Finite Group Databasebeta

← #14762341

Subgroups — #14762341

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×#10622328C211yesmaximal, characteristic
2C2×#10622466C212yesmaximal, complemented
3C2×#10622502C212yesmaximal
4#13071183C211yesmaximal, characteristic, complemented
5#13071155C211yesmaximal, characteristic
6#13069475C212yesmaximal, complemented
7#13069468C212yesmaximal
8#13069435C211yesmaximal, characteristic, complemented
9#13069430C211yesmaximal, characteristic
10#97×Dic11C211yesmaximal, characteristic, complemented
11C11×#1847C211yesmaximal, characteristic, complemented
12C22×Dic44C2212yes—
13C22×#4314C2212yes—
14C2×#66946C2211yescharacteristic
15C2×#66940C2211yescharacteristic
16C2×#66940C2212yes—
17C2×#66928C2211yescharacteristic
18C2×#66922C2211yescharacteristic
19C2×C11×#107C2212yes—
20C2×C11×#106C2212yes—
21C2×C11×#97C2211yescharacteristic
22C11×#384C2211yescharacteristic
23C11×#382C2211yescharacteristic
24C2×#66879C2212yes—
25C2×C8×Dic11C2212yes—
26#10622601C2211yescharacteristic
27C4⋊C4×Dic11—22no—
28#10622587C2211yescharacteristic
29#10622587C2212yes—
30#10622586—22no—
31C2×#66874C2212yes—
32C2×#66874C2212yes—
33C2×#66874C2212yes—
34C2×#66873C2212yes—
35C42×Dic11C2211yescharacteristic
36C2×#66867C2211yescharacteristic
37#10622502—28no—
38#10622466—28no—
39#10622328C418yescomplemented
40#10622282—22no—
41#10622279—22no—
42C22×D44C2311yescharacteristic
43C22×C4×D11—21no—
44C22×Dic22C2312yes—
45C22×Dic22C2311yescharacteristic
46C22×C8×C11C2312yes—
47C2×C11×C4⋊C4—22no—
48C2×C11×C4⋊C4C2312yes—
49C2×C11×C4⋊C4C2311yescharacteristic
50C2×C11×C4⋊C4C2311yescharacteristic
51C2×C42×C11C2311yescharacteristic
52C2×(C2×D11)⋊C4—22no—
53C2×(C2×D11)⋊C4—21no—
54C2×(C2×D11)⋊C4—22no—
55C2×C4⋊Dic11—22no—
56C2×Dic11⋊C4—21no—
57C2×Dic11⋊C4—22no—
58C2×C4×Dic11—21no—
59C2×C4×Dic11—22no—
60C2×C4×Dic11D412yes—
61C2×C4×Dic11D412yes—
62C2×C4×Dic11C2311yescharacteristic
63C2×C4×Dic11C2311yescharacteristic
64C22×C11⋊C8C2312yes—
65C2×Dic44—24no—
66C2×Dic44—24no—
67C2×Dic44C2×C418yescomplemented
68C2×#4314—24no—
69C2×#4314—24no—
70C2×#4314C2×C418yes—
71#66946—24no—
72#66940—24no—
73#66940—24no—
74#66940—24no—
75#66928—22no—
76#66928C2×C414yes—
77#66922—22no—
78#66922C2×C414yescomplemented
79C11×#107—24no—
80C11×#106—24no—
81C11×#97C2×C414yescomplemented
82C11×#95—22no—
83C11⋊#95—22no—
84C11⋊#95—24no—
85#66879D418yes—
86C8×Dic11—24no—
87#66874—24no—
88#66874—24no—
89#66874—24no—
90#66873—24no—
91#66867—22no—
92#21702—111nomaximal, Sylow
93C23×D11—21no—
94C22×C4×C11—21no—
95C22×C4×C11—22no—
96C22×C4×C11—21no—
97C22×C4×C11C2×D412yes—
98C22×C4×C11C2411yescharacteristic
99C22×Dic11—22no—
100C22×Dic11—21no—
101C22×Dic11C2×D411yescharacteristic
102C22×Dic11C2×D411yescharacteristic
103C22×Dic11C2×D412yes—
104C2×D44—22no—
105C2×D44—21no—
106C2×D44—22no—
107C2×D44C22×C412yes—
108C2×C4×D11—44no—
109C2×C4×D11—42no—
110C2×Dic22—22no—
111C2×Dic22—22no—
112C2×Dic22—22no—
113C2×Dic22—22no—
114C2×Dic22—22no—
115C2×Dic22—22no—
116C2×Dic22—22no—
117C2×Dic22—21no—
118C2×Dic22C22×C414yes—
119C2×Dic22C22×C412yes—
120C2×C8×C11C22×C414yes—
121C2×C8×C11C2×D414yes—
122C2×C8×C11#4114yes—
123C11×C4⋊C4—22no—
124C11×C4⋊C4—22no—
125C11×C4⋊C4—22no—
126C11×C4⋊C4—22no—
127C11×C4⋊C4—44no—
128C42×C11C22×C412yes—
129C42×C11#4112yes—
130(C2×D11)⋊C4—28no—
131(C2×D11)⋊C4—42no—
132(C2×D11)⋊C4—44no—
133C4⋊Dic11—28no—
134Dic11⋊C4—42no—
135Dic11⋊C4—44no—
136C4×Dic11—24no—
137C4×Dic11—22no—
138C4×Dic11—42no—
139C4×Dic11—44no—
140C4×Dic11—42no—
141C4×Dic11C2×D414yes—
142C2×C11⋊C8—22no—
143C2×C11⋊C8—22no—
144C2×C11⋊C8C2×D414yes—
145Dic44—216no—
146#4314—216no—
147C2×#497—111no—
148C2×#441—112no—
149C2×#440—112no—
150C4×C4⋊Q8—111no—
151C4×#124—111no—
152#1969—112no—
153#1968—112no—
154#1960—111no—
155#1959—111no—
156#1847D1111yescharacteristic, complemented
157C4×#97—111no—
158C23×C11C22×D411yescharacteristic
159C22×D11—22no—
160C22×D11—41no—
161C22×D11—41no—
162C22×D11—42no—
163C22×D11—42no—
164C2×C4×C11—22no—
165C2×C4×C11—22no—
166C2×C4×C11—41no—
167C2×C4×C11—42no—
168C2×C4×C11—41no—
169C2×C4×C11—42no—
170C2×C4×C11—44no—
171C2×C4×C11—42no—
172C2×C4×C11C4×D414yes—
173C2×C4×C11C23×C411yescharacteristic
174C2×C4×C11C22×D412yes—
175C2×C4×C11C2×#4112yes—
176C2×C4×C11C2×#4111yescharacteristic
177C2×Dic11—22no—
178C2×Dic11—22no—
179C2×Dic11—22no—
180C2×Dic11—22no—
181C2×Dic11—24no—
182C2×Dic11—22no—
183C2×Dic11—42no—
184C2×Dic11—41no—
185C2×Dic11—42no—
186C2×Dic11—41no—
187C2×Dic11#12712yes—
188C2×Dic11#12712yes—
189C2×Dic11#13714yes—
190D44—24no—
191D44—42no—
192C4×D11—84no—
193Dic22—24no—
194Dic22—24no—
195Dic22—24no—
196Dic22—42no—
197Dic22—42no—
198Dic22—42no—
199C8×C11C4×D418yes—
200C11⋊C8—24no—
201C22×Q16—112no—
202C22×SD16—112no—
203C2×C4⋊Q8—111no—
204C2×#124—111no—
205C2×C4×Q8—112no—
206C2×C4×Q8—111no—
207C2×C4×D4—111no—
208#497—118no—
209#441—228no—
210#440—228no—
211C2×#107C2×D1112yes—
212C2×#106C2×D1112yes—
213C2×#103—112no—
214C2×#103—112no—
215C2×#103—112no—
216C2×#102—112no—
217C2×#97—112no—
218C2×#97—111no—
219C2×#97C2×D1111yescharacteristic
220C2×C4×C8—112no—
221#391—112no—
222#391—111no—
223#390—111no—
224#389—222no—
225#388—222no—
226#384C2×D1111yescharacteristic
227#382C2×D1111yescharacteristic
228C4×C4⋊C4—222no—
229C4×C22⋊C4—222no—
230C43—111no—
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—24no—
242C4×C11—81no—
243C4×C11—82no—
244C4×C11—81no—
245C4×C11C2×C4×D412yes—
246C4×C11#53212yes—
247Dic11—22no—
248Dic11—22no—
249Dic11—24no—
250Dic11—44no—
251Dic11—42no—
252C22×Q8—111no—
253C22×Q8—112no—
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×C8C22×D1112yes—
264C4⋊Q8—114no—
265C4⋊Q8—222no—
266#124—114no—
267#124—222no—
268C4×Q8—224no—
269C4×Q8—224no—
270C4×Q8—224no—
271C4×D4—224no—
272C2×C4⋊C4—22no—
273C2×C4⋊C4—222no—
274C2×C4⋊C4—221no—
275C2×C4⋊C4—222no—
276C2×C4⋊C4C22×D1111yescharacteristic
277C2×C4⋊C4C22×D1111yescharacteristic
278C2×C4⋊C4C22×D1112yes—
279C2×C22⋊C4—222no—
280C2×C22⋊C4—221no—
281C2×C22⋊C4—222no—
282C2×C42—111no—
283C2×C42—112no—
284C2×C42—111no—
285C2×C42—112no—
286C2×C42—221no—
287C2×C42—222no—
288C2×C42C22×D1111yescharacteristic
289#107—24no—
290#106—24no—
291#103—224no—
292#103—224no—
293#103—224no—
294#102—224no—
295#97—118no—
296#97—222no—
297#97C4×D1114yescomplemented
298C4×C8—224no—
299#95—22no—
300#95—222no—
301#95—224no—
302C2×C11C4×#12711yescharacteristic
303C2×C11C4×#13712yes—
304C2×C11#315211yescharacteristic
305C2×C11#315311yescharacteristic
306C2×C11#318112yes—
307D11—82no—
308C24—221no—
309C2×Q8—112no—
310C2×Q8—114no—
311C2×Q8—221no—
312C2×Q8—222no—
313C2×Q8—222no—
314C2×Q8—222no—
315C2×Q8—222no—
316C2×Q8—222no—
317C2×Q8—222no—
318C2×Q8—222no—
319C2×D4—112no—
320C2×D4—222no—
321C2×D4—222no—
322C2×D4—221no—
323C22×C4—21no—
324C22×C4—21no—
325C22×C4—22no—
326C22×C4—112no—
327C22×C4—111no—
328C22×C4—111no—
329C22×C4—221no—
330C22×C4—222no—
331C22×C4—442no—
332C22×C4—444no—
333C22×C4D4×D1112yes—
334C22×C4C23×D1111yescharacteristic
335Q16—2216no—
336SD16—2216no—
337C2×C8—114no—
338C2×C8—222no—
339C2×C8—222no—
340C2×C8C2×C4×D1114yes—
341C2×C8D4×D1114yes—
342C2×C8#434314yes—
343C4⋊C4—22no—
344C4⋊C4—22no—
345C4⋊C4—22no—
346C4⋊C4—22no—
347C4⋊C4—44no—
348C4⋊C4—228no—
349C4⋊C4—442no—
350C4⋊C4—444no—
351C22⋊C4—228no—
352C22⋊C4—442no—
353C22⋊C4—444no—
354C42—114no—
355C42—224no—
356C42—222no—
357C42—442no—
358C42—444no—
359C42—442no—
360C42C2×C4×D1112yes—
361C42#434312yes—
362C11#2170211yescharacteristic, complemented, Sylow
363C23—222no—
364C23—441no—
365C23—441no—
366C23—442no—
367C23—442no—
368C23C2×D4×D1111yescharacteristic
369Q8—224no—
370Q8—224no—
371Q8—224no—
372Q8—442no—
373Q8—442no—
374Q8—442no—
375D4—224no—
376D4—442no—
377C2×C4—22no—
378C2×C4—22no—
379C2×C4—41no—
380C2×C4—42no—
381C2×C4—41no—
382C2×C4—44no—
383C2×C4—42no—
384C2×C4—42no—
385C2×C4—112no—
386C2×C4—112no—
387C2×C4—114no—
388C2×C4—222no—
389C2×C4—222no—
390C2×C4—222no—
391C2×C4—222no—
392C2×C4—222no—
393C2×C4—224no—
394C2×C4—441no—
395C2×C4—442no—
396C2×C4—441no—
397C2×C4—442no—
398C2×C4—884no—
399C2×C4#6694614yes—
400C2×C4C22×C4×D1111yescharacteristic
401C2×C4C2×D4×D1112yes—
402C2×C4C2×#434311yescharacteristic
403C2×C4C2×#434312yes—
404C8—224no—
405C8#6694618yes—
406C22—442no—
407C22—444no—
408C22—882no—
409C22—881no—
410C22—881no—
411C22C2×#6694611yescharacteristic
412C22D11×#12711yescharacteristic
413C22#1062325611yescharacteristic
414C22#1062330412yes—
415C22D11×#13712yes—
416C4—24no—
417C4—81no—
418C4—81no—
419C4—82no—
420C4—224no—
421C4—222no—
422C4—222no—
423C4—442no—
424C4—444no—
425C4C2×#6694612yes—
426C4#1062325612yes—
427C2—882no—
428C2#1307117811yescharacteristic
429C2#1307743412yes—
430C2#1307907211yescharacteristic
431C2#1307908111yescharacteristic
432C2#1307932712yes—
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1847C2
socleC23×C11C22×D4
prime radicalC22×D44C23
cosocleC22×C4×C11C24
hypercenter#1847D11
hypocenterC11#21702
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1847

Complements

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

NH ≅ G/Ntype
2. C2×#10622466C2semidirect
4. #13071183C2semidirect
6. #13069475C2semidirect
8. #13069435C2semidirect
10. #97×Dic11C2semidirect
11. C11×#1847C2semidirect
39. #10622328C4semidirect
67. C2×Dic44C2×C4semidirect
78. #66922C2×C4semidirect
81. C11×#97C2×C4semidirect
156. #1847D11semidirect
297. #97C4×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×#106223282
C2×#106224662
C2×#106225022
#130711832
#130711552
#130694752
#130694682
#130694352
#130694302
#97×Dic112
C11×#18472
#2170211