Finite Group Databasebeta

← #14650138

Subgroups — #14650138

Order 2816.

544 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D4×#4318C211yesmaximal, characteristic
2#13069606C211yesmaximal, characteristic, complemented
3#13067297C211yesmaximal, characteristic, complemented
4#13067041C211yesmaximal, characteristic
5#13066491C211yesmaximal, characteristic, complemented
6#13066466C211yesmaximal, characteristic, complemented
7C2×C11×#461C211yesmaximal, characteristic
8C22×C11×SD16C412yes—
9C2×C11×C4⋊Q8C2211yescharacteristic
10C2×C4×D4×C11C2211yescharacteristic
11C22×#4318—21no—
12C11×#461—21no—
13C11×#461—21no—
14C11×#461—21no—
15C11×#461—21no—
16C2×C11×C4⋊C8C2211yescharacteristic
17C2×C11×#103C412yes—
18#10622820—21no—
19#10622625—21no—
20#10622624—22no—
21D4×C11⋊C8—21no—
22#10622538C2211yescharacteristic
23#10622537C2211yescharacteristic
24#10622537C2211yescharacteristic
25C4×#4318C2211yescharacteristic
26#10622184—22no—
27D4⋊(C11⋊C8)—21no—
28D4⋊(C11⋊C8)—21no—
29#10622168—21no—
30#10622168—21no—
31C22×Q8×C11C2×C412yes—
32C22×D4×C11C2×C411yescharacteristic
33C23×C4×C11—21no—
34C2×C11×SD16—22no—
35C2×C11×SD16—22no—
36C2×C11×SD16—44no—
37C22×C8×C11C2×C412yes—
38C11×C4⋊Q8—21no—
39C11×C4⋊Q8—21no—
40C11×C4⋊Q8—21no—
41C11×C4⋊Q8—21no—
42C4×D4×C11—21no—
43C4×D4×C11—21no—
44C4×D4×C11D411yescharacteristic
45C4×D4×C11D411yescharacteristic
46C4×D4×C11D411yescharacteristic
47C4×D4×C11D411yescharacteristic
48C2×C11×C4⋊C4—21no—
49C2×C11×C4⋊C4—21no—
50C2×C11×C4⋊C4C2×C411yescharacteristic
51C2×C11×C22⋊C4—21no—
52C2×C42×C11C2311yescharacteristic
53C2×#4318—22no—
54C2×#4318—21no—
55C2×#4318—21no—
56C2×#4318—42no—
57C2×#4318—42no—
58C2×#4318D411yescharacteristic
59C2×#4318D411yescharacteristic
60C22×C11⋊C8—22no—
61C11×C4⋊C8—21no—
62C11×C4⋊C8—21no—
63C11×#103—22no—
64C11×#103—22no—
65C22⋊(C11⋊C8)—22no—
66C22⋊(C11⋊C8)—22no—
67C22⋊(C11⋊C8)—21no—
68C4⋊(C11⋊C8)—21no—
69C4⋊(C11⋊C8)—21no—
70C4⋊(C11⋊C8)—21no—
71C4⋊(C11⋊C8)—21no—
72C4⋊(C11⋊C8)D412yes—
73#66867—21no—
74C4×C11⋊C8—21no—
75C4×C11⋊C8—21no—
76#9247—111nomaximal, Sylow
77C24×C11—21no—
78C2×Q8×C11—22no—
79C2×Q8×C11—22no—
80C2×Q8×C11—42no—
81C2×Q8×C11—42no—
82C2×D4×C11—22no—
83C2×D4×C11—21no—
84C2×D4×C11—41no—
85C2×D4×C11C22⋊C411yescharacteristic
86C2×D4×C11C22⋊C411yescharacteristic
87C22×C4×C11—21no—
88C22×C4×C11—21no—
89C22×C4×C11—21no—
90C22×C4×C11—21no—
91C22×C4×C11—21no—
92C22×C4×C11—22no—
93C22×C4×C11—41no—
94C22×C4×C11—41no—
95C22×C4×C11—41no—
96C22×C4×C11—41no—
97C22×C4×C11C22×C411yescharacteristic
98C22×C4×C11C2×D411yescharacteristic
99C22×C4×C11#4111yescharacteristic
100C11×SD16—44no—
101C11×SD16—44no—
102C2×C8×C11—22no—
103C2×C8×C11—42no—
104C11×C4⋊C4—21no—
105C11×C4⋊C4—41no—
106C11×C4⋊C4—41no—
107C11×C4⋊C4—41no—
108C11×C4⋊C4—41no—
109C11×C4⋊C4C22⋊C411yescharacteristic
110C11×C4⋊C4C22⋊C411yescharacteristic
111C11×C22⋊C4—21no—
112C11×C22⋊C4—21no—
113C11×C22⋊C4—21no—
114C11×C22⋊C4—21no—
115C42×C11C2×D411yescharacteristic
116C42×C11C2×D411yescharacteristic
117C42×C11C2×D411yescharacteristic
118C42×C11#4111yescharacteristic
119#4318—21no—
120#4318—21no—
121#4318—21no—
122#4318—44no—
123#4318—41no—
124#4318—41no—
125#4318—41no—
126#4318—41no—
127#4318SD1612yescomplemented
128C2×C11⋊C8—21no—
129C2×C11⋊C8—21no—
130C2×C11⋊C8—22no—
131C2×C11⋊C8—44no—
132C2×C11⋊C8—41no—
133C2×C11⋊C8—41no—
134C2×#461D1111yescharacteristic
135D4×M16—111no—
136#1997—111no—
137#1548—111no—
138#1486—111no—
139#1292—111no—
140#1283—111no—
141C23×C11—21no—
142C23×C11—21no—
143C23×C11—42no—
144C23×C11—41no—
145C23×C11—41no—
146C23×C11—81no—
147C23×C11C4×D411yescharacteristic
148Q8×C11—42no—
149Q8×C11—42no—
150Q8×C11—82no—
151D4×C11—21no—
152D4×C11—21no—
153D4×C11—21no—
154D4×C11—42no—
155D4×C11#10012yes—
156C2×C4×C11—21no—
157C2×C4×C11—21no—
158C2×C4×C11—21no—
159C2×C4×C11—21no—
160C2×C4×C11—41no—
161C2×C4×C11—41no—
162C2×C4×C11—41no—
163C2×C4×C11—41no—
164C2×C4×C11—41no—
165C2×C4×C11—41no—
166C2×C4×C11—41no—
167C2×C4×C11—41no—
168C2×C4×C11—41no—
169C2×C4×C11—41no—
170C2×C4×C11—41no—
171C2×C4×C11—42no—
172C2×C4×C11—82no—
173C2×C4×C11C2×C22⋊C411yescharacteristic
174C2×C4×C11C4×D411yescharacteristic
175C2×C4×C11#12011yescharacteristic
176C2×C4×C11#12111yescharacteristic
177C2×C4×C11#12111yescharacteristic
178C2×C4×C11#12311yescharacteristic
179C2×C4×C11C2×SD1611yescharacteristic
180C2×C4×C11#13511yescharacteristic
181C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
182C2×C4×C11#13711yescharacteristic
183C8×C11—42no—
184C11⋊C8—22no—
185C11⋊C8—42no—
186C11⋊C8—41no—
187C11⋊C8—81no—
188C11⋊C8—81no—
189C22×SD16Dic1112yes—
190C22×M16—221no—
191C2×C4⋊Q8C2×D1111yescharacteristic
192C2×C4×D4C2×D1111yescharacteristic
193#461—21no—
194#461—21no—
195#461—21no—
196#461—21no—
197#436—221no—
198#435—222no—
199C8×D4—221no—
200#431—111no—
201#423—111no—
202#423—111no—
203C2×C4⋊C8C2×D1111yescharacteristic
204C2×#103Dic1112yes—
205#407—221no—
206C4×M16—111no—
207#343—221no—
208#343—221no—
209#333—222no—
210D4⋊C8—221no—
211D4⋊C8—221no—
212C22×C11—21no—
213C22×C11—21no—
214C22×C11—22no—
215C22×C11—41no—
216C22×C11—41no—
217C22×C11—41no—
218C22×C11—41no—
219C22×C11—41no—
220C22×C11—82no—
221C22×C11—82no—
222C22×C11#38611yescharacteristic
223C22×C11C4×SD1611yescharacteristic
224C22×C11#44011yescharacteristic
225C4×C11—21no—
226C4×C11—21no—
227C4×C11—21no—
228C4×C11—41no—
229C4×C11—41no—
230C4×C11—82no—
231C4×C11C2×#10011yescharacteristic
232C4×C11#41311yescharacteristic
233C4×C11#45011yescharacteristic
234C4×C11#45211yescharacteristic
235C4×C11#46111yescharacteristic
236C4×C11#46311yescharacteristic
237C22×Q8C2×Dic1112yes—
238C22×D4C2×Dic1111yescharacteristic
239C23×C4—21no—
240C2×SD16—22no—
241C2×SD16—22no—
242C2×SD16—44no—
243C2×M16—111no—
244C2×M16—111no—
245C2×M16—222no—
246C2×M16—221no—
247C2×M16—221no—
248C2×M16—442no—
249C2×M16—442no—
250C22×C8—222no—
251C22×C8C2×Dic1112yes—
252C4⋊Q8—21no—
253C4⋊Q8—21no—
254C4⋊Q8—21no—
255C4⋊Q8—21no—
256C4×D4—21no—
257C4×D4—21no—
258C4×D4C22⋊D1111yescharacteristic
259C4×D4C22⋊D1111yescharacteristic
260C4×D4C22⋊D1111yescharacteristic
261C4×D4C22⋊D1111yescharacteristic
262C2×C4⋊C4—21no—
263C2×C4⋊C4—21no—
264C2×C4⋊C4C2×Dic1111yescharacteristic
265C2×C22⋊C4—21no—
266C2×C42C22×D1111yescharacteristic
267C4⋊C8—21no—
268C4⋊C8—21no—
269C4⋊C8—112no—
270C4⋊C8—221no—
271C4⋊C8—221no—
272C4⋊C8—221no—
273C4⋊C8—221no—
274#103—22no—
275#103—22no—
276C22⋊C8—222no—
277C22⋊C8—222no—
278C22⋊C8—221no—
279#97—221no—
280C4×C8—221no—
281C4×C8—221no—
282C2×C11—21no—
283C2×C11—21no—
284C2×C11—42no—
285C2×C11—81no—
286C2×C11#187711yescharacteristic
287C2×C11#190011yescharacteristic
288C2×C11#190211yescharacteristic
289C24—21no—
290C2×Q8—22no—
291C2×Q8—22no—
292C2×Q8—42no—
293C2×Q8—42no—
294C2×D4—22no—
295C2×D4—21no—
296C2×D4—41no—
297C2×D4C22⋊Dic1111yescharacteristic
298C2×D4C22⋊Dic1111yescharacteristic
299C22×C4—21no—
300C22×C4—21no—
301C22×C4—21no—
302C22×C4—21no—
303C22×C4—21no—
304C22×C4—22no—
305C22×C4—41no—
306C22×C4—41no—
307C22×C4—41no—
308C22×C4—41no—
309C22×C4D4×D1111yescharacteristic
310C22×C4#434111yescharacteristic
311C22×C4C22×Dic1111yescharacteristic
312SD16—44no—
313SD16—44no—
314M16—112no—
315M16—221no—
316M16—221no—
317M16—221no—
318M16—444no—
319M16—441no—
320M16—441no—
321M16—441no—
322M16—441no—
323C2×C8—22no—
324C2×C8—42no—
325C2×C8—221no—
326C2×C8—221no—
327C2×C8—222no—
328C2×C8—444no—
329C2×C8—441no—
330C2×C8—441no—
331C4⋊C4—21no—
332C4⋊C4—41no—
333C4⋊C4—41no—
334C4⋊C4—41no—
335C4⋊C4—41no—
336C4⋊C4C22⋊Dic1111yescharacteristic
337C4⋊C4C22⋊Dic1111yescharacteristic
338C22⋊C4—21no—
339C22⋊C4—21no—
340C22⋊C4—21no—
341C22⋊C4—21no—
342C42D4×D1111yescharacteristic
343C42#434111yescharacteristic
344C42C2×C22⋊D1111yescharacteristic
345C42C2×C22⋊D1111yescharacteristic
346C11#924711yescharacteristic, complemented, Sylow
347C23—21no—
348C23—21no—
349C23—42no—
350C23—41no—
351C23—41no—
352C23—81no—
353C23D4×Dic1111yescharacteristic
354Q8—42no—
355Q8—42no—
356Q8—82no—
357D4—21no—
358D4—21no—
359D4—21no—
360D4—42no—
361D4#6689712yes—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—42no—
378C2×C4—82no—
379C2×C4SD16×D1111yescharacteristic
380C2×C4#6696711yescharacteristic
381C2×C4#6696811yescharacteristic
382C2×C4#6696911yescharacteristic
383C2×C4D4×Dic1111yescharacteristic
384C2×C4#6698811yescharacteristic
385C2×C4#6699011yescharacteristic
386C2×C4#6699211yescharacteristic
387C2×C4#6699211yescharacteristic
388C2×C4C2×C22⋊Dic1111yescharacteristic
389C8—42no—
390C8—222no—
391C8—442no—
392C8—441no—
393C8—881no—
394C8—881no—
395C22—21no—
396C22—21no—
397C22—22no—
398C22—41no—
399C22—41no—
400C22—41no—
401C22—41no—
402C22—41no—
403C22—82no—
404C22—82no—
405C22SD16×Dic1111yescharacteristic
406C22#1062277711yescharacteristic
407C22#1062283311yescharacteristic
408C4—21no—
409C4—21no—
410C4—21no—
411C4—41no—
412C4—41no—
413C4—82no—
414C4#1062277511yescharacteristic
415C4#1062277811yescharacteristic
416C4#1062278211yescharacteristic
417C4#1062278611yescharacteristic
418C4C2×#6689711yescharacteristic
419C4#1062285011yescharacteristic
420C2—21no—
421C2—21no—
422C2—42no—
423C2—81no—
424C2#1306895211yescharacteristic
425C2#1306908011yescharacteristic
426C2#1306909111yescharacteristic
subgroupG/H
centerC22#10622833
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC2×C11×#461C2
socleC22×C11#386
prime radicalC22×D4×C11C2×C4
cosocleC2×C42×C11C23
hypercenterC2×#461D11
hypocenterC11#9247
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#461

Complements

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

NH ≅ G/Ntype
2. #13069606C2semidirect
3. #13067297C2semidirect
5. #13066491C2semidirect
6. #13066466C2semidirect
127. #4318SD16semidirect
346. C11#9247semidirect

Maximal subgroups

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

subgroupindex
D4×#43182
#130696062
#130672972
#130670412
#130664912
#130664662
C2×C11×#4612
#924711