Finite Group Databasebeta

← #14648592

Subgroups — #14648592

Order 2816.

680 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D4×C4⋊Dic11C211yesmaximal, characteristic
2#13069578C211yesmaximal, characteristic, complemented
3#13069569C211yesmaximal, characteristic, complemented
4C2×D4⋊(C11⋊C8)C211yesmaximal, characteristic
5#13066500C211yesmaximal, characteristic, complemented
6#13066455C211yesmaximal, characteristic, complemented
7C2×C11×#461C211yesmaximal, characteristic
8C22×C11×SD16—21no—
9C2×C11×C4⋊Q8C2211yescharacteristic
10C2×C4×D4×C11C2211yescharacteristic
11C2×D4×Dic11—21no—
12C22×C4⋊Dic11—21no—
13C11×#461—22no—
14C11×#461C414yescomplemented
15C2×C11×C4⋊C8C2211yescharacteristic
16C2×C11×#103—21no—
17#10622825—21no—
18#10622598—21no—
19#10622563—22no—
20#10622548C2211yescharacteristic
21C4×C4⋊Dic11C2211yescharacteristic
22C2×C4⋊(C11⋊C8)C2211yescharacteristic
23C2×C4×C11⋊C8C2211yescharacteristic
24D4⋊(C11⋊C8)—22no—
25#10622167—21no—
26#10622167—21no—
27#10622167—22no—
28C22×Q8×C11—21no—
29C22×D4×C11D411yescharacteristic
30C23×C4×C11—21no—
31C23×Dic11—22no—
32C2×C11×SD16—24no—
33C2×C11×SD16—42no—
34C2×C11×SD16—42no—
35C22×C8×C11—21no—
36C11×C4⋊Q8—21no—
37C11×C4⋊Q8—21no—
38C11×C4⋊Q8—21no—
39C11×C4⋊Q8C2×C412yescomplemented
40C4×D4×C11—21no—
41C4×D4×C11—21no—
42C4×D4×C11C2×C412yes—
43C4×D4×C11D412yes—
44C2×C11×C4⋊C4—21no—
45C2×C11×C4⋊C4—21no—
46C2×C11×C4⋊C4D411yescharacteristic
47C2×C11×C22⋊C4—21no—
48C2×C42×C11C2311yescharacteristic
49C2×C22⋊Dic11—22no—
50D4×Dic11—42no—
51D4×Dic11—42no—
52C2×C4⋊Dic11—22no—
53C2×C4⋊Dic11—21no—
54C2×C4⋊Dic11—21no—
55C2×C4⋊Dic11—42no—
56C2×C4⋊Dic11—42no—
57C2×C4⋊Dic11D411yescharacteristic
58C2×C4⋊Dic11D411yescharacteristic
59C2×C4⋊Dic11D412yes—
60C2×C4×Dic11—21no—
61C22×C11⋊C8—21no—
62C22×C11⋊C8—21no—
63C11×C4⋊C8—21no—
64C11×C4⋊C8C2×C412yescomplemented
65C11×#103—24no—
66C11⋊#95—22no—
67C11⋊#95—21no—
68C4⋊(C11⋊C8)—21no—
69C4⋊(C11⋊C8)—21no—
70C4×C11⋊C8—21no—
71C4×C11⋊C8—21no—
72#8985—111nomaximal, Sylow
73C24×C11—21no—
74C2×Q8×C11—22no—
75C2×Q8×C11—41no—
76C2×Q8×C11—41no—
77C2×Q8×C11—41no—
78C2×Q8×C11—41no—
79C2×Q8×C11—41no—
80C2×D4×C11—21no—
81C2×D4×C11—21no—
82C2×D4×C11—21no—
83C2×D4×C11C22⋊C412yes—
84C2×D4×C11D812yes—
85C2×D4×C11SD1612yes—
86C22×C4×C11—21no—
87C22×C4×C11—22no—
88C22×C4×C11—22no—
89C22×C4×C11—41no—
90C22×C4×C11—41no—
91C22×C4×C11—41no—
92C22×C4×C11—41no—
93C22×C4×C11—41no—
94C22×C4×C11C2×D411yescharacteristic
95C22×C4×C11C2×D411yescharacteristic
96C22×C4×C11C2×D411yescharacteristic
97C22×Dic11—21no—
98C22×Dic11—21no—
99C22×Dic11—22no—
100C22×Dic11—44no—
101C22×Dic11—44no—
102C22×Dic11—82no—
103C11×SD16—48no—
104C2×C8×C11—22no—
105C2×C8×C11—41no—
106C2×C8×C11—41no—
107C11×C4⋊C4—21no—
108C11×C4⋊C4—22no—
109C11×C4⋊C4—22no—
110C11×C4⋊C4—41no—
111C11×C4⋊C4—41no—
112C11×C4⋊C4C22⋊C412yes—
113C11×C22⋊C4—22no—
114C11×C22⋊C4—22no—
115C42×C11C22×C411yescharacteristic
116C42×C11C2×D411yescharacteristic
117C42×C11#4111yescharacteristic
118C42×C11#4111yescharacteristic
119C22⋊Dic11—44no—
120C4⋊Dic11—21no—
121C4⋊Dic11—21no—
122C4⋊Dic11—21no—
123C4⋊Dic11—42no—
124C4⋊Dic11—44no—
125C4⋊Dic11—41no—
126C4⋊Dic11—41no—
127C4⋊Dic11—41no—
128C4⋊Dic11—41no—
129C4⋊Dic11SD1612yescomplemented
130C4×Dic11—41no—
131C4×Dic11—41no—
132C2×C11⋊C8—22no—
133C2×C11⋊C8—41no—
134C2×C11⋊C8—41no—
135C2×C11⋊C8—41no—
136C2×C11⋊C8—41no—
137C2×C11⋊C8—41no—
138C2×#461D1111yescharacteristic
139D4×C4⋊C4—111no—
140#1990—111no—
141#1988—111no—
142C2×D4⋊C8—111no—
143#1296—111no—
144#1279—111no—
145C23×C11—22no—
146C23×C11—22no—
147C23×C11—22no—
148C23×C11—41no—
149C23×C11—41no—
150C23×C11—41no—
151C23×C11—41no—
152C23×C11#12011yescharacteristic
153Q8×C11—42no—
154Q8×C11—42no—
155Q8×C11—81no—
156Q8×C11—81no—
157D4×C11—22no—
158D4×C11—22no—
159D4×C11—22no—
160D4×C11#10214yes—
161C2×C4×C11—21no—
162C2×C4×C11—21no—
163C2×C4×C11—22no—
164C2×C4×C11—41no—
165C2×C4×C11—41no—
166C2×C4×C11—42no—
167C2×C4×C11—42no—
168C2×C4×C11—42no—
169C2×C4×C11—42no—
170C2×C4×C11—42no—
171C2×C4×C11—81no—
172C2×C4×C11—81no—
173C2×C4×C11C2×C22⋊C411yescharacteristic
174C2×C4×C11C4×D411yescharacteristic
175C2×C4×C11C4×D411yescharacteristic
176C2×C4×C11#12111yescharacteristic
177C2×C4×C11#12111yescharacteristic
178C2×C4×C11#12311yescharacteristic
179C2×C4×C11C2×D811yescharacteristic
180C2×C4×C11C2×SD1611yescharacteristic
181C2×C4×C11C2×SD1611yescharacteristic
182C2×C4×C11#13511yescharacteristic
183C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
184C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
185C2×C4×C11#13711yescharacteristic
186C2×C4×C11#13711yescharacteristic
187C2×Dic11—22no—
188C2×Dic11—41no—
189C2×Dic11—41no—
190C2×Dic11—41no—
191C2×Dic11—42no—
192C2×Dic11—42no—
193C2×Dic11—41no—
194C2×Dic11—42no—
195C2×Dic11—41no—
196C2×Dic11—88no—
197C8×C11—42no—
198C11⋊C8—42no—
199C11⋊C8—81no—
200C22×SD16—21no—
201C2×C4⋊Q8C2×D1111yescharacteristic
202C2×C4×D4—221no—
203C2×C4×D4C2×D1111yescharacteristic
204C22×C4⋊C4—221no—
205#461—22no—
206#461Dic1114yescomplemented
207C2×C4⋊C8—111no—
208C2×C4⋊C8C2×D1111yescharacteristic
209C2×#103—21no—
210C2×C4×C8—111no—
211#389—221no—
212#385—222no—
213#384—111no—
214#380—221no—
215C4×C4⋊C4—111no—
216#340—221no—
217#340—221no—
218#340—222no—
219D4⋊C8—222no—
220C22×C11—24no—
221C22×C11—42no—
222C22×C11—42no—
223C22×C11—42no—
224C22×C11—42no—
225C22×C11—42no—
226C22×C11—42no—
227C22×C11#38611yescharacteristic
228C22×C11#44711yescharacteristic
229C22×C11#44811yescharacteristic
230C22×C11#45011yescharacteristic
231C22×C11#45211yescharacteristic
232C22×C11#45511yescharacteristic
233C22×C11#45611yescharacteristic
234C4×C11—21no—
235C4×C11—21no—
236C4×C11—42no—
237C4×C11—82no—
238C4×C11C2×#10211yescharacteristic
239C4×C11#41711yescharacteristic
240C4×C11C4×SD1611yescharacteristic
241C4×C11#44011yescharacteristic
242C4×C11#46111yescharacteristic
243C4×C11#46311yescharacteristic
244C4×C11#48011yescharacteristic
245C4×C11#48111yescharacteristic
246Dic11—42no—
247Dic11—82no—
248Dic11—81no—
249C22×Q8—21no—
250C22×D4C22⋊D1111yescharacteristic
251C23×C4—21no—
252C23×C4—222no—
253C2×SD16—24no—
254C2×SD16—42no—
255C2×SD16—42no—
256C22×C8—21no—
257C22×C8—221no—
258C22×C8—221no—
259C4⋊Q8—21no—
260C4⋊Q8—21no—
261C4⋊Q8—21no—
262C4⋊Q8C2×Dic1112yescomplemented
263C4×D4—21no—
264C4×D4—21no—
265C4×D4—442no—
266C4×D4—442no—
267C4×D4C2×Dic1112yes—
268C4×D4C22⋊D1112yes—
269C2×C4⋊C4—21no—
270C2×C4⋊C4—21no—
271C2×C4⋊C4—111no—
272C2×C4⋊C4—111no—
273C2×C4⋊C4—112no—
274C2×C4⋊C4—222no—
275C2×C4⋊C4—221no—
276C2×C4⋊C4—221no—
277C2×C4⋊C4—442no—
278C2×C4⋊C4—442no—
279C2×C4⋊C4C22⋊D1111yescharacteristic
280C2×C22⋊C4—21no—
281C2×C22⋊C4—222no—
282C2×C42—221no—
283C2×C42C22×D1111yescharacteristic
284C4⋊C8—21no—
285C4⋊C8—221no—
286C4⋊C8—221no—
287C4⋊C8C2×Dic1112yescomplemented
288#103—24no—
289C4×C8—221no—
290C4×C8—221no—
291#95—222no—
292#95—221no—
293C2×C11—44no—
294C2×C11#163911yescharacteristic
295C2×C11#164311yescharacteristic
296C2×C11#164711yescharacteristic
297C2×C11#165111yescharacteristic
298C2×C11#187411yescharacteristic
299C2×C11#187711yescharacteristic
300C2×C11#188211yescharacteristic
301C24—21no—
302C2×Q8—22no—
303C2×Q8—41no—
304C2×Q8—41no—
305C2×Q8—41no—
306C2×Q8—41no—
307C2×Q8—41no—
308C2×D4—21no—
309C2×D4—21no—
310C2×D4—21no—
311C2×D4#432312yes—
312C2×D4#432412yes—
313C2×D4C22⋊Dic1112yes—
314C22×C4—21no—
315C22×C4—22no—
316C22×C4—22no—
317C22×C4—41no—
318C22×C4—41no—
319C22×C4—41no—
320C22×C4—41no—
321C22×C4—41no—
322C22×C4—221no—
323C22×C4—221no—
324C22×C4—222no—
325C22×C4—444no—
326C22×C4—444no—
327C22×C4—882no—
328C22×C4D4×D1111yescharacteristic
329C22×C4D4×D1111yescharacteristic
330C22×C4C2×C22⋊D1111yescharacteristic
331SD16—48no—
332C2×C8—22no—
333C2×C8—41no—
334C2×C8—41no—
335C2×C8—222no—
336C2×C8—441no—
337C2×C8—441no—
338C2×C8—441no—
339C2×C8—441no—
340C2×C8—441no—
341C4⋊C4—21no—
342C4⋊C4—22no—
343C4⋊C4—22no—
344C4⋊C4—41no—
345C4⋊C4—41no—
346C4⋊C4—112no—
347C4⋊C4—221no—
348C4⋊C4—221no—
349C4⋊C4—221no—
350C4⋊C4—442no—
351C4⋊C4—444no—
352C4⋊C4—441no—
353C4⋊C4—441no—
354C4⋊C4—441no—
355C4⋊C4—441no—
356C4⋊C4C22⋊Dic1112yes—
357C22⋊C4—22no—
358C22⋊C4—22no—
359C22⋊C4—444no—
360C42—441no—
361C42—441no—
362C42#434111yescharacteristic
363C42#434111yescharacteristic
364C42C22×Dic1111yescharacteristic
365C42C2×C22⋊D1111yescharacteristic
366C11#898511yescharacteristic, complemented, Sylow
367C23—22no—
368C23—22no—
369C23—22no—
370C23—41no—
371C23—41no—
372C23—41no—
373C23—41no—
374C23#6699011yescharacteristic
375Q8—42no—
376Q8—42no—
377Q8—81no—
378Q8—81no—
379D4—22no—
380D4—22no—
381D4—22no—
382D4#6689614yes—
383C2×C4—21no—
384C2×C4—21no—
385C2×C4—22no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—42no—
389C2×C4—42no—
390C2×C4—42no—
391C2×C4—42no—
392C2×C4—42no—
393C2×C4—81no—
394C2×C4—81no—
395C2×C4—222no—
396C2×C4—441no—
397C2×C4—441no—
398C2×C4—442no—
399C2×C4—441no—
400C2×C4—442no—
401C2×C4—441no—
402C2×C4—441no—
403C2×C4—442no—
404C2×C4—888no—
405C2×C4SD16×D1111yescharacteristic
406C2×C4#6696711yescharacteristic
407C2×C4#6696811yescharacteristic
408C2×C4#6696911yescharacteristic
409C2×C4C2×#432311yescharacteristic
410C2×C4C2×#432411yescharacteristic
411C2×C4D4×Dic1111yescharacteristic
412C2×C4D4×Dic1111yescharacteristic
413C2×C4#6698811yescharacteristic
414C2×C4#6699211yescharacteristic
415C2×C4#6699211yescharacteristic
416C2×C4#6700211yescharacteristic
417C2×C4#6700411yescharacteristic
418C2×C4C2×C22⋊Dic1111yescharacteristic
419C8—42no—
420C8—442no—
421C8—881no—
422C22—24no—
423C22—42no—
424C22—42no—
425C22—42no—
426C22—42no—
427C22—42no—
428C22—42no—
429C22#1062264911yescharacteristic
430C22#1062265311yescharacteristic
431C22#1062278211yescharacteristic
432C22#1062278611yescharacteristic
433C22#1062281511yescharacteristic
434C22#1062281811yescharacteristic
435C22#1062283311yescharacteristic
436C4—21no—
437C4—21no—
438C4—42no—
439C4—82no—
440C4—442no—
441C4—882no—
442C4—881no—
443C4#1062264611yescharacteristic
444C4#1062264711yescharacteristic
445C4SD16×Dic1111yescharacteristic
446C4#1062277511yescharacteristic
447C4#1062277711yescharacteristic
448C4#1062277811yescharacteristic
449C4C2×#6689611yescharacteristic
450C4#1062284511yescharacteristic
451C2—44no—
452C2#1306779311yescharacteristic
453C2#1306782111yescharacteristic
454C2#1306784911yescharacteristic
455C2#1306787711yescharacteristic
456C2#1306893411yescharacteristic
457C2#1306895211yescharacteristic
458C2#1306898711yescharacteristic
subgroupG/H
centerC23#66990
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC2×C11×#461C2
socleC23×C11#120
prime radicalC22×D4×C11D4
cosocleC2×C42×C11C23
hypercenterC2×#461D11
hypocenterC11#8985
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#461

Complements

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

NH ≅ G/Ntype
2. #13069578C2semidirect
3. #13069569C2semidirect
5. #13066500C2semidirect
6. #13066455C2semidirect
14. C11×#461C4semidirect
39. C11×C4⋊Q8C2×C4semidirect
64. C11×C4⋊C8C2×C4semidirect
129. C4⋊Dic11SD16semidirect
206. #461Dic11semidirect
262. C4⋊Q8C2×Dic11semidirect
287. C4⋊C8C2×Dic11semidirect
366. C11#8985semidirect

Maximal subgroups

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

subgroupindex
D4×C4⋊Dic112
#130695782
#130695692
C2×D4⋊(C11⋊C8)2
#130665002
#130664552
C2×C11×#4612
#898511