Finite Group Databasebeta

← #14753835

Subgroups — #14753835

Order 2816.

1306 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66940C211yesmaximal, characteristic
2C2×#10622332C211yesmaximal, characteristic
3#13071011C211yesmaximal, characteristic
4#13068706C211yesmaximal, characteristic
5#13068630C214yesmaximal, complemented
6#13068552C211yesmaximal, characteristic
7#13068550C211yesmaximal, characteristic
8#13068445C214yesmaximal, complemented
9C11×#1824C211yesmaximal, characteristic
10C23×Dic22C2211yescharacteristic
11C22×C11×C4⋊C4C2211yescharacteristic
12C22×Dic11⋊C4—21no—
13C22×C4×Dic11—21no—
14C22×C4×Dic11C2211yescharacteristic
15C2×#66940—21no—
16C2×#66940—21no—
17C2×#66940—24no—
18C2×#66940C418yescomplemented
19C2×#66940C2212yes—
20C2×#66940C2212yes—
21C2×C11×C22⋊C8C2211yescharacteristic
22C11×#380C2211yescharacteristic
23#10622825C2211yescharacteristic
24C2×C22⋊(C11⋊C8)C2211yescharacteristic
25C2×#66880C2214yes—
26C2×#66879C2212yes—
27C2×Dic11⋊C8C2212yes—
28#10622590C2212yes—
29C4⋊C4×Dic11C2212yes—
30C2×#66874C2214yes—
31#10622556—21no—
32C22⋊C4×Dic11—21no—
33#10622332—24no—
34#10622264—21no—
35#10622261—21no—
36C11×#340C2214yes—
37#10622167C2214yes—
38C23×C4×C11—21no—
39C23×C4×C11C2311yescharacteristic
40C23×Dic11—21no—
41C23×Dic11D411yescharacteristic
42C23×Dic11D411yescharacteristic
43C22×Dic22—21no—
44C22×Dic22—22no—
45C22×Dic22—28no—
46C22×Dic22C2×C414yes—
47C22×Dic22C2312yes—
48C22×C8×C11C2312yes—
49C2×C11×C4⋊C4—21no—
50C2×C11×C4⋊C4—22no—
51C2×C11×C4⋊C4C2×C414yes—
52C2×C11×C4⋊C4C2312yes—
53C2×C11×C4⋊C4C2312yes—
54C2×C11×C22⋊C4—21no—
55C2×C22⋊Dic11—21no—
56C2×C4⋊Dic11C2312yes—
57C2×Dic11⋊C4—28no—
58C2×Dic11⋊C4—22no—
59C2×Dic11⋊C4—22no—
60C2×C4×Dic11—28no—
61C2×C4×Dic11—22no—
62C2×C4×Dic11—22no—
63C2×C4×Dic11—22no—
64C2×C4×Dic11C2×C414yes—
65C2×C4×Dic11D411yescharacteristic
66C2×C4×Dic11D411yescharacteristic
67C2×C4×Dic11D414yes—
68C2×C4×Dic11C2311yescharacteristic
69C2×C4×Dic11C2311yescharacteristic
70C22×C11⋊C8C2312yes—
71#66940—28no—
72#66940—28no—
73#66940—24no—
74#66940—24no—
75#66940C2×C418yes—
76#66940C2×C418yes—
77C11×C22⋊C8—22no—
78C11×#95—21no—
79C11⋊#95—21no—
80C11⋊#95—22no—
81C11⋊#95—22no—
82C11⋊#95—22no—
83C22⋊(C11⋊C8)—22no—
84#66880—28no—
85#66879—24no—
86Dic11⋊C8—24no—
87#66874—28no—
88#20741—111nomaximal, Sylow
89C24×C11C2×D411yescharacteristic
90C22×C4×C11—24no—
91C22×C4×C11—24no—
92C22×C4×C11—22no—
93C22×C4×C11—22no—
94C22×C4×C11—44no—
95C22×C4×C11C22×C412yes—
96C22×C4×C11C2×D411yescharacteristic
97C22×C4×C11C2×D412yes—
98C22×C4×C11C2411yescharacteristic
99C22×Dic11—28no—
100C22×Dic11—24no—
101C22×Dic11—22no—
102C22×Dic11—22no—
103C22×Dic11—22no—
104C22×Dic11—22no—
105C22×Dic11—42no—
106C22×Dic11C22⋊C414yes—
107C22×Dic11C22⋊C414yes—
108C22×Dic11C2×D411yescharacteristic
109C22×Dic11C2×D411yescharacteristic
110C22×Dic11C2×D411yescharacteristic
111C22×Dic11C2×D411yescharacteristic
112C2×Dic22—28no—
113C2×Dic22—216no—
114C2×Dic22—216no—
115C2×Dic22—24no—
116C2×Dic22—22no—
117C2×Dic22—24no—
118C2×Dic22C22×C414yes—
119C2×Dic22#4118yes—
120C2×C8×C11—22no—
121C2×C8×C11—24no—
122C11×C4⋊C4—24no—
123C11×C4⋊C4—22no—
124C11×C4⋊C4—24no—
125C11×C4⋊C4C22×C414yes—
126C11×C22⋊C4—42no—
127C22⋊Dic11—42no—
128C4⋊Dic11—24no—
129Dic11⋊C4—28no—
130Dic11⋊C4—28no—
131C4×Dic11—28no—
132C4×Dic11—28no—
133C4×Dic11—44no—
134C4×Dic11C22⋊C414yes—
135C4×Dic11C22⋊C414yes—
136C4×Dic11C22×C412yes—
137C4×Dic11C22×C412yes—
138C4×Dic11C2×D412yes—
139C4×Dic11C2×D412yes—
140C2×C11⋊C8—22no—
141C2×C11⋊C8—24no—
142C22×C4×Q8—111no—
143C2×#432—111no—
144#2283—111no—
145#1824—111no—
146#1824D1111yescharacteristic
147#1805—114no—
148#1787—111no—
149#1787—111no—
150#1763—114no—
151C23×C11—22no—
152C23×C11—22no—
153C23×C11C2×C22⋊C412yes—
154C23×C11#13712yes—
155C23×C11#13712yes—
156C23×C11C22×D411yescharacteristic
157C2×C4×C11—22no—
158C2×C4×C11—24no—
159C2×C4×C11—24no—
160C2×C4×C11—24no—
161C2×C4×C11—48no—
162C2×C4×C11—44no—
163C2×C4×C11—42no—
164C2×C4×C11—42no—
165C2×C4×C11—42no—
166C2×C4×C11C2×C22⋊C412yes—
167C2×C4×C11C23×C411yescharacteristic
168C2×C4×C11C22×D411yescharacteristic
169C2×C4×C11C2×#4114yes—
170C2×Dic11—216no—
171C2×Dic11—24no—
172C2×Dic11—28no—
173C2×Dic11—21no—
174C2×Dic11—21no—
175C2×Dic11—21no—
176C2×Dic11—21no—
177C2×Dic11—22no—
178C2×Dic11—22no—
179C2×Dic11—28no—
180C2×Dic11—44no—
181C2×Dic11—42no—
182C2×Dic11—42no—
183C2×Dic11—42no—
184C2×Dic11C2×C22⋊C412yes—
185C2×Dic11C2×C22⋊C412yes—
186C2×Dic11C2×C22⋊C412yes—
187C2×Dic11C2×C22⋊C412yes—
188Dic22—216no—
189Dic22—24no—
190Dic22—28no—
191Dic22#11718yes—
192C8×C11—42no—
193C11⋊C8—42no—
194C23×Q8—111no—
195C2×C4×Q8—112no—
196C2×C4×Q8—112no—
197C2×C4×Q8—118no—
198C2×C4×Q8—221no—
199C2×C4×Q8—221no—
200C2×C4×Q8—224no—
201C22×C4⋊C4—221no—
202C22×C4⋊C4C2×D1111yescharacteristic
203C22×C42—111no—
204C22×C42—221no—
205#432—224no—
206C2×C4⋊C8—112no—
207C2×#103—114no—
208C2×#103—114no—
209C2×C22⋊C8—111no—
210C2×C22⋊C8C2×D1111yescharacteristic
211C2×#97—112no—
212#383—221no—
213#382—112no—
214#381—221no—
215#380—111no—
216#380C2×D1111yescharacteristic
217C4×C4⋊C4—112no—
218C4×C22⋊C4—221no—
219#376—221no—
220#340—114no—
221#340C2×D1114yes—
222C22×C11—24no—
223C22×C11—24no—
224C22×C11—22no—
225C22×C11—22no—
226C22×C11#41914yes—
227C22×C11C22×C22⋊C411yescharacteristic
228C22×C11#52512yes—
229C22×C11C2×#13711yescharacteristic
230C22×C11C2×#13711yescharacteristic
231C22×C11#57512yes—
232C4×C11—22no—
233C4×C11—44no—
234C4×C11—82no—
235C4×C11C2×#11712yes—
236C4×C11#52512yes—
237Dic11—22no—
238Dic11—22no—
239Dic11—22no—
240Dic11—22no—
241Dic11—28no—
242Dic11—82no—
243C22×Q8—114no—
244C22×Q8—112no—
245C22×Q8—228no—
246C22×Q8—222no—
247C22×Q8—221no—
248C23×C4—21no—
249C23×C4—111no—
250C23×C4—111no—
251C23×C4—221no—
252C23×C4C22×D1111yescharacteristic
253C22×C8—112no—
254C22×C8C22×D1112yes—
255C4×Q8—118no—
256C4×Q8—118no—
257C4×Q8—228no—
258C4×Q8—228no—
259C4×Q8—224no—
260C4×Q8—224no—
261C2×C4⋊C4—21no—
262C2×C4⋊C4—22no—
263C2×C4⋊C4—112no—
264C2×C4⋊C4—228no—
265C2×C4⋊C4—222no—
266C2×C4⋊C4—222no—
267C2×C4⋊C4C4×D1114yes—
268C2×C4⋊C4C22×D1112yes—
269C2×C4⋊C4C22×D1112yes—
270C2×C22⋊C4—21no—
271C2×C22⋊C4—221no—
272C2×C42—114no—
273C2×C42—111no—
274C2×C42—111no—
275C2×C42—114no—
276C2×C42—111no—
277C2×C42—111no—
278C2×C42—228no—
279C2×C42—222no—
280C2×C42—222no—
281C2×C42—222no—
282C4⋊C8—224no—
283#103—228no—
284#103—228no—
285C22⋊C8—22no—
286C22⋊C8—222no—
287#97—224no—
288#95—21no—
289#95—222no—
290#95—222no—
291#95—222no—
292#95—221no—
293C2×C11—24no—
294C2×C11#228011yescharacteristic
295C2×C11C2×#41911yescharacteristic
296C2×C11#289611yescharacteristic
297C2×C11#311712yes—
298C2×C11#311712yes—
299C24D4×D1111yescharacteristic
300C2×Q8—114no—
301C2×Q8—118no—
302C2×Q8—2216no—
303C2×Q8—228no—
304C2×Q8—2216no—
305C2×Q8—224no—
306C2×Q8—222no—
307C2×Q8—224no—
308C22×C4—24no—
309C22×C4—24no—
310C22×C4—22no—
311C22×C4—22no—
312C22×C4—44no—
313C22×C4—114no—
314C22×C4—111no—
315C22×C4—111no—
316C22×C4—111no—
317C22×C4—111no—
318C22×C4—114no—
319C22×C4—228no—
320C22×C4—224no—
321C22×C4—222no—
322C22×C4—222no—
323C22×C4—222no—
324C22×C4—222no—
325C22×C4—442no—
326C22×C4C2×C4×D1112yes—
327C22×C4D4×D1111yescharacteristic
328C22×C4D4×D1112yes—
329C22×C4C23×D1111yescharacteristic
330C2×C8—22no—
331C2×C8—24no—
332C2×C8—222no—
333C2×C8—224no—
334C4⋊C4—24no—
335C4⋊C4—22no—
336C4⋊C4—24no—
337C4⋊C4—228no—
338C4⋊C4—228no—
339C4⋊C4—224no—
340C4⋊C4C2×C4×D1114yes—
341C22⋊C4—42no—
342C22⋊C4—442no—
343C42—114no—
344C42—114no—
345C42—112no—
346C42—112no—
347C42—112no—
348C42—112no—
349C42—228no—
350C42—228no—
351C42—444no—
352C11#2074111yescharacteristic, complemented, Sylow
353C23—22no—
354C23—22no—
355C23C22⋊C4×D1112yes—
356C23#6696812yes—
357C23#6697112yes—
358C23C2×D4×D1111yescharacteristic
359Q8—118no—
360Q8—2216no—
361Q8—224no—
362Q8—228no—
363C2×C4—22no—
364C2×C4—24no—
365C2×C4—24no—
366C2×C4—24no—
367C2×C4—48no—
368C2×C4—44no—
369C2×C4—42no—
370C2×C4—42no—
371C2×C4—42no—
372C2×C4—112no—
373C2×C4—112no—
374C2×C4—112no—
375C2×C4—112no—
376C2×C4—2216no—
377C2×C4—224no—
378C2×C4—221no—
379C2×C4—221no—
380C2×C4—221no—
381C2×C4—221no—
382C2×C4—222no—
383C2×C4—222no—
384C2×C4—228no—
385C2×C4—228no—
386C2×C4—444no—
387C2×C4—442no—
388C2×C4—442no—
389C2×C4—442no—
390C2×C4C22⋊C4×D1112yes—
391C2×C4C22×C4×D1111yescharacteristic
392C2×C4C2×D4×D1111yescharacteristic
393C2×C4#41×D1114yes—
394C8—42no—
395C8—442no—
396C22—24no—
397C22—24no—
398C22—22no—
399C22—22no—
400C22#1062241514yes—
401C22C2×C22⋊C4×D1111yescharacteristic
402C22#1062318712yes—
403C22C2×#6696811yescharacteristic
404C22C2×#6697111yescharacteristic
405C22#1062330412yes—
406C4—22no—
407C4—44no—
408C4—82no—
409C4—222no—
410C4—222no—
411C4—222no—
412C4—222no—
413C4—228no—
414C4—882no—
415C4D11×#11712yes—
416C4#1062318712yes—
417C2—24no—
418C2#1307099611yescharacteristic
419C2C2×#1062241511yescharacteristic
420C2#1307713011yescharacteristic
421C2#1307878412yes—
422C2#1307879012yes—
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1824C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
cosocleC22×C4×C11C24
hypercenter#1824D11
hypocenterC11#20741
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1824

Complements

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

NH ≅ G/Ntype
5. #13068630C2semidirect
8. #13068445C2semidirect
18. C2×#66940C4semidirect
352. C11#20741semidirect

Maximal subgroups

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

subgroupindex
C22×#669402
C2×#106223322
#130710112
#130687062
#130686302
#130685522
#130685502
#130684452
C11×#18242
#2074111