Finite Group Databasebeta

← #14668917

Subgroups — #14668917

Order 2816.

548 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13071288C211yesmaximal, characteristic
2C2×#10622177C211yesmaximal, characteristic
3#100×Dic11C211yesmaximal, characteristic
4#99×Dic11C211yesmaximal, characteristic
5#13066735C211yesmaximal, characteristic
6#13066733C211yesmaximal, characteristic
7C2×C11×#352C211yesmaximal, characteristic
8C2×C11×#123C2211yescharacteristic
9C2×D4×Dic11C2211yescharacteristic
10C22×C4⋊Dic11C411yescharacteristic, complemented
11C2×C11×#100C2211yescharacteristic
12C2×C11×#99C2211yescharacteristic
13#10622833C2211yescharacteristic
14C2×#66898C2211yescharacteristic
15C2×#66897C2211yescharacteristic
16#10622824C411yescharacteristic, complemented
17M16×Dic11—21no—
18#10622598—21no—
19#10622594—21no—
20#10622564—21no—
21#10622563—21no—
22#10622563C411yescharacteristic, complemented
23C22⋊C4×Dic11—21no—
24C22⋊C4×Dic11C411yescharacteristic, complemented
25C11×#352C414yescomplemented
26#10622192—21no—
27#10622177C414yescomplemented
28#10622165—21no—
29C22×D4×C11C2311yescharacteristic
30C23×C4×C11C2×C411yescharacteristic
31C23×Dic11C2×C411yescharacteristic
32C23×Dic11C2×C411yescharacteristic
33C23×Dic11D411yescharacteristic
34C2×C11×M16—21no—
35C11×#123—21no—
36C11×#123—21no—
37C11×#123C2×C412yes—
38C11×#123C2×C412yes—
39C2×C11×C4⋊C4—21no—
40C2×C11×C22⋊C4—21no—
41C2×C11×C22⋊C4—21no—
42C2×C11×C22⋊C4C2×C411yescharacteristic
43C2×C22⋊Dic11—21no—
44C2×C22⋊Dic11—21no—
45C2×C22⋊Dic11C2×C411yescharacteristic
46C2×C22⋊Dic11C2×C411yescharacteristic
47C2×C22⋊Dic11D411yescharacteristic
48D4×Dic11—41no—
49D4×Dic11—41no—
50C2×C4⋊Dic11—21no—
51C2×C4⋊Dic11—21no—
52C2×C4⋊Dic11—21no—
53C2×C4⋊Dic11—41no—
54C2×C4⋊Dic11—41no—
55C2×C4⋊Dic11D411yescharacteristic
56C2×C4×Dic11—21no—
57C2×C4×Dic11—41no—
58C2×C4×Dic11D411yescharacteristic
59C2×#4318—21no—
60C11×#100—21no—
61C11×#100C2×C412yes—
62C11×#99—21no—
63C11×#99C2×C412yes—
64#66898—21no—
65#66898C2×C412yes—
66#66897—21no—
67#66897C2×C412yes—
68C11⋊#95—21no—
69C11⋊#95—21no—
70C11⋊#95—21no—
71C11⋊#95—21no—
72C11⋊#95—21no—
73C11⋊#95—41no—
74#66879—41no—
75C8×Dic11—41no—
76#12621—111nomaximal, Sylow
77C24×C11C22×C411yescharacteristic
78C24×C11C2×D411yescharacteristic
79C2×D4×C11—41no—
80C2×D4×C11—41no—
81C2×D4×C11C22×C411yescharacteristic
82C2×D4×C11C22×C411yescharacteristic
83C2×D4×C11#4111yescharacteristic
84C2×D4×C11#4111yescharacteristic
85C22×C4×C11—21no—
86C22×C4×C11—21no—
87C22×C4×C11—21no—
88C22×C4×C11—41no—
89C22×C4×C11—41no—
90C22×C4×C11—41no—
91C22×C4×C11C4212yescomplemented
92C22×C4×C11C2×D411yescharacteristic
93C22×Dic11—21no—
94C22×Dic11—21no—
95C22×Dic11—21no—
96C22×Dic11—21no—
97C22×Dic11—21no—
98C22×Dic11—21no—
99C22×Dic11—41no—
100C22×Dic11—41no—
101C22×Dic11—81no—
102C22×Dic11—81no—
103C22×Dic11—81no—
104C22×Dic11C22⋊C411yescharacteristic
105C22×Dic11C22⋊C411yescharacteristic
106C22×Dic11C22⋊C411yescharacteristic
107C22×Dic11C22⋊C411yescharacteristic
108C11×M16—22no—
109C11×M16—41no—
110C2×C8×C11—41no—
111C11×C4⋊C4—22no—
112C11×C4⋊C4—22no—
113C11×C22⋊C4—21no—
114C11×C22⋊C4—22no—
115C11×C22⋊C4—22no—
116C11×C22⋊C4—22no—
117C11×C22⋊C4—41no—
118C11×C22⋊C4C4212yescomplemented
119C22⋊Dic11—22no—
120C22⋊Dic11—41no—
121C22⋊Dic11—41no—
122C22⋊Dic11—41no—
123C22⋊Dic11—41no—
124C22⋊Dic11—81no—
125C4⋊Dic11—41no—
126C4⋊Dic11—42no—
127C4⋊Dic11—41no—
128C4⋊Dic11—41no—
129C4⋊Dic11—81no—
130C4×Dic11—21no—
131C4×Dic11—21no—
132C4×Dic11—81no—
133C4×Dic11—82no—
134#4318—22no—
135#4318—41no—
136C2×C11⋊C8—41no—
137#2322—111no—
138C2×#352—111no—
139C2×#352D1111yescharacteristic
140C4×#100—111no—
141C4×#99—111no—
142#1390—111no—
143#1390—111no—
144C23×C11—21no—
145C23×C11—21no—
146C23×C11—21no—
147C23×C11—21no—
148C23×C11—41no—
149C23×C11—41no—
150C23×C11—41no—
151C23×C11—41no—
152C23×C11C2×C4211yescharacteristic
153C23×C11C2×C22⋊C411yescharacteristic
154C23×C11#11711yescharacteristic
155C23×C11C4×D411yescharacteristic
156C23×C11C4×D411yescharacteristic
157D4×C11—41no—
158D4×C11—41no—
159D4×C11—41no—
160D4×C11—41no—
161C2×C4×C11—21no—
162C2×C4×C11—21no—
163C2×C4×C11—22no—
164C2×C4×C11—22no—
165C2×C4×C11—41no—
166C2×C4×C11—41no—
167C2×C4×C11—42no—
168C2×C4×C11—41no—
169C2×C4×C11—41no—
170C2×C4×C11—42no—
171C2×C4×C11—42no—
172C2×C4×C11—81no—
173C2×C4×C11—81no—
174C2×C4×C11C4×D411yescharacteristic
175C2×C4×C11C4×D411yescharacteristic
176C2×Dic11—21no—
177C2×Dic11—21no—
178C2×Dic11—21no—
179C2×Dic11—41no—
180C2×Dic11—42no—
181C2×Dic11—41no—
182C2×Dic11—41no—
183C2×Dic11—41no—
184C2×Dic11—41no—
185C2×Dic11—41no—
186C2×Dic11—42no—
187C2×Dic11—41no—
188C2×Dic11—41no—
189C2×Dic11—41no—
190C2×Dic11—41no—
191C2×Dic11—81no—
192C2×Dic11—81no—
193C2×Dic11—81no—
194C2×Dic11—81no—
195C2×Dic11—81no—
196C2×Dic11—82no—
197C2×Dic11#9911yescharacteristic
198C2×Dic11#9911yescharacteristic
199C8×C11—42no—
200C11⋊C8—42no—
201C2×#123C2×D1111yescharacteristic
202C2×C4×D4—111no—
203C22×C4⋊C4—111no—
204C2×#100—111no—
205C2×#100C2×D1111yescharacteristic
206C2×#99—111no—
207C2×#99C2×D1111yescharacteristic
208C4×M16—221no—
209#389—221no—
210#388—221no—
211#387—221no—
212#386—111no—
213#385—111no—
214#385—221no—
215#381—111no—
216C4×C22⋊C4—111no—
217C4×C22⋊C4—221no—
218#352—114no—
219#352Dic1114yescomplemented
220#343—221no—
221#342—221no—
222C22×C11—21no—
223C22×C11—21no—
224C22×C11—21no—
225C22×C11—21no—
226C22×C11—21no—
227C22×C11—21no—
228C22×C11—41no—
229C22×C11—41no—
230C22×C11—41no—
231C22×C11—41no—
232C22×C11—42no—
233C22×C11—41no—
234C22×C11—41no—
235C22×C11—41no—
236C22×C11—41no—
237C22×C11—81no—
238C22×C11C4×C22⋊C411yescharacteristic
239C22×C11C2×#9911yescharacteristic
240C22×C11#41011yescharacteristic
241C4×C11—21no—
242C4×C11—21no—
243C4×C11—42no—
244C4×C11—42no—
245C4×C11—82no—
246Dic11—21no—
247Dic11—21no—
248Dic11—41no—
249Dic11—41no—
250Dic11—41no—
251Dic11—81no—
252Dic11—82no—
253Dic11—81no—
254C22×D4C22×D1111yescharacteristic
255C23×C4—111no—
256C23×C4—111no—
257C23×C4—111no—
258C23×C4C4×D1111yescharacteristic
259C2×M16—21no—
260C2×M16—221no—
261#123—21no—
262#123—21no—
263#123C4×D1112yes—
264#123C2×Dic1112yes—
265C4×D4—441no—
266C4×D4—441no—
267C2×C4⋊C4—21no—
268C2×C4⋊C4—111no—
269C2×C4⋊C4—221no—
270C2×C4⋊C4—221no—
271C2×C4⋊C4—221no—
272C2×C4⋊C4—441no—
273C2×C4⋊C4—441no—
274C2×C22⋊C4—21no—
275C2×C22⋊C4—21no—
276C2×C22⋊C4—111no—
277C2×C22⋊C4—111no—
278C2×C22⋊C4—111no—
279C2×C22⋊C4—221no—
280C2×C22⋊C4—221no—
281C2×C22⋊C4C4×D1111yescharacteristic
282C2×C42—111no—
283C2×C42—221no—
284C2×C42—441no—
285#100—21no—
286#100—112no—
287#100—221no—
288#100C2×Dic1112yes—
289#99—21no—
290#99—112no—
291#99—221no—
292#99C2×Dic1112yes—
293#97—441no—
294C4×C8—441no—
295#95—221no—
296#95—221no—
297#95—221no—
298#95—221no—
299#95—221no—
300#95—441no—
301C2×C11—21no—
302C2×C11—21no—
303C2×C11—41no—
304C2×C11—41no—
305C2×C11—41no—
306C2×C11—41no—
307C2×C11C4×#9911yescharacteristic
308C2×C11#212111yescharacteristic
309C2×C11#212311yescharacteristic
310C24C2×C4×D1111yescharacteristic
311C24D4×D1111yescharacteristic
312C2×D4—41no—
313C2×D4—41no—
314C2×D4C2×C4×D1111yescharacteristic
315C2×D4#434111yescharacteristic
316C2×D4#434111yescharacteristic
317C2×D4C22×Dic1111yescharacteristic
318C22×C4—21no—
319C22×C4—21no—
320C22×C4—21no—
321C22×C4—41no—
322C22×C4—41no—
323C22×C4—41no—
324C22×C4—111no—
325C22×C4—111no—
326C22×C4—111no—
327C22×C4—111no—
328C22×C4—221no—
329C22×C4—221no—
330C22×C4—221no—
331C22×C4—221no—
332C22×C4—221no—
333C22×C4—221no—
334C22×C4—441no—
335C22×C4—441no—
336C22×C4—881no—
337C22×C4—881no—
338C22×C4—881no—
339C22×C4C4×Dic1112yescomplemented
340C22×C4D4×D1111yescharacteristic
341M16—22no—
342M16—41no—
343M16—222no—
344M16—441no—
345C2×C8—41no—
346C2×C8—441no—
347C4⋊C4—22no—
348C4⋊C4—22no—
349C4⋊C4—441no—
350C4⋊C4—441no—
351C4⋊C4—441no—
352C4⋊C4—442no—
353C4⋊C4—881no—
354C22⋊C4—21no—
355C22⋊C4—22no—
356C22⋊C4—22no—
357C22⋊C4—22no—
358C22⋊C4—41no—
359C22⋊C4—222no—
360C22⋊C4—441no—
361C22⋊C4—441no—
362C22⋊C4—441no—
363C22⋊C4—441no—
364C22⋊C4—881no—
365C22⋊C4C4×Dic1112yescomplemented
366C42—221no—
367C42—221no—
368C42—881no—
369C42—882no—
370C11#1262111yescharacteristic, complemented, Sylow
371C23—21no—
372C23—21no—
373C23—21no—
374C23—21no—
375C23—41no—
376C23—41no—
377C23—41no—
378C23—41no—
379C23#6693011yescharacteristic
380C23C22⋊C4×D1111yescharacteristic
381C23(C22⋊D11)⋊C411yescharacteristic
382C23C2×C4×Dic1111yescharacteristic
383C23D4×Dic1111yescharacteristic
384D4—41no—
385D4—41no—
386D4—41no—
387D4—41no—
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—22no—
391C2×C4—22no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—42no—
395C2×C4—41no—
396C2×C4—41no—
397C2×C4—42no—
398C2×C4—42no—
399C2×C4—81no—
400C2×C4—81no—
401C2×C4—111no—
402C2×C4—111no—
403C2×C4—221no—
404C2×C4—221no—
405C2×C4—221no—
406C2×C4—441no—
407C2×C4—442no—
408C2×C4—441no—
409C2×C4—441no—
410C2×C4—441no—
411C2×C4—441no—
412C2×C4—442no—
413C2×C4—441no—
414C2×C4—441no—
415C2×C4—441no—
416C2×C4—441no—
417C2×C4—441no—
418C2×C4—881no—
419C2×C4—881no—
420C2×C4—881no—
421C2×C4—881no—
422C2×C4—881no—
423C2×C4—882no—
424C2×C4(C22⋊D11)⋊C411yescharacteristic
425C2×C4D4×Dic1111yescharacteristic
426C8—42no—
427C8—442no—
428C22—21no—
429C22—21no—
430C22—21no—
431C22—21no—
432C22—21no—
433C22—21no—
434C22—41no—
435C22—41no—
436C22—41no—
437C22—41no—
438C22—42no—
439C22—41no—
440C22—41no—
441C22—41no—
442C22—41no—
443C22—81no—
444C22#1062235311yescharacteristic
445C22D11×#9911yescharacteristic
446C22C22⋊C4×Dic1111yescharacteristic
447C4—21no—
448C4—21no—
449C4—42no—
450C4—42no—
451C4—82no—
452C4—221no—
453C4—221no—
454C4—441no—
455C4—441no—
456C4—441no—
457C4—881no—
458C4—882no—
459C4—881no—
460C2—21no—
461C2—21no—
462C2—41no—
463C2—41no—
464C2—41no—
465C2—41no—
466C2#99×Dic1111yescharacteristic
467C2#1307026111yescharacteristic
468C2#1307026811yescharacteristic
subgroupG/H
centerC22D11×#99
commutatorC23×C11C2×C42
FrattiniC22×D4C22×D11
FittingC2×C11×#352C2
socleC22×C11C2×#99
prime radical, cosocleC22×D4×C11C23
hypercenterC2×#352D11
hypocenterC11#12621
LCSG ▷ C23×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C22×D4 ◁ C2×#352

Complements

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

NH ≅ G/Ntype
10. C22×C4⋊Dic11C4semidirect
16. #10622824C4semidirect
22. #10622563C4semidirect
24. C22⋊C4×Dic11C4semidirect
25. C11×#352C4semidirect
27. #10622177C4semidirect
91. C22×C4×C11C42semidirect
118. C11×C22⋊C4C42semidirect
219. #352Dic11semidirect
339. C22×C4C4×Dic11semidirect
365. C22⋊C4C4×Dic11semidirect
370. C11#12621semidirect

Maximal subgroups

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

subgroupindex
#130712882
C2×#106221772
#100×Dic112
#99×Dic112
#130667352
#130667332
C2×C11×#3522
#1262111