Finite Group Databasebeta

← #14908831

Subgroups — #14908831

Order 2816.

612 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×D88C211yesmaximal, characteristic, complemented
2#13070811C211yesmaximal, characteristic, complemented
3#13070794C211yesmaximal, characteristic, complemented
4#13070770C212yesmaximal, complemented
5#13070668C212yesmaximal, complemented
6#13070544C211yesmaximal, characteristic, complemented
7#13070527C211yesmaximal, characteristic
8#13070490C212yesmaximal, complemented
9#13070478C212yesmaximal, complemented
10#13070419C211yesmaximal, characteristic, complemented
11C11×#3168C211yesmaximal, characteristic, complemented
12C11×#529—21no—
13C22×D88C2211yescharacteristic
14C2×C4×D44—21no—
15C11×#499C2211yescharacteristic, complemented
16C11×#495C2211yescharacteristic, complemented
17C11×#488—21no—
18C11×#467C2211yescharacteristic
19C11×#466C2211yescharacteristic
20C11×#465—21no—
21C4×C11×Q16C2211yescharacteristic, complemented
22C4×C11×SD16—21no—
23C4×C11×D8C2211yescharacteristic, complemented
24C2×C4×C8×C11C2211yescharacteristic
25C2×#66892C2212yes—
26C2×#66890C2212yes—
27C2×#66885—21no—
28C2×#66882C2211yescharacteristic
29C4×D88—21no—
30C4×D88—21no—
31C4×D88C2212yes—
32C4×D88C2212yes—
33#10622202C2212yescomplemented
34#10622200C2212yescomplemented
35C22⋊(C11⋊C16)C2211yescharacteristic
36C22⋊(C11⋊C16)C2211yescharacteristic
37#10622129C2212yes—
38#10622129C2212yes—
39#10622128C2212yescomplemented
40#10622127C2212yescomplemented
41C4⋊(C11⋊C16)C2212yescomplemented
42#10622099C2212yescomplemented
43C22×D44—21no—
44C22×C4×D11—41no—
45C2×C11×Q16C2311yescharacteristic
46C2×C11×SD16—21no—
47C2×C11×D8C2311yescharacteristic
48C22×C8×C11D411yescharacteristic
49C22×C8×C11C2311yescharacteristic
50C11×#126—41no—
51C11×#125—21no—
52C11×#124—21no—
53C11×#123—41no—
54C11×C22⋊Q8—21no—
55C11×#121—21no—
56C4×Q8×C11—21no—
57C4×D4×C11—21no—
58C4×D4×C11—41no—
59C11×#117—41no—
60C2×C42×C11D411yescharacteristic
61C2×(C2×D11)⋊C4—41no—
62C2×C4⋊Dic11—21no—
63C2×D88—21no—
64C2×D88—24no—
65C2×D88C2312yes—
66C4×D44—22no—
67C4×D44—22no—
68C4×D44—41no—
69C4×D44—41no—
70C11×#107C2311yescharacteristic
71C11×#107C2311yescharacteristic
72C11×#106—21no—
73C11×#103—21no—
74C11×#103—21no—
75C11×#102—21no—
76C11×#102—21no—
77C4×C8×C11D411yescharacteristic
78C4×C8×C11D411yescharacteristic
79C4×C8×C11C2311yescharacteristic
80C4×C8×C11C2311yescharacteristic
81#66892—24no—
82#66890—24no—
83#66885—22no—
84#66885—22no—
85#66882—21no—
86#66882C2312yes—
87C2×C11⋊C16C2312yes—
88C2×C11⋊C16C2312yes—
89#33674—111nomaximal, Sylow
90C23×D11—41no—
91C2×Q8×C11—21no—
92C2×D4×C11—21no—
93C2×D4×C11—41no—
94C22×C4×C11—41no—
95C22×C4×C11D811yescharacteristic
96C22×C4×C11D811yescharacteristic
97C22×C4×C11C2×D411yescharacteristic
98C22×Dic11—41no—
99C2×D44—24no—
100C2×D44—22no—
101C2×D44—42no—
102C2×D44—41no—
103C2×C4×D11—42no—
104C2×C4×D11—42no—
105C2×C4×D11—84no—
106C11×Q16—22no—
107C11×SD16—42no—
108C11×D8—22no—
109C2×C8×C11—22no—
110C2×C8×C11—41no—
111C2×C8×C11C2×D411yescharacteristic
112C2×C8×C11C2×D411yescharacteristic
113C2×C8×C11C2×D411yescharacteristic
114C2×C8×C11C2411yescharacteristic
115C11×C4⋊C4—21no—
116C11×C4⋊C4—21no—
117C11×C4⋊C4—41no—
118C11×C4⋊C4—41no—
119C11×C4⋊C4—41no—
120C11×C4⋊C4—41no—
121C11×C22⋊C4—41no—
122C11×C22⋊C4—41no—
123C11×C22⋊C4—41no—
124C11×C22⋊C4—41no—
125C11×C22⋊C4—41no—
126C42×C11—41no—
127C42×C11D811yescharacteristic
128C42×C11D811yescharacteristic
129C42×C11C2×D411yescharacteristic
130C42×C11C2×D411yescharacteristic
131(C2×D11)⋊C4—42no—
132(C2×D11)⋊C4—42no—
133C4⋊Dic11—22no—
134C4⋊Dic11—41no—
135D88—24no—
136D88—22no—
137D88#4114yes—
138C11⋊C16—22no—
139C11⋊C16—22no—
140#3168D1111yescharacteristic, complemented
141C2×C4×D8—111no—
142#2235—111no—
143#2232—111no—
144#2228—112no—
145#2210—112no—
146#2187—111no—
147#2184—111no—
148#2177—112no—
149#2175—112no—
150#2163—111no—
151C23×C11—41no—
152C23×C11C2×D811yescharacteristic
153C22×D11—44no—
154C22×D11—42no—
155C22×D11—82no—
156C22×D11—82no—
157Q8×C11—41no—
158Q8×C11—41no—
159D4×C11—41no—
160D4×C11—41no—
161D4×C11—82no—
162C2×C4×C11—22no—
163C2×C4×C11—21no—
164C2×C4×C11—21no—
165C2×C4×C11—41no—
166C2×C4×C11—41no—
167C2×C4×C11—41no—
168C2×C4×C11—41no—
169C2×C4×C11—82no—
170C2×C4×C11C2×D811yescharacteristic
171C2×C4×C11C2×D811yescharacteristic
172C2×C4×C11C2×D811yescharacteristic
173C2×C4×C11C2×D811yescharacteristic
174C2×C4×C11C2×D811yescharacteristic
175C2×C4×C11C22×D411yescharacteristic
176C2×Dic11—42no—
177C2×Dic11—82no—
178D44—24no—
179D44—44no—
180D44—42no—
181C4×D11—84no—
182C4×D11—84no—
183C8×C11—21no—
184C8×C11—21no—
185C8×C11—21no—
186C8×C11C2×#4112yes—
187C22×D8—111no—
188#529—21no—
189C2×C4×D4—221no—
190C2×SD32—112no—
191C2×D16—112no—
192#499C2×D1111yescharacteristic, complemented
193#495C2×D1111yescharacteristic, complemented
194#488—21no—
195#467C2×D1111yescharacteristic
196#466C2×D1111yescharacteristic
197#465—21no—
198C4×Q16C2×D1111yescharacteristic, complemented
199C4×SD16—21no—
200C4×D8—112no—
201C4×D8—112no—
202C4×D8—221no—
203C4×D8—221no—
204C4×D8C2×D1111yescharacteristic, complemented
205C2×#107—111no—
206C2×#102—221no—
207C2×C4×C8C2×D1111yescharacteristic
208#367—112no—
209#366—112no—
210C4⋊C16—112no—
211#358—112no—
212#357—112no—
213#357—112no—
214#357—112no—
215C22⋊C16—111no—
216C22⋊C16—111no—
217#346—112no—
218C22×C11—21no—
219C22×C11—21no—
220C22×C11—81no—
221C22×C11—81no—
222C22×C11—81no—
223C22×C11#50912yes—
224C22×C11C22×D811yescharacteristic
225C2×D11—44no—
226C2×D11—88no—
227C2×D11—82no—
228C2×D11—82no—
229C4×C11—21no—
230C4×C11—21no—
231C4×C11—21no—
232C4×C11—21no—
233C4×C11—21no—
234C4×C11—81no—
235C4×C11—81no—
236C4×C11—81no—
237C4×C11#52511yescharacteristic
238C4×C11#57511yescharacteristic
239Dic11—82no—
240C22×D4—221no—
241C23×C4—441no—
242C2×Q16C22×D1111yescharacteristic
243C2×SD16—21no—
244C2×D8—112no—
245C2×D8—224no—
246C2×D8—221no—
247C2×D8C22×D1111yescharacteristic
248C22×C8C22⋊D1111yescharacteristic
249C22×C8C22×D1111yescharacteristic
250#126—41no—
251#125—21no—
252#124—21no—
253#123—41no—
254C22⋊Q8—21no—
255#121—21no—
256C4×Q8—21no—
257C4×D4—21no—
258C4×D4—41no—
259C4×D4—222no—
260C4×D4—222no—
261C4×D4—441no—
262C4×D4—441no—
263#117—41no—
264C2×C4⋊C4—221no—
265C2×C22⋊C4—441no—
266C2×C42C22⋊D1111yescharacteristic
267SD32—224no—
268D16—224no—
269C2×C16—112no—
270C2×C16—112no—
271#107—112no—
272#107—221no—
273#107C22×D1111yescharacteristic
274#107C22×D1111yescharacteristic
275#106—21no—
276#103—21no—
277#103—21no—
278#102—21no—
279#102—21no—
280#102—222no—
281#102—222no—
282C4×C8C22⋊D1111yescharacteristic
283C4×C8C22⋊D1111yescharacteristic
284C4×C8C22×D1111yescharacteristic
285C4×C8C22×D1111yescharacteristic
286C2×C11—22no—
287C2×C11—161no—
288C2×C11#310011yescharacteristic
289C2×C11C2×#50911yescharacteristic
290C2×C11#341411yescharacteristic
291D11—84no—
292C24—441no—
293C2×Q8—21no—
294C2×D4—21no—
295C2×D4—41no—
296C2×D4—224no—
297C2×D4—222no—
298C2×D4—442no—
299C2×D4—441no—
300C22×C4—41no—
301C22×C4—441no—
302C22×C4—442no—
303C22×C4—442no—
304C22×C4—884no—
305C22×C4#432311yescharacteristic
306C22×C4#432311yescharacteristic
307C22×C4C2×C22⋊D1111yescharacteristic
308Q16—22no—
309SD16—42no—
310D8—22no—
311D8—114no—
312D8—224no—
313D8—222no—
314C2×C8—22no—
315C2×C8—41no—
316C2×C8C2×C22⋊D1111yescharacteristic
317C2×C8C2×C22⋊D1111yescharacteristic
318C2×C8C2×C22⋊D1111yescharacteristic
319C2×C8C23×D1111yescharacteristic
320C4⋊C4—21no—
321C4⋊C4—21no—
322C4⋊C4—41no—
323C4⋊C4—41no—
324C4⋊C4—41no—
325C4⋊C4—41no—
326C4⋊C4—222no—
327C4⋊C4—441no—
328C22⋊C4—41no—
329C22⋊C4—41no—
330C22⋊C4—41no—
331C22⋊C4—41no—
332C22⋊C4—41no—
333C22⋊C4—442no—
334C22⋊C4—442no—
335C42—41no—
336C42#432311yescharacteristic
337C42#432311yescharacteristic
338C42C2×C22⋊D1111yescharacteristic
339C42C2×C22⋊D1111yescharacteristic
340C16—222no—
341C16—222no—
342C11#3367411yescharacteristic, complemented, Sylow
343C23—41no—
344C23—444no—
345C23—442no—
346C23—882no—
347C23—882no—
348C23C2×#432311yescharacteristic
349Q8—41no—
350Q8—41no—
351D4—41no—
352D4—41no—
353D4—82no—
354D4—224no—
355D4—444no—
356D4—442no—
357C2×C4—22no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—82no—
365C2×C4—442no—
366C2×C4—884no—
367C2×C4—884no—
368C2×C4—882no—
369C2×C4C2×#432311yescharacteristic
370C2×C4C2×#432311yescharacteristic
371C2×C4C2×#432311yescharacteristic
372C2×C4C2×#432311yescharacteristic
373C2×C4C2×#432311yescharacteristic
374C2×C4C22×C22⋊D1111yescharacteristic
375C8—21no—
376C8—21no—
377C8—21no—
378C8#41×D1112yes—
379C22—21no—
380C22—21no—
381C22—81no—
382C22—81no—
383C22—81no—
384C22—444no—
385C22—888no—
386C22—882no—
387C22—882no—
388C22#1062280612yes—
389C22C22×#432311yescharacteristic
390C4—21no—
391C4—21no—
392C4—21no—
393C4—21no—
394C4—21no—
395C4—81no—
396C4—81no—
397C4—81no—
398C4—882no—
399C4#1062335311yescharacteristic
400C4#1062335911yescharacteristic
401C2—22no—
402C2—161no—
403C2—884no—
404C2#1307861211yescharacteristic
405C2C2×#1062280611yescharacteristic
406C2#1308175011yescharacteristic
subgroupG/H
centerC22C22×#4323
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#3168C2
socleC22×C11C22×D8
prime radical#13070527C2
hypercenter#3168D11
hypocenterC11#33674
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C4×C8 ◁ #3168

Complements

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

NH ≅ G/Ntype
1. C2×C4×D88C2semidirect
2. #13070811C2semidirect
3. #13070794C2semidirect
4. #13070770C2semidirect
5. #13070668C2semidirect
6. #13070544C2semidirect
8. #13070490C2semidirect
9. #13070478C2semidirect
10. #13070419C2semidirect
11. C11×#3168C2semidirect
15. C11×#499C22semidirect
16. C11×#495C22semidirect
21. C4×C11×Q16C22semidirect
23. C4×C11×D8C22semidirect
33. #10622202C22semidirect
34. #10622200C22semidirect
39. #10622128C22semidirect
40. #10622127C22semidirect
41. C4⋊(C11⋊C16)C22semidirect
42. #10622099C22semidirect
140. #3168D11semidirect
192. #499C2×D11semidirect
193. #495C2×D11semidirect
198. C4×Q16C2×D11semidirect
204. C4×D8C2×D11semidirect
342. C11#33674semidirect

Maximal subgroups

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

subgroupindex
C2×C4×D882
#130708112
#130707942
#130707702
#130706682
#130705442
#130705272
#130704902
#130704782
#130704192
C11×#31682
#3367411