Finite Group Databasebeta

← #14658516

Subgroups — #14658516

Order 2816.

402 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13069409C211yesmaximal, characteristic
2#13068743C211yesmaximal, characteristic, complemented
3#13068617C211yesmaximal, characteristic
4#13068613C211yesmaximal, characteristic
5#13066500C211yesmaximal, characteristic, complemented
6#13066450C211yesmaximal, characteristic, complemented
7C11×#1296C211yesmaximal, characteristic, complemented
8C2×C4×D44C2211yescharacteristic
9C2×C11×C4⋊C8C2211yescharacteristic
10C2×C11×C4⋊C8C2211yescharacteristic
11C11×#384C2211yescharacteristic
12C2×#66885—21no—
13C2×(C2×D11)⋊C8—21no—
14C2×(C2×D11)⋊C8—21no—
15C2×#66873—21no—
16#10622548C2211yescharacteristic
17C2×C4⋊(C11⋊C8)C2211yescharacteristic
18C2×C4×C11⋊C8C2211yescharacteristic
19#10622189—21no—
20#10622167—21no—
21#10622167—21no—
22#10622167—21no—
23C22×D44D411yescharacteristic
24C22×C4×D11—21no—
25C22×C8×C11—21no—
26C22×C8×C11—21no—
27C2×C11×C4⋊C4—21no—
28C2×C11×C4⋊C4—21no—
29C2×C11×C4⋊C4—21no—
30C2×C42×C11C2311yescharacteristic
31C2×(C2×D11)⋊C4—21no—
32C2×C4⋊Dic11—21no—
33C2×C4⋊Dic11—21no—
34C2×C4⋊Dic11—21no—
35C2×C4⋊Dic11D411yescharacteristic
36C22×C11⋊C8—21no—
37C22×C11⋊C8D411yescharacteristic
38C22×C11⋊C8D411yescharacteristic
39C4×D44—21no—
40C4×D44—21no—
41C4×D44—21no—
42C4×D44—21no—
43C11×C4⋊C8—21no—
44C11×C4⋊C8—21no—
45C11×C4⋊C8—21no—
46C11×C4⋊C8—21no—
47#66885—42no—
48(C2×D11)⋊C8—42no—
49(C2×D11)⋊C8—42no—
50#66873—42no—
51C4⋊(C11⋊C8)—21no—
52C4⋊(C11⋊C8)—21no—
53C4×C11⋊C8—21no—
54C4×C11⋊C8—21no—
55#10622—111nomaximal, Sylow
56C23×D11—21no—
57C22×C4×C11—41no—
58C22×C4×C11C2×D411yescharacteristic
59C22×C4×C11C2×D411yescharacteristic
60C22×C4×C11#4111yescharacteristic
61C22×Dic11—21no—
62C22×Dic11—41no—
63C2×D44—21no—
64C2×D44—21no—
65C2×D44—21no—
66C2×D44—21no—
67C2×D44—21no—
68C2×D44Q1612yes—
69C2×C4×D11—41no—
70C2×C4×D11—41no—
71C2×C4×D11—41no—
72C2×C4×D11—41no—
73C2×C4×D11—41no—
74C2×C4×D11—41no—
75C2×C8×C11—41no—
76C2×C8×C11—41no—
77C2×C8×C11—41no—
78C2×C8×C11—41no—
79C2×C8×C11—41no—
80C2×C8×C11—41no—
81C11×C4⋊C4—41no—
82C11×C4⋊C4—41no—
83C11×C4⋊C4—41no—
84C11×C4⋊C4—41no—
85C11×C4⋊C4—81no—
86C42×C11#4111yescharacteristic
87C42×C11#4111yescharacteristic
88C42×C11#4111yescharacteristic
89C42×C11#4111yescharacteristic
90(C2×D11)⋊C4—41no—
91(C2×D11)⋊C4—41no—
92C4⋊Dic11—21no—
93C4⋊Dic11—21no—
94C4⋊Dic11—41no—
95C4⋊Dic11—41no—
96C4⋊Dic11—41no—
97C4⋊Dic11—41no—
98C4⋊Dic11—81no—
99C2×C11⋊C8—21no—
100C2×C11⋊C8—21no—
101C2×C11⋊C8—21no—
102C2×C11⋊C8—21no—
103C2×C11⋊C8—21no—
104C2×C11⋊C8—21no—
105C2×C11⋊C8—41no—
106C2×C11⋊C8—41no—
107C2×C11⋊C8—41no—
108#1954—111no—
109#1834—111no—
110#1802—111no—
111#1802—111no—
112#1296—111no—
113#1296D1111yescharacteristic, complemented
114#1277—111no—
115C23×C11#12111yescharacteristic
116C22×D11—22no—
117C22×D11—41no—
118C22×D11—41no—
119C22×D11—41no—
120C22×D11—41no—
121C22×D11—41no—
122C22×D11—41no—
123C2×C4×C11—21no—
124C2×C4×C11—21no—
125C2×C4×C11—81no—
126C2×C4×C11—81no—
127C2×C4×C11—81no—
128C2×C4×C11#12311yescharacteristic
129C2×C4×C11#12311yescharacteristic
130C2×C4×C11#12311yescharacteristic
131C2×C4×C11#12411yescharacteristic
132C2×C4×C11#12611yescharacteristic
133C2×C4×C11#12611yescharacteristic
134C2×C4×C11C2×Q1611yescharacteristic
135C2×C4×C11#13511yescharacteristic
136C2×C4×C11#13511yescharacteristic
137C2×C4×C11#13511yescharacteristic
138C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
139C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
140C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
141C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
142C2×Dic11—41no—
143C2×Dic11—41no—
144C2×Dic11—41no—
145C2×Dic11—81no—
146C2×Dic11—81no—
147C2×Dic11—81no—
148D44—22no—
149D44—22no—
150D44—41no—
151D44—41no—
152C4×D11—81no—
153C4×D11—81no—
154C4×D11—81no—
155C4×D11—81no—
156C8×C11—81no—
157C8×C11—81no—
158C11⋊C8—41no—
159C11⋊C8—41no—
160C11⋊C8—81no—
161C2×C4×D4—111no—
162C2×C4⋊C8—111no—
163C2×C4⋊C8C2×D1111yescharacteristic
164C2×C4⋊C8C2×D1111yescharacteristic
165C2×#102—221no—
166C2×#102—221no—
167C2×C22⋊C8—221no—
168C2×C22⋊C8—221no—
169C2×C4×C8—111no—
170#384—111no—
171#384C2×D1111yescharacteristic
172#340—221no—
173#340—221no—
174#340—221no—
175#340—221no—
176C22×C11#39711yescharacteristic
177C22×C11#46311yescharacteristic
178C22×C11#46311yescharacteristic
179C22×C11#46711yescharacteristic
180C22×C11#46911yescharacteristic
181C22×C11#47111yescharacteristic
182C22×C11#47111yescharacteristic
183C2×D11—42no—
184C2×D11—42no—
185C2×D11—42no—
186C2×D11—81no—
187C2×D11—81no—
188C2×D11—81no—
189C2×D11—81no—
190C4×C11—21no—
191C4×C11—21no—
192C4×C11—161no—
193C4×C11#48211yescharacteristic
194C4×C11#48211yescharacteristic
195C4×C11#48211yescharacteristic
196C4×C11#48211yescharacteristic
197C4×C11#48411yescharacteristic
198C4×C11#48411yescharacteristic
199C4×C11#48811yescharacteristic
200C4×C11#49011yescharacteristic
201Dic11—81no—
202Dic11—161no—
203C22×D4—111no—
204C23×C4—221no—
205C22×C8—21no—
206C22×C8—21no—
207C22×C8—111no—
208C22×C8—111no—
209C22×C8—221no—
210C4×D4—221no—
211C4×D4—221no—
212C4×D4—221no—
213C4×D4—221no—
214C2×C4⋊C4—21no—
215C2×C4⋊C4—21no—
216C2×C4⋊C4—21no—
217C2×C4⋊C4—111no—
218C2×C4⋊C4—221no—
219C2×C4⋊C4—221no—
220C2×C4⋊C4—221no—
221C2×C22⋊C4—221no—
222C2×C42C22×D1111yescharacteristic
223C4⋊C8—21no—
224C4⋊C8—21no—
225C4⋊C8—21no—
226C4⋊C8—21no—
227C4⋊C8—221no—
228C4⋊C8—221no—
229#102—442no—
230#102—442no—
231C22⋊C8—442no—
232C22⋊C8—442no—
233C4×C8—221no—
234C4×C8—221no—
235C2×C11#168311yescharacteristic
236C2×C11#168311yescharacteristic
237C2×C11#170111yescharacteristic
238C2×C11#170111yescharacteristic
239C2×C11#207311yescharacteristic
240C2×C11#207611yescharacteristic
241C2×C11#207911yescharacteristic
242D11—82no—
243C24—221no—
244C2×D4—112no—
245C2×D4—221no—
246C2×D4—221no—
247C2×D4—221no—
248C2×D4—221no—
249C2×D4—221no—
250C22×C4—41no—
251C22×C4—221no—
252C22×C4—441no—
253C22×C4—441no—
254C22×C4—441no—
255C22×C4—441no—
256C22×C4—441no—
257C22×C4—441no—
258C22×C4—441no—
259C22×C4#433911yescharacteristic
260C22×C4D4×D1111yescharacteristic
261C22×C4D4×D1111yescharacteristic
262C2×C8—41no—
263C2×C8—41no—
264C2×C8—41no—
265C2×C8—41no—
266C2×C8—41no—
267C2×C8—41no—
268C2×C8—221no—
269C2×C8—221no—
270C2×C8—221no—
271C2×C8—221no—
272C2×C8—221no—
273C2×C8—221no—
274C2×C8—441no—
275C2×C8—441no—
276C2×C8—441no—
277C4⋊C4—41no—
278C4⋊C4—41no—
279C4⋊C4—41no—
280C4⋊C4—41no—
281C4⋊C4—81no—
282C4⋊C4—221no—
283C4⋊C4—221no—
284C4⋊C4—441no—
285C4⋊C4—441no—
286C4⋊C4—441no—
287C4⋊C4—441no—
288C4⋊C4—881no—
289C22⋊C4—441no—
290C22⋊C4—441no—
291C42#433911yescharacteristic
292C42#433911yescharacteristic
293C42#434111yescharacteristic
294C42#434311yescharacteristic
295C11#1062211yescharacteristic, complemented, Sylow
296C23—222no—
297C23—441no—
298C23—441no—
299C23—441no—
300C23—441no—
301C23—441no—
302C23—441no—
303C23#6693711yescharacteristic
304D4—222no—
305D4—222no—
306D4—441no—
307D4—441no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—81no—
311C2×C4—81no—
312C2×C4—81no—
313C2×C4—441no—
314C2×C4—441no—
315C2×C4—441no—
316C2×C4—881no—
317C2×C4—881no—
318C2×C4—881no—
319C2×C4—881no—
320C2×C4—881no—
321C2×C4—881no—
322C2×C4—881no—
323C2×C4#6692911yescharacteristic
324C2×C4#6693611yescharacteristic
325C2×C4#6693811yescharacteristic
326C2×C4#6694711yescharacteristic
327C2×C4#6694711yescharacteristic
328C2×C4#6695111yescharacteristic
329C2×C4#6696411yescharacteristic
330C2×C4#6696411yescharacteristic
331C2×C4#6696711yescharacteristic
332C2×C4#6696711yescharacteristic
333C2×C4#6696911yescharacteristic
334C2×C4#6696911yescharacteristic
335C2×C4Q16×D1111yescharacteristic
336C2×C4#6697211yescharacteristic
337C8—81no—
338C8—81no—
339C8—441no—
340C8—441no—
341C8—881no—
342C22—442no—
343C22—442no—
344C22—442no—
345C22—881no—
346C22—881no—
347C22—881no—
348C22—881no—
349C22#1062228811yescharacteristic
350C22#1062236111yescharacteristic
351C22#1062236711yescharacteristic
352C22#1062239511yescharacteristic
353C22#1062240011yescharacteristic
354C22#1062242611yescharacteristic
355C22#1062243211yescharacteristic
356C4—21no—
357C4—21no—
358C4—161no—
359C4—881no—
360C4—1761no—
361C4#1062237711yescharacteristic
362C4#1062239211yescharacteristic
363C4#1062241311yescharacteristic
364C4#1062242211yescharacteristic
365C4#1062247911yescharacteristic
366C4#1062247911yescharacteristic
367C4#1062249711yescharacteristic
368C4#1062249811yescharacteristic
369C2—882no—
370C2#1306806611yescharacteristic
371C2#1306807011yescharacteristic
372C2#1306817611yescharacteristic
373C2#1306818011yescharacteristic
374C2#1307003311yescharacteristic
375C2#1307004811yescharacteristic
376C2#1307006511yescharacteristic
subgroupG/H
centerC23#66937
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1296C2
socleC23×C11#121
prime radicalC22×D44D4
hypercenter#1296D11
hypocenterC11#10622
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1296

Complements

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

NH ≅ G/Ntype
2. #13068743C2semidirect
5. #13066500C2semidirect
6. #13066450C2semidirect
7. C11×#1296C2semidirect
113. #1296D11semidirect
295. C11#10622semidirect

Maximal subgroups

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

subgroupindex
#130694092
#130687432
#130686172
#130686132
#130665002
#130664502
C11×#12962
#1062211