Finite Group Databasebeta

← #14646528

Subgroups — #14646528

Order 2816.

658 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#66977C211yesmaximal, characteristic
2#13068596C211yesmaximal, characteristic
3C2×#10622090C212yesmaximal
4#13066495C212yesmaximal
5C11×C4⋊#95C211yesmaximal, characteristic
6C22×C11×C4⋊C4—21no—
7C22×C42×C11C2211yescharacteristic
8C2×#66977C2211yescharacteristic
9C2×C4×Dic22C411yescharacteristic, complemented
10C2×C11×#95—21no—
11C2×C11×#95C2212yes—
12#10622825C2211yescharacteristic
13#10622823—21no—
14C4×C22⋊Dic11—21no—
15C2×C22⋊(C11⋊C8)C2212yes—
16C4×C4⋊Dic11C411yescharacteristic, complemented
17#10622546—21no—
18C4×Dic11⋊C4—21no—
19#10622542C411yescharacteristic, complemented
20#10622541C411yescharacteristic, complemented
21C2×C4⋊(C11⋊C8)—21no—
22#10622162—21no—
23#10622090—24no—
24C23×C4×C11—22no—
25C23×C4×C11D411yescharacteristic
26C23×C4×C11D411yescharacteristic
27C23×C4×C11C2311yescharacteristic
28C22×Dic22C2×C411yescharacteristic
29C2×C11×C4⋊C4—24no—
30C2×C11×C4⋊C4—42no—
31C2×C11×C4⋊C4—42no—
32C2×C42×C11—42no—
33C2×C42×C11C2×C411yescharacteristic
34C2×C42×C11C2×C411yescharacteristic
35C2×C42×C11D411yescharacteristic
36C2×C42×C11D411yescharacteristic
37C2×C22⋊Dic11—21no—
38C2×C22⋊Dic11—21no—
39C2×C4⋊Dic11C2×C411yescharacteristic
40C2×C4⋊Dic11C2×C411yescharacteristic
41C2×C4⋊Dic11C2×C411yescharacteristic
42#66977—21no—
43#66977—21no—
44#66977D412yes—
45#66977Q812yes—
46C2×Dic11⋊C4—21no—
47C2×Dic11⋊C4—21no—
48C2×Dic11⋊C4—21no—
49C2×C4×Dic11—21no—
50C2×C4×Dic11—21no—
51C22×C11⋊C8—22no—
52C4×Dic22—42no—
53C11×#95—22no—
54C11×#95—22no—
55C11×#95—42no—
56C11⋊#95—21no—
57C11⋊#95—21no—
58C11⋊#95—21no—
59C11⋊#95—21no—
60C11⋊#95—21no—
61C22⋊(C11⋊C8)—22no—
62C22⋊(C11⋊C8)—22no—
63C4⋊(C11⋊C8)—42no—
64#8578—111nomaximal, Sylow
65C24×C11C2×D411yescharacteristic
66C22×C4×C11—21no—
67C22×C4×C11—21no—
68C22×C4×C11—22no—
69C22×C4×C11—22no—
70C22×C4×C11—24no—
71C22×C4×C11—41no—
72C22×C4×C11—41no—
73C22×C4×C11—41no—
74C22×C4×C11—41no—
75C22×C4×C11—42no—
76C22×C4×C11—42no—
77C22×C4×C11—42no—
78C22×C4×C11—42no—
79C22×C4×C11—42no—
80C22×C4×C11—42no—
81C22×C4×C11C22⋊C411yescharacteristic
82C22×C4×C11C22⋊C411yescharacteristic
83C22×C4×C11C22⋊C411yescharacteristic
84C22×C4×C11C22⋊C411yescharacteristic
85C22×C4×C11SD1612yes—
86C22×C4×C11Q1612yes—
87C22×C4×C11C22×C411yescharacteristic
88C22×C4×C11C2×D411yescharacteristic
89C22×C4×C11C2×D411yescharacteristic
90C22×C4×C11C2×Q811yescharacteristic
91C22×C4×C11#4111yescharacteristic
92C22×C4×C11#4111yescharacteristic
93C22×Dic11—21no—
94C22×Dic11—21no—
95C22×Dic11—21no—
96C22×Dic11—21no—
97C2×Dic22—21no—
98C2×Dic22—41no—
99C2×Dic22—41no—
100C2×Dic22C4⋊C412yescomplemented
101C11×C4⋊C4—48no—
102C42×C11—22no—
103C42×C11—22no—
104C42×C11—41no—
105C42×C11—41no—
106C22⋊Dic11—22no—
107C22⋊Dic11—22no—
108C22⋊Dic11—41no—
109C22⋊Dic11—41no—
110C4⋊Dic11—21no—
111C4⋊Dic11—41no—
112C4⋊Dic11—41no—
113C4⋊Dic11C4⋊C412yescomplemented
114Dic11⋊C4—22no—
115Dic11⋊C4—22no—
116Dic11⋊C4—42no—
117Dic11⋊C4—42no—
118C4×Dic11—42no—
119C4×Dic11—42no—
120C2×C11⋊C8—42no—
121C2×C11⋊C8—42no—
122C2×C11⋊C8—42no—
123C4×C22⋊Q8—111no—
124#1797—111no—
125C2×#328—112no—
126C4⋊#95D1111yescharacteristic
127#1294—112no—
128C23×C11—21no—
129C23×C11—21no—
130C23×C11—21no—
131C23×C11—21no—
132C23×C11C2×C22⋊C411yescharacteristic
133C23×C11#12111yescharacteristic
134C23×C11C22⋊Q811yescharacteristic
135C23×C11C2×SD1611yescharacteristic
136C23×C11C2×Q1611yescharacteristic
137C23×C11AGL(1,ℤ/8)11yescharacteristic
138C23×C11#13711yescharacteristic
139C2×C4×C11—24no—
140C2×C4×C11—24no—
141C2×C4×C11—21no—
142C2×C4×C11—21no—
143C2×C4×C11—21no—
144C2×C4×C11—21no—
145C2×C4×C11—21no—
146C2×C4×C11—21no—
147C2×C4×C11—21no—
148C2×C4×C11—21no—
149C2×C4×C11—21no—
150C2×C4×C11—21no—
151C2×C4×C11—21no—
152C2×C4×C11—21no—
153C2×C4×C11—42no—
154C2×C4×C11—42no—
155C2×C4×C11—41no—
156C2×C4×C11—41no—
157C2×C4×C11—41no—
158C2×C4×C11—41no—
159C2×C4×C11—44no—
160C2×C4×C11—44no—
161C2×C4×C11—44no—
162C2×C4×C11—82no—
163C2×C4×C11—82no—
164C2×C4×C11—82no—
165C2×C4×C11—82no—
166C2×C4×C11#9912yes—
167C2×C4×C11#10312yes—
168C2×C4×C11#10312yes—
169C2×C4×C11#10412yes—
170C2×C4×C11C2×C4⋊C411yescharacteristic
171C2×C4×C11#11711yescharacteristic
172C2×C4×C11#12111yescharacteristic
173C2×C4×C11C22⋊Q811yescharacteristic
174C2×Dic11—22no—
175C2×Dic11—22no—
176C2×Dic11—41no—
177C2×Dic11—41no—
178C2×Dic11—41no—
179C2×Dic11—41no—
180C2×Dic11—41no—
181C2×Dic11—41no—
182C2×Dic11—41no—
183C2×Dic11—41no—
184C2×Dic11—41no—
185C2×Dic11—41no—
186Dic22—42no—
187Dic22—42no—
188C11⋊C8—82no—
189C2×C22⋊Q8—111no—
190C2×C4×Q8—111no—
191C22×C4⋊C4—21no—
192C22×C42C2×D1111yescharacteristic
193C2×C4⋊C8—221no—
194C2×C22⋊C8—112no—
195#391—111no—
196#389—111no—
197#387—221no—
198#385—221no—
199#380—111no—
200C4×C4⋊C4—111no—
201C4×C4⋊C4—221no—
202C4×C22⋊C4—221no—
203C2×#95—21no—
204C2×#95C2×D1112yes—
205#336—221no—
206#328—224no—
207C22×C11—21no—
208C22×C11—21no—
209C22×C11—21no—
210C22×C11—21no—
211C22×C11—21no—
212C22×C11—21no—
213C22×C11—21no—
214C22×C11—21no—
215C22×C11—21no—
216C22×C11—21no—
217C22×C11—21no—
218C22×C11—21no—
219C22×C11#38011yescharacteristic
220C22×C11C2×#9911yescharacteristic
221C22×C11#41011yescharacteristic
222C22×C11C2×#10311yescharacteristic
223C22×C11#41711yescharacteristic
224C22×C11C2×#10411yescharacteristic
225C22×C11#42111yescharacteristic
226C22×C11#46011yescharacteristic
227C22×C11#46211yescharacteristic
228C22×C11#47511yescharacteristic
229C22×C11#47711yescharacteristic
230C4×C11—21no—
231C4×C11—21no—
232C4×C11—21no—
233C4×C11—21no—
234C4×C11—22no—
235C4×C11—22no—
236C4×C11—22no—
237C4×C11—22no—
238C4×C11—84no—
239Dic11—42no—
240Dic11—42no—
241Dic11—81no—
242Dic11—81no—
243C22×Q8—111no—
244C23×C4—22no—
245C23×C4C22⋊D1111yescharacteristic
246C23×C4C22⋊D1111yescharacteristic
247C23×C4C22×D1111yescharacteristic
248C22×C8—222no—
249C22⋊Q8—112no—
250C22⋊Q8—112no—
251C22⋊Q8—221no—
252C22⋊Q8—221no—
253C4×Q8—442no—
254C2×C4⋊C4—24no—
255C2×C4⋊C4—42no—
256C2×C4⋊C4—42no—
257C2×C4⋊C4—111no—
258C2×C4⋊C4—111no—
259C2×C4⋊C4—111no—
260C2×C4⋊C4—221no—
261C2×C4⋊C4—221no—
262C2×C4⋊C4—221no—
263C2×C22⋊C4—221no—
264C2×C22⋊C4—221no—
265C2×C42—42no—
266C2×C42—221no—
267C2×C42—221no—
268C2×C42C4×D1111yescharacteristic
269C2×C42C4×D1111yescharacteristic
270C2×C42D4411yescharacteristic
271C2×C42D4411yescharacteristic
272C4⋊C8—442no—
273C22⋊C8—222no—
274C22⋊C8—222no—
275#95—22no—
276#95—22no—
277#95—42no—
278#95—221no—
279#95—221no—
280#95—221no—
281#95—221no—
282#95—221no—
283C2×C11—21no—
284C2×C11—21no—
285C2×C11—21no—
286C2×C11—21no—
287C2×C11#150311yescharacteristic
288C2×C11#150411yescharacteristic
289C2×C11#151211yescharacteristic
290C2×C11#152011yescharacteristic
291C2×C11#179911yescharacteristic
292C2×C11#180311yescharacteristic
293C2×C11#180611yescharacteristic
294C24C2×C22⋊D1111yescharacteristic
295C2×Q8—112no—
296C2×Q8—221no—
297C2×Q8—441no—
298C2×Q8—441no—
299C22×C4—21no—
300C22×C4—21no—
301C22×C4—22no—
302C22×C4—22no—
303C22×C4—24no—
304C22×C4—41no—
305C22×C4—41no—
306C22×C4—41no—
307C22×C4—41no—
308C22×C4—42no—
309C22×C4—42no—
310C22×C4—42no—
311C22×C4—42no—
312C22×C4—42no—
313C22×C4—42no—
314C22×C4—221no—
315C22×C4—221no—
316C22×C4—221no—
317C22×C4—221no—
318C22×C4(C2×D11)⋊C411yescharacteristic
319C22×C4(C2×D11)⋊C411yescharacteristic
320C22×C4(C2×D11)⋊C411yescharacteristic
321C22×C4(C2×D11)⋊C411yescharacteristic
322C22×C4#432412yes—
323C22×C4#432612yes—
324C22×C4C2×C4×D1111yescharacteristic
325C22×C4C2×D4411yescharacteristic
326C22×C4D4×D1111yescharacteristic
327C22×C4#434111yescharacteristic
328C22×C4Q8×D1111yescharacteristic
329C22×C4#434311yescharacteristic
330C2×C8—442no—
331C2×C8—442no—
332C2×C8—442no—
333C4⋊C4—48no—
334C4⋊C4—112no—
335C4⋊C4—221no—
336C4⋊C4—222no—
337C4⋊C4—222no—
338C4⋊C4—441no—
339C4⋊C4—441no—
340C4⋊C4—442no—
341C4⋊C4—442no—
342C22⋊C4—222no—
343C22⋊C4—222no—
344C22⋊C4—441no—
345C22⋊C4—441no—
346C42—22no—
347C42—22no—
348C42—41no—
349C42—41no—
350C42—442no—
351C42—442no—
352C11#857811yescharacteristic, complemented, Sylow
353C23—21no—
354C23—21no—
355C23—21no—
356C23—21no—
357C23C2×(C2×D11)⋊C411yescharacteristic
358C23#6698511yescharacteristic
359C23C2×#432411yescharacteristic
360C23#6699111yescharacteristic
361C23#6699511yescharacteristic
362C23C2×#432611yescharacteristic
363C23#6699911yescharacteristic
364Q8—442no—
365Q8—442no—
366C2×C4—24no—
367C2×C4—24no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—42no—
381C2×C4—42no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—44no—
387C2×C4—44no—
388C2×C4—44no—
389C2×C4—82no—
390C2×C4—82no—
391C2×C4—82no—
392C2×C4—82no—
393C2×C4—222no—
394C2×C4—222no—
395C2×C4—441no—
396C2×C4—441no—
397C2×C4—441no—
398C2×C4—441no—
399C2×C4—441no—
400C2×C4—441no—
401C2×C4—441no—
402C2×C4—441no—
403C2×C4—441no—
404C2×C4—441no—
405C2×C4#6686912yes—
406C2×C4#6687012yes—
407C2×C4#6687412yes—
408C2×C4#6687412yes—
409C2×C4C4⋊C4×D1111yescharacteristic
410C2×C4#6694511yescharacteristic
411C2×C4#6694811yescharacteristic
412C2×C4#6695011yescharacteristic
413C8—882no—
414C22—21no—
415C22—21no—
416C22—21no—
417C22—21no—
418C22—21no—
419C22—21no—
420C22—21no—
421C22—21no—
422C22—21no—
423C22—21no—
424C22—21no—
425C22—21no—
426C22C2×#6686911yescharacteristic
427C22C2×#6687011yescharacteristic
428C22#1062257911yescharacteristic
429C22C2×#6687411yescharacteristic
430C22#1062260011yescharacteristic
431C22#1062261811yescharacteristic
432C22#1062261911yescharacteristic
433C22#1062268811yescharacteristic
434C22#1062270311yescharacteristic
435C22#1062270411yescharacteristic
436C22#1062270711yescharacteristic
437C4—21no—
438C4—21no—
439C4—21no—
440C4—21no—
441C4—22no—
442C4—22no—
443C4—22no—
444C4—22no—
445C4—84no—
446C4—442no—
447C4—442no—
448C4—881no—
449C4—881no—
450C2—21no—
451C2—21no—
452C2—21no—
453C2—21no—
454C2#1306711411yescharacteristic
455C2#1306711811yescharacteristic
456C2#1306715211yescharacteristic
457C2#1306718711yescharacteristic
458C2#1306860111yescharacteristic
459C2#1306861811yescharacteristic
460C2#1306863711yescharacteristic
subgroupG/H
centerC23C2×(C2×D11)⋊C4
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×C4⋊#95C2
socleC23×C11C2×C22⋊C4
prime radicalC24×C11C2×D4
cosocleC23×C4×C11C23
hypercenterC4⋊#95D11
hypocenterC11#8578
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
9. C2×C4×Dic22C4semidirect
16. C4×C4⋊Dic11C4semidirect
19. #10622542C4semidirect
20. #10622541C4semidirect
100. C2×Dic22C4⋊C4semidirect
113. C4⋊Dic11C4⋊C4semidirect
352. C11#8578semidirect

Maximal subgroups

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

subgroupindex
C4×#669772
#130685962
C2×#106220902
#130664952
C11×C4⋊#952
#857811