Finite Group Databasebeta

← #14790016

Subgroups — #14790016

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#13082419C211yesmaximal, characteristic
2#13078421C212yesmaximal, complemented
3#13069966C212yesmaximal, complemented
4#13069777C212yesmaximal, complemented
5#13069593C212yesmaximal, complemented
6#13069005C212yesmaximal
7#13068825C212yesmaximal
8#13068608C211yesmaximal, characteristic
9C4×C11×#124C211yesmaximal, characteristic
10C2×C11×#124C2211yescharacteristic
11C2×C4×Q8×C11C2211yescharacteristic
12C2×C4×D4×C11C2211yescharacteristic
13#10623329C2212yes—
14C2×#66977—22no—
15#10623074—22no—
16#10623070—24no—
17D4×Dic22—22no—
18#10623031C2212yes—
19#10623014—22no—
20#10623001C2212yes—
21C11×#391C2211yescharacteristic
22C11×#390C2211yescharacteristic
23C11×#388—22no—
24C11×#382C2211yescharacteristic
25C4×C11×C22⋊C4—22no—
26C43×C11C2211yescharacteristic
27#10622838C2214yes—
28C2×#66897C2212yes—
29#10622635—24no—
30#10622634—22no—
31#10622633—22no—
32#10622577C2214yes—
33#10622537C2212yes—
34#10622168C2212yes—
35#10622161C2214yes—
36#10622161C2214yes—
37C22×Q8×C11C2311yescharacteristic
38C22×D4×C11C2311yescharacteristic
39C23×C4×C11D412yes—
40C22×Dic22—22no—
41C11×#124—22no—
42C11×#124Q814yescomplemented
43C4×Q8×C11—22no—
44C4×Q8×C11—22no—
45C4×D4×C11—22no—
46C4×D4×C11—22no—
47C2×C11×C4⋊C4—21no—
48C2×C11×C4⋊C4C2311yescharacteristic
49C2×C11×C4⋊C4C2311yescharacteristic
50C2×C11×C22⋊C4—22no—
51C2×C11×C22⋊C4—22no—
52C2×C11×C22⋊C4D412yes—
53C2×C42×C11—21no—
54C2×C42×C11—21no—
55C2×C42×C11—21no—
56C2×C42×C11C2311yescharacteristic
57C2×C42×C11C2311yescharacteristic
58C2×C42×C11C2311yescharacteristic
59C2×C22⋊Dic11—24no—
60D4×Dic11—24no—
61D4×Dic11—24no—
62#66979C2314yes—
63C2×C4⋊Dic11—22no—
64#66977—24no—
65#66977—24no—
66#66977—22no—
67#66977—22no—
68#66977—24no—
69C2×Dic11⋊C4—24no—
70C2×#4318C2314yes—
71#66943—24no—
72#66941—24no—
73#66931—28no—
74#66931—28no—
75#66923D414yes—
76#66922D412yes—
77#66922D412yes—
78C4×Dic22—22no—
79C4×Dic22—22no—
80C11×#95—22no—
81C11×#95—22no—
82#66899—24no—
83#66899—24no—
84#66897—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—21no—
92C2×Q8×C11—22no—
93C2×Q8×C11—22no—
94C2×Q8×C11C2×Q812yescomplemented
95C2×D4×C11—22no—
96C2×D4×C11—22no—
97C2×D4×C11C2×Q812yes—
98C2×D4×C11#4112yes—
99C22×C4×C11—21no—
100C22×C4×C11—21no—
101C22×C4×C11—21no—
102C22×C4×C11—22no—
103C22×C4×C11—22no—
104C22×C4×C11—21no—
105C22×C4×C11—44no—
106C22×C4×C11C2×D411yescharacteristic
107C22×C4×C11C2×D412yes—
108C22×C4×C11C2×D411yescharacteristic
109C22×C4×C11C2411yescharacteristic
110C22×Dic11—24no—
111C22×Dic11—24no—
112C2×Dic22—24no—
113C2×Dic22—22no—
114C2×Dic22—22no—
115C2×Dic22—84no—
116C11×C4⋊C4—22no—
117C11×C4⋊C4—22no—
118C11×C4⋊C4—42no—
119C11×C22⋊C4—28no—
120C11×C22⋊C4—24no—
121C11×C22⋊C4—44no—
122C42×C11—21no—
123C42×C11—22no—
124C42×C11—42no—
125C42×C11—42no—
126C42×C11—41no—
127C42×C11—41no—
128C42×C11C2×D412yes—
129C42×C11C2×D412yes—
130C42×C11C2×Q812yescomplemented
131C22⋊Dic11—28no—
132C22⋊Dic11—24no—
133C4⋊Dic11—24no—
134C4⋊Dic11—22no—
135C4⋊Dic11—22no—
136C4⋊Dic11C2×D414yes—
137C4⋊Dic11C2×D414yes—
138Dic11⋊C4—28no—
139Dic11⋊C4—24no—
140Dic11⋊C4—24no—
141C4×Dic11—24no—
142#4318—24no—
143#4318—24no—
144C2×C11⋊C8—24no—
145#3501—111no—
146#3078—112no—
147C4×#124D1111yescharacteristic
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—24no—
161Q8×C11—42no—
162D4×C11—24no—
163D4×C11—24no—
164C2×C4×C11—22no—
165C2×C4×C11—22no—
166C2×C4×C11—22no—
167C2×C4×C11—22no—
168C2×C4×C11—22no—
169C2×C4×C11—41no—
170C2×C4×C11—41no—
171C2×C4×C11—41no—
172C2×C4×C11—41no—
173C2×C4×C11—41no—
174C2×C4×C11—41no—
175C2×C4×C11—41no—
176C2×C4×C11—44no—
177C2×C4×C11—42no—
178C2×C4×C11—42no—
179C2×C4×C11—41no—
180C2×C4×C11—82no—
181C2×C4×C11#12011yescharacteristic
182C2×C4×C11#12012yes—
183C2×C4×C11#12011yescharacteristic
184C2×C4×C11C22×D412yes—
185C2×C4×C11C22×Q811yescharacteristic
186C2×C4×C11C2×#4111yescharacteristic
187C2×C4×C112−1+412yes—
188C2×Dic11—24no—
189C2×Dic11—24no—
190C2×Dic11—84no—
191C2×Dic11—84no—
192Dic22—44no—
193Dic22—82no—
194Dic22—84no—
195C11⋊C8—44no—
196#554—224no—
197#554—222no—
198D4×Q8—222no—
199#544—112no—
200#543—222no—
201#533—112no—
202C2×#124C2×D1111yescharacteristic
203C2×C22⋊Q8—222no—
204#518—112no—
205C2×C4×Q8C2×D1111yescharacteristic
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#391C2×D1111yescharacteristic
215#390C2×D1111yescharacteristic
216#388—22no—
217#382C2×D1111yescharacteristic
218C4×C22⋊C4—22no—
219C43C2×D1111yescharacteristic
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—42no—
237C4×C11—42no—
238C4×C11—42no—
239C4×C11—81no—
240C4×C11#45512yes—
241C4×C11#54812yes—
242C4×C11D4×Q812yes—
243Dic11—44no—
244Dic11—44no—
245C22×Q8—222no—
246C22×Q8C22×D1111yescharacteristic
247C22×D4C22×D1111yescharacteristic
248C23×C4C22⋊D1112yes—
249C2×M16—114no—
250C4⋊Q8—112no—
251C4⋊Q8—112no—
252C4⋊Q8—224no—
253#125—114no—
254#125—224no—
255#124—22no—
256#124Dic2214yescomplemented
257C22⋊Q8—228no—
258C22⋊Q8—228no—
259C22⋊Q8—224no—
260C22⋊Q8—224no—
261C22⋊Q8—222no—
262C22⋊Q8—224no—
263C22⋊Q8—222no—
264C4×Q8—22no—
265C4×Q8—22no—
266C4×Q8—222no—
267C4×Q8—222no—
268C4×D4—22no—
269C4×D4—22no—
270C4×D4—224no—
271C4×D4—224no—
272#117—114no—
273C2×C4⋊C4—21no—
274C2×C4⋊C4—224no—
275C2×C4⋊C4—222no—
276C2×C4⋊C4C22×D1111yescharacteristic
277C2×C4⋊C4C22×D1111yescharacteristic
278C2×C22⋊C4—22no—
279C2×C22⋊C4—22no—
280C2×C22⋊C4—224no—
281C2×C22⋊C4C22⋊D1112yes—
282C2×C42—21no—
283C2×C42—21no—
284C2×C42—21no—
285C2×C42C22×D1111yescharacteristic
286C2×C42C22×D1111yescharacteristic
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—22no—
296#95—22no—
297C2×C11—21no—
298C2×C11—21no—
299C2×C11—44no—
300C2×C11#240911yescharacteristic
301C2×C11C2×#45511yescharacteristic
302C2×C11#301811yescharacteristic
303C24C2×C22⋊D1112yes—
304C2×Q8—21no—
305C2×Q8—22no—
306C2×Q8—22no—
307C2×Q8—224no—
308C2×Q8—222no—
309C2×Q8—222no—
310C2×Q8—884no—
311C2×Q8C2×Dic2212yescomplemented
312C2×D4—22no—
313C2×D4—22no—
314C2×D4C2×Dic2212yes—
315C2×D4#433912yes—
316C22×C4—21no—
317C22×C4—21no—
318C22×C4—21no—
319C22×C4—22no—
320C22×C4—22no—
321C22×C4—21no—
322C22×C4—44no—
323C22×C4—224no—
324C22×C4—224no—
325C22×C4C2×C22⋊D1111yescharacteristic
326C22×C4C2×C22⋊D1112yes—
327C22×C4C2×C22⋊D1111yescharacteristic
328C22×C4C23×D1111yescharacteristic
329M16—224no—
330M16—224no—
331C2×C8—224no—
332C4⋊C4—22no—
333C4⋊C4—22no—
334C4⋊C4—42no—
335C4⋊C4—114no—
336C4⋊C4—114no—
337C4⋊C4—224no—
338C4⋊C4—228no—
339C4⋊C4—224no—
340C4⋊C4—222no—
341C4⋊C4—224no—
342C4⋊C4—222no—
343C22⋊C4—28no—
344C22⋊C4—24no—
345C22⋊C4—44no—
346C22⋊C4—228no—
347C22⋊C4—224no—
348C42—21no—
349C42—22no—
350C42—42no—
351C42—42no—
352C42—41no—
353C42—41no—
354C42—224no—
355C42C2×Dic2212yescomplemented
356C42D4×D1112yes—
357C42D4×D1112yes—
358C11#2431411yescharacteristic, complemented, Sylow
359C23—22no—
360C23—22no—
361C23—42no—
362C23—42no—
363C23#6697714yes—
364C23C22×C22⋊D1111yescharacteristic
365Q8—24no—
366Q8—42no—
367Q8—444no—
368Q8—882no—
369Q8—884no—
370D4—24no—
371D4—24no—
372C2×C4—22no—
373C2×C4—22no—
374C2×C4—22no—
375C2×C4—22no—
376C2×C4—22no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—44no—
385C2×C4—42no—
386C2×C4—42no—
387C2×C4—41no—
388C2×C4—82no—
389C2×C4—224no—
390C2×C4—224no—
391C2×C4—884no—
392C2×C4—884no—
393C2×C4#6699011yescharacteristic
394C2×C4#6699012yes—
395C2×C4#6699011yescharacteristic
396C2×C4C22×Dic2211yescharacteristic
397C2×C4C2×#433911yescharacteristic
398C2×C4C2×D4×D1112yes—
399C2×C4#6704312yes—
400C8—444no—
401C22—21no—
402C22—21no—
403C22—24no—
404C22—44no—
405C22—42no—
406C22—42no—
407C22—82no—
408C22C2×#6697711yescharacteristic
409C22C2×#6699011yescharacteristic
410C22#1062335611yescharacteristic
411C4—21no—
412C4—22no—
413C4—42no—
414C4—42no—
415C4—42no—
416C4—42no—
417C4—81no—
418C4—444no—
419C4—444no—
420C4#1062267412yes—
421C4D4×Dic2212yes—
422C4#1062308312yes—
423C2—21no—
424C2—21no—
425C2—44no—
426C2#1307198111yescharacteristic
427C2C2×#1062267411yescharacteristic
428C2#1307796411yescharacteristic
subgroupG/H
centerC22C2×#66990
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC4×C11×#124C2
socleC22×C11C2×#120
prime radicalC22×D4×C11C23
hypercenterC4×#124D11
hypocenterC11#24314
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C4×#124

Complements

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

NH ≅ G/Ntype
2. #13078421C2semidirect
3. #13069966C2semidirect
4. #13069777C2semidirect
5. #13069593C2semidirect
42. C11×#124Q8semidirect
94. C2×Q8×C11C2×Q8semidirect
130. C42×C11C2×Q8semidirect
256. #124Dic22semidirect
311. C2×Q8C2×Dic22semidirect
355. C42C2×Dic22semidirect
358. C11#24314semidirect

Maximal subgroups

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

subgroupindex
#130824192
#130784212
#130699662
#130697772
#130695932
#130690052
#130688252
#130686082
C4×C11×#1242
#2431411