Finite Group Databasebeta

← #14648317

Subgroups — #14648317

Order 2816.

648 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622537C211yesmaximal, characteristic
2C4×#66977C211yesmaximal, characteristic
3C2×#10622094C212yesmaximal, complemented
4#13066456C212yesmaximal, complemented
5C4×C11×C22⋊C8C211yesmaximal, characteristic
6C22×C42×C11C2211yescharacteristic
7C2×#66977C411yescharacteristic
8C22×#4318—21no—
9C2×C4×Dic22C2211yescharacteristic
10C2×C11×C22⋊C8—21no—
11C2×C4×C8×C11C2212yes—
12#10622825C411yescharacteristic
13#10622823—21no—
14C4×C22⋊Dic11—21no—
15C4×C4⋊Dic11C2211yescharacteristic
16#10622546—21no—
17C4×Dic11⋊C4—21no—
18#10622542C411yescharacteristic
19#10622541C411yescharacteristic
20#10622537—24no—
21C2×C4⋊(C11⋊C8)—21no—
22C2×C4⋊(C11⋊C8)C2212yes—
23C11×#336—21no—
24#10622094—24no—
25C23×C4×C11C2×C411yescharacteristic
26C23×C4×C11D411yescharacteristic
27C23×C4×C11D411yescharacteristic
28C22×Dic22C2×C411yescharacteristic
29C22×C8×C11—22no—
30C2×C42×C11—22no—
31C2×C42×C11—22no—
32C2×C42×C11C2×C411yescharacteristic
33C2×C42×C11D411yescharacteristic
34C2×C42×C11D411yescharacteristic
35C2×C42×C11C2311yescharacteristic
36C2×C22⋊Dic11—21no—
37C2×C22⋊Dic11—21no—
38C2×C4⋊Dic11C2×C411yescharacteristic
39C2×C4⋊Dic11C2×C411yescharacteristic
40C2×C4⋊Dic11C2×C411yescharacteristic
41#66977—22no—
42#66977—22no—
43C2×Dic11⋊C4—21no—
44C2×Dic11⋊C4—21no—
45C2×Dic11⋊C4—21no—
46C2×C4×Dic11—21no—
47C2×C4×Dic11—21no—
48C2×#4318—24no—
49C2×#4318—42no—
50C2×#4318—42no—
51C22×C11⋊C8—22no—
52C4×Dic22—22no—
53C4×Dic22—22no—
54C11×C22⋊C8—24no—
55C4×C8×C11—22no—
56C4×C8×C11—22no—
57C11⋊#95—21no—
58C11⋊#95—21no—
59C11⋊#95—21no—
60C11⋊#95—21no—
61C11⋊#95—21no—
62C4⋊(C11⋊C8)—24no—
63C4⋊(C11⋊C8)—22no—
64C4⋊(C11⋊C8)D414yes—
65#8942—111nomaximal, Sylow
66C24×C11C22⋊C411yescharacteristic
67C22×C4×C11—21no—
68C22×C4×C11—21no—
69C22×C4×C11—21no—
70C22×C4×C11—21no—
71C22×C4×C11—22no—
72C22×C4×C11—22no—
73C22×C4×C11—22no—
74C22×C4×C11—21no—
75C22×C4×C11—21no—
76C22×C4×C11—22no—
77C22×C4×C11—41no—
78C22×C4×C11C22⋊C411yescharacteristic
79C22×C4×C11C22⋊C411yescharacteristic
80C22×C4×C11C22⋊C411yescharacteristic
81C22×C4×C11SD1612yes—
82C22×C4×C11Q1612yes—
83C22×C4×C11C22×C411yescharacteristic
84C22×C4×C11C2×D411yescharacteristic
85C22×C4×C11C2×D411yescharacteristic
86C22×Dic11—21no—
87C22×Dic11—21no—
88C22×Dic11—21no—
89C22×Dic11—21no—
90C2×Dic22—22no—
91C2×Dic22—21no—
92C2×Dic22—22no—
93C2×Dic22M1612yescomplemented
94C2×C8×C11—24no—
95C2×C8×C11—42no—
96C2×C8×C11—42no—
97C42×C11—22no—
98C42×C11—21no—
99C42×C11—22no—
100C42×C11—21no—
101C42×C11C2×D412yes—
102C42×C11#4112yes—
103C22⋊Dic11—24no—
104C22⋊Dic11—42no—
105C4⋊Dic11—22no—
106C4⋊Dic11—21no—
107C4⋊Dic11—22no—
108C4⋊Dic11M1612yescomplemented
109Dic11⋊C4—24no—
110Dic11⋊C4—42no—
111Dic11⋊C4—42no—
112C4×Dic11—41no—
113C4×Dic11—41no—
114C4×Dic11—41no—
115C4×Dic11—41no—
116#4318—48no—
117C2×C11⋊C8—24no—
118C2×C11⋊C8—42no—
119C2×C11⋊C8—42no—
120C2×#423—111no—
121C4×C22⋊Q8—111no—
122C4×C22⋊C8D1111yescharacteristic
123C2×Q8⋊C8—112no—
124#1279—112no—
125C23×C11—21no—
126C23×C11—21no—
127C23×C11—21no—
128C23×C11—21no—
129C23×C11—21no—
130C23×C11—21no—
131C23×C11#10312yes—
132C23×C11C2×C22⋊C411yescharacteristic
133C2×C4×C11—21no—
134C2×C4×C11—21no—
135C2×C4×C11—21no—
136C2×C4×C11—21no—
137C2×C4×C11—21no—
138C2×C4×C11—21no—
139C2×C4×C11—22no—
140C2×C4×C11—22no—
141C2×C4×C11—22no—
142C2×C4×C11—22no—
143C2×C4×C11—21no—
144C2×C4×C11—21no—
145C2×C4×C11—21no—
146C2×C4×C11—44no—
147C2×C4×C11—42no—
148C2×C4×C11—42no—
149C2×C4×C11#10312yes—
150C2×C4×C11#10412yes—
151C2×C4×C11C4×D412yes—
152C2×C4×C11#12011yescharacteristic
153C2×C4×C11#12112yes—
154C2×C4×C11#12311yescharacteristic
155C2×C4×C11C2×M1611yescharacteristic
156C2×C4×C11C2×M1611yescharacteristic
157C2×C4×C11#13112yes—
158C2×C4×C11C2×SD1611yescharacteristic
159C2×C4×C11C2×Q1611yescharacteristic
160C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
161C2×C4×C11#13711yescharacteristic
162C2×Dic11—22no—
163C2×Dic11—22no—
164C2×Dic11—41no—
165C2×Dic11—41no—
166C2×Dic11—41no—
167C2×Dic11—41no—
168C2×Dic11—41no—
169C2×Dic11—41no—
170C2×Dic11—41no—
171C2×Dic11—41no—
172C2×Dic11—41no—
173C2×Dic11—41no—
174Dic22—24no—
175Dic22—42no—
176C8×C11—44no—
177C11⋊C8—44no—
178C22×M16—221no—
179C2×C22⋊Q8—111no—
180C2×C4×Q8—111no—
181C22×C42C2×D1111yescharacteristic
182#423—224no—
183C2×C4⋊C8—112no—
184C2×C4⋊C8—221no—
185C2×C22⋊C8—21no—
186C2×C4×C8C2×D1112yes—
187#391—111no—
188#389—111no—
189#387—221no—
190#385—221no—
191#380—111no—
192C4×C4⋊C4—111no—
193C4×C4⋊C4—221no—
194C4×C22⋊C4—221no—
195#336—21no—
196Q8⋊C8—224no—
197C22×C11—22no—
198C22×C11—22no—
199C22×C11—22no—
200C22×C11—41no—
201C22×C11—41no—
202C22×C11—41no—
203C22×C11—41no—
204C22×C11#38611yescharacteristic
205C22×C11#40711yescharacteristic
206C22×C11#40811yescharacteristic
207C22×C11C2×#10311yescharacteristic
208C22×C11#41711yescharacteristic
209C22×C11C2×#10411yescharacteristic
210C22×C11#42111yescharacteristic
211C4×C11—22no—
212C4×C11—22no—
213C4×C11—22no—
214C4×C11—41no—
215C4×C11#43512yes—
216C4×C11#43612yes—
217C4×C11#45011yescharacteristic
218C4×C11#45111yescharacteristic
219C4×C11#48311yescharacteristic
220C4×C11#48411yescharacteristic
221Dic11—42no—
222Dic11—42no—
223Dic11—81no—
224Dic11—81no—
225C22×Q8—111no—
226C23×C4C4×D1111yescharacteristic
227C23×C4D4411yescharacteristic
228C23×C4C22⋊D1111yescharacteristic
229C2×M16—224no—
230C2×M16—442no—
231C2×M16—442no—
232C22×C8—22no—
233C22×C8—222no—
234C22⋊Q8—222no—
235C22⋊Q8—222no—
236C4×Q8—222no—
237C4×Q8—222no—
238C2×C4⋊C4—111no—
239C2×C4⋊C4—111no—
240C2×C4⋊C4—111no—
241C2×C4⋊C4—221no—
242C2×C4⋊C4—221no—
243C2×C4⋊C4—221no—
244C2×C22⋊C4—221no—
245C2×C22⋊C4—221no—
246C2×C42—22no—
247C2×C42—22no—
248C2×C42—221no—
249C2×C42—221no—
250C2×C42C4×D1111yescharacteristic
251C2×C42D4411yescharacteristic
252C2×C42C22⋊D1111yescharacteristic
253C2×C42C22×D1111yescharacteristic
254C4⋊C8—114no—
255C4⋊C8—224no—
256C4⋊C8—222no—
257C22⋊C8—24no—
258C4×C8—22no—
259C4×C8—22no—
260#95—221no—
261#95—221no—
262#95—221no—
263#95—221no—
264#95—221no—
265C2×C11—42no—
266C2×C11#148711yescharacteristic
267C2×C11#148911yescharacteristic
268C2×C11#149311yescharacteristic
269C2×C11#149511yescharacteristic
270C2×C11#187011yescharacteristic
271C2×C11#187111yescharacteristic
272C2×C11#187211yescharacteristic
273C24(C2×D11)⋊C411yescharacteristic
274C2×Q8—112no—
275C2×Q8—221no—
276C2×Q8—222no—
277C2×Q8—222no—
278C22×C4—21no—
279C22×C4—21no—
280C22×C4—21no—
281C22×C4—21no—
282C22×C4—22no—
283C22×C4—22no—
284C22×C4—22no—
285C22×C4—21no—
286C22×C4—21no—
287C22×C4—22no—
288C22×C4—41no—
289C22×C4—221no—
290C22×C4—221no—
291C22×C4—221no—
292C22×C4—221no—
293C22×C4#431412yes—
294C22×C4Dic4412yes—
295C22×C4(C2×D11)⋊C411yescharacteristic
296C22×C4(C2×D11)⋊C411yescharacteristic
297C22×C4(C2×D11)⋊C411yescharacteristic
298C22×C4C2×C4×D1111yescharacteristic
299C22×C4C2×D4411yescharacteristic
300C22×C4C2×C22⋊D1111yescharacteristic
301M16—448no—
302C2×C8—24no—
303C2×C8—42no—
304C2×C8—42no—
305C2×C8—224no—
306C2×C8—442no—
307C2×C8—442no—
308C4⋊C4—112no—
309C4⋊C4—224no—
310C4⋊C4—221no—
311C4⋊C4—222no—
312C4⋊C4—222no—
313C4⋊C4—442no—
314C4⋊C4—442no—
315C22⋊C4—224no—
316C22⋊C4—442no—
317C42—22no—
318C42—21no—
319C42—21no—
320C42—22no—
321C42—441no—
322C42—441no—
323C42—441no—
324C42—441no—
325C42D4×D1112yes—
326C42#434112yes—
327C11#894211yescharacteristic, complemented, Sylow
328C23—21no—
329C23—21no—
330C23—21no—
331C23—21no—
332C23—21no—
333C23—21no—
334C23#6688012yes—
335C23C2×(C2×D11)⋊C411yescharacteristic
336Q8—224no—
337Q8—442no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—22no—
345C2×C4—22no—
346C2×C4—22no—
347C2×C4—22no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—44no—
352C2×C4—42no—
353C2×C4—42no—
354C2×C4—222no—
355C2×C4—222no—
356C2×C4—441no—
357C2×C4—441no—
358C2×C4—441no—
359C2×C4—441no—
360C2×C4—441no—
361C2×C4—441no—
362C2×C4—441no—
363C2×C4—441no—
364C2×C4—441no—
365C2×C4—441no—
366C2×C4#6686912yes—
367C2×C4#6688012yes—
368C2×C4(C22⋊D11)⋊C412yes—
369C2×C4#6693511yescharacteristic
370C2×C4#6693911yescharacteristic
371C2×C4#6695412yes—
372C2×C4C2×#431411yescharacteristic
373C2×C4C2×Dic4411yescharacteristic
374C2×C4M16×D1111yescharacteristic
375C2×C4M16×D1111yescharacteristic
376C2×C4#6696111yescharacteristic
377C2×C4#6696211yescharacteristic
378C2×C4#6699212yes—
379C8—44no—
380C8—444no—
381C22—22no—
382C22—22no—
383C22—22no—
384C22—41no—
385C22—41no—
386C22—41no—
387C22—41no—
388C22C2×#6686911yescharacteristic
389C22#1062257111yescharacteristic
390C22#1062261811yescharacteristic
391C22C2×#6688011yescharacteristic
392C22#1062272311yescharacteristic
393C22#1062273911yescharacteristic
394C22#1062274611yescharacteristic
395C4—22no—
396C4—22no—
397C4—22no—
398C4—41no—
399C4—442no—
400C4—442no—
401C4—881no—
402C4—881no—
403C4#1062233411yescharacteristic
404C4#1062233511yescharacteristic
405C4#1062234112yes—
406C4#1062234212yes—
407C4#1062234411yescharacteristic
408C4#1062235211yescharacteristic
409C2—42no—
410C2#1306704611yescharacteristic
411C2#1306705611yescharacteristic
412C2#1306707211yescharacteristic
413C2#1306708211yescharacteristic
414C2#1306891111yescharacteristic
415C2#1306891611yescharacteristic
416C2#1306892111yescharacteristic
subgroupG/H
centerC22×C4C2×D44
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC4×C11×C22⋊C8C2
socleC23×C11C2×C22⋊C4
prime radicalC24×C11C22⋊C4
cosocleC2×C42×C11C23
hypercenterC4×C22⋊C8D11
hypocenterC11#8942
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C4×C22⋊C8

Complements

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

NH ≅ G/Ntype
3. C2×#10622094C2semidirect
4. #13066456C2semidirect
93. C2×Dic22M16semidirect
108. C4⋊Dic11M16semidirect
327. C11#8942semidirect

Maximal subgroups

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

subgroupindex
C2×#106225372
C4×#669772
C2×#106220942
#130664562
C4×C11×C22⋊C82
#894211