Finite Group Databasebeta

← #14645274

Subgroups — #14645274

Order 2816.

802 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623001C211yesmaximal, characteristic
2#13068596C211yesmaximal, characteristic
3C2×#10622119C212yesmaximal, complemented
4C2×#10622124C212yesmaximal, complemented
5C11×#1797C211yesmaximal, characteristic
6C22×C42×C11C2211yescharacteristic
7C2×#66979—21no—
8C2×#66977—21no—
9C2×#66977C412yes—
10#10623001—24no—
11#10623001—24no—
12C2×#66923—21no—
13C2×#66922C2211yescharacteristic
14C2×#66922C2211yescharacteristic
15C2×C4×Dic22—21no—
16C2×C4×Dic22C412yes—
17C2×C11×C4⋊C8C2212yes—
18C2×C11×C22⋊C8—21no—
19C2×C22⋊(C11⋊C8)—21no—
20C2×C4⋊(C11⋊C8)C2212yes—
21C11×#336—21no—
22#10622162—21no—
23#10622124—24no—
24#10622119—24no—
25C23×C4×C11C2×C411yescharacteristic
26C23×C4×C11D411yescharacteristic
27C23×C4×C11D411yescharacteristic
28C22×Dic22—21no—
29C22×Dic22C2×C412yes—
30C22×C8×C11—22no—
31C2×C42×C11—22no—
32C2×C42×C11—22no—
33C2×C42×C11C2×C411yescharacteristic
34C2×C42×C11D411yescharacteristic
35C2×C42×C11D411yescharacteristic
36C2×C42×C11C2311yescharacteristic
37C2×C22⋊Dic11—22no—
38#66979—28no—
39C2×C4⋊Dic11—21no—
40C2×C4⋊Dic11—21no—
41C2×C4⋊Dic11—21no—
42C2×C4⋊Dic11C2×C412yes—
43#66977—28no—
44#66977—24no—
45#66977—24no—
46C2×Dic11⋊C4—22no—
47C2×Dic11⋊C4—22no—
48C2×C4×Dic11—22no—
49C22×C11⋊C8—22no—
50#66923—28no—
51#66922—22no—
52#66922—22no—
53#66922D414yes—
54#66922D414yes—
55C4×Dic22—28no—
56C4×Dic22—24no—
57C4×Dic22—24no—
58C11×C4⋊C8—22no—
59C11×C4⋊C8—22no—
60C11×C22⋊C8—42no—
61C22⋊(C11⋊C8)—42no—
62C4⋊(C11⋊C8)—22no—
63C4⋊(C11⋊C8)—22no—
64#8343—111nomaximal, Sylow
65C24×C11C22⋊C411yescharacteristic
66C22×C4×C11—22no—
67C22×C4×C11—22no—
68C22×C4×C11—21no—
69C22×C4×C11—21no—
70C22×C4×C11—22no—
71C22×C4×C11—22no—
72C22×C4×C11—21no—
73C22×C4×C11—21no—
74C22×C4×C11—41no—
75C22×C4×C11—41no—
76C22×C4×C11C22⋊C411yescharacteristic
77C22×C4×C11C22⋊C411yescharacteristic
78C22×C4×C11C22⋊C411yescharacteristic
79C22×C4×C11SD1612yes—
80C22×C4×C11Q1612yes—
81C22×C4×C11C22×C411yescharacteristic
82C22×C4×C11C2×D411yescharacteristic
83C22×C4×C11C2×D411yescharacteristic
84C22×Dic11—22no—
85C22×Dic11—22no—
86C2×Dic22—22no—
87C2×Dic22—24no—
88C2×Dic22—42no—
89C2×Dic22—42no—
90C2×Dic22—42no—
91C2×Dic22—41no—
92C2×Dic22—41no—
93C2×Dic22C22⋊C414yes—
94C2×C8×C11—42no—
95C2×C8×C11—42no—
96C2×C8×C11—42no—
97C42×C11—21no—
98C42×C11—21no—
99C42×C11—22no—
100C42×C11—22no—
101C42×C11C2×D412yes—
102C42×C11C2×D412yes—
103C22⋊Dic11—28no—
104C4⋊Dic11—22no—
105C4⋊Dic11—24no—
106C4⋊Dic11—24no—
107C4⋊Dic11—24no—
108C4⋊Dic11C22⋊C414yes—
109Dic11⋊C4—28no—
110Dic11⋊C4—28no—
111C4×Dic11—28no—
112C2×C11⋊C8—42no—
113C2×C11⋊C8—42no—
114C2×C11⋊C8—42no—
115C2×#533—111no—
116#1797—111no—
117#1797D1111yescharacteristic
118C2×#333—112no—
119C2×#332—112no—
120C23×C11—21no—
121C23×C11—21no—
122C23×C11—21no—
123C23×C11—21no—
124C23×C11—21no—
125C23×C11—21no—
126C23×C11#10312yes—
127C23×C11C2×C22⋊C411yescharacteristic
128C2×C4×C11—21no—
129C2×C4×C11—21no—
130C2×C4×C11—21no—
131C2×C4×C11—21no—
132C2×C4×C11—24no—
133C2×C4×C11—24no—
134C2×C4×C11—21no—
135C2×C4×C11—21no—
136C2×C4×C11—21no—
137C2×C4×C11—21no—
138C2×C4×C11—21no—
139C2×C4×C11—21no—
140C2×C4×C11—42no—
141C2×C4×C11—42no—
142C2×C4×C11—42no—
143C2×C4×C11—42no—
144C2×C4×C11#10312yes—
145C2×C4×C11C2×C22⋊C411yescharacteristic
146C2×C4×C11C2×C22⋊C411yescharacteristic
147C2×C4×C11#12012yes—
148C2×C4×C11#12012yes—
149C2×C4×C11C2×SD1611yescharacteristic
150C2×C4×C11C2×Q1611yescharacteristic
151C2×C4×C11#13512yes—
152C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
153C2×C4×C11#13711yescharacteristic
154C2×C4×C11#13712yes—
155C2×Dic11—24no—
156C2×Dic11—24no—
157C2×Dic11—42no—
158C2×Dic11—42no—
159C2×Dic11—42no—
160C2×Dic11—42no—
161Dic22—44no—
162Dic22—44no—
163Dic22—44no—
164Dic22—44no—
165C8×C11—82no—
166C11⋊C8—82no—
167#533—224no—
168#533—224no—
169C2×C4⋊Q8—111no—
170C2×C4⋊Q8—111no—
171C2×#125—221no—
172C2×C22⋊Q8—112no—
173C2×C22⋊Q8—221no—
174C2×C4×Q8—112no—
175C2×C4×Q8—221no—
176C2×#117—221no—
177C22×C42C2×D1111yescharacteristic
178C2×C4⋊C8—112no—
179C2×C4⋊C8C2×D1112yes—
180C2×C22⋊C8—21no—
181C2×C22⋊C8—221no—
182#336—21no—
183#336—221no—
184#333—224no—
185#332—224no—
186C22×C11—22no—
187C22×C11—22no—
188C22×C11—22no—
189C22×C11—41no—
190C22×C11—41no—
191C22×C11—41no—
192C22×C11—41no—
193C22×C11#37911yescharacteristic
194C22×C11#41311yescharacteristic
195C22×C11#41311yescharacteristic
196C22×C11C2×#10311yescharacteristic
197C22×C11#41611yescharacteristic
198C22×C11#41711yescharacteristic
199C22×C11#41911yescharacteristic
200C4×C11—21no—
201C4×C11—21no—
202C4×C11—22no—
203C4×C11—41no—
204C4×C11—41no—
205C4×C11#44812yes—
206C4×C11#44912yes—
207C4×C11#45112yes—
208C4×C11#45212yes—
209Dic11—44no—
210Dic11—44no—
211C22×Q8—112no—
212C22×Q8—221no—
213C23×C4C4×D1111yescharacteristic
214C23×C4D4411yescharacteristic
215C23×C4C22⋊D1111yescharacteristic
216C22×C8—22no—
217C22×C8—222no—
218C4⋊Q8—114no—
219C4⋊Q8—114no—
220C4⋊Q8—222no—
221C4⋊Q8—222no—
222#125—228no—
223C22⋊Q8—224no—
224C22⋊Q8—224no—
225C22⋊Q8—228no—
226C4×Q8—224no—
227C4×Q8—224no—
228C4×Q8—228no—
229#117—228no—
230C2×C4⋊C4—112no—
231C2×C4⋊C4—222no—
232C2×C4⋊C4—222no—
233C2×C4⋊C4—221no—
234C2×C4⋊C4—221no—
235C2×C4⋊C4—221no—
236C2×C22⋊C4—222no—
237C2×C42—22no—
238C2×C42—22no—
239C2×C42—222no—
240C2×C42C4×D1111yescharacteristic
241C2×C42D4411yescharacteristic
242C2×C42C22⋊D1111yescharacteristic
243C2×C42C22×D1111yescharacteristic
244C4⋊C8—22no—
245C4⋊C8—22no—
246C4⋊C8—222no—
247C4⋊C8—222no—
248C22⋊C8—42no—
249C22⋊C8—442no—
250C2×C11—42no—
251C2×C11#154211yescharacteristic
252C2×C11#155011yescharacteristic
253C2×C11#155411yescharacteristic
254C2×C11#155911yescharacteristic
255C2×C11#178511yescharacteristic
256C2×C11#178711yescharacteristic
257C2×C11#178811yescharacteristic
258C24(C2×D11)⋊C411yescharacteristic
259C2×Q8—114no—
260C2×Q8—222no—
261C2×Q8—224no—
262C2×Q8—442no—
263C2×Q8—442no—
264C2×Q8—442no—
265C2×Q8—441no—
266C2×Q8—441no—
267C22×C4—22no—
268C22×C4—22no—
269C22×C4—21no—
270C22×C4—21no—
271C22×C4—22no—
272C22×C4—22no—
273C22×C4—21no—
274C22×C4—21no—
275C22×C4—41no—
276C22×C4—41no—
277C22×C4—222no—
278C22×C4—222no—
279C22×C4(C2×D11)⋊C411yescharacteristic
280C22×C4(C2×D11)⋊C411yescharacteristic
281C22×C4(C2×D11)⋊C411yescharacteristic
282C22×C4#432412yes—
283C22×C4#432612yes—
284C22×C4C2×C4×D1111yescharacteristic
285C22×C4C2×D4411yescharacteristic
286C22×C4C2×C22⋊D1111yescharacteristic
287C2×C8—42no—
288C2×C8—42no—
289C2×C8—42no—
290C2×C8—442no—
291C2×C8—442no—
292C2×C8—442no—
293C4⋊C4—114no—
294C4⋊C4—228no—
295C4⋊C4—228no—
296C4⋊C4—222no—
297C4⋊C4—224no—
298C4⋊C4—224no—
299C4⋊C4—224no—
300C22⋊C4—228no—
301C42—21no—
302C42—21no—
303C42—22no—
304C42—22no—
305C42—228no—
306C42D4×D1112yes—
307C42D4×D1112yes—
308C11#834311yescharacteristic, complemented, Sylow
309C23—21no—
310C23—21no—
311C23—21no—
312C23—21no—
313C23—21no—
314C23—21no—
315C23#6687412yes—
316C23C2×(C2×D11)⋊C411yescharacteristic
317Q8—444no—
318Q8—444no—
319Q8—444no—
320Q8—444no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—24no—
326C2×C4—24no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—42no—
334C2×C4—42no—
335C2×C4—42no—
336C2×C4—42no—
337C2×C4—224no—
338C2×C4—224no—
339C2×C4—442no—
340C2×C4—442no—
341C2×C4—442no—
342C2×C4—442no—
343C2×C4#6687412yes—
344C2×C4C22⋊C4×D1111yescharacteristic
345C2×C4C22⋊C4×D1111yescharacteristic
346C2×C4#6693512yes—
347C2×C4#6695712yes—
348C2×C4#6696111yescharacteristic
349C2×C4#6696211yescharacteristic
350C2×C4C2×#432411yescharacteristic
351C2×C4#6699012yes—
352C2×C4C2×#432611yescharacteristic
353C2×C4#6700412yes—
354C8—82no—
355C8—882no—
356C22—22no—
357C22—22no—
358C22—22no—
359C22—41no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22#1062256811yescharacteristic
364C22C2×#6687411yescharacteristic
365C22#1062261711yescharacteristic
366C22#1062272611yescharacteristic
367C22#1062274511yescharacteristic
368C22#1062274511yescharacteristic
369C22#1062274611yescharacteristic
370C4—22no—
371C4—21no—
372C4—21no—
373C4—41no—
374C4—41no—
375C4—444no—
376C4—444no—
377C4#1062234612yes—
378C4#1062234712yes—
379C4#1062265312yes—
380C4#1062266312yes—
381C2—42no—
382C2#1306727411yescharacteristic
383C2#1306730711yescharacteristic
384C2#1306732411yescharacteristic
385C2#1306734711yescharacteristic
386C2#1306854211yescharacteristic
387C2#1306855011yescharacteristic
388C2#1306855711yescharacteristic
subgroupG/H
centerC23C2×(C2×D11)⋊C4
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1797C2
socleC23×C11C2×C22⋊C4
prime radicalC24×C11C22⋊C4
cosocleC2×C42×C11C23
hypercenter#1797D11
hypocenterC11#8343
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ #1797

Complements

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

NH ≅ G/Ntype
3. C2×#10622119C2semidirect
4. C2×#10622124C2semidirect
308. C11#8343semidirect

Maximal subgroups

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

subgroupindex
C2×#106230012
#130685962
C2×#106221192
C2×#106221242
C11×#17972
#834311