Finite Group Databasebeta

← #14647191

Subgroups — #14647191

Order 2816.

630 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D11×#384C211yesmaximal, characteristic
2#13068593C211yesmaximal, characteristic
3#13068593C211yesmaximal, characteristic
4#13066500C211yesmaximal, characteristic, complemented
5#13066500C211yesmaximal, characteristic, complemented
6#13066499C211yesmaximal, characteristic, complemented
7C11×#1296C211yesmaximal, characteristic, complemented
8C2×C4⋊C4×D11—21no—
9C2×C4⋊C4×D11—21no—
10C2×C4⋊C4×D11C412yes—
11C2×C42×D11C2211yescharacteristic
12C2×C11×C4⋊C8C2211yescharacteristic
13C2×C11×C4⋊C8C2211yescharacteristic
14C11×#384C2211yescharacteristic
15C2×(C2×D11)⋊C8—21no—
16C2×(C2×D11)⋊C8—21no—
17#10622589—21no—
18#10622589—21no—
19#10622589C412yes—
20#10622548C2211yescharacteristic
21C2×C4⋊(C11⋊C8)C2211yescharacteristic
22C2×C4⋊(C11⋊C8)C2211yescharacteristic
23#10622188—21no—
24#10622188—21no—
25C22×C4×D11—22no—
26C22×C4×D11C2×C411yescharacteristic
27C22×C4×D11D411yescharacteristic
28C22×C4×D11D411yescharacteristic
29C22×C8×C11—21no—
30C22×C8×C11—21no—
31C2×C11×C4⋊C4—21no—
32C2×C11×C4⋊C4—21no—
33C2×C11×C4⋊C4C2×C412yes—
34C2×C42×C11C2311yescharacteristic
35C2×C4⋊Dic11—21no—
36C2×C4⋊Dic11—21no—
37C2×C4⋊Dic11C2×C412yes—
38C2×Dic11⋊C4—22no—
39C2×Dic11⋊C4—22no—
40C2×Dic11⋊C4—22no—
41C2×C4×Dic11C2×C411yescharacteristic
42C2×C4×Dic11D411yescharacteristic
43C2×C4×Dic11D411yescharacteristic
44C22×C11⋊C8—21no—
45C22×C11⋊C8—21no—
46C4⋊C4×D11—42no—
47C4⋊C4×D11—42no—
48C4⋊C4×D11—42no—
49C4⋊C4×D11—42no—
50C4⋊C4×D11—44no—
51C42×D11—21no—
52C42×D11—21no—
53C42×D11—21no—
54C42×D11—21no—
55C11×C4⋊C8—21no—
56C11×C4⋊C8—21no—
57C11×C4⋊C8—21no—
58C11×C4⋊C8—21no—
59(C2×D11)⋊C8—42no—
60(C2×D11)⋊C8—42no—
61C4⋊(C11⋊C8)—21no—
62C4⋊(C11⋊C8)—21no—
63C4⋊(C11⋊C8)—21no—
64C4⋊(C11⋊C8)—21no—
65#8724—111nomaximal, Sylow
66C23×D11C22⋊C411yescharacteristic
67C22×C4×C11—22no—
68C22×C4×C11C22×C411yescharacteristic
69C22×C4×C11C2×D411yescharacteristic
70C22×C4×C11C2×D411yescharacteristic
71C22×Dic11—22no—
72C22×Dic11C22⋊C411yescharacteristic
73C22×Dic11C22⋊C411yescharacteristic
74C22×Dic11C22⋊C411yescharacteristic
75C2×C4×D11—22no—
76C2×C4×D11—22no—
77C2×C4×D11—21no—
78C2×C4×D11—21no—
79C2×C4×D11—21no—
80C2×C4×D11—21no—
81C2×C4×D11—21no—
82C2×C4×D11—21no—
83C2×C4×D11—21no—
84C2×C4×D11—21no—
85C2×C4×D11—21no—
86C2×C4×D11—21no—
87C2×C4×D11—44no—
88C2×C4×D11—44no—
89C2×C4×D11—44no—
90C2×C4×D11D812yes—
91C2×C4×D11SD1612yes—
92C2×C4×D11SD1612yes—
93C2×C4×D11Q1612yes—
94C2×C8×C11—41no—
95C2×C8×C11—41no—
96C2×C8×C11—41no—
97C2×C8×C11—41no—
98C2×C8×C11—41no—
99C2×C8×C11—41no—
100C11×C4⋊C4—42no—
101C11×C4⋊C4—41no—
102C11×C4⋊C4—41no—
103C11×C4⋊C4—41no—
104C11×C4⋊C4—41no—
105C42×C11#4111yescharacteristic
106C42×C11#4111yescharacteristic
107C42×C11#4111yescharacteristic
108C42×C11#4111yescharacteristic
109C4⋊Dic11—42no—
110C4⋊Dic11—41no—
111C4⋊Dic11—41no—
112C4⋊Dic11—41no—
113C4⋊Dic11—41no—
114Dic11⋊C4—44no—
115Dic11⋊C4—44no—
116Dic11⋊C4—44no—
117C4×Dic11—21no—
118C4×Dic11—21no—
119C4×Dic11—21no—
120C4×Dic11—21no—
121C4×Dic11—21no—
122C4×Dic11—21no—
123C2×C11⋊C8—41no—
124C2×C11⋊C8—41no—
125C2×C11⋊C8—41no—
126C2×C11⋊C8—41no—
127C2×C11⋊C8—41no—
128C2×C11⋊C8—41no—
129C2×#384—111no—
130#1797—111no—
131#1797—111no—
132#1296—111no—
133#1296—111no—
134#1296—111no—
135#1296D1111yescharacteristic, complemented
136C23×C11C2×C22⋊C411yescharacteristic
137C22×D11—21no—
138C22×D11—21no—
139C22×D11—21no—
140C22×D11—21no—
141C22×D11#10112yes—
142C22×D11#10212yes—
143C22×D11#10312yes—
144C2×C4×C11—21no—
145C2×C4×C11—21no—
146C2×C4×C11—42no—
147C2×C4×C11—42no—
148C2×C4×C11—42no—
149C2×C4×C11#11711yescharacteristic
150C2×C4×C11#11711yescharacteristic
151C2×C4×C11#12311yescharacteristic
152C2×C4×C11#12311yescharacteristic
153C2×C4×C11#12311yescharacteristic
154C2×C4×C11#12311yescharacteristic
155C2×C4×C11C2×D811yescharacteristic
156C2×C4×C11C2×SD1611yescharacteristic
157C2×C4×C11C2×SD1611yescharacteristic
158C2×C4×C11C2×Q1611yescharacteristic
159C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
160C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
161C2×C4×C11#13711yescharacteristic
162C2×C4×C11#13711yescharacteristic
163C2×Dic11—21no—
164C2×Dic11—21no—
165C2×Dic11—21no—
166C2×Dic11—21no—
167C2×Dic11—21no—
168C2×Dic11—21no—
169C2×Dic11—42no—
170C2×Dic11—42no—
171C2×Dic11—42no—
172C2×Dic11#10012yes—
173C2×Dic11#10212yes—
174C2×Dic11#10312yes—
175C4×D11—24no—
176C4×D11—24no—
177C4×D11—22no—
178C4×D11—22no—
179C4×D11—22no—
180C4×D11—22no—
181C4×D11—22no—
182C4×D11—22no—
183C4×D11—22no—
184C4×D11—22no—
185C4×D11—88no—
186C8×C11—81no—
187C8×C11—81no—
188C11⋊C8—81no—
189C11⋊C8—81no—
190C22×C4⋊C4—112no—
191C22×C4⋊C4—221no—
192C22×C4⋊C4—221no—
193C22×C42—111no—
194C2×C4⋊C8—111no—
195C2×C4⋊C8—111no—
196C2×C4⋊C8C2×D1111yescharacteristic
197C2×C4⋊C8C2×D1111yescharacteristic
198C2×C22⋊C8—221no—
199C2×C22⋊C8—221no—
200#384—112no—
201#384—111no—
202#384—221no—
203#384—221no—
204#384C2×D1111yescharacteristic
205#336—221no—
206#336—221no—
207C22×C11#38111yescharacteristic
208C22×C11C2×#10011yescharacteristic
209C22×C11C2×#10111yescharacteristic
210C22×C11C2×#10211yescharacteristic
211C22×C11C2×#10311yescharacteristic
212C22×C11#41811yescharacteristic
213C22×C11#41911yescharacteristic
214C2×D11—22no—
215C2×D11—22no—
216C2×D11—22no—
217C2×D11—22no—
218C2×D11—22no—
219C2×D11—22no—
220C2×D11#33214yes—
221C4×C11—21no—
222C4×C11—21no—
223C4×C11—82no—
224C4×C11#48011yescharacteristic
225C4×C11#48011yescharacteristic
226C4×C11#48111yescharacteristic
227C4×C11#48111yescharacteristic
228C4×C11#48311yescharacteristic
229C4×C11#48311yescharacteristic
230C4×C11#48411yescharacteristic
231C4×C11#48411yescharacteristic
232Dic11—22no—
233Dic11—22no—
234Dic11—22no—
235Dic11—82no—
236C23×C4—111no—
237C23×C4—111no—
238C23×C4—111no—
239C23×C4—222no—
240C22×C8—21no—
241C22×C8—21no—
242C22×C8—221no—
243C22×C8—221no—
244C2×C4⋊C4—21no—
245C2×C4⋊C4—21no—
246C2×C4⋊C4—112no—
247C2×C4⋊C4—222no—
248C2×C4⋊C4—222no—
249C2×C4⋊C4—222no—
250C2×C4⋊C4—221no—
251C2×C4⋊C4—221no—
252C2×C4⋊C4—442no—
253C2×C4⋊C4—442no—
254C2×C4⋊C4—442no—
255C2×C4⋊C4—442no—
256C2×C4⋊C4—444no—
257C2×C4⋊C4C4×D1112yes—
258C2×C42—111no—
259C2×C42—111no—
260C2×C42—111no—
261C2×C42—221no—
262C2×C42—221no—
263C2×C42—221no—
264C2×C42—221no—
265C2×C42C22×D1111yescharacteristic
266C4⋊C8—21no—
267C4⋊C8—21no—
268C4⋊C8—21no—
269C4⋊C8—21no—
270C4⋊C8—221no—
271C4⋊C8—221no—
272C4⋊C8—221no—
273C4⋊C8—221no—
274C22⋊C8—442no—
275C22⋊C8—442no—
276C2×C11C2×#33211yescharacteristic
277C2×C11#154511yescharacteristic
278C2×C11#154811yescharacteristic
279C2×C11#155611yescharacteristic
280C2×C11#182111yescharacteristic
281C2×C11#182311yescharacteristic
282C2×C11#182411yescharacteristic
283D11—24no—
284C24—111no—
285C22×C4—22no—
286C22×C4—111no—
287C22×C4—111no—
288C22×C4—111no—
289C22×C4—112no—
290C22×C4—112no—
291C22×C4—112no—
292C22×C4—112no—
293C22×C4—222no—
294C22×C4—222no—
295C22×C4—221no—
296C22×C4—221no—
297C22×C4—221no—
298C22×C4—221no—
299C22×C4—221no—
300C22×C4—221no—
301C22×C4—221no—
302C22×C4—221no—
303C22×C4—221no—
304C22×C4—221no—
305C22×C4—222no—
306C22×C4—444no—
307C22×C4—444no—
308C22×C4—444no—
309C22×C4C2×C4×D1111yescharacteristic
310C22×C4D4×D1111yescharacteristic
311C22×C4D4×D1111yescharacteristic
312C2×C8—41no—
313C2×C8—41no—
314C2×C8—41no—
315C2×C8—41no—
316C2×C8—41no—
317C2×C8—41no—
318C2×C8—441no—
319C2×C8—441no—
320C2×C8—441no—
321C2×C8—441no—
322C2×C8—441no—
323C2×C8—441no—
324C4⋊C4—42no—
325C4⋊C4—41no—
326C4⋊C4—41no—
327C4⋊C4—41no—
328C4⋊C4—41no—
329C4⋊C4—442no—
330C4⋊C4—444no—
331C4⋊C4—444no—
332C4⋊C4—444no—
333C4⋊C4—441no—
334C4⋊C4—441no—
335C4⋊C4—441no—
336C4⋊C4—441no—
337C42—221no—
338C42—221no—
339C42—221no—
340C42—221no—
341C42—221no—
342C42—221no—
343C42#433911yescharacteristic
344C42#433911yescharacteristic
345C42#434111yescharacteristic
346C42#434311yescharacteristic
347C11#872411yescharacteristic, complemented, Sylow
348C23—112no—
349C23—112no—
350C23—112no—
351C23—221no—
352C23—221no—
353C23—221no—
354C23—221no—
355C23C22⋊C4×D1111yescharacteristic
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—42no—
359C2×C4—42no—
360C2×C4—42no—
361C2×C4—112no—
362C2×C4—112no—
363C2×C4—112no—
364C2×C4—224no—
365C2×C4—224no—
366C2×C4—221no—
367C2×C4—221no—
368C2×C4—221no—
369C2×C4—221no—
370C2×C4—221no—
371C2×C4—221no—
372C2×C4—222no—
373C2×C4—222no—
374C2×C4—222no—
375C2×C4—222no—
376C2×C4—222no—
377C2×C4—222no—
378C2×C4—222no—
379C2×C4—222no—
380C2×C4—442no—
381C2×C4—442no—
382C2×C4—442no—
383C2×C4—888no—
384C2×C4#6692511yescharacteristic
385C2×C4#6693611yescharacteristic
386C2×C4#6693611yescharacteristic
387C2×C4#6694511yescharacteristic
388C2×C4#6694711yescharacteristic
389C2×C4#6694711yescharacteristic
390C2×C4D8×D1111yescharacteristic
391C2×C4#6696411yescharacteristic
392C2×C4SD16×D1111yescharacteristic
393C2×C4SD16×D1111yescharacteristic
394C2×C4#6696711yescharacteristic
395C2×C4#6696811yescharacteristic
396C2×C4Q16×D1111yescharacteristic
397C2×C4#6697111yescharacteristic
398C8—81no—
399C8—81no—
400C8—881no—
401C8—881no—
402C22—114no—
403C22—222no—
404C22—222no—
405C22—222no—
406C22—222no—
407C22—222no—
408C22—222no—
409C22#1062227711yescharacteristic
410C22D11×#10011yescharacteristic
411C22D11×#10111yescharacteristic
412C22D11×#10211yescharacteristic
413C22#1062238311yescharacteristic
414C22D11×#10311yescharacteristic
415C22#1062241511yescharacteristic
416C4—21no—
417C4—21no—
418C4—82no—
419C4—222no—
420C4—222no—
421C4—222no—
422C4—882no—
423C4#1062238711yescharacteristic
424C4#1062239011yescharacteristic
425C4#1062241811yescharacteristic
426C4#1062242211yescharacteristic
427C4#1062247511yescharacteristic
428C4#1062247611yescharacteristic
429C4#1062249511yescharacteristic
430C4#1062249711yescharacteristic
431C2—224no—
432C2D11×#33211yescharacteristic
433C2#1306728211yescharacteristic
434C2#1306729511yescharacteristic
435C2#1306733111yescharacteristic
436C2#1306869511yescharacteristic
437C2#1306870111yescharacteristic
438C2#1306870511yescharacteristic
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#8724
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. #13066500C2semidirect
5. #13066500C2semidirect
6. #13066499C2semidirect
7. C11×#1296C2semidirect
135. #1296D11semidirect
347. C11#8724semidirect

Maximal subgroups

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

subgroupindex
D11×#3842
#130685932
#130665002
#130664992
C11×#12962
#872411