Finite Group Databasebeta

← #14648104

Subgroups — #14648104

Order 2816.

454 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1M16×D44C211yesmaximal, characteristic
2#13069391C211yesmaximal, characteristic, complemented
3#13067375C211yesmaximal, characteristic, complemented
4#13067042C211yesmaximal, characteristic
5C2×#10622097C211yesmaximal, characteristic
6#13066512C211yesmaximal, characteristic, complemented
7C11×#1278C211yesmaximal, characteristic, complemented
8C2×M16×D11—21no—
9C2×C4×D44C2211yescharacteristic
10C11×#431C2211yescharacteristic
11C4×C11×M16C2211yescharacteristic
12C2×C4×C8×C11C2211yescharacteristic
13#10622739—21no—
14C2×#66886—21no—
15#10622537C2211yescharacteristic
16#10622537C2211yescharacteristic
17C2×C4⋊(C11⋊C8)C2211yescharacteristic
18#10622319—22no—
19#10622301—21no—
20C8×D44—21no—
21#10622196—21no—
22#10622097—21no—
23#10622097—21no—
24#10622097C411yescharacteristic
25#10622097C411yescharacteristic
26#10622097C411yescharacteristic
27#10622097C411yescharacteristic
28#10622096—22no—
29C22×D44Q811yescharacteristic
30C22×C4×D11—21no—
31C2×C11×M16D411yescharacteristic
32C2×C11×M16D411yescharacteristic
33C22×C8×C11—21no—
34C2×C42×C11C2311yescharacteristic
35C2×(C2×D11)⋊C4—21no—
36C2×C4⋊Dic11Q811yescharacteristic
37C2×#4318—21no—
38C2×#4318—21no—
39C22×C11⋊C8—21no—
40M16×D11—42no—
41M16×D11—42no—
42C2×#4313—22no—
43C2×C8×D11—22no—
44C4×D44—21no—
45C4×D44—21no—
46C4×D44C2×C411yescharacteristic
47C4×D44C2×C411yescharacteristic
48C4×D44D411yescharacteristic
49C4×D44D411yescharacteristic
50C11×C4⋊C8—21no—
51C11×C22⋊C8—21no—
52C11×#97—21no—
53C4×C8×C11—21no—
54C4×C8×C11—21no—
55C4×C8×C11—21no—
56C4×C8×C11C2×C411yescharacteristic
57C4×C8×C11C2×C411yescharacteristic
58#66886—42no—
59(C2×D11)⋊C8—22no—
60(C2×D11)⋊C8—22no—
61C4⋊(C11⋊C8)—21no—
62C4⋊(C11⋊C8)—21no—
63C4⋊(C11⋊C8)—21no—
64C4⋊(C11⋊C8)—21no—
65C4⋊(C11⋊C8)C2×C411yescharacteristic
66C4⋊(C11⋊C8)C2×C411yescharacteristic
67C4⋊(C11⋊C8)D412yes—
68#8906—111nomaximal, Sylow
69C23×D11—21no—
70C22×C4×C11C2×D411yescharacteristic
71C22×C4×C11C2×Q811yescharacteristic
72C22×C4×C11#4111yescharacteristic
73C22×Dic11—21no—
74C2×D44—22no—
75C2×D44—21no—
76C2×D44—41no—
77C2×D44C4⋊C411yescharacteristic
78C2×D44C4⋊C411yescharacteristic
79C2×C4×D11—21no—
80C2×C4×D11—21no—
81C2×C4×D11—21no—
82C2×C4×D11—21no—
83C2×C4×D11—41no—
84C2×C4×D11—41no—
85C2×C4×D11—41no—
86C2×C4×D11—41no—
87C11×M16—21no—
88C11×M16—21no—
89C11×M16—21no—
90C11×M16D812yes—
91C2×C8×C11—21no—
92C2×C8×C11—21no—
93C2×C8×C11—21no—
94C2×C8×C11—21no—
95C2×C8×C11—42no—
96C2×C8×C11—41no—
97C42×C11C22×C411yescharacteristic
98C42×C11C2×D411yescharacteristic
99C42×C11C2×D411yescharacteristic
100C42×C11#4111yescharacteristic
101(C2×D11)⋊C4—21no—
102(C2×D11)⋊C4—21no—
103(C2×D11)⋊C4—21no—
104(C2×D11)⋊C4—21no—
105C4⋊Dic11—21no—
106C4⋊Dic11C4⋊C411yescharacteristic
107C4⋊Dic11C4⋊C411yescharacteristic
108#4318—41no—
109#4318—41no—
110#4318—41no—
111#4318—41no—
112C2×C11⋊C8—21no—
113C2×C11⋊C8—21no—
114C2×C11⋊C8—22no—
115C2×C11⋊C8—41no—
116C2×C11⋊C8—41no—
117C2×C11⋊C8—41no—
118#4313—44no—
119C8×D11—44no—
120D4×M16—111no—
121#1950—111no—
122#1567—111no—
123#1486—111no—
124C2×D4⋊C8—111no—
125#1301—111no—
126#1278D1111yescharacteristic, complemented
127C23×C11C22⋊Q811yescharacteristic
128C22×D11—21no—
129C22×D11—21no—
130C22×D11—42no—
131C22×D11—41no—
132C22×D11—41no—
133C22×D11—81no—
134C2×C4×C11—21no—
135C2×C4×C11—21no—
136C2×C4×C11—41no—
137C2×C4×C11C2×C4⋊C411yescharacteristic
138C2×C4×C11C4×D411yescharacteristic
139C2×C4×C11C4×D411yescharacteristic
140C2×C4×C11#12011yescharacteristic
141C2×C4×C11C22⋊Q811yescharacteristic
142C2×C4×C11#12311yescharacteristic
143C2×C4×C11C2×D811yescharacteristic
144C2×C4×C11#13511yescharacteristic
145C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
146C2×C4×C11#13711yescharacteristic
147C2×Dic11—21no—
148C2×Dic11—21no—
149C2×Dic11—41no—
150C2×Dic11—41no—
151D44—21no—
152D44—21no—
153D44—21no—
154D44—42no—
155D44#10812yescomplemented
156C4×D11—41no—
157C4×D11—41no—
158C4×D11—41no—
159C4×D11—41no—
160C4×D11—41no—
161C4×D11—41no—
162C4×D11—41no—
163C4×D11—41no—
164C8×C11—22no—
165C8×C11—22no—
166C8×C11—41no—
167C8×C11—41no—
168C8×C11—81no—
169C11⋊C8—41no—
170C11⋊C8—41no—
171C11⋊C8—42no—
172C11⋊C8—81no—
173C22×M16—221no—
174C2×C4×D4—111no—
175#436—221no—
176#435—222no—
177C8×D4—221no—
178#431C2×D1111yescharacteristic
179C2×#108—221no—
180#423—111no—
181#423—111no—
182C2×C4⋊C8—111no—
183#407—221no—
184C4×M16C2×D1111yescharacteristic
185C2×C4×C8C2×D1111yescharacteristic
186#341—221no—
187#335—222no—
188D4⋊C8—111no—
189D4⋊C8—111no—
190D4⋊C8—111no—
191D4⋊C8—111no—
192D4⋊C8—221no—
193D4⋊C8—221no—
194C22×C11—21no—
195C22×C11—21no—
196C22×C11#38511yescharacteristic
197C22×C11#47411yescharacteristic
198C22×C11#47811yescharacteristic
199C2×D11—22no—
200C2×D11—41no—
201C2×D11—41no—
202C2×D11—41no—
203C2×D11—41no—
204C2×D11—41no—
205C2×D11—82no—
206C2×D11—82no—
207C4×C11—21no—
208C4×C11—21no—
209C4×C11—21no—
210C4×C11C2×#10811yescharacteristic
211C4×C11#43011yescharacteristic
212C4×C11C4×D811yescharacteristic
213C4×C11#44011yescharacteristic
214C4×C11#44711yescharacteristic
215C4×C11#45211yescharacteristic
216Dic11—41no—
217Dic11—41no—
218C22×D4—111no—
219C23×C4—221no—
220C2×M16—222no—
221C2×M16—221no—
222C2×M16—221no—
223C2×M16—442no—
224C2×M16—442no—
225C2×M16D4411yescharacteristic
226C2×M16D4411yescharacteristic
227C22×C8—21no—
228C22×C8—222no—
229C22×C8—221no—
230C4×D4—111no—
231C4×D4—111no—
232C4×D4—111no—
233C4×D4—111no—
234C4×D4—221no—
235C4×D4—221no—
236C2×C4⋊C4—111no—
237C2×C22⋊C4—221no—
238C2×C42C22×D1111yescharacteristic
239#108—442no—
240C4⋊C8—21no—
241C4⋊C8—111no—
242C4⋊C8—111no—
243C4⋊C8—112no—
244C4⋊C8—221no—
245C4⋊C8—221no—
246C4⋊C8—221no—
247C4⋊C8—221no—
248C22⋊C8—21no—
249C22⋊C8—222no—
250C22⋊C8—222no—
251#97—21no—
252C4×C8—21no—
253C4×C8—21no—
254C4×C8—21no—
255C4×C8C4×D1111yescharacteristic
256C4×C8C4×D1111yescharacteristic
257C2×C11—21no—
258C2×C11—21no—
259C2×C11#185511yescharacteristic
260C2×C11#186111yescharacteristic
261C2×C11#186211yescharacteristic
262D11—42no—
263D11—81no—
264C24—221no—
265C2×D4—111no—
266C2×D4—111no—
267C2×D4—222no—
268C2×D4—221no—
269C2×D4—441no—
270C22×C4—221no—
271C22×C4—221no—
272C22×C4—221no—
273C22×C4—221no—
274C22×C4—221no—
275C22×C4—441no—
276C22×C4—441no—
277C22×C4—441no—
278C22×C4—441no—
279C22×C4C2×D4411yescharacteristic
280C22×C4#434111yescharacteristic
281C22×C4Q8×D1111yescharacteristic
282M16—21no—
283M16—21no—
284M16—21no—
285M16—444no—
286M16—441no—
287M16—441no—
288M16—441no—
289M16—441no—
290M16D8812yes—
291C2×C8—21no—
292C2×C8—21no—
293C2×C8—21no—
294C2×C8—21no—
295C2×C8—42no—
296C2×C8—41no—
297C2×C8—221no—
298C2×C8—221no—
299C2×C8—222no—
300C2×C8—444no—
301C2×C8—441no—
302C2×C8—441no—
303C2×C8—441no—
304C4⋊C4—111no—
305C4⋊C4—111no—
306C4⋊C4—221no—
307C22⋊C4—221no—
308C22⋊C4—221no—
309C22⋊C4—221no—
310C22⋊C4—221no—
311C42C2×C4×D1111yescharacteristic
312C42#433911yescharacteristic
313C42D4×D1111yescharacteristic
314C42D4×D1111yescharacteristic
315C11#890611yescharacteristic, complemented, Sylow
316C23—221no—
317C23—221no—
318C23—442no—
319C23—441no—
320C23—441no—
321C23—881no—
322C23#6695011yescharacteristic
323D4—112no—
324D4—221no—
325D4—221no—
326D4—221no—
327D4—442no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—41no—
331C2×C4—221no—
332C2×C4—221no—
333C2×C4—441no—
334C2×C4—441no—
335C2×C4—441no—
336C2×C4—441no—
337C2×C4—441no—
338C2×C4—441no—
339C2×C4—441no—
340C2×C4—441no—
341C2×C4—441no—
342C2×C4—441no—
343C2×C4C4×D4411yescharacteristic
344C2×C4(C22⋊D11)⋊C411yescharacteristic
345C2×C4#6693511yescharacteristic
346C2×C4#6693611yescharacteristic
347C2×C4C4⋊C4×D1111yescharacteristic
348C2×C4#6694911yescharacteristic
349C2×C4C2×D8811yescharacteristic
350C2×C4#6695711yescharacteristic
351C2×C4#6696111yescharacteristic
352C2×C4#6696211yescharacteristic
353C8—22no—
354C8—22no—
355C8—41no—
356C8—41no—
357C8—81no—
358C8—441no—
359C8—441no—
360C8—442no—
361C8—881no—
362C22—21no—
363C22—21no—
364C22—222no—
365C22—441no—
366C22—441no—
367C22—441no—
368C22—441no—
369C22—441no—
370C22—882no—
371C22—882no—
372C22#1062228111yescharacteristic
373C22#1062245911yescharacteristic
374C22#1062246011yescharacteristic
375C4—21no—
376C4—21no—
377C4—21no—
378C4—441no—
379C4—441no—
380C4C4×D8811yescharacteristic
381C4#1062232311yescharacteristic
382C4#1062234511yescharacteristic
383C4#1062234611yescharacteristic
384C4D11×#10811yescharacteristic
385C4#1062250611yescharacteristic
386C2—21no—
387C2—21no—
388C2—442no—
389C2—881no—
390C2#1306882211yescharacteristic
391C2#1306885711yescharacteristic
392C2#1306886611yescharacteristic
subgroupG/H
centerC2×C4#66935
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1278C2
socleC22×C11#385
prime radicalC22×D44Q8
cosocleC2×C42×C11C23
hypercenter#1278D11
hypocenterC11#8906
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1278

Complements

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

NH ≅ G/Ntype
2. #13069391C2semidirect
3. #13067375C2semidirect
6. #13066512C2semidirect
7. C11×#1278C2semidirect
126. #1278D11semidirect
155. D44#108semidirect
315. C11#8906semidirect

Maximal subgroups

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

subgroupindex
M16×D442
#130693912
#130673752
#130670422
C2×#106220972
#130665122
C11×#12782
#890611