Finite Group Databasebeta

← #14908699

Subgroups — #14908699

Order 2816.

654 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079196C211yesmaximal, characteristic, complemented
2C4×D8×D11C211yesmaximal, characteristic, complemented
3#13070798C212yesmaximal, complemented
4#13070750C211yesmaximal, characteristic, complemented
5#13070652C211yesmaximal, characteristic, complemented
6#13070651C211yesmaximal, characteristic, complemented
7#13070529C212yesmaximal, complemented
8#13070462C212yesmaximal, complemented
9#13070460C212yesmaximal, complemented
10#13070414C211yesmaximal, characteristic, complemented
11C11×#2224C211yesmaximal, characteristic, complemented
12C2×D8×D11C2211yescharacteristic
13#10623256—21no—
14C4×D4×D11—21no—
15C11×#500C2211yescharacteristic, complemented
16C4×C11×D8C2211yescharacteristic
17D8×Dic11C2211yescharacteristic
18C2×#66890C2212yes—
19#10622701—21no—
20C4×#4323—21no—
21C2×D176C2212yes—
22#10622496—21no—
23#10622496C2212yes—
24D11×#107C2211yescharacteristic
25#10622485—21no—
26#10622485C2211yescharacteristic
27#10622485C2212yescomplemented
28D11×#102—21no—
29#10622369—21no—
30#10622308C2211yescharacteristic, complemented
31C4×D88C2211yescharacteristic
32C4×C8×D11C2211yescharacteristic
33C11×#366C2212yescomplemented
34C11×C4⋊C16C2211yescharacteristic, complemented
35C11×#357C2212yes—
36#10622147C2212yescomplemented
37(C2×D11)⋊C16C2212yes—
38C16×Dic11C2212yescomplemented
39#10622129C2212yes—
40#10622129C2212yescomplemented
41#10622127C2212yescomplemented
42C4⋊(C11⋊C16)C2211yescharacteristic, complemented
43C2×#4343—41no—
44C2×D4×D11—21no—
45C22×C4×D11—41no—
46C2×C11×D8C2311yescharacteristic
47C11×C4⋊Q8—21no—
48C4×D4×C11—21no—
49#67000—41no—
50D4×Dic11—21no—
51C2×#4323—21no—
52C4×C22⋊D11—41no—
53D8×D11—22no—
54D8×D11—22no—
55C2×D88—21no—
56C2×D88C2312yes—
57C2×D88C2311yescharacteristic
58C2×C8×D11D411yescharacteristic
59C2×C8×D11C2311yescharacteristic
60#66948—22no—
61#66948—41no—
62#66946—22no—
63#66946—21no—
64#66946—41no—
65C4⋊C4×D11—21no—
66(C22⋊D11)⋊C4—41no—
67C22⋊C4×D11—41no—
68#66927—21no—
69C4×D44—21no—
70C42×D11D411yescharacteristic
71C2×C11×C16C2312yes—
72C11×#107—21no—
73C11×#107C2312yes—
74C11×#107C2311yescharacteristic
75C11×#102—21no—
76C4×C8×C11C2311yescharacteristic
77#66896—21no—
78#66890—24no—
79#66885—21no—
80#66882C2311yescharacteristic
81C8×Dic11D411yescharacteristic
82C8×Dic11C2311yescharacteristic
83C2×C11⋊C16C2312yes—
84#66873—22no—
85#66873—21no—
86#66873—22no—
87#66871—21no—
88C4×C11⋊C8D411yescharacteristic
89D176—24no—
90#33660—111nomaximal, Sylow
91C23×D11—41no—
92C2×Q8×C11—41no—
93C2×D4×C11—21no—
94C22×C4×C11—41no—
95C2×C22⋊D11—41no—
96C22×Dic11—41no—
97#4343—84no—
98D4×D11—24no—
99D4×D11—42no—
100C2×D44—21no—
101C2×D44—22no—
102C2×D44—42no—
103C2×D44—41no—
104C2×D44—41no—
105C2×C4×D11—41no—
106C2×C4×D11—42no—
107C2×C4×D11—41no—
108C2×C4×D11—41no—
109C2×C4×D11—84no—
110C2×C4×D11D811yescharacteristic
111C2×C4×D11D811yescharacteristic
112C2×C4×D11C2×D411yescharacteristic
113C11×D8—21no—
114C11×D8#4112yescomplemented
115C2×C8×C11C2×D411yescharacteristic
116C2×C8×C11C2411yescharacteristic
117C11×C4⋊C4—21no—
118C11×C4⋊C4—22no—
119C11×C4⋊C4—41no—
120C11×C22⋊C4—41no—
121C42×C11C2×D411yescharacteristic
122C22⋊Dic11—41no—
123#4323—24no—
124(C2×D11)⋊C4—41no—
125(C2×D11)⋊C4—42no—
126(C2×D11)⋊C4—42no—
127(C2×D11)⋊C4—41no—
128C4⋊Dic11—21no—
129Dic11⋊C4—41no—
130C4×Dic11D811yescharacteristic
131C4×Dic11D811yescharacteristic
132C4×Dic11C2×D411yescharacteristic
133C2×C11⋊C8C2×D411yescharacteristic
134C2×C11⋊C8C2×D411yescharacteristic
135D88—21no—
136D88—22no—
137D88—22no—
138D88—42no—
139D88#4112yescomplemented
140C8×D11—21no—
141C8×D11—21no—
142C8×D11—41no—
143C11×C16—22no—
144C11⋊C16—22no—
145#3169—111no—
146C2×C4×D8—111no—
147#2232—112no—
148#2224—111no—
149#2224D1111yescharacteristic, complemented
150#2206—111no—
151#2206—111no—
152#2184—112no—
153C4×D16—112no—
154C4×D16—112no—
155#2162—111no—
156C23×C11—41no—
157C22×D11—44no—
158C22×D11—41no—
159C22×D11—42no—
160C22×D11—82no—
161C22×D11—82no—
162C22×D11C2×D811yescharacteristic
163Q8×C11—82no—
164D4×C11—22no—
165D4×C11—41no—
166C2×C4×C11—41no—
167C2×C4×C11—42no—
168C2×C4×C11—82no—
169C2×C4×C11C2×D811yescharacteristic
170C2×C4×C11C2×D811yescharacteristic
171C2×C4×C11C22×D411yescharacteristic
172C22⋊D11—44no—
173C2×Dic11—41no—
174C2×Dic11—82no—
175C2×Dic11C2×D811yescharacteristic
176C2×Dic11C2×D811yescharacteristic
177C2×Dic11C2×D811yescharacteristic
178D44—22no—
179D44—42no—
180D44—41no—
181D44—42no—
182D44—82no—
183D44—84no—
184D44—82no—
185C4×D11—21no—
186C4×D11—21no—
187C4×D11—41no—
188C4×D11—82no—
189C4×D11—82no—
190C4×D11—82no—
191C4×D11—84no—
192C4×D11D1614yescomplemented
193C8×C11—21no—
194C8×C11C2×#4111yescharacteristic
195C8×C11C2×#4111yescharacteristic
196C11⋊C8—21no—
197C11⋊C8—21no—
198C22×D8—111no—
199#532—221no—
200C2×C4×D4—221no—
201C2×D16—112no—
202C2×D16—112no—
203#500C2×D1111yescharacteristic, complemented
204#493—111no—
205#486—221no—
206#466—112no—
207#466—221no—
208C4×D8—111no—
209C4×D8—111no—
210C4×D8—112no—
211C4×D8—111no—
212C4×D8—221no—
213C4×D8—221no—
214C4×D8—221no—
215C4×D8C2×D1111yescharacteristic
216C2×#107—111no—
217C2×#102—221no—
218C2×C4×C8—111no—
219#366—112no—
220#366C2×D1112yescomplemented
221C4⋊C16—111no—
222C4⋊C16C2×D1111yescharacteristic, complemented
223#357—112no—
224#357—112no—
225#357—112no—
226#357C2×D1112yes—
227C22⋊C16—112no—
228C4×C16—112no—
229C22×C11—42no—
230C22×C11—81no—
231C22×C11—81no—
232C22×C11C22×D811yescharacteristic
233C2×D11—21no—
234C2×D11—21no—
235C2×D11—42no—
236C2×D11—88no—
237C2×D11—81no—
238C2×D11—81no—
239C2×D11—82no—
240C2×D11—82no—
241C2×D11—82no—
242C2×D11C2×D1612yes—
243C4×C11—21no—
244C4×C11—81no—
245C4×C11—82no—
246C4×C11C2×D1612yes—
247C4×C11#52511yescharacteristic
248C4×C11#57511yescharacteristic
249Dic11—21no—
250Dic11—21no—
251Dic11—81no—
252Dic11C2×D1612yes—
253C2×#41—441no—
254C22×D4—221no—
255C23×C4—441no—
256C2×D8—111no—
257C2×D8—112no—
258C2×D8—221no—
259C2×D8—222no—
260C2×D8—222no—
261C2×D8—221no—
262C2×D8C22×D1111yescharacteristic
263C22×C8—111no—
264C22×C8—111no—
265C4⋊Q8—21no—
266#127—221no—
267#124—441no—
268#121—222no—
269#121—441no—
270C4×D4—21no—
271C4×D4—221no—
272C4×D4—222no—
273C4×D4—221no—
274C4×D4—221no—
275C4×D4—441no—
276C4×D4—441no—
277C4×D4—441no—
278C2×C4⋊C4—221no—
279C2×C22⋊C4—441no—
280C2×C42—111no—
281D16—224no—
282D16—224no—
283C2×C16—112no—
284C2×C16C22×D1112yes—
285#107—21no—
286#107—111no—
287#107—221no—
288#107C22×D1111yescharacteristic
289#107C22×D1112yes—
290#102—21no—
291#102—221no—
292#102—222no—
293#102—222no—
294#102—221no—
295#102—221no—
296C4×C8—111no—
297C4×C8—111no—
298C4×C8—111no—
299C4×C8C22×D1111yescharacteristic
300C2×C11—82no—
301C2×C11#310011yescharacteristic
302C2×C11C22×D1611yescharacteristic
303C2×C11#341411yescharacteristic
304D11—22no—
305D11—82no—
306D11—162no—
307C24—441no—
308#41—884no—
309C2×Q8—41no—
310C2×D4—21no—
311C2×D4—224no—
312C2×D4—221no—
313C2×D4—222no—
314C2×D4—442no—
315C2×D4—441no—
316C2×D4—442no—
317C2×D4—441no—
318C2×D4—441no—
319C22×C4—41no—
320C22×C4—111no—
321C22×C4—111no—
322C22×C4—111no—
323C22×C4—441no—
324C22×C4—442no—
325C22×C4—441no—
326C22×C4—441no—
327C22×C4—441no—
328C22×C4—884no—
329D8—21no—
330D8—112no—
331D8—224no—
332D8—221no—
333D8—222no—
334D8—222no—
335D8—442no—
336D8#434312yescomplemented
337C2×C8—111no—
338C2×C8—111no—
339C2×C8—221no—
340C2×C8—221no—
341C2×C8—441no—
342C2×C8D4×D1111yescharacteristic
343C2×C8C23×D1111yescharacteristic
344C4⋊C4—21no—
345C4⋊C4—22no—
346C4⋊C4—41no—
347C4⋊C4—221no—
348C4⋊C4—441no—
349C22⋊C4—41no—
350C22⋊C4—441no—
351C22⋊C4—442no—
352C22⋊C4—442no—
353C22⋊C4—441no—
354C22⋊C4—441no—
355C42—111no—
356C42—111no—
357C42—111no—
358C42D4×D1111yescharacteristic
359C16—22no—
360C16—222no—
361C11#3366011yescharacteristic, complemented, Sylow
362C23—41no—
363C23—111no—
364C23—444no—
365C23—441no—
366C23—442no—
367C23—882no—
368C23—882no—
369Q8—82no—
370D4—22no—
371D4—41no—
372D4—222no—
373D4—444no—
374D4—441no—
375D4—442no—
376D4—442no—
377D4—882no—
378D4—884no—
379D4—882no—
380C2×C4—41no—
381C2×C4—42no—
382C2×C4—82no—
383C2×C4—111no—
384C2×C4—114no—
385C2×C4—111no—
386C2×C4—111no—
387C2×C4—221no—
388C2×C4—221no—
389C2×C4—441no—
390C2×C4—441no—
391C2×C4—882no—
392C2×C4—884no—
393C2×C4—882no—
394C2×C4—882no—
395C2×C4—882no—
396C2×C4D8×D1111yescharacteristic
397C2×C4D8×D1111yescharacteristic
398C2×C4C2×D4×D1111yescharacteristic
399C8—21no—
400C8—221no—
401C8—221no—
402C8C2×#434311yescharacteristic
403C8#41×D1111yescharacteristic
404C22—42no—
405C22—81no—
406C22—81no—
407C22—112no—
408C22—221no—
409C22—221no—
410C22—442no—
411C22—888no—
412C22—881no—
413C22—881no—
414C22—882no—
415C22—882no—
416C22—882no—
417C22C2×D8×D1111yescharacteristic
418C4—21no—
419C4—81no—
420C4—82no—
421C4—112no—
422C4—221no—
423C4—221no—
424C4—881no—
425C4D11×D1612yes—
426C4#1062315811yescharacteristic
427C4#1062330811yescharacteristic
428C2—82no—
429C2—222no—
430C2—882no—
431C2—1762no—
432C2#1307861811yescharacteristic
433C2C2×D11×D1611yescharacteristic
434C2#1308175111yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2224C2
socleC22×C11C22×D8
hypercenter#2224D11
hypocenterC11#33660
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2224

Complements

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

NH ≅ G/Ntype
1. #13079196C2semidirect
2. C4×D8×D11C2semidirect
3. #13070798C2semidirect
4. #13070750C2semidirect
5. #13070652C2semidirect
6. #13070651C2semidirect
7. #13070529C2semidirect
8. #13070462C2semidirect
9. #13070460C2semidirect
10. #13070414C2semidirect
11. C11×#2224C2semidirect
15. C11×#500C22semidirect
27. #10622485C22semidirect
30. #10622308C22semidirect
33. C11×#366C22semidirect
34. C11×C4⋊C16C22semidirect
36. #10622147C22semidirect
38. C16×Dic11C22semidirect
40. #10622129C22semidirect
41. #10622127C22semidirect
42. C4⋊(C11⋊C16)C22semidirect
114. C11×D8#41semidirect
139. D88#41semidirect
149. #2224D11semidirect
192. C4×D11D16semidirect
203. #500C2×D11semidirect
220. #366C2×D11semidirect
222. C4⋊C16C2×D11semidirect
336. D8#4343semidirect
361. C11#33660semidirect

Maximal subgroups

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

subgroupindex
#130791962
C4×D8×D112
#130707982
#130707502
#130706522
#130706512
#130705292
#130704622
#130704602
#130704142
C11×#22242
#3366011