Finite Group Databasebeta

← #14911384

Subgroups — #14911384

Order 2816.

488 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081021C211yesmaximal, characteristic, complemented
2#13081013C211yesmaximal, characteristic, complemented
3#13070894C211yesmaximal, characteristic, complemented
4#13070806C211yesmaximal, characteristic, complemented
5#13070804C211yesmaximal, characteristic, complemented
6#13070795C211yesmaximal, characteristic, complemented
7#13070794C211yesmaximal, characteristic, complemented
8#13070775C211yesmaximal, characteristic, complemented
9#13070771C211yesmaximal, characteristic, complemented
10#13070716C211yesmaximal, characteristic, complemented
11D16×Dic11C211yesmaximal, characteristic, complemented
12#13070446C211yesmaximal, characteristic, complemented
13#13070404C211yesmaximal, characteristic, complemented
14#13070403C211yesmaximal, characteristic, complemented
15C11×#2218C211yesmaximal, characteristic, complemented
16#10623149—21no—
17#10623145—21no—
18C2×C11×D16C2211yescharacteristic
19C2×C11×M32C2211yescharacteristic
20C11×#466C2211yescharacteristic
21C11×#466C2211yescharacteristic
22#10622770C2211yescharacteristic
23#10622770C2211yescharacteristic
24D8×Dic11C2211yescharacteristic
25D8×Dic11C2211yescharacteristic
26C8×C22⋊D11C2211yescharacteristic
27#10622719C2211yescharacteristic
28C2×#66882C2211yescharacteristic
29#10622648—21no—
30#10622647—21no—
31C2×#66862C2211yescharacteristic
32#10622493C2211yescharacteristic
33D11×#107C2211yescharacteristic
34#10622491C2211yescharacteristic
35#10622491C2211yescharacteristic
36#10622397—21no—
37#10622390—21no—
38#10622379—21no—
39#10622376—21no—
40C11×#367C2211yescharacteristic
41C11×#357C2211yescharacteristic
42C11×#357C2211yescharacteristic
43#10622200C2211yescharacteristic
44#10622200C2211yescharacteristic
45#10622200C2211yescharacteristic
46#10622200C2211yescharacteristic
47C22⋊(C11⋊C16)C2211yescharacteristic
48(C2×D11)⋊C16C2211yescharacteristic
49#10622143C2211yescharacteristic
50#10622143C2211yescharacteristic
51#10622142C2211yescharacteristic
52#10622142C2211yescharacteristic
53Dic11⋊C16C2211yescharacteristic
54C16×Dic11C2211yescharacteristic
55#10622128C2211yescharacteristic
56#10622127C2211yescharacteristic
57#10622127C2211yescharacteristic
58#10622127C2211yescharacteristic
59C2×C11×D8C2311yescharacteristic
60C2×C11×D8C2311yescharacteristic
61C22×C8×C11C2311yescharacteristic
62C11×#121—21no—
63C11×#121—21no—
64#66992—41no—
65#66991—21no—
66#66991—21no—
67#66991—41no—
68#66988—41no—
69D4×Dic11—21no—
70D4×Dic11—21no—
71D4×Dic11—41no—
72C4×C22⋊D11D411yescharacteristic
73#66979—21no—
74C2×C4⋊Dic11—21no—
75C2×C8×D11C2311yescharacteristic
76#66945—21no—
77C4⋊C4×D11—21no—
78#66943—21no—
79#66943—21no—
80#66939—41no—
81(C22⋊D11)⋊C4—41no—
82#66932—41no—
83#66932—41no—
84C11×D16—22no—
85C11×M32—22no—
86C2×C11×C16C2311yescharacteristic
87C2×C11×C16C2311yescharacteristic
88C11×#107C2311yescharacteristic
89C11×#107C2311yescharacteristic
90C11×#102—21no—
91C11×#102—21no—
92#66896—21no—
93#66896—21no—
94#66896—21no—
95#66896—21no—
96C22⋊(C11⋊C8)D411yescharacteristic
97(C2×D11)⋊C8D411yescharacteristic
98#66882—21no—
99#66882C2311yescharacteristic
100#66882C2311yescharacteristic
101#66882C2311yescharacteristic
102#66882C2311yescharacteristic
103#66881—21no—
104Dic11⋊C8D411yescharacteristic
105C8×Dic11C2311yescharacteristic
106C2×C11⋊C16C2311yescharacteristic
107C2×C11⋊C16C2311yescharacteristic
108#66872—21no—
109#66872—21no—
110#66872—21no—
111#66871—21no—
112#66862—22no—
113#33922—111nomaximal, Sylow
114C2×D4×C11—21no—
115C2×D4×C11—21no—
116C2×D4×C11—41no—
117C2×D4×C11—41no—
118C22×C4×C11C2×D411yescharacteristic
119C2×C22⋊D11—41no—
120C2×C22⋊D11—41no—
121C2×C22⋊D11D811yescharacteristic
122C22×Dic11—41no—
123C22×Dic11—41no—
124C22×Dic11—41no—
125C2×C4×D11—41no—
126C2×C4×D11C2×D411yescharacteristic
127C11×D8—21no—
128C11×D8—21no—
129C11×D8—21no—
130C11×D8—21no—
131C2×C8×C11—21no—
132C2×C8×C11—21no—
133C2×C8×C11C2×D411yescharacteristic
134C2×C8×C11C2411yescharacteristic
135C11×C4⋊C4—21no—
136C11×C4⋊C4—21no—
137C11×C22⋊C4—41no—
138C11×C22⋊C4—41no—
139C22⋊Dic11—41no—
140C22⋊Dic11—41no—
141C22⋊Dic11—41no—
142C22⋊Dic11—41no—
143C22⋊Dic11—41no—
144C22⋊Dic11D811yescharacteristic
145(C2×D11)⋊C4—41no—
146(C2×D11)⋊C4D811yescharacteristic
147C4⋊Dic11—21no—
148C4⋊Dic11—21no—
149C4⋊Dic11—21no—
150C4⋊Dic11—21no—
151C4⋊Dic11—41no—
152C4⋊Dic11—41no—
153C4⋊Dic11—41no—
154Dic11⋊C4—41no—
155Dic11⋊C4—41no—
156Dic11⋊C4—41no—
157Dic11⋊C4D811yescharacteristic
158C4×Dic11—41no—
159C4×Dic11—41no—
160C4×Dic11C2×D411yescharacteristic
161C2×C11⋊C8C2×D411yescharacteristic
162C2×C11⋊C8C2×D411yescharacteristic
163C8×D11—21no—
164C8×D11—21no—
165C11×C16—21no—
166C11×C16#4112yes—
167C11⋊C16—21no—
168C11⋊C16—21no—
169#3339—111no—
170#3339—111no—
171#2253—111no—
172#2234—111no—
173#2234—111no—
174#2232—111no—
175#2232—111no—
176#2228—111no—
177#2228—111no—
178#2218—111no—
179#2218D1111yescharacteristic, complemented
180C4×D16—111no—
181#2169—111no—
182#2159—111no—
183#2159—111no—
184C23×C11—41no—
185C23×C11—41no—
186C23×C11C2×D811yescharacteristic
187C22×D11C2×D811yescharacteristic
188D4×C11—41no—
189D4×C11—41no—
190D4×C11—41no—
191D4×C11—41no—
192D4×C11—82no—
193D4×C11—161no—
194C2×C4×C11—21no—
195C2×C4×C11—21no—
196C2×C4×C11—41no—
197C2×C4×C11—41no—
198C2×C4×C11C2×D811yescharacteristic
199C2×C4×C11C22×D411yescharacteristic
200C22⋊D11—41no—
201C22⋊D11—82no—
202C22⋊D11—161no—
203C2×Dic11—41no—
204C2×Dic11—41no—
205C2×Dic11—41no—
206C2×Dic11—41no—
207C2×Dic11—161no—
208C2×Dic11—161no—
209C2×Dic11—161no—
210C2×Dic11C2×D811yescharacteristic
211C2×Dic11C2×D811yescharacteristic
212C2×Dic11C2×D811yescharacteristic
213C4×D11—21no—
214C4×D11—21no—
215C4×D11—161no—
216C8×C11—21no—
217C8×C11C2×#4111yescharacteristic
218C8×C112−1+411yescharacteristic
219C11⋊C8—21no—
220C11⋊C8—21no—
221#553—221no—
222#553—221no—
223C2×D16C2×D1111yescharacteristic
224C2×M32—111no—
225C2×M32C2×D1111yescharacteristic
226#499—111no—
227#499—111no—
228#482—221no—
229#482—221no—
230#481—221no—
231#481—221no—
232#478—221no—
233#478—221no—
234#466—111no—
235#466—111no—
236#466C2×D1111yescharacteristic
237#466C2×D1111yescharacteristic
238C4×D8—111no—
239C4×D8—111no—
240C8×D4—111no—
241#427—111no—
242#427—111no—
243C2×#107—111no—
244C2×#107—111no—
245#367—111no—
246#367—111no—
247#367—111no—
248#367C2×D1111yescharacteristic
249#366—111no—
250#366—111no—
251#366—111no—
252#366—111no—
253#366—111no—
254C4⋊C16—111no—
255#357—111no—
256#357—111no—
257#357—111no—
258#357—111no—
259#357C2×D1111yescharacteristic
260#357C2×D1111yescharacteristic
261C22⋊C16—111no—
262C22⋊C16—111no—
263C4×C16—111no—
264C22×C11—21no—
265C22×C11—21no—
266C22×C11—21no—
267C22×C11—81no—
268C22×C11—81no—
269C22×C11—81no—
270C22×C11—81no—
271C22×C11—81no—
272C22×C11—81no—
273C22×C11C22×D811yescharacteristic
274C2×D11—21no—
275C2×D11—21no—
276C2×D11—21no—
277C4×C11—21no—
278C4×C11—81no—
279C4×C11—81no—
280C4×C11#54711yescharacteristic
281C4×C11#57811yescharacteristic
282Dic11—21no—
283Dic11—21no—
284Dic11—21no—
285Dic11—81no—
286Dic11—81no—
287Dic11—81no—
288Dic11—81no—
289C2×D8C22×D1111yescharacteristic
290C2×D8C22×D1111yescharacteristic
291C22×C8—111no—
292C22×C8C22×D1111yescharacteristic
293#126—441no—
294#126—441no—
295#125—221no—
296#125—221no—
297#123—441no—
298#123—441no—
299#121—21no—
300#121—21no—
301#121—221no—
302#121—221no—
303#121—441no—
304#121—441no—
305C4×D4—111no—
306C4×D4—221no—
307C4×D4—221no—
308C4×D4—441no—
309C4×D4—441no—
310#117—221no—
311#117—221no—
312C2×C4⋊C4—221no—
313C2×C4⋊C4—221no—
314D16—22no—
315M32—22no—
316M32—222no—
317C2×C16—111no—
318C2×C16—111no—
319C2×C16C22×D1111yescharacteristic
320C2×C16C22×D1111yescharacteristic
321#107—111no—
322#107—111no—
323#107—111no—
324#107—111no—
325#107—221no—
326#107—221no—
327#107C22×D1111yescharacteristic
328#107C22×D1111yescharacteristic
329#106—221no—
330#106—221no—
331#106—221no—
332#106—221no—
333C4⋊C8—111no—
334#102—21no—
335#102—21no—
336#102—221no—
337#102—221no—
338#102—221no—
339#102—221no—
340C22⋊C8—111no—
341C22⋊C8—111no—
342C4×C8—111no—
343C2×C11—41no—
344C2×C11—161no—
345C2×C11—161no—
346C2×C11#333411yescharacteristic
347C2×C11#341411yescharacteristic
348C2×C11#341511yescharacteristic
349D11—41no—
350C2×D4—21no—
351C2×D4—21no—
352C2×D4—41no—
353C2×D4—41no—
354C2×D4—111no—
355C2×D4—441no—
356C2×D4—441no—
357C22×C4—111no—
358C22×C4—441no—
359C22×C4—441no—
360C22×C4—441no—
361C22×C4—441no—
362C22×C4D4×D1111yescharacteristic
363D8—21no—
364D8—21no—
365D8—21no—
366D8—21no—
367C2×C8—21no—
368C2×C8—21no—
369C2×C8—111no—
370C2×C8—111no—
371C2×C8—221no—
372C2×C8—221no—
373C2×C8D4×D1111yescharacteristic
374C2×C8C23×D1111yescharacteristic
375C4⋊C4—21no—
376C4⋊C4—21no—
377C4⋊C4—111no—
378C4⋊C4—221no—
379C4⋊C4—221no—
380C4⋊C4—221no—
381C4⋊C4—221no—
382C4⋊C4—441no—
383C4⋊C4—441no—
384C4⋊C4—441no—
385C4⋊C4—441no—
386C4⋊C4—441no—
387C4⋊C4—441no—
388C22⋊C4—41no—
389C22⋊C4—41no—
390C22⋊C4—111no—
391C22⋊C4—111no—
392C22⋊C4—441no—
393C22⋊C4—441no—
394C22⋊C4—441no—
395C22⋊C4—441no—
396C22⋊C4—441no—
397C22⋊C4—441no—
398C42—111no—
399C42—441no—
400C42—441no—
401C16—21no—
402C16—221no—
403C16—221no—
404C16#434112yes—
405C11#3392211yescharacteristic, complemented, Sylow
406C23—41no—
407C23—41no—
408C23—111no—
409C23D8×D1111yescharacteristic
410D4—41no—
411D4—41no—
412D4—41no—
413D4—41no—
414D4—82no—
415D4—161no—
416D4—441no—
417D4—882no—
418D4—1761no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—111no—
424C2×C4—111no—
425C2×C4—111no—
426C2×C4—221no—
427C2×C4—221no—
428C2×C4—441no—
429C2×C4—441no—
430C2×C4—441no—
431C2×C4—441no—
432C2×C4—1761no—
433C2×C4—1761no—
434C2×C4—1761no—
435C2×C4—1761no—
436C2×C4D8×D1111yescharacteristic
437C2×C4C2×D4×D1111yescharacteristic
438C8—21no—
439C8—221no—
440C8—221no—
441C8C2×#434111yescharacteristic
442C8#6704311yescharacteristic
443C22—21no—
444C22—21no—
445C22—21no—
446C22—81no—
447C22—81no—
448C22—81no—
449C22—81no—
450C22—81no—
451C22—81no—
452C22—221no—
453C22—221no—
454C22—221no—
455C22C2×D8×D1111yescharacteristic
456C4—21no—
457C4—81no—
458C4—81no—
459C4—221no—
460C4—221no—
461C4—221no—
462C4—881no—
463C4—881no—
464C4—881no—
465C4—881no—
466C4#1062314211yescharacteristic
467C4#1062330211yescharacteristic
468C2—41no—
469C2—161no—
470C2—161no—
471C2—441no—
472C2#1308096011yescharacteristic
473C2#1308174811yescharacteristic
474C2#1308175611yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2218C2
socleC22×C11C22×D8
hypercenter#2218D11
hypocenterC11#33922
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2218

Complements

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

NH ≅ G/Ntype
1. #13081021C2semidirect
2. #13081013C2semidirect
3. #13070894C2semidirect
4. #13070806C2semidirect
5. #13070804C2semidirect
6. #13070795C2semidirect
7. #13070794C2semidirect
8. #13070775C2semidirect
9. #13070771C2semidirect
10. #13070716C2semidirect
11. D16×Dic11C2semidirect
12. #13070446C2semidirect
13. #13070404C2semidirect
14. #13070403C2semidirect
15. C11×#2218C2semidirect
179. #2218D11semidirect
405. C11#33922semidirect

Maximal subgroups

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

subgroupindex
#130810212
#130810132
#130708942
#130708062
#130708042
#130707952
#130707942
#130707752
#130707712
#130707162
D16×Dic112
#130704462
#130704042
#130704032
C11×#22182
#3392211