Finite Group Databasebeta

← #14790010

Subgroups — #14790010

Order 2816.

1034 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078417C212yesmaximal, complemented
2C4×#66989C211yesmaximal, characteristic
3#13069963C212yesmaximal, complemented
4#13069774C212yesmaximal, complemented
5#13069594C212yesmaximal, complemented
6#13069004C212yesmaximal
7#13068826C212yesmaximal
8#13068608C211yesmaximal, characteristic
9C11×#3501C211yesmaximal, characteristic
10C11×#554—22no—
11C11×#554—24no—
12D4×Q8×C11—22no—
13C11×#544C2212yes—
14C11×#543—22no—
15C11×#533C2212yes—
16C2×C11×C22⋊Q8—22no—
17C11×#518C2212yes—
18C2×C4×D4×C11C2211yescharacteristic
19C2×#66989C2211yescharacteristic
20C2×C4×Dic22C2211yescharacteristic
21#10622834C2211yescharacteristic
22C2×#66897C2212yes—
23C4×C22⋊Dic11—22no—
24#10622707—22no—
25#10622704—22no—
26#10622676—24no—
27#10622617C2214yes—
28#10622608C2214yes—
29#10622590C2211yescharacteristic
30#10622587C2211yescharacteristic
31#10622558—22no—
32C42×Dic11C2211yescharacteristic
33#10622537C2212yes—
34#10622170C2214yes—
35#10622170C2214yes—
36#10622168C2212yes—
37C22×Q8×C11—22no—
38C22×D4×C11C2311yescharacteristic
39C23×C4×C11D412yes—
40C22×Dic22C2311yescharacteristic
41C11×C4⋊Q8—24no—
42C11×C4⋊Q8D412yes—
43C11×C4⋊Q8D412yes—
44C11×#125—24no—
45C11×#125D414yes—
46C11×C22⋊Q8—24no—
47C11×C22⋊Q8—24no—
48C11×C22⋊Q8—28no—
49C11×C22⋊Q8—28no—
50C11×C22⋊Q8—22no—
51C11×C22⋊Q8—24no—
52C11×C22⋊Q8—22no—
53C4×Q8×C11—22no—
54C4×Q8×C11—22no—
55C4×D4×C11—24no—
56C4×D4×C11—24no—
57C4×D4×C11—22no—
58C4×D4×C11—22no—
59C11×#117C2314yes—
60C2×C11×C4⋊C4—22no—
61C2×C11×C4⋊C4—24no—
62C2×C11×C4⋊C4C2311yescharacteristic
63C2×C11×C22⋊C4—24no—
64C2×C11×C22⋊C4D412yes—
65C2×C42×C11C2311yescharacteristic
66C2×C22⋊Dic11—22no—
67C2×C22⋊Dic11—22no—
68#66989—22no—
69#66989Q814yescomplemented
70C2×C4⋊Dic11C2311yescharacteristic
71C2×Dic11⋊C4—21no—
72C2×C4×Dic11—21no—
73C2×C4×Dic11—21no—
74C2×C4×Dic11—21no—
75C2×C4×Dic11C2311yescharacteristic
76C2×C4×Dic11C2311yescharacteristic
77C2×#4318C2314yes—
78C4×Dic22—22no—
79C4×Dic22—22no—
80#66897—24no—
81C11⋊#95—22no—
82C11⋊#95—22no—
83#66874—24no—
84#66874—24no—
85#66872—24no—
86#66871—24no—
87C4⋊(C11⋊C8)—22no—
88C4⋊(C11⋊C8)—22no—
89#24314—111nomaximal, Sylow
90C24×C11C2×D412yes—
91C2×Q8×C11—24no—
92C2×Q8×C11—22no—
93C2×Q8×C11—22no—
94C2×Q8×C11—84no—
95C2×D4×C11—22no—
96C2×D4×C11—22no—
97C2×D4×C11C2×Q812yes—
98C2×D4×C11#4112yes—
99C22×C4×C11—24no—
100C22×C4×C11—24no—
101C22×C4×C11—22no—
102C22×C4×C11—22no—
103C22×C4×C11—44no—
104C22×C4×C11C2×D411yescharacteristic
105C22×C4×C11C2×D412yes—
106C22×C4×C11C2×D411yescharacteristic
107C22×C4×C11C2411yescharacteristic
108C22×Dic11—21no—
109C22×Dic11—21no—
110C22×Dic11—21no—
111C22×Dic11—21no—
112C2×Dic22—22no—
113C2×Dic22—21no—
114C2×Dic22—22no—
115C2×Dic22C2×Q812yescomplemented
116C11×C4⋊C4—24no—
117C11×C4⋊C4—28no—
118C11×C4⋊C4—24no—
119C11×C4⋊C4—22no—
120C11×C4⋊C4—24no—
121C11×C4⋊C4—22no—
122C11×C4⋊C4—22no—
123C11×C4⋊C4C2×D414yes—
124C11×C4⋊C4C2×D414yes—
125C11×C22⋊C4—28no—
126C11×C22⋊C4—24no—
127C11×C22⋊C4—24no—
128C42×C11—24no—
129C42×C11C2×D412yes—
130C42×C11C2×D412yes—
131C22⋊Dic11—28no—
132C22⋊Dic11—44no—
133C4⋊Dic11—22no—
134Dic11⋊C4—42no—
135C4×Dic11—21no—
136C4×Dic11—22no—
137C4×Dic11—42no—
138C4×Dic11—42no—
139C4×Dic11—41no—
140C4×Dic11—41no—
141C4×Dic11C2×Q812yescomplemented
142#4318—24no—
143#4318—24no—
144C2×C11⋊C8—24no—
145#3501D1111yescharacteristic
146#3078—112no—
147C4×#124—111no—
148#2061—112no—
149#2028—112no—
150#1994—112no—
151#1885—112no—
152#1856—112no—
153#1800—111no—
154C23×C11—22no—
155C23×C11—22no—
156C23×C11—42no—
157C23×C11—42no—
158C23×C11C22⋊Q814yes—
159C23×C11C22×D411yescharacteristic
160Q8×C11—44no—
161Q8×C11—82no—
162Q8×C11—84no—
163D4×C11—24no—
164D4×C11—24no—
165C2×C4×C11—22no—
166C2×C4×C11—24no—
167C2×C4×C11—24no—
168C2×C4×C11—22no—
169C2×C4×C11—41no—
170C2×C4×C11—44no—
171C2×C4×C11—42no—
172C2×C4×C11—82no—
173C2×C4×C11—84no—
174C2×C4×C11—84no—
175C2×C4×C11#12011yescharacteristic
176C2×C4×C11#12012yes—
177C2×C4×C11#12011yescharacteristic
178C2×C4×C11C22×D412yes—
179C2×C4×C11C22×Q811yescharacteristic
180C2×C4×C11C2×#4111yescharacteristic
181C2×C4×C112−1+412yes—
182C2×Dic11—22no—
183C2×Dic11—22no—
184C2×Dic11—22no—
185C2×Dic11—41no—
186C2×Dic11—41no—
187C2×Dic11—41no—
188C2×Dic11—41no—
189C2×Dic11—41no—
190C2×Dic11—41no—
191C2×Dic11—42no—
192C2×Dic11—41no—
193Dic22—24no—
194Dic22—42no—
195C11⋊C8—44no—
196#554—22no—
197#554—24no—
198D4×Q8—22no—
199#544C2×D1112yes—
200#543—22no—
201#533C2×D1112yes—
202C2×#124—111no—
203C2×C22⋊Q8—22no—
204#518C2×D1112yes—
205C2×C4×Q8—111no—
206C2×C4×D4C2×D1111yescharacteristic
207#479—224no—
208#477—222no—
209#475—222no—
210#428—114no—
211#423—112no—
212#419—114no—
213C2×#100—112no—
214#391—111no—
215#390—111no—
216#388—222no—
217#382—111no—
218C4×C22⋊C4—222no—
219C43—111no—
220#343—112no—
221#339—114no—
222#339—114no—
223C22×C11—21no—
224C22×C11—21no—
225C22×C11—24no—
226C22×C11—44no—
227C22×C11—42no—
228C22×C11—42no—
229C22×C11—82no—
230C22×C11C2×#12011yescharacteristic
231C22×C11C2×C22⋊Q811yescharacteristic
232C22×C11#53611yescharacteristic
233C4×C11—21no—
234C4×C11—22no—
235C4×C11—42no—
236C4×C11—44no—
237C4×C11—44no—
238C4×C11#45512yes—
239C4×C11#54812yes—
240C4×C11D4×Q812yes—
241Dic11—42no—
242Dic11—42no—
243Dic11—42no—
244Dic11—81no—
245C22×Q8—22no—
246C22×Q8—111no—
247C22×D4C22×D1111yescharacteristic
248C23×C4C22⋊D1112yes—
249C2×M16—114no—
250C4⋊Q8—24no—
251C4⋊Q8C22⋊D1112yes—
252C4⋊Q8C22⋊D1112yes—
253#125—24no—
254#125C22⋊D1114yes—
255#124—114no—
256#124—222no—
257C22⋊Q8—24no—
258C22⋊Q8—24no—
259C22⋊Q8—28no—
260C22⋊Q8—28no—
261C22⋊Q8—22no—
262C22⋊Q8—24no—
263C22⋊Q8—22no—
264C4×Q8—22no—
265C4×Q8—22no—
266C4×Q8—222no—
267C4×Q8—222no—
268C4×D4—24no—
269C4×D4—24no—
270C4×D4—22no—
271C4×D4—22no—
272#117C22×D1114yes—
273C2×C4⋊C4—22no—
274C2×C4⋊C4—24no—
275C2×C4⋊C4—111no—
276C2×C4⋊C4—221no—
277C2×C4⋊C4C22×D1111yescharacteristic
278C2×C22⋊C4—24no—
279C2×C22⋊C4—222no—
280C2×C22⋊C4—222no—
281C2×C22⋊C4C22⋊D1112yes—
282C2×C42—111no—
283C2×C42—111no—
284C2×C42—221no—
285C2×C42—221no—
286C2×C42—221no—
287C2×C42C22×D1111yescharacteristic
288#107—224no—
289#106—224no—
290C4⋊C8—222no—
291C4⋊C8—222no—
292#103—224no—
293#103—224no—
294#100—224no—
295#95—222no—
296#95—222no—
297C2×C11—21no—
298C2×C11—21no—
299C2×C11—44no—
300C2×C11#240911yescharacteristic
301C2×C11C2×#45511yescharacteristic
302C2×C11#301811yescharacteristic
303C24C2×C22⋊D1112yes—
304C2×Q8—24no—
305C2×Q8—22no—
306C2×Q8—22no—
307C2×Q8—84no—
308C2×Q8—112no—
309C2×Q8—221no—
310C2×Q8—222no—
311C2×Q8—222no—
312C2×D4—22no—
313C2×D4—22no—
314C2×D4Q8×D1112yes—
315C2×D4#434312yes—
316C22×C4—24no—
317C22×C4—24no—
318C22×C4—22no—
319C22×C4—22no—
320C22×C4—44no—
321C22×C4—221no—
322C22×C4—221no—
323C22×C4—221no—
324C22×C4—221no—
325C22×C4C2×C22⋊D1111yescharacteristic
326C22×C4C2×C22⋊D1112yes—
327C22×C4C2×C22⋊D1111yescharacteristic
328C22×C4C23×D1111yescharacteristic
329M16—224no—
330M16—224no—
331C2×C8—224no—
332C4⋊C4—24no—
333C4⋊C4—28no—
334C4⋊C4—24no—
335C4⋊C4—22no—
336C4⋊C4—24no—
337C4⋊C4—22no—
338C4⋊C4—22no—
339C4⋊C4—222no—
340C4⋊C4—442no—
341C4⋊C4C2×C22⋊D1114yes—
342C4⋊C4C2×C22⋊D1114yes—
343C22⋊C4—28no—
344C22⋊C4—24no—
345C22⋊C4—24no—
346C22⋊C4—228no—
347C22⋊C4—444no—
348C42—24no—
349C42—112no—
350C42—221no—
351C42—222no—
352C42—442no—
353C42—442no—
354C42—441no—
355C42—441no—
356C42C2×C22⋊D1112yes—
357C42C2×C22⋊D1112yes—
358C11#2431411yescharacteristic, complemented, Sylow
359C23—22no—
360C23—22no—
361C23—42no—
362C23—42no—
363C23#6699914yes—
364C23C22×C22⋊D1111yescharacteristic
365Q8—44no—
366Q8—82no—
367Q8—84no—
368Q8—224no—
369Q8—442no—
370D4—24no—
371D4—24no—
372C2×C4—22no—
373C2×C4—24no—
374C2×C4—24no—
375C2×C4—22no—
376C2×C4—41no—
377C2×C4—44no—
378C2×C4—42no—
379C2×C4—82no—
380C2×C4—84no—
381C2×C4—84no—
382C2×C4—222no—
383C2×C4—222no—
384C2×C4—222no—
385C2×C4—441no—
386C2×C4—441no—
387C2×C4—441no—
388C2×C4—441no—
389C2×C4—441no—
390C2×C4—441no—
391C2×C4—442no—
392C2×C4—441no—
393C2×C4#6700611yescharacteristic
394C2×C4#6700612yes—
395C2×C4#6700611yescharacteristic
396C2×C4C2×Q8×D1111yescharacteristic
397C2×C4C2×#434311yescharacteristic
398C2×C4#6704012yes—
399C2×C4C22×C22⋊D1112yes—
400C8—444no—
401C22—21no—
402C22—21no—
403C22—24no—
404C22—44no—
405C22—42no—
406C22—42no—
407C22—82no—
408C22C2×#6699911yescharacteristic
409C22#1062334711yescharacteristic
410C22C2×#6700611yescharacteristic
411C4—21no—
412C4—22no—
413C4—42no—
414C4—44no—
415C4—44no—
416C4—442no—
417C4—442no—
418C4—442no—
419C4—881no—
420C4#1062285512yes—
421C4Q8×C22⋊D1112yes—
422C4#1062334812yes—
423C2—21no—
424C2—21no—
425C2—44no—
426C2#1307197511yescharacteristic
427C2C2×#1062285511yescharacteristic
428C2#1307796511yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#3501C2
socleC22×C11C2×#120
prime radicalC22×D4×C11C23
hypercenter#3501D11
hypocenterC11#24314
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3501

Complements

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

NH ≅ G/Ntype
1. #13078417C2semidirect
3. #13069963C2semidirect
4. #13069774C2semidirect
5. #13069594C2semidirect
69. #66989Q8semidirect
115. C2×Dic22C2×Q8semidirect
141. C4×Dic11C2×Q8semidirect
358. C11#24314semidirect

Maximal subgroups

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

subgroupindex
#130784172
C4×#669892
#130699632
#130697742
#130695942
#130690042
#130688262
#130686082
C11×#35012
#2431411