Finite Group Databasebeta

← #14649447

Subgroups — #14649447

Order 2816.

612 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622450C211yesmaximal, characteristic
2#13076969C211yesmaximal, characteristic
3#13068593C211yesmaximal, characteristic
4C2×#10622119C211yesmaximal, characteristic, complemented
5C2×#10622119C211yesmaximal, characteristic, complemented
6#13066499C211yesmaximal, characteristic, complemented
7C11×#1296C211yesmaximal, characteristic, complemented
8C22×#4313—21no—
9C2×#66950C412yes—
10C2×C42×D11C2211yescharacteristic
11C2×#66922C2211yescharacteristic
12C2×C11×C4⋊C8C2211yescharacteristic
13C2×C11×C4⋊C8C2211yescharacteristic
14C11×#384C2211yescharacteristic
15C2×(C2×D11)⋊C8—21no—
16C2×Dic11⋊C8—21no—
17#10622600—21no—
18#10622600—21no—
19#10622598—21no—
20#10622598—21no—
21#10622587C412yes—
22C2×C4⋊(C11⋊C8)C2211yescharacteristic
23C2×C4⋊(C11⋊C8)C2211yescharacteristic
24#10622450—22no—
25#10622450—22no—
26#10622188—21no—
27#10622119—22no—
28#10622119—22no—
29C22×C4×D11C2×C411yescharacteristic
30C22×C4×D11D411yescharacteristic
31C22×C4×D11D411yescharacteristic
32C22×Dic22C2×C412yes—
33C22×C8×C11—21no—
34C22×C8×C11—21no—
35C2×C11×C4⋊C4—21no—
36C2×C11×C4⋊C4—21no—
37C2×C11×C4⋊C4C2×C412yes—
38C2×C42×C11C2311yescharacteristic
39C2×(C2×D11)⋊C4—22no—
40C2×C4⋊Dic11—21no—
41C2×C4⋊Dic11—21no—
42C2×C4⋊Dic11—22no—
43C2×C4×Dic11C2×C411yescharacteristic
44C2×C4×Dic11D411yescharacteristic
45C2×C4×Dic11D411yescharacteristic
46C22×C11⋊C8—21no—
47C22×C11⋊C8—21no—
48C2×#4313—24no—
49C2×#4313—42no—
50C2×#4313—42no—
51#66950—44no—
52C42×D11—21no—
53C42×D11—21no—
54C42×D11—21no—
55C42×D11—21no—
56#66922—21no—
57#66922—21no—
58#66922—21no—
59#66922—21no—
60C11×C4⋊C8—21no—
61C11×C4⋊C8—21no—
62C11×C4⋊C8—21no—
63C11×C4⋊C8D412yes—
64C11⋊#95—22no—
65C11⋊#95—22no—
66(C2×D11)⋊C8—42no—
67Dic11⋊C8—24no—
68C4⋊(C11⋊C8)—21no—
69C4⋊(C11⋊C8)—21no—
70C4⋊(C11⋊C8)—21no—
71C4⋊(C11⋊C8)D412yes—
72#9135—111nomaximal, Sylow
73C23×D11C22⋊C411yescharacteristic
74C22×C4×C11—22no—
75C22×C4×C11C22×C411yescharacteristic
76C22×C4×C11C2×D411yescharacteristic
77C22×C4×C11C2×D411yescharacteristic
78C22×Dic11—22no—
79C22×Dic11C22⋊C411yescharacteristic
80C22×Dic11C22⋊C411yescharacteristic
81C22×Dic11C22⋊C411yescharacteristic
82C2×C4×D11—22no—
83C2×C4×D11—21no—
84C2×C4×D11—21no—
85C2×C4×D11—21no—
86C2×C4×D11—21no—
87C2×C4×D11—21no—
88C2×C4×D11—21no—
89C2×C4×D11—21no—
90C2×C4×D11—21no—
91C2×C4×D11—21no—
92C2×C4×D11—21no—
93C2×C4×D11—21no—
94C2×C4×D11—21no—
95C2×C4×D11—41no—
96C2×C4×D11SD1612yes—
97C2×C4×D11Q1612yes—
98C2×Dic22—22no—
99C2×Dic22—22no—
100C2×Dic22—42no—
101C2×Dic22—42no—
102C2×C8×C11—22no—
103C2×C8×C11—41no—
104C2×C8×C11—41no—
105C2×C8×C11—41no—
106C2×C8×C11—41no—
107C2×C8×C11—41no—
108C11×C4⋊C4—42no—
109C11×C4⋊C4—41no—
110C11×C4⋊C4—41no—
111C11×C4⋊C4—41no—
112C11×C4⋊C4—41no—
113C42×C11C2×D411yescharacteristic
114C42×C11C2×D411yescharacteristic
115C42×C11#4111yescharacteristic
116C42×C11#4111yescharacteristic
117(C2×D11)⋊C4—44no—
118C4⋊Dic11—44no—
119C4⋊Dic11—41no—
120C4⋊Dic11—41no—
121C4⋊Dic11—41no—
122C4⋊Dic11—41no—
123C4×Dic11—21no—
124C4×Dic11—21no—
125C4×Dic11—21no—
126C4×Dic11—21no—
127C4×Dic11—21no—
128C4×Dic11—21no—
129C2×C11⋊C8—22no—
130C2×C11⋊C8—41no—
131C2×C11⋊C8—41no—
132C2×C11⋊C8—41no—
133C2×C11⋊C8—41no—
134C2×C11⋊C8—41no—
135#4313—48no—
136C2×#423—111no—
137#2857—111no—
138#1797—111no—
139C2×#333—111no—
140C2×#333—111no—
141#1296—111no—
142#1296D1111yescharacteristic, complemented
143C23×C11C2×C22⋊C411yescharacteristic
144C22×D11—21no—
145C22×D11—21no—
146C22×D11—21no—
147C22×D11—21no—
148C22×D11—21no—
149C22×D11—21no—
150C22×D11#10312yes—
151C2×C4×C11—21no—
152C2×C4×C11—21no—
153C2×C4×C11—42no—
154C2×C4×C11—42no—
155C2×C4×C11—42no—
156C2×C4×C11C4×D411yescharacteristic
157C2×C4×C11C4×D411yescharacteristic
158C2×C4×C11#12011yescharacteristic
159C2×C4×C11#12111yescharacteristic
160C2×C4×C11#12111yescharacteristic
161C2×C4×C11#12311yescharacteristic
162C2×C4×C11C2×SD1611yescharacteristic
163C2×C4×C11C2×Q1611yescharacteristic
164C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
165C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
166C2×C4×C11#13711yescharacteristic
167C2×C4×C11#13711yescharacteristic
168C2×C4×C11#13711yescharacteristic
169C2×C4×C11#13711yescharacteristic
170C2×Dic11—21no—
171C2×Dic11—21no—
172C2×Dic11—21no—
173C2×Dic11—21no—
174C2×Dic11—21no—
175C2×Dic11—21no—
176C2×Dic11—21no—
177C2×Dic11—42no—
178C2×Dic11—42no—
179C2×Dic11—42no—
180C2×Dic11#10012yes—
181C2×Dic11#10312yes—
182C4×D11—22no—
183C4×D11—22no—
184C4×D11—22no—
185C4×D11—22no—
186C4×D11—42no—
187C4×D11—42no—
188C4×D11—41no—
189C4×D11—41no—
190C4×D11—41no—
191C4×D11—41no—
192Dic22—82no—
193Dic22—82no—
194C8×C11—42no—
195C8×C11—81no—
196C11⋊C8—42no—
197C11⋊C8—81no—
198C22×M16—221no—
199C2×C4⋊Q8—111no—
200C2×C22⋊Q8—112no—
201C22×C42—111no—
202#423—222no—
203#423—222no—
204C2×C4⋊C8—111no—
205C2×C4⋊C8—111no—
206C2×C4⋊C8—221no—
207C2×C4⋊C8C2×D1111yescharacteristic
208C2×C4⋊C8C2×D1111yescharacteristic
209C2×C22⋊C8—221no—
210#391—112no—
211#389—221no—
212#389—221no—
213#384C2×D1111yescharacteristic
214#380—221no—
215#380—221no—
216#336—221no—
217#333—222no—
218#333—222no—
219C22×C11#38611yescharacteristic
220C22×C11C2×#10011yescharacteristic
221C22×C11#41311yescharacteristic
222C22×C11C2×#10311yescharacteristic
223C22×C11#41711yescharacteristic
224C22×C11#41711yescharacteristic
225C22×C11#41911yescharacteristic
226C2×D11—22no—
227C2×D11—22no—
228C2×D11—22no—
229C2×D11—41no—
230C2×D11—41no—
231C2×D11—41no—
232C2×D11—41no—
233C4×C11—21no—
234C4×C11—21no—
235C4×C11—82no—
236C4×C11#45011yescharacteristic
237C4×C11#45111yescharacteristic
238C4×C11#46811yescharacteristic
239C4×C11#46811yescharacteristic
240C4×C11#47011yescharacteristic
241C4×C11#47011yescharacteristic
242C4×C11#48311yescharacteristic
243C4×C11#48411yescharacteristic
244Dic11—22no—
245Dic11—22no—
246Dic11—41no—
247Dic11—82no—
248C22×Q8—112no—
249C23×C4—111no—
250C23×C4—111no—
251C23×C4—111no—
252C2×M16—224no—
253C2×M16—442no—
254C2×M16—442no—
255C22×C8—21no—
256C22×C8—21no—
257C22×C8—221no—
258C22×C8—221no—
259C4⋊Q8—221no—
260C4⋊Q8—221no—
261C4⋊Q8—221no—
262C4⋊Q8—221no—
263C22⋊Q8—444no—
264C2×C4⋊C4—21no—
265C2×C4⋊C4—21no—
266C2×C4⋊C4—222no—
267C2×C4⋊C4—221no—
268C2×C4⋊C4—221no—
269C2×C4⋊C4C4×D1112yes—
270C2×C22⋊C4—222no—
271C2×C42—111no—
272C2×C42—111no—
273C2×C42—111no—
274C2×C42—221no—
275C2×C42—221no—
276C2×C42—221no—
277C2×C42—221no—
278C2×C42C22×D1111yescharacteristic
279C4⋊C8—21no—
280C4⋊C8—21no—
281C4⋊C8—21no—
282C4⋊C8—112no—
283C4⋊C8—224no—
284C4⋊C8—221no—
285C4⋊C8—221no—
286C4⋊C8—221no—
287C4⋊C8D4412yes—
288C22⋊C8—442no—
289#95—222no—
290#95—222no—
291C2×C11#154811yescharacteristic
292C2×C11#155011yescharacteristic
293C2×C11#155911yescharacteristic
294C2×C11#156011yescharacteristic
295C2×C11#187211yescharacteristic
296C2×C11#189411yescharacteristic
297C2×C11#190011yescharacteristic
298D11—42no—
299C24—111no—
300C2×Q8—222no—
301C2×Q8—222no—
302C2×Q8—442no—
303C2×Q8—442no—
304C22×C4—22no—
305C22×C4—111no—
306C22×C4—111no—
307C22×C4—112no—
308C22×C4—112no—
309C22×C4—111no—
310C22×C4—222no—
311C22×C4—221no—
312C22×C4—221no—
313C22×C4—221no—
314C22×C4—221no—
315C22×C4—221no—
316C22×C4—221no—
317C22×C4—221no—
318C22×C4—221no—
319C22×C4—221no—
320C22×C4—221no—
321C22×C4—221no—
322C22×C4—221no—
323C22×C4—222no—
324C22×C4—441no—
325C22×C4C2×C4×D1111yescharacteristic
326C22×C4D4×D1111yescharacteristic
327C22×C4D4×D1111yescharacteristic
328M16—448no—
329C2×C8—22no—
330C2×C8—41no—
331C2×C8—41no—
332C2×C8—41no—
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—42no—
342C4⋊C4—41no—
343C4⋊C4—41no—
344C4⋊C4—41no—
345C4⋊C4—41no—
346C4⋊C4—444no—
347C4⋊C4—441no—
348C4⋊C4—441no—
349C4⋊C4—441no—
350C4⋊C4—441no—
351C22⋊C4—444no—
352C42—221no—
353C42—221no—
354C42—221no—
355C42—221no—
356C42—221no—
357C42—221no—
358C42C2×D4411yescharacteristic
359C42#433911yescharacteristic
360C42D4×D1111yescharacteristic
361C42#434311yescharacteristic
362C11#913511yescharacteristic, complemented, Sylow
363C23—112no—
364C23—221no—
365C23—221no—
366C23—221no—
367C23—221no—
368C23—221no—
369C23—221no—
370C23C22⋊C4×D1111yescharacteristic
371Q8—882no—
372Q8—882no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—42no—
376C2×C4—42no—
377C2×C4—42no—
378C2×C4—112no—
379C2×C4—112no—
380C2×C4—221no—
381C2×C4—221no—
382C2×C4—221no—
383C2×C4—221no—
384C2×C4—222no—
385C2×C4—222no—
386C2×C4—222no—
387C2×C4—222no—
388C2×C4—221no—
389C2×C4—221no—
390C2×C4—221no—
391C2×C4—442no—
392C2×C4—442no—
393C2×C4—441no—
394C2×C4—441no—
395C2×C4—441no—
396C2×C4—441no—
397C2×C4—442no—
398C2×C4—442no—
399C2×C4—442no—
400C2×C4C4×D4411yescharacteristic
401C2×C4#6693511yescharacteristic
402C2×C4#6693711yescharacteristic
403C2×C4#6694611yescharacteristic
404C2×C4#6694711yescharacteristic
405C2×C4#6694811yescharacteristic
406C2×C4#6696411yescharacteristic
407C2×C4#6696411yescharacteristic
408C2×C4SD16×D1111yescharacteristic
409C2×C4#6696811yescharacteristic
410C2×C4#6696811yescharacteristic
411C2×C4#6696811yescharacteristic
412C2×C4Q16×D1111yescharacteristic
413C2×C4#6697111yescharacteristic
414C8—42no—
415C8—81no—
416C8—442no—
417C8—881no—
418C22—222no—
419C22—222no—
420C22—222no—
421C22—441no—
422C22—441no—
423C22—441no—
424C22—441no—
425C22#1062227811yescharacteristic
426C22D11×#10011yescharacteristic
427C22#1062236411yescharacteristic
428C22#1062238411yescharacteristic
429C22#1062238411yescharacteristic
430C22D11×#10311yescharacteristic
431C22#1062241511yescharacteristic
432C4—21no—
433C4—21no—
434C4—82no—
435C4—222no—
436C4—222no—
437C4—441no—
438C4—882no—
439C4#1062238911yescharacteristic
440C4#1062239311yescharacteristic
441C4#1062242111yescharacteristic
442C4#1062242911yescharacteristic
443C4#1062247511yescharacteristic
444C4#1062248111yescharacteristic
445C4#1062249711yescharacteristic
446C4#1062249911yescharacteristic
447C2—442no—
448C2#1306729511yescharacteristic
449C2#1306730511yescharacteristic
450C2#1306734511yescharacteristic
451C2#1306734811yescharacteristic
452C2#1306892211yescharacteristic
453C2#1306904811yescharacteristic
454C2#1306907811yescharacteristic
subgroupG/H
centerC23C22⋊C4×D11
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1296C2
socleC23×C11C2×C22⋊C4
prime radicalC23×D11C22⋊C4
cosocleC2×C42×C11C23
hypercenter#1296D11
hypocenterC11#9135
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1296

Complements

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

NH ≅ G/Ntype
4. C2×#10622119C2semidirect
5. C2×#10622119C2semidirect
6. #13066499C2semidirect
7. C11×#1296C2semidirect
142. #1296D11semidirect
362. C11#9135semidirect

Maximal subgroups

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

subgroupindex
C2×#106224502
#130769692
#130685932
C2×#106221192
#130664992
C11×#12962
#913511