Finite Group Databasebeta

← #14755416

Subgroups — #14755416

Order 2816.

1742 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623356C211yesmaximal, characteristic
2#13081819C211yesmaximal, characteristic
3#13071200C212yesmaximal, complemented
4#13069027C218yesmaximal, complemented
5#13068348C212yesmaximal, complemented
6C2×C11×#410C211yesmaximal, characteristic
7C22×C11×#41C2211yescharacteristic
8C23×Dic22C2211yescharacteristic
9C2×C11×#117C2212yes—
10#10623358—24no—
11#41×Dic11—24no—
12#10623356—24no—
13#10623356C418yescomplemented
14#10623343—21no—
15C2×#66997—21no—
16#10623329—21no—
17#10623329C2214yes—
18C2×#66989—21no—
19C2×#66988C2214yes—
20C2×#66979—22no—
21C2×#66979C2211yescharacteristic
22C2×#66979C2212yes—
23C2×#66977—22no—
24C11×#410—24no—
25C2×C11×#99C2214yes—
26#10622587—24no—
27#10622556C2218yes—
28#10622542—24no—
29#10622165C2218yes—
30C2×C11×#41—22no—
31C2×C11×#41—22no—
32C2×C11×#41—24no—
33C2×C11×#41C2×C414yes—
34C2×C11×#41D414yes—
35C22×Q8×C11D411yescharacteristic
36C22×D4×C11D411yescharacteristic
37C22×D4×C11C2312yes—
38C23×C4×C11D412yes—
39C23×C4×C11C2311yescharacteristic
40C23×Dic11C2312yes—
41C22×Dic22—22no—
42C22×Dic22—21no—
43C22×Dic22—21no—
44C22×Dic22—22no—
45C22×Dic22—22no—
46C22×Dic22—24no—
47C22×Dic22C2×C414yescomplemented
48C11×#117—24no—
49C11×#117—24no—
50C2×C11×C4⋊C4—22no—
51C2×C11×C22⋊C4C2314yes—
52C2×C42×C11—22no—
53C2×C22⋊Dic11—24no—
54C2×C22⋊Dic11—24no—
55C2×C22⋊Dic11C2314yes—
56C2×C22⋊Dic11C2312yes—
57Q8×Dic11—28no—
58#66997—28no—
59#66989—28no—
60#66988—28no—
61#66988C2×C4116yescomplemented
62D4×Dic11—28no—
63D4×Dic11—216no—
64#66979—24no—
65#66979—24no—
66#66979—22no—
67#66979—24no—
68#66979—22no—
69#66979—22no—
70#66979—22no—
71#66979—22no—
72#66979C2×C414yescomplemented
73C2×C4⋊Dic11—24no—
74C2×C4⋊Dic11—21no—
75C2×C4⋊Dic11D414yes—
76#66977—216no—
77C2×Dic11⋊C4—24no—
78C2×C4×Dic11—24no—
79C2×C4×Dic11—21no—
80C2×C4×Dic11D414yes—
81C11×#99—28no—
82C11⋊#95—216no—
83#20962—111nomaximal, Sylow
84C24×C11C2×D412yes—
85C24×C11C2411yescharacteristic
86C11×#41—28no—
87C11×#41—28no—
88C11×#41—28no—
89C11×#41—28no—
90C2×Q8×C11—22no—
91C2×Q8×C11—22no—
92C2×Q8×C11C22⋊C414yes—
93C2×D4×C11—24no—
94C2×D4×C11—24no—
95C2×D4×C11—22no—
96C2×D4×C11—22no—
97C2×D4×C11C22⋊C414yes—
98C2×D4×C11C22×C414yes—
99C2×D4×C11C2×D414yes—
100C22×C4×C11—22no—
101C22×C4×C11—22no—
102C22×C4×C11—24no—
103C22×C4×C11—24no—
104C22×C4×C11C22⋊C418yes—
105C22×C4×C11C22×C412yes—
106C22×C4×C11C2×D412yes—
107C22×C4×C11C2×D411yescharacteristic
108C22×C4×C11C2×D411yescharacteristic
109C22×C4×C11C2×D412yes—
110C22×C4×C11C2×D412yes—
111C22×C4×C11C2×D412yes—
112C22×C4×C11#4114yes—
113C22×Dic11—28no—
114C22×Dic11—24no—
115C22×Dic11—22no—
116C22×Dic11—22no—
117C22×Dic11—22no—
118C22×Dic11—24no—
119C22×Dic11C22×C414yes—
120C22×Dic11C2×D418yes—
121C2×Dic22—24no—
122C2×Dic22—24no—
123C2×Dic22—28no—
124C2×Dic22—28no—
125C2×Dic22—41no—
126C2×Dic22—42no—
127C2×Dic22—41no—
128C2×Dic22—44no—
129C2×Dic22—44no—
130C2×Dic22—42no—
131C2×Dic22—42no—
132C11×C4⋊C4—44no—
133C11×C22⋊C4—24no—
134C11×C22⋊C4—24no—
135C42×C11—44no—
136C22⋊Dic11—28no—
137C22⋊Dic11—216no—
138C22⋊Dic11—24no—
139C22⋊Dic11—24no—
140C22⋊Dic11—22no—
141C22⋊Dic11C22×C414yes—
142C4⋊Dic11—28no—
143C4⋊Dic11—24no—
144C4⋊Dic11—24no—
145C4⋊Dic11—24no—
146Dic11⋊C4—216no—
147C4×Dic11—28no—
148C4×Dic11—24no—
149C4×Dic11—24no—
150C4×Dic11—24no—
151C2×#536—111no—
152#3428—111no—
153C2×#410D1111yescharacteristic
154#2310—112no—
155#1890—118no—
156#1740—112no—
157C23×C11—22no—
158C23×C11—22no—
159C23×C11—42no—
160C23×C11—44no—
161C23×C11C2×C22⋊C414yes—
162C23×C11C23×C411yescharacteristic
163C23×C11C22×D411yescharacteristic
164C23×C11C22×D412yes—
165C23×C11C22×D411yescharacteristic
166C23×C11C2×#4112yes—
167Q8×C11—28no—
168D4×C11—28no—
169D4×C11—28no—
170D4×C11—28no—
171C2×C4×C11—22no—
172C2×C4×C11—22no—
173C2×C4×C11—28no—
174C2×C4×C11—28no—
175C2×C4×C11—48no—
176C2×C4×C11—44no—
177C2×C4×C11C2×C22⋊C414yes—
178C2×C4×C11C2×C22⋊C412yes—
179C2×C4×C11C2×C22⋊C412yes—
180C2×C4×C11C4×D414yes—
181C2×C4×C11C4×D414yes—
182C2×C4×C11#12011yescharacteristic
183C2×C4×C11#12012yes—
184C2×C4×C11#12011yescharacteristic
185C2×C4×C11#12114yes—
186C2×C4×C11#12114yes—
187C2×C4×C11#12312yes—
188C2×C4×C11#12312yes—
189C2×Dic11—24no—
190C2×Dic11—24no—
191C2×Dic11—28no—
192C2×Dic11—28no—
193C2×Dic11—44no—
194C2×Dic11—42no—
195C2×Dic11—44no—
196C2×Dic11—42no—
197C2×Dic11—48no—
198C2×Dic11—88no—
199Dic22—44no—
200Dic22—44no—
201Dic22—48no—
202C22×#41C2×D1111yescharacteristic
203C23×Q8—111no—
204#536—118no—
205#536—224no—
206C2×C4⋊Q8—221no—
207C2×#124—221no—
208C2×#123—114no—
209C2×C22⋊Q8—222no—
210#520—224no—
211#519—221no—
212#518—114no—
213#518—221no—
214C4×#41—224no—
215C2×#117—112no—
216C2×#117—111no—
217C2×#117—222no—
218C2×#117C2×D1112yes—
219#410—24no—
220C2×#99C2×D1114yes—
221#391—224no—
222#391—224no—
223#381—118no—
224#342—118no—
225C22×C11—24no—
226C22×C11—22no—
227C22×C11—24no—
228C22×C11—41no—
229C22×C11—41no—
230C22×C11—42no—
231C22×C11—44no—
232C22×C11—44no—
233C22×C11—82no—
234C22×C11C22×C22⋊C411yescharacteristic
235C22×C11C2×C4×D412yes—
236C22×C11C2×#12011yescharacteristic
237C22×C11C2×#12112yes—
238C22×C11C2×#12311yescharacteristic
239C4×C11—24no—
240C4×C11—84no—
241C4×C11#38612yes—
242C4×C11#38612yes—
243C4×C11#38614yes—
244Dic11—44no—
245Dic11—48no—
246Dic11—44no—
247C2×#41—22no—
248C2×#41—22no—
249C2×#41—24no—
250C2×#41C4×D1114yes—
251C2×#41C22⋊D1114yes—
252C22×Q8—114no—
253C22×Q8—221no—
254C22×Q8—221no—
255C22×Q8—222no—
256C22×Q8—222no—
257C22×Q8—224no—
258C22×Q8—222no—
259C22×Q8D4411yescharacteristic
260C22×D4D4411yescharacteristic
261C22×D4C22×D1112yes—
262C23×C4—112no—
263C23×C4D4412yes—
264C23×C4C22×D1111yescharacteristic
265C4⋊Q8—228no—
266#124—228no—
267#123—1116no—
268#123—228no—
269C22⋊Q8—2216no—
270C4×Q8—228no—
271C4×D4—2216no—
272C4×D4—228no—
273#117—24no—
274#117—24no—
275#117—114no—
276#117—224no—
277#117—224no—
278#117—222no—
279#117—222no—
280#117—224no—
281#117—222no—
282#117—222no—
283#117—222no—
284C2×C4⋊C4—22no—
285C2×C4⋊C4—114no—
286C2×C4⋊C4—224no—
287C2×C4⋊C4—221no—
288C2×C4⋊C4—224no—
289C2×C22⋊C4—112no—
290C2×C22⋊C4—114no—
291C2×C22⋊C4—224no—
292C2×C22⋊C4—224no—
293C2×C22⋊C4C22×D1114yes—
294C2×C42—22no—
295C2×C42—114no—
296C2×C42—224no—
297C2×C42—221no—
298#99—28no—
299#95—2216no—
300C2×C11—21no—
301C2×C11—22no—
302C2×C11—21no—
303C2×C11—22no—
304C2×C11—44no—
305C2×C11C2×#38611yescharacteristic
306C2×C11#302812yes—
307C24C2×D4412yes—
308C24C23×D1111yescharacteristic
309#41—28no—
310#41—28no—
311#41—28no—
312#41—28no—
313C2×Q8—22no—
314C2×Q8—22no—
315C2×Q8—228no—
316C2×Q8—228no—
317C2×Q8—224no—
318C2×Q8—224no—
319C2×Q8—441no—
320C2×Q8—442no—
321C2×Q8—441no—
322C2×Q8—442no—
323C2×Q8—442no—
324C2×Q8—444no—
325C2×Q8—444no—
326C2×Q8(C2×D11)⋊C414yes—
327C2×D4—24no—
328C2×D4—24no—
329C2×D4—22no—
330C2×D4—22no—
331C2×D4(C2×D11)⋊C414yes—
332C2×D4C2×C4×D1114yes—
333C2×D4C2×C22⋊D1114yes—
334C22×C4—22no—
335C22×C4—22no—
336C22×C4—24no—
337C22×C4—24no—
338C22×C4—114no—
339C22×C4—118no—
340C22×C4—222no—
341C22×C4—222no—
342C22×C4—224no—
343C22×C4—224no—
344C22×C4—222no—
345C22×C4—228no—
346C22×C4(C2×D11)⋊C418yes—
347C22×C4C2×C4×D1112yes—
348C22×C4C2×D4412yes—
349C22×C4C2×D4411yescharacteristic
350C22×C4C2×D4411yescharacteristic
351C22×C4D4×D1112yes—
352C22×C4D4×D1112yes—
353C22×C4#434114yes—
354C22×C4C2×C22⋊D1112yes—
355C4⋊C4—44no—
356C4⋊C4—228no—
357C4⋊C4—224no—
358C4⋊C4—224no—
359C4⋊C4—224no—
360C4⋊C4—2216no—
361C22⋊C4—24no—
362C22⋊C4—24no—
363C22⋊C4—114no—
364C22⋊C4—228no—
365C22⋊C4—2216no—
366C22⋊C4—224no—
367C22⋊C4—224no—
368C22⋊C4—222no—
369C42—44no—
370C42—228no—
371C42—224no—
372C42—224no—
373C42—224no—
374C11#2096211yescharacteristic, complemented, Sylow
375C23—22no—
376C23—22no—
377C23—42no—
378C23—44no—
379C23C2×(C2×D11)⋊C414yes—
380C23C22×C4×D1111yescharacteristic
381C23C22×D4411yescharacteristic
382C23C2×D4×D1112yes—
383C23C2×#434112yes—
384C23C22×C22⋊D1111yescharacteristic
385Q8—28no—
386Q8—444no—
387Q8—444no—
388Q8—448no—
389D4—28no—
390D4—28no—
391D4—28no—
392C2×C4—22no—
393C2×C4—22no—
394C2×C4—28no—
395C2×C4—28no—
396C2×C4—48no—
397C2×C4—44no—
398C2×C4—228no—
399C2×C4—228no—
400C2×C4—224no—
401C2×C4—224no—
402C2×C4—444no—
403C2×C4—442no—
404C2×C4—442no—
405C2×C4—444no—
406C2×C4—448no—
407C2×C4—888no—
408C2×C4(C22⋊D11)⋊C414yes—
409C2×C4(C22⋊D11)⋊C414yes—
410C2×C4#6693511yescharacteristic
411C2×C4#6693512yes—
412C2×C4#6693511yescharacteristic
413C2×C4#6693912yes—
414C2×C4#6693912yes—
415C2×C4C2×(C2×D11)⋊C414yes—
416C2×C4C2×(C2×D11)⋊C412yes—
417C2×C4C2×(C2×D11)⋊C412yes—
418C2×C4#6699214yes—
419C2×C4#6699214yes—
420C22—24no—
421C22—22no—
422C22—24no—
423C22—41no—
424C22—42no—
425C22—41no—
426C22—44no—
427C22—44no—
428C22—82no—
429C22C2×(C22⋊D11)⋊C412yes—
430C22C2×#6693511yescharacteristic
431C22C2×#6693911yescharacteristic
432C22C22×(C2×D11)⋊C411yescharacteristic
433C22C2×#6699212yes—
434C4—24no—
435C4—84no—
436C4—444no—
437C4—448no—
438C4—444no—
439C4#1062257112yes—
440C4#1062257112yes—
441C4#1062257114yes—
442C2—22no—
443C2—21no—
444C2—21no—
445C2—22no—
446C2—44no—
447C2C2×#1062257111yescharacteristic
448C2#1307802312yes—
subgroupG/H
centerC22C2×#66935
commutatorC23×C11C23×C4
FrattiniC24C23×D11
FittingC2×C11×#410C2
socleC22×C11C2×#120
prime radicalC22×C11×#41C22
cosocleC24×C11C24
hypercenterC2×#410D11
hypocenterC11#20962
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#410

Complements

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

NH ≅ G/Ntype
3. #13071200C2semidirect
4. #13069027C2semidirect
5. #13068348C2semidirect
13. #10623356C4semidirect
47. C22×Dic22C2×C4semidirect
61. #66988C2×C4semidirect
72. #66979C2×C4semidirect
374. C11#20962semidirect

Maximal subgroups

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

subgroupindex
C2×#106233562
#130818192
#130712002
#130690272
#130683482
C2×C11×#4102
#2096211