Finite Group Databasebeta

← #14756708

Subgroups — #14756708

Order 2816.

978 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#4324C211yesmaximal, characteristic
2#13071090C211yesmaximal, characteristic, complemented
3C4×D4×Dic11C211yesmaximal, characteristic
4#13069255C212yesmaximal, complemented
5#13069192C212yesmaximal, complemented
6#13068948C212yesmaximal
7#13068861C212yesmaximal
8C4×#66871C211yesmaximal, characteristic, complemented
9C4×#66880C211yesmaximal, characteristic, complemented
10#13068361C211yesmaximal, characteristic, complemented
11C4×C11×#102C211yesmaximal, characteristic
12C2×C4×D4×C11C2211yescharacteristic
13C2×D4×Dic11C2212yes—
14C22×#4324C2211yescharacteristic
15C22×C4×Dic11—21no—
16C2×C4×Dic22C2211yescharacteristic
17C2×C11×#102C2212yes—
18C2×C4×C8×C11C2211yescharacteristic
19C4×C11×C4⋊C4C2211yescharacteristic
20C2×#66896C2211yescharacteristic
21C4×C22⋊Dic11—21no—
22C2×#66880C2212yes—
23C4×#4324C418yescomplemented
24C4⋊C4×Dic11C2212yes—
25#10622587C2212yes—
26#10622586C2212yes—
27C2×#66874C2211yescharacteristic
28C2×#66872C2211yescharacteristic
29C2×#66871C2212yes—
30C22⋊C4×Dic11—22no—
31C4×C4⋊Dic11C2211yescharacteristic
32#10622545—21no—
33C4×Dic11⋊C4—21no—
34C42×Dic11C2211yescharacteristic
35C2×C4×C11⋊C8C2211yescharacteristic
36#10622265—22no—
37C11×#340C2212yes—
38#10622189C2212yes—
39#10622188C2212yes—
40#10622188C2212yes—
41#10622167C2212yes—
42C22×D4×C11C2311yescharacteristic
43C23×C4×C11—21no—
44C23×Dic11—22no—
45C22×Dic22C2311yescharacteristic
46C22×C8×C11C2312yes—
47C4×D4×C11—22no—
48C4×D4×C11C2×C414yes—
49C2×C11×C4⋊C4C2312yes—
50C2×C11×C4⋊C4C2311yescharacteristic
51C2×C11×C22⋊C4—21no—
52C2×C42×C11—21no—
53C2×C42×C11C2311yescharacteristic
54C2×C22⋊Dic11—22no—
55D4×Dic11—24no—
56D4×Dic11—24no—
57C2×#4324—24no—
58C2×#4324C2×C414yes—
59C2×C4⋊Dic11C2311yescharacteristic
60C2×C4⋊Dic11C2312yes—
61C2×Dic11⋊C4—21no—
62C2×Dic11⋊C4—22no—
63C2×C4×Dic11—21no—
64C2×C4×Dic11—21no—
65C2×C4×Dic11—22no—
66C2×C4×Dic11—44no—
67C2×C4×Dic11D412yes—
68C2×C4×Dic11D411yescharacteristic
69C2×C4×Dic11D411yescharacteristic
70C2×C4×Dic11C2312yes—
71C22×C11⋊C8C2311yescharacteristic
72C22×C11⋊C8C2311yescharacteristic
73C4×Dic22—22no—
74C4×Dic22C2×C414yescomplemented
75C11×#102—24no—
76C4×C8×C11—22no—
77C11×#95—21no—
78#66896C2×C414yes—
79C11⋊#95—21no—
80C11⋊#95—22no—
81C11⋊#95—22no—
82C11⋊#95—22no—
83C11⋊#95—22no—
84#66880—24no—
85#66874C2×C414yescomplemented
86#66872C2×C414yescomplemented
87#66871—24no—
88C4×C11⋊C8C2×C414yescomplemented
89#21114—111nomaximal, Sylow
90C24×C11—21no—
91C2×D4×C11—22no—
92C2×D4×C11—21no—
93C2×D4×C11C22×C412yes—
94C2×D4×C11#4114yes—
95C22×C4×C11—21no—
96C22×C4×C11—24no—
97C22×C4×C11—22no—
98C22×C4×C11—42no—
99C22×C4×C11—42no—
100C22×C4×C11C2×D411yescharacteristic
101C22×C4×C11C2×D411yescharacteristic
102C22×C4×C11C2411yescharacteristic
103C22×Dic11—28no—
104C22×Dic11—21no—
105C22×Dic11—22no—
106C22×Dic11—21no—
107C22×Dic11—44no—
108C22×Dic11—44no—
109C22×Dic11C2×D412yes—
110C22×Dic11C2×D412yes—
111C2×Dic22—22no—
112C2×Dic22—22no—
113C2×Dic22—21no—
114C2×Dic22C22×C412yes—
115C2×C8×C11—22no—
116C2×C8×C11—22no—
117C2×C8×C11—22no—
118C11×C4⋊C4—21no—
119C11×C4⋊C4—22no—
120C11×C4⋊C4—22no—
121C11×C4⋊C4C22×C412yes—
122C11×C22⋊C4—24no—
123C42×C11—42no—
124C42×C11C22×C412yes—
125C42×C11#4112yes—
126C22⋊Dic11—28no—
127#4324—28no—
128C4⋊Dic11—21no—
129C4⋊Dic11—22no—
130C4⋊Dic11C22×C412yes—
131C4⋊Dic11#4114yes—
132Dic11⋊C4—24no—
133Dic11⋊C4—44no—
134C4×Dic11—24no—
135C4×Dic11—24no—
136C4×Dic11—22no—
137C4×Dic11—22no—
138C4×Dic11—22no—
139C4×Dic11—22no—
140C4×Dic11—44no—
141C4×Dic11—42no—
142C2×C11⋊C8—22no—
143C2×C11⋊C8—22no—
144C2×C11⋊C8C22×C412yes—
145C2×C11⋊C8C22×C412yes—
146C2×C4×SD16—111no—
147#2295—111no—
148C42×D4—111no—
149#1928—112no—
150#1919—112no—
151#1877—112no—
152#1862—112no—
153C4×#107—111no—
154C4×#103—111no—
155C4×#102D1111yescharacteristic
156#1744—111no—
157C23×C11—22no—
158C23×C11—24no—
159C23×C11—42no—
160C23×C11—41no—
161C23×C11—41no—
162C23×C11C22×D411yescharacteristic
163D4×C11—22no—
164D4×C11—24no—
165D4×C11#11714yes—
166C2×C4×C11—22no—
167C2×C4×C11—22no—
168C2×C4×C11—41no—
169C2×C4×C11—41no—
170C2×C4×C11—48no—
171C2×C4×C11—42no—
172C2×C4×C11—42no—
173C2×C4×C11—42no—
174C2×C4×C11C4×D412yes—
175C2×C4×C11C4×D412yes—
176C2×C4×C11AGL(1,ℤ/8)12yes—
177C2×C4×C11#13712yes—
178C2×C4×C11C23×C411yescharacteristic
179C2×C4×C11C2×#4112yes—
180C2×C4×C11C2×#4111yescharacteristic
181C2×C4×C11C2×#4112yes—
182C2×Dic11—22no—
183C2×Dic11—22no—
184C2×Dic11—22no—
185C2×Dic11—22no—
186C2×Dic11—22no—
187C2×Dic11—24no—
188C2×Dic11—22no—
189C2×Dic11—22no—
190C2×Dic11—416no—
191C2×Dic11—42no—
192C2×Dic11—42no—
193C2×Dic11—42no—
194C2×Dic11—42no—
195C2×Dic11#13514yes—
196Dic22—22no—
197Dic22—22no—
198Dic22—42no—
199C8×C11—42no—
200C11⋊C8—22no—
201C11⋊C8—22no—
202C22×SD16—111no—
203C2×C4×Q8—111no—
204C2×C4×D4—112no—
205C2×C4×D4C2×D1111yescharacteristic
206C22×C42—221no—
207C4×SD16—118no—
208C2×#107—112no—
209C2×#106—111no—
210C2×#103—111no—
211C2×#103—112no—
212C2×#102—111no—
213C2×#102C2×D1112yes—
214C2×C4×C8—111no—
215C2×C4×C8C2×D1111yescharacteristic
216#391—112no—
217#389—112no—
218#387—222no—
219C4×C4⋊C4—112no—
220C4×C4⋊C4—111no—
221C4×C4⋊C4—221no—
222C4×C4⋊C4C2×D1111yescharacteristic
223C4×C22⋊C4—222no—
224C4×C22⋊C4—221no—
225#376—221no—
226C43—111no—
227#340—112no—
228#340—112no—
229#340C2×D1112yes—
230#336—112no—
231#336—112no—
232C22×C11—24no—
233C22×C11—44no—
234C22×C11—44no—
235C22×C11—42no—
236C22×C11—42no—
237C22×C11C2×C4×D411yescharacteristic
238C22×C11#52512yes—
239C22×C11C2×#13512yes—
240C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
241C22×C11C2×#13711yescharacteristic
242C4×C11—22no—
243C4×C11—42no—
244C4×C11—82no—
245C4×C11#44014yes—
246C4×C11C2×#11711yescharacteristic
247C4×C11C4×#4111yescharacteristic
248C4×C11#52912yes—
249Dic11—24no—
250Dic11—44no—
251Dic11—42no—
252Dic11—42no—
253Dic11—42no—
254C22×Q8—111no—
255C22×D4C22×D1111yescharacteristic
256C23×C4—21no—
257C23×C4—222no—
258C2×SD16—114no—
259C2×SD16—224no—
260C22×C8—111no—
261C22×C8—111no—
262C22×C8C22×D1112yes—
263C4×Q8—114no—
264C4×Q8—222no—
265C4×D4—22no—
266C4×D4—224no—
267C4×D4—224no—
268C4×D4C4×D1114yes—
269C2×C4⋊C4—112no—
270C2×C4⋊C4—111no—
271C2×C4⋊C4—221no—
272C2×C4⋊C4—222no—
273C2×C4⋊C4C22×D1112yes—
274C2×C4⋊C4C22×D1111yescharacteristic
275C2×C22⋊C4—21no—
276C2×C22⋊C4—222no—
277C2×C42—21no—
278C2×C42—112no—
279C2×C42—111no—
280C2×C42—111no—
281C2×C42—112no—
282C2×C42—221no—
283C2×C42—222no—
284C2×C42—221no—
285C2×C42—444no—
286C2×C42C22×D1111yescharacteristic
287#107—224no—
288#106—114no—
289#103—114no—
290#103—224no—
291#102—24no—
292#102—114no—
293C4×C8—22no—
294C4×C8—114no—
295#95—21no—
296#95—222no—
297#95—222no—
298#95—222no—
299#95—222no—
300#95—221no—
301C2×C11—44no—
302C2×C11#229011yescharacteristic
303C2×C11C4×#13511yescharacteristic
304C2×C11C2×#44011yescharacteristic
305C2×C11#310512yes—
306C2×C11#310712yes—
307C24—21no—
308C2×Q8—112no—
309C2×Q8—221no—
310C2×Q8—222no—
311C2×Q8—222no—
312C2×D4—21no—
313C2×D4—22no—
314C2×D4C2×C4×D1112yes—
315C2×D4#433914yes—
316C22×C4—21no—
317C22×C4—24no—
318C22×C4—22no—
319C22×C4—42no—
320C22×C4—42no—
321C22×C4—112no—
322C22×C4—112no—
323C22×C4—228no—
324C22×C4—221no—
325C22×C4—222no—
326C22×C4—221no—
327C22×C4—444no—
328C22×C4—444no—
329C22×C4D4×D1111yescharacteristic
330C22×C4D4×D1111yescharacteristic
331C22×C4C23×D1111yescharacteristic
332SD16—228no—
333C2×C8—22no—
334C2×C8—22no—
335C2×C8—22no—
336C2×C8—112no—
337C2×C8—112no—
338C2×C8—222no—
339C2×C8—222no—
340C4⋊C4—21no—
341C4⋊C4—22no—
342C4⋊C4—22no—
343C4⋊C4—112no—
344C4⋊C4—114no—
345C4⋊C4—224no—
346C4⋊C4—222no—
347C4⋊C4—221no—
348C4⋊C4—444no—
349C4⋊C4C2×C4×D1112yes—
350C22⋊C4—24no—
351C22⋊C4—228no—
352C42—42no—
353C42—224no—
354C42—224no—
355C42—222no—
356C42—222no—
357C42—222no—
358C42—222no—
359C42—444no—
360C42—442no—
361C42C2×C4×D1112yes—
362C42#434112yes—
363C11#2111411yescharacteristic, complemented, Sylow
364C23—22no—
365C23—24no—
366C23—41no—
367C23—41no—
368C23—42no—
369C23C2×D4×D1111yescharacteristic
370Q8—222no—
371Q8—222no—
372Q8—442no—
373D4—22no—
374D4—24no—
375D4#6692514yes—
376C2×C4—22no—
377C2×C4—22no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—48no—
381C2×C4—42no—
382C2×C4—42no—
383C2×C4—42no—
384C2×C4—114no—
385C2×C4—222no—
386C2×C4—222no—
387C2×C4—222no—
388C2×C4—222no—
389C2×C4—222no—
390C2×C4—222no—
391C2×C4—222no—
392C2×C4—224no—
393C2×C4—4416no—
394C2×C4—442no—
395C2×C4—442no—
396C2×C4—442no—
397C2×C4—442no—
398C2×C4(C22⋊D11)⋊C412yes—
399C2×C4(C22⋊D11)⋊C412yes—
400C2×C4#6696412yes—
401C2×C4#6696812yes—
402C2×C4C22×C4×D1111yescharacteristic
403C2×C4C2×#433912yes—
404C2×C4C2×#434111yescharacteristic
405C2×C4#41×D1112yes—
406C8—42no—
407C8—222no—
408C8—222no—
409C22—24no—
410C22—44no—
411C22—42no—
412C22—42no—
413C22—44no—
414C22C2×(C22⋊D11)⋊C411yescharacteristic
415C22#1062307812yes—
416C22C2×#6696411yescharacteristic
417C22C2×#6696811yescharacteristic
418C22D11×#13512yes—
419C4—22no—
420C4—42no—
421C4—82no—
422C4—224no—
423C4—444no—
424C4—442no—
425C4—442no—
426C4—442no—
427C4#1062237014yes—
428C4C2×#6692511yescharacteristic
429C4#1062305311yescharacteristic
430C4#1062306912yes—
431C2—44no—
432C2#1307105511yescharacteristic
433C2#1307738411yescharacteristic
434C2C2×#1062237011yescharacteristic
435C2#1307866112yes—
436C2#1307868312yes—
subgroupG/H
centerC22×C4D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC4×C11×#102C2
socleC23×C11C22×D4
prime radicalC22×D4×C11C23
cosocleC22×C4×C11C24
hypercenterC4×#102D11
hypocenterC11#21114
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C4×#102

Complements

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

NH ≅ G/Ntype
2. #13071090C2semidirect
4. #13069255C2semidirect
5. #13069192C2semidirect
8. C4×#66871C2semidirect
9. C4×#66880C2semidirect
10. #13068361C2semidirect
23. C4×#4324C4semidirect
74. C4×Dic22C2×C4semidirect
85. #66874C2×C4semidirect
86. #66872C2×C4semidirect
88. C4×C11⋊C8C2×C4semidirect
363. C11#21114semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#43242
#130710902
C4×D4×Dic112
#130692552
#130691922
#130689482
#130688612
C4×#668712
C4×#668802
#130683612
C4×C11×#1022
#2111411