Finite Group Databasebeta

← #14649375

Subgroups — #14649375

Order 2816.

626 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D11×#97C211yesmaximal, characteristic
2#13076921C211yesmaximal, characteristic
3#13068379C211yesmaximal, characteristic
4C2×#10622181C211yesmaximal, characteristic, complemented
5#13066498C211yesmaximal, characteristic, complemented
6#13066498C211yesmaximal, characteristic, complemented
7C2×C11×#330C211yesmaximal, characteristic, complemented
8C2×C11×#125C2211yescharacteristic
9C22×C8×D11—21no—
10C2×C42×D11C2211yescharacteristic
11C2×C11×#97C2211yescharacteristic
12C2×C11×#97C2211yescharacteristic
13C2×(C2×D11)⋊C8—21no—
14C2×#66879—21no—
15#10622602—21no—
16#10622602—21no—
17#10622600C411yescharacteristic
18#10622600C411yescharacteristic
19#10622591—21no—
20#10622591—21no—
21#10622586C411yescharacteristic
22#10622586C411yescharacteristic
23#10622549C2211yescharacteristic
24C2×#66867C2211yescharacteristic
25C2×#66867C2211yescharacteristic
26D11×#97—22no—
27D11×#97—22no—
28C11×#330—22no—
29#10622188—21no—
30#10622181—22no—
31C22×C4×D11C2×C411yescharacteristic
32C22×C4×D11D411yescharacteristic
33C22×C4×D11D411yescharacteristic
34C22×C8×C11—21no—
35C22×C8×C11—21no—
36C11×#125—21no—
37C11×#125—21no—
38C11×#125—21no—
39C11×#125—21no—
40C2×C11×C4⋊C4—21no—
41C2×C11×C4⋊C4—21no—
42C2×C11×C4⋊C4C2×C411yescharacteristic
43C2×C11×C4⋊C4C2×C411yescharacteristic
44C2×C42×C11C2311yescharacteristic
45C2×(C2×D11)⋊C4—21no—
46C2×(C2×D11)⋊C4—21no—
47C2×C4⋊Dic11C2×C411yescharacteristic
48C2×C4⋊Dic11C2×C411yescharacteristic
49C2×Dic11⋊C4—21no—
50C2×Dic11⋊C4—21no—
51C2×C4×Dic11C2×C411yescharacteristic
52C2×C4×Dic11D411yescharacteristic
53C2×C4×Dic11D411yescharacteristic
54C22×C11⋊C8—21no—
55C22×C11⋊C8—21no—
56C2×C8×D11—24no—
57C2×C8×D11—24no—
58C2×C8×D11—24no—
59C42×D11—21no—
60C42×D11—21no—
61C42×D11—21no—
62C42×D11—21no—
63C11×#97—21no—
64C11×#97—21no—
65C11×#97—21no—
66C11×#97D412yes—
67C11⋊#95—21no—
68C11⋊#95—21no—
69C11⋊#95—21no—
70C11⋊#95—21no—
71C11⋊#95—21no—
72C11⋊#95—21no—
73(C2×D11)⋊C8—24no—
74#66879—24no—
75#66867—21no—
76#66867—21no—
77#66867—21no—
78#66867D412yes—
79#9121—111nomaximal, Sylow
80C23×D11C22⋊C411yescharacteristic
81C22×C4×C11—21no—
82C22×C4×C11—21no—
83C22×C4×C11C22×C411yescharacteristic
84C22×C4×C11C2×D411yescharacteristic
85C22×C4×C11C2×D411yescharacteristic
86C22×Dic11—21no—
87C22×Dic11—21no—
88C22×Dic11C22⋊C411yescharacteristic
89C22×Dic11C22⋊C411yescharacteristic
90C22×Dic11C22⋊C411yescharacteristic
91C2×C4×D11—22no—
92C2×C4×D11—22no—
93C2×C4×D11—22no—
94C2×C4×D11—22no—
95C2×C4×D11—21no—
96C2×C4×D11—21no—
97C2×C4×D11—21no—
98C2×C4×D11—21no—
99C2×C4×D11—21no—
100C2×C4×D11—21no—
101C2×C4×D11—41no—
102C2×C4×D11—41no—
103C2×C8×C11—22no—
104C2×C8×C11—22no—
105C2×C8×C11—22no—
106C2×C8×C11—22no—
107C2×C8×C11—41no—
108C2×C8×C11—41no—
109C11×C4⋊C4—21no—
110C11×C4⋊C4—21no—
111C11×C4⋊C4—21no—
112C11×C4⋊C4—21no—
113C11×C4⋊C4—41no—
114C11×C4⋊C4—41no—
115C11×C4⋊C4—41no—
116C11×C4⋊C4—41no—
117C42×C11C2×D411yescharacteristic
118C42×C11C2×D411yescharacteristic
119C42×C11#4111yescharacteristic
120C42×C11#4111yescharacteristic
121(C2×D11)⋊C4—42no—
122(C2×D11)⋊C4—42no—
123C4⋊Dic11—41no—
124C4⋊Dic11—41no—
125Dic11⋊C4—42no—
126Dic11⋊C4—42no—
127C4×Dic11—21no—
128C4×Dic11—21no—
129C4×Dic11—21no—
130C4×Dic11—21no—
131C4×Dic11—21no—
132C4×Dic11—21no—
133C2×C11⋊C8—22no—
134C2×C11⋊C8—22no—
135C2×C11⋊C8—22no—
136C2×C11⋊C8—22no—
137C2×C11⋊C8—41no—
138C2×C11⋊C8—41no—
139C8×D11—216no—
140C22×#97—111no—
141#2851—111no—
142#1749—111no—
143C2×#330—111no—
144C2×#330D1111yescharacteristic, complemented
145#1295—111no—
146#1295—111no—
147C23×C11C2×C22⋊C411yescharacteristic
148C22×D11—21no—
149C22×D11—21no—
150C22×D11—21no—
151C22×D11—21no—
152C22×D11#10112yes—
153C22×D11#10412yes—
154C22×D11#10412yes—
155C2×C4×C11—21no—
156C2×C4×C11—21no—
157C2×C4×C11—21no—
158C2×C4×C11—21no—
159C2×C4×C11—21no—
160C2×C4×C11—21no—
161C2×C4×C11—41no—
162C2×C4×C11—41no—
163C2×C4×C11—41no—
164C2×C4×C11—41no—
165C2×C4×C11—41no—
166C2×C4×C11—41no—
167C2×C4×C11C4×D411yescharacteristic
168C2×C4×C11C4×D411yescharacteristic
169C2×C4×C11#12011yescharacteristic
170C2×C4×C11#12111yescharacteristic
171C2×C4×C11#12111yescharacteristic
172C2×C4×C11#12311yescharacteristic
173C2×Dic11—21no—
174C2×Dic11—21no—
175C2×Dic11—21no—
176C2×Dic11—21no—
177C2×Dic11—21no—
178C2×Dic11—21no—
179C2×Dic11—21no—
180C2×Dic11—21no—
181C2×Dic11—41no—
182C2×Dic11—41no—
183C2×Dic11—41no—
184C2×Dic11—41no—
185C2×Dic11—41no—
186C2×Dic11—41no—
187C2×Dic11#10412yes—
188C4×D11—24no—
189C4×D11—24no—
190C4×D11—42no—
191C4×D11—42no—
192C4×D11—42no—
193C4×D11—42no—
194C8×C11—24no—
195C8×C11—42no—
196C11⋊C8—24no—
197C11⋊C8—42no—
198C23×C8—221no—
199C2×#125C2×D1111yescharacteristic
200C22×C42—111no—
201C2×C22⋊C8—221no—
202C2×#97—111no—
203C2×#97—111no—
204C2×#97—222no—
205C2×#97—221no—
206C2×#97—222no—
207C2×#97C2×D1111yescharacteristic
208C2×#97C2×D1111yescharacteristic
209#389—111no—
210#389—111no—
211#387—221no—
212#387—221no—
213#385—221no—
214#385—221no—
215#382—111no—
216#380—111no—
217#380—111no—
218#336—221no—
219#330—22no—
220#330—222no—
221C22×C11#38611yescharacteristic
222C22×C11C2×#10111yescharacteristic
223C22×C11#41311yescharacteristic
224C22×C11C2×#10411yescharacteristic
225C22×C11C2×#10411yescharacteristic
226C22×C11C2×#10411yescharacteristic
227C22×C11#42111yescharacteristic
228C2×D11—22no—
229C2×D11—22no—
230C2×D11—22no—
231C2×D11—22no—
232C2×D11—22no—
233C2×D11—22no—
234C2×D11#33014yescomplemented
235C4×C11—21no—
236C4×C11—21no—
237C4×C11—21no—
238C4×C11—21no—
239C4×C11—21no—
240C4×C11—21no—
241C4×C11—81no—
242C4×C11—81no—
243Dic11—22no—
244Dic11—41no—
245Dic11—41no—
246Dic11—81no—
247Dic11—81no—
248C23×C4—111no—
249C23×C4—111no—
250C23×C4—111no—
251C22×C8—21no—
252C22×C8—21no—
253C22×C8—224no—
254C22×C8—224no—
255C22×C8—224no—
256C22×C8—221no—
257C22×C8—221no—
258#125—21no—
259#125—21no—
260#125—21no—
261#125—21no—
262C2×C4⋊C4—21no—
263C2×C4⋊C4—21no—
264C2×C4⋊C4—111no—
265C2×C4⋊C4—111no—
266C2×C4⋊C4—221no—
267C2×C4⋊C4—221no—
268C2×C4⋊C4C4×D1111yescharacteristic
269C2×C4⋊C4C4×D1111yescharacteristic
270C2×C22⋊C4—221no—
271C2×C22⋊C4—221no—
272C2×C42—111no—
273C2×C42—111no—
274C2×C42—111no—
275C2×C42—221no—
276C2×C42—221no—
277C2×C42—221no—
278C2×C42—221no—
279C2×C42C22×D1111yescharacteristic
280C22⋊C8—224no—
281#97—21no—
282#97—21no—
283#97—21no—
284#97—112no—
285#97—224no—
286#97—221no—
287#97—221no—
288#97—221no—
289#97C22⋊D1112yes—
290#95—221no—
291#95—221no—
292#95—221no—
293#95—221no—
294#95—221no—
295#95—221no—
296C2×C11C2×#33011yescharacteristic
297C2×C11#152411yescharacteristic
298C2×C11#153111yescharacteristic
299C2×C11#153211yescharacteristic
300C2×C11#187111yescharacteristic
301C2×C11#189611yescharacteristic
302C2×C11#190111yescharacteristic
303D11—24no—
304C24—111no—
305C22×C4—21no—
306C22×C4—21no—
307C22×C4—111no—
308C22×C4—111no—
309C22×C4—111no—
310C22×C4—222no—
311C22×C4—222no—
312C22×C4—222no—
313C22×C4—222no—
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—441no—
323C22×C4—441no—
324C22×C4C2×C4×D1111yescharacteristic
325C22×C4D4×D1111yescharacteristic
326C22×C4D4×D1111yescharacteristic
327C2×C8—22no—
328C2×C8—22no—
329C2×C8—22no—
330C2×C8—22no—
331C2×C8—41no—
332C2×C8—41no—
333C2×C8—2216no—
334C2×C8—222no—
335C2×C8—222no—
336C2×C8—222no—
337C2×C8—222no—
338C2×C8—441no—
339C2×C8—441no—
340C4⋊C4—21no—
341C4⋊C4—21no—
342C4⋊C4—21no—
343C4⋊C4—21no—
344C4⋊C4—41no—
345C4⋊C4—41no—
346C4⋊C4—41no—
347C4⋊C4—41no—
348C4⋊C4—441no—
349C4⋊C4—441no—
350C4⋊C4—442no—
351C4⋊C4—442no—
352C22⋊C4—442no—
353C22⋊C4—442no—
354C42—221no—
355C42—221no—
356C42—221no—
357C42—221no—
358C42—221no—
359C42—221no—
360C42#433911yescharacteristic
361C42D4×D1111yescharacteristic
362C42#434111yescharacteristic
363C42C2×C22⋊D1111yescharacteristic
364C11#912111yescharacteristic, complemented, Sylow
365C23—112no—
366C23—112no—
367C23—112no—
368C23—221no—
369C23—221no—
370C23—221no—
371C23—221no—
372C23C22⋊C4×D1111yescharacteristic
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—112no—
386C2×C4—224no—
387C2×C4—224no—
388C2×C4—221no—
389C2×C4—221no—
390C2×C4—221no—
391C2×C4—221no—
392C2×C4—221no—
393C2×C4—221no—
394C2×C4—221no—
395C2×C4—221no—
396C2×C4—442no—
397C2×C4—442no—
398C2×C4—442no—
399C2×C4—442no—
400C2×C4—441no—
401C2×C4—441no—
402C2×C4—441no—
403C2×C4—441no—
404C2×C4—441no—
405C2×C4—441no—
406C2×C4(C22⋊D11)⋊C411yescharacteristic
407C2×C4#6693611yescharacteristic
408C2×C4#6693711yescharacteristic
409C2×C4C4×C22⋊D1111yescharacteristic
410C2×C4#6699011yescharacteristic
411C2×C4#6699111yescharacteristic
412C8—24no—
413C8—42no—
414C8—224no—
415C8—442no—
416C22—114no—
417C22—222no—
418C22—222no—
419C22—222no—
420C22—222no—
421C22—222no—
422C22—222no—
423C22D11×#10111yescharacteristic
424C22#1062236411yescharacteristic
425C22D11×#10411yescharacteristic
426C22D11×#10411yescharacteristic
427C22D11×#10411yescharacteristic
428C22#1062243411yescharacteristic
429C22#1062256911yescharacteristic
430C4—21no—
431C4—21no—
432C4—21no—
433C4—21no—
434C4—21no—
435C4—21no—
436C4—81no—
437C4—81no—
438C4—222no—
439C4—441no—
440C4—441no—
441C4—881no—
442C4—881no—
443C2—224no—
444C2D11×#33011yescharacteristic
445C2#1306720311yescharacteristic
446C2#1306722911yescharacteristic
447C2#1306723511yescharacteristic
448C2#1306891511yescharacteristic
449C2#1306905611yescharacteristic
450C2#1306908111yescharacteristic
subgroupG/H
centerC23C22⋊C4×D11
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC2×C11×#330C2
socleC23×C11C2×C22⋊C4
prime radicalC23×D11C22⋊C4
cosocleC2×C42×C11C23
hypercenterC2×#330D11
hypocenterC11#9121
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#330

Complements

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

NH ≅ G/Ntype
4. C2×#10622181C2semidirect
5. #13066498C2semidirect
6. #13066498C2semidirect
7. C2×C11×#330C2semidirect
144. C2×#330D11semidirect
234. C2×D11#330semidirect
364. C11#9121semidirect

Maximal subgroups

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

subgroupindex
C2×D11×#972
#130769212
#130683792
C2×#106221812
#130664982
C2×C11×#3302
#912111