Finite Group Databasebeta

← #14660316

Subgroups — #14660316

Order 2816.

1462 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×#10622828C212yesmaximal
2C22×#66900C211yesmaximal, characteristic, complemented
3#13071202C211yesmaximal, characteristic, complemented
4C2×#10622161C212yesmaximal, complemented
5C22×C11×#124C211yesmaximal, characteristic
6C23×Q8×C11C2211yescharacteristic
7C23×D4×C11C2211yescharacteristic
8C2×C11×#124—22no—
9C2×C11×#124—24no—
10C2×C11×#124—24no—
11C2×C11×#124C414yescomplemented
12C22×C11×C22⋊C4—22no—
13C22×C42×C11C2211yescharacteristic
14C2×#66979C2212yes—
15C22×#4318C2212yes—
16#10622843—24no—
17C2×#66900—22no—
18C2×#66900—24no—
19#10622828—24no—
20#10622828—24no—
21C2×#66896—24no—
22#10622824—22no—
23#10622161—24no—
24C25×C11—21no—
25C22×Q8×C11—22no—
26C22×Q8×C11—22no—
27C22×Q8×C11—22no—
28C22×Q8×C11—22no—
29C22×Q8×C11—22no—
30C22×Q8×C11—22no—
31C22×Q8×C11C2×C412yes—
32C22×Q8×C11D412yes—
33C22×D4×C11—22no—
34C22×D4×C11—22no—
35C22×D4×C11—22no—
36C22×D4×C11—21no—
37C22×D4×C11—22no—
38C22×D4×C11—22no—
39C22×D4×C11C2×C412yes—
40C22×D4×C11D414yes—
41C23×C4×C11—21no—
42C23×C4×C11D412yes—
43C23×C4×C11C2311yescharacteristic
44C11×#124—216no—
45C11×#124—28no—
46C11×#124—28no—
47C2×C11×C22⋊C4—216no—
48C2×C11×C22⋊C4—28no—
49C2×C42×C11—22no—
50C2×C42×C11—21no—
51C2×C42×C11C2×C412yes—
52C2×C42×C11D414yes—
53C2×C22⋊Dic11—22no—
54#66979—22no—
55#66979—22no—
56#66979—22no—
57#66979—22no—
58C2×C4⋊Dic11D414yes—
59C2×C4×Dic11—22no—
60C2×#4318—22no—
61C2×#4318—22no—
62C2×#4318—22no—
63C2×#4318—22no—
64C2×#4318—22no—
65C2×#4318D414yes—
66C22×C11⋊C8—22no—
67#66900—28no—
68#66896—216no—
69C11⋊#95—28no—
70#10976—111nomaximal, Sylow
71C24×C11—22no—
72C24×C11—24no—
73C24×C11—48no—
74C24×C11—41no—
75C24×C11—42no—
76C24×C11—41no—
77C24×C11C2×D411yescharacteristic
78C2×Q8×C11—22no—
79C2×Q8×C11—22no—
80C2×Q8×C11—24no—
81C2×Q8×C11—24no—
82C2×Q8×C11—22no—
83C2×Q8×C11—24no—
84C2×Q8×C11—24no—
85C2×Q8×C11—22no—
86C2×Q8×C11—42no—
87C2×Q8×C11—42no—
88C2×Q8×C11—42no—
89C2×Q8×C11—42no—
90C2×Q8×C11—42no—
91C2×Q8×C11—42no—
92C2×Q8×C11—42no—
93C2×Q8×C11—42no—
94C2×D4×C11—22no—
95C2×D4×C11—24no—
96C2×D4×C11—24no—
97C2×D4×C11—24no—
98C2×D4×C11—24no—
99C2×D4×C11—24no—
100C2×D4×C11—24no—
101C2×D4×C11—24no—
102C2×D4×C11—41no—
103C2×D4×C11—42no—
104C2×D4×C11—42no—
105C2×D4×C11—42no—
106C2×D4×C11—41no—
107C2×D4×C11—42no—
108C2×D4×C11—42no—
109C2×D4×C11C22⋊C414yes—
110C22×C4×C11—22no—
111C22×C4×C11—22no—
112C22×C4×C11—24no—
113C22×C4×C11—24no—
114C22×C4×C11—24no—
115C22×C4×C11—22no—
116C22×C4×C11—44no—
117C22×C4×C11C22⋊C414yes—
118C22×C4×C11C22×C411yescharacteristic
119C22×C4×C11C2×D412yes—
120C22×C4×C11C2×D412yes—
121C22×C4×C11C2×D412yes—
122C22×C4×C11C2×D412yes—
123C22×C4×C11C2×D411yescharacteristic
124C22×C4×C11#4112yes—
125C22×C4×C11#4112yes—
126C22×Dic11—24no—
127C11×C22⋊C4—232no—
128C42×C11—22no—
129C42×C11—24no—
130C42×C11C22⋊C414yes—
131C22⋊Dic11—42no—
132C22⋊Dic11—42no—
133C4⋊Dic11—24no—
134C4⋊Dic11—24no—
135C4×Dic11—42no—
136C4×Dic11—42no—
137#4318—24no—
138#4318—24no—
139#4318—42no—
140#4318—42no—
141C2×C11⋊C8—24no—
142C2×C11⋊C8—42no—
143C2×C11⋊C8—42no—
144C22×#124D1111yescharacteristic
145C2×#418—112no—
146C22×#101—111no—
147#2310—111no—
148C2×#339—112no—
149C23×C11—24no—
150C23×C11—24no—
151C23×C11—48no—
152C23×C11—416no—
153C23×C11—42no—
154C23×C11—42no—
155C23×C11—44no—
156C23×C11—44no—
157C23×C11—84no—
158C23×C11—88no—
159C23×C11—84no—
160C23×C11C2×C22⋊C411yescharacteristic
161C23×C11#12011yescharacteristic
162C23×C11#12012yes—
163C23×C11#12112yes—
164C23×C11#12311yescharacteristic
165Q8×C11—44no—
166Q8×C11—44no—
167Q8×C11—44no—
168Q8×C11—44no—
169D4×C11—28no—
170D4×C11—44no—
171D4×C11—44no—
172D4×C11—44no—
173C2×C4×C11—24no—
174C2×C4×C11—24no—
175C2×C4×C11—24no—
176C2×C4×C11—24no—
177C2×C4×C11—44no—
178C2×C4×C11—48no—
179C2×C4×C11—44no—
180C2×C4×C11—44no—
181C2×C4×C11C2×C22⋊C411yescharacteristic
182C2×C4×C11C2×C22⋊C411yescharacteristic
183C2×C4×C11C4×D412yes—
184C2×C4×C11C4×D412yes—
185C2×C4×C11#12012yes—
186C2×C4×C11#12011yescharacteristic
187C2×C4×C11#12012yes—
188C2×C4×C11#12112yes—
189C2×C4×C11#12112yes—
190C2×C4×C11#12112yes—
191C2×C4×C11#12112yes—
192C2×C4×C11#12112yes—
193C2×C4×C11#12312yes—
194C2×C4×C11#12311yescharacteristic
195C2×C4×C11#12412yes—
196C2×C4×C11#12712yes—
197C2×Dic11—44no—
198C2×Dic11—48no—
199C11⋊C8—44no—
200C23×Q8C2×D1111yescharacteristic
201C23×D4C2×D1111yescharacteristic
202C22×M16—112no—
203C2×#124—22no—
204C2×#124—24no—
205C2×#124—24no—
206C2×#124Dic1114yescomplemented
207C2×#117—112no—
208C22×C22⋊C4—22no—
209C22×C42C2×D1111yescharacteristic
210#418—224no—
211#418—224no—
212C2×#102—224no—
213C2×#101—224no—
214C2×#101—222no—
215#391—224no—
216#381—222no—
217#339—224no—
218C22×C11—22no—
219C22×C11—22no—
220C22×C11—24no—
221C22×C11—24no—
222C22×C11—48no—
223C22×C11—44no—
224C22×C11—84no—
225C22×C11—88no—
226C22×C11—84no—
227C22×C11—88no—
228C22×C11#37911yescharacteristic
229C22×C11#38611yescharacteristic
230C22×C11#38611yescharacteristic
231C22×C11#39212yes—
232C22×C11#39412yes—
233C22×C11#45414yes—
234C4×C11—44no—
235C4×C11—44no—
236C4×C11#38612yes—
237C4×C11#39012yes—
238C4×C11#39212yes—
239C4×C11#39412yes—
240Dic11—84no—
241C25—21no—
242C22×Q8—22no—
243C22×Q8—22no—
244C22×Q8—22no—
245C22×Q8—22no—
246C22×Q8—22no—
247C22×Q8—22no—
248C22×Q8C2×Dic1112yes—
249C22×Q8C22⋊D1112yes—
250C22×D4—22no—
251C22×D4—22no—
252C22×D4—22no—
253C22×D4—22no—
254C22×D4—21no—
255C22×D4—22no—
256C22×D4C2×Dic1112yes—
257C22×D4C22⋊D1114yes—
258C23×C4—21no—
259C23×C4C22⋊D1112yes—
260C23×C4C22×D1111yescharacteristic
261C2×M16—114no—
262C2×M16—222no—
263C2×M16—222no—
264C2×M16—222no—
265C2×M16—222no—
266C2×M16—222no—
267C22×C8—222no—
268#124—216no—
269#124—28no—
270#124—28no—
271#117—222no—
272#117—222no—
273#117—222no—
274#117—222no—
275C2×C4⋊C4—114no—
276C2×C22⋊C4—216no—
277C2×C22⋊C4—28no—
278C2×C22⋊C4—222no—
279C2×C42—22no—
280C2×C42—21no—
281C2×C42—222no—
282C2×C42C2×Dic1112yes—
283C2×C42C22⋊D1114yes—
284#102—2216no—
285#101—228no—
286#95—228no—
287C2×C11—21no—
288C2×C11—21no—
289C2×C11—22no—
290C2×C11—84no—
291C2×C11#143811yescharacteristic
292C2×C11#188812yes—
293C2×C11#200314yes—
294C24—22no—
295C24—24no—
296C24—48no—
297C24—41no—
298C24—41no—
299C24—42no—
300C24C2×C22⋊D1111yescharacteristic
301C2×Q8—24no—
302C2×Q8—24no—
303C2×Q8—22no—
304C2×Q8—22no—
305C2×Q8—24no—
306C2×Q8—22no—
307C2×Q8—22no—
308C2×Q8—24no—
309C2×Q8—42no—
310C2×Q8—42no—
311C2×Q8—42no—
312C2×Q8—42no—
313C2×Q8—42no—
314C2×Q8—42no—
315C2×Q8—42no—
316C2×Q8—42no—
317C2×D4—24no—
318C2×D4—24no—
319C2×D4—24no—
320C2×D4—24no—
321C2×D4—24no—
322C2×D4—24no—
323C2×D4—22no—
324C2×D4—24no—
325C2×D4—41no—
326C2×D4—42no—
327C2×D4—41no—
328C2×D4—42no—
329C2×D4—42no—
330C2×D4—42no—
331C2×D4—42no—
332C2×D4C22⋊Dic1114yes—
333C22×C4—22no—
334C22×C4—22no—
335C22×C4—24no—
336C22×C4—22no—
337C22×C4—24no—
338C22×C4—24no—
339C22×C4—44no—
340C22×C4—224no—
341C22×C4C22⋊Dic1114yes—
342C22×C4D4×D1112yes—
343C22×C4D4×D1112yes—
344C22×C4#434112yes—
345C22×C4#434112yes—
346C22×C4C22×Dic1111yescharacteristic
347C22×C4C2×C22⋊D1112yes—
348C22×C4C2×C22⋊D1111yescharacteristic
349C22×C4C2×C22⋊D1112yes—
350M16—224no—
351M16—224no—
352M16—442no—
353M16—442no—
354C2×C8—224no—
355C2×C8—442no—
356C2×C8—442no—
357C4⋊C4—224no—
358C4⋊C4—224no—
359C22⋊C4—232no—
360C22⋊C4—442no—
361C22⋊C4—442no—
362C42—22no—
363C42—24no—
364C42—442no—
365C42—442no—
366C42C22⋊Dic1114yes—
367C11#1097611yescharacteristic, complemented, Sylow
368C23—24no—
369C23—24no—
370C23—416no—
371C23—48no—
372C23—42no—
373C23—42no—
374C23—44no—
375C23—44no—
376C23—88no—
377C23—84no—
378C23—84no—
379C23#6698811yescharacteristic
380C23#6699011yescharacteristic
381C23#6699212yes—
382C23C2×C22⋊Dic1111yescharacteristic
383C23#6700612yes—
384Q8—44no—
385Q8—44no—
386Q8—44no—
387Q8—44no—
388D4—28no—
389D4—44no—
390D4—44no—
391D4—44no—
392C2×C4—24no—
393C2×C4—24no—
394C2×C4—24no—
395C2×C4—24no—
396C2×C4—48no—
397C2×C4—44no—
398C2×C4—44no—
399C2×C4—44no—
400C2×C4—444no—
401C2×C4—448no—
402C2×C4D4×Dic1112yes—
403C2×C4D4×Dic1112yes—
404C2×C4#6698812yes—
405C2×C4#6698811yescharacteristic
406C2×C4#6698912yes—
407C2×C4#6699012yes—
408C2×C4#6699011yescharacteristic
409C2×C4#6699112yes—
410C2×C4#6699112yes—
411C2×C4#6699212yes—
412C2×C4#6699212yes—
413C2×C4#6699212yes—
414C2×C4#6699312yes—
415C2×C4C2×C22⋊Dic1111yescharacteristic
416C2×C4C2×C22⋊Dic1111yescharacteristic
417C2×C4#6700612yes—
418C8—444no—
419C22—24no—
420C22—24no—
421C22—22no—
422C22—22no—
423C22—48no—
424C22—44no—
425C22—84no—
426C22—88no—
427C22—88no—
428C22—84no—
429C22#1062267514yes—
430C22#1062283311yescharacteristic
431C22#1062283311yescharacteristic
432C22#1062283512yes—
433C22#1062283612yes—
434C22#1062286011yescharacteristic
435C4—44no—
436C4—44no—
437C4—884no—
438C4#1062283312yes—
439C4#1062283412yes—
440C4#1062283512yes—
441C4#1062283612yes—
442C2—21no—
443C2—21no—
444C2—22no—
445C2—84no—
446C2#1306685711yescharacteristic
447C2#1306902012yes—
448C2#1306963814yes—
subgroupG/H
centerC23#66990
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC22×C11×#124C2
socleC23×C11#120
prime radicalC23×D4×C11C22
cosocleC23×C4×C11C23
hypercenterC22×#124D11
hypocenterC11#10976
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#124

Complements

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

NH ≅ G/Ntype
2. C22×#66900C2semidirect
3. #13071202C2semidirect
4. C2×#10622161C2semidirect
11. C2×C11×#124C4semidirect
206. C2×#124Dic11semidirect
367. C11#10976semidirect

Maximal subgroups

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

subgroupindex
C2×#106228282
C22×#669002
#130712022
C2×#106221612
C22×C11×#1242
#1097611