Finite Group Databasebeta

← #14762344

Subgroups — #14762344

Order 2816.

1094 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622699C211yesmaximal, characteristic
2C2×#10622643C212yesmaximal, complemented
3C2×#10622639C212yesmaximal
4C4×#66928C211yesmaximal, characteristic
5#13069476C212yesmaximal, complemented
6#13069473C212yesmaximal
7#13069437C211yesmaximal, characteristic, complemented
8#13069430C211yesmaximal, characteristic
9#13068782C211yesmaximal, characteristic, complemented
10C4×#66867C211yesmaximal, characteristic, complemented
11C4×C11×C4⋊Q8C211yesmaximal, characteristic, complemented
12C2×C11×C4⋊Q8C2211yescharacteristic
13C2×C4×Q8×C11C2212yes—
14C22×#4326C2212yes—
15C22×#4325C2212yes—
16C2×#66928C2211yescharacteristic
17C2×C4×D44C2211yescharacteristic
18C2×C4×Dic22C2211yescharacteristic
19C11×#391C2212yes—
20C11×#389—22no—
21C11×#384C2211yescharacteristic
22C4×C11×C4⋊C4—22no—
23C43×C11C2211yescharacteristic
24C2×#66899C2212yes—
25C2×#66899C2212yes—
26#10622699C418yescomplemented
27#10622643—28no—
28#10622639—28no—
29C2×#66874C2212yes—
30C2×#66873C2212yes—
31C2×#66872C2212yes—
32C2×#66871C2212yes—
33#10622553—22no—
34#10622552C2211yescharacteristic
35C4×(C2×D11)⋊C4—22no—
36#10622549C2211yescharacteristic
37#10622542C2211yescharacteristic
38C2×#66867C2211yescharacteristic
39C2×#66867C2211yescharacteristic
40C2×#66867C2212yes—
41C2×C4×C11⋊C8C2212yes—
42C22×Q8×C11C2312yes—
43C22×D44C2311yescharacteristic
44C22×C4×D11—21no—
45C22×Dic22C2311yescharacteristic
46C11×C4⋊Q8—22no—
47C11×C4⋊Q8C2×C414yescomplemented
48C4×Q8×C11—24no—
49C4×Q8×C11—24no—
50C2×C11×C4⋊C4—22no—
51C2×C11×C4⋊C4—22no—
52C2×C11×C4⋊C4—22no—
53C2×C11×C4⋊C4C2312yes—
54C2×C42×C11—22no—
55C2×C42×C11D412yes—
56C2×C42×C11D412yes—
57C2×C42×C11C2311yescharacteristic
58C2×C42×C11C2311yescharacteristic
59C2×C42×C11C2311yescharacteristic
60C2×#4326—24no—
61C2×#4326—24no—
62C2×#4326C2×C418yescomplemented
63C2×#4325—24no—
64C2×#4325—24no—
65C2×#4325C2×C418yes—
66C2×(C2×D11)⋊C4—22no—
67C2×(C2×D11)⋊C4—21no—
68C2×(C2×D11)⋊C4—22no—
69C2×C4⋊Dic11C2311yescharacteristic
70C2×C4⋊Dic11C2311yescharacteristic
71C2×Dic11⋊C4—21no—
72C2×C4×Dic11—21no—
73C22×C11⋊C8C2312yes—
74C22×C11⋊C8C2312yes—
75#66928—22no—
76#66928C2×C414yes—
77C4×D44—24no—
78C4×Dic22—24no—
79C11×#95—24no—
80#66899—24no—
81#66899—24no—
82C11⋊#95—22no—
83C11⋊#95—22no—
84#66874—24no—
85#66873—24no—
86#66872—24no—
87#66871—24no—
88#66867—22no—
89#66867C2×C414yescomplemented
90#66867D418yes—
91C4×C11⋊C8—24no—
92#21702—111nomaximal, Sylow
93C23×D11—21no—
94C2×Q8×C11—22no—
95C2×Q8×C11—22no—
96C2×Q8×C11—22no—
97C2×Q8×C11—22no—
98C2×Q8×C11—22no—
99C2×Q8×C11C22×C414yes—
100C22×C4×C11—22no—
101C22×C4×C11—22no—
102C22×C4×C11C2×D412yes—
103C22×C4×C11C2×D411yescharacteristic
104C22×C4×C11C2×D411yescharacteristic
105C22×C4×C11C2×D412yes—
106C22×C4×C11C2411yescharacteristic
107C22×Dic11—21no—
108C22×Dic11—21no—
109C22×Dic11—21no—
110C2×D44—22no—
111C2×D44—21no—
112C2×D44—22no—
113C2×D44C22×C412yes—
114C2×C4×D11—44no—
115C2×C4×D11—42no—
116C2×Dic22—22no—
117C2×Dic22—22no—
118C2×Dic22—21no—
119C2×Dic22C22×C412yes—
120C11×C4⋊C4—28no—
121C11×C4⋊C4—22no—
122C11×C4⋊C4—22no—
123C11×C4⋊C4—44no—
124C11×C4⋊C4—44no—
125C42×C11—24no—
126C42×C11—22no—
127C42×C11—42no—
128C42×C11—44no—
129C42×C11C22×C412yes—
130C42×C11C2×D414yes—
131C42×C11#4112yes—
132#4326—216no—
133#4325—216no—
134(C2×D11)⋊C4—28no—
135(C2×D11)⋊C4—42no—
136(C2×D11)⋊C4—44no—
137C4⋊Dic11—22no—
138C4⋊Dic11—22no—
139Dic11⋊C4—42no—
140C4×Dic11—42no—
141C2×C11⋊C8—22no—
142C2×C11⋊C8—22no—
143C2×C11⋊C8C22×C414yes—
144C2×C11⋊C8C2×D414yes—
145C2×C11⋊C8C2×D414yes—
146C2×C11⋊C8#4114yes—
147C2×#497—111no—
148C2×#441—112no—
149C2×#440—112no—
150C4×C4⋊Q8D1111yescharacteristic, complemented
151C4×#124—111no—
152#1969—112no—
153#1968—112no—
154#1960—111no—
155#1959—111no—
156#1847—111no—
157C4×#97—111no—
158C23×C11C22×D411yescharacteristic
159C22×D11—22no—
160C22×D11—41no—
161C22×D11—41no—
162C22×D11—42no—
163C22×D11—42no—
164Q8×C11—24no—
165Q8×C11—24no—
166Q8×C11—42no—
167Q8×C11—42no—
168C2×C4×C11—22no—
169C2×C4×C11—22no—
170C2×C4×C11—22no—
171C2×C4×C11—22no—
172C2×C4×C11—22no—
173C2×C4×C11—22no—
174C2×C4×C11—24no—
175C2×C4×C11—42no—
176C2×C4×C11—42no—
177C2×C4×C11—42no—
178C2×C4×C11—44no—
179C2×C4×C11C4×D414yes—
180C2×C4×C11#12712yes—
181C2×C4×C11#12712yes—
182C2×C4×C11#13714yes—
183C2×C4×C11C23×C411yescharacteristic
184C2×C4×C11C22×D412yes—
185C2×C4×C11C2×#4111yescharacteristic
186C2×C4×C11C2×#4112yes—
187C2×Dic11—22no—
188C2×Dic11—41no—
189C2×Dic11—41no—
190C2×Dic11—41no—
191C2×Dic11—41no—
192C2×Dic11—42no—
193C2×Dic11—42no—
194D44—24no—
195D44—42no—
196C4×D11—84no—
197Dic22—24no—
198Dic22—42no—
199C11⋊C8—24no—
200C11⋊C8C4×D418yes—
201C22×Q16—112no—
202C22×SD16—112no—
203C2×C4⋊Q8C2×D1111yescharacteristic
204C2×#124—111no—
205C2×C4×Q8—111no—
206C2×C4×Q8C2×D1112yes—
207C2×C4×D4—111no—
208#497—118no—
209#441—228no—
210#440—228no—
211C2×#107—112no—
212C2×#106—112no—
213C2×#103—112no—
214C2×#103—112no—
215C2×#103—112no—
216C2×#102—112no—
217C2×#97—111no—
218C2×#97—112no—
219C2×#97—111no—
220C2×C4×C8—112no—
221#391—111no—
222#391C2×D1112yes—
223#390—111no—
224#389—22no—
225#388—222no—
226#384C2×D1111yescharacteristic
227#382—111no—
228C4×C4⋊C4—22no—
229C4×C22⋊C4—222no—
230C43C2×D1111yescharacteristic
231C22×C11C2×C4×D411yescharacteristic
232C22×C11C2×#12711yescharacteristic
233C22×C11#53211yescharacteristic
234C22×C11C2×#13712yes—
235C22×C11#57512yes—
236C2×D11—42no—
237C2×D11—44no—
238C2×D11—81no—
239C2×D11—81no—
240C2×D11—82no—
241C4×C11—22no—
242C4×C11—22no—
243C4×C11—24no—
244C4×C11—24no—
245C4×C11—44no—
246C4×C11—82no—
247C4×C11C2×C4×D412yes—
248C4×C11#53212yes—
249Dic11—42no—
250Dic11—81no—
251Dic11—81no—
252C22×Q8—111no—
253C22×Q8C22×D1112yes—
254C22×D4—111no—
255C23×C4—221no—
256C2×Q16—118no—
257C2×Q16—224no—
258C2×Q16—224no—
259C2×SD16—118no—
260C2×SD16—224no—
261C2×SD16—224no—
262C22×C8—112no—
263C22×C8—112no—
264C4⋊Q8—22no—
265C4⋊Q8C4×D1114yescomplemented
266#124—114no—
267#124—222no—
268C4×Q8—24no—
269C4×Q8—24no—
270C4×Q8—224no—
271C4×D4—224no—
272C2×C4⋊C4—22no—
273C2×C4⋊C4—22no—
274C2×C4⋊C4—22no—
275C2×C4⋊C4—111no—
276C2×C4⋊C4—111no—
277C2×C4⋊C4—221no—
278C2×C4⋊C4C22×D1112yes—
279C2×C22⋊C4—222no—
280C2×C22⋊C4—221no—
281C2×C22⋊C4—222no—
282C2×C42—22no—
283C2×C42—221no—
284C2×C42C22⋊D1112yes—
285C2×C42C22⋊D1112yes—
286C2×C42C22×D1111yescharacteristic
287C2×C42C22×D1111yescharacteristic
288C2×C42C22×D1111yescharacteristic
289#107—224no—
290#106—224no—
291#103—224no—
292#103—224no—
293#103—224no—
294#102—224no—
295#97—114no—
296#97—118no—
297#97—222no—
298C4×C8—224no—
299#95—24no—
300#95—222no—
301#95—222no—
302C2×C11C4×#12711yescharacteristic
303C2×C11C4×#13712yes—
304C2×C11#315211yescharacteristic
305C2×C11#315311yescharacteristic
306C2×C11#318112yes—
307D11—82no—
308C24—221no—
309C2×Q8—22no—
310C2×Q8—22no—
311C2×Q8—22no—
312C2×Q8—22no—
313C2×Q8—22no—
314C2×Q8—112no—
315C2×Q8—221no—
316C2×Q8—222no—
317C2×Q8—222no—
318C2×Q8C2×C4×D1114yes—
319C2×D4—112no—
320C2×D4—221no—
321C2×D4—222no—
322C2×D4—222no—
323C22×C4—22no—
324C22×C4—22no—
325C22×C4—221no—
326C22×C4—221no—
327C22×C4—221no—
328C22×C4—444no—
329C22×C4—442no—
330C22×C4C2×C22⋊D1112yes—
331C22×C4C2×C22⋊D1111yescharacteristic
332C22×C4C2×C22⋊D1111yescharacteristic
333C22×C4C2×C22⋊D1112yes—
334C22×C4C23×D1111yescharacteristic
335Q16—2216no—
336SD16—2216no—
337C2×C8—114no—
338C2×C8—114no—
339C2×C8—114no—
340C2×C8—114no—
341C2×C8—222no—
342C2×C8—222no—
343C4⋊C4—28no—
344C4⋊C4—22no—
345C4⋊C4—22no—
346C4⋊C4—44no—
347C4⋊C4—44no—
348C4⋊C4—222no—
349C4⋊C4—222no—
350C4⋊C4—442no—
351C22⋊C4—228no—
352C22⋊C4—442no—
353C22⋊C4—444no—
354C42—24no—
355C42—22no—
356C42—42no—
357C42—44no—
358C42—442no—
359C42C2×C4×D1112yes—
360C42#433912yes—
361C42D4×D1114yes—
362C11#2170211yescharacteristic, complemented, Sylow
363C23—222no—
364C23—441no—
365C23—442no—
366C23—442no—
367C23—441no—
368C23C22×C22⋊D1111yescharacteristic
369Q8—24no—
370Q8—24no—
371Q8—42no—
372Q8—42no—
373Q8—224no—
374Q8—442no—
375D4—224no—
376D4—442no—
377C2×C4—22no—
378C2×C4—22no—
379C2×C4—22no—
380C2×C4—22no—
381C2×C4—22no—
382C2×C4—22no—
383C2×C4—24no—
384C2×C4—42no—
385C2×C4—42no—
386C2×C4—42no—
387C2×C4—44no—
388C2×C4—222no—
389C2×C4—441no—
390C2×C4—441no—
391C2×C4—441no—
392C2×C4—441no—
393C2×C4—442no—
394C2×C4—442no—
395C2×C4—884no—
396C2×C4C4×C22⋊D1114yes—
397C2×C4#6699312yes—
398C2×C4#6699312yes—
399C2×C4#6699514yes—
400C2×C4C22×C4×D1111yescharacteristic
401C2×C4C2×#433911yescharacteristic
402C2×C4C2×D4×D1112yes—
403C2×C4#41×D1112yes—
404C8—118no—
405C8—224no—
406C22—442no—
407C22—444no—
408C22—882no—
409C22—881no—
410C22—881no—
411C22C2×C4×C22⋊D1111yescharacteristic
412C22C2×#6699311yescharacteristic
413C22C2×#6699512yes—
414C22#1062335312yes—
415C22#1062336311yescharacteristic
416C4—24no—
417C4—22no—
418C4—22no—
419C4—24no—
420C4—44no—
421C4—82no—
422C4—442no—
423C4—881no—
424C4—881no—
425C4C4×D4×D1112yes—
426C4#1062307912yes—
427C2—882no—
428C2C4×#6699311yescharacteristic
429C2C4×#6699512yes—
430C2#1307907311yescharacteristic
431C2#1307908411yescharacteristic
432C2#1307931912yes—
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC4×C11×C4⋊Q8C2
socleC23×C11C22×D4
prime radicalC22×D44C23
cosocleC22×C4×C11C24
hypercenterC4×C4⋊Q8D11
hypocenterC11#21702
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C43 ◁ C4×C4⋊Q8

Complements

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

NH ≅ G/Ntype
2. C2×#10622643C2semidirect
5. #13069476C2semidirect
7. #13069437C2semidirect
9. #13068782C2semidirect
10. C4×#66867C2semidirect
11. C4×C11×C4⋊Q8C2semidirect
26. #10622699C4semidirect
47. C11×C4⋊Q8C2×C4semidirect
62. C2×#4326C2×C4semidirect
89. #66867C2×C4semidirect
150. C4×C4⋊Q8D11semidirect
265. C4⋊Q8C4×D11semidirect
362. C11#21702semidirect

Maximal subgroups

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

subgroupindex
C2×#106226992
C2×#106226432
C2×#106226392
C4×#669282
#130694762
#130694732
#130694372
#130694302
#130687822
C4×#668672
C4×C11×C4⋊Q82
#2170211