
49C22×C8×C11C2311yescharacteristic
50C11×#121—21no—
51C2×C11×C4⋊C4—21no—
52#66992—41no—
53#66991—21no—
54C2×#4323—21no—
55#66983—21no—
56C2×(C2×D11)⋊C4—41no—
57C22×C11⋊C8D411yescharacteristic
58D8×D11—42no—
59C2×D88—21no—
60C2×D88—42no—
61C2×D88C2311yescharacteristic
62C2×D88C2312yes—
63C2×C8×D11—42no—
64C2×C8×D11D411yescharacteristic
65C2×C8×D11D411yescharacteristic
66C2×C8×D11C2311yescharacteristic
67C2×C8×D11C2311yescharacteristic
68#66948—22no—
69#66948—22no—
70#66948—21no—
71#66948—41no—
72#66948—41no—
73C4⋊C4×D11—21no—
74#66937—41no—
75C22⋊C4×D11—41no—
76C2×C11×C16C2312yes—
77C11×#107—21no—
78C11×#107C2311yescharacteristic
79C11×#107C2312yes—
80C11×#102—21no—
81#66896—21no—
82#66890—42no—
83#66885—21no—
84#66882C2311yescharacteristic
85C2×C11⋊C16C2312yes—
86#66873—22no—
87#66873—22no—
88#66873—21no—
89#66871—21no—
90D176—42no—
91C16×D11—42no—
92#33752—111nomaximal, Sylow
93C23×D11—41no—
94C23×D11—41no—
95C23×D11D811yescharacteristic
96C2×D4×C11—21no—
97C2×D4×C11—41no—
98C22×C4×C11—41no—
99C22×C4×C11C2×D411yescharacteristic
100C2×C22⋊D11—41no—
101C2×C22⋊D11—41no—
102C2×C22⋊D11—41no—
103C22×Dic11D811yescharacteristic
104D4×D11—42no—
105D4×D11—42no—
106D4×D11—84no—
107C2×D44—22no—
108C2×D44—21no—
109C2×D44—42no—
110C2×D44—42no—
111C2×D44—41no—
112C2×D44—42no—
113C2×D44—42no—
114C2×D44—41no—
115C2×D44—84no—
116C2×C4×D11—41no—
117C2×C4×D11—41no—
118C2×C4×D11—41no—
119C2×C4×D11D811yescharacteristic
120C2×C4×D11D811yescharacteristic
121C2×C4×D11C2×D411yescharacteristic
122C2×C4×D11C2×D411yescharacteristic
123C11×D8—22no—
124C2×C8×C11—22no—
125C2×C8×C11C2×D411yescharacteristic
126C2×C8×C11C2411yescharacteristic
127C11×C4⋊C4—21no—
128C11×C4⋊C4—22no—
129C11×C4⋊C4—41no—
130C11×C22⋊C4—41no—
131C22⋊Dic11—41no—
132#4323—42no—
133(C2×D11)⋊C4—41no—
134(C2×D11)⋊C4—42no—
135(C2×D11)⋊C4—42no—
136(C2×D11)⋊C4—41no—
137C4⋊Dic11—21no—
138Dic11⋊C4—41no—
139C2×C11⋊C8—41no—
140C2×C11⋊C8C2×D411yescharacteristic
141C2×C11⋊C8C2×D411yescharacteristic
142D88—22no—
143D88—22no—
144D88—22no—
145D88—42no—
146C8×D11—22no—
147C8×D11—22no—
148C8×D11—41no—
149C8×D11—41no—
150C11×C16—22no—
151C11⋊C16—22no—
152C2×#466—111no—
153C2×#466—111no—
154#2232—111no—
155#2232—112no—
156#2232D1111yescharacteristic, complemented
157#2215—112no—
158#2215—112no—
159#2184—111no—
160#2184—112no—
161#2184—111no—
162C2×C22⋊C16—111no—
163C23×C11—41no—
164C23×C11C2×D811yescharacteristic
165C22×D11—41no—
166C22×D11—41no—
167C22×D11—42no—
168C22×D11—41no—
169C22×D11—82no—
170C22×D11—82no—
171C22×D11—82no—
172C22×D11—82no—
173C22×D11—82no—
174C22×D11—82no—
175C22×D11D1614yescomplemented
176C22×D11C2×D811yescharacteristic
177C22×D11C2×D811yescharacteristic
178D4×C11—41no—
179D4×C11—41no—
180D4×C11—82no—
181C2×C4×C11—21no—
182C2×C4×C11—21no—
183C2×C4×C11—41no—
184C2×C4×C11—42no—
185C2×C4×C11—82no—
186C2×C4×C11C2×D811yescharacteristic
187C2×C4×C11C22×D411yescharacteristic
188C22⋊D11—82no—
189C22⋊D11—82no—
190C22⋊D11—82no—
191C2×Dic11—41no—
192C2×Dic11—41no—
193C2×Dic11C2×D811yescharacteristic
194C2×Dic11C2×D811yescharacteristic
195D44—42no—
196D44—41no—
197D44—42no—
198D44—41no—
199D44—82no—
200D44—84no—
201D44—84no—
202D44—82no—
203C4×D11—21no—
204C4×D11—21no—
205C4×D11—21no—
206C4×D11—21no—
207C4×D11—41no—
208C4×D11—41no—
209C4×D11—82no—
210C8×C11—21no—
211C8×C11H(5,𝔽2)12yes—
212C11⋊C8—21no—
213C11⋊C8—21no—
214C22×D8—111no—
215C22×D8—111no—
216C23×C8—111no—
217C2×#121—221no—
218C2×#121—221no—
219C2×D16—112no—
220C2×D16—112no—
221C22×C16—112no—
222#466—111no—
223#466—111no—
224#466—112no—
225#466—111no—
226#466—112no—
227#466—221no—
228#466—221no—
229#466—221no—
230#466—221no—
231#466C2×D1111yescharacteristic
232C2×#107—111no—
233C2×#107C2×D1111yescharacteristic, complemented
234C2×#102—221no—
235C2×#102—221no—
236#366—112no—
237#366C2×D1112yescomplemented
238#357—112no—
239#357—112no—
240#357—112no—
241#357C2×D1112yescomplemented
242C22⋊C16—111no—
243C22⋊C16—112no—
244C22⋊C16C2×D1111yescharacteristic, complemented
245C22×C11—21no—
246C22×C11—21no—
247C22×C11—81no—
248C22×C11—81no—
249C22×C11—81no—
250C22×C11C2×D1612yes—
251C22×C11C22×D811yescharacteristic
252C2×D11—21no—
253C2×D11—21no—
254C2×D11—21no—
255C2×D11—21no—
256C2×D11—44no—
257C2×D11—82no—
258C2×D11—81no—
259C2×D11—82no—
260C2×D11—81no—
261C2×D11—82no—
262C2×D11—81no—
263C2×D11—164no—
264C2×D11—164no—
265C2×D11C2×D1612yes—
266C2×D11C2×D1612yes—
267C4×C11—21no—
268C4×C11—82no—
269C4×C11—81no—
270C4×C11#53411yescharacteristic
271C4×C11#57511yescharacteristic
272Dic11—21no—
273Dic11—21no—
274Dic11—81no—
275C22×D4—221no—
276C22×D4—221no—
277C22×D4—441no—
278C22×D4—441no—
279C23×C4—111no—
280C2×D8—111no—
281C2×D8—112no—
282C2×D8—221no—
283C2×D8—221no—
284C2×D8—442no—
285C2×D8—442no—
286C2×D8C22×D1111yescharacteristic
287C22×C8—111no—
288C22×C8—111no—
289C22×C8—111no—
290C22×C8—111no—
291C22×C8—111no—
292C22×C8—442no—
293C22×C8C22×D1111yescharacteristic
294#121—21no—
295#121—221no—
296#121—222no—
297#121—222no—
298#121—221no—
299#121—221no—
300#121—441no—
301#121—441no—
302#121—441no—
303#121—441no—
304C2×C4⋊C4—21no—
305C2×C4⋊C4—221no—
306C2×C22⋊C4—441no—
307C2×C22⋊C4—441no—
308D16—442no—
309D16—442no—
310C2×C16—112no—
311C2×C16—442no—
312C2×C16C22×D1112yes—
313#107—21no—
314#107—111no—
315#107—221no—
316#107C22×D1111yescharacteristic
317#107C22×D1112yes—
318#102—21no—
319#102—221no—
320#102—222no—
321#102—222no—
322#102—221no—
323#102—221no—
324C2×C11—22no—
325C2×C11—161no—
326C2×C11#318611yescharacteristic
327C2×C11C22×D1611yescharacteristic
328C2×C11#341411yescharacteristic
329D11—22no—
330D11—22no—
331D11—162no—
332D11—161no—
333C24—111no—
334C24—441no—
335C24—441no—
336C2×D4—21no—
337C2×D4—41no—
338C2×D4—222no—
339C2×D4—221no—
340C2×D4—442no—
341C2×D4—442no—
342C2×D4—441no—
343C2×D4—442no—
344C2×D4—442no—
345C2×D4—441no—
346C2×D4—442no—
347C2×D4—442no—
348C2×D4—441no—
349C2×D4—441no—
350C2×D4—441no—
351C2×D4—884no—
352C2×D4—884no—
353C22×C4—41no—
354C22×C4—111no—
355C22×C4—111no—
356C22×C4—111no—
357C22×C4—111no—
358C22×C4—111no—
359C22×C4—441no—
360C22×C4—441no—
361C22×C4—441no—
362C22×C4D4×D1111yescharacteristic
363D8—22no—
364D8—222no—
365D8—222no—
366D8—222no—
367D8—442no—
368D8—442no—
369C2×C8—22no—
370C2×C8—111no—
371C2×C8—111no—
372C2×C8—222no—
373C2×C8—222no—
374C2×C8—441no—
375C2×C8—441no—
376C2×C8—441no—
377C2×C8D4×D1111yescharacteristic
378C2×C8C23×D1111yescharacteristic
379C4⋊C4—21no—
380C4⋊C4—22no—
381C4⋊C4—41no—
382C4⋊C4—221no—
383C4⋊C4—441no—
384C22⋊C4—41no—
385C22⋊C4—441no—
386C22⋊C4—442no—
387C22⋊C4—442no—
388C22⋊C4—441no—
389C22⋊C4—441no—
390C16—22no—
391C16—222no—
392C11#3375211yescharacteristic, complemented, Sylow
393C23—41no—
394C23—111no—
395C23—111no—
396C23—114no—
397C23—441no—
398C23—441no—
399C23—442no—
400C23—441no—
401C23—882no—
402C23—882no—
403C23—882no—
404C23—882no—
405C23—882no—
406C23—882no—
407C23D8×D1111yescharacteristic
408D4—41no—
409D4—41no—
410D4—82no—
411D4—442no—
412D4—441no—
413D4—442no—
414D4—441no—
415D4—882no—
416D4—884no—
417D4—884no—
418D4—882no—
419D4—882no—
420D4—882no—
421D4—882no—
422C2×C4—21no—
423C2×C4—21no—
424C2×C4—41no—
425C2×C4—42no—
426C2×C4—82no—
427C2×C4—111no—
428C2×C4—111no—
429C2×C4—221no—
430C2×C4—221no—
431C2×C4—221no—
432C2×C4—221no—
433C2×C4—441no—
434C2×C4—441no—
435C2×C4—441no—
436C2×C4—441no—
437C2×C4—882no—
438C2×C4D8×D1111yescharacteristic
439C2×C4C2×D4×D1111yescharacteristic
440C8—21no—
441C8—221no—
442C8—221no—
443C8#6704212yes—
444C22—21no—
445C22—21no—
446C22—81no—
447C22—81no—
448C22—81no—
449C22—112no—
450C22—112no—
451C22—221no—
452C22—221no—
453C22—221no—
454C22—221no—
455C22—444no—
456C22—882no—
457C22—881no—
458C22—882no—
459C22—881no—
460C22—882no—
461C22—881no—
462C22—1764no—
463C22—1764no—
464C22D11×D1612yes—
465C22C2×D8×D1111yescharacteristic
466C4—21no—
467C4—82no—
468C4—81no—
469C4—221no—
470C4—221no—
471C4—881no—
472C4#1062318411yescharacteristic
473C4#1062330811yescharacteristic
474C2—22no—
475C2—161no—
476C2—222no—
477C2—222no—
478C2—1762no—
479C2—1761no—
480C2#1307936611yescharacteristic
481C2C2×D11×D1611yescharacteristic
482C2#1308175111yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2232C2
socleC22×C11C22×D8
hypercenter#2232D11
hypocenterC11#33752
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2232

Complements

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

NH ≅ G/Ntype
1. C2×#10622496C2semidirect
2. D11×#466C2semidirect
3. #13070798C2semidirect
4. #13070796C2semidirect
5. #13070703C2semidirect
6. #13070701C2semidirect
7. #13070530C2semidirect
8. #13070529C2semidirect
9. #13070527C2semidirect
10. D11×C22⋊C16C2semidirect
11. C11×#2232C2semidirect
12. C2×D8×D11C22semidirect
13. C22×D88C22semidirect
18. C2×C11×#107C22semidirect
19. #10622770C22semidirect
20. C2×#66890C22semidirect
24. C2×D176C22semidirect
25. C2×C16×D11C22semidirect
29. #10622496C22semidirect
30. #10622496C22semidirect
31. D11×#107C22semidirect
34. C11×#366C22semidirect
35. C11×#357C22semidirect
36. C11×C22⋊C16C22semidirect
37. C22⋊(C11⋊C16)C22semidirect
38. #10622147C22semidirect
39. (C2×D11)⋊C16C22semidirect
40. #10622129C22semidirect
41. #10622129C22semidirect
42. #10622127C22semidirect
156. #2232D11semidirect
175. C22×D11D16semidirect
233. C2×#107C2×D11semidirect
237. #366C2×D11semidirect
241. #357C2×D11semidirect
244. C22⋊C16C2×D11semidirect
392. C11#33752semidirect

Maximal subgroups

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

subgroupindex
C2×#106224962
D11×#4662
#130707982
#130707962
#130707032
#130707012
#130705302
#130705292
#130705272
D11×C22⋊C162
C11×#22322
#3375211