Finite Group Databasebeta

← #14810385

Subgroups — #14810385

Order 2816.

1446 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622701C212yesmaximal, complemented
2#13076961C211yesmaximal, characteristic
3#13069749C214yesmaximal, complemented
4#13069578C212yesmaximal, complemented
5#13068933C214yesmaximal, complemented
6C4×C22⋊(C11⋊C8)C211yesmaximal, characteristic, complemented
7C22×C11×C4⋊Q8C211yesmaximal, characteristic, complemented
8C23×Q8×C11—21no—
9C2×C11×C4⋊Q8—28no—
10C2×C11×C4⋊Q8—21no—
11C2×C11×C4⋊Q8—21no—
12C2×C11×C4⋊Q8C2212yes—
13C2×C11×C4⋊Q8C2212yes—
14C22×C11×C4⋊C4—21no—
15C22×C11×C4⋊C4C2212yes—
16C22×C42×C11C2211yescharacteristic
17C2×#66983—21no—
18C2×#66983—21no—
19C2×#66983C2212yes—
20C2×#66927C2211yescharacteristic
21C2×C22⋊(C11⋊C8)C2212yes—
22#10622701—28no—
23C2×#66873C2218yes—
24#10622552—21no—
25#10622552—21no—
26#10622552C2212yes—
27#10622548C2211yescharacteristic
28C2×C4×C11⋊C8C2212yes—
29#10622167C2218yes—
30#10622162C2212yes—
31C22×Q8×C11—28no—
32C22×Q8×C11—22no—
33C22×Q8×C11—22no—
34C22×Q8×C11—44no—
35C22×Q8×C11—44no—
36C23×C4×C11—22no—
37C23×C4×C11D411yescharacteristic
38C23×C4×C11D411yescharacteristic
39C23×C4×C11C2311yescharacteristic
40C22×C22⋊D11—22no—
41C22×D44—21no—
42C22×D44—21no—
43C22×D44C2312yes—
44C11×C4⋊Q8—28no—
45C11×C4⋊Q8—28no—
46C11×C4⋊Q8—28no—
47C11×C4⋊Q8—24no—
48C11×C4⋊Q8D418yescomplemented
49C2×C11×C4⋊C4—28no—
50C2×C11×C4⋊C4—22no—
51C2×C11×C4⋊C4—22no—
52C2×C11×C4⋊C4—22no—
53C2×C11×C4⋊C4—28no—
54C2×C11×C4⋊C4C2314yes—
55C2×C42×C11—24no—
56C2×C42×C11D411yescharacteristic
57C2×C42×C11D411yescharacteristic
58C2×C42×C11C2311yescharacteristic
59C2×C42×C11C2311yescharacteristic
60#66983—28no—
61#66983—44no—
62#66983—44no—
63C2×(C2×D11)⋊C4—22no—
64C2×(C2×D11)⋊C4—22no—
65C2×(C2×D11)⋊C4—22no—
66C2×C4⋊Dic11—21no—
67C2×C4⋊Dic11—21no—
68C2×C4⋊Dic11C2312yes—
69C22×C11⋊C8C2314yes—
70#66927—24no—
71C22⋊(C11⋊C8)—24no—
72#66873—216no—
73C4×C11⋊C8—24no—
74#25903—111nomaximal, Sylow
75C24×C11C2×D411yescharacteristic
76C23×D11—22no—
77C2×Q8×C11—28no—
78C2×Q8×C11—28no—
79C2×Q8×C11—44no—
80C2×Q8×C11—432no—
81C2×Q8×C11—44no—
82C2×Q8×C11—44no—
83C2×Q8×C11—44no—
84C22×C4×C11—22no—
85C22×C4×C11—22no—
86C22×C4×C11—22no—
87C22×C4×C11—22no—
88C22×C4×C11—22no—
89C22×C4×C11—22no—
90C22×C4×C11—28no—
91C22×C4×C11—24no—
92C22×C4×C11—44no—
93C22×C4×C11—44no—
94C22×C4×C11D814yes—
95C22×C4×C11SD1614yes—
96C22×C4×C11C2×D411yescharacteristic
97C22×C4×C11C2×D411yescharacteristic
98C22×C4×C11C2×D411yescharacteristic
99C22×C4×C11C2×D411yescharacteristic
100C22×C4×C11C2×D411yescharacteristic
101C22×C4×C11#4114yes—
102C22×C4×C11C2411yescharacteristic
103C2×C22⋊D11—44no—
104C2×C22⋊D11—44no—
105C2×C22⋊D11—44no—
106C22×Dic11—22no—
107C2×D44—24no—
108C2×D44—24no—
109C2×D44—24no—
110C2×D44—42no—
111C2×D44—42no—
112C2×D44—42no—
113C2×D44—42no—
114C2×D44—42no—
115C2×D44—42no—
116C11×C4⋊C4—28no—
117C11×C4⋊C4—28no—
118C11×C4⋊C4—28no—
119C11×C4⋊C4—24no—
120C11×C4⋊C4C2×D418yes—
121C42×C11—22no—
122C42×C11—22no—
123C42×C11—22no—
124C42×C11C2×D414yes—
125(C2×D11)⋊C4—44no—
126(C2×D11)⋊C4—44no—
127(C2×D11)⋊C4—44no—
128C4⋊Dic11—24no—
129C4⋊Dic11—42no—
130C4⋊Dic11—42no—
131C2×C11⋊C8—24no—
132C2×C11⋊C8—24no—
133C2×C11⋊C8—24no—
134C22×C4⋊Q8D1111yescharacteristic, complemented
135C2×#486—112no—
136#2856—111no—
137#2023—114no—
138#1990—112no—
139#1874—114no—
140C4×C22⋊C8—111no—
141C23×C11—21no—
142C23×C11—21no—
143C23×C11—21no—
144C23×C11—21no—
145C23×C11#12412yes—
146C23×C11C2×D812yes—
147C23×C11C2×SD1612yes—
148C23×C11C22×D411yescharacteristic
149C22×D11—42no—
150C22×D11—42no—
151C22×D11—42no—
152C22×D11—42no—
153C22×D11—42no—
154C22×D11—42no—
155C22×D11—42no—
156Q8×C11—416no—
157Q8×C11—416no—
158C2×C4×C11—21no—
159C2×C4×C11—21no—
160C2×C4×C11—21no—
161C2×C4×C11—21no—
162C2×C4×C11—21no—
163C2×C4×C11—21no—
164C2×C4×C11—28no—
165C2×C4×C11—28no—
166C2×C4×C11—28no—
167C2×C4×C11—28no—
168C2×C4×C11—416no—
169C2×C4×C11—44no—
170C2×C4×C11—44no—
171C2×C4×C11#12012yes—
172C2×C4×C11#12012yes—
173C2×C4×C11#12412yes—
174C2×C4×C11C2×D812yes—
175C2×C4×C11C2×D812yes—
176C2×C4×C11C2×SD1612yes—
177C2×C4×C11C2×SD1612yes—
178C2×C4×C11AGL(1,ℤ/8)12yes—
179C2×C4×C11#13712yes—
180C2×C4×C11C22×D412yes—
181C2×C4×C11C2×#4112yes—
182C2×C4×C112−1+412yes—
183C22⋊D11—88no—
184C2×Dic11—42no—
185C2×Dic11—42no—
186C2×Dic11—42no—
187D44—48no—
188D44—84no—
189D44—84no—
190C11⋊C8—44no—
191C23×Q8—21no—
192C2×C4⋊Q8—28no—
193C2×C4⋊Q8—21no—
194C2×C4⋊Q8—21no—
195C2×C4⋊Q8C2×D1112yes—
196C2×C4⋊Q8C2×D1112yes—
197C2×#127—111no—
198C2×#121—112no—
199C2×#121—221no—
200C2×#121—221no—
201C22×C4⋊C4—21no—
202C22×C4⋊C4C2×D1112yes—
203C22×C42C2×D1111yescharacteristic
204#486—228no—
205C2×#102—118no—
206C2×C22⋊C8—112no—
207C2×C4×C8—112no—
208#390—112no—
209#390—221no—
210#390—221no—
211#384—111no—
212#340—118no—
213#336—112no—
214C22×C11—22no—
215C22×C11—22no—
216C22×C11—22no—
217C22×C11—22no—
218C22×C11—22no—
219C22×C11—22no—
220C22×C11#48614yescomplemented
221C22×C11C2×#12011yescharacteristic
222C22×C11C2×#12411yescharacteristic
223C22×C11#53611yescharacteristic
224C22×C11C22×D811yescharacteristic
225C22×C11C22×SD1611yescharacteristic
226C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
227C22×C11C2×#13711yescharacteristic
228C2×D11—82no—
229C2×D11—82no—
230C2×D11—82no—
231C2×D11—82no—
232C2×D11—82no—
233C2×D11—82no—
234C2×D11—82no—
235C4×C11—22no—
236C4×C11—22no—
237C4×C11—22no—
238C4×C11—48no—
239C4×C11#44714yes—
240C4×C11#44814yes—
241C4×C11#54814yes—
242Dic11—82no—
243C22×Q8—28no—
244C22×Q8—22no—
245C22×Q8—22no—
246C22×Q8—44no—
247C22×Q8—44no—
248C22×D4—112no—
249C22×D4—222no—
250C22×D4—221no—
251C22×D4—221no—
252C23×C4—22no—
253C23×C4C22⋊D1111yescharacteristic
254C23×C4C22⋊D1111yescharacteristic
255C23×C4C22×D1111yescharacteristic
256C22×C8—114no—
257C4⋊Q8—28no—
258C4⋊Q8—28no—
259C4⋊Q8—28no—
260C4⋊Q8—24no—
261C4⋊Q8C22⋊D1118yescomplemented
262#127—224no—
263#121—228no—
264#121—444no—
265#121—444no—
266C2×C4⋊C4—28no—
267C2×C4⋊C4—22no—
268C2×C4⋊C4—22no—
269C2×C4⋊C4—22no—
270C2×C4⋊C4—28no—
271C2×C4⋊C4—112no—
272C2×C4⋊C4—221no—
273C2×C4⋊C4—221no—
274C2×C4⋊C4C22×D1114yes—
275C2×C22⋊C4—222no—
276C2×C22⋊C4—222no—
277C2×C22⋊C4—222no—
278C2×C42—24no—
279C2×C42C22⋊D1111yescharacteristic
280C2×C42C22⋊D1111yescharacteristic
281C2×C42C22×D1111yescharacteristic
282C2×C42C22×D1111yescharacteristic
283#102—2216no—
284C22⋊C8—224no—
285C4×C8—224no—
286C2×C11—24no—
287C2×C11#243611yescharacteristic
288C2×C11C2×#44711yescharacteristic
289C2×C11C2×#44811yescharacteristic
290C2×C11C2×#48611yescharacteristic
291C2×C11#314111yescharacteristic
292C2×C11#322611yescharacteristic
293C2×C11#322711yescharacteristic
294D11—162no—
295C24—222no—
296C24C2×C22⋊D1111yescharacteristic
297C2×Q8—28no—
298C2×Q8—28no—
299C2×Q8—44no—
300C2×Q8—432no—
301C2×Q8—44no—
302C2×Q8—44no—
303C2×Q8—44no—
304C2×D4—224no—
305C2×D4—224no—
306C2×D4—224no—
307C2×D4—444no—
308C2×D4—444no—
309C2×D4—444no—
310C2×D4—442no—
311C2×D4—442no—
312C2×D4—442no—
313C2×D4—442no—
314C2×D4—442no—
315C2×D4—442no—
316C22×C4—22no—
317C22×C4—22no—
318C22×C4—22no—
319C22×C4—22no—
320C22×C4—22no—
321C22×C4—22no—
322C22×C4—28no—
323C22×C4—24no—
324C22×C4—44no—
325C22×C4—44no—
326C22×C4—222no—
327C22×C4#432314yes—
328C22×C4#432514yes—
329C22×C4#434314yes—
330C22×C4C2×C22⋊D1111yescharacteristic
331C22×C4C2×C22⋊D1111yescharacteristic
332C22×C4C2×C22⋊D1111yescharacteristic
333C22×C4C2×C22⋊D1111yescharacteristic
334C22×C4C2×C22⋊D1111yescharacteristic
335C22×C4C23×D1111yescharacteristic
336C2×C8—224no—
337C2×C8—224no—
338C2×C8—224no—
339C4⋊C4—28no—
340C4⋊C4—28no—
341C4⋊C4—28no—
342C4⋊C4—24no—
343C4⋊C4—224no—
344C4⋊C4—442no—
345C4⋊C4—442no—
346C4⋊C4C2×C22⋊D1118yes—
347C22⋊C4—444no—
348C22⋊C4—444no—
349C22⋊C4—444no—
350C42—22no—
351C42—22no—
352C42—22no—
353C42C2×C22⋊D1114yes—
354C11#2590311yescharacteristic, complemented, Sylow
355C23—21no—
356C23—21no—
357C23—21no—
358C23—21no—
359C23—442no—
360C23—442no—
361C23—442no—
362C23—442no—
363C23—442no—
364C23—442no—
365C23—442no—
366C23C2×#432312yes—
367C23C2×#432512yes—
368C23#6700012yes—
369C23C22×C22⋊D1111yescharacteristic
370Q8—416no—
371Q8—416no—
372D4—448no—
373D4—888no—
374D4—884no—
375D4—884no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—28no—
383C2×C4—28no—
384C2×C4—28no—
385C2×C4—28no—
386C2×C4—416no—
387C2×C4—44no—
388C2×C4—44no—
389C2×C4—442no—
390C2×C4—442no—
391C2×C4—442no—
392C2×C4C2×#432312yes—
393C2×C4C2×#432312yes—
394C2×C4#6698512yes—
395C2×C4C2×#432512yes—
396C2×C4C2×#432512yes—
397C2×C4#6699512yes—
398C2×C4#6700012yes—
399C2×C4#6700612yes—
400C2×C4#6700612yes—
401C2×C4C2×#434312yes—
402C2×C4#6704012yes—
403C2×C4C22×C22⋊D1112yes—
404C8—444no—
405C22—22no—
406C22—22no—
407C22—22no—
408C22—22no—
409C22—22no—
410C22—22no—
411C22—882no—
412C22—882no—
413C22—882no—
414C22—882no—
415C22—882no—
416C22—882no—
417C22—882no—
418C22#1062270114yescomplemented
419C22C22×#432311yescharacteristic
420C22C2×#6698511yescharacteristic
421C22C22×#432511yescharacteristic
422C22C2×#6699511yescharacteristic
423C22C2×#6700011yescharacteristic
424C22#1062334711yescharacteristic
425C22C2×#6700611yescharacteristic
426C4—22no—
427C4—22no—
428C4—22no—
429C4—48no—
430C4—882no—
431C4#1062283014yes—
432C4#1062284014yes—
433C4#1062334814yes—
434C2—24no—
435C2—1762no—
436C2#1307227011yescharacteristic
437C2C2×#1062283011yescharacteristic
438C2C2×#1062284011yescharacteristic
439C2C2×#1062270111yescharacteristic
440C2#1307901211yescharacteristic
441C2#1307973711yescharacteristic
442C2#1307974411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC22×C11×C4⋊Q8C2
socleC23×C11C22×D4
prime radical#13076961C2
hypercenterC22×C4⋊Q8D11
hypocenterC11#25903
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ C22×C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. C2×#10622701C2semidirect
3. #13069749C2semidirect
4. #13069578C2semidirect
5. #13068933C2semidirect
6. C4×C22⋊(C11⋊C8)C2semidirect
7. C22×C11×C4⋊Q8C2semidirect
48. C11×C4⋊Q8D4semidirect
134. C22×C4⋊Q8D11semidirect
220. C22×C11#486semidirect
261. C4⋊Q8C22⋊D11semidirect
354. C11#25903semidirect
418. C22#10622701semidirect

Maximal subgroups

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

subgroupindex
C2×#106227012
#130769612
#130697492
#130695782
#130689332
C4×C22⋊(C11⋊C8)2
C22×C11×C4⋊Q82
#2590311