Finite Group Databasebeta

← #14645270

Subgroups — #14645270

Order 2816.

802 conjugacy classes of subgroups.

The subgroup lattice has 508 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623259C211yesmaximal, characteristic
2#13068593C211yesmaximal, characteristic
3#13068593C211yesmaximal, characteristic
4C2×#10622184C211yesmaximal, characteristic, complemented
5C2×#10622120C211yesmaximal, characteristic, complemented
6C2×#10622124C211yesmaximal, characteristic, complemented
7C2×C11×#333C211yesmaximal, characteristic, complemented
8C2×C11×C4⋊Q8C2211yescharacteristic
9C2×#66999C412yes—
10C2×Q8×Dic11C412yes—
11#10623259—22no—
12#10623259—22no—
13#10623259—22no—
14#10623259—22no—
15C2×#66950—21no—
16C2×#66945—21no—
17C2×#66943—21no—
18C2×#66940—21no—
19C2×C42×D11C2211yescharacteristic
20C2×#66922C2211yescharacteristic
21C2×C11×C4⋊C8C2211yescharacteristic
22C2×C11×C4⋊C8C2211yescharacteristic
23C2×(C2×D11)⋊C8—21no—
24C2×(C2×D11)⋊C8—21no—
25C2×C4⋊(C11⋊C8)C2211yescharacteristic
26C2×C4⋊(C11⋊C8)C2211yescharacteristic
27C11×#333—22no—
28#10622188—21no—
29#10622188—21no—
30#10622184—22no—
31#10622124—22no—
32#10622120—22no—
33C22×Q8×C11C2×C412yes—
34C22×C4×D11C2×C411yescharacteristic
35C22×C4×D11D411yescharacteristic
36C22×C4×D11D411yescharacteristic
37C22×Dic22—21no—
38C22×C8×C11—21no—
39C22×C8×C11—21no—
40C11×C4⋊Q8—21no—
41C11×C4⋊Q8—21no—
42C11×C4⋊Q8D412yes—
43C11×C4⋊Q8D412yes—
44C2×C11×C4⋊C4—21no—
45C2×C11×C4⋊C4—21no—
46C2×C42×C11C2311yescharacteristic
47#66999—24no—
48#66999—24no—
49Q8×Dic11—24no—
50Q8×Dic11—24no—
51C2×(C2×D11)⋊C4—22no—
52C2×C4⋊Dic11—21no—
53C2×C4⋊Dic11—22no—
54C2×C4⋊Dic11C2×C412yes—
55C2×Dic11⋊C4—22no—
56C2×C4×Dic11—22no—
57C2×C4×Dic11C2×C411yescharacteristic
58C2×C4×Dic11D411yescharacteristic
59C2×C4×Dic11D411yescharacteristic
60C22×C11⋊C8—21no—
61C22×C11⋊C8—21no—
62#66950—24no—
63#66950—24no—
64#66945—24no—
65#66945—24no—
66#66943—24no—
67#66943—24no—
68#66940—24no—
69#66940—24no—
70C42×D11—21no—
71C42×D11—21no—
72C42×D11—21no—
73C42×D11—21no—
74#66922—21no—
75#66922—21no—
76#66922D412yes—
77#66922D412yes—
78C11×C4⋊C8—21no—
79C11×C4⋊C8—21no—
80C11×C4⋊C8—21no—
81C11×C4⋊C8—21no—
82(C2×D11)⋊C8—42no—
83(C2×D11)⋊C8—42no—
84C4⋊(C11⋊C8)—21no—
85C4⋊(C11⋊C8)—21no—
86C4⋊(C11⋊C8)—21no—
87C4⋊(C11⋊C8)—21no—
88#8343—111nomaximal, Sylow
89C23×D11C22⋊C411yescharacteristic
90C2×Q8×C11—22no—
91C2×Q8×C11—42no—
92C2×Q8×C11—42no—
93C2×Q8×C11C22⋊C414yes—
94C22×C4×C11—22no—
95C22×C4×C11C22×C411yescharacteristic
96C22×C4×C11C2×D411yescharacteristic
97C22×C4×C11C2×D411yescharacteristic
98C22×Dic11—22no—
99C22×Dic11C22⋊C411yescharacteristic
100C22×Dic11C22⋊C411yescharacteristic
101C22×Dic11C22⋊C411yescharacteristic
102C2×C4×D11—21no—
103C2×C4×D11—21no—
104C2×C4×D11—21no—
105C2×C4×D11—21no—
106C2×C4×D11—21no—
107C2×C4×D11—21no—
108C2×C4×D11—21no—
109C2×C4×D11—21no—
110C2×C4×D11—21no—
111C2×C4×D11—21no—
112C2×C4×D11—21no—
113C2×C4×D11—21no—
114C2×C4×D11—41no—
115C2×C4×D11—41no—
116C2×C4×D11SD1612yes—
117C2×C4×D11Q1612yes—
118C2×Dic22—22no—
119C2×Dic22—22no—
120C2×Dic22—41no—
121C2×Dic22—41no—
122C2×Dic22—41no—
123C2×Dic22—41no—
124C2×C8×C11—41no—
125C2×C8×C11—41no—
126C2×C8×C11—41no—
127C2×C8×C11—41no—
128C2×C8×C11—41no—
129C2×C8×C11—41no—
130C11×C4⋊C4—22no—
131C11×C4⋊C4—22no—
132C11×C4⋊C4—22no—
133C11×C4⋊C4—22no—
134C42×C11C2×D411yescharacteristic
135C42×C11C2×D411yescharacteristic
136C42×C11C2×D411yescharacteristic
137C42×C11C2×D411yescharacteristic
138(C2×D11)⋊C4—28no—
139C4⋊Dic11—28no—
140C4⋊Dic11—22no—
141C4⋊Dic11—22no—
142C4⋊Dic11—22no—
143C4⋊Dic11C22⋊C414yes—
144Dic11⋊C4—28no—
145C4×Dic11—28no—
146C4×Dic11—21no—
147C4×Dic11—21no—
148C4×Dic11—21no—
149C4×Dic11—21no—
150C4×Dic11—21no—
151C4×Dic11—21no—
152C2×C11⋊C8—41no—
153C2×C11⋊C8—41no—
154C2×C11⋊C8—41no—
155C2×C11⋊C8—41no—
156C2×C11⋊C8—41no—
157C2×C11⋊C8—41no—
158C2×#533—111no—
159#1797—111no—
160#1797—111no—
161C2×#333—111no—
162C2×#333D1111yescharacteristic, complemented
163C2×#332—111no—
164C2×#332—111no—
165C23×C11C2×C22⋊C411yescharacteristic
166C22×D11—21no—
167C22×D11—21no—
168C22×D11—21no—
169C22×D11—21no—
170C22×D11—21no—
171C22×D11—21no—
172C22×D11#10312yes—
173Q8×C11—44no—
174Q8×C11—44no—
175C2×C4×C11—21no—
176C2×C4×C11—21no—
177C2×C4×C11—24no—
178C2×C4×C11—42no—
179C2×C4×C11—42no—
180C2×C4×C11C2×C22⋊C411yescharacteristic
181C2×C4×C11C2×C22⋊C411yescharacteristic
182C2×C4×C11#12011yescharacteristic
183C2×C4×C11#12011yescharacteristic
184C2×C4×C11#12011yescharacteristic
185C2×C4×C11#12011yescharacteristic
186C2×C4×C11C2×SD1611yescharacteristic
187C2×C4×C11C2×Q1611yescharacteristic
188C2×C4×C11#13511yescharacteristic
189C2×C4×C11#13511yescharacteristic
190C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
191C2×C4×C11#13711yescharacteristic
192C2×C4×C11#13711yescharacteristic
193C2×C4×C11#13711yescharacteristic
194C2×Dic11—21no—
195C2×Dic11—21no—
196C2×Dic11—21no—
197C2×Dic11—21no—
198C2×Dic11—24no—
199C2×Dic11—21no—
200C2×Dic11—21no—
201C2×Dic11—21no—
202C2×Dic11—21no—
203C2×Dic11—42no—
204C2×Dic11—42no—
205C2×Dic11#10312yes—
206C4×D11—22no—
207C4×D11—22no—
208C4×D11—22no—
209C4×D11—22no—
210C4×D11—42no—
211C4×D11—42no—
212C4×D11—41no—
213C4×D11—41no—
214C4×D11—41no—
215C4×D11—41no—
216Dic22—42no—
217Dic22—42no—
218Dic22—42no—
219Dic22—42no—
220C8×C11—81no—
221C8×C11—81no—
222C11⋊C8—81no—
223C11⋊C8—81no—
224#533—222no—
225#533—222no—
226#533—222no—
227#533—222no—
228C2×C4⋊Q8—111no—
229C2×C4⋊Q8C2×D1111yescharacteristic
230C2×#125—221no—
231C2×C22⋊Q8—112no—
232C2×C22⋊Q8—221no—
233C2×C4×Q8—112no—
234C2×C4×Q8—221no—
235C2×#117—221no—
236C22×C42—111no—
237C2×C4⋊C8—111no—
238C2×C4⋊C8—111no—
239C2×C4⋊C8C2×D1111yescharacteristic
240C2×C4⋊C8C2×D1111yescharacteristic
241C2×C22⋊C8—221no—
242C2×C22⋊C8—221no—
243#336—221no—
244#336—221no—
245#333—22no—
246#333—222no—
247#332—222no—
248#332—222no—
249C22×C11#37911yescharacteristic
250C22×C11#41311yescharacteristic
251C22×C11#41311yescharacteristic
252C22×C11C2×#10311yescharacteristic
253C22×C11#41611yescharacteristic
254C22×C11#41711yescharacteristic
255C22×C11#41911yescharacteristic
256C2×D11—22no—
257C2×D11—22no—
258C2×D11—22no—
259C2×D11—41no—
260C2×D11—41no—
261C2×D11—41no—
262C2×D11—41no—
263C4×C11—21no—
264C4×C11—21no—
265C4×C11—44no—
266C4×C11#44811yescharacteristic
267C4×C11#44811yescharacteristic
268C4×C11#44911yescharacteristic
269C4×C11#44911yescharacteristic
270C4×C11#45111yescharacteristic
271C4×C11#45111yescharacteristic
272C4×C11#45211yescharacteristic
273C4×C11#45211yescharacteristic
274Dic11—22no—
275Dic11—41no—
276Dic11—44no—
277Dic11—41no—
278C22×Q8—221no—
279C22×Q8C4×D1112yes—
280C23×C4—111no—
281C23×C4—111no—
282C23×C4—111no—
283C22×C8—21no—
284C22×C8—21no—
285C22×C8—221no—
286C22×C8—221no—
287C4⋊Q8—21no—
288C4⋊Q8—21no—
289C4⋊Q8—112no—
290C4⋊Q8—112no—
291C4⋊Q8—221no—
292C4⋊Q8—221no—
293C4⋊Q8D4412yes—
294C4⋊Q8C22⋊D1112yes—
295#125—224no—
296#125—224no—
297C22⋊Q8—224no—
298C22⋊Q8—224no—
299C22⋊Q8—224no—
300C22⋊Q8—224no—
301C4×Q8—224no—
302C4×Q8—224no—
303C4×Q8—224no—
304C4×Q8—224no—
305#117—224no—
306#117—224no—
307C2×C4⋊C4—21no—
308C2×C4⋊C4—21no—
309C2×C4⋊C4—112no—
310C2×C4⋊C4—222no—
311C2×C4⋊C4—222no—
312C2×C4⋊C4—221no—
313C2×C22⋊C4—222no—
314C2×C42—111no—
315C2×C42—111no—
316C2×C42—111no—
317C2×C42—222no—
318C2×C42—221no—
319C2×C42—221no—
320C2×C42—221no—
321C2×C42—221no—
322C2×C42C22×D1111yescharacteristic
323C4⋊C8—21no—
324C4⋊C8—21no—
325C4⋊C8—21no—
326C4⋊C8—21no—
327C4⋊C8—221no—
328C4⋊C8—221no—
329C4⋊C8—221no—
330C4⋊C8—221no—
331C22⋊C8—442no—
332C22⋊C8—442no—
333C2×C11#154211yescharacteristic
334C2×C11#155011yescharacteristic
335C2×C11#155411yescharacteristic
336C2×C11#155911yescharacteristic
337C2×C11#178511yescharacteristic
338C2×C11#178711yescharacteristic
339C2×C11#178811yescharacteristic
340D11—42no—
341C24—111no—
342C2×Q8—22no—
343C2×Q8—42no—
344C2×Q8—42no—
345C2×Q8—222no—
346C2×Q8—222no—
347C2×Q8—441no—
348C2×Q8—441no—
349C2×Q8—441no—
350C2×Q8—441no—
351C2×Q8(C2×D11)⋊C414yes—
352C22×C4—22no—
353C22×C4—111no—
354C22×C4—112no—
355C22×C4—112no—
356C22×C4—111no—
357C22×C4—111no—
358C22×C4—221no—
359C22×C4—221no—
360C22×C4—221no—
361C22×C4—221no—
362C22×C4—222no—
363C22×C4—221no—
364C22×C4—221no—
365C22×C4—221no—
366C22×C4—221no—
367C22×C4—221no—
368C22×C4—221no—
369C22×C4—221no—
370C22×C4—221no—
371C22×C4—441no—
372C22×C4—441no—
373C22×C4C2×C4×D1111yescharacteristic
374C22×C4D4×D1111yescharacteristic
375C22×C4D4×D1111yescharacteristic
376C2×C8—41no—
377C2×C8—41no—
378C2×C8—41no—
379C2×C8—41no—
380C2×C8—41no—
381C2×C8—41no—
382C2×C8—441no—
383C2×C8—441no—
384C2×C8—441no—
385C2×C8—441no—
386C2×C8—441no—
387C2×C8—441no—
388C4⋊C4—22no—
389C4⋊C4—22no—
390C4⋊C4—22no—
391C4⋊C4—22no—
392C4⋊C4—114no—
393C4⋊C4—228no—
394C4⋊C4—228no—
395C4⋊C4—222no—
396C4⋊C4—222no—
397C4⋊C4—222no—
398C22⋊C4—228no—
399C42—228no—
400C42—221no—
401C42—221no—
402C42—221no—
403C42—221no—
404C42—221no—
405C42—221no—
406C42C2×D4411yescharacteristic
407C42D4×D1111yescharacteristic
408C42D4×D1111yescharacteristic
409C42C2×C22⋊D1111yescharacteristic
410C11#834311yescharacteristic, complemented, Sylow
411C23—112no—
412C23—221no—
413C23—221no—
414C23—221no—
415C23—221no—
416C23—221no—
417C23—221no—
418C23C22⋊C4×D1111yescharacteristic
419Q8—44no—
420Q8—44no—
421Q8—442no—
422Q8—442no—
423Q8—442no—
424Q8—442no—
425C2×C4—21no—
426C2×C4—21no—
427C2×C4—24no—
428C2×C4—42no—
429C2×C4—42no—
430C2×C4—112no—
431C2×C4—221no—
432C2×C4—221no—
433C2×C4—222no—
434C2×C4—222no—
435C2×C4—222no—
436C2×C4—222no—
437C2×C4—221no—
438C2×C4—221no—
439C2×C4—224no—
440C2×C4—221no—
441C2×C4—221no—
442C2×C4—221no—
443C2×C4—221no—
444C2×C4—442no—
445C2×C4—442no—
446C2×C4—442no—
447C2×C4—442no—
448C2×C4—441no—
449C2×C4—441no—
450C2×C4—441no—
451C2×C4—441no—
452C2×C4C22⋊C4×D1111yescharacteristic
453C2×C4#6693511yescharacteristic
454C2×C4#6693511yescharacteristic
455C2×C4SD16×D1111yescharacteristic
456C2×C4#6696711yescharacteristic
457C2×C4#6696811yescharacteristic
458C2×C4#6696911yescharacteristic
459C2×C4Q16×D1111yescharacteristic
460C2×C4#6697111yescharacteristic
461C2×C4#6697111yescharacteristic
462C2×C4#6697211yescharacteristic
463C2×C4C2×(C2×D11)⋊C411yescharacteristic
464C2×C4#6699011yescharacteristic
465C2×C4#6699011yescharacteristic
466C8—81no—
467C8—81no—
468C8—881no—
469C8—881no—
470C22—222no—
471C22—222no—
472C22—222no—
473C22—441no—
474C22—441no—
475C22—441no—
476C22—441no—
477C22#1062235811yescharacteristic
478C22#1062235811yescharacteristic
479C22D11×#10311yescharacteristic
480C22#1062241511yescharacteristic
481C22#1062241611yescharacteristic
482C22#1062241711yescharacteristic
483C22#1062256811yescharacteristic
484C4—21no—
485C4—21no—
486C4—44no—
487C4—222no—
488C4—441no—
489C4—444no—
490C4—441no—
491C4#1062241911yescharacteristic
492C4#1062242111yescharacteristic
493C4#1062242311yescharacteristic
494C4#1062242411yescharacteristic
495C4#1062278311yescharacteristic
496C4#1062278511yescharacteristic
497C4#1062279911yescharacteristic
498C4#1062280011yescharacteristic
499C2—442no—
500C2#1306727011yescharacteristic
501C2#1306730311yescharacteristic
502C2#1306732511yescharacteristic
503C2#1306734311yescharacteristic
504C2#1306854111yescharacteristic
505C2#1306854911yescharacteristic
506C2#1306855511yescharacteristic
subgroupG/H
centerC23C22⋊C4×D11
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC2×C11×#333C2
socleC23×C11C2×C22⋊C4
prime radicalC23×D11C22⋊C4
cosocleC2×C42×C11C23
hypercenterC2×#333D11
hypocenterC11#8343
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#333

Complements

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

NH ≅ G/Ntype
4. C2×#10622184C2semidirect
5. C2×#10622120C2semidirect
6. C2×#10622124C2semidirect
7. C2×C11×#333C2semidirect
162. C2×#333D11semidirect
410. C11#8343semidirect

Maximal subgroups

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

subgroupindex
C2×#106232592
#130685932
C2×#106221842
C2×#106221202
C2×#106221242
C2×C11×#3332
#834311