Finite Group Databasebeta

← #14647212

Subgroups — #14647212

Order 2816.

514 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13071021C211yesmaximal, characteristic
2#13068593C211yesmaximal, characteristic
3#13068593C211yesmaximal, characteristic
4#13066500C211yesmaximal, characteristic, complemented
5#13066500C211yesmaximal, characteristic, complemented
6#13066499C211yesmaximal, characteristic, complemented
7C11×#1296C211yesmaximal, characteristic, complemented
8C2×#66945C412yes—
9C2×C42×D11C2211yescharacteristic
10C2×C11×C4⋊C8C2211yescharacteristic
11C2×C11×C4⋊C8C2211yescharacteristic
12C11×#384C2211yescharacteristic
13C2×(C2×D11)⋊C8—21no—
14C2×(C2×D11)⋊C8—21no—
15#10622600—21no—
16#10622600—21no—
17#10622590C412yes—
18C4⋊C4×Dic11—21no—
19C4⋊C4×Dic11—21no—
20#10622548C2211yescharacteristic
21C2×C4⋊(C11⋊C8)C2211yescharacteristic
22C2×C4⋊(C11⋊C8)C2211yescharacteristic
23#10622188—21no—
24#10622188—21no—
25C22×C4×D11C2×C411yescharacteristic
26C22×C4×D11D411yescharacteristic
27C22×C4×D11D411yescharacteristic
28C22×C8×C11—21no—
29C22×C8×C11—21no—
30C2×C11×C4⋊C4—21no—
31C2×C11×C4⋊C4—21no—
32C2×C11×C4⋊C4C2×C412yes—
33C2×C42×C11C2311yescharacteristic
34C2×(C2×D11)⋊C4—22no—
35C2×C4⋊Dic11—21no—
36C2×C4⋊Dic11—21no—
37C2×C4⋊Dic11C2×C412yes—
38C2×C4×Dic11—22no—
39C2×C4×Dic11C2×C411yescharacteristic
40C2×C4×Dic11D411yescharacteristic
41C2×C4×Dic11D411yescharacteristic
42C22×C11⋊C8—21no—
43C22×C11⋊C8—21no—
44#66945—44no—
45C42×D11—21no—
46C42×D11—21no—
47C42×D11—21no—
48C42×D11—21no—
49C11×C4⋊C8—21no—
50C11×C4⋊C8—21no—
51C11×C4⋊C8—21no—
52C11×C4⋊C8—21no—
53C11⋊#95—22no—
54C11⋊#95—22no—
55(C2×D11)⋊C8—42no—
56(C2×D11)⋊C8—42no—
57C4⋊(C11⋊C8)—21no—
58C4⋊(C11⋊C8)—21no—
59C4⋊(C11⋊C8)—21no—
60C4⋊(C11⋊C8)—21no—
61#8729—111nomaximal, Sylow
62C23×D11C22⋊C411yescharacteristic
63C22×C4×C11—22no—
64C22×C4×C11C22×C411yescharacteristic
65C22×C4×C11C2×D411yescharacteristic
66C22×C4×C11C2×D411yescharacteristic
67C22×Dic11—22no—
68C22×Dic11C22⋊C411yescharacteristic
69C22×Dic11C22⋊C411yescharacteristic
70C22×Dic11C22⋊C411yescharacteristic
71C2×C4×D11—22no—
72C2×C4×D11—22no—
73C2×C4×D11—21no—
74C2×C4×D11—21no—
75C2×C4×D11—21no—
76C2×C4×D11—21no—
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×C8×C11—41no—
88C2×C8×C11—41no—
89C2×C8×C11—41no—
90C2×C8×C11—41no—
91C2×C8×C11—41no—
92C2×C8×C11—41no—
93C11×C4⋊C4—42no—
94C11×C4⋊C4—41no—
95C11×C4⋊C4—41no—
96C11×C4⋊C4—41no—
97C11×C4⋊C4—41no—
98C42×C11#4111yescharacteristic
99C42×C11#4111yescharacteristic
100C42×C11#4111yescharacteristic
101C42×C11#4111yescharacteristic
102(C2×D11)⋊C4—44no—
103C4⋊Dic11—42no—
104C4⋊Dic11—41no—
105C4⋊Dic11—41no—
106C4⋊Dic11—41no—
107C4⋊Dic11—41no—
108C4×Dic11—21no—
109C4×Dic11—21no—
110C4×Dic11—21no—
111C4×Dic11—21no—
112C4×Dic11—21no—
113C4×Dic11—21no—
114C4×Dic11—44no—
115C2×C11⋊C8—41no—
116C2×C11⋊C8—41no—
117C2×C11⋊C8—41no—
118C2×C11⋊C8—41no—
119C2×C11⋊C8—41no—
120C2×C11⋊C8—41no—
121#2285—111no—
122#1797—111no—
123#1797—111no—
124#1296—111no—
125#1296—111no—
126#1296—111no—
127#1296D1111yescharacteristic, complemented
128C23×C11C2×C22⋊C411yescharacteristic
129C22×D11—21no—
130C22×D11—21no—
131C22×D11—21no—
132C22×D11—21no—
133C22×D11—21no—
134C22×D11—21no—
135C22×D11#10012yes—
136C2×C4×C11—21no—
137C2×C4×C11—21no—
138C2×C4×C11—42no—
139C2×C4×C11—42no—
140C2×C4×C11—42no—
141C2×C4×C11#11711yescharacteristic
142C2×C4×C11#11711yescharacteristic
143C2×C4×C11#12311yescharacteristic
144C2×C4×C11#12311yescharacteristic
145C2×C4×C11#12311yescharacteristic
146C2×C4×C11#12311yescharacteristic
147C2×C4×C11#13511yescharacteristic
148C2×C4×C11#13511yescharacteristic
149C2×C4×C11#13511yescharacteristic
150C2×C4×C11#13511yescharacteristic
151C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
152C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
153C2×C4×C11#13711yescharacteristic
154C2×C4×C11#13711yescharacteristic
155C2×Dic11—21no—
156C2×Dic11—21no—
157C2×Dic11—21no—
158C2×Dic11—21no—
159C2×Dic11—21no—
160C2×Dic11—21no—
161C2×Dic11—21no—
162C2×Dic11—21no—
163C2×Dic11—42no—
164C2×Dic11—42no—
165C2×Dic11—42no—
166C2×Dic11#10112yes—
167C4×D11—24no—
168C4×D11—24no—
169C4×D11—41no—
170C4×D11—41no—
171C4×D11—41no—
172C4×D11—41no—
173C4×D11—41no—
174C4×D11—41no—
175C4×D11—41no—
176C4×D11—41no—
177C8×C11—81no—
178C8×C11—81no—
179C11⋊C8—81no—
180C11⋊C8—81no—
181C2×#117—112no—
182C22×C42—111no—
183C2×C4⋊C8—111no—
184C2×C4⋊C8—111no—
185C2×C4⋊C8C2×D1111yescharacteristic
186C2×C4⋊C8C2×D1111yescharacteristic
187C2×C22⋊C8—221no—
188C2×C22⋊C8—221no—
189#384—111no—
190#384C2×D1111yescharacteristic
191#382—112no—
192#380—221no—
193#380—221no—
194C4×C4⋊C4—221no—
195C4×C4⋊C4—221no—
196#336—221no—
197#336—221no—
198C22×C11#38111yescharacteristic
199C22×C11C2×#10011yescharacteristic
200C22×C11C2×#10111yescharacteristic
201C22×C11#41611yescharacteristic
202C22×C11#41611yescharacteristic
203C22×C11#41711yescharacteristic
204C22×C11#41711yescharacteristic
205C2×D11—22no—
206C2×D11—22no—
207C2×D11—22no—
208C2×D11—41no—
209C2×D11—41no—
210C2×D11—41no—
211C2×D11—41no—
212C4×C11—21no—
213C4×C11—21no—
214C4×C11—82no—
215C4×C11#48211yescharacteristic
216C4×C11#48211yescharacteristic
217C4×C11#48211yescharacteristic
218C4×C11#48211yescharacteristic
219C4×C11#48511yescharacteristic
220C4×C11#48511yescharacteristic
221C4×C11#48511yescharacteristic
222C4×C11#48511yescharacteristic
223Dic11—22no—
224Dic11—41no—
225Dic11—41no—
226Dic11—82no—
227C23×C4—111no—
228C23×C4—111no—
229C23×C4—111no—
230C22×C8—21no—
231C22×C8—21no—
232C22×C8—221no—
233C22×C8—221no—
234#117—444no—
235C2×C4⋊C4—21no—
236C2×C4⋊C4—21no—
237C2×C4⋊C4—112no—
238C2×C4⋊C4—221no—
239C2×C4⋊C4—221no—
240C2×C4⋊C4C4×D1112yes—
241C2×C22⋊C4—222no—
242C2×C42—111no—
243C2×C42—111no—
244C2×C42—111no—
245C2×C42—221no—
246C2×C42—221no—
247C2×C42—221no—
248C2×C42—221no—
249C2×C42—222no—
250C2×C42C22×D1111yescharacteristic
251C4⋊C8—21no—
252C4⋊C8—21no—
253C4⋊C8—21no—
254C4⋊C8—21no—
255C4⋊C8—221no—
256C4⋊C8—221no—
257C4⋊C8—221no—
258C4⋊C8—221no—
259C22⋊C8—442no—
260C22⋊C8—442no—
261#95—222no—
262#95—222no—
263C2×C11#154411yescharacteristic
264C2×C11#155111yescharacteristic
265C2×C11#155111yescharacteristic
266C2×C11#156111yescharacteristic
267C2×C11#182111yescharacteristic
268C2×C11#182511yescharacteristic
269C2×C11#182511yescharacteristic
270D11—42no—
271C24—111no—
272C22×C4—22no—
273C22×C4—111no—
274C22×C4—111no—
275C22×C4—111no—
276C22×C4—222no—
277C22×C4—222no—
278C22×C4—221no—
279C22×C4—221no—
280C22×C4—221no—
281C22×C4—221no—
282C22×C4—221no—
283C22×C4—221no—
284C22×C4—221no—
285C22×C4—221no—
286C22×C4—221no—
287C22×C4—221no—
288C22×C4—221no—
289C22×C4—221no—
290C22×C4—221no—
291C22×C4—221no—
292C22×C4—222no—
293C22×C4C2×C4×D1111yescharacteristic
294C22×C4D4×D1111yescharacteristic
295C22×C4D4×D1111yescharacteristic
296C2×C8—41no—
297C2×C8—41no—
298C2×C8—41no—
299C2×C8—41no—
300C2×C8—41no—
301C2×C8—41no—
302C2×C8—441no—
303C2×C8—441no—
304C2×C8—441no—
305C2×C8—441no—
306C2×C8—441no—
307C2×C8—441no—
308C4⋊C4—42no—
309C4⋊C4—41no—
310C4⋊C4—41no—
311C4⋊C4—41no—
312C4⋊C4—41no—
313C4⋊C4—442no—
314C4⋊C4—441no—
315C4⋊C4—441no—
316C4⋊C4—441no—
317C4⋊C4—441no—
318C22⋊C4—444no—
319C42—221no—
320C42—221no—
321C42—221no—
322C42—221no—
323C42—221no—
324C42—221no—
325C42—444no—
326C42#433911yescharacteristic
327C42#433911yescharacteristic
328C42#434111yescharacteristic
329C42#434311yescharacteristic
330C11#872911yescharacteristic, complemented, Sylow
331C23—112no—
332C23—221no—
333C23—221no—
334C23—221no—
335C23—221no—
336C23—221no—
337C23—221no—
338C23C22⋊C4×D1111yescharacteristic
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—42no—
342C2×C4—42no—
343C2×C4—42no—
344C2×C4—112no—
345C2×C4—224no—
346C2×C4—224no—
347C2×C4—221no—
348C2×C4—221no—
349C2×C4—221no—
350C2×C4—221no—
351C2×C4—221no—
352C2×C4—221no—
353C2×C4—221no—
354C2×C4—221no—
355C2×C4—441no—
356C2×C4—441no—
357C2×C4—441no—
358C2×C4—441no—
359C2×C4—441no—
360C2×C4—441no—
361C2×C4—441no—
362C2×C4—441no—
363C2×C4—442no—
364C2×C4—442no—
365C2×C4—442no—
366C2×C4#6692511yescharacteristic
367C2×C4#6693611yescharacteristic
368C2×C4#6693611yescharacteristic
369C2×C4#6694511yescharacteristic
370C2×C4#6694711yescharacteristic
371C2×C4#6694711yescharacteristic
372C2×C4#6696411yescharacteristic
373C2×C4#6696511yescharacteristic
374C2×C4#6696711yescharacteristic
375C2×C4#6696811yescharacteristic
376C2×C4#6696911yescharacteristic
377C2×C4#6696911yescharacteristic
378C2×C4#6697111yescharacteristic
379C2×C4#6697211yescharacteristic
380C8—81no—
381C8—81no—
382C8—881no—
383C8—881no—
384C22—222no—
385C22—222no—
386C22—222no—
387C22—441no—
388C22—441no—
389C22—441no—
390C22—441no—
391C22#1062227711yescharacteristic
392C22D11×#10011yescharacteristic
393C22D11×#10111yescharacteristic
394C22#1062238411yescharacteristic
395C22#1062238511yescharacteristic
396C22#1062241611yescharacteristic
397C22#1062241711yescharacteristic
398C4—21no—
399C4—21no—
400C4—82no—
401C4—222no—
402C4—441no—
403C4—441no—
404C4—882no—
405C4#1062239211yescharacteristic
406C4#1062239711yescharacteristic
407C4#1062242711yescharacteristic
408C4#1062242811yescharacteristic
409C4#1062247911yescharacteristic
410C4#1062248011yescharacteristic
411C4#1062249811yescharacteristic
412C4#1062250111yescharacteristic
413C2—442no—
414C2#1306727911yescharacteristic
415C2#1306730811yescharacteristic
416C2#1306731011yescharacteristic
417C2#1306735211yescharacteristic
418C2#1306869511yescharacteristic
419C2#1306870911yescharacteristic
420C2#1306871011yescharacteristic
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#8729
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
127. #1296D11semidirect
330. C11#8729semidirect

Maximal subgroups

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

subgroupindex
#130710212
#130685932
#130665002
#130664992
C11×#12962
#872911