Finite Group Databasebeta

← #14649402

Subgroups — #14649402

Order 2816.

530 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622318C211yesmaximal, characteristic
2#13076927C211yesmaximal, characteristic
3#13068379C211yesmaximal, characteristic
4C2×#10622103C211yesmaximal, characteristic, complemented
5C2×#10622103C211yesmaximal, characteristic, complemented
6#13066497C211yesmaximal, characteristic, complemented
7C11×#1295C211yesmaximal, characteristic, complemented
8C2×C42×D11C2211yescharacteristic
9C2×#66923C2211yescharacteristic
10C2×C11×#97C2211yescharacteristic
11C2×C11×#97C2211yescharacteristic
12C11×#382C2211yescharacteristic
13C2×(C2×D11)⋊C8—21no—
14C2×(C2×D11)⋊C8—21no—
15C2×Dic11⋊C8—21no—
16#10622600C411yescharacteristic
17#10622600C411yescharacteristic
18#10622598C411yescharacteristic
19#10622598C411yescharacteristic
20C2×#66867C2211yescharacteristic
21C2×#66867C2211yescharacteristic
22#10622318—22no—
23#10622318—22no—
24#10622281—21no—
25#10622281—21no—
26#10622266—21no—
27#10622266—21no—
28#10622188—21no—
29#10622103—22no—
30#10622103—22no—
31C22×C4×D11C2×C411yescharacteristic
32C22×C4×D11D411yescharacteristic
33C22×C4×D11D411yescharacteristic
34C22×C8×C11—21no—
35C22×C8×C11—21no—
36C2×C11×C4⋊C4C2×C411yescharacteristic
37C2×C11×C4⋊C4C2×C411yescharacteristic
38C2×C42×C11C2311yescharacteristic
39C2×(C2×D11)⋊C4—21no—
40C2×(C2×D11)⋊C4—21no—
41C2×C4⋊Dic11—21no—
42C2×C4⋊Dic11—21no—
43C2×C4⋊Dic11C2×C411yescharacteristic
44C2×C4⋊Dic11C2×C411yescharacteristic
45C2×Dic11⋊C4—21no—
46C2×Dic11⋊C4—21no—
47C2×C4×Dic11C2×C411yescharacteristic
48C2×C4×Dic11D411yescharacteristic
49C2×C4×Dic11D411yescharacteristic
50C22×C11⋊C8—21no—
51C22×C11⋊C8—21no—
52C42×D11—21no—
53C42×D11—21no—
54C42×D11—21no—
55C42×D11—21no—
56#66923—21no—
57#66923—21no—
58#66923—21no—
59#66923—21no—
60C11×#97—21no—
61C11×#97—21no—
62C11×#97—21no—
63C11×#97D412yes—
64C11×#95—21no—
65C11×#95—21no—
66C11⋊#95—21no—
67C11⋊#95—21no—
68C11⋊#95—21no—
69C11⋊#95—21no—
70(C2×D11)⋊C8—24no—
71(C2×D11)⋊C8—24no—
72Dic11⋊C8—24no—
73#66867—21no—
74#66867—21no—
75#66867—21no—
76#66867D412yes—
77#9126—111nomaximal, Sylow
78C23×D11C22⋊C411yescharacteristic
79C22×C4×C11—21no—
80C22×C4×C11—21no—
81C22×C4×C11C22×C411yescharacteristic
82C22×C4×C11C2×D411yescharacteristic
83C22×C4×C11C2×D411yescharacteristic
84C22×Dic11—21no—
85C22×Dic11—21no—
86C22×Dic11C22⋊C411yescharacteristic
87C22×Dic11C22⋊C411yescharacteristic
88C22×Dic11C22⋊C411yescharacteristic
89C2×C4×D11—22no—
90C2×C4×D11—22no—
91C2×C4×D11—21no—
92C2×C4×D11—21no—
93C2×C4×D11—21no—
94C2×C4×D11—21no—
95C2×C4×D11—21no—
96C2×C4×D11—21no—
97C2×C4×D11—41no—
98C2×C4×D11—41no—
99C2×C4×D11—41no—
100C2×C4×D11—41no—
101C2×C8×C11—22no—
102C2×C8×C11—22no—
103C2×C8×C11—41no—
104C2×C8×C11—41no—
105C2×C8×C11—41no—
106C2×C8×C11—41no—
107C11×C4⋊C4—41no—
108C11×C4⋊C4—41no—
109C42×C11C2×D411yescharacteristic
110C42×C11C2×D411yescharacteristic
111C42×C11#4111yescharacteristic
112C42×C11#4111yescharacteristic
113(C2×D11)⋊C4—42no—
114(C2×D11)⋊C4—42no—
115C4⋊Dic11—21no—
116C4⋊Dic11—21no—
117C4⋊Dic11—21no—
118C4⋊Dic11—21no—
119C4⋊Dic11—42no—
120C4⋊Dic11—42no—
121Dic11⋊C4—41no—
122Dic11⋊C4—41no—
123Dic11⋊C4—41no—
124Dic11⋊C4—41no—
125C4×Dic11—21no—
126C4×Dic11—21no—
127C4×Dic11—21no—
128C4×Dic11—21no—
129C4×Dic11—21no—
130C4×Dic11—21no—
131C2×C11⋊C8—22no—
132C2×C11⋊C8—22no—
133C2×C11⋊C8—41no—
134C2×C11⋊C8—41no—
135C2×C11⋊C8—41no—
136C2×C11⋊C8—41no—
137C2×#432—111no—
138#2851—111no—
139#1749—111no—
140C2×#330—111no—
141C2×#330—111no—
142#1295—111no—
143#1295D1111yescharacteristic, complemented
144C23×C11C2×C22⋊C411yescharacteristic
145C22×D11—21no—
146C22×D11—21no—
147C22×D11—21no—
148C22×D11—21no—
149C22×D11—21no—
150C22×D11—21no—
151C22×D11#10112yes—
152C2×C4×C11—21no—
153C2×C4×C11—21no—
154C2×C4×C11—21no—
155C2×C4×C11—21no—
156C2×C4×C11—21no—
157C2×C4×C11—21no—
158C2×C4×C11—41no—
159C2×C4×C11—41no—
160C2×C4×C11—41no—
161C2×C4×C11—41no—
162C2×C4×C11—41no—
163C2×C4×C11—41no—
164C2×C4×C11C4×D411yescharacteristic
165C2×C4×C11C4×D411yescharacteristic
166C2×C4×C11#12011yescharacteristic
167C2×C4×C11#12111yescharacteristic
168C2×C4×C11#12111yescharacteristic
169C2×C4×C11#12311yescharacteristic
170C2×Dic11—21no—
171C2×Dic11—21no—
172C2×Dic11—21no—
173C2×Dic11—21no—
174C2×Dic11—21no—
175C2×Dic11—21no—
176C2×Dic11—21no—
177C2×Dic11—21no—
178C2×Dic11—41no—
179C2×Dic11—41no—
180C2×Dic11—41no—
181C2×Dic11—41no—
182C2×Dic11—41no—
183C2×Dic11—41no—
184C2×Dic11#10412yes—
185C4×D11—42no—
186C4×D11—42no—
187C4×D11—42no—
188C4×D11—42no—
189C4×D11—42no—
190C4×D11—42no—
191C8×C11—42no—
192C8×C11—42no—
193C11⋊C8—42no—
194C11⋊C8—42no—
195C2×#125—111no—
196C22×C42—111no—
197#432—222no—
198#432—222no—
199C2×C4⋊C8—221no—
200C2×C22⋊C8—221no—
201C2×C22⋊C8—221no—
202C2×#97—111no—
203C2×#97—111no—
204C2×#97C2×D1111yescharacteristic
205C2×#97C2×D1111yescharacteristic
206#389—111no—
207#389—111no—
208#387—221no—
209#387—221no—
210#385—221no—
211#385—221no—
212#382C2×D1111yescharacteristic
213#380—111no—
214#380—111no—
215#336—221no—
216#330—222no—
217#330—222no—
218C22×C11#38611yescharacteristic
219C22×C11C2×#10111yescharacteristic
220C22×C11#41311yescharacteristic
221C22×C11C2×#10411yescharacteristic
222C22×C11#42111yescharacteristic
223C22×C11#42111yescharacteristic
224C22×C11#42111yescharacteristic
225C2×D11—22no—
226C2×D11—22no—
227C2×D11—22no—
228C2×D11—41no—
229C2×D11—41no—
230C2×D11—41no—
231C2×D11—41no—
232C4×C11—21no—
233C4×C11—21no—
234C4×C11—21no—
235C4×C11—21no—
236C4×C11—21no—
237C4×C11—21no—
238C4×C11—81no—
239C4×C11—81no—
240Dic11—22no—
241Dic11—41no—
242Dic11—41no—
243Dic11—81no—
244Dic11—81no—
245C23×C4—111no—
246C23×C4—111no—
247C23×C4—111no—
248C22×C8—21no—
249C22×C8—21no—
250C22×C8—221no—
251C22×C8—221no—
252#125—221no—
253#125—221no—
254#125—221no—
255#125—221no—
256C2×C4⋊C4—111no—
257C2×C4⋊C4—111no—
258C2×C4⋊C4—221no—
259C2×C4⋊C4—221no—
260C2×C4⋊C4—221no—
261C2×C4⋊C4—221no—
262C2×C4⋊C4C4×D1111yescharacteristic
263C2×C4⋊C4C4×D1111yescharacteristic
264C2×C22⋊C4—221no—
265C2×C22⋊C4—221no—
266C2×C42—111no—
267C2×C42—111no—
268C2×C42—111no—
269C2×C42—221no—
270C2×C42—221no—
271C2×C42—221no—
272C2×C42—221no—
273C2×C42C22×D1111yescharacteristic
274C4⋊C8—224no—
275C22⋊C8—224no—
276C22⋊C8—224no—
277#97—21no—
278#97—21no—
279#97—21no—
280#97—112no—
281#97—221no—
282#97—221no—
283#97—221no—
284#97D4412yes—
285#95—21no—
286#95—21no—
287#95—221no—
288#95—221no—
289#95—221no—
290#95—221no—
291C2×C11#152911yescharacteristic
292C2×C11#153111yescharacteristic
293C2×C11#153411yescharacteristic
294C2×C11#153511yescharacteristic
295C2×C11#187111yescharacteristic
296C2×C11#189711yescharacteristic
297C2×C11#190111yescharacteristic
298D11—42no—
299C24—111no—
300C22×C4—21no—
301C22×C4—21no—
302C22×C4—111no—
303C22×C4—111no—
304C22×C4—111no—
305C22×C4—222no—
306C22×C4—222no—
307C22×C4—221no—
308C22×C4—221no—
309C22×C4—221no—
310C22×C4—221no—
311C22×C4—221no—
312C22×C4—221no—
313C22×C4—221no—
314C22×C4—221no—
315C22×C4—441no—
316C22×C4—441no—
317C22×C4—441no—
318C22×C4—441no—
319C22×C4C2×C4×D1111yescharacteristic
320C22×C4D4×D1111yescharacteristic
321C22×C4D4×D1111yescharacteristic
322C2×C8—22no—
323C2×C8—22no—
324C2×C8—41no—
325C2×C8—41no—
326C2×C8—41no—
327C2×C8—41no—
328C2×C8—222no—
329C2×C8—222no—
330C2×C8—441no—
331C2×C8—441no—
332C2×C8—441no—
333C2×C8—441no—
334C4⋊C4—41no—
335C4⋊C4—41no—
336C4⋊C4—221no—
337C4⋊C4—221no—
338C4⋊C4—221no—
339C4⋊C4—221no—
340C4⋊C4—442no—
341C4⋊C4—442no—
342C4⋊C4—441no—
343C4⋊C4—441no—
344C4⋊C4—441no—
345C4⋊C4—441no—
346C22⋊C4—442no—
347C22⋊C4—442no—
348C42—221no—
349C42—221no—
350C42—221no—
351C42—221no—
352C42—221no—
353C42—221no—
354C42C2×D4411yescharacteristic
355C42#433911yescharacteristic
356C42D4×D1111yescharacteristic
357C42#434311yescharacteristic
358C11#912611yescharacteristic, complemented, Sylow
359C23—112no—
360C23—221no—
361C23—221no—
362C23—221no—
363C23—221no—
364C23—221no—
365C23—221no—
366C23C22⋊C4×D1111yescharacteristic
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—112no—
380C2×C4—221no—
381C2×C4—221no—
382C2×C4—221no—
383C2×C4—221no—
384C2×C4—221no—
385C2×C4—221no—
386C2×C4—221no—
387C2×C4—221no—
388C2×C4—442no—
389C2×C4—442no—
390C2×C4—442no—
391C2×C4—442no—
392C2×C4—442no—
393C2×C4—442no—
394C2×C4—441no—
395C2×C4—441no—
396C2×C4—441no—
397C2×C4—441no—
398C2×C4—441no—
399C2×C4—441no—
400C2×C4C4×D4411yescharacteristic
401C2×C4#6693511yescharacteristic
402C2×C4#6693711yescharacteristic
403C2×C4#6694611yescharacteristic
404C2×C4#6694711yescharacteristic
405C2×C4#6694811yescharacteristic
406C8—42no—
407C8—42no—
408C8—442no—
409C8—442no—
410C22—222no—
411C22—222no—
412C22—222no—
413C22—441no—
414C22—441no—
415C22—441no—
416C22—441no—
417C22#1062227811yescharacteristic
418C22#1062235811yescharacteristic
419C22D11×#10111yescharacteristic
420C22D11×#10411yescharacteristic
421C22#1062243411yescharacteristic
422C22#1062243411yescharacteristic
423C22#1062243411yescharacteristic
424C4—21no—
425C4—21no—
426C4—21no—
427C4—21no—
428C4—21no—
429C4—21no—
430C4—81no—
431C4—81no—
432C4—222no—
433C4—441no—
434C4—441no—
435C4—881no—
436C4—881no—
437C2—442no—
438C2#1306722011yescharacteristic
439C2#1306722911yescharacteristic
440C2#1306724111yescharacteristic
441C2#1306724411yescharacteristic
442C2#1306891711yescharacteristic
443C2#1306906311yescharacteristic
444C2#1306908311yescharacteristic
subgroupG/H
centerC23C22⋊C4×D11
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1295C2
socleC23×C11C2×C22⋊C4
prime radicalC23×D11C22⋊C4
cosocleC2×C42×C11C23
hypercenter#1295D11
hypocenterC11#9126
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1295

Complements

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

NH ≅ G/Ntype
4. C2×#10622103C2semidirect
5. C2×#10622103C2semidirect
6. #13066497C2semidirect
7. C11×#1295C2semidirect
143. #1295D11semidirect
358. C11#9126semidirect

Maximal subgroups

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

subgroupindex
C2×#106223182
#130769272
#130683792
C2×#106221032
#130664972
C11×#12952
#912611